DT2H2X---1.9.5.THM-Ref.s

%------------------------------------------------------------------------------
% File     : DT2H2X---1.9.5
% Problem  : ITP210^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300

% Computer : n007.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 09:04:06 AM UTC 2026

% Result   : Theorem 21.04s 7.59s
% Output   : Refutation 21.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   13
% Syntax   : Number of formulae    :  112 (   4 unt;   0 typ;  12 def)
%            Number of atoms       :  736 ( 217 equ;   0 cnn)
%            Maximal formula atoms :    6 (   6 avg)
%            Number of connectives : 1057 ( 153   ~; 190   |; 122   &; 580   @)
%                                         (  12 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Number of types       :  124 ( 123 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     : 1526 (1523 usr; 144 con; 0-11 aty)
%            Number of variables   :   84 (  84   ^;   0   !;   0   ?;  84   :)

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

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

thf(type_def_8,type,
    produc3658429121746597890et_nat: $tType ).

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

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

thf(type_def_11,type,
    heap_e7401611519738050253t_unit: $tType ).

thf(type_def_12,type,
    produc2732055786443039994et_nat: $tType ).

thf(type_def_13,type,
    set_Pr5094982260447487303t_unit: $tType ).

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

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

thf(type_def_16,type,
    set_Pr1261947904930325089at_nat: $tType ).

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

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

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

thf(type_def_20,type,
    produc3843707927480180839at_nat: $tType ).

thf(type_def_21,type,
    set_Pr958786334691620121nt_int: $tType ).

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

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

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

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

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

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

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

thf(type_def_29,type,
    set_Pr1932065953672099015od_o_o: $tType ).

thf(type_def_30,type,
    set_Pr4329608150637261639at_nat: $tType ).

thf(type_def_31,type,
    set_Pr457366540195662369at_nat: $tType ).

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

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

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

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

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

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

thf(type_def_38,type,
    set_Pr8551490117392284871at_nat: $tType ).

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

thf(type_def_40,type,
    produc6271795597528267376eger_o: $tType ).

thf(type_def_41,type,
    produc8923325533196201883nteger: $tType ).

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

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

thf(type_def_44,type,
    filter1242075044329608583at_nat: $tType ).

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

thf(type_def_46,type,
    set_Pr4532377907799695533_nat_o: $tType ).

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

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

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

thf(type_def_50,type,
    set_se6260736226359567993nt_int: $tType ).

thf(type_def_51,type,
    set_se7855581050983116737at_nat: $tType ).

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

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

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

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

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

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

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

thf(type_def_59,type,
    set_op4508134149509766951at_nat: $tType ).

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

thf(type_def_61,type,
    set_Pr8834758594704517033_o_int: $tType ).

thf(type_def_62,type,
    set_Pr2101469702781467981_o_nat: $tType ).

thf(type_def_63,type,
    set_Pr4944855402158566229_o_rat: $tType ).

thf(type_def_64,type,
    set_Pr3149072824959771635_nat_o: $tType ).

thf(type_def_65,type,
    set_Pr4105333604307423337at_rat: $tType ).

thf(type_def_66,type,
    set_Pr2399638329824935915_rat_o: $tType ).

thf(type_def_67,type,
    set_Pr3594552606344371909at_int: $tType ).

thf(type_def_68,type,
    set_Pr6084635751276098665at_nat: $tType ).

thf(type_def_69,type,
    set_Pr8928021450653196913at_rat: $tType ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(type_def_85,type,
    set_Pr8693737435421807431at_nat: $tType ).

thf(type_def_86,type,
    produc4193628355235574503at_nat: $tType ).

thf(type_def_87,type,
    produc1319942482725812455at_nat: $tType ).

thf(type_def_88,type,
    multis2468970476368604999at_nat: $tType ).

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

thf(type_def_90,type,
    produc4166570645942440679at_nat: $tType ).

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

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

thf(type_def_93,type,
    produc4675096598859438275atural: $tType ).

thf(type_def_94,type,
    option6357759511663192854e_term: $tType ).

thf(type_def_95,type,
    produc6241069584506657477e_term: $tType ).

thf(type_def_96,type,
    produc3925858234332021118et_nat: $tType ).

thf(type_def_97,type,
    produc8551481072490612790e_term: $tType ).

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

thf(type_def_99,type,
    set_Pr1872883991513573699nt_int: $tType ).

thf(type_def_100,type,
    set_Pr1281608226676607948nteger: $tType ).

thf(type_def_101,type,
    set_Pr8536935166611901872et_nat: $tType ).

thf(type_def_102,type,
    set_Pr3286484037609594932et_nat: $tType ).

thf(type_def_103,type,
    set_Pr9222295170931077689nt_int: $tType ).

thf(type_def_104,type,
    produc6576344331059438605e_term: $tType ).

thf(type_def_105,type,
    produc7773217078559923341nt_int: $tType ).

thf(type_def_106,type,
    set_Pr2161125870931222855_nat_o: $tType ).

thf(type_def_107,type,
    set_Pr4759807026041935047at_nat: $tType ).

thf(type_def_108,type,
    set_Pr5564308138774400199at_nat: $tType ).

thf(type_def_109,type,
    set_Pr5488025237498180813et_nat: $tType ).

thf(type_def_110,type,
    set_Pr8057934254988874055nt_int: $tType ).

thf(type_def_111,type,
    produc8763457246119570046nteger: $tType ).

thf(type_def_112,type,
    produc7822875418678951345atural: $tType ).

thf(type_def_113,type,
    produc8731074985263844745atural: $tType ).

thf(type_def_114,type,
    produc7248412053542808358at_nat: $tType ).

thf(type_def_115,type,
    produc4471711990508489141at_nat: $tType ).

thf(type_def_116,type,
    produc1908205239877642774nteger: $tType ).

thf(type_def_117,type,
    produc4972180933644002618e_term: $tType ).

thf(type_def_118,type,
    produc989692990947075319atural: $tType ).

thf(type_def_119,type,
    produc4928098042776334183_nat_o: $tType ).

thf(type_def_120,type,
    produc2285326912895808259nt_int: $tType ).

thf(type_def_121,type,
    produc5835291356934675326atural: $tType ).

thf(type_def_122,type,
    product_prod_nat_num: $tType ).

thf(type_def_123,type,
    produc6756470014200349799atural: $tType ).

thf(type_def_124,type,
    produc859450856879609959at_nat: $tType ).

thf(type_def_125,type,
    produc7819656566062154093et_nat: $tType ).

thf(type_def_126,type,
    produc2934264451710624999od_o_o: $tType ).

thf(type_def_127,type,
    produc732395585841259969at_nat: $tType ).

thf(type_def_128,type,
    produc412284730452459111nt_int: $tType ).

thf(func_def_0,type,
    set_Pr8536935166611901872et_nat: $tType ).

thf(func_def_1,type,
    produc4193628355235574503at_nat: $tType ).

thf(func_def_2,type,
    produc2732055786443039994et_nat: $tType ).

thf(func_def_3,type,
    set_Pr4759807026041935047at_nat: $tType ).

thf(func_def_4,type,
    produc1319942482725812455at_nat: $tType ).

thf(func_def_5,type,
    set_Pr5564308138774400199at_nat: $tType ).

thf(func_def_6,type,
    set_Pr1281608226676607948nteger: $tType ).

thf(func_def_7,type,
    produc989692990947075319atural: $tType ).

thf(func_def_8,type,
    produc1908205239877642774nteger: $tType ).

thf(func_def_9,type,
    set_Pr9222295170931077689nt_int: $tType ).

thf(func_def_10,type,
    set_Pr2161125870931222855_nat_o: $tType ).

thf(func_def_11,type,
    produc2285326912895808259nt_int: $tType ).

thf(func_def_12,type,
    set_Pr3286484037609594932et_nat: $tType ).

thf(func_def_13,type,
    produc4928098042776334183_nat_o: $tType ).

thf(func_def_14,type,
    produc3925858234332021118et_nat: $tType ).

thf(func_def_15,type,
    produc8731074985263844745atural: $tType ).

thf(func_def_16,type,
    produc8763457246119570046nteger: $tType ).

thf(func_def_17,type,
    produc6576344331059438605e_term: $tType ).

thf(func_def_18,type,
    set_Pr1872883991513573699nt_int: $tType ).

thf(func_def_19,type,
    produc7773217078559923341nt_int: $tType ).

thf(func_def_20,type,
    set_Pr8551490117392284871at_nat: $tType ).

thf(func_def_21,type,
    produc6756470014200349799atural: $tType ).

thf(func_def_22,type,
    produc4166570645942440679at_nat: $tType ).

thf(func_def_23,type,
    set_Pr4329608150637261639at_nat: $tType ).

thf(func_def_24,type,
    set_Pr8057934254988874055nt_int: $tType ).

thf(func_def_25,type,
    produc4471711990508489141at_nat: $tType ).

thf(func_def_26,type,
    produc3843707927480180839at_nat: $tType ).

thf(func_def_27,type,
    produc412284730452459111nt_int: $tType ).

thf(func_def_28,type,
    set_Pr457366540195662369at_nat: $tType ).

thf(func_def_29,type,
    produc4675096598859438275atural: $tType ).

thf(func_def_30,type,
    set_Pr8693737435421807431at_nat: $tType ).

thf(func_def_31,type,
    produc732395585841259969at_nat: $tType ).

thf(func_def_32,type,
    set_Pr1932065953672099015od_o_o: $tType ).

thf(func_def_33,type,
    produc5835291356934675326atural: $tType ).

thf(func_def_34,type,
    set_Pr4532377907799695533_nat_o: $tType ).

thf(func_def_35,type,
    produc859450856879609959at_nat: $tType ).

thf(func_def_36,type,
    produc2934264451710624999od_o_o: $tType ).

thf(func_def_37,type,
    produc4972180933644002618e_term: $tType ).

thf(func_def_38,type,
    produc6241069584506657477e_term: $tType ).

thf(func_def_39,type,
    produc3658429121746597890et_nat: $tType ).

thf(func_def_40,type,
    produc8551481072490612790e_term: $tType ).

thf(func_def_41,type,
    set_Pr5488025237498180813et_nat: $tType ).

thf(func_def_42,type,
    option6357759511663192854e_term: $tType ).

thf(func_def_43,type,
    produc7248412053542808358at_nat: $tType ).

thf(func_def_44,type,
    set_Pr5094982260447487303t_unit: $tType ).

thf(func_def_45,type,
    set_op4508134149509766951at_nat: $tType ).

thf(func_def_46,type,
    set_se7855581050983116737at_nat: $tType ).

thf(func_def_47,type,
    set_se6260736226359567993nt_int: $tType ).

thf(func_def_48,type,
    produc7819656566062154093et_nat: $tType ).

thf(func_def_49,type,
    produc7822875418678951345atural: $tType ).

thf(func_def_50,type,
    produc8923325533196201883nteger: $tType ).

thf(func_def_51,type,
    multis2468970476368604999at_nat: $tType ).

thf(func_def_52,type,
    filter1242075044329608583at_nat: $tType ).

thf(func_def_53,type,
    set_Pr8928021450653196913at_rat: $tType ).

thf(func_def_54,type,
    set_Pr6084635751276098665at_nat: $tType ).

thf(func_def_55,type,
    set_Pr3594552606344371909at_int: $tType ).

thf(func_def_56,type,
    set_Pr4105333604307423337at_rat: $tType ).

thf(func_def_57,type,
    set_Pr1261947904930325089at_nat: $tType ).

thf(func_def_58,type,
    set_Pr958786334691620121nt_int: $tType ).

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

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

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

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

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

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

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

thf(func_def_66,type,
    set_Pr2399638329824935915_rat_o: $tType ).

thf(func_def_67,type,
    set_Pr3149072824959771635_nat_o: $tType ).

thf(func_def_68,type,
    set_Pr4944855402158566229_o_rat: $tType ).

thf(func_def_69,type,
    set_Pr2101469702781467981_o_nat: $tType ).

thf(func_def_70,type,
    set_Pr8834758594704517033_o_int: $tType ).

thf(func_def_71,type,
    produc6271795597528267376eger_o: $tType ).

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

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

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

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

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

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

thf(func_def_78,type,
    heap_e7401611519738050253t_unit: $tType ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(func_def_98,type,
    set_Code_integer: $tType ).

thf(func_def_99,type,
    set_Product_unit: $tType ).

thf(func_def_100,type,
    set_option_o: $tType ).

thf(func_def_101,type,
    set_literal: $tType ).

thf(func_def_102,type,
    set_set_o: $tType ).

thf(func_def_103,type,
    option_num: $tType ).

thf(func_def_104,type,
    list_char: $tType ).

thf(func_def_105,type,
    filter_nat: $tType ).

thf(func_def_106,type,
    set_char: $tType ).

thf(func_def_107,type,
    list_nat: $tType ).

thf(func_def_108,type,
    list_int: $tType ).

thf(func_def_109,type,
    set_rat: $tType ).

thf(func_def_110,type,
    set_nat: $tType ).

thf(func_def_111,type,
    set_int: $tType ).

thf(func_def_112,type,
    code_natural: $tType ).

thf(func_def_113,type,
    code_integer: $tType ).

thf(func_def_114,type,
    product_unit: $tType ).

thf(func_def_115,type,
    assn: $tType ).

thf(func_def_116,type,
    literal: $tType ).

thf(func_def_117,type,
    set_o: $tType ).

thf(func_def_118,type,
    char: $tType ).

thf(func_def_119,type,
    rat: $tType ).

thf(func_def_120,type,
    num: $tType ).

thf(func_def_121,type,
    nat: $tType ).

thf(func_def_122,type,
    int: $tType ).

thf(func_def_123,type,
    archim2889992004027027881ng_rat: rat > int ).

thf(func_def_124,type,
    archim3151403230148437115or_rat: rat > int ).

thf(func_def_125,type,
    archimedean_frac_rat: rat > rat ).

thf(func_def_126,type,
    archim7778729529865785530nd_rat: rat > int ).

thf(func_def_127,type,
    abs_assn: ( produc3658429121746597890et_nat > $o ) > assn ).

thf(func_def_128,type,
    rep_assn: assn > produc3658429121746597890et_nat > $o ).

thf(func_def_129,type,
    in_range: produc3658429121746597890et_nat > $o ).

thf(func_def_130,type,
    one_assn_raw: produc3658429121746597890et_nat > $o ).

thf(func_def_131,type,
    proper: ( produc3658429121746597890et_nat > $o ) > $o ).

thf(func_def_132,type,
    relH: set_nat > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o ).

thf(func_def_133,type,
    times_assn_raw: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).

thf(func_def_134,type,
    times_assn_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ).

thf(func_def_135,type,
    wand_assn: assn > assn > assn ).

thf(func_def_136,type,
    wand_raw: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).

thf(func_def_137,type,
    wand_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ).

thf(func_def_138,type,
    bNF_Cardinal_cone: set_Pr5094982260447487303t_unit ).

thf(func_def_139,type,
    bNF_Cardinal_ctwo: set_Product_prod_o_o ).

thf(func_def_140,type,
    bNF_Cardinal_czero_o: set_Product_prod_o_o ).

thf(func_def_141,type,
    bNF_Ca3172636760949973492d_of_o: set_o > set_Product_prod_o_o ).

thf(func_def_142,type,
    bNF_Ca3793111618940312692of_nat: set_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_143,type,
    bNF_Ca7083678892733797993t_unit: set_Product_unit > set_Pr5094982260447487303t_unit ).

thf(func_def_144,type,
    bNF_Ca8331644756375544342r_on_o: set_o > set_Product_prod_o_o > $o ).

thf(func_def_145,type,
    bNF_Ca1281551314933786834on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_146,type,
    bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat ).

thf(func_def_147,type,
    bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat ).

thf(func_def_148,type,
    bNF_id2059982186938784458at_o_o: ( ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ) > ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ).

thf(func_def_149,type,
    bNF_id4470576313039291732at_o_o: ( ( produc3658429121746597890et_nat > $o ) > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ).

thf(func_def_150,type,
    bNF_id_bnf_o_o_o: ( $o > $o > $o ) > $o > $o > $o ).

thf(func_def_151,type,
    bNF_id_bnf_o_int_o: ( $o > int > $o ) > $o > int > $o ).

thf(func_def_152,type,
    bNF_id_bnf_o_nat_o: ( $o > nat > $o ) > $o > nat > $o ).

thf(func_def_153,type,
    bNF_id_bnf_o_o: ( $o > $o ) > $o > $o ).

thf(func_def_154,type,
    bNF_id_bnf_int_o_o: ( int > $o > $o ) > int > $o > $o ).

thf(func_def_155,type,
    bNF_id_bnf_int_int_o: ( int > int > $o ) > int > int > $o ).

thf(func_def_156,type,
    bNF_id_bnf_int_nat_o: ( int > nat > $o ) > int > nat > $o ).

thf(func_def_157,type,
    bNF_id_bnf_int_o: ( int > $o ) > int > $o ).

thf(func_def_158,type,
    bNF_id_bnf_nat_o_o: ( nat > $o > $o ) > nat > $o > $o ).

thf(func_def_159,type,
    bNF_id_bnf_nat_int_o: ( nat > int > $o ) > nat > int > $o ).

thf(func_def_160,type,
    bNF_id_bnf_nat_nat_o: ( nat > nat > $o ) > nat > nat > $o ).

thf(func_def_161,type,
    bNF_id_bnf_nat_o: ( nat > $o ) > nat > $o ).

thf(func_def_162,type,
    bNF_id146787821168362314_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_163,type,
    bNF_id5045731369644952736_nat_o: ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).

thf(func_def_164,type,
    bNF_id5557877041440844106_nat_o: ( produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o ) > produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o ).

thf(func_def_165,type,
    bNF_id1044457264471098170_nat_o: ( produc3843707927480180839at_nat > $o ) > produc3843707927480180839at_nat > $o ).

thf(func_def_166,type,
    bNF_id1382368747416007662at_o_o: ( set_nat > $o > $o ) > set_nat > $o > $o ).

thf(func_def_167,type,
    bNF_id293821497076346774_nat_o: ( set_nat > set_nat > $o ) > set_nat > set_nat > $o ).

thf(func_def_168,type,
    bNF_id_bnf_set_nat_o: ( set_nat > $o ) > set_nat > $o ).

thf(func_def_169,type,
    bNF_id745042670895148362_int_o: ( set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o ) > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o ).

thf(func_def_170,type,
    bNF_id9176111459293603464_int_o: ( set_Pr958786334691620121nt_int > $o ) > set_Pr958786334691620121nt_int > $o ).

thf(func_def_171,type,
    bNF_id_bnf_o: $o > $o ).

thf(func_def_172,type,
    bNF_id_bnf_int: int > int ).

thf(func_def_173,type,
    bNF_id_bnf_list_nat: list_nat > list_nat ).

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

thf(func_def_175,type,
    bNF_id_bnf_rat: rat > rat ).

thf(func_def_176,type,
    bNF_eq_onp_list_char: ( list_char > $o ) > list_char > list_char > $o ).

thf(func_def_177,type,
    bNF_re5598663031114558885t_char: ( $o > $o > $o ) > ( ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > $o ) > ( $o > $o > $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > $o > $o > list_char > list_char ) > $o ).

thf(func_def_178,type,
    bNF_re8691941649098027561iteral: ( $o > $o > $o ) > ( ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > $o > literal > literal ) > $o ) > ( $o > $o > $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > $o > $o > literal > literal ) > $o ).

thf(func_def_179,type,
    bNF_re7347849368244578525t_char: ( $o > $o > $o ) > ( ( $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > list_char > list_char ) > $o ) > ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > $o ).

thf(func_def_180,type,
    bNF_re5719858693005739489iteral: ( $o > $o > $o ) > ( ( $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > literal > literal ) > $o ) > ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > $o > literal > literal ) > $o ).

thf(func_def_181,type,
    bNF_re7972843584066424825t_char: ( $o > $o > $o ) > ( ( $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > list_char > list_char ) > $o ) > ( $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > list_char > list_char ) > $o ).

thf(func_def_182,type,
    bNF_re136309367175754621iteral: ( $o > $o > $o ) > ( ( $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > literal > literal ) > $o ) > ( $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > literal > literal ) > $o ).

thf(func_def_183,type,
    bNF_re796896441190010845t_char: ( $o > $o > $o ) > ( ( $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > list_char > list_char ) > $o ) > ( $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > list_char > list_char ) > $o ).

thf(func_def_184,type,
    bNF_re2365650225897248225iteral: ( $o > $o > $o ) > ( ( $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > literal > literal ) > $o ) > ( $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > literal > literal ) > $o ).

thf(func_def_185,type,
    bNF_re4583855572895197261t_char: ( $o > $o > $o ) > ( ( $o > $o > list_char > list_char ) > ( $o > $o > list_char > list_char ) > $o ) > ( $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > list_char > list_char ) > $o ).

thf(func_def_186,type,
    bNF_re5778109699181701841iteral: ( $o > $o > $o ) > ( ( $o > $o > list_char > list_char ) > ( $o > $o > literal > literal ) > $o ) > ( $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > literal > literal ) > $o ).

thf(func_def_187,type,
    bNF_re441219624009962717t_char: ( $o > $o > $o ) > ( ( $o > list_char > list_char ) > ( $o > list_char > list_char ) > $o ) > ( $o > $o > list_char > list_char ) > ( $o > $o > list_char > list_char ) > $o ).

thf(func_def_188,type,
    bNF_re1595102025518187489iteral: ( $o > $o > $o ) > ( ( $o > list_char > list_char ) > ( $o > literal > literal ) > $o ) > ( $o > $o > list_char > list_char ) > ( $o > $o > literal > literal ) > $o ).

thf(func_def_189,type,
    bNF_re6157522605288126113t_char: ( $o > $o > $o ) > ( ( list_char > list_char ) > ( list_char > list_char ) > $o ) > ( $o > list_char > list_char ) > ( $o > list_char > list_char ) > $o ).

thf(func_def_190,type,
    bNF_re6148748351543924773iteral: ( $o > $o > $o ) > ( ( list_char > list_char ) > ( literal > literal ) > $o ) > ( $o > list_char > list_char ) > ( $o > literal > literal ) > $o ).

thf(func_def_191,type,
    bNF_re3379532845092657523nteger: ( int > code_integer > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( code_integer > code_integer ) > $o ).

thf(func_def_192,type,
    bNF_re3804157879324367682nt_int: ( int > code_integer > $o ) > ( int > int > $o ) > ( int > int ) > ( code_integer > int ) > $o ).

thf(func_def_193,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_194,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_195,type,
    bNF_re982302072995117890nteger: ( int > int > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( int > code_integer ) > $o ).

thf(func_def_196,type,
    bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).

thf(func_def_197,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_198,type,
    bNF_re2214769303045360666nt_rat: ( int > int > $o ) > ( product_prod_int_int > rat > $o ) > ( int > product_prod_int_int ) > ( int > rat ) > $o ).

thf(func_def_199,type,
    bNF_re5828396963709814525t_char: ( list_Code_integer > list_Code_integer > $o ) > ( list_char > list_char > $o ) > ( list_Code_integer > list_char ) > ( list_Code_integer > list_char ) > $o ).

thf(func_def_200,type,
    bNF_re7775871201573978401char_o: ( list_char > list_char > $o ) > ( ( list_char > $o ) > ( list_char > $o ) > $o ) > ( list_char > list_char > $o ) > ( list_char > list_char > $o ) > $o ).

thf(func_def_201,type,
    bNF_re7399511318543894245t_char: ( list_char > list_char > $o ) > ( ( list_char > list_char ) > ( list_char > list_char ) > $o ) > ( list_char > list_char > list_char ) > ( list_char > list_char > list_char ) > $o ).

thf(func_def_202,type,
    bNF_re6668474094832959905ar_o_o: ( list_char > list_char > $o ) > ( $o > $o > $o ) > ( list_char > $o ) > ( list_char > $o ) > $o ).

thf(func_def_203,type,
    bNF_re901197953848981245nteger: ( list_char > list_char > $o ) > ( list_Code_integer > list_Code_integer > $o ) > ( list_char > list_Code_integer ) > ( list_char > list_Code_integer ) > $o ).

thf(func_def_204,type,
    bNF_re1407854171455731685t_char: ( list_char > list_char > $o ) > ( list_char > list_char > $o ) > ( list_char > list_char ) > ( list_char > list_char ) > $o ).

thf(func_def_205,type,
    bNF_re76688982720252355at_nat: ( list_char > list_char > $o ) > ( nat > nat > $o ) > ( list_char > nat ) > ( list_char > nat ) > $o ).

thf(func_def_206,type,
    bNF_re7831395832754058691eral_o: ( list_char > literal > $o ) > ( ( list_char > $o ) > ( literal > $o ) > $o ) > ( list_char > list_char > $o ) > ( literal > literal > $o ) > $o ).

thf(func_def_207,type,
    bNF_re8730477052009823892al_o_o: ( list_char > literal > $o ) > ( $o > $o > $o ) > ( list_char > $o ) > ( literal > $o ) > $o ).

thf(func_def_208,type,
    bNF_re4991257583289732696t_char: ( list_char > literal > $o ) > ( list_char > list_char > $o ) > ( list_char > list_char ) > ( literal > list_char ) > $o ).

thf(func_def_209,type,
    bNF_re5453467372598631581iteral: ( list_char > literal > $o ) > ( list_char > literal > $o ) > ( list_char > list_char ) > ( literal > literal ) > $o ).

thf(func_def_210,type,
    bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).

thf(func_def_211,type,
    bNF_re7876454716742015248nteger: ( num > num > $o ) > ( ( num > int ) > ( num > code_integer ) > $o ) > ( num > num > int ) > ( num > num > code_integer ) > $o ).

thf(func_def_212,type,
    bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).

thf(func_def_213,type,
    bNF_re6501075790457514782nteger: ( num > num > $o ) > ( int > code_integer > $o ) > ( num > int ) > ( num > code_integer ) > $o ).

thf(func_def_214,type,
    bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).

thf(func_def_215,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_216,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_217,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_218,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_219,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_220,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_221,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_222,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_223,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_224,type,
    bNF_re4555766996558763186at_nat: ( product_prod_nat_nat > int > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ).

thf(func_def_225,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_226,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_227,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_228,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_229,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_230,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_231,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_232,type,
    bNF_We2654380646378065620so_o_o: set_Pr1932065953672099015od_o_o ).

thf(func_def_233,type,
    bNF_We5258908940166488438at_nat: set_Pr4329608150637261639at_nat ).

thf(func_def_234,type,
    bNF_We8182288985678559134_o_nat: set_Pr457366540195662369at_nat ).

thf(func_def_235,type,
    bNF_We3818239936649020644el_nat: set_Pr1261947904930325089at_nat > $o ).

thf(func_def_236,type,
    basic_1567116559311922317nt_int: ( int > $o ) > ( int > $o ) > product_prod_int_int > $o ).

thf(func_def_237,type,
    basic_4387203522000727145nt_int: ( int > int > $o ) > ( int > int > $o ) > product_prod_int_int > product_prod_int_int > $o ).

thf(func_def_238,type,
    basic_5328504652464829177at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_239,type,
    binomial: nat > nat > nat ).

thf(func_def_240,type,
    gbinom8545251970709558553nteger: code_integer > nat > code_integer ).

thf(func_def_241,type,
    gbinom7368847122466276068atural: code_natural > nat > code_natural ).

thf(func_def_242,type,
    gbinomial_int: int > nat > int ).

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

thf(func_def_244,type,
    gbinomial_rat: rat > nat > rat ).

thf(func_def_245,type,
    bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).

thf(func_def_246,type,
    bit_and_not_num: num > num > option_num ).

thf(func_def_247,type,
    bit_and_not_num_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_248,type,
    bit_concat_bit: nat > int > int > int ).

thf(func_def_249,type,
    bit_or_not_num_neg: num > num > num ).

thf(func_def_250,type,
    bit_or3848514188828904588eg_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_251,type,
    bit_ri7632146776885996613nteger: code_integer > code_integer ).

thf(func_def_252,type,
    bit_ri7919022796975470100ot_int: int > int ).

thf(func_def_253,type,
    bit_ri6519982836138164636nteger: nat > code_integer > code_integer ).

thf(func_def_254,type,
    bit_ri631733984087533419it_int: nat > int > int ).

thf(func_def_255,type,
    bit_se3949692690581998587nteger: code_integer > code_integer > code_integer ).

thf(func_def_256,type,
    bit_se2773287842338716102atural: code_natural > code_natural > code_natural ).

thf(func_def_257,type,
    bit_se725231765392027082nd_int: int > int > int ).

thf(func_def_258,type,
    bit_se727722235901077358nd_nat: nat > nat > nat ).

thf(func_def_259,type,
    bit_se3928097537394005634nteger: nat > code_integer > code_integer ).

thf(func_def_260,type,
    bit_se2751692689150723149atural: nat > code_natural > code_natural ).

thf(func_def_261,type,
    bit_se8568078237143864401it_int: nat > int > int ).

thf(func_def_262,type,
    bit_se8570568707652914677it_nat: nat > nat > nat ).

thf(func_def_263,type,
    bit_se1345352211410354436nteger: nat > code_integer > code_integer ).

thf(func_def_264,type,
    bit_se168947363167071951atural: nat > code_natural > code_natural ).

thf(func_def_265,type,
    bit_se2159334234014336723it_int: nat > int > int ).

thf(func_def_266,type,
    bit_se2161824704523386999it_nat: nat > nat > nat ).

thf(func_def_267,type,
    bit_se2119862282449309892nteger: nat > code_integer ).

thf(func_def_268,type,
    bit_se943457434206027407atural: nat > code_natural ).

thf(func_def_269,type,
    bit_se2000444600071755411sk_int: nat > int ).

thf(func_def_270,type,
    bit_se2002935070580805687sk_nat: nat > nat ).

thf(func_def_271,type,
    bit_se1409905431419307370or_int: int > int > int ).

thf(func_def_272,type,
    bit_se1412395901928357646or_nat: nat > nat > nat ).

thf(func_def_273,type,
    bit_se7788150548672797655nteger: nat > code_integer > code_integer ).

thf(func_def_274,type,
    bit_se6611745700429515170atural: nat > code_natural > code_natural ).

thf(func_def_275,type,
    bit_se545348938243370406it_int: nat > int > int ).

thf(func_def_276,type,
    bit_se547839408752420682it_nat: nat > nat > nat ).

thf(func_def_277,type,
    bit_se2793503036327961859nteger: nat > code_integer > code_integer ).

thf(func_def_278,type,
    bit_se1617098188084679374atural: nat > code_natural > code_natural ).

thf(func_def_279,type,
    bit_se7879613467334960850it_int: nat > int > int ).

thf(func_def_280,type,
    bit_se7882103937844011126it_nat: nat > nat > nat ).

thf(func_def_281,type,
    bit_se1745604003318907178nteger: nat > code_integer > code_integer ).

thf(func_def_282,type,
    bit_se569199155075624693atural: nat > code_natural > code_natural ).

thf(func_def_283,type,
    bit_se2923211474154528505it_int: nat > int > int ).

thf(func_def_284,type,
    bit_se2925701944663578781it_nat: nat > nat > nat ).

thf(func_def_285,type,
    bit_se8260200283734997820nteger: nat > code_integer > code_integer ).

thf(func_def_286,type,
    bit_se7083795435491715335atural: nat > code_natural > code_natural ).

thf(func_def_287,type,
    bit_se4203085406695923979it_int: nat > int > int ).

thf(func_def_288,type,
    bit_se4205575877204974255it_nat: nat > nat > nat ).

thf(func_def_289,type,
    bit_se3222712562003087583nteger: code_integer > code_integer > code_integer ).

thf(func_def_290,type,
    bit_se2046307713759805098atural: code_natural > code_natural > code_natural ).

thf(func_def_291,type,
    bit_se6526347334894502574or_int: int > int > int ).

thf(func_def_292,type,
    bit_se6528837805403552850or_nat: nat > nat > nat ).

thf(func_def_293,type,
    bit_se1146084159140164899it_int: int > nat > $o ).

thf(func_def_294,type,
    bit_take_bit_num: nat > num > option_num ).

thf(func_def_295,type,
    bit_un7362597486090784418nd_num: num > num > option_num ).

thf(func_def_296,type,
    bit_un4731106466462545111um_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_297,type,
    bit_un6697907153464112080or_num: num > num > num ).

thf(func_def_298,type,
    bit_un4773296044027857193um_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_299,type,
    bit_un2480387367778600638or_num: num > num > option_num ).

thf(func_def_300,type,
    bit_un2901131394128224187um_rel: product_prod_num_num > product_prod_num_num > $o ).

thf(func_def_301,type,
    boolea934052484356091300char_o: ( ( list_char > $o ) > ( list_char > $o ) > list_char > $o ) > ( ( list_char > $o ) > ( list_char > $o ) > list_char > $o ) > ( ( list_char > $o ) > list_char > $o ) > ( list_char > $o ) > ( list_char > $o ) > $o ).

thf(func_def_302,type,
    boolea1849928419393854478_int_o: ( ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ) > ( ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ) > ( ( product_prod_int_int > $o ) > product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).

thf(func_def_303,type,
    boolea7165431671056489859t_unit: ( product_unit > product_unit > product_unit ) > ( product_unit > product_unit > product_unit ) > ( product_unit > product_unit ) > product_unit > product_unit > $o ).

thf(func_def_304,type,
    boolea379910186789422830_set_o: ( set_o > set_o > set_o ) > ( set_o > set_o > set_o ) > ( set_o > set_o ) > set_o > set_o > $o ).

thf(func_def_305,type,
    boolea5824373010784320748et_int: ( set_int > set_int > set_int ) > ( set_int > set_int > set_int ) > ( set_int > set_int ) > set_int > set_int > $o ).

thf(func_def_306,type,
    boolea9074081411689916704st_nat: ( set_list_nat > set_list_nat > set_list_nat ) > ( set_list_nat > set_list_nat > set_list_nat ) > ( set_list_nat > set_list_nat ) > set_list_nat > set_list_nat > $o ).

thf(func_def_307,type,
    boolea778851993438741648et_nat: ( set_nat > set_nat > set_nat ) > ( set_nat > set_nat > set_nat ) > ( set_nat > set_nat ) > set_nat > set_nat > $o ).

thf(func_def_308,type,
    boolea51845251928480829at_nat: ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ) > ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ) > ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ) > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > $o ).

thf(func_def_309,type,
    boolea949959532490082519at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_310,type,
    boolea6493995471900120728et_rat: ( set_rat > set_rat > set_rat ) > ( set_rat > set_rat > set_rat ) > ( set_rat > set_rat ) > set_rat > set_rat > $o ).

thf(func_def_311,type,
    code_Suc: code_natural > code_natural ).

thf(func_def_312,type,
    code_bit_cut_integer: code_integer > produc6271795597528267376eger_o ).

thf(func_def_313,type,
    code_cr_integer: int > code_integer > $o ).

thf(func_def_314,type,
    code_cr_natural: nat > code_natural > $o ).

thf(func_def_315,type,
    code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger ).

thf(func_def_316,type,
    code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger ).

thf(func_def_317,type,
    code_dup: code_integer > code_integer ).

thf(func_def_318,type,
    code_int_of_integer: code_integer > int ).

thf(func_def_319,type,
    code_integer_of_int: int > code_integer ).

thf(func_def_320,type,
    code_integer_of_nat: nat > code_integer ).

thf(func_def_321,type,
    code_integer_of_num: num > code_integer ).

thf(func_def_322,type,
    code_nat_of_integer: code_integer > nat ).

thf(func_def_323,type,
    code_nat_of_natural: code_natural > nat ).

thf(func_def_324,type,
    code_natural_of_nat: nat > code_natural ).

thf(func_def_325,type,
    code_negative: num > code_integer ).

thf(func_def_326,type,
    code_num_of_integer: code_integer > num ).

thf(func_def_327,type,
    code_pcr_integer: int > code_integer > $o ).

thf(func_def_328,type,
    code_sub: num > num > code_integer ).

thf(func_def_329,type,
    complete_Inf_Inf_int: set_int > int ).

thf(func_def_330,type,
    complete_Inf_Inf_nat: set_nat > nat ).

thf(func_def_331,type,
    comple7806235888213564991et_nat: set_set_nat > set_nat ).

thf(func_def_332,type,
    complete_Sup_Sup_int: set_int > int ).

thf(func_def_333,type,
    complete_Sup_Sup_nat: set_nat > nat ).

thf(func_def_334,type,
    comple7399068483239264473et_nat: set_set_nat > set_nat ).

thf(func_def_335,type,
    nat_to_rat_surj: nat > rat ).

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

thf(func_def_337,type,
    adjust_div: product_prod_int_int > int ).

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

thf(func_def_339,type,
    divmod_nat: nat > nat > product_prod_nat_nat ).

thf(func_def_340,type,
    eucl_rel_int: int > int > product_prod_int_int > $o ).

thf(func_def_341,type,
    unique5706413561485394159nteger: produc8923325533196201883nteger > $o ).

thf(func_def_342,type,
    unique6319869463603278526ux_int: product_prod_int_int > $o ).

thf(func_def_343,type,
    unique6322359934112328802ux_nat: product_prod_nat_nat > $o ).

thf(func_def_344,type,
    unique3479559517661332726nteger: num > num > produc8923325533196201883nteger ).

thf(func_def_345,type,
    unique5052692396658037445od_int: num > num > product_prod_int_int ).

thf(func_def_346,type,
    unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).

thf(func_def_347,type,
    unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_348,type,
    unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).

thf(func_def_349,type,
    unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_350,type,
    euclid3395696857347342551nt_int: int > int ).

thf(func_def_351,type,
    euclid3398187327856392827nt_nat: nat > nat ).

thf(func_def_352,type,
    comm_s8582702949713902594nteger: code_integer > nat > code_integer ).

thf(func_def_353,type,
    comm_s4660882817536571857er_int: int > nat > int ).

thf(func_def_354,type,
    comm_s4663373288045622133er_nat: nat > nat > nat ).

thf(func_def_355,type,
    comm_s4028243227959126397er_rat: rat > nat > rat ).

thf(func_def_356,type,
    semiri3624122377584611663nteger: nat > code_integer ).

thf(func_def_357,type,
    semiri2447717529341329178atural: nat > code_natural ).

thf(func_def_358,type,
    semiri1406184849735516958ct_int: nat > int ).

thf(func_def_359,type,
    semiri1408675320244567234ct_nat: nat > nat ).

thf(func_def_360,type,
    semiri773545260158071498ct_rat: nat > rat ).

thf(func_def_361,type,
    inverse_inverse_rat: rat > rat ).

thf(func_def_362,type,
    at_top_nat: filter_nat ).

thf(func_def_363,type,
    cofinite_nat: filter_nat ).

thf(func_def_364,type,
    eventually_nat: ( nat > $o ) > filter_nat > $o ).

thf(func_def_365,type,
    eventu1038000079068216329at_nat: ( product_prod_nat_nat > $o ) > filter1242075044329608583at_nat > $o ).

thf(func_def_366,type,
    filter3212408913953519116et_nat: ( nat > set_nat ) > filter_set_nat > filter_nat > $o ).

thf(func_def_367,type,
    finite3254316476582989077op_nat: set_nat > filter_set_nat ).

thf(func_def_368,type,
    frequently_nat: ( nat > $o ) > filter_nat > $o ).

thf(func_def_369,type,
    prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat ).

thf(func_def_370,type,
    finite1363419556375932405_nat_o: set_Pr4532377907799695533_nat_o > nat ).

thf(func_def_371,type,
    finite_card_o: set_o > nat ).

thf(func_def_372,type,
    finite_card_int: set_int > nat ).

thf(func_def_373,type,
    finite_card_list_nat: set_list_nat > nat ).

thf(func_def_374,type,
    finite_card_nat: set_nat > nat ).

thf(func_def_375,type,
    finite6756421564338198497nt_int: set_Pr958786334691620121nt_int > nat ).

thf(func_def_376,type,
    finite711546835091564841at_nat: set_Pr1261947904930325089at_nat > nat ).

thf(func_def_377,type,
    finite3771342082235030671at_nat: set_Pr4329608150637261639at_nat > nat ).

thf(func_def_378,type,
    finite410649719033368117t_unit: set_Product_unit > nat ).

thf(func_def_379,type,
    finite_card_rat: set_rat > nat ).

thf(func_def_380,type,
    finite_card_set_o: set_set_o > nat ).

thf(func_def_381,type,
    finite_card_set_int: set_set_int > nat ).

thf(func_def_382,type,
    finite2364142230527598318st_nat: set_set_list_nat > nat ).

thf(func_def_383,type,
    finite_card_set_nat: set_set_nat > nat ).

thf(func_def_384,type,
    finite4053189226111446337nt_int: set_se6260736226359567993nt_int > nat ).

thf(func_def_385,type,
    finite4356350796350151305at_nat: set_se7855581050983116737at_nat > nat ).

thf(func_def_386,type,
    finite1149291290879098388et_nat: set_set_set_nat > nat ).

thf(func_def_387,type,
    finite_card_char: set_char > nat ).

thf(func_def_388,type,
    finite3252695134891459830_nat_o: set_Pr4532377907799695533_nat_o > $o ).

thf(func_def_389,type,
    finite_finite_o: set_o > $o ).

thf(func_def_390,type,
    finite2119507909894593271er_nat: set_filter_nat > $o ).

thf(func_def_391,type,
    finite_finite_int: set_int > $o ).

thf(func_def_392,type,
    finite8100373058378681591st_nat: set_list_nat > $o ).

thf(func_def_393,type,
    finite_finite_nat: set_nat > $o ).

thf(func_def_394,type,
    finite4093902646404507527tion_o: set_option_o > $o ).

thf(func_def_395,type,
    finite1345302120164226195on_int: set_option_int > $o ).

thf(func_def_396,type,
    finite7857960318081769799st_nat: set_option_list_nat > $o ).

thf(func_def_397,type,
    finite5523153139673422903on_nat: set_option_nat > $o ).

thf(func_def_398,type,
    finite6732403688824079472at_nat: set_op4508134149509766951at_nat > $o ).

thf(func_def_399,type,
    finite2014924581280026175on_rat: set_option_rat > $o ).

thf(func_def_400,type,
    finite6120865539452801872od_o_o: set_Product_prod_o_o > $o ).

thf(func_def_401,type,
    finite6891994925333515530_o_int: set_Pr8834758594704517033_o_int > $o ).

thf(func_def_402,type,
    finite1846473907987936430_o_nat: set_Pr2101469702781467981_o_nat > $o ).

thf(func_def_403,type,
    finite7561617386449315510_o_rat: set_Pr4944855402158566229_o_rat > $o ).

thf(func_def_404,type,
    finite2998713641127702882nt_int: set_Pr958786334691620121nt_int > $o ).

thf(func_def_405,type,
    finite1918287321285529104at_nat: set_Pr8551490117392284871at_nat > $o ).

thf(func_def_406,type,
    finite5355008432043429460_nat_o: set_Pr3149072824959771635_nat_o > $o ).

thf(func_def_407,type,
    finite6177210948735845034at_nat: set_Pr1261947904930325089at_nat > $o ).

thf(func_def_408,type,
    finite2668982390342448306at_rat: set_Pr4105333604307423337at_rat > $o ).

thf(func_def_409,type,
    finite1617675504726861388_rat_o: set_Pr2399638329824935915_rat_o > $o ).

thf(func_def_410,type,
    finite1682805285291782414at_int: set_Pr3594552606344371909at_int > $o ).

thf(func_def_411,type,
    finite5860656304800979122at_nat: set_Pr6084635751276098665at_nat > $o ).

thf(func_def_412,type,
    finite2352427746407582394at_rat: set_Pr8928021450653196913at_rat > $o ).

thf(func_def_413,type,
    finite4343798906461161616at_nat: set_Pr4329608150637261639at_nat > $o ).

thf(func_def_414,type,
    finite_finite_rat: set_rat > $o ).

thf(func_def_415,type,
    finite_finite_set_o: set_set_o > $o ).

thf(func_def_416,type,
    finite6197958912794628473et_int: set_set_int > $o ).

thf(func_def_417,type,
    finite7047420756378620717st_nat: set_set_list_nat > $o ).

thf(func_def_418,type,
    finite1152437895449049373et_nat: set_set_nat > $o ).

thf(func_def_419,type,
    finite8744585540193469122nt_int: set_se6260736226359567993nt_int > $o ).

thf(func_def_420,type,
    finite9047747110432174090at_nat: set_se7855581050983116737at_nat > $o ).

thf(func_def_421,type,
    finite6867581373910428453et_rat: set_set_rat > $o ).

thf(func_def_422,type,
    finite5847741373460823677iteral: set_literal > $o ).

thf(func_def_423,type,
    finite6699802884135759036um_o_o: set_Sum_sum_o_o > $o ).

thf(func_def_424,type,
    finite1631874702275618462_o_int: set_Sum_sum_o_int > $o ).

thf(func_def_425,type,
    finite5809725721784815170_o_nat: set_Sum_sum_o_nat > $o ).

thf(func_def_426,type,
    finite2301497163391418442_o_rat: set_Sum_sum_o_rat > $o ).

thf(func_def_427,type,
    finite94888208985532392_nat_o: set_Sum_sum_nat_o > $o ).

thf(func_def_428,type,
    finite2679478125380364318at_rat: set_Sum_sum_nat_rat > $o ).

thf(func_def_429,type,
    finite5580927318523740128_rat_o: set_Sum_sum_rat_o > $o ).

thf(func_def_430,type,
    finite1693301020329698426at_int: set_Sum_sum_rat_int > $o ).

thf(func_def_431,type,
    finite5871152039838895134at_nat: set_Sum_sum_rat_nat > $o ).

thf(func_def_432,type,
    finite2362923481445498406at_rat: set_Sum_sum_rat_rat > $o ).

thf(func_def_433,type,
    bij_betw_int_nat: ( int > nat ) > set_int > set_nat > $o ).

thf(func_def_434,type,
    bij_be8532844293280997160at_nat: ( list_nat > nat ) > set_list_nat > set_nat > $o ).

thf(func_def_435,type,
    bij_betw_nat_int: ( nat > int ) > set_nat > set_int > $o ).

thf(func_def_436,type,
    bij_be6293887246118711976st_nat: ( nat > list_nat ) > set_nat > set_list_nat > $o ).

thf(func_def_437,type,
    bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).

thf(func_def_438,type,
    bij_be8693218025023041337at_nat: ( nat > product_prod_nat_nat ) > set_nat > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_439,type,
    bij_be4790990086886966983at_nat: ( nat > sum_sum_nat_nat ) > set_nat > set_Sum_sum_nat_nat > $o ).

thf(func_def_440,type,
    bij_be5333170631980326235at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > set_nat > $o ).

thf(func_def_441,type,
    bij_be5432664580149595207at_nat: ( sum_sum_nat_nat > nat ) > set_Sum_sum_nat_nat > set_nat > $o ).

thf(func_def_442,type,
    comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_443,type,
    comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_444,type,
    comp_C3531382070062128313er_num: ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ).

thf(func_def_445,type,
    comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).

thf(func_def_446,type,
    comp_c4562247934908617188nteger: ( char > char ) > ( code_integer > char ) > code_integer > char ).

thf(func_def_447,type,
    id_o: $o > $o ).

thf(func_def_448,type,
    id_int: int > int ).

thf(func_def_449,type,
    id_nat: nat > nat ).

thf(func_def_450,type,
    id_num: num > num ).

thf(func_def_451,type,
    inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).

thf(func_def_452,type,
    map_fu1104370778922912482iteral: ( $o > $o ) > ( ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > $o > $o > $o > $o > $o > $o > literal > literal ) > ( $o > $o > $o > $o > $o > $o > $o > list_char > list_char ) > $o > $o > $o > $o > $o > $o > $o > literal > literal ).

thf(func_def_453,type,
    map_fu7309004089335677210iteral: ( $o > $o ) > ( ( $o > $o > $o > $o > $o > list_char > list_char ) > $o > $o > $o > $o > $o > literal > literal ) > ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > $o > $o > $o > $o > $o > $o > literal > literal ).

thf(func_def_454,type,
    map_fu1929762555066093878iteral: ( $o > $o ) > ( ( $o > $o > $o > $o > list_char > list_char ) > $o > $o > $o > $o > literal > literal ) > ( $o > $o > $o > $o > $o > list_char > list_char ) > $o > $o > $o > $o > $o > literal > literal ).

thf(func_def_455,type,
    map_fu5333924603067766298iteral: ( $o > $o ) > ( ( $o > $o > $o > list_char > list_char ) > $o > $o > $o > literal > literal ) > ( $o > $o > $o > $o > list_char > list_char ) > $o > $o > $o > $o > literal > literal ).

thf(func_def_456,type,
    map_fu1888220742600445322iteral: ( $o > $o ) > ( ( $o > $o > list_char > list_char ) > $o > $o > literal > literal ) > ( $o > $o > $o > list_char > list_char ) > $o > $o > $o > literal > literal ).

thf(func_def_457,type,
    map_fu5700776415251466522iteral: ( $o > $o ) > ( ( $o > list_char > list_char ) > $o > literal > literal ) > ( $o > $o > list_char > list_char ) > $o > $o > literal > literal ).

thf(func_def_458,type,
    map_fu4627020735845646302iteral: ( $o > $o ) > ( ( list_char > list_char ) > literal > literal ) > ( $o > list_char > list_char ) > $o > literal > literal ).

thf(func_def_459,type,
    map_fu2599414010547811884nteger: ( code_integer > int ) > ( int > code_integer ) > ( int > int ) > code_integer > code_integer ).

thf(func_def_460,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_461,type,
    map_fu3424225382358772769nt_rat: ( int > int ) > ( product_prod_int_int > rat ) > ( int > product_prod_int_int ) > int > rat ).

thf(func_def_462,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_463,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_464,type,
    map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).

thf(func_def_465,type,
    map_fu2345160673673942751at_nat: ( int > product_prod_nat_nat ) > ( nat > nat ) > ( product_prod_nat_nat > nat ) > int > nat ).

thf(func_def_466,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_467,type,
    map_fu6891787308814931657nteger: ( num > num ) > ( ( num > int ) > num > code_integer ) > ( num > num > int ) > num > num > code_integer ).

thf(func_def_468,type,
    map_fu8638147718074629079nteger: ( num > num ) > ( int > code_integer ) > ( num > int ) > num > code_integer ).

thf(func_def_469,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_470,type,
    map_fu898904425404107465nt_o_o: ( rat > product_prod_int_int ) > ( $o > $o ) > ( product_prod_int_int > $o ) > rat > $o ).

thf(func_def_471,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_472,type,
    map_fu2661873803724901240eral_o: ( literal > list_char ) > ( ( list_char > $o ) > literal > $o ) > ( list_char > list_char > $o ) > literal > literal > $o ).

thf(func_def_473,type,
    map_fu6698795530259886495ar_o_o: ( literal > list_char ) > ( $o > $o ) > ( list_char > $o ) > literal > $o ).

thf(func_def_474,type,
    map_fu7398138089906338514iteral: ( literal > list_char ) > ( list_char > literal ) > ( list_char > list_char ) > literal > literal ).

thf(func_def_475,type,
    fun_max_strict: set_Pr4329608150637261639at_nat ).

thf(func_def_476,type,
    fun_max_weak: set_Pr4329608150637261639at_nat ).

thf(func_def_477,type,
    fun_min_strict: set_Pr4329608150637261639at_nat ).

thf(func_def_478,type,
    fun_min_weak: set_Pr4329608150637261639at_nat ).

thf(func_def_479,type,
    fun_pair_leq: set_Pr8693737435421807431at_nat ).

thf(func_def_480,type,
    fun_pair_less: set_Pr8693737435421807431at_nat ).

thf(func_def_481,type,
    fun_re7357418987779152907at_nat: produc4193628355235574503at_nat > $o ).

thf(func_def_482,type,
    fun_re2478310338295953701at_nat: produc1319942482725812455at_nat > $o ).

thf(func_def_483,type,
    gcd_Gcd_int: set_int > int ).

thf(func_def_484,type,
    gcd_Gcd_nat: set_nat > nat ).

thf(func_def_485,type,
    gcd_Lcm_int: set_int > int ).

thf(func_def_486,type,
    gcd_Lcm_nat: set_nat > nat ).

thf(func_def_487,type,
    bezw: nat > nat > product_prod_int_int ).

thf(func_def_488,type,
    bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_489,type,
    gcd_gcd_int: int > int > int ).

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

thf(func_def_491,type,
    gcd_lcm_int: int > int > int ).

thf(func_def_492,type,
    gcd_lcm_nat: nat > nat > nat ).

thf(func_def_493,type,
    gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_494,type,
    abs_abs_Code_integer: code_integer > code_integer ).

thf(func_def_495,type,
    abs_abs_int: int > int ).

thf(func_def_496,type,
    abs_abs_rat: rat > rat ).

thf(func_def_497,type,
    comm_m8764728085499324515char_o: ( ( list_char > $o ) > ( list_char > $o ) > list_char > $o ) > ( list_char > $o ) > $o ).

thf(func_def_498,type,
    comm_m5839176995973721103_int_o: ( ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).

thf(func_def_499,type,
    comm_monoid_assn: ( assn > assn > assn ) > assn > $o ).

thf(func_def_500,type,
    comm_m1654649897431166824nteger: ( code_integer > code_integer > code_integer ) > code_integer > $o ).

thf(func_def_501,type,
    comm_monoid_int: ( int > int > int ) > int > $o ).

thf(func_def_502,type,
    comm_m1862543879040115196at_nat: ( multis2468970476368604999at_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat ) > multis2468970476368604999at_nat > $o ).

thf(func_def_503,type,
    comm_monoid_nat: ( nat > nat > nat ) > nat > $o ).

thf(func_def_504,type,
    comm_monoid_rat: ( rat > rat > rat ) > rat > $o ).

thf(func_def_505,type,
    comm_monoid_set_o: ( set_o > set_o > set_o ) > set_o > $o ).

thf(func_def_506,type,
    comm_monoid_set_int: ( set_int > set_int > set_int ) > set_int > $o ).

thf(func_def_507,type,
    comm_m4511514676032769697st_nat: ( set_list_nat > set_list_nat > set_list_nat ) > set_list_nat > $o ).

thf(func_def_508,type,
    comm_monoid_set_nat: ( set_nat > set_nat > set_nat ) > set_nat > $o ).

thf(func_def_509,type,
    comm_m4707310049023135612at_nat: ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ) > set_Pr8551490117392284871at_nat > $o ).

thf(func_def_510,type,
    comm_m5709050211238513046at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_511,type,
    comm_m2457627138559323900at_nat: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ) > set_Pr4329608150637261639at_nat > $o ).

thf(func_def_512,type,
    comm_monoid_set_rat: ( set_rat > set_rat > set_rat ) > set_rat > $o ).

thf(func_def_513,type,
    minus_2803741817741520073at_o_o: ( ( produc3658429121746597890et_nat > $o ) > $o ) > ( ( produc3658429121746597890et_nat > $o ) > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ).

thf(func_def_514,type,
    minus_minus_int_o: ( int > $o ) > ( int > $o ) > int > $o ).

thf(func_def_515,type,
    minus_6821098565838606101char_o: ( list_char > $o ) > ( list_char > $o ) > list_char > $o ).

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

thf(func_def_517,type,
    minus_711738161318947805_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ).

thf(func_def_518,type,
    minus_6910147592129066416_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > set_nat > $o ).

thf(func_def_519,type,
    minus_357216186751819389_int_o: ( set_Pr958786334691620121nt_int > $o ) > ( set_Pr958786334691620121nt_int > $o ) > set_Pr958786334691620121nt_int > $o ).

thf(func_def_520,type,
    minus_minus_assn: assn > assn > assn ).

thf(func_def_521,type,
    minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).

thf(func_def_522,type,
    minus_7197305767214868737atural: code_natural > code_natural > code_natural ).

thf(func_def_523,type,
    minus_minus_int: int > int > int ).

thf(func_def_524,type,
    minus_4286766774447292334at_nat: multis2468970476368604999at_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat ).

thf(func_def_525,type,
    minus_minus_nat: nat > nat > nat ).

thf(func_def_526,type,
    minus_3524152463667985524t_unit: product_unit > product_unit > product_unit ).

thf(func_def_527,type,
    minus_minus_rat: rat > rat > rat ).

thf(func_def_528,type,
    minus_1801376950450012436_nat_o: set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o ).

thf(func_def_529,type,
    minus_minus_set_o: set_o > set_o > set_o ).

thf(func_def_530,type,
    minus_2355218937544613996nteger: set_Code_integer > set_Code_integer > set_Code_integer ).

thf(func_def_531,type,
    minus_minus_set_int: set_int > set_int > set_int ).

thf(func_def_532,type,
    minus_7954133019191499631st_nat: set_list_nat > set_list_nat > set_list_nat ).

thf(func_def_533,type,
    minus_minus_set_nat: set_nat > set_nat > set_nat ).

thf(func_def_534,type,
    minus_1052850069191792384nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).

thf(func_def_535,type,
    minus_5060654252129873198at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ).

thf(func_def_536,type,
    minus_1356011639430497352at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_537,type,
    minus_3314409938677909166at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).

thf(func_def_538,type,
    minus_minus_set_rat: set_rat > set_rat > set_rat ).

thf(func_def_539,type,
    minus_2163939370556025621et_nat: set_set_nat > set_set_nat > set_set_nat ).

thf(func_def_540,type,
    minus_2612819937483484256nt_int: set_se6260736226359567993nt_int > set_se6260736226359567993nt_int > set_se6260736226359567993nt_int ).

thf(func_def_541,type,
    monoid_list_char_o: ( ( list_char > $o ) > ( list_char > $o ) > list_char > $o ) > ( list_char > $o ) > $o ).

thf(func_def_542,type,
    monoid6910981727789844035_int_o: ( ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).

thf(func_def_543,type,
    monoid_assn: ( assn > assn > assn ) > assn > $o ).

thf(func_def_544,type,
    monoid_Code_integer: ( code_integer > code_integer > code_integer ) > code_integer > $o ).

thf(func_def_545,type,
    monoid_int: ( int > int > int ) > int > $o ).

thf(func_def_546,type,
    monoid66256789251010760at_nat: ( multis2468970476368604999at_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat ) > multis2468970476368604999at_nat > $o ).

thf(func_def_547,type,
    monoid_nat: ( nat > nat > nat ) > nat > $o ).

thf(func_def_548,type,
    monoid_rat: ( rat > rat > rat ) > rat > $o ).

thf(func_def_549,type,
    monoid_set_o: ( set_o > set_o > set_o ) > set_o > $o ).

thf(func_def_550,type,
    monoid_set_int: ( set_int > set_int > set_int ) > set_int > $o ).

thf(func_def_551,type,
    monoid_set_list_nat: ( set_list_nat > set_list_nat > set_list_nat ) > set_list_nat > $o ).

thf(func_def_552,type,
    monoid_set_nat: ( set_nat > set_nat > set_nat ) > set_nat > $o ).

thf(func_def_553,type,
    monoid3323479476634721864at_nat: ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ) > set_Pr8551490117392284871at_nat > $o ).

thf(func_def_554,type,
    monoid1519094961268053602at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_555,type,
    monoid534952638934301128at_nat: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ) > set_Pr4329608150637261639at_nat > $o ).

thf(func_def_556,type,
    monoid_set_rat: ( set_rat > set_rat > set_rat ) > set_rat > $o ).

thf(func_def_557,type,
    monoid_literal: ( literal > literal > literal ) > literal > $o ).

thf(func_def_558,type,
    one_one_assn: assn ).

thf(func_def_559,type,
    one_one_Code_integer: code_integer ).

thf(func_def_560,type,
    one_one_Code_natural: code_natural ).

thf(func_def_561,type,
    one_one_int: int ).

thf(func_def_562,type,
    one_one_nat: nat ).

thf(func_def_563,type,
    one_one_rat: rat ).

thf(func_def_564,type,
    plus_p5714425477246183910nteger: code_integer > code_integer > code_integer ).

thf(func_def_565,type,
    plus_p4538020629002901425atural: code_natural > code_natural > code_natural ).

thf(func_def_566,type,
    plus_plus_int: int > int > int ).

thf(func_def_567,type,
    plus_p7104986032573967614at_nat: multis2468970476368604999at_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat ).

thf(func_def_568,type,
    plus_plus_nat: nat > nat > nat ).

thf(func_def_569,type,
    plus_plus_num: num > num > num ).

thf(func_def_570,type,
    plus_plus_rat: rat > rat > rat ).

thf(func_def_571,type,
    plus_plus_literal: literal > literal > literal ).

thf(func_def_572,type,
    sgn_sgn_Code_integer: code_integer > code_integer ).

thf(func_def_573,type,
    sgn_sgn_int: int > int ).

thf(func_def_574,type,
    sgn_sgn_rat: rat > rat ).

thf(func_def_575,type,
    times_times_assn: assn > assn > assn ).

thf(func_def_576,type,
    times_3573771949741848930nteger: code_integer > code_integer > code_integer ).

thf(func_def_577,type,
    times_2397367101498566445atural: code_natural > code_natural > code_natural ).

thf(func_def_578,type,
    times_times_int: int > int > int ).

thf(func_def_579,type,
    times_times_nat: nat > nat > nat ).

thf(func_def_580,type,
    times_times_num: num > num > num ).

thf(func_def_581,type,
    times_times_rat: rat > rat > rat ).

thf(func_def_582,type,
    uminus8928876914783121465at_o_o: ( ( produc3658429121746597890et_nat > $o ) > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ).

thf(func_def_583,type,
    uminus_uminus_int_o: ( int > $o ) > int > $o ).

thf(func_def_584,type,
    uminus7154032370948614053char_o: ( list_char > $o ) > list_char > $o ).

thf(func_def_585,type,
    uminus_uminus_nat_o: ( nat > $o ) > nat > $o ).

thf(func_def_586,type,
    uminus7117520113953359693_int_o: ( product_prod_int_int > $o ) > product_prod_int_int > $o ).

thf(func_def_587,type,
    uminus6401447641752708672_nat_o: ( set_nat > $o ) > set_nat > $o ).

thf(func_def_588,type,
    uminus8147837162492574189_int_o: ( set_Pr958786334691620121nt_int > $o ) > set_Pr958786334691620121nt_int > $o ).

thf(func_def_589,type,
    uminus_uminus_assn: assn > assn ).

thf(func_def_590,type,
    uminus1351360451143612070nteger: code_integer > code_integer ).

thf(func_def_591,type,
    uminus_uminus_int: int > int ).

thf(func_def_592,type,
    uminus2952777764628376836t_unit: product_unit > product_unit ).

thf(func_def_593,type,
    uminus_uminus_rat: rat > rat ).

thf(func_def_594,type,
    uminus5254974436814262692_nat_o: set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o ).

thf(func_def_595,type,
    uminus_uminus_set_o: set_o > set_o ).

thf(func_def_596,type,
    uminus1532241313380277803et_int: set_int > set_int ).

thf(func_def_597,type,
    uminus3195874150345416415st_nat: set_list_nat > set_list_nat ).

thf(func_def_598,type,
    uminus5710092332889474511et_nat: set_nat > set_nat ).

thf(func_def_599,type,
    uminus2330091110623919550at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ).

thf(func_def_600,type,
    uminus6524753893492686040at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_601,type,
    uminus935396558254630718at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).

thf(func_def_602,type,
    uminus2201863774496077783et_rat: set_rat > set_rat ).

thf(func_def_603,type,
    uminus613421341184616069et_nat: set_set_nat > set_set_nat ).

thf(func_def_604,type,
    uminus6423885277529793776nt_int: set_se6260736226359567993nt_int > set_se6260736226359567993nt_int ).

thf(func_def_605,type,
    zero_z3403309356797280102nteger: code_integer ).

thf(func_def_606,type,
    zero_z2226904508553997617atural: code_natural ).

thf(func_def_607,type,
    zero_zero_int: int ).

thf(func_def_608,type,
    zero_z1048942125864253310at_nat: multis2468970476368604999at_nat ).

thf(func_def_609,type,
    zero_zero_nat: nat ).

thf(func_def_610,type,
    zero_zero_rat: rat ).

thf(func_def_611,type,
    zero_zero_literal: literal ).

thf(func_def_612,type,
    groups6742167275697360483_o_nat: ( ( produc3658429121746597890et_nat > $o ) > nat ) > set_Pr4532377907799695533_nat_o > nat ).

thf(func_def_613,type,
    groups4406642042086082107nteger: ( $o > code_integer ) > set_o > code_integer ).

thf(func_def_614,type,
    groups3230237193842799622atural: ( $o > code_natural ) > set_o > code_natural ).

thf(func_def_615,type,
    groups8505340233167759370_o_int: ( $o > int ) > set_o > int ).

thf(func_def_616,type,
    groups8507830703676809646_o_nat: ( $o > nat ) > set_o > nat ).

thf(func_def_617,type,
    groups7872700643590313910_o_rat: ( $o > rat ) > set_o > rat ).

thf(func_def_618,type,
    groups7873554091576472773nteger: ( int > code_integer ) > set_int > code_integer ).

thf(func_def_619,type,
    groups6697149243333190288atural: ( int > code_natural ) > set_int > code_natural ).

thf(func_def_620,type,
    groups4538972089207619220nt_int: ( int > int ) > set_int > int ).

thf(func_def_621,type,
    groups4541462559716669496nt_nat: ( int > nat ) > set_int > nat ).

thf(func_def_622,type,
    groups3906332499630173760nt_rat: ( int > rat ) > set_int > rat ).

thf(func_def_623,type,
    groups4396056296759096172at_nat: ( list_nat > nat ) > set_list_nat > nat ).

thf(func_def_624,type,
    groups3760926236672600436at_rat: ( list_nat > rat ) > set_list_nat > rat ).

thf(func_def_625,type,
    groups7501900531339628137nteger: ( nat > code_integer ) > set_nat > code_integer ).

thf(func_def_626,type,
    groups6325495683096345652atural: ( nat > code_natural ) > set_nat > code_natural ).

thf(func_def_627,type,
    groups3539618377306564664at_int: ( nat > int ) > set_nat > int ).

thf(func_def_628,type,
    groups6857163185585827899at_nat: ( nat > multis2468970476368604999at_nat ) > set_nat > multis2468970476368604999at_nat ).

thf(func_def_629,type,
    groups3542108847815614940at_nat: ( nat > nat ) > set_nat > nat ).

thf(func_def_630,type,
    groups2906978787729119204at_rat: ( nat > rat ) > set_nat > rat ).

thf(func_def_631,type,
    groups7057407298757096921at_int: ( produc4166570645942440679at_nat > int ) > set_Pr8551490117392284871at_nat > int ).

thf(func_def_632,type,
    groups7059897769266147197at_nat: ( produc4166570645942440679at_nat > nat ) > set_Pr8551490117392284871at_nat > nat ).

thf(func_def_633,type,
    groups6424767709179651461at_rat: ( produc4166570645942440679at_nat > rat ) > set_Pr8551490117392284871at_nat > rat ).

thf(func_def_634,type,
    groups196832835297161892nteger: ( product_prod_nat_nat > code_integer ) > set_Pr1261947904930325089at_nat > code_integer ).

thf(func_def_635,type,
    groups975429370522433651at_int: ( product_prod_nat_nat > int ) > set_Pr1261947904930325089at_nat > int ).

thf(func_def_636,type,
    groups977919841031483927at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > nat ).

thf(func_def_637,type,
    groups342789780944988191at_rat: ( product_prod_nat_nat > rat ) > set_Pr1261947904930325089at_nat > rat ).

thf(func_def_638,type,
    groups3858419854409063513at_int: ( produc3843707927480180839at_nat > int ) > set_Pr4329608150637261639at_nat > int ).

thf(func_def_639,type,
    groups3860910324918113789at_nat: ( produc3843707927480180839at_nat > nat ) > set_Pr4329608150637261639at_nat > nat ).

thf(func_def_640,type,
    groups3225780264831618053at_rat: ( produc3843707927480180839at_nat > rat ) > set_Pr4329608150637261639at_nat > rat ).

thf(func_def_641,type,
    groups9190459664516455967nteger: ( set_nat > code_integer ) > set_set_nat > code_integer ).

thf(func_def_642,type,
    groups8292507037921071086at_int: ( set_nat > int ) > set_set_nat > int ).

thf(func_def_643,type,
    groups8294997508430121362at_nat: ( set_nat > nat ) > set_set_nat > nat ).

thf(func_def_644,type,
    groups7659867448343625626at_rat: ( set_nat > rat ) > set_set_nat > rat ).

thf(func_def_645,type,
    groups3738144136874984124nteger: ( set_Pr958786334691620121nt_int > code_integer ) > set_se6260736226359567993nt_int > code_integer ).

thf(func_def_646,type,
    groups185207323561075247nt_nat: ( set_Pr958786334691620121nt_int > nat ) > set_se6260736226359567993nt_int > nat ).

thf(func_def_647,type,
    groups8773449300329355319nt_rat: ( set_Pr958786334691620121nt_int > rat ) > set_se6260736226359567993nt_int > rat ).

thf(func_def_648,type,
    groups1402912129352969042nteger: ( $o > code_integer ) > set_o > code_integer ).

thf(func_def_649,type,
    groups4553916814277028129_o_int: ( $o > int ) > set_o > int ).

thf(func_def_650,type,
    groups4556407284786078405_o_nat: ( $o > nat ) > set_o > nat ).

thf(func_def_651,type,
    groups3921277224699582669_o_rat: ( $o > rat ) > set_o > rat ).

thf(func_def_652,type,
    groups926780983652909934nteger: ( int > code_integer ) > set_int > code_integer ).

thf(func_def_653,type,
    groups2983280209131991357nt_int: ( int > int ) > set_int > int ).

thf(func_def_654,type,
    groups2985770679641041633nt_nat: ( int > nat ) > set_int > nat ).

thf(func_def_655,type,
    groups2350640619554545897nt_rat: ( int > rat ) > set_int > rat ).

thf(func_def_656,type,
    groups555127423416065298nteger: ( nat > code_integer ) > set_nat > code_integer ).

thf(func_def_657,type,
    groups1983926497230936801at_int: ( nat > int ) > set_nat > int ).

thf(func_def_658,type,
    groups1986416967739987077at_nat: ( nat > nat ) > set_nat > nat ).

thf(func_def_659,type,
    groups1351286907653491341at_rat: ( nat > rat ) > set_nat > rat ).

thf(func_def_660,type,
    groups9221925307898054856nteger: ( set_nat > code_integer ) > set_set_nat > code_integer ).

thf(func_def_661,type,
    groups713094340420062787at_rat: ( set_nat > rat ) > set_set_nat > rat ).

thf(func_def_662,type,
    groups5301882518646026715o_assn: ( $o > assn ) > set_o > assn ).

thf(func_def_663,type,
    groups7694694392188491536nteger: ( $o > code_integer ) > set_o > code_integer ).

thf(func_def_664,type,
    groups6518289543945209051atural: ( $o > code_natural ) > set_o > code_natural ).

thf(func_def_665,type,
    groups3502327434004483295_o_int: ( $o > int ) > set_o > int ).

thf(func_def_666,type,
    groups3504817904513533571_o_nat: ( $o > nat ) > set_o > nat ).

thf(func_def_667,type,
    groups2869687844427037835_o_rat: ( $o > rat ) > set_o > rat ).

thf(func_def_668,type,
    groups7882442080178216443t_assn: ( int > assn ) > set_int > assn ).

thf(func_def_669,type,
    groups3827104343326376752nteger: ( int > code_integer ) > set_int > code_integer ).

thf(func_def_670,type,
    groups1705073143266064639nt_int: ( int > int ) > set_int > int ).

thf(func_def_671,type,
    groups1707563613775114915nt_nat: ( int > nat ) > set_int > nat ).

thf(func_def_672,type,
    groups1072433553688619179nt_rat: ( int > rat ) > set_int > rat ).

thf(func_def_673,type,
    groups2905156660866384563at_int: ( list_nat > int ) > set_list_nat > int ).

thf(func_def_674,type,
    groups2907647131375434839at_nat: ( list_nat > nat ) > set_list_nat > nat ).

thf(func_def_675,type,
    groups6906906614972039071t_assn: ( nat > assn ) > set_nat > assn ).

thf(func_def_676,type,
    groups3455450783089532116nteger: ( nat > code_integer ) > set_nat > code_integer ).

thf(func_def_677,type,
    groups2279045934846249631atural: ( nat > code_natural ) > set_nat > code_natural ).

thf(func_def_678,type,
    groups705719431365010083at_int: ( nat > int ) > set_nat > int ).

thf(func_def_679,type,
    groups708209901874060359at_nat: ( nat > nat ) > set_nat > nat ).

thf(func_def_680,type,
    groups73079841787564623at_rat: ( nat > rat ) > set_nat > rat ).

thf(func_def_681,type,
    groups5938585286922990810at_rat: ( produc4166570645942440679at_nat > rat ) > set_Pr8551490117392284871at_nat > rat ).

thf(func_def_682,type,
    groups1230400874837758585nteger: ( product_prod_nat_nat > code_integer ) > set_Pr1261947904930325089at_nat > code_integer ).

thf(func_def_683,type,
    groups4075276357253098568at_int: ( product_prod_nat_nat > int ) > set_Pr1261947904930325089at_nat > int ).

thf(func_def_684,type,
    groups4077766827762148844at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > nat ).

thf(func_def_685,type,
    groups3442636767675653108at_rat: ( product_prod_nat_nat > rat ) > set_Pr1261947904930325089at_nat > rat ).

thf(func_def_686,type,
    groups8874911130973611098at_rat: ( produc3843707927480180839at_nat > rat ) > set_Pr4329608150637261639at_nat > rat ).

thf(func_def_687,type,
    groups2761809935038513290nteger: ( set_nat > code_integer ) > set_set_nat > code_integer ).

thf(func_def_688,type,
    groups4246057289670975065at_int: ( set_nat > int ) > set_set_nat > int ).

thf(func_def_689,type,
    groups4248547760180025341at_nat: ( set_nat > nat ) > set_set_nat > nat ).

thf(func_def_690,type,
    groups3613417700093529605at_rat: ( set_nat > rat ) > set_set_nat > rat ).

thf(func_def_691,type,
    groups4561878855575611511st_nat: list_nat > nat ).

thf(func_def_692,type,
    nO_MAT8252062027627875367nteger: code_integer > code_integer > $o ).

thf(func_def_693,type,
    nO_MAT8427913294028938742er_int: code_integer > int > $o ).

thf(func_def_694,type,
    nO_MAT7795273704451493282er_rat: code_integer > rat > $o ).

thf(func_def_695,type,
    nO_MAT9066612773553876470nteger: int > code_integer > $o ).

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

thf(func_def_697,type,
    nO_MATCH_int_nat: int > nat > $o ).

thf(func_def_698,type,
    nO_MATCH_int_rat: int > rat > $o ).

thf(func_def_699,type,
    nO_MAT8694959213317031834nteger: nat > code_integer > $o ).

thf(func_def_700,type,
    nO_MATCH_nat_int: nat > int > $o ).

thf(func_def_701,type,
    nO_MATCH_nat_nat: nat > nat > $o ).

thf(func_def_702,type,
    nO_MATCH_nat_rat: nat > rat > $o ).

thf(func_def_703,type,
    nO_MAT243659986023775650nteger: rat > code_integer > $o ).

thf(func_def_704,type,
    nO_MATCH_rat_rat: rat > rat > $o ).

thf(func_def_705,type,
    the_int: ( int > $o ) > int ).

thf(func_def_706,type,
    the_Pr4378521158711661632nt_int: ( product_prod_int_int > $o ) > product_prod_int_int ).

thf(func_def_707,type,
    lim_Product_unit: heap_e7401611519738050253t_unit > nat ).

thf(func_def_708,type,
    if_assn: $o > assn > assn > assn ).

thf(func_def_709,type,
    if_Code_integer: $o > code_integer > code_integer > code_integer ).

thf(func_def_710,type,
    if_Code_natural: $o > code_natural > code_natural > code_natural ).

thf(func_def_711,type,
    if_int: $o > int > int > int ).

thf(func_def_712,type,
    if_list_int: $o > list_int > list_int > list_int ).

thf(func_def_713,type,
    if_mul8430962117462786573at_nat: $o > multis2468970476368604999at_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat ).

thf(func_def_714,type,
    if_nat: $o > nat > nat > nat ).

thf(func_def_715,type,
    if_num: $o > num > num > num ).

thf(func_def_716,type,
    if_option_num: $o > option_num > option_num > option_num ).

thf(func_def_717,type,
    if_pred_Product_unit: $o > pred_Product_unit > pred_Product_unit > pred_Product_unit ).

thf(func_def_718,type,
    if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o ).

thf(func_def_719,type,
    if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_720,type,
    if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).

thf(func_def_721,type,
    if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_722,type,
    if_Pro3444522238938527101atural: $o > produc4675096598859438275atural > produc4675096598859438275atural > produc4675096598859438275atural ).

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

thf(func_def_724,type,
    if_set_int: $o > set_int > set_int > set_int ).

thf(func_def_725,type,
    if_Sum_sum_nat_nat: $o > sum_sum_nat_nat > sum_sum_nat_nat > sum_sum_nat_nat ).

thf(func_def_726,type,
    infini8530281810654367211te_nat: set_nat > nat > nat ).

thf(func_def_727,type,
    abs_Integ: product_prod_nat_nat > int ).

thf(func_def_728,type,
    rep_Integ: int > product_prod_nat_nat ).

thf(func_def_729,type,
    cr_int: product_prod_nat_nat > int > $o ).

thf(func_def_730,type,
    dup: int > int ).

thf(func_def_731,type,
    abs_int: set_Pr1261947904930325089at_nat > int ).

thf(func_def_732,type,
    rep_int: int > set_Pr1261947904930325089at_nat ).

thf(func_def_733,type,
    int_ge_less_than: int > set_Pr958786334691620121nt_int ).

thf(func_def_734,type,
    int_ge_less_than2: int > set_Pr958786334691620121nt_int ).

thf(func_def_735,type,
    intrel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_736,type,
    nat2: int > nat ).

thf(func_def_737,type,
    pcr_int: product_prod_nat_nat > int > $o ).

thf(func_def_738,type,
    ring_18347121197199848620nteger: int > code_integer ).

thf(func_def_739,type,
    ring_1_of_int_int: int > int ).

thf(func_def_740,type,
    ring_1_of_int_rat: int > rat ).

thf(func_def_741,type,
    sub: num > num > int ).

thf(func_def_742,type,
    inf_in8201999774870019094_int_o: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ).

thf(func_def_743,type,
    inf_in3563340378267265229eger_o: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ).

thf(func_def_744,type,
    inf_in2641120393918057659_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).

thf(func_def_745,type,
    inf_in3295504058751909687_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).

thf(func_def_746,type,
    inf_in9018898317438245890at_o_o: ( ( produc3658429121746597890et_nat > $o ) > $o ) > ( ( produc3658429121746597890et_nat > $o ) > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ).

thf(func_def_747,type,
    inf_in8045883074377559328_int_o: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ).

thf(func_def_748,type,
    inf_inf_int_o: ( int > $o ) > ( int > $o ) > int > $o ).

thf(func_def_749,type,
    inf_inf_list_char_o: ( list_char > $o ) > ( list_char > $o ) > list_char > $o ).

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

thf(func_def_751,type,
    inf_inf_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).

thf(func_def_752,type,
    inf_in3604695632404883862_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ).

thf(func_def_753,type,
    inf_in5163264567034779214_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).

thf(func_def_754,type,
    inf_inf_set_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > set_nat > $o ).

thf(func_def_755,type,
    inf_in5102985939729578038_int_o: ( set_Pr958786334691620121nt_int > $o ) > ( set_Pr958786334691620121nt_int > $o ) > set_Pr958786334691620121nt_int > $o ).

thf(func_def_756,type,
    inf_inf_o: $o > $o > $o ).

thf(func_def_757,type,
    inf_inf_assn: assn > assn > assn ).

thf(func_def_758,type,
    inf_inf_filter_nat: filter_nat > filter_nat > filter_nat ).

thf(func_def_759,type,
    inf_inf_int: int > int > int ).

thf(func_def_760,type,
    inf_inf_nat: nat > nat > nat ).

thf(func_def_761,type,
    inf_inf_Product_unit: product_unit > product_unit > product_unit ).

thf(func_def_762,type,
    inf_inf_rat: rat > rat > rat ).

thf(func_def_763,type,
    inf_in1906310914598751387_nat_o: set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o ).

thf(func_def_764,type,
    inf_inf_set_o: set_o > set_o > set_o ).

thf(func_def_765,type,
    inf_in1364745209274528805nteger: set_Code_integer > set_Code_integer > set_Code_integer ).

thf(func_def_766,type,
    inf_inf_set_int: set_int > set_int > set_int ).

thf(func_def_767,type,
    inf_inf_set_list_nat: set_list_nat > set_list_nat > set_list_nat ).

thf(func_def_768,type,
    inf_in6177012701088388009t_char: set_list_char > set_list_char > set_list_char ).

thf(func_def_769,type,
    inf_inf_set_nat: set_nat > set_nat > set_nat ).

thf(func_def_770,type,
    inf_in8806012763027673301nt_int: set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int ).

thf(func_def_771,type,
    inf_in3408396081536963678nteger: set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger ).

thf(func_def_772,type,
    inf_in3088352823822785602et_nat: set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat ).

thf(func_def_773,type,
    inf_in1768905781608824518et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat ).

thf(func_def_774,type,
    inf_in2576786181675586251nt_int: set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int ).

thf(func_def_775,type,
    inf_in2269163501485487111nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).

thf(func_def_776,type,
    inf_in1697001100524423349at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ).

thf(func_def_777,type,
    inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_778,type,
    inf_in7913087082777306421at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).

thf(func_def_779,type,
    inf_inf_set_rat: set_rat > set_rat > set_rat ).

thf(func_def_780,type,
    inf_inf_set_set_nat: set_set_nat > set_set_nat > set_set_nat ).

thf(func_def_781,type,
    inf_in8396524679539076455nt_int: set_se6260736226359567993nt_int > set_se6260736226359567993nt_int > set_se6260736226359567993nt_int ).

thf(func_def_782,type,
    inf_inf_set_literal: set_literal > set_literal > set_literal ).

thf(func_def_783,type,
    semila3963277552210239504char_o: ( ( list_char > $o ) > ( list_char > $o ) > list_char > $o ) > ( list_char > $o ) > $o ).

thf(func_def_784,type,
    semila6538661356715008162_int_o: ( ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).

thf(func_def_785,type,
    semila6106414119144251899nteger: ( code_integer > code_integer > code_integer ) > code_integer > $o ).

thf(func_def_786,type,
    semila9079005292280841162tr_int: ( int > int > int ) > int > $o ).

thf(func_def_787,type,
    semila9081495762789891438tr_nat: ( nat > nat > nat ) > nat > $o ).

thf(func_def_788,type,
    semila1065760912024005978_set_o: ( set_o > set_o > set_o ) > set_o > $o ).

thf(func_def_789,type,
    semila6287294981380917632et_int: ( set_int > set_int > set_int ) > set_int > $o ).

thf(func_def_790,type,
    semila7136768128396663732st_nat: ( set_list_nat > set_list_nat > set_list_nat ) > set_list_nat > $o ).

thf(func_def_791,type,
    semila1241773964035338532et_nat: ( set_nat > set_nat > set_nat ) > set_nat > $o ).

thf(func_def_792,type,
    semila6683195626996185257at_nat: ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ) > set_Pr8551490117392284871at_nat > $o ).

thf(func_def_793,type,
    semila858173770281612099at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_794,type,
    semila3675781407871293737at_nat: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ) > set_Pr4329608150637261639at_nat > $o ).

thf(func_def_795,type,
    semila6956917442496717612et_rat: ( set_rat > set_rat > set_rat ) > set_rat > $o ).

thf(func_def_796,type,
    semila3134969884451571676char_o: ( ( list_char > $o ) > ( list_char > $o ) > list_char > $o ) > ( list_char > $o ) > ( ( list_char > $o ) > ( list_char > $o ) > $o ) > ( ( list_char > $o ) > ( list_char > $o ) > $o ) > $o ).

thf(func_def_797,type,
    semila8052717425514686422_int_o: ( ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > ( ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ) > ( ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ) > $o ).

thf(func_def_798,type,
    semila5926144314033625522er_nat: ( filter_nat > filter_nat > filter_nat ) > filter_nat > ( filter_nat > filter_nat > $o ) > ( filter_nat > filter_nat > $o ) > $o ).

thf(func_def_799,type,
    semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).

thf(func_def_800,type,
    semila2554085542299052326_set_o: ( set_o > set_o > set_o ) > set_o > ( set_o > set_o > $o ) > ( set_o > set_o > $o ) > $o ).

thf(func_def_801,type,
    semila6712789903965657268et_int: ( set_int > set_int > set_int ) > set_int > ( set_int > set_int > $o ) > ( set_int > set_int > $o ) > $o ).

thf(func_def_802,type,
    semila2613578647866687720st_nat: ( set_list_nat > set_list_nat > set_list_nat ) > set_list_nat > ( set_list_nat > set_list_nat > $o ) > ( set_list_nat > set_list_nat > $o ) > $o ).

thf(func_def_803,type,
    semila1667268886620078168et_nat: ( set_nat > set_nat > set_nat ) > set_nat > ( set_nat > set_nat > $o ) > ( set_nat > set_nat > $o ) > $o ).

thf(func_def_804,type,
    semila5207306265035627125at_nat: ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ) > set_Pr8551490117392284871at_nat > ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > $o ) > ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > $o ) > $o ).

thf(func_def_805,type,
    semila4918476307565957903at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > $o ).

thf(func_def_806,type,
    semila6534579987270727413at_nat: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ) > set_Pr4329608150637261639at_nat > ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > $o ).

thf(func_def_807,type,
    semila7382412365081457248et_rat: ( set_rat > set_rat > set_rat ) > set_rat > ( set_rat > set_rat > $o ) > ( set_rat > set_rat > $o ) > $o ).

thf(func_def_808,type,
    semila1248733672344298208er_nat: ( nat > nat > nat ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).

thf(func_def_809,type,
    sup_su600977994968626096_int_o: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ).

thf(func_def_810,type,
    sup_su234547053653886311eger_o: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ).

thf(func_def_811,type,
    sup_su6535292691877529429_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).

thf(func_def_812,type,
    sup_su1630790145277462993_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).

thf(func_def_813,type,
    sup_su8003631835303541148at_o_o: ( ( produc3658429121746597890et_nat > $o ) > $o ) > ( ( produc3658429121746597890et_nat > $o ) > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ).

thf(func_def_814,type,
    sup_su4182031696650224058_int_o: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ).

thf(func_def_815,type,
    sup_sup_int_o: ( int > $o ) > ( int > $o ) > int > $o ).

thf(func_def_816,type,
    sup_sup_list_char_o: ( list_char > $o ) > ( list_char > $o ) > list_char > $o ).

thf(func_def_817,type,
    sup_su2200014604384089602_nat_o: ( multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o ) > ( multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o ) > multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o ).

thf(func_def_818,type,
    sup_sup_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).

thf(func_def_819,type,
    sup_su8463660629351352368_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ).

thf(func_def_820,type,
    sup_su6256023009775730178_nat_o: ( produc4166570645942440679at_nat > $o ) > ( produc4166570645942440679at_nat > $o ) > produc4166570645942440679at_nat > $o ).

thf(func_def_821,type,
    sup_su2080679670758317954_nat_o: ( produc3843707927480180839at_nat > $o ) > ( produc3843707927480180839at_nat > $o ) > produc3843707927480180839at_nat > $o ).

thf(func_def_822,type,
    sup_sup_set_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > set_nat > $o ).

thf(func_def_823,type,
    sup_su1852724690005176016_int_o: ( set_Pr958786334691620121nt_int > $o ) > ( set_Pr958786334691620121nt_int > $o ) > set_Pr958786334691620121nt_int > $o ).

thf(func_def_824,type,
    sup_su7519161239522478338_nat_o: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_825,type,
    sup_sup_assn: assn > assn > assn ).

thf(func_def_826,type,
    sup_sup_filter_nat: filter_nat > filter_nat > filter_nat ).

thf(func_def_827,type,
    sup_sup_int: int > int > int ).

thf(func_def_828,type,
    sup_sup_nat: nat > nat > nat ).

thf(func_def_829,type,
    sup_sup_Product_unit: product_unit > product_unit > product_unit ).

thf(func_def_830,type,
    sup_sup_rat: rat > rat > rat ).

thf(func_def_831,type,
    sup_su5209123915105501825_nat_o: set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o ).

thf(func_def_832,type,
    sup_sup_set_o: set_o > set_o > set_o ).

thf(func_def_833,type,
    sup_su848401254843788991nteger: set_Code_integer > set_Code_integer > set_Code_integer ).

thf(func_def_834,type,
    sup_sup_set_int: set_int > set_int > set_int ).

thf(func_def_835,type,
    sup_sup_set_list_nat: set_list_nat > set_list_nat > set_list_nat ).

thf(func_def_836,type,
    sup_sup_set_nat: set_nat > set_nat > set_nat ).

thf(func_def_837,type,
    sup_su3298353300217089135nt_int: set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int ).

thf(func_def_838,type,
    sup_su4591284015454442744nteger: set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger ).

thf(func_def_839,type,
    sup_su8975264963432250076et_nat: set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat ).

thf(func_def_840,type,
    sup_su7128418612487073120et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat ).

thf(func_def_841,type,
    sup_su3382966977382714213nt_int: set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int ).

thf(func_def_842,type,
    sup_su3035147773818789531at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ).

thf(func_def_843,type,
    sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_844,type,
    sup_su718114333110466843at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat ).

thf(func_def_845,type,
    sup_su5525570899277871387at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).

thf(func_def_846,type,
    sup_sup_set_rat: set_rat > set_rat > set_rat ).

thf(func_def_847,type,
    sup_sup_set_set_nat: set_set_nat > set_set_nat > set_set_nat ).

thf(func_def_848,type,
    sup_su2047564715030645325nt_int: set_se6260736226359567993nt_int > set_se6260736226359567993nt_int > set_se6260736226359567993nt_int ).

thf(func_def_849,type,
    sup_sup_set_literal: set_literal > set_literal > set_literal ).

thf(func_def_850,type,
    lattic8263393255366662781ax_int: set_int > int ).

thf(func_def_851,type,
    lattic8265883725875713057ax_nat: set_nat > nat ).

thf(func_def_852,type,
    lattic7826324295020591184_F_nat: ( nat > nat > nat ) > nat > set_nat > nat ).

thf(func_def_853,type,
    quotie6109894551476798619iteral: ( list_char > list_char > $o ) > ( list_char > literal ) > ( literal > list_char ) > ( list_char > literal > $o ) > $o ).

thf(func_def_854,type,
    append_int: list_int > list_int > list_int ).

thf(func_def_855,type,
    append_char: list_char > list_char > list_char ).

thf(func_def_856,type,
    butlast_nat: list_nat > list_nat ).

thf(func_def_857,type,
    filter_nat2: ( nat > $o ) > list_nat > list_nat ).

thf(func_def_858,type,
    fold_int_int: ( int > int > int ) > list_int > int > int ).

thf(func_def_859,type,
    fold_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).

thf(func_def_860,type,
    last_nat: list_nat > nat ).

thf(func_def_861,type,
    linord1735203802627413978nt_int: ( int > int ) > list_int > list_int ).

thf(func_def_862,type,
    linord738340561235409698at_nat: ( nat > nat ) > list_nat > list_nat ).

thf(func_def_863,type,
    cons_int: int > list_int > list_int ).

thf(func_def_864,type,
    cons_nat: nat > list_nat > list_nat ).

thf(func_def_865,type,
    cons_char: char > list_char > list_char ).

thf(func_def_866,type,
    nil_int: list_int ).

thf(func_def_867,type,
    nil_nat: list_nat ).

thf(func_def_868,type,
    nil_char: list_char ).

thf(func_def_869,type,
    list_all2_char_char: ( char > char > $o ) > list_char > list_char > $o ).

thf(func_def_870,type,
    list_all_char: ( char > $o ) > list_char > $o ).

thf(func_def_871,type,
    map_Co843364623960961780r_char: ( code_integer > char ) > list_Code_integer > list_char ).

thf(func_def_872,type,
    map_nat_nat: ( nat > nat ) > list_nat > list_nat ).

thf(func_def_873,type,
    map_ch5843194146513361140nteger: ( char > code_integer ) > list_char > list_Code_integer ).

thf(func_def_874,type,
    map_char_char: ( char > char ) > list_char > list_char ).

thf(func_def_875,type,
    set_int2: list_int > set_int ).

thf(func_def_876,type,
    set_nat2: list_nat > set_nat ).

thf(func_def_877,type,
    set_char2: list_char > set_char ).

thf(func_def_878,type,
    lexordp_char: ( char > char > $o ) > list_char > list_char > $o ).

thf(func_def_879,type,
    lexordp_eq_char: ( char > char > $o ) > list_char > list_char > $o ).

thf(func_def_880,type,
    upt: nat > nat > list_nat ).

thf(func_def_881,type,
    upto: int > int > list_int ).

thf(func_def_882,type,
    upto_aux: int > int > list_int > list_int ).

thf(func_def_883,type,
    upto_rel: product_prod_int_int > product_prod_int_int > $o ).

thf(func_def_884,type,
    biject576505603616484041nt_int: set_Pr1872883991513573699nt_int > $o ).

thf(func_def_885,type,
    biject9051520373387432658nteger: set_Pr1281608226676607948nteger > $o ).

thf(func_def_886,type,
    biject1468766312547416318et_nat: set_Pr8536935166611901872et_nat > $o ).

thf(func_def_887,type,
    biject2615096655818420098et_nat: set_Pr3286484037609594932et_nat > $o ).

thf(func_def_888,type,
    biject383251550997737151nt_int: set_Pr9222295170931077689nt_int > $o ).

thf(func_def_889,type,
    bijective_nat_nat: set_Pr1261947904930325089at_nat > $o ).

thf(func_def_890,type,
    pairse3534876335208825186e_term: ( int > option6357759511663192854e_term ) > product_prod_int_int > produc6576344331059438605e_term ).

thf(func_def_891,type,
    pairse6848479906795794847e_term: produc7773217078559923341nt_int > produc7773217078559923341nt_int > $o ).

thf(func_def_892,type,
    rel_re3331361160397388719_nat_o: set_Pr2161125870931222855_nat_o > set_Pr4532377907799695533_nat_o > set_Pr2161125870931222855_nat_o ).

thf(func_def_893,type,
    rel_restrict_o: set_Product_prod_o_o > set_o > set_Product_prod_o_o ).

thf(func_def_894,type,
    rel_restrict_int: set_Pr958786334691620121nt_int > set_int > set_Pr958786334691620121nt_int ).

thf(func_def_895,type,
    rel_restrict_nat: set_Pr1261947904930325089at_nat > set_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_896,type,
    rel_re2197483123211154633at_nat: set_Pr4759807026041935047at_nat > set_Pr8551490117392284871at_nat > set_Pr4759807026041935047at_nat ).

thf(func_def_897,type,
    rel_re36662636952045539at_nat: set_Pr8693737435421807431at_nat > set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat ).

thf(func_def_898,type,
    rel_re2767227651283840073at_nat: set_Pr5564308138774400199at_nat > set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat ).

thf(func_def_899,type,
    rel_restrict_set_nat: set_Pr5488025237498180813et_nat > set_set_nat > set_Pr5488025237498180813et_nat ).

thf(func_def_900,type,
    rel_re4349003428253852667nt_int: set_Pr8057934254988874055nt_int > set_se6260736226359567993nt_int > set_Pr8057934254988874055nt_int ).

thf(func_def_901,type,
    uncurry_int_int_o: ( int > int > $o ) > product_prod_int_int > $o ).

thf(func_def_902,type,
    uncurry_int_int_int: ( int > int > int ) > product_prod_int_int > int ).

thf(func_def_903,type,
    uncurr7650761721940715016nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).

thf(func_def_904,type,
    uncurr7511940902602773877_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_905,type,
    uncurr8011562610307062878at_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_906,type,
    add_ms2612439473150266591at_nat: product_prod_nat_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat ).

thf(func_def_907,type,
    ms_strict: set_Pr8551490117392284871at_nat ).

thf(func_def_908,type,
    ms_weak: set_Pr8551490117392284871at_nat ).

thf(func_def_909,type,
    pw_leq: multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o ).

thf(func_def_910,type,
    set_ms8126754132646256062at_nat: multis2468970476368604999at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_911,type,
    suc: nat > nat ).

thf(func_def_912,type,
    case_nat_o: $o > ( nat > $o ) > nat > $o ).

thf(func_def_913,type,
    case_nat_nat: nat > ( nat > nat ) > nat > nat ).

thf(func_def_914,type,
    case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).

thf(func_def_915,type,
    pred: nat > nat ).

thf(func_def_916,type,
    semiring_1_Nats_int: set_int ).

thf(func_def_917,type,
    semiri4939895301339042750nteger: nat > code_integer ).

thf(func_def_918,type,
    semiri3763490453095760265atural: nat > code_natural ).

thf(func_def_919,type,
    semiri1314217659103216013at_int: nat > int ).

thf(func_def_920,type,
    semiri1316708129612266289at_nat: nat > nat ).

thf(func_def_921,type,
    semiri681578069525770553at_rat: nat > rat ).

thf(func_def_922,type,
    semiri4055485073559036834nteger: ( code_integer > code_integer ) > nat > code_integer > code_integer ).

thf(func_def_923,type,
    semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).

thf(func_def_924,type,
    semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).

thf(func_def_925,type,
    semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).

thf(func_def_926,type,
    size_size_list_int: list_int > nat ).

thf(func_def_927,type,
    size_size_list_nat: list_nat > nat ).

thf(func_def_928,type,
    size_size_list_char: list_char > nat ).

thf(func_def_929,type,
    size_size_literal: literal > nat ).

thf(func_def_930,type,
    nat_int_decode: nat > int ).

thf(func_def_931,type,
    nat_int_encode: int > nat ).

thf(func_def_932,type,
    nat_list_decode: nat > list_nat ).

thf(func_def_933,type,
    nat_list_decode_rel: nat > nat > $o ).

thf(func_def_934,type,
    nat_list_encode: list_nat > nat ).

thf(func_def_935,type,
    nat_list_encode_rel: list_nat > list_nat > $o ).

thf(func_def_936,type,
    nat_prod_decode: nat > product_prod_nat_nat ).

thf(func_def_937,type,
    nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).

thf(func_def_938,type,
    nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_939,type,
    nat_prod_encode: product_prod_nat_nat > nat ).

thf(func_def_940,type,
    nat_set_decode: nat > set_nat ).

thf(func_def_941,type,
    nat_set_encode: set_nat > nat ).

thf(func_def_942,type,
    nat_sum_decode: nat > sum_sum_nat_nat ).

thf(func_def_943,type,
    nat_sum_encode: sum_sum_nat_nat > nat ).

thf(func_def_944,type,
    nat_triangle: nat > nat ).

thf(func_def_945,type,
    bitM: num > num ).

thf(func_def_946,type,
    inc: num > num ).

thf(func_def_947,type,
    nat_of_num: num > nat ).

thf(func_def_948,type,
    neg_nu8804712462038260780nteger: code_integer > code_integer ).

thf(func_def_949,type,
    neg_numeral_dbl_int: int > int ).

thf(func_def_950,type,
    neg_numeral_dbl_rat: rat > rat ).

thf(func_def_951,type,
    neg_nu7757733837767384882nteger: code_integer > code_integer ).

thf(func_def_952,type,
    neg_nu3811975205180677377ec_int: int > int ).

thf(func_def_953,type,
    neg_nu3179335615603231917ec_rat: rat > rat ).

thf(func_def_954,type,
    neg_nu5831290666863070958nteger: code_integer > code_integer ).

thf(func_def_955,type,
    neg_nu5851722552734809277nc_int: int > int ).

thf(func_def_956,type,
    neg_nu5219082963157363817nc_rat: rat > rat ).

thf(func_def_957,type,
    neg_nu5755505904847501662nteger: num > num > code_integer ).

thf(func_def_958,type,
    neg_numeral_sub_int: num > num > int ).

thf(func_def_959,type,
    neg_numeral_sub_rat: num > num > rat ).

thf(func_def_960,type,
    bit0: num > num ).

thf(func_def_961,type,
    bit1: num > num ).

thf(func_def_962,type,
    one: num ).

thf(func_def_963,type,
    case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).

thf(func_def_964,type,
    num_of_nat: nat > num ).

thf(func_def_965,type,
    numera6620942414471956472nteger: num > code_integer ).

thf(func_def_966,type,
    numera5444537566228673987atural: num > code_natural ).

thf(func_def_967,type,
    numeral_numeral_int: num > int ).

thf(func_def_968,type,
    numeral_numeral_nat: num > nat ).

thf(func_def_969,type,
    numeral_numeral_rat: num > rat ).

thf(func_def_970,type,
    pred_numeral: num > nat ).

thf(func_def_971,type,
    ring_16219924574208605041nteger: code_integer > $o ).

thf(func_def_972,type,
    ring_1_iszero_int: int > $o ).

thf(func_def_973,type,
    ring_1_iszero_rat: rat > $o ).

thf(func_def_974,type,
    none_num: option_num ).

thf(func_def_975,type,
    some_num: num > option_num ).

thf(func_def_976,type,
    case_option_int_num: int > ( num > int ) > option_num > int ).

thf(func_def_977,type,
    case_option_num_num: num > ( num > num ) > option_num > num ).

thf(func_def_978,type,
    case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).

thf(func_def_979,type,
    map_option_num_num: ( num > num ) > option_num > option_num ).

thf(func_def_980,type,
    order_underS_nat: set_Pr1261947904930325089at_nat > nat > set_nat ).

thf(func_def_981,type,
    order_2888998067076097458on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_982,type,
    bot_bo1403522918969695512_int_o: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ).

thf(func_def_983,type,
    bot_bo3000040243691356879eger_o: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ).

thf(func_def_984,type,
    bot_bo3790638025767943357_nat_o: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).

thf(func_def_985,type,
    bot_bo5580076615179976505_nat_o: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).

thf(func_def_986,type,
    bot_bo7963750851167320836at_o_o: ( produc3658429121746597890et_nat > $o ) > $o ).

thf(func_def_987,type,
    bot_bo8662317086119403298_int_o: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ).

thf(func_def_988,type,
    bot_bot_o_o: $o > $o ).

thf(func_def_989,type,
    bot_bot_int_o: int > $o ).

thf(func_def_990,type,
    bot_bot_list_char_o: list_char > $o ).

thf(func_def_991,type,
    bot_bot_nat_nat_o: nat > nat > $o ).

thf(func_def_992,type,
    bot_bot_nat_o: nat > $o ).

thf(func_def_993,type,
    bot_bo8147686125503663512_int_o: product_prod_int_int > $o ).

thf(func_def_994,type,
    bot_bo482883023278783056_nat_o: product_prod_nat_nat > $o ).

thf(func_def_995,type,
    bot_bot_set_nat_o: set_nat > $o ).

thf(func_def_996,type,
    bot_bo2686080419298087992_int_o: set_Pr958786334691620121nt_int > $o ).

thf(func_def_998,type,
    bot_bot_assn: assn ).

thf(func_def_999,type,
    bot_bot_filter_nat: filter_nat ).

thf(func_def_1000,type,
    bot_bot_nat: nat ).

thf(func_def_1001,type,
    bot_bo2717538794563056311t_unit: pred_Product_unit ).

thf(func_def_1002,type,
    bot_bot_Product_unit: product_unit ).

thf(func_def_1003,type,
    bot_bo7824918357723582233_nat_o: set_Pr4532377907799695533_nat_o ).

thf(func_def_1004,type,
    bot_bot_set_o: set_o ).

thf(func_def_1005,type,
    bot_bo3990330152332043303nteger: set_Code_integer ).

thf(func_def_1006,type,
    bot_bo498966703094740906er_nat: set_filter_nat ).

thf(func_def_1007,type,
    bot_bot_set_int: set_int ).

thf(func_def_1008,type,
    bot_bot_set_list_nat: set_list_nat ).

thf(func_def_1009,type,
    bot_bot_set_nat: set_nat ).

thf(func_def_1010,type,
    bot_bo4508923176915781079nt_int: set_Pr1872883991513573699nt_int ).

thf(func_def_1011,type,
    bot_bo5443222936135328352nteger: set_Pr1281608226676607948nteger ).

thf(func_def_1012,type,
    bot_bo5635537948650799172et_nat: set_Pr8536935166611901872et_nat ).

thf(func_def_1013,type,
    bot_bo1481135142794719944et_nat: set_Pr3286484037609594932et_nat ).

thf(func_def_1014,type,
    bot_bo572930865798478029nt_int: set_Pr9222295170931077689nt_int ).

thf(func_def_1015,type,
    bot_bo7073875226086086771od_o_o: set_Product_prod_o_o ).

thf(func_def_1016,type,
    bot_bo1796632182523588997nt_int: set_Pr958786334691620121nt_int ).

thf(func_def_1017,type,
    bot_bo8422036546324065075at_nat: set_Pr8551490117392284871at_nat ).

thf(func_def_1018,type,
    bot_bo2099793752762293965at_nat: set_Pr1261947904930325089at_nat ).

thf(func_def_1019,type,
    bot_bo5327735625951526323at_nat: set_Pr8693737435421807431at_nat ).

thf(func_def_1020,type,
    bot_bo228742789529271731at_nat: set_Pr4329608150637261639at_nat ).

thf(func_def_1021,type,
    bot_bo3957492148770167129t_unit: set_Product_unit ).

thf(func_def_1022,type,
    bot_bot_set_rat: set_rat ).

thf(func_def_1023,type,
    bot_bot_set_set_nat: set_set_nat ).

thf(func_def_1024,type,
    bot_bo1488462491386950373nt_int: set_se6260736226359567993nt_int ).

thf(func_def_1025,type,
    bot_bot_set_literal: set_literal ).

thf(func_def_1026,type,
    ord_Least_nat: ( nat > $o ) > nat ).

thf(func_def_1027,type,
    ord_le5728734702541193924at_o_o: ( ( produc3658429121746597890et_nat > $o ) > $o ) > ( ( produc3658429121746597890et_nat > $o ) > $o ) > $o ).

thf(func_def_1028,type,
    ord_less_int_o: ( int > $o ) > ( int > $o ) > $o ).

thf(func_def_1029,type,
    ord_less_list_char_o: ( list_char > $o ) > ( list_char > $o ) > $o ).

thf(func_def_1030,type,
    ord_less_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).

thf(func_def_1031,type,
    ord_le8176553561544679545_nat_o: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ).

thf(func_def_1032,type,
    ord_le8213806771718485336_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).

thf(func_def_1033,type,
    ord_less_set_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > $o ).

thf(func_def_1034,type,
    ord_le2688692977766382584_int_o: ( set_Pr958786334691620121nt_int > $o ) > ( set_Pr958786334691620121nt_int > $o ) > $o ).

thf(func_def_1035,type,
    ord_less_o: $o > $o > $o ).

thf(func_def_1036,type,
    ord_less_assn: assn > assn > $o ).

thf(func_def_1037,type,
    ord_le6747313008572928689nteger: code_integer > code_integer > $o ).

thf(func_def_1038,type,
    ord_le5570908160329646204atural: code_natural > code_natural > $o ).

thf(func_def_1039,type,
    ord_less_filter_nat: filter_nat > filter_nat > $o ).

thf(func_def_1040,type,
    ord_less_int: int > int > $o ).

thf(func_def_1041,type,
    ord_less_nat: nat > nat > $o ).

thf(func_def_1042,type,
    ord_less_num: num > num > $o ).

thf(func_def_1043,type,
    ord_le361264281704409273t_unit: product_unit > product_unit > $o ).

thf(func_def_1044,type,
    ord_less_rat: rat > rat > $o ).

thf(func_def_1045,type,
    ord_le2453136405763929_nat_o: set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o > $o ).

thf(func_def_1046,type,
    ord_less_set_o: set_o > set_o > $o ).

thf(func_def_1047,type,
    ord_le1307284697595431911nteger: set_Code_integer > set_Code_integer > $o ).

thf(func_def_1048,type,
    ord_less_set_int: set_int > set_int > $o ).

thf(func_def_1049,type,
    ord_le1190675801316882794st_nat: set_list_nat > set_list_nat > $o ).

thf(func_def_1050,type,
    ord_less_set_nat: set_nat > set_nat > $o ).

thf(func_def_1051,type,
    ord_le7563427860532173253nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o ).

thf(func_def_1052,type,
    ord_le7642048601412989811at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > $o ).

thf(func_def_1053,type,
    ord_le7866589430770878221at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_1054,type,
    ord_le2604355607129572851at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ).

thf(func_def_1055,type,
    ord_less_set_rat: set_rat > set_rat > $o ).

thf(func_def_1056,type,
    ord_less_set_set_nat: set_set_nat > set_set_nat > $o ).

thf(func_def_1057,type,
    ord_le1924305788584680229nt_int: set_se6260736226359567993nt_int > set_se6260736226359567993nt_int > $o ).

thf(func_def_1058,type,
    ord_less_literal: literal > literal > $o ).

thf(func_def_1059,type,
    ord_le2124322318746777828_int_o: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > $o ).

thf(func_def_1060,type,
    ord_le4340812435750786203eger_o: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > $o ).

thf(func_def_1061,type,
    ord_le6753239538765779593_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > $o ).

thf(func_def_1062,type,
    ord_le8000401564054156549_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > $o ).

thf(func_def_1063,type,
    ord_le1304494283415849680at_o_o: ( ( produc3658429121746597890et_nat > $o ) > $o ) > ( ( produc3658429121746597890et_nat > $o ) > $o ) > $o ).

thf(func_def_1064,type,
    ord_le5643404153117327598_int_o: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > $o ).

thf(func_def_1065,type,
    ord_less_eq_int_o: ( int > $o ) > ( int > $o ) > $o ).

thf(func_def_1066,type,
    ord_le4796328588573674190char_o: ( list_char > $o ) > ( list_char > $o ) > $o ).

thf(func_def_1067,type,
    ord_less_eq_nat_o: ( nat > $o ) > ( nat > $o ) > $o ).

thf(func_def_1068,type,
    ord_le729326519192465773_nat_o: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ).

thf(func_def_1069,type,
    ord_le8369615600986905444_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).

thf(func_def_1070,type,
    ord_le3964352015994296041_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > $o ).

thf(func_def_1071,type,
    ord_le8334417538754933252_int_o: ( set_Pr958786334691620121nt_int > $o ) > ( set_Pr958786334691620121nt_int > $o ) > $o ).

thf(func_def_1072,type,
    ord_less_eq_o: $o > $o > $o ).

thf(func_def_1073,type,
    ord_less_eq_assn: assn > assn > $o ).

thf(func_def_1074,type,
    ord_le3102999989581377725nteger: code_integer > code_integer > $o ).

thf(func_def_1075,type,
    ord_le1926595141338095240atural: code_natural > code_natural > $o ).

thf(func_def_1076,type,
    ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o ).

thf(func_def_1077,type,
    ord_less_eq_int: int > int > $o ).

thf(func_def_1078,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(func_def_1079,type,
    ord_less_eq_num: num > num > $o ).

thf(func_def_1080,type,
    ord_le3221252021190050221t_unit: product_unit > product_unit > $o ).

thf(func_def_1081,type,
    ord_less_eq_rat: rat > rat > $o ).

thf(func_def_1082,type,
    ord_le2965882846123202637_nat_o: set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o > $o ).

thf(func_def_1083,type,
    ord_less_eq_set_o: set_o > set_o > $o ).

thf(func_def_1084,type,
    ord_le7084787975880047091nteger: set_Code_integer > set_Code_integer > $o ).

thf(func_def_1085,type,
    ord_less_eq_set_int: set_int > set_int > $o ).

thf(func_def_1086,type,
    ord_le6045566169113846134st_nat: set_list_nat > set_list_nat > $o ).

thf(func_def_1087,type,
    ord_less_eq_set_nat: set_nat > set_nat > $o ).

thf(func_def_1088,type,
    ord_le135402666524580259nt_int: set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int > $o ).

thf(func_def_1089,type,
    ord_le653643898420964396nteger: set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger > $o ).

thf(func_def_1090,type,
    ord_le4763372923235995152et_nat: set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat > $o ).

thf(func_def_1091,type,
    ord_le5966269811547037844et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > $o ).

thf(func_def_1092,type,
    ord_le8725513860283290265nt_int: set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int > $o ).

thf(func_def_1093,type,
    ord_le2843351958646193337nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o ).

thf(func_def_1094,type,
    ord_le8081472938463900775at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > $o ).

thf(func_def_1095,type,
    ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_1096,type,
    ord_le1268244103169919719at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ).

thf(func_def_1097,type,
    ord_less_eq_set_rat: set_rat > set_rat > $o ).

thf(func_def_1098,type,
    ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o ).

thf(func_def_1099,type,
    ord_le483042692224249369nt_int: set_se6260736226359567993nt_int > set_se6260736226359567993nt_int > $o ).

thf(func_def_1100,type,
    ord_less_eq_literal: literal > literal > $o ).

thf(func_def_1101,type,
    ord_max_int: int > int > int ).

thf(func_def_1102,type,
    ord_max_nat: nat > nat > nat ).

thf(func_def_1103,type,
    ord_min_nat: nat > nat > nat ).

thf(func_def_1104,type,
    order_mono_nat_nat: ( nat > nat ) > $o ).

thf(func_def_1105,type,
    ordering_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).

thf(func_def_1106,type,
    orderi2807725203697798511er_nat: ( filter_nat > filter_nat > $o ) > ( filter_nat > filter_nat > $o ) > filter_nat > $o ).

thf(func_def_1107,type,
    ordering_top_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > $o ).

thf(func_def_1108,type,
    ordering_top_set_o: ( set_o > set_o > $o ) > ( set_o > set_o > $o ) > set_o > $o ).

thf(func_def_1109,type,
    ordering_top_set_int: ( set_int > set_int > $o ) > ( set_int > set_int > $o ) > set_int > $o ).

thf(func_def_1110,type,
    orderi7613023277850353061st_nat: ( set_list_nat > set_list_nat > $o ) > ( set_list_nat > set_list_nat > $o ) > set_list_nat > $o ).

thf(func_def_1111,type,
    ordering_top_set_nat: ( set_nat > set_nat > $o ) > ( set_nat > set_nat > $o ) > set_nat > $o ).

thf(func_def_1112,type,
    orderi2172309028950807442at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_1113,type,
    ordering_top_set_rat: ( set_rat > set_rat > $o ) > ( set_rat > set_rat > $o ) > set_rat > $o ).

thf(func_def_1114,type,
    preordering_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).

thf(func_def_1115,type,
    top_to6513043852502318900_int_o: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ).

thf(func_def_1116,type,
    top_to8112647782992986859eger_o: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ).

thf(func_def_1117,type,
    top_to7190503160269336793_nat_o: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).

thf(func_def_1118,type,
    top_to2428096842796733269_nat_o: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).

thf(func_def_1119,type,
    top_to2462227307520033056at_o_o: ( produc3658429121746597890et_nat > $o ) > $o ).

thf(func_def_1120,type,
    top_to6261655714344447806_int_o: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ).

thf(func_def_1121,type,
    top_top_o_o: $o > $o ).

thf(func_def_1122,type,
    top_top_int_o: int > $o ).

thf(func_def_1123,type,
    top_top_list_nat_o: list_nat > $o ).

thf(func_def_1124,type,
    top_top_list_char_o: list_char > $o ).

thf(func_def_1125,type,
    top_top_nat_o: nat > $o ).

thf(func_def_1126,type,
    top_to1578927101902068148_int_o: product_prod_int_int > $o ).

thf(func_def_1127,type,
    top_top_rat_o: rat > $o ).

thf(func_def_1128,type,
    top_top_set_nat_o: set_nat > $o ).

thf(func_def_1129,type,
    top_to6187514276045680724_int_o: set_Pr958786334691620121nt_int > $o ).

thf(func_def_1131,type,
    top_top_assn: assn ).

thf(func_def_1132,type,
    top_top_filter_nat: filter_nat ).

thf(func_def_1133,type,
    top_top_Product_unit: product_unit ).

thf(func_def_1134,type,
    top_to4869887016220417533_nat_o: set_Pr4532377907799695533_nat_o ).

thf(func_def_1135,type,
    top_top_set_o: set_o ).

thf(func_def_1136,type,
    top_top_set_int: set_int ).

thf(func_def_1137,type,
    top_top_set_list_nat: set_list_nat ).

thf(func_def_1138,type,
    top_to3190553582279535303t_char: set_list_char ).

thf(func_def_1139,type,
    top_top_set_nat: set_nat ).

thf(func_def_1140,type,
    top_top_set_option_o: set_option_o ).

thf(func_def_1141,type,
    top_to6430115241214627170on_int: set_option_int ).

thf(func_def_1142,type,
    top_to1113147461230312982st_nat: set_option_list_nat ).

thf(func_def_1143,type,
    top_to8920198386146353926on_nat: set_option_nat ).

thf(func_def_1144,type,
    top_to3251141154256563319at_nat: set_op4508134149509766951at_nat ).

thf(func_def_1145,type,
    top_to2540212048668676366on_rat: set_option_rat ).

thf(func_def_1146,type,
    top_to2069137843433766899nt_int: set_Pr1872883991513573699nt_int ).

thf(func_def_1147,type,
    top_to7512759353274530428nteger: set_Pr1281608226676607948nteger ).

thf(func_def_1148,type,
    top_to1599102959340997728et_nat: set_Pr8536935166611901872et_nat ).

thf(func_def_1149,type,
    top_to8753217654552796900et_nat: set_Pr3286484037609594932et_nat ).

thf(func_def_1150,type,
    top_to3181862456159035625nt_int: set_Pr9222295170931077689nt_int ).

thf(func_def_1151,type,
    top_to7721136755696657239od_o_o: set_Product_prod_o_o ).

thf(func_def_1152,type,
    top_to4532601362410810969_o_int: set_Pr8834758594704517033_o_int ).

thf(func_def_1153,type,
    top_to7022684507342537725_o_nat: set_Pr2101469702781467981_o_nat ).

thf(func_def_1154,type,
    top_to642698169864860165_o_rat: set_Pr4944855402158566229_o_rat ).

thf(func_def_1155,type,
    top_to4366644338036079209nt_int: set_Pr958786334691620121nt_int ).

thf(func_def_1156,type,
    top_to8764741339697478167at_nat: set_Pr8551490117392284871at_nat ).

thf(func_def_1157,type,
    top_to8070287629520841379_nat_o: set_Pr3149072824959771635_nat_o ).

thf(func_def_1158,type,
    top_to4669805908274784177at_nat: set_Pr1261947904930325089at_nat ).

thf(func_def_1159,type,
    top_to7513191607651882425at_rat: set_Pr4105333604307423337at_rat ).

thf(func_def_1160,type,
    top_to7320853134386005659_rat_o: set_Pr2399638329824935915_rat_o ).

thf(func_def_1161,type,
    top_to7002410609688830997at_int: set_Pr3594552606344371909at_int ).

thf(func_def_1162,type,
    top_to269121717765781945at_nat: set_Pr6084635751276098665at_nat ).

thf(func_def_1163,type,
    top_to3112507417142880193at_rat: set_Pr8928021450653196913at_rat ).

thf(func_def_1164,type,
    top_to6833984726390702231at_nat: set_Pr4329608150637261639at_nat ).

thf(func_def_1165,type,
    top_to1996260823553986621t_unit: set_Product_unit ).

thf(func_def_1166,type,
    top_top_set_rat: set_rat ).

thf(func_def_1167,type,
    top_top_set_set_o: set_set_o ).

thf(func_def_1168,type,
    top_top_set_set_int: set_set_int ).

thf(func_def_1169,type,
    top_to1619013496918823676st_nat: set_set_list_nat ).

thf(func_def_1170,type,
    top_top_set_set_nat: set_set_nat ).

thf(func_def_1171,type,
    top_to6034159466715884489nt_int: set_se6260736226359567993nt_int ).

thf(func_def_1172,type,
    top_to7629004291339433233at_nat: set_se7855581050983116737at_nat ).

thf(func_def_1173,type,
    top_top_set_set_rat: set_set_rat ).

thf(func_def_1174,type,
    top_top_set_char: set_char ).

thf(func_def_1175,type,
    top_to1686961084667892491um_o_o: set_Sum_sum_o_o ).

thf(func_def_1176,type,
    top_to3582428612079801253_o_int: set_Sum_sum_o_int ).

thf(func_def_1177,type,
    top_to6072511757011528009_o_nat: set_Sum_sum_o_nat ).

thf(func_def_1178,type,
    top_to8915897456388626257_o_rat: set_Sum_sum_o_rat ).

thf(func_def_1179,type,
    top_to7120114879189831663_nat_o: set_Sum_sum_nat_o ).

thf(func_def_1180,type,
    top_to6661820994512907621at_nat: set_Sum_sum_nat_nat ).

thf(func_def_1181,type,
    top_to281834657035230061at_rat: set_Sum_sum_nat_rat ).

thf(func_def_1182,type,
    top_to6370680384054995943_rat_o: set_Sum_sum_rat_o ).

thf(func_def_1183,type,
    top_to8994425695926954441at_int: set_Sum_sum_rat_int ).

thf(func_def_1184,type,
    top_to2261136804003905389at_nat: set_Sum_sum_rat_nat ).

thf(func_def_1185,type,
    top_to5104522503381003637at_rat: set_Sum_sum_rat_rat ).

thf(func_def_1186,type,
    power_power_assn: assn > nat > assn ).

thf(func_def_1187,type,
    power_8256067586552552935nteger: code_integer > nat > code_integer ).

thf(func_def_1188,type,
    power_7079662738309270450atural: code_natural > nat > code_natural ).

thf(func_def_1189,type,
    power_power_int: int > nat > int ).

thf(func_def_1190,type,
    power_power_nat: nat > nat > nat ).

thf(func_def_1191,type,
    power_power_rat: rat > nat > rat ).

thf(func_def_1192,type,
    if_pred: $o > pred_Product_unit ).

thf(func_def_1193,type,
    not_pred: pred_Product_unit > pred_Product_unit ).

thf(func_def_1194,type,
    pred_Product_unit2: ( product_unit > $o ) > pred_Product_unit ).

thf(func_def_1195,type,
    eval_Product_unit: pred_Product_unit > product_unit > $o ).

thf(func_def_1196,type,
    single_Product_unit: product_unit > pred_Product_unit ).

thf(func_def_1197,type,
    produc6137756002093451184nteger: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > produc8763457246119570046nteger ).

thf(func_def_1198,type,
    produc2252593628808123835atural: ( code_natural > option6357759511663192854e_term ) > produc7822875418678951345atural > produc8731074985263844745atural ).

thf(func_def_1199,type,
    produc4305682042979456191nt_int: ( int > option6357759511663192854e_term ) > product_prod_int_int > produc7773217078559923341nt_int ).

thf(func_def_1200,type,
    produc3209952032786966637at_nat: ( nat > nat > nat ) > produc7248412053542808358at_nat > produc4471711990508489141at_nat ).

thf(func_def_1201,type,
    produc8603105652947943368nteger: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > produc1908205239877642774nteger ).

thf(func_def_1202,type,
    produc3831813291587773865atural: ( produc4972180933644002618e_term > option6357759511663192854e_term ) > produc7822875418678951345atural > produc989692990947075319atural ).

thf(func_def_1203,type,
    produc7368190662567826135_nat_o: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc4928098042776334183_nat_o ).

thf(func_def_1204,type,
    produc2245416461498447860et_nat: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > produc2732055786443039994et_nat ).

thf(func_def_1205,type,
    produc5001842942810119800et_nat: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > produc3925858234332021118et_nat ).

thf(func_def_1206,type,
    produc5700946648718959541nt_int: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > produc2285326912895808259nt_int ).

thf(func_def_1207,type,
    produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o ).

thf(func_def_1208,type,
    produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).

thf(func_def_1209,type,
    produc3574140220909816553atural: code_natural > code_natural > produc7822875418678951345atural ).

thf(func_def_1210,type,
    produc6639722614265839536atural: code_natural > produc7822875418678951345atural > produc5835291356934675326atural ).

thf(func_def_1211,type,
    produc7507926704131184380et_nat: heap_e7401611519738050253t_unit > set_nat > produc3658429121746597890et_nat ).

thf(func_def_1212,type,
    product_Pair_int_int: int > int > product_prod_int_int ).

thf(func_def_1213,type,
    produc4348348721325984599at_nat: multis2468970476368604999at_nat > multis2468970476368604999at_nat > produc4166570645942440679at_nat ).

thf(func_def_1214,type,
    product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).

thf(func_def_1215,type,
    product_Pair_nat_num: nat > num > product_prod_nat_num ).

thf(func_def_1216,type,
    produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat ).

thf(func_def_1217,type,
    product_Pair_num_num: num > num > product_prod_num_num ).

thf(func_def_1218,type,
    produc5950683997804057413e_term: option6357759511663192854e_term > option6357759511663192854e_term > produc6576344331059438605e_term ).

thf(func_def_1219,type,
    produc5069803637994805237atural: pred_Product_unit > produc7822875418678951345atural > produc4675096598859438275atural ).

thf(func_def_1220,type,
    produc4480994950612372183atural: produc7822875418678951345atural > produc7822875418678951345atural > produc6756470014200349799atural ).

thf(func_def_1221,type,
    produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat ).

thf(func_def_1222,type,
    produc4532415448927165861et_nat: set_nat > set_nat > produc7819656566062154093et_nat ).

thf(func_def_1223,type,
    produc763777882069021527od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > produc2934264451710624999od_o_o ).

thf(func_def_1224,type,
    produc8517790099723286449at_nat: set_Product_prod_o_o > set_Pr1261947904930325089at_nat > produc732395585841259969at_nat ).

thf(func_def_1225,type,
    produc782388162306416855nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > produc412284730452459111nt_int ).

thf(func_def_1226,type,
    produc5245064249948416855at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > produc4193628355235574503at_nat ).

thf(func_def_1227,type,
    produc2922128104949294807at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat ).

thf(func_def_1228,type,
    produc9060074326276436823at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > produc1319942482725812455at_nat ).

thf(func_def_1229,type,
    produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).

thf(func_def_1230,type,
    product_Unity: product_unit ).

thf(func_def_1231,type,
    produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_1232,type,
    produc969530845752564945_nat_o: ( produc3925858234332021118et_nat > produc3925858234332021118et_nat ) > produc2732055786443039994et_nat > produc2732055786443039994et_nat ).

thf(func_def_1233,type,
    produc1515462096303866701_nat_o: ( produc3925858234332021118et_nat > produc3658429121746597890et_nat ) > produc2732055786443039994et_nat > produc3925858234332021118et_nat ).

thf(func_def_1234,type,
    produc717174245515237944e_term: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc1908205239877642774nteger > produc1908205239877642774nteger ).

thf(func_def_1235,type,
    produc7714581247149323085_nat_o: ( produc3658429121746597890et_nat > produc3925858234332021118et_nat ) > produc3925858234332021118et_nat > produc2732055786443039994et_nat ).

thf(func_def_1236,type,
    produc8750854537940449737_nat_o: ( produc3658429121746597890et_nat > produc3658429121746597890et_nat ) > produc3925858234332021118et_nat > produc3925858234332021118et_nat ).

thf(func_def_1237,type,
    produc7011684061226097695e_term: ( product_prod_int_int > product_prod_int_int ) > produc7773217078559923341nt_int > produc7773217078559923341nt_int ).

thf(func_def_1238,type,
    produc4973430039190721449e_term: ( product_prod_int_int > product_prod_int_int ) > produc2285326912895808259nt_int > produc2285326912895808259nt_int ).

thf(func_def_1239,type,
    produc2558449545302689196_int_o: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc7773217078559923341nt_int > $o ).

thf(func_def_1240,type,
    produc5122537100556696953nt_int: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > produc7773217078559923341nt_int ) > produc7773217078559923341nt_int > produc7773217078559923341nt_int ).

thf(func_def_1241,type,
    produc4111701587417901774et_int: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_int ) > produc7773217078559923341nt_int > set_int ).

thf(func_def_1242,type,
    produc8289552606927098482et_nat: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat ) > produc7773217078559923341nt_int > set_nat ).

thf(func_def_1243,type,
    produc3577156405726439208et_nat: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_set_nat ) > produc7773217078559923341nt_int > set_set_nat ).

thf(func_def_1244,type,
    produc575502675617541261nt_int: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_se6260736226359567993nt_int ) > produc7773217078559923341nt_int > set_se6260736226359567993nt_int ).

thf(func_def_1245,type,
    produc6253627499356882019eger_o: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc1908205239877642774nteger > $o ).

thf(func_def_1246,type,
    produc6512950862096126219nteger: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > produc1908205239877642774nteger ) > produc1908205239877642774nteger > produc1908205239877642774nteger ).

thf(func_def_1247,type,
    produc5700143819190870999et_int: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int ) > produc1908205239877642774nteger > set_int ).

thf(func_def_1248,type,
    produc654622801845291899et_nat: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat ) > produc1908205239877642774nteger > set_nat ).

thf(func_def_1249,type,
    produc5150382289251079596at_o_o: ( ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ) > produc4928098042776334183_nat_o > $o ).

thf(func_def_1250,type,
    produc838355143741117751_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > produc2732055786443039994et_nat > $o ).

thf(func_def_1251,type,
    produc2377985495875741467et_nat: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > produc2732055786443039994et_nat ) > produc2732055786443039994et_nat > produc2732055786443039994et_nat ).

thf(func_def_1252,type,
    produc1437786849005270451_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).

thf(func_def_1253,type,
    produc4058941399401191971et_nat: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > produc3925858234332021118et_nat ) > produc3925858234332021118et_nat > produc3925858234332021118et_nat ).

thf(func_def_1254,type,
    produc4627640435386541703et_int: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_int ) > produc3925858234332021118et_nat > set_int ).

thf(func_def_1255,type,
    produc8805491454895738411et_nat: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_nat ) > produc3925858234332021118et_nat > set_nat ).

thf(func_def_1256,type,
    produc2333231157791014625et_nat: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_set_nat ) > produc3925858234332021118et_nat > set_set_nat ).

thf(func_def_1257,type,
    produc1573362020775583542_int_o: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc2285326912895808259nt_int > $o ).

thf(func_def_1258,type,
    produc8492565224438309093nt_int: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > produc2285326912895808259nt_int ) > produc2285326912895808259nt_int > produc2285326912895808259nt_int ).

thf(func_def_1259,type,
    produc3619988815162578792et_nat: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > set_nat ) > produc2285326912895808259nt_int > set_nat ).

thf(func_def_1260,type,
    produc4188289175737317920o_char: ( code_integer > $o > char ) > produc6271795597528267376eger_o > char ).

thf(func_def_1261,type,
    produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).

thf(func_def_1262,type,
    produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).

thf(func_def_1263,type,
    produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).

thf(func_def_1264,type,
    produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).

thf(func_def_1265,type,
    produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).

thf(func_def_1266,type,
    produc8282080750456430313atural: ( code_natural > code_natural > produc6756470014200349799atural ) > produc7822875418678951345atural > produc6756470014200349799atural ).

thf(func_def_1267,type,
    produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).

thf(func_def_1268,type,
    produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).

thf(func_def_1269,type,
    produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).

thf(func_def_1270,type,
    produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).

thf(func_def_1271,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_1272,type,
    produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).

thf(func_def_1273,type,
    produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).

thf(func_def_1274,type,
    produc2761476792215241774st_nat: ( nat > nat > list_nat ) > product_prod_nat_nat > list_nat ).

thf(func_def_1275,type,
    produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).

thf(func_def_1276,type,
    produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).

thf(func_def_1277,type,
    produc6207742614233964070at_rat: ( nat > nat > rat ) > product_prod_nat_nat > rat ).

thf(func_def_1278,type,
    produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).

thf(func_def_1279,type,
    produc6665183775751917029atural: ( pred_Product_unit > produc7822875418678951345atural > produc4675096598859438275atural ) > produc4675096598859438275atural > produc4675096598859438275atural ).

thf(func_def_1280,type,
    produc6247414631856714078_nat_o: ( set_nat > set_nat > $o ) > produc7819656566062154093et_nat > $o ).

thf(func_def_1281,type,
    produc1547782455048856492_int_o: ( set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o ) > produc412284730452459111nt_int > $o ).

thf(func_def_1282,type,
    product_fst_int_int: product_prod_int_int > int ).

thf(func_def_1283,type,
    produc6591912806276919810atural: produc5835291356934675326atural > produc7822875418678951345atural ).

thf(func_def_1284,type,
    product_snd_int_int: product_prod_int_int > int ).

thf(func_def_1285,type,
    produc5538323210962509403atural: ( produc7822875418678951345atural > produc5835291356934675326atural ) > ( code_natural > produc7822875418678951345atural > produc5835291356934675326atural ) > produc7822875418678951345atural > produc5835291356934675326atural ).

thf(func_def_1286,type,
    product_Abs_unit: $o > product_unit ).

thf(func_def_1287,type,
    product_Rep_unit: product_unit > $o ).

thf(func_def_1288,type,
    inc_shift: code_natural > code_natural > code_natural ).

thf(func_def_1289,type,
    iterat8892046348760725948atural: code_natural > ( code_natural > produc7822875418678951345atural > produc5835291356934675326atural ) > code_natural > produc7822875418678951345atural > produc5835291356934675326atural ).

thf(func_def_1290,type,
    log: code_natural > code_natural > code_natural ).

thf(func_def_1291,type,
    log_rel: produc7822875418678951345atural > produc7822875418678951345atural > $o ).

thf(func_def_1292,type,
    minus_shift: code_natural > code_natural > code_natural > code_natural ).

thf(func_def_1293,type,
    next: produc7822875418678951345atural > produc5835291356934675326atural ).

thf(func_def_1294,type,
    range: code_natural > produc7822875418678951345atural > produc5835291356934675326atural ).

thf(func_def_1295,type,
    split_seed: produc7822875418678951345atural > produc6756470014200349799atural ).

thf(func_def_1296,type,
    random6974930770145893639ompred: ( produc7822875418678951345atural > produc4675096598859438275atural ) > produc7822875418678951345atural > produc4675096598859438275atural ).

thf(func_def_1297,type,
    abs_Rat: product_prod_int_int > rat ).

thf(func_def_1298,type,
    fract: int > int > rat ).

thf(func_def_1299,type,
    frct: product_prod_int_int > rat ).

thf(func_def_1300,type,
    rep_Rat: rat > product_prod_int_int ).

thf(func_def_1301,type,
    cr_rat: product_prod_int_int > rat > $o ).

thf(func_def_1302,type,
    field_6020823756834552118ts_rat: set_rat ).

thf(func_def_1303,type,
    normalize: product_prod_int_int > product_prod_int_int ).

thf(func_def_1304,type,
    of_int: int > rat ).

thf(func_def_1305,type,
    pcr_rat: product_prod_int_int > rat > $o ).

thf(func_def_1306,type,
    positive: rat > $o ).

thf(func_def_1307,type,
    quotient_of: rat > product_prod_int_int ).

thf(func_def_1308,type,
    abs_rat: set_Pr958786334691620121nt_int > rat ).

thf(func_def_1309,type,
    rep_rat: rat > set_Pr958786334691620121nt_int ).

thf(func_def_1310,type,
    ratrel: product_prod_int_int > product_prod_int_int > $o ).

thf(func_def_1311,type,
    domainp_int_int: ( int > int > $o ) > int > $o ).

thf(func_def_1312,type,
    domain7888411570377768909iteral: ( list_char > literal > $o ) > list_char > $o ).

thf(func_def_1313,type,
    domain9213661015745956397nt_rat: ( product_prod_int_int > rat > $o ) > product_prod_int_int > $o ).

thf(func_def_1314,type,
    domainp_char_char: ( char > char > $o ) > char > $o ).

thf(func_def_1315,type,
    field_o: set_Product_prod_o_o > set_o ).

thf(func_def_1316,type,
    field_nat: set_Pr1261947904930325089at_nat > set_nat ).

thf(func_def_1317,type,
    id_mul2649389997224486051at_nat: set_Pr8551490117392284871at_nat ).

thf(func_def_1318,type,
    id_Pro2258643101195443293at_nat: set_Pr8693737435421807431at_nat ).

thf(func_def_1319,type,
    id_on_7438695062414216554_nat_o: set_Pr4532377907799695533_nat_o > set_Pr2161125870931222855_nat_o ).

thf(func_def_1320,type,
    id_on_o: set_o > set_Product_prod_o_o ).

thf(func_def_1321,type,
    id_on_int: set_int > set_Pr958786334691620121nt_int ).

thf(func_def_1322,type,
    id_on_nat: set_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_1323,type,
    id_on_2554058798563519774at_nat: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat ).

thf(func_def_1324,type,
    id_on_set_nat: set_set_nat > set_Pr5488025237498180813et_nat ).

thf(func_def_1325,type,
    id_on_6410342593070439734nt_int: set_se6260736226359567993nt_int > set_Pr8057934254988874055nt_int ).

thf(func_def_1326,type,
    total_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_1327,type,
    algebr932160517623751201me_int: int > int > $o ).

thf(func_def_1328,type,
    algebr934650988132801477me_nat: nat > nat > $o ).

thf(func_def_1329,type,
    divide6298287555418463151nteger: code_integer > code_integer > code_integer ).

thf(func_def_1330,type,
    divide5121882707175180666atural: code_natural > code_natural > code_natural ).

thf(func_def_1331,type,
    divide_divide_int: int > int > int ).

thf(func_def_1332,type,
    divide_divide_nat: nat > nat > nat ).

thf(func_def_1333,type,
    divide_divide_rat: rat > rat > rat ).

thf(func_def_1334,type,
    dvd_dvd_assn: assn > assn > $o ).

thf(func_def_1335,type,
    dvd_dvd_Code_integer: code_integer > code_integer > $o ).

thf(func_def_1336,type,
    dvd_dvd_Code_natural: code_natural > code_natural > $o ).

thf(func_def_1337,type,
    dvd_dvd_int: int > int > $o ).

thf(func_def_1338,type,
    dvd_dvd_nat: nat > nat > $o ).

thf(func_def_1339,type,
    dvd_dvd_rat: rat > rat > $o ).

thf(func_def_1340,type,
    modulo364778990260209775nteger: code_integer > code_integer > code_integer ).

thf(func_def_1341,type,
    modulo8411746178871703098atural: code_natural > code_natural > code_natural ).

thf(func_def_1342,type,
    modulo_modulo_int: int > int > int ).

thf(func_def_1343,type,
    modulo_modulo_nat: nat > nat > nat ).

thf(func_def_1344,type,
    unit_f2748546683901255202or_nat: nat > nat ).

thf(func_def_1345,type,
    zero_n356916108424825756nteger: $o > code_integer ).

thf(func_def_1346,type,
    zero_n8403883297036319079atural: $o > code_natural ).

thf(func_def_1347,type,
    zero_n2684676970156552555ol_int: $o > int ).

thf(func_def_1348,type,
    zero_n2687167440665602831ol_nat: $o > nat ).

thf(func_def_1349,type,
    zero_n2052037380579107095ol_rat: $o > rat ).

thf(func_def_1350,type,
    collec939566748876313656_nat_o: ( ( produc3658429121746597890et_nat > $o ) > $o ) > set_Pr4532377907799695533_nat_o ).

thf(func_def_1351,type,
    collect_o: ( $o > $o ) > set_o ).

thf(func_def_1352,type,
    collect_Code_integer: ( code_integer > $o ) > set_Code_integer ).

thf(func_def_1353,type,
    collect_filter_nat: ( filter_nat > $o ) > set_filter_nat ).

thf(func_def_1354,type,
    collect_int: ( int > $o ) > set_int ).

thf(func_def_1355,type,
    collect_list_nat: ( list_nat > $o ) > set_list_nat ).

thf(func_def_1356,type,
    collect_list_char: ( list_char > $o ) > set_list_char ).

thf(func_def_1357,type,
    collect_nat: ( nat > $o ) > set_nat ).

thf(func_def_1358,type,
    collec7086185654880424402_nat_o: ( produc4928098042776334183_nat_o > $o ) > set_Pr2161125870931222855_nat_o ).

thf(func_def_1359,type,
    collec213857154873943460nt_int: ( product_prod_int_int > $o ) > set_Pr958786334691620121nt_int ).

thf(func_def_1360,type,
    collec5204685387357076818at_nat: ( produc4166570645942440679at_nat > $o ) > set_Pr8551490117392284871at_nat ).

thf(func_def_1361,type,
    collec3392354462482085612at_nat: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).

thf(func_def_1362,type,
    collec6662362479098859352et_nat: ( produc7819656566062154093et_nat > $o ) > set_Pr5488025237498180813et_nat ).

thf(func_def_1363,type,
    collec2889756465124990930nt_int: ( produc412284730452459111nt_int > $o ) > set_Pr8057934254988874055nt_int ).

thf(func_def_1364,type,
    collec6321179662152712658at_nat: ( produc3843707927480180839at_nat > $o ) > set_Pr4329608150637261639at_nat ).

thf(func_def_1365,type,
    collect_rat: ( rat > $o ) > set_rat ).

thf(func_def_1366,type,
    collect_set_o: ( set_o > $o ) > set_set_o ).

thf(func_def_1367,type,
    collect_set_int: ( set_int > $o ) > set_set_int ).

thf(func_def_1368,type,
    collect_set_list_nat: ( set_list_nat > $o ) > set_set_list_nat ).

thf(func_def_1369,type,
    collect_set_nat: ( set_nat > $o ) > set_set_nat ).

thf(func_def_1370,type,
    collec5210948495886036740nt_int: ( set_Pr958786334691620121nt_int > $o ) > set_se6260736226359567993nt_int ).

thf(func_def_1371,type,
    collec5514110066124741708at_nat: ( set_Pr1261947904930325089at_nat > $o ) > set_se7855581050983116737at_nat ).

thf(func_def_1372,type,
    collect_set_set_nat: ( set_set_nat > $o ) > set_set_set_nat ).

thf(func_def_1373,type,
    collect_literal: ( literal > $o ) > set_literal ).

thf(func_def_1374,type,
    pow_nat: set_nat > set_set_nat ).

thf(func_def_1375,type,
    image_4470545334726330049nteger: ( code_integer > code_integer ) > set_Code_integer > set_Code_integer ).

thf(func_def_1376,type,
    image_int_int: ( int > int ) > set_int > set_int ).

thf(func_def_1377,type,
    image_int_nat: ( int > nat ) > set_int > set_nat ).

thf(func_def_1378,type,
    image_list_nat_nat: ( list_nat > nat ) > set_list_nat > set_nat ).

thf(func_def_1379,type,
    image_nat_int: ( nat > int ) > set_nat > set_int ).

thf(func_def_1380,type,
    image_nat_list_nat: ( nat > list_nat ) > set_nat > set_list_nat ).

thf(func_def_1381,type,
    image_nat_nat: ( nat > nat ) > set_nat > set_nat ).

thf(func_def_1382,type,
    image_5846123807819985514at_nat: ( nat > product_prod_nat_nat ) > set_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_1383,type,
    image_nat_rat: ( nat > rat ) > set_nat > set_rat ).

thf(func_def_1384,type,
    image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).

thf(func_def_1385,type,
    image_nat_char: ( nat > char ) > set_nat > set_char ).

thf(func_def_1386,type,
    image_678696785212003926at_nat: ( nat > sum_sum_nat_nat ) > set_nat > set_Sum_sum_nat_nat ).

thf(func_def_1387,type,
    image_2486076414777270412at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > set_nat ).

thf(func_def_1388,type,
    image_char_nat: ( char > nat ) > set_char > set_nat ).

thf(func_def_1389,type,
    image_1320371278474632150at_nat: ( sum_sum_nat_nat > nat ) > set_Sum_sum_nat_nat > set_nat ).

thf(func_def_1390,type,
    insert5175938949040314269_nat_o: ( produc3658429121746597890et_nat > $o ) > set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o ).

thf(func_def_1391,type,
    insert_o: $o > set_o > set_o ).

thf(func_def_1392,type,
    insert_Code_integer: code_integer > set_Code_integer > set_Code_integer ).

thf(func_def_1393,type,
    insert_int: int > set_int > set_int ).

thf(func_def_1394,type,
    insert_list_nat: list_nat > set_list_nat > set_list_nat ).

thf(func_def_1395,type,
    insert_nat: nat > set_nat > set_nat ).

thf(func_def_1396,type,
    insert6337962749363155127at_nat: produc4166570645942440679at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ).

thf(func_def_1397,type,
    insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_1398,type,
    insert9069300056098147895at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).

thf(func_def_1399,type,
    insert_Product_unit: product_unit > set_Product_unit > set_Product_unit ).

thf(func_def_1400,type,
    insert_rat: rat > set_rat > set_rat ).

thf(func_def_1401,type,
    insert_set_nat: set_nat > set_set_nat > set_set_nat ).

thf(func_def_1402,type,
    insert8897473484851387113nt_int: set_Pr958786334691620121nt_int > set_se6260736226359567993nt_int > set_se6260736226359567993nt_int ).

thf(func_def_1403,type,
    insert_literal: literal > set_literal > set_literal ).

thf(func_def_1404,type,
    is_empty_o: set_o > $o ).

thf(func_def_1405,type,
    is_empty_int: set_int > $o ).

thf(func_def_1406,type,
    is_empty_nat: set_nat > $o ).

thf(func_def_1407,type,
    is_emp1662574758705540307at_nat: set_Pr1261947904930325089at_nat > $o ).

thf(func_def_1408,type,
    is_sin5180296473474724033_nat_o: set_Pr4532377907799695533_nat_o > $o ).

thf(func_def_1409,type,
    is_singleton_o: set_o > $o ).

thf(func_def_1410,type,
    is_singleton_int: set_int > $o ).

thf(func_def_1411,type,
    is_singleton_nat: set_nat > $o ).

thf(func_def_1412,type,
    is_sin2850979758926227957at_nat: set_Pr1261947904930325089at_nat > $o ).

thf(func_def_1413,type,
    is_sin2937591304547752795at_nat: set_Pr4329608150637261639at_nat > $o ).

thf(func_def_1414,type,
    is_singleton_set_nat: set_set_nat > $o ).

thf(func_def_1415,type,
    is_sin6299389887212142093nt_int: set_se6260736226359567993nt_int > $o ).

thf(func_def_1416,type,
    the_elem_o: set_o > $o ).

thf(func_def_1417,type,
    the_elem_int: set_int > int ).

thf(func_def_1418,type,
    the_elem_nat: set_nat > nat ).

thf(func_def_1419,type,
    the_el2281957884133575798at_nat: set_Pr1261947904930325089at_nat > product_prod_nat_nat ).

thf(func_def_1420,type,
    the_el221668144340439132at_nat: set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat ).

thf(func_def_1421,type,
    vimage_o_o: ( $o > $o ) > set_o > set_o ).

thf(func_def_1422,type,
    vimage_o_int: ( $o > int ) > set_int > set_o ).

thf(func_def_1423,type,
    vimage_o_nat: ( $o > nat ) > set_nat > set_o ).

thf(func_def_1424,type,
    vimage2606541041029201316at_nat: ( $o > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > set_o ).

thf(func_def_1425,type,
    vimage_o_rat: ( $o > rat ) > set_rat > set_o ).

thf(func_def_1426,type,
    vimage_int_o: ( int > $o ) > set_o > set_int ).

thf(func_def_1427,type,
    vimage_int_int: ( int > int ) > set_int > set_int ).

thf(func_def_1428,type,
    vimage_int_nat: ( int > nat ) > set_nat > set_int ).

thf(func_def_1429,type,
    vimage1827798767263827160at_nat: ( int > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > set_int ).

thf(func_def_1430,type,
    vimage_int_rat: ( int > rat ) > set_rat > set_int ).

thf(func_def_1431,type,
    vimage_int_set_nat: ( int > set_nat ) > set_set_nat > set_int ).

thf(func_def_1432,type,
    vimage_list_nat_int: ( list_nat > int ) > set_int > set_list_nat ).

thf(func_def_1433,type,
    vimage_list_nat_nat: ( list_nat > nat ) > set_nat > set_list_nat ).

thf(func_def_1434,type,
    vimage_nat_o: ( nat > $o ) > set_o > set_nat ).

thf(func_def_1435,type,
    vimage_nat_int: ( nat > int ) > set_int > set_nat ).

thf(func_def_1436,type,
    vimage_nat_nat: ( nat > nat ) > set_nat > set_nat ).

thf(func_def_1437,type,
    vimage7262694317370708122at_nat: ( nat > produc4166570645942440679at_nat ) > set_Pr8551490117392284871at_nat > set_nat ).

thf(func_def_1438,type,
    vimage8013328719654469172at_nat: ( nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > set_nat ).

thf(func_def_1439,type,
    vimage6435164912253009178at_nat: ( nat > produc3843707927480180839at_nat ) > set_Pr4329608150637261639at_nat > set_nat ).

thf(func_def_1440,type,
    vimage_nat_rat: ( nat > rat ) > set_rat > set_nat ).

thf(func_def_1441,type,
    vimage_nat_set_nat: ( nat > set_nat ) > set_set_nat > set_nat ).

thf(func_def_1442,type,
    vimage2935056327143036492nt_int: ( nat > set_Pr958786334691620121nt_int ) > set_se6260736226359567993nt_int > set_nat ).

thf(func_def_1443,type,
    vimage2280073292226551852_nat_o: ( produc4166570645942440679at_nat > $o ) > set_o > set_Pr8551490117392284871at_nat ).

thf(func_def_1444,type,
    vimage7949981338974167704at_int: ( produc4166570645942440679at_nat > int ) > set_int > set_Pr8551490117392284871at_nat ).

thf(func_def_1445,type,
    vimage7952471809483217980at_nat: ( produc4166570645942440679at_nat > nat ) > set_nat > set_Pr8551490117392284871at_nat ).

thf(func_def_1446,type,
    vimage3529983231074640251at_nat: ( produc4166570645942440679at_nat > produc4166570645942440679at_nat ) > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ).

thf(func_def_1447,type,
    vimage5412736291816116987at_nat: ( produc4166570645942440679at_nat > produc3843707927480180839at_nat ) > set_Pr4329608150637261639at_nat > set_Pr8551490117392284871at_nat ).

thf(func_def_1448,type,
    vimage4653281326611754070at_nat: ( product_prod_nat_nat > nat ) > set_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_1449,type,
    vimage2449269961533847803at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_1450,type,
    vimage3307185822755684012_nat_o: ( produc3843707927480180839at_nat > $o ) > set_o > set_Pr4329608150637261639at_nat ).

thf(func_def_1451,type,
    vimage7134676753939176892at_nat: ( produc3843707927480180839at_nat > nat ) > set_nat > set_Pr4329608150637261639at_nat ).

thf(func_def_1452,type,
    vimage2716263466903273467at_nat: ( produc3843707927480180839at_nat > produc4166570645942440679at_nat ) > set_Pr8551490117392284871at_nat > set_Pr4329608150637261639at_nat ).

thf(func_def_1453,type,
    vimage6896080417876799867at_nat: ( produc3843707927480180839at_nat > produc3843707927480180839at_nat ) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).

thf(func_def_1454,type,
    vimage_rat_o: ( rat > $o ) > set_o > set_rat ).

thf(func_def_1455,type,
    vimage_rat_int: ( rat > int ) > set_int > set_rat ).

thf(func_def_1456,type,
    vimage_rat_nat: ( rat > nat ) > set_nat > set_rat ).

thf(func_def_1457,type,
    vimage_rat_rat: ( rat > rat ) > set_rat > set_rat ).

thf(func_def_1458,type,
    vimage_set_nat_o: ( set_nat > $o ) > set_o > set_set_nat ).

thf(func_def_1459,type,
    vimage_set_nat_int: ( set_nat > int ) > set_int > set_set_nat ).

thf(func_def_1460,type,
    vimage_set_nat_nat: ( set_nat > nat ) > set_nat > set_set_nat ).

thf(func_def_1461,type,
    vimage4765135879290611145et_nat: ( set_nat > set_nat ) > set_set_nat > set_set_nat ).

thf(func_def_1462,type,
    vimage928727498438615150nt_nat: ( set_Pr958786334691620121nt_int > nat ) > set_nat > set_se6260736226359567993nt_int ).

thf(func_def_1463,type,
    set_fo1959793692361082170t_assn: ( nat > assn > assn ) > nat > nat > assn > assn ).

thf(func_def_1464,type,
    set_fo1084959871951514735nteger: ( nat > code_integer > code_integer ) > nat > nat > code_integer > code_integer ).

thf(func_def_1465,type,
    set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).

thf(func_def_1466,type,
    set_fo4497565046347964853at_nat: ( nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat ) > nat > nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat ).

thf(func_def_1467,type,
    set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).

thf(func_def_1468,type,
    set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).

thf(func_def_1469,type,
    set_fo3699595496184130361el_nat: produc4471711990508489141at_nat > produc4471711990508489141at_nat > $o ).

thf(func_def_1470,type,
    set_or8904488021354931149Most_o: $o > $o > set_o ).

thf(func_def_1471,type,
    set_or189985376899183464nteger: code_integer > code_integer > set_Code_integer ).

thf(func_def_1472,type,
    set_or1955772592623580779er_nat: filter_nat > filter_nat > set_filter_nat ).

thf(func_def_1473,type,
    set_or1266510415728281911st_int: int > int > set_int ).

thf(func_def_1474,type,
    set_or1269000886237332187st_nat: nat > nat > set_nat ).

thf(func_def_1475,type,
    set_or633870826150836451st_rat: rat > rat > set_rat ).

thf(func_def_1476,type,
    set_or266616469461849773_set_o: set_o > set_o > set_set_o ).

thf(func_def_1477,type,
    set_or370866239135849197et_int: set_int > set_int > set_set_int ).

thf(func_def_1478,type,
    set_or1270514513317581473st_nat: set_list_nat > set_list_nat > set_set_list_nat ).

thf(func_def_1479,type,
    set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat ).

thf(func_def_1480,type,
    set_or2784603332384507286at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat ).

thf(func_def_1481,type,
    set_or1040488700251649177et_rat: set_rat > set_rat > set_set_rat ).

thf(func_def_1482,type,
    set_or8436436507035938825iteral: literal > literal > set_literal ).

thf(func_def_1483,type,
    set_or7139685690850216873Than_o: $o > $o > set_o ).

thf(func_def_1484,type,
    set_or8404916559141939852nteger: code_integer > code_integer > set_Code_integer ).

thf(func_def_1485,type,
    set_or1773934645810362255er_nat: filter_nat > filter_nat > set_filter_nat ).

thf(func_def_1486,type,
    set_or4662586982721622107an_int: int > int > set_int ).

thf(func_def_1487,type,
    set_or4665077453230672383an_nat: nat > nat > set_nat ).

thf(func_def_1488,type,
    set_or4029947393144176647an_rat: rat > rat > set_rat ).

thf(func_def_1489,type,
    set_or3540276404033026485et_nat: set_nat > set_nat > set_set_nat ).

thf(func_def_1490,type,
    set_or4828121863581493221iteral: literal > literal > set_literal ).

thf(func_def_1491,type,
    set_ord_atLeast_nat: nat > set_nat ).

thf(func_def_1492,type,
    set_or1537382583742010260_nat_o: ( produc3658429121746597890et_nat > $o ) > set_Pr4532377907799695533_nat_o ).

thf(func_def_1493,type,
    set_ord_atMost_o: $o > set_o ).

thf(func_def_1494,type,
    set_or9101266186257409494nteger: code_integer > set_Code_integer ).

thf(func_def_1495,type,
    set_or9144418160755794905er_nat: filter_nat > set_filter_nat ).

thf(func_def_1496,type,
    set_ord_atMost_int: int > set_int ).

thf(func_def_1497,type,
    set_ord_atMost_nat: nat > set_nat ).

thf(func_def_1498,type,
    set_ord_atMost_rat: rat > set_rat ).

thf(func_def_1499,type,
    set_ord_atMost_set_o: set_o > set_set_o ).

thf(func_def_1500,type,
    set_or58775011639299419et_int: set_int > set_set_int ).

thf(func_def_1501,type,
    set_or2492388921469580815st_nat: set_list_nat > set_set_list_nat ).

thf(func_def_1502,type,
    set_or4236626031148496127et_nat: set_nat > set_set_nat ).

thf(func_def_1503,type,
    set_or2459421552957432928nt_int: set_Pr958786334691620121nt_int > set_se6260736226359567993nt_int ).

thf(func_def_1504,type,
    set_or728397472755099399et_rat: set_rat > set_set_rat ).

thf(func_def_1505,type,
    set_or2715278749043346189nteger: code_integer > code_integer > set_Code_integer ).

thf(func_def_1506,type,
    set_or6656581121297822940st_int: int > int > set_int ).

thf(func_def_1507,type,
    set_or4266950643985792945nteger: code_integer > code_integer > set_Code_integer ).

thf(func_def_1508,type,
    set_or5832277885323065728an_int: int > int > set_int ).

thf(func_def_1509,type,
    set_or1210151606488870762an_nat: nat > set_nat ).

thf(func_def_1510,type,
    set_or7240481858991947888_nat_o: ( produc3658429121746597890et_nat > $o ) > set_Pr4532377907799695533_nat_o ).

thf(func_def_1511,type,
    set_ord_lessThan_o: $o > set_o ).

thf(func_def_1512,type,
    set_or5754767410780653050nteger: code_integer > set_Code_integer ).

thf(func_def_1513,type,
    set_ord_lessThan_int: int > set_int ).

thf(func_def_1514,type,
    set_ord_lessThan_nat: nat > set_nat ).

thf(func_def_1515,type,
    set_ord_lessThan_rat: rat > set_rat ).

thf(func_def_1516,type,
    set_or890127255671739683et_nat: set_nat > set_set_nat ).

thf(func_def_1517,type,
    set_or4940836740269066044nt_int: set_Pr958786334691620121nt_int > set_se6260736226359567993nt_int ).

thf(func_def_1518,type,
    set_or2436086697161274615iteral: literal > set_literal ).

thf(func_def_1519,type,
    literal2: $o > $o > $o > $o > $o > $o > $o > literal > literal ).

thf(func_def_1520,type,
    ascii_of: char > char ).

thf(func_def_1521,type,
    asciis_of_literal: literal > list_Code_integer ).

thf(func_def_1522,type,
    char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).

thf(func_def_1523,type,
    digit7: char > $o ).

thf(func_def_1524,type,
    char_of_integer: code_integer > char ).

thf(func_def_1525,type,
    comm_s4049598766089966537nteger: char > code_integer ).

thf(func_def_1526,type,
    comm_s629917340098488124ar_nat: char > nat ).

thf(func_def_1527,type,
    cr_literal: list_char > literal > $o ).

thf(func_def_1528,type,
    abs_literal: list_char > literal ).

thf(func_def_1529,type,
    explode: literal > list_char ).

thf(func_def_1530,type,
    pcr_literal: list_char > literal > $o ).

thf(func_def_1531,type,
    unique1708501630192214702nteger: code_integer > char ).

thf(func_def_1532,type,
    unique3096191561947761185of_nat: nat > char ).

thf(func_def_1533,type,
    sum_Inl_nat_nat: nat > sum_sum_nat_nat ).

thf(func_def_1534,type,
    sum_Inr_nat_nat: nat > sum_sum_nat_nat ).

thf(func_def_1535,type,
    sum_ca7763040182479039464nt_nat: ( nat > int ) > ( nat > int ) > sum_sum_nat_nat > int ).

thf(func_def_1536,type,
    sum_ca6763686470577984908at_nat: ( nat > nat ) > ( nat > nat ) > sum_sum_nat_nat > nat ).

thf(func_def_1537,type,
    syntax7398250324933576852n_assn: assn > assn > $o ).

thf(func_def_1538,type,
    syntax380677951125133566nteger: code_integer > code_integer > $o ).

thf(func_def_1539,type,
    syntax5678989248478167196nt_int: int > int > $o ).

thf(func_def_1540,type,
    syntax4682126007086162916at_nat: nat > nat > $o ).

thf(func_def_1541,type,
    syntax3730441303064801268at_rat: rat > rat > $o ).

thf(func_def_1542,type,
    left_t8440299596084406506t_char: ( list_char > list_char > $o ) > $o ).

thf(func_def_1543,type,
    left_t3131394472396969446nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > $o ).

thf(func_def_1544,type,
    transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_1545,type,
    transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).

thf(func_def_1546,type,
    transi2163837189807498211lp_nat: ( nat > nat > $o ) > nat > nat > $o ).

thf(func_def_1547,type,
    type_definition_o_o: ( $o > $o ) > ( $o > $o ) > set_o > $o ).

thf(func_def_1548,type,
    type_d3909072315231072503_nat_o: ( assn > produc3658429121746597890et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > assn ) > set_Pr4532377907799695533_nat_o > $o ).

thf(func_def_1549,type,
    type_d8366093980585677751er_int: ( code_integer > int ) > ( int > code_integer ) > set_int > $o ).

thf(func_def_1550,type,
    type_d4410041424927559462al_nat: ( code_natural > nat ) > ( nat > code_natural ) > set_nat > $o ).

thf(func_def_1551,type,
    type_d7247357190169752966nt_int: ( int > int ) > ( int > int ) > set_int > $o ).

thf(func_def_1552,type,
    type_d8752208705193531015at_nat: ( int > set_Pr1261947904930325089at_nat ) > ( set_Pr1261947904930325089at_nat > int ) > set_se7855581050983116737at_nat > $o ).

thf(func_def_1553,type,
    type_d5972188401318659438st_nat: ( list_nat > list_nat ) > ( list_nat > list_nat ) > set_list_nat > $o ).

thf(func_def_1554,type,
    type_d6250493948777748686at_nat: ( nat > nat ) > ( nat > nat ) > set_nat > $o ).

thf(func_def_1555,type,
    type_d6188575255521822967unit_o: ( product_unit > $o ) > ( $o > product_unit ) > set_o > $o ).

thf(func_def_1556,type,
    type_d5298809244756387038at_rat: ( rat > rat ) > ( rat > rat ) > set_rat > $o ).

thf(func_def_1557,type,
    type_d8554052265237484179nt_int: ( rat > set_Pr958786334691620121nt_int ) > ( set_Pr958786334691620121nt_int > rat ) > set_se6260736226359567993nt_int > $o ).

thf(func_def_1558,type,
    type_d4752411451802217481t_char: ( literal > list_char ) > ( list_char > literal ) > set_list_char > $o ).

thf(func_def_1559,type,
    accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).

thf(func_def_1560,type,
    accp_nat: ( nat > nat > $o ) > nat > $o ).

thf(func_def_1561,type,
    accp_P8928870874622223812nt_int: ( produc7773217078559923341nt_int > produc7773217078559923341nt_int > $o ) > produc7773217078559923341nt_int > $o ).

thf(func_def_1562,type,
    accp_P6019419558468335806at_nat: ( produc4471711990508489141at_nat > produc4471711990508489141at_nat > $o ) > produc4471711990508489141at_nat > $o ).

thf(func_def_1563,type,
    accp_P1862375125659990705et_nat: ( produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ) > produc2732055786443039994et_nat > $o ).

thf(func_def_1564,type,
    accp_P8126237942716283194atural: ( produc7822875418678951345atural > produc7822875418678951345atural > $o ) > produc7822875418678951345atural > $o ).

thf(func_def_1565,type,
    accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).

thf(func_def_1566,type,
    accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).

thf(func_def_1567,type,
    accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).

thf(func_def_1568,type,
    less_than: set_Pr1261947904930325089at_nat ).

thf(func_def_1569,type,
    max_ex8135407076693332796at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat ).

thf(func_def_1570,type,
    min_ex6901939911449802026at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat ).

thf(func_def_1571,type,
    pred_nat: set_Pr1261947904930325089at_nat ).

thf(func_def_1572,type,
    wf_nat: set_Pr1261947904930325089at_nat > $o ).

thf(func_def_1573,type,
    member6576561426505652726_nat_o: ( produc3658429121746597890et_nat > $o ) > set_Pr4532377907799695533_nat_o > $o ).

thf(func_def_1574,type,
    member_o: $o > set_o > $o ).

thf(func_def_1575,type,
    member_filter_nat: filter_nat > set_filter_nat > $o ).

thf(func_def_1576,type,
    member_int: int > set_int > $o ).

thf(func_def_1577,type,
    member_list_nat: list_nat > set_list_nat > $o ).

thf(func_def_1578,type,
    member_list_char: list_char > set_list_char > $o ).

thf(func_def_1579,type,
    member_nat: nat > set_nat > $o ).

thf(func_def_1580,type,
    member7034335876925520548nt_int: produc7773217078559923341nt_int > set_Pr1872883991513573699nt_int > $o ).

thf(func_def_1581,type,
    member4164122664394876845nteger: produc1908205239877642774nteger > set_Pr1281608226676607948nteger > $o ).

thf(func_def_1582,type,
    member8781333585448626064_nat_o: produc4928098042776334183_nat_o > set_Pr2161125870931222855_nat_o > $o ).

thf(func_def_1583,type,
    member6124377750444531601et_nat: produc2732055786443039994et_nat > set_Pr8536935166611901872et_nat > $o ).

thf(func_def_1584,type,
    member1996754912294343701et_nat: produc3925858234332021118et_nat > set_Pr3286484037609594932et_nat > $o ).

thf(func_def_1585,type,
    member7618704894036264090nt_int: produc2285326912895808259nt_int > set_Pr9222295170931077689nt_int > $o ).

thf(func_def_1586,type,
    member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).

thf(func_def_1587,type,
    member6689249552917799696at_nat: produc4166570645942440679at_nat > set_Pr8551490117392284871at_nat > $o ).

thf(func_def_1588,type,
    member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).

thf(func_def_1589,type,
    member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).

thf(func_def_1590,type,
    member8277197624267554838et_nat: produc7819656566062154093et_nat > set_Pr5488025237498180813et_nat > $o ).

thf(func_def_1591,type,
    member444158400953824016od_o_o: produc2934264451710624999od_o_o > set_Pr1932065953672099015od_o_o > $o ).

thf(func_def_1592,type,
    member4095101504841534314at_nat: produc732395585841259969at_nat > set_Pr457366540195662369at_nat > $o ).

thf(func_def_1593,type,
    member5325734588016868240nt_int: produc412284730452459111nt_int > set_Pr8057934254988874055nt_int > $o ).

thf(func_def_1594,type,
    member8757157785044589968at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > $o ).

thf(func_def_1595,type,
    member_rat: rat > set_rat > $o ).

thf(func_def_1596,type,
    member_set_nat: set_nat > set_set_nat > $o ).

thf(func_def_1597,type,
    member2340774599025711042nt_int: set_Pr958786334691620121nt_int > set_se6260736226359567993nt_int > $o ).

thf(func_def_1598,type,
    member2643936169264416010at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat > $o ).

thf(func_def_1599,type,
    member_char: char > set_char > $o ).

thf(func_def_1600,type,
    member_literal: literal > set_literal > $o ).

thf(func_def_1601,type,
    x: assn ).

thf(func_def_1602,type,
    y: assn ).

thf(func_def_1625,type,
    sK0: assn > assn > produc3658429121746597890et_nat ).

thf(func_def_1626,type,
    sK1: assn > assn > produc3658429121746597890et_nat ).

thf(func_def_1627,type,
    sK2: assn > produc3658429121746597890et_nat ).

thf(func_def_1628,type,
    sK3: assn > produc3658429121746597890et_nat ).

thf(func_def_1629,type,
    sK4: assn > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat ).

thf(func_def_1630,type,
    sK5: ( produc3658429121746597890et_nat > $o ) > assn > produc3658429121746597890et_nat ).

thf(func_def_1631,type,
    sK6: assn > produc3658429121746597890et_nat > $o ).

thf(func_def_1632,type,
    sK7: ( assn > $o ) > produc3658429121746597890et_nat > $o ).

thf(func_def_1634,type,
    ph9: 
      !>[X0: $tType] : X0 ).

thf(func_def_1635,type,
    sK10: assn > produc3658429121746597890et_nat ).

thf(func_def_1636,type,
    sK11: assn > produc3658429121746597890et_nat ).

thf(func_def_1637,type,
    sK12: assn > produc3658429121746597890et_nat ).

thf(func_def_1638,type,
    sK13: assn > produc3658429121746597890et_nat ).

thf(func_def_1639,type,
    sK14: assn > produc3658429121746597890et_nat ).

thf(func_def_1640,type,
    sK15: assn > produc3658429121746597890et_nat ).

thf(func_def_1641,type,
    sK16: ( assn > $o ) > produc3658429121746597890et_nat ).

thf(func_def_1642,type,
    sK17: produc3658429121746597890et_nat ).

thf(func_def_1643,type,
    sK18: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat ).

thf(func_def_1644,type,
    sK19: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat ).

thf(func_def_1645,type,
    sK20: assn > assn > produc3658429121746597890et_nat ).

thf(func_def_1646,type,
    sK21: assn > assn > produc3658429121746597890et_nat ).

thf(func_def_1647,type,
    sK22: assn > assn > produc3658429121746597890et_nat ).

thf(func_def_1648,type,
    sK23: assn > produc3658429121746597890et_nat ).

thf(func_def_1649,type,
    sK24: assn > produc3658429121746597890et_nat ).

thf(func_def_1650,type,
    sK25: assn > produc3658429121746597890et_nat ).

thf(func_def_1651,type,
    sK26: assn > produc3658429121746597890et_nat ).

thf(func_def_1652,type,
    sK27: ( assn > $o ) > produc3658429121746597890et_nat ).

thf(func_def_1653,type,
    sK28: produc3658429121746597890et_nat ).

thf(func_def_1654,type,
    sK29: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat ).

thf(func_def_1655,type,
    sK30: assn > assn > produc3658429121746597890et_nat ).

thf(func_def_1656,type,
    sK31: assn > assn > produc3658429121746597890et_nat ).

thf(func_def_1657,type,
    sK32: assn > assn > produc3658429121746597890et_nat ).

thf(func_def_1658,type,
    sK33: assn > assn > produc3658429121746597890et_nat ).

thf(f24177,plain,
    $false,
    inference(avatar_sat_refutation,[status(thm)],[f23046,f23051,f23053,f23536,f23549,f23554,f23557,f23715,f23788,f23815,f23994,f23995,f24005,f24067,f24174]) ).

thf(f24174,plain,
    ( ~ spl8_32
    | ~ spl8_34 ),
    inference(avatar_contradiction_clause,[status(thm)],[f24173]) ).

thf(f24173,plain,
    ( $false
    | ~ spl8_32
    | ~ spl8_34 ),
    inference(trivial_inequality_removal,[status(thm)],[f24162]) ).

thf(f24162,plain,
    ( ( $false = $true )
    | ~ spl8_32
    | ~ spl8_34 ),
    inference(superposition,[status(thm)],[f23992,f24004]) ).

thf(f24004,plain,
    ( ( $false
      = ( rep_assn @ y @ sK28 ) )
    | ~ spl8_34 ),
    inference(avatar_component_clause,[status(thm)],[f24002]) ).

thf(f24002,definition,
    ( spl8_34
  <=> ( $false
      = ( rep_assn @ y @ sK28 ) ) ),
    introduced(definition,[new_symbols(naming,[spl8_34])],[avatar_definition]) ).

thf(f23992,plain,
    ( ( ( rep_assn @ y @ sK28 )
      = $true )
    | ~ spl8_32 ),
    inference(avatar_component_clause,[status(thm)],[f23990]) ).

thf(f23990,definition,
    ( spl8_32
  <=> ( ( rep_assn @ y @ sK28 )
      = $true ) ),
    introduced(definition,[new_symbols(naming,[spl8_32])],[avatar_definition]) ).

thf(f24067,plain,
    ( ~ spl8_31
    | ~ spl8_33 ),
    inference(avatar_contradiction_clause,[status(thm)],[f24066]) ).

thf(f24066,plain,
    ( $false
    | ~ spl8_31
    | ~ spl8_33 ),
    inference(trivial_inequality_removal,[status(thm)],[f24056]) ).

thf(f24056,plain,
    ( ( $false = $true )
    | ~ spl8_31
    | ~ spl8_33 ),
    inference(superposition,[status(thm)],[f23988,f24000]) ).

thf(f24000,plain,
    ( ( $false
      = ( rep_assn @ x @ sK28 ) )
    | ~ spl8_33 ),
    inference(avatar_component_clause,[status(thm)],[f23998]) ).

thf(f23998,definition,
    ( spl8_33
  <=> ( $false
      = ( rep_assn @ x @ sK28 ) ) ),
    introduced(definition,[new_symbols(naming,[spl8_33])],[avatar_definition]) ).

thf(f23988,plain,
    ( ( ( rep_assn @ x @ sK28 )
      = $true )
    | ~ spl8_31 ),
    inference(avatar_component_clause,[status(thm)],[f23986]) ).

thf(f23986,definition,
    ( spl8_31
  <=> ( ( rep_assn @ x @ sK28 )
      = $true ) ),
    introduced(definition,[new_symbols(naming,[spl8_31])],[avatar_definition]) ).

thf(f24005,plain,
    ( spl8_33
    | spl8_34
    | spl8_2
    | ~ spl8_4 ),
    inference(avatar_split_clause,[status(thm)],[f23976,f23048,f23038,f24002,f23998]) ).

thf(f23038,definition,
    ( spl8_2
  <=> ( x
      = ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ x @ Y0 )
            & ( rep_assn @ y @ Y0 ) ) ) ) ),
    introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition]) ).

thf(f23048,definition,
    ( spl8_4
  <=> ( x
      = ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) ) ) ) ),
    introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition]) ).

thf(f23976,plain,
    ( ( $false
      = ( rep_assn @ y @ sK28 ) )
    | ( $false
      = ( rep_assn @ x @ sK28 ) )
    | spl8_2
    | ~ spl8_4 ),
    inference(duplicate_literal_removal,[status(thm)],[f23975]) ).

thf(f23975,plain,
    ( ( $false
      = ( rep_assn @ x @ sK28 ) )
    | ( $false
      = ( rep_assn @ y @ sK28 ) )
    | ( $false
      = ( rep_assn @ x @ sK28 ) )
    | ( $false
      = ( rep_assn @ y @ sK28 ) )
    | spl8_2
    | ~ spl8_4 ),
    inference(binary_proxy_clausification,[status(thm)],[f23974]) ).

thf(f23974,plain,
    ( ( $false
      = ( rep_assn @ y @ sK28 ) )
    | ( $false
      = ( rep_assn @ x @ sK28 ) )
    | ( $false
      = ( ( rep_assn @ x @ sK28 )
        & ( rep_assn @ y @ sK28 ) ) )
    | spl8_2
    | ~ spl8_4 ),
    inference(binary_proxy_clausification,[status(thm)],[f23973]) ).

thf(f23973,plain,
    ( ( $false
      = ( ( rep_assn @ y @ sK28 )
        & ( rep_assn @ x @ sK28 ) ) )
    | ( $false
      = ( ( rep_assn @ x @ sK28 )
        & ( rep_assn @ y @ sK28 ) ) )
    | spl8_2
    | ~ spl8_4 ),
    inference(binary_proxy_clausification,[status(thm)],[f23971]) ).

thf(f23971,plain,
    ( ( ( ( rep_assn @ x @ sK28 )
        & ( rep_assn @ y @ sK28 ) )
     != ( ( rep_assn @ y @ sK28 )
        & ( rep_assn @ x @ sK28 ) ) )
    | spl8_2
    | ~ spl8_4 ),
    inference(beta_eta_normalization,[status(thm)],[f23969]) ).

thf(f23969,plain,
    ( ( ( ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ x @ Y0 )
            & ( rep_assn @ y @ Y0 ) )
        @ sK28 )
     != ( ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) )
        @ sK28 ) )
    | spl8_2
    | ~ spl8_4 ),
    inference(negative_extensionality,[status(thm)],[f23835]) ).

thf(f23835,plain,
    ( ( ( ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ x @ Y0 )
            & ( rep_assn @ y @ Y0 ) ) )
     != ( ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) ) ) )
    | spl8_2
    | ~ spl8_4 ),
    inference(trivial_inequality_removal,[status(thm)],[f23818]) ).

thf(f23818,plain,
    ( ( x != x )
    | ( ( ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ x @ Y0 )
            & ( rep_assn @ y @ Y0 ) ) )
     != ( ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) ) ) )
    | spl8_2
    | ~ spl8_4 ),
    inference(constrained_superposition,[status(thm)],[f23039,f23050]) ).

thf(f23050,plain,
    ( ( x
      = ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) ) ) )
    | ~ spl8_4 ),
    inference(avatar_component_clause,[status(thm)],[f23048]) ).

thf(f23039,plain,
    ( ( x
     != ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ x @ Y0 )
            & ( rep_assn @ y @ Y0 ) ) ) )
    | spl8_2 ),
    inference(avatar_component_clause,[status(thm)],[f23038]) ).

thf(f23995,plain,
    ( spl8_32
    | spl8_2
    | ~ spl8_4 ),
    inference(avatar_split_clause,[status(thm)],[f23981,f23048,f23038,f23990]) ).

thf(f23981,plain,
    ( ( ( rep_assn @ y @ sK28 )
      = $true )
    | spl8_2
    | ~ spl8_4 ),
    inference(duplicate_literal_removal,[status(thm)],[f23979]) ).

thf(f23979,plain,
    ( ( ( rep_assn @ y @ sK28 )
      = $true )
    | ( ( rep_assn @ y @ sK28 )
      = $true )
    | spl8_2
    | ~ spl8_4 ),
    inference(binary_proxy_clausification,[status(thm)],[f23978]) ).

thf(f23978,plain,
    ( ( ( rep_assn @ y @ sK28 )
      = $true )
    | ( ( ( rep_assn @ x @ sK28 )
        & ( rep_assn @ y @ sK28 ) )
      = $true )
    | spl8_2
    | ~ spl8_4 ),
    inference(binary_proxy_clausification,[status(thm)],[f23972]) ).

thf(f23972,plain,
    ( ( ( ( rep_assn @ y @ sK28 )
        & ( rep_assn @ x @ sK28 ) )
      = $true )
    | ( ( ( rep_assn @ x @ sK28 )
        & ( rep_assn @ y @ sK28 ) )
      = $true )
    | spl8_2
    | ~ spl8_4 ),
    inference(binary_proxy_clausification,[status(thm)],[f23971]) ).

thf(f23994,plain,
    ( spl8_31
    | spl8_2
    | ~ spl8_4 ),
    inference(avatar_split_clause,[status(thm)],[f23984,f23048,f23038,f23986]) ).

thf(f23984,plain,
    ( ( ( rep_assn @ x @ sK28 )
      = $true )
    | spl8_2
    | ~ spl8_4 ),
    inference(duplicate_literal_removal,[status(thm)],[f23983]) ).

thf(f23983,plain,
    ( ( ( rep_assn @ x @ sK28 )
      = $true )
    | ( ( rep_assn @ x @ sK28 )
      = $true )
    | spl8_2
    | ~ spl8_4 ),
    inference(binary_proxy_clausification,[status(thm)],[f23977]) ).

thf(f23977,plain,
    ( ( ( ( rep_assn @ x @ sK28 )
        & ( rep_assn @ y @ sK28 ) )
      = $true )
    | ( ( rep_assn @ x @ sK28 )
      = $true )
    | spl8_2
    | ~ spl8_4 ),
    inference(binary_proxy_clausification,[status(thm)],[f23972]) ).

thf(f23815,plain,
    ( ~ spl8_1
    | spl8_3
    | ~ spl8_4 ),
    inference(avatar_contradiction_clause,[status(thm)],[f23814]) ).

thf(f23814,plain,
    ( $false
    | ~ spl8_1
    | spl8_3
    | ~ spl8_4 ),
    inference(subsumption_resolution,[status(thm)],[f23813,f23045]) ).

thf(f23045,plain,
    ( ( x != y )
    | spl8_3 ),
    inference(avatar_component_clause,[status(thm)],[f23043]) ).

thf(f23043,definition,
    ( spl8_3
  <=> ( x = y ) ),
    introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition]) ).

thf(f23813,plain,
    ( ( x = y )
    | ~ spl8_1
    | ~ spl8_4 ),
    inference(forward_demodulation,[status(thm)],[f23035,f23050]) ).

thf(f23035,plain,
    ( ( y
      = ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) ) ) )
    | ~ spl8_1 ),
    inference(avatar_component_clause,[status(thm)],[f23034]) ).

thf(f23034,definition,
    ( spl8_1
  <=> ( y
      = ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) ) ) ) ),
    introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition]) ).

thf(f23788,plain,
    ( spl8_1
    | ~ spl8_3
    | ~ spl8_4 ),
    inference(avatar_contradiction_clause,[status(thm)],[f23787]) ).

thf(f23787,plain,
    ( $false
    | spl8_1
    | ~ spl8_3
    | ~ spl8_4 ),
    inference(subsumption_resolution,[status(thm)],[f23744,f23044]) ).

thf(f23044,plain,
    ( ( x = y )
    | ~ spl8_3 ),
    inference(avatar_component_clause,[status(thm)],[f23043]) ).

thf(f23744,plain,
    ( ( x != y )
    | spl8_1
    | ~ spl8_4 ),
    inference(superposition,[status(thm)],[f23036,f23050]) ).

thf(f23036,plain,
    ( ( y
     != ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) ) ) )
    | spl8_1 ),
    inference(avatar_component_clause,[status(thm)],[f23034]) ).

thf(f23715,plain,
    ( ~ spl8_23
    | ~ spl8_25 ),
    inference(avatar_contradiction_clause,[status(thm)],[f23714]) ).

thf(f23714,plain,
    ( $false
    | ~ spl8_23
    | ~ spl8_25 ),
    inference(trivial_inequality_removal,[status(thm)],[f23705]) ).

thf(f23705,plain,
    ( ( $false = $true )
    | ~ spl8_23
    | ~ spl8_25 ),
    inference(superposition,[status(thm)],[f23535,f23544]) ).

thf(f23544,plain,
    ( ( ( rep_assn @ x @ sK17 )
      = $true )
    | ~ spl8_25 ),
    inference(avatar_component_clause,[status(thm)],[f23542]) ).

thf(f23542,definition,
    ( spl8_25
  <=> ( ( rep_assn @ x @ sK17 )
      = $true ) ),
    introduced(definition,[new_symbols(naming,[spl8_25])],[avatar_definition]) ).

thf(f23535,plain,
    ( ( $false
      = ( rep_assn @ x @ sK17 ) )
    | ~ spl8_23 ),
    inference(avatar_component_clause,[status(thm)],[f23533]) ).

thf(f23533,definition,
    ( spl8_23
  <=> ( $false
      = ( rep_assn @ x @ sK17 ) ) ),
    introduced(definition,[new_symbols(naming,[spl8_23])],[avatar_definition]) ).

thf(f23557,plain,
    ( ~ spl8_22
    | ~ spl8_24 ),
    inference(avatar_contradiction_clause,[status(thm)],[f23556]) ).

thf(f23556,plain,
    ( $false
    | ~ spl8_22
    | ~ spl8_24 ),
    inference(trivial_inequality_removal,[status(thm)],[f23555]) ).

thf(f23555,plain,
    ( ( $false = $true )
    | ~ spl8_22
    | ~ spl8_24 ),
    inference(forward_demodulation,[status(thm)],[f23540,f23531]) ).

thf(f23531,plain,
    ( ( $false
      = ( rep_assn @ y @ sK17 ) )
    | ~ spl8_22 ),
    inference(avatar_component_clause,[status(thm)],[f23529]) ).

thf(f23529,definition,
    ( spl8_22
  <=> ( $false
      = ( rep_assn @ y @ sK17 ) ) ),
    introduced(definition,[new_symbols(naming,[spl8_22])],[avatar_definition]) ).

thf(f23540,plain,
    ( ( ( rep_assn @ y @ sK17 )
      = $true )
    | ~ spl8_24 ),
    inference(avatar_component_clause,[status(thm)],[f23538]) ).

thf(f23538,definition,
    ( spl8_24
  <=> ( ( rep_assn @ y @ sK17 )
      = $true ) ),
    introduced(definition,[new_symbols(naming,[spl8_24])],[avatar_definition]) ).

thf(f23554,plain,
    ( spl8_25
    | ~ spl8_2
    | spl8_4 ),
    inference(avatar_split_clause,[status(thm)],[f23521,f23048,f23038,f23542]) ).

thf(f23521,plain,
    ( ( ( rep_assn @ x @ sK17 )
      = $true )
    | ~ spl8_2
    | spl8_4 ),
    inference(duplicate_literal_removal,[status(thm)],[f23519]) ).

thf(f23519,plain,
    ( ( ( rep_assn @ x @ sK17 )
      = $true )
    | ( ( rep_assn @ x @ sK17 )
      = $true )
    | ~ spl8_2
    | spl8_4 ),
    inference(binary_proxy_clausification,[status(thm)],[f23518]) ).

thf(f23518,plain,
    ( ( ( ( rep_assn @ y @ sK17 )
        & ( rep_assn @ x @ sK17 ) )
      = $true )
    | ( ( rep_assn @ x @ sK17 )
      = $true )
    | ~ spl8_2
    | spl8_4 ),
    inference(binary_proxy_clausification,[status(thm)],[f23512]) ).

thf(f23512,plain,
    ( ( ( ( rep_assn @ x @ sK17 )
        & ( rep_assn @ y @ sK17 ) )
      = $true )
    | ( ( ( rep_assn @ y @ sK17 )
        & ( rep_assn @ x @ sK17 ) )
      = $true )
    | ~ spl8_2
    | spl8_4 ),
    inference(binary_proxy_clausification,[status(thm)],[f23511]) ).

thf(f23511,plain,
    ( ( ( ( rep_assn @ y @ sK17 )
        & ( rep_assn @ x @ sK17 ) )
     != ( ( rep_assn @ x @ sK17 )
        & ( rep_assn @ y @ sK17 ) ) )
    | ~ spl8_2
    | spl8_4 ),
    inference(beta_eta_normalization,[status(thm)],[f23509]) ).

thf(f23509,plain,
    ( ( ( ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ x @ Y0 )
            & ( rep_assn @ y @ Y0 ) )
        @ sK17 )
     != ( ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) )
        @ sK17 ) )
    | ~ spl8_2
    | spl8_4 ),
    inference(negative_extensionality,[status(thm)],[f23359]) ).

thf(f23359,plain,
    ( ( ( ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ x @ Y0 )
            & ( rep_assn @ y @ Y0 ) ) )
     != ( ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) ) ) )
    | ~ spl8_2
    | spl8_4 ),
    inference(trivial_inequality_removal,[status(thm)],[f23354]) ).

thf(f23354,plain,
    ( ( x != x )
    | ( ( ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ x @ Y0 )
            & ( rep_assn @ y @ Y0 ) ) )
     != ( ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) ) ) )
    | ~ spl8_2
    | spl8_4 ),
    inference(constrained_superposition,[status(thm)],[f23049,f23040]) ).

thf(f23040,plain,
    ( ( x
      = ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ x @ Y0 )
            & ( rep_assn @ y @ Y0 ) ) ) )
    | ~ spl8_2 ),
    inference(avatar_component_clause,[status(thm)],[f23038]) ).

thf(f23049,plain,
    ( ( x
     != ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) ) ) )
    | spl8_4 ),
    inference(avatar_component_clause,[status(thm)],[f23048]) ).

thf(f23549,plain,
    ( spl8_24
    | ~ spl8_2
    | spl8_4 ),
    inference(avatar_split_clause,[status(thm)],[f23524,f23048,f23038,f23538]) ).

thf(f23524,plain,
    ( ( ( rep_assn @ y @ sK17 )
      = $true )
    | ~ spl8_2
    | spl8_4 ),
    inference(duplicate_literal_removal,[status(thm)],[f23523]) ).

thf(f23523,plain,
    ( ( ( rep_assn @ y @ sK17 )
      = $true )
    | ( ( rep_assn @ y @ sK17 )
      = $true )
    | ~ spl8_2
    | spl8_4 ),
    inference(binary_proxy_clausification,[status(thm)],[f23517]) ).

thf(f23517,plain,
    ( ( ( rep_assn @ y @ sK17 )
      = $true )
    | ( ( ( rep_assn @ y @ sK17 )
        & ( rep_assn @ x @ sK17 ) )
      = $true )
    | ~ spl8_2
    | spl8_4 ),
    inference(binary_proxy_clausification,[status(thm)],[f23512]) ).

thf(f23536,plain,
    ( spl8_22
    | spl8_23
    | ~ spl8_2
    | spl8_4 ),
    inference(avatar_split_clause,[status(thm)],[f23516,f23048,f23038,f23533,f23529]) ).

thf(f23516,plain,
    ( ( $false
      = ( rep_assn @ x @ sK17 ) )
    | ( $false
      = ( rep_assn @ y @ sK17 ) )
    | ~ spl8_2
    | spl8_4 ),
    inference(duplicate_literal_removal,[status(thm)],[f23515]) ).

thf(f23515,plain,
    ( ( $false
      = ( rep_assn @ y @ sK17 ) )
    | ( $false
      = ( rep_assn @ x @ sK17 ) )
    | ( $false
      = ( rep_assn @ y @ sK17 ) )
    | ( $false
      = ( rep_assn @ x @ sK17 ) )
    | ~ spl8_2
    | spl8_4 ),
    inference(binary_proxy_clausification,[status(thm)],[f23514]) ).

thf(f23514,plain,
    ( ( $false
      = ( rep_assn @ y @ sK17 ) )
    | ( $false
      = ( rep_assn @ x @ sK17 ) )
    | ( $false
      = ( ( rep_assn @ y @ sK17 )
        & ( rep_assn @ x @ sK17 ) ) )
    | ~ spl8_2
    | spl8_4 ),
    inference(binary_proxy_clausification,[status(thm)],[f23513]) ).

thf(f23513,plain,
    ( ( $false
      = ( ( rep_assn @ x @ sK17 )
        & ( rep_assn @ y @ sK17 ) ) )
    | ( $false
      = ( ( rep_assn @ y @ sK17 )
        & ( rep_assn @ x @ sK17 ) ) )
    | ~ spl8_2
    | spl8_4 ),
    inference(binary_proxy_clausification,[status(thm)],[f23511]) ).

thf(f23053,plain,
    ( spl8_3
    | ~ spl8_4
    | ~ spl8_2
    | spl8_1 ),
    inference(avatar_split_clause,[status(thm)],[f23015,f23034,f23038,f23048,f23043]) ).

thf(f23015,plain,
    ( ( x
     != ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ x @ Y0 )
            & ( rep_assn @ y @ Y0 ) ) ) )
    | ( x
     != ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) ) ) )
    | ( y
      = ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) ) ) )
    | ( x = y ) ),
    inference(equality_proxy_clausification,[status(thm)],[f23014]) ).

thf(f23014,plain,
    ( ( x
     != ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) ) ) )
    | ( ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ y @ Y0 )
              & ( rep_assn @ x @ Y0 ) ) )
        = y )
      = $true )
    | ( x = y )
    | ( x
     != ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ x @ Y0 )
            & ( rep_assn @ y @ Y0 ) ) ) ) ),
    inference(equality_proxy_clausification,[status(thm)],[f23013]) ).

thf(f23013,plain,
    ( ( x
     != ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) ) ) )
    | ( $true
      = ( x = y ) )
    | ( ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ y @ Y0 )
              & ( rep_assn @ x @ Y0 ) ) )
        = y )
      = $true )
    | ( x
     != ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ x @ Y0 )
            & ( rep_assn @ y @ Y0 ) ) ) ) ),
    inference(not_proxy_clausification,[status(thm)],[f23012]) ).

thf(f23012,plain,
    ( ( x
     != ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) ) ) )
    | ( x
     != ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ x @ Y0 )
            & ( rep_assn @ y @ Y0 ) ) ) )
    | ( $false
      = ( x != y ) )
    | ( ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ y @ Y0 )
              & ( rep_assn @ x @ Y0 ) ) )
        = y )
      = $true ) ),
    inference(not_proxy_clausification,[status(thm)],[f23011]) ).

thf(f23011,plain,
    ( ( $false
      = ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ y @ Y0 )
              & ( rep_assn @ x @ Y0 ) ) )
       != y ) )
    | ( x
     != ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ x @ Y0 )
            & ( rep_assn @ y @ Y0 ) ) ) )
    | ( $false
      = ( x != y ) )
    | ( x
     != ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) ) ) ) ),
    inference(equality_proxy_clausification,[status(thm)],[f23010]) ).

thf(f23010,plain,
    ( ( x
     != ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) ) ) )
    | ( $false
      = ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ x @ Y0 )
              & ( rep_assn @ y @ Y0 ) ) )
        = x ) )
    | ( $false
      = ( x != y ) )
    | ( $false
      = ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ y @ Y0 )
              & ( rep_assn @ x @ Y0 ) ) )
       != y ) ) ),
    inference(equality_proxy_clausification,[status(thm)],[f23009]) ).

thf(f23009,plain,
    ( ( $false
      = ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ y @ Y0 )
              & ( rep_assn @ x @ Y0 ) ) )
        = x ) )
    | ( $false
      = ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ y @ Y0 )
              & ( rep_assn @ x @ Y0 ) ) )
       != y ) )
    | ( $false
      = ( x != y ) )
    | ( $false
      = ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ x @ Y0 )
              & ( rep_assn @ y @ Y0 ) ) )
        = x ) ) ),
    inference(binary_proxy_clausification,[status(thm)],[f23008]) ).

thf(f23008,plain,
    ( ( $false
      = ( ( ( abs_assn
            @ ^ [Y0: produc3658429121746597890et_nat] :
                ( ( rep_assn @ y @ Y0 )
                & ( rep_assn @ x @ Y0 ) ) )
          = x )
        & ( ( abs_assn
            @ ^ [Y0: produc3658429121746597890et_nat] :
                ( ( rep_assn @ y @ Y0 )
                & ( rep_assn @ x @ Y0 ) ) )
         != y ) ) )
    | ( $false
      = ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ x @ Y0 )
              & ( rep_assn @ y @ Y0 ) ) )
        = x ) )
    | ( $false
      = ( x != y ) ) ),
    inference(binary_proxy_clausification,[status(thm)],[f23007]) ).

thf(f23007,plain,
    ( ( $false
      = ( ( x != y )
        & ( ( abs_assn
            @ ^ [Y0: produc3658429121746597890et_nat] :
                ( ( rep_assn @ x @ Y0 )
                & ( rep_assn @ y @ Y0 ) ) )
          = x ) ) )
    | ( $false
      = ( ( ( abs_assn
            @ ^ [Y0: produc3658429121746597890et_nat] :
                ( ( rep_assn @ y @ Y0 )
                & ( rep_assn @ x @ Y0 ) ) )
          = x )
        & ( ( abs_assn
            @ ^ [Y0: produc3658429121746597890et_nat] :
                ( ( rep_assn @ y @ Y0 )
                & ( rep_assn @ x @ Y0 ) ) )
         != y ) ) ) ),
    inference(binary_proxy_clausification,[status(thm)],[f22968]) ).

thf(f22968,plain,
    ( ( ( x != y )
      & ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ x @ Y0 )
              & ( rep_assn @ y @ Y0 ) ) )
        = x ) )
   != ( ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ y @ Y0 )
              & ( rep_assn @ x @ Y0 ) ) )
        = x )
      & ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ y @ Y0 )
              & ( rep_assn @ x @ Y0 ) ) )
       != y ) ) ),
    inference(cnf_transformation,[status(thm)],[f22935]) ).

thf(f22935,plain,
    ( ( ( x != y )
      & ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ x @ Y0 )
              & ( rep_assn @ y @ Y0 ) ) )
        = x ) )
   != ( ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ y @ Y0 )
              & ( rep_assn @ x @ Y0 ) ) )
        = x )
      & ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ y @ Y0 )
              & ( rep_assn @ x @ Y0 ) ) )
       != y ) ) ),
    inference(flattening,[status(thm)],[f20009]) ).

thf(f20009,plain,
    ( ( ( x != y )
      & ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ x @ Y0 )
              & ( rep_assn @ y @ Y0 ) ) )
        = x ) )
   != ( ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ y @ Y0 )
              & ( rep_assn @ x @ Y0 ) ) )
        = x )
      & ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ y @ Y0 )
              & ( rep_assn @ x @ Y0 ) ) )
       != y ) ) ),
    inference(fool_elimination,[status(thm)],[f20008]) ).

thf(f20008,plain,
    ~ ( ( ( abs_assn
          @ ^ [X0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ y @ X0 )
              & ( rep_assn @ x @ X0 ) ) )
        = x )
      & ( ( x != y )
        = ( ( abs_assn
            @ ^ [X1: produc3658429121746597890et_nat] :
                ( ( rep_assn @ x @ X1 )
                & ( rep_assn @ y @ X1 ) ) )
         != y ) )
      & ( ( abs_assn
          @ ^ [X2: produc3658429121746597890et_nat] :
              ( ( rep_assn @ x @ X2 )
              & ( rep_assn @ y @ X2 ) ) )
        = x ) ),
    inference(rectify,[status(thm)],[f9727]) ).

thf(f9727,negated_conjecture,
    ~ ( ( ( abs_assn
          @ ^ [X7: produc3658429121746597890et_nat] :
              ( ( rep_assn @ y @ X7 )
              & ( rep_assn @ x @ X7 ) ) )
        = x )
      & ( ( x != y )
        = ( ( abs_assn
            @ ^ [X7: produc3658429121746597890et_nat] :
                ( ( rep_assn @ x @ X7 )
                & ( rep_assn @ y @ X7 ) ) )
         != y ) )
      & ( ( abs_assn
          @ ^ [X7: produc3658429121746597890et_nat] :
              ( ( rep_assn @ x @ X7 )
              & ( rep_assn @ y @ X7 ) ) )
        = x ) ),
    inference(negated_conjecture,[status(cth)],[f9726]) ).

thf(f9726,conjecture,
    ( ( ( abs_assn
        @ ^ [X7: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ X7 )
            & ( rep_assn @ x @ X7 ) ) )
      = x )
    & ( ( x != y )
      = ( ( abs_assn
          @ ^ [X7: produc3658429121746597890et_nat] :
              ( ( rep_assn @ x @ X7 )
              & ( rep_assn @ y @ X7 ) ) )
       != y ) )
    & ( ( abs_assn
        @ ^ [X7: produc3658429121746597890et_nat] :
            ( ( rep_assn @ x @ X7 )
            & ( rep_assn @ y @ X7 ) ) )
      = x ) ),
    file('/export/starexec/sandbox2/tmp/tmp.q4ZIkRLcku/DTF2THF_32141.p',conj_0) ).

thf(f23051,plain,
    ( spl8_4
    | spl8_2 ),
    inference(avatar_split_clause,[status(thm)],[f23023,f23038,f23048]) ).

thf(f23023,plain,
    ( ( x
      = ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ x @ Y0 )
            & ( rep_assn @ y @ Y0 ) ) ) )
    | ( x
      = ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) ) ) ) ),
    inference(equality_proxy_clausification,[status(thm)],[f23019]) ).

thf(f23019,plain,
    ( ( ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ x @ Y0 )
              & ( rep_assn @ y @ Y0 ) ) )
        = x )
      = $true )
    | ( x
      = ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) ) ) ) ),
    inference(binary_proxy_clausification,[status(thm)],[f23018]) ).

thf(f23018,plain,
    ( ( ( ( x != y )
        & ( ( abs_assn
            @ ^ [Y0: produc3658429121746597890et_nat] :
                ( ( rep_assn @ x @ Y0 )
                & ( rep_assn @ y @ Y0 ) ) )
          = x ) )
      = $true )
    | ( x
      = ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) ) ) ) ),
    inference(equality_proxy_clausification,[status(thm)],[f23017]) ).

thf(f23017,plain,
    ( ( ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ y @ Y0 )
              & ( rep_assn @ x @ Y0 ) ) )
        = x )
      = $true )
    | ( ( ( x != y )
        & ( ( abs_assn
            @ ^ [Y0: produc3658429121746597890et_nat] :
                ( ( rep_assn @ x @ Y0 )
                & ( rep_assn @ y @ Y0 ) ) )
          = x ) )
      = $true ) ),
    inference(binary_proxy_clausification,[status(thm)],[f23006]) ).

thf(f23006,plain,
    ( ( ( ( ( abs_assn
            @ ^ [Y0: produc3658429121746597890et_nat] :
                ( ( rep_assn @ y @ Y0 )
                & ( rep_assn @ x @ Y0 ) ) )
          = x )
        & ( ( abs_assn
            @ ^ [Y0: produc3658429121746597890et_nat] :
                ( ( rep_assn @ y @ Y0 )
                & ( rep_assn @ x @ Y0 ) ) )
         != y ) )
      = $true )
    | ( ( ( x != y )
        & ( ( abs_assn
            @ ^ [Y0: produc3658429121746597890et_nat] :
                ( ( rep_assn @ x @ Y0 )
                & ( rep_assn @ y @ Y0 ) ) )
          = x ) )
      = $true ) ),
    inference(binary_proxy_clausification,[status(thm)],[f22968]) ).

thf(f23046,plain,
    ( ~ spl8_1
    | ~ spl8_3 ),
    inference(avatar_split_clause,[status(thm)],[f23029,f23043,f23034]) ).

thf(f23029,plain,
    ( ( y
     != ( abs_assn
        @ ^ [Y0: produc3658429121746597890et_nat] :
            ( ( rep_assn @ y @ Y0 )
            & ( rep_assn @ x @ Y0 ) ) ) )
    | ( x != y ) ),
    inference(equality_proxy_clausification,[status(thm)],[f23028]) ).

thf(f23028,plain,
    ( ( $false
      = ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ y @ Y0 )
              & ( rep_assn @ x @ Y0 ) ) )
        = y ) )
    | ( x != y ) ),
    inference(equality_proxy_clausification,[status(thm)],[f23027]) ).

thf(f23027,plain,
    ( ( $false
      = ( x = y ) )
    | ( $false
      = ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ y @ Y0 )
              & ( rep_assn @ x @ Y0 ) ) )
        = y ) ) ),
    inference(not_proxy_clausification,[status(thm)],[f23026]) ).

thf(f23026,plain,
    ( ( ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ y @ Y0 )
              & ( rep_assn @ x @ Y0 ) ) )
       != y )
      = $true )
    | ( $false
      = ( x = y ) ) ),
    inference(not_proxy_clausification,[status(thm)],[f23025]) ).

thf(f23025,plain,
    ( ( ( x != y )
      = $true )
    | ( ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ y @ Y0 )
              & ( rep_assn @ x @ Y0 ) ) )
       != y )
      = $true ) ),
    inference(binary_proxy_clausification,[status(thm)],[f23016]) ).

thf(f23016,plain,
    ( ( ( ( x != y )
        & ( ( abs_assn
            @ ^ [Y0: produc3658429121746597890et_nat] :
                ( ( rep_assn @ x @ Y0 )
                & ( rep_assn @ y @ Y0 ) ) )
          = x ) )
      = $true )
    | ( ( ( abs_assn
          @ ^ [Y0: produc3658429121746597890et_nat] :
              ( ( rep_assn @ y @ Y0 )
              & ( rep_assn @ x @ Y0 ) ) )
       != y )
      = $true ) ),
    inference(binary_proxy_clausification,[status(thm)],[f23006]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : ITP210^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.12/0.13  % Command  : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34  % Computer : n007.cluster.edu
% 0.15/0.34  % Model    : x86_64 x86_64
% 0.15/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34  % Memory   : 8042.1875MB
% 0.15/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34  % CPULimit : 300
% 0.15/0.34  % WCLimit  : 300
% 0.15/0.34  % DateTime : Thu Feb 26 02:30:38 EST 2026
% 0.15/0.34  % CPUTime  : 
% 0.15/0.34  Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46  ---- Original DTF file ---
% 0.29/0.46  thf(spec,logic,$$dhol).
% 0.29/0.46  %------------------------------------------------------------------------------
% 0.29/0.46  % File     : ITP210^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.29/0.46  % Domain   : Interactive Theorem Proving
% 0.29/0.46  % Problem  : Sledgehammer problem Assertions 00353_010205
% 0.29/0.46  % Version  : [Des22] axioms.
% 0.29/0.46  % English  :
% 0.29/0.46  
% 0.29/0.46  % Refs     : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.46  %          : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 0.29/0.46  % Source   : [Des22]
% 0.29/0.46  % Names    : 0024_Assertions_00353_010205 [Des22]
% 0.29/0.46  
% 0.29/0.46  % Status   : Theorem
% 0.29/0.46  % Rating   : ? v9.2.1
% 0.29/0.46  % Syntax   : Number of formulae    : 11329 (5578 unt;1603 typ;   0 def)
% 0.29/0.46  %            Number of atoms       : 25969 (11559 equ;   0 cnn)
% 0.29/0.46  %            Maximal formula atoms :   48 (   2 avg)
% 0.29/0.46  %            Number of connectives : 96556 (2581   ~; 330   |;1588   &;82679   @)
% 0.29/0.46  %                                         (   0 <=>;9378  =>;   0  <=;   0 <~>)
% 0.29/0.46  %            Maximal formula depth :   25 (   5 avg)
% 0.29/0.46  %            Number of types       :  124 ( 123 usr)
% 0.29/0.46  %            Number of type conns  : 8510 (8510   >;   0   *;   0   +;   0  <<)
% 0.29/0.46  %            Number of symbols     : 1483 (1480 usr; 132 con; 0-11 aty)
% 0.29/0.46  %            Number of variables   : 25098 (3455   ^;21378   !; 265   ?;25098   :)
% 0.29/0.46  % SPC      : TH0_THM_EQU_NAR
% 0.29/0.46  
% 0.29/0.46  % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.29/0.46  %            from the van Emde Boas Trees session in the Archive of Formal
% 0.29/0.46  %            proofs - 
% 0.29/0.46  %            www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 0.29/0.46  %            2022-02-17 14:36:05.698
% 0.29/0.46  % Bugfixes : Added ()s around negated sides of equations.
% 0.29/0.46  %------------------------------------------------------------------------------
% 0.29/0.46  % Could-be-implicit typings (123)
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% 0.29/0.46  thf(ty_n_t__Set__Oset_It__String__Ochar_J,type,
% 0.29/0.46      set_char: $tType ).
% 0.29/0.46  
% 0.29/0.46  thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 0.29/0.46      list_nat: $tType ).
% 0.29/0.46  
% 0.29/0.46  thf(ty_n_t__List__Olist_It__Int__Oint_J,type,
% 0.29/0.46      list_int: $tType ).
% 0.29/0.46  
% 0.29/0.46  thf(ty_n_t__Set__Oset_It__Rat__Orat_J,type,
% 0.29/0.46      set_rat: $tType ).
% 0.29/0.46  
% 0.29/0.46  thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.29/0.46      set_nat: $tType ).
% 0.29/0.46  
% 0.29/0.46  thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
% 0.29/0.46      set_int: $tType ).
% 0.29/0.46  
% 0.29/0.46  thf(ty_n_t__Code____Numeral__Onatural,type,
% 0.29/0.46      code_natural: $tType ).
% 0.29/0.46  
% 0.29/0.46  thf(ty_n_t__Code____Numeral__Ointeger,type,
% 0.29/0.46      code_integer: $tType ).
% 0.29/0.46  
% 0.29/0.46  thf(ty_n_t__Product____Type__Ounit,type,
% 0.29/0.46      product_unit: $tType ).
% 0.29/0.46  
% 0.29/0.46  thf(ty_n_t__Assertions__Oassn,type,
% 0.29/0.46      assn: $tType ).
% 0.29/0.46  
% 0.29/0.46  thf(ty_n_t__String__Oliteral,type,
% 0.29/0.46      literal: $tType ).
% 0.29/0.46  
% 0.29/0.46  thf(ty_n_t__Set__Oset_I_Eo_J,type,
% 0.29/0.46      set_o: $tType ).
% 0.29/0.46  
% 0.29/0.46  thf(ty_n_t__String__Ochar,type,
% 0.29/0.46      char: $tType ).
% 0.29/0.46  
% 0.29/0.46  thf(ty_n_t__Rat__Orat,type,
% 0.29/0.46      rat: $tType ).
% 0.29/0.46  
% 0.29/0.46  thf(ty_n_t__Num__Onum,type,
% 0.29/0.46      num: $tType ).
% 0.29/0.46  
% 0.29/0.46  thf(ty_n_t__Nat__Onat,type,
% 0.29/0.46      nat: $tType ).
% 0.29/0.46  
% 0.29/0.46  thf(ty_n_t__Int__Oint,type,
% 0.29/0.46      int: $tType ).
% 0.29/0.46  
% 0.29/0.46  % Explicit typings (1480)
% 0.29/0.46  thf(sy_c_Archimedean__Field_Oceiling_001t__Rat__Orat,type,
% 0.29/0.46      archim2889992004027027881ng_rat: rat > int ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Rat__Orat,type,
% 0.29/0.46      archim3151403230148437115or_rat: rat > int ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Archimedean__Field_Ofrac_001t__Rat__Orat,type,
% 0.29/0.46      archimedean_frac_rat: rat > rat ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Archimedean__Field_Oround_001t__Rat__Orat,type,
% 0.29/0.46      archim7778729529865785530nd_rat: rat > int ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Assertions_Oassn_OAbs__assn,type,
% 0.29/0.46      abs_assn: ( produc3658429121746597890et_nat > $o ) > assn ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Assertions_Oassn_ORep__assn,type,
% 0.29/0.46      rep_assn: assn > produc3658429121746597890et_nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Assertions_Oin__range,type,
% 0.29/0.46      in_range: produc3658429121746597890et_nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Assertions_Oone__assn__raw,type,
% 0.29/0.46      one_assn_raw: produc3658429121746597890et_nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Assertions_Oproper,type,
% 0.29/0.46      proper: ( produc3658429121746597890et_nat > $o ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Assertions_OrelH,type,
% 0.29/0.46      relH: set_nat > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Assertions_Otimes__assn__raw,type,
% 0.29/0.46      times_assn_raw: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Assertions_Otimes__assn__raw__rel,type,
% 0.29/0.46      times_assn_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Assertions_Owand__assn,type,
% 0.29/0.46      wand_assn: assn > assn > assn ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Assertions_Owand__raw,type,
% 0.29/0.46      wand_raw: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Assertions_Owand__raw__rel,type,
% 0.29/0.46      wand_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Cardinal__Arithmetic_Ocone,type,
% 0.29/0.46      bNF_Cardinal_cone: set_Pr5094982260447487303t_unit ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Cardinal__Arithmetic_Octwo,type,
% 0.29/0.46      bNF_Cardinal_ctwo: set_Product_prod_o_o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Cardinal__Arithmetic_Oczero_001_Eo,type,
% 0.29/0.46      bNF_Cardinal_czero_o: set_Product_prod_o_o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001_Eo,type,
% 0.29/0.46      bNF_Ca3172636760949973492d_of_o: set_o > set_Product_prod_o_o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001t__Nat__Onat,type,
% 0.29/0.46      bNF_Ca3793111618940312692of_nat: set_nat > set_Pr1261947904930325089at_nat ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001t__Product____Type__Ounit,type,
% 0.29/0.46      bNF_Ca7083678892733797993t_unit: set_Product_unit > set_Pr5094982260447487303t_unit ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__order__on_001_Eo,type,
% 0.29/0.46      bNF_Ca8331644756375544342r_on_o: set_o > set_Product_prod_o_o > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__order__on_001t__Nat__Onat,type,
% 0.29/0.46      bNF_Ca1281551314933786834on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Cardinal__Order__Relation_OnatLeq,type,
% 0.29/0.46      bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Cardinal__Order__Relation_OnatLess,type,
% 0.29/0.46      bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_Eo_J_J,type,
% 0.29/0.46      bNF_id2059982186938784458at_o_o: ( ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ) > ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_Eo_J,type,
% 0.29/0.46      bNF_id4470576313039291732at_o_o: ( ( produc3658429121746597890et_nat > $o ) > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_I_Eo_M_062_I_Eo_M_Eo_J_J,type,
% 0.29/0.46      bNF_id_bnf_o_o_o: ( $o > $o > $o ) > $o > $o > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_I_Eo_M_062_It__Int__Oint_M_Eo_J_J,type,
% 0.29/0.46      bNF_id_bnf_o_int_o: ( $o > int > $o ) > $o > int > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_I_Eo_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 0.29/0.46      bNF_id_bnf_o_nat_o: ( $o > nat > $o ) > $o > nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_I_Eo_M_Eo_J,type,
% 0.29/0.46      bNF_id_bnf_o_o: ( $o > $o ) > $o > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Int__Oint_M_062_I_Eo_M_Eo_J_J,type,
% 0.29/0.46      bNF_id_bnf_int_o_o: ( int > $o > $o ) > int > $o > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
% 0.29/0.46      bNF_id_bnf_int_int_o: ( int > int > $o ) > int > int > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 0.29/0.46      bNF_id_bnf_int_nat_o: ( int > nat > $o ) > int > nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Int__Oint_M_Eo_J,type,
% 0.29/0.46      bNF_id_bnf_int_o: ( int > $o ) > int > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Nat__Onat_M_062_I_Eo_M_Eo_J_J,type,
% 0.29/0.46      bNF_id_bnf_nat_o_o: ( nat > $o > $o ) > nat > $o > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Nat__Onat_M_062_It__Int__Oint_M_Eo_J_J,type,
% 0.29/0.46      bNF_id_bnf_nat_int_o: ( nat > int > $o ) > nat > int > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 0.29/0.46      bNF_id_bnf_nat_nat_o: ( nat > nat > $o ) > nat > nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Nat__Onat_M_Eo_J,type,
% 0.29/0.46      bNF_id_bnf_nat_o: ( nat > $o ) > nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
% 0.29/0.46      bNF_id146787821168362314_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 0.29/0.46      bNF_id5045731369644952736_nat_o: ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_062_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J_J,type,
% 0.29/0.46      bNF_id5557877041440844106_nat_o: ( produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o ) > produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
% 0.29/0.46      bNF_id1044457264471098170_nat_o: ( produc3843707927480180839at_nat > $o ) > produc3843707927480180839at_nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Set__Oset_It__Nat__Onat_J_M_062_I_Eo_M_Eo_J_J,type,
% 0.29/0.46      bNF_id1382368747416007662at_o_o: ( set_nat > $o > $o ) > set_nat > $o > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Set__Oset_It__Nat__Onat_J_M_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J_J,type,
% 0.29/0.46      bNF_id293821497076346774_nat_o: ( set_nat > set_nat > $o ) > set_nat > set_nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
% 0.29/0.46      bNF_id_bnf_set_nat_o: ( set_nat > $o ) > set_nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_062_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_J,type,
% 0.29/0.46      bNF_id745042670895148362_int_o: ( set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o ) > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
% 0.29/0.46      bNF_id9176111459293603464_int_o: ( set_Pr958786334691620121nt_int > $o ) > set_Pr958786334691620121nt_int > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001_Eo,type,
% 0.29/0.46      bNF_id_bnf_o: $o > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001t__Int__Oint,type,
% 0.29/0.46      bNF_id_bnf_int: int > int ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001t__List__Olist_It__Nat__Onat_J,type,
% 0.29/0.46      bNF_id_bnf_list_nat: list_nat > list_nat ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001t__Nat__Onat,type,
% 0.29/0.46      bNF_id_bnf_nat: nat > nat ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Composition_Oid__bnf_001t__Rat__Orat,type,
% 0.29/0.46      bNF_id_bnf_rat: rat > rat ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Oeq__onp_001t__List__Olist_It__String__Ochar_J,type,
% 0.29/0.46      bNF_eq_onp_list_char: ( list_char > $o ) > list_char > list_char > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J_J_J,type,
% 0.29/0.46      bNF_re5598663031114558885t_char: ( $o > $o > $o ) > ( ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > $o ) > ( $o > $o > $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > $o > $o > list_char > list_char ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J_J_J_J_J_J,type,
% 0.29/0.46      bNF_re8691941649098027561iteral: ( $o > $o > $o ) > ( ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > $o > literal > literal ) > $o ) > ( $o > $o > $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > $o > $o > literal > literal ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J_J,type,
% 0.29/0.46      bNF_re7347849368244578525t_char: ( $o > $o > $o ) > ( ( $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > list_char > list_char ) > $o ) > ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J_J_J_J_J,type,
% 0.29/0.46      bNF_re5719858693005739489iteral: ( $o > $o > $o ) > ( ( $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > literal > literal ) > $o ) > ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > $o > literal > literal ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J,type,
% 0.29/0.46      bNF_re7972843584066424825t_char: ( $o > $o > $o ) > ( ( $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > list_char > list_char ) > $o ) > ( $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > list_char > list_char ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J_J_J_J,type,
% 0.29/0.46      bNF_re136309367175754621iteral: ( $o > $o > $o ) > ( ( $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > literal > literal ) > $o ) > ( $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > literal > literal ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J,type,
% 0.29/0.46      bNF_re796896441190010845t_char: ( $o > $o > $o ) > ( ( $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > list_char > list_char ) > $o ) > ( $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > list_char > list_char ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J_J_J,type,
% 0.29/0.46      bNF_re2365650225897248225iteral: ( $o > $o > $o ) > ( ( $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > literal > literal ) > $o ) > ( $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > literal > literal ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J,type,
% 0.29/0.46      bNF_re4583855572895197261t_char: ( $o > $o > $o ) > ( ( $o > $o > list_char > list_char ) > ( $o > $o > list_char > list_char ) > $o ) > ( $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > list_char > list_char ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J_J,type,
% 0.29/0.46      bNF_re5778109699181701841iteral: ( $o > $o > $o ) > ( ( $o > $o > list_char > list_char ) > ( $o > $o > literal > literal ) > $o ) > ( $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > literal > literal ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_001_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J,type,
% 0.29/0.46      bNF_re441219624009962717t_char: ( $o > $o > $o ) > ( ( $o > list_char > list_char ) > ( $o > list_char > list_char ) > $o ) > ( $o > $o > list_char > list_char ) > ( $o > $o > list_char > list_char ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_001_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J,type,
% 0.29/0.46      bNF_re1595102025518187489iteral: ( $o > $o > $o ) > ( ( $o > list_char > list_char ) > ( $o > literal > literal ) > $o ) > ( $o > $o > list_char > list_char ) > ( $o > $o > literal > literal ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J,type,
% 0.29/0.46      bNF_re6157522605288126113t_char: ( $o > $o > $o ) > ( ( list_char > list_char ) > ( list_char > list_char ) > $o ) > ( $o > list_char > list_char ) > ( $o > list_char > list_char ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_001_062_It__String__Oliteral_Mt__String__Oliteral_J,type,
% 0.29/0.46      bNF_re6148748351543924773iteral: ( $o > $o > $o ) > ( ( list_char > list_char ) > ( literal > literal ) > $o ) > ( $o > list_char > list_char ) > ( $o > literal > literal ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 0.29/0.46      bNF_re3379532845092657523nteger: ( int > code_integer > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( code_integer > code_integer ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.46      bNF_re3804157879324367682nt_int: ( int > code_integer > $o ) > ( int > int > $o ) > ( int > int ) > ( code_integer > int ) > $o ).
% 0.29/0.46  
% 0.29/0.46  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,
% 0.29/0.46      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 ).
% 0.29/0.46  
% 0.29/0.46  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,
% 0.29/0.46      bNF_re3461391660133120880nt_rat: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > rat ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 0.29/0.46      bNF_re982302072995117890nteger: ( int > int > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( int > code_integer ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.46      bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
% 0.29/0.46  
% 0.29/0.46  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,
% 0.29/0.46      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 ).
% 0.29/0.46  
% 0.29/0.46  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,
% 0.29/0.46      bNF_re2214769303045360666nt_rat: ( int > int > $o ) > ( product_prod_int_int > rat > $o ) > ( int > product_prod_int_int ) > ( int > rat ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__Code____Numeral__Ointeger_J_001t__List__Olist_It__Code____Numeral__Ointeger_J_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J,type,
% 0.29/0.46      bNF_re5828396963709814525t_char: ( list_Code_integer > list_Code_integer > $o ) > ( list_char > list_char > $o ) > ( list_Code_integer > list_char ) > ( list_Code_integer > list_char ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J,type,
% 0.29/0.46      bNF_re7775871201573978401char_o: ( list_char > list_char > $o ) > ( ( list_char > $o ) > ( list_char > $o ) > $o ) > ( list_char > list_char > $o ) > ( list_char > list_char > $o ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J,type,
% 0.29/0.46      bNF_re7399511318543894245t_char: ( list_char > list_char > $o ) > ( ( list_char > list_char ) > ( list_char > list_char ) > $o ) > ( list_char > list_char > list_char ) > ( list_char > list_char > list_char ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J_001_Eo_001_Eo,type,
% 0.29/0.46      bNF_re6668474094832959905ar_o_o: ( list_char > list_char > $o ) > ( $o > $o > $o ) > ( list_char > $o ) > ( list_char > $o ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__Code____Numeral__Ointeger_J_001t__List__Olist_It__Code____Numeral__Ointeger_J,type,
% 0.29/0.46      bNF_re901197953848981245nteger: ( list_char > list_char > $o ) > ( list_Code_integer > list_Code_integer > $o ) > ( list_char > list_Code_integer ) > ( list_char > list_Code_integer ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J,type,
% 0.29/0.46      bNF_re1407854171455731685t_char: ( list_char > list_char > $o ) > ( list_char > list_char > $o ) > ( list_char > list_char ) > ( list_char > list_char ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.46      bNF_re76688982720252355at_nat: ( list_char > list_char > $o ) > ( nat > nat > $o ) > ( list_char > nat ) > ( list_char > nat ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__String__Ochar_J_001t__String__Oliteral_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J_001_062_It__String__Oliteral_M_Eo_J,type,
% 0.29/0.46      bNF_re7831395832754058691eral_o: ( list_char > literal > $o ) > ( ( list_char > $o ) > ( literal > $o ) > $o ) > ( list_char > list_char > $o ) > ( literal > literal > $o ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__String__Ochar_J_001t__String__Oliteral_001_Eo_001_Eo,type,
% 0.29/0.46      bNF_re8730477052009823892al_o_o: ( list_char > literal > $o ) > ( $o > $o > $o ) > ( list_char > $o ) > ( literal > $o ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__String__Ochar_J_001t__String__Oliteral_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J,type,
% 0.29/0.46      bNF_re4991257583289732696t_char: ( list_char > literal > $o ) > ( list_char > list_char > $o ) > ( list_char > list_char ) > ( literal > list_char ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__String__Ochar_J_001t__String__Oliteral_001t__List__Olist_It__String__Ochar_J_001t__String__Oliteral,type,
% 0.29/0.46      bNF_re5453467372598631581iteral: ( list_char > literal > $o ) > ( list_char > literal > $o ) > ( list_char > list_char ) > ( literal > literal ) > $o ).
% 0.29/0.46  
% 0.29/0.46  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,
% 0.29/0.46      bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
% 0.29/0.46  
% 0.29/0.46  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,
% 0.29/0.46      bNF_re7876454716742015248nteger: ( num > num > $o ) > ( ( num > int ) > ( num > code_integer ) > $o ) > ( num > num > int ) > ( num > num > code_integer ) > $o ).
% 0.29/0.46  
% 0.29/0.46  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,
% 0.29/0.46      bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 0.29/0.46      bNF_re6501075790457514782nteger: ( num > num > $o ) > ( int > code_integer > $o ) > ( num > int ) > ( num > code_integer ) > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Int__Oint,type,
% 0.29/0.46      bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).
% 0.29/0.46  
% 0.29/0.46  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,
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% 0.29/0.46      comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 0.29/0.46      comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 0.29/0.46      comp_C3531382070062128313er_num: ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
% 0.29/0.46      comp_int_nat_int: ( int > nat ) > ( int > int ) > int > nat ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Ocomp_001t__String__Ochar_001t__String__Ochar_001t__Code____Numeral__Ointeger,type,
% 0.29/0.46      comp_c4562247934908617188nteger: ( char > char ) > ( code_integer > char ) > code_integer > char ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Oid_001_Eo,type,
% 0.29/0.46      id_o: $o > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Oid_001t__Int__Oint,type,
% 0.29/0.46      id_int: int > int ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Oid_001t__Nat__Onat,type,
% 0.29/0.46      id_nat: nat > nat ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Oid_001t__Num__Onum,type,
% 0.29/0.46      id_num: num > num ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.46      inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Omap__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J_J_J_J_J_J,type,
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% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Omap__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J_J_J_J_J,type,
% 0.29/0.46      map_fu7309004089335677210iteral: ( $o > $o ) > ( ( $o > $o > $o > $o > $o > list_char > list_char ) > $o > $o > $o > $o > $o > literal > literal ) > ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > $o > $o > $o > $o > $o > $o > literal > literal ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Omap__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J_J_J_J,type,
% 0.29/0.46      map_fu1929762555066093878iteral: ( $o > $o ) > ( ( $o > $o > $o > $o > list_char > list_char ) > $o > $o > $o > $o > literal > literal ) > ( $o > $o > $o > $o > $o > list_char > list_char ) > $o > $o > $o > $o > $o > literal > literal ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Omap__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J_J_J,type,
% 0.29/0.46      map_fu5333924603067766298iteral: ( $o > $o ) > ( ( $o > $o > $o > list_char > list_char ) > $o > $o > $o > literal > literal ) > ( $o > $o > $o > $o > list_char > list_char ) > $o > $o > $o > $o > literal > literal ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Omap__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J_J,type,
% 0.29/0.46      map_fu1888220742600445322iteral: ( $o > $o ) > ( ( $o > $o > list_char > list_char ) > $o > $o > literal > literal ) > ( $o > $o > $o > list_char > list_char ) > $o > $o > $o > literal > literal ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Omap__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_001_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J,type,
% 0.29/0.46      map_fu5700776415251466522iteral: ( $o > $o ) > ( ( $o > list_char > list_char ) > $o > literal > literal ) > ( $o > $o > list_char > list_char ) > $o > $o > literal > literal ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Omap__fun_001_Eo_001_Eo_001_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_001_062_It__String__Oliteral_Mt__String__Oliteral_J,type,
% 0.29/0.46      map_fu4627020735845646302iteral: ( $o > $o ) > ( ( list_char > list_char ) > literal > literal ) > ( $o > list_char > list_char ) > $o > literal > literal ).
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% 0.29/0.46  thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
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% 0.29/0.46  
% 0.29/0.46  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,
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% 0.29/0.46  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,
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% 0.29/0.46  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 0.29/0.46      map_fu434086159418415080_int_o: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > int > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 0.29/0.46      map_fu4960017516451851995nt_int: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > int > int > int ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 0.29/0.46      map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.29/0.46      map_fu2345160673673942751at_nat: ( int > product_prod_nat_nat ) > ( nat > nat ) > ( product_prod_nat_nat > nat ) > int > nat ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 0.29/0.46      map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
% 0.29/0.46  
% 0.29/0.46  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,
% 0.29/0.46      map_fu6891787308814931657nteger: ( num > num ) > ( ( num > int ) > num > code_integer ) > ( num > num > int ) > num > num > code_integer ).
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% 0.29/0.46  thf(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
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% 0.29/0.46  
% 0.29/0.46  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,
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% 0.29/0.46  
% 0.29/0.46  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,
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% 0.29/0.46  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,
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% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Omap__fun_001t__String__Oliteral_001t__List__Olist_It__String__Ochar_J_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J_001_062_It__String__Oliteral_M_Eo_J,type,
% 0.29/0.46      map_fu2661873803724901240eral_o: ( literal > list_char ) > ( ( list_char > $o ) > literal > $o ) > ( list_char > list_char > $o ) > literal > literal > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Omap__fun_001t__String__Oliteral_001t__List__Olist_It__String__Ochar_J_001_Eo_001_Eo,type,
% 0.29/0.46      map_fu6698795530259886495ar_o_o: ( literal > list_char ) > ( $o > $o ) > ( list_char > $o ) > literal > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun_Omap__fun_001t__String__Oliteral_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J_001t__String__Oliteral,type,
% 0.29/0.46      map_fu7398138089906338514iteral: ( literal > list_char ) > ( list_char > literal ) > ( list_char > list_char ) > literal > literal ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun__Def_Omax__strict,type,
% 0.29/0.46      fun_max_strict: set_Pr4329608150637261639at_nat ).
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% 0.29/0.46  thf(sy_c_Fun__Def_Omax__weak,type,
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% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun__Def_Omin__strict,type,
% 0.29/0.46      fun_min_strict: set_Pr4329608150637261639at_nat ).
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% 0.29/0.46  thf(sy_c_Fun__Def_Omin__weak,type,
% 0.29/0.46      fun_min_weak: set_Pr4329608150637261639at_nat ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun__Def_Opair__leq,type,
% 0.29/0.46      fun_pair_leq: set_Pr8693737435421807431at_nat ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Fun__Def_Opair__less,type,
% 0.29/0.46      fun_pair_less: set_Pr8693737435421807431at_nat ).
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% 0.29/0.46  thf(sy_c_Fun__Def_Oreduction__pair_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 0.29/0.46  thf(sy_c_Fun__Def_Oreduction__pair_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.29/0.46      fun_re2478310338295953701at_nat: produc1319942482725812455at_nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_GCD_OGcd__class_OGcd_001t__Int__Oint,type,
% 0.29/0.46      gcd_Gcd_int: set_int > int ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_GCD_OGcd__class_OGcd_001t__Nat__Onat,type,
% 0.29/0.46      gcd_Gcd_nat: set_nat > nat ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_GCD_OGcd__class_OLcm_001t__Int__Oint,type,
% 0.29/0.46      gcd_Lcm_int: set_int > int ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_GCD_OGcd__class_OLcm_001t__Nat__Onat,type,
% 0.29/0.46      gcd_Lcm_nat: set_nat > nat ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_GCD_Obezw,type,
% 0.29/0.46      bezw: nat > nat > product_prod_int_int ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_GCD_Obezw__rel,type,
% 0.29/0.46      bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Int__Oint,type,
% 0.29/0.46      gcd_gcd_int: int > int > int ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
% 0.29/0.46      gcd_gcd_nat: nat > nat > nat ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_GCD_Ogcd__class_Olcm_001t__Int__Oint,type,
% 0.29/0.46      gcd_lcm_int: int > int > int ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_GCD_Ogcd__class_Olcm_001t__Nat__Onat,type,
% 0.29/0.46      gcd_lcm_nat: nat > nat > nat ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_GCD_Ogcd__nat__rel,type,
% 0.29/0.46      gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Groups_Oabs__class_Oabs_001t__Code____Numeral__Ointeger,type,
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% 0.29/0.46  thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
% 0.29/0.46      abs_abs_int: int > int ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Groups_Oabs__class_Oabs_001t__Rat__Orat,type,
% 0.29/0.46      abs_abs_rat: rat > rat ).
% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Groups_Ocomm__monoid_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J,type,
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% 0.29/0.46  thf(sy_c_Groups_Ocomm__monoid_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
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% 0.29/0.46  
% 0.29/0.46  thf(sy_c_Groups_Ocomm__monoid_001t__Assertions__Oassn,type,
% 0.29/0.46      comm_monoid_assn: ( assn > assn > assn ) > assn > $o ).
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% 0.29/0.46  thf(sy_c_Groups_Ocomm__monoid_001t__Code____Numeral__Ointeger,type,
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% 0.29/0.46  thf(sy_c_Groups_Ocomm__monoid_001t__Int__Oint,type,
% 0.29/0.46      comm_monoid_int: ( int > int > int ) > int > $o ).
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% 0.29/0.47  
% 0.29/0.47  thf(sy_c_If_001t__Rat__Orat,type,
% 0.29/0.47      if_rat: $o > rat > rat > rat ).
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% 0.29/0.47  thf(sy_c_If_001t__Set__Oset_It__Int__Oint_J,type,
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% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Infinite__Set_Owellorder__class_Oenumerate_001t__Nat__Onat,type,
% 0.29/0.47      infini8530281810654367211te_nat: set_nat > nat > nat ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Int_OAbs__Integ,type,
% 0.29/0.47      abs_Integ: product_prod_nat_nat > int ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Int_ORep__Integ,type,
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% 0.29/0.47  thf(sy_c_Int_Ocr__int,type,
% 0.29/0.47      cr_int: product_prod_nat_nat > int > $o ).
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% 0.29/0.47  thf(sy_c_Int_Odup,type,
% 0.29/0.47      dup: int > int ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Int_Oint_OAbs__int,type,
% 0.29/0.47      abs_int: set_Pr1261947904930325089at_nat > int ).
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% 0.29/0.47  thf(sy_c_Int_Oint_ORep__int,type,
% 0.29/0.47      rep_int: int > set_Pr1261947904930325089at_nat ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Int_Oint__ge__less__than,type,
% 0.29/0.47      int_ge_less_than: int > set_Pr958786334691620121nt_int ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Int_Oint__ge__less__than2,type,
% 0.29/0.47      int_ge_less_than2: int > set_Pr958786334691620121nt_int ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Int_Ointrel,type,
% 0.29/0.47      intrel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Int_Onat,type,
% 0.29/0.47      nat2: int > nat ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Int_Opcr__int,type,
% 0.29/0.47      pcr_int: product_prod_nat_nat > int > $o ).
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% 0.29/0.47  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Code____Numeral__Ointeger,type,
% 0.29/0.47      ring_18347121197199848620nteger: int > code_integer ).
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% 0.29/0.47  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 0.29/0.47      ring_1_of_int_int: int > int ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 0.29/0.47      ring_1_of_int_rat: int > rat ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Int_Osub,type,
% 0.29/0.47      sub: num > num > int ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
% 0.29/0.47      inf_in8201999774870019094_int_o: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ).
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% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
% 0.29/0.47      inf_in3563340378267265229eger_o: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_062_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J,type,
% 0.29/0.47      inf_in2641120393918057659_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
% 0.29/0.47      inf_in3295504058751909687_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_Eo_J,type,
% 0.29/0.47      inf_in9018898317438245890at_o_o: ( ( produc3658429121746597890et_nat > $o ) > $o ) > ( ( produc3658429121746597890et_nat > $o ) > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
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% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Int__Oint_M_Eo_J,type,
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% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J,type,
% 0.29/0.47      inf_inf_list_char_o: ( list_char > $o ) > ( list_char > $o ) > list_char > $o ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 0.29/0.47      inf_inf_nat_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > nat > $o ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Nat__Onat_M_Eo_J,type,
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% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
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% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001_Eo,type,
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% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Assertions__Oassn,type,
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% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 0.29/0.47      inf_inf_filter_nat: filter_nat > filter_nat > filter_nat ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Int__Oint,type,
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% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
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% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Product____Type__Ounit,type,
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% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Rat__Orat,type,
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% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
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% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_Eo_J,type,
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% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
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% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Int__Oint_J,type,
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% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 0.29/0.47      inf_inf_set_list_nat: set_list_nat > set_list_nat > set_list_nat ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J,type,
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% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Nat__Onat_J,type,
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% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
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% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
% 0.29/0.47      inf_in3408396081536963678nteger: set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger ).
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% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
% 0.29/0.47      inf_in3088352823822785602et_nat: set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
% 0.29/0.47      inf_in1768905781608824518et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 0.29/0.47      inf_in2576786181675586251nt_int: set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 0.29/0.47      inf_in2269163501485487111nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 0.29/0.47      inf_in1697001100524423349at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ).
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% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 0.29/0.47      inf_in7913087082777306421at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Rat__Orat_J,type,
% 0.29/0.47      inf_inf_set_rat: set_rat > set_rat > set_rat ).
% 0.29/0.47  
% 0.29/0.47  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 0.29/0.48      accp_P6019419558468335806at_nat: ( produc4471711990508489141at_nat > produc4471711990508489141at_nat > $o ) > produc4471711990508489141at_nat > $o ).
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% 0.29/0.48  thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
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% 0.29/0.48  thf(sy_c_Wellfounded_Oless__than,type,
% 0.29/0.48      less_than: set_Pr1261947904930325089at_nat ).
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% 0.29/0.48  thf(sy_c_Wellfounded_Omax__ext_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 0.29/0.48  
% 0.29/0.48  thf(sy_c_Wellfounded_Omin__ext_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 0.29/0.48  
% 0.29/0.48  thf(sy_c_Wellfounded_Opred__nat,type,
% 0.29/0.48      pred_nat: set_Pr1261947904930325089at_nat ).
% 0.29/0.48  
% 0.29/0.48  thf(sy_c_Wellfounded_Owf_001t__Nat__Onat,type,
% 0.29/0.48      wf_nat: set_Pr1261947904930325089at_nat > $o ).
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% 0.29/0.48  thf(sy_c_member_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
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% 0.29/0.48  thf(sy_c_member_001_Eo,type,
% 0.29/0.48      member_o: $o > set_o > $o ).
% 0.29/0.48  
% 0.29/0.48  thf(sy_c_member_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 0.29/0.48      member_filter_nat: filter_nat > set_filter_nat > $o ).
% 0.29/0.48  
% 0.29/0.48  thf(sy_c_member_001t__Int__Oint,type,
% 0.29/0.48      member_int: int > set_int > $o ).
% 0.29/0.48  
% 0.29/0.48  thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 0.29/0.48      member_list_nat: list_nat > set_list_nat > $o ).
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% 0.29/0.48  thf(sy_c_member_001t__List__Olist_It__String__Ochar_J,type,
% 0.29/0.48      member_list_char: list_char > set_list_char > $o ).
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% 0.29/0.48  thf(sy_c_member_001t__Nat__Onat,type,
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% 0.29/0.48  thf(sy_v_y,type,
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% 0.29/0.48  
% 0.29/0.48  % Relevant facts (9688)
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% 0.29/0.48        ( ( ( rep_assn @ X )
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% 0.29/0.48  
% 0.29/0.48  % Rep_assn_inject
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% 0.29/0.48  % Rep_assn_inverse
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% 0.29/0.48        ( ! [H: produc3658429121746597890et_nat] :
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% 0.29/0.48            ( ( P @ H )
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% 0.29/0.48  
% 0.29/0.48  % Abs_assn_eqI(1)
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% 0.29/0.48                ( ( rep_assn @ P2 @ H2 )
% 0.29/0.48                | ( rep_assn @ Q @ H2 ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_assn_def
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% 0.29/0.48  
% 0.29/0.48  % bot_assn_def
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% 0.29/0.48            ( ( X
% 0.29/0.48              = ( abs_assn @ Y2 ) )
% 0.29/0.48           => ~ ( member6576561426505652726_nat_o @ Y2 @ ( collec939566748876313656_nat_o @ proper ) ) ) ).
% 0.29/0.48  
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% 0.29/0.48      ! [P: assn > $o,X: assn] :
% 0.29/0.48        ( ! [Y2: produc3658429121746597890et_nat > $o] :
% 0.29/0.48            ( ( member6576561426505652726_nat_o @ Y2 @ ( collec939566748876313656_nat_o @ proper ) )
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% 0.29/0.48       => ( P @ X ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Abs_assn_induct
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% 0.29/0.48       => ( ( member6576561426505652726_nat_o @ Y @ ( collec939566748876313656_nat_o @ proper ) )
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% 0.29/0.48            = ( X = Y ) ) ) ) ).
% 0.29/0.48  
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% 0.29/0.48  
% 0.29/0.48  % Rep_assn
% 0.29/0.48  thf(fact_13_Rep__assn__cases,axiom,
% 0.29/0.48      ! [Y: produc3658429121746597890et_nat > $o] :
% 0.29/0.48        ( ( member6576561426505652726_nat_o @ Y @ ( collec939566748876313656_nat_o @ proper ) )
% 0.29/0.48       => ~ ! [X2: assn] :
% 0.29/0.48              ( Y
% 0.29/0.48             != ( rep_assn @ X2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Rep_assn_cases
% 0.29/0.48  thf(fact_14_Rep__assn__induct,axiom,
% 0.29/0.48      ! [Y: produc3658429121746597890et_nat > $o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.29/0.48        ( ( member6576561426505652726_nat_o @ Y @ ( collec939566748876313656_nat_o @ proper ) )
% 0.29/0.48       => ( ! [X2: assn] : ( P @ ( rep_assn @ X2 ) )
% 0.29/0.48         => ( P @ Y ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Rep_assn_induct
% 0.29/0.48  thf(fact_15_times__assn__def,axiom,
% 0.29/0.48      ( times_times_assn
% 0.29/0.48      = ( ^ [P2: assn,Q: assn] : ( abs_assn @ ( times_assn_raw @ ( rep_assn @ P2 ) @ ( rep_assn @ Q ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % times_assn_def
% 0.29/0.48  thf(fact_16_bool__assn__proper_I2_J,axiom,
% 0.29/0.48      ( proper
% 0.29/0.48      @ ^ [Uu: produc3658429121746597890et_nat] : $false ) ).
% 0.29/0.48  
% 0.29/0.48  % bool_assn_proper(2)
% 0.29/0.48  thf(fact_17_bool__assn__proper_I3_J,axiom,
% 0.29/0.48      ! [P: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o] :
% 0.29/0.48        ( ( proper @ P )
% 0.29/0.48       => ( ( proper @ Q2 )
% 0.29/0.48         => ( proper
% 0.29/0.48            @ ^ [H2: produc3658429121746597890et_nat] :
% 0.29/0.48                ( ( P @ H2 )
% 0.29/0.48                | ( Q2 @ H2 ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % bool_assn_proper(3)
% 0.29/0.48  thf(fact_18_bool__assn__proper_I4_J,axiom,
% 0.29/0.48      ! [P: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o] :
% 0.29/0.48        ( ( proper @ P )
% 0.29/0.48       => ( ( proper @ Q2 )
% 0.29/0.48         => ( proper
% 0.29/0.48            @ ^ [H2: produc3658429121746597890et_nat] :
% 0.29/0.48                ( ( P @ H2 )
% 0.29/0.48                & ( Q2 @ H2 ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % bool_assn_proper(4)
% 0.29/0.48  thf(fact_19_wand__proper,axiom,
% 0.29/0.48      ! [P: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o] : ( proper @ ( wand_raw @ P @ Q2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % wand_proper
% 0.29/0.48  thf(fact_20_times__assn__proper,axiom,
% 0.29/0.48      ! [P: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o] :
% 0.29/0.48        ( ( proper @ P )
% 0.29/0.48       => ( ( proper @ Q2 )
% 0.29/0.48         => ( proper @ ( times_assn_raw @ P @ Q2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % times_assn_proper
% 0.29/0.48  thf(fact_21_assn__times__comm,axiom,
% 0.29/0.48      ( times_times_assn
% 0.29/0.48      = ( ^ [P2: assn,Q: assn] : ( times_times_assn @ Q @ P2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % assn_times_comm
% 0.29/0.48  thf(fact_22_assn__times__assoc,axiom,
% 0.29/0.48      ! [P: assn,Q2: assn,R: assn] :
% 0.29/0.48        ( ( times_times_assn @ ( times_times_assn @ P @ Q2 ) @ R )
% 0.29/0.48        = ( times_times_assn @ P @ ( times_times_assn @ Q2 @ R ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % assn_times_assoc
% 0.29/0.48  thf(fact_23_mod__starE,axiom,
% 0.29/0.48      ! [A: assn,B: assn,H3: produc3658429121746597890et_nat] :
% 0.29/0.48        ( ( rep_assn @ ( times_times_assn @ A @ B ) @ H3 )
% 0.29/0.48       => ~ ( ? [X_1: produc3658429121746597890et_nat] : ( rep_assn @ A @ X_1 )
% 0.29/0.48           => ! [H_2: produc3658429121746597890et_nat] :
% 0.29/0.48                ~ ( rep_assn @ B @ H_2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % mod_starE
% 0.29/0.48  thf(fact_24_mod__starD,axiom,
% 0.29/0.48      ! [A2: assn,B2: assn,H3: produc3658429121746597890et_nat] :
% 0.29/0.48        ( ( rep_assn @ ( times_times_assn @ A2 @ B2 ) @ H3 )
% 0.29/0.48       => ? [H1: produc3658429121746597890et_nat,H22: produc3658429121746597890et_nat] :
% 0.29/0.48            ( ( rep_assn @ A2 @ H1 )
% 0.29/0.48            & ( rep_assn @ B2 @ H22 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % mod_starD
% 0.29/0.48  thf(fact_25_inf__sup__absorb,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ X @ Y ) )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_absorb
% 0.29/0.48  thf(fact_26_inf__sup__absorb,axiom,
% 0.29/0.48      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ X @ ( sup_su8463660629351352368_int_o @ X @ Y ) )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_absorb
% 0.29/0.48  thf(fact_27_inf__sup__absorb,axiom,
% 0.29/0.48      ! [X: list_char > $o,Y: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ X @ ( sup_sup_list_char_o @ X @ Y ) )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_absorb
% 0.29/0.48  thf(fact_28_inf__sup__absorb,axiom,
% 0.29/0.48      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( inf_in1697001100524423349at_nat @ X @ ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_absorb
% 0.29/0.48  thf(fact_29_inf__sup__absorb,axiom,
% 0.29/0.48      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_absorb
% 0.29/0.48  thf(fact_30_inf__sup__absorb,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_absorb
% 0.29/0.48  thf(fact_31_inf__sup__absorb,axiom,
% 0.29/0.48      ! [X: nat,Y: nat] :
% 0.29/0.48        ( ( inf_inf_nat @ X @ ( sup_sup_nat @ X @ Y ) )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_absorb
% 0.29/0.48  thf(fact_32_inf__sup__absorb,axiom,
% 0.29/0.48      ! [X: int,Y: int] :
% 0.29/0.48        ( ( inf_inf_int @ X @ ( sup_sup_int @ X @ Y ) )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_absorb
% 0.29/0.48  thf(fact_33_sup__inf__absorb,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_absorb
% 0.29/0.48  thf(fact_34_sup__inf__absorb,axiom,
% 0.29/0.48      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 0.29/0.48        ( ( sup_su8463660629351352368_int_o @ X @ ( inf_in3604695632404883862_int_o @ X @ Y ) )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_absorb
% 0.29/0.48  thf(fact_35_sup__inf__absorb,axiom,
% 0.29/0.48      ! [X: list_char > $o,Y: list_char > $o] :
% 0.29/0.48        ( ( sup_sup_list_char_o @ X @ ( inf_inf_list_char_o @ X @ Y ) )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_absorb
% 0.29/0.48  thf(fact_36_sup__inf__absorb,axiom,
% 0.29/0.48      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ X @ ( inf_in1697001100524423349at_nat @ X @ Y ) )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_absorb
% 0.29/0.48  thf(fact_37_sup__inf__absorb,axiom,
% 0.29/0.48      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ X @ Y ) )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_absorb
% 0.29/0.48  thf(fact_38_sup__inf__absorb,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ X @ Y ) )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_absorb
% 0.29/0.48  thf(fact_39_sup__inf__absorb,axiom,
% 0.29/0.48      ! [X: nat,Y: nat] :
% 0.29/0.48        ( ( sup_sup_nat @ X @ ( inf_inf_nat @ X @ Y ) )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_absorb
% 0.29/0.48  thf(fact_40_sup__inf__absorb,axiom,
% 0.29/0.48      ! [X: int,Y: int] :
% 0.29/0.48        ( ( sup_sup_int @ X @ ( inf_inf_int @ X @ Y ) )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_absorb
% 0.29/0.48  thf(fact_41_sup__bot__left,axiom,
% 0.29/0.48      ! [X: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat @ X )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot_left
% 0.29/0.48  thf(fact_42_sup__bot__left,axiom,
% 0.29/0.48      ! [X: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat @ X )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot_left
% 0.29/0.48  thf(fact_43_sup__bot__left,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat @ X )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot_left
% 0.29/0.48  thf(fact_44_sup__bot__left,axiom,
% 0.29/0.48      ! [X: set_o] :
% 0.29/0.48        ( ( sup_sup_set_o @ bot_bot_set_o @ X )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot_left
% 0.29/0.48  thf(fact_45_sup__bot__left,axiom,
% 0.29/0.48      ! [X: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ bot_bot_set_nat @ X )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot_left
% 0.29/0.48  thf(fact_46_sup__bot__left,axiom,
% 0.29/0.48      ! [X: set_int] :
% 0.29/0.48        ( ( sup_sup_set_int @ bot_bot_set_int @ X )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot_left
% 0.29/0.48  thf(fact_47_sup__bot__right,axiom,
% 0.29/0.48      ! [X: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ X @ bot_bo8422036546324065075at_nat )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot_right
% 0.29/0.48  thf(fact_48_sup__bot__right,axiom,
% 0.29/0.48      ! [X: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ X @ bot_bo228742789529271731at_nat )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot_right
% 0.29/0.48  thf(fact_49_sup__bot__right,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( sup_su6327502436637775413at_nat @ X @ bot_bo2099793752762293965at_nat )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot_right
% 0.29/0.48  thf(fact_50_sup__bot__right,axiom,
% 0.29/0.48      ! [X: set_o] :
% 0.29/0.48        ( ( sup_sup_set_o @ X @ bot_bot_set_o )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot_right
% 0.29/0.48  thf(fact_51_sup__bot__right,axiom,
% 0.29/0.48      ! [X: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ X @ bot_bot_set_nat )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot_right
% 0.29/0.48  thf(fact_52_sup__bot__right,axiom,
% 0.29/0.48      ! [X: set_int] :
% 0.29/0.48        ( ( sup_sup_set_int @ X @ bot_bot_set_int )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot_right
% 0.29/0.48  thf(fact_53_bot__eq__sup__iff,axiom,
% 0.29/0.48      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( bot_bo8422036546324065075at_nat
% 0.29/0.48          = ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 0.29/0.48        = ( ( X = bot_bo8422036546324065075at_nat )
% 0.29/0.48          & ( Y = bot_bo8422036546324065075at_nat ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % bot_eq_sup_iff
% 0.29/0.48  thf(fact_54_bot__eq__sup__iff,axiom,
% 0.29/0.48      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( bot_bo228742789529271731at_nat
% 0.29/0.48          = ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 0.29/0.48        = ( ( X = bot_bo228742789529271731at_nat )
% 0.29/0.48          & ( Y = bot_bo228742789529271731at_nat ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % bot_eq_sup_iff
% 0.29/0.48  thf(fact_55_bot__eq__sup__iff,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( bot_bo2099793752762293965at_nat
% 0.29/0.48          = ( sup_su6327502436637775413at_nat @ X @ Y ) )
% 0.29/0.48        = ( ( X = bot_bo2099793752762293965at_nat )
% 0.29/0.48          & ( Y = bot_bo2099793752762293965at_nat ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % bot_eq_sup_iff
% 0.29/0.48  thf(fact_56_bot__eq__sup__iff,axiom,
% 0.29/0.48      ! [X: set_o,Y: set_o] :
% 0.29/0.48        ( ( bot_bot_set_o
% 0.29/0.48          = ( sup_sup_set_o @ X @ Y ) )
% 0.29/0.48        = ( ( X = bot_bot_set_o )
% 0.29/0.48          & ( Y = bot_bot_set_o ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % bot_eq_sup_iff
% 0.29/0.48  thf(fact_57_bot__eq__sup__iff,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat] :
% 0.29/0.48        ( ( bot_bot_set_nat
% 0.29/0.48          = ( sup_sup_set_nat @ X @ Y ) )
% 0.29/0.48        = ( ( X = bot_bot_set_nat )
% 0.29/0.48          & ( Y = bot_bot_set_nat ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % bot_eq_sup_iff
% 0.29/0.48  thf(fact_58_bot__eq__sup__iff,axiom,
% 0.29/0.48      ! [X: set_int,Y: set_int] :
% 0.29/0.48        ( ( bot_bot_set_int
% 0.29/0.48          = ( sup_sup_set_int @ X @ Y ) )
% 0.29/0.48        = ( ( X = bot_bot_set_int )
% 0.29/0.48          & ( Y = bot_bot_set_int ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % bot_eq_sup_iff
% 0.29/0.48  thf(fact_59_sup__eq__bot__iff,axiom,
% 0.29/0.48      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( ( sup_su3035147773818789531at_nat @ X @ Y )
% 0.29/0.48          = bot_bo8422036546324065075at_nat )
% 0.29/0.48        = ( ( X = bot_bo8422036546324065075at_nat )
% 0.29/0.48          & ( Y = bot_bo8422036546324065075at_nat ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_eq_bot_iff
% 0.29/0.48  thf(fact_60_sup__eq__bot__iff,axiom,
% 0.29/0.48      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 0.29/0.48          = bot_bo228742789529271731at_nat )
% 0.29/0.48        = ( ( X = bot_bo228742789529271731at_nat )
% 0.29/0.48          & ( Y = bot_bo228742789529271731at_nat ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_eq_bot_iff
% 0.29/0.48  thf(fact_61_sup__eq__bot__iff,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( ( sup_su6327502436637775413at_nat @ X @ Y )
% 0.29/0.48          = bot_bo2099793752762293965at_nat )
% 0.29/0.48        = ( ( X = bot_bo2099793752762293965at_nat )
% 0.29/0.48          & ( Y = bot_bo2099793752762293965at_nat ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_eq_bot_iff
% 0.29/0.48  thf(fact_62_sup__eq__bot__iff,axiom,
% 0.29/0.48      ! [X: set_o,Y: set_o] :
% 0.29/0.48        ( ( ( sup_sup_set_o @ X @ Y )
% 0.29/0.48          = bot_bot_set_o )
% 0.29/0.48        = ( ( X = bot_bot_set_o )
% 0.29/0.48          & ( Y = bot_bot_set_o ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_eq_bot_iff
% 0.29/0.48  thf(fact_63_sup__eq__bot__iff,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat] :
% 0.29/0.48        ( ( ( sup_sup_set_nat @ X @ Y )
% 0.29/0.48          = bot_bot_set_nat )
% 0.29/0.48        = ( ( X = bot_bot_set_nat )
% 0.29/0.48          & ( Y = bot_bot_set_nat ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_eq_bot_iff
% 0.29/0.48  thf(fact_64_sup__eq__bot__iff,axiom,
% 0.29/0.48      ! [X: set_int,Y: set_int] :
% 0.29/0.48        ( ( ( sup_sup_set_int @ X @ Y )
% 0.29/0.48          = bot_bot_set_int )
% 0.29/0.48        = ( ( X = bot_bot_set_int )
% 0.29/0.48          & ( Y = bot_bot_set_int ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_eq_bot_iff
% 0.29/0.48  thf(fact_65_sup__bot_Oeq__neutr__iff,axiom,
% 0.29/0.48      ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( ( sup_su3035147773818789531at_nat @ A @ B )
% 0.29/0.48          = bot_bo8422036546324065075at_nat )
% 0.29/0.48        = ( ( A = bot_bo8422036546324065075at_nat )
% 0.29/0.48          & ( B = bot_bo8422036546324065075at_nat ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.eq_neutr_iff
% 0.29/0.48  thf(fact_66_sup__bot_Oeq__neutr__iff,axiom,
% 0.29/0.48      ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( ( sup_su5525570899277871387at_nat @ A @ B )
% 0.29/0.48          = bot_bo228742789529271731at_nat )
% 0.29/0.48        = ( ( A = bot_bo228742789529271731at_nat )
% 0.29/0.48          & ( B = bot_bo228742789529271731at_nat ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.eq_neutr_iff
% 0.29/0.48  thf(fact_67_sup__bot_Oeq__neutr__iff,axiom,
% 0.29/0.48      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( ( sup_su6327502436637775413at_nat @ A @ B )
% 0.29/0.48          = bot_bo2099793752762293965at_nat )
% 0.29/0.48        = ( ( A = bot_bo2099793752762293965at_nat )
% 0.29/0.48          & ( B = bot_bo2099793752762293965at_nat ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.eq_neutr_iff
% 0.29/0.48  thf(fact_68_sup__bot_Oeq__neutr__iff,axiom,
% 0.29/0.48      ! [A: set_o,B: set_o] :
% 0.29/0.48        ( ( ( sup_sup_set_o @ A @ B )
% 0.29/0.48          = bot_bot_set_o )
% 0.29/0.48        = ( ( A = bot_bot_set_o )
% 0.29/0.48          & ( B = bot_bot_set_o ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.eq_neutr_iff
% 0.29/0.48  thf(fact_69_sup__bot_Oeq__neutr__iff,axiom,
% 0.29/0.48      ! [A: set_nat,B: set_nat] :
% 0.29/0.48        ( ( ( sup_sup_set_nat @ A @ B )
% 0.29/0.48          = bot_bot_set_nat )
% 0.29/0.48        = ( ( A = bot_bot_set_nat )
% 0.29/0.48          & ( B = bot_bot_set_nat ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.eq_neutr_iff
% 0.29/0.48  thf(fact_70_sup__bot_Oeq__neutr__iff,axiom,
% 0.29/0.48      ! [A: set_int,B: set_int] :
% 0.29/0.48        ( ( ( sup_sup_set_int @ A @ B )
% 0.29/0.48          = bot_bot_set_int )
% 0.29/0.48        = ( ( A = bot_bot_set_int )
% 0.29/0.48          & ( B = bot_bot_set_int ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.eq_neutr_iff
% 0.29/0.48  thf(fact_71_sup__bot_Oleft__neutral,axiom,
% 0.29/0.48      ! [A: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat @ A )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.left_neutral
% 0.29/0.48  thf(fact_72_sup__bot_Oleft__neutral,axiom,
% 0.29/0.48      ! [A: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat @ A )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.left_neutral
% 0.29/0.48  thf(fact_73_sup__bot_Oleft__neutral,axiom,
% 0.29/0.48      ! [A: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat @ A )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.left_neutral
% 0.29/0.48  thf(fact_74_sup__bot_Oleft__neutral,axiom,
% 0.29/0.48      ! [A: set_o] :
% 0.29/0.48        ( ( sup_sup_set_o @ bot_bot_set_o @ A )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.left_neutral
% 0.29/0.48  thf(fact_75_sup__bot_Oleft__neutral,axiom,
% 0.29/0.48      ! [A: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ bot_bot_set_nat @ A )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.left_neutral
% 0.29/0.48  thf(fact_76_sup__bot_Oleft__neutral,axiom,
% 0.29/0.48      ! [A: set_int] :
% 0.29/0.48        ( ( sup_sup_set_int @ bot_bot_set_int @ A )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.left_neutral
% 0.29/0.48  thf(fact_77_sup__bot_Oneutr__eq__iff,axiom,
% 0.29/0.48      ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( bot_bo8422036546324065075at_nat
% 0.29/0.48          = ( sup_su3035147773818789531at_nat @ A @ B ) )
% 0.29/0.48        = ( ( A = bot_bo8422036546324065075at_nat )
% 0.29/0.48          & ( B = bot_bo8422036546324065075at_nat ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.neutr_eq_iff
% 0.29/0.48  thf(fact_78_sup__bot_Oneutr__eq__iff,axiom,
% 0.29/0.48      ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( bot_bo228742789529271731at_nat
% 0.29/0.48          = ( sup_su5525570899277871387at_nat @ A @ B ) )
% 0.29/0.48        = ( ( A = bot_bo228742789529271731at_nat )
% 0.29/0.48          & ( B = bot_bo228742789529271731at_nat ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.neutr_eq_iff
% 0.29/0.48  thf(fact_79_sup__bot_Oneutr__eq__iff,axiom,
% 0.29/0.48      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( bot_bo2099793752762293965at_nat
% 0.29/0.48          = ( sup_su6327502436637775413at_nat @ A @ B ) )
% 0.29/0.48        = ( ( A = bot_bo2099793752762293965at_nat )
% 0.29/0.48          & ( B = bot_bo2099793752762293965at_nat ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.neutr_eq_iff
% 0.29/0.48  thf(fact_80_sup__bot_Oneutr__eq__iff,axiom,
% 0.29/0.48      ! [A: set_o,B: set_o] :
% 0.29/0.48        ( ( bot_bot_set_o
% 0.29/0.48          = ( sup_sup_set_o @ A @ B ) )
% 0.29/0.48        = ( ( A = bot_bot_set_o )
% 0.29/0.48          & ( B = bot_bot_set_o ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.neutr_eq_iff
% 0.29/0.48  thf(fact_81_sup__bot_Oneutr__eq__iff,axiom,
% 0.29/0.48      ! [A: set_nat,B: set_nat] :
% 0.29/0.48        ( ( bot_bot_set_nat
% 0.29/0.48          = ( sup_sup_set_nat @ A @ B ) )
% 0.29/0.48        = ( ( A = bot_bot_set_nat )
% 0.29/0.48          & ( B = bot_bot_set_nat ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.neutr_eq_iff
% 0.29/0.48  thf(fact_82_sup__bot_Oneutr__eq__iff,axiom,
% 0.29/0.48      ! [A: set_int,B: set_int] :
% 0.29/0.48        ( ( bot_bot_set_int
% 0.29/0.48          = ( sup_sup_set_int @ A @ B ) )
% 0.29/0.48        = ( ( A = bot_bot_set_int )
% 0.29/0.48          & ( B = bot_bot_set_int ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.neutr_eq_iff
% 0.29/0.48  thf(fact_83_sup__bot_Oright__neutral,axiom,
% 0.29/0.48      ! [A: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ A @ bot_bo8422036546324065075at_nat )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.right_neutral
% 0.29/0.48  thf(fact_84_sup__bot_Oright__neutral,axiom,
% 0.29/0.48      ! [A: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ A @ bot_bo228742789529271731at_nat )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.right_neutral
% 0.29/0.48  thf(fact_85_sup__bot_Oright__neutral,axiom,
% 0.29/0.48      ! [A: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( sup_su6327502436637775413at_nat @ A @ bot_bo2099793752762293965at_nat )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.right_neutral
% 0.29/0.48  thf(fact_86_sup__bot_Oright__neutral,axiom,
% 0.29/0.48      ! [A: set_o] :
% 0.29/0.48        ( ( sup_sup_set_o @ A @ bot_bot_set_o )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.right_neutral
% 0.29/0.48  thf(fact_87_sup__bot_Oright__neutral,axiom,
% 0.29/0.48      ! [A: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ A @ bot_bot_set_nat )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.right_neutral
% 0.29/0.48  thf(fact_88_sup__bot_Oright__neutral,axiom,
% 0.29/0.48      ! [A: set_int] :
% 0.29/0.48        ( ( sup_sup_set_int @ A @ bot_bot_set_int )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_bot.right_neutral
% 0.29/0.48  thf(fact_89_inf__bot__left,axiom,
% 0.29/0.48      ! [X: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ bot_bo8147686125503663512_int_o @ X )
% 0.29/0.48        = bot_bo8147686125503663512_int_o ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_bot_left
% 0.29/0.48  thf(fact_90_inf__bot__left,axiom,
% 0.29/0.48      ! [X: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ bot_bot_list_char_o @ X )
% 0.29/0.48        = bot_bot_list_char_o ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_bot_left
% 0.29/0.48  thf(fact_91_inf__bot__left,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ bot_bo2099793752762293965at_nat @ X )
% 0.29/0.48        = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_bot_left
% 0.29/0.48  thf(fact_92_inf__bot__left,axiom,
% 0.29/0.48      ! [X: set_o] :
% 0.29/0.48        ( ( inf_inf_set_o @ bot_bot_set_o @ X )
% 0.29/0.48        = bot_bot_set_o ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_bot_left
% 0.29/0.48  thf(fact_93_inf__bot__left,axiom,
% 0.29/0.48      ! [X: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ bot_bot_set_nat @ X )
% 0.29/0.48        = bot_bot_set_nat ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_bot_left
% 0.29/0.48  thf(fact_94_inf__bot__left,axiom,
% 0.29/0.48      ! [X: set_int] :
% 0.29/0.48        ( ( inf_inf_set_int @ bot_bot_set_int @ X )
% 0.29/0.48        = bot_bot_set_int ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_bot_left
% 0.29/0.48  thf(fact_95_inf__bot__right,axiom,
% 0.29/0.48      ! [X: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ X @ bot_bo8147686125503663512_int_o )
% 0.29/0.48        = bot_bo8147686125503663512_int_o ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_bot_right
% 0.29/0.48  thf(fact_96_inf__bot__right,axiom,
% 0.29/0.48      ! [X: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ X @ bot_bot_list_char_o )
% 0.29/0.48        = bot_bot_list_char_o ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_bot_right
% 0.29/0.48  thf(fact_97_inf__bot__right,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ X @ bot_bo2099793752762293965at_nat )
% 0.29/0.48        = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_bot_right
% 0.29/0.48  thf(fact_98_inf__bot__right,axiom,
% 0.29/0.48      ! [X: set_o] :
% 0.29/0.48        ( ( inf_inf_set_o @ X @ bot_bot_set_o )
% 0.29/0.48        = bot_bot_set_o ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_bot_right
% 0.29/0.48  thf(fact_99_inf__bot__right,axiom,
% 0.29/0.48      ! [X: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ X @ bot_bot_set_nat )
% 0.29/0.48        = bot_bot_set_nat ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_bot_right
% 0.29/0.48  thf(fact_100_inf__bot__right,axiom,
% 0.29/0.48      ! [X: set_int] :
% 0.29/0.48        ( ( inf_inf_set_int @ X @ bot_bot_set_int )
% 0.29/0.48        = bot_bot_set_int ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_bot_right
% 0.29/0.48  thf(fact_101_inf__apply,axiom,
% 0.29/0.48      ( inf_in3604695632404883862_int_o
% 0.29/0.48      = ( ^ [F: product_prod_int_int > $o,G: product_prod_int_int > $o,X3: product_prod_int_int] : ( inf_inf_o @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_apply
% 0.29/0.48  thf(fact_102_inf__apply,axiom,
% 0.29/0.48      ( inf_inf_list_char_o
% 0.29/0.48      = ( ^ [F: list_char > $o,G: list_char > $o,X3: list_char] : ( inf_inf_o @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_apply
% 0.29/0.48  thf(fact_103_inf__right__idem,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y )
% 0.29/0.48        = ( inf_in2572325071724192079at_nat @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_right_idem
% 0.29/0.48  thf(fact_104_inf__right__idem,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y )
% 0.29/0.48        = ( inf_inf_set_nat @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_right_idem
% 0.29/0.48  thf(fact_105_inf__right__idem,axiom,
% 0.29/0.48      ! [X: nat,Y: nat] :
% 0.29/0.48        ( ( inf_inf_nat @ ( inf_inf_nat @ X @ Y ) @ Y )
% 0.29/0.48        = ( inf_inf_nat @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_right_idem
% 0.29/0.48  thf(fact_106_inf__right__idem,axiom,
% 0.29/0.48      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ Y )
% 0.29/0.48        = ( inf_in3604695632404883862_int_o @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_right_idem
% 0.29/0.48  thf(fact_107_inf__right__idem,axiom,
% 0.29/0.48      ! [X: list_char > $o,Y: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ ( inf_inf_list_char_o @ X @ Y ) @ Y )
% 0.29/0.48        = ( inf_inf_list_char_o @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_right_idem
% 0.29/0.48  thf(fact_108_inf_Oright__idem,axiom,
% 0.29/0.48      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ B )
% 0.29/0.48        = ( inf_in2572325071724192079at_nat @ A @ B ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.right_idem
% 0.29/0.48  thf(fact_109_inf_Oright__idem,axiom,
% 0.29/0.48      ! [A: set_nat,B: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A @ B ) @ B )
% 0.29/0.48        = ( inf_inf_set_nat @ A @ B ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.right_idem
% 0.29/0.48  thf(fact_110_inf_Oright__idem,axiom,
% 0.29/0.48      ! [A: nat,B: nat] :
% 0.29/0.48        ( ( inf_inf_nat @ ( inf_inf_nat @ A @ B ) @ B )
% 0.29/0.48        = ( inf_inf_nat @ A @ B ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.right_idem
% 0.29/0.48  thf(fact_111_inf_Oright__idem,axiom,
% 0.29/0.48      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ B )
% 0.29/0.48        = ( inf_in3604695632404883862_int_o @ A @ B ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.right_idem
% 0.29/0.48  thf(fact_112_inf_Oright__idem,axiom,
% 0.29/0.48      ! [A: list_char > $o,B: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ ( inf_inf_list_char_o @ A @ B ) @ B )
% 0.29/0.48        = ( inf_inf_list_char_o @ A @ B ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.right_idem
% 0.29/0.48  thf(fact_113_inf__left__idem,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 0.29/0.48        = ( inf_in2572325071724192079at_nat @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_left_idem
% 0.29/0.48  thf(fact_114_inf__left__idem,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ X @ Y ) )
% 0.29/0.48        = ( inf_inf_set_nat @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_left_idem
% 0.29/0.48  thf(fact_115_inf__left__idem,axiom,
% 0.29/0.48      ! [X: nat,Y: nat] :
% 0.29/0.48        ( ( inf_inf_nat @ X @ ( inf_inf_nat @ X @ Y ) )
% 0.29/0.48        = ( inf_inf_nat @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_left_idem
% 0.29/0.48  thf(fact_116_inf__left__idem,axiom,
% 0.29/0.48      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ X @ Y ) )
% 0.29/0.48        = ( inf_in3604695632404883862_int_o @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_left_idem
% 0.29/0.48  thf(fact_117_inf__left__idem,axiom,
% 0.29/0.48      ! [X: list_char > $o,Y: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ X @ ( inf_inf_list_char_o @ X @ Y ) )
% 0.29/0.48        = ( inf_inf_list_char_o @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_left_idem
% 0.29/0.48  thf(fact_118_inf_Oleft__idem,axiom,
% 0.29/0.48      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ A @ ( inf_in2572325071724192079at_nat @ A @ B ) )
% 0.29/0.48        = ( inf_in2572325071724192079at_nat @ A @ B ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.left_idem
% 0.29/0.48  thf(fact_119_inf_Oleft__idem,axiom,
% 0.29/0.48      ! [A: set_nat,B: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ A @ ( inf_inf_set_nat @ A @ B ) )
% 0.29/0.48        = ( inf_inf_set_nat @ A @ B ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.left_idem
% 0.29/0.48  thf(fact_120_inf_Oleft__idem,axiom,
% 0.29/0.48      ! [A: nat,B: nat] :
% 0.29/0.48        ( ( inf_inf_nat @ A @ ( inf_inf_nat @ A @ B ) )
% 0.29/0.48        = ( inf_inf_nat @ A @ B ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.left_idem
% 0.29/0.48  thf(fact_121_inf_Oleft__idem,axiom,
% 0.29/0.48      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ A @ ( inf_in3604695632404883862_int_o @ A @ B ) )
% 0.29/0.48        = ( inf_in3604695632404883862_int_o @ A @ B ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.left_idem
% 0.29/0.48  thf(fact_122_inf_Oleft__idem,axiom,
% 0.29/0.48      ! [A: list_char > $o,B: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ A @ ( inf_inf_list_char_o @ A @ B ) )
% 0.29/0.48        = ( inf_inf_list_char_o @ A @ B ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.left_idem
% 0.29/0.48  thf(fact_123_inf__idem,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ X @ X )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_idem
% 0.29/0.48  thf(fact_124_inf__idem,axiom,
% 0.29/0.48      ! [X: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ X @ X )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_idem
% 0.29/0.48  thf(fact_125_inf__idem,axiom,
% 0.29/0.48      ! [X: nat] :
% 0.29/0.48        ( ( inf_inf_nat @ X @ X )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_idem
% 0.29/0.48  thf(fact_126_inf__idem,axiom,
% 0.29/0.48      ! [X: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ X @ X )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_idem
% 0.29/0.48  thf(fact_127_inf__idem,axiom,
% 0.29/0.48      ! [X: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ X @ X )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_idem
% 0.29/0.48  thf(fact_128_inf_Oidem,axiom,
% 0.29/0.48      ! [A: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ A @ A )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.idem
% 0.29/0.48  thf(fact_129_inf_Oidem,axiom,
% 0.29/0.48      ! [A: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ A @ A )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.idem
% 0.29/0.48  thf(fact_130_inf_Oidem,axiom,
% 0.29/0.48      ! [A: nat] :
% 0.29/0.48        ( ( inf_inf_nat @ A @ A )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.idem
% 0.29/0.48  thf(fact_131_inf_Oidem,axiom,
% 0.29/0.48      ! [A: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ A @ A )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.idem
% 0.29/0.48  thf(fact_132_inf_Oidem,axiom,
% 0.29/0.48      ! [A: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ A @ A )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.idem
% 0.29/0.48  thf(fact_133_mem__Collect__eq,axiom,
% 0.29/0.48      ! [A: set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 0.29/0.48        ( ( member2340774599025711042nt_int @ A @ ( collec5210948495886036740nt_int @ P ) )
% 0.29/0.48        = ( P @ A ) ) ).
% 0.29/0.48  
% 0.29/0.48  % mem_Collect_eq
% 0.29/0.48  thf(fact_134_mem__Collect__eq,axiom,
% 0.29/0.48      ! [A: set_nat,P: set_nat > $o] :
% 0.29/0.48        ( ( member_set_nat @ A @ ( collect_set_nat @ P ) )
% 0.29/0.48        = ( P @ A ) ) ).
% 0.29/0.48  
% 0.29/0.48  % mem_Collect_eq
% 0.29/0.48  thf(fact_135_mem__Collect__eq,axiom,
% 0.29/0.48      ! [A: nat,P: nat > $o] :
% 0.29/0.48        ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.29/0.48        = ( P @ A ) ) ).
% 0.29/0.48  
% 0.29/0.48  % mem_Collect_eq
% 0.29/0.48  thf(fact_136_mem__Collect__eq,axiom,
% 0.29/0.48      ! [A: int,P: int > $o] :
% 0.29/0.48        ( ( member_int @ A @ ( collect_int @ P ) )
% 0.29/0.48        = ( P @ A ) ) ).
% 0.29/0.48  
% 0.29/0.48  % mem_Collect_eq
% 0.29/0.48  thf(fact_137_mem__Collect__eq,axiom,
% 0.29/0.48      ! [A: produc3658429121746597890et_nat > $o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.29/0.48        ( ( member6576561426505652726_nat_o @ A @ ( collec939566748876313656_nat_o @ P ) )
% 0.29/0.48        = ( P @ A ) ) ).
% 0.29/0.48  
% 0.29/0.48  % mem_Collect_eq
% 0.29/0.48  thf(fact_138_Collect__mem__eq,axiom,
% 0.29/0.48      ! [A2: set_se6260736226359567993nt_int] :
% 0.29/0.48        ( ( collec5210948495886036740nt_int
% 0.29/0.48          @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ A2 ) )
% 0.29/0.48        = A2 ) ).
% 0.29/0.48  
% 0.29/0.48  % Collect_mem_eq
% 0.29/0.48  thf(fact_139_Collect__mem__eq,axiom,
% 0.29/0.48      ! [A2: set_set_nat] :
% 0.29/0.48        ( ( collect_set_nat
% 0.29/0.48          @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A2 ) )
% 0.29/0.48        = A2 ) ).
% 0.29/0.48  
% 0.29/0.48  % Collect_mem_eq
% 0.29/0.48  thf(fact_140_Collect__mem__eq,axiom,
% 0.29/0.48      ! [A2: set_nat] :
% 0.29/0.48        ( ( collect_nat
% 0.29/0.48          @ ^ [X3: nat] : ( member_nat @ X3 @ A2 ) )
% 0.29/0.48        = A2 ) ).
% 0.29/0.48  
% 0.29/0.48  % Collect_mem_eq
% 0.29/0.48  thf(fact_141_Collect__mem__eq,axiom,
% 0.29/0.48      ! [A2: set_int] :
% 0.29/0.48        ( ( collect_int
% 0.29/0.48          @ ^ [X3: int] : ( member_int @ X3 @ A2 ) )
% 0.29/0.48        = A2 ) ).
% 0.29/0.48  
% 0.29/0.48  % Collect_mem_eq
% 0.29/0.48  thf(fact_142_Collect__mem__eq,axiom,
% 0.29/0.48      ! [A2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.48        ( ( collec939566748876313656_nat_o
% 0.29/0.48          @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ A2 ) )
% 0.29/0.48        = A2 ) ).
% 0.29/0.48  
% 0.29/0.48  % Collect_mem_eq
% 0.29/0.48  thf(fact_143_Collect__cong,axiom,
% 0.29/0.48      ! [P: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 0.29/0.48        ( ! [X2: set_Pr958786334691620121nt_int] :
% 0.29/0.48            ( ( P @ X2 )
% 0.29/0.48            = ( Q2 @ X2 ) )
% 0.29/0.48       => ( ( collec5210948495886036740nt_int @ P )
% 0.29/0.48          = ( collec5210948495886036740nt_int @ Q2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Collect_cong
% 0.29/0.48  thf(fact_144_Collect__cong,axiom,
% 0.29/0.48      ! [P: set_nat > $o,Q2: set_nat > $o] :
% 0.29/0.48        ( ! [X2: set_nat] :
% 0.29/0.48            ( ( P @ X2 )
% 0.29/0.48            = ( Q2 @ X2 ) )
% 0.29/0.48       => ( ( collect_set_nat @ P )
% 0.29/0.48          = ( collect_set_nat @ Q2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Collect_cong
% 0.29/0.48  thf(fact_145_Collect__cong,axiom,
% 0.29/0.48      ! [P: nat > $o,Q2: nat > $o] :
% 0.29/0.48        ( ! [X2: nat] :
% 0.29/0.48            ( ( P @ X2 )
% 0.29/0.48            = ( Q2 @ X2 ) )
% 0.29/0.48       => ( ( collect_nat @ P )
% 0.29/0.48          = ( collect_nat @ Q2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Collect_cong
% 0.29/0.48  thf(fact_146_Collect__cong,axiom,
% 0.29/0.48      ! [P: int > $o,Q2: int > $o] :
% 0.29/0.48        ( ! [X2: int] :
% 0.29/0.48            ( ( P @ X2 )
% 0.29/0.48            = ( Q2 @ X2 ) )
% 0.29/0.48       => ( ( collect_int @ P )
% 0.29/0.48          = ( collect_int @ Q2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Collect_cong
% 0.29/0.48  thf(fact_147_Collect__cong,axiom,
% 0.29/0.48      ! [P: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.29/0.48        ( ! [X2: produc3658429121746597890et_nat > $o] :
% 0.29/0.48            ( ( P @ X2 )
% 0.29/0.48            = ( Q2 @ X2 ) )
% 0.29/0.48       => ( ( collec939566748876313656_nat_o @ P )
% 0.29/0.48          = ( collec939566748876313656_nat_o @ Q2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % Collect_cong
% 0.29/0.48  thf(fact_148_sup_Oright__idem,axiom,
% 0.29/0.48      ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ A @ B ) @ B )
% 0.29/0.48        = ( sup_su3035147773818789531at_nat @ A @ B ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.right_idem
% 0.29/0.48  thf(fact_149_sup_Oright__idem,axiom,
% 0.29/0.48      ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ B )
% 0.29/0.48        = ( sup_su5525570899277871387at_nat @ A @ B ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.right_idem
% 0.29/0.48  thf(fact_150_sup_Oright__idem,axiom,
% 0.29/0.48      ! [A: set_nat,B: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A @ B ) @ B )
% 0.29/0.48        = ( sup_sup_set_nat @ A @ B ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.right_idem
% 0.29/0.48  thf(fact_151_sup_Oright__idem,axiom,
% 0.29/0.48      ! [A: nat,B: nat] :
% 0.29/0.48        ( ( sup_sup_nat @ ( sup_sup_nat @ A @ B ) @ B )
% 0.29/0.48        = ( sup_sup_nat @ A @ B ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.right_idem
% 0.29/0.48  thf(fact_152_sup_Oright__idem,axiom,
% 0.29/0.48      ! [A: int,B: int] :
% 0.29/0.48        ( ( sup_sup_int @ ( sup_sup_int @ A @ B ) @ B )
% 0.29/0.48        = ( sup_sup_int @ A @ B ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.right_idem
% 0.29/0.48  thf(fact_153_sup__left__idem,axiom,
% 0.29/0.48      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 0.29/0.48        = ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_left_idem
% 0.29/0.48  thf(fact_154_sup__left__idem,axiom,
% 0.29/0.48      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 0.29/0.48        = ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_left_idem
% 0.29/0.48  thf(fact_155_sup__left__idem,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) )
% 0.29/0.48        = ( sup_sup_set_nat @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_left_idem
% 0.29/0.48  thf(fact_156_sup__left__idem,axiom,
% 0.29/0.48      ! [X: nat,Y: nat] :
% 0.29/0.48        ( ( sup_sup_nat @ X @ ( sup_sup_nat @ X @ Y ) )
% 0.29/0.48        = ( sup_sup_nat @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_left_idem
% 0.29/0.48  thf(fact_157_sup__left__idem,axiom,
% 0.29/0.48      ! [X: int,Y: int] :
% 0.29/0.48        ( ( sup_sup_int @ X @ ( sup_sup_int @ X @ Y ) )
% 0.29/0.48        = ( sup_sup_int @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_left_idem
% 0.29/0.48  thf(fact_158_sup_Oleft__idem,axiom,
% 0.29/0.48      ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ A @ ( sup_su3035147773818789531at_nat @ A @ B ) )
% 0.29/0.48        = ( sup_su3035147773818789531at_nat @ A @ B ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.left_idem
% 0.29/0.48  thf(fact_159_sup_Oleft__idem,axiom,
% 0.29/0.48      ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ A @ ( sup_su5525570899277871387at_nat @ A @ B ) )
% 0.29/0.48        = ( sup_su5525570899277871387at_nat @ A @ B ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.left_idem
% 0.29/0.48  thf(fact_160_sup_Oleft__idem,axiom,
% 0.29/0.48      ! [A: set_nat,B: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ A @ B ) )
% 0.29/0.48        = ( sup_sup_set_nat @ A @ B ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.left_idem
% 0.29/0.48  thf(fact_161_sup_Oleft__idem,axiom,
% 0.29/0.48      ! [A: nat,B: nat] :
% 0.29/0.48        ( ( sup_sup_nat @ A @ ( sup_sup_nat @ A @ B ) )
% 0.29/0.48        = ( sup_sup_nat @ A @ B ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.left_idem
% 0.29/0.48  thf(fact_162_sup_Oleft__idem,axiom,
% 0.29/0.48      ! [A: int,B: int] :
% 0.29/0.48        ( ( sup_sup_int @ A @ ( sup_sup_int @ A @ B ) )
% 0.29/0.48        = ( sup_sup_int @ A @ B ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.left_idem
% 0.29/0.48  thf(fact_163_sup__idem,axiom,
% 0.29/0.48      ! [X: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ X @ X )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_idem
% 0.29/0.48  thf(fact_164_sup__idem,axiom,
% 0.29/0.48      ! [X: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ X @ X )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_idem
% 0.29/0.48  thf(fact_165_sup__idem,axiom,
% 0.29/0.48      ! [X: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ X @ X )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_idem
% 0.29/0.48  thf(fact_166_sup__idem,axiom,
% 0.29/0.48      ! [X: nat] :
% 0.29/0.48        ( ( sup_sup_nat @ X @ X )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_idem
% 0.29/0.48  thf(fact_167_sup__idem,axiom,
% 0.29/0.48      ! [X: int] :
% 0.29/0.48        ( ( sup_sup_int @ X @ X )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_idem
% 0.29/0.48  thf(fact_168_sup_Oidem,axiom,
% 0.29/0.48      ! [A: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ A @ A )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.idem
% 0.29/0.48  thf(fact_169_sup_Oidem,axiom,
% 0.29/0.48      ! [A: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ A @ A )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.idem
% 0.29/0.48  thf(fact_170_sup_Oidem,axiom,
% 0.29/0.48      ! [A: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ A @ A )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.idem
% 0.29/0.48  thf(fact_171_sup_Oidem,axiom,
% 0.29/0.48      ! [A: nat] :
% 0.29/0.48        ( ( sup_sup_nat @ A @ A )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.idem
% 0.29/0.48  thf(fact_172_sup_Oidem,axiom,
% 0.29/0.48      ! [A: int] :
% 0.29/0.48        ( ( sup_sup_int @ A @ A )
% 0.29/0.48        = A ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.idem
% 0.29/0.48  thf(fact_173_inf__fun__def,axiom,
% 0.29/0.48      ( inf_in3604695632404883862_int_o
% 0.29/0.48      = ( ^ [F: product_prod_int_int > $o,G: product_prod_int_int > $o,X3: product_prod_int_int] : ( inf_inf_o @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_fun_def
% 0.29/0.48  thf(fact_174_inf__fun__def,axiom,
% 0.29/0.48      ( inf_inf_list_char_o
% 0.29/0.48      = ( ^ [F: list_char > $o,G: list_char > $o,X3: list_char] : ( inf_inf_o @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_fun_def
% 0.29/0.48  thf(fact_175_inf__left__commute,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 0.29/0.48        = ( inf_in2572325071724192079at_nat @ Y @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_left_commute
% 0.29/0.48  thf(fact_176_inf__left__commute,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 0.29/0.48        = ( inf_inf_set_nat @ Y @ ( inf_inf_set_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_left_commute
% 0.29/0.48  thf(fact_177_inf__left__commute,axiom,
% 0.29/0.48      ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.48        ( ( inf_inf_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 0.29/0.48        = ( inf_inf_nat @ Y @ ( inf_inf_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_left_commute
% 0.29/0.48  thf(fact_178_inf__left__commute,axiom,
% 0.29/0.48      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) )
% 0.29/0.48        = ( inf_in3604695632404883862_int_o @ Y @ ( inf_in3604695632404883862_int_o @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_left_commute
% 0.29/0.48  thf(fact_179_inf__left__commute,axiom,
% 0.29/0.48      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ X @ ( inf_inf_list_char_o @ Y @ Z ) )
% 0.29/0.48        = ( inf_inf_list_char_o @ Y @ ( inf_inf_list_char_o @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_left_commute
% 0.29/0.48  thf(fact_180_inf_Oleft__commute,axiom,
% 0.29/0.48      ! [B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ B @ ( inf_in2572325071724192079at_nat @ A @ C ) )
% 0.29/0.48        = ( inf_in2572325071724192079at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.left_commute
% 0.29/0.48  thf(fact_181_inf_Oleft__commute,axiom,
% 0.29/0.48      ! [B: set_nat,A: set_nat,C: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ B @ ( inf_inf_set_nat @ A @ C ) )
% 0.29/0.48        = ( inf_inf_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.left_commute
% 0.29/0.48  thf(fact_182_inf_Oleft__commute,axiom,
% 0.29/0.48      ! [B: nat,A: nat,C: nat] :
% 0.29/0.48        ( ( inf_inf_nat @ B @ ( inf_inf_nat @ A @ C ) )
% 0.29/0.48        = ( inf_inf_nat @ A @ ( inf_inf_nat @ B @ C ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.left_commute
% 0.29/0.48  thf(fact_183_inf_Oleft__commute,axiom,
% 0.29/0.48      ! [B: product_prod_int_int > $o,A: product_prod_int_int > $o,C: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ B @ ( inf_in3604695632404883862_int_o @ A @ C ) )
% 0.29/0.48        = ( inf_in3604695632404883862_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.left_commute
% 0.29/0.48  thf(fact_184_inf_Oleft__commute,axiom,
% 0.29/0.48      ! [B: list_char > $o,A: list_char > $o,C: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ B @ ( inf_inf_list_char_o @ A @ C ) )
% 0.29/0.48        = ( inf_inf_list_char_o @ A @ ( inf_inf_list_char_o @ B @ C ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.left_commute
% 0.29/0.48  thf(fact_185_inf__commute,axiom,
% 0.29/0.48      ( inf_in2572325071724192079at_nat
% 0.29/0.48      = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ Y3 @ X3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_commute
% 0.29/0.48  thf(fact_186_inf__commute,axiom,
% 0.29/0.48      ( inf_inf_set_nat
% 0.29/0.48      = ( ^ [X3: set_nat,Y3: set_nat] : ( inf_inf_set_nat @ Y3 @ X3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_commute
% 0.29/0.48  thf(fact_187_inf__commute,axiom,
% 0.29/0.48      ( inf_inf_nat
% 0.29/0.48      = ( ^ [X3: nat,Y3: nat] : ( inf_inf_nat @ Y3 @ X3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_commute
% 0.29/0.48  thf(fact_188_inf__commute,axiom,
% 0.29/0.48      ( inf_in3604695632404883862_int_o
% 0.29/0.48      = ( ^ [X3: product_prod_int_int > $o,Y3: product_prod_int_int > $o] : ( inf_in3604695632404883862_int_o @ Y3 @ X3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_commute
% 0.29/0.48  thf(fact_189_inf__commute,axiom,
% 0.29/0.48      ( inf_inf_list_char_o
% 0.29/0.48      = ( ^ [X3: list_char > $o,Y3: list_char > $o] : ( inf_inf_list_char_o @ Y3 @ X3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_commute
% 0.29/0.48  thf(fact_190_inf_Ocommute,axiom,
% 0.29/0.48      ( inf_in2572325071724192079at_nat
% 0.29/0.48      = ( ^ [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ B3 @ A3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.commute
% 0.29/0.48  thf(fact_191_inf_Ocommute,axiom,
% 0.29/0.48      ( inf_inf_set_nat
% 0.29/0.48      = ( ^ [A3: set_nat,B3: set_nat] : ( inf_inf_set_nat @ B3 @ A3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.commute
% 0.29/0.48  thf(fact_192_inf_Ocommute,axiom,
% 0.29/0.48      ( inf_inf_nat
% 0.29/0.48      = ( ^ [A3: nat,B3: nat] : ( inf_inf_nat @ B3 @ A3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.commute
% 0.29/0.48  thf(fact_193_inf_Ocommute,axiom,
% 0.29/0.48      ( inf_in3604695632404883862_int_o
% 0.29/0.48      = ( ^ [A3: product_prod_int_int > $o,B3: product_prod_int_int > $o] : ( inf_in3604695632404883862_int_o @ B3 @ A3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.commute
% 0.29/0.48  thf(fact_194_inf_Ocommute,axiom,
% 0.29/0.48      ( inf_inf_list_char_o
% 0.29/0.48      = ( ^ [A3: list_char > $o,B3: list_char > $o] : ( inf_inf_list_char_o @ B3 @ A3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.commute
% 0.29/0.48  thf(fact_195_inf__assoc,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Z )
% 0.29/0.48        = ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_assoc
% 0.29/0.48  thf(fact_196_inf__assoc,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Z )
% 0.29/0.48        = ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_assoc
% 0.29/0.48  thf(fact_197_inf__assoc,axiom,
% 0.29/0.48      ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.48        ( ( inf_inf_nat @ ( inf_inf_nat @ X @ Y ) @ Z )
% 0.29/0.48        = ( inf_inf_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_assoc
% 0.29/0.48  thf(fact_198_inf__assoc,axiom,
% 0.29/0.48      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ Z )
% 0.29/0.48        = ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_assoc
% 0.29/0.48  thf(fact_199_inf__assoc,axiom,
% 0.29/0.48      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ ( inf_inf_list_char_o @ X @ Y ) @ Z )
% 0.29/0.48        = ( inf_inf_list_char_o @ X @ ( inf_inf_list_char_o @ Y @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_assoc
% 0.29/0.48  thf(fact_200_inf_Oassoc,axiom,
% 0.29/0.48      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C )
% 0.29/0.48        = ( inf_in2572325071724192079at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.assoc
% 0.29/0.48  thf(fact_201_inf_Oassoc,axiom,
% 0.29/0.48      ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C )
% 0.29/0.48        = ( inf_inf_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.assoc
% 0.29/0.48  thf(fact_202_inf_Oassoc,axiom,
% 0.29/0.48      ! [A: nat,B: nat,C: nat] :
% 0.29/0.48        ( ( inf_inf_nat @ ( inf_inf_nat @ A @ B ) @ C )
% 0.29/0.48        = ( inf_inf_nat @ A @ ( inf_inf_nat @ B @ C ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.assoc
% 0.29/0.48  thf(fact_203_inf_Oassoc,axiom,
% 0.29/0.48      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o,C: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ C )
% 0.29/0.48        = ( inf_in3604695632404883862_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.assoc
% 0.29/0.48  thf(fact_204_inf_Oassoc,axiom,
% 0.29/0.48      ! [A: list_char > $o,B: list_char > $o,C: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ ( inf_inf_list_char_o @ A @ B ) @ C )
% 0.29/0.48        = ( inf_inf_list_char_o @ A @ ( inf_inf_list_char_o @ B @ C ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf.assoc
% 0.29/0.48  thf(fact_205_inf__sup__aci_I1_J,axiom,
% 0.29/0.48      ( inf_in2572325071724192079at_nat
% 0.29/0.48      = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ Y3 @ X3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(1)
% 0.29/0.48  thf(fact_206_inf__sup__aci_I1_J,axiom,
% 0.29/0.48      ( inf_inf_set_nat
% 0.29/0.48      = ( ^ [X3: set_nat,Y3: set_nat] : ( inf_inf_set_nat @ Y3 @ X3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(1)
% 0.29/0.48  thf(fact_207_inf__sup__aci_I1_J,axiom,
% 0.29/0.48      ( inf_inf_nat
% 0.29/0.48      = ( ^ [X3: nat,Y3: nat] : ( inf_inf_nat @ Y3 @ X3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(1)
% 0.29/0.48  thf(fact_208_inf__sup__aci_I1_J,axiom,
% 0.29/0.48      ( inf_in3604695632404883862_int_o
% 0.29/0.48      = ( ^ [X3: product_prod_int_int > $o,Y3: product_prod_int_int > $o] : ( inf_in3604695632404883862_int_o @ Y3 @ X3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(1)
% 0.29/0.48  thf(fact_209_inf__sup__aci_I1_J,axiom,
% 0.29/0.48      ( inf_inf_list_char_o
% 0.29/0.48      = ( ^ [X3: list_char > $o,Y3: list_char > $o] : ( inf_inf_list_char_o @ Y3 @ X3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(1)
% 0.29/0.48  thf(fact_210_inf__sup__aci_I2_J,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Z )
% 0.29/0.48        = ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(2)
% 0.29/0.48  thf(fact_211_inf__sup__aci_I2_J,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Z )
% 0.29/0.48        = ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(2)
% 0.29/0.48  thf(fact_212_inf__sup__aci_I2_J,axiom,
% 0.29/0.48      ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.48        ( ( inf_inf_nat @ ( inf_inf_nat @ X @ Y ) @ Z )
% 0.29/0.48        = ( inf_inf_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(2)
% 0.29/0.48  thf(fact_213_inf__sup__aci_I2_J,axiom,
% 0.29/0.48      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ Z )
% 0.29/0.48        = ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(2)
% 0.29/0.48  thf(fact_214_inf__sup__aci_I2_J,axiom,
% 0.29/0.48      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ ( inf_inf_list_char_o @ X @ Y ) @ Z )
% 0.29/0.48        = ( inf_inf_list_char_o @ X @ ( inf_inf_list_char_o @ Y @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(2)
% 0.29/0.48  thf(fact_215_inf__sup__aci_I3_J,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 0.29/0.48        = ( inf_in2572325071724192079at_nat @ Y @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(3)
% 0.29/0.48  thf(fact_216_inf__sup__aci_I3_J,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 0.29/0.48        = ( inf_inf_set_nat @ Y @ ( inf_inf_set_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(3)
% 0.29/0.48  thf(fact_217_inf__sup__aci_I3_J,axiom,
% 0.29/0.48      ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.48        ( ( inf_inf_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 0.29/0.48        = ( inf_inf_nat @ Y @ ( inf_inf_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(3)
% 0.29/0.48  thf(fact_218_inf__sup__aci_I3_J,axiom,
% 0.29/0.48      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) )
% 0.29/0.48        = ( inf_in3604695632404883862_int_o @ Y @ ( inf_in3604695632404883862_int_o @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(3)
% 0.29/0.48  thf(fact_219_inf__sup__aci_I3_J,axiom,
% 0.29/0.48      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ X @ ( inf_inf_list_char_o @ Y @ Z ) )
% 0.29/0.48        = ( inf_inf_list_char_o @ Y @ ( inf_inf_list_char_o @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(3)
% 0.29/0.48  thf(fact_220_inf__sup__aci_I4_J,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 0.29/0.48        = ( inf_in2572325071724192079at_nat @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(4)
% 0.29/0.48  thf(fact_221_inf__sup__aci_I4_J,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ X @ Y ) )
% 0.29/0.48        = ( inf_inf_set_nat @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(4)
% 0.29/0.48  thf(fact_222_inf__sup__aci_I4_J,axiom,
% 0.29/0.48      ! [X: nat,Y: nat] :
% 0.29/0.48        ( ( inf_inf_nat @ X @ ( inf_inf_nat @ X @ Y ) )
% 0.29/0.48        = ( inf_inf_nat @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(4)
% 0.29/0.48  thf(fact_223_inf__sup__aci_I4_J,axiom,
% 0.29/0.48      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ X @ Y ) )
% 0.29/0.48        = ( inf_in3604695632404883862_int_o @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(4)
% 0.29/0.48  thf(fact_224_inf__sup__aci_I4_J,axiom,
% 0.29/0.48      ! [X: list_char > $o,Y: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ X @ ( inf_inf_list_char_o @ X @ Y ) )
% 0.29/0.48        = ( inf_inf_list_char_o @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(4)
% 0.29/0.48  thf(fact_225_sup__left__commute,axiom,
% 0.29/0.48      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) )
% 0.29/0.48        = ( sup_su3035147773818789531at_nat @ Y @ ( sup_su3035147773818789531at_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_left_commute
% 0.29/0.48  thf(fact_226_sup__left__commute,axiom,
% 0.29/0.48      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) )
% 0.29/0.48        = ( sup_su5525570899277871387at_nat @ Y @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_left_commute
% 0.29/0.48  thf(fact_227_sup__left__commute,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 0.29/0.48        = ( sup_sup_set_nat @ Y @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_left_commute
% 0.29/0.48  thf(fact_228_sup__left__commute,axiom,
% 0.29/0.48      ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.48        ( ( sup_sup_nat @ X @ ( sup_sup_nat @ Y @ Z ) )
% 0.29/0.48        = ( sup_sup_nat @ Y @ ( sup_sup_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_left_commute
% 0.29/0.48  thf(fact_229_sup__left__commute,axiom,
% 0.29/0.48      ! [X: int,Y: int,Z: int] :
% 0.29/0.48        ( ( sup_sup_int @ X @ ( sup_sup_int @ Y @ Z ) )
% 0.29/0.48        = ( sup_sup_int @ Y @ ( sup_sup_int @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_left_commute
% 0.29/0.48  thf(fact_230_sup_Oleft__commute,axiom,
% 0.29/0.48      ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,C: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ B @ ( sup_su3035147773818789531at_nat @ A @ C ) )
% 0.29/0.48        = ( sup_su3035147773818789531at_nat @ A @ ( sup_su3035147773818789531at_nat @ B @ C ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.left_commute
% 0.29/0.48  thf(fact_231_sup_Oleft__commute,axiom,
% 0.29/0.48      ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ B @ ( sup_su5525570899277871387at_nat @ A @ C ) )
% 0.29/0.48        = ( sup_su5525570899277871387at_nat @ A @ ( sup_su5525570899277871387at_nat @ B @ C ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.left_commute
% 0.29/0.48  thf(fact_232_sup_Oleft__commute,axiom,
% 0.29/0.48      ! [B: set_nat,A: set_nat,C: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ B @ ( sup_sup_set_nat @ A @ C ) )
% 0.29/0.48        = ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ B @ C ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.left_commute
% 0.29/0.48  thf(fact_233_sup_Oleft__commute,axiom,
% 0.29/0.48      ! [B: nat,A: nat,C: nat] :
% 0.29/0.48        ( ( sup_sup_nat @ B @ ( sup_sup_nat @ A @ C ) )
% 0.29/0.48        = ( sup_sup_nat @ A @ ( sup_sup_nat @ B @ C ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.left_commute
% 0.29/0.48  thf(fact_234_sup_Oleft__commute,axiom,
% 0.29/0.48      ! [B: int,A: int,C: int] :
% 0.29/0.48        ( ( sup_sup_int @ B @ ( sup_sup_int @ A @ C ) )
% 0.29/0.48        = ( sup_sup_int @ A @ ( sup_sup_int @ B @ C ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.left_commute
% 0.29/0.48  thf(fact_235_sup__commute,axiom,
% 0.29/0.48      ( sup_su3035147773818789531at_nat
% 0.29/0.48      = ( ^ [X3: set_Pr8551490117392284871at_nat,Y3: set_Pr8551490117392284871at_nat] : ( sup_su3035147773818789531at_nat @ Y3 @ X3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_commute
% 0.29/0.48  thf(fact_236_sup__commute,axiom,
% 0.29/0.48      ( sup_su5525570899277871387at_nat
% 0.29/0.48      = ( ^ [X3: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ Y3 @ X3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_commute
% 0.29/0.48  thf(fact_237_sup__commute,axiom,
% 0.29/0.48      ( sup_sup_set_nat
% 0.29/0.48      = ( ^ [X3: set_nat,Y3: set_nat] : ( sup_sup_set_nat @ Y3 @ X3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_commute
% 0.29/0.48  thf(fact_238_sup__commute,axiom,
% 0.29/0.48      ( sup_sup_nat
% 0.29/0.48      = ( ^ [X3: nat,Y3: nat] : ( sup_sup_nat @ Y3 @ X3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_commute
% 0.29/0.48  thf(fact_239_sup__commute,axiom,
% 0.29/0.48      ( sup_sup_int
% 0.29/0.48      = ( ^ [X3: int,Y3: int] : ( sup_sup_int @ Y3 @ X3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_commute
% 0.29/0.48  thf(fact_240_sup_Ocommute,axiom,
% 0.29/0.48      ( sup_su3035147773818789531at_nat
% 0.29/0.48      = ( ^ [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] : ( sup_su3035147773818789531at_nat @ B3 @ A3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.commute
% 0.29/0.48  thf(fact_241_sup_Ocommute,axiom,
% 0.29/0.48      ( sup_su5525570899277871387at_nat
% 0.29/0.48      = ( ^ [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ B3 @ A3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.commute
% 0.29/0.48  thf(fact_242_sup_Ocommute,axiom,
% 0.29/0.48      ( sup_sup_set_nat
% 0.29/0.48      = ( ^ [A3: set_nat,B3: set_nat] : ( sup_sup_set_nat @ B3 @ A3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.commute
% 0.29/0.48  thf(fact_243_sup_Ocommute,axiom,
% 0.29/0.48      ( sup_sup_nat
% 0.29/0.48      = ( ^ [A3: nat,B3: nat] : ( sup_sup_nat @ B3 @ A3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.commute
% 0.29/0.48  thf(fact_244_sup_Ocommute,axiom,
% 0.29/0.48      ( sup_sup_int
% 0.29/0.48      = ( ^ [A3: int,B3: int] : ( sup_sup_int @ B3 @ A3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.commute
% 0.29/0.48  thf(fact_245_sup__assoc,axiom,
% 0.29/0.48      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ Z )
% 0.29/0.48        = ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_assoc
% 0.29/0.48  thf(fact_246_sup__assoc,axiom,
% 0.29/0.48      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ Z )
% 0.29/0.48        = ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_assoc
% 0.29/0.48  thf(fact_247_sup__assoc,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z )
% 0.29/0.48        = ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_assoc
% 0.29/0.48  thf(fact_248_sup__assoc,axiom,
% 0.29/0.48      ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.48        ( ( sup_sup_nat @ ( sup_sup_nat @ X @ Y ) @ Z )
% 0.29/0.48        = ( sup_sup_nat @ X @ ( sup_sup_nat @ Y @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_assoc
% 0.29/0.48  thf(fact_249_sup__assoc,axiom,
% 0.29/0.48      ! [X: int,Y: int,Z: int] :
% 0.29/0.48        ( ( sup_sup_int @ ( sup_sup_int @ X @ Y ) @ Z )
% 0.29/0.48        = ( sup_sup_int @ X @ ( sup_sup_int @ Y @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_assoc
% 0.29/0.48  thf(fact_250_sup_Oassoc,axiom,
% 0.29/0.48      ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,C: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ A @ B ) @ C )
% 0.29/0.48        = ( sup_su3035147773818789531at_nat @ A @ ( sup_su3035147773818789531at_nat @ B @ C ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.assoc
% 0.29/0.48  thf(fact_251_sup_Oassoc,axiom,
% 0.29/0.48      ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ C )
% 0.29/0.48        = ( sup_su5525570899277871387at_nat @ A @ ( sup_su5525570899277871387at_nat @ B @ C ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.assoc
% 0.29/0.48  thf(fact_252_sup_Oassoc,axiom,
% 0.29/0.48      ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A @ B ) @ C )
% 0.29/0.48        = ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ B @ C ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.assoc
% 0.29/0.48  thf(fact_253_sup_Oassoc,axiom,
% 0.29/0.48      ! [A: nat,B: nat,C: nat] :
% 0.29/0.48        ( ( sup_sup_nat @ ( sup_sup_nat @ A @ B ) @ C )
% 0.29/0.48        = ( sup_sup_nat @ A @ ( sup_sup_nat @ B @ C ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.assoc
% 0.29/0.48  thf(fact_254_sup_Oassoc,axiom,
% 0.29/0.48      ! [A: int,B: int,C: int] :
% 0.29/0.48        ( ( sup_sup_int @ ( sup_sup_int @ A @ B ) @ C )
% 0.29/0.48        = ( sup_sup_int @ A @ ( sup_sup_int @ B @ C ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup.assoc
% 0.29/0.48  thf(fact_255_inf__sup__aci_I5_J,axiom,
% 0.29/0.48      ( sup_su3035147773818789531at_nat
% 0.29/0.48      = ( ^ [X3: set_Pr8551490117392284871at_nat,Y3: set_Pr8551490117392284871at_nat] : ( sup_su3035147773818789531at_nat @ Y3 @ X3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(5)
% 0.29/0.48  thf(fact_256_inf__sup__aci_I5_J,axiom,
% 0.29/0.48      ( sup_su5525570899277871387at_nat
% 0.29/0.48      = ( ^ [X3: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ Y3 @ X3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(5)
% 0.29/0.48  thf(fact_257_inf__sup__aci_I5_J,axiom,
% 0.29/0.48      ( sup_sup_set_nat
% 0.29/0.48      = ( ^ [X3: set_nat,Y3: set_nat] : ( sup_sup_set_nat @ Y3 @ X3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(5)
% 0.29/0.48  thf(fact_258_inf__sup__aci_I5_J,axiom,
% 0.29/0.48      ( sup_sup_nat
% 0.29/0.48      = ( ^ [X3: nat,Y3: nat] : ( sup_sup_nat @ Y3 @ X3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(5)
% 0.29/0.48  thf(fact_259_inf__sup__aci_I5_J,axiom,
% 0.29/0.48      ( sup_sup_int
% 0.29/0.48      = ( ^ [X3: int,Y3: int] : ( sup_sup_int @ Y3 @ X3 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(5)
% 0.29/0.48  thf(fact_260_inf__sup__aci_I6_J,axiom,
% 0.29/0.48      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ Z )
% 0.29/0.48        = ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(6)
% 0.29/0.48  thf(fact_261_inf__sup__aci_I6_J,axiom,
% 0.29/0.48      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ Z )
% 0.29/0.48        = ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(6)
% 0.29/0.48  thf(fact_262_inf__sup__aci_I6_J,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z )
% 0.29/0.48        = ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(6)
% 0.29/0.48  thf(fact_263_inf__sup__aci_I6_J,axiom,
% 0.29/0.48      ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.48        ( ( sup_sup_nat @ ( sup_sup_nat @ X @ Y ) @ Z )
% 0.29/0.48        = ( sup_sup_nat @ X @ ( sup_sup_nat @ Y @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(6)
% 0.29/0.48  thf(fact_264_inf__sup__aci_I6_J,axiom,
% 0.29/0.48      ! [X: int,Y: int,Z: int] :
% 0.29/0.48        ( ( sup_sup_int @ ( sup_sup_int @ X @ Y ) @ Z )
% 0.29/0.48        = ( sup_sup_int @ X @ ( sup_sup_int @ Y @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(6)
% 0.29/0.48  thf(fact_265_inf__sup__aci_I7_J,axiom,
% 0.29/0.48      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) )
% 0.29/0.48        = ( sup_su3035147773818789531at_nat @ Y @ ( sup_su3035147773818789531at_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(7)
% 0.29/0.48  thf(fact_266_inf__sup__aci_I7_J,axiom,
% 0.29/0.48      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) )
% 0.29/0.48        = ( sup_su5525570899277871387at_nat @ Y @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(7)
% 0.29/0.48  thf(fact_267_inf__sup__aci_I7_J,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 0.29/0.48        = ( sup_sup_set_nat @ Y @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(7)
% 0.29/0.48  thf(fact_268_inf__sup__aci_I7_J,axiom,
% 0.29/0.48      ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.48        ( ( sup_sup_nat @ X @ ( sup_sup_nat @ Y @ Z ) )
% 0.29/0.48        = ( sup_sup_nat @ Y @ ( sup_sup_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(7)
% 0.29/0.48  thf(fact_269_inf__sup__aci_I7_J,axiom,
% 0.29/0.48      ! [X: int,Y: int,Z: int] :
% 0.29/0.48        ( ( sup_sup_int @ X @ ( sup_sup_int @ Y @ Z ) )
% 0.29/0.48        = ( sup_sup_int @ Y @ ( sup_sup_int @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(7)
% 0.29/0.48  thf(fact_270_inf__sup__aci_I8_J,axiom,
% 0.29/0.48      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 0.29/0.48        = ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(8)
% 0.29/0.48  thf(fact_271_inf__sup__aci_I8_J,axiom,
% 0.29/0.48      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 0.29/0.48        = ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(8)
% 0.29/0.48  thf(fact_272_inf__sup__aci_I8_J,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) )
% 0.29/0.48        = ( sup_sup_set_nat @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(8)
% 0.29/0.48  thf(fact_273_inf__sup__aci_I8_J,axiom,
% 0.29/0.48      ! [X: nat,Y: nat] :
% 0.29/0.48        ( ( sup_sup_nat @ X @ ( sup_sup_nat @ X @ Y ) )
% 0.29/0.48        = ( sup_sup_nat @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(8)
% 0.29/0.48  thf(fact_274_inf__sup__aci_I8_J,axiom,
% 0.29/0.48      ! [X: int,Y: int] :
% 0.29/0.48        ( ( sup_sup_int @ X @ ( sup_sup_int @ X @ Y ) )
% 0.29/0.48        = ( sup_sup_int @ X @ Y ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_aci(8)
% 0.29/0.48  thf(fact_275_sup__inf__distrib2,axiom,
% 0.29/0.48      ! [Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ Z ) @ X )
% 0.29/0.48        = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ X ) @ ( sup_su6327502436637775413at_nat @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_distrib2
% 0.29/0.48  thf(fact_276_sup__inf__distrib2,axiom,
% 0.29/0.48      ! [Y: product_prod_int_int > $o,Z: product_prod_int_int > $o,X: product_prod_int_int > $o] :
% 0.29/0.48        ( ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ Y @ Z ) @ X )
% 0.29/0.48        = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ Y @ X ) @ ( sup_su8463660629351352368_int_o @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_distrib2
% 0.29/0.48  thf(fact_277_sup__inf__distrib2,axiom,
% 0.29/0.48      ! [Y: list_char > $o,Z: list_char > $o,X: list_char > $o] :
% 0.29/0.48        ( ( sup_sup_list_char_o @ ( inf_inf_list_char_o @ Y @ Z ) @ X )
% 0.29/0.48        = ( inf_inf_list_char_o @ ( sup_sup_list_char_o @ Y @ X ) @ ( sup_sup_list_char_o @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_distrib2
% 0.29/0.48  thf(fact_278_sup__inf__distrib2,axiom,
% 0.29/0.48      ! [Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ Y @ Z ) @ X )
% 0.29/0.48        = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ Y @ X ) @ ( sup_su3035147773818789531at_nat @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_distrib2
% 0.29/0.48  thf(fact_279_sup__inf__distrib2,axiom,
% 0.29/0.48      ! [Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ Y @ Z ) @ X )
% 0.29/0.48        = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ Y @ X ) @ ( sup_su5525570899277871387at_nat @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_distrib2
% 0.29/0.48  thf(fact_280_sup__inf__distrib2,axiom,
% 0.29/0.48      ! [Y: set_nat,Z: set_nat,X: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ Z ) @ X )
% 0.29/0.48        = ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ X ) @ ( sup_sup_set_nat @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_distrib2
% 0.29/0.48  thf(fact_281_sup__inf__distrib2,axiom,
% 0.29/0.48      ! [Y: nat,Z: nat,X: nat] :
% 0.29/0.48        ( ( sup_sup_nat @ ( inf_inf_nat @ Y @ Z ) @ X )
% 0.29/0.48        = ( inf_inf_nat @ ( sup_sup_nat @ Y @ X ) @ ( sup_sup_nat @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_distrib2
% 0.29/0.48  thf(fact_282_sup__inf__distrib2,axiom,
% 0.29/0.48      ! [Y: int,Z: int,X: int] :
% 0.29/0.48        ( ( sup_sup_int @ ( inf_inf_int @ Y @ Z ) @ X )
% 0.29/0.48        = ( inf_inf_int @ ( sup_sup_int @ Y @ X ) @ ( sup_sup_int @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_distrib2
% 0.29/0.48  thf(fact_283_sup__inf__distrib1,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 0.29/0.48        = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_distrib1
% 0.29/0.48  thf(fact_284_sup__inf__distrib1,axiom,
% 0.29/0.48      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 0.29/0.48        ( ( sup_su8463660629351352368_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) )
% 0.29/0.48        = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ X @ Y ) @ ( sup_su8463660629351352368_int_o @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_distrib1
% 0.29/0.48  thf(fact_285_sup__inf__distrib1,axiom,
% 0.29/0.48      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 0.29/0.48        ( ( sup_sup_list_char_o @ X @ ( inf_inf_list_char_o @ Y @ Z ) )
% 0.29/0.48        = ( inf_inf_list_char_o @ ( sup_sup_list_char_o @ X @ Y ) @ ( sup_sup_list_char_o @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_distrib1
% 0.29/0.48  thf(fact_286_sup__inf__distrib1,axiom,
% 0.29/0.48      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ X @ ( inf_in1697001100524423349at_nat @ Y @ Z ) )
% 0.29/0.48        = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ ( sup_su3035147773818789531at_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_distrib1
% 0.29/0.48  thf(fact_287_sup__inf__distrib1,axiom,
% 0.29/0.48      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ Y @ Z ) )
% 0.29/0.48        = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_distrib1
% 0.29/0.48  thf(fact_288_sup__inf__distrib1,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 0.29/0.48        = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_distrib1
% 0.29/0.48  thf(fact_289_sup__inf__distrib1,axiom,
% 0.29/0.48      ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.48        ( ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 0.29/0.48        = ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_distrib1
% 0.29/0.48  thf(fact_290_sup__inf__distrib1,axiom,
% 0.29/0.48      ! [X: int,Y: int,Z: int] :
% 0.29/0.48        ( ( sup_sup_int @ X @ ( inf_inf_int @ Y @ Z ) )
% 0.29/0.48        = ( inf_inf_int @ ( sup_sup_int @ X @ Y ) @ ( sup_sup_int @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % sup_inf_distrib1
% 0.29/0.48  thf(fact_291_inf__sup__distrib2,axiom,
% 0.29/0.48      ! [Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ Z ) @ X )
% 0.29/0.48        = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ X ) @ ( inf_in2572325071724192079at_nat @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_distrib2
% 0.29/0.48  thf(fact_292_inf__sup__distrib2,axiom,
% 0.29/0.48      ! [Y: product_prod_int_int > $o,Z: product_prod_int_int > $o,X: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ Y @ Z ) @ X )
% 0.29/0.48        = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ Y @ X ) @ ( inf_in3604695632404883862_int_o @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_distrib2
% 0.29/0.48  thf(fact_293_inf__sup__distrib2,axiom,
% 0.29/0.48      ! [Y: list_char > $o,Z: list_char > $o,X: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ ( sup_sup_list_char_o @ Y @ Z ) @ X )
% 0.29/0.48        = ( sup_sup_list_char_o @ ( inf_inf_list_char_o @ Y @ X ) @ ( inf_inf_list_char_o @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_distrib2
% 0.29/0.48  thf(fact_294_inf__sup__distrib2,axiom,
% 0.29/0.48      ! [Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ Y @ Z ) @ X )
% 0.29/0.48        = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ Y @ X ) @ ( inf_in1697001100524423349at_nat @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_distrib2
% 0.29/0.48  thf(fact_295_inf__sup__distrib2,axiom,
% 0.29/0.48      ! [Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ Y @ Z ) @ X )
% 0.29/0.48        = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ Y @ X ) @ ( inf_in7913087082777306421at_nat @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_distrib2
% 0.29/0.48  thf(fact_296_inf__sup__distrib2,axiom,
% 0.29/0.48      ! [Y: set_nat,Z: set_nat,X: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ Z ) @ X )
% 0.29/0.48        = ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ X ) @ ( inf_inf_set_nat @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_distrib2
% 0.29/0.48  thf(fact_297_inf__sup__distrib2,axiom,
% 0.29/0.48      ! [Y: nat,Z: nat,X: nat] :
% 0.29/0.48        ( ( inf_inf_nat @ ( sup_sup_nat @ Y @ Z ) @ X )
% 0.29/0.48        = ( sup_sup_nat @ ( inf_inf_nat @ Y @ X ) @ ( inf_inf_nat @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_distrib2
% 0.29/0.48  thf(fact_298_inf__sup__distrib2,axiom,
% 0.29/0.48      ! [Y: int,Z: int,X: int] :
% 0.29/0.48        ( ( inf_inf_int @ ( sup_sup_int @ Y @ Z ) @ X )
% 0.29/0.48        = ( sup_sup_int @ ( inf_inf_int @ Y @ X ) @ ( inf_inf_int @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_distrib2
% 0.29/0.48  thf(fact_299_inf__sup__distrib1,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) )
% 0.29/0.48        = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_distrib1
% 0.29/0.48  thf(fact_300_inf__sup__distrib1,axiom,
% 0.29/0.48      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ X @ ( sup_su8463660629351352368_int_o @ Y @ Z ) )
% 0.29/0.48        = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ ( inf_in3604695632404883862_int_o @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_distrib1
% 0.29/0.48  thf(fact_301_inf__sup__distrib1,axiom,
% 0.29/0.48      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ X @ ( sup_sup_list_char_o @ Y @ Z ) )
% 0.29/0.48        = ( sup_sup_list_char_o @ ( inf_inf_list_char_o @ X @ Y ) @ ( inf_inf_list_char_o @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_distrib1
% 0.29/0.48  thf(fact_302_inf__sup__distrib1,axiom,
% 0.29/0.48      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( inf_in1697001100524423349at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) )
% 0.29/0.48        = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) @ ( inf_in1697001100524423349at_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_distrib1
% 0.29/0.48  thf(fact_303_inf__sup__distrib1,axiom,
% 0.29/0.48      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) )
% 0.29/0.48        = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ ( inf_in7913087082777306421at_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_distrib1
% 0.29/0.48  thf(fact_304_inf__sup__distrib1,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 0.29/0.48        = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_distrib1
% 0.29/0.48  thf(fact_305_inf__sup__distrib1,axiom,
% 0.29/0.48      ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.48        ( ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z ) )
% 0.29/0.48        = ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_distrib1
% 0.29/0.48  thf(fact_306_inf__sup__distrib1,axiom,
% 0.29/0.48      ! [X: int,Y: int,Z: int] :
% 0.29/0.48        ( ( inf_inf_int @ X @ ( sup_sup_int @ Y @ Z ) )
% 0.29/0.48        = ( sup_sup_int @ ( inf_inf_int @ X @ Y ) @ ( inf_inf_int @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % inf_sup_distrib1
% 0.29/0.48  thf(fact_307_distrib__imp2,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ! [X2: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
% 0.29/0.48            ( ( sup_su6327502436637775413at_nat @ X2 @ ( inf_in2572325071724192079at_nat @ Y2 @ Z2 ) )
% 0.29/0.48            = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X2 @ Y2 ) @ ( sup_su6327502436637775413at_nat @ X2 @ Z2 ) ) )
% 0.29/0.48       => ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) )
% 0.29/0.48          = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % distrib_imp2
% 0.29/0.48  thf(fact_308_distrib__imp2,axiom,
% 0.29/0.48      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 0.29/0.48        ( ! [X2: product_prod_int_int > $o,Y2: product_prod_int_int > $o,Z2: product_prod_int_int > $o] :
% 0.29/0.48            ( ( sup_su8463660629351352368_int_o @ X2 @ ( inf_in3604695632404883862_int_o @ Y2 @ Z2 ) )
% 0.29/0.48            = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ X2 @ Y2 ) @ ( sup_su8463660629351352368_int_o @ X2 @ Z2 ) ) )
% 0.29/0.48       => ( ( inf_in3604695632404883862_int_o @ X @ ( sup_su8463660629351352368_int_o @ Y @ Z ) )
% 0.29/0.48          = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ ( inf_in3604695632404883862_int_o @ X @ Z ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % distrib_imp2
% 0.29/0.48  thf(fact_309_distrib__imp2,axiom,
% 0.29/0.48      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 0.29/0.48        ( ! [X2: list_char > $o,Y2: list_char > $o,Z2: list_char > $o] :
% 0.29/0.48            ( ( sup_sup_list_char_o @ X2 @ ( inf_inf_list_char_o @ Y2 @ Z2 ) )
% 0.29/0.48            = ( inf_inf_list_char_o @ ( sup_sup_list_char_o @ X2 @ Y2 ) @ ( sup_sup_list_char_o @ X2 @ Z2 ) ) )
% 0.29/0.48       => ( ( inf_inf_list_char_o @ X @ ( sup_sup_list_char_o @ Y @ Z ) )
% 0.29/0.48          = ( sup_sup_list_char_o @ ( inf_inf_list_char_o @ X @ Y ) @ ( inf_inf_list_char_o @ X @ Z ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % distrib_imp2
% 0.29/0.48  thf(fact_310_distrib__imp2,axiom,
% 0.29/0.48      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ! [X2: set_Pr8551490117392284871at_nat,Y2: set_Pr8551490117392284871at_nat,Z2: set_Pr8551490117392284871at_nat] :
% 0.29/0.48            ( ( sup_su3035147773818789531at_nat @ X2 @ ( inf_in1697001100524423349at_nat @ Y2 @ Z2 ) )
% 0.29/0.48            = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ X2 @ Y2 ) @ ( sup_su3035147773818789531at_nat @ X2 @ Z2 ) ) )
% 0.29/0.48       => ( ( inf_in1697001100524423349at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) )
% 0.29/0.48          = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) @ ( inf_in1697001100524423349at_nat @ X @ Z ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % distrib_imp2
% 0.29/0.48  thf(fact_311_distrib__imp2,axiom,
% 0.29/0.48      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ! [X2: set_Pr4329608150637261639at_nat,Y2: set_Pr4329608150637261639at_nat,Z2: set_Pr4329608150637261639at_nat] :
% 0.29/0.48            ( ( sup_su5525570899277871387at_nat @ X2 @ ( inf_in7913087082777306421at_nat @ Y2 @ Z2 ) )
% 0.29/0.48            = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X2 @ Y2 ) @ ( sup_su5525570899277871387at_nat @ X2 @ Z2 ) ) )
% 0.29/0.48       => ( ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) )
% 0.29/0.48          = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ ( inf_in7913087082777306421at_nat @ X @ Z ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % distrib_imp2
% 0.29/0.48  thf(fact_312_distrib__imp2,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.29/0.48        ( ! [X2: set_nat,Y2: set_nat,Z2: set_nat] :
% 0.29/0.48            ( ( sup_sup_set_nat @ X2 @ ( inf_inf_set_nat @ Y2 @ Z2 ) )
% 0.29/0.48            = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X2 @ Y2 ) @ ( sup_sup_set_nat @ X2 @ Z2 ) ) )
% 0.29/0.48       => ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 0.29/0.48          = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % distrib_imp2
% 0.29/0.48  thf(fact_313_distrib__imp2,axiom,
% 0.29/0.48      ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.48        ( ! [X2: nat,Y2: nat,Z2: nat] :
% 0.29/0.48            ( ( sup_sup_nat @ X2 @ ( inf_inf_nat @ Y2 @ Z2 ) )
% 0.29/0.48            = ( inf_inf_nat @ ( sup_sup_nat @ X2 @ Y2 ) @ ( sup_sup_nat @ X2 @ Z2 ) ) )
% 0.29/0.48       => ( ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z ) )
% 0.29/0.48          = ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % distrib_imp2
% 0.29/0.48  thf(fact_314_distrib__imp2,axiom,
% 0.29/0.48      ! [X: int,Y: int,Z: int] :
% 0.29/0.48        ( ! [X2: int,Y2: int,Z2: int] :
% 0.29/0.48            ( ( sup_sup_int @ X2 @ ( inf_inf_int @ Y2 @ Z2 ) )
% 0.29/0.48            = ( inf_inf_int @ ( sup_sup_int @ X2 @ Y2 ) @ ( sup_sup_int @ X2 @ Z2 ) ) )
% 0.29/0.48       => ( ( inf_inf_int @ X @ ( sup_sup_int @ Y @ Z ) )
% 0.29/0.48          = ( sup_sup_int @ ( inf_inf_int @ X @ Y ) @ ( inf_inf_int @ X @ Z ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % distrib_imp2
% 0.29/0.48  thf(fact_315_distrib__imp1,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ! [X2: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
% 0.29/0.48            ( ( inf_in2572325071724192079at_nat @ X2 @ ( sup_su6327502436637775413at_nat @ Y2 @ Z2 ) )
% 0.29/0.48            = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X2 @ Y2 ) @ ( inf_in2572325071724192079at_nat @ X2 @ Z2 ) ) )
% 0.29/0.48       => ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 0.29/0.48          = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % distrib_imp1
% 0.29/0.48  thf(fact_316_distrib__imp1,axiom,
% 0.29/0.48      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 0.29/0.48        ( ! [X2: product_prod_int_int > $o,Y2: product_prod_int_int > $o,Z2: product_prod_int_int > $o] :
% 0.29/0.48            ( ( inf_in3604695632404883862_int_o @ X2 @ ( sup_su8463660629351352368_int_o @ Y2 @ Z2 ) )
% 0.29/0.48            = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ X2 @ Y2 ) @ ( inf_in3604695632404883862_int_o @ X2 @ Z2 ) ) )
% 0.29/0.48       => ( ( sup_su8463660629351352368_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) )
% 0.29/0.48          = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ X @ Y ) @ ( sup_su8463660629351352368_int_o @ X @ Z ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % distrib_imp1
% 0.29/0.48  thf(fact_317_distrib__imp1,axiom,
% 0.29/0.48      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 0.29/0.48        ( ! [X2: list_char > $o,Y2: list_char > $o,Z2: list_char > $o] :
% 0.29/0.48            ( ( inf_inf_list_char_o @ X2 @ ( sup_sup_list_char_o @ Y2 @ Z2 ) )
% 0.29/0.48            = ( sup_sup_list_char_o @ ( inf_inf_list_char_o @ X2 @ Y2 ) @ ( inf_inf_list_char_o @ X2 @ Z2 ) ) )
% 0.29/0.48       => ( ( sup_sup_list_char_o @ X @ ( inf_inf_list_char_o @ Y @ Z ) )
% 0.29/0.48          = ( inf_inf_list_char_o @ ( sup_sup_list_char_o @ X @ Y ) @ ( sup_sup_list_char_o @ X @ Z ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % distrib_imp1
% 0.29/0.48  thf(fact_318_distrib__imp1,axiom,
% 0.29/0.48      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ! [X2: set_Pr8551490117392284871at_nat,Y2: set_Pr8551490117392284871at_nat,Z2: set_Pr8551490117392284871at_nat] :
% 0.29/0.48            ( ( inf_in1697001100524423349at_nat @ X2 @ ( sup_su3035147773818789531at_nat @ Y2 @ Z2 ) )
% 0.29/0.48            = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ X2 @ Y2 ) @ ( inf_in1697001100524423349at_nat @ X2 @ Z2 ) ) )
% 0.29/0.48       => ( ( sup_su3035147773818789531at_nat @ X @ ( inf_in1697001100524423349at_nat @ Y @ Z ) )
% 0.29/0.48          = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ ( sup_su3035147773818789531at_nat @ X @ Z ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % distrib_imp1
% 0.29/0.48  thf(fact_319_distrib__imp1,axiom,
% 0.29/0.48      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ! [X2: set_Pr4329608150637261639at_nat,Y2: set_Pr4329608150637261639at_nat,Z2: set_Pr4329608150637261639at_nat] :
% 0.29/0.48            ( ( inf_in7913087082777306421at_nat @ X2 @ ( sup_su5525570899277871387at_nat @ Y2 @ Z2 ) )
% 0.29/0.48            = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X2 @ Y2 ) @ ( inf_in7913087082777306421at_nat @ X2 @ Z2 ) ) )
% 0.29/0.48       => ( ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ Y @ Z ) )
% 0.29/0.48          = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % distrib_imp1
% 0.29/0.48  thf(fact_320_distrib__imp1,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.29/0.48        ( ! [X2: set_nat,Y2: set_nat,Z2: set_nat] :
% 0.29/0.48            ( ( inf_inf_set_nat @ X2 @ ( sup_sup_set_nat @ Y2 @ Z2 ) )
% 0.29/0.48            = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X2 @ Y2 ) @ ( inf_inf_set_nat @ X2 @ Z2 ) ) )
% 0.29/0.48       => ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 0.29/0.48          = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % distrib_imp1
% 0.29/0.48  thf(fact_321_distrib__imp1,axiom,
% 0.29/0.48      ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.48        ( ! [X2: nat,Y2: nat,Z2: nat] :
% 0.29/0.48            ( ( inf_inf_nat @ X2 @ ( sup_sup_nat @ Y2 @ Z2 ) )
% 0.29/0.48            = ( sup_sup_nat @ ( inf_inf_nat @ X2 @ Y2 ) @ ( inf_inf_nat @ X2 @ Z2 ) ) )
% 0.29/0.48       => ( ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 0.29/0.48          = ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % distrib_imp1
% 0.29/0.48  thf(fact_322_distrib__imp1,axiom,
% 0.29/0.48      ! [X: int,Y: int,Z: int] :
% 0.29/0.48        ( ! [X2: int,Y2: int,Z2: int] :
% 0.29/0.48            ( ( inf_inf_int @ X2 @ ( sup_sup_int @ Y2 @ Z2 ) )
% 0.29/0.48            = ( sup_sup_int @ ( inf_inf_int @ X2 @ Y2 ) @ ( inf_inf_int @ X2 @ Z2 ) ) )
% 0.29/0.48       => ( ( sup_sup_int @ X @ ( inf_inf_int @ Y @ Z ) )
% 0.29/0.48          = ( inf_inf_int @ ( sup_sup_int @ X @ Y ) @ ( sup_sup_int @ X @ Z ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % distrib_imp1
% 0.29/0.48  thf(fact_323_boolean__algebra_Oconj__zero__right,axiom,
% 0.29/0.48      ! [X: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ X @ bot_bo8147686125503663512_int_o )
% 0.29/0.48        = bot_bo8147686125503663512_int_o ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_zero_right
% 0.29/0.48  thf(fact_324_boolean__algebra_Oconj__zero__right,axiom,
% 0.29/0.48      ! [X: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ X @ bot_bot_list_char_o )
% 0.29/0.48        = bot_bot_list_char_o ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_zero_right
% 0.29/0.48  thf(fact_325_boolean__algebra_Oconj__zero__right,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ X @ bot_bo2099793752762293965at_nat )
% 0.29/0.48        = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_zero_right
% 0.29/0.48  thf(fact_326_boolean__algebra_Oconj__zero__right,axiom,
% 0.29/0.48      ! [X: set_o] :
% 0.29/0.48        ( ( inf_inf_set_o @ X @ bot_bot_set_o )
% 0.29/0.48        = bot_bot_set_o ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_zero_right
% 0.29/0.48  thf(fact_327_boolean__algebra_Oconj__zero__right,axiom,
% 0.29/0.48      ! [X: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ X @ bot_bot_set_nat )
% 0.29/0.48        = bot_bot_set_nat ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_zero_right
% 0.29/0.48  thf(fact_328_boolean__algebra_Oconj__zero__right,axiom,
% 0.29/0.48      ! [X: set_int] :
% 0.29/0.48        ( ( inf_inf_set_int @ X @ bot_bot_set_int )
% 0.29/0.48        = bot_bot_set_int ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_zero_right
% 0.29/0.48  thf(fact_329_boolean__algebra_Oconj__zero__left,axiom,
% 0.29/0.48      ! [X: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ bot_bo8147686125503663512_int_o @ X )
% 0.29/0.48        = bot_bo8147686125503663512_int_o ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_zero_left
% 0.29/0.48  thf(fact_330_boolean__algebra_Oconj__zero__left,axiom,
% 0.29/0.48      ! [X: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ bot_bot_list_char_o @ X )
% 0.29/0.48        = bot_bot_list_char_o ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_zero_left
% 0.29/0.48  thf(fact_331_boolean__algebra_Oconj__zero__left,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ bot_bo2099793752762293965at_nat @ X )
% 0.29/0.48        = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_zero_left
% 0.29/0.48  thf(fact_332_boolean__algebra_Oconj__zero__left,axiom,
% 0.29/0.48      ! [X: set_o] :
% 0.29/0.48        ( ( inf_inf_set_o @ bot_bot_set_o @ X )
% 0.29/0.48        = bot_bot_set_o ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_zero_left
% 0.29/0.48  thf(fact_333_boolean__algebra_Oconj__zero__left,axiom,
% 0.29/0.48      ! [X: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ bot_bot_set_nat @ X )
% 0.29/0.48        = bot_bot_set_nat ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_zero_left
% 0.29/0.48  thf(fact_334_boolean__algebra_Oconj__zero__left,axiom,
% 0.29/0.48      ! [X: set_int] :
% 0.29/0.48        ( ( inf_inf_set_int @ bot_bot_set_int @ X )
% 0.29/0.48        = bot_bot_set_int ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_zero_left
% 0.29/0.48  thf(fact_335_boolean__algebra_Odisj__conj__distrib2,axiom,
% 0.29/0.48      ! [Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ Z ) @ X )
% 0.29/0.48        = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ X ) @ ( sup_su6327502436637775413at_nat @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.disj_conj_distrib2
% 0.29/0.48  thf(fact_336_boolean__algebra_Odisj__conj__distrib2,axiom,
% 0.29/0.48      ! [Y: product_prod_int_int > $o,Z: product_prod_int_int > $o,X: product_prod_int_int > $o] :
% 0.29/0.48        ( ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ Y @ Z ) @ X )
% 0.29/0.48        = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ Y @ X ) @ ( sup_su8463660629351352368_int_o @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.disj_conj_distrib2
% 0.29/0.48  thf(fact_337_boolean__algebra_Odisj__conj__distrib2,axiom,
% 0.29/0.48      ! [Y: list_char > $o,Z: list_char > $o,X: list_char > $o] :
% 0.29/0.48        ( ( sup_sup_list_char_o @ ( inf_inf_list_char_o @ Y @ Z ) @ X )
% 0.29/0.48        = ( inf_inf_list_char_o @ ( sup_sup_list_char_o @ Y @ X ) @ ( sup_sup_list_char_o @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.disj_conj_distrib2
% 0.29/0.48  thf(fact_338_boolean__algebra_Odisj__conj__distrib2,axiom,
% 0.29/0.48      ! [Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ Y @ Z ) @ X )
% 0.29/0.48        = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ Y @ X ) @ ( sup_su3035147773818789531at_nat @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.disj_conj_distrib2
% 0.29/0.48  thf(fact_339_boolean__algebra_Odisj__conj__distrib2,axiom,
% 0.29/0.48      ! [Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ Y @ Z ) @ X )
% 0.29/0.48        = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ Y @ X ) @ ( sup_su5525570899277871387at_nat @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.disj_conj_distrib2
% 0.29/0.48  thf(fact_340_boolean__algebra_Odisj__conj__distrib2,axiom,
% 0.29/0.48      ! [Y: set_nat,Z: set_nat,X: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ Z ) @ X )
% 0.29/0.48        = ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ X ) @ ( sup_sup_set_nat @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.disj_conj_distrib2
% 0.29/0.48  thf(fact_341_boolean__algebra_Oconj__disj__distrib2,axiom,
% 0.29/0.48      ! [Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ Z ) @ X )
% 0.29/0.48        = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ X ) @ ( inf_in2572325071724192079at_nat @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_disj_distrib2
% 0.29/0.48  thf(fact_342_boolean__algebra_Oconj__disj__distrib2,axiom,
% 0.29/0.48      ! [Y: product_prod_int_int > $o,Z: product_prod_int_int > $o,X: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ Y @ Z ) @ X )
% 0.29/0.48        = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ Y @ X ) @ ( inf_in3604695632404883862_int_o @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_disj_distrib2
% 0.29/0.48  thf(fact_343_boolean__algebra_Oconj__disj__distrib2,axiom,
% 0.29/0.48      ! [Y: list_char > $o,Z: list_char > $o,X: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ ( sup_sup_list_char_o @ Y @ Z ) @ X )
% 0.29/0.48        = ( sup_sup_list_char_o @ ( inf_inf_list_char_o @ Y @ X ) @ ( inf_inf_list_char_o @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_disj_distrib2
% 0.29/0.48  thf(fact_344_boolean__algebra_Oconj__disj__distrib2,axiom,
% 0.29/0.48      ! [Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ Y @ Z ) @ X )
% 0.29/0.48        = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ Y @ X ) @ ( inf_in1697001100524423349at_nat @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_disj_distrib2
% 0.29/0.48  thf(fact_345_boolean__algebra_Oconj__disj__distrib2,axiom,
% 0.29/0.48      ! [Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ Y @ Z ) @ X )
% 0.29/0.48        = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ Y @ X ) @ ( inf_in7913087082777306421at_nat @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_disj_distrib2
% 0.29/0.48  thf(fact_346_boolean__algebra_Oconj__disj__distrib2,axiom,
% 0.29/0.48      ! [Y: set_nat,Z: set_nat,X: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ Z ) @ X )
% 0.29/0.48        = ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ X ) @ ( inf_inf_set_nat @ Z @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_disj_distrib2
% 0.29/0.48  thf(fact_347_boolean__algebra_Odisj__conj__distrib,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 0.29/0.48        = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.disj_conj_distrib
% 0.29/0.48  thf(fact_348_boolean__algebra_Odisj__conj__distrib,axiom,
% 0.29/0.48      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 0.29/0.48        ( ( sup_su8463660629351352368_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) )
% 0.29/0.48        = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ X @ Y ) @ ( sup_su8463660629351352368_int_o @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.disj_conj_distrib
% 0.29/0.48  thf(fact_349_boolean__algebra_Odisj__conj__distrib,axiom,
% 0.29/0.48      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 0.29/0.48        ( ( sup_sup_list_char_o @ X @ ( inf_inf_list_char_o @ Y @ Z ) )
% 0.29/0.48        = ( inf_inf_list_char_o @ ( sup_sup_list_char_o @ X @ Y ) @ ( sup_sup_list_char_o @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.disj_conj_distrib
% 0.29/0.48  thf(fact_350_boolean__algebra_Odisj__conj__distrib,axiom,
% 0.29/0.48      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ X @ ( inf_in1697001100524423349at_nat @ Y @ Z ) )
% 0.29/0.48        = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ ( sup_su3035147773818789531at_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.disj_conj_distrib
% 0.29/0.48  thf(fact_351_boolean__algebra_Odisj__conj__distrib,axiom,
% 0.29/0.48      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ Y @ Z ) )
% 0.29/0.48        = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.disj_conj_distrib
% 0.29/0.48  thf(fact_352_boolean__algebra_Odisj__conj__distrib,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 0.29/0.48        = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.disj_conj_distrib
% 0.29/0.48  thf(fact_353_boolean__algebra_Oconj__disj__distrib,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) )
% 0.29/0.48        = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_disj_distrib
% 0.29/0.48  thf(fact_354_boolean__algebra_Oconj__disj__distrib,axiom,
% 0.29/0.48      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 0.29/0.48        ( ( inf_in3604695632404883862_int_o @ X @ ( sup_su8463660629351352368_int_o @ Y @ Z ) )
% 0.29/0.48        = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ ( inf_in3604695632404883862_int_o @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_disj_distrib
% 0.29/0.48  thf(fact_355_boolean__algebra_Oconj__disj__distrib,axiom,
% 0.29/0.48      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 0.29/0.48        ( ( inf_inf_list_char_o @ X @ ( sup_sup_list_char_o @ Y @ Z ) )
% 0.29/0.48        = ( sup_sup_list_char_o @ ( inf_inf_list_char_o @ X @ Y ) @ ( inf_inf_list_char_o @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_disj_distrib
% 0.29/0.48  thf(fact_356_boolean__algebra_Oconj__disj__distrib,axiom,
% 0.29/0.48      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( inf_in1697001100524423349at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) )
% 0.29/0.48        = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) @ ( inf_in1697001100524423349at_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_disj_distrib
% 0.29/0.48  thf(fact_357_boolean__algebra_Oconj__disj__distrib,axiom,
% 0.29/0.48      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) )
% 0.29/0.48        = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ ( inf_in7913087082777306421at_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_disj_distrib
% 0.29/0.48  thf(fact_358_boolean__algebra_Oconj__disj__distrib,axiom,
% 0.29/0.48      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.29/0.48        ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 0.29/0.48        = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.conj_disj_distrib
% 0.29/0.48  thf(fact_359_boolean__algebra_Odisj__zero__right,axiom,
% 0.29/0.48      ! [X: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( sup_su3035147773818789531at_nat @ X @ bot_bo8422036546324065075at_nat )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.disj_zero_right
% 0.29/0.48  thf(fact_360_boolean__algebra_Odisj__zero__right,axiom,
% 0.29/0.48      ! [X: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( sup_su5525570899277871387at_nat @ X @ bot_bo228742789529271731at_nat )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.disj_zero_right
% 0.29/0.48  thf(fact_361_boolean__algebra_Odisj__zero__right,axiom,
% 0.29/0.48      ! [X: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( sup_su6327502436637775413at_nat @ X @ bot_bo2099793752762293965at_nat )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.disj_zero_right
% 0.29/0.48  thf(fact_362_boolean__algebra_Odisj__zero__right,axiom,
% 0.29/0.48      ! [X: set_o] :
% 0.29/0.48        ( ( sup_sup_set_o @ X @ bot_bot_set_o )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.disj_zero_right
% 0.29/0.48  thf(fact_363_boolean__algebra_Odisj__zero__right,axiom,
% 0.29/0.48      ! [X: set_nat] :
% 0.29/0.48        ( ( sup_sup_set_nat @ X @ bot_bot_set_nat )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.disj_zero_right
% 0.29/0.48  thf(fact_364_boolean__algebra_Odisj__zero__right,axiom,
% 0.29/0.48      ! [X: set_int] :
% 0.29/0.48        ( ( sup_sup_set_int @ X @ bot_bot_set_int )
% 0.29/0.48        = X ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra.disj_zero_right
% 0.29/0.48  thf(fact_365_one__assn__proper,axiom,
% 0.29/0.48      proper @ one_assn_raw ).
% 0.29/0.48  
% 0.29/0.48  % one_assn_proper
% 0.29/0.48  thf(fact_366_type__definition__assn,axiom,
% 0.29/0.48      type_d3909072315231072503_nat_o @ rep_assn @ abs_assn @ ( collec939566748876313656_nat_o @ proper ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition_assn
% 0.29/0.48  thf(fact_367_boolean__algebra__cancel_Osup2,axiom,
% 0.29/0.48      ! [B2: set_Pr8551490117392284871at_nat,K: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( B2
% 0.29/0.48          = ( sup_su3035147773818789531at_nat @ K @ B ) )
% 0.29/0.48       => ( ( sup_su3035147773818789531at_nat @ A @ B2 )
% 0.29/0.48          = ( sup_su3035147773818789531at_nat @ K @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra_cancel.sup2
% 0.29/0.48  thf(fact_368_boolean__algebra__cancel_Osup2,axiom,
% 0.29/0.48      ! [B2: set_Pr4329608150637261639at_nat,K: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( B2
% 0.29/0.48          = ( sup_su5525570899277871387at_nat @ K @ B ) )
% 0.29/0.48       => ( ( sup_su5525570899277871387at_nat @ A @ B2 )
% 0.29/0.48          = ( sup_su5525570899277871387at_nat @ K @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra_cancel.sup2
% 0.29/0.48  thf(fact_369_boolean__algebra__cancel_Osup2,axiom,
% 0.29/0.48      ! [B2: set_nat,K: set_nat,B: set_nat,A: set_nat] :
% 0.29/0.48        ( ( B2
% 0.29/0.48          = ( sup_sup_set_nat @ K @ B ) )
% 0.29/0.48       => ( ( sup_sup_set_nat @ A @ B2 )
% 0.29/0.48          = ( sup_sup_set_nat @ K @ ( sup_sup_set_nat @ A @ B ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra_cancel.sup2
% 0.29/0.48  thf(fact_370_boolean__algebra__cancel_Osup2,axiom,
% 0.29/0.48      ! [B2: nat,K: nat,B: nat,A: nat] :
% 0.29/0.48        ( ( B2
% 0.29/0.48          = ( sup_sup_nat @ K @ B ) )
% 0.29/0.48       => ( ( sup_sup_nat @ A @ B2 )
% 0.29/0.48          = ( sup_sup_nat @ K @ ( sup_sup_nat @ A @ B ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra_cancel.sup2
% 0.29/0.48  thf(fact_371_boolean__algebra__cancel_Osup2,axiom,
% 0.29/0.48      ! [B2: int,K: int,B: int,A: int] :
% 0.29/0.48        ( ( B2
% 0.29/0.48          = ( sup_sup_int @ K @ B ) )
% 0.29/0.48       => ( ( sup_sup_int @ A @ B2 )
% 0.29/0.48          = ( sup_sup_int @ K @ ( sup_sup_int @ A @ B ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra_cancel.sup2
% 0.29/0.48  thf(fact_372_boolean__algebra__cancel_Osup1,axiom,
% 0.29/0.48      ! [A2: set_Pr8551490117392284871at_nat,K: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 0.29/0.48        ( ( A2
% 0.29/0.48          = ( sup_su3035147773818789531at_nat @ K @ A ) )
% 0.29/0.48       => ( ( sup_su3035147773818789531at_nat @ A2 @ B )
% 0.29/0.48          = ( sup_su3035147773818789531at_nat @ K @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra_cancel.sup1
% 0.29/0.48  thf(fact_373_boolean__algebra__cancel_Osup1,axiom,
% 0.29/0.48      ! [A2: set_Pr4329608150637261639at_nat,K: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.29/0.48        ( ( A2
% 0.29/0.48          = ( sup_su5525570899277871387at_nat @ K @ A ) )
% 0.29/0.48       => ( ( sup_su5525570899277871387at_nat @ A2 @ B )
% 0.29/0.48          = ( sup_su5525570899277871387at_nat @ K @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra_cancel.sup1
% 0.29/0.48  thf(fact_374_boolean__algebra__cancel_Osup1,axiom,
% 0.29/0.48      ! [A2: set_nat,K: set_nat,A: set_nat,B: set_nat] :
% 0.29/0.48        ( ( A2
% 0.29/0.48          = ( sup_sup_set_nat @ K @ A ) )
% 0.29/0.48       => ( ( sup_sup_set_nat @ A2 @ B )
% 0.29/0.48          = ( sup_sup_set_nat @ K @ ( sup_sup_set_nat @ A @ B ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra_cancel.sup1
% 0.29/0.48  thf(fact_375_boolean__algebra__cancel_Osup1,axiom,
% 0.29/0.48      ! [A2: nat,K: nat,A: nat,B: nat] :
% 0.29/0.48        ( ( A2
% 0.29/0.48          = ( sup_sup_nat @ K @ A ) )
% 0.29/0.48       => ( ( sup_sup_nat @ A2 @ B )
% 0.29/0.48          = ( sup_sup_nat @ K @ ( sup_sup_nat @ A @ B ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra_cancel.sup1
% 0.29/0.48  thf(fact_376_boolean__algebra__cancel_Osup1,axiom,
% 0.29/0.48      ! [A2: int,K: int,A: int,B: int] :
% 0.29/0.48        ( ( A2
% 0.29/0.48          = ( sup_sup_int @ K @ A ) )
% 0.29/0.48       => ( ( sup_sup_int @ A2 @ B )
% 0.29/0.48          = ( sup_sup_int @ K @ ( sup_sup_int @ A @ B ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra_cancel.sup1
% 0.29/0.48  thf(fact_377_boolean__algebra__cancel_Oinf1,axiom,
% 0.29/0.48      ! [A2: set_Pr1261947904930325089at_nat,K: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( A2
% 0.29/0.48          = ( inf_in2572325071724192079at_nat @ K @ A ) )
% 0.29/0.48       => ( ( inf_in2572325071724192079at_nat @ A2 @ B )
% 0.29/0.48          = ( inf_in2572325071724192079at_nat @ K @ ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra_cancel.inf1
% 0.29/0.48  thf(fact_378_boolean__algebra__cancel_Oinf1,axiom,
% 0.29/0.48      ! [A2: set_nat,K: set_nat,A: set_nat,B: set_nat] :
% 0.29/0.48        ( ( A2
% 0.29/0.48          = ( inf_inf_set_nat @ K @ A ) )
% 0.29/0.48       => ( ( inf_inf_set_nat @ A2 @ B )
% 0.29/0.48          = ( inf_inf_set_nat @ K @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra_cancel.inf1
% 0.29/0.48  thf(fact_379_boolean__algebra__cancel_Oinf1,axiom,
% 0.29/0.48      ! [A2: nat,K: nat,A: nat,B: nat] :
% 0.29/0.48        ( ( A2
% 0.29/0.48          = ( inf_inf_nat @ K @ A ) )
% 0.29/0.48       => ( ( inf_inf_nat @ A2 @ B )
% 0.29/0.48          = ( inf_inf_nat @ K @ ( inf_inf_nat @ A @ B ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra_cancel.inf1
% 0.29/0.48  thf(fact_380_boolean__algebra__cancel_Oinf1,axiom,
% 0.29/0.48      ! [A2: product_prod_int_int > $o,K: product_prod_int_int > $o,A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 0.29/0.48        ( ( A2
% 0.29/0.48          = ( inf_in3604695632404883862_int_o @ K @ A ) )
% 0.29/0.48       => ( ( inf_in3604695632404883862_int_o @ A2 @ B )
% 0.29/0.48          = ( inf_in3604695632404883862_int_o @ K @ ( inf_in3604695632404883862_int_o @ A @ B ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra_cancel.inf1
% 0.29/0.48  thf(fact_381_boolean__algebra__cancel_Oinf1,axiom,
% 0.29/0.48      ! [A2: list_char > $o,K: list_char > $o,A: list_char > $o,B: list_char > $o] :
% 0.29/0.48        ( ( A2
% 0.29/0.48          = ( inf_inf_list_char_o @ K @ A ) )
% 0.29/0.48       => ( ( inf_inf_list_char_o @ A2 @ B )
% 0.29/0.48          = ( inf_inf_list_char_o @ K @ ( inf_inf_list_char_o @ A @ B ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra_cancel.inf1
% 0.29/0.48  thf(fact_382_boolean__algebra__cancel_Oinf2,axiom,
% 0.29/0.48      ! [B2: set_Pr1261947904930325089at_nat,K: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( B2
% 0.29/0.48          = ( inf_in2572325071724192079at_nat @ K @ B ) )
% 0.29/0.48       => ( ( inf_in2572325071724192079at_nat @ A @ B2 )
% 0.29/0.48          = ( inf_in2572325071724192079at_nat @ K @ ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra_cancel.inf2
% 0.29/0.48  thf(fact_383_boolean__algebra__cancel_Oinf2,axiom,
% 0.29/0.48      ! [B2: set_nat,K: set_nat,B: set_nat,A: set_nat] :
% 0.29/0.48        ( ( B2
% 0.29/0.48          = ( inf_inf_set_nat @ K @ B ) )
% 0.29/0.48       => ( ( inf_inf_set_nat @ A @ B2 )
% 0.29/0.48          = ( inf_inf_set_nat @ K @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra_cancel.inf2
% 0.29/0.48  thf(fact_384_boolean__algebra__cancel_Oinf2,axiom,
% 0.29/0.48      ! [B2: nat,K: nat,B: nat,A: nat] :
% 0.29/0.48        ( ( B2
% 0.29/0.48          = ( inf_inf_nat @ K @ B ) )
% 0.29/0.48       => ( ( inf_inf_nat @ A @ B2 )
% 0.29/0.48          = ( inf_inf_nat @ K @ ( inf_inf_nat @ A @ B ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra_cancel.inf2
% 0.29/0.48  thf(fact_385_boolean__algebra__cancel_Oinf2,axiom,
% 0.29/0.48      ! [B2: product_prod_int_int > $o,K: product_prod_int_int > $o,B: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 0.29/0.48        ( ( B2
% 0.29/0.48          = ( inf_in3604695632404883862_int_o @ K @ B ) )
% 0.29/0.48       => ( ( inf_in3604695632404883862_int_o @ A @ B2 )
% 0.29/0.48          = ( inf_in3604695632404883862_int_o @ K @ ( inf_in3604695632404883862_int_o @ A @ B ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra_cancel.inf2
% 0.29/0.48  thf(fact_386_boolean__algebra__cancel_Oinf2,axiom,
% 0.29/0.48      ! [B2: list_char > $o,K: list_char > $o,B: list_char > $o,A: list_char > $o] :
% 0.29/0.48        ( ( B2
% 0.29/0.48          = ( inf_inf_list_char_o @ K @ B ) )
% 0.29/0.48       => ( ( inf_inf_list_char_o @ A @ B2 )
% 0.29/0.48          = ( inf_inf_list_char_o @ K @ ( inf_inf_list_char_o @ A @ B ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % boolean_algebra_cancel.inf2
% 0.29/0.48  thf(fact_387_type__definition_ORep,axiom,
% 0.29/0.48      ! [Rep: product_unit > $o,Abs: $o > product_unit,A2: set_o,X: product_unit] :
% 0.29/0.48        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( member_o @ ( Rep @ X ) @ A2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep
% 0.29/0.48  thf(fact_388_type__definition_ORep,axiom,
% 0.29/0.48      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,A2: set_Pr4532377907799695533_nat_o,X: assn] :
% 0.29/0.48        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( member6576561426505652726_nat_o @ ( Rep @ X ) @ A2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep
% 0.29/0.48  thf(fact_389_type__definition_ORep,axiom,
% 0.29/0.48      ! [Rep: literal > list_char,Abs: list_char > literal,A2: set_list_char,X: literal] :
% 0.29/0.48        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( member_list_char @ ( Rep @ X ) @ A2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep
% 0.29/0.48  thf(fact_390_type__definition_ORep,axiom,
% 0.29/0.48      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,A2: set_se6260736226359567993nt_int,X: rat] :
% 0.29/0.48        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( member2340774599025711042nt_int @ ( Rep @ X ) @ A2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep
% 0.29/0.48  thf(fact_391_type__definition_ORep,axiom,
% 0.29/0.48      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,A2: set_se7855581050983116737at_nat,X: int] :
% 0.29/0.48        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( member2643936169264416010at_nat @ ( Rep @ X ) @ A2 ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep
% 0.29/0.48  thf(fact_392_type__definition_Ointro,axiom,
% 0.29/0.48      ! [Rep: product_unit > $o,A2: set_o,Abs: $o > product_unit] :
% 0.29/0.48        ( ! [X2: product_unit] : ( member_o @ ( Rep @ X2 ) @ A2 )
% 0.29/0.48       => ( ! [X2: product_unit] :
% 0.29/0.48              ( ( Abs @ ( Rep @ X2 ) )
% 0.29/0.48              = X2 )
% 0.29/0.48         => ( ! [Y2: $o] :
% 0.29/0.48                ( ( member_o @ Y2 @ A2 )
% 0.29/0.48               => ( ( Rep @ ( Abs @ Y2 ) )
% 0.29/0.48                  = Y2 ) )
% 0.29/0.48           => ( type_d6188575255521822967unit_o @ Rep @ Abs @ A2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.intro
% 0.29/0.48  thf(fact_393_type__definition_Ointro,axiom,
% 0.29/0.48      ! [Rep: assn > produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,Abs: ( produc3658429121746597890et_nat > $o ) > assn] :
% 0.29/0.48        ( ! [X2: assn] : ( member6576561426505652726_nat_o @ ( Rep @ X2 ) @ A2 )
% 0.29/0.48       => ( ! [X2: assn] :
% 0.29/0.48              ( ( Abs @ ( Rep @ X2 ) )
% 0.29/0.48              = X2 )
% 0.29/0.48         => ( ! [Y2: produc3658429121746597890et_nat > $o] :
% 0.29/0.48                ( ( member6576561426505652726_nat_o @ Y2 @ A2 )
% 0.29/0.48               => ( ( Rep @ ( Abs @ Y2 ) )
% 0.29/0.48                  = Y2 ) )
% 0.29/0.48           => ( type_d3909072315231072503_nat_o @ Rep @ Abs @ A2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.intro
% 0.29/0.48  thf(fact_394_type__definition_Ointro,axiom,
% 0.29/0.48      ! [Rep: literal > list_char,A2: set_list_char,Abs: list_char > literal] :
% 0.29/0.48        ( ! [X2: literal] : ( member_list_char @ ( Rep @ X2 ) @ A2 )
% 0.29/0.48       => ( ! [X2: literal] :
% 0.29/0.48              ( ( Abs @ ( Rep @ X2 ) )
% 0.29/0.48              = X2 )
% 0.29/0.48         => ( ! [Y2: list_char] :
% 0.29/0.48                ( ( member_list_char @ Y2 @ A2 )
% 0.29/0.48               => ( ( Rep @ ( Abs @ Y2 ) )
% 0.29/0.48                  = Y2 ) )
% 0.29/0.48           => ( type_d4752411451802217481t_char @ Rep @ Abs @ A2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.intro
% 0.29/0.48  thf(fact_395_type__definition_Ointro,axiom,
% 0.29/0.48      ! [Rep: rat > set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,Abs: set_Pr958786334691620121nt_int > rat] :
% 0.29/0.48        ( ! [X2: rat] : ( member2340774599025711042nt_int @ ( Rep @ X2 ) @ A2 )
% 0.29/0.48       => ( ! [X2: rat] :
% 0.29/0.48              ( ( Abs @ ( Rep @ X2 ) )
% 0.29/0.48              = X2 )
% 0.29/0.48         => ( ! [Y2: set_Pr958786334691620121nt_int] :
% 0.29/0.48                ( ( member2340774599025711042nt_int @ Y2 @ A2 )
% 0.29/0.48               => ( ( Rep @ ( Abs @ Y2 ) )
% 0.29/0.48                  = Y2 ) )
% 0.29/0.48           => ( type_d8554052265237484179nt_int @ Rep @ Abs @ A2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.intro
% 0.29/0.48  thf(fact_396_type__definition_Ointro,axiom,
% 0.29/0.48      ! [Rep: int > set_Pr1261947904930325089at_nat,A2: set_se7855581050983116737at_nat,Abs: set_Pr1261947904930325089at_nat > int] :
% 0.29/0.48        ( ! [X2: int] : ( member2643936169264416010at_nat @ ( Rep @ X2 ) @ A2 )
% 0.29/0.48       => ( ! [X2: int] :
% 0.29/0.48              ( ( Abs @ ( Rep @ X2 ) )
% 0.29/0.48              = X2 )
% 0.29/0.48         => ( ! [Y2: set_Pr1261947904930325089at_nat] :
% 0.29/0.48                ( ( member2643936169264416010at_nat @ Y2 @ A2 )
% 0.29/0.48               => ( ( Rep @ ( Abs @ Y2 ) )
% 0.29/0.48                  = Y2 ) )
% 0.29/0.48           => ( type_d8752208705193531015at_nat @ Rep @ Abs @ A2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.intro
% 0.29/0.48  thf(fact_397_type__definition_OAbs__cases,axiom,
% 0.29/0.48      ! [Rep: product_unit > $o,Abs: $o > product_unit,A2: set_o,X: product_unit] :
% 0.29/0.48        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A2 )
% 0.29/0.48       => ~ ! [Y2: $o] :
% 0.29/0.48              ( ( X
% 0.29/0.48                = ( Abs @ Y2 ) )
% 0.29/0.48             => ~ ( member_o @ Y2 @ A2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Abs_cases
% 0.29/0.48  thf(fact_398_type__definition_OAbs__cases,axiom,
% 0.29/0.48      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,A2: set_Pr4532377907799695533_nat_o,X: assn] :
% 0.29/0.48        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ A2 )
% 0.29/0.48       => ~ ! [Y2: produc3658429121746597890et_nat > $o] :
% 0.29/0.48              ( ( X
% 0.29/0.48                = ( Abs @ Y2 ) )
% 0.29/0.48             => ~ ( member6576561426505652726_nat_o @ Y2 @ A2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Abs_cases
% 0.29/0.48  thf(fact_399_type__definition_OAbs__cases,axiom,
% 0.29/0.48      ! [Rep: literal > list_char,Abs: list_char > literal,A2: set_list_char,X: literal] :
% 0.29/0.48        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ A2 )
% 0.29/0.48       => ~ ! [Y2: list_char] :
% 0.29/0.48              ( ( X
% 0.29/0.48                = ( Abs @ Y2 ) )
% 0.29/0.48             => ~ ( member_list_char @ Y2 @ A2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Abs_cases
% 0.29/0.48  thf(fact_400_type__definition_OAbs__cases,axiom,
% 0.29/0.48      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,A2: set_se6260736226359567993nt_int,X: rat] :
% 0.29/0.48        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ A2 )
% 0.29/0.48       => ~ ! [Y2: set_Pr958786334691620121nt_int] :
% 0.29/0.48              ( ( X
% 0.29/0.48                = ( Abs @ Y2 ) )
% 0.29/0.48             => ~ ( member2340774599025711042nt_int @ Y2 @ A2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Abs_cases
% 0.29/0.48  thf(fact_401_type__definition_OAbs__cases,axiom,
% 0.29/0.48      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,A2: set_se7855581050983116737at_nat,X: int] :
% 0.29/0.48        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ A2 )
% 0.29/0.48       => ~ ! [Y2: set_Pr1261947904930325089at_nat] :
% 0.29/0.48              ( ( X
% 0.29/0.48                = ( Abs @ Y2 ) )
% 0.29/0.48             => ~ ( member2643936169264416010at_nat @ Y2 @ A2 ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Abs_cases
% 0.29/0.48  thf(fact_402_type__definition_ORep__cases,axiom,
% 0.29/0.48      ! [Rep: product_unit > $o,Abs: $o > product_unit,A2: set_o,Y: $o] :
% 0.29/0.48        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( member_o @ Y @ A2 )
% 0.29/0.48         => ~ ! [X2: product_unit] :
% 0.29/0.48                ( Y
% 0.29/0.48                = ( ~ ( Rep @ X2 ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep_cases
% 0.29/0.48  thf(fact_403_type__definition_ORep__cases,axiom,
% 0.29/0.48      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,A2: set_Pr4532377907799695533_nat_o,Y: produc3658429121746597890et_nat > $o] :
% 0.29/0.48        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( member6576561426505652726_nat_o @ Y @ A2 )
% 0.29/0.48         => ~ ! [X2: assn] :
% 0.29/0.48                ( Y
% 0.29/0.48               != ( Rep @ X2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep_cases
% 0.29/0.48  thf(fact_404_type__definition_ORep__cases,axiom,
% 0.29/0.48      ! [Rep: literal > list_char,Abs: list_char > literal,A2: set_list_char,Y: list_char] :
% 0.29/0.48        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( member_list_char @ Y @ A2 )
% 0.29/0.48         => ~ ! [X2: literal] :
% 0.29/0.48                ( Y
% 0.29/0.48               != ( Rep @ X2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep_cases
% 0.29/0.48  thf(fact_405_type__definition_ORep__cases,axiom,
% 0.29/0.48      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,A2: set_se6260736226359567993nt_int,Y: set_Pr958786334691620121nt_int] :
% 0.29/0.48        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( member2340774599025711042nt_int @ Y @ A2 )
% 0.29/0.48         => ~ ! [X2: rat] :
% 0.29/0.48                ( Y
% 0.29/0.48               != ( Rep @ X2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep_cases
% 0.29/0.48  thf(fact_406_type__definition_ORep__cases,axiom,
% 0.29/0.48      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,A2: set_se7855581050983116737at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( member2643936169264416010at_nat @ Y @ A2 )
% 0.29/0.48         => ~ ! [X2: int] :
% 0.29/0.48                ( Y
% 0.29/0.48               != ( Rep @ X2 ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep_cases
% 0.29/0.48  thf(fact_407_type__definition_OAbs__induct,axiom,
% 0.29/0.48      ! [Rep: product_unit > $o,Abs: $o > product_unit,A2: set_o,P: product_unit > $o,X: product_unit] :
% 0.29/0.48        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ! [Y2: $o] :
% 0.29/0.48              ( ( member_o @ Y2 @ A2 )
% 0.29/0.48             => ( P @ ( Abs @ Y2 ) ) )
% 0.29/0.48         => ( P @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Abs_induct
% 0.29/0.48  thf(fact_408_type__definition_OAbs__induct,axiom,
% 0.29/0.48      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,A2: set_Pr4532377907799695533_nat_o,P: assn > $o,X: assn] :
% 0.29/0.48        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ! [Y2: produc3658429121746597890et_nat > $o] :
% 0.29/0.48              ( ( member6576561426505652726_nat_o @ Y2 @ A2 )
% 0.29/0.48             => ( P @ ( Abs @ Y2 ) ) )
% 0.29/0.48         => ( P @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Abs_induct
% 0.29/0.48  thf(fact_409_type__definition_OAbs__induct,axiom,
% 0.29/0.48      ! [Rep: literal > list_char,Abs: list_char > literal,A2: set_list_char,P: literal > $o,X: literal] :
% 0.29/0.48        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ! [Y2: list_char] :
% 0.29/0.48              ( ( member_list_char @ Y2 @ A2 )
% 0.29/0.48             => ( P @ ( Abs @ Y2 ) ) )
% 0.29/0.48         => ( P @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Abs_induct
% 0.29/0.48  thf(fact_410_type__definition_OAbs__induct,axiom,
% 0.29/0.48      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,A2: set_se6260736226359567993nt_int,P: rat > $o,X: rat] :
% 0.29/0.48        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ! [Y2: set_Pr958786334691620121nt_int] :
% 0.29/0.48              ( ( member2340774599025711042nt_int @ Y2 @ A2 )
% 0.29/0.48             => ( P @ ( Abs @ Y2 ) ) )
% 0.29/0.48         => ( P @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Abs_induct
% 0.29/0.48  thf(fact_411_type__definition_OAbs__induct,axiom,
% 0.29/0.48      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,A2: set_se7855581050983116737at_nat,P: int > $o,X: int] :
% 0.29/0.48        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ! [Y2: set_Pr1261947904930325089at_nat] :
% 0.29/0.48              ( ( member2643936169264416010at_nat @ Y2 @ A2 )
% 0.29/0.48             => ( P @ ( Abs @ Y2 ) ) )
% 0.29/0.48         => ( P @ X ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Abs_induct
% 0.29/0.48  thf(fact_412_type__definition_OAbs__inject,axiom,
% 0.29/0.48      ! [Rep: product_unit > $o,Abs: $o > product_unit,A2: set_o,X: $o,Y: $o] :
% 0.29/0.48        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( member_o @ X @ A2 )
% 0.29/0.48         => ( ( member_o @ Y @ A2 )
% 0.29/0.48           => ( ( ( Abs @ X )
% 0.29/0.48                = ( Abs @ Y ) )
% 0.29/0.48              = ( X = Y ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Abs_inject
% 0.29/0.48  thf(fact_413_type__definition_OAbs__inject,axiom,
% 0.29/0.48      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,A2: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 0.29/0.48        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( member6576561426505652726_nat_o @ X @ A2 )
% 0.29/0.48         => ( ( member6576561426505652726_nat_o @ Y @ A2 )
% 0.29/0.48           => ( ( ( Abs @ X )
% 0.29/0.48                = ( Abs @ Y ) )
% 0.29/0.48              = ( X = Y ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Abs_inject
% 0.29/0.48  thf(fact_414_type__definition_OAbs__inject,axiom,
% 0.29/0.48      ! [Rep: literal > list_char,Abs: list_char > literal,A2: set_list_char,X: list_char,Y: list_char] :
% 0.29/0.48        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( member_list_char @ X @ A2 )
% 0.29/0.48         => ( ( member_list_char @ Y @ A2 )
% 0.29/0.48           => ( ( ( Abs @ X )
% 0.29/0.48                = ( Abs @ Y ) )
% 0.29/0.48              = ( X = Y ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Abs_inject
% 0.29/0.48  thf(fact_415_type__definition_OAbs__inject,axiom,
% 0.29/0.48      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,A2: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
% 0.29/0.48        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( member2340774599025711042nt_int @ X @ A2 )
% 0.29/0.48         => ( ( member2340774599025711042nt_int @ Y @ A2 )
% 0.29/0.48           => ( ( ( Abs @ X )
% 0.29/0.48                = ( Abs @ Y ) )
% 0.29/0.48              = ( X = Y ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Abs_inject
% 0.29/0.48  thf(fact_416_type__definition_OAbs__inject,axiom,
% 0.29/0.48      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,A2: set_se7855581050983116737at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( member2643936169264416010at_nat @ X @ A2 )
% 0.29/0.48         => ( ( member2643936169264416010at_nat @ Y @ A2 )
% 0.29/0.48           => ( ( ( Abs @ X )
% 0.29/0.48                = ( Abs @ Y ) )
% 0.29/0.48              = ( X = Y ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Abs_inject
% 0.29/0.48  thf(fact_417_type__definition_ORep__induct,axiom,
% 0.29/0.48      ! [Rep: product_unit > $o,Abs: $o > product_unit,A2: set_o,Y: $o,P: $o > $o] :
% 0.29/0.48        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( member_o @ Y @ A2 )
% 0.29/0.48         => ( ! [X2: product_unit] : ( P @ ( Rep @ X2 ) )
% 0.29/0.48           => ( P @ Y ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep_induct
% 0.29/0.48  thf(fact_418_type__definition_ORep__induct,axiom,
% 0.29/0.48      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,A2: set_Pr4532377907799695533_nat_o,Y: produc3658429121746597890et_nat > $o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.29/0.48        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( member6576561426505652726_nat_o @ Y @ A2 )
% 0.29/0.48         => ( ! [X2: assn] : ( P @ ( Rep @ X2 ) )
% 0.29/0.48           => ( P @ Y ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep_induct
% 0.29/0.48  thf(fact_419_type__definition_ORep__induct,axiom,
% 0.29/0.48      ! [Rep: literal > list_char,Abs: list_char > literal,A2: set_list_char,Y: list_char,P: list_char > $o] :
% 0.29/0.48        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( member_list_char @ Y @ A2 )
% 0.29/0.48         => ( ! [X2: literal] : ( P @ ( Rep @ X2 ) )
% 0.29/0.48           => ( P @ Y ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep_induct
% 0.29/0.48  thf(fact_420_type__definition_ORep__induct,axiom,
% 0.29/0.48      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,A2: set_se6260736226359567993nt_int,Y: set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 0.29/0.48        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( member2340774599025711042nt_int @ Y @ A2 )
% 0.29/0.48         => ( ! [X2: rat] : ( P @ ( Rep @ X2 ) )
% 0.29/0.48           => ( P @ Y ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep_induct
% 0.29/0.48  thf(fact_421_type__definition_ORep__induct,axiom,
% 0.29/0.48      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,A2: set_se7855581050983116737at_nat,Y: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 0.29/0.48        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( member2643936169264416010at_nat @ Y @ A2 )
% 0.29/0.48         => ( ! [X2: int] : ( P @ ( Rep @ X2 ) )
% 0.29/0.48           => ( P @ Y ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep_induct
% 0.29/0.48  thf(fact_422_type__definition_ORep__inject,axiom,
% 0.29/0.48      ! [Rep: product_unit > $o,Abs: $o > product_unit,A2: set_o,X: product_unit,Y: product_unit] :
% 0.29/0.48        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( ( Rep @ X )
% 0.29/0.48            = ( Rep @ Y ) )
% 0.29/0.48          = ( X = Y ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep_inject
% 0.29/0.48  thf(fact_423_type__definition_ORep__inject,axiom,
% 0.29/0.48      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,A2: set_Pr4532377907799695533_nat_o,X: assn,Y: assn] :
% 0.29/0.48        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( ( Rep @ X )
% 0.29/0.48            = ( Rep @ Y ) )
% 0.29/0.48          = ( X = Y ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep_inject
% 0.29/0.48  thf(fact_424_type__definition_ORep__inject,axiom,
% 0.29/0.48      ! [Rep: literal > list_char,Abs: list_char > literal,A2: set_list_char,X: literal,Y: literal] :
% 0.29/0.48        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( ( Rep @ X )
% 0.29/0.48            = ( Rep @ Y ) )
% 0.29/0.48          = ( X = Y ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep_inject
% 0.29/0.48  thf(fact_425_type__definition_ORep__inject,axiom,
% 0.29/0.48      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,A2: set_se6260736226359567993nt_int,X: rat,Y: rat] :
% 0.29/0.48        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( ( Rep @ X )
% 0.29/0.48            = ( Rep @ Y ) )
% 0.29/0.48          = ( X = Y ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep_inject
% 0.29/0.48  thf(fact_426_type__definition_ORep__inject,axiom,
% 0.29/0.48      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,A2: set_se7855581050983116737at_nat,X: int,Y: int] :
% 0.29/0.48        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( ( Rep @ X )
% 0.29/0.48            = ( Rep @ Y ) )
% 0.29/0.48          = ( X = Y ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep_inject
% 0.29/0.48  thf(fact_427_type__definition_OAbs__inverse,axiom,
% 0.29/0.48      ! [Rep: product_unit > $o,Abs: $o > product_unit,A2: set_o,Y: $o] :
% 0.29/0.48        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( member_o @ Y @ A2 )
% 0.29/0.48         => ( ( Rep @ ( Abs @ Y ) )
% 0.29/0.48            = Y ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Abs_inverse
% 0.29/0.48  thf(fact_428_type__definition_OAbs__inverse,axiom,
% 0.29/0.48      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,A2: set_Pr4532377907799695533_nat_o,Y: produc3658429121746597890et_nat > $o] :
% 0.29/0.48        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( member6576561426505652726_nat_o @ Y @ A2 )
% 0.29/0.48         => ( ( Rep @ ( Abs @ Y ) )
% 0.29/0.48            = Y ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Abs_inverse
% 0.29/0.48  thf(fact_429_type__definition_OAbs__inverse,axiom,
% 0.29/0.48      ! [Rep: literal > list_char,Abs: list_char > literal,A2: set_list_char,Y: list_char] :
% 0.29/0.48        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( member_list_char @ Y @ A2 )
% 0.29/0.48         => ( ( Rep @ ( Abs @ Y ) )
% 0.29/0.48            = Y ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Abs_inverse
% 0.29/0.48  thf(fact_430_type__definition_OAbs__inverse,axiom,
% 0.29/0.48      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,A2: set_se6260736226359567993nt_int,Y: set_Pr958786334691620121nt_int] :
% 0.29/0.48        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( member2340774599025711042nt_int @ Y @ A2 )
% 0.29/0.48         => ( ( Rep @ ( Abs @ Y ) )
% 0.29/0.48            = Y ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Abs_inverse
% 0.29/0.48  thf(fact_431_type__definition_OAbs__inverse,axiom,
% 0.29/0.48      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,A2: set_se7855581050983116737at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.29/0.48        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( member2643936169264416010at_nat @ Y @ A2 )
% 0.29/0.48         => ( ( Rep @ ( Abs @ Y ) )
% 0.29/0.48            = Y ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Abs_inverse
% 0.29/0.48  thf(fact_432_type__definition_ORep__inverse,axiom,
% 0.29/0.48      ! [Rep: product_unit > $o,Abs: $o > product_unit,A2: set_o,X: product_unit] :
% 0.29/0.48        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( Abs @ ( Rep @ X ) )
% 0.29/0.48          = X ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep_inverse
% 0.29/0.48  thf(fact_433_type__definition_ORep__inverse,axiom,
% 0.29/0.48      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,A2: set_Pr4532377907799695533_nat_o,X: assn] :
% 0.29/0.48        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( Abs @ ( Rep @ X ) )
% 0.29/0.48          = X ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep_inverse
% 0.29/0.48  thf(fact_434_type__definition_ORep__inverse,axiom,
% 0.29/0.48      ! [Rep: literal > list_char,Abs: list_char > literal,A2: set_list_char,X: literal] :
% 0.29/0.48        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( Abs @ ( Rep @ X ) )
% 0.29/0.48          = X ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep_inverse
% 0.29/0.48  thf(fact_435_type__definition_ORep__inverse,axiom,
% 0.29/0.48      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,A2: set_se6260736226359567993nt_int,X: rat] :
% 0.29/0.48        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( Abs @ ( Rep @ X ) )
% 0.29/0.48          = X ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep_inverse
% 0.29/0.48  thf(fact_436_type__definition_ORep__inverse,axiom,
% 0.29/0.48      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,A2: set_se7855581050983116737at_nat,X: int] :
% 0.29/0.48        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ A2 )
% 0.29/0.48       => ( ( Abs @ ( Rep @ X ) )
% 0.29/0.48          = X ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition.Rep_inverse
% 0.29/0.48  thf(fact_437_type__definition__def,axiom,
% 0.29/0.48      ( type_d6188575255521822967unit_o
% 0.29/0.48      = ( ^ [Rep2: product_unit > $o,Abs2: $o > product_unit,A4: set_o] :
% 0.29/0.48            ( ! [X3: product_unit] : ( member_o @ ( Rep2 @ X3 ) @ A4 )
% 0.29/0.48            & ! [X3: product_unit] :
% 0.29/0.48                ( ( Abs2 @ ( Rep2 @ X3 ) )
% 0.29/0.48                = X3 )
% 0.29/0.48            & ! [Y3: $o] :
% 0.29/0.48                ( ( member_o @ Y3 @ A4 )
% 0.29/0.48               => ( ( Rep2 @ ( Abs2 @ Y3 ) )
% 0.29/0.48                  = Y3 ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition_def
% 0.29/0.48  thf(fact_438_type__definition__def,axiom,
% 0.29/0.48      ( type_d3909072315231072503_nat_o
% 0.29/0.48      = ( ^ [Rep2: assn > produc3658429121746597890et_nat > $o,Abs2: ( produc3658429121746597890et_nat > $o ) > assn,A4: set_Pr4532377907799695533_nat_o] :
% 0.29/0.48            ( ! [X3: assn] : ( member6576561426505652726_nat_o @ ( Rep2 @ X3 ) @ A4 )
% 0.29/0.48            & ! [X3: assn] :
% 0.29/0.48                ( ( Abs2 @ ( Rep2 @ X3 ) )
% 0.29/0.48                = X3 )
% 0.29/0.48            & ! [Y3: produc3658429121746597890et_nat > $o] :
% 0.29/0.48                ( ( member6576561426505652726_nat_o @ Y3 @ A4 )
% 0.29/0.48               => ( ( Rep2 @ ( Abs2 @ Y3 ) )
% 0.29/0.48                  = Y3 ) ) ) ) ) ).
% 0.29/0.48  
% 0.29/0.48  % type_definition_def
% 0.29/0.48  thf(fact_439_type__definition__def,axiom,
% 0.29/0.48      ( type_d4752411451802217481t_char
% 0.29/0.48      = ( ^ [Rep2: literal > list_char,Abs2: list_char > literal,A4: set_list_char] :
% 0.29/0.48            ( ! [X3: literal] : ( member_list_char @ ( Rep2 @ X3 ) @ A4 )
% 0.29/0.48            & ! [X3: literal] :
% 0.29/0.48                ( ( Abs2 @ ( Rep2 @ X3 ) )
% 0.29/0.48                = X3 )
% 0.29/0.48            & ! [Y3: list_char] :
% 0.29/0.48                ( ( member_list_char @ Y3 @ A4 )
% 0.29/0.48               => ( ( Rep2 @ ( Abs2 @ Y3 ) )
% 0.29/0.48                  = Y3 ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % type_definition_def
% 0.29/0.49  thf(fact_440_type__definition__def,axiom,
% 0.29/0.49      ( type_d8554052265237484179nt_int
% 0.29/0.49      = ( ^ [Rep2: rat > set_Pr958786334691620121nt_int,Abs2: set_Pr958786334691620121nt_int > rat,A4: set_se6260736226359567993nt_int] :
% 0.29/0.49            ( ! [X3: rat] : ( member2340774599025711042nt_int @ ( Rep2 @ X3 ) @ A4 )
% 0.29/0.49            & ! [X3: rat] :
% 0.29/0.49                ( ( Abs2 @ ( Rep2 @ X3 ) )
% 0.29/0.49                = X3 )
% 0.29/0.49            & ! [Y3: set_Pr958786334691620121nt_int] :
% 0.29/0.49                ( ( member2340774599025711042nt_int @ Y3 @ A4 )
% 0.29/0.49               => ( ( Rep2 @ ( Abs2 @ Y3 ) )
% 0.29/0.49                  = Y3 ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % type_definition_def
% 0.29/0.49  thf(fact_441_type__definition__def,axiom,
% 0.29/0.49      ( type_d8752208705193531015at_nat
% 0.29/0.49      = ( ^ [Rep2: int > set_Pr1261947904930325089at_nat,Abs2: set_Pr1261947904930325089at_nat > int,A4: set_se7855581050983116737at_nat] :
% 0.29/0.49            ( ! [X3: int] : ( member2643936169264416010at_nat @ ( Rep2 @ X3 ) @ A4 )
% 0.29/0.49            & ! [X3: int] :
% 0.29/0.49                ( ( Abs2 @ ( Rep2 @ X3 ) )
% 0.29/0.49                = X3 )
% 0.29/0.49            & ! [Y3: set_Pr1261947904930325089at_nat] :
% 0.29/0.49                ( ( member2643936169264416010at_nat @ Y3 @ A4 )
% 0.29/0.49               => ( ( Rep2 @ ( Abs2 @ Y3 ) )
% 0.29/0.49                  = Y3 ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % type_definition_def
% 0.29/0.49  thf(fact_442_mult_Oright__assoc,axiom,
% 0.29/0.49      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.49        ( ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.29/0.49        = ( times_3573771949741848930nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.right_assoc
% 0.29/0.49  thf(fact_443_mult_Oright__assoc,axiom,
% 0.29/0.49      ! [A: assn,B: assn,C: assn] :
% 0.29/0.49        ( ( times_times_assn @ ( times_times_assn @ A @ B ) @ C )
% 0.29/0.49        = ( times_times_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.right_assoc
% 0.29/0.49  thf(fact_444_mult_Oright__assoc,axiom,
% 0.29/0.49      ! [A: rat,B: rat,C: rat] :
% 0.29/0.49        ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 0.29/0.49        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.right_assoc
% 0.29/0.49  thf(fact_445_mult_Oright__assoc,axiom,
% 0.29/0.49      ! [A: nat,B: nat,C: nat] :
% 0.29/0.49        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.29/0.49        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.right_assoc
% 0.29/0.49  thf(fact_446_mult_Oright__assoc,axiom,
% 0.29/0.49      ! [A: int,B: int,C: int] :
% 0.29/0.49        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 0.29/0.49        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.right_assoc
% 0.29/0.49  thf(fact_447_mult_Oright__commute,axiom,
% 0.29/0.49      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.49        ( ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.29/0.49        = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.right_commute
% 0.29/0.49  thf(fact_448_mult_Oright__commute,axiom,
% 0.29/0.49      ! [A: assn,B: assn,C: assn] :
% 0.29/0.49        ( ( times_times_assn @ ( times_times_assn @ A @ B ) @ C )
% 0.29/0.49        = ( times_times_assn @ ( times_times_assn @ A @ C ) @ B ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.right_commute
% 0.29/0.49  thf(fact_449_mult_Oright__commute,axiom,
% 0.29/0.49      ! [A: rat,B: rat,C: rat] :
% 0.29/0.49        ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 0.29/0.49        = ( times_times_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.right_commute
% 0.29/0.49  thf(fact_450_mult_Oright__commute,axiom,
% 0.29/0.49      ! [A: nat,B: nat,C: nat] :
% 0.29/0.49        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.29/0.49        = ( times_times_nat @ ( times_times_nat @ A @ C ) @ B ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.right_commute
% 0.29/0.49  thf(fact_451_mult_Oright__commute,axiom,
% 0.29/0.49      ! [A: int,B: int,C: int] :
% 0.29/0.49        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 0.29/0.49        = ( times_times_int @ ( times_times_int @ A @ C ) @ B ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.right_commute
% 0.29/0.49  thf(fact_452_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 0.29/0.49      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.29/0.49        ( ( times_3573771949741848930nteger @ B @ ( times_3573771949741848930nteger @ A @ C ) )
% 0.29/0.49        = ( times_3573771949741848930nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % ab_semigroup_mult_class.mult.left_commute
% 0.29/0.49  thf(fact_453_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 0.29/0.49      ! [B: assn,A: assn,C: assn] :
% 0.29/0.49        ( ( times_times_assn @ B @ ( times_times_assn @ A @ C ) )
% 0.29/0.49        = ( times_times_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % ab_semigroup_mult_class.mult.left_commute
% 0.29/0.49  thf(fact_454_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 0.29/0.49      ! [B: rat,A: rat,C: rat] :
% 0.29/0.49        ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 0.29/0.49        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % ab_semigroup_mult_class.mult.left_commute
% 0.29/0.49  thf(fact_455_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 0.29/0.49      ! [B: nat,A: nat,C: nat] :
% 0.29/0.49        ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 0.29/0.49        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % ab_semigroup_mult_class.mult.left_commute
% 0.29/0.49  thf(fact_456_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 0.29/0.49      ! [B: int,A: int,C: int] :
% 0.29/0.49        ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 0.29/0.49        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % ab_semigroup_mult_class.mult.left_commute
% 0.29/0.49  thf(fact_457_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 0.29/0.49      ( times_3573771949741848930nteger
% 0.29/0.49      = ( ^ [A3: code_integer,B3: code_integer] : ( times_3573771949741848930nteger @ B3 @ A3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % ab_semigroup_mult_class.mult.commute
% 0.29/0.49  thf(fact_458_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 0.29/0.49      ( times_times_assn
% 0.29/0.49      = ( ^ [A3: assn,B3: assn] : ( times_times_assn @ B3 @ A3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % ab_semigroup_mult_class.mult.commute
% 0.29/0.49  thf(fact_459_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 0.29/0.49      ( times_times_rat
% 0.29/0.49      = ( ^ [A3: rat,B3: rat] : ( times_times_rat @ B3 @ A3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % ab_semigroup_mult_class.mult.commute
% 0.29/0.49  thf(fact_460_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 0.29/0.49      ( times_times_nat
% 0.29/0.49      = ( ^ [A3: nat,B3: nat] : ( times_times_nat @ B3 @ A3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % ab_semigroup_mult_class.mult.commute
% 0.29/0.49  thf(fact_461_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 0.29/0.49      ( times_times_int
% 0.29/0.49      = ( ^ [A3: int,B3: int] : ( times_times_int @ B3 @ A3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % ab_semigroup_mult_class.mult.commute
% 0.29/0.49  thf(fact_462_mult_Oassoc,axiom,
% 0.29/0.49      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.49        ( ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.29/0.49        = ( times_3573771949741848930nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.assoc
% 0.29/0.49  thf(fact_463_mult_Oassoc,axiom,
% 0.29/0.49      ! [A: assn,B: assn,C: assn] :
% 0.29/0.49        ( ( times_times_assn @ ( times_times_assn @ A @ B ) @ C )
% 0.29/0.49        = ( times_times_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.assoc
% 0.29/0.49  thf(fact_464_mult_Oassoc,axiom,
% 0.29/0.49      ! [A: rat,B: rat,C: rat] :
% 0.29/0.49        ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 0.29/0.49        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.assoc
% 0.29/0.49  thf(fact_465_mult_Oassoc,axiom,
% 0.29/0.49      ! [A: nat,B: nat,C: nat] :
% 0.29/0.49        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.29/0.49        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.assoc
% 0.29/0.49  thf(fact_466_mult_Oassoc,axiom,
% 0.29/0.49      ! [A: int,B: int,C: int] :
% 0.29/0.49        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 0.29/0.49        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.assoc
% 0.29/0.49  thf(fact_467_mult_Osafe__commute,axiom,
% 0.29/0.49      ! [X: code_integer,Y: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.49        ( ( syntax380677951125133566nteger @ ( times_3573771949741848930nteger @ X @ Y ) @ A )
% 0.29/0.49       => ( ( times_3573771949741848930nteger @ A @ B )
% 0.29/0.49          = ( times_3573771949741848930nteger @ B @ A ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.safe_commute
% 0.29/0.49  thf(fact_468_mult_Osafe__commute,axiom,
% 0.29/0.49      ! [X: assn,Y: assn,A: assn,B: assn] :
% 0.29/0.49        ( ( syntax7398250324933576852n_assn @ ( times_times_assn @ X @ Y ) @ A )
% 0.29/0.49       => ( ( times_times_assn @ A @ B )
% 0.29/0.49          = ( times_times_assn @ B @ A ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.safe_commute
% 0.29/0.49  thf(fact_469_mult_Osafe__commute,axiom,
% 0.29/0.49      ! [X: rat,Y: rat,A: rat,B: rat] :
% 0.29/0.49        ( ( syntax3730441303064801268at_rat @ ( times_times_rat @ X @ Y ) @ A )
% 0.29/0.49       => ( ( times_times_rat @ A @ B )
% 0.29/0.49          = ( times_times_rat @ B @ A ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.safe_commute
% 0.29/0.49  thf(fact_470_mult_Osafe__commute,axiom,
% 0.29/0.49      ! [X: nat,Y: nat,A: nat,B: nat] :
% 0.29/0.49        ( ( syntax4682126007086162916at_nat @ ( times_times_nat @ X @ Y ) @ A )
% 0.29/0.49       => ( ( times_times_nat @ A @ B )
% 0.29/0.49          = ( times_times_nat @ B @ A ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.safe_commute
% 0.29/0.49  thf(fact_471_mult_Osafe__commute,axiom,
% 0.29/0.49      ! [X: int,Y: int,A: int,B: int] :
% 0.29/0.49        ( ( syntax5678989248478167196nt_int @ ( times_times_int @ X @ Y ) @ A )
% 0.29/0.49       => ( ( times_times_int @ A @ B )
% 0.29/0.49          = ( times_times_int @ B @ A ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.safe_commute
% 0.29/0.49  thf(fact_472_sup__bot_Osemilattice__neutr__axioms,axiom,
% 0.29/0.49      semila6683195626996185257at_nat @ sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat ).
% 0.29/0.49  
% 0.29/0.49  % sup_bot.semilattice_neutr_axioms
% 0.29/0.49  thf(fact_473_sup__bot_Osemilattice__neutr__axioms,axiom,
% 0.29/0.49      semila3675781407871293737at_nat @ sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat ).
% 0.29/0.49  
% 0.29/0.49  % sup_bot.semilattice_neutr_axioms
% 0.29/0.49  thf(fact_474_sup__bot_Osemilattice__neutr__axioms,axiom,
% 0.29/0.49      semila858173770281612099at_nat @ sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat ).
% 0.29/0.49  
% 0.29/0.49  % sup_bot.semilattice_neutr_axioms
% 0.29/0.49  thf(fact_475_sup__bot_Osemilattice__neutr__axioms,axiom,
% 0.29/0.49      semila1065760912024005978_set_o @ sup_sup_set_o @ bot_bot_set_o ).
% 0.29/0.49  
% 0.29/0.49  % sup_bot.semilattice_neutr_axioms
% 0.29/0.49  thf(fact_476_sup__bot_Osemilattice__neutr__axioms,axiom,
% 0.29/0.49      semila1241773964035338532et_nat @ sup_sup_set_nat @ bot_bot_set_nat ).
% 0.29/0.49  
% 0.29/0.49  % sup_bot.semilattice_neutr_axioms
% 0.29/0.49  thf(fact_477_sup__bot_Osemilattice__neutr__axioms,axiom,
% 0.29/0.49      semila6287294981380917632et_int @ sup_sup_set_int @ bot_bot_set_int ).
% 0.29/0.49  
% 0.29/0.49  % sup_bot.semilattice_neutr_axioms
% 0.29/0.49  thf(fact_478_sup__bot_Omonoid__axioms,axiom,
% 0.29/0.49      monoid3323479476634721864at_nat @ sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat ).
% 0.29/0.49  
% 0.29/0.49  % sup_bot.monoid_axioms
% 0.29/0.49  thf(fact_479_sup__bot_Omonoid__axioms,axiom,
% 0.29/0.49      monoid534952638934301128at_nat @ sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat ).
% 0.29/0.49  
% 0.29/0.49  % sup_bot.monoid_axioms
% 0.29/0.49  thf(fact_480_sup__bot_Omonoid__axioms,axiom,
% 0.29/0.49      monoid1519094961268053602at_nat @ sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat ).
% 0.29/0.49  
% 0.29/0.49  % sup_bot.monoid_axioms
% 0.29/0.49  thf(fact_481_sup__bot_Omonoid__axioms,axiom,
% 0.29/0.49      monoid_set_o @ sup_sup_set_o @ bot_bot_set_o ).
% 0.29/0.49  
% 0.29/0.49  % sup_bot.monoid_axioms
% 0.29/0.49  thf(fact_482_sup__bot_Omonoid__axioms,axiom,
% 0.29/0.49      monoid_set_nat @ sup_sup_set_nat @ bot_bot_set_nat ).
% 0.29/0.49  
% 0.29/0.49  % sup_bot.monoid_axioms
% 0.29/0.49  thf(fact_483_sup__bot_Omonoid__axioms,axiom,
% 0.29/0.49      monoid_set_int @ sup_sup_set_int @ bot_bot_set_int ).
% 0.29/0.49  
% 0.29/0.49  % sup_bot.monoid_axioms
% 0.29/0.49  thf(fact_484_one__assn__def,axiom,
% 0.29/0.49      ( one_one_assn
% 0.29/0.49      = ( abs_assn @ one_assn_raw ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_assn_def
% 0.29/0.49  thf(fact_485_boolean__algebra_Ocomplement__unique,axiom,
% 0.29/0.49      ! [A: product_prod_int_int > $o,X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 0.29/0.49        ( ( ( inf_in3604695632404883862_int_o @ A @ X )
% 0.29/0.49          = bot_bo8147686125503663512_int_o )
% 0.29/0.49       => ( ( ( sup_su8463660629351352368_int_o @ A @ X )
% 0.29/0.49            = top_to1578927101902068148_int_o )
% 0.29/0.49         => ( ( ( inf_in3604695632404883862_int_o @ A @ Y )
% 0.29/0.49              = bot_bo8147686125503663512_int_o )
% 0.29/0.49           => ( ( ( sup_su8463660629351352368_int_o @ A @ Y )
% 0.29/0.49                = top_to1578927101902068148_int_o )
% 0.29/0.49             => ( X = Y ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.complement_unique
% 0.29/0.49  thf(fact_486_boolean__algebra_Ocomplement__unique,axiom,
% 0.29/0.49      ! [A: list_char > $o,X: list_char > $o,Y: list_char > $o] :
% 0.29/0.49        ( ( ( inf_inf_list_char_o @ A @ X )
% 0.29/0.49          = bot_bot_list_char_o )
% 0.29/0.49       => ( ( ( sup_sup_list_char_o @ A @ X )
% 0.29/0.49            = top_top_list_char_o )
% 0.29/0.49         => ( ( ( inf_inf_list_char_o @ A @ Y )
% 0.29/0.49              = bot_bot_list_char_o )
% 0.29/0.49           => ( ( ( sup_sup_list_char_o @ A @ Y )
% 0.29/0.49                = top_top_list_char_o )
% 0.29/0.49             => ( X = Y ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.complement_unique
% 0.29/0.49  thf(fact_487_boolean__algebra_Ocomplement__unique,axiom,
% 0.29/0.49      ! [A: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( ( inf_in1697001100524423349at_nat @ A @ X )
% 0.29/0.49          = bot_bo8422036546324065075at_nat )
% 0.29/0.49       => ( ( ( sup_su3035147773818789531at_nat @ A @ X )
% 0.29/0.49            = top_to8764741339697478167at_nat )
% 0.29/0.49         => ( ( ( inf_in1697001100524423349at_nat @ A @ Y )
% 0.29/0.49              = bot_bo8422036546324065075at_nat )
% 0.29/0.49           => ( ( ( sup_su3035147773818789531at_nat @ A @ Y )
% 0.29/0.49                = top_to8764741339697478167at_nat )
% 0.29/0.49             => ( X = Y ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.complement_unique
% 0.29/0.49  thf(fact_488_boolean__algebra_Ocomplement__unique,axiom,
% 0.29/0.49      ! [A: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( ( inf_in7913087082777306421at_nat @ A @ X )
% 0.29/0.49          = bot_bo228742789529271731at_nat )
% 0.29/0.49       => ( ( ( sup_su5525570899277871387at_nat @ A @ X )
% 0.29/0.49            = top_to6833984726390702231at_nat )
% 0.29/0.49         => ( ( ( inf_in7913087082777306421at_nat @ A @ Y )
% 0.29/0.49              = bot_bo228742789529271731at_nat )
% 0.29/0.49           => ( ( ( sup_su5525570899277871387at_nat @ A @ Y )
% 0.29/0.49                = top_to6833984726390702231at_nat )
% 0.29/0.49             => ( X = Y ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.complement_unique
% 0.29/0.49  thf(fact_489_boolean__algebra_Ocomplement__unique,axiom,
% 0.29/0.49      ! [A: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( ( inf_in2572325071724192079at_nat @ A @ X )
% 0.29/0.49          = bot_bo2099793752762293965at_nat )
% 0.29/0.49       => ( ( ( sup_su6327502436637775413at_nat @ A @ X )
% 0.29/0.49            = top_to4669805908274784177at_nat )
% 0.29/0.49         => ( ( ( inf_in2572325071724192079at_nat @ A @ Y )
% 0.29/0.49              = bot_bo2099793752762293965at_nat )
% 0.29/0.49           => ( ( ( sup_su6327502436637775413at_nat @ A @ Y )
% 0.29/0.49                = top_to4669805908274784177at_nat )
% 0.29/0.49             => ( X = Y ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.complement_unique
% 0.29/0.49  thf(fact_490_boolean__algebra_Ocomplement__unique,axiom,
% 0.29/0.49      ! [A: set_list_nat,X: set_list_nat,Y: set_list_nat] :
% 0.29/0.49        ( ( ( inf_inf_set_list_nat @ A @ X )
% 0.29/0.49          = bot_bot_set_list_nat )
% 0.29/0.49       => ( ( ( sup_sup_set_list_nat @ A @ X )
% 0.29/0.49            = top_top_set_list_nat )
% 0.29/0.49         => ( ( ( inf_inf_set_list_nat @ A @ Y )
% 0.29/0.49              = bot_bot_set_list_nat )
% 0.29/0.49           => ( ( ( sup_sup_set_list_nat @ A @ Y )
% 0.29/0.49                = top_top_set_list_nat )
% 0.29/0.49             => ( X = Y ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.complement_unique
% 0.29/0.49  thf(fact_491_boolean__algebra_Ocomplement__unique,axiom,
% 0.29/0.49      ! [A: set_o,X: set_o,Y: set_o] :
% 0.29/0.49        ( ( ( inf_inf_set_o @ A @ X )
% 0.29/0.49          = bot_bot_set_o )
% 0.29/0.49       => ( ( ( sup_sup_set_o @ A @ X )
% 0.29/0.49            = top_top_set_o )
% 0.29/0.49         => ( ( ( inf_inf_set_o @ A @ Y )
% 0.29/0.49              = bot_bot_set_o )
% 0.29/0.49           => ( ( ( sup_sup_set_o @ A @ Y )
% 0.29/0.49                = top_top_set_o )
% 0.29/0.49             => ( X = Y ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.complement_unique
% 0.29/0.49  thf(fact_492_boolean__algebra_Ocomplement__unique,axiom,
% 0.29/0.49      ! [A: set_rat,X: set_rat,Y: set_rat] :
% 0.29/0.49        ( ( ( inf_inf_set_rat @ A @ X )
% 0.29/0.49          = bot_bot_set_rat )
% 0.29/0.49       => ( ( ( sup_sup_set_rat @ A @ X )
% 0.29/0.49            = top_top_set_rat )
% 0.29/0.49         => ( ( ( inf_inf_set_rat @ A @ Y )
% 0.29/0.49              = bot_bot_set_rat )
% 0.29/0.49           => ( ( ( sup_sup_set_rat @ A @ Y )
% 0.29/0.49                = top_top_set_rat )
% 0.29/0.49             => ( X = Y ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.complement_unique
% 0.29/0.49  thf(fact_493_boolean__algebra_Ocomplement__unique,axiom,
% 0.29/0.49      ! [A: set_nat,X: set_nat,Y: set_nat] :
% 0.29/0.49        ( ( ( inf_inf_set_nat @ A @ X )
% 0.29/0.49          = bot_bot_set_nat )
% 0.29/0.49       => ( ( ( sup_sup_set_nat @ A @ X )
% 0.29/0.49            = top_top_set_nat )
% 0.29/0.49         => ( ( ( inf_inf_set_nat @ A @ Y )
% 0.29/0.49              = bot_bot_set_nat )
% 0.29/0.49           => ( ( ( sup_sup_set_nat @ A @ Y )
% 0.29/0.49                = top_top_set_nat )
% 0.29/0.49             => ( X = Y ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.complement_unique
% 0.29/0.49  thf(fact_494_boolean__algebra_Ocomplement__unique,axiom,
% 0.29/0.49      ! [A: set_int,X: set_int,Y: set_int] :
% 0.29/0.49        ( ( ( inf_inf_set_int @ A @ X )
% 0.29/0.49          = bot_bot_set_int )
% 0.29/0.49       => ( ( ( sup_sup_set_int @ A @ X )
% 0.29/0.49            = top_top_set_int )
% 0.29/0.49         => ( ( ( inf_inf_set_int @ A @ Y )
% 0.29/0.49              = bot_bot_set_int )
% 0.29/0.49           => ( ( ( sup_sup_set_int @ A @ Y )
% 0.29/0.49                = top_top_set_int )
% 0.29/0.49             => ( X = Y ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.complement_unique
% 0.29/0.49  thf(fact_495_mod__star__conv,axiom,
% 0.29/0.49      ! [A2: assn,B2: assn,H3: produc3658429121746597890et_nat] :
% 0.29/0.49        ( ( rep_assn @ ( times_times_assn @ A2 @ B2 ) @ H3 )
% 0.29/0.49        = ( ? [Hr: heap_e7401611519738050253t_unit,As1: set_nat,As2: set_nat] :
% 0.29/0.49              ( ( H3
% 0.29/0.49                = ( produc7507926704131184380et_nat @ Hr @ ( sup_sup_set_nat @ As1 @ As2 ) ) )
% 0.29/0.49              & ( ( inf_inf_set_nat @ As1 @ As2 )
% 0.29/0.49                = bot_bot_set_nat )
% 0.29/0.49              & ( rep_assn @ A2 @ ( produc7507926704131184380et_nat @ Hr @ As1 ) )
% 0.29/0.49              & ( rep_assn @ B2 @ ( produc7507926704131184380et_nat @ Hr @ As2 ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mod_star_conv
% 0.29/0.49  thf(fact_496_star__assnI,axiom,
% 0.29/0.49      ! [P: assn,H3: heap_e7401611519738050253t_unit,As: set_nat,Q2: assn,As3: set_nat] :
% 0.29/0.49        ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 0.29/0.49       => ( ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 0.29/0.49         => ( ( ( inf_inf_set_nat @ As @ As3 )
% 0.29/0.49              = bot_bot_set_nat )
% 0.29/0.49           => ( rep_assn @ ( times_times_assn @ P @ Q2 ) @ ( produc7507926704131184380et_nat @ H3 @ ( sup_sup_set_nat @ As @ As3 ) ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % star_assnI
% 0.29/0.49  thf(fact_497_sup__bot_Ocomm__monoid__axioms,axiom,
% 0.29/0.49      comm_m4707310049023135612at_nat @ sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat ).
% 0.29/0.49  
% 0.29/0.49  % sup_bot.comm_monoid_axioms
% 0.29/0.49  thf(fact_498_sup__bot_Ocomm__monoid__axioms,axiom,
% 0.29/0.49      comm_m2457627138559323900at_nat @ sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat ).
% 0.29/0.49  
% 0.29/0.49  % sup_bot.comm_monoid_axioms
% 0.29/0.49  thf(fact_499_sup__bot_Ocomm__monoid__axioms,axiom,
% 0.29/0.49      comm_m5709050211238513046at_nat @ sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat ).
% 0.29/0.49  
% 0.29/0.49  % sup_bot.comm_monoid_axioms
% 0.29/0.49  thf(fact_500_sup__bot_Ocomm__monoid__axioms,axiom,
% 0.29/0.49      comm_monoid_set_o @ sup_sup_set_o @ bot_bot_set_o ).
% 0.29/0.49  
% 0.29/0.49  % sup_bot.comm_monoid_axioms
% 0.29/0.49  thf(fact_501_sup__bot_Ocomm__monoid__axioms,axiom,
% 0.29/0.49      comm_monoid_set_nat @ sup_sup_set_nat @ bot_bot_set_nat ).
% 0.29/0.49  
% 0.29/0.49  % sup_bot.comm_monoid_axioms
% 0.29/0.49  thf(fact_502_sup__bot_Ocomm__monoid__axioms,axiom,
% 0.29/0.49      comm_monoid_set_int @ sup_sup_set_int @ bot_bot_set_int ).
% 0.29/0.49  
% 0.29/0.49  % sup_bot.comm_monoid_axioms
% 0.29/0.49  thf(fact_503_boolean__algebra_Ode__Morgan__disj,axiom,
% 0.29/0.49      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( uminus6524753893492686040at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) )
% 0.29/0.49        = ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ ( uminus6524753893492686040at_nat @ Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.de_Morgan_disj
% 0.29/0.49  thf(fact_504_boolean__algebra_Ode__Morgan__disj,axiom,
% 0.29/0.49      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 0.29/0.49        ( ( uminus7117520113953359693_int_o @ ( sup_su8463660629351352368_int_o @ X @ Y ) )
% 0.29/0.49        = ( inf_in3604695632404883862_int_o @ ( uminus7117520113953359693_int_o @ X ) @ ( uminus7117520113953359693_int_o @ Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.de_Morgan_disj
% 0.29/0.49  thf(fact_505_boolean__algebra_Ode__Morgan__disj,axiom,
% 0.29/0.49      ! [X: list_char > $o,Y: list_char > $o] :
% 0.29/0.49        ( ( uminus7154032370948614053char_o @ ( sup_sup_list_char_o @ X @ Y ) )
% 0.29/0.49        = ( inf_inf_list_char_o @ ( uminus7154032370948614053char_o @ X ) @ ( uminus7154032370948614053char_o @ Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.de_Morgan_disj
% 0.29/0.49  thf(fact_506_boolean__algebra_Ode__Morgan__disj,axiom,
% 0.29/0.49      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( uminus2330091110623919550at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 0.29/0.49        = ( inf_in1697001100524423349at_nat @ ( uminus2330091110623919550at_nat @ X ) @ ( uminus2330091110623919550at_nat @ Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.de_Morgan_disj
% 0.29/0.49  thf(fact_507_boolean__algebra_Ode__Morgan__disj,axiom,
% 0.29/0.49      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( uminus935396558254630718at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 0.29/0.49        = ( inf_in7913087082777306421at_nat @ ( uminus935396558254630718at_nat @ X ) @ ( uminus935396558254630718at_nat @ Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.de_Morgan_disj
% 0.29/0.49  thf(fact_508_boolean__algebra_Ode__Morgan__disj,axiom,
% 0.29/0.49      ! [X: set_nat,Y: set_nat] :
% 0.29/0.49        ( ( uminus5710092332889474511et_nat @ ( sup_sup_set_nat @ X @ Y ) )
% 0.29/0.49        = ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.de_Morgan_disj
% 0.29/0.49  thf(fact_509_boolean__algebra_Ode__Morgan__disj,axiom,
% 0.29/0.49      ! [X: product_unit,Y: product_unit] :
% 0.29/0.49        ( ( uminus2952777764628376836t_unit @ ( sup_sup_Product_unit @ X @ Y ) )
% 0.29/0.49        = ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( uminus2952777764628376836t_unit @ Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.de_Morgan_disj
% 0.29/0.49  thf(fact_510_add_Oinverse__inverse,axiom,
% 0.29/0.49      ! [A: int] :
% 0.29/0.49        ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % add.inverse_inverse
% 0.29/0.49  thf(fact_511_add_Oinverse__inverse,axiom,
% 0.29/0.49      ! [A: code_integer] :
% 0.29/0.49        ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % add.inverse_inverse
% 0.29/0.49  thf(fact_512_add_Oinverse__inverse,axiom,
% 0.29/0.49      ! [A: rat] :
% 0.29/0.49        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % add.inverse_inverse
% 0.29/0.49  thf(fact_513_neg__equal__iff__equal,axiom,
% 0.29/0.49      ! [A: int,B: int] :
% 0.29/0.49        ( ( ( uminus_uminus_int @ A )
% 0.29/0.49          = ( uminus_uminus_int @ B ) )
% 0.29/0.49        = ( A = B ) ) ).
% 0.29/0.49  
% 0.29/0.49  % neg_equal_iff_equal
% 0.29/0.49  thf(fact_514_neg__equal__iff__equal,axiom,
% 0.29/0.49      ! [A: code_integer,B: code_integer] :
% 0.29/0.49        ( ( ( uminus1351360451143612070nteger @ A )
% 0.29/0.49          = ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.49        = ( A = B ) ) ).
% 0.29/0.49  
% 0.29/0.49  % neg_equal_iff_equal
% 0.29/0.49  thf(fact_515_neg__equal__iff__equal,axiom,
% 0.29/0.49      ! [A: rat,B: rat] :
% 0.29/0.49        ( ( ( uminus_uminus_rat @ A )
% 0.29/0.49          = ( uminus_uminus_rat @ B ) )
% 0.29/0.49        = ( A = B ) ) ).
% 0.29/0.49  
% 0.29/0.49  % neg_equal_iff_equal
% 0.29/0.49  thf(fact_516_boolean__algebra__class_Oboolean__algebra_Ocompl__eq__compl__iff,axiom,
% 0.29/0.49      ! [X: product_unit,Y: product_unit] :
% 0.29/0.49        ( ( ( uminus2952777764628376836t_unit @ X )
% 0.29/0.49          = ( uminus2952777764628376836t_unit @ Y ) )
% 0.29/0.49        = ( X = Y ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra_class.boolean_algebra.compl_eq_compl_iff
% 0.29/0.49  thf(fact_517_boolean__algebra__class_Oboolean__algebra_Odouble__compl,axiom,
% 0.29/0.49      ! [X: product_unit] :
% 0.29/0.49        ( ( uminus2952777764628376836t_unit @ ( uminus2952777764628376836t_unit @ X ) )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra_class.boolean_algebra.double_compl
% 0.29/0.49  thf(fact_518_mult_Oright__neutral,axiom,
% 0.29/0.49      ! [A: code_integer] :
% 0.29/0.49        ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.right_neutral
% 0.29/0.49  thf(fact_519_mult_Oright__neutral,axiom,
% 0.29/0.49      ! [A: assn] :
% 0.29/0.49        ( ( times_times_assn @ A @ one_one_assn )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.right_neutral
% 0.29/0.49  thf(fact_520_mult_Oright__neutral,axiom,
% 0.29/0.49      ! [A: rat] :
% 0.29/0.49        ( ( times_times_rat @ A @ one_one_rat )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.right_neutral
% 0.29/0.49  thf(fact_521_mult_Oright__neutral,axiom,
% 0.29/0.49      ! [A: nat] :
% 0.29/0.49        ( ( times_times_nat @ A @ one_one_nat )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.right_neutral
% 0.29/0.49  thf(fact_522_mult_Oright__neutral,axiom,
% 0.29/0.49      ! [A: int] :
% 0.29/0.49        ( ( times_times_int @ A @ one_one_int )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.right_neutral
% 0.29/0.49  thf(fact_523_mult__1,axiom,
% 0.29/0.49      ! [A: code_integer] :
% 0.29/0.49        ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % mult_1
% 0.29/0.49  thf(fact_524_mult__1,axiom,
% 0.29/0.49      ! [A: assn] :
% 0.29/0.49        ( ( times_times_assn @ one_one_assn @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % mult_1
% 0.29/0.49  thf(fact_525_mult__1,axiom,
% 0.29/0.49      ! [A: rat] :
% 0.29/0.49        ( ( times_times_rat @ one_one_rat @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % mult_1
% 0.29/0.49  thf(fact_526_mult__1,axiom,
% 0.29/0.49      ! [A: nat] :
% 0.29/0.49        ( ( times_times_nat @ one_one_nat @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % mult_1
% 0.29/0.49  thf(fact_527_mult__1,axiom,
% 0.29/0.49      ! [A: int] :
% 0.29/0.49        ( ( times_times_int @ one_one_int @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % mult_1
% 0.29/0.49  thf(fact_528_inf__top__left,axiom,
% 0.29/0.49      ! [X: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( inf_in2572325071724192079at_nat @ top_to4669805908274784177at_nat @ X )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top_left
% 0.29/0.49  thf(fact_529_inf__top__left,axiom,
% 0.29/0.49      ! [X: product_prod_int_int > $o] :
% 0.29/0.49        ( ( inf_in3604695632404883862_int_o @ top_to1578927101902068148_int_o @ X )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top_left
% 0.29/0.49  thf(fact_530_inf__top__left,axiom,
% 0.29/0.49      ! [X: list_char > $o] :
% 0.29/0.49        ( ( inf_inf_list_char_o @ top_top_list_char_o @ X )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top_left
% 0.29/0.49  thf(fact_531_inf__top__left,axiom,
% 0.29/0.49      ! [X: set_list_nat] :
% 0.29/0.49        ( ( inf_inf_set_list_nat @ top_top_set_list_nat @ X )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top_left
% 0.29/0.49  thf(fact_532_inf__top__left,axiom,
% 0.29/0.49      ! [X: set_o] :
% 0.29/0.49        ( ( inf_inf_set_o @ top_top_set_o @ X )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top_left
% 0.29/0.49  thf(fact_533_inf__top__left,axiom,
% 0.29/0.49      ! [X: set_rat] :
% 0.29/0.49        ( ( inf_inf_set_rat @ top_top_set_rat @ X )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top_left
% 0.29/0.49  thf(fact_534_inf__top__left,axiom,
% 0.29/0.49      ! [X: set_nat] :
% 0.29/0.49        ( ( inf_inf_set_nat @ top_top_set_nat @ X )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top_left
% 0.29/0.49  thf(fact_535_inf__top__left,axiom,
% 0.29/0.49      ! [X: set_int] :
% 0.29/0.49        ( ( inf_inf_set_int @ top_top_set_int @ X )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top_left
% 0.29/0.49  thf(fact_536_inf__top__right,axiom,
% 0.29/0.49      ! [X: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( inf_in2572325071724192079at_nat @ X @ top_to4669805908274784177at_nat )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top_right
% 0.29/0.49  thf(fact_537_inf__top__right,axiom,
% 0.29/0.49      ! [X: product_prod_int_int > $o] :
% 0.29/0.49        ( ( inf_in3604695632404883862_int_o @ X @ top_to1578927101902068148_int_o )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top_right
% 0.29/0.49  thf(fact_538_inf__top__right,axiom,
% 0.29/0.49      ! [X: list_char > $o] :
% 0.29/0.49        ( ( inf_inf_list_char_o @ X @ top_top_list_char_o )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top_right
% 0.29/0.49  thf(fact_539_inf__top__right,axiom,
% 0.29/0.49      ! [X: set_list_nat] :
% 0.29/0.49        ( ( inf_inf_set_list_nat @ X @ top_top_set_list_nat )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top_right
% 0.29/0.49  thf(fact_540_inf__top__right,axiom,
% 0.29/0.49      ! [X: set_o] :
% 0.29/0.49        ( ( inf_inf_set_o @ X @ top_top_set_o )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top_right
% 0.29/0.49  thf(fact_541_inf__top__right,axiom,
% 0.29/0.49      ! [X: set_rat] :
% 0.29/0.49        ( ( inf_inf_set_rat @ X @ top_top_set_rat )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top_right
% 0.29/0.49  thf(fact_542_inf__top__right,axiom,
% 0.29/0.49      ! [X: set_nat] :
% 0.29/0.49        ( ( inf_inf_set_nat @ X @ top_top_set_nat )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top_right
% 0.29/0.49  thf(fact_543_inf__top__right,axiom,
% 0.29/0.49      ! [X: set_int] :
% 0.29/0.49        ( ( inf_inf_set_int @ X @ top_top_set_int )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top_right
% 0.29/0.49  thf(fact_544_inf__eq__top__iff,axiom,
% 0.29/0.49      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 0.29/0.49          = top_to4669805908274784177at_nat )
% 0.29/0.49        = ( ( X = top_to4669805908274784177at_nat )
% 0.29/0.49          & ( Y = top_to4669805908274784177at_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_eq_top_iff
% 0.29/0.49  thf(fact_545_inf__eq__top__iff,axiom,
% 0.29/0.49      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 0.29/0.49        ( ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 0.29/0.49          = top_to1578927101902068148_int_o )
% 0.29/0.49        = ( ( X = top_to1578927101902068148_int_o )
% 0.29/0.49          & ( Y = top_to1578927101902068148_int_o ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_eq_top_iff
% 0.29/0.49  thf(fact_546_inf__eq__top__iff,axiom,
% 0.29/0.49      ! [X: list_char > $o,Y: list_char > $o] :
% 0.29/0.49        ( ( ( inf_inf_list_char_o @ X @ Y )
% 0.29/0.49          = top_top_list_char_o )
% 0.29/0.49        = ( ( X = top_top_list_char_o )
% 0.29/0.49          & ( Y = top_top_list_char_o ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_eq_top_iff
% 0.29/0.49  thf(fact_547_inf__eq__top__iff,axiom,
% 0.29/0.49      ! [X: set_list_nat,Y: set_list_nat] :
% 0.29/0.49        ( ( ( inf_inf_set_list_nat @ X @ Y )
% 0.29/0.49          = top_top_set_list_nat )
% 0.29/0.49        = ( ( X = top_top_set_list_nat )
% 0.29/0.49          & ( Y = top_top_set_list_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_eq_top_iff
% 0.29/0.49  thf(fact_548_inf__eq__top__iff,axiom,
% 0.29/0.49      ! [X: set_o,Y: set_o] :
% 0.29/0.49        ( ( ( inf_inf_set_o @ X @ Y )
% 0.29/0.49          = top_top_set_o )
% 0.29/0.49        = ( ( X = top_top_set_o )
% 0.29/0.49          & ( Y = top_top_set_o ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_eq_top_iff
% 0.29/0.49  thf(fact_549_inf__eq__top__iff,axiom,
% 0.29/0.49      ! [X: set_rat,Y: set_rat] :
% 0.29/0.49        ( ( ( inf_inf_set_rat @ X @ Y )
% 0.29/0.49          = top_top_set_rat )
% 0.29/0.49        = ( ( X = top_top_set_rat )
% 0.29/0.49          & ( Y = top_top_set_rat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_eq_top_iff
% 0.29/0.49  thf(fact_550_inf__eq__top__iff,axiom,
% 0.29/0.49      ! [X: set_nat,Y: set_nat] :
% 0.29/0.49        ( ( ( inf_inf_set_nat @ X @ Y )
% 0.29/0.49          = top_top_set_nat )
% 0.29/0.49        = ( ( X = top_top_set_nat )
% 0.29/0.49          & ( Y = top_top_set_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_eq_top_iff
% 0.29/0.49  thf(fact_551_inf__eq__top__iff,axiom,
% 0.29/0.49      ! [X: set_int,Y: set_int] :
% 0.29/0.49        ( ( ( inf_inf_set_int @ X @ Y )
% 0.29/0.49          = top_top_set_int )
% 0.29/0.49        = ( ( X = top_top_set_int )
% 0.29/0.49          & ( Y = top_top_set_int ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_eq_top_iff
% 0.29/0.49  thf(fact_552_top__eq__inf__iff,axiom,
% 0.29/0.49      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( top_to4669805908274784177at_nat
% 0.29/0.49          = ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 0.29/0.49        = ( ( X = top_to4669805908274784177at_nat )
% 0.29/0.49          & ( Y = top_to4669805908274784177at_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % top_eq_inf_iff
% 0.29/0.49  thf(fact_553_top__eq__inf__iff,axiom,
% 0.29/0.49      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 0.29/0.49        ( ( top_to1578927101902068148_int_o
% 0.29/0.49          = ( inf_in3604695632404883862_int_o @ X @ Y ) )
% 0.29/0.49        = ( ( X = top_to1578927101902068148_int_o )
% 0.29/0.49          & ( Y = top_to1578927101902068148_int_o ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % top_eq_inf_iff
% 0.29/0.49  thf(fact_554_top__eq__inf__iff,axiom,
% 0.29/0.49      ! [X: list_char > $o,Y: list_char > $o] :
% 0.29/0.49        ( ( top_top_list_char_o
% 0.29/0.49          = ( inf_inf_list_char_o @ X @ Y ) )
% 0.29/0.49        = ( ( X = top_top_list_char_o )
% 0.29/0.49          & ( Y = top_top_list_char_o ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % top_eq_inf_iff
% 0.29/0.49  thf(fact_555_top__eq__inf__iff,axiom,
% 0.29/0.49      ! [X: set_list_nat,Y: set_list_nat] :
% 0.29/0.49        ( ( top_top_set_list_nat
% 0.29/0.49          = ( inf_inf_set_list_nat @ X @ Y ) )
% 0.29/0.49        = ( ( X = top_top_set_list_nat )
% 0.29/0.49          & ( Y = top_top_set_list_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % top_eq_inf_iff
% 0.29/0.49  thf(fact_556_top__eq__inf__iff,axiom,
% 0.29/0.49      ! [X: set_o,Y: set_o] :
% 0.29/0.49        ( ( top_top_set_o
% 0.29/0.49          = ( inf_inf_set_o @ X @ Y ) )
% 0.29/0.49        = ( ( X = top_top_set_o )
% 0.29/0.49          & ( Y = top_top_set_o ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % top_eq_inf_iff
% 0.29/0.49  thf(fact_557_top__eq__inf__iff,axiom,
% 0.29/0.49      ! [X: set_rat,Y: set_rat] :
% 0.29/0.49        ( ( top_top_set_rat
% 0.29/0.49          = ( inf_inf_set_rat @ X @ Y ) )
% 0.29/0.49        = ( ( X = top_top_set_rat )
% 0.29/0.49          & ( Y = top_top_set_rat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % top_eq_inf_iff
% 0.29/0.49  thf(fact_558_top__eq__inf__iff,axiom,
% 0.29/0.49      ! [X: set_nat,Y: set_nat] :
% 0.29/0.49        ( ( top_top_set_nat
% 0.29/0.49          = ( inf_inf_set_nat @ X @ Y ) )
% 0.29/0.49        = ( ( X = top_top_set_nat )
% 0.29/0.49          & ( Y = top_top_set_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % top_eq_inf_iff
% 0.29/0.49  thf(fact_559_top__eq__inf__iff,axiom,
% 0.29/0.49      ! [X: set_int,Y: set_int] :
% 0.29/0.49        ( ( top_top_set_int
% 0.29/0.49          = ( inf_inf_set_int @ X @ Y ) )
% 0.29/0.49        = ( ( X = top_top_set_int )
% 0.29/0.49          & ( Y = top_top_set_int ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % top_eq_inf_iff
% 0.29/0.49  thf(fact_560_inf__top_Oeq__neutr__iff,axiom,
% 0.29/0.49      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( ( inf_in2572325071724192079at_nat @ A @ B )
% 0.29/0.49          = top_to4669805908274784177at_nat )
% 0.29/0.49        = ( ( A = top_to4669805908274784177at_nat )
% 0.29/0.49          & ( B = top_to4669805908274784177at_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.eq_neutr_iff
% 0.29/0.49  thf(fact_561_inf__top_Oeq__neutr__iff,axiom,
% 0.29/0.49      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 0.29/0.49        ( ( ( inf_in3604695632404883862_int_o @ A @ B )
% 0.29/0.49          = top_to1578927101902068148_int_o )
% 0.29/0.49        = ( ( A = top_to1578927101902068148_int_o )
% 0.29/0.49          & ( B = top_to1578927101902068148_int_o ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.eq_neutr_iff
% 0.29/0.49  thf(fact_562_inf__top_Oeq__neutr__iff,axiom,
% 0.29/0.49      ! [A: list_char > $o,B: list_char > $o] :
% 0.29/0.49        ( ( ( inf_inf_list_char_o @ A @ B )
% 0.29/0.49          = top_top_list_char_o )
% 0.29/0.49        = ( ( A = top_top_list_char_o )
% 0.29/0.49          & ( B = top_top_list_char_o ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.eq_neutr_iff
% 0.29/0.49  thf(fact_563_inf__top_Oeq__neutr__iff,axiom,
% 0.29/0.49      ! [A: set_list_nat,B: set_list_nat] :
% 0.29/0.49        ( ( ( inf_inf_set_list_nat @ A @ B )
% 0.29/0.49          = top_top_set_list_nat )
% 0.29/0.49        = ( ( A = top_top_set_list_nat )
% 0.29/0.49          & ( B = top_top_set_list_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.eq_neutr_iff
% 0.29/0.49  thf(fact_564_inf__top_Oeq__neutr__iff,axiom,
% 0.29/0.49      ! [A: set_o,B: set_o] :
% 0.29/0.49        ( ( ( inf_inf_set_o @ A @ B )
% 0.29/0.49          = top_top_set_o )
% 0.29/0.49        = ( ( A = top_top_set_o )
% 0.29/0.49          & ( B = top_top_set_o ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.eq_neutr_iff
% 0.29/0.49  thf(fact_565_inf__top_Oeq__neutr__iff,axiom,
% 0.29/0.49      ! [A: set_rat,B: set_rat] :
% 0.29/0.49        ( ( ( inf_inf_set_rat @ A @ B )
% 0.29/0.49          = top_top_set_rat )
% 0.29/0.49        = ( ( A = top_top_set_rat )
% 0.29/0.49          & ( B = top_top_set_rat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.eq_neutr_iff
% 0.29/0.49  thf(fact_566_inf__top_Oeq__neutr__iff,axiom,
% 0.29/0.49      ! [A: set_nat,B: set_nat] :
% 0.29/0.49        ( ( ( inf_inf_set_nat @ A @ B )
% 0.29/0.49          = top_top_set_nat )
% 0.29/0.49        = ( ( A = top_top_set_nat )
% 0.29/0.49          & ( B = top_top_set_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.eq_neutr_iff
% 0.29/0.49  thf(fact_567_inf__top_Oeq__neutr__iff,axiom,
% 0.29/0.49      ! [A: set_int,B: set_int] :
% 0.29/0.49        ( ( ( inf_inf_set_int @ A @ B )
% 0.29/0.49          = top_top_set_int )
% 0.29/0.49        = ( ( A = top_top_set_int )
% 0.29/0.49          & ( B = top_top_set_int ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.eq_neutr_iff
% 0.29/0.49  thf(fact_568_inf__top_Oleft__neutral,axiom,
% 0.29/0.49      ! [A: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( inf_in2572325071724192079at_nat @ top_to4669805908274784177at_nat @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.left_neutral
% 0.29/0.49  thf(fact_569_inf__top_Oleft__neutral,axiom,
% 0.29/0.49      ! [A: product_prod_int_int > $o] :
% 0.29/0.49        ( ( inf_in3604695632404883862_int_o @ top_to1578927101902068148_int_o @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.left_neutral
% 0.29/0.49  thf(fact_570_inf__top_Oleft__neutral,axiom,
% 0.29/0.49      ! [A: list_char > $o] :
% 0.29/0.49        ( ( inf_inf_list_char_o @ top_top_list_char_o @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.left_neutral
% 0.29/0.49  thf(fact_571_inf__top_Oleft__neutral,axiom,
% 0.29/0.49      ! [A: set_list_nat] :
% 0.29/0.49        ( ( inf_inf_set_list_nat @ top_top_set_list_nat @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.left_neutral
% 0.29/0.49  thf(fact_572_inf__top_Oleft__neutral,axiom,
% 0.29/0.49      ! [A: set_o] :
% 0.29/0.49        ( ( inf_inf_set_o @ top_top_set_o @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.left_neutral
% 0.29/0.49  thf(fact_573_inf__top_Oleft__neutral,axiom,
% 0.29/0.49      ! [A: set_rat] :
% 0.29/0.49        ( ( inf_inf_set_rat @ top_top_set_rat @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.left_neutral
% 0.29/0.49  thf(fact_574_inf__top_Oleft__neutral,axiom,
% 0.29/0.49      ! [A: set_nat] :
% 0.29/0.49        ( ( inf_inf_set_nat @ top_top_set_nat @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.left_neutral
% 0.29/0.49  thf(fact_575_inf__top_Oleft__neutral,axiom,
% 0.29/0.49      ! [A: set_int] :
% 0.29/0.49        ( ( inf_inf_set_int @ top_top_set_int @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.left_neutral
% 0.29/0.49  thf(fact_576_inf__top_Oneutr__eq__iff,axiom,
% 0.29/0.49      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( top_to4669805908274784177at_nat
% 0.29/0.49          = ( inf_in2572325071724192079at_nat @ A @ B ) )
% 0.29/0.49        = ( ( A = top_to4669805908274784177at_nat )
% 0.29/0.49          & ( B = top_to4669805908274784177at_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.neutr_eq_iff
% 0.29/0.49  thf(fact_577_inf__top_Oneutr__eq__iff,axiom,
% 0.29/0.49      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 0.29/0.49        ( ( top_to1578927101902068148_int_o
% 0.29/0.49          = ( inf_in3604695632404883862_int_o @ A @ B ) )
% 0.29/0.49        = ( ( A = top_to1578927101902068148_int_o )
% 0.29/0.49          & ( B = top_to1578927101902068148_int_o ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.neutr_eq_iff
% 0.29/0.49  thf(fact_578_inf__top_Oneutr__eq__iff,axiom,
% 0.29/0.49      ! [A: list_char > $o,B: list_char > $o] :
% 0.29/0.49        ( ( top_top_list_char_o
% 0.29/0.49          = ( inf_inf_list_char_o @ A @ B ) )
% 0.29/0.49        = ( ( A = top_top_list_char_o )
% 0.29/0.49          & ( B = top_top_list_char_o ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.neutr_eq_iff
% 0.29/0.49  thf(fact_579_inf__top_Oneutr__eq__iff,axiom,
% 0.29/0.49      ! [A: set_list_nat,B: set_list_nat] :
% 0.29/0.49        ( ( top_top_set_list_nat
% 0.29/0.49          = ( inf_inf_set_list_nat @ A @ B ) )
% 0.29/0.49        = ( ( A = top_top_set_list_nat )
% 0.29/0.49          & ( B = top_top_set_list_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.neutr_eq_iff
% 0.29/0.49  thf(fact_580_inf__top_Oneutr__eq__iff,axiom,
% 0.29/0.49      ! [A: set_o,B: set_o] :
% 0.29/0.49        ( ( top_top_set_o
% 0.29/0.49          = ( inf_inf_set_o @ A @ B ) )
% 0.29/0.49        = ( ( A = top_top_set_o )
% 0.29/0.49          & ( B = top_top_set_o ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.neutr_eq_iff
% 0.29/0.49  thf(fact_581_inf__top_Oneutr__eq__iff,axiom,
% 0.29/0.49      ! [A: set_rat,B: set_rat] :
% 0.29/0.49        ( ( top_top_set_rat
% 0.29/0.49          = ( inf_inf_set_rat @ A @ B ) )
% 0.29/0.49        = ( ( A = top_top_set_rat )
% 0.29/0.49          & ( B = top_top_set_rat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.neutr_eq_iff
% 0.29/0.49  thf(fact_582_inf__top_Oneutr__eq__iff,axiom,
% 0.29/0.49      ! [A: set_nat,B: set_nat] :
% 0.29/0.49        ( ( top_top_set_nat
% 0.29/0.49          = ( inf_inf_set_nat @ A @ B ) )
% 0.29/0.49        = ( ( A = top_top_set_nat )
% 0.29/0.49          & ( B = top_top_set_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.neutr_eq_iff
% 0.29/0.49  thf(fact_583_inf__top_Oneutr__eq__iff,axiom,
% 0.29/0.49      ! [A: set_int,B: set_int] :
% 0.29/0.49        ( ( top_top_set_int
% 0.29/0.49          = ( inf_inf_set_int @ A @ B ) )
% 0.29/0.49        = ( ( A = top_top_set_int )
% 0.29/0.49          & ( B = top_top_set_int ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.neutr_eq_iff
% 0.29/0.49  thf(fact_584_inf__top_Oright__neutral,axiom,
% 0.29/0.49      ! [A: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( inf_in2572325071724192079at_nat @ A @ top_to4669805908274784177at_nat )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.right_neutral
% 0.29/0.49  thf(fact_585_inf__top_Oright__neutral,axiom,
% 0.29/0.49      ! [A: product_prod_int_int > $o] :
% 0.29/0.49        ( ( inf_in3604695632404883862_int_o @ A @ top_to1578927101902068148_int_o )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.right_neutral
% 0.29/0.49  thf(fact_586_inf__top_Oright__neutral,axiom,
% 0.29/0.49      ! [A: list_char > $o] :
% 0.29/0.49        ( ( inf_inf_list_char_o @ A @ top_top_list_char_o )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.right_neutral
% 0.29/0.49  thf(fact_587_inf__top_Oright__neutral,axiom,
% 0.29/0.49      ! [A: set_list_nat] :
% 0.29/0.49        ( ( inf_inf_set_list_nat @ A @ top_top_set_list_nat )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.right_neutral
% 0.29/0.49  thf(fact_588_inf__top_Oright__neutral,axiom,
% 0.29/0.49      ! [A: set_o] :
% 0.29/0.49        ( ( inf_inf_set_o @ A @ top_top_set_o )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.right_neutral
% 0.29/0.49  thf(fact_589_inf__top_Oright__neutral,axiom,
% 0.29/0.49      ! [A: set_rat] :
% 0.29/0.49        ( ( inf_inf_set_rat @ A @ top_top_set_rat )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.right_neutral
% 0.29/0.49  thf(fact_590_inf__top_Oright__neutral,axiom,
% 0.29/0.49      ! [A: set_nat] :
% 0.29/0.49        ( ( inf_inf_set_nat @ A @ top_top_set_nat )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.right_neutral
% 0.29/0.49  thf(fact_591_inf__top_Oright__neutral,axiom,
% 0.29/0.49      ! [A: set_int] :
% 0.29/0.49        ( ( inf_inf_set_int @ A @ top_top_set_int )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.right_neutral
% 0.29/0.49  thf(fact_592_boolean__algebra_Odisj__one__left,axiom,
% 0.29/0.49      ! [X: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( sup_su3035147773818789531at_nat @ top_to8764741339697478167at_nat @ X )
% 0.29/0.49        = top_to8764741339697478167at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_one_left
% 0.29/0.49  thf(fact_593_boolean__algebra_Odisj__one__left,axiom,
% 0.29/0.49      ! [X: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( sup_su5525570899277871387at_nat @ top_to6833984726390702231at_nat @ X )
% 0.29/0.49        = top_to6833984726390702231at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_one_left
% 0.29/0.49  thf(fact_594_boolean__algebra_Odisj__one__left,axiom,
% 0.29/0.49      ! [X: set_list_nat] :
% 0.29/0.49        ( ( sup_sup_set_list_nat @ top_top_set_list_nat @ X )
% 0.29/0.49        = top_top_set_list_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_one_left
% 0.29/0.49  thf(fact_595_boolean__algebra_Odisj__one__left,axiom,
% 0.29/0.49      ! [X: set_o] :
% 0.29/0.49        ( ( sup_sup_set_o @ top_top_set_o @ X )
% 0.29/0.49        = top_top_set_o ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_one_left
% 0.29/0.49  thf(fact_596_boolean__algebra_Odisj__one__left,axiom,
% 0.29/0.49      ! [X: set_rat] :
% 0.29/0.49        ( ( sup_sup_set_rat @ top_top_set_rat @ X )
% 0.29/0.49        = top_top_set_rat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_one_left
% 0.29/0.49  thf(fact_597_boolean__algebra_Odisj__one__left,axiom,
% 0.29/0.49      ! [X: set_nat] :
% 0.29/0.49        ( ( sup_sup_set_nat @ top_top_set_nat @ X )
% 0.29/0.49        = top_top_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_one_left
% 0.29/0.49  thf(fact_598_boolean__algebra_Odisj__one__left,axiom,
% 0.29/0.49      ! [X: set_int] :
% 0.29/0.49        ( ( sup_sup_set_int @ top_top_set_int @ X )
% 0.29/0.49        = top_top_set_int ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_one_left
% 0.29/0.49  thf(fact_599_boolean__algebra_Odisj__one__right,axiom,
% 0.29/0.49      ! [X: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( sup_su3035147773818789531at_nat @ X @ top_to8764741339697478167at_nat )
% 0.29/0.49        = top_to8764741339697478167at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_one_right
% 0.29/0.49  thf(fact_600_boolean__algebra_Odisj__one__right,axiom,
% 0.29/0.49      ! [X: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( sup_su5525570899277871387at_nat @ X @ top_to6833984726390702231at_nat )
% 0.29/0.49        = top_to6833984726390702231at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_one_right
% 0.29/0.49  thf(fact_601_boolean__algebra_Odisj__one__right,axiom,
% 0.29/0.49      ! [X: set_list_nat] :
% 0.29/0.49        ( ( sup_sup_set_list_nat @ X @ top_top_set_list_nat )
% 0.29/0.49        = top_top_set_list_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_one_right
% 0.29/0.49  thf(fact_602_boolean__algebra_Odisj__one__right,axiom,
% 0.29/0.49      ! [X: set_o] :
% 0.29/0.49        ( ( sup_sup_set_o @ X @ top_top_set_o )
% 0.29/0.49        = top_top_set_o ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_one_right
% 0.29/0.49  thf(fact_603_boolean__algebra_Odisj__one__right,axiom,
% 0.29/0.49      ! [X: set_rat] :
% 0.29/0.49        ( ( sup_sup_set_rat @ X @ top_top_set_rat )
% 0.29/0.49        = top_top_set_rat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_one_right
% 0.29/0.49  thf(fact_604_boolean__algebra_Odisj__one__right,axiom,
% 0.29/0.49      ! [X: set_nat] :
% 0.29/0.49        ( ( sup_sup_set_nat @ X @ top_top_set_nat )
% 0.29/0.49        = top_top_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_one_right
% 0.29/0.49  thf(fact_605_boolean__algebra_Odisj__one__right,axiom,
% 0.29/0.49      ! [X: set_int] :
% 0.29/0.49        ( ( sup_sup_set_int @ X @ top_top_set_int )
% 0.29/0.49        = top_top_set_int ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_one_right
% 0.29/0.49  thf(fact_606_sup__top__left,axiom,
% 0.29/0.49      ! [X: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( sup_su3035147773818789531at_nat @ top_to8764741339697478167at_nat @ X )
% 0.29/0.49        = top_to8764741339697478167at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_top_left
% 0.29/0.49  thf(fact_607_sup__top__left,axiom,
% 0.29/0.49      ! [X: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( sup_su5525570899277871387at_nat @ top_to6833984726390702231at_nat @ X )
% 0.29/0.49        = top_to6833984726390702231at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_top_left
% 0.29/0.49  thf(fact_608_sup__top__left,axiom,
% 0.29/0.49      ! [X: set_list_nat] :
% 0.29/0.49        ( ( sup_sup_set_list_nat @ top_top_set_list_nat @ X )
% 0.29/0.49        = top_top_set_list_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_top_left
% 0.29/0.49  thf(fact_609_sup__top__left,axiom,
% 0.29/0.49      ! [X: set_o] :
% 0.29/0.49        ( ( sup_sup_set_o @ top_top_set_o @ X )
% 0.29/0.49        = top_top_set_o ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_top_left
% 0.29/0.49  thf(fact_610_sup__top__left,axiom,
% 0.29/0.49      ! [X: set_rat] :
% 0.29/0.49        ( ( sup_sup_set_rat @ top_top_set_rat @ X )
% 0.29/0.49        = top_top_set_rat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_top_left
% 0.29/0.49  thf(fact_611_sup__top__left,axiom,
% 0.29/0.49      ! [X: set_nat] :
% 0.29/0.49        ( ( sup_sup_set_nat @ top_top_set_nat @ X )
% 0.29/0.49        = top_top_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_top_left
% 0.29/0.49  thf(fact_612_sup__top__left,axiom,
% 0.29/0.49      ! [X: set_int] :
% 0.29/0.49        ( ( sup_sup_set_int @ top_top_set_int @ X )
% 0.29/0.49        = top_top_set_int ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_top_left
% 0.29/0.49  thf(fact_613_sup__top__right,axiom,
% 0.29/0.49      ! [X: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( sup_su3035147773818789531at_nat @ X @ top_to8764741339697478167at_nat )
% 0.29/0.49        = top_to8764741339697478167at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_top_right
% 0.29/0.49  thf(fact_614_sup__top__right,axiom,
% 0.29/0.49      ! [X: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( sup_su5525570899277871387at_nat @ X @ top_to6833984726390702231at_nat )
% 0.29/0.49        = top_to6833984726390702231at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_top_right
% 0.29/0.49  thf(fact_615_sup__top__right,axiom,
% 0.29/0.49      ! [X: set_list_nat] :
% 0.29/0.49        ( ( sup_sup_set_list_nat @ X @ top_top_set_list_nat )
% 0.29/0.49        = top_top_set_list_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_top_right
% 0.29/0.49  thf(fact_616_sup__top__right,axiom,
% 0.29/0.49      ! [X: set_o] :
% 0.29/0.49        ( ( sup_sup_set_o @ X @ top_top_set_o )
% 0.29/0.49        = top_top_set_o ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_top_right
% 0.29/0.49  thf(fact_617_sup__top__right,axiom,
% 0.29/0.49      ! [X: set_rat] :
% 0.29/0.49        ( ( sup_sup_set_rat @ X @ top_top_set_rat )
% 0.29/0.49        = top_top_set_rat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_top_right
% 0.29/0.49  thf(fact_618_sup__top__right,axiom,
% 0.29/0.49      ! [X: set_nat] :
% 0.29/0.49        ( ( sup_sup_set_nat @ X @ top_top_set_nat )
% 0.29/0.49        = top_top_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_top_right
% 0.29/0.49  thf(fact_619_sup__top__right,axiom,
% 0.29/0.49      ! [X: set_int] :
% 0.29/0.49        ( ( sup_sup_set_int @ X @ top_top_set_int )
% 0.29/0.49        = top_top_set_int ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_top_right
% 0.29/0.49  thf(fact_620_boolean__algebra_Ocompl__one,axiom,
% 0.29/0.49      ( ( uminus6524753893492686040at_nat @ top_to4669805908274784177at_nat )
% 0.29/0.49      = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.compl_one
% 0.29/0.49  thf(fact_621_boolean__algebra_Ocompl__one,axiom,
% 0.29/0.49      ( ( uminus3195874150345416415st_nat @ top_top_set_list_nat )
% 0.29/0.49      = bot_bot_set_list_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.compl_one
% 0.29/0.49  thf(fact_622_boolean__algebra_Ocompl__one,axiom,
% 0.29/0.49      ( ( uminus_uminus_set_o @ top_top_set_o )
% 0.29/0.49      = bot_bot_set_o ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.compl_one
% 0.29/0.49  thf(fact_623_boolean__algebra_Ocompl__one,axiom,
% 0.29/0.49      ( ( uminus2201863774496077783et_rat @ top_top_set_rat )
% 0.29/0.49      = bot_bot_set_rat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.compl_one
% 0.29/0.49  thf(fact_624_boolean__algebra_Ocompl__one,axiom,
% 0.29/0.49      ( ( uminus5710092332889474511et_nat @ top_top_set_nat )
% 0.29/0.49      = bot_bot_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.compl_one
% 0.29/0.49  thf(fact_625_boolean__algebra_Ocompl__one,axiom,
% 0.29/0.49      ( ( uminus1532241313380277803et_int @ top_top_set_int )
% 0.29/0.49      = bot_bot_set_int ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.compl_one
% 0.29/0.49  thf(fact_626_boolean__algebra_Ocompl__one,axiom,
% 0.29/0.49      ( ( uminus2952777764628376836t_unit @ top_top_Product_unit )
% 0.29/0.49      = bot_bot_Product_unit ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.compl_one
% 0.29/0.49  thf(fact_627_boolean__algebra_Ocompl__zero,axiom,
% 0.29/0.49      ( ( uminus6524753893492686040at_nat @ bot_bo2099793752762293965at_nat )
% 0.29/0.49      = top_to4669805908274784177at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.compl_zero
% 0.29/0.49  thf(fact_628_boolean__algebra_Ocompl__zero,axiom,
% 0.29/0.49      ( ( uminus3195874150345416415st_nat @ bot_bot_set_list_nat )
% 0.29/0.49      = top_top_set_list_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.compl_zero
% 0.29/0.49  thf(fact_629_boolean__algebra_Ocompl__zero,axiom,
% 0.29/0.49      ( ( uminus_uminus_set_o @ bot_bot_set_o )
% 0.29/0.49      = top_top_set_o ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.compl_zero
% 0.29/0.49  thf(fact_630_boolean__algebra_Ocompl__zero,axiom,
% 0.29/0.49      ( ( uminus2201863774496077783et_rat @ bot_bot_set_rat )
% 0.29/0.49      = top_top_set_rat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.compl_zero
% 0.29/0.49  thf(fact_631_boolean__algebra_Ocompl__zero,axiom,
% 0.29/0.49      ( ( uminus5710092332889474511et_nat @ bot_bot_set_nat )
% 0.29/0.49      = top_top_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.compl_zero
% 0.29/0.49  thf(fact_632_boolean__algebra_Ocompl__zero,axiom,
% 0.29/0.49      ( ( uminus1532241313380277803et_int @ bot_bot_set_int )
% 0.29/0.49      = top_top_set_int ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.compl_zero
% 0.29/0.49  thf(fact_633_boolean__algebra_Ocompl__zero,axiom,
% 0.29/0.49      ( ( uminus2952777764628376836t_unit @ bot_bot_Product_unit )
% 0.29/0.49      = top_top_Product_unit ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.compl_zero
% 0.29/0.49  thf(fact_634_inf__compl__bot__left1,axiom,
% 0.29/0.49      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 0.29/0.49        ( ( inf_in3604695632404883862_int_o @ ( uminus7117520113953359693_int_o @ X ) @ ( inf_in3604695632404883862_int_o @ X @ Y ) )
% 0.29/0.49        = bot_bo8147686125503663512_int_o ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_compl_bot_left1
% 0.29/0.49  thf(fact_635_inf__compl__bot__left1,axiom,
% 0.29/0.49      ! [X: list_char > $o,Y: list_char > $o] :
% 0.29/0.49        ( ( inf_inf_list_char_o @ ( uminus7154032370948614053char_o @ X ) @ ( inf_inf_list_char_o @ X @ Y ) )
% 0.29/0.49        = bot_bot_list_char_o ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_compl_bot_left1
% 0.29/0.49  thf(fact_636_inf__compl__bot__left1,axiom,
% 0.29/0.49      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 0.29/0.49        = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_compl_bot_left1
% 0.29/0.49  thf(fact_637_inf__compl__bot__left1,axiom,
% 0.29/0.49      ! [X: set_o,Y: set_o] :
% 0.29/0.49        ( ( inf_inf_set_o @ ( uminus_uminus_set_o @ X ) @ ( inf_inf_set_o @ X @ Y ) )
% 0.29/0.49        = bot_bot_set_o ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_compl_bot_left1
% 0.29/0.49  thf(fact_638_inf__compl__bot__left1,axiom,
% 0.29/0.49      ! [X: set_nat,Y: set_nat] :
% 0.29/0.49        ( ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( inf_inf_set_nat @ X @ Y ) )
% 0.29/0.49        = bot_bot_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_compl_bot_left1
% 0.29/0.49  thf(fact_639_inf__compl__bot__left1,axiom,
% 0.29/0.49      ! [X: set_int,Y: set_int] :
% 0.29/0.49        ( ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ ( inf_inf_set_int @ X @ Y ) )
% 0.29/0.49        = bot_bot_set_int ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_compl_bot_left1
% 0.29/0.49  thf(fact_640_inf__compl__bot__left1,axiom,
% 0.29/0.49      ! [X: product_unit,Y: product_unit] :
% 0.29/0.49        ( ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( inf_inf_Product_unit @ X @ Y ) )
% 0.29/0.49        = bot_bot_Product_unit ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_compl_bot_left1
% 0.29/0.49  thf(fact_641_inf__compl__bot__left2,axiom,
% 0.29/0.49      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 0.29/0.49        ( ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ ( uminus7117520113953359693_int_o @ X ) @ Y ) )
% 0.29/0.49        = bot_bo8147686125503663512_int_o ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_compl_bot_left2
% 0.29/0.49  thf(fact_642_inf__compl__bot__left2,axiom,
% 0.29/0.49      ! [X: list_char > $o,Y: list_char > $o] :
% 0.29/0.49        ( ( inf_inf_list_char_o @ X @ ( inf_inf_list_char_o @ ( uminus7154032370948614053char_o @ X ) @ Y ) )
% 0.29/0.49        = bot_bot_list_char_o ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_compl_bot_left2
% 0.29/0.49  thf(fact_643_inf__compl__bot__left2,axiom,
% 0.29/0.49      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ Y ) )
% 0.29/0.49        = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_compl_bot_left2
% 0.29/0.49  thf(fact_644_inf__compl__bot__left2,axiom,
% 0.29/0.49      ! [X: set_o,Y: set_o] :
% 0.29/0.49        ( ( inf_inf_set_o @ X @ ( inf_inf_set_o @ ( uminus_uminus_set_o @ X ) @ Y ) )
% 0.29/0.49        = bot_bot_set_o ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_compl_bot_left2
% 0.29/0.49  thf(fact_645_inf__compl__bot__left2,axiom,
% 0.29/0.49      ! [X: set_nat,Y: set_nat] :
% 0.29/0.49        ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ Y ) )
% 0.29/0.49        = bot_bot_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_compl_bot_left2
% 0.29/0.49  thf(fact_646_inf__compl__bot__left2,axiom,
% 0.29/0.49      ! [X: set_int,Y: set_int] :
% 0.29/0.49        ( ( inf_inf_set_int @ X @ ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ Y ) )
% 0.29/0.49        = bot_bot_set_int ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_compl_bot_left2
% 0.29/0.49  thf(fact_647_inf__compl__bot__left2,axiom,
% 0.29/0.49      ! [X: product_unit,Y: product_unit] :
% 0.29/0.49        ( ( inf_inf_Product_unit @ X @ ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ Y ) )
% 0.29/0.49        = bot_bot_Product_unit ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_compl_bot_left2
% 0.29/0.49  thf(fact_648_inf__compl__bot__right,axiom,
% 0.29/0.49      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 0.29/0.49        ( ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ ( uminus7117520113953359693_int_o @ X ) ) )
% 0.29/0.49        = bot_bo8147686125503663512_int_o ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_compl_bot_right
% 0.29/0.49  thf(fact_649_inf__compl__bot__right,axiom,
% 0.29/0.49      ! [X: list_char > $o,Y: list_char > $o] :
% 0.29/0.49        ( ( inf_inf_list_char_o @ X @ ( inf_inf_list_char_o @ Y @ ( uminus7154032370948614053char_o @ X ) ) )
% 0.29/0.49        = bot_bot_list_char_o ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_compl_bot_right
% 0.29/0.49  thf(fact_650_inf__compl__bot__right,axiom,
% 0.29/0.49      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ ( uminus6524753893492686040at_nat @ X ) ) )
% 0.29/0.49        = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_compl_bot_right
% 0.29/0.49  thf(fact_651_inf__compl__bot__right,axiom,
% 0.29/0.49      ! [X: set_o,Y: set_o] :
% 0.29/0.49        ( ( inf_inf_set_o @ X @ ( inf_inf_set_o @ Y @ ( uminus_uminus_set_o @ X ) ) )
% 0.29/0.49        = bot_bot_set_o ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_compl_bot_right
% 0.29/0.49  thf(fact_652_inf__compl__bot__right,axiom,
% 0.29/0.49      ! [X: set_nat,Y: set_nat] :
% 0.29/0.49        ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ ( uminus5710092332889474511et_nat @ X ) ) )
% 0.29/0.49        = bot_bot_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_compl_bot_right
% 0.29/0.49  thf(fact_653_inf__compl__bot__right,axiom,
% 0.29/0.49      ! [X: set_int,Y: set_int] :
% 0.29/0.49        ( ( inf_inf_set_int @ X @ ( inf_inf_set_int @ Y @ ( uminus1532241313380277803et_int @ X ) ) )
% 0.29/0.49        = bot_bot_set_int ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_compl_bot_right
% 0.29/0.49  thf(fact_654_inf__compl__bot__right,axiom,
% 0.29/0.49      ! [X: product_unit,Y: product_unit] :
% 0.29/0.49        ( ( inf_inf_Product_unit @ X @ ( inf_inf_Product_unit @ Y @ ( uminus2952777764628376836t_unit @ X ) ) )
% 0.29/0.49        = bot_bot_Product_unit ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_compl_bot_right
% 0.29/0.49  thf(fact_655_boolean__algebra_Oconj__cancel__left,axiom,
% 0.29/0.49      ! [X: product_prod_int_int > $o] :
% 0.29/0.49        ( ( inf_in3604695632404883862_int_o @ ( uminus7117520113953359693_int_o @ X ) @ X )
% 0.29/0.49        = bot_bo8147686125503663512_int_o ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_cancel_left
% 0.29/0.49  thf(fact_656_boolean__algebra_Oconj__cancel__left,axiom,
% 0.29/0.49      ! [X: list_char > $o] :
% 0.29/0.49        ( ( inf_inf_list_char_o @ ( uminus7154032370948614053char_o @ X ) @ X )
% 0.29/0.49        = bot_bot_list_char_o ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_cancel_left
% 0.29/0.49  thf(fact_657_boolean__algebra_Oconj__cancel__left,axiom,
% 0.29/0.49      ! [X: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ X )
% 0.29/0.49        = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_cancel_left
% 0.29/0.49  thf(fact_658_boolean__algebra_Oconj__cancel__left,axiom,
% 0.29/0.49      ! [X: set_o] :
% 0.29/0.49        ( ( inf_inf_set_o @ ( uminus_uminus_set_o @ X ) @ X )
% 0.29/0.49        = bot_bot_set_o ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_cancel_left
% 0.29/0.49  thf(fact_659_boolean__algebra_Oconj__cancel__left,axiom,
% 0.29/0.49      ! [X: set_nat] :
% 0.29/0.49        ( ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ X )
% 0.29/0.49        = bot_bot_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_cancel_left
% 0.29/0.49  thf(fact_660_boolean__algebra_Oconj__cancel__left,axiom,
% 0.29/0.49      ! [X: set_int] :
% 0.29/0.49        ( ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ X )
% 0.29/0.49        = bot_bot_set_int ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_cancel_left
% 0.29/0.49  thf(fact_661_boolean__algebra_Oconj__cancel__left,axiom,
% 0.29/0.49      ! [X: product_unit] :
% 0.29/0.49        ( ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ X )
% 0.29/0.49        = bot_bot_Product_unit ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_cancel_left
% 0.29/0.49  thf(fact_662_boolean__algebra_Oconj__cancel__right,axiom,
% 0.29/0.49      ! [X: product_prod_int_int > $o] :
% 0.29/0.49        ( ( inf_in3604695632404883862_int_o @ X @ ( uminus7117520113953359693_int_o @ X ) )
% 0.29/0.49        = bot_bo8147686125503663512_int_o ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_cancel_right
% 0.29/0.49  thf(fact_663_boolean__algebra_Oconj__cancel__right,axiom,
% 0.29/0.49      ! [X: list_char > $o] :
% 0.29/0.49        ( ( inf_inf_list_char_o @ X @ ( uminus7154032370948614053char_o @ X ) )
% 0.29/0.49        = bot_bot_list_char_o ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_cancel_right
% 0.29/0.49  thf(fact_664_boolean__algebra_Oconj__cancel__right,axiom,
% 0.29/0.49      ! [X: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( inf_in2572325071724192079at_nat @ X @ ( uminus6524753893492686040at_nat @ X ) )
% 0.29/0.49        = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_cancel_right
% 0.29/0.49  thf(fact_665_boolean__algebra_Oconj__cancel__right,axiom,
% 0.29/0.49      ! [X: set_o] :
% 0.29/0.49        ( ( inf_inf_set_o @ X @ ( uminus_uminus_set_o @ X ) )
% 0.29/0.49        = bot_bot_set_o ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_cancel_right
% 0.29/0.49  thf(fact_666_boolean__algebra_Oconj__cancel__right,axiom,
% 0.29/0.49      ! [X: set_nat] :
% 0.29/0.49        ( ( inf_inf_set_nat @ X @ ( uminus5710092332889474511et_nat @ X ) )
% 0.29/0.49        = bot_bot_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_cancel_right
% 0.29/0.49  thf(fact_667_boolean__algebra_Oconj__cancel__right,axiom,
% 0.29/0.49      ! [X: set_int] :
% 0.29/0.49        ( ( inf_inf_set_int @ X @ ( uminus1532241313380277803et_int @ X ) )
% 0.29/0.49        = bot_bot_set_int ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_cancel_right
% 0.29/0.49  thf(fact_668_boolean__algebra_Oconj__cancel__right,axiom,
% 0.29/0.49      ! [X: product_unit] :
% 0.29/0.49        ( ( inf_inf_Product_unit @ X @ ( uminus2952777764628376836t_unit @ X ) )
% 0.29/0.49        = bot_bot_Product_unit ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_cancel_right
% 0.29/0.49  thf(fact_669_sup__compl__top__left1,axiom,
% 0.29/0.49      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ X ) @ ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 0.29/0.49        = top_to8764741339697478167at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_compl_top_left1
% 0.29/0.49  thf(fact_670_sup__compl__top__left1,axiom,
% 0.29/0.49      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ X ) @ ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 0.29/0.49        = top_to6833984726390702231at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_compl_top_left1
% 0.29/0.49  thf(fact_671_sup__compl__top__left1,axiom,
% 0.29/0.49      ! [X: set_list_nat,Y: set_list_nat] :
% 0.29/0.49        ( ( sup_sup_set_list_nat @ ( uminus3195874150345416415st_nat @ X ) @ ( sup_sup_set_list_nat @ X @ Y ) )
% 0.29/0.49        = top_top_set_list_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_compl_top_left1
% 0.29/0.49  thf(fact_672_sup__compl__top__left1,axiom,
% 0.29/0.49      ! [X: set_o,Y: set_o] :
% 0.29/0.49        ( ( sup_sup_set_o @ ( uminus_uminus_set_o @ X ) @ ( sup_sup_set_o @ X @ Y ) )
% 0.29/0.49        = top_top_set_o ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_compl_top_left1
% 0.29/0.49  thf(fact_673_sup__compl__top__left1,axiom,
% 0.29/0.49      ! [X: set_rat,Y: set_rat] :
% 0.29/0.49        ( ( sup_sup_set_rat @ ( uminus2201863774496077783et_rat @ X ) @ ( sup_sup_set_rat @ X @ Y ) )
% 0.29/0.49        = top_top_set_rat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_compl_top_left1
% 0.29/0.49  thf(fact_674_sup__compl__top__left1,axiom,
% 0.29/0.49      ! [X: set_nat,Y: set_nat] :
% 0.29/0.49        ( ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( sup_sup_set_nat @ X @ Y ) )
% 0.29/0.49        = top_top_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_compl_top_left1
% 0.29/0.49  thf(fact_675_sup__compl__top__left1,axiom,
% 0.29/0.49      ! [X: set_int,Y: set_int] :
% 0.29/0.49        ( ( sup_sup_set_int @ ( uminus1532241313380277803et_int @ X ) @ ( sup_sup_set_int @ X @ Y ) )
% 0.29/0.49        = top_top_set_int ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_compl_top_left1
% 0.29/0.49  thf(fact_676_sup__compl__top__left1,axiom,
% 0.29/0.49      ! [X: product_unit,Y: product_unit] :
% 0.29/0.49        ( ( sup_sup_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( sup_sup_Product_unit @ X @ Y ) )
% 0.29/0.49        = top_top_Product_unit ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_compl_top_left1
% 0.29/0.49  thf(fact_677_sup__compl__top__left2,axiom,
% 0.29/0.49      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ X ) @ Y ) )
% 0.29/0.49        = top_to8764741339697478167at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_compl_top_left2
% 0.29/0.49  thf(fact_678_sup__compl__top__left2,axiom,
% 0.29/0.49      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ X ) @ Y ) )
% 0.29/0.49        = top_to6833984726390702231at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_compl_top_left2
% 0.29/0.49  thf(fact_679_sup__compl__top__left2,axiom,
% 0.29/0.49      ! [X: set_list_nat,Y: set_list_nat] :
% 0.29/0.49        ( ( sup_sup_set_list_nat @ X @ ( sup_sup_set_list_nat @ ( uminus3195874150345416415st_nat @ X ) @ Y ) )
% 0.29/0.49        = top_top_set_list_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_compl_top_left2
% 0.29/0.49  thf(fact_680_sup__compl__top__left2,axiom,
% 0.29/0.49      ! [X: set_o,Y: set_o] :
% 0.29/0.49        ( ( sup_sup_set_o @ X @ ( sup_sup_set_o @ ( uminus_uminus_set_o @ X ) @ Y ) )
% 0.29/0.49        = top_top_set_o ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_compl_top_left2
% 0.29/0.49  thf(fact_681_sup__compl__top__left2,axiom,
% 0.29/0.49      ! [X: set_rat,Y: set_rat] :
% 0.29/0.49        ( ( sup_sup_set_rat @ X @ ( sup_sup_set_rat @ ( uminus2201863774496077783et_rat @ X ) @ Y ) )
% 0.29/0.49        = top_top_set_rat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_compl_top_left2
% 0.29/0.49  thf(fact_682_sup__compl__top__left2,axiom,
% 0.29/0.49      ! [X: set_nat,Y: set_nat] :
% 0.29/0.49        ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ Y ) )
% 0.29/0.49        = top_top_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_compl_top_left2
% 0.29/0.49  thf(fact_683_sup__compl__top__left2,axiom,
% 0.29/0.49      ! [X: set_int,Y: set_int] :
% 0.29/0.49        ( ( sup_sup_set_int @ X @ ( sup_sup_set_int @ ( uminus1532241313380277803et_int @ X ) @ Y ) )
% 0.29/0.49        = top_top_set_int ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_compl_top_left2
% 0.29/0.49  thf(fact_684_sup__compl__top__left2,axiom,
% 0.29/0.49      ! [X: product_unit,Y: product_unit] :
% 0.29/0.49        ( ( sup_sup_Product_unit @ X @ ( sup_sup_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ Y ) )
% 0.29/0.49        = top_top_Product_unit ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_compl_top_left2
% 0.29/0.49  thf(fact_685_boolean__algebra_Odisj__cancel__left,axiom,
% 0.29/0.49      ! [X: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ X ) @ X )
% 0.29/0.49        = top_to8764741339697478167at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_cancel_left
% 0.29/0.49  thf(fact_686_boolean__algebra_Odisj__cancel__left,axiom,
% 0.29/0.49      ! [X: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ X ) @ X )
% 0.29/0.49        = top_to6833984726390702231at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_cancel_left
% 0.29/0.49  thf(fact_687_boolean__algebra_Odisj__cancel__left,axiom,
% 0.29/0.49      ! [X: set_list_nat] :
% 0.29/0.49        ( ( sup_sup_set_list_nat @ ( uminus3195874150345416415st_nat @ X ) @ X )
% 0.29/0.49        = top_top_set_list_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_cancel_left
% 0.29/0.49  thf(fact_688_boolean__algebra_Odisj__cancel__left,axiom,
% 0.29/0.49      ! [X: set_o] :
% 0.29/0.49        ( ( sup_sup_set_o @ ( uminus_uminus_set_o @ X ) @ X )
% 0.29/0.49        = top_top_set_o ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_cancel_left
% 0.29/0.49  thf(fact_689_boolean__algebra_Odisj__cancel__left,axiom,
% 0.29/0.49      ! [X: set_rat] :
% 0.29/0.49        ( ( sup_sup_set_rat @ ( uminus2201863774496077783et_rat @ X ) @ X )
% 0.29/0.49        = top_top_set_rat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_cancel_left
% 0.29/0.49  thf(fact_690_boolean__algebra_Odisj__cancel__left,axiom,
% 0.29/0.49      ! [X: set_nat] :
% 0.29/0.49        ( ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ X )
% 0.29/0.49        = top_top_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_cancel_left
% 0.29/0.49  thf(fact_691_boolean__algebra_Odisj__cancel__left,axiom,
% 0.29/0.49      ! [X: set_int] :
% 0.29/0.49        ( ( sup_sup_set_int @ ( uminus1532241313380277803et_int @ X ) @ X )
% 0.29/0.49        = top_top_set_int ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_cancel_left
% 0.29/0.49  thf(fact_692_boolean__algebra_Odisj__cancel__left,axiom,
% 0.29/0.49      ! [X: product_unit] :
% 0.29/0.49        ( ( sup_sup_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ X )
% 0.29/0.49        = top_top_Product_unit ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_cancel_left
% 0.29/0.49  thf(fact_693_boolean__algebra_Odisj__cancel__right,axiom,
% 0.29/0.49      ! [X: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( sup_su3035147773818789531at_nat @ X @ ( uminus2330091110623919550at_nat @ X ) )
% 0.29/0.49        = top_to8764741339697478167at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_cancel_right
% 0.29/0.49  thf(fact_694_boolean__algebra_Odisj__cancel__right,axiom,
% 0.29/0.49      ! [X: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( sup_su5525570899277871387at_nat @ X @ ( uminus935396558254630718at_nat @ X ) )
% 0.29/0.49        = top_to6833984726390702231at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_cancel_right
% 0.29/0.49  thf(fact_695_boolean__algebra_Odisj__cancel__right,axiom,
% 0.29/0.49      ! [X: set_list_nat] :
% 0.29/0.49        ( ( sup_sup_set_list_nat @ X @ ( uminus3195874150345416415st_nat @ X ) )
% 0.29/0.49        = top_top_set_list_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_cancel_right
% 0.29/0.49  thf(fact_696_boolean__algebra_Odisj__cancel__right,axiom,
% 0.29/0.49      ! [X: set_o] :
% 0.29/0.49        ( ( sup_sup_set_o @ X @ ( uminus_uminus_set_o @ X ) )
% 0.29/0.49        = top_top_set_o ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_cancel_right
% 0.29/0.49  thf(fact_697_boolean__algebra_Odisj__cancel__right,axiom,
% 0.29/0.49      ! [X: set_rat] :
% 0.29/0.49        ( ( sup_sup_set_rat @ X @ ( uminus2201863774496077783et_rat @ X ) )
% 0.29/0.49        = top_top_set_rat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_cancel_right
% 0.29/0.49  thf(fact_698_boolean__algebra_Odisj__cancel__right,axiom,
% 0.29/0.49      ! [X: set_nat] :
% 0.29/0.49        ( ( sup_sup_set_nat @ X @ ( uminus5710092332889474511et_nat @ X ) )
% 0.29/0.49        = top_top_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_cancel_right
% 0.29/0.49  thf(fact_699_boolean__algebra_Odisj__cancel__right,axiom,
% 0.29/0.49      ! [X: set_int] :
% 0.29/0.49        ( ( sup_sup_set_int @ X @ ( uminus1532241313380277803et_int @ X ) )
% 0.29/0.49        = top_top_set_int ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_cancel_right
% 0.29/0.49  thf(fact_700_boolean__algebra_Odisj__cancel__right,axiom,
% 0.29/0.49      ! [X: product_unit] :
% 0.29/0.49        ( ( sup_sup_Product_unit @ X @ ( uminus2952777764628376836t_unit @ X ) )
% 0.29/0.49        = top_top_Product_unit ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.disj_cancel_right
% 0.29/0.49  thf(fact_701_boolean__algebra_Ode__Morgan__conj,axiom,
% 0.29/0.49      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( uminus6524753893492686040at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 0.29/0.49        = ( sup_su6327502436637775413at_nat @ ( uminus6524753893492686040at_nat @ X ) @ ( uminus6524753893492686040at_nat @ Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.de_Morgan_conj
% 0.29/0.49  thf(fact_702_boolean__algebra_Ode__Morgan__conj,axiom,
% 0.29/0.49      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 0.29/0.49        ( ( uminus7117520113953359693_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) )
% 0.29/0.49        = ( sup_su8463660629351352368_int_o @ ( uminus7117520113953359693_int_o @ X ) @ ( uminus7117520113953359693_int_o @ Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.de_Morgan_conj
% 0.29/0.49  thf(fact_703_boolean__algebra_Ode__Morgan__conj,axiom,
% 0.29/0.49      ! [X: list_char > $o,Y: list_char > $o] :
% 0.29/0.49        ( ( uminus7154032370948614053char_o @ ( inf_inf_list_char_o @ X @ Y ) )
% 0.29/0.49        = ( sup_sup_list_char_o @ ( uminus7154032370948614053char_o @ X ) @ ( uminus7154032370948614053char_o @ Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.de_Morgan_conj
% 0.29/0.49  thf(fact_704_boolean__algebra_Ode__Morgan__conj,axiom,
% 0.29/0.49      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( uminus2330091110623919550at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) )
% 0.29/0.49        = ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ X ) @ ( uminus2330091110623919550at_nat @ Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.de_Morgan_conj
% 0.29/0.49  thf(fact_705_boolean__algebra_Ode__Morgan__conj,axiom,
% 0.29/0.49      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( uminus935396558254630718at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) )
% 0.29/0.49        = ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ X ) @ ( uminus935396558254630718at_nat @ Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.de_Morgan_conj
% 0.29/0.49  thf(fact_706_boolean__algebra_Ode__Morgan__conj,axiom,
% 0.29/0.49      ! [X: set_nat,Y: set_nat] :
% 0.29/0.49        ( ( uminus5710092332889474511et_nat @ ( inf_inf_set_nat @ X @ Y ) )
% 0.29/0.49        = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.de_Morgan_conj
% 0.29/0.49  thf(fact_707_boolean__algebra_Ode__Morgan__conj,axiom,
% 0.29/0.49      ! [X: product_unit,Y: product_unit] :
% 0.29/0.49        ( ( uminus2952777764628376836t_unit @ ( inf_inf_Product_unit @ X @ Y ) )
% 0.29/0.49        = ( sup_sup_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( uminus2952777764628376836t_unit @ Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.de_Morgan_conj
% 0.29/0.49  thf(fact_708_mult_Omonoid__axioms,axiom,
% 0.29/0.49      monoid_Code_integer @ times_3573771949741848930nteger @ one_one_Code_integer ).
% 0.29/0.49  
% 0.29/0.49  % mult.monoid_axioms
% 0.29/0.49  thf(fact_709_mult_Omonoid__axioms,axiom,
% 0.29/0.49      monoid_assn @ times_times_assn @ one_one_assn ).
% 0.29/0.49  
% 0.29/0.49  % mult.monoid_axioms
% 0.29/0.49  thf(fact_710_mult_Omonoid__axioms,axiom,
% 0.29/0.49      monoid_rat @ times_times_rat @ one_one_rat ).
% 0.29/0.49  
% 0.29/0.49  % mult.monoid_axioms
% 0.29/0.49  thf(fact_711_mult_Omonoid__axioms,axiom,
% 0.29/0.49      monoid_nat @ times_times_nat @ one_one_nat ).
% 0.29/0.49  
% 0.29/0.49  % mult.monoid_axioms
% 0.29/0.49  thf(fact_712_mult_Omonoid__axioms,axiom,
% 0.29/0.49      monoid_int @ times_times_int @ one_one_int ).
% 0.29/0.49  
% 0.29/0.49  % mult.monoid_axioms
% 0.29/0.49  thf(fact_713_mult_Ocomm__monoid__axioms,axiom,
% 0.29/0.49      comm_m1654649897431166824nteger @ times_3573771949741848930nteger @ one_one_Code_integer ).
% 0.29/0.49  
% 0.29/0.49  % mult.comm_monoid_axioms
% 0.29/0.49  thf(fact_714_mult_Ocomm__monoid__axioms,axiom,
% 0.29/0.49      comm_monoid_assn @ times_times_assn @ one_one_assn ).
% 0.29/0.49  
% 0.29/0.49  % mult.comm_monoid_axioms
% 0.29/0.49  thf(fact_715_mult_Ocomm__monoid__axioms,axiom,
% 0.29/0.49      comm_monoid_rat @ times_times_rat @ one_one_rat ).
% 0.29/0.49  
% 0.29/0.49  % mult.comm_monoid_axioms
% 0.29/0.49  thf(fact_716_mult_Ocomm__monoid__axioms,axiom,
% 0.29/0.49      comm_monoid_nat @ times_times_nat @ one_one_nat ).
% 0.29/0.49  
% 0.29/0.49  % mult.comm_monoid_axioms
% 0.29/0.49  thf(fact_717_mult_Ocomm__monoid__axioms,axiom,
% 0.29/0.49      comm_monoid_int @ times_times_int @ one_one_int ).
% 0.29/0.49  
% 0.29/0.49  % mult.comm_monoid_axioms
% 0.29/0.49  thf(fact_718_semilattice__neutr_Oaxioms_I2_J,axiom,
% 0.29/0.49      ! [F2: nat > nat > nat,Z: nat] :
% 0.29/0.49        ( ( semila9081495762789891438tr_nat @ F2 @ Z )
% 0.29/0.49       => ( comm_monoid_nat @ F2 @ Z ) ) ).
% 0.29/0.49  
% 0.29/0.49  % semilattice_neutr.axioms(2)
% 0.29/0.49  thf(fact_719_monoid_Oleft__neutral,axiom,
% 0.29/0.49      ! [F2: nat > nat > nat,Z: nat,A: nat] :
% 0.29/0.49        ( ( monoid_nat @ F2 @ Z )
% 0.29/0.49       => ( ( F2 @ Z @ A )
% 0.29/0.49          = A ) ) ).
% 0.29/0.49  
% 0.29/0.49  % monoid.left_neutral
% 0.29/0.49  thf(fact_720_monoid_Oright__neutral,axiom,
% 0.29/0.49      ! [F2: nat > nat > nat,Z: nat,A: nat] :
% 0.29/0.49        ( ( monoid_nat @ F2 @ Z )
% 0.29/0.49       => ( ( F2 @ A @ Z )
% 0.29/0.49          = A ) ) ).
% 0.29/0.49  
% 0.29/0.49  % monoid.right_neutral
% 0.29/0.49  thf(fact_721_one__assn__raw_Ocases,axiom,
% 0.29/0.49      ! [X: produc3658429121746597890et_nat] :
% 0.29/0.49        ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 0.29/0.49            ( X
% 0.29/0.49           != ( produc7507926704131184380et_nat @ H @ As4 ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_assn_raw.cases
% 0.29/0.49  thf(fact_722_comm__monoid_Ocomm__neutral,axiom,
% 0.29/0.49      ! [F2: nat > nat > nat,Z: nat,A: nat] :
% 0.29/0.49        ( ( comm_monoid_nat @ F2 @ Z )
% 0.29/0.49       => ( ( F2 @ A @ Z )
% 0.29/0.49          = A ) ) ).
% 0.29/0.49  
% 0.29/0.49  % comm_monoid.comm_neutral
% 0.29/0.49  thf(fact_723_equation__minus__iff,axiom,
% 0.29/0.49      ! [A: int,B: int] :
% 0.29/0.49        ( ( A
% 0.29/0.49          = ( uminus_uminus_int @ B ) )
% 0.29/0.49        = ( B
% 0.29/0.49          = ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % equation_minus_iff
% 0.29/0.49  thf(fact_724_equation__minus__iff,axiom,
% 0.29/0.49      ! [A: code_integer,B: code_integer] :
% 0.29/0.49        ( ( A
% 0.29/0.49          = ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.49        = ( B
% 0.29/0.49          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % equation_minus_iff
% 0.29/0.49  thf(fact_725_equation__minus__iff,axiom,
% 0.29/0.49      ! [A: rat,B: rat] :
% 0.29/0.49        ( ( A
% 0.29/0.49          = ( uminus_uminus_rat @ B ) )
% 0.29/0.49        = ( B
% 0.29/0.49          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % equation_minus_iff
% 0.29/0.49  thf(fact_726_minus__equation__iff,axiom,
% 0.29/0.49      ! [A: int,B: int] :
% 0.29/0.49        ( ( ( uminus_uminus_int @ A )
% 0.29/0.49          = B )
% 0.29/0.49        = ( ( uminus_uminus_int @ B )
% 0.29/0.49          = A ) ) ).
% 0.29/0.49  
% 0.29/0.49  % minus_equation_iff
% 0.29/0.49  thf(fact_727_minus__equation__iff,axiom,
% 0.29/0.49      ! [A: code_integer,B: code_integer] :
% 0.29/0.49        ( ( ( uminus1351360451143612070nteger @ A )
% 0.29/0.49          = B )
% 0.29/0.49        = ( ( uminus1351360451143612070nteger @ B )
% 0.29/0.49          = A ) ) ).
% 0.29/0.49  
% 0.29/0.49  % minus_equation_iff
% 0.29/0.49  thf(fact_728_minus__equation__iff,axiom,
% 0.29/0.49      ! [A: rat,B: rat] :
% 0.29/0.49        ( ( ( uminus_uminus_rat @ A )
% 0.29/0.49          = B )
% 0.29/0.49        = ( ( uminus_uminus_rat @ B )
% 0.29/0.49          = A ) ) ).
% 0.29/0.49  
% 0.29/0.49  % minus_equation_iff
% 0.29/0.49  thf(fact_729_one__reorient,axiom,
% 0.29/0.49      ! [X: code_integer] :
% 0.29/0.49        ( ( one_one_Code_integer = X )
% 0.29/0.49        = ( X = one_one_Code_integer ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_reorient
% 0.29/0.49  thf(fact_730_one__reorient,axiom,
% 0.29/0.49      ! [X: assn] :
% 0.29/0.49        ( ( one_one_assn = X )
% 0.29/0.49        = ( X = one_one_assn ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_reorient
% 0.29/0.49  thf(fact_731_one__reorient,axiom,
% 0.29/0.49      ! [X: rat] :
% 0.29/0.49        ( ( one_one_rat = X )
% 0.29/0.49        = ( X = one_one_rat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_reorient
% 0.29/0.49  thf(fact_732_one__reorient,axiom,
% 0.29/0.49      ! [X: nat] :
% 0.29/0.49        ( ( one_one_nat = X )
% 0.29/0.49        = ( X = one_one_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_reorient
% 0.29/0.49  thf(fact_733_one__reorient,axiom,
% 0.29/0.49      ! [X: int] :
% 0.29/0.49        ( ( one_one_int = X )
% 0.29/0.49        = ( X = one_one_int ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_reorient
% 0.29/0.49  thf(fact_734_sup__cancel__left1,axiom,
% 0.29/0.49      ! [X: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ X @ A ) @ ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ X ) @ B ) )
% 0.29/0.49        = top_to8764741339697478167at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_cancel_left1
% 0.29/0.49  thf(fact_735_sup__cancel__left1,axiom,
% 0.29/0.49      ! [X: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ X @ A ) @ ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ X ) @ B ) )
% 0.29/0.49        = top_to6833984726390702231at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_cancel_left1
% 0.29/0.49  thf(fact_736_sup__cancel__left1,axiom,
% 0.29/0.49      ! [X: set_list_nat,A: set_list_nat,B: set_list_nat] :
% 0.29/0.49        ( ( sup_sup_set_list_nat @ ( sup_sup_set_list_nat @ X @ A ) @ ( sup_sup_set_list_nat @ ( uminus3195874150345416415st_nat @ X ) @ B ) )
% 0.29/0.49        = top_top_set_list_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_cancel_left1
% 0.29/0.49  thf(fact_737_sup__cancel__left1,axiom,
% 0.29/0.49      ! [X: set_o,A: set_o,B: set_o] :
% 0.29/0.49        ( ( sup_sup_set_o @ ( sup_sup_set_o @ X @ A ) @ ( sup_sup_set_o @ ( uminus_uminus_set_o @ X ) @ B ) )
% 0.29/0.49        = top_top_set_o ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_cancel_left1
% 0.29/0.49  thf(fact_738_sup__cancel__left1,axiom,
% 0.29/0.49      ! [X: set_rat,A: set_rat,B: set_rat] :
% 0.29/0.49        ( ( sup_sup_set_rat @ ( sup_sup_set_rat @ X @ A ) @ ( sup_sup_set_rat @ ( uminus2201863774496077783et_rat @ X ) @ B ) )
% 0.29/0.49        = top_top_set_rat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_cancel_left1
% 0.29/0.49  thf(fact_739_sup__cancel__left1,axiom,
% 0.29/0.49      ! [X: set_nat,A: set_nat,B: set_nat] :
% 0.29/0.49        ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ X @ A ) @ ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ B ) )
% 0.29/0.49        = top_top_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_cancel_left1
% 0.29/0.49  thf(fact_740_sup__cancel__left1,axiom,
% 0.29/0.49      ! [X: set_int,A: set_int,B: set_int] :
% 0.29/0.49        ( ( sup_sup_set_int @ ( sup_sup_set_int @ X @ A ) @ ( sup_sup_set_int @ ( uminus1532241313380277803et_int @ X ) @ B ) )
% 0.29/0.49        = top_top_set_int ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_cancel_left1
% 0.29/0.49  thf(fact_741_sup__cancel__left1,axiom,
% 0.29/0.49      ! [X: product_unit,A: product_unit,B: product_unit] :
% 0.29/0.49        ( ( sup_sup_Product_unit @ ( sup_sup_Product_unit @ X @ A ) @ ( sup_sup_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ B ) )
% 0.29/0.49        = top_top_Product_unit ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_cancel_left1
% 0.29/0.49  thf(fact_742_sup__cancel__left2,axiom,
% 0.29/0.49      ! [X: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ X ) @ A ) @ ( sup_su3035147773818789531at_nat @ X @ B ) )
% 0.29/0.49        = top_to8764741339697478167at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_cancel_left2
% 0.29/0.49  thf(fact_743_sup__cancel__left2,axiom,
% 0.29/0.49      ! [X: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ X ) @ A ) @ ( sup_su5525570899277871387at_nat @ X @ B ) )
% 0.29/0.49        = top_to6833984726390702231at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_cancel_left2
% 0.29/0.49  thf(fact_744_sup__cancel__left2,axiom,
% 0.29/0.49      ! [X: set_list_nat,A: set_list_nat,B: set_list_nat] :
% 0.29/0.49        ( ( sup_sup_set_list_nat @ ( sup_sup_set_list_nat @ ( uminus3195874150345416415st_nat @ X ) @ A ) @ ( sup_sup_set_list_nat @ X @ B ) )
% 0.29/0.49        = top_top_set_list_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_cancel_left2
% 0.29/0.49  thf(fact_745_sup__cancel__left2,axiom,
% 0.29/0.49      ! [X: set_o,A: set_o,B: set_o] :
% 0.29/0.49        ( ( sup_sup_set_o @ ( sup_sup_set_o @ ( uminus_uminus_set_o @ X ) @ A ) @ ( sup_sup_set_o @ X @ B ) )
% 0.29/0.49        = top_top_set_o ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_cancel_left2
% 0.29/0.49  thf(fact_746_sup__cancel__left2,axiom,
% 0.29/0.49      ! [X: set_rat,A: set_rat,B: set_rat] :
% 0.29/0.49        ( ( sup_sup_set_rat @ ( sup_sup_set_rat @ ( uminus2201863774496077783et_rat @ X ) @ A ) @ ( sup_sup_set_rat @ X @ B ) )
% 0.29/0.49        = top_top_set_rat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_cancel_left2
% 0.29/0.49  thf(fact_747_sup__cancel__left2,axiom,
% 0.29/0.49      ! [X: set_nat,A: set_nat,B: set_nat] :
% 0.29/0.49        ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ A ) @ ( sup_sup_set_nat @ X @ B ) )
% 0.29/0.49        = top_top_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_cancel_left2
% 0.29/0.49  thf(fact_748_sup__cancel__left2,axiom,
% 0.29/0.49      ! [X: set_int,A: set_int,B: set_int] :
% 0.29/0.49        ( ( sup_sup_set_int @ ( sup_sup_set_int @ ( uminus1532241313380277803et_int @ X ) @ A ) @ ( sup_sup_set_int @ X @ B ) )
% 0.29/0.49        = top_top_set_int ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_cancel_left2
% 0.29/0.49  thf(fact_749_sup__cancel__left2,axiom,
% 0.29/0.49      ! [X: product_unit,A: product_unit,B: product_unit] :
% 0.29/0.49        ( ( sup_sup_Product_unit @ ( sup_sup_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ A ) @ ( sup_sup_Product_unit @ X @ B ) )
% 0.29/0.49        = top_top_Product_unit ) ).
% 0.29/0.49  
% 0.29/0.49  % sup_cancel_left2
% 0.29/0.49  thf(fact_750_inf__top_Ocomm__monoid__axioms,axiom,
% 0.29/0.49      comm_m5709050211238513046at_nat @ inf_in2572325071724192079at_nat @ top_to4669805908274784177at_nat ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.comm_monoid_axioms
% 0.29/0.49  thf(fact_751_inf__top_Ocomm__monoid__axioms,axiom,
% 0.29/0.49      comm_m5839176995973721103_int_o @ inf_in3604695632404883862_int_o @ top_to1578927101902068148_int_o ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.comm_monoid_axioms
% 0.29/0.49  thf(fact_752_inf__top_Ocomm__monoid__axioms,axiom,
% 0.29/0.49      comm_m8764728085499324515char_o @ inf_inf_list_char_o @ top_top_list_char_o ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.comm_monoid_axioms
% 0.29/0.49  thf(fact_753_inf__top_Ocomm__monoid__axioms,axiom,
% 0.29/0.49      comm_m4511514676032769697st_nat @ inf_inf_set_list_nat @ top_top_set_list_nat ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.comm_monoid_axioms
% 0.29/0.49  thf(fact_754_inf__top_Ocomm__monoid__axioms,axiom,
% 0.29/0.49      comm_monoid_set_o @ inf_inf_set_o @ top_top_set_o ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.comm_monoid_axioms
% 0.29/0.49  thf(fact_755_inf__top_Ocomm__monoid__axioms,axiom,
% 0.29/0.49      comm_monoid_set_rat @ inf_inf_set_rat @ top_top_set_rat ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.comm_monoid_axioms
% 0.29/0.49  thf(fact_756_inf__top_Ocomm__monoid__axioms,axiom,
% 0.29/0.49      comm_monoid_set_nat @ inf_inf_set_nat @ top_top_set_nat ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.comm_monoid_axioms
% 0.29/0.49  thf(fact_757_inf__top_Ocomm__monoid__axioms,axiom,
% 0.29/0.49      comm_monoid_set_int @ inf_inf_set_int @ top_top_set_int ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.comm_monoid_axioms
% 0.29/0.49  thf(fact_758_inf__top_Omonoid__axioms,axiom,
% 0.29/0.49      monoid1519094961268053602at_nat @ inf_in2572325071724192079at_nat @ top_to4669805908274784177at_nat ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.monoid_axioms
% 0.29/0.49  thf(fact_759_inf__top_Omonoid__axioms,axiom,
% 0.29/0.49      monoid6910981727789844035_int_o @ inf_in3604695632404883862_int_o @ top_to1578927101902068148_int_o ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.monoid_axioms
% 0.29/0.49  thf(fact_760_inf__top_Omonoid__axioms,axiom,
% 0.29/0.49      monoid_list_char_o @ inf_inf_list_char_o @ top_top_list_char_o ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.monoid_axioms
% 0.29/0.49  thf(fact_761_inf__top_Omonoid__axioms,axiom,
% 0.29/0.49      monoid_set_list_nat @ inf_inf_set_list_nat @ top_top_set_list_nat ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.monoid_axioms
% 0.29/0.49  thf(fact_762_inf__top_Omonoid__axioms,axiom,
% 0.29/0.49      monoid_set_o @ inf_inf_set_o @ top_top_set_o ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.monoid_axioms
% 0.29/0.49  thf(fact_763_inf__top_Omonoid__axioms,axiom,
% 0.29/0.49      monoid_set_rat @ inf_inf_set_rat @ top_top_set_rat ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.monoid_axioms
% 0.29/0.49  thf(fact_764_inf__top_Omonoid__axioms,axiom,
% 0.29/0.49      monoid_set_nat @ inf_inf_set_nat @ top_top_set_nat ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.monoid_axioms
% 0.29/0.49  thf(fact_765_inf__top_Omonoid__axioms,axiom,
% 0.29/0.49      monoid_set_int @ inf_inf_set_int @ top_top_set_int ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.monoid_axioms
% 0.29/0.49  thf(fact_766_comm__monoid__mult__class_Omult__1,axiom,
% 0.29/0.49      ! [A: code_integer] :
% 0.29/0.49        ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % comm_monoid_mult_class.mult_1
% 0.29/0.49  thf(fact_767_comm__monoid__mult__class_Omult__1,axiom,
% 0.29/0.49      ! [A: assn] :
% 0.29/0.49        ( ( times_times_assn @ one_one_assn @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % comm_monoid_mult_class.mult_1
% 0.29/0.49  thf(fact_768_comm__monoid__mult__class_Omult__1,axiom,
% 0.29/0.49      ! [A: rat] :
% 0.29/0.49        ( ( times_times_rat @ one_one_rat @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % comm_monoid_mult_class.mult_1
% 0.29/0.49  thf(fact_769_comm__monoid__mult__class_Omult__1,axiom,
% 0.29/0.49      ! [A: nat] :
% 0.29/0.49        ( ( times_times_nat @ one_one_nat @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % comm_monoid_mult_class.mult_1
% 0.29/0.49  thf(fact_770_comm__monoid__mult__class_Omult__1,axiom,
% 0.29/0.49      ! [A: int] :
% 0.29/0.49        ( ( times_times_int @ one_one_int @ A )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % comm_monoid_mult_class.mult_1
% 0.29/0.49  thf(fact_771_mult_Ocomm__neutral,axiom,
% 0.29/0.49      ! [A: code_integer] :
% 0.29/0.49        ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.comm_neutral
% 0.29/0.49  thf(fact_772_mult_Ocomm__neutral,axiom,
% 0.29/0.49      ! [A: assn] :
% 0.29/0.49        ( ( times_times_assn @ A @ one_one_assn )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.comm_neutral
% 0.29/0.49  thf(fact_773_mult_Ocomm__neutral,axiom,
% 0.29/0.49      ! [A: rat] :
% 0.29/0.49        ( ( times_times_rat @ A @ one_one_rat )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.comm_neutral
% 0.29/0.49  thf(fact_774_mult_Ocomm__neutral,axiom,
% 0.29/0.49      ! [A: nat] :
% 0.29/0.49        ( ( times_times_nat @ A @ one_one_nat )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.comm_neutral
% 0.29/0.49  thf(fact_775_mult_Ocomm__neutral,axiom,
% 0.29/0.49      ! [A: int] :
% 0.29/0.49        ( ( times_times_int @ A @ one_one_int )
% 0.29/0.49        = A ) ).
% 0.29/0.49  
% 0.29/0.49  % mult.comm_neutral
% 0.29/0.49  thf(fact_776_inf__top_Osemilattice__neutr__axioms,axiom,
% 0.29/0.49      semila858173770281612099at_nat @ inf_in2572325071724192079at_nat @ top_to4669805908274784177at_nat ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.semilattice_neutr_axioms
% 0.29/0.49  thf(fact_777_inf__top_Osemilattice__neutr__axioms,axiom,
% 0.29/0.49      semila6538661356715008162_int_o @ inf_in3604695632404883862_int_o @ top_to1578927101902068148_int_o ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.semilattice_neutr_axioms
% 0.29/0.49  thf(fact_778_inf__top_Osemilattice__neutr__axioms,axiom,
% 0.29/0.49      semila3963277552210239504char_o @ inf_inf_list_char_o @ top_top_list_char_o ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.semilattice_neutr_axioms
% 0.29/0.49  thf(fact_779_inf__top_Osemilattice__neutr__axioms,axiom,
% 0.29/0.49      semila7136768128396663732st_nat @ inf_inf_set_list_nat @ top_top_set_list_nat ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.semilattice_neutr_axioms
% 0.29/0.49  thf(fact_780_inf__top_Osemilattice__neutr__axioms,axiom,
% 0.29/0.49      semila1065760912024005978_set_o @ inf_inf_set_o @ top_top_set_o ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.semilattice_neutr_axioms
% 0.29/0.49  thf(fact_781_inf__top_Osemilattice__neutr__axioms,axiom,
% 0.29/0.49      semila6956917442496717612et_rat @ inf_inf_set_rat @ top_top_set_rat ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.semilattice_neutr_axioms
% 0.29/0.49  thf(fact_782_inf__top_Osemilattice__neutr__axioms,axiom,
% 0.29/0.49      semila1241773964035338532et_nat @ inf_inf_set_nat @ top_top_set_nat ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.semilattice_neutr_axioms
% 0.29/0.49  thf(fact_783_inf__top_Osemilattice__neutr__axioms,axiom,
% 0.29/0.49      semila6287294981380917632et_int @ inf_inf_set_int @ top_top_set_int ).
% 0.29/0.49  
% 0.29/0.49  % inf_top.semilattice_neutr_axioms
% 0.29/0.49  thf(fact_784_boolean__algebra_Oconj__one__right,axiom,
% 0.29/0.49      ! [X: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( inf_in2572325071724192079at_nat @ X @ top_to4669805908274784177at_nat )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_one_right
% 0.29/0.49  thf(fact_785_boolean__algebra_Oconj__one__right,axiom,
% 0.29/0.49      ! [X: product_prod_int_int > $o] :
% 0.29/0.49        ( ( inf_in3604695632404883862_int_o @ X @ top_to1578927101902068148_int_o )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_one_right
% 0.29/0.49  thf(fact_786_boolean__algebra_Oconj__one__right,axiom,
% 0.29/0.49      ! [X: list_char > $o] :
% 0.29/0.49        ( ( inf_inf_list_char_o @ X @ top_top_list_char_o )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_one_right
% 0.29/0.49  thf(fact_787_boolean__algebra_Oconj__one__right,axiom,
% 0.29/0.49      ! [X: set_list_nat] :
% 0.29/0.49        ( ( inf_inf_set_list_nat @ X @ top_top_set_list_nat )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_one_right
% 0.29/0.49  thf(fact_788_boolean__algebra_Oconj__one__right,axiom,
% 0.29/0.49      ! [X: set_o] :
% 0.29/0.49        ( ( inf_inf_set_o @ X @ top_top_set_o )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_one_right
% 0.29/0.49  thf(fact_789_boolean__algebra_Oconj__one__right,axiom,
% 0.29/0.49      ! [X: set_rat] :
% 0.29/0.49        ( ( inf_inf_set_rat @ X @ top_top_set_rat )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_one_right
% 0.29/0.49  thf(fact_790_boolean__algebra_Oconj__one__right,axiom,
% 0.29/0.49      ! [X: set_nat] :
% 0.29/0.49        ( ( inf_inf_set_nat @ X @ top_top_set_nat )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_one_right
% 0.29/0.49  thf(fact_791_boolean__algebra_Oconj__one__right,axiom,
% 0.29/0.49      ! [X: set_int] :
% 0.29/0.49        ( ( inf_inf_set_int @ X @ top_top_set_int )
% 0.29/0.49        = X ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra.conj_one_right
% 0.29/0.49  thf(fact_792_mod__h__bot__indep,axiom,
% 0.29/0.49      ! [P: assn,H3: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 0.29/0.49        ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) )
% 0.29/0.49        = ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H4 @ bot_bot_set_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mod_h_bot_indep
% 0.29/0.49  thf(fact_793_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 0.29/0.49      ! [X: product_unit,Y: product_unit] :
% 0.29/0.49        ( ( ( inf_inf_Product_unit @ X @ Y )
% 0.29/0.49          = bot_bot_Product_unit )
% 0.29/0.49       => ( ( ( sup_sup_Product_unit @ X @ Y )
% 0.29/0.49            = top_top_Product_unit )
% 0.29/0.49         => ( ( uminus2952777764628376836t_unit @ X )
% 0.29/0.49            = Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra_class.boolean_algebra.compl_unique
% 0.29/0.49  thf(fact_794_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 0.29/0.49      ! [X: set_o,Y: set_o] :
% 0.29/0.49        ( ( ( inf_inf_set_o @ X @ Y )
% 0.29/0.49          = bot_bot_set_o )
% 0.29/0.49       => ( ( ( sup_sup_set_o @ X @ Y )
% 0.29/0.49            = top_top_set_o )
% 0.29/0.49         => ( ( uminus_uminus_set_o @ X )
% 0.29/0.49            = Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra_class.boolean_algebra.compl_unique
% 0.29/0.49  thf(fact_795_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 0.29/0.49      ! [X: set_rat,Y: set_rat] :
% 0.29/0.49        ( ( ( inf_inf_set_rat @ X @ Y )
% 0.29/0.49          = bot_bot_set_rat )
% 0.29/0.49       => ( ( ( sup_sup_set_rat @ X @ Y )
% 0.29/0.49            = top_top_set_rat )
% 0.29/0.49         => ( ( uminus2201863774496077783et_rat @ X )
% 0.29/0.49            = Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra_class.boolean_algebra.compl_unique
% 0.29/0.49  thf(fact_796_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 0.29/0.49      ! [X: set_nat,Y: set_nat] :
% 0.29/0.49        ( ( ( inf_inf_set_nat @ X @ Y )
% 0.29/0.49          = bot_bot_set_nat )
% 0.29/0.49       => ( ( ( sup_sup_set_nat @ X @ Y )
% 0.29/0.49            = top_top_set_nat )
% 0.29/0.49         => ( ( uminus5710092332889474511et_nat @ X )
% 0.29/0.49            = Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra_class.boolean_algebra.compl_unique
% 0.29/0.49  thf(fact_797_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 0.29/0.49      ! [X: set_int,Y: set_int] :
% 0.29/0.49        ( ( ( inf_inf_set_int @ X @ Y )
% 0.29/0.49          = bot_bot_set_int )
% 0.29/0.49       => ( ( ( sup_sup_set_int @ X @ Y )
% 0.29/0.49            = top_top_set_int )
% 0.29/0.49         => ( ( uminus1532241313380277803et_int @ X )
% 0.29/0.49            = Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra_class.boolean_algebra.compl_unique
% 0.29/0.49  thf(fact_798_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 0.29/0.49      ! [X: set_list_nat,Y: set_list_nat] :
% 0.29/0.49        ( ( ( inf_inf_set_list_nat @ X @ Y )
% 0.29/0.49          = bot_bot_set_list_nat )
% 0.29/0.49       => ( ( ( sup_sup_set_list_nat @ X @ Y )
% 0.29/0.49            = top_top_set_list_nat )
% 0.29/0.49         => ( ( uminus3195874150345416415st_nat @ X )
% 0.29/0.49            = Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra_class.boolean_algebra.compl_unique
% 0.29/0.49  thf(fact_799_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 0.29/0.49      ! [X: list_char > $o,Y: list_char > $o] :
% 0.29/0.49        ( ( ( inf_inf_list_char_o @ X @ Y )
% 0.29/0.49          = bot_bot_list_char_o )
% 0.29/0.49       => ( ( ( sup_sup_list_char_o @ X @ Y )
% 0.29/0.49            = top_top_list_char_o )
% 0.29/0.49         => ( ( uminus7154032370948614053char_o @ X )
% 0.29/0.49            = Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra_class.boolean_algebra.compl_unique
% 0.29/0.49  thf(fact_800_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 0.29/0.49      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 0.29/0.49          = bot_bo2099793752762293965at_nat )
% 0.29/0.49       => ( ( ( sup_su6327502436637775413at_nat @ X @ Y )
% 0.29/0.49            = top_to4669805908274784177at_nat )
% 0.29/0.49         => ( ( uminus6524753893492686040at_nat @ X )
% 0.29/0.49            = Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra_class.boolean_algebra.compl_unique
% 0.29/0.49  thf(fact_801_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 0.29/0.49      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 0.29/0.49        ( ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 0.29/0.49          = bot_bo8147686125503663512_int_o )
% 0.29/0.49       => ( ( ( sup_su8463660629351352368_int_o @ X @ Y )
% 0.29/0.49            = top_to1578927101902068148_int_o )
% 0.29/0.49         => ( ( uminus7117520113953359693_int_o @ X )
% 0.29/0.49            = Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra_class.boolean_algebra.compl_unique
% 0.29/0.49  thf(fact_802_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 0.29/0.49      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( ( inf_in1697001100524423349at_nat @ X @ Y )
% 0.29/0.49          = bot_bo8422036546324065075at_nat )
% 0.29/0.49       => ( ( ( sup_su3035147773818789531at_nat @ X @ Y )
% 0.29/0.49            = top_to8764741339697478167at_nat )
% 0.29/0.49         => ( ( uminus2330091110623919550at_nat @ X )
% 0.29/0.49            = Y ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % boolean_algebra_class.boolean_algebra.compl_unique
% 0.29/0.49  thf(fact_803_one__assn__raw_Oelims_I3_J,axiom,
% 0.29/0.49      ! [X: produc3658429121746597890et_nat] :
% 0.29/0.49        ( ~ ( one_assn_raw @ X )
% 0.29/0.49       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 0.29/0.49              ( ( X
% 0.29/0.49                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.49             => ( As4 = bot_bot_set_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_assn_raw.elims(3)
% 0.29/0.49  thf(fact_804_one__assn__raw_Oelims_I2_J,axiom,
% 0.29/0.49      ! [X: produc3658429121746597890et_nat] :
% 0.29/0.49        ( ( one_assn_raw @ X )
% 0.29/0.49       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 0.29/0.49              ( ( X
% 0.29/0.49                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.49             => ( As4 != bot_bot_set_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_assn_raw.elims(2)
% 0.29/0.49  thf(fact_805_one__assn__raw_Oelims_I1_J,axiom,
% 0.29/0.49      ! [X: produc3658429121746597890et_nat,Y: $o] :
% 0.29/0.49        ( ( ( one_assn_raw @ X )
% 0.29/0.49          = Y )
% 0.29/0.49       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 0.29/0.49              ( ( X
% 0.29/0.49                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.49             => ( Y
% 0.29/0.49                = ( As4 != bot_bot_set_nat ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_assn_raw.elims(1)
% 0.29/0.49  thf(fact_806_one__assn__raw_Osimps,axiom,
% 0.29/0.49      ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.29/0.49        ( ( one_assn_raw @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 0.29/0.49        = ( As = bot_bot_set_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % one_assn_raw.simps
% 0.29/0.49  thf(fact_807_times__assn__raw_Osimps,axiom,
% 0.29/0.49      ! [P: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o,H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.29/0.49        ( ( times_assn_raw @ P @ Q2 @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 0.29/0.49        = ( ? [As1: set_nat,As2: set_nat] :
% 0.29/0.49              ( ( As
% 0.29/0.49                = ( sup_sup_set_nat @ As1 @ As2 ) )
% 0.29/0.49              & ( ( inf_inf_set_nat @ As1 @ As2 )
% 0.29/0.49                = bot_bot_set_nat )
% 0.29/0.49              & ( P @ ( produc7507926704131184380et_nat @ H3 @ As1 ) )
% 0.29/0.49              & ( Q2 @ ( produc7507926704131184380et_nat @ H3 @ As2 ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % times_assn_raw.simps
% 0.29/0.49  thf(fact_808_times__assn__raw_Oelims_I1_J,axiom,
% 0.29/0.49      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 0.29/0.49        ( ( ( times_assn_raw @ X @ Xa @ Xb )
% 0.29/0.49          = Y )
% 0.29/0.49       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 0.29/0.49              ( ( Xb
% 0.29/0.49                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.49             => ( Y
% 0.29/0.49                = ( ~ ? [As1: set_nat,As2: set_nat] :
% 0.29/0.49                        ( ( As4
% 0.29/0.49                          = ( sup_sup_set_nat @ As1 @ As2 ) )
% 0.29/0.49                        & ( ( inf_inf_set_nat @ As1 @ As2 )
% 0.29/0.49                          = bot_bot_set_nat )
% 0.29/0.49                        & ( X @ ( produc7507926704131184380et_nat @ H @ As1 ) )
% 0.29/0.49                        & ( Xa @ ( produc7507926704131184380et_nat @ H @ As2 ) ) ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % times_assn_raw.elims(1)
% 0.29/0.49  thf(fact_809_times__assn__raw_Oelims_I2_J,axiom,
% 0.29/0.49      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 0.29/0.49        ( ( times_assn_raw @ X @ Xa @ Xb )
% 0.29/0.49       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 0.29/0.49              ( ( Xb
% 0.29/0.49                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.49             => ~ ? [As12: set_nat,As22: set_nat] :
% 0.29/0.49                    ( ( As4
% 0.29/0.49                      = ( sup_sup_set_nat @ As12 @ As22 ) )
% 0.29/0.49                    & ( ( inf_inf_set_nat @ As12 @ As22 )
% 0.29/0.49                      = bot_bot_set_nat )
% 0.29/0.49                    & ( X @ ( produc7507926704131184380et_nat @ H @ As12 ) )
% 0.29/0.49                    & ( Xa @ ( produc7507926704131184380et_nat @ H @ As22 ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % times_assn_raw.elims(2)
% 0.29/0.49  thf(fact_810_times__assn__raw_Oelims_I3_J,axiom,
% 0.29/0.49      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 0.29/0.49        ( ~ ( times_assn_raw @ X @ Xa @ Xb )
% 0.29/0.49       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 0.29/0.49              ( ( Xb
% 0.29/0.49                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.49             => ? [As13: set_nat,As23: set_nat] :
% 0.29/0.49                  ( ( As4
% 0.29/0.49                    = ( sup_sup_set_nat @ As13 @ As23 ) )
% 0.29/0.49                  & ( ( inf_inf_set_nat @ As13 @ As23 )
% 0.29/0.49                    = bot_bot_set_nat )
% 0.29/0.49                  & ( X @ ( produc7507926704131184380et_nat @ H @ As13 ) )
% 0.29/0.49                  & ( Xa @ ( produc7507926704131184380et_nat @ H @ As23 ) ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % times_assn_raw.elims(3)
% 0.29/0.49  thf(fact_811_assn__one__left,axiom,
% 0.29/0.49      ! [P: assn] :
% 0.29/0.49        ( ( times_times_assn @ one_one_assn @ P )
% 0.29/0.49        = P ) ).
% 0.29/0.49  
% 0.29/0.49  % assn_one_left
% 0.29/0.49  thf(fact_812_inf__cancel__left1,axiom,
% 0.29/0.49      ! [X: product_prod_int_int > $o,A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 0.29/0.49        ( ( inf_in3604695632404883862_int_o @ ( inf_in3604695632404883862_int_o @ X @ A ) @ ( inf_in3604695632404883862_int_o @ ( uminus7117520113953359693_int_o @ X ) @ B ) )
% 0.29/0.49        = bot_bo8147686125503663512_int_o ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_cancel_left1
% 0.29/0.49  thf(fact_813_inf__cancel__left1,axiom,
% 0.29/0.49      ! [X: list_char > $o,A: list_char > $o,B: list_char > $o] :
% 0.29/0.49        ( ( inf_inf_list_char_o @ ( inf_inf_list_char_o @ X @ A ) @ ( inf_inf_list_char_o @ ( uminus7154032370948614053char_o @ X ) @ B ) )
% 0.29/0.49        = bot_bot_list_char_o ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_cancel_left1
% 0.29/0.49  thf(fact_814_inf__cancel__left1,axiom,
% 0.29/0.49      ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ X @ A ) @ ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ B ) )
% 0.29/0.49        = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_cancel_left1
% 0.29/0.49  thf(fact_815_inf__cancel__left1,axiom,
% 0.29/0.49      ! [X: set_o,A: set_o,B: set_o] :
% 0.29/0.49        ( ( inf_inf_set_o @ ( inf_inf_set_o @ X @ A ) @ ( inf_inf_set_o @ ( uminus_uminus_set_o @ X ) @ B ) )
% 0.29/0.49        = bot_bot_set_o ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_cancel_left1
% 0.29/0.49  thf(fact_816_inf__cancel__left1,axiom,
% 0.29/0.49      ! [X: set_nat,A: set_nat,B: set_nat] :
% 0.29/0.49        ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ A ) @ ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ B ) )
% 0.29/0.49        = bot_bot_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_cancel_left1
% 0.29/0.49  thf(fact_817_inf__cancel__left1,axiom,
% 0.29/0.49      ! [X: set_int,A: set_int,B: set_int] :
% 0.29/0.49        ( ( inf_inf_set_int @ ( inf_inf_set_int @ X @ A ) @ ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ B ) )
% 0.29/0.49        = bot_bot_set_int ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_cancel_left1
% 0.29/0.49  thf(fact_818_inf__cancel__left1,axiom,
% 0.29/0.49      ! [X: product_unit,A: product_unit,B: product_unit] :
% 0.29/0.49        ( ( inf_inf_Product_unit @ ( inf_inf_Product_unit @ X @ A ) @ ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ B ) )
% 0.29/0.49        = bot_bot_Product_unit ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_cancel_left1
% 0.29/0.49  thf(fact_819_inf__cancel__left2,axiom,
% 0.29/0.49      ! [X: product_prod_int_int > $o,A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 0.29/0.49        ( ( inf_in3604695632404883862_int_o @ ( inf_in3604695632404883862_int_o @ ( uminus7117520113953359693_int_o @ X ) @ A ) @ ( inf_in3604695632404883862_int_o @ X @ B ) )
% 0.29/0.49        = bot_bo8147686125503663512_int_o ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_cancel_left2
% 0.29/0.49  thf(fact_820_inf__cancel__left2,axiom,
% 0.29/0.49      ! [X: list_char > $o,A: list_char > $o,B: list_char > $o] :
% 0.29/0.49        ( ( inf_inf_list_char_o @ ( inf_inf_list_char_o @ ( uminus7154032370948614053char_o @ X ) @ A ) @ ( inf_inf_list_char_o @ X @ B ) )
% 0.29/0.49        = bot_bot_list_char_o ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_cancel_left2
% 0.29/0.49  thf(fact_821_inf__cancel__left2,axiom,
% 0.29/0.49      ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ A ) @ ( inf_in2572325071724192079at_nat @ X @ B ) )
% 0.29/0.49        = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_cancel_left2
% 0.29/0.49  thf(fact_822_inf__cancel__left2,axiom,
% 0.29/0.49      ! [X: set_o,A: set_o,B: set_o] :
% 0.29/0.49        ( ( inf_inf_set_o @ ( inf_inf_set_o @ ( uminus_uminus_set_o @ X ) @ A ) @ ( inf_inf_set_o @ X @ B ) )
% 0.29/0.49        = bot_bot_set_o ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_cancel_left2
% 0.29/0.49  thf(fact_823_inf__cancel__left2,axiom,
% 0.29/0.49      ! [X: set_nat,A: set_nat,B: set_nat] :
% 0.29/0.49        ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ A ) @ ( inf_inf_set_nat @ X @ B ) )
% 0.29/0.49        = bot_bot_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_cancel_left2
% 0.29/0.49  thf(fact_824_inf__cancel__left2,axiom,
% 0.29/0.49      ! [X: set_int,A: set_int,B: set_int] :
% 0.29/0.49        ( ( inf_inf_set_int @ ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ A ) @ ( inf_inf_set_int @ X @ B ) )
% 0.29/0.49        = bot_bot_set_int ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_cancel_left2
% 0.29/0.49  thf(fact_825_inf__cancel__left2,axiom,
% 0.29/0.49      ! [X: product_unit,A: product_unit,B: product_unit] :
% 0.29/0.49        ( ( inf_inf_Product_unit @ ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ A ) @ ( inf_inf_Product_unit @ X @ B ) )
% 0.29/0.49        = bot_bot_Product_unit ) ).
% 0.29/0.49  
% 0.29/0.49  % inf_cancel_left2
% 0.29/0.49  thf(fact_826_mult__minus1,axiom,
% 0.29/0.49      ! [Z: int] :
% 0.29/0.49        ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 0.29/0.49        = ( uminus_uminus_int @ Z ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult_minus1
% 0.29/0.49  thf(fact_827_mult__minus1,axiom,
% 0.29/0.49      ! [Z: code_integer] :
% 0.29/0.49        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 0.29/0.49        = ( uminus1351360451143612070nteger @ Z ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult_minus1
% 0.29/0.49  thf(fact_828_mult__minus1,axiom,
% 0.29/0.49      ! [Z: rat] :
% 0.29/0.49        ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 0.29/0.49        = ( uminus_uminus_rat @ Z ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult_minus1
% 0.29/0.49  thf(fact_829_mult__minus1__right,axiom,
% 0.29/0.49      ! [Z: int] :
% 0.29/0.49        ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.49        = ( uminus_uminus_int @ Z ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult_minus1_right
% 0.29/0.49  thf(fact_830_mult__minus1__right,axiom,
% 0.29/0.49      ! [Z: code_integer] :
% 0.29/0.49        ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.49        = ( uminus1351360451143612070nteger @ Z ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult_minus1_right
% 0.29/0.49  thf(fact_831_mult__minus1__right,axiom,
% 0.29/0.49      ! [Z: rat] :
% 0.29/0.49        ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.49        = ( uminus_uminus_rat @ Z ) ) ).
% 0.29/0.49  
% 0.29/0.49  % mult_minus1_right
% 0.29/0.49  thf(fact_832_Un__Int__eq_I1_J,axiom,
% 0.29/0.49      ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ S @ T ) @ S )
% 0.29/0.49        = S ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_Int_eq(1)
% 0.29/0.49  thf(fact_833_Un__Int__eq_I1_J,axiom,
% 0.29/0.49      ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ S @ T ) @ S )
% 0.29/0.49        = S ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_Int_eq(1)
% 0.29/0.49  thf(fact_834_Un__Int__eq_I1_J,axiom,
% 0.29/0.49      ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ S @ T ) @ S )
% 0.29/0.49        = S ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_Int_eq(1)
% 0.29/0.49  thf(fact_835_Un__Int__eq_I1_J,axiom,
% 0.29/0.49      ! [S: set_nat,T: set_nat] :
% 0.29/0.49        ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ S @ T ) @ S )
% 0.29/0.49        = S ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_Int_eq(1)
% 0.29/0.49  thf(fact_836_Un__Int__eq_I2_J,axiom,
% 0.29/0.49      ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ S @ T ) @ T )
% 0.29/0.49        = T ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_Int_eq(2)
% 0.29/0.49  thf(fact_837_Un__Int__eq_I2_J,axiom,
% 0.29/0.49      ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ S @ T ) @ T )
% 0.29/0.49        = T ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_Int_eq(2)
% 0.29/0.49  thf(fact_838_Un__Int__eq_I2_J,axiom,
% 0.29/0.49      ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ S @ T ) @ T )
% 0.29/0.49        = T ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_Int_eq(2)
% 0.29/0.49  thf(fact_839_Un__Int__eq_I2_J,axiom,
% 0.29/0.49      ! [S: set_nat,T: set_nat] :
% 0.29/0.49        ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ S @ T ) @ T )
% 0.29/0.49        = T ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_Int_eq(2)
% 0.29/0.49  thf(fact_840_Un__Int__eq_I3_J,axiom,
% 0.29/0.49      ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( inf_in2572325071724192079at_nat @ S @ ( sup_su6327502436637775413at_nat @ S @ T ) )
% 0.29/0.49        = S ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_Int_eq(3)
% 0.29/0.49  thf(fact_841_Un__Int__eq_I3_J,axiom,
% 0.29/0.49      ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( inf_in1697001100524423349at_nat @ S @ ( sup_su3035147773818789531at_nat @ S @ T ) )
% 0.29/0.49        = S ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_Int_eq(3)
% 0.29/0.49  thf(fact_842_Un__Int__eq_I3_J,axiom,
% 0.29/0.49      ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( inf_in7913087082777306421at_nat @ S @ ( sup_su5525570899277871387at_nat @ S @ T ) )
% 0.29/0.49        = S ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_Int_eq(3)
% 0.29/0.49  thf(fact_843_Un__Int__eq_I3_J,axiom,
% 0.29/0.49      ! [S: set_nat,T: set_nat] :
% 0.29/0.49        ( ( inf_inf_set_nat @ S @ ( sup_sup_set_nat @ S @ T ) )
% 0.29/0.49        = S ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_Int_eq(3)
% 0.29/0.49  thf(fact_844_Un__Int__eq_I4_J,axiom,
% 0.29/0.49      ! [T: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( inf_in2572325071724192079at_nat @ T @ ( sup_su6327502436637775413at_nat @ S @ T ) )
% 0.29/0.49        = T ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_Int_eq(4)
% 0.29/0.49  thf(fact_845_Un__Int__eq_I4_J,axiom,
% 0.29/0.49      ! [T: set_Pr8551490117392284871at_nat,S: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( inf_in1697001100524423349at_nat @ T @ ( sup_su3035147773818789531at_nat @ S @ T ) )
% 0.29/0.49        = T ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_Int_eq(4)
% 0.29/0.49  thf(fact_846_Un__Int__eq_I4_J,axiom,
% 0.29/0.49      ! [T: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( inf_in7913087082777306421at_nat @ T @ ( sup_su5525570899277871387at_nat @ S @ T ) )
% 0.29/0.49        = T ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_Int_eq(4)
% 0.29/0.49  thf(fact_847_Un__Int__eq_I4_J,axiom,
% 0.29/0.49      ! [T: set_nat,S: set_nat] :
% 0.29/0.49        ( ( inf_inf_set_nat @ T @ ( sup_sup_set_nat @ S @ T ) )
% 0.29/0.49        = T ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_Int_eq(4)
% 0.29/0.49  thf(fact_848_Int__Un__eq_I1_J,axiom,
% 0.29/0.49      ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ S @ T ) @ S )
% 0.29/0.49        = S ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_Un_eq(1)
% 0.29/0.49  thf(fact_849_Int__Un__eq_I1_J,axiom,
% 0.29/0.49      ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ S @ T ) @ S )
% 0.29/0.49        = S ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_Un_eq(1)
% 0.29/0.49  thf(fact_850_Int__Un__eq_I1_J,axiom,
% 0.29/0.49      ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ S @ T ) @ S )
% 0.29/0.49        = S ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_Un_eq(1)
% 0.29/0.49  thf(fact_851_Int__Un__eq_I1_J,axiom,
% 0.29/0.49      ! [S: set_nat,T: set_nat] :
% 0.29/0.49        ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ S @ T ) @ S )
% 0.29/0.49        = S ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_Un_eq(1)
% 0.29/0.49  thf(fact_852_Int__Un__eq_I2_J,axiom,
% 0.29/0.49      ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ S @ T ) @ T )
% 0.29/0.49        = T ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_Un_eq(2)
% 0.29/0.49  thf(fact_853_Int__Un__eq_I2_J,axiom,
% 0.29/0.49      ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ S @ T ) @ T )
% 0.29/0.49        = T ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_Un_eq(2)
% 0.29/0.49  thf(fact_854_Int__Un__eq_I2_J,axiom,
% 0.29/0.49      ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ S @ T ) @ T )
% 0.29/0.49        = T ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_Un_eq(2)
% 0.29/0.49  thf(fact_855_Int__Un__eq_I2_J,axiom,
% 0.29/0.49      ! [S: set_nat,T: set_nat] :
% 0.29/0.49        ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ S @ T ) @ T )
% 0.29/0.49        = T ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_Un_eq(2)
% 0.29/0.49  thf(fact_856_Int__Un__eq_I3_J,axiom,
% 0.29/0.49      ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( sup_su6327502436637775413at_nat @ S @ ( inf_in2572325071724192079at_nat @ S @ T ) )
% 0.29/0.49        = S ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_Un_eq(3)
% 0.29/0.49  thf(fact_857_Int__Un__eq_I3_J,axiom,
% 0.29/0.49      ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( sup_su3035147773818789531at_nat @ S @ ( inf_in1697001100524423349at_nat @ S @ T ) )
% 0.29/0.49        = S ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_Un_eq(3)
% 0.29/0.49  thf(fact_858_Int__Un__eq_I3_J,axiom,
% 0.29/0.49      ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( sup_su5525570899277871387at_nat @ S @ ( inf_in7913087082777306421at_nat @ S @ T ) )
% 0.29/0.49        = S ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_Un_eq(3)
% 0.29/0.49  thf(fact_859_Int__Un__eq_I3_J,axiom,
% 0.29/0.49      ! [S: set_nat,T: set_nat] :
% 0.29/0.49        ( ( sup_sup_set_nat @ S @ ( inf_inf_set_nat @ S @ T ) )
% 0.29/0.49        = S ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_Un_eq(3)
% 0.29/0.49  thf(fact_860_Int__Un__eq_I4_J,axiom,
% 0.29/0.49      ! [T: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( sup_su6327502436637775413at_nat @ T @ ( inf_in2572325071724192079at_nat @ S @ T ) )
% 0.29/0.49        = T ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_Un_eq(4)
% 0.29/0.49  thf(fact_861_Int__Un__eq_I4_J,axiom,
% 0.29/0.49      ! [T: set_Pr8551490117392284871at_nat,S: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( sup_su3035147773818789531at_nat @ T @ ( inf_in1697001100524423349at_nat @ S @ T ) )
% 0.29/0.49        = T ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_Un_eq(4)
% 0.29/0.49  thf(fact_862_Int__Un__eq_I4_J,axiom,
% 0.29/0.49      ! [T: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( sup_su5525570899277871387at_nat @ T @ ( inf_in7913087082777306421at_nat @ S @ T ) )
% 0.29/0.49        = T ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_Un_eq(4)
% 0.29/0.49  thf(fact_863_Int__Un__eq_I4_J,axiom,
% 0.29/0.49      ! [T: set_nat,S: set_nat] :
% 0.29/0.49        ( ( sup_sup_set_nat @ T @ ( inf_inf_set_nat @ S @ T ) )
% 0.29/0.49        = T ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_Un_eq(4)
% 0.29/0.49  thf(fact_864_Un__empty,axiom,
% 0.29/0.49      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( ( sup_su3035147773818789531at_nat @ A2 @ B2 )
% 0.29/0.49          = bot_bo8422036546324065075at_nat )
% 0.29/0.49        = ( ( A2 = bot_bo8422036546324065075at_nat )
% 0.29/0.49          & ( B2 = bot_bo8422036546324065075at_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_empty
% 0.29/0.49  thf(fact_865_Un__empty,axiom,
% 0.29/0.49      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( ( sup_su5525570899277871387at_nat @ A2 @ B2 )
% 0.29/0.49          = bot_bo228742789529271731at_nat )
% 0.29/0.49        = ( ( A2 = bot_bo228742789529271731at_nat )
% 0.29/0.49          & ( B2 = bot_bo228742789529271731at_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_empty
% 0.29/0.49  thf(fact_866_Un__empty,axiom,
% 0.29/0.49      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( ( sup_su6327502436637775413at_nat @ A2 @ B2 )
% 0.29/0.49          = bot_bo2099793752762293965at_nat )
% 0.29/0.49        = ( ( A2 = bot_bo2099793752762293965at_nat )
% 0.29/0.49          & ( B2 = bot_bo2099793752762293965at_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_empty
% 0.29/0.49  thf(fact_867_Un__empty,axiom,
% 0.29/0.49      ! [A2: set_o,B2: set_o] :
% 0.29/0.49        ( ( ( sup_sup_set_o @ A2 @ B2 )
% 0.29/0.49          = bot_bot_set_o )
% 0.29/0.49        = ( ( A2 = bot_bot_set_o )
% 0.29/0.49          & ( B2 = bot_bot_set_o ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_empty
% 0.29/0.49  thf(fact_868_Un__empty,axiom,
% 0.29/0.49      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.49        ( ( ( sup_sup_set_nat @ A2 @ B2 )
% 0.29/0.49          = bot_bot_set_nat )
% 0.29/0.49        = ( ( A2 = bot_bot_set_nat )
% 0.29/0.49          & ( B2 = bot_bot_set_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_empty
% 0.29/0.49  thf(fact_869_Un__empty,axiom,
% 0.29/0.49      ! [A2: set_int,B2: set_int] :
% 0.29/0.49        ( ( ( sup_sup_set_int @ A2 @ B2 )
% 0.29/0.49          = bot_bot_set_int )
% 0.29/0.49        = ( ( A2 = bot_bot_set_int )
% 0.29/0.49          & ( B2 = bot_bot_set_int ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_empty
% 0.29/0.49  thf(fact_870_Compl__disjoint2,axiom,
% 0.29/0.49      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ A2 ) @ A2 )
% 0.29/0.49        = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % Compl_disjoint2
% 0.29/0.49  thf(fact_871_Compl__disjoint2,axiom,
% 0.29/0.49      ! [A2: set_o] :
% 0.29/0.49        ( ( inf_inf_set_o @ ( uminus_uminus_set_o @ A2 ) @ A2 )
% 0.29/0.49        = bot_bot_set_o ) ).
% 0.29/0.49  
% 0.29/0.49  % Compl_disjoint2
% 0.29/0.49  thf(fact_872_Compl__disjoint2,axiom,
% 0.29/0.49      ! [A2: set_nat] :
% 0.29/0.49        ( ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ A2 )
% 0.29/0.49        = bot_bot_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % Compl_disjoint2
% 0.29/0.49  thf(fact_873_Compl__disjoint2,axiom,
% 0.29/0.49      ! [A2: set_int] :
% 0.29/0.49        ( ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ A2 )
% 0.29/0.49        = bot_bot_set_int ) ).
% 0.29/0.49  
% 0.29/0.49  % Compl_disjoint2
% 0.29/0.49  thf(fact_874_empty__iff,axiom,
% 0.29/0.49      ! [C: set_Pr958786334691620121nt_int] :
% 0.29/0.49        ~ ( member2340774599025711042nt_int @ C @ bot_bo1488462491386950373nt_int ) ).
% 0.29/0.49  
% 0.29/0.49  % empty_iff
% 0.29/0.49  thf(fact_875_empty__iff,axiom,
% 0.29/0.49      ! [C: set_nat] :
% 0.29/0.49        ~ ( member_set_nat @ C @ bot_bot_set_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % empty_iff
% 0.29/0.49  thf(fact_876_empty__iff,axiom,
% 0.29/0.49      ! [C: produc3658429121746597890et_nat > $o] :
% 0.29/0.49        ~ ( member6576561426505652726_nat_o @ C @ bot_bo7824918357723582233_nat_o ) ).
% 0.29/0.49  
% 0.29/0.49  % empty_iff
% 0.29/0.49  thf(fact_877_empty__iff,axiom,
% 0.29/0.49      ! [C: product_prod_nat_nat] :
% 0.29/0.49        ~ ( member8440522571783428010at_nat @ C @ bot_bo2099793752762293965at_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % empty_iff
% 0.29/0.49  thf(fact_878_empty__iff,axiom,
% 0.29/0.49      ! [C: $o] :
% 0.29/0.49        ~ ( member_o @ C @ bot_bot_set_o ) ).
% 0.29/0.49  
% 0.29/0.49  % empty_iff
% 0.29/0.49  thf(fact_879_empty__iff,axiom,
% 0.29/0.49      ! [C: nat] :
% 0.29/0.49        ~ ( member_nat @ C @ bot_bot_set_nat ) ).
% 0.29/0.49  
% 0.29/0.49  % empty_iff
% 0.29/0.49  thf(fact_880_empty__iff,axiom,
% 0.29/0.49      ! [C: int] :
% 0.29/0.49        ~ ( member_int @ C @ bot_bot_set_int ) ).
% 0.29/0.49  
% 0.29/0.49  % empty_iff
% 0.29/0.49  thf(fact_881_all__not__in__conv,axiom,
% 0.29/0.49      ! [A2: set_se6260736226359567993nt_int] :
% 0.29/0.49        ( ( ! [X3: set_Pr958786334691620121nt_int] :
% 0.29/0.49              ~ ( member2340774599025711042nt_int @ X3 @ A2 ) )
% 0.29/0.49        = ( A2 = bot_bo1488462491386950373nt_int ) ) ).
% 0.29/0.49  
% 0.29/0.49  % all_not_in_conv
% 0.29/0.49  thf(fact_882_all__not__in__conv,axiom,
% 0.29/0.49      ! [A2: set_set_nat] :
% 0.29/0.49        ( ( ! [X3: set_nat] :
% 0.29/0.49              ~ ( member_set_nat @ X3 @ A2 ) )
% 0.29/0.49        = ( A2 = bot_bot_set_set_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % all_not_in_conv
% 0.29/0.49  thf(fact_883_all__not__in__conv,axiom,
% 0.29/0.49      ! [A2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.49        ( ( ! [X3: produc3658429121746597890et_nat > $o] :
% 0.29/0.49              ~ ( member6576561426505652726_nat_o @ X3 @ A2 ) )
% 0.29/0.49        = ( A2 = bot_bo7824918357723582233_nat_o ) ) ).
% 0.29/0.49  
% 0.29/0.49  % all_not_in_conv
% 0.29/0.49  thf(fact_884_all__not__in__conv,axiom,
% 0.29/0.49      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( ! [X3: product_prod_nat_nat] :
% 0.29/0.49              ~ ( member8440522571783428010at_nat @ X3 @ A2 ) )
% 0.29/0.49        = ( A2 = bot_bo2099793752762293965at_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % all_not_in_conv
% 0.29/0.49  thf(fact_885_all__not__in__conv,axiom,
% 0.29/0.49      ! [A2: set_o] :
% 0.29/0.49        ( ( ! [X3: $o] :
% 0.29/0.49              ~ ( member_o @ X3 @ A2 ) )
% 0.29/0.49        = ( A2 = bot_bot_set_o ) ) ).
% 0.29/0.49  
% 0.29/0.49  % all_not_in_conv
% 0.29/0.49  thf(fact_886_all__not__in__conv,axiom,
% 0.29/0.49      ! [A2: set_nat] :
% 0.29/0.49        ( ( ! [X3: nat] :
% 0.29/0.49              ~ ( member_nat @ X3 @ A2 ) )
% 0.29/0.49        = ( A2 = bot_bot_set_nat ) ) ).
% 0.29/0.49  
% 0.29/0.49  % all_not_in_conv
% 0.29/0.49  thf(fact_887_all__not__in__conv,axiom,
% 0.29/0.49      ! [A2: set_int] :
% 0.29/0.49        ( ( ! [X3: int] :
% 0.29/0.49              ~ ( member_int @ X3 @ A2 ) )
% 0.29/0.49        = ( A2 = bot_bot_set_int ) ) ).
% 0.29/0.49  
% 0.29/0.49  % all_not_in_conv
% 0.29/0.49  thf(fact_888_Collect__empty__eq,axiom,
% 0.29/0.49      ! [P: set_Pr958786334691620121nt_int > $o] :
% 0.29/0.49        ( ( ( collec5210948495886036740nt_int @ P )
% 0.29/0.49          = bot_bo1488462491386950373nt_int )
% 0.29/0.49        = ( ! [X3: set_Pr958786334691620121nt_int] :
% 0.29/0.49              ~ ( P @ X3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Collect_empty_eq
% 0.29/0.49  thf(fact_889_Collect__empty__eq,axiom,
% 0.29/0.49      ! [P: set_nat > $o] :
% 0.29/0.49        ( ( ( collect_set_nat @ P )
% 0.29/0.49          = bot_bot_set_set_nat )
% 0.29/0.49        = ( ! [X3: set_nat] :
% 0.29/0.49              ~ ( P @ X3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Collect_empty_eq
% 0.29/0.49  thf(fact_890_Collect__empty__eq,axiom,
% 0.29/0.49      ! [P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.29/0.49        ( ( ( collec939566748876313656_nat_o @ P )
% 0.29/0.49          = bot_bo7824918357723582233_nat_o )
% 0.29/0.49        = ( ! [X3: produc3658429121746597890et_nat > $o] :
% 0.29/0.49              ~ ( P @ X3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Collect_empty_eq
% 0.29/0.49  thf(fact_891_Collect__empty__eq,axiom,
% 0.29/0.49      ! [P: product_prod_nat_nat > $o] :
% 0.29/0.49        ( ( ( collec3392354462482085612at_nat @ P )
% 0.29/0.49          = bot_bo2099793752762293965at_nat )
% 0.29/0.49        = ( ! [X3: product_prod_nat_nat] :
% 0.29/0.49              ~ ( P @ X3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Collect_empty_eq
% 0.29/0.49  thf(fact_892_Collect__empty__eq,axiom,
% 0.29/0.49      ! [P: $o > $o] :
% 0.29/0.49        ( ( ( collect_o @ P )
% 0.29/0.49          = bot_bot_set_o )
% 0.29/0.49        = ( ! [X3: $o] :
% 0.29/0.49              ~ ( P @ X3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Collect_empty_eq
% 0.29/0.49  thf(fact_893_Collect__empty__eq,axiom,
% 0.29/0.49      ! [P: nat > $o] :
% 0.29/0.49        ( ( ( collect_nat @ P )
% 0.29/0.49          = bot_bot_set_nat )
% 0.29/0.49        = ( ! [X3: nat] :
% 0.29/0.49              ~ ( P @ X3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Collect_empty_eq
% 0.29/0.49  thf(fact_894_Collect__empty__eq,axiom,
% 0.29/0.49      ! [P: int > $o] :
% 0.29/0.49        ( ( ( collect_int @ P )
% 0.29/0.49          = bot_bot_set_int )
% 0.29/0.49        = ( ! [X3: int] :
% 0.29/0.49              ~ ( P @ X3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Collect_empty_eq
% 0.29/0.49  thf(fact_895_empty__Collect__eq,axiom,
% 0.29/0.49      ! [P: set_Pr958786334691620121nt_int > $o] :
% 0.29/0.49        ( ( bot_bo1488462491386950373nt_int
% 0.29/0.49          = ( collec5210948495886036740nt_int @ P ) )
% 0.29/0.49        = ( ! [X3: set_Pr958786334691620121nt_int] :
% 0.29/0.49              ~ ( P @ X3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % empty_Collect_eq
% 0.29/0.49  thf(fact_896_empty__Collect__eq,axiom,
% 0.29/0.49      ! [P: set_nat > $o] :
% 0.29/0.49        ( ( bot_bot_set_set_nat
% 0.29/0.49          = ( collect_set_nat @ P ) )
% 0.29/0.49        = ( ! [X3: set_nat] :
% 0.29/0.49              ~ ( P @ X3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % empty_Collect_eq
% 0.29/0.49  thf(fact_897_empty__Collect__eq,axiom,
% 0.29/0.49      ! [P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.29/0.49        ( ( bot_bo7824918357723582233_nat_o
% 0.29/0.49          = ( collec939566748876313656_nat_o @ P ) )
% 0.29/0.49        = ( ! [X3: produc3658429121746597890et_nat > $o] :
% 0.29/0.49              ~ ( P @ X3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % empty_Collect_eq
% 0.29/0.49  thf(fact_898_empty__Collect__eq,axiom,
% 0.29/0.49      ! [P: product_prod_nat_nat > $o] :
% 0.29/0.49        ( ( bot_bo2099793752762293965at_nat
% 0.29/0.49          = ( collec3392354462482085612at_nat @ P ) )
% 0.29/0.49        = ( ! [X3: product_prod_nat_nat] :
% 0.29/0.49              ~ ( P @ X3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % empty_Collect_eq
% 0.29/0.49  thf(fact_899_empty__Collect__eq,axiom,
% 0.29/0.49      ! [P: $o > $o] :
% 0.29/0.49        ( ( bot_bot_set_o
% 0.29/0.49          = ( collect_o @ P ) )
% 0.29/0.49        = ( ! [X3: $o] :
% 0.29/0.49              ~ ( P @ X3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % empty_Collect_eq
% 0.29/0.49  thf(fact_900_empty__Collect__eq,axiom,
% 0.29/0.49      ! [P: nat > $o] :
% 0.29/0.49        ( ( bot_bot_set_nat
% 0.29/0.49          = ( collect_nat @ P ) )
% 0.29/0.49        = ( ! [X3: nat] :
% 0.29/0.49              ~ ( P @ X3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % empty_Collect_eq
% 0.29/0.49  thf(fact_901_empty__Collect__eq,axiom,
% 0.29/0.49      ! [P: int > $o] :
% 0.29/0.49        ( ( bot_bot_set_int
% 0.29/0.49          = ( collect_int @ P ) )
% 0.29/0.49        = ( ! [X3: int] :
% 0.29/0.49              ~ ( P @ X3 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % empty_Collect_eq
% 0.29/0.49  thf(fact_902_IntI,axiom,
% 0.29/0.49      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 0.29/0.49        ( ( member2340774599025711042nt_int @ C @ A2 )
% 0.29/0.49       => ( ( member2340774599025711042nt_int @ C @ B2 )
% 0.29/0.49         => ( member2340774599025711042nt_int @ C @ ( inf_in8396524679539076455nt_int @ A2 @ B2 ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % IntI
% 0.29/0.49  thf(fact_903_IntI,axiom,
% 0.29/0.49      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.29/0.49        ( ( member_set_nat @ C @ A2 )
% 0.29/0.49       => ( ( member_set_nat @ C @ B2 )
% 0.29/0.49         => ( member_set_nat @ C @ ( inf_inf_set_set_nat @ A2 @ B2 ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % IntI
% 0.29/0.49  thf(fact_904_IntI,axiom,
% 0.29/0.49      ! [C: int,A2: set_int,B2: set_int] :
% 0.29/0.49        ( ( member_int @ C @ A2 )
% 0.29/0.49       => ( ( member_int @ C @ B2 )
% 0.29/0.49         => ( member_int @ C @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % IntI
% 0.29/0.49  thf(fact_905_IntI,axiom,
% 0.29/0.49      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.49        ( ( member6576561426505652726_nat_o @ C @ A2 )
% 0.29/0.49       => ( ( member6576561426505652726_nat_o @ C @ B2 )
% 0.29/0.49         => ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % IntI
% 0.29/0.49  thf(fact_906_IntI,axiom,
% 0.29/0.49      ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( member8440522571783428010at_nat @ C @ A2 )
% 0.29/0.49       => ( ( member8440522571783428010at_nat @ C @ B2 )
% 0.29/0.49         => ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % IntI
% 0.29/0.49  thf(fact_907_IntI,axiom,
% 0.29/0.49      ! [C: nat,A2: set_nat,B2: set_nat] :
% 0.29/0.49        ( ( member_nat @ C @ A2 )
% 0.29/0.49       => ( ( member_nat @ C @ B2 )
% 0.29/0.49         => ( member_nat @ C @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % IntI
% 0.29/0.49  thf(fact_908_Int__iff,axiom,
% 0.29/0.49      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 0.29/0.49        ( ( member2340774599025711042nt_int @ C @ ( inf_in8396524679539076455nt_int @ A2 @ B2 ) )
% 0.29/0.49        = ( ( member2340774599025711042nt_int @ C @ A2 )
% 0.29/0.49          & ( member2340774599025711042nt_int @ C @ B2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_iff
% 0.29/0.49  thf(fact_909_Int__iff,axiom,
% 0.29/0.49      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.29/0.49        ( ( member_set_nat @ C @ ( inf_inf_set_set_nat @ A2 @ B2 ) )
% 0.29/0.49        = ( ( member_set_nat @ C @ A2 )
% 0.29/0.49          & ( member_set_nat @ C @ B2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_iff
% 0.29/0.49  thf(fact_910_Int__iff,axiom,
% 0.29/0.49      ! [C: int,A2: set_int,B2: set_int] :
% 0.29/0.49        ( ( member_int @ C @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.29/0.49        = ( ( member_int @ C @ A2 )
% 0.29/0.49          & ( member_int @ C @ B2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_iff
% 0.29/0.49  thf(fact_911_Int__iff,axiom,
% 0.29/0.49      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.49        ( ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) )
% 0.29/0.49        = ( ( member6576561426505652726_nat_o @ C @ A2 )
% 0.29/0.49          & ( member6576561426505652726_nat_o @ C @ B2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_iff
% 0.29/0.49  thf(fact_912_Int__iff,axiom,
% 0.29/0.49      ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 0.29/0.49        = ( ( member8440522571783428010at_nat @ C @ A2 )
% 0.29/0.49          & ( member8440522571783428010at_nat @ C @ B2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_iff
% 0.29/0.49  thf(fact_913_Int__iff,axiom,
% 0.29/0.49      ! [C: nat,A2: set_nat,B2: set_nat] :
% 0.29/0.49        ( ( member_nat @ C @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.29/0.49        = ( ( member_nat @ C @ A2 )
% 0.29/0.49          & ( member_nat @ C @ B2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_iff
% 0.29/0.49  thf(fact_914_Int__UNIV,axiom,
% 0.29/0.49      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.49        ( ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 0.29/0.49          = top_to4669805908274784177at_nat )
% 0.29/0.49        = ( ( A2 = top_to4669805908274784177at_nat )
% 0.29/0.49          & ( B2 = top_to4669805908274784177at_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_UNIV
% 0.29/0.49  thf(fact_915_Int__UNIV,axiom,
% 0.29/0.49      ! [A2: set_list_nat,B2: set_list_nat] :
% 0.29/0.49        ( ( ( inf_inf_set_list_nat @ A2 @ B2 )
% 0.29/0.49          = top_top_set_list_nat )
% 0.29/0.49        = ( ( A2 = top_top_set_list_nat )
% 0.29/0.49          & ( B2 = top_top_set_list_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_UNIV
% 0.29/0.49  thf(fact_916_Int__UNIV,axiom,
% 0.29/0.49      ! [A2: set_o,B2: set_o] :
% 0.29/0.49        ( ( ( inf_inf_set_o @ A2 @ B2 )
% 0.29/0.49          = top_top_set_o )
% 0.29/0.49        = ( ( A2 = top_top_set_o )
% 0.29/0.49          & ( B2 = top_top_set_o ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_UNIV
% 0.29/0.49  thf(fact_917_Int__UNIV,axiom,
% 0.29/0.49      ! [A2: set_rat,B2: set_rat] :
% 0.29/0.49        ( ( ( inf_inf_set_rat @ A2 @ B2 )
% 0.29/0.49          = top_top_set_rat )
% 0.29/0.49        = ( ( A2 = top_top_set_rat )
% 0.29/0.49          & ( B2 = top_top_set_rat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_UNIV
% 0.29/0.49  thf(fact_918_Int__UNIV,axiom,
% 0.29/0.49      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.49        ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 0.29/0.49          = top_top_set_nat )
% 0.29/0.49        = ( ( A2 = top_top_set_nat )
% 0.29/0.49          & ( B2 = top_top_set_nat ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_UNIV
% 0.29/0.49  thf(fact_919_Int__UNIV,axiom,
% 0.29/0.49      ! [A2: set_int,B2: set_int] :
% 0.29/0.49        ( ( ( inf_inf_set_int @ A2 @ B2 )
% 0.29/0.49          = top_top_set_int )
% 0.29/0.49        = ( ( A2 = top_top_set_int )
% 0.29/0.49          & ( B2 = top_top_set_int ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Int_UNIV
% 0.29/0.49  thf(fact_920_UnCI,axiom,
% 0.29/0.49      ! [C: set_Pr958786334691620121nt_int,B2: set_se6260736226359567993nt_int,A2: set_se6260736226359567993nt_int] :
% 0.29/0.49        ( ( ~ ( member2340774599025711042nt_int @ C @ B2 )
% 0.29/0.49         => ( member2340774599025711042nt_int @ C @ A2 ) )
% 0.29/0.49       => ( member2340774599025711042nt_int @ C @ ( sup_su2047564715030645325nt_int @ A2 @ B2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % UnCI
% 0.29/0.49  thf(fact_921_UnCI,axiom,
% 0.29/0.49      ! [C: set_nat,B2: set_set_nat,A2: set_set_nat] :
% 0.29/0.49        ( ( ~ ( member_set_nat @ C @ B2 )
% 0.29/0.49         => ( member_set_nat @ C @ A2 ) )
% 0.29/0.49       => ( member_set_nat @ C @ ( sup_sup_set_set_nat @ A2 @ B2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % UnCI
% 0.29/0.49  thf(fact_922_UnCI,axiom,
% 0.29/0.49      ! [C: int,B2: set_int,A2: set_int] :
% 0.29/0.49        ( ( ~ ( member_int @ C @ B2 )
% 0.29/0.49         => ( member_int @ C @ A2 ) )
% 0.29/0.49       => ( member_int @ C @ ( sup_sup_set_int @ A2 @ B2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % UnCI
% 0.29/0.49  thf(fact_923_UnCI,axiom,
% 0.29/0.49      ! [C: produc3658429121746597890et_nat > $o,B2: set_Pr4532377907799695533_nat_o,A2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.49        ( ( ~ ( member6576561426505652726_nat_o @ C @ B2 )
% 0.29/0.49         => ( member6576561426505652726_nat_o @ C @ A2 ) )
% 0.29/0.49       => ( member6576561426505652726_nat_o @ C @ ( sup_su5209123915105501825_nat_o @ A2 @ B2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % UnCI
% 0.29/0.49  thf(fact_924_UnCI,axiom,
% 0.29/0.49      ! [C: produc4166570645942440679at_nat,B2: set_Pr8551490117392284871at_nat,A2: set_Pr8551490117392284871at_nat] :
% 0.29/0.49        ( ( ~ ( member6689249552917799696at_nat @ C @ B2 )
% 0.29/0.49         => ( member6689249552917799696at_nat @ C @ A2 ) )
% 0.29/0.49       => ( member6689249552917799696at_nat @ C @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % UnCI
% 0.29/0.49  thf(fact_925_UnCI,axiom,
% 0.29/0.49      ! [C: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.29/0.49        ( ( ~ ( member8757157785044589968at_nat @ C @ B2 )
% 0.29/0.49         => ( member8757157785044589968at_nat @ C @ A2 ) )
% 0.29/0.49       => ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % UnCI
% 0.29/0.49  thf(fact_926_UnCI,axiom,
% 0.29/0.49      ! [C: nat,B2: set_nat,A2: set_nat] :
% 0.29/0.49        ( ( ~ ( member_nat @ C @ B2 )
% 0.29/0.49         => ( member_nat @ C @ A2 ) )
% 0.29/0.49       => ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % UnCI
% 0.29/0.49  thf(fact_927_Un__iff,axiom,
% 0.29/0.49      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 0.29/0.49        ( ( member2340774599025711042nt_int @ C @ ( sup_su2047564715030645325nt_int @ A2 @ B2 ) )
% 0.29/0.49        = ( ( member2340774599025711042nt_int @ C @ A2 )
% 0.29/0.49          | ( member2340774599025711042nt_int @ C @ B2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_iff
% 0.29/0.49  thf(fact_928_Un__iff,axiom,
% 0.29/0.49      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.29/0.49        ( ( member_set_nat @ C @ ( sup_sup_set_set_nat @ A2 @ B2 ) )
% 0.29/0.49        = ( ( member_set_nat @ C @ A2 )
% 0.29/0.49          | ( member_set_nat @ C @ B2 ) ) ) ).
% 0.29/0.49  
% 0.29/0.49  % Un_iff
% 0.29/0.49  thf(fact_929_Un__iff,axiom,
% 0.29/0.50      ! [C: int,A2: set_int,B2: set_int] :
% 0.29/0.50        ( ( member_int @ C @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.29/0.50        = ( ( member_int @ C @ A2 )
% 0.29/0.50          | ( member_int @ C @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_iff
% 0.29/0.50  thf(fact_930_Un__iff,axiom,
% 0.29/0.50      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50        ( ( member6576561426505652726_nat_o @ C @ ( sup_su5209123915105501825_nat_o @ A2 @ B2 ) )
% 0.29/0.50        = ( ( member6576561426505652726_nat_o @ C @ A2 )
% 0.29/0.50          | ( member6576561426505652726_nat_o @ C @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_iff
% 0.29/0.50  thf(fact_931_Un__iff,axiom,
% 0.29/0.50      ! [C: produc4166570645942440679at_nat,A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 0.29/0.50        ( ( member6689249552917799696at_nat @ C @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 0.29/0.50        = ( ( member6689249552917799696at_nat @ C @ A2 )
% 0.29/0.50          | ( member6689249552917799696at_nat @ C @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_iff
% 0.29/0.50  thf(fact_932_Un__iff,axiom,
% 0.29/0.50      ! [C: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.29/0.50        ( ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 0.29/0.50        = ( ( member8757157785044589968at_nat @ C @ A2 )
% 0.29/0.50          | ( member8757157785044589968at_nat @ C @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_iff
% 0.29/0.50  thf(fact_933_Un__iff,axiom,
% 0.29/0.50      ! [C: nat,A2: set_nat,B2: set_nat] :
% 0.29/0.50        ( ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.29/0.50        = ( ( member_nat @ C @ A2 )
% 0.29/0.50          | ( member_nat @ C @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_iff
% 0.29/0.50  thf(fact_934_ComplI,axiom,
% 0.29/0.50      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int] :
% 0.29/0.50        ( ~ ( member2340774599025711042nt_int @ C @ A2 )
% 0.29/0.50       => ( member2340774599025711042nt_int @ C @ ( uminus6423885277529793776nt_int @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ComplI
% 0.29/0.50  thf(fact_935_ComplI,axiom,
% 0.29/0.50      ! [C: set_nat,A2: set_set_nat] :
% 0.29/0.50        ( ~ ( member_set_nat @ C @ A2 )
% 0.29/0.50       => ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ComplI
% 0.29/0.50  thf(fact_936_ComplI,axiom,
% 0.29/0.50      ! [C: nat,A2: set_nat] :
% 0.29/0.50        ( ~ ( member_nat @ C @ A2 )
% 0.29/0.50       => ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ComplI
% 0.29/0.50  thf(fact_937_ComplI,axiom,
% 0.29/0.50      ! [C: int,A2: set_int] :
% 0.29/0.50        ( ~ ( member_int @ C @ A2 )
% 0.29/0.50       => ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ComplI
% 0.29/0.50  thf(fact_938_ComplI,axiom,
% 0.29/0.50      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50        ( ~ ( member6576561426505652726_nat_o @ C @ A2 )
% 0.29/0.50       => ( member6576561426505652726_nat_o @ C @ ( uminus5254974436814262692_nat_o @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ComplI
% 0.29/0.50  thf(fact_939_Compl__iff,axiom,
% 0.29/0.50      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int] :
% 0.29/0.50        ( ( member2340774599025711042nt_int @ C @ ( uminus6423885277529793776nt_int @ A2 ) )
% 0.29/0.50        = ( ~ ( member2340774599025711042nt_int @ C @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_iff
% 0.29/0.50  thf(fact_940_Compl__iff,axiom,
% 0.29/0.50      ! [C: set_nat,A2: set_set_nat] :
% 0.29/0.50        ( ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) )
% 0.29/0.50        = ( ~ ( member_set_nat @ C @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_iff
% 0.29/0.50  thf(fact_941_Compl__iff,axiom,
% 0.29/0.50      ! [C: nat,A2: set_nat] :
% 0.29/0.50        ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) )
% 0.29/0.50        = ( ~ ( member_nat @ C @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_iff
% 0.29/0.50  thf(fact_942_Compl__iff,axiom,
% 0.29/0.50      ! [C: int,A2: set_int] :
% 0.29/0.50        ( ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) )
% 0.29/0.50        = ( ~ ( member_int @ C @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_iff
% 0.29/0.50  thf(fact_943_Compl__iff,axiom,
% 0.29/0.50      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50        ( ( member6576561426505652726_nat_o @ C @ ( uminus5254974436814262692_nat_o @ A2 ) )
% 0.29/0.50        = ( ~ ( member6576561426505652726_nat_o @ C @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_iff
% 0.29/0.50  thf(fact_944_Collect__const,axiom,
% 0.29/0.50      ! [P: $o] :
% 0.29/0.50        ( ( P
% 0.29/0.50         => ( ( collec5210948495886036740nt_int
% 0.29/0.50              @ ^ [S2: set_Pr958786334691620121nt_int] : P )
% 0.29/0.50            = top_to6034159466715884489nt_int ) )
% 0.29/0.50        & ( ~ P
% 0.29/0.50         => ( ( collec5210948495886036740nt_int
% 0.29/0.50              @ ^ [S2: set_Pr958786334691620121nt_int] : P )
% 0.29/0.50            = bot_bo1488462491386950373nt_int ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_const
% 0.29/0.50  thf(fact_945_Collect__const,axiom,
% 0.29/0.50      ! [P: $o] :
% 0.29/0.50        ( ( P
% 0.29/0.50         => ( ( collect_set_nat
% 0.29/0.50              @ ^ [S2: set_nat] : P )
% 0.29/0.50            = top_top_set_set_nat ) )
% 0.29/0.50        & ( ~ P
% 0.29/0.50         => ( ( collect_set_nat
% 0.29/0.50              @ ^ [S2: set_nat] : P )
% 0.29/0.50            = bot_bot_set_set_nat ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_const
% 0.29/0.50  thf(fact_946_Collect__const,axiom,
% 0.29/0.50      ! [P: $o] :
% 0.29/0.50        ( ( P
% 0.29/0.50         => ( ( collec939566748876313656_nat_o
% 0.29/0.50              @ ^ [S2: produc3658429121746597890et_nat > $o] : P )
% 0.29/0.50            = top_to4869887016220417533_nat_o ) )
% 0.29/0.50        & ( ~ P
% 0.29/0.50         => ( ( collec939566748876313656_nat_o
% 0.29/0.50              @ ^ [S2: produc3658429121746597890et_nat > $o] : P )
% 0.29/0.50            = bot_bo7824918357723582233_nat_o ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_const
% 0.29/0.50  thf(fact_947_Collect__const,axiom,
% 0.29/0.50      ! [P: $o] :
% 0.29/0.50        ( ( P
% 0.29/0.50         => ( ( collec3392354462482085612at_nat
% 0.29/0.50              @ ^ [S2: product_prod_nat_nat] : P )
% 0.29/0.50            = top_to4669805908274784177at_nat ) )
% 0.29/0.50        & ( ~ P
% 0.29/0.50         => ( ( collec3392354462482085612at_nat
% 0.29/0.50              @ ^ [S2: product_prod_nat_nat] : P )
% 0.29/0.50            = bot_bo2099793752762293965at_nat ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_const
% 0.29/0.50  thf(fact_948_Collect__const,axiom,
% 0.29/0.50      ! [P: $o] :
% 0.29/0.50        ( ( P
% 0.29/0.50         => ( ( collect_list_nat
% 0.29/0.50              @ ^ [S2: list_nat] : P )
% 0.29/0.50            = top_top_set_list_nat ) )
% 0.29/0.50        & ( ~ P
% 0.29/0.50         => ( ( collect_list_nat
% 0.29/0.50              @ ^ [S2: list_nat] : P )
% 0.29/0.50            = bot_bot_set_list_nat ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_const
% 0.29/0.50  thf(fact_949_Collect__const,axiom,
% 0.29/0.50      ! [P: $o] :
% 0.29/0.50        ( ( P
% 0.29/0.50         => ( ( collect_o
% 0.29/0.50              @ ^ [S2: $o] : P )
% 0.29/0.50            = top_top_set_o ) )
% 0.29/0.50        & ( ~ P
% 0.29/0.50         => ( ( collect_o
% 0.29/0.50              @ ^ [S2: $o] : P )
% 0.29/0.50            = bot_bot_set_o ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_const
% 0.29/0.50  thf(fact_950_Collect__const,axiom,
% 0.29/0.50      ! [P: $o] :
% 0.29/0.50        ( ( P
% 0.29/0.50         => ( ( collect_rat
% 0.29/0.50              @ ^ [S2: rat] : P )
% 0.29/0.50            = top_top_set_rat ) )
% 0.29/0.50        & ( ~ P
% 0.29/0.50         => ( ( collect_rat
% 0.29/0.50              @ ^ [S2: rat] : P )
% 0.29/0.50            = bot_bot_set_rat ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_const
% 0.29/0.50  thf(fact_951_Collect__const,axiom,
% 0.29/0.50      ! [P: $o] :
% 0.29/0.50        ( ( P
% 0.29/0.50         => ( ( collect_nat
% 0.29/0.50              @ ^ [S2: nat] : P )
% 0.29/0.50            = top_top_set_nat ) )
% 0.29/0.50        & ( ~ P
% 0.29/0.50         => ( ( collect_nat
% 0.29/0.50              @ ^ [S2: nat] : P )
% 0.29/0.50            = bot_bot_set_nat ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_const
% 0.29/0.50  thf(fact_952_Collect__const,axiom,
% 0.29/0.50      ! [P: $o] :
% 0.29/0.50        ( ( P
% 0.29/0.50         => ( ( collect_int
% 0.29/0.50              @ ^ [S2: int] : P )
% 0.29/0.50            = top_top_set_int ) )
% 0.29/0.50        & ( ~ P
% 0.29/0.50         => ( ( collect_int
% 0.29/0.50              @ ^ [S2: int] : P )
% 0.29/0.50            = bot_bot_set_int ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_const
% 0.29/0.50  thf(fact_953_Compl__disjoint,axiom,
% 0.29/0.50      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( inf_in2572325071724192079at_nat @ A2 @ ( uminus6524753893492686040at_nat @ A2 ) )
% 0.29/0.50        = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_disjoint
% 0.29/0.50  thf(fact_954_Compl__disjoint,axiom,
% 0.29/0.50      ! [A2: set_o] :
% 0.29/0.50        ( ( inf_inf_set_o @ A2 @ ( uminus_uminus_set_o @ A2 ) )
% 0.29/0.50        = bot_bot_set_o ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_disjoint
% 0.29/0.50  thf(fact_955_Compl__disjoint,axiom,
% 0.29/0.50      ! [A2: set_nat] :
% 0.29/0.50        ( ( inf_inf_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ A2 ) )
% 0.29/0.50        = bot_bot_set_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_disjoint
% 0.29/0.50  thf(fact_956_Compl__disjoint,axiom,
% 0.29/0.50      ! [A2: set_int] :
% 0.29/0.50        ( ( inf_inf_set_int @ A2 @ ( uminus1532241313380277803et_int @ A2 ) )
% 0.29/0.50        = bot_bot_set_int ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_disjoint
% 0.29/0.50  thf(fact_957_ComplD,axiom,
% 0.29/0.50      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int] :
% 0.29/0.50        ( ( member2340774599025711042nt_int @ C @ ( uminus6423885277529793776nt_int @ A2 ) )
% 0.29/0.50       => ~ ( member2340774599025711042nt_int @ C @ A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ComplD
% 0.29/0.50  thf(fact_958_ComplD,axiom,
% 0.29/0.50      ! [C: set_nat,A2: set_set_nat] :
% 0.29/0.50        ( ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) )
% 0.29/0.50       => ~ ( member_set_nat @ C @ A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ComplD
% 0.29/0.50  thf(fact_959_ComplD,axiom,
% 0.29/0.50      ! [C: nat,A2: set_nat] :
% 0.29/0.50        ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) )
% 0.29/0.50       => ~ ( member_nat @ C @ A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ComplD
% 0.29/0.50  thf(fact_960_ComplD,axiom,
% 0.29/0.50      ! [C: int,A2: set_int] :
% 0.29/0.50        ( ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) )
% 0.29/0.50       => ~ ( member_int @ C @ A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ComplD
% 0.29/0.50  thf(fact_961_ComplD,axiom,
% 0.29/0.50      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50        ( ( member6576561426505652726_nat_o @ C @ ( uminus5254974436814262692_nat_o @ A2 ) )
% 0.29/0.50       => ~ ( member6576561426505652726_nat_o @ C @ A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ComplD
% 0.29/0.50  thf(fact_962_Compl__eq,axiom,
% 0.29/0.50      ( uminus6423885277529793776nt_int
% 0.29/0.50      = ( ^ [A4: set_se6260736226359567993nt_int] :
% 0.29/0.50            ( collec5210948495886036740nt_int
% 0.29/0.50            @ ^ [X3: set_Pr958786334691620121nt_int] :
% 0.29/0.50                ~ ( member2340774599025711042nt_int @ X3 @ A4 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_eq
% 0.29/0.50  thf(fact_963_Compl__eq,axiom,
% 0.29/0.50      ( uminus613421341184616069et_nat
% 0.29/0.50      = ( ^ [A4: set_set_nat] :
% 0.29/0.50            ( collect_set_nat
% 0.29/0.50            @ ^ [X3: set_nat] :
% 0.29/0.50                ~ ( member_set_nat @ X3 @ A4 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_eq
% 0.29/0.50  thf(fact_964_Compl__eq,axiom,
% 0.29/0.50      ( uminus5710092332889474511et_nat
% 0.29/0.50      = ( ^ [A4: set_nat] :
% 0.29/0.50            ( collect_nat
% 0.29/0.50            @ ^ [X3: nat] :
% 0.29/0.50                ~ ( member_nat @ X3 @ A4 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_eq
% 0.29/0.50  thf(fact_965_Compl__eq,axiom,
% 0.29/0.50      ( uminus1532241313380277803et_int
% 0.29/0.50      = ( ^ [A4: set_int] :
% 0.29/0.50            ( collect_int
% 0.29/0.50            @ ^ [X3: int] :
% 0.29/0.50                ~ ( member_int @ X3 @ A4 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_eq
% 0.29/0.50  thf(fact_966_Compl__eq,axiom,
% 0.29/0.50      ( uminus5254974436814262692_nat_o
% 0.29/0.50      = ( ^ [A4: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50            ( collec939566748876313656_nat_o
% 0.29/0.50            @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.29/0.50                ~ ( member6576561426505652726_nat_o @ X3 @ A4 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_eq
% 0.29/0.50  thf(fact_967_Collect__neg__eq,axiom,
% 0.29/0.50      ! [P: set_Pr958786334691620121nt_int > $o] :
% 0.29/0.50        ( ( collec5210948495886036740nt_int
% 0.29/0.50          @ ^ [X3: set_Pr958786334691620121nt_int] :
% 0.29/0.50              ~ ( P @ X3 ) )
% 0.29/0.50        = ( uminus6423885277529793776nt_int @ ( collec5210948495886036740nt_int @ P ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_neg_eq
% 0.29/0.50  thf(fact_968_Collect__neg__eq,axiom,
% 0.29/0.50      ! [P: set_nat > $o] :
% 0.29/0.50        ( ( collect_set_nat
% 0.29/0.50          @ ^ [X3: set_nat] :
% 0.29/0.50              ~ ( P @ X3 ) )
% 0.29/0.50        = ( uminus613421341184616069et_nat @ ( collect_set_nat @ P ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_neg_eq
% 0.29/0.50  thf(fact_969_Collect__neg__eq,axiom,
% 0.29/0.50      ! [P: nat > $o] :
% 0.29/0.50        ( ( collect_nat
% 0.29/0.50          @ ^ [X3: nat] :
% 0.29/0.50              ~ ( P @ X3 ) )
% 0.29/0.50        = ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_neg_eq
% 0.29/0.50  thf(fact_970_Collect__neg__eq,axiom,
% 0.29/0.50      ! [P: int > $o] :
% 0.29/0.50        ( ( collect_int
% 0.29/0.50          @ ^ [X3: int] :
% 0.29/0.50              ~ ( P @ X3 ) )
% 0.29/0.50        = ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_neg_eq
% 0.29/0.50  thf(fact_971_Collect__neg__eq,axiom,
% 0.29/0.50      ! [P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.29/0.50        ( ( collec939566748876313656_nat_o
% 0.29/0.50          @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.29/0.50              ~ ( P @ X3 ) )
% 0.29/0.50        = ( uminus5254974436814262692_nat_o @ ( collec939566748876313656_nat_o @ P ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_neg_eq
% 0.29/0.50  thf(fact_972_uminus__set__def,axiom,
% 0.29/0.50      ( uminus6423885277529793776nt_int
% 0.29/0.50      = ( ^ [A4: set_se6260736226359567993nt_int] :
% 0.29/0.50            ( collec5210948495886036740nt_int
% 0.29/0.50            @ ( uminus8147837162492574189_int_o
% 0.29/0.50              @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ A4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % uminus_set_def
% 0.29/0.50  thf(fact_973_uminus__set__def,axiom,
% 0.29/0.50      ( uminus613421341184616069et_nat
% 0.29/0.50      = ( ^ [A4: set_set_nat] :
% 0.29/0.50            ( collect_set_nat
% 0.29/0.50            @ ( uminus6401447641752708672_nat_o
% 0.29/0.50              @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % uminus_set_def
% 0.29/0.50  thf(fact_974_uminus__set__def,axiom,
% 0.29/0.50      ( uminus5710092332889474511et_nat
% 0.29/0.50      = ( ^ [A4: set_nat] :
% 0.29/0.50            ( collect_nat
% 0.29/0.50            @ ( uminus_uminus_nat_o
% 0.29/0.50              @ ^ [X3: nat] : ( member_nat @ X3 @ A4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % uminus_set_def
% 0.29/0.50  thf(fact_975_uminus__set__def,axiom,
% 0.29/0.50      ( uminus1532241313380277803et_int
% 0.29/0.50      = ( ^ [A4: set_int] :
% 0.29/0.50            ( collect_int
% 0.29/0.50            @ ( uminus_uminus_int_o
% 0.29/0.50              @ ^ [X3: int] : ( member_int @ X3 @ A4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % uminus_set_def
% 0.29/0.50  thf(fact_976_uminus__set__def,axiom,
% 0.29/0.50      ( uminus5254974436814262692_nat_o
% 0.29/0.50      = ( ^ [A4: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50            ( collec939566748876313656_nat_o
% 0.29/0.50            @ ( uminus8928876914783121465at_o_o
% 0.29/0.50              @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ A4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % uminus_set_def
% 0.29/0.50  thf(fact_977_emptyE,axiom,
% 0.29/0.50      ! [A: set_Pr958786334691620121nt_int] :
% 0.29/0.50        ~ ( member2340774599025711042nt_int @ A @ bot_bo1488462491386950373nt_int ) ).
% 0.29/0.50  
% 0.29/0.50  % emptyE
% 0.29/0.50  thf(fact_978_emptyE,axiom,
% 0.29/0.50      ! [A: set_nat] :
% 0.29/0.50        ~ ( member_set_nat @ A @ bot_bot_set_set_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % emptyE
% 0.29/0.50  thf(fact_979_emptyE,axiom,
% 0.29/0.50      ! [A: produc3658429121746597890et_nat > $o] :
% 0.29/0.50        ~ ( member6576561426505652726_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ).
% 0.29/0.50  
% 0.29/0.50  % emptyE
% 0.29/0.50  thf(fact_980_emptyE,axiom,
% 0.29/0.50      ! [A: product_prod_nat_nat] :
% 0.29/0.50        ~ ( member8440522571783428010at_nat @ A @ bot_bo2099793752762293965at_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % emptyE
% 0.29/0.50  thf(fact_981_emptyE,axiom,
% 0.29/0.50      ! [A: $o] :
% 0.29/0.50        ~ ( member_o @ A @ bot_bot_set_o ) ).
% 0.29/0.50  
% 0.29/0.50  % emptyE
% 0.29/0.50  thf(fact_982_emptyE,axiom,
% 0.29/0.50      ! [A: nat] :
% 0.29/0.50        ~ ( member_nat @ A @ bot_bot_set_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % emptyE
% 0.29/0.50  thf(fact_983_emptyE,axiom,
% 0.29/0.50      ! [A: int] :
% 0.29/0.50        ~ ( member_int @ A @ bot_bot_set_int ) ).
% 0.29/0.50  
% 0.29/0.50  % emptyE
% 0.29/0.50  thf(fact_984_equals0D,axiom,
% 0.29/0.50      ! [A2: set_se6260736226359567993nt_int,A: set_Pr958786334691620121nt_int] :
% 0.29/0.50        ( ( A2 = bot_bo1488462491386950373nt_int )
% 0.29/0.50       => ~ ( member2340774599025711042nt_int @ A @ A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % equals0D
% 0.29/0.50  thf(fact_985_equals0D,axiom,
% 0.29/0.50      ! [A2: set_set_nat,A: set_nat] :
% 0.29/0.50        ( ( A2 = bot_bot_set_set_nat )
% 0.29/0.50       => ~ ( member_set_nat @ A @ A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % equals0D
% 0.29/0.50  thf(fact_986_equals0D,axiom,
% 0.29/0.50      ! [A2: set_Pr4532377907799695533_nat_o,A: produc3658429121746597890et_nat > $o] :
% 0.29/0.50        ( ( A2 = bot_bo7824918357723582233_nat_o )
% 0.29/0.50       => ~ ( member6576561426505652726_nat_o @ A @ A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % equals0D
% 0.29/0.50  thf(fact_987_equals0D,axiom,
% 0.29/0.50      ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
% 0.29/0.50        ( ( A2 = bot_bo2099793752762293965at_nat )
% 0.29/0.50       => ~ ( member8440522571783428010at_nat @ A @ A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % equals0D
% 0.29/0.50  thf(fact_988_equals0D,axiom,
% 0.29/0.50      ! [A2: set_o,A: $o] :
% 0.29/0.50        ( ( A2 = bot_bot_set_o )
% 0.29/0.50       => ~ ( member_o @ A @ A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % equals0D
% 0.29/0.50  thf(fact_989_equals0D,axiom,
% 0.29/0.50      ! [A2: set_nat,A: nat] :
% 0.29/0.50        ( ( A2 = bot_bot_set_nat )
% 0.29/0.50       => ~ ( member_nat @ A @ A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % equals0D
% 0.29/0.50  thf(fact_990_equals0D,axiom,
% 0.29/0.50      ! [A2: set_int,A: int] :
% 0.29/0.50        ( ( A2 = bot_bot_set_int )
% 0.29/0.50       => ~ ( member_int @ A @ A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % equals0D
% 0.29/0.50  thf(fact_991_equals0I,axiom,
% 0.29/0.50      ! [A2: set_se6260736226359567993nt_int] :
% 0.29/0.50        ( ! [Y2: set_Pr958786334691620121nt_int] :
% 0.29/0.50            ~ ( member2340774599025711042nt_int @ Y2 @ A2 )
% 0.29/0.50       => ( A2 = bot_bo1488462491386950373nt_int ) ) ).
% 0.29/0.50  
% 0.29/0.50  % equals0I
% 0.29/0.50  thf(fact_992_equals0I,axiom,
% 0.29/0.50      ! [A2: set_set_nat] :
% 0.29/0.50        ( ! [Y2: set_nat] :
% 0.29/0.50            ~ ( member_set_nat @ Y2 @ A2 )
% 0.29/0.50       => ( A2 = bot_bot_set_set_nat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % equals0I
% 0.29/0.50  thf(fact_993_equals0I,axiom,
% 0.29/0.50      ! [A2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50        ( ! [Y2: produc3658429121746597890et_nat > $o] :
% 0.29/0.50            ~ ( member6576561426505652726_nat_o @ Y2 @ A2 )
% 0.29/0.50       => ( A2 = bot_bo7824918357723582233_nat_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % equals0I
% 0.29/0.50  thf(fact_994_equals0I,axiom,
% 0.29/0.50      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ! [Y2: product_prod_nat_nat] :
% 0.29/0.50            ~ ( member8440522571783428010at_nat @ Y2 @ A2 )
% 0.29/0.50       => ( A2 = bot_bo2099793752762293965at_nat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % equals0I
% 0.29/0.50  thf(fact_995_equals0I,axiom,
% 0.29/0.50      ! [A2: set_o] :
% 0.29/0.50        ( ! [Y2: $o] :
% 0.29/0.50            ~ ( member_o @ Y2 @ A2 )
% 0.29/0.50       => ( A2 = bot_bot_set_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % equals0I
% 0.29/0.50  thf(fact_996_equals0I,axiom,
% 0.29/0.50      ! [A2: set_nat] :
% 0.29/0.50        ( ! [Y2: nat] :
% 0.29/0.50            ~ ( member_nat @ Y2 @ A2 )
% 0.29/0.50       => ( A2 = bot_bot_set_nat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % equals0I
% 0.29/0.50  thf(fact_997_equals0I,axiom,
% 0.29/0.50      ! [A2: set_int] :
% 0.29/0.50        ( ! [Y2: int] :
% 0.29/0.50            ~ ( member_int @ Y2 @ A2 )
% 0.29/0.50       => ( A2 = bot_bot_set_int ) ) ).
% 0.29/0.50  
% 0.29/0.50  % equals0I
% 0.29/0.50  thf(fact_998_ex__in__conv,axiom,
% 0.29/0.50      ! [A2: set_se6260736226359567993nt_int] :
% 0.29/0.50        ( ( ? [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ A2 ) )
% 0.29/0.50        = ( A2 != bot_bo1488462491386950373nt_int ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ex_in_conv
% 0.29/0.50  thf(fact_999_ex__in__conv,axiom,
% 0.29/0.50      ! [A2: set_set_nat] :
% 0.29/0.50        ( ( ? [X3: set_nat] : ( member_set_nat @ X3 @ A2 ) )
% 0.29/0.50        = ( A2 != bot_bot_set_set_nat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ex_in_conv
% 0.29/0.50  thf(fact_1000_ex__in__conv,axiom,
% 0.29/0.50      ! [A2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50        ( ( ? [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ A2 ) )
% 0.29/0.50        = ( A2 != bot_bo7824918357723582233_nat_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ex_in_conv
% 0.29/0.50  thf(fact_1001_ex__in__conv,axiom,
% 0.29/0.50      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( ? [X3: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X3 @ A2 ) )
% 0.29/0.50        = ( A2 != bot_bo2099793752762293965at_nat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ex_in_conv
% 0.29/0.50  thf(fact_1002_ex__in__conv,axiom,
% 0.29/0.50      ! [A2: set_o] :
% 0.29/0.50        ( ( ? [X3: $o] : ( member_o @ X3 @ A2 ) )
% 0.29/0.50        = ( A2 != bot_bot_set_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ex_in_conv
% 0.29/0.50  thf(fact_1003_ex__in__conv,axiom,
% 0.29/0.50      ! [A2: set_nat] :
% 0.29/0.50        ( ( ? [X3: nat] : ( member_nat @ X3 @ A2 ) )
% 0.29/0.50        = ( A2 != bot_bot_set_nat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ex_in_conv
% 0.29/0.50  thf(fact_1004_ex__in__conv,axiom,
% 0.29/0.50      ! [A2: set_int] :
% 0.29/0.50        ( ( ? [X3: int] : ( member_int @ X3 @ A2 ) )
% 0.29/0.50        = ( A2 != bot_bot_set_int ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ex_in_conv
% 0.29/0.50  thf(fact_1005_bot__set__def,axiom,
% 0.29/0.50      ( bot_bo1488462491386950373nt_int
% 0.29/0.50      = ( collec5210948495886036740nt_int @ bot_bo2686080419298087992_int_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % bot_set_def
% 0.29/0.50  thf(fact_1006_bot__set__def,axiom,
% 0.29/0.50      ( bot_bot_set_set_nat
% 0.29/0.50      = ( collect_set_nat @ bot_bot_set_nat_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % bot_set_def
% 0.29/0.50  thf(fact_1007_bot__set__def,axiom,
% 0.29/0.50      ( bot_bo7824918357723582233_nat_o
% 0.29/0.50      = ( collec939566748876313656_nat_o @ bot_bo7963750851167320836at_o_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % bot_set_def
% 0.29/0.50  thf(fact_1008_bot__set__def,axiom,
% 0.29/0.50      ( bot_bo2099793752762293965at_nat
% 0.29/0.50      = ( collec3392354462482085612at_nat @ bot_bo482883023278783056_nat_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % bot_set_def
% 0.29/0.50  thf(fact_1009_bot__set__def,axiom,
% 0.29/0.50      ( bot_bot_set_o
% 0.29/0.50      = ( collect_o @ bot_bot_o_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % bot_set_def
% 0.29/0.50  thf(fact_1010_bot__set__def,axiom,
% 0.29/0.50      ( bot_bot_set_nat
% 0.29/0.50      = ( collect_nat @ bot_bot_nat_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % bot_set_def
% 0.29/0.50  thf(fact_1011_bot__set__def,axiom,
% 0.29/0.50      ( bot_bot_set_int
% 0.29/0.50      = ( collect_int @ bot_bot_int_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % bot_set_def
% 0.29/0.50  thf(fact_1012_Compl__UNIV__eq,axiom,
% 0.29/0.50      ( ( uminus6524753893492686040at_nat @ top_to4669805908274784177at_nat )
% 0.29/0.50      = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_UNIV_eq
% 0.29/0.50  thf(fact_1013_Compl__UNIV__eq,axiom,
% 0.29/0.50      ( ( uminus3195874150345416415st_nat @ top_top_set_list_nat )
% 0.29/0.50      = bot_bot_set_list_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_UNIV_eq
% 0.29/0.50  thf(fact_1014_Compl__UNIV__eq,axiom,
% 0.29/0.50      ( ( uminus_uminus_set_o @ top_top_set_o )
% 0.29/0.50      = bot_bot_set_o ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_UNIV_eq
% 0.29/0.50  thf(fact_1015_Compl__UNIV__eq,axiom,
% 0.29/0.50      ( ( uminus2201863774496077783et_rat @ top_top_set_rat )
% 0.29/0.50      = bot_bot_set_rat ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_UNIV_eq
% 0.29/0.50  thf(fact_1016_Compl__UNIV__eq,axiom,
% 0.29/0.50      ( ( uminus5710092332889474511et_nat @ top_top_set_nat )
% 0.29/0.50      = bot_bot_set_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_UNIV_eq
% 0.29/0.50  thf(fact_1017_Compl__UNIV__eq,axiom,
% 0.29/0.50      ( ( uminus1532241313380277803et_int @ top_top_set_int )
% 0.29/0.50      = bot_bot_set_int ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_UNIV_eq
% 0.29/0.50  thf(fact_1018_Compl__empty__eq,axiom,
% 0.29/0.50      ( ( uminus6524753893492686040at_nat @ bot_bo2099793752762293965at_nat )
% 0.29/0.50      = top_to4669805908274784177at_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_empty_eq
% 0.29/0.50  thf(fact_1019_Compl__empty__eq,axiom,
% 0.29/0.50      ( ( uminus3195874150345416415st_nat @ bot_bot_set_list_nat )
% 0.29/0.50      = top_top_set_list_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_empty_eq
% 0.29/0.50  thf(fact_1020_Compl__empty__eq,axiom,
% 0.29/0.50      ( ( uminus_uminus_set_o @ bot_bot_set_o )
% 0.29/0.50      = top_top_set_o ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_empty_eq
% 0.29/0.50  thf(fact_1021_Compl__empty__eq,axiom,
% 0.29/0.50      ( ( uminus2201863774496077783et_rat @ bot_bot_set_rat )
% 0.29/0.50      = top_top_set_rat ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_empty_eq
% 0.29/0.50  thf(fact_1022_Compl__empty__eq,axiom,
% 0.29/0.50      ( ( uminus5710092332889474511et_nat @ bot_bot_set_nat )
% 0.29/0.50      = top_top_set_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_empty_eq
% 0.29/0.50  thf(fact_1023_Compl__empty__eq,axiom,
% 0.29/0.50      ( ( uminus1532241313380277803et_int @ bot_bot_set_int )
% 0.29/0.50      = top_top_set_int ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_empty_eq
% 0.29/0.50  thf(fact_1024_empty__not__UNIV,axiom,
% 0.29/0.50      bot_bo2099793752762293965at_nat != top_to4669805908274784177at_nat ).
% 0.29/0.50  
% 0.29/0.50  % empty_not_UNIV
% 0.29/0.50  thf(fact_1025_empty__not__UNIV,axiom,
% 0.29/0.50      bot_bot_set_list_nat != top_top_set_list_nat ).
% 0.29/0.50  
% 0.29/0.50  % empty_not_UNIV
% 0.29/0.50  thf(fact_1026_empty__not__UNIV,axiom,
% 0.29/0.50      bot_bot_set_o != top_top_set_o ).
% 0.29/0.50  
% 0.29/0.50  % empty_not_UNIV
% 0.29/0.50  thf(fact_1027_empty__not__UNIV,axiom,
% 0.29/0.50      bot_bot_set_rat != top_top_set_rat ).
% 0.29/0.50  
% 0.29/0.50  % empty_not_UNIV
% 0.29/0.50  thf(fact_1028_empty__not__UNIV,axiom,
% 0.29/0.50      bot_bot_set_nat != top_top_set_nat ).
% 0.29/0.50  
% 0.29/0.50  % empty_not_UNIV
% 0.29/0.50  thf(fact_1029_empty__not__UNIV,axiom,
% 0.29/0.50      bot_bot_set_int != top_top_set_int ).
% 0.29/0.50  
% 0.29/0.50  % empty_not_UNIV
% 0.29/0.50  thf(fact_1030_IntE,axiom,
% 0.29/0.50      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 0.29/0.50        ( ( member2340774599025711042nt_int @ C @ ( inf_in8396524679539076455nt_int @ A2 @ B2 ) )
% 0.29/0.50       => ~ ( ( member2340774599025711042nt_int @ C @ A2 )
% 0.29/0.50           => ~ ( member2340774599025711042nt_int @ C @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % IntE
% 0.29/0.50  thf(fact_1031_IntE,axiom,
% 0.29/0.50      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.29/0.50        ( ( member_set_nat @ C @ ( inf_inf_set_set_nat @ A2 @ B2 ) )
% 0.29/0.50       => ~ ( ( member_set_nat @ C @ A2 )
% 0.29/0.50           => ~ ( member_set_nat @ C @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % IntE
% 0.29/0.50  thf(fact_1032_IntE,axiom,
% 0.29/0.50      ! [C: int,A2: set_int,B2: set_int] :
% 0.29/0.50        ( ( member_int @ C @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.29/0.50       => ~ ( ( member_int @ C @ A2 )
% 0.29/0.50           => ~ ( member_int @ C @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % IntE
% 0.29/0.50  thf(fact_1033_IntE,axiom,
% 0.29/0.50      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50        ( ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) )
% 0.29/0.50       => ~ ( ( member6576561426505652726_nat_o @ C @ A2 )
% 0.29/0.50           => ~ ( member6576561426505652726_nat_o @ C @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % IntE
% 0.29/0.50  thf(fact_1034_IntE,axiom,
% 0.29/0.50      ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 0.29/0.50       => ~ ( ( member8440522571783428010at_nat @ C @ A2 )
% 0.29/0.50           => ~ ( member8440522571783428010at_nat @ C @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % IntE
% 0.29/0.50  thf(fact_1035_IntE,axiom,
% 0.29/0.50      ! [C: nat,A2: set_nat,B2: set_nat] :
% 0.29/0.50        ( ( member_nat @ C @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.29/0.50       => ~ ( ( member_nat @ C @ A2 )
% 0.29/0.50           => ~ ( member_nat @ C @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % IntE
% 0.29/0.50  thf(fact_1036_IntD1,axiom,
% 0.29/0.50      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 0.29/0.50        ( ( member2340774599025711042nt_int @ C @ ( inf_in8396524679539076455nt_int @ A2 @ B2 ) )
% 0.29/0.50       => ( member2340774599025711042nt_int @ C @ A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % IntD1
% 0.29/0.50  thf(fact_1037_IntD1,axiom,
% 0.29/0.50      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.29/0.50        ( ( member_set_nat @ C @ ( inf_inf_set_set_nat @ A2 @ B2 ) )
% 0.29/0.50       => ( member_set_nat @ C @ A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % IntD1
% 0.29/0.50  thf(fact_1038_IntD1,axiom,
% 0.29/0.50      ! [C: int,A2: set_int,B2: set_int] :
% 0.29/0.50        ( ( member_int @ C @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.29/0.50       => ( member_int @ C @ A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % IntD1
% 0.29/0.50  thf(fact_1039_IntD1,axiom,
% 0.29/0.50      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50        ( ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) )
% 0.29/0.50       => ( member6576561426505652726_nat_o @ C @ A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % IntD1
% 0.29/0.50  thf(fact_1040_IntD1,axiom,
% 0.29/0.50      ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 0.29/0.50       => ( member8440522571783428010at_nat @ C @ A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % IntD1
% 0.29/0.50  thf(fact_1041_IntD1,axiom,
% 0.29/0.50      ! [C: nat,A2: set_nat,B2: set_nat] :
% 0.29/0.50        ( ( member_nat @ C @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.29/0.50       => ( member_nat @ C @ A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % IntD1
% 0.29/0.50  thf(fact_1042_IntD2,axiom,
% 0.29/0.50      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 0.29/0.50        ( ( member2340774599025711042nt_int @ C @ ( inf_in8396524679539076455nt_int @ A2 @ B2 ) )
% 0.29/0.50       => ( member2340774599025711042nt_int @ C @ B2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % IntD2
% 0.29/0.50  thf(fact_1043_IntD2,axiom,
% 0.29/0.50      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.29/0.50        ( ( member_set_nat @ C @ ( inf_inf_set_set_nat @ A2 @ B2 ) )
% 0.29/0.50       => ( member_set_nat @ C @ B2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % IntD2
% 0.29/0.50  thf(fact_1044_IntD2,axiom,
% 0.29/0.50      ! [C: int,A2: set_int,B2: set_int] :
% 0.29/0.50        ( ( member_int @ C @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.29/0.50       => ( member_int @ C @ B2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % IntD2
% 0.29/0.50  thf(fact_1045_IntD2,axiom,
% 0.29/0.50      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50        ( ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) )
% 0.29/0.50       => ( member6576561426505652726_nat_o @ C @ B2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % IntD2
% 0.29/0.50  thf(fact_1046_IntD2,axiom,
% 0.29/0.50      ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 0.29/0.50       => ( member8440522571783428010at_nat @ C @ B2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % IntD2
% 0.29/0.50  thf(fact_1047_IntD2,axiom,
% 0.29/0.50      ! [C: nat,A2: set_nat,B2: set_nat] :
% 0.29/0.50        ( ( member_nat @ C @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.29/0.50       => ( member_nat @ C @ B2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % IntD2
% 0.29/0.50  thf(fact_1048_Int__assoc,axiom,
% 0.29/0.50      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ C2 )
% 0.29/0.50        = ( inf_in2572325071724192079at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_assoc
% 0.29/0.50  thf(fact_1049_Int__assoc,axiom,
% 0.29/0.50      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 0.29/0.50        ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ C2 )
% 0.29/0.50        = ( inf_inf_set_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_assoc
% 0.29/0.50  thf(fact_1050_Int__absorb,axiom,
% 0.29/0.50      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( inf_in2572325071724192079at_nat @ A2 @ A2 )
% 0.29/0.50        = A2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_absorb
% 0.29/0.50  thf(fact_1051_Int__absorb,axiom,
% 0.29/0.50      ! [A2: set_nat] :
% 0.29/0.50        ( ( inf_inf_set_nat @ A2 @ A2 )
% 0.29/0.50        = A2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_absorb
% 0.29/0.50  thf(fact_1052_Int__commute,axiom,
% 0.29/0.50      ( inf_in2572325071724192079at_nat
% 0.29/0.50      = ( ^ [A4: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ B4 @ A4 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_commute
% 0.29/0.50  thf(fact_1053_Int__commute,axiom,
% 0.29/0.50      ( inf_inf_set_nat
% 0.29/0.50      = ( ^ [A4: set_nat,B4: set_nat] : ( inf_inf_set_nat @ B4 @ A4 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_commute
% 0.29/0.50  thf(fact_1054_Int__UNIV__left,axiom,
% 0.29/0.50      ! [B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( inf_in2572325071724192079at_nat @ top_to4669805908274784177at_nat @ B2 )
% 0.29/0.50        = B2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_UNIV_left
% 0.29/0.50  thf(fact_1055_Int__UNIV__left,axiom,
% 0.29/0.50      ! [B2: set_list_nat] :
% 0.29/0.50        ( ( inf_inf_set_list_nat @ top_top_set_list_nat @ B2 )
% 0.29/0.50        = B2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_UNIV_left
% 0.29/0.50  thf(fact_1056_Int__UNIV__left,axiom,
% 0.29/0.50      ! [B2: set_o] :
% 0.29/0.50        ( ( inf_inf_set_o @ top_top_set_o @ B2 )
% 0.29/0.50        = B2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_UNIV_left
% 0.29/0.50  thf(fact_1057_Int__UNIV__left,axiom,
% 0.29/0.50      ! [B2: set_rat] :
% 0.29/0.50        ( ( inf_inf_set_rat @ top_top_set_rat @ B2 )
% 0.29/0.50        = B2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_UNIV_left
% 0.29/0.50  thf(fact_1058_Int__UNIV__left,axiom,
% 0.29/0.50      ! [B2: set_nat] :
% 0.29/0.50        ( ( inf_inf_set_nat @ top_top_set_nat @ B2 )
% 0.29/0.50        = B2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_UNIV_left
% 0.29/0.50  thf(fact_1059_Int__UNIV__left,axiom,
% 0.29/0.50      ! [B2: set_int] :
% 0.29/0.50        ( ( inf_inf_set_int @ top_top_set_int @ B2 )
% 0.29/0.50        = B2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_UNIV_left
% 0.29/0.50  thf(fact_1060_Int__UNIV__right,axiom,
% 0.29/0.50      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( inf_in2572325071724192079at_nat @ A2 @ top_to4669805908274784177at_nat )
% 0.29/0.50        = A2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_UNIV_right
% 0.29/0.50  thf(fact_1061_Int__UNIV__right,axiom,
% 0.29/0.50      ! [A2: set_list_nat] :
% 0.29/0.50        ( ( inf_inf_set_list_nat @ A2 @ top_top_set_list_nat )
% 0.29/0.50        = A2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_UNIV_right
% 0.29/0.50  thf(fact_1062_Int__UNIV__right,axiom,
% 0.29/0.50      ! [A2: set_o] :
% 0.29/0.50        ( ( inf_inf_set_o @ A2 @ top_top_set_o )
% 0.29/0.50        = A2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_UNIV_right
% 0.29/0.50  thf(fact_1063_Int__UNIV__right,axiom,
% 0.29/0.50      ! [A2: set_rat] :
% 0.29/0.50        ( ( inf_inf_set_rat @ A2 @ top_top_set_rat )
% 0.29/0.50        = A2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_UNIV_right
% 0.29/0.50  thf(fact_1064_Int__UNIV__right,axiom,
% 0.29/0.50      ! [A2: set_nat] :
% 0.29/0.50        ( ( inf_inf_set_nat @ A2 @ top_top_set_nat )
% 0.29/0.50        = A2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_UNIV_right
% 0.29/0.50  thf(fact_1065_Int__UNIV__right,axiom,
% 0.29/0.50      ! [A2: set_int] :
% 0.29/0.50        ( ( inf_inf_set_int @ A2 @ top_top_set_int )
% 0.29/0.50        = A2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_UNIV_right
% 0.29/0.50  thf(fact_1066_Int__left__absorb,axiom,
% 0.29/0.50      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( inf_in2572325071724192079at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 0.29/0.50        = ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_left_absorb
% 0.29/0.50  thf(fact_1067_Int__left__absorb,axiom,
% 0.29/0.50      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.50        ( ( inf_inf_set_nat @ A2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.29/0.50        = ( inf_inf_set_nat @ A2 @ B2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_left_absorb
% 0.29/0.50  thf(fact_1068_Int__left__commute,axiom,
% 0.29/0.50      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( inf_in2572325071724192079at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) )
% 0.29/0.50        = ( inf_in2572325071724192079at_nat @ B2 @ ( inf_in2572325071724192079at_nat @ A2 @ C2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_left_commute
% 0.29/0.50  thf(fact_1069_Int__left__commute,axiom,
% 0.29/0.50      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 0.29/0.50        ( ( inf_inf_set_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C2 ) )
% 0.29/0.50        = ( inf_inf_set_nat @ B2 @ ( inf_inf_set_nat @ A2 @ C2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_left_commute
% 0.29/0.50  thf(fact_1070_UnE,axiom,
% 0.29/0.50      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 0.29/0.50        ( ( member2340774599025711042nt_int @ C @ ( sup_su2047564715030645325nt_int @ A2 @ B2 ) )
% 0.29/0.50       => ( ~ ( member2340774599025711042nt_int @ C @ A2 )
% 0.29/0.50         => ( member2340774599025711042nt_int @ C @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UnE
% 0.29/0.50  thf(fact_1071_UnE,axiom,
% 0.29/0.50      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.29/0.50        ( ( member_set_nat @ C @ ( sup_sup_set_set_nat @ A2 @ B2 ) )
% 0.29/0.50       => ( ~ ( member_set_nat @ C @ A2 )
% 0.29/0.50         => ( member_set_nat @ C @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UnE
% 0.29/0.50  thf(fact_1072_UnE,axiom,
% 0.29/0.50      ! [C: int,A2: set_int,B2: set_int] :
% 0.29/0.50        ( ( member_int @ C @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.29/0.50       => ( ~ ( member_int @ C @ A2 )
% 0.29/0.50         => ( member_int @ C @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UnE
% 0.29/0.50  thf(fact_1073_UnE,axiom,
% 0.29/0.50      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50        ( ( member6576561426505652726_nat_o @ C @ ( sup_su5209123915105501825_nat_o @ A2 @ B2 ) )
% 0.29/0.50       => ( ~ ( member6576561426505652726_nat_o @ C @ A2 )
% 0.29/0.50         => ( member6576561426505652726_nat_o @ C @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UnE
% 0.29/0.50  thf(fact_1074_UnE,axiom,
% 0.29/0.50      ! [C: produc4166570645942440679at_nat,A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 0.29/0.50        ( ( member6689249552917799696at_nat @ C @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 0.29/0.50       => ( ~ ( member6689249552917799696at_nat @ C @ A2 )
% 0.29/0.50         => ( member6689249552917799696at_nat @ C @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UnE
% 0.29/0.50  thf(fact_1075_UnE,axiom,
% 0.29/0.50      ! [C: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.29/0.50        ( ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 0.29/0.50       => ( ~ ( member8757157785044589968at_nat @ C @ A2 )
% 0.29/0.50         => ( member8757157785044589968at_nat @ C @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UnE
% 0.29/0.50  thf(fact_1076_UnE,axiom,
% 0.29/0.50      ! [C: nat,A2: set_nat,B2: set_nat] :
% 0.29/0.50        ( ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.29/0.50       => ( ~ ( member_nat @ C @ A2 )
% 0.29/0.50         => ( member_nat @ C @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UnE
% 0.29/0.50  thf(fact_1077_UnI1,axiom,
% 0.29/0.50      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 0.29/0.50        ( ( member2340774599025711042nt_int @ C @ A2 )
% 0.29/0.50       => ( member2340774599025711042nt_int @ C @ ( sup_su2047564715030645325nt_int @ A2 @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UnI1
% 0.29/0.50  thf(fact_1078_UnI1,axiom,
% 0.29/0.50      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.29/0.50        ( ( member_set_nat @ C @ A2 )
% 0.29/0.50       => ( member_set_nat @ C @ ( sup_sup_set_set_nat @ A2 @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UnI1
% 0.29/0.50  thf(fact_1079_UnI1,axiom,
% 0.29/0.50      ! [C: int,A2: set_int,B2: set_int] :
% 0.29/0.50        ( ( member_int @ C @ A2 )
% 0.29/0.50       => ( member_int @ C @ ( sup_sup_set_int @ A2 @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UnI1
% 0.29/0.50  thf(fact_1080_UnI1,axiom,
% 0.29/0.50      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50        ( ( member6576561426505652726_nat_o @ C @ A2 )
% 0.29/0.50       => ( member6576561426505652726_nat_o @ C @ ( sup_su5209123915105501825_nat_o @ A2 @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UnI1
% 0.29/0.50  thf(fact_1081_UnI1,axiom,
% 0.29/0.50      ! [C: produc4166570645942440679at_nat,A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 0.29/0.50        ( ( member6689249552917799696at_nat @ C @ A2 )
% 0.29/0.50       => ( member6689249552917799696at_nat @ C @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UnI1
% 0.29/0.50  thf(fact_1082_UnI1,axiom,
% 0.29/0.50      ! [C: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.29/0.50        ( ( member8757157785044589968at_nat @ C @ A2 )
% 0.29/0.50       => ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UnI1
% 0.29/0.50  thf(fact_1083_UnI1,axiom,
% 0.29/0.50      ! [C: nat,A2: set_nat,B2: set_nat] :
% 0.29/0.50        ( ( member_nat @ C @ A2 )
% 0.29/0.50       => ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UnI1
% 0.29/0.50  thf(fact_1084_UnI2,axiom,
% 0.29/0.50      ! [C: set_Pr958786334691620121nt_int,B2: set_se6260736226359567993nt_int,A2: set_se6260736226359567993nt_int] :
% 0.29/0.50        ( ( member2340774599025711042nt_int @ C @ B2 )
% 0.29/0.50       => ( member2340774599025711042nt_int @ C @ ( sup_su2047564715030645325nt_int @ A2 @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UnI2
% 0.29/0.50  thf(fact_1085_UnI2,axiom,
% 0.29/0.50      ! [C: set_nat,B2: set_set_nat,A2: set_set_nat] :
% 0.29/0.50        ( ( member_set_nat @ C @ B2 )
% 0.29/0.50       => ( member_set_nat @ C @ ( sup_sup_set_set_nat @ A2 @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UnI2
% 0.29/0.50  thf(fact_1086_UnI2,axiom,
% 0.29/0.50      ! [C: int,B2: set_int,A2: set_int] :
% 0.29/0.50        ( ( member_int @ C @ B2 )
% 0.29/0.50       => ( member_int @ C @ ( sup_sup_set_int @ A2 @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UnI2
% 0.29/0.50  thf(fact_1087_UnI2,axiom,
% 0.29/0.50      ! [C: produc3658429121746597890et_nat > $o,B2: set_Pr4532377907799695533_nat_o,A2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50        ( ( member6576561426505652726_nat_o @ C @ B2 )
% 0.29/0.50       => ( member6576561426505652726_nat_o @ C @ ( sup_su5209123915105501825_nat_o @ A2 @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UnI2
% 0.29/0.50  thf(fact_1088_UnI2,axiom,
% 0.29/0.50      ! [C: produc4166570645942440679at_nat,B2: set_Pr8551490117392284871at_nat,A2: set_Pr8551490117392284871at_nat] :
% 0.29/0.50        ( ( member6689249552917799696at_nat @ C @ B2 )
% 0.29/0.50       => ( member6689249552917799696at_nat @ C @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UnI2
% 0.29/0.50  thf(fact_1089_UnI2,axiom,
% 0.29/0.50      ! [C: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.29/0.50        ( ( member8757157785044589968at_nat @ C @ B2 )
% 0.29/0.50       => ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UnI2
% 0.29/0.50  thf(fact_1090_UnI2,axiom,
% 0.29/0.50      ! [C: nat,B2: set_nat,A2: set_nat] :
% 0.29/0.50        ( ( member_nat @ C @ B2 )
% 0.29/0.50       => ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UnI2
% 0.29/0.50  thf(fact_1091_bex__Un,axiom,
% 0.29/0.50      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,P: produc4166570645942440679at_nat > $o] :
% 0.29/0.50        ( ( ? [X3: produc4166570645942440679at_nat] :
% 0.29/0.50              ( ( member6689249552917799696at_nat @ X3 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 0.29/0.50              & ( P @ X3 ) ) )
% 0.29/0.50        = ( ? [X3: produc4166570645942440679at_nat] :
% 0.29/0.50              ( ( member6689249552917799696at_nat @ X3 @ A2 )
% 0.29/0.50              & ( P @ X3 ) )
% 0.29/0.50          | ? [X3: produc4166570645942440679at_nat] :
% 0.29/0.50              ( ( member6689249552917799696at_nat @ X3 @ B2 )
% 0.29/0.50              & ( P @ X3 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % bex_Un
% 0.29/0.50  thf(fact_1092_bex__Un,axiom,
% 0.29/0.50      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,P: produc3843707927480180839at_nat > $o] :
% 0.29/0.50        ( ( ? [X3: produc3843707927480180839at_nat] :
% 0.29/0.50              ( ( member8757157785044589968at_nat @ X3 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 0.29/0.50              & ( P @ X3 ) ) )
% 0.29/0.50        = ( ? [X3: produc3843707927480180839at_nat] :
% 0.29/0.50              ( ( member8757157785044589968at_nat @ X3 @ A2 )
% 0.29/0.50              & ( P @ X3 ) )
% 0.29/0.50          | ? [X3: produc3843707927480180839at_nat] :
% 0.29/0.50              ( ( member8757157785044589968at_nat @ X3 @ B2 )
% 0.29/0.50              & ( P @ X3 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % bex_Un
% 0.29/0.50  thf(fact_1093_bex__Un,axiom,
% 0.29/0.50      ! [A2: set_nat,B2: set_nat,P: nat > $o] :
% 0.29/0.50        ( ( ? [X3: nat] :
% 0.29/0.50              ( ( member_nat @ X3 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.29/0.50              & ( P @ X3 ) ) )
% 0.29/0.50        = ( ? [X3: nat] :
% 0.29/0.50              ( ( member_nat @ X3 @ A2 )
% 0.29/0.50              & ( P @ X3 ) )
% 0.29/0.50          | ? [X3: nat] :
% 0.29/0.50              ( ( member_nat @ X3 @ B2 )
% 0.29/0.50              & ( P @ X3 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % bex_Un
% 0.29/0.50  thf(fact_1094_ball__Un,axiom,
% 0.29/0.50      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,P: produc4166570645942440679at_nat > $o] :
% 0.29/0.50        ( ( ! [X3: produc4166570645942440679at_nat] :
% 0.29/0.50              ( ( member6689249552917799696at_nat @ X3 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 0.29/0.50             => ( P @ X3 ) ) )
% 0.29/0.50        = ( ! [X3: produc4166570645942440679at_nat] :
% 0.29/0.50              ( ( member6689249552917799696at_nat @ X3 @ A2 )
% 0.29/0.50             => ( P @ X3 ) )
% 0.29/0.50          & ! [X3: produc4166570645942440679at_nat] :
% 0.29/0.50              ( ( member6689249552917799696at_nat @ X3 @ B2 )
% 0.29/0.50             => ( P @ X3 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ball_Un
% 0.29/0.50  thf(fact_1095_ball__Un,axiom,
% 0.29/0.50      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,P: produc3843707927480180839at_nat > $o] :
% 0.29/0.50        ( ( ! [X3: produc3843707927480180839at_nat] :
% 0.29/0.50              ( ( member8757157785044589968at_nat @ X3 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 0.29/0.50             => ( P @ X3 ) ) )
% 0.29/0.50        = ( ! [X3: produc3843707927480180839at_nat] :
% 0.29/0.50              ( ( member8757157785044589968at_nat @ X3 @ A2 )
% 0.29/0.50             => ( P @ X3 ) )
% 0.29/0.50          & ! [X3: produc3843707927480180839at_nat] :
% 0.29/0.50              ( ( member8757157785044589968at_nat @ X3 @ B2 )
% 0.29/0.50             => ( P @ X3 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ball_Un
% 0.29/0.50  thf(fact_1096_ball__Un,axiom,
% 0.29/0.50      ! [A2: set_nat,B2: set_nat,P: nat > $o] :
% 0.29/0.50        ( ( ! [X3: nat] :
% 0.29/0.50              ( ( member_nat @ X3 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.29/0.50             => ( P @ X3 ) ) )
% 0.29/0.50        = ( ! [X3: nat] :
% 0.29/0.50              ( ( member_nat @ X3 @ A2 )
% 0.29/0.50             => ( P @ X3 ) )
% 0.29/0.50          & ! [X3: nat] :
% 0.29/0.50              ( ( member_nat @ X3 @ B2 )
% 0.29/0.50             => ( P @ X3 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % ball_Un
% 0.29/0.50  thf(fact_1097_Un__assoc,axiom,
% 0.29/0.50      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 0.29/0.50        ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) @ C2 )
% 0.29/0.50        = ( sup_su3035147773818789531at_nat @ A2 @ ( sup_su3035147773818789531at_nat @ B2 @ C2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_assoc
% 0.29/0.50  thf(fact_1098_Un__assoc,axiom,
% 0.29/0.50      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 0.29/0.50        ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) @ C2 )
% 0.29/0.50        = ( sup_su5525570899277871387at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_assoc
% 0.29/0.50  thf(fact_1099_Un__assoc,axiom,
% 0.29/0.50      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 0.29/0.50        ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ C2 )
% 0.29/0.50        = ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ B2 @ C2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_assoc
% 0.29/0.50  thf(fact_1100_Un__absorb,axiom,
% 0.29/0.50      ! [A2: set_Pr8551490117392284871at_nat] :
% 0.29/0.50        ( ( sup_su3035147773818789531at_nat @ A2 @ A2 )
% 0.29/0.50        = A2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_absorb
% 0.29/0.50  thf(fact_1101_Un__absorb,axiom,
% 0.29/0.50      ! [A2: set_Pr4329608150637261639at_nat] :
% 0.29/0.50        ( ( sup_su5525570899277871387at_nat @ A2 @ A2 )
% 0.29/0.50        = A2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_absorb
% 0.29/0.50  thf(fact_1102_Un__absorb,axiom,
% 0.29/0.50      ! [A2: set_nat] :
% 0.29/0.50        ( ( sup_sup_set_nat @ A2 @ A2 )
% 0.29/0.50        = A2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_absorb
% 0.29/0.50  thf(fact_1103_Un__commute,axiom,
% 0.29/0.50      ( sup_su3035147773818789531at_nat
% 0.29/0.50      = ( ^ [A4: set_Pr8551490117392284871at_nat,B4: set_Pr8551490117392284871at_nat] : ( sup_su3035147773818789531at_nat @ B4 @ A4 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_commute
% 0.29/0.50  thf(fact_1104_Un__commute,axiom,
% 0.29/0.50      ( sup_su5525570899277871387at_nat
% 0.29/0.50      = ( ^ [A4: set_Pr4329608150637261639at_nat,B4: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ B4 @ A4 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_commute
% 0.29/0.50  thf(fact_1105_Un__commute,axiom,
% 0.29/0.50      ( sup_sup_set_nat
% 0.29/0.50      = ( ^ [A4: set_nat,B4: set_nat] : ( sup_sup_set_nat @ B4 @ A4 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_commute
% 0.29/0.50  thf(fact_1106_Un__UNIV__left,axiom,
% 0.29/0.50      ! [B2: set_Pr8551490117392284871at_nat] :
% 0.29/0.50        ( ( sup_su3035147773818789531at_nat @ top_to8764741339697478167at_nat @ B2 )
% 0.29/0.50        = top_to8764741339697478167at_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_UNIV_left
% 0.29/0.50  thf(fact_1107_Un__UNIV__left,axiom,
% 0.29/0.50      ! [B2: set_Pr4329608150637261639at_nat] :
% 0.29/0.50        ( ( sup_su5525570899277871387at_nat @ top_to6833984726390702231at_nat @ B2 )
% 0.29/0.50        = top_to6833984726390702231at_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_UNIV_left
% 0.29/0.50  thf(fact_1108_Un__UNIV__left,axiom,
% 0.29/0.50      ! [B2: set_list_nat] :
% 0.29/0.50        ( ( sup_sup_set_list_nat @ top_top_set_list_nat @ B2 )
% 0.29/0.50        = top_top_set_list_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_UNIV_left
% 0.29/0.50  thf(fact_1109_Un__UNIV__left,axiom,
% 0.29/0.50      ! [B2: set_o] :
% 0.29/0.50        ( ( sup_sup_set_o @ top_top_set_o @ B2 )
% 0.29/0.50        = top_top_set_o ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_UNIV_left
% 0.29/0.50  thf(fact_1110_Un__UNIV__left,axiom,
% 0.29/0.50      ! [B2: set_rat] :
% 0.29/0.50        ( ( sup_sup_set_rat @ top_top_set_rat @ B2 )
% 0.29/0.50        = top_top_set_rat ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_UNIV_left
% 0.29/0.50  thf(fact_1111_Un__UNIV__left,axiom,
% 0.29/0.50      ! [B2: set_nat] :
% 0.29/0.50        ( ( sup_sup_set_nat @ top_top_set_nat @ B2 )
% 0.29/0.50        = top_top_set_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_UNIV_left
% 0.29/0.50  thf(fact_1112_Un__UNIV__left,axiom,
% 0.29/0.50      ! [B2: set_int] :
% 0.29/0.50        ( ( sup_sup_set_int @ top_top_set_int @ B2 )
% 0.29/0.50        = top_top_set_int ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_UNIV_left
% 0.29/0.50  thf(fact_1113_Un__UNIV__right,axiom,
% 0.29/0.50      ! [A2: set_Pr8551490117392284871at_nat] :
% 0.29/0.50        ( ( sup_su3035147773818789531at_nat @ A2 @ top_to8764741339697478167at_nat )
% 0.29/0.50        = top_to8764741339697478167at_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_UNIV_right
% 0.29/0.50  thf(fact_1114_Un__UNIV__right,axiom,
% 0.29/0.50      ! [A2: set_Pr4329608150637261639at_nat] :
% 0.29/0.50        ( ( sup_su5525570899277871387at_nat @ A2 @ top_to6833984726390702231at_nat )
% 0.29/0.50        = top_to6833984726390702231at_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_UNIV_right
% 0.29/0.50  thf(fact_1115_Un__UNIV__right,axiom,
% 0.29/0.50      ! [A2: set_list_nat] :
% 0.29/0.50        ( ( sup_sup_set_list_nat @ A2 @ top_top_set_list_nat )
% 0.29/0.50        = top_top_set_list_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_UNIV_right
% 0.29/0.50  thf(fact_1116_Un__UNIV__right,axiom,
% 0.29/0.50      ! [A2: set_o] :
% 0.29/0.50        ( ( sup_sup_set_o @ A2 @ top_top_set_o )
% 0.29/0.50        = top_top_set_o ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_UNIV_right
% 0.29/0.50  thf(fact_1117_Un__UNIV__right,axiom,
% 0.29/0.50      ! [A2: set_rat] :
% 0.29/0.50        ( ( sup_sup_set_rat @ A2 @ top_top_set_rat )
% 0.29/0.50        = top_top_set_rat ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_UNIV_right
% 0.29/0.50  thf(fact_1118_Un__UNIV__right,axiom,
% 0.29/0.50      ! [A2: set_nat] :
% 0.29/0.50        ( ( sup_sup_set_nat @ A2 @ top_top_set_nat )
% 0.29/0.50        = top_top_set_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_UNIV_right
% 0.29/0.50  thf(fact_1119_Un__UNIV__right,axiom,
% 0.29/0.50      ! [A2: set_int] :
% 0.29/0.50        ( ( sup_sup_set_int @ A2 @ top_top_set_int )
% 0.29/0.50        = top_top_set_int ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_UNIV_right
% 0.29/0.50  thf(fact_1120_Un__left__absorb,axiom,
% 0.29/0.50      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 0.29/0.50        ( ( sup_su3035147773818789531at_nat @ A2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 0.29/0.50        = ( sup_su3035147773818789531at_nat @ A2 @ B2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_left_absorb
% 0.29/0.50  thf(fact_1121_Un__left__absorb,axiom,
% 0.29/0.50      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.29/0.50        ( ( sup_su5525570899277871387at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 0.29/0.50        = ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_left_absorb
% 0.29/0.50  thf(fact_1122_Un__left__absorb,axiom,
% 0.29/0.50      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.50        ( ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.29/0.50        = ( sup_sup_set_nat @ A2 @ B2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_left_absorb
% 0.29/0.50  thf(fact_1123_Compl__partition,axiom,
% 0.29/0.50      ! [A2: set_Pr8551490117392284871at_nat] :
% 0.29/0.50        ( ( sup_su3035147773818789531at_nat @ A2 @ ( uminus2330091110623919550at_nat @ A2 ) )
% 0.29/0.50        = top_to8764741339697478167at_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_partition
% 0.29/0.50  thf(fact_1124_Compl__partition,axiom,
% 0.29/0.50      ! [A2: set_Pr4329608150637261639at_nat] :
% 0.29/0.50        ( ( sup_su5525570899277871387at_nat @ A2 @ ( uminus935396558254630718at_nat @ A2 ) )
% 0.29/0.50        = top_to6833984726390702231at_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_partition
% 0.29/0.50  thf(fact_1125_Compl__partition,axiom,
% 0.29/0.50      ! [A2: set_list_nat] :
% 0.29/0.50        ( ( sup_sup_set_list_nat @ A2 @ ( uminus3195874150345416415st_nat @ A2 ) )
% 0.29/0.50        = top_top_set_list_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_partition
% 0.29/0.50  thf(fact_1126_Compl__partition,axiom,
% 0.29/0.50      ! [A2: set_o] :
% 0.29/0.50        ( ( sup_sup_set_o @ A2 @ ( uminus_uminus_set_o @ A2 ) )
% 0.29/0.50        = top_top_set_o ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_partition
% 0.29/0.50  thf(fact_1127_Compl__partition,axiom,
% 0.29/0.50      ! [A2: set_rat] :
% 0.29/0.50        ( ( sup_sup_set_rat @ A2 @ ( uminus2201863774496077783et_rat @ A2 ) )
% 0.29/0.50        = top_top_set_rat ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_partition
% 0.29/0.50  thf(fact_1128_Compl__partition,axiom,
% 0.29/0.50      ! [A2: set_nat] :
% 0.29/0.50        ( ( sup_sup_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ A2 ) )
% 0.29/0.50        = top_top_set_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_partition
% 0.29/0.50  thf(fact_1129_Compl__partition,axiom,
% 0.29/0.50      ! [A2: set_int] :
% 0.29/0.50        ( ( sup_sup_set_int @ A2 @ ( uminus1532241313380277803et_int @ A2 ) )
% 0.29/0.50        = top_top_set_int ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_partition
% 0.29/0.50  thf(fact_1130_Un__left__commute,axiom,
% 0.29/0.50      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 0.29/0.50        ( ( sup_su3035147773818789531at_nat @ A2 @ ( sup_su3035147773818789531at_nat @ B2 @ C2 ) )
% 0.29/0.50        = ( sup_su3035147773818789531at_nat @ B2 @ ( sup_su3035147773818789531at_nat @ A2 @ C2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_left_commute
% 0.29/0.50  thf(fact_1131_Un__left__commute,axiom,
% 0.29/0.50      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 0.29/0.50        ( ( sup_su5525570899277871387at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) )
% 0.29/0.50        = ( sup_su5525570899277871387at_nat @ B2 @ ( sup_su5525570899277871387at_nat @ A2 @ C2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_left_commute
% 0.29/0.50  thf(fact_1132_Un__left__commute,axiom,
% 0.29/0.50      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 0.29/0.50        ( ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ B2 @ C2 ) )
% 0.29/0.50        = ( sup_sup_set_nat @ B2 @ ( sup_sup_set_nat @ A2 @ C2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_left_commute
% 0.29/0.50  thf(fact_1133_Compl__partition2,axiom,
% 0.29/0.50      ! [A2: set_Pr8551490117392284871at_nat] :
% 0.29/0.50        ( ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ A2 ) @ A2 )
% 0.29/0.50        = top_to8764741339697478167at_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_partition2
% 0.29/0.50  thf(fact_1134_Compl__partition2,axiom,
% 0.29/0.50      ! [A2: set_Pr4329608150637261639at_nat] :
% 0.29/0.50        ( ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ A2 ) @ A2 )
% 0.29/0.50        = top_to6833984726390702231at_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_partition2
% 0.29/0.50  thf(fact_1135_Compl__partition2,axiom,
% 0.29/0.50      ! [A2: set_list_nat] :
% 0.29/0.50        ( ( sup_sup_set_list_nat @ ( uminus3195874150345416415st_nat @ A2 ) @ A2 )
% 0.29/0.50        = top_top_set_list_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_partition2
% 0.29/0.50  thf(fact_1136_Compl__partition2,axiom,
% 0.29/0.50      ! [A2: set_o] :
% 0.29/0.50        ( ( sup_sup_set_o @ ( uminus_uminus_set_o @ A2 ) @ A2 )
% 0.29/0.50        = top_top_set_o ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_partition2
% 0.29/0.50  thf(fact_1137_Compl__partition2,axiom,
% 0.29/0.50      ! [A2: set_rat] :
% 0.29/0.50        ( ( sup_sup_set_rat @ ( uminus2201863774496077783et_rat @ A2 ) @ A2 )
% 0.29/0.50        = top_top_set_rat ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_partition2
% 0.29/0.50  thf(fact_1138_Compl__partition2,axiom,
% 0.29/0.50      ! [A2: set_nat] :
% 0.29/0.50        ( ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ A2 )
% 0.29/0.50        = top_top_set_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_partition2
% 0.29/0.50  thf(fact_1139_Compl__partition2,axiom,
% 0.29/0.50      ! [A2: set_int] :
% 0.29/0.50        ( ( sup_sup_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ A2 )
% 0.29/0.50        = top_top_set_int ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_partition2
% 0.29/0.50  thf(fact_1140_Set_Oempty__def,axiom,
% 0.29/0.50      ( bot_bo1488462491386950373nt_int
% 0.29/0.50      = ( collec5210948495886036740nt_int
% 0.29/0.50        @ ^ [X3: set_Pr958786334691620121nt_int] : $false ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Set.empty_def
% 0.29/0.50  thf(fact_1141_Set_Oempty__def,axiom,
% 0.29/0.50      ( bot_bot_set_set_nat
% 0.29/0.50      = ( collect_set_nat
% 0.29/0.50        @ ^ [X3: set_nat] : $false ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Set.empty_def
% 0.29/0.50  thf(fact_1142_Set_Oempty__def,axiom,
% 0.29/0.50      ( bot_bo7824918357723582233_nat_o
% 0.29/0.50      = ( collec939566748876313656_nat_o
% 0.29/0.50        @ ^ [X3: produc3658429121746597890et_nat > $o] : $false ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Set.empty_def
% 0.29/0.50  thf(fact_1143_Set_Oempty__def,axiom,
% 0.29/0.50      ( bot_bo2099793752762293965at_nat
% 0.29/0.50      = ( collec3392354462482085612at_nat
% 0.29/0.50        @ ^ [X3: product_prod_nat_nat] : $false ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Set.empty_def
% 0.29/0.50  thf(fact_1144_Set_Oempty__def,axiom,
% 0.29/0.50      ( bot_bot_set_o
% 0.29/0.50      = ( collect_o
% 0.29/0.50        @ ^ [X3: $o] : $false ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Set.empty_def
% 0.29/0.50  thf(fact_1145_Set_Oempty__def,axiom,
% 0.29/0.50      ( bot_bot_set_nat
% 0.29/0.50      = ( collect_nat
% 0.29/0.50        @ ^ [X3: nat] : $false ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Set.empty_def
% 0.29/0.50  thf(fact_1146_Set_Oempty__def,axiom,
% 0.29/0.50      ( bot_bot_set_int
% 0.29/0.50      = ( collect_int
% 0.29/0.50        @ ^ [X3: int] : $false ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Set.empty_def
% 0.29/0.50  thf(fact_1147_Int__def,axiom,
% 0.29/0.50      ( inf_in8396524679539076455nt_int
% 0.29/0.50      = ( ^ [A4: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
% 0.29/0.50            ( collec5210948495886036740nt_int
% 0.29/0.50            @ ^ [X3: set_Pr958786334691620121nt_int] :
% 0.29/0.50                ( ( member2340774599025711042nt_int @ X3 @ A4 )
% 0.29/0.50                & ( member2340774599025711042nt_int @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_def
% 0.29/0.50  thf(fact_1148_Int__def,axiom,
% 0.29/0.50      ( inf_inf_set_set_nat
% 0.29/0.50      = ( ^ [A4: set_set_nat,B4: set_set_nat] :
% 0.29/0.50            ( collect_set_nat
% 0.29/0.50            @ ^ [X3: set_nat] :
% 0.29/0.50                ( ( member_set_nat @ X3 @ A4 )
% 0.29/0.50                & ( member_set_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_def
% 0.29/0.50  thf(fact_1149_Int__def,axiom,
% 0.29/0.50      ( inf_inf_set_int
% 0.29/0.50      = ( ^ [A4: set_int,B4: set_int] :
% 0.29/0.50            ( collect_int
% 0.29/0.50            @ ^ [X3: int] :
% 0.29/0.50                ( ( member_int @ X3 @ A4 )
% 0.29/0.50                & ( member_int @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_def
% 0.29/0.50  thf(fact_1150_Int__def,axiom,
% 0.29/0.50      ( inf_in1906310914598751387_nat_o
% 0.29/0.50      = ( ^ [A4: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50            ( collec939566748876313656_nat_o
% 0.29/0.50            @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.29/0.50                ( ( member6576561426505652726_nat_o @ X3 @ A4 )
% 0.29/0.50                & ( member6576561426505652726_nat_o @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_def
% 0.29/0.50  thf(fact_1151_Int__def,axiom,
% 0.29/0.50      ( inf_in2572325071724192079at_nat
% 0.29/0.50      = ( ^ [A4: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 0.29/0.50            ( collec3392354462482085612at_nat
% 0.29/0.50            @ ^ [X3: product_prod_nat_nat] :
% 0.29/0.50                ( ( member8440522571783428010at_nat @ X3 @ A4 )
% 0.29/0.50                & ( member8440522571783428010at_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_def
% 0.29/0.50  thf(fact_1152_Int__def,axiom,
% 0.29/0.50      ( inf_inf_set_nat
% 0.29/0.50      = ( ^ [A4: set_nat,B4: set_nat] :
% 0.29/0.50            ( collect_nat
% 0.29/0.50            @ ^ [X3: nat] :
% 0.29/0.50                ( ( member_nat @ X3 @ A4 )
% 0.29/0.50                & ( member_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_def
% 0.29/0.50  thf(fact_1153_Int__Collect,axiom,
% 0.29/0.50      ! [X: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 0.29/0.50        ( ( member2340774599025711042nt_int @ X @ ( inf_in8396524679539076455nt_int @ A2 @ ( collec5210948495886036740nt_int @ P ) ) )
% 0.29/0.50        = ( ( member2340774599025711042nt_int @ X @ A2 )
% 0.29/0.50          & ( P @ X ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_Collect
% 0.29/0.50  thf(fact_1154_Int__Collect,axiom,
% 0.29/0.50      ! [X: set_nat,A2: set_set_nat,P: set_nat > $o] :
% 0.29/0.50        ( ( member_set_nat @ X @ ( inf_inf_set_set_nat @ A2 @ ( collect_set_nat @ P ) ) )
% 0.29/0.50        = ( ( member_set_nat @ X @ A2 )
% 0.29/0.50          & ( P @ X ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_Collect
% 0.29/0.50  thf(fact_1155_Int__Collect,axiom,
% 0.29/0.50      ! [X: int,A2: set_int,P: int > $o] :
% 0.29/0.50        ( ( member_int @ X @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) )
% 0.29/0.50        = ( ( member_int @ X @ A2 )
% 0.29/0.50          & ( P @ X ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_Collect
% 0.29/0.50  thf(fact_1156_Int__Collect,axiom,
% 0.29/0.50      ! [X: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.29/0.50        ( ( member6576561426505652726_nat_o @ X @ ( inf_in1906310914598751387_nat_o @ A2 @ ( collec939566748876313656_nat_o @ P ) ) )
% 0.29/0.50        = ( ( member6576561426505652726_nat_o @ X @ A2 )
% 0.29/0.50          & ( P @ X ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_Collect
% 0.29/0.50  thf(fact_1157_Int__Collect,axiom,
% 0.29/0.50      ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o] :
% 0.29/0.50        ( ( member8440522571783428010at_nat @ X @ ( inf_in2572325071724192079at_nat @ A2 @ ( collec3392354462482085612at_nat @ P ) ) )
% 0.29/0.50        = ( ( member8440522571783428010at_nat @ X @ A2 )
% 0.29/0.50          & ( P @ X ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_Collect
% 0.29/0.50  thf(fact_1158_Int__Collect,axiom,
% 0.29/0.50      ! [X: nat,A2: set_nat,P: nat > $o] :
% 0.29/0.50        ( ( member_nat @ X @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) )
% 0.29/0.50        = ( ( member_nat @ X @ A2 )
% 0.29/0.50          & ( P @ X ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_Collect
% 0.29/0.50  thf(fact_1159_inf__set__def,axiom,
% 0.29/0.50      ( inf_in8396524679539076455nt_int
% 0.29/0.50      = ( ^ [A4: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
% 0.29/0.50            ( collec5210948495886036740nt_int
% 0.29/0.50            @ ( inf_in5102985939729578038_int_o
% 0.29/0.50              @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ A4 )
% 0.29/0.50              @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inf_set_def
% 0.29/0.50  thf(fact_1160_inf__set__def,axiom,
% 0.29/0.50      ( inf_inf_set_set_nat
% 0.29/0.50      = ( ^ [A4: set_set_nat,B4: set_set_nat] :
% 0.29/0.50            ( collect_set_nat
% 0.29/0.50            @ ( inf_inf_set_nat_o
% 0.29/0.50              @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A4 )
% 0.29/0.50              @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inf_set_def
% 0.29/0.50  thf(fact_1161_inf__set__def,axiom,
% 0.29/0.50      ( inf_inf_set_int
% 0.29/0.50      = ( ^ [A4: set_int,B4: set_int] :
% 0.29/0.50            ( collect_int
% 0.29/0.50            @ ( inf_inf_int_o
% 0.29/0.50              @ ^ [X3: int] : ( member_int @ X3 @ A4 )
% 0.29/0.50              @ ^ [X3: int] : ( member_int @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inf_set_def
% 0.29/0.50  thf(fact_1162_inf__set__def,axiom,
% 0.29/0.50      ( inf_in1906310914598751387_nat_o
% 0.29/0.50      = ( ^ [A4: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50            ( collec939566748876313656_nat_o
% 0.29/0.50            @ ( inf_in9018898317438245890at_o_o
% 0.29/0.50              @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ A4 )
% 0.29/0.50              @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inf_set_def
% 0.29/0.50  thf(fact_1163_inf__set__def,axiom,
% 0.29/0.50      ( inf_in2269163501485487111nt_int
% 0.29/0.50      = ( ^ [A4: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
% 0.29/0.50            ( collec213857154873943460nt_int
% 0.29/0.50            @ ( inf_in3604695632404883862_int_o
% 0.29/0.50              @ ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ A4 )
% 0.29/0.50              @ ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inf_set_def
% 0.29/0.50  thf(fact_1164_inf__set__def,axiom,
% 0.29/0.50      ( inf_in6177012701088388009t_char
% 0.29/0.50      = ( ^ [A4: set_list_char,B4: set_list_char] :
% 0.29/0.50            ( collect_list_char
% 0.29/0.50            @ ( inf_inf_list_char_o
% 0.29/0.50              @ ^ [X3: list_char] : ( member_list_char @ X3 @ A4 )
% 0.29/0.50              @ ^ [X3: list_char] : ( member_list_char @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inf_set_def
% 0.29/0.50  thf(fact_1165_inf__set__def,axiom,
% 0.29/0.50      ( inf_in2572325071724192079at_nat
% 0.29/0.50      = ( ^ [A4: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 0.29/0.50            ( collec3392354462482085612at_nat
% 0.29/0.50            @ ( inf_in5163264567034779214_nat_o
% 0.29/0.50              @ ^ [X3: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X3 @ A4 )
% 0.29/0.50              @ ^ [X3: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inf_set_def
% 0.29/0.50  thf(fact_1166_inf__set__def,axiom,
% 0.29/0.50      ( inf_inf_set_nat
% 0.29/0.50      = ( ^ [A4: set_nat,B4: set_nat] :
% 0.29/0.50            ( collect_nat
% 0.29/0.50            @ ( inf_inf_nat_o
% 0.29/0.50              @ ^ [X3: nat] : ( member_nat @ X3 @ A4 )
% 0.29/0.50              @ ^ [X3: nat] : ( member_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inf_set_def
% 0.29/0.50  thf(fact_1167_Collect__conj__eq,axiom,
% 0.29/0.50      ! [P: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 0.29/0.50        ( ( collec5210948495886036740nt_int
% 0.29/0.50          @ ^ [X3: set_Pr958786334691620121nt_int] :
% 0.29/0.50              ( ( P @ X3 )
% 0.29/0.50              & ( Q2 @ X3 ) ) )
% 0.29/0.50        = ( inf_in8396524679539076455nt_int @ ( collec5210948495886036740nt_int @ P ) @ ( collec5210948495886036740nt_int @ Q2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_conj_eq
% 0.29/0.50  thf(fact_1168_Collect__conj__eq,axiom,
% 0.29/0.50      ! [P: set_nat > $o,Q2: set_nat > $o] :
% 0.29/0.50        ( ( collect_set_nat
% 0.29/0.50          @ ^ [X3: set_nat] :
% 0.29/0.50              ( ( P @ X3 )
% 0.29/0.50              & ( Q2 @ X3 ) ) )
% 0.29/0.50        = ( inf_inf_set_set_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_conj_eq
% 0.29/0.50  thf(fact_1169_Collect__conj__eq,axiom,
% 0.29/0.50      ! [P: int > $o,Q2: int > $o] :
% 0.29/0.50        ( ( collect_int
% 0.29/0.50          @ ^ [X3: int] :
% 0.29/0.50              ( ( P @ X3 )
% 0.29/0.50              & ( Q2 @ X3 ) ) )
% 0.29/0.50        = ( inf_inf_set_int @ ( collect_int @ P ) @ ( collect_int @ Q2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_conj_eq
% 0.29/0.50  thf(fact_1170_Collect__conj__eq,axiom,
% 0.29/0.50      ! [P: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.29/0.50        ( ( collec939566748876313656_nat_o
% 0.29/0.50          @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.29/0.50              ( ( P @ X3 )
% 0.29/0.50              & ( Q2 @ X3 ) ) )
% 0.29/0.50        = ( inf_in1906310914598751387_nat_o @ ( collec939566748876313656_nat_o @ P ) @ ( collec939566748876313656_nat_o @ Q2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_conj_eq
% 0.29/0.50  thf(fact_1171_Collect__conj__eq,axiom,
% 0.29/0.50      ! [P: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > $o] :
% 0.29/0.50        ( ( collec3392354462482085612at_nat
% 0.29/0.50          @ ^ [X3: product_prod_nat_nat] :
% 0.29/0.50              ( ( P @ X3 )
% 0.29/0.50              & ( Q2 @ X3 ) ) )
% 0.29/0.50        = ( inf_in2572325071724192079at_nat @ ( collec3392354462482085612at_nat @ P ) @ ( collec3392354462482085612at_nat @ Q2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_conj_eq
% 0.29/0.50  thf(fact_1172_Collect__conj__eq,axiom,
% 0.29/0.50      ! [P: nat > $o,Q2: nat > $o] :
% 0.29/0.50        ( ( collect_nat
% 0.29/0.50          @ ^ [X3: nat] :
% 0.29/0.50              ( ( P @ X3 )
% 0.29/0.50              & ( Q2 @ X3 ) ) )
% 0.29/0.50        = ( inf_inf_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_conj_eq
% 0.29/0.50  thf(fact_1173_Un__def,axiom,
% 0.29/0.50      ( sup_su2047564715030645325nt_int
% 0.29/0.50      = ( ^ [A4: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
% 0.29/0.50            ( collec5210948495886036740nt_int
% 0.29/0.50            @ ^ [X3: set_Pr958786334691620121nt_int] :
% 0.29/0.50                ( ( member2340774599025711042nt_int @ X3 @ A4 )
% 0.29/0.50                | ( member2340774599025711042nt_int @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_def
% 0.29/0.50  thf(fact_1174_Un__def,axiom,
% 0.29/0.50      ( sup_sup_set_set_nat
% 0.29/0.50      = ( ^ [A4: set_set_nat,B4: set_set_nat] :
% 0.29/0.50            ( collect_set_nat
% 0.29/0.50            @ ^ [X3: set_nat] :
% 0.29/0.50                ( ( member_set_nat @ X3 @ A4 )
% 0.29/0.50                | ( member_set_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_def
% 0.29/0.50  thf(fact_1175_Un__def,axiom,
% 0.29/0.50      ( sup_sup_set_int
% 0.29/0.50      = ( ^ [A4: set_int,B4: set_int] :
% 0.29/0.50            ( collect_int
% 0.29/0.50            @ ^ [X3: int] :
% 0.29/0.50                ( ( member_int @ X3 @ A4 )
% 0.29/0.50                | ( member_int @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_def
% 0.29/0.50  thf(fact_1176_Un__def,axiom,
% 0.29/0.50      ( sup_su5209123915105501825_nat_o
% 0.29/0.50      = ( ^ [A4: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50            ( collec939566748876313656_nat_o
% 0.29/0.50            @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.29/0.50                ( ( member6576561426505652726_nat_o @ X3 @ A4 )
% 0.29/0.50                | ( member6576561426505652726_nat_o @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_def
% 0.29/0.50  thf(fact_1177_Un__def,axiom,
% 0.29/0.50      ( sup_su3035147773818789531at_nat
% 0.29/0.50      = ( ^ [A4: set_Pr8551490117392284871at_nat,B4: set_Pr8551490117392284871at_nat] :
% 0.29/0.50            ( collec5204685387357076818at_nat
% 0.29/0.50            @ ^ [X3: produc4166570645942440679at_nat] :
% 0.29/0.50                ( ( member6689249552917799696at_nat @ X3 @ A4 )
% 0.29/0.50                | ( member6689249552917799696at_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_def
% 0.29/0.50  thf(fact_1178_Un__def,axiom,
% 0.29/0.50      ( sup_su5525570899277871387at_nat
% 0.29/0.50      = ( ^ [A4: set_Pr4329608150637261639at_nat,B4: set_Pr4329608150637261639at_nat] :
% 0.29/0.50            ( collec6321179662152712658at_nat
% 0.29/0.50            @ ^ [X3: produc3843707927480180839at_nat] :
% 0.29/0.50                ( ( member8757157785044589968at_nat @ X3 @ A4 )
% 0.29/0.50                | ( member8757157785044589968at_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_def
% 0.29/0.50  thf(fact_1179_Un__def,axiom,
% 0.29/0.50      ( sup_sup_set_nat
% 0.29/0.50      = ( ^ [A4: set_nat,B4: set_nat] :
% 0.29/0.50            ( collect_nat
% 0.29/0.50            @ ^ [X3: nat] :
% 0.29/0.50                ( ( member_nat @ X3 @ A4 )
% 0.29/0.50                | ( member_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_def
% 0.29/0.50  thf(fact_1180_sup__set__def,axiom,
% 0.29/0.50      ( sup_su2047564715030645325nt_int
% 0.29/0.50      = ( ^ [A4: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
% 0.29/0.50            ( collec5210948495886036740nt_int
% 0.29/0.50            @ ( sup_su1852724690005176016_int_o
% 0.29/0.50              @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ A4 )
% 0.29/0.50              @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % sup_set_def
% 0.29/0.50  thf(fact_1181_sup__set__def,axiom,
% 0.29/0.50      ( sup_sup_set_set_nat
% 0.29/0.50      = ( ^ [A4: set_set_nat,B4: set_set_nat] :
% 0.29/0.50            ( collect_set_nat
% 0.29/0.50            @ ( sup_sup_set_nat_o
% 0.29/0.50              @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A4 )
% 0.29/0.50              @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % sup_set_def
% 0.29/0.50  thf(fact_1182_sup__set__def,axiom,
% 0.29/0.50      ( sup_sup_set_int
% 0.29/0.50      = ( ^ [A4: set_int,B4: set_int] :
% 0.29/0.50            ( collect_int
% 0.29/0.50            @ ( sup_sup_int_o
% 0.29/0.50              @ ^ [X3: int] : ( member_int @ X3 @ A4 )
% 0.29/0.50              @ ^ [X3: int] : ( member_int @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % sup_set_def
% 0.29/0.50  thf(fact_1183_sup__set__def,axiom,
% 0.29/0.50      ( sup_su5209123915105501825_nat_o
% 0.29/0.50      = ( ^ [A4: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50            ( collec939566748876313656_nat_o
% 0.29/0.50            @ ( sup_su8003631835303541148at_o_o
% 0.29/0.50              @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ A4 )
% 0.29/0.50              @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % sup_set_def
% 0.29/0.50  thf(fact_1184_sup__set__def,axiom,
% 0.29/0.50      ( sup_su3035147773818789531at_nat
% 0.29/0.50      = ( ^ [A4: set_Pr8551490117392284871at_nat,B4: set_Pr8551490117392284871at_nat] :
% 0.29/0.50            ( collec5204685387357076818at_nat
% 0.29/0.50            @ ( sup_su6256023009775730178_nat_o
% 0.29/0.50              @ ^ [X3: produc4166570645942440679at_nat] : ( member6689249552917799696at_nat @ X3 @ A4 )
% 0.29/0.50              @ ^ [X3: produc4166570645942440679at_nat] : ( member6689249552917799696at_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % sup_set_def
% 0.29/0.50  thf(fact_1185_sup__set__def,axiom,
% 0.29/0.50      ( sup_su5525570899277871387at_nat
% 0.29/0.50      = ( ^ [A4: set_Pr4329608150637261639at_nat,B4: set_Pr4329608150637261639at_nat] :
% 0.29/0.50            ( collec6321179662152712658at_nat
% 0.29/0.50            @ ( sup_su2080679670758317954_nat_o
% 0.29/0.50              @ ^ [X3: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X3 @ A4 )
% 0.29/0.50              @ ^ [X3: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % sup_set_def
% 0.29/0.50  thf(fact_1186_sup__set__def,axiom,
% 0.29/0.50      ( sup_sup_set_nat
% 0.29/0.50      = ( ^ [A4: set_nat,B4: set_nat] :
% 0.29/0.50            ( collect_nat
% 0.29/0.50            @ ( sup_sup_nat_o
% 0.29/0.50              @ ^ [X3: nat] : ( member_nat @ X3 @ A4 )
% 0.29/0.50              @ ^ [X3: nat] : ( member_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % sup_set_def
% 0.29/0.50  thf(fact_1187_Collect__imp__eq,axiom,
% 0.29/0.50      ! [P: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 0.29/0.50        ( ( collec5210948495886036740nt_int
% 0.29/0.50          @ ^ [X3: set_Pr958786334691620121nt_int] :
% 0.29/0.50              ( ( P @ X3 )
% 0.29/0.50             => ( Q2 @ X3 ) ) )
% 0.29/0.50        = ( sup_su2047564715030645325nt_int @ ( uminus6423885277529793776nt_int @ ( collec5210948495886036740nt_int @ P ) ) @ ( collec5210948495886036740nt_int @ Q2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_imp_eq
% 0.29/0.50  thf(fact_1188_Collect__imp__eq,axiom,
% 0.29/0.50      ! [P: set_nat > $o,Q2: set_nat > $o] :
% 0.29/0.50        ( ( collect_set_nat
% 0.29/0.50          @ ^ [X3: set_nat] :
% 0.29/0.50              ( ( P @ X3 )
% 0.29/0.50             => ( Q2 @ X3 ) ) )
% 0.29/0.50        = ( sup_sup_set_set_nat @ ( uminus613421341184616069et_nat @ ( collect_set_nat @ P ) ) @ ( collect_set_nat @ Q2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_imp_eq
% 0.29/0.50  thf(fact_1189_Collect__imp__eq,axiom,
% 0.29/0.50      ! [P: int > $o,Q2: int > $o] :
% 0.29/0.50        ( ( collect_int
% 0.29/0.50          @ ^ [X3: int] :
% 0.29/0.50              ( ( P @ X3 )
% 0.29/0.50             => ( Q2 @ X3 ) ) )
% 0.29/0.50        = ( sup_sup_set_int @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) @ ( collect_int @ Q2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_imp_eq
% 0.29/0.50  thf(fact_1190_Collect__imp__eq,axiom,
% 0.29/0.50      ! [P: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.29/0.50        ( ( collec939566748876313656_nat_o
% 0.29/0.50          @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.29/0.50              ( ( P @ X3 )
% 0.29/0.50             => ( Q2 @ X3 ) ) )
% 0.29/0.50        = ( sup_su5209123915105501825_nat_o @ ( uminus5254974436814262692_nat_o @ ( collec939566748876313656_nat_o @ P ) ) @ ( collec939566748876313656_nat_o @ Q2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_imp_eq
% 0.29/0.50  thf(fact_1191_Collect__imp__eq,axiom,
% 0.29/0.50      ! [P: produc4166570645942440679at_nat > $o,Q2: produc4166570645942440679at_nat > $o] :
% 0.29/0.50        ( ( collec5204685387357076818at_nat
% 0.29/0.50          @ ^ [X3: produc4166570645942440679at_nat] :
% 0.29/0.50              ( ( P @ X3 )
% 0.29/0.50             => ( Q2 @ X3 ) ) )
% 0.29/0.50        = ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ ( collec5204685387357076818at_nat @ P ) ) @ ( collec5204685387357076818at_nat @ Q2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_imp_eq
% 0.29/0.50  thf(fact_1192_Collect__imp__eq,axiom,
% 0.29/0.50      ! [P: produc3843707927480180839at_nat > $o,Q2: produc3843707927480180839at_nat > $o] :
% 0.29/0.50        ( ( collec6321179662152712658at_nat
% 0.29/0.50          @ ^ [X3: produc3843707927480180839at_nat] :
% 0.29/0.50              ( ( P @ X3 )
% 0.29/0.50             => ( Q2 @ X3 ) ) )
% 0.29/0.50        = ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ ( collec6321179662152712658at_nat @ P ) ) @ ( collec6321179662152712658at_nat @ Q2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_imp_eq
% 0.29/0.50  thf(fact_1193_Collect__imp__eq,axiom,
% 0.29/0.50      ! [P: nat > $o,Q2: nat > $o] :
% 0.29/0.50        ( ( collect_nat
% 0.29/0.50          @ ^ [X3: nat] :
% 0.29/0.50              ( ( P @ X3 )
% 0.29/0.50             => ( Q2 @ X3 ) ) )
% 0.29/0.50        = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) @ ( collect_nat @ Q2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_imp_eq
% 0.29/0.50  thf(fact_1194_Collect__disj__eq,axiom,
% 0.29/0.50      ! [P: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 0.29/0.50        ( ( collec5210948495886036740nt_int
% 0.29/0.50          @ ^ [X3: set_Pr958786334691620121nt_int] :
% 0.29/0.50              ( ( P @ X3 )
% 0.29/0.50              | ( Q2 @ X3 ) ) )
% 0.29/0.50        = ( sup_su2047564715030645325nt_int @ ( collec5210948495886036740nt_int @ P ) @ ( collec5210948495886036740nt_int @ Q2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_disj_eq
% 0.29/0.50  thf(fact_1195_Collect__disj__eq,axiom,
% 0.29/0.50      ! [P: set_nat > $o,Q2: set_nat > $o] :
% 0.29/0.50        ( ( collect_set_nat
% 0.29/0.50          @ ^ [X3: set_nat] :
% 0.29/0.50              ( ( P @ X3 )
% 0.29/0.50              | ( Q2 @ X3 ) ) )
% 0.29/0.50        = ( sup_sup_set_set_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_disj_eq
% 0.29/0.50  thf(fact_1196_Collect__disj__eq,axiom,
% 0.29/0.50      ! [P: int > $o,Q2: int > $o] :
% 0.29/0.50        ( ( collect_int
% 0.29/0.50          @ ^ [X3: int] :
% 0.29/0.50              ( ( P @ X3 )
% 0.29/0.50              | ( Q2 @ X3 ) ) )
% 0.29/0.50        = ( sup_sup_set_int @ ( collect_int @ P ) @ ( collect_int @ Q2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_disj_eq
% 0.29/0.50  thf(fact_1197_Collect__disj__eq,axiom,
% 0.29/0.50      ! [P: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.29/0.50        ( ( collec939566748876313656_nat_o
% 0.29/0.50          @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.29/0.50              ( ( P @ X3 )
% 0.29/0.50              | ( Q2 @ X3 ) ) )
% 0.29/0.50        = ( sup_su5209123915105501825_nat_o @ ( collec939566748876313656_nat_o @ P ) @ ( collec939566748876313656_nat_o @ Q2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_disj_eq
% 0.29/0.50  thf(fact_1198_Collect__disj__eq,axiom,
% 0.29/0.50      ! [P: produc4166570645942440679at_nat > $o,Q2: produc4166570645942440679at_nat > $o] :
% 0.29/0.50        ( ( collec5204685387357076818at_nat
% 0.29/0.50          @ ^ [X3: produc4166570645942440679at_nat] :
% 0.29/0.50              ( ( P @ X3 )
% 0.29/0.50              | ( Q2 @ X3 ) ) )
% 0.29/0.50        = ( sup_su3035147773818789531at_nat @ ( collec5204685387357076818at_nat @ P ) @ ( collec5204685387357076818at_nat @ Q2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_disj_eq
% 0.29/0.50  thf(fact_1199_Collect__disj__eq,axiom,
% 0.29/0.50      ! [P: produc3843707927480180839at_nat > $o,Q2: produc3843707927480180839at_nat > $o] :
% 0.29/0.50        ( ( collec6321179662152712658at_nat
% 0.29/0.50          @ ^ [X3: produc3843707927480180839at_nat] :
% 0.29/0.50              ( ( P @ X3 )
% 0.29/0.50              | ( Q2 @ X3 ) ) )
% 0.29/0.50        = ( sup_su5525570899277871387at_nat @ ( collec6321179662152712658at_nat @ P ) @ ( collec6321179662152712658at_nat @ Q2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_disj_eq
% 0.29/0.50  thf(fact_1200_Collect__disj__eq,axiom,
% 0.29/0.50      ! [P: nat > $o,Q2: nat > $o] :
% 0.29/0.50        ( ( collect_nat
% 0.29/0.50          @ ^ [X3: nat] :
% 0.29/0.50              ( ( P @ X3 )
% 0.29/0.50              | ( Q2 @ X3 ) ) )
% 0.29/0.50        = ( sup_sup_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Collect_disj_eq
% 0.29/0.50  thf(fact_1201_one__neq__neg__one,axiom,
% 0.29/0.50      ( one_one_int
% 0.29/0.50     != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.50  
% 0.29/0.50  % one_neq_neg_one
% 0.29/0.50  thf(fact_1202_one__neq__neg__one,axiom,
% 0.29/0.50      ( one_one_Code_integer
% 0.29/0.50     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.50  
% 0.29/0.50  % one_neq_neg_one
% 0.29/0.50  thf(fact_1203_one__neq__neg__one,axiom,
% 0.29/0.50      ( one_one_rat
% 0.29/0.50     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % one_neq_neg_one
% 0.29/0.50  thf(fact_1204_Int__emptyI,axiom,
% 0.29/0.50      ! [A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 0.29/0.50        ( ! [X2: set_Pr958786334691620121nt_int] :
% 0.29/0.50            ( ( member2340774599025711042nt_int @ X2 @ A2 )
% 0.29/0.50           => ~ ( member2340774599025711042nt_int @ X2 @ B2 ) )
% 0.29/0.50       => ( ( inf_in8396524679539076455nt_int @ A2 @ B2 )
% 0.29/0.50          = bot_bo1488462491386950373nt_int ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_emptyI
% 0.29/0.50  thf(fact_1205_Int__emptyI,axiom,
% 0.29/0.50      ! [A2: set_set_nat,B2: set_set_nat] :
% 0.29/0.50        ( ! [X2: set_nat] :
% 0.29/0.50            ( ( member_set_nat @ X2 @ A2 )
% 0.29/0.50           => ~ ( member_set_nat @ X2 @ B2 ) )
% 0.29/0.50       => ( ( inf_inf_set_set_nat @ A2 @ B2 )
% 0.29/0.50          = bot_bot_set_set_nat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_emptyI
% 0.29/0.50  thf(fact_1206_Int__emptyI,axiom,
% 0.29/0.50      ! [A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50        ( ! [X2: produc3658429121746597890et_nat > $o] :
% 0.29/0.50            ( ( member6576561426505652726_nat_o @ X2 @ A2 )
% 0.29/0.50           => ~ ( member6576561426505652726_nat_o @ X2 @ B2 ) )
% 0.29/0.50       => ( ( inf_in1906310914598751387_nat_o @ A2 @ B2 )
% 0.29/0.50          = bot_bo7824918357723582233_nat_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_emptyI
% 0.29/0.50  thf(fact_1207_Int__emptyI,axiom,
% 0.29/0.50      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ! [X2: product_prod_nat_nat] :
% 0.29/0.50            ( ( member8440522571783428010at_nat @ X2 @ A2 )
% 0.29/0.50           => ~ ( member8440522571783428010at_nat @ X2 @ B2 ) )
% 0.29/0.50       => ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 0.29/0.50          = bot_bo2099793752762293965at_nat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_emptyI
% 0.29/0.50  thf(fact_1208_Int__emptyI,axiom,
% 0.29/0.50      ! [A2: set_o,B2: set_o] :
% 0.29/0.50        ( ! [X2: $o] :
% 0.29/0.50            ( ( member_o @ X2 @ A2 )
% 0.29/0.50           => ~ ( member_o @ X2 @ B2 ) )
% 0.29/0.50       => ( ( inf_inf_set_o @ A2 @ B2 )
% 0.29/0.50          = bot_bot_set_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_emptyI
% 0.29/0.50  thf(fact_1209_Int__emptyI,axiom,
% 0.29/0.50      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.50        ( ! [X2: nat] :
% 0.29/0.50            ( ( member_nat @ X2 @ A2 )
% 0.29/0.50           => ~ ( member_nat @ X2 @ B2 ) )
% 0.29/0.50       => ( ( inf_inf_set_nat @ A2 @ B2 )
% 0.29/0.50          = bot_bot_set_nat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_emptyI
% 0.29/0.50  thf(fact_1210_Int__emptyI,axiom,
% 0.29/0.50      ! [A2: set_int,B2: set_int] :
% 0.29/0.50        ( ! [X2: int] :
% 0.29/0.50            ( ( member_int @ X2 @ A2 )
% 0.29/0.50           => ~ ( member_int @ X2 @ B2 ) )
% 0.29/0.50       => ( ( inf_inf_set_int @ A2 @ B2 )
% 0.29/0.50          = bot_bot_set_int ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_emptyI
% 0.29/0.50  thf(fact_1211_disjoint__iff,axiom,
% 0.29/0.50      ! [A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 0.29/0.50        ( ( ( inf_in8396524679539076455nt_int @ A2 @ B2 )
% 0.29/0.50          = bot_bo1488462491386950373nt_int )
% 0.29/0.50        = ( ! [X3: set_Pr958786334691620121nt_int] :
% 0.29/0.50              ( ( member2340774599025711042nt_int @ X3 @ A2 )
% 0.29/0.50             => ~ ( member2340774599025711042nt_int @ X3 @ B2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % disjoint_iff
% 0.29/0.50  thf(fact_1212_disjoint__iff,axiom,
% 0.29/0.50      ! [A2: set_set_nat,B2: set_set_nat] :
% 0.29/0.50        ( ( ( inf_inf_set_set_nat @ A2 @ B2 )
% 0.29/0.50          = bot_bot_set_set_nat )
% 0.29/0.50        = ( ! [X3: set_nat] :
% 0.29/0.50              ( ( member_set_nat @ X3 @ A2 )
% 0.29/0.50             => ~ ( member_set_nat @ X3 @ B2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % disjoint_iff
% 0.29/0.50  thf(fact_1213_disjoint__iff,axiom,
% 0.29/0.50      ! [A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50        ( ( ( inf_in1906310914598751387_nat_o @ A2 @ B2 )
% 0.29/0.50          = bot_bo7824918357723582233_nat_o )
% 0.29/0.50        = ( ! [X3: produc3658429121746597890et_nat > $o] :
% 0.29/0.50              ( ( member6576561426505652726_nat_o @ X3 @ A2 )
% 0.29/0.50             => ~ ( member6576561426505652726_nat_o @ X3 @ B2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % disjoint_iff
% 0.29/0.50  thf(fact_1214_disjoint__iff,axiom,
% 0.29/0.50      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 0.29/0.50          = bot_bo2099793752762293965at_nat )
% 0.29/0.50        = ( ! [X3: product_prod_nat_nat] :
% 0.29/0.50              ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 0.29/0.50             => ~ ( member8440522571783428010at_nat @ X3 @ B2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % disjoint_iff
% 0.29/0.50  thf(fact_1215_disjoint__iff,axiom,
% 0.29/0.50      ! [A2: set_o,B2: set_o] :
% 0.29/0.50        ( ( ( inf_inf_set_o @ A2 @ B2 )
% 0.29/0.50          = bot_bot_set_o )
% 0.29/0.50        = ( ! [X3: $o] :
% 0.29/0.50              ( ( member_o @ X3 @ A2 )
% 0.29/0.50             => ~ ( member_o @ X3 @ B2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % disjoint_iff
% 0.29/0.50  thf(fact_1216_disjoint__iff,axiom,
% 0.29/0.50      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.50        ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 0.29/0.50          = bot_bot_set_nat )
% 0.29/0.50        = ( ! [X3: nat] :
% 0.29/0.50              ( ( member_nat @ X3 @ A2 )
% 0.29/0.50             => ~ ( member_nat @ X3 @ B2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % disjoint_iff
% 0.29/0.50  thf(fact_1217_disjoint__iff,axiom,
% 0.29/0.50      ! [A2: set_int,B2: set_int] :
% 0.29/0.50        ( ( ( inf_inf_set_int @ A2 @ B2 )
% 0.29/0.50          = bot_bot_set_int )
% 0.29/0.50        = ( ! [X3: int] :
% 0.29/0.50              ( ( member_int @ X3 @ A2 )
% 0.29/0.50             => ~ ( member_int @ X3 @ B2 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % disjoint_iff
% 0.29/0.50  thf(fact_1218_Int__empty__left,axiom,
% 0.29/0.50      ! [B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( inf_in2572325071724192079at_nat @ bot_bo2099793752762293965at_nat @ B2 )
% 0.29/0.50        = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_empty_left
% 0.29/0.50  thf(fact_1219_Int__empty__left,axiom,
% 0.29/0.50      ! [B2: set_o] :
% 0.29/0.50        ( ( inf_inf_set_o @ bot_bot_set_o @ B2 )
% 0.29/0.50        = bot_bot_set_o ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_empty_left
% 0.29/0.50  thf(fact_1220_Int__empty__left,axiom,
% 0.29/0.50      ! [B2: set_nat] :
% 0.29/0.50        ( ( inf_inf_set_nat @ bot_bot_set_nat @ B2 )
% 0.29/0.50        = bot_bot_set_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_empty_left
% 0.29/0.50  thf(fact_1221_Int__empty__left,axiom,
% 0.29/0.50      ! [B2: set_int] :
% 0.29/0.50        ( ( inf_inf_set_int @ bot_bot_set_int @ B2 )
% 0.29/0.50        = bot_bot_set_int ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_empty_left
% 0.29/0.50  thf(fact_1222_Int__empty__right,axiom,
% 0.29/0.50      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( inf_in2572325071724192079at_nat @ A2 @ bot_bo2099793752762293965at_nat )
% 0.29/0.50        = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_empty_right
% 0.29/0.50  thf(fact_1223_Int__empty__right,axiom,
% 0.29/0.50      ! [A2: set_o] :
% 0.29/0.50        ( ( inf_inf_set_o @ A2 @ bot_bot_set_o )
% 0.29/0.50        = bot_bot_set_o ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_empty_right
% 0.29/0.50  thf(fact_1224_Int__empty__right,axiom,
% 0.29/0.50      ! [A2: set_nat] :
% 0.29/0.50        ( ( inf_inf_set_nat @ A2 @ bot_bot_set_nat )
% 0.29/0.50        = bot_bot_set_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_empty_right
% 0.29/0.50  thf(fact_1225_Int__empty__right,axiom,
% 0.29/0.50      ! [A2: set_int] :
% 0.29/0.50        ( ( inf_inf_set_int @ A2 @ bot_bot_set_int )
% 0.29/0.50        = bot_bot_set_int ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_empty_right
% 0.29/0.50  thf(fact_1226_disjoint__iff__not__equal,axiom,
% 0.29/0.50      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 0.29/0.50          = bot_bo2099793752762293965at_nat )
% 0.29/0.50        = ( ! [X3: product_prod_nat_nat] :
% 0.29/0.50              ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 0.29/0.50             => ! [Y3: product_prod_nat_nat] :
% 0.29/0.50                  ( ( member8440522571783428010at_nat @ Y3 @ B2 )
% 0.29/0.50                 => ( X3 != Y3 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % disjoint_iff_not_equal
% 0.29/0.50  thf(fact_1227_disjoint__iff__not__equal,axiom,
% 0.29/0.50      ! [A2: set_o,B2: set_o] :
% 0.29/0.50        ( ( ( inf_inf_set_o @ A2 @ B2 )
% 0.29/0.50          = bot_bot_set_o )
% 0.29/0.50        = ( ! [X3: $o] :
% 0.29/0.50              ( ( member_o @ X3 @ A2 )
% 0.29/0.50             => ! [Y3: $o] :
% 0.29/0.50                  ( ( member_o @ Y3 @ B2 )
% 0.29/0.50                 => ( X3 = ( ~ Y3 ) ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % disjoint_iff_not_equal
% 0.29/0.50  thf(fact_1228_disjoint__iff__not__equal,axiom,
% 0.29/0.50      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.50        ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 0.29/0.50          = bot_bot_set_nat )
% 0.29/0.50        = ( ! [X3: nat] :
% 0.29/0.50              ( ( member_nat @ X3 @ A2 )
% 0.29/0.50             => ! [Y3: nat] :
% 0.29/0.50                  ( ( member_nat @ Y3 @ B2 )
% 0.29/0.50                 => ( X3 != Y3 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % disjoint_iff_not_equal
% 0.29/0.50  thf(fact_1229_disjoint__iff__not__equal,axiom,
% 0.29/0.50      ! [A2: set_int,B2: set_int] :
% 0.29/0.50        ( ( ( inf_inf_set_int @ A2 @ B2 )
% 0.29/0.50          = bot_bot_set_int )
% 0.29/0.50        = ( ! [X3: int] :
% 0.29/0.50              ( ( member_int @ X3 @ A2 )
% 0.29/0.50             => ! [Y3: int] :
% 0.29/0.50                  ( ( member_int @ Y3 @ B2 )
% 0.29/0.50                 => ( X3 != Y3 ) ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % disjoint_iff_not_equal
% 0.29/0.50  thf(fact_1230_Un__empty__left,axiom,
% 0.29/0.50      ! [B2: set_Pr8551490117392284871at_nat] :
% 0.29/0.50        ( ( sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat @ B2 )
% 0.29/0.50        = B2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_empty_left
% 0.29/0.50  thf(fact_1231_Un__empty__left,axiom,
% 0.29/0.50      ! [B2: set_Pr4329608150637261639at_nat] :
% 0.29/0.50        ( ( sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat @ B2 )
% 0.29/0.50        = B2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_empty_left
% 0.29/0.50  thf(fact_1232_Un__empty__left,axiom,
% 0.29/0.50      ! [B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat @ B2 )
% 0.29/0.50        = B2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_empty_left
% 0.29/0.50  thf(fact_1233_Un__empty__left,axiom,
% 0.29/0.50      ! [B2: set_o] :
% 0.29/0.50        ( ( sup_sup_set_o @ bot_bot_set_o @ B2 )
% 0.29/0.50        = B2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_empty_left
% 0.29/0.50  thf(fact_1234_Un__empty__left,axiom,
% 0.29/0.50      ! [B2: set_nat] :
% 0.29/0.50        ( ( sup_sup_set_nat @ bot_bot_set_nat @ B2 )
% 0.29/0.50        = B2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_empty_left
% 0.29/0.50  thf(fact_1235_Un__empty__left,axiom,
% 0.29/0.50      ! [B2: set_int] :
% 0.29/0.50        ( ( sup_sup_set_int @ bot_bot_set_int @ B2 )
% 0.29/0.50        = B2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_empty_left
% 0.29/0.50  thf(fact_1236_Un__empty__right,axiom,
% 0.29/0.50      ! [A2: set_Pr8551490117392284871at_nat] :
% 0.29/0.50        ( ( sup_su3035147773818789531at_nat @ A2 @ bot_bo8422036546324065075at_nat )
% 0.29/0.50        = A2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_empty_right
% 0.29/0.50  thf(fact_1237_Un__empty__right,axiom,
% 0.29/0.50      ! [A2: set_Pr4329608150637261639at_nat] :
% 0.29/0.50        ( ( sup_su5525570899277871387at_nat @ A2 @ bot_bo228742789529271731at_nat )
% 0.29/0.50        = A2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_empty_right
% 0.29/0.50  thf(fact_1238_Un__empty__right,axiom,
% 0.29/0.50      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( sup_su6327502436637775413at_nat @ A2 @ bot_bo2099793752762293965at_nat )
% 0.29/0.50        = A2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_empty_right
% 0.29/0.50  thf(fact_1239_Un__empty__right,axiom,
% 0.29/0.50      ! [A2: set_o] :
% 0.29/0.50        ( ( sup_sup_set_o @ A2 @ bot_bot_set_o )
% 0.29/0.50        = A2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_empty_right
% 0.29/0.50  thf(fact_1240_Un__empty__right,axiom,
% 0.29/0.50      ! [A2: set_nat] :
% 0.29/0.50        ( ( sup_sup_set_nat @ A2 @ bot_bot_set_nat )
% 0.29/0.50        = A2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_empty_right
% 0.29/0.50  thf(fact_1241_Un__empty__right,axiom,
% 0.29/0.50      ! [A2: set_int] :
% 0.29/0.50        ( ( sup_sup_set_int @ A2 @ bot_bot_set_int )
% 0.29/0.50        = A2 ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_empty_right
% 0.29/0.50  thf(fact_1242_Compl__Un,axiom,
% 0.29/0.50      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( uminus6524753893492686040at_nat @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 0.29/0.50        = ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ A2 ) @ ( uminus6524753893492686040at_nat @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_Un
% 0.29/0.50  thf(fact_1243_Compl__Un,axiom,
% 0.29/0.50      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 0.29/0.50        ( ( uminus2330091110623919550at_nat @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 0.29/0.50        = ( inf_in1697001100524423349at_nat @ ( uminus2330091110623919550at_nat @ A2 ) @ ( uminus2330091110623919550at_nat @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_Un
% 0.29/0.50  thf(fact_1244_Compl__Un,axiom,
% 0.29/0.50      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.29/0.50        ( ( uminus935396558254630718at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 0.29/0.50        = ( inf_in7913087082777306421at_nat @ ( uminus935396558254630718at_nat @ A2 ) @ ( uminus935396558254630718at_nat @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_Un
% 0.29/0.50  thf(fact_1245_Compl__Un,axiom,
% 0.29/0.50      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.50        ( ( uminus5710092332889474511et_nat @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.29/0.50        = ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( uminus5710092332889474511et_nat @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_Un
% 0.29/0.50  thf(fact_1246_Compl__Int,axiom,
% 0.29/0.50      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( uminus6524753893492686040at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 0.29/0.50        = ( sup_su6327502436637775413at_nat @ ( uminus6524753893492686040at_nat @ A2 ) @ ( uminus6524753893492686040at_nat @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_Int
% 0.29/0.50  thf(fact_1247_Compl__Int,axiom,
% 0.29/0.50      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 0.29/0.50        ( ( uminus2330091110623919550at_nat @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) )
% 0.29/0.50        = ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ A2 ) @ ( uminus2330091110623919550at_nat @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_Int
% 0.29/0.50  thf(fact_1248_Compl__Int,axiom,
% 0.29/0.50      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.29/0.50        ( ( uminus935396558254630718at_nat @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) )
% 0.29/0.50        = ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ A2 ) @ ( uminus935396558254630718at_nat @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_Int
% 0.29/0.50  thf(fact_1249_Compl__Int,axiom,
% 0.29/0.50      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.50        ( ( uminus5710092332889474511et_nat @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.29/0.50        = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( uminus5710092332889474511et_nat @ B2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Compl_Int
% 0.29/0.50  thf(fact_1250_Un__Int__crazy,axiom,
% 0.29/0.50      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( sup_su6327502436637775413at_nat @ ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) ) @ ( inf_in2572325071724192079at_nat @ C2 @ A2 ) )
% 0.29/0.50        = ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) @ ( sup_su6327502436637775413at_nat @ B2 @ C2 ) ) @ ( sup_su6327502436637775413at_nat @ C2 @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_Int_crazy
% 0.29/0.50  thf(fact_1251_Un__Int__crazy,axiom,
% 0.29/0.50      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 0.29/0.50        ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) @ ( inf_in1697001100524423349at_nat @ B2 @ C2 ) ) @ ( inf_in1697001100524423349at_nat @ C2 @ A2 ) )
% 0.29/0.50        = ( inf_in1697001100524423349at_nat @ ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) @ ( sup_su3035147773818789531at_nat @ B2 @ C2 ) ) @ ( sup_su3035147773818789531at_nat @ C2 @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_Int_crazy
% 0.29/0.50  thf(fact_1252_Un__Int__crazy,axiom,
% 0.29/0.50      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 0.29/0.50        ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) @ ( inf_in7913087082777306421at_nat @ B2 @ C2 ) ) @ ( inf_in7913087082777306421at_nat @ C2 @ A2 ) )
% 0.29/0.50        = ( inf_in7913087082777306421at_nat @ ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) ) @ ( sup_su5525570899277871387at_nat @ C2 @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_Int_crazy
% 0.29/0.50  thf(fact_1253_Un__Int__crazy,axiom,
% 0.29/0.50      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 0.29/0.50        ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ ( inf_inf_set_nat @ B2 @ C2 ) ) @ ( inf_inf_set_nat @ C2 @ A2 ) )
% 0.29/0.50        = ( inf_inf_set_nat @ ( inf_inf_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ ( sup_sup_set_nat @ B2 @ C2 ) ) @ ( sup_sup_set_nat @ C2 @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_Int_crazy
% 0.29/0.50  thf(fact_1254_Int__Un__distrib,axiom,
% 0.29/0.50      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( inf_in2572325071724192079at_nat @ A2 @ ( sup_su6327502436637775413at_nat @ B2 @ C2 ) )
% 0.29/0.50        = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ ( inf_in2572325071724192079at_nat @ A2 @ C2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_Un_distrib
% 0.29/0.50  thf(fact_1255_Int__Un__distrib,axiom,
% 0.29/0.50      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 0.29/0.50        ( ( inf_in1697001100524423349at_nat @ A2 @ ( sup_su3035147773818789531at_nat @ B2 @ C2 ) )
% 0.29/0.50        = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) @ ( inf_in1697001100524423349at_nat @ A2 @ C2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_Un_distrib
% 0.29/0.50  thf(fact_1256_Int__Un__distrib,axiom,
% 0.29/0.50      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 0.29/0.50        ( ( inf_in7913087082777306421at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) )
% 0.29/0.50        = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) @ ( inf_in7913087082777306421at_nat @ A2 @ C2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_Un_distrib
% 0.29/0.50  thf(fact_1257_Int__Un__distrib,axiom,
% 0.29/0.50      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 0.29/0.50        ( ( inf_inf_set_nat @ A2 @ ( sup_sup_set_nat @ B2 @ C2 ) )
% 0.29/0.50        = ( sup_sup_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ ( inf_inf_set_nat @ A2 @ C2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_Un_distrib
% 0.29/0.50  thf(fact_1258_Un__Int__distrib,axiom,
% 0.29/0.50      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( sup_su6327502436637775413at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) )
% 0.29/0.50        = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) @ ( sup_su6327502436637775413at_nat @ A2 @ C2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_Int_distrib
% 0.29/0.50  thf(fact_1259_Un__Int__distrib,axiom,
% 0.29/0.50      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 0.29/0.50        ( ( sup_su3035147773818789531at_nat @ A2 @ ( inf_in1697001100524423349at_nat @ B2 @ C2 ) )
% 0.29/0.50        = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) @ ( sup_su3035147773818789531at_nat @ A2 @ C2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_Int_distrib
% 0.29/0.50  thf(fact_1260_Un__Int__distrib,axiom,
% 0.29/0.50      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 0.29/0.50        ( ( sup_su5525570899277871387at_nat @ A2 @ ( inf_in7913087082777306421at_nat @ B2 @ C2 ) )
% 0.29/0.50        = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) @ ( sup_su5525570899277871387at_nat @ A2 @ C2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_Int_distrib
% 0.29/0.50  thf(fact_1261_Un__Int__distrib,axiom,
% 0.29/0.50      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 0.29/0.50        ( ( sup_sup_set_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C2 ) )
% 0.29/0.50        = ( inf_inf_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ ( sup_sup_set_nat @ A2 @ C2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_Int_distrib
% 0.29/0.50  thf(fact_1262_Int__Un__distrib2,axiom,
% 0.29/0.50      ! [B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ B2 @ C2 ) @ A2 )
% 0.29/0.50        = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ B2 @ A2 ) @ ( inf_in2572325071724192079at_nat @ C2 @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_Un_distrib2
% 0.29/0.50  thf(fact_1263_Int__Un__distrib2,axiom,
% 0.29/0.50      ! [B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat,A2: set_Pr8551490117392284871at_nat] :
% 0.29/0.50        ( ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ B2 @ C2 ) @ A2 )
% 0.29/0.50        = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ B2 @ A2 ) @ ( inf_in1697001100524423349at_nat @ C2 @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_Un_distrib2
% 0.29/0.50  thf(fact_1264_Int__Un__distrib2,axiom,
% 0.29/0.50      ! [B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.29/0.50        ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) @ A2 )
% 0.29/0.50        = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ B2 @ A2 ) @ ( inf_in7913087082777306421at_nat @ C2 @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_Un_distrib2
% 0.29/0.50  thf(fact_1265_Int__Un__distrib2,axiom,
% 0.29/0.50      ! [B2: set_nat,C2: set_nat,A2: set_nat] :
% 0.29/0.50        ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ B2 @ C2 ) @ A2 )
% 0.29/0.50        = ( sup_sup_set_nat @ ( inf_inf_set_nat @ B2 @ A2 ) @ ( inf_inf_set_nat @ C2 @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Int_Un_distrib2
% 0.29/0.50  thf(fact_1266_Un__Int__distrib2,axiom,
% 0.29/0.50      ! [B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) @ A2 )
% 0.29/0.50        = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ B2 @ A2 ) @ ( sup_su6327502436637775413at_nat @ C2 @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_Int_distrib2
% 0.29/0.50  thf(fact_1267_Un__Int__distrib2,axiom,
% 0.29/0.50      ! [B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat,A2: set_Pr8551490117392284871at_nat] :
% 0.29/0.50        ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ B2 @ C2 ) @ A2 )
% 0.29/0.50        = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ B2 @ A2 ) @ ( sup_su3035147773818789531at_nat @ C2 @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_Int_distrib2
% 0.29/0.50  thf(fact_1268_Un__Int__distrib2,axiom,
% 0.29/0.50      ! [B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.29/0.50        ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ B2 @ C2 ) @ A2 )
% 0.29/0.50        = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ B2 @ A2 ) @ ( sup_su5525570899277871387at_nat @ C2 @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_Int_distrib2
% 0.29/0.50  thf(fact_1269_Un__Int__distrib2,axiom,
% 0.29/0.50      ! [B2: set_nat,C2: set_nat,A2: set_nat] :
% 0.29/0.50        ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ B2 @ C2 ) @ A2 )
% 0.29/0.50        = ( inf_inf_set_nat @ ( sup_sup_set_nat @ B2 @ A2 ) @ ( sup_sup_set_nat @ C2 @ A2 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Un_Int_distrib2
% 0.29/0.50  thf(fact_1270_mult__minus__right,axiom,
% 0.29/0.50      ! [A: int,B: int] :
% 0.29/0.50        ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 0.29/0.50        = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_minus_right
% 0.29/0.50  thf(fact_1271_mult__minus__right,axiom,
% 0.29/0.50      ! [A: code_integer,B: code_integer] :
% 0.29/0.50        ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.50        = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_minus_right
% 0.29/0.50  thf(fact_1272_mult__minus__right,axiom,
% 0.29/0.50      ! [A: rat,B: rat] :
% 0.29/0.50        ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.29/0.50        = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_minus_right
% 0.29/0.50  thf(fact_1273_minus__mult__minus,axiom,
% 0.29/0.50      ! [A: int,B: int] :
% 0.29/0.50        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 0.29/0.50        = ( times_times_int @ A @ B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % minus_mult_minus
% 0.29/0.50  thf(fact_1274_minus__mult__minus,axiom,
% 0.29/0.50      ! [A: code_integer,B: code_integer] :
% 0.29/0.50        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.50        = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % minus_mult_minus
% 0.29/0.50  thf(fact_1275_minus__mult__minus,axiom,
% 0.29/0.50      ! [A: rat,B: rat] :
% 0.29/0.50        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.29/0.50        = ( times_times_rat @ A @ B ) ) ).
% 0.29/0.50  
% 0.29/0.50  % minus_mult_minus
% 0.29/0.50  thf(fact_1276_mult__minus__left,axiom,
% 0.29/0.50      ! [A: int,B: int] :
% 0.29/0.50        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 0.29/0.50        = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_minus_left
% 0.29/0.50  thf(fact_1277_mult__minus__left,axiom,
% 0.29/0.50      ! [A: code_integer,B: code_integer] :
% 0.29/0.50        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.29/0.50        = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_minus_left
% 0.29/0.50  thf(fact_1278_mult__minus__left,axiom,
% 0.29/0.50      ! [A: rat,B: rat] :
% 0.29/0.50        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.29/0.50        = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % mult_minus_left
% 0.29/0.50  thf(fact_1279_square__eq__1__iff,axiom,
% 0.29/0.50      ! [X: int] :
% 0.29/0.50        ( ( ( times_times_int @ X @ X )
% 0.29/0.50          = one_one_int )
% 0.29/0.50        = ( ( X = one_one_int )
% 0.29/0.50          | ( X
% 0.29/0.50            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % square_eq_1_iff
% 0.29/0.50  thf(fact_1280_square__eq__1__iff,axiom,
% 0.29/0.50      ! [X: code_integer] :
% 0.29/0.50        ( ( ( times_3573771949741848930nteger @ X @ X )
% 0.29/0.50          = one_one_Code_integer )
% 0.29/0.50        = ( ( X = one_one_Code_integer )
% 0.29/0.50          | ( X
% 0.29/0.50            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % square_eq_1_iff
% 0.29/0.50  thf(fact_1281_square__eq__1__iff,axiom,
% 0.29/0.50      ! [X: rat] :
% 0.29/0.50        ( ( ( times_times_rat @ X @ X )
% 0.29/0.50          = one_one_rat )
% 0.29/0.50        = ( ( X = one_one_rat )
% 0.29/0.50          | ( X
% 0.29/0.50            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % square_eq_1_iff
% 0.29/0.50  thf(fact_1282_verit__minus__simplify_I4_J,axiom,
% 0.29/0.50      ! [B: int] :
% 0.29/0.50        ( ( uminus_uminus_int @ ( uminus_uminus_int @ B ) )
% 0.29/0.50        = B ) ).
% 0.29/0.50  
% 0.29/0.50  % verit_minus_simplify(4)
% 0.29/0.50  thf(fact_1283_verit__minus__simplify_I4_J,axiom,
% 0.29/0.50      ! [B: code_integer] :
% 0.29/0.50        ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.50        = B ) ).
% 0.29/0.50  
% 0.29/0.50  % verit_minus_simplify(4)
% 0.29/0.50  thf(fact_1284_verit__minus__simplify_I4_J,axiom,
% 0.29/0.50      ! [B: rat] :
% 0.29/0.50        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ B ) )
% 0.29/0.50        = B ) ).
% 0.29/0.50  
% 0.29/0.50  % verit_minus_simplify(4)
% 0.29/0.50  thf(fact_1285_old_Oprod_Oinject,axiom,
% 0.29/0.50      ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 0.29/0.50        ( ( ( produc8603105652947943368nteger @ A @ B )
% 0.29/0.50          = ( produc8603105652947943368nteger @ A5 @ B5 ) )
% 0.29/0.50        = ( ( A = A5 )
% 0.29/0.50          & ( B = B5 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % old.prod.inject
% 0.29/0.50  thf(fact_1286_old_Oprod_Oinject,axiom,
% 0.29/0.50      ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A5: produc3658429121746597890et_nat > $o,B5: produc3658429121746597890et_nat] :
% 0.29/0.50        ( ( ( produc5001842942810119800et_nat @ A @ B )
% 0.29/0.50          = ( produc5001842942810119800et_nat @ A5 @ B5 ) )
% 0.29/0.50        = ( ( A = A5 )
% 0.29/0.50          & ( B = B5 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % old.prod.inject
% 0.29/0.50  thf(fact_1287_old_Oprod_Oinject,axiom,
% 0.29/0.50      ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A5: produc3658429121746597890et_nat > $o,B5: produc3925858234332021118et_nat] :
% 0.29/0.50        ( ( ( produc2245416461498447860et_nat @ A @ B )
% 0.29/0.50          = ( produc2245416461498447860et_nat @ A5 @ B5 ) )
% 0.29/0.50        = ( ( A = A5 )
% 0.29/0.50          & ( B = B5 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % old.prod.inject
% 0.29/0.50  thf(fact_1288_old_Oprod_Oinject,axiom,
% 0.29/0.50      ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: product_prod_int_int] :
% 0.29/0.50        ( ( ( produc5700946648718959541nt_int @ A @ B )
% 0.29/0.50          = ( produc5700946648718959541nt_int @ A5 @ B5 ) )
% 0.29/0.50        = ( ( A = A5 )
% 0.29/0.50          & ( B = B5 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % old.prod.inject
% 0.29/0.50  thf(fact_1289_old_Oprod_Oinject,axiom,
% 0.29/0.50      ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A5: int > option6357759511663192854e_term,B5: product_prod_int_int] :
% 0.29/0.50        ( ( ( produc4305682042979456191nt_int @ A @ B )
% 0.29/0.50          = ( produc4305682042979456191nt_int @ A5 @ B5 ) )
% 0.29/0.50        = ( ( A = A5 )
% 0.29/0.50          & ( B = B5 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % old.prod.inject
% 0.29/0.50  thf(fact_1290_prod_Oinject,axiom,
% 0.29/0.50      ! [X1: produc6241069584506657477e_term > option6357759511663192854e_term,X22: produc8923325533196201883nteger,Y1: produc6241069584506657477e_term > option6357759511663192854e_term,Y22: produc8923325533196201883nteger] :
% 0.29/0.50        ( ( ( produc8603105652947943368nteger @ X1 @ X22 )
% 0.29/0.50          = ( produc8603105652947943368nteger @ Y1 @ Y22 ) )
% 0.29/0.50        = ( ( X1 = Y1 )
% 0.29/0.50          & ( X22 = Y22 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % prod.inject
% 0.29/0.50  thf(fact_1291_prod_Oinject,axiom,
% 0.29/0.50      ! [X1: produc3658429121746597890et_nat > $o,X22: produc3658429121746597890et_nat,Y1: produc3658429121746597890et_nat > $o,Y22: produc3658429121746597890et_nat] :
% 0.29/0.50        ( ( ( produc5001842942810119800et_nat @ X1 @ X22 )
% 0.29/0.50          = ( produc5001842942810119800et_nat @ Y1 @ Y22 ) )
% 0.29/0.50        = ( ( X1 = Y1 )
% 0.29/0.50          & ( X22 = Y22 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % prod.inject
% 0.29/0.50  thf(fact_1292_prod_Oinject,axiom,
% 0.29/0.50      ! [X1: produc3658429121746597890et_nat > $o,X22: produc3925858234332021118et_nat,Y1: produc3658429121746597890et_nat > $o,Y22: produc3925858234332021118et_nat] :
% 0.29/0.50        ( ( ( produc2245416461498447860et_nat @ X1 @ X22 )
% 0.29/0.50          = ( produc2245416461498447860et_nat @ Y1 @ Y22 ) )
% 0.29/0.50        = ( ( X1 = Y1 )
% 0.29/0.50          & ( X22 = Y22 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % prod.inject
% 0.29/0.50  thf(fact_1293_prod_Oinject,axiom,
% 0.29/0.50      ! [X1: produc8551481072490612790e_term > option6357759511663192854e_term,X22: product_prod_int_int,Y1: produc8551481072490612790e_term > option6357759511663192854e_term,Y22: product_prod_int_int] :
% 0.29/0.50        ( ( ( produc5700946648718959541nt_int @ X1 @ X22 )
% 0.29/0.50          = ( produc5700946648718959541nt_int @ Y1 @ Y22 ) )
% 0.29/0.50        = ( ( X1 = Y1 )
% 0.29/0.50          & ( X22 = Y22 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % prod.inject
% 0.29/0.50  thf(fact_1294_prod_Oinject,axiom,
% 0.29/0.50      ! [X1: int > option6357759511663192854e_term,X22: product_prod_int_int,Y1: int > option6357759511663192854e_term,Y22: product_prod_int_int] :
% 0.29/0.50        ( ( ( produc4305682042979456191nt_int @ X1 @ X22 )
% 0.29/0.50          = ( produc4305682042979456191nt_int @ Y1 @ Y22 ) )
% 0.29/0.50        = ( ( X1 = Y1 )
% 0.29/0.50          & ( X22 = Y22 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % prod.inject
% 0.29/0.50  thf(fact_1295_lambda__one,axiom,
% 0.29/0.50      ( ( ^ [X3: code_integer] : X3 )
% 0.29/0.50      = ( times_3573771949741848930nteger @ one_one_Code_integer ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lambda_one
% 0.29/0.50  thf(fact_1296_lambda__one,axiom,
% 0.29/0.50      ( ( ^ [X3: assn] : X3 )
% 0.29/0.50      = ( times_times_assn @ one_one_assn ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lambda_one
% 0.29/0.50  thf(fact_1297_lambda__one,axiom,
% 0.29/0.50      ( ( ^ [X3: rat] : X3 )
% 0.29/0.50      = ( times_times_rat @ one_one_rat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lambda_one
% 0.29/0.50  thf(fact_1298_lambda__one,axiom,
% 0.29/0.50      ( ( ^ [X3: nat] : X3 )
% 0.29/0.50      = ( times_times_nat @ one_one_nat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lambda_one
% 0.29/0.50  thf(fact_1299_lambda__one,axiom,
% 0.29/0.50      ( ( ^ [X3: int] : X3 )
% 0.29/0.50      = ( times_times_int @ one_one_int ) ) ).
% 0.29/0.50  
% 0.29/0.50  % lambda_one
% 0.29/0.50  thf(fact_1300_disjointI,axiom,
% 0.29/0.50      ! [A: set_se6260736226359567993nt_int,B: set_se6260736226359567993nt_int] :
% 0.29/0.50        ( ! [X2: set_Pr958786334691620121nt_int] :
% 0.29/0.50            ( ( member2340774599025711042nt_int @ X2 @ A )
% 0.29/0.50           => ~ ( member2340774599025711042nt_int @ X2 @ B ) )
% 0.29/0.50       => ( ( inf_in8396524679539076455nt_int @ A @ B )
% 0.29/0.50          = bot_bo1488462491386950373nt_int ) ) ).
% 0.29/0.50  
% 0.29/0.50  % disjointI
% 0.29/0.50  thf(fact_1301_disjointI,axiom,
% 0.29/0.50      ! [A: set_set_nat,B: set_set_nat] :
% 0.29/0.50        ( ! [X2: set_nat] :
% 0.29/0.50            ( ( member_set_nat @ X2 @ A )
% 0.29/0.50           => ~ ( member_set_nat @ X2 @ B ) )
% 0.29/0.50       => ( ( inf_inf_set_set_nat @ A @ B )
% 0.29/0.50          = bot_bot_set_set_nat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % disjointI
% 0.29/0.50  thf(fact_1302_disjointI,axiom,
% 0.29/0.50      ! [A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50        ( ! [X2: produc3658429121746597890et_nat > $o] :
% 0.29/0.50            ( ( member6576561426505652726_nat_o @ X2 @ A )
% 0.29/0.50           => ~ ( member6576561426505652726_nat_o @ X2 @ B ) )
% 0.29/0.50       => ( ( inf_in1906310914598751387_nat_o @ A @ B )
% 0.29/0.50          = bot_bo7824918357723582233_nat_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % disjointI
% 0.29/0.50  thf(fact_1303_disjointI,axiom,
% 0.29/0.50      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.29/0.50        ( ! [X2: product_prod_nat_nat] :
% 0.29/0.50            ( ( member8440522571783428010at_nat @ X2 @ A )
% 0.29/0.50           => ~ ( member8440522571783428010at_nat @ X2 @ B ) )
% 0.29/0.50       => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 0.29/0.50          = bot_bo2099793752762293965at_nat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % disjointI
% 0.29/0.50  thf(fact_1304_disjointI,axiom,
% 0.29/0.50      ! [A: set_o,B: set_o] :
% 0.29/0.50        ( ! [X2: $o] :
% 0.29/0.50            ( ( member_o @ X2 @ A )
% 0.29/0.50           => ~ ( member_o @ X2 @ B ) )
% 0.29/0.50       => ( ( inf_inf_set_o @ A @ B )
% 0.29/0.50          = bot_bot_set_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % disjointI
% 0.29/0.50  thf(fact_1305_disjointI,axiom,
% 0.29/0.50      ! [A: set_nat,B: set_nat] :
% 0.29/0.50        ( ! [X2: nat] :
% 0.29/0.50            ( ( member_nat @ X2 @ A )
% 0.29/0.50           => ~ ( member_nat @ X2 @ B ) )
% 0.29/0.50       => ( ( inf_inf_set_nat @ A @ B )
% 0.29/0.50          = bot_bot_set_nat ) ) ).
% 0.29/0.50  
% 0.29/0.50  % disjointI
% 0.29/0.50  thf(fact_1306_disjointI,axiom,
% 0.29/0.50      ! [A: set_int,B: set_int] :
% 0.29/0.50        ( ! [X2: int] :
% 0.29/0.50            ( ( member_int @ X2 @ A )
% 0.29/0.50           => ~ ( member_int @ X2 @ B ) )
% 0.29/0.50       => ( ( inf_inf_set_int @ A @ B )
% 0.29/0.50          = bot_bot_set_int ) ) ).
% 0.29/0.50  
% 0.29/0.50  % disjointI
% 0.29/0.50  thf(fact_1307_minus__mult__commute,axiom,
% 0.29/0.50      ! [A: int,B: int] :
% 0.29/0.50        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 0.29/0.50        = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % minus_mult_commute
% 0.29/0.50  thf(fact_1308_minus__mult__commute,axiom,
% 0.29/0.50      ! [A: code_integer,B: code_integer] :
% 0.29/0.50        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.29/0.50        = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % minus_mult_commute
% 0.29/0.50  thf(fact_1309_minus__mult__commute,axiom,
% 0.29/0.50      ! [A: rat,B: rat] :
% 0.29/0.50        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.29/0.50        = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % minus_mult_commute
% 0.29/0.50  thf(fact_1310_square__eq__iff,axiom,
% 0.29/0.50      ! [A: int,B: int] :
% 0.29/0.50        ( ( ( times_times_int @ A @ A )
% 0.29/0.50          = ( times_times_int @ B @ B ) )
% 0.29/0.50        = ( ( A = B )
% 0.29/0.50          | ( A
% 0.29/0.50            = ( uminus_uminus_int @ B ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % square_eq_iff
% 0.29/0.50  thf(fact_1311_square__eq__iff,axiom,
% 0.29/0.50      ! [A: code_integer,B: code_integer] :
% 0.29/0.50        ( ( ( times_3573771949741848930nteger @ A @ A )
% 0.29/0.50          = ( times_3573771949741848930nteger @ B @ B ) )
% 0.29/0.50        = ( ( A = B )
% 0.29/0.50          | ( A
% 0.29/0.50            = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % square_eq_iff
% 0.29/0.50  thf(fact_1312_square__eq__iff,axiom,
% 0.29/0.50      ! [A: rat,B: rat] :
% 0.29/0.50        ( ( ( times_times_rat @ A @ A )
% 0.29/0.50          = ( times_times_rat @ B @ B ) )
% 0.29/0.50        = ( ( A = B )
% 0.29/0.50          | ( A
% 0.29/0.50            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % square_eq_iff
% 0.29/0.50  thf(fact_1313_UNIV__I,axiom,
% 0.29/0.50      ! [X: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X @ top_to6034159466715884489nt_int ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_I
% 0.29/0.50  thf(fact_1314_UNIV__I,axiom,
% 0.29/0.50      ! [X: set_nat] : ( member_set_nat @ X @ top_top_set_set_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_I
% 0.29/0.50  thf(fact_1315_UNIV__I,axiom,
% 0.29/0.50      ! [X: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X @ top_to4869887016220417533_nat_o ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_I
% 0.29/0.50  thf(fact_1316_UNIV__I,axiom,
% 0.29/0.50      ! [X: list_nat] : ( member_list_nat @ X @ top_top_set_list_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_I
% 0.29/0.50  thf(fact_1317_UNIV__I,axiom,
% 0.29/0.50      ! [X: $o] : ( member_o @ X @ top_top_set_o ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_I
% 0.29/0.50  thf(fact_1318_UNIV__I,axiom,
% 0.29/0.50      ! [X: rat] : ( member_rat @ X @ top_top_set_rat ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_I
% 0.29/0.50  thf(fact_1319_UNIV__I,axiom,
% 0.29/0.50      ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_I
% 0.29/0.50  thf(fact_1320_UNIV__I,axiom,
% 0.29/0.50      ! [X: int] : ( member_int @ X @ top_top_set_int ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_I
% 0.29/0.50  thf(fact_1321_inf1I,axiom,
% 0.29/0.50      ! [A2: product_prod_int_int > $o,X: product_prod_int_int,B2: product_prod_int_int > $o] :
% 0.29/0.50        ( ( A2 @ X )
% 0.29/0.50       => ( ( B2 @ X )
% 0.29/0.50         => ( inf_in3604695632404883862_int_o @ A2 @ B2 @ X ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inf1I
% 0.29/0.50  thf(fact_1322_inf1I,axiom,
% 0.29/0.50      ! [A2: list_char > $o,X: list_char,B2: list_char > $o] :
% 0.29/0.50        ( ( A2 @ X )
% 0.29/0.50       => ( ( B2 @ X )
% 0.29/0.50         => ( inf_inf_list_char_o @ A2 @ B2 @ X ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inf1I
% 0.29/0.50  thf(fact_1323_UNIV__def,axiom,
% 0.29/0.50      ( top_to6034159466715884489nt_int
% 0.29/0.50      = ( collec5210948495886036740nt_int
% 0.29/0.50        @ ^ [X3: set_Pr958786334691620121nt_int] : $true ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_def
% 0.29/0.50  thf(fact_1324_UNIV__def,axiom,
% 0.29/0.50      ( top_top_set_set_nat
% 0.29/0.50      = ( collect_set_nat
% 0.29/0.50        @ ^ [X3: set_nat] : $true ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_def
% 0.29/0.50  thf(fact_1325_UNIV__def,axiom,
% 0.29/0.50      ( top_to4869887016220417533_nat_o
% 0.29/0.50      = ( collec939566748876313656_nat_o
% 0.29/0.50        @ ^ [X3: produc3658429121746597890et_nat > $o] : $true ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_def
% 0.29/0.50  thf(fact_1326_UNIV__def,axiom,
% 0.29/0.50      ( top_top_set_list_nat
% 0.29/0.50      = ( collect_list_nat
% 0.29/0.50        @ ^ [X3: list_nat] : $true ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_def
% 0.29/0.50  thf(fact_1327_UNIV__def,axiom,
% 0.29/0.50      ( top_top_set_o
% 0.29/0.50      = ( collect_o
% 0.29/0.50        @ ^ [X3: $o] : $true ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_def
% 0.29/0.50  thf(fact_1328_UNIV__def,axiom,
% 0.29/0.50      ( top_top_set_rat
% 0.29/0.50      = ( collect_rat
% 0.29/0.50        @ ^ [X3: rat] : $true ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_def
% 0.29/0.50  thf(fact_1329_UNIV__def,axiom,
% 0.29/0.50      ( top_top_set_nat
% 0.29/0.50      = ( collect_nat
% 0.29/0.50        @ ^ [X3: nat] : $true ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_def
% 0.29/0.50  thf(fact_1330_UNIV__def,axiom,
% 0.29/0.50      ( top_top_set_int
% 0.29/0.50      = ( collect_int
% 0.29/0.50        @ ^ [X3: int] : $true ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_def
% 0.29/0.50  thf(fact_1331_UNIV__eq__I,axiom,
% 0.29/0.50      ! [A2: set_se6260736226359567993nt_int] :
% 0.29/0.50        ( ! [X2: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X2 @ A2 )
% 0.29/0.50       => ( top_to6034159466715884489nt_int = A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_eq_I
% 0.29/0.50  thf(fact_1332_UNIV__eq__I,axiom,
% 0.29/0.50      ! [A2: set_set_nat] :
% 0.29/0.50        ( ! [X2: set_nat] : ( member_set_nat @ X2 @ A2 )
% 0.29/0.50       => ( top_top_set_set_nat = A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_eq_I
% 0.29/0.50  thf(fact_1333_UNIV__eq__I,axiom,
% 0.29/0.50      ! [A2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.50        ( ! [X2: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X2 @ A2 )
% 0.29/0.50       => ( top_to4869887016220417533_nat_o = A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_eq_I
% 0.29/0.50  thf(fact_1334_UNIV__eq__I,axiom,
% 0.29/0.50      ! [A2: set_list_nat] :
% 0.29/0.50        ( ! [X2: list_nat] : ( member_list_nat @ X2 @ A2 )
% 0.29/0.50       => ( top_top_set_list_nat = A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_eq_I
% 0.29/0.50  thf(fact_1335_UNIV__eq__I,axiom,
% 0.29/0.50      ! [A2: set_o] :
% 0.29/0.50        ( ! [X2: $o] : ( member_o @ X2 @ A2 )
% 0.29/0.50       => ( top_top_set_o = A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_eq_I
% 0.29/0.50  thf(fact_1336_UNIV__eq__I,axiom,
% 0.29/0.50      ! [A2: set_rat] :
% 0.29/0.50        ( ! [X2: rat] : ( member_rat @ X2 @ A2 )
% 0.29/0.50       => ( top_top_set_rat = A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_eq_I
% 0.29/0.50  thf(fact_1337_UNIV__eq__I,axiom,
% 0.29/0.50      ! [A2: set_nat] :
% 0.29/0.50        ( ! [X2: nat] : ( member_nat @ X2 @ A2 )
% 0.29/0.50       => ( top_top_set_nat = A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_eq_I
% 0.29/0.50  thf(fact_1338_UNIV__eq__I,axiom,
% 0.29/0.50      ! [A2: set_int] :
% 0.29/0.50        ( ! [X2: int] : ( member_int @ X2 @ A2 )
% 0.29/0.50       => ( top_top_set_int = A2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_eq_I
% 0.29/0.50  thf(fact_1339_top__set__def,axiom,
% 0.29/0.50      ( top_to6034159466715884489nt_int
% 0.29/0.50      = ( collec5210948495886036740nt_int @ top_to6187514276045680724_int_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % top_set_def
% 0.29/0.50  thf(fact_1340_top__set__def,axiom,
% 0.29/0.50      ( top_top_set_set_nat
% 0.29/0.50      = ( collect_set_nat @ top_top_set_nat_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % top_set_def
% 0.29/0.50  thf(fact_1341_top__set__def,axiom,
% 0.29/0.50      ( top_to4869887016220417533_nat_o
% 0.29/0.50      = ( collec939566748876313656_nat_o @ top_to2462227307520033056at_o_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % top_set_def
% 0.29/0.50  thf(fact_1342_top__set__def,axiom,
% 0.29/0.50      ( top_top_set_list_nat
% 0.29/0.50      = ( collect_list_nat @ top_top_list_nat_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % top_set_def
% 0.29/0.50  thf(fact_1343_top__set__def,axiom,
% 0.29/0.50      ( top_top_set_o
% 0.29/0.50      = ( collect_o @ top_top_o_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % top_set_def
% 0.29/0.50  thf(fact_1344_top__set__def,axiom,
% 0.29/0.50      ( top_top_set_rat
% 0.29/0.50      = ( collect_rat @ top_top_rat_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % top_set_def
% 0.29/0.50  thf(fact_1345_top__set__def,axiom,
% 0.29/0.50      ( top_top_set_nat
% 0.29/0.50      = ( collect_nat @ top_top_nat_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % top_set_def
% 0.29/0.50  thf(fact_1346_top__set__def,axiom,
% 0.29/0.50      ( top_top_set_int
% 0.29/0.50      = ( collect_int @ top_top_int_o ) ) ).
% 0.29/0.50  
% 0.29/0.50  % top_set_def
% 0.29/0.50  thf(fact_1347_UNIV__witness,axiom,
% 0.29/0.50      ? [X2: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X2 @ top_to6034159466715884489nt_int ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_witness
% 0.29/0.50  thf(fact_1348_UNIV__witness,axiom,
% 0.29/0.50      ? [X2: set_nat] : ( member_set_nat @ X2 @ top_top_set_set_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_witness
% 0.29/0.50  thf(fact_1349_UNIV__witness,axiom,
% 0.29/0.50      ? [X2: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X2 @ top_to4869887016220417533_nat_o ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_witness
% 0.29/0.50  thf(fact_1350_UNIV__witness,axiom,
% 0.29/0.50      ? [X2: list_nat] : ( member_list_nat @ X2 @ top_top_set_list_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_witness
% 0.29/0.50  thf(fact_1351_UNIV__witness,axiom,
% 0.29/0.50      ? [X2: $o] : ( member_o @ X2 @ top_top_set_o ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_witness
% 0.29/0.50  thf(fact_1352_UNIV__witness,axiom,
% 0.29/0.50      ? [X2: rat] : ( member_rat @ X2 @ top_top_set_rat ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_witness
% 0.29/0.50  thf(fact_1353_UNIV__witness,axiom,
% 0.29/0.50      ? [X2: nat] : ( member_nat @ X2 @ top_top_set_nat ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_witness
% 0.29/0.50  thf(fact_1354_UNIV__witness,axiom,
% 0.29/0.50      ? [X2: int] : ( member_int @ X2 @ top_top_set_int ) ).
% 0.29/0.50  
% 0.29/0.50  % UNIV_witness
% 0.29/0.50  thf(fact_1355_inf1D2,axiom,
% 0.29/0.50      ! [A2: product_prod_int_int > $o,B2: product_prod_int_int > $o,X: product_prod_int_int] :
% 0.29/0.50        ( ( inf_in3604695632404883862_int_o @ A2 @ B2 @ X )
% 0.29/0.50       => ( B2 @ X ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inf1D2
% 0.29/0.50  thf(fact_1356_inf1D2,axiom,
% 0.29/0.50      ! [A2: list_char > $o,B2: list_char > $o,X: list_char] :
% 0.29/0.50        ( ( inf_inf_list_char_o @ A2 @ B2 @ X )
% 0.29/0.50       => ( B2 @ X ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inf1D2
% 0.29/0.50  thf(fact_1357_inf1D1,axiom,
% 0.29/0.50      ! [A2: product_prod_int_int > $o,B2: product_prod_int_int > $o,X: product_prod_int_int] :
% 0.29/0.50        ( ( inf_in3604695632404883862_int_o @ A2 @ B2 @ X )
% 0.29/0.50       => ( A2 @ X ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inf1D1
% 0.29/0.50  thf(fact_1358_inf1D1,axiom,
% 0.29/0.50      ! [A2: list_char > $o,B2: list_char > $o,X: list_char] :
% 0.29/0.50        ( ( inf_inf_list_char_o @ A2 @ B2 @ X )
% 0.29/0.50       => ( A2 @ X ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inf1D1
% 0.29/0.50  thf(fact_1359_inf1E,axiom,
% 0.29/0.50      ! [A2: product_prod_int_int > $o,B2: product_prod_int_int > $o,X: product_prod_int_int] :
% 0.29/0.50        ( ( inf_in3604695632404883862_int_o @ A2 @ B2 @ X )
% 0.29/0.50       => ~ ( ( A2 @ X )
% 0.29/0.50           => ~ ( B2 @ X ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inf1E
% 0.29/0.50  thf(fact_1360_inf1E,axiom,
% 0.29/0.50      ! [A2: list_char > $o,B2: list_char > $o,X: list_char] :
% 0.29/0.50        ( ( inf_inf_list_char_o @ A2 @ B2 @ X )
% 0.29/0.50       => ~ ( ( A2 @ X )
% 0.29/0.50           => ~ ( B2 @ X ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % inf1E
% 0.29/0.50  thf(fact_1361_times__assn__raw_Ocases,axiom,
% 0.29/0.50      ! [X: produc2732055786443039994et_nat] :
% 0.29/0.50        ~ ! [P3: produc3658429121746597890et_nat > $o,Q3: produc3658429121746597890et_nat > $o,H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 0.29/0.50            ( X
% 0.29/0.50           != ( produc2245416461498447860et_nat @ P3 @ ( produc5001842942810119800et_nat @ Q3 @ ( produc7507926704131184380et_nat @ H @ As4 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % times_assn_raw.cases
% 0.29/0.50  thf(fact_1362_pairself_Ocases,axiom,
% 0.29/0.50      ! [X: produc7773217078559923341nt_int] :
% 0.29/0.50        ~ ! [F3: int > option6357759511663192854e_term,A6: int,B6: int] :
% 0.29/0.50            ( X
% 0.29/0.50           != ( produc4305682042979456191nt_int @ F3 @ ( product_Pair_int_int @ A6 @ B6 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % pairself.cases
% 0.29/0.50  thf(fact_1363_old_Oprod_Oexhaust,axiom,
% 0.29/0.50      ! [Y: produc1908205239877642774nteger] :
% 0.29/0.50        ~ ! [A6: produc6241069584506657477e_term > option6357759511663192854e_term,B6: produc8923325533196201883nteger] :
% 0.29/0.50            ( Y
% 0.29/0.50           != ( produc8603105652947943368nteger @ A6 @ B6 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % old.prod.exhaust
% 0.29/0.50  thf(fact_1364_old_Oprod_Oexhaust,axiom,
% 0.29/0.50      ! [Y: produc3925858234332021118et_nat] :
% 0.29/0.50        ~ ! [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat] :
% 0.29/0.50            ( Y
% 0.29/0.50           != ( produc5001842942810119800et_nat @ A6 @ B6 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % old.prod.exhaust
% 0.29/0.50  thf(fact_1365_old_Oprod_Oexhaust,axiom,
% 0.29/0.50      ! [Y: produc2732055786443039994et_nat] :
% 0.29/0.50        ~ ! [A6: produc3658429121746597890et_nat > $o,B6: produc3925858234332021118et_nat] :
% 0.29/0.50            ( Y
% 0.29/0.50           != ( produc2245416461498447860et_nat @ A6 @ B6 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % old.prod.exhaust
% 0.29/0.50  thf(fact_1366_old_Oprod_Oexhaust,axiom,
% 0.29/0.50      ! [Y: produc2285326912895808259nt_int] :
% 0.29/0.50        ~ ! [A6: produc8551481072490612790e_term > option6357759511663192854e_term,B6: product_prod_int_int] :
% 0.29/0.50            ( Y
% 0.29/0.50           != ( produc5700946648718959541nt_int @ A6 @ B6 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % old.prod.exhaust
% 0.29/0.50  thf(fact_1367_old_Oprod_Oexhaust,axiom,
% 0.29/0.50      ! [Y: produc7773217078559923341nt_int] :
% 0.29/0.50        ~ ! [A6: int > option6357759511663192854e_term,B6: product_prod_int_int] :
% 0.29/0.50            ( Y
% 0.29/0.50           != ( produc4305682042979456191nt_int @ A6 @ B6 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % old.prod.exhaust
% 0.29/0.50  thf(fact_1368_bex2I,axiom,
% 0.29/0.50      ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,S: set_Pr1281608226676607948nteger,P: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o] :
% 0.29/0.50        ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A @ B ) @ S )
% 0.29/0.50       => ( ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A @ B ) @ S )
% 0.29/0.50           => ( P @ A @ B ) )
% 0.29/0.50         => ? [A6: produc6241069584506657477e_term > option6357759511663192854e_term,B6: produc8923325533196201883nteger] :
% 0.29/0.50              ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A6 @ B6 ) @ S )
% 0.29/0.50              & ( P @ A6 @ B6 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % bex2I
% 0.29/0.50  thf(fact_1369_bex2I,axiom,
% 0.29/0.50      ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,S: set_Pr3286484037609594932et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 0.29/0.50        ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S )
% 0.29/0.50       => ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S )
% 0.29/0.50           => ( P @ A @ B ) )
% 0.29/0.50         => ? [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat] :
% 0.29/0.50              ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A6 @ B6 ) @ S )
% 0.29/0.50              & ( P @ A6 @ B6 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % bex2I
% 0.29/0.50  thf(fact_1370_bex2I,axiom,
% 0.29/0.50      ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,S: set_Pr8536935166611901872et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 0.29/0.50        ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S )
% 0.29/0.50       => ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S )
% 0.29/0.50           => ( P @ A @ B ) )
% 0.29/0.50         => ? [A6: produc3658429121746597890et_nat > $o,B6: produc3925858234332021118et_nat] :
% 0.29/0.50              ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A6 @ B6 ) @ S )
% 0.29/0.50              & ( P @ A6 @ B6 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % bex2I
% 0.29/0.50  thf(fact_1371_bex2I,axiom,
% 0.29/0.50      ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,S: set_Pr9222295170931077689nt_int,P: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 0.29/0.50        ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A @ B ) @ S )
% 0.29/0.50       => ( ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A @ B ) @ S )
% 0.29/0.50           => ( P @ A @ B ) )
% 0.29/0.50         => ? [A6: produc8551481072490612790e_term > option6357759511663192854e_term,B6: product_prod_int_int] :
% 0.29/0.50              ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A6 @ B6 ) @ S )
% 0.29/0.50              & ( P @ A6 @ B6 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % bex2I
% 0.29/0.50  thf(fact_1372_bex2I,axiom,
% 0.29/0.50      ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,S: set_Pr1872883991513573699nt_int,P: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 0.29/0.50        ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A @ B ) @ S )
% 0.29/0.50       => ( ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A @ B ) @ S )
% 0.29/0.50           => ( P @ A @ B ) )
% 0.29/0.50         => ? [A6: int > option6357759511663192854e_term,B6: product_prod_int_int] :
% 0.29/0.50              ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A6 @ B6 ) @ S )
% 0.29/0.50              & ( P @ A6 @ B6 ) ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % bex2I
% 0.29/0.50  thf(fact_1373_surj__pair,axiom,
% 0.29/0.50      ! [P4: produc1908205239877642774nteger] :
% 0.29/0.50      ? [X2: produc6241069584506657477e_term > option6357759511663192854e_term,Y2: produc8923325533196201883nteger] :
% 0.29/0.50        ( P4
% 0.29/0.50        = ( produc8603105652947943368nteger @ X2 @ Y2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % surj_pair
% 0.29/0.50  thf(fact_1374_surj__pair,axiom,
% 0.29/0.50      ! [P4: produc3925858234332021118et_nat] :
% 0.29/0.50      ? [X2: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 0.29/0.50        ( P4
% 0.29/0.50        = ( produc5001842942810119800et_nat @ X2 @ Y2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % surj_pair
% 0.29/0.50  thf(fact_1375_surj__pair,axiom,
% 0.29/0.50      ! [P4: produc2732055786443039994et_nat] :
% 0.29/0.50      ? [X2: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat] :
% 0.29/0.50        ( P4
% 0.29/0.50        = ( produc2245416461498447860et_nat @ X2 @ Y2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % surj_pair
% 0.29/0.50  thf(fact_1376_surj__pair,axiom,
% 0.29/0.50      ! [P4: produc2285326912895808259nt_int] :
% 0.29/0.50      ? [X2: produc8551481072490612790e_term > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 0.29/0.50        ( P4
% 0.29/0.50        = ( produc5700946648718959541nt_int @ X2 @ Y2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % surj_pair
% 0.29/0.50  thf(fact_1377_surj__pair,axiom,
% 0.29/0.50      ! [P4: produc7773217078559923341nt_int] :
% 0.29/0.50      ? [X2: int > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 0.29/0.50        ( P4
% 0.29/0.50        = ( produc4305682042979456191nt_int @ X2 @ Y2 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % surj_pair
% 0.29/0.50  thf(fact_1378_prod__cases,axiom,
% 0.29/0.50      ! [P: produc1908205239877642774nteger > $o,P4: produc1908205239877642774nteger] :
% 0.29/0.50        ( ! [A6: produc6241069584506657477e_term > option6357759511663192854e_term,B6: produc8923325533196201883nteger] : ( P @ ( produc8603105652947943368nteger @ A6 @ B6 ) )
% 0.29/0.50       => ( P @ P4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % prod_cases
% 0.29/0.50  thf(fact_1379_prod__cases,axiom,
% 0.29/0.50      ! [P: produc3925858234332021118et_nat > $o,P4: produc3925858234332021118et_nat] :
% 0.29/0.50        ( ! [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat] : ( P @ ( produc5001842942810119800et_nat @ A6 @ B6 ) )
% 0.29/0.50       => ( P @ P4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % prod_cases
% 0.29/0.50  thf(fact_1380_prod__cases,axiom,
% 0.29/0.50      ! [P: produc2732055786443039994et_nat > $o,P4: produc2732055786443039994et_nat] :
% 0.29/0.50        ( ! [A6: produc3658429121746597890et_nat > $o,B6: produc3925858234332021118et_nat] : ( P @ ( produc2245416461498447860et_nat @ A6 @ B6 ) )
% 0.29/0.50       => ( P @ P4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % prod_cases
% 0.29/0.50  thf(fact_1381_prod__cases,axiom,
% 0.29/0.50      ! [P: produc2285326912895808259nt_int > $o,P4: produc2285326912895808259nt_int] :
% 0.29/0.50        ( ! [A6: produc8551481072490612790e_term > option6357759511663192854e_term,B6: product_prod_int_int] : ( P @ ( produc5700946648718959541nt_int @ A6 @ B6 ) )
% 0.29/0.50       => ( P @ P4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % prod_cases
% 0.29/0.50  thf(fact_1382_prod__cases,axiom,
% 0.29/0.50      ! [P: produc7773217078559923341nt_int > $o,P4: produc7773217078559923341nt_int] :
% 0.29/0.50        ( ! [A6: int > option6357759511663192854e_term,B6: product_prod_int_int] : ( P @ ( produc4305682042979456191nt_int @ A6 @ B6 ) )
% 0.29/0.50       => ( P @ P4 ) ) ).
% 0.29/0.50  
% 0.29/0.50  % prod_cases
% 0.29/0.50  thf(fact_1383_Pair__inject,axiom,
% 0.29/0.50      ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 0.29/0.50        ( ( ( produc8603105652947943368nteger @ A @ B )
% 0.29/0.50          = ( produc8603105652947943368nteger @ A5 @ B5 ) )
% 0.29/0.50       => ~ ( ( A = A5 )
% 0.29/0.50           => ( B != B5 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Pair_inject
% 0.29/0.50  thf(fact_1384_Pair__inject,axiom,
% 0.29/0.50      ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A5: produc3658429121746597890et_nat > $o,B5: produc3658429121746597890et_nat] :
% 0.29/0.50        ( ( ( produc5001842942810119800et_nat @ A @ B )
% 0.29/0.50          = ( produc5001842942810119800et_nat @ A5 @ B5 ) )
% 0.29/0.50       => ~ ( ( A = A5 )
% 0.29/0.50           => ( B != B5 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Pair_inject
% 0.29/0.50  thf(fact_1385_Pair__inject,axiom,
% 0.29/0.50      ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A5: produc3658429121746597890et_nat > $o,B5: produc3925858234332021118et_nat] :
% 0.29/0.50        ( ( ( produc2245416461498447860et_nat @ A @ B )
% 0.29/0.50          = ( produc2245416461498447860et_nat @ A5 @ B5 ) )
% 0.29/0.50       => ~ ( ( A = A5 )
% 0.29/0.50           => ( B != B5 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Pair_inject
% 0.29/0.50  thf(fact_1386_Pair__inject,axiom,
% 0.29/0.50      ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: product_prod_int_int] :
% 0.29/0.50        ( ( ( produc5700946648718959541nt_int @ A @ B )
% 0.29/0.50          = ( produc5700946648718959541nt_int @ A5 @ B5 ) )
% 0.29/0.50       => ~ ( ( A = A5 )
% 0.29/0.50           => ( B != B5 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Pair_inject
% 0.29/0.50  thf(fact_1387_Pair__inject,axiom,
% 0.29/0.50      ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A5: int > option6357759511663192854e_term,B5: product_prod_int_int] :
% 0.29/0.50        ( ( ( produc4305682042979456191nt_int @ A @ B )
% 0.29/0.50          = ( produc4305682042979456191nt_int @ A5 @ B5 ) )
% 0.29/0.50       => ~ ( ( A = A5 )
% 0.29/0.50           => ( B != B5 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % Pair_inject
% 0.29/0.50  thf(fact_1388_prod__cases3,axiom,
% 0.29/0.50      ! [Y: produc1908205239877642774nteger] :
% 0.29/0.50        ~ ! [A6: produc6241069584506657477e_term > option6357759511663192854e_term,B6: code_integer,C3: code_integer] :
% 0.29/0.50            ( Y
% 0.29/0.50           != ( produc8603105652947943368nteger @ A6 @ ( produc1086072967326762835nteger @ B6 @ C3 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % prod_cases3
% 0.29/0.50  thf(fact_1389_prod__cases3,axiom,
% 0.29/0.50      ! [Y: produc3925858234332021118et_nat] :
% 0.29/0.50        ~ ! [A6: produc3658429121746597890et_nat > $o,B6: heap_e7401611519738050253t_unit,C3: set_nat] :
% 0.29/0.50            ( Y
% 0.29/0.50           != ( produc5001842942810119800et_nat @ A6 @ ( produc7507926704131184380et_nat @ B6 @ C3 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % prod_cases3
% 0.29/0.50  thf(fact_1390_prod__cases3,axiom,
% 0.29/0.50      ! [Y: produc2732055786443039994et_nat] :
% 0.29/0.50        ~ ! [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat > $o,C3: produc3658429121746597890et_nat] :
% 0.29/0.50            ( Y
% 0.29/0.50           != ( produc2245416461498447860et_nat @ A6 @ ( produc5001842942810119800et_nat @ B6 @ C3 ) ) ) ).
% 0.29/0.50  
% 0.29/0.50  % prod_cases3
% 0.29/0.50  thf(fact_1391_prod__cases3,axiom,
% 0.29/0.50      ! [Y: produc2285326912895808259nt_int] :
% 0.29/0.50        ~ ! [A6: produc8551481072490612790e_term > option6357759511663192854e_term,B6: int,C3: int] :
% 0.29/0.51            ( Y
% 0.29/0.51           != ( produc5700946648718959541nt_int @ A6 @ ( product_Pair_int_int @ B6 @ C3 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % prod_cases3
% 0.29/0.51  thf(fact_1392_prod__cases3,axiom,
% 0.29/0.51      ! [Y: produc7773217078559923341nt_int] :
% 0.29/0.51        ~ ! [A6: int > option6357759511663192854e_term,B6: int,C3: int] :
% 0.29/0.51            ( Y
% 0.29/0.51           != ( produc4305682042979456191nt_int @ A6 @ ( product_Pair_int_int @ B6 @ C3 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % prod_cases3
% 0.29/0.51  thf(fact_1393_prod__cases4,axiom,
% 0.29/0.51      ! [Y: produc2732055786443039994et_nat] :
% 0.29/0.51        ~ ! [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat > $o,C3: heap_e7401611519738050253t_unit,D: set_nat] :
% 0.29/0.51            ( Y
% 0.29/0.51           != ( produc2245416461498447860et_nat @ A6 @ ( produc5001842942810119800et_nat @ B6 @ ( produc7507926704131184380et_nat @ C3 @ D ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % prod_cases4
% 0.29/0.51  thf(fact_1394_prod__induct3,axiom,
% 0.29/0.51      ! [P: produc1908205239877642774nteger > $o,X: produc1908205239877642774nteger] :
% 0.29/0.51        ( ! [A6: produc6241069584506657477e_term > option6357759511663192854e_term,B6: code_integer,C3: code_integer] : ( P @ ( produc8603105652947943368nteger @ A6 @ ( produc1086072967326762835nteger @ B6 @ C3 ) ) )
% 0.29/0.51       => ( P @ X ) ) ).
% 0.29/0.51  
% 0.29/0.51  % prod_induct3
% 0.29/0.51  thf(fact_1395_prod__induct3,axiom,
% 0.29/0.51      ! [P: produc3925858234332021118et_nat > $o,X: produc3925858234332021118et_nat] :
% 0.29/0.51        ( ! [A6: produc3658429121746597890et_nat > $o,B6: heap_e7401611519738050253t_unit,C3: set_nat] : ( P @ ( produc5001842942810119800et_nat @ A6 @ ( produc7507926704131184380et_nat @ B6 @ C3 ) ) )
% 0.29/0.51       => ( P @ X ) ) ).
% 0.29/0.51  
% 0.29/0.51  % prod_induct3
% 0.29/0.51  thf(fact_1396_prod__induct3,axiom,
% 0.29/0.51      ! [P: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 0.29/0.51        ( ! [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat > $o,C3: produc3658429121746597890et_nat] : ( P @ ( produc2245416461498447860et_nat @ A6 @ ( produc5001842942810119800et_nat @ B6 @ C3 ) ) )
% 0.29/0.51       => ( P @ X ) ) ).
% 0.29/0.51  
% 0.29/0.51  % prod_induct3
% 0.29/0.51  thf(fact_1397_prod__induct3,axiom,
% 0.29/0.51      ! [P: produc2285326912895808259nt_int > $o,X: produc2285326912895808259nt_int] :
% 0.29/0.51        ( ! [A6: produc8551481072490612790e_term > option6357759511663192854e_term,B6: int,C3: int] : ( P @ ( produc5700946648718959541nt_int @ A6 @ ( product_Pair_int_int @ B6 @ C3 ) ) )
% 0.29/0.51       => ( P @ X ) ) ).
% 0.29/0.51  
% 0.29/0.51  % prod_induct3
% 0.29/0.51  thf(fact_1398_prod__induct3,axiom,
% 0.29/0.51      ! [P: produc7773217078559923341nt_int > $o,X: produc7773217078559923341nt_int] :
% 0.29/0.51        ( ! [A6: int > option6357759511663192854e_term,B6: int,C3: int] : ( P @ ( produc4305682042979456191nt_int @ A6 @ ( product_Pair_int_int @ B6 @ C3 ) ) )
% 0.29/0.51       => ( P @ X ) ) ).
% 0.29/0.51  
% 0.29/0.51  % prod_induct3
% 0.29/0.51  thf(fact_1399_prod__induct4,axiom,
% 0.29/0.51      ! [P: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 0.29/0.51        ( ! [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat > $o,C3: heap_e7401611519738050253t_unit,D: set_nat] : ( P @ ( produc2245416461498447860et_nat @ A6 @ ( produc5001842942810119800et_nat @ B6 @ ( produc7507926704131184380et_nat @ C3 @ D ) ) ) )
% 0.29/0.51       => ( P @ X ) ) ).
% 0.29/0.51  
% 0.29/0.51  % prod_induct4
% 0.29/0.51  thf(fact_1400_memb__imp__not__empty,axiom,
% 0.29/0.51      ! [X: set_Pr958786334691620121nt_int,S: set_se6260736226359567993nt_int] :
% 0.29/0.51        ( ( member2340774599025711042nt_int @ X @ S )
% 0.29/0.51       => ( S != bot_bo1488462491386950373nt_int ) ) ).
% 0.29/0.51  
% 0.29/0.51  % memb_imp_not_empty
% 0.29/0.51  thf(fact_1401_memb__imp__not__empty,axiom,
% 0.29/0.51      ! [X: set_nat,S: set_set_nat] :
% 0.29/0.51        ( ( member_set_nat @ X @ S )
% 0.29/0.51       => ( S != bot_bot_set_set_nat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % memb_imp_not_empty
% 0.29/0.51  thf(fact_1402_memb__imp__not__empty,axiom,
% 0.29/0.51      ! [X: produc3658429121746597890et_nat > $o,S: set_Pr4532377907799695533_nat_o] :
% 0.29/0.51        ( ( member6576561426505652726_nat_o @ X @ S )
% 0.29/0.51       => ( S != bot_bo7824918357723582233_nat_o ) ) ).
% 0.29/0.51  
% 0.29/0.51  % memb_imp_not_empty
% 0.29/0.51  thf(fact_1403_memb__imp__not__empty,axiom,
% 0.29/0.51      ! [X: product_prod_nat_nat,S: set_Pr1261947904930325089at_nat] :
% 0.29/0.51        ( ( member8440522571783428010at_nat @ X @ S )
% 0.29/0.51       => ( S != bot_bo2099793752762293965at_nat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % memb_imp_not_empty
% 0.29/0.51  thf(fact_1404_memb__imp__not__empty,axiom,
% 0.29/0.51      ! [X: $o,S: set_o] :
% 0.29/0.51        ( ( member_o @ X @ S )
% 0.29/0.51       => ( S != bot_bot_set_o ) ) ).
% 0.29/0.51  
% 0.29/0.51  % memb_imp_not_empty
% 0.29/0.51  thf(fact_1405_memb__imp__not__empty,axiom,
% 0.29/0.51      ! [X: nat,S: set_nat] :
% 0.29/0.51        ( ( member_nat @ X @ S )
% 0.29/0.51       => ( S != bot_bot_set_nat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % memb_imp_not_empty
% 0.29/0.51  thf(fact_1406_memb__imp__not__empty,axiom,
% 0.29/0.51      ! [X: int,S: set_int] :
% 0.29/0.51        ( ( member_int @ X @ S )
% 0.29/0.51       => ( S != bot_bot_set_int ) ) ).
% 0.29/0.51  
% 0.29/0.51  % memb_imp_not_empty
% 0.29/0.51  thf(fact_1407_set__notEmptyE,axiom,
% 0.29/0.51      ! [S: set_se6260736226359567993nt_int] :
% 0.29/0.51        ( ( S != bot_bo1488462491386950373nt_int )
% 0.29/0.51       => ~ ! [X2: set_Pr958786334691620121nt_int] :
% 0.29/0.51              ~ ( member2340774599025711042nt_int @ X2 @ S ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_notEmptyE
% 0.29/0.51  thf(fact_1408_set__notEmptyE,axiom,
% 0.29/0.51      ! [S: set_set_nat] :
% 0.29/0.51        ( ( S != bot_bot_set_set_nat )
% 0.29/0.51       => ~ ! [X2: set_nat] :
% 0.29/0.51              ~ ( member_set_nat @ X2 @ S ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_notEmptyE
% 0.29/0.51  thf(fact_1409_set__notEmptyE,axiom,
% 0.29/0.51      ! [S: set_Pr4532377907799695533_nat_o] :
% 0.29/0.51        ( ( S != bot_bo7824918357723582233_nat_o )
% 0.29/0.51       => ~ ! [X2: produc3658429121746597890et_nat > $o] :
% 0.29/0.51              ~ ( member6576561426505652726_nat_o @ X2 @ S ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_notEmptyE
% 0.29/0.51  thf(fact_1410_set__notEmptyE,axiom,
% 0.29/0.51      ! [S: set_Pr1261947904930325089at_nat] :
% 0.29/0.51        ( ( S != bot_bo2099793752762293965at_nat )
% 0.29/0.51       => ~ ! [X2: product_prod_nat_nat] :
% 0.29/0.51              ~ ( member8440522571783428010at_nat @ X2 @ S ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_notEmptyE
% 0.29/0.51  thf(fact_1411_set__notEmptyE,axiom,
% 0.29/0.51      ! [S: set_o] :
% 0.29/0.51        ( ( S != bot_bot_set_o )
% 0.29/0.51       => ~ ! [X2: $o] :
% 0.29/0.51              ~ ( member_o @ X2 @ S ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_notEmptyE
% 0.29/0.51  thf(fact_1412_set__notEmptyE,axiom,
% 0.29/0.51      ! [S: set_nat] :
% 0.29/0.51        ( ( S != bot_bot_set_nat )
% 0.29/0.51       => ~ ! [X2: nat] :
% 0.29/0.51              ~ ( member_nat @ X2 @ S ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_notEmptyE
% 0.29/0.51  thf(fact_1413_set__notEmptyE,axiom,
% 0.29/0.51      ! [S: set_int] :
% 0.29/0.51        ( ( S != bot_bot_set_int )
% 0.29/0.51       => ~ ! [X2: int] :
% 0.29/0.51              ~ ( member_int @ X2 @ S ) ) ).
% 0.29/0.51  
% 0.29/0.51  % set_notEmptyE
% 0.29/0.51  thf(fact_1414_verit__negate__coefficient_I3_J,axiom,
% 0.29/0.51      ! [A: int,B: int] :
% 0.29/0.51        ( ( A = B )
% 0.29/0.51       => ( ( uminus_uminus_int @ A )
% 0.29/0.51          = ( uminus_uminus_int @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % verit_negate_coefficient(3)
% 0.29/0.51  thf(fact_1415_verit__negate__coefficient_I3_J,axiom,
% 0.29/0.51      ! [A: code_integer,B: code_integer] :
% 0.29/0.51        ( ( A = B )
% 0.29/0.51       => ( ( uminus1351360451143612070nteger @ A )
% 0.29/0.51          = ( uminus1351360451143612070nteger @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % verit_negate_coefficient(3)
% 0.29/0.51  thf(fact_1416_verit__negate__coefficient_I3_J,axiom,
% 0.29/0.51      ! [A: rat,B: rat] :
% 0.29/0.51        ( ( A = B )
% 0.29/0.51       => ( ( uminus_uminus_rat @ A )
% 0.29/0.51          = ( uminus_uminus_rat @ B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % verit_negate_coefficient(3)
% 0.29/0.51  thf(fact_1417_sup__Un__eq,axiom,
% 0.29/0.51      ! [R: set_se6260736226359567993nt_int,S: set_se6260736226359567993nt_int] :
% 0.29/0.51        ( ( sup_su1852724690005176016_int_o
% 0.29/0.51          @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ R )
% 0.29/0.51          @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ S ) )
% 0.29/0.51        = ( ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ ( sup_su2047564715030645325nt_int @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sup_Un_eq
% 0.29/0.51  thf(fact_1418_sup__Un__eq,axiom,
% 0.29/0.51      ! [R: set_set_nat,S: set_set_nat] :
% 0.29/0.51        ( ( sup_sup_set_nat_o
% 0.29/0.51          @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ R )
% 0.29/0.51          @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ S ) )
% 0.29/0.51        = ( ^ [X3: set_nat] : ( member_set_nat @ X3 @ ( sup_sup_set_set_nat @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sup_Un_eq
% 0.29/0.51  thf(fact_1419_sup__Un__eq,axiom,
% 0.29/0.51      ! [R: set_int,S: set_int] :
% 0.29/0.51        ( ( sup_sup_int_o
% 0.29/0.51          @ ^ [X3: int] : ( member_int @ X3 @ R )
% 0.29/0.51          @ ^ [X3: int] : ( member_int @ X3 @ S ) )
% 0.29/0.51        = ( ^ [X3: int] : ( member_int @ X3 @ ( sup_sup_set_int @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sup_Un_eq
% 0.29/0.51  thf(fact_1420_sup__Un__eq,axiom,
% 0.29/0.51      ! [R: set_Pr4532377907799695533_nat_o,S: set_Pr4532377907799695533_nat_o] :
% 0.29/0.51        ( ( sup_su8003631835303541148at_o_o
% 0.29/0.51          @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ R )
% 0.29/0.51          @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ S ) )
% 0.29/0.51        = ( ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ ( sup_su5209123915105501825_nat_o @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sup_Un_eq
% 0.29/0.51  thf(fact_1421_sup__Un__eq,axiom,
% 0.29/0.51      ! [R: set_Pr8551490117392284871at_nat,S: set_Pr8551490117392284871at_nat] :
% 0.29/0.51        ( ( sup_su6256023009775730178_nat_o
% 0.29/0.51          @ ^ [X3: produc4166570645942440679at_nat] : ( member6689249552917799696at_nat @ X3 @ R )
% 0.29/0.51          @ ^ [X3: produc4166570645942440679at_nat] : ( member6689249552917799696at_nat @ X3 @ S ) )
% 0.29/0.51        = ( ^ [X3: produc4166570645942440679at_nat] : ( member6689249552917799696at_nat @ X3 @ ( sup_su3035147773818789531at_nat @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sup_Un_eq
% 0.29/0.51  thf(fact_1422_sup__Un__eq,axiom,
% 0.29/0.51      ! [R: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 0.29/0.51        ( ( sup_su2080679670758317954_nat_o
% 0.29/0.51          @ ^ [X3: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X3 @ R )
% 0.29/0.51          @ ^ [X3: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X3 @ S ) )
% 0.29/0.51        = ( ^ [X3: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X3 @ ( sup_su5525570899277871387at_nat @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sup_Un_eq
% 0.29/0.51  thf(fact_1423_sup__Un__eq,axiom,
% 0.29/0.51      ! [R: set_nat,S: set_nat] :
% 0.29/0.51        ( ( sup_sup_nat_o
% 0.29/0.51          @ ^ [X3: nat] : ( member_nat @ X3 @ R )
% 0.29/0.51          @ ^ [X3: nat] : ( member_nat @ X3 @ S ) )
% 0.29/0.51        = ( ^ [X3: nat] : ( member_nat @ X3 @ ( sup_sup_set_nat @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sup_Un_eq
% 0.29/0.51  thf(fact_1424_inf__Int__eq,axiom,
% 0.29/0.51      ! [R: set_se6260736226359567993nt_int,S: set_se6260736226359567993nt_int] :
% 0.29/0.51        ( ( inf_in5102985939729578038_int_o
% 0.29/0.51          @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ R )
% 0.29/0.51          @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ S ) )
% 0.29/0.51        = ( ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ ( inf_in8396524679539076455nt_int @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % inf_Int_eq
% 0.29/0.51  thf(fact_1425_inf__Int__eq,axiom,
% 0.29/0.51      ! [R: set_set_nat,S: set_set_nat] :
% 0.29/0.51        ( ( inf_inf_set_nat_o
% 0.29/0.51          @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ R )
% 0.29/0.51          @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ S ) )
% 0.29/0.51        = ( ^ [X3: set_nat] : ( member_set_nat @ X3 @ ( inf_inf_set_set_nat @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % inf_Int_eq
% 0.29/0.51  thf(fact_1426_inf__Int__eq,axiom,
% 0.29/0.51      ! [R: set_int,S: set_int] :
% 0.29/0.51        ( ( inf_inf_int_o
% 0.29/0.51          @ ^ [X3: int] : ( member_int @ X3 @ R )
% 0.29/0.51          @ ^ [X3: int] : ( member_int @ X3 @ S ) )
% 0.29/0.51        = ( ^ [X3: int] : ( member_int @ X3 @ ( inf_inf_set_int @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % inf_Int_eq
% 0.29/0.51  thf(fact_1427_inf__Int__eq,axiom,
% 0.29/0.51      ! [R: set_Pr4532377907799695533_nat_o,S: set_Pr4532377907799695533_nat_o] :
% 0.29/0.51        ( ( inf_in9018898317438245890at_o_o
% 0.29/0.51          @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ R )
% 0.29/0.51          @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ S ) )
% 0.29/0.51        = ( ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ ( inf_in1906310914598751387_nat_o @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % inf_Int_eq
% 0.29/0.51  thf(fact_1428_inf__Int__eq,axiom,
% 0.29/0.51      ! [R: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 0.29/0.51        ( ( inf_in5163264567034779214_nat_o
% 0.29/0.51          @ ^ [X3: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X3 @ R )
% 0.29/0.51          @ ^ [X3: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X3 @ S ) )
% 0.29/0.51        = ( ^ [X3: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X3 @ ( inf_in2572325071724192079at_nat @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % inf_Int_eq
% 0.29/0.51  thf(fact_1429_inf__Int__eq,axiom,
% 0.29/0.51      ! [R: set_nat,S: set_nat] :
% 0.29/0.51        ( ( inf_inf_nat_o
% 0.29/0.51          @ ^ [X3: nat] : ( member_nat @ X3 @ R )
% 0.29/0.51          @ ^ [X3: nat] : ( member_nat @ X3 @ S ) )
% 0.29/0.51        = ( ^ [X3: nat] : ( member_nat @ X3 @ ( inf_inf_set_nat @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % inf_Int_eq
% 0.29/0.51  thf(fact_1430_inf__Int__eq,axiom,
% 0.29/0.51      ! [R: set_Pr958786334691620121nt_int,S: set_Pr958786334691620121nt_int] :
% 0.29/0.51        ( ( inf_in3604695632404883862_int_o
% 0.29/0.51          @ ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ R )
% 0.29/0.51          @ ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ S ) )
% 0.29/0.51        = ( ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ ( inf_in2269163501485487111nt_int @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % inf_Int_eq
% 0.29/0.51  thf(fact_1431_inf__Int__eq,axiom,
% 0.29/0.51      ! [R: set_list_char,S: set_list_char] :
% 0.29/0.51        ( ( inf_inf_list_char_o
% 0.29/0.51          @ ^ [X3: list_char] : ( member_list_char @ X3 @ R )
% 0.29/0.51          @ ^ [X3: list_char] : ( member_list_char @ X3 @ S ) )
% 0.29/0.51        = ( ^ [X3: list_char] : ( member_list_char @ X3 @ ( inf_in6177012701088388009t_char @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % inf_Int_eq
% 0.29/0.51  thf(fact_1432_iso__tuple__UNIV__I,axiom,
% 0.29/0.51      ! [X: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X @ top_to6034159466715884489nt_int ) ).
% 0.29/0.51  
% 0.29/0.51  % iso_tuple_UNIV_I
% 0.29/0.51  thf(fact_1433_iso__tuple__UNIV__I,axiom,
% 0.29/0.51      ! [X: set_nat] : ( member_set_nat @ X @ top_top_set_set_nat ) ).
% 0.29/0.51  
% 0.29/0.51  % iso_tuple_UNIV_I
% 0.29/0.51  thf(fact_1434_iso__tuple__UNIV__I,axiom,
% 0.29/0.51      ! [X: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X @ top_to4869887016220417533_nat_o ) ).
% 0.29/0.51  
% 0.29/0.51  % iso_tuple_UNIV_I
% 0.29/0.51  thf(fact_1435_iso__tuple__UNIV__I,axiom,
% 0.29/0.51      ! [X: list_nat] : ( member_list_nat @ X @ top_top_set_list_nat ) ).
% 0.29/0.51  
% 0.29/0.51  % iso_tuple_UNIV_I
% 0.29/0.51  thf(fact_1436_iso__tuple__UNIV__I,axiom,
% 0.29/0.51      ! [X: $o] : ( member_o @ X @ top_top_set_o ) ).
% 0.29/0.51  
% 0.29/0.51  % iso_tuple_UNIV_I
% 0.29/0.51  thf(fact_1437_iso__tuple__UNIV__I,axiom,
% 0.29/0.51      ! [X: rat] : ( member_rat @ X @ top_top_set_rat ) ).
% 0.29/0.51  
% 0.29/0.51  % iso_tuple_UNIV_I
% 0.29/0.51  thf(fact_1438_iso__tuple__UNIV__I,axiom,
% 0.29/0.51      ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 0.29/0.51  
% 0.29/0.51  % iso_tuple_UNIV_I
% 0.29/0.51  thf(fact_1439_iso__tuple__UNIV__I,axiom,
% 0.29/0.51      ! [X: int] : ( member_int @ X @ top_top_set_int ) ).
% 0.29/0.51  
% 0.29/0.51  % iso_tuple_UNIV_I
% 0.29/0.51  thf(fact_1440_Collect__empty__eq__bot,axiom,
% 0.29/0.51      ! [P: set_Pr958786334691620121nt_int > $o] :
% 0.29/0.51        ( ( ( collec5210948495886036740nt_int @ P )
% 0.29/0.51          = bot_bo1488462491386950373nt_int )
% 0.29/0.51        = ( P = bot_bo2686080419298087992_int_o ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Collect_empty_eq_bot
% 0.29/0.51  thf(fact_1441_Collect__empty__eq__bot,axiom,
% 0.29/0.51      ! [P: set_nat > $o] :
% 0.29/0.51        ( ( ( collect_set_nat @ P )
% 0.29/0.51          = bot_bot_set_set_nat )
% 0.29/0.51        = ( P = bot_bot_set_nat_o ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Collect_empty_eq_bot
% 0.29/0.51  thf(fact_1442_Collect__empty__eq__bot,axiom,
% 0.29/0.51      ! [P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.29/0.51        ( ( ( collec939566748876313656_nat_o @ P )
% 0.29/0.51          = bot_bo7824918357723582233_nat_o )
% 0.29/0.51        = ( P = bot_bo7963750851167320836at_o_o ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Collect_empty_eq_bot
% 0.29/0.51  thf(fact_1443_Collect__empty__eq__bot,axiom,
% 0.29/0.51      ! [P: product_prod_nat_nat > $o] :
% 0.29/0.51        ( ( ( collec3392354462482085612at_nat @ P )
% 0.29/0.51          = bot_bo2099793752762293965at_nat )
% 0.29/0.51        = ( P = bot_bo482883023278783056_nat_o ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Collect_empty_eq_bot
% 0.29/0.51  thf(fact_1444_Collect__empty__eq__bot,axiom,
% 0.29/0.51      ! [P: $o > $o] :
% 0.29/0.51        ( ( ( collect_o @ P )
% 0.29/0.51          = bot_bot_set_o )
% 0.29/0.51        = ( P = bot_bot_o_o ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Collect_empty_eq_bot
% 0.29/0.51  thf(fact_1445_Collect__empty__eq__bot,axiom,
% 0.29/0.51      ! [P: nat > $o] :
% 0.29/0.51        ( ( ( collect_nat @ P )
% 0.29/0.51          = bot_bot_set_nat )
% 0.29/0.51        = ( P = bot_bot_nat_o ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Collect_empty_eq_bot
% 0.29/0.51  thf(fact_1446_Collect__empty__eq__bot,axiom,
% 0.29/0.51      ! [P: int > $o] :
% 0.29/0.51        ( ( ( collect_int @ P )
% 0.29/0.51          = bot_bot_set_int )
% 0.29/0.51        = ( P = bot_bot_int_o ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Collect_empty_eq_bot
% 0.29/0.51  thf(fact_1447_bot__empty__eq,axiom,
% 0.29/0.51      ( bot_bo2686080419298087992_int_o
% 0.29/0.51      = ( ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ bot_bo1488462491386950373nt_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % bot_empty_eq
% 0.29/0.51  thf(fact_1448_bot__empty__eq,axiom,
% 0.29/0.51      ( bot_bot_set_nat_o
% 0.29/0.51      = ( ^ [X3: set_nat] : ( member_set_nat @ X3 @ bot_bot_set_set_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % bot_empty_eq
% 0.29/0.51  thf(fact_1449_bot__empty__eq,axiom,
% 0.29/0.51      ( bot_bo7963750851167320836at_o_o
% 0.29/0.51      = ( ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ bot_bo7824918357723582233_nat_o ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % bot_empty_eq
% 0.29/0.51  thf(fact_1450_bot__empty__eq,axiom,
% 0.29/0.51      ( bot_bo482883023278783056_nat_o
% 0.29/0.51      = ( ^ [X3: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X3 @ bot_bo2099793752762293965at_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % bot_empty_eq
% 0.29/0.51  thf(fact_1451_bot__empty__eq,axiom,
% 0.29/0.51      ( bot_bot_o_o
% 0.29/0.51      = ( ^ [X3: $o] : ( member_o @ X3 @ bot_bot_set_o ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % bot_empty_eq
% 0.29/0.51  thf(fact_1452_bot__empty__eq,axiom,
% 0.29/0.51      ( bot_bot_nat_o
% 0.29/0.51      = ( ^ [X3: nat] : ( member_nat @ X3 @ bot_bot_set_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % bot_empty_eq
% 0.29/0.51  thf(fact_1453_bot__empty__eq,axiom,
% 0.29/0.51      ( bot_bot_int_o
% 0.29/0.51      = ( ^ [X3: int] : ( member_int @ X3 @ bot_bot_set_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % bot_empty_eq
% 0.29/0.51  thf(fact_1454_type__copy__ex__RepI,axiom,
% 0.29/0.51      ! [Rep: product_unit > $o,Abs: $o > product_unit,F4: $o > $o] :
% 0.29/0.51        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ top_top_set_o )
% 0.29/0.51       => ( ( ? [X4: $o] : ( F4 @ X4 ) )
% 0.29/0.51          = ( ? [B3: product_unit] : ( F4 @ ( Rep @ B3 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % type_copy_ex_RepI
% 0.29/0.51  thf(fact_1455_type__copy__ex__RepI,axiom,
% 0.29/0.51      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,F4: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.29/0.51        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ top_to4869887016220417533_nat_o )
% 0.29/0.51       => ( ( ? [X4: produc3658429121746597890et_nat > $o] : ( F4 @ X4 ) )
% 0.29/0.51          = ( ? [B3: assn] : ( F4 @ ( Rep @ B3 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % type_copy_ex_RepI
% 0.29/0.51  thf(fact_1456_type__copy__ex__RepI,axiom,
% 0.29/0.51      ! [Rep: literal > list_char,Abs: list_char > literal,F4: list_char > $o] :
% 0.29/0.51        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ top_to3190553582279535303t_char )
% 0.29/0.51       => ( ( ? [X4: list_char] : ( F4 @ X4 ) )
% 0.29/0.51          = ( ? [B3: literal] : ( F4 @ ( Rep @ B3 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % type_copy_ex_RepI
% 0.29/0.51  thf(fact_1457_type__copy__ex__RepI,axiom,
% 0.29/0.51      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,F4: set_Pr958786334691620121nt_int > $o] :
% 0.29/0.51        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ top_to6034159466715884489nt_int )
% 0.29/0.51       => ( ( ? [X4: set_Pr958786334691620121nt_int] : ( F4 @ X4 ) )
% 0.29/0.51          = ( ? [B3: rat] : ( F4 @ ( Rep @ B3 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % type_copy_ex_RepI
% 0.29/0.51  thf(fact_1458_type__copy__ex__RepI,axiom,
% 0.29/0.51      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,F4: set_Pr1261947904930325089at_nat > $o] :
% 0.29/0.51        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ top_to7629004291339433233at_nat )
% 0.29/0.51       => ( ( ? [X4: set_Pr1261947904930325089at_nat] : ( F4 @ X4 ) )
% 0.29/0.51          = ( ? [B3: int] : ( F4 @ ( Rep @ B3 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % type_copy_ex_RepI
% 0.29/0.51  thf(fact_1459_type__copy__obj__one__point__absE,axiom,
% 0.29/0.51      ! [Rep: product_unit > $o,Abs: $o > product_unit,S3: product_unit] :
% 0.29/0.51        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ top_top_set_o )
% 0.29/0.51       => ~ ! [X2: $o] :
% 0.29/0.51              ( S3
% 0.29/0.51             != ( Abs @ X2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % type_copy_obj_one_point_absE
% 0.29/0.51  thf(fact_1460_type__copy__obj__one__point__absE,axiom,
% 0.29/0.51      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,S3: assn] :
% 0.29/0.51        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ top_to4869887016220417533_nat_o )
% 0.29/0.51       => ~ ! [X2: produc3658429121746597890et_nat > $o] :
% 0.29/0.51              ( S3
% 0.29/0.51             != ( Abs @ X2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % type_copy_obj_one_point_absE
% 0.29/0.51  thf(fact_1461_type__copy__obj__one__point__absE,axiom,
% 0.29/0.51      ! [Rep: literal > list_char,Abs: list_char > literal,S3: literal] :
% 0.29/0.51        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ top_to3190553582279535303t_char )
% 0.29/0.51       => ~ ! [X2: list_char] :
% 0.29/0.51              ( S3
% 0.29/0.51             != ( Abs @ X2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % type_copy_obj_one_point_absE
% 0.29/0.51  thf(fact_1462_type__copy__obj__one__point__absE,axiom,
% 0.29/0.51      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,S3: rat] :
% 0.29/0.51        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ top_to6034159466715884489nt_int )
% 0.29/0.51       => ~ ! [X2: set_Pr958786334691620121nt_int] :
% 0.29/0.51              ( S3
% 0.29/0.51             != ( Abs @ X2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % type_copy_obj_one_point_absE
% 0.29/0.51  thf(fact_1463_type__copy__obj__one__point__absE,axiom,
% 0.29/0.51      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,S3: int] :
% 0.29/0.51        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ top_to7629004291339433233at_nat )
% 0.29/0.51       => ~ ! [X2: set_Pr1261947904930325089at_nat] :
% 0.29/0.51              ( S3
% 0.29/0.51             != ( Abs @ X2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % type_copy_obj_one_point_absE
% 0.29/0.51  thf(fact_1464_dbl__inc__simps_I4_J,axiom,
% 0.29/0.51      ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.51      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dbl_inc_simps(4)
% 0.29/0.51  thf(fact_1465_dbl__inc__simps_I4_J,axiom,
% 0.29/0.51      ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.51      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dbl_inc_simps(4)
% 0.29/0.51  thf(fact_1466_dbl__inc__simps_I4_J,axiom,
% 0.29/0.51      ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.51      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dbl_inc_simps(4)
% 0.29/0.51  thf(fact_1467_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 0.29/0.51      boolea7165431671056489859t_unit @ inf_inf_Product_unit @ sup_sup_Product_unit @ uminus2952777764628376836t_unit @ bot_bot_Product_unit @ top_top_Product_unit ).
% 0.29/0.51  
% 0.29/0.51  % boolean_algebra.abstract_boolean_algebra_axioms
% 0.29/0.51  thf(fact_1468_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 0.29/0.51      boolea379910186789422830_set_o @ inf_inf_set_o @ sup_sup_set_o @ uminus_uminus_set_o @ bot_bot_set_o @ top_top_set_o ).
% 0.29/0.51  
% 0.29/0.51  % boolean_algebra.abstract_boolean_algebra_axioms
% 0.29/0.51  thf(fact_1469_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 0.29/0.51      boolea6493995471900120728et_rat @ inf_inf_set_rat @ sup_sup_set_rat @ uminus2201863774496077783et_rat @ bot_bot_set_rat @ top_top_set_rat ).
% 0.29/0.51  
% 0.29/0.51  % boolean_algebra.abstract_boolean_algebra_axioms
% 0.29/0.51  thf(fact_1470_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 0.29/0.51      boolea778851993438741648et_nat @ inf_inf_set_nat @ sup_sup_set_nat @ uminus5710092332889474511et_nat @ bot_bot_set_nat @ top_top_set_nat ).
% 0.29/0.51  
% 0.29/0.51  % boolean_algebra.abstract_boolean_algebra_axioms
% 0.29/0.51  thf(fact_1471_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 0.29/0.51      boolea5824373010784320748et_int @ inf_inf_set_int @ sup_sup_set_int @ uminus1532241313380277803et_int @ bot_bot_set_int @ top_top_set_int ).
% 0.29/0.51  
% 0.29/0.51  % boolean_algebra.abstract_boolean_algebra_axioms
% 0.29/0.51  thf(fact_1472_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 0.29/0.51      boolea9074081411689916704st_nat @ inf_inf_set_list_nat @ sup_sup_set_list_nat @ uminus3195874150345416415st_nat @ bot_bot_set_list_nat @ top_top_set_list_nat ).
% 0.29/0.51  
% 0.29/0.51  % boolean_algebra.abstract_boolean_algebra_axioms
% 0.29/0.51  thf(fact_1473_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 0.29/0.51      boolea934052484356091300char_o @ inf_inf_list_char_o @ sup_sup_list_char_o @ uminus7154032370948614053char_o @ bot_bot_list_char_o @ top_top_list_char_o ).
% 0.29/0.51  
% 0.29/0.51  % boolean_algebra.abstract_boolean_algebra_axioms
% 0.29/0.51  thf(fact_1474_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 0.29/0.51      boolea949959532490082519at_nat @ inf_in2572325071724192079at_nat @ sup_su6327502436637775413at_nat @ uminus6524753893492686040at_nat @ bot_bo2099793752762293965at_nat @ top_to4669805908274784177at_nat ).
% 0.29/0.51  
% 0.29/0.51  % boolean_algebra.abstract_boolean_algebra_axioms
% 0.29/0.51  thf(fact_1475_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 0.29/0.51      boolea1849928419393854478_int_o @ inf_in3604695632404883862_int_o @ sup_su8463660629351352368_int_o @ uminus7117520113953359693_int_o @ bot_bo8147686125503663512_int_o @ top_to1578927101902068148_int_o ).
% 0.29/0.51  
% 0.29/0.51  % boolean_algebra.abstract_boolean_algebra_axioms
% 0.29/0.51  thf(fact_1476_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 0.29/0.51      boolea51845251928480829at_nat @ inf_in1697001100524423349at_nat @ sup_su3035147773818789531at_nat @ uminus2330091110623919550at_nat @ bot_bo8422036546324065075at_nat @ top_to8764741339697478167at_nat ).
% 0.29/0.51  
% 0.29/0.51  % boolean_algebra.abstract_boolean_algebra_axioms
% 0.29/0.51  thf(fact_1477_top__empty__eq,axiom,
% 0.29/0.51      ( top_to6187514276045680724_int_o
% 0.29/0.51      = ( ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ top_to6034159466715884489nt_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % top_empty_eq
% 0.29/0.51  thf(fact_1478_top__empty__eq,axiom,
% 0.29/0.51      ( top_top_set_nat_o
% 0.29/0.51      = ( ^ [X3: set_nat] : ( member_set_nat @ X3 @ top_top_set_set_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % top_empty_eq
% 0.29/0.51  thf(fact_1479_top__empty__eq,axiom,
% 0.29/0.51      ( top_to2462227307520033056at_o_o
% 0.29/0.51      = ( ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ top_to4869887016220417533_nat_o ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % top_empty_eq
% 0.29/0.51  thf(fact_1480_top__empty__eq,axiom,
% 0.29/0.51      ( top_top_list_nat_o
% 0.29/0.51      = ( ^ [X3: list_nat] : ( member_list_nat @ X3 @ top_top_set_list_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % top_empty_eq
% 0.29/0.51  thf(fact_1481_top__empty__eq,axiom,
% 0.29/0.51      ( top_top_o_o
% 0.29/0.51      = ( ^ [X3: $o] : ( member_o @ X3 @ top_top_set_o ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % top_empty_eq
% 0.29/0.51  thf(fact_1482_top__empty__eq,axiom,
% 0.29/0.51      ( top_top_rat_o
% 0.29/0.51      = ( ^ [X3: rat] : ( member_rat @ X3 @ top_top_set_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % top_empty_eq
% 0.29/0.51  thf(fact_1483_top__empty__eq,axiom,
% 0.29/0.51      ( top_top_nat_o
% 0.29/0.51      = ( ^ [X3: nat] : ( member_nat @ X3 @ top_top_set_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % top_empty_eq
% 0.29/0.51  thf(fact_1484_top__empty__eq,axiom,
% 0.29/0.51      ( top_top_int_o
% 0.29/0.51      = ( ^ [X3: int] : ( member_int @ X3 @ top_top_set_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % top_empty_eq
% 0.29/0.51  thf(fact_1485_sup__Un__eq2,axiom,
% 0.29/0.51      ! [R: set_Pr1281608226676607948nteger,S: set_Pr1281608226676607948nteger] :
% 0.29/0.51        ( ( sup_su234547053653886311eger_o
% 0.29/0.51          @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ R )
% 0.29/0.51          @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ S ) )
% 0.29/0.51        = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ ( sup_su4591284015454442744nteger @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sup_Un_eq2
% 0.29/0.51  thf(fact_1486_sup__Un__eq2,axiom,
% 0.29/0.51      ! [R: set_Pr3286484037609594932et_nat,S: set_Pr3286484037609594932et_nat] :
% 0.29/0.51        ( ( sup_su1630790145277462993_nat_o
% 0.29/0.51          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R )
% 0.29/0.51          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ S ) )
% 0.29/0.51        = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ ( sup_su7128418612487073120et_nat @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sup_Un_eq2
% 0.29/0.51  thf(fact_1487_sup__Un__eq2,axiom,
% 0.29/0.51      ! [R: set_Pr8536935166611901872et_nat,S: set_Pr8536935166611901872et_nat] :
% 0.29/0.51        ( ( sup_su6535292691877529429_nat_o
% 0.29/0.51          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R )
% 0.29/0.51          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ S ) )
% 0.29/0.51        = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ ( sup_su8975264963432250076et_nat @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sup_Un_eq2
% 0.29/0.51  thf(fact_1488_sup__Un__eq2,axiom,
% 0.29/0.51      ! [R: set_Pr9222295170931077689nt_int,S: set_Pr9222295170931077689nt_int] :
% 0.29/0.51        ( ( sup_su4182031696650224058_int_o
% 0.29/0.51          @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ R )
% 0.29/0.51          @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ S ) )
% 0.29/0.51        = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ ( sup_su3382966977382714213nt_int @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sup_Un_eq2
% 0.29/0.51  thf(fact_1489_sup__Un__eq2,axiom,
% 0.29/0.51      ! [R: set_Pr1872883991513573699nt_int,S: set_Pr1872883991513573699nt_int] :
% 0.29/0.51        ( ( sup_su600977994968626096_int_o
% 0.29/0.51          @ ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ R )
% 0.29/0.51          @ ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ S ) )
% 0.29/0.51        = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ ( sup_su3298353300217089135nt_int @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sup_Un_eq2
% 0.29/0.51  thf(fact_1490_sup__Un__eq2,axiom,
% 0.29/0.51      ! [R: set_Pr8551490117392284871at_nat,S: set_Pr8551490117392284871at_nat] :
% 0.29/0.51        ( ( sup_su2200014604384089602_nat_o
% 0.29/0.51          @ ^ [X3: multis2468970476368604999at_nat,Y3: multis2468970476368604999at_nat] : ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ X3 @ Y3 ) @ R )
% 0.29/0.51          @ ^ [X3: multis2468970476368604999at_nat,Y3: multis2468970476368604999at_nat] : ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ X3 @ Y3 ) @ S ) )
% 0.29/0.51        = ( ^ [X3: multis2468970476368604999at_nat,Y3: multis2468970476368604999at_nat] : ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ X3 @ Y3 ) @ ( sup_su3035147773818789531at_nat @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sup_Un_eq2
% 0.29/0.51  thf(fact_1491_sup__Un__eq2,axiom,
% 0.29/0.51      ! [R: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 0.29/0.51        ( ( sup_su7519161239522478338_nat_o
% 0.29/0.51          @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R )
% 0.29/0.51          @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ S ) )
% 0.29/0.51        = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ ( sup_su5525570899277871387at_nat @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % sup_Un_eq2
% 0.29/0.51  thf(fact_1492_inf__Int__eq2,axiom,
% 0.29/0.51      ! [R: set_Pr1281608226676607948nteger,S: set_Pr1281608226676607948nteger] :
% 0.29/0.51        ( ( inf_in3563340378267265229eger_o
% 0.29/0.51          @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ R )
% 0.29/0.51          @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ S ) )
% 0.29/0.51        = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ ( inf_in3408396081536963678nteger @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % inf_Int_eq2
% 0.29/0.51  thf(fact_1493_inf__Int__eq2,axiom,
% 0.29/0.51      ! [R: set_Pr3286484037609594932et_nat,S: set_Pr3286484037609594932et_nat] :
% 0.29/0.51        ( ( inf_in3295504058751909687_nat_o
% 0.29/0.51          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R )
% 0.29/0.51          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ S ) )
% 0.29/0.51        = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ ( inf_in1768905781608824518et_nat @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % inf_Int_eq2
% 0.29/0.51  thf(fact_1494_inf__Int__eq2,axiom,
% 0.29/0.51      ! [R: set_Pr8536935166611901872et_nat,S: set_Pr8536935166611901872et_nat] :
% 0.29/0.51        ( ( inf_in2641120393918057659_nat_o
% 0.29/0.51          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R )
% 0.29/0.51          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ S ) )
% 0.29/0.51        = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ ( inf_in3088352823822785602et_nat @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % inf_Int_eq2
% 0.29/0.51  thf(fact_1495_inf__Int__eq2,axiom,
% 0.29/0.51      ! [R: set_Pr9222295170931077689nt_int,S: set_Pr9222295170931077689nt_int] :
% 0.29/0.51        ( ( inf_in8045883074377559328_int_o
% 0.29/0.51          @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ R )
% 0.29/0.51          @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ S ) )
% 0.29/0.51        = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ ( inf_in2576786181675586251nt_int @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % inf_Int_eq2
% 0.29/0.51  thf(fact_1496_inf__Int__eq2,axiom,
% 0.29/0.51      ! [R: set_Pr1872883991513573699nt_int,S: set_Pr1872883991513573699nt_int] :
% 0.29/0.51        ( ( inf_in8201999774870019094_int_o
% 0.29/0.51          @ ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ R )
% 0.29/0.51          @ ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ S ) )
% 0.29/0.51        = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ ( inf_in8806012763027673301nt_int @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % inf_Int_eq2
% 0.29/0.51  thf(fact_1497_inf__Int__eq2,axiom,
% 0.29/0.51      ! [R: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 0.29/0.51        ( ( inf_inf_nat_nat_o
% 0.29/0.51          @ ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R )
% 0.29/0.51          @ ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ S ) )
% 0.29/0.51        = ( ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( inf_in2572325071724192079at_nat @ R @ S ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % inf_Int_eq2
% 0.29/0.51  thf(fact_1498_bot__empty__eq2,axiom,
% 0.29/0.51      ( bot_bo3000040243691356879eger_o
% 0.29/0.51      = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ bot_bo5443222936135328352nteger ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % bot_empty_eq2
% 0.29/0.51  thf(fact_1499_bot__empty__eq2,axiom,
% 0.29/0.51      ( bot_bo5580076615179976505_nat_o
% 0.29/0.51      = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ bot_bo1481135142794719944et_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % bot_empty_eq2
% 0.29/0.51  thf(fact_1500_bot__empty__eq2,axiom,
% 0.29/0.51      ( bot_bo3790638025767943357_nat_o
% 0.29/0.51      = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ bot_bo5635537948650799172et_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % bot_empty_eq2
% 0.29/0.51  thf(fact_1501_bot__empty__eq2,axiom,
% 0.29/0.51      ( bot_bo8662317086119403298_int_o
% 0.29/0.51      = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ bot_bo572930865798478029nt_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % bot_empty_eq2
% 0.29/0.51  thf(fact_1502_bot__empty__eq2,axiom,
% 0.29/0.51      ( bot_bo1403522918969695512_int_o
% 0.29/0.51      = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ bot_bo4508923176915781079nt_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % bot_empty_eq2
% 0.29/0.51  thf(fact_1503_bot__empty__eq2,axiom,
% 0.29/0.51      ( bot_bot_nat_nat_o
% 0.29/0.51      = ( ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ bot_bo2099793752762293965at_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % bot_empty_eq2
% 0.29/0.51  thf(fact_1504_pred__equals__eq2,axiom,
% 0.29/0.51      ! [R: set_Pr1281608226676607948nteger,S: set_Pr1281608226676607948nteger] :
% 0.29/0.51        ( ( ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ R ) )
% 0.29/0.51          = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ S ) ) )
% 0.29/0.51        = ( R = S ) ) ).
% 0.29/0.51  
% 0.29/0.51  % pred_equals_eq2
% 0.29/0.51  thf(fact_1505_pred__equals__eq2,axiom,
% 0.29/0.51      ! [R: set_Pr3286484037609594932et_nat,S: set_Pr3286484037609594932et_nat] :
% 0.29/0.51        ( ( ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R ) )
% 0.29/0.51          = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ S ) ) )
% 0.29/0.51        = ( R = S ) ) ).
% 0.29/0.51  
% 0.29/0.51  % pred_equals_eq2
% 0.29/0.51  thf(fact_1506_pred__equals__eq2,axiom,
% 0.29/0.51      ! [R: set_Pr8536935166611901872et_nat,S: set_Pr8536935166611901872et_nat] :
% 0.29/0.51        ( ( ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R ) )
% 0.29/0.51          = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ S ) ) )
% 0.29/0.51        = ( R = S ) ) ).
% 0.29/0.51  
% 0.29/0.51  % pred_equals_eq2
% 0.29/0.51  thf(fact_1507_pred__equals__eq2,axiom,
% 0.29/0.51      ! [R: set_Pr9222295170931077689nt_int,S: set_Pr9222295170931077689nt_int] :
% 0.29/0.51        ( ( ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ R ) )
% 0.29/0.51          = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ S ) ) )
% 0.29/0.51        = ( R = S ) ) ).
% 0.29/0.51  
% 0.29/0.51  % pred_equals_eq2
% 0.29/0.51  thf(fact_1508_pred__equals__eq2,axiom,
% 0.29/0.51      ! [R: set_Pr1872883991513573699nt_int,S: set_Pr1872883991513573699nt_int] :
% 0.29/0.51        ( ( ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ R ) )
% 0.29/0.51          = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ S ) ) )
% 0.29/0.51        = ( R = S ) ) ).
% 0.29/0.51  
% 0.29/0.51  % pred_equals_eq2
% 0.29/0.51  thf(fact_1509_top__empty__eq2,axiom,
% 0.29/0.51      ( top_to8112647782992986859eger_o
% 0.29/0.51      = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ top_to7512759353274530428nteger ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % top_empty_eq2
% 0.29/0.51  thf(fact_1510_top__empty__eq2,axiom,
% 0.29/0.51      ( top_to2428096842796733269_nat_o
% 0.29/0.51      = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ top_to8753217654552796900et_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % top_empty_eq2
% 0.29/0.51  thf(fact_1511_top__empty__eq2,axiom,
% 0.29/0.51      ( top_to7190503160269336793_nat_o
% 0.29/0.51      = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ top_to1599102959340997728et_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % top_empty_eq2
% 0.29/0.51  thf(fact_1512_top__empty__eq2,axiom,
% 0.29/0.51      ( top_to6261655714344447806_int_o
% 0.29/0.51      = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ top_to3181862456159035625nt_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % top_empty_eq2
% 0.29/0.51  thf(fact_1513_top__empty__eq2,axiom,
% 0.29/0.51      ( top_to6513043852502318900_int_o
% 0.29/0.51      = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ top_to2069137843433766899nt_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % top_empty_eq2
% 0.29/0.51  thf(fact_1514_times__assn__raw_Opelims_I3_J,axiom,
% 0.29/0.51      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 0.29/0.51        ( ~ ( times_assn_raw @ X @ Xa @ Xb )
% 0.29/0.51       => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 0.29/0.51         => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 0.29/0.51                ( ( Xb
% 0.29/0.51                  = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.51               => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As4 ) ) ) )
% 0.29/0.51                 => ? [As13: set_nat,As23: set_nat] :
% 0.29/0.51                      ( ( As4
% 0.29/0.51                        = ( sup_sup_set_nat @ As13 @ As23 ) )
% 0.29/0.51                      & ( ( inf_inf_set_nat @ As13 @ As23 )
% 0.29/0.51                        = bot_bot_set_nat )
% 0.29/0.51                      & ( X @ ( produc7507926704131184380et_nat @ H @ As13 ) )
% 0.29/0.51                      & ( Xa @ ( produc7507926704131184380et_nat @ H @ As23 ) ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % times_assn_raw.pelims(3)
% 0.29/0.51  thf(fact_1515_times__assn__raw_Opelims_I2_J,axiom,
% 0.29/0.51      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 0.29/0.51        ( ( times_assn_raw @ X @ Xa @ Xb )
% 0.29/0.51       => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 0.29/0.51         => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 0.29/0.51                ( ( Xb
% 0.29/0.51                  = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.51               => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As4 ) ) ) )
% 0.29/0.51                 => ~ ? [As12: set_nat,As22: set_nat] :
% 0.29/0.51                        ( ( As4
% 0.29/0.51                          = ( sup_sup_set_nat @ As12 @ As22 ) )
% 0.29/0.51                        & ( ( inf_inf_set_nat @ As12 @ As22 )
% 0.29/0.51                          = bot_bot_set_nat )
% 0.29/0.51                        & ( X @ ( produc7507926704131184380et_nat @ H @ As12 ) )
% 0.29/0.51                        & ( Xa @ ( produc7507926704131184380et_nat @ H @ As22 ) ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % times_assn_raw.pelims(2)
% 0.29/0.51  thf(fact_1516_times__assn__raw_Opelims_I1_J,axiom,
% 0.29/0.51      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 0.29/0.51        ( ( ( times_assn_raw @ X @ Xa @ Xb )
% 0.29/0.51          = Y )
% 0.29/0.51       => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 0.29/0.51         => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 0.29/0.51                ( ( Xb
% 0.29/0.51                  = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.51               => ( ( Y
% 0.29/0.51                    = ( ? [As1: set_nat,As2: set_nat] :
% 0.29/0.51                          ( ( As4
% 0.29/0.51                            = ( sup_sup_set_nat @ As1 @ As2 ) )
% 0.29/0.51                          & ( ( inf_inf_set_nat @ As1 @ As2 )
% 0.29/0.51                            = bot_bot_set_nat )
% 0.29/0.51                          & ( X @ ( produc7507926704131184380et_nat @ H @ As1 ) )
% 0.29/0.51                          & ( Xa @ ( produc7507926704131184380et_nat @ H @ As2 ) ) ) ) )
% 0.29/0.51                 => ~ ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As4 ) ) ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % times_assn_raw.pelims(1)
% 0.29/0.51  thf(fact_1517_Set_Ois__empty__def,axiom,
% 0.29/0.51      ( is_emp1662574758705540307at_nat
% 0.29/0.51      = ( ^ [A4: set_Pr1261947904930325089at_nat] : ( A4 = bot_bo2099793752762293965at_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Set.is_empty_def
% 0.29/0.51  thf(fact_1518_Set_Ois__empty__def,axiom,
% 0.29/0.51      ( is_empty_o
% 0.29/0.51      = ( ^ [A4: set_o] : ( A4 = bot_bot_set_o ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Set.is_empty_def
% 0.29/0.51  thf(fact_1519_Set_Ois__empty__def,axiom,
% 0.29/0.51      ( is_empty_nat
% 0.29/0.51      = ( ^ [A4: set_nat] : ( A4 = bot_bot_set_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Set.is_empty_def
% 0.29/0.51  thf(fact_1520_Set_Ois__empty__def,axiom,
% 0.29/0.51      ( is_empty_int
% 0.29/0.51      = ( ^ [A4: set_int] : ( A4 = bot_bot_set_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Set.is_empty_def
% 0.29/0.51  thf(fact_1521_wand__assnI,axiom,
% 0.29/0.51      ! [H3: heap_e7401611519738050253t_unit,As: set_nat,Q2: assn,R: assn] :
% 0.29/0.51        ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 0.29/0.51       => ( ! [H5: heap_e7401611519738050253t_unit,As5: set_nat] :
% 0.29/0.51              ( ( ( inf_inf_set_nat @ As @ As5 )
% 0.29/0.51                = bot_bot_set_nat )
% 0.29/0.51             => ( ( relH @ As @ H3 @ H5 )
% 0.29/0.51               => ( ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As ) )
% 0.29/0.51                 => ( ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H5 @ As5 ) )
% 0.29/0.51                   => ( rep_assn @ R @ ( produc7507926704131184380et_nat @ H5 @ ( sup_sup_set_nat @ As @ As5 ) ) ) ) ) ) )
% 0.29/0.51         => ( rep_assn @ ( wand_assn @ Q2 @ R ) @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % wand_assnI
% 0.29/0.51  thf(fact_1522_vimage__if,axiom,
% 0.29/0.51      ! [C: nat,A2: set_nat,D2: nat,B2: set_o] :
% 0.29/0.51        ( ( ( member_nat @ C @ A2 )
% 0.29/0.51         => ( ( ( member_nat @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_o_nat
% 0.29/0.51                  @ ^ [X3: $o] : ( if_nat @ ( member_o @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = top_top_set_o ) )
% 0.29/0.51            & ( ~ ( member_nat @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_o_nat
% 0.29/0.51                  @ ^ [X3: $o] : ( if_nat @ ( member_o @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = B2 ) ) ) )
% 0.29/0.51        & ( ~ ( member_nat @ C @ A2 )
% 0.29/0.51         => ( ( ( member_nat @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_o_nat
% 0.29/0.51                  @ ^ [X3: $o] : ( if_nat @ ( member_o @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = ( uminus_uminus_set_o @ B2 ) ) )
% 0.29/0.51            & ( ~ ( member_nat @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_o_nat
% 0.29/0.51                  @ ^ [X3: $o] : ( if_nat @ ( member_o @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = bot_bot_set_o ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_if
% 0.29/0.51  thf(fact_1523_vimage__if,axiom,
% 0.29/0.51      ! [C: int,A2: set_int,D2: int,B2: set_o] :
% 0.29/0.51        ( ( ( member_int @ C @ A2 )
% 0.29/0.51         => ( ( ( member_int @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_o_int
% 0.29/0.51                  @ ^ [X3: $o] : ( if_int @ ( member_o @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = top_top_set_o ) )
% 0.29/0.51            & ( ~ ( member_int @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_o_int
% 0.29/0.51                  @ ^ [X3: $o] : ( if_int @ ( member_o @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = B2 ) ) ) )
% 0.29/0.51        & ( ~ ( member_int @ C @ A2 )
% 0.29/0.51         => ( ( ( member_int @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_o_int
% 0.29/0.51                  @ ^ [X3: $o] : ( if_int @ ( member_o @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = ( uminus_uminus_set_o @ B2 ) ) )
% 0.29/0.51            & ( ~ ( member_int @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_o_int
% 0.29/0.51                  @ ^ [X3: $o] : ( if_int @ ( member_o @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = bot_bot_set_o ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_if
% 0.29/0.51  thf(fact_1524_vimage__if,axiom,
% 0.29/0.51      ! [C: nat,A2: set_nat,D2: nat,B2: set_rat] :
% 0.29/0.51        ( ( ( member_nat @ C @ A2 )
% 0.29/0.51         => ( ( ( member_nat @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_rat_nat
% 0.29/0.51                  @ ^ [X3: rat] : ( if_nat @ ( member_rat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = top_top_set_rat ) )
% 0.29/0.51            & ( ~ ( member_nat @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_rat_nat
% 0.29/0.51                  @ ^ [X3: rat] : ( if_nat @ ( member_rat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = B2 ) ) ) )
% 0.29/0.51        & ( ~ ( member_nat @ C @ A2 )
% 0.29/0.51         => ( ( ( member_nat @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_rat_nat
% 0.29/0.51                  @ ^ [X3: rat] : ( if_nat @ ( member_rat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = ( uminus2201863774496077783et_rat @ B2 ) ) )
% 0.29/0.51            & ( ~ ( member_nat @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_rat_nat
% 0.29/0.51                  @ ^ [X3: rat] : ( if_nat @ ( member_rat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = bot_bot_set_rat ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_if
% 0.29/0.51  thf(fact_1525_vimage__if,axiom,
% 0.29/0.51      ! [C: int,A2: set_int,D2: int,B2: set_rat] :
% 0.29/0.51        ( ( ( member_int @ C @ A2 )
% 0.29/0.51         => ( ( ( member_int @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_rat_int
% 0.29/0.51                  @ ^ [X3: rat] : ( if_int @ ( member_rat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = top_top_set_rat ) )
% 0.29/0.51            & ( ~ ( member_int @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_rat_int
% 0.29/0.51                  @ ^ [X3: rat] : ( if_int @ ( member_rat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = B2 ) ) ) )
% 0.29/0.51        & ( ~ ( member_int @ C @ A2 )
% 0.29/0.51         => ( ( ( member_int @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_rat_int
% 0.29/0.51                  @ ^ [X3: rat] : ( if_int @ ( member_rat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = ( uminus2201863774496077783et_rat @ B2 ) ) )
% 0.29/0.51            & ( ~ ( member_int @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_rat_int
% 0.29/0.51                  @ ^ [X3: rat] : ( if_int @ ( member_rat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = bot_bot_set_rat ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_if
% 0.29/0.51  thf(fact_1526_vimage__if,axiom,
% 0.29/0.51      ! [C: nat,A2: set_nat,D2: nat,B2: set_nat] :
% 0.29/0.51        ( ( ( member_nat @ C @ A2 )
% 0.29/0.51         => ( ( ( member_nat @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_nat_nat
% 0.29/0.51                  @ ^ [X3: nat] : ( if_nat @ ( member_nat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = top_top_set_nat ) )
% 0.29/0.51            & ( ~ ( member_nat @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_nat_nat
% 0.29/0.51                  @ ^ [X3: nat] : ( if_nat @ ( member_nat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = B2 ) ) ) )
% 0.29/0.51        & ( ~ ( member_nat @ C @ A2 )
% 0.29/0.51         => ( ( ( member_nat @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_nat_nat
% 0.29/0.51                  @ ^ [X3: nat] : ( if_nat @ ( member_nat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = ( uminus5710092332889474511et_nat @ B2 ) ) )
% 0.29/0.51            & ( ~ ( member_nat @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_nat_nat
% 0.29/0.51                  @ ^ [X3: nat] : ( if_nat @ ( member_nat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = bot_bot_set_nat ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_if
% 0.29/0.51  thf(fact_1527_vimage__if,axiom,
% 0.29/0.51      ! [C: int,A2: set_int,D2: int,B2: set_nat] :
% 0.29/0.51        ( ( ( member_int @ C @ A2 )
% 0.29/0.51         => ( ( ( member_int @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_nat_int
% 0.29/0.51                  @ ^ [X3: nat] : ( if_int @ ( member_nat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = top_top_set_nat ) )
% 0.29/0.51            & ( ~ ( member_int @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_nat_int
% 0.29/0.51                  @ ^ [X3: nat] : ( if_int @ ( member_nat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = B2 ) ) ) )
% 0.29/0.51        & ( ~ ( member_int @ C @ A2 )
% 0.29/0.51         => ( ( ( member_int @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_nat_int
% 0.29/0.51                  @ ^ [X3: nat] : ( if_int @ ( member_nat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = ( uminus5710092332889474511et_nat @ B2 ) ) )
% 0.29/0.51            & ( ~ ( member_int @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_nat_int
% 0.29/0.51                  @ ^ [X3: nat] : ( if_int @ ( member_nat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = bot_bot_set_nat ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_if
% 0.29/0.51  thf(fact_1528_vimage__if,axiom,
% 0.29/0.51      ! [C: nat,A2: set_nat,D2: nat,B2: set_int] :
% 0.29/0.51        ( ( ( member_nat @ C @ A2 )
% 0.29/0.51         => ( ( ( member_nat @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_int_nat
% 0.29/0.51                  @ ^ [X3: int] : ( if_nat @ ( member_int @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = top_top_set_int ) )
% 0.29/0.51            & ( ~ ( member_nat @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_int_nat
% 0.29/0.51                  @ ^ [X3: int] : ( if_nat @ ( member_int @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = B2 ) ) ) )
% 0.29/0.51        & ( ~ ( member_nat @ C @ A2 )
% 0.29/0.51         => ( ( ( member_nat @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_int_nat
% 0.29/0.51                  @ ^ [X3: int] : ( if_nat @ ( member_int @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = ( uminus1532241313380277803et_int @ B2 ) ) )
% 0.29/0.51            & ( ~ ( member_nat @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_int_nat
% 0.29/0.51                  @ ^ [X3: int] : ( if_nat @ ( member_int @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = bot_bot_set_int ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_if
% 0.29/0.51  thf(fact_1529_vimage__if,axiom,
% 0.29/0.51      ! [C: int,A2: set_int,D2: int,B2: set_int] :
% 0.29/0.51        ( ( ( member_int @ C @ A2 )
% 0.29/0.51         => ( ( ( member_int @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_int_int
% 0.29/0.51                  @ ^ [X3: int] : ( if_int @ ( member_int @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = top_top_set_int ) )
% 0.29/0.51            & ( ~ ( member_int @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_int_int
% 0.29/0.51                  @ ^ [X3: int] : ( if_int @ ( member_int @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = B2 ) ) ) )
% 0.29/0.51        & ( ~ ( member_int @ C @ A2 )
% 0.29/0.51         => ( ( ( member_int @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_int_int
% 0.29/0.51                  @ ^ [X3: int] : ( if_int @ ( member_int @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = ( uminus1532241313380277803et_int @ B2 ) ) )
% 0.29/0.51            & ( ~ ( member_int @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_int_int
% 0.29/0.51                  @ ^ [X3: int] : ( if_int @ ( member_int @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = bot_bot_set_int ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_if
% 0.29/0.51  thf(fact_1530_vimage__if,axiom,
% 0.29/0.51      ! [C: nat,A2: set_nat,D2: nat,B2: set_set_nat] :
% 0.29/0.51        ( ( ( member_nat @ C @ A2 )
% 0.29/0.51         => ( ( ( member_nat @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_set_nat_nat
% 0.29/0.51                  @ ^ [X3: set_nat] : ( if_nat @ ( member_set_nat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = top_top_set_set_nat ) )
% 0.29/0.51            & ( ~ ( member_nat @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_set_nat_nat
% 0.29/0.51                  @ ^ [X3: set_nat] : ( if_nat @ ( member_set_nat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = B2 ) ) ) )
% 0.29/0.51        & ( ~ ( member_nat @ C @ A2 )
% 0.29/0.51         => ( ( ( member_nat @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_set_nat_nat
% 0.29/0.51                  @ ^ [X3: set_nat] : ( if_nat @ ( member_set_nat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = ( uminus613421341184616069et_nat @ B2 ) ) )
% 0.29/0.51            & ( ~ ( member_nat @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_set_nat_nat
% 0.29/0.51                  @ ^ [X3: set_nat] : ( if_nat @ ( member_set_nat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = bot_bot_set_set_nat ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_if
% 0.29/0.51  thf(fact_1531_vimage__if,axiom,
% 0.29/0.51      ! [C: int,A2: set_int,D2: int,B2: set_set_nat] :
% 0.29/0.51        ( ( ( member_int @ C @ A2 )
% 0.29/0.51         => ( ( ( member_int @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_set_nat_int
% 0.29/0.51                  @ ^ [X3: set_nat] : ( if_int @ ( member_set_nat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = top_top_set_set_nat ) )
% 0.29/0.51            & ( ~ ( member_int @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_set_nat_int
% 0.29/0.51                  @ ^ [X3: set_nat] : ( if_int @ ( member_set_nat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = B2 ) ) ) )
% 0.29/0.51        & ( ~ ( member_int @ C @ A2 )
% 0.29/0.51         => ( ( ( member_int @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_set_nat_int
% 0.29/0.51                  @ ^ [X3: set_nat] : ( if_int @ ( member_set_nat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = ( uminus613421341184616069et_nat @ B2 ) ) )
% 0.29/0.51            & ( ~ ( member_int @ D2 @ A2 )
% 0.29/0.51             => ( ( vimage_set_nat_int
% 0.29/0.51                  @ ^ [X3: set_nat] : ( if_int @ ( member_set_nat @ X3 @ B2 ) @ C @ D2 )
% 0.29/0.51                  @ A2 )
% 0.29/0.51                = bot_bot_set_set_nat ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_if
% 0.29/0.51  thf(fact_1532_BNF__Composition_Otype__definition__id__bnf__UNIV,axiom,
% 0.29/0.51      type_d5972188401318659438st_nat @ bNF_id_bnf_list_nat @ bNF_id_bnf_list_nat @ top_top_set_list_nat ).
% 0.29/0.51  
% 0.29/0.51  % BNF_Composition.type_definition_id_bnf_UNIV
% 0.29/0.51  thf(fact_1533_BNF__Composition_Otype__definition__id__bnf__UNIV,axiom,
% 0.29/0.51      type_definition_o_o @ bNF_id_bnf_o @ bNF_id_bnf_o @ top_top_set_o ).
% 0.29/0.51  
% 0.29/0.51  % BNF_Composition.type_definition_id_bnf_UNIV
% 0.29/0.51  thf(fact_1534_BNF__Composition_Otype__definition__id__bnf__UNIV,axiom,
% 0.29/0.51      type_d5298809244756387038at_rat @ bNF_id_bnf_rat @ bNF_id_bnf_rat @ top_top_set_rat ).
% 0.29/0.51  
% 0.29/0.51  % BNF_Composition.type_definition_id_bnf_UNIV
% 0.29/0.51  thf(fact_1535_BNF__Composition_Otype__definition__id__bnf__UNIV,axiom,
% 0.29/0.51      type_d6250493948777748686at_nat @ bNF_id_bnf_nat @ bNF_id_bnf_nat @ top_top_set_nat ).
% 0.29/0.51  
% 0.29/0.51  % BNF_Composition.type_definition_id_bnf_UNIV
% 0.29/0.51  thf(fact_1536_BNF__Composition_Otype__definition__id__bnf__UNIV,axiom,
% 0.29/0.51      type_d7247357190169752966nt_int @ bNF_id_bnf_int @ bNF_id_bnf_int @ top_top_set_int ).
% 0.29/0.51  
% 0.29/0.51  % BNF_Composition.type_definition_id_bnf_UNIV
% 0.29/0.51  thf(fact_1537_dbl__dec__simps_I3_J,axiom,
% 0.29/0.51      ( ( neg_nu7757733837767384882nteger @ one_one_Code_integer )
% 0.29/0.51      = one_one_Code_integer ) ).
% 0.29/0.51  
% 0.29/0.51  % dbl_dec_simps(3)
% 0.29/0.51  thf(fact_1538_dbl__dec__simps_I3_J,axiom,
% 0.29/0.51      ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 0.29/0.51      = one_one_rat ) ).
% 0.29/0.51  
% 0.29/0.51  % dbl_dec_simps(3)
% 0.29/0.51  thf(fact_1539_dbl__dec__simps_I3_J,axiom,
% 0.29/0.51      ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 0.29/0.51      = one_one_int ) ).
% 0.29/0.51  
% 0.29/0.51  % dbl_dec_simps(3)
% 0.29/0.51  thf(fact_1540_wand__raw_Oelims_I3_J,axiom,
% 0.29/0.51      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 0.29/0.51        ( ~ ( wand_raw @ X @ Xa @ Xb )
% 0.29/0.51       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 0.29/0.51              ( ( Xb
% 0.29/0.51                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.51             => ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.51                & ! [H5: heap_e7401611519738050253t_unit,As5: set_nat] :
% 0.29/0.51                    ( ( ( ( inf_inf_set_nat @ As4 @ As5 )
% 0.29/0.51                        = bot_bot_set_nat )
% 0.29/0.51                      & ( relH @ As4 @ H @ H5 )
% 0.29/0.51                      & ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As4 ) )
% 0.29/0.51                      & ( X @ ( produc7507926704131184380et_nat @ H5 @ As5 ) ) )
% 0.29/0.51                   => ( Xa @ ( produc7507926704131184380et_nat @ H5 @ ( sup_sup_set_nat @ As4 @ As5 ) ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % wand_raw.elims(3)
% 0.29/0.51  thf(fact_1541_wand__raw_Oelims_I2_J,axiom,
% 0.29/0.51      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 0.29/0.51        ( ( wand_raw @ X @ Xa @ Xb )
% 0.29/0.51       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 0.29/0.51              ( ( Xb
% 0.29/0.51                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.51             => ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.51                  & ! [H6: heap_e7401611519738050253t_unit,As6: set_nat] :
% 0.29/0.51                      ( ( ( ( inf_inf_set_nat @ As4 @ As6 )
% 0.29/0.51                          = bot_bot_set_nat )
% 0.29/0.51                        & ( relH @ As4 @ H @ H6 )
% 0.29/0.51                        & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As4 ) )
% 0.29/0.51                        & ( X @ ( produc7507926704131184380et_nat @ H6 @ As6 ) ) )
% 0.29/0.51                     => ( Xa @ ( produc7507926704131184380et_nat @ H6 @ ( sup_sup_set_nat @ As4 @ As6 ) ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % wand_raw.elims(2)
% 0.29/0.51  thf(fact_1542_vimage__Collect__eq,axiom,
% 0.29/0.51      ! [F2: nat > nat,P: nat > $o] :
% 0.29/0.51        ( ( vimage_nat_nat @ F2 @ ( collect_nat @ P ) )
% 0.29/0.51        = ( collect_nat
% 0.29/0.51          @ ^ [Y3: nat] : ( P @ ( F2 @ Y3 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Collect_eq
% 0.29/0.51  thf(fact_1543_vimage__Collect__eq,axiom,
% 0.29/0.51      ! [F2: int > nat,P: nat > $o] :
% 0.29/0.51        ( ( vimage_int_nat @ F2 @ ( collect_nat @ P ) )
% 0.29/0.51        = ( collect_int
% 0.29/0.51          @ ^ [Y3: int] : ( P @ ( F2 @ Y3 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Collect_eq
% 0.29/0.51  thf(fact_1544_vimage__Collect__eq,axiom,
% 0.29/0.51      ! [F2: nat > int,P: int > $o] :
% 0.29/0.51        ( ( vimage_nat_int @ F2 @ ( collect_int @ P ) )
% 0.29/0.51        = ( collect_nat
% 0.29/0.51          @ ^ [Y3: nat] : ( P @ ( F2 @ Y3 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Collect_eq
% 0.29/0.51  thf(fact_1545_vimage__Collect__eq,axiom,
% 0.29/0.51      ! [F2: int > int,P: int > $o] :
% 0.29/0.51        ( ( vimage_int_int @ F2 @ ( collect_int @ P ) )
% 0.29/0.51        = ( collect_int
% 0.29/0.51          @ ^ [Y3: int] : ( P @ ( F2 @ Y3 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Collect_eq
% 0.29/0.51  thf(fact_1546_vimage__Collect__eq,axiom,
% 0.29/0.51      ! [F2: nat > set_nat,P: set_nat > $o] :
% 0.29/0.51        ( ( vimage_nat_set_nat @ F2 @ ( collect_set_nat @ P ) )
% 0.29/0.51        = ( collect_nat
% 0.29/0.51          @ ^ [Y3: nat] : ( P @ ( F2 @ Y3 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Collect_eq
% 0.29/0.51  thf(fact_1547_vimage__Collect__eq,axiom,
% 0.29/0.51      ! [F2: int > set_nat,P: set_nat > $o] :
% 0.29/0.51        ( ( vimage_int_set_nat @ F2 @ ( collect_set_nat @ P ) )
% 0.29/0.51        = ( collect_int
% 0.29/0.51          @ ^ [Y3: int] : ( P @ ( F2 @ Y3 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Collect_eq
% 0.29/0.51  thf(fact_1548_vimage__Collect__eq,axiom,
% 0.29/0.51      ! [F2: set_nat > nat,P: nat > $o] :
% 0.29/0.51        ( ( vimage_set_nat_nat @ F2 @ ( collect_nat @ P ) )
% 0.29/0.51        = ( collect_set_nat
% 0.29/0.51          @ ^ [Y3: set_nat] : ( P @ ( F2 @ Y3 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Collect_eq
% 0.29/0.51  thf(fact_1549_vimage__Collect__eq,axiom,
% 0.29/0.51      ! [F2: set_nat > int,P: int > $o] :
% 0.29/0.51        ( ( vimage_set_nat_int @ F2 @ ( collect_int @ P ) )
% 0.29/0.51        = ( collect_set_nat
% 0.29/0.51          @ ^ [Y3: set_nat] : ( P @ ( F2 @ Y3 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Collect_eq
% 0.29/0.51  thf(fact_1550_vimage__Collect__eq,axiom,
% 0.29/0.51      ! [F2: set_nat > set_nat,P: set_nat > $o] :
% 0.29/0.51        ( ( vimage4765135879290611145et_nat @ F2 @ ( collect_set_nat @ P ) )
% 0.29/0.51        = ( collect_set_nat
% 0.29/0.51          @ ^ [Y3: set_nat] : ( P @ ( F2 @ Y3 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Collect_eq
% 0.29/0.51  thf(fact_1551_vimage__Collect__eq,axiom,
% 0.29/0.51      ! [F2: nat > set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 0.29/0.51        ( ( vimage2935056327143036492nt_int @ F2 @ ( collec5210948495886036740nt_int @ P ) )
% 0.29/0.51        = ( collect_nat
% 0.29/0.51          @ ^ [Y3: nat] : ( P @ ( F2 @ Y3 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Collect_eq
% 0.29/0.51  thf(fact_1552_vimage__empty,axiom,
% 0.29/0.51      ! [F2: $o > $o] :
% 0.29/0.51        ( ( vimage_o_o @ F2 @ bot_bot_set_o )
% 0.29/0.51        = bot_bot_set_o ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_empty
% 0.29/0.51  thf(fact_1553_vimage__empty,axiom,
% 0.29/0.51      ! [F2: nat > $o] :
% 0.29/0.51        ( ( vimage_nat_o @ F2 @ bot_bot_set_o )
% 0.29/0.51        = bot_bot_set_nat ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_empty
% 0.29/0.51  thf(fact_1554_vimage__empty,axiom,
% 0.29/0.51      ! [F2: int > $o] :
% 0.29/0.51        ( ( vimage_int_o @ F2 @ bot_bot_set_o )
% 0.29/0.51        = bot_bot_set_int ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_empty
% 0.29/0.51  thf(fact_1555_vimage__empty,axiom,
% 0.29/0.51      ! [F2: $o > nat] :
% 0.29/0.51        ( ( vimage_o_nat @ F2 @ bot_bot_set_nat )
% 0.29/0.51        = bot_bot_set_o ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_empty
% 0.29/0.51  thf(fact_1556_vimage__empty,axiom,
% 0.29/0.51      ! [F2: nat > nat] :
% 0.29/0.51        ( ( vimage_nat_nat @ F2 @ bot_bot_set_nat )
% 0.29/0.51        = bot_bot_set_nat ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_empty
% 0.29/0.51  thf(fact_1557_vimage__empty,axiom,
% 0.29/0.51      ! [F2: int > nat] :
% 0.29/0.51        ( ( vimage_int_nat @ F2 @ bot_bot_set_nat )
% 0.29/0.51        = bot_bot_set_int ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_empty
% 0.29/0.51  thf(fact_1558_vimage__empty,axiom,
% 0.29/0.51      ! [F2: $o > int] :
% 0.29/0.51        ( ( vimage_o_int @ F2 @ bot_bot_set_int )
% 0.29/0.51        = bot_bot_set_o ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_empty
% 0.29/0.51  thf(fact_1559_vimage__empty,axiom,
% 0.29/0.51      ! [F2: nat > int] :
% 0.29/0.51        ( ( vimage_nat_int @ F2 @ bot_bot_set_int )
% 0.29/0.51        = bot_bot_set_nat ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_empty
% 0.29/0.51  thf(fact_1560_vimage__empty,axiom,
% 0.29/0.51      ! [F2: int > int] :
% 0.29/0.51        ( ( vimage_int_int @ F2 @ bot_bot_set_int )
% 0.29/0.51        = bot_bot_set_int ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_empty
% 0.29/0.51  thf(fact_1561_vimage__empty,axiom,
% 0.29/0.51      ! [F2: $o > product_prod_nat_nat] :
% 0.29/0.51        ( ( vimage2606541041029201316at_nat @ F2 @ bot_bo2099793752762293965at_nat )
% 0.29/0.51        = bot_bot_set_o ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_empty
% 0.29/0.51  thf(fact_1562_vimage__UNIV,axiom,
% 0.29/0.51      ! [F2: $o > $o] :
% 0.29/0.51        ( ( vimage_o_o @ F2 @ top_top_set_o )
% 0.29/0.51        = top_top_set_o ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_UNIV
% 0.29/0.51  thf(fact_1563_vimage__UNIV,axiom,
% 0.29/0.51      ! [F2: rat > $o] :
% 0.29/0.51        ( ( vimage_rat_o @ F2 @ top_top_set_o )
% 0.29/0.51        = top_top_set_rat ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_UNIV
% 0.29/0.51  thf(fact_1564_vimage__UNIV,axiom,
% 0.29/0.51      ! [F2: nat > $o] :
% 0.29/0.51        ( ( vimage_nat_o @ F2 @ top_top_set_o )
% 0.29/0.51        = top_top_set_nat ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_UNIV
% 0.29/0.51  thf(fact_1565_vimage__UNIV,axiom,
% 0.29/0.51      ! [F2: int > $o] :
% 0.29/0.51        ( ( vimage_int_o @ F2 @ top_top_set_o )
% 0.29/0.51        = top_top_set_int ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_UNIV
% 0.29/0.51  thf(fact_1566_vimage__UNIV,axiom,
% 0.29/0.51      ! [F2: $o > rat] :
% 0.29/0.51        ( ( vimage_o_rat @ F2 @ top_top_set_rat )
% 0.29/0.51        = top_top_set_o ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_UNIV
% 0.29/0.51  thf(fact_1567_vimage__UNIV,axiom,
% 0.29/0.51      ! [F2: rat > rat] :
% 0.29/0.51        ( ( vimage_rat_rat @ F2 @ top_top_set_rat )
% 0.29/0.51        = top_top_set_rat ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_UNIV
% 0.29/0.51  thf(fact_1568_vimage__UNIV,axiom,
% 0.29/0.51      ! [F2: nat > rat] :
% 0.29/0.51        ( ( vimage_nat_rat @ F2 @ top_top_set_rat )
% 0.29/0.51        = top_top_set_nat ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_UNIV
% 0.29/0.51  thf(fact_1569_vimage__UNIV,axiom,
% 0.29/0.51      ! [F2: int > rat] :
% 0.29/0.51        ( ( vimage_int_rat @ F2 @ top_top_set_rat )
% 0.29/0.51        = top_top_set_int ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_UNIV
% 0.29/0.51  thf(fact_1570_vimage__UNIV,axiom,
% 0.29/0.51      ! [F2: $o > nat] :
% 0.29/0.51        ( ( vimage_o_nat @ F2 @ top_top_set_nat )
% 0.29/0.51        = top_top_set_o ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_UNIV
% 0.29/0.51  thf(fact_1571_vimage__UNIV,axiom,
% 0.29/0.51      ! [F2: rat > nat] :
% 0.29/0.51        ( ( vimage_rat_nat @ F2 @ top_top_set_nat )
% 0.29/0.51        = top_top_set_rat ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_UNIV
% 0.29/0.51  thf(fact_1572_vimage__Int,axiom,
% 0.29/0.51      ! [F2: product_prod_nat_nat > product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.51        ( ( vimage2449269961533847803at_nat @ F2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 0.29/0.51        = ( inf_in2572325071724192079at_nat @ ( vimage2449269961533847803at_nat @ F2 @ A2 ) @ ( vimage2449269961533847803at_nat @ F2 @ B2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Int
% 0.29/0.51  thf(fact_1573_vimage__Int,axiom,
% 0.29/0.51      ! [F2: nat > product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.51        ( ( vimage8013328719654469172at_nat @ F2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 0.29/0.51        = ( inf_inf_set_nat @ ( vimage8013328719654469172at_nat @ F2 @ A2 ) @ ( vimage8013328719654469172at_nat @ F2 @ B2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Int
% 0.29/0.51  thf(fact_1574_vimage__Int,axiom,
% 0.29/0.51      ! [F2: product_prod_nat_nat > nat,A2: set_nat,B2: set_nat] :
% 0.29/0.51        ( ( vimage4653281326611754070at_nat @ F2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.29/0.51        = ( inf_in2572325071724192079at_nat @ ( vimage4653281326611754070at_nat @ F2 @ A2 ) @ ( vimage4653281326611754070at_nat @ F2 @ B2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Int
% 0.29/0.51  thf(fact_1575_vimage__Int,axiom,
% 0.29/0.51      ! [F2: nat > nat,A2: set_nat,B2: set_nat] :
% 0.29/0.51        ( ( vimage_nat_nat @ F2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.29/0.51        = ( inf_inf_set_nat @ ( vimage_nat_nat @ F2 @ A2 ) @ ( vimage_nat_nat @ F2 @ B2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Int
% 0.29/0.51  thf(fact_1576_vimage__Un,axiom,
% 0.29/0.51      ! [F2: produc4166570645942440679at_nat > produc4166570645942440679at_nat,A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 0.29/0.51        ( ( vimage3529983231074640251at_nat @ F2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 0.29/0.51        = ( sup_su3035147773818789531at_nat @ ( vimage3529983231074640251at_nat @ F2 @ A2 ) @ ( vimage3529983231074640251at_nat @ F2 @ B2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Un
% 0.29/0.51  thf(fact_1577_vimage__Un,axiom,
% 0.29/0.51      ! [F2: produc3843707927480180839at_nat > produc4166570645942440679at_nat,A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 0.29/0.51        ( ( vimage2716263466903273467at_nat @ F2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 0.29/0.51        = ( sup_su5525570899277871387at_nat @ ( vimage2716263466903273467at_nat @ F2 @ A2 ) @ ( vimage2716263466903273467at_nat @ F2 @ B2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Un
% 0.29/0.51  thf(fact_1578_vimage__Un,axiom,
% 0.29/0.51      ! [F2: nat > produc4166570645942440679at_nat,A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 0.29/0.51        ( ( vimage7262694317370708122at_nat @ F2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 0.29/0.51        = ( sup_sup_set_nat @ ( vimage7262694317370708122at_nat @ F2 @ A2 ) @ ( vimage7262694317370708122at_nat @ F2 @ B2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Un
% 0.29/0.51  thf(fact_1579_vimage__Un,axiom,
% 0.29/0.51      ! [F2: produc4166570645942440679at_nat > produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.29/0.51        ( ( vimage5412736291816116987at_nat @ F2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 0.29/0.51        = ( sup_su3035147773818789531at_nat @ ( vimage5412736291816116987at_nat @ F2 @ A2 ) @ ( vimage5412736291816116987at_nat @ F2 @ B2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Un
% 0.29/0.51  thf(fact_1580_vimage__Un,axiom,
% 0.29/0.51      ! [F2: produc3843707927480180839at_nat > produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.29/0.51        ( ( vimage6896080417876799867at_nat @ F2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 0.29/0.51        = ( sup_su5525570899277871387at_nat @ ( vimage6896080417876799867at_nat @ F2 @ A2 ) @ ( vimage6896080417876799867at_nat @ F2 @ B2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Un
% 0.29/0.51  thf(fact_1581_vimage__Un,axiom,
% 0.29/0.51      ! [F2: nat > produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.29/0.51        ( ( vimage6435164912253009178at_nat @ F2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 0.29/0.51        = ( sup_sup_set_nat @ ( vimage6435164912253009178at_nat @ F2 @ A2 ) @ ( vimage6435164912253009178at_nat @ F2 @ B2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Un
% 0.29/0.51  thf(fact_1582_vimage__Un,axiom,
% 0.29/0.51      ! [F2: produc4166570645942440679at_nat > nat,A2: set_nat,B2: set_nat] :
% 0.29/0.51        ( ( vimage7952471809483217980at_nat @ F2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.29/0.51        = ( sup_su3035147773818789531at_nat @ ( vimage7952471809483217980at_nat @ F2 @ A2 ) @ ( vimage7952471809483217980at_nat @ F2 @ B2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Un
% 0.29/0.51  thf(fact_1583_vimage__Un,axiom,
% 0.29/0.51      ! [F2: produc3843707927480180839at_nat > nat,A2: set_nat,B2: set_nat] :
% 0.29/0.51        ( ( vimage7134676753939176892at_nat @ F2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.29/0.51        = ( sup_su5525570899277871387at_nat @ ( vimage7134676753939176892at_nat @ F2 @ A2 ) @ ( vimage7134676753939176892at_nat @ F2 @ B2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Un
% 0.29/0.51  thf(fact_1584_vimage__Un,axiom,
% 0.29/0.51      ! [F2: nat > nat,A2: set_nat,B2: set_nat] :
% 0.29/0.51        ( ( vimage_nat_nat @ F2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.29/0.51        = ( sup_sup_set_nat @ ( vimage_nat_nat @ F2 @ A2 ) @ ( vimage_nat_nat @ F2 @ B2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_Un
% 0.29/0.51  thf(fact_1585_bool__assn__proper_I1_J,axiom,
% 0.29/0.51      proper @ in_range ).
% 0.29/0.51  
% 0.29/0.51  % bool_assn_proper(1)
% 0.29/0.51  thf(fact_1586_relH__dist__union,axiom,
% 0.29/0.51      ! [As: set_nat,As3: set_nat,H3: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 0.29/0.51        ( ( relH @ ( sup_sup_set_nat @ As @ As3 ) @ H3 @ H4 )
% 0.29/0.51        = ( ( relH @ As @ H3 @ H4 )
% 0.29/0.51          & ( relH @ As3 @ H3 @ H4 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % relH_dist_union
% 0.29/0.51  thf(fact_1587_bool__assn__proper_I5_J,axiom,
% 0.29/0.51      ! [P: produc3658429121746597890et_nat > $o] :
% 0.29/0.51        ( ( proper @ P )
% 0.29/0.51       => ( proper
% 0.29/0.51          @ ^ [H2: produc3658429121746597890et_nat] :
% 0.29/0.51              ( ( in_range @ H2 )
% 0.29/0.51              & ~ ( P @ H2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % bool_assn_proper(5)
% 0.29/0.51  thf(fact_1588_in__range__empty,axiom,
% 0.29/0.51      ! [H3: heap_e7401611519738050253t_unit] : ( in_range @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % in_range_empty
% 0.29/0.51  thf(fact_1589_vimage__const,axiom,
% 0.29/0.51      ! [C: nat,A2: set_nat] :
% 0.29/0.51        ( ( ( member_nat @ C @ A2 )
% 0.29/0.51         => ( ( vimage_o_nat
% 0.29/0.51              @ ^ [X3: $o] : C
% 0.29/0.51              @ A2 )
% 0.29/0.51            = top_top_set_o ) )
% 0.29/0.51        & ( ~ ( member_nat @ C @ A2 )
% 0.29/0.51         => ( ( vimage_o_nat
% 0.29/0.51              @ ^ [X3: $o] : C
% 0.29/0.51              @ A2 )
% 0.29/0.51            = bot_bot_set_o ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_const
% 0.29/0.51  thf(fact_1590_vimage__const,axiom,
% 0.29/0.51      ! [C: int,A2: set_int] :
% 0.29/0.51        ( ( ( member_int @ C @ A2 )
% 0.29/0.51         => ( ( vimage_o_int
% 0.29/0.51              @ ^ [X3: $o] : C
% 0.29/0.51              @ A2 )
% 0.29/0.51            = top_top_set_o ) )
% 0.29/0.51        & ( ~ ( member_int @ C @ A2 )
% 0.29/0.51         => ( ( vimage_o_int
% 0.29/0.51              @ ^ [X3: $o] : C
% 0.29/0.51              @ A2 )
% 0.29/0.51            = bot_bot_set_o ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_const
% 0.29/0.51  thf(fact_1591_vimage__const,axiom,
% 0.29/0.51      ! [C: nat,A2: set_nat] :
% 0.29/0.51        ( ( ( member_nat @ C @ A2 )
% 0.29/0.51         => ( ( vimage_rat_nat
% 0.29/0.51              @ ^ [X3: rat] : C
% 0.29/0.51              @ A2 )
% 0.29/0.51            = top_top_set_rat ) )
% 0.29/0.51        & ( ~ ( member_nat @ C @ A2 )
% 0.29/0.51         => ( ( vimage_rat_nat
% 0.29/0.51              @ ^ [X3: rat] : C
% 0.29/0.51              @ A2 )
% 0.29/0.51            = bot_bot_set_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_const
% 0.29/0.51  thf(fact_1592_vimage__const,axiom,
% 0.29/0.51      ! [C: int,A2: set_int] :
% 0.29/0.51        ( ( ( member_int @ C @ A2 )
% 0.29/0.51         => ( ( vimage_rat_int
% 0.29/0.51              @ ^ [X3: rat] : C
% 0.29/0.51              @ A2 )
% 0.29/0.51            = top_top_set_rat ) )
% 0.29/0.51        & ( ~ ( member_int @ C @ A2 )
% 0.29/0.51         => ( ( vimage_rat_int
% 0.29/0.51              @ ^ [X3: rat] : C
% 0.29/0.51              @ A2 )
% 0.29/0.51            = bot_bot_set_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_const
% 0.29/0.51  thf(fact_1593_vimage__const,axiom,
% 0.29/0.51      ! [C: nat,A2: set_nat] :
% 0.29/0.51        ( ( ( member_nat @ C @ A2 )
% 0.29/0.51         => ( ( vimage_nat_nat
% 0.29/0.51              @ ^ [X3: nat] : C
% 0.29/0.51              @ A2 )
% 0.29/0.51            = top_top_set_nat ) )
% 0.29/0.51        & ( ~ ( member_nat @ C @ A2 )
% 0.29/0.51         => ( ( vimage_nat_nat
% 0.29/0.51              @ ^ [X3: nat] : C
% 0.29/0.51              @ A2 )
% 0.29/0.51            = bot_bot_set_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_const
% 0.29/0.51  thf(fact_1594_vimage__const,axiom,
% 0.29/0.51      ! [C: int,A2: set_int] :
% 0.29/0.51        ( ( ( member_int @ C @ A2 )
% 0.29/0.51         => ( ( vimage_nat_int
% 0.29/0.51              @ ^ [X3: nat] : C
% 0.29/0.51              @ A2 )
% 0.29/0.51            = top_top_set_nat ) )
% 0.29/0.51        & ( ~ ( member_int @ C @ A2 )
% 0.29/0.51         => ( ( vimage_nat_int
% 0.29/0.51              @ ^ [X3: nat] : C
% 0.29/0.51              @ A2 )
% 0.29/0.51            = bot_bot_set_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_const
% 0.29/0.51  thf(fact_1595_vimage__const,axiom,
% 0.29/0.51      ! [C: nat,A2: set_nat] :
% 0.29/0.51        ( ( ( member_nat @ C @ A2 )
% 0.29/0.51         => ( ( vimage_int_nat
% 0.29/0.51              @ ^ [X3: int] : C
% 0.29/0.51              @ A2 )
% 0.29/0.51            = top_top_set_int ) )
% 0.29/0.51        & ( ~ ( member_nat @ C @ A2 )
% 0.29/0.51         => ( ( vimage_int_nat
% 0.29/0.51              @ ^ [X3: int] : C
% 0.29/0.51              @ A2 )
% 0.29/0.51            = bot_bot_set_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_const
% 0.29/0.51  thf(fact_1596_vimage__const,axiom,
% 0.29/0.51      ! [C: int,A2: set_int] :
% 0.29/0.51        ( ( ( member_int @ C @ A2 )
% 0.29/0.51         => ( ( vimage_int_int
% 0.29/0.51              @ ^ [X3: int] : C
% 0.29/0.51              @ A2 )
% 0.29/0.51            = top_top_set_int ) )
% 0.29/0.51        & ( ~ ( member_int @ C @ A2 )
% 0.29/0.51         => ( ( vimage_int_int
% 0.29/0.51              @ ^ [X3: int] : C
% 0.29/0.51              @ A2 )
% 0.29/0.51            = bot_bot_set_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_const
% 0.29/0.51  thf(fact_1597_vimage__const,axiom,
% 0.29/0.51      ! [C: nat,A2: set_nat] :
% 0.29/0.51        ( ( ( member_nat @ C @ A2 )
% 0.29/0.51         => ( ( vimage_list_nat_nat
% 0.29/0.51              @ ^ [X3: list_nat] : C
% 0.29/0.51              @ A2 )
% 0.29/0.51            = top_top_set_list_nat ) )
% 0.29/0.51        & ( ~ ( member_nat @ C @ A2 )
% 0.29/0.51         => ( ( vimage_list_nat_nat
% 0.29/0.51              @ ^ [X3: list_nat] : C
% 0.29/0.51              @ A2 )
% 0.29/0.51            = bot_bot_set_list_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_const
% 0.29/0.51  thf(fact_1598_vimage__const,axiom,
% 0.29/0.51      ! [C: int,A2: set_int] :
% 0.29/0.51        ( ( ( member_int @ C @ A2 )
% 0.29/0.51         => ( ( vimage_list_nat_int
% 0.29/0.51              @ ^ [X3: list_nat] : C
% 0.29/0.51              @ A2 )
% 0.29/0.51            = top_top_set_list_nat ) )
% 0.29/0.51        & ( ~ ( member_int @ C @ A2 )
% 0.29/0.51         => ( ( vimage_list_nat_int
% 0.29/0.51              @ ^ [X3: list_nat] : C
% 0.29/0.51              @ A2 )
% 0.29/0.51            = bot_bot_set_list_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_const
% 0.29/0.51  thf(fact_1599_in__range__dist__union,axiom,
% 0.29/0.51      ! [H3: heap_e7401611519738050253t_unit,As: set_nat,As3: set_nat] :
% 0.29/0.51        ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ ( sup_sup_set_nat @ As @ As3 ) ) )
% 0.29/0.51        = ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 0.29/0.51          & ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As3 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % in_range_dist_union
% 0.29/0.51  thf(fact_1600_relH__sym,axiom,
% 0.29/0.51      ! [As: set_nat,H3: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 0.29/0.51        ( ( relH @ As @ H3 @ H4 )
% 0.29/0.51       => ( relH @ As @ H4 @ H3 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % relH_sym
% 0.29/0.51  thf(fact_1601_relH__trans,axiom,
% 0.29/0.51      ! [As: set_nat,H12: heap_e7401611519738050253t_unit,H23: heap_e7401611519738050253t_unit,H32: heap_e7401611519738050253t_unit] :
% 0.29/0.51        ( ( relH @ As @ H12 @ H23 )
% 0.29/0.51       => ( ( relH @ As @ H23 @ H32 )
% 0.29/0.51         => ( relH @ As @ H12 @ H32 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % relH_trans
% 0.29/0.51  thf(fact_1602_vimage__def,axiom,
% 0.29/0.51      ( vimage_nat_nat
% 0.29/0.51      = ( ^ [F: nat > nat,B4: set_nat] :
% 0.29/0.51            ( collect_nat
% 0.29/0.51            @ ^ [X3: nat] : ( member_nat @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_def
% 0.29/0.51  thf(fact_1603_vimage__def,axiom,
% 0.29/0.51      ( vimage_nat_int
% 0.29/0.51      = ( ^ [F: nat > int,B4: set_int] :
% 0.29/0.51            ( collect_nat
% 0.29/0.51            @ ^ [X3: nat] : ( member_int @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_def
% 0.29/0.51  thf(fact_1604_vimage__def,axiom,
% 0.29/0.51      ( vimage_int_nat
% 0.29/0.51      = ( ^ [F: int > nat,B4: set_nat] :
% 0.29/0.51            ( collect_int
% 0.29/0.51            @ ^ [X3: int] : ( member_nat @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_def
% 0.29/0.51  thf(fact_1605_vimage__def,axiom,
% 0.29/0.51      ( vimage_int_int
% 0.29/0.51      = ( ^ [F: int > int,B4: set_int] :
% 0.29/0.51            ( collect_int
% 0.29/0.51            @ ^ [X3: int] : ( member_int @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_def
% 0.29/0.51  thf(fact_1606_vimage__def,axiom,
% 0.29/0.51      ( vimage_set_nat_nat
% 0.29/0.51      = ( ^ [F: set_nat > nat,B4: set_nat] :
% 0.29/0.51            ( collect_set_nat
% 0.29/0.51            @ ^ [X3: set_nat] : ( member_nat @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_def
% 0.29/0.51  thf(fact_1607_vimage__def,axiom,
% 0.29/0.51      ( vimage_set_nat_int
% 0.29/0.51      = ( ^ [F: set_nat > int,B4: set_int] :
% 0.29/0.51            ( collect_set_nat
% 0.29/0.51            @ ^ [X3: set_nat] : ( member_int @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_def
% 0.29/0.51  thf(fact_1608_vimage__def,axiom,
% 0.29/0.51      ( vimage_nat_set_nat
% 0.29/0.51      = ( ^ [F: nat > set_nat,B4: set_set_nat] :
% 0.29/0.51            ( collect_nat
% 0.29/0.51            @ ^ [X3: nat] : ( member_set_nat @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_def
% 0.29/0.51  thf(fact_1609_vimage__def,axiom,
% 0.29/0.51      ( vimage_int_set_nat
% 0.29/0.51      = ( ^ [F: int > set_nat,B4: set_set_nat] :
% 0.29/0.51            ( collect_int
% 0.29/0.51            @ ^ [X3: int] : ( member_set_nat @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_def
% 0.29/0.51  thf(fact_1610_vimage__def,axiom,
% 0.29/0.51      ( vimage4765135879290611145et_nat
% 0.29/0.51      = ( ^ [F: set_nat > set_nat,B4: set_set_nat] :
% 0.29/0.51            ( collect_set_nat
% 0.29/0.51            @ ^ [X3: set_nat] : ( member_set_nat @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_def
% 0.29/0.51  thf(fact_1611_vimage__def,axiom,
% 0.29/0.51      ( vimage928727498438615150nt_nat
% 0.29/0.51      = ( ^ [F: set_Pr958786334691620121nt_int > nat,B4: set_nat] :
% 0.29/0.51            ( collec5210948495886036740nt_int
% 0.29/0.51            @ ^ [X3: set_Pr958786334691620121nt_int] : ( member_nat @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % vimage_def
% 0.29/0.51  thf(fact_1612_relH__in__rangeI_I2_J,axiom,
% 0.29/0.51      ! [As: set_nat,H3: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 0.29/0.51        ( ( relH @ As @ H3 @ H4 )
% 0.29/0.51       => ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % relH_in_rangeI(2)
% 0.29/0.51  thf(fact_1613_relH__in__rangeI_I1_J,axiom,
% 0.29/0.51      ! [As: set_nat,H3: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 0.29/0.51        ( ( relH @ As @ H3 @ H4 )
% 0.29/0.51       => ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % relH_in_rangeI(1)
% 0.29/0.51  thf(fact_1614_relH__refl,axiom,
% 0.29/0.51      ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.29/0.51        ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 0.29/0.51       => ( relH @ As @ H3 @ H3 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % relH_refl
% 0.29/0.51  thf(fact_1615_proper__iff,axiom,
% 0.29/0.51      ! [P: produc3658429121746597890et_nat > $o,As: set_nat,H3: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 0.29/0.51        ( ( proper @ P )
% 0.29/0.51       => ( ( relH @ As @ H3 @ H4 )
% 0.29/0.51         => ( ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As ) )
% 0.29/0.51           => ( ( P @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 0.29/0.51              = ( P @ ( produc7507926704131184380et_nat @ H4 @ As ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % proper_iff
% 0.29/0.51  thf(fact_1616_proper__def,axiom,
% 0.29/0.51      ( proper
% 0.29/0.51      = ( ^ [P2: produc3658429121746597890et_nat > $o] :
% 0.29/0.51          ! [H2: heap_e7401611519738050253t_unit,H7: heap_e7401611519738050253t_unit,As7: set_nat] :
% 0.29/0.51            ( ( ( P2 @ ( produc7507926704131184380et_nat @ H2 @ As7 ) )
% 0.29/0.51             => ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As7 ) ) )
% 0.29/0.51            & ( ( ( P2 @ ( produc7507926704131184380et_nat @ H2 @ As7 ) )
% 0.29/0.51                & ( relH @ As7 @ H2 @ H7 )
% 0.29/0.51                & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As7 ) ) )
% 0.29/0.51             => ( P2 @ ( produc7507926704131184380et_nat @ H7 @ As7 ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % proper_def
% 0.29/0.51  thf(fact_1617_properD2,axiom,
% 0.29/0.51      ! [P: produc3658429121746597890et_nat > $o,H3: heap_e7401611519738050253t_unit,As: set_nat,H4: heap_e7401611519738050253t_unit] :
% 0.29/0.51        ( ( proper @ P )
% 0.29/0.51       => ( ( P @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 0.29/0.51         => ( ( relH @ As @ H3 @ H4 )
% 0.29/0.51           => ( ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As ) )
% 0.29/0.51             => ( P @ ( produc7507926704131184380et_nat @ H4 @ As ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % properD2
% 0.29/0.51  thf(fact_1618_properI,axiom,
% 0.29/0.51      ! [P: produc3658429121746597890et_nat > $o] :
% 0.29/0.51        ( ! [As4: set_nat,H: heap_e7401611519738050253t_unit] :
% 0.29/0.51            ( ( P @ ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.51           => ( in_range @ ( produc7507926704131184380et_nat @ H @ As4 ) ) )
% 0.29/0.51       => ( ! [As4: set_nat,H: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 0.29/0.51              ( ( P @ ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.51             => ( ( relH @ As4 @ H @ H5 )
% 0.29/0.51               => ( ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As4 ) )
% 0.29/0.51                 => ( P @ ( produc7507926704131184380et_nat @ H5 @ As4 ) ) ) ) )
% 0.29/0.51         => ( proper @ P ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % properI
% 0.29/0.51  thf(fact_1619_models__in__range,axiom,
% 0.29/0.51      ! [P: assn,H3: produc3658429121746597890et_nat] :
% 0.29/0.51        ( ( rep_assn @ P @ H3 )
% 0.29/0.51       => ( in_range @ H3 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % models_in_range
% 0.29/0.51  thf(fact_1620_top__assn__def,axiom,
% 0.29/0.51      ( top_top_assn
% 0.29/0.51      = ( abs_assn @ in_range ) ) ).
% 0.29/0.51  
% 0.29/0.51  % top_assn_def
% 0.29/0.51  thf(fact_1621_properD1,axiom,
% 0.29/0.51      ! [P: produc3658429121746597890et_nat > $o,H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.29/0.51        ( ( proper @ P )
% 0.29/0.51       => ( ( P @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 0.29/0.51         => ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % properD1
% 0.29/0.51  thf(fact_1622_mod__relH,axiom,
% 0.29/0.51      ! [As: set_nat,H3: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit,P: assn] :
% 0.29/0.51        ( ( relH @ As @ H3 @ H4 )
% 0.29/0.51       => ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 0.29/0.51          = ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H4 @ As ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mod_relH
% 0.29/0.51  thf(fact_1623_uminus__assn__def,axiom,
% 0.29/0.51      ( uminus_uminus_assn
% 0.29/0.51      = ( ^ [P2: assn] :
% 0.29/0.51            ( abs_assn
% 0.29/0.51            @ ^ [H2: produc3658429121746597890et_nat] :
% 0.29/0.51                ( ( in_range @ H2 )
% 0.29/0.51                & ~ ( rep_assn @ P2 @ H2 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % uminus_assn_def
% 0.29/0.51  thf(fact_1624_wand__raw_Osimps,axiom,
% 0.29/0.51      ! [P: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o,H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.29/0.51        ( ( wand_raw @ P @ Q2 @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 0.29/0.51        = ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 0.29/0.51          & ! [H7: heap_e7401611519738050253t_unit,As8: set_nat] :
% 0.29/0.51              ( ( ( ( inf_inf_set_nat @ As @ As8 )
% 0.29/0.51                  = bot_bot_set_nat )
% 0.29/0.51                & ( relH @ As @ H3 @ H7 )
% 0.29/0.51                & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As ) )
% 0.29/0.51                & ( P @ ( produc7507926704131184380et_nat @ H7 @ As8 ) ) )
% 0.29/0.51             => ( Q2 @ ( produc7507926704131184380et_nat @ H7 @ ( sup_sup_set_nat @ As @ As8 ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % wand_raw.simps
% 0.29/0.51  thf(fact_1625_wand__raw_Oelims_I1_J,axiom,
% 0.29/0.51      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 0.29/0.51        ( ( ( wand_raw @ X @ Xa @ Xb )
% 0.29/0.51          = Y )
% 0.29/0.51       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 0.29/0.51              ( ( Xb
% 0.29/0.51                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.51             => ( Y
% 0.29/0.51                = ( ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.51                      & ! [H7: heap_e7401611519738050253t_unit,As8: set_nat] :
% 0.29/0.51                          ( ( ( ( inf_inf_set_nat @ As4 @ As8 )
% 0.29/0.51                              = bot_bot_set_nat )
% 0.29/0.51                            & ( relH @ As4 @ H @ H7 )
% 0.29/0.51                            & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As4 ) )
% 0.29/0.51                            & ( X @ ( produc7507926704131184380et_nat @ H7 @ As8 ) ) )
% 0.29/0.51                         => ( Xa @ ( produc7507926704131184380et_nat @ H7 @ ( sup_sup_set_nat @ As4 @ As8 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % wand_raw.elims(1)
% 0.29/0.51  thf(fact_1626_wand__raw_Opelims_I1_J,axiom,
% 0.29/0.51      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 0.29/0.51        ( ( ( wand_raw @ X @ Xa @ Xb )
% 0.29/0.51          = Y )
% 0.29/0.51       => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 0.29/0.51         => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 0.29/0.51                ( ( Xb
% 0.29/0.51                  = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.51               => ( ( Y
% 0.29/0.51                    = ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.51                      & ! [H7: heap_e7401611519738050253t_unit,As8: set_nat] :
% 0.29/0.51                          ( ( ( ( inf_inf_set_nat @ As4 @ As8 )
% 0.29/0.51                              = bot_bot_set_nat )
% 0.29/0.51                            & ( relH @ As4 @ H @ H7 )
% 0.29/0.51                            & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As4 ) )
% 0.29/0.51                            & ( X @ ( produc7507926704131184380et_nat @ H7 @ As8 ) ) )
% 0.29/0.51                         => ( Xa @ ( produc7507926704131184380et_nat @ H7 @ ( sup_sup_set_nat @ As4 @ As8 ) ) ) ) ) )
% 0.29/0.51                 => ~ ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As4 ) ) ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % wand_raw.pelims(1)
% 0.29/0.51  thf(fact_1627_wand__raw_Opelims_I2_J,axiom,
% 0.29/0.51      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 0.29/0.51        ( ( wand_raw @ X @ Xa @ Xb )
% 0.29/0.51       => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 0.29/0.51         => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 0.29/0.51                ( ( Xb
% 0.29/0.51                  = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.51               => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As4 ) ) ) )
% 0.29/0.51                 => ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.51                      & ! [H6: heap_e7401611519738050253t_unit,As6: set_nat] :
% 0.29/0.51                          ( ( ( ( inf_inf_set_nat @ As4 @ As6 )
% 0.29/0.51                              = bot_bot_set_nat )
% 0.29/0.51                            & ( relH @ As4 @ H @ H6 )
% 0.29/0.51                            & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As4 ) )
% 0.29/0.51                            & ( X @ ( produc7507926704131184380et_nat @ H6 @ As6 ) ) )
% 0.29/0.51                         => ( Xa @ ( produc7507926704131184380et_nat @ H6 @ ( sup_sup_set_nat @ As4 @ As6 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % wand_raw.pelims(2)
% 0.29/0.51  thf(fact_1628_wand__raw_Opelims_I3_J,axiom,
% 0.29/0.51      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 0.29/0.51        ( ~ ( wand_raw @ X @ Xa @ Xb )
% 0.29/0.51       => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 0.29/0.51         => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 0.29/0.51                ( ( Xb
% 0.29/0.51                  = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.51               => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As4 ) ) ) )
% 0.29/0.51                 => ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.29/0.51                    & ! [H5: heap_e7401611519738050253t_unit,As5: set_nat] :
% 0.29/0.51                        ( ( ( ( inf_inf_set_nat @ As4 @ As5 )
% 0.29/0.51                            = bot_bot_set_nat )
% 0.29/0.51                          & ( relH @ As4 @ H @ H5 )
% 0.29/0.51                          & ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As4 ) )
% 0.29/0.51                          & ( X @ ( produc7507926704131184380et_nat @ H5 @ As5 ) ) )
% 0.29/0.51                       => ( Xa @ ( produc7507926704131184380et_nat @ H5 @ ( sup_sup_set_nat @ As4 @ As5 ) ) ) ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % wand_raw.pelims(3)
% 0.29/0.51  thf(fact_1629_bijective__Empty,axiom,
% 0.29/0.51      bijective_nat_nat @ bot_bo2099793752762293965at_nat ).
% 0.29/0.51  
% 0.29/0.51  % bijective_Empty
% 0.29/0.51  thf(fact_1630_dbl__inc__simps_I1_J,axiom,
% 0.29/0.51      ! [K: num] :
% 0.29/0.51        ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.29/0.51        = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dbl_inc_simps(1)
% 0.29/0.51  thf(fact_1631_dbl__inc__simps_I1_J,axiom,
% 0.29/0.51      ! [K: num] :
% 0.29/0.51        ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.29/0.51        = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dbl_inc_simps(1)
% 0.29/0.51  thf(fact_1632_dbl__inc__simps_I1_J,axiom,
% 0.29/0.51      ! [K: num] :
% 0.29/0.51        ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.29/0.51        = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dbl_inc_simps(1)
% 0.29/0.51  thf(fact_1633_dbl__dec__simps_I1_J,axiom,
% 0.29/0.51      ! [K: num] :
% 0.29/0.51        ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.29/0.51        = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dbl_dec_simps(1)
% 0.29/0.51  thf(fact_1634_dbl__dec__simps_I1_J,axiom,
% 0.29/0.51      ! [K: num] :
% 0.29/0.51        ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.29/0.51        = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dbl_dec_simps(1)
% 0.29/0.51  thf(fact_1635_dbl__dec__simps_I1_J,axiom,
% 0.29/0.51      ! [K: num] :
% 0.29/0.51        ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.29/0.51        = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dbl_dec_simps(1)
% 0.29/0.51  thf(fact_1636_dbl__dec__simps_I2_J,axiom,
% 0.29/0.51      ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 0.29/0.51      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dbl_dec_simps(2)
% 0.29/0.51  thf(fact_1637_dbl__dec__simps_I2_J,axiom,
% 0.29/0.51      ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 0.29/0.51      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dbl_dec_simps(2)
% 0.29/0.51  thf(fact_1638_dbl__dec__simps_I2_J,axiom,
% 0.29/0.51      ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 0.29/0.51      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % dbl_dec_simps(2)
% 0.29/0.51  thf(fact_1639_pairself_Opelims,axiom,
% 0.29/0.51      ! [X: int > option6357759511663192854e_term,Xa: product_prod_int_int,Y: produc6576344331059438605e_term] :
% 0.29/0.51        ( ( ( pairse3534876335208825186e_term @ X @ Xa )
% 0.29/0.51          = Y )
% 0.29/0.51       => ( ( accp_P8928870874622223812nt_int @ pairse6848479906795794847e_term @ ( produc4305682042979456191nt_int @ X @ Xa ) )
% 0.29/0.51         => ~ ! [A6: int,B6: int] :
% 0.29/0.51                ( ( Xa
% 0.29/0.51                  = ( product_Pair_int_int @ A6 @ B6 ) )
% 0.29/0.51               => ( ( Y
% 0.29/0.51                    = ( produc5950683997804057413e_term @ ( X @ A6 ) @ ( X @ B6 ) ) )
% 0.29/0.51                 => ~ ( accp_P8928870874622223812nt_int @ pairse6848479906795794847e_term @ ( produc4305682042979456191nt_int @ X @ ( product_Pair_int_int @ A6 @ B6 ) ) ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % pairself.pelims
% 0.29/0.51  thf(fact_1640_rel__restrict__compl,axiom,
% 0.29/0.51      ! [R: set_Pr1261947904930325089at_nat,A2: set_nat] :
% 0.29/0.51        ( ( inf_in2572325071724192079at_nat @ ( rel_restrict_nat @ R @ A2 ) @ ( rel_restrict_nat @ R @ ( uminus5710092332889474511et_nat @ A2 ) ) )
% 0.29/0.51        = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrict_compl
% 0.29/0.51  thf(fact_1641_Id__on__empty,axiom,
% 0.29/0.51      ( ( id_on_2554058798563519774at_nat @ bot_bo2099793752762293965at_nat )
% 0.29/0.51      = bot_bo5327735625951526323at_nat ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_on_empty
% 0.29/0.51  thf(fact_1642_Id__on__empty,axiom,
% 0.29/0.51      ( ( id_on_o @ bot_bot_set_o )
% 0.29/0.51      = bot_bo7073875226086086771od_o_o ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_on_empty
% 0.29/0.51  thf(fact_1643_Id__on__empty,axiom,
% 0.29/0.51      ( ( id_on_nat @ bot_bot_set_nat )
% 0.29/0.51      = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_on_empty
% 0.29/0.51  thf(fact_1644_Id__on__empty,axiom,
% 0.29/0.51      ( ( id_on_int @ bot_bot_set_int )
% 0.29/0.51      = bot_bo1796632182523588997nt_int ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_on_empty
% 0.29/0.51  thf(fact_1645_mult__cancel__right,axiom,
% 0.29/0.51      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.51        ( ( ( times_3573771949741848930nteger @ A @ C )
% 0.29/0.51          = ( times_3573771949741848930nteger @ B @ C ) )
% 0.29/0.51        = ( ( C = zero_z3403309356797280102nteger )
% 0.29/0.51          | ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_cancel_right
% 0.29/0.51  thf(fact_1646_mult__cancel__right,axiom,
% 0.29/0.51      ! [A: rat,C: rat,B: rat] :
% 0.29/0.51        ( ( ( times_times_rat @ A @ C )
% 0.29/0.51          = ( times_times_rat @ B @ C ) )
% 0.29/0.51        = ( ( C = zero_zero_rat )
% 0.29/0.51          | ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_cancel_right
% 0.29/0.51  thf(fact_1647_mult__cancel__right,axiom,
% 0.29/0.51      ! [A: nat,C: nat,B: nat] :
% 0.29/0.51        ( ( ( times_times_nat @ A @ C )
% 0.29/0.51          = ( times_times_nat @ B @ C ) )
% 0.29/0.51        = ( ( C = zero_zero_nat )
% 0.29/0.51          | ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_cancel_right
% 0.29/0.51  thf(fact_1648_mult__cancel__right,axiom,
% 0.29/0.51      ! [A: int,C: int,B: int] :
% 0.29/0.51        ( ( ( times_times_int @ A @ C )
% 0.29/0.51          = ( times_times_int @ B @ C ) )
% 0.29/0.51        = ( ( C = zero_zero_int )
% 0.29/0.51          | ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_cancel_right
% 0.29/0.51  thf(fact_1649_mult__cancel__left,axiom,
% 0.29/0.51      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.51        ( ( ( times_3573771949741848930nteger @ C @ A )
% 0.29/0.51          = ( times_3573771949741848930nteger @ C @ B ) )
% 0.29/0.51        = ( ( C = zero_z3403309356797280102nteger )
% 0.29/0.51          | ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_cancel_left
% 0.29/0.51  thf(fact_1650_mult__cancel__left,axiom,
% 0.29/0.51      ! [C: rat,A: rat,B: rat] :
% 0.29/0.51        ( ( ( times_times_rat @ C @ A )
% 0.29/0.51          = ( times_times_rat @ C @ B ) )
% 0.29/0.51        = ( ( C = zero_zero_rat )
% 0.29/0.51          | ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_cancel_left
% 0.29/0.51  thf(fact_1651_mult__cancel__left,axiom,
% 0.29/0.51      ! [C: nat,A: nat,B: nat] :
% 0.29/0.51        ( ( ( times_times_nat @ C @ A )
% 0.29/0.51          = ( times_times_nat @ C @ B ) )
% 0.29/0.51        = ( ( C = zero_zero_nat )
% 0.29/0.51          | ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_cancel_left
% 0.29/0.51  thf(fact_1652_mult__cancel__left,axiom,
% 0.29/0.51      ! [C: int,A: int,B: int] :
% 0.29/0.51        ( ( ( times_times_int @ C @ A )
% 0.29/0.51          = ( times_times_int @ C @ B ) )
% 0.29/0.51        = ( ( C = zero_zero_int )
% 0.29/0.51          | ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_cancel_left
% 0.29/0.51  thf(fact_1653_mult__eq__0__iff,axiom,
% 0.29/0.51      ! [A: code_integer,B: code_integer] :
% 0.29/0.51        ( ( ( times_3573771949741848930nteger @ A @ B )
% 0.29/0.51          = zero_z3403309356797280102nteger )
% 0.29/0.51        = ( ( A = zero_z3403309356797280102nteger )
% 0.29/0.51          | ( B = zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_eq_0_iff
% 0.29/0.51  thf(fact_1654_mult__eq__0__iff,axiom,
% 0.29/0.51      ! [A: rat,B: rat] :
% 0.29/0.51        ( ( ( times_times_rat @ A @ B )
% 0.29/0.51          = zero_zero_rat )
% 0.29/0.51        = ( ( A = zero_zero_rat )
% 0.29/0.51          | ( B = zero_zero_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_eq_0_iff
% 0.29/0.51  thf(fact_1655_mult__eq__0__iff,axiom,
% 0.29/0.51      ! [A: nat,B: nat] :
% 0.29/0.51        ( ( ( times_times_nat @ A @ B )
% 0.29/0.51          = zero_zero_nat )
% 0.29/0.51        = ( ( A = zero_zero_nat )
% 0.29/0.51          | ( B = zero_zero_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_eq_0_iff
% 0.29/0.51  thf(fact_1656_mult__eq__0__iff,axiom,
% 0.29/0.51      ! [A: int,B: int] :
% 0.29/0.51        ( ( ( times_times_int @ A @ B )
% 0.29/0.51          = zero_zero_int )
% 0.29/0.51        = ( ( A = zero_zero_int )
% 0.29/0.51          | ( B = zero_zero_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_eq_0_iff
% 0.29/0.51  thf(fact_1657_mult__zero__right,axiom,
% 0.29/0.51      ! [A: code_integer] :
% 0.29/0.51        ( ( times_3573771949741848930nteger @ A @ zero_z3403309356797280102nteger )
% 0.29/0.51        = zero_z3403309356797280102nteger ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_zero_right
% 0.29/0.51  thf(fact_1658_mult__zero__right,axiom,
% 0.29/0.51      ! [A: rat] :
% 0.29/0.51        ( ( times_times_rat @ A @ zero_zero_rat )
% 0.29/0.51        = zero_zero_rat ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_zero_right
% 0.29/0.51  thf(fact_1659_mult__zero__right,axiom,
% 0.29/0.51      ! [A: nat] :
% 0.29/0.51        ( ( times_times_nat @ A @ zero_zero_nat )
% 0.29/0.51        = zero_zero_nat ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_zero_right
% 0.29/0.51  thf(fact_1660_mult__zero__right,axiom,
% 0.29/0.51      ! [A: int] :
% 0.29/0.51        ( ( times_times_int @ A @ zero_zero_int )
% 0.29/0.51        = zero_zero_int ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_zero_right
% 0.29/0.51  thf(fact_1661_mult__zero__left,axiom,
% 0.29/0.51      ! [A: code_integer] :
% 0.29/0.51        ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.51        = zero_z3403309356797280102nteger ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_zero_left
% 0.29/0.51  thf(fact_1662_mult__zero__left,axiom,
% 0.29/0.51      ! [A: rat] :
% 0.29/0.51        ( ( times_times_rat @ zero_zero_rat @ A )
% 0.29/0.51        = zero_zero_rat ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_zero_left
% 0.29/0.51  thf(fact_1663_mult__zero__left,axiom,
% 0.29/0.51      ! [A: nat] :
% 0.29/0.51        ( ( times_times_nat @ zero_zero_nat @ A )
% 0.29/0.51        = zero_zero_nat ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_zero_left
% 0.29/0.51  thf(fact_1664_mult__zero__left,axiom,
% 0.29/0.51      ! [A: int] :
% 0.29/0.51        ( ( times_times_int @ zero_zero_int @ A )
% 0.29/0.51        = zero_zero_int ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_zero_left
% 0.29/0.51  thf(fact_1665_mult__numeral__left__semiring__numeral,axiom,
% 0.29/0.51      ! [V: num,W: num,Z: nat] :
% 0.29/0.51        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 0.29/0.51        = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_numeral_left_semiring_numeral
% 0.29/0.51  thf(fact_1666_mult__numeral__left__semiring__numeral,axiom,
% 0.29/0.51      ! [V: num,W: num,Z: int] :
% 0.29/0.51        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 0.29/0.51        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_numeral_left_semiring_numeral
% 0.29/0.51  thf(fact_1667_mult__numeral__left__semiring__numeral,axiom,
% 0.29/0.51      ! [V: num,W: num,Z: code_integer] :
% 0.29/0.51        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Z ) )
% 0.29/0.51        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_numeral_left_semiring_numeral
% 0.29/0.51  thf(fact_1668_mult__numeral__left__semiring__numeral,axiom,
% 0.29/0.51      ! [V: num,W: num,Z: rat] :
% 0.29/0.51        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 0.29/0.51        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_numeral_left_semiring_numeral
% 0.29/0.51  thf(fact_1669_mult__numeral__left__semiring__numeral,axiom,
% 0.29/0.51      ! [V: num,W: num,Z: code_natural] :
% 0.29/0.51        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ W ) @ Z ) )
% 0.29/0.51        = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_numeral_left_semiring_numeral
% 0.29/0.51  thf(fact_1670_numeral__times__numeral,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 0.29/0.51        = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % numeral_times_numeral
% 0.29/0.51  thf(fact_1671_numeral__times__numeral,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.29/0.51        = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % numeral_times_numeral
% 0.29/0.51  thf(fact_1672_numeral__times__numeral,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 0.29/0.51        = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % numeral_times_numeral
% 0.29/0.51  thf(fact_1673_numeral__times__numeral,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 0.29/0.51        = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % numeral_times_numeral
% 0.29/0.51  thf(fact_1674_numeral__times__numeral,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ M ) @ ( numera5444537566228673987atural @ N ) )
% 0.29/0.51        = ( numera5444537566228673987atural @ ( times_times_num @ M @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % numeral_times_numeral
% 0.29/0.51  thf(fact_1675_neg__equal__zero,axiom,
% 0.29/0.51      ! [A: int] :
% 0.29/0.51        ( ( ( uminus_uminus_int @ A )
% 0.29/0.51          = A )
% 0.29/0.51        = ( A = zero_zero_int ) ) ).
% 0.29/0.51  
% 0.29/0.51  % neg_equal_zero
% 0.29/0.51  thf(fact_1676_neg__equal__zero,axiom,
% 0.29/0.51      ! [A: code_integer] :
% 0.29/0.51        ( ( ( uminus1351360451143612070nteger @ A )
% 0.29/0.51          = A )
% 0.29/0.51        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.51  
% 0.29/0.51  % neg_equal_zero
% 0.29/0.51  thf(fact_1677_neg__equal__zero,axiom,
% 0.29/0.51      ! [A: rat] :
% 0.29/0.51        ( ( ( uminus_uminus_rat @ A )
% 0.29/0.51          = A )
% 0.29/0.51        = ( A = zero_zero_rat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % neg_equal_zero
% 0.29/0.51  thf(fact_1678_equal__neg__zero,axiom,
% 0.29/0.51      ! [A: int] :
% 0.29/0.51        ( ( A
% 0.29/0.51          = ( uminus_uminus_int @ A ) )
% 0.29/0.51        = ( A = zero_zero_int ) ) ).
% 0.29/0.51  
% 0.29/0.51  % equal_neg_zero
% 0.29/0.51  thf(fact_1679_equal__neg__zero,axiom,
% 0.29/0.51      ! [A: code_integer] :
% 0.29/0.51        ( ( A
% 0.29/0.51          = ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.51        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.51  
% 0.29/0.51  % equal_neg_zero
% 0.29/0.51  thf(fact_1680_equal__neg__zero,axiom,
% 0.29/0.51      ! [A: rat] :
% 0.29/0.51        ( ( A
% 0.29/0.51          = ( uminus_uminus_rat @ A ) )
% 0.29/0.51        = ( A = zero_zero_rat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % equal_neg_zero
% 0.29/0.51  thf(fact_1681_neg__equal__0__iff__equal,axiom,
% 0.29/0.51      ! [A: int] :
% 0.29/0.51        ( ( ( uminus_uminus_int @ A )
% 0.29/0.51          = zero_zero_int )
% 0.29/0.51        = ( A = zero_zero_int ) ) ).
% 0.29/0.51  
% 0.29/0.51  % neg_equal_0_iff_equal
% 0.29/0.51  thf(fact_1682_neg__equal__0__iff__equal,axiom,
% 0.29/0.51      ! [A: code_integer] :
% 0.29/0.51        ( ( ( uminus1351360451143612070nteger @ A )
% 0.29/0.51          = zero_z3403309356797280102nteger )
% 0.29/0.51        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.51  
% 0.29/0.51  % neg_equal_0_iff_equal
% 0.29/0.51  thf(fact_1683_neg__equal__0__iff__equal,axiom,
% 0.29/0.51      ! [A: rat] :
% 0.29/0.51        ( ( ( uminus_uminus_rat @ A )
% 0.29/0.51          = zero_zero_rat )
% 0.29/0.51        = ( A = zero_zero_rat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % neg_equal_0_iff_equal
% 0.29/0.51  thf(fact_1684_neg__0__equal__iff__equal,axiom,
% 0.29/0.51      ! [A: int] :
% 0.29/0.51        ( ( zero_zero_int
% 0.29/0.51          = ( uminus_uminus_int @ A ) )
% 0.29/0.51        = ( zero_zero_int = A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % neg_0_equal_iff_equal
% 0.29/0.51  thf(fact_1685_neg__0__equal__iff__equal,axiom,
% 0.29/0.51      ! [A: code_integer] :
% 0.29/0.51        ( ( zero_z3403309356797280102nteger
% 0.29/0.51          = ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.51        = ( zero_z3403309356797280102nteger = A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % neg_0_equal_iff_equal
% 0.29/0.51  thf(fact_1686_neg__0__equal__iff__equal,axiom,
% 0.29/0.51      ! [A: rat] :
% 0.29/0.51        ( ( zero_zero_rat
% 0.29/0.51          = ( uminus_uminus_rat @ A ) )
% 0.29/0.51        = ( zero_zero_rat = A ) ) ).
% 0.29/0.51  
% 0.29/0.51  % neg_0_equal_iff_equal
% 0.29/0.51  thf(fact_1687_add_Oinverse__neutral,axiom,
% 0.29/0.51      ( ( uminus_uminus_int @ zero_zero_int )
% 0.29/0.51      = zero_zero_int ) ).
% 0.29/0.51  
% 0.29/0.51  % add.inverse_neutral
% 0.29/0.51  thf(fact_1688_add_Oinverse__neutral,axiom,
% 0.29/0.51      ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 0.29/0.51      = zero_z3403309356797280102nteger ) ).
% 0.29/0.51  
% 0.29/0.51  % add.inverse_neutral
% 0.29/0.51  thf(fact_1689_add_Oinverse__neutral,axiom,
% 0.29/0.51      ( ( uminus_uminus_rat @ zero_zero_rat )
% 0.29/0.51      = zero_zero_rat ) ).
% 0.29/0.51  
% 0.29/0.51  % add.inverse_neutral
% 0.29/0.51  thf(fact_1690_neg__numeral__eq__iff,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 0.29/0.51          = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.29/0.51        = ( M = N ) ) ).
% 0.29/0.51  
% 0.29/0.51  % neg_numeral_eq_iff
% 0.29/0.51  thf(fact_1691_neg__numeral__eq__iff,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 0.29/0.51          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.29/0.51        = ( M = N ) ) ).
% 0.29/0.51  
% 0.29/0.51  % neg_numeral_eq_iff
% 0.29/0.51  thf(fact_1692_neg__numeral__eq__iff,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 0.29/0.51          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.29/0.51        = ( M = N ) ) ).
% 0.29/0.51  
% 0.29/0.51  % neg_numeral_eq_iff
% 0.29/0.51  thf(fact_1693_rel__restrict__empty,axiom,
% 0.29/0.51      ! [R: set_Pr8693737435421807431at_nat] :
% 0.29/0.51        ( ( rel_re36662636952045539at_nat @ R @ bot_bo2099793752762293965at_nat )
% 0.29/0.51        = R ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrict_empty
% 0.29/0.51  thf(fact_1694_rel__restrict__empty,axiom,
% 0.29/0.51      ! [R: set_Product_prod_o_o] :
% 0.29/0.51        ( ( rel_restrict_o @ R @ bot_bot_set_o )
% 0.29/0.51        = R ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrict_empty
% 0.29/0.51  thf(fact_1695_rel__restrict__empty,axiom,
% 0.29/0.51      ! [R: set_Pr1261947904930325089at_nat] :
% 0.29/0.51        ( ( rel_restrict_nat @ R @ bot_bot_set_nat )
% 0.29/0.51        = R ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrict_empty
% 0.29/0.51  thf(fact_1696_rel__restrict__empty,axiom,
% 0.29/0.51      ! [R: set_Pr958786334691620121nt_int] :
% 0.29/0.51        ( ( rel_restrict_int @ R @ bot_bot_set_int )
% 0.29/0.51        = R ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrict_empty
% 0.29/0.51  thf(fact_1697_Id__onI,axiom,
% 0.29/0.51      ! [A: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int] :
% 0.29/0.51        ( ( member2340774599025711042nt_int @ A @ A2 )
% 0.29/0.51       => ( member5325734588016868240nt_int @ ( produc782388162306416855nt_int @ A @ A ) @ ( id_on_6410342593070439734nt_int @ A2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_onI
% 0.29/0.51  thf(fact_1698_Id__onI,axiom,
% 0.29/0.51      ! [A: set_nat,A2: set_set_nat] :
% 0.29/0.51        ( ( member_set_nat @ A @ A2 )
% 0.29/0.51       => ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A @ A ) @ ( id_on_set_nat @ A2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_onI
% 0.29/0.51  thf(fact_1699_Id__onI,axiom,
% 0.29/0.51      ! [A: nat,A2: set_nat] :
% 0.29/0.51        ( ( member_nat @ A @ A2 )
% 0.29/0.51       => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ A ) @ ( id_on_nat @ A2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_onI
% 0.29/0.51  thf(fact_1700_Id__onI,axiom,
% 0.29/0.51      ! [A: int,A2: set_int] :
% 0.29/0.51        ( ( member_int @ A @ A2 )
% 0.29/0.51       => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ A ) @ ( id_on_int @ A2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_onI
% 0.29/0.51  thf(fact_1701_Id__onI,axiom,
% 0.29/0.51      ! [A: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.51        ( ( member6576561426505652726_nat_o @ A @ A2 )
% 0.29/0.51       => ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A @ A ) @ ( id_on_7438695062414216554_nat_o @ A2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_onI
% 0.29/0.51  thf(fact_1702_mult__cancel__right2,axiom,
% 0.29/0.51      ! [A: code_integer,C: code_integer] :
% 0.29/0.51        ( ( ( times_3573771949741848930nteger @ A @ C )
% 0.29/0.51          = C )
% 0.29/0.51        = ( ( C = zero_z3403309356797280102nteger )
% 0.29/0.51          | ( A = one_one_Code_integer ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_cancel_right2
% 0.29/0.51  thf(fact_1703_mult__cancel__right2,axiom,
% 0.29/0.51      ! [A: rat,C: rat] :
% 0.29/0.51        ( ( ( times_times_rat @ A @ C )
% 0.29/0.51          = C )
% 0.29/0.51        = ( ( C = zero_zero_rat )
% 0.29/0.51          | ( A = one_one_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_cancel_right2
% 0.29/0.51  thf(fact_1704_mult__cancel__right2,axiom,
% 0.29/0.51      ! [A: int,C: int] :
% 0.29/0.51        ( ( ( times_times_int @ A @ C )
% 0.29/0.51          = C )
% 0.29/0.51        = ( ( C = zero_zero_int )
% 0.29/0.51          | ( A = one_one_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_cancel_right2
% 0.29/0.51  thf(fact_1705_mult__cancel__right1,axiom,
% 0.29/0.51      ! [C: code_integer,B: code_integer] :
% 0.29/0.51        ( ( C
% 0.29/0.51          = ( times_3573771949741848930nteger @ B @ C ) )
% 0.29/0.51        = ( ( C = zero_z3403309356797280102nteger )
% 0.29/0.51          | ( B = one_one_Code_integer ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_cancel_right1
% 0.29/0.51  thf(fact_1706_mult__cancel__right1,axiom,
% 0.29/0.51      ! [C: rat,B: rat] :
% 0.29/0.51        ( ( C
% 0.29/0.51          = ( times_times_rat @ B @ C ) )
% 0.29/0.51        = ( ( C = zero_zero_rat )
% 0.29/0.51          | ( B = one_one_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_cancel_right1
% 0.29/0.51  thf(fact_1707_mult__cancel__right1,axiom,
% 0.29/0.51      ! [C: int,B: int] :
% 0.29/0.51        ( ( C
% 0.29/0.51          = ( times_times_int @ B @ C ) )
% 0.29/0.51        = ( ( C = zero_zero_int )
% 0.29/0.51          | ( B = one_one_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_cancel_right1
% 0.29/0.51  thf(fact_1708_mult__cancel__left2,axiom,
% 0.29/0.51      ! [C: code_integer,A: code_integer] :
% 0.29/0.51        ( ( ( times_3573771949741848930nteger @ C @ A )
% 0.29/0.51          = C )
% 0.29/0.51        = ( ( C = zero_z3403309356797280102nteger )
% 0.29/0.51          | ( A = one_one_Code_integer ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_cancel_left2
% 0.29/0.51  thf(fact_1709_mult__cancel__left2,axiom,
% 0.29/0.51      ! [C: rat,A: rat] :
% 0.29/0.51        ( ( ( times_times_rat @ C @ A )
% 0.29/0.51          = C )
% 0.29/0.51        = ( ( C = zero_zero_rat )
% 0.29/0.51          | ( A = one_one_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_cancel_left2
% 0.29/0.51  thf(fact_1710_mult__cancel__left2,axiom,
% 0.29/0.51      ! [C: int,A: int] :
% 0.29/0.51        ( ( ( times_times_int @ C @ A )
% 0.29/0.51          = C )
% 0.29/0.51        = ( ( C = zero_zero_int )
% 0.29/0.51          | ( A = one_one_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_cancel_left2
% 0.29/0.51  thf(fact_1711_mult__cancel__left1,axiom,
% 0.29/0.51      ! [C: code_integer,B: code_integer] :
% 0.29/0.51        ( ( C
% 0.29/0.51          = ( times_3573771949741848930nteger @ C @ B ) )
% 0.29/0.51        = ( ( C = zero_z3403309356797280102nteger )
% 0.29/0.51          | ( B = one_one_Code_integer ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_cancel_left1
% 0.29/0.51  thf(fact_1712_mult__cancel__left1,axiom,
% 0.29/0.51      ! [C: rat,B: rat] :
% 0.29/0.51        ( ( C
% 0.29/0.51          = ( times_times_rat @ C @ B ) )
% 0.29/0.51        = ( ( C = zero_zero_rat )
% 0.29/0.51          | ( B = one_one_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_cancel_left1
% 0.29/0.51  thf(fact_1713_mult__cancel__left1,axiom,
% 0.29/0.51      ! [C: int,B: int] :
% 0.29/0.51        ( ( C
% 0.29/0.51          = ( times_times_int @ C @ B ) )
% 0.29/0.51        = ( ( C = zero_zero_int )
% 0.29/0.51          | ( B = one_one_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_cancel_left1
% 0.29/0.51  thf(fact_1714_mult__neg__numeral__simps_I1_J,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.29/0.51        = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_neg_numeral_simps(1)
% 0.29/0.51  thf(fact_1715_mult__neg__numeral__simps_I1_J,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.29/0.51        = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_neg_numeral_simps(1)
% 0.29/0.51  thf(fact_1716_mult__neg__numeral__simps_I1_J,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.29/0.51        = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_neg_numeral_simps(1)
% 0.29/0.51  thf(fact_1717_mult__neg__numeral__simps_I2_J,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.29/0.51        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_neg_numeral_simps(2)
% 0.29/0.51  thf(fact_1718_mult__neg__numeral__simps_I2_J,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 0.29/0.51        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_neg_numeral_simps(2)
% 0.29/0.51  thf(fact_1719_mult__neg__numeral__simps_I2_J,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 0.29/0.51        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_neg_numeral_simps(2)
% 0.29/0.51  thf(fact_1720_mult__neg__numeral__simps_I3_J,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.29/0.51        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_neg_numeral_simps(3)
% 0.29/0.51  thf(fact_1721_mult__neg__numeral__simps_I3_J,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.29/0.51        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_neg_numeral_simps(3)
% 0.29/0.51  thf(fact_1722_mult__neg__numeral__simps_I3_J,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.29/0.51        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_neg_numeral_simps(3)
% 0.29/0.51  thf(fact_1723_dbl__inc__simps_I2_J,axiom,
% 0.29/0.51      ( ( neg_nu5831290666863070958nteger @ zero_z3403309356797280102nteger )
% 0.29/0.51      = one_one_Code_integer ) ).
% 0.29/0.51  
% 0.29/0.51  % dbl_inc_simps(2)
% 0.29/0.51  thf(fact_1724_dbl__inc__simps_I2_J,axiom,
% 0.29/0.51      ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 0.29/0.51      = one_one_rat ) ).
% 0.29/0.51  
% 0.29/0.51  % dbl_inc_simps(2)
% 0.29/0.51  thf(fact_1725_dbl__inc__simps_I2_J,axiom,
% 0.29/0.51      ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 0.29/0.51      = one_one_int ) ).
% 0.29/0.51  
% 0.29/0.51  % dbl_inc_simps(2)
% 0.29/0.51  thf(fact_1726_zero__reorient,axiom,
% 0.29/0.51      ! [X: code_integer] :
% 0.29/0.51        ( ( zero_z3403309356797280102nteger = X )
% 0.29/0.51        = ( X = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_reorient
% 0.29/0.51  thf(fact_1727_zero__reorient,axiom,
% 0.29/0.51      ! [X: multis2468970476368604999at_nat] :
% 0.29/0.51        ( ( zero_z1048942125864253310at_nat = X )
% 0.29/0.51        = ( X = zero_z1048942125864253310at_nat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_reorient
% 0.29/0.51  thf(fact_1728_zero__reorient,axiom,
% 0.29/0.51      ! [X: rat] :
% 0.29/0.51        ( ( zero_zero_rat = X )
% 0.29/0.51        = ( X = zero_zero_rat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_reorient
% 0.29/0.51  thf(fact_1729_zero__reorient,axiom,
% 0.29/0.51      ! [X: nat] :
% 0.29/0.51        ( ( zero_zero_nat = X )
% 0.29/0.51        = ( X = zero_zero_nat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_reorient
% 0.29/0.51  thf(fact_1730_zero__reorient,axiom,
% 0.29/0.51      ! [X: int] :
% 0.29/0.51        ( ( zero_zero_int = X )
% 0.29/0.51        = ( X = zero_zero_int ) ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_reorient
% 0.29/0.51  thf(fact_1731_zero__neq__neg__numeral,axiom,
% 0.29/0.51      ! [N: num] :
% 0.29/0.51        ( zero_zero_int
% 0.29/0.51       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_neq_neg_numeral
% 0.29/0.51  thf(fact_1732_zero__neq__neg__numeral,axiom,
% 0.29/0.51      ! [N: num] :
% 0.29/0.51        ( zero_z3403309356797280102nteger
% 0.29/0.51       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_neq_neg_numeral
% 0.29/0.51  thf(fact_1733_zero__neq__neg__numeral,axiom,
% 0.29/0.51      ! [N: num] :
% 0.29/0.51        ( zero_zero_rat
% 0.29/0.51       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_neq_neg_numeral
% 0.29/0.51  thf(fact_1734_numeral__neq__neg__numeral,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( numeral_numeral_int @ M )
% 0.29/0.51       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % numeral_neq_neg_numeral
% 0.29/0.51  thf(fact_1735_numeral__neq__neg__numeral,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( numera6620942414471956472nteger @ M )
% 0.29/0.51       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % numeral_neq_neg_numeral
% 0.29/0.51  thf(fact_1736_numeral__neq__neg__numeral,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( numeral_numeral_rat @ M )
% 0.29/0.51       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % numeral_neq_neg_numeral
% 0.29/0.51  thf(fact_1737_neg__numeral__neq__numeral,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 0.29/0.51       != ( numeral_numeral_int @ N ) ) ).
% 0.29/0.51  
% 0.29/0.51  % neg_numeral_neq_numeral
% 0.29/0.51  thf(fact_1738_neg__numeral__neq__numeral,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 0.29/0.51       != ( numera6620942414471956472nteger @ N ) ) ).
% 0.29/0.51  
% 0.29/0.51  % neg_numeral_neq_numeral
% 0.29/0.51  thf(fact_1739_neg__numeral__neq__numeral,axiom,
% 0.29/0.51      ! [M: num,N: num] :
% 0.29/0.51        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 0.29/0.51       != ( numeral_numeral_rat @ N ) ) ).
% 0.29/0.51  
% 0.29/0.51  % neg_numeral_neq_numeral
% 0.29/0.51  thf(fact_1740_mult__right__cancel,axiom,
% 0.29/0.51      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.51        ( ( C != zero_z3403309356797280102nteger )
% 0.29/0.51       => ( ( ( times_3573771949741848930nteger @ A @ C )
% 0.29/0.51            = ( times_3573771949741848930nteger @ B @ C ) )
% 0.29/0.51          = ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_right_cancel
% 0.29/0.51  thf(fact_1741_mult__right__cancel,axiom,
% 0.29/0.51      ! [C: rat,A: rat,B: rat] :
% 0.29/0.51        ( ( C != zero_zero_rat )
% 0.29/0.51       => ( ( ( times_times_rat @ A @ C )
% 0.29/0.51            = ( times_times_rat @ B @ C ) )
% 0.29/0.51          = ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_right_cancel
% 0.29/0.51  thf(fact_1742_mult__right__cancel,axiom,
% 0.29/0.51      ! [C: nat,A: nat,B: nat] :
% 0.29/0.51        ( ( C != zero_zero_nat )
% 0.29/0.51       => ( ( ( times_times_nat @ A @ C )
% 0.29/0.51            = ( times_times_nat @ B @ C ) )
% 0.29/0.51          = ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_right_cancel
% 0.29/0.51  thf(fact_1743_mult__right__cancel,axiom,
% 0.29/0.51      ! [C: int,A: int,B: int] :
% 0.29/0.51        ( ( C != zero_zero_int )
% 0.29/0.51       => ( ( ( times_times_int @ A @ C )
% 0.29/0.51            = ( times_times_int @ B @ C ) )
% 0.29/0.51          = ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_right_cancel
% 0.29/0.51  thf(fact_1744_mult__left__cancel,axiom,
% 0.29/0.51      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.51        ( ( C != zero_z3403309356797280102nteger )
% 0.29/0.51       => ( ( ( times_3573771949741848930nteger @ C @ A )
% 0.29/0.51            = ( times_3573771949741848930nteger @ C @ B ) )
% 0.29/0.51          = ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_left_cancel
% 0.29/0.51  thf(fact_1745_mult__left__cancel,axiom,
% 0.29/0.51      ! [C: rat,A: rat,B: rat] :
% 0.29/0.51        ( ( C != zero_zero_rat )
% 0.29/0.51       => ( ( ( times_times_rat @ C @ A )
% 0.29/0.51            = ( times_times_rat @ C @ B ) )
% 0.29/0.51          = ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_left_cancel
% 0.29/0.51  thf(fact_1746_mult__left__cancel,axiom,
% 0.29/0.51      ! [C: nat,A: nat,B: nat] :
% 0.29/0.51        ( ( C != zero_zero_nat )
% 0.29/0.51       => ( ( ( times_times_nat @ C @ A )
% 0.29/0.51            = ( times_times_nat @ C @ B ) )
% 0.29/0.51          = ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_left_cancel
% 0.29/0.51  thf(fact_1747_mult__left__cancel,axiom,
% 0.29/0.51      ! [C: int,A: int,B: int] :
% 0.29/0.51        ( ( C != zero_zero_int )
% 0.29/0.51       => ( ( ( times_times_int @ C @ A )
% 0.29/0.51            = ( times_times_int @ C @ B ) )
% 0.29/0.51          = ( A = B ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_left_cancel
% 0.29/0.51  thf(fact_1748_no__zero__divisors,axiom,
% 0.29/0.51      ! [A: code_integer,B: code_integer] :
% 0.29/0.51        ( ( A != zero_z3403309356797280102nteger )
% 0.29/0.51       => ( ( B != zero_z3403309356797280102nteger )
% 0.29/0.51         => ( ( times_3573771949741848930nteger @ A @ B )
% 0.29/0.51           != zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % no_zero_divisors
% 0.29/0.51  thf(fact_1749_no__zero__divisors,axiom,
% 0.29/0.51      ! [A: rat,B: rat] :
% 0.29/0.51        ( ( A != zero_zero_rat )
% 0.29/0.51       => ( ( B != zero_zero_rat )
% 0.29/0.51         => ( ( times_times_rat @ A @ B )
% 0.29/0.51           != zero_zero_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % no_zero_divisors
% 0.29/0.51  thf(fact_1750_no__zero__divisors,axiom,
% 0.29/0.51      ! [A: nat,B: nat] :
% 0.29/0.51        ( ( A != zero_zero_nat )
% 0.29/0.51       => ( ( B != zero_zero_nat )
% 0.29/0.51         => ( ( times_times_nat @ A @ B )
% 0.29/0.51           != zero_zero_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % no_zero_divisors
% 0.29/0.51  thf(fact_1751_no__zero__divisors,axiom,
% 0.29/0.51      ! [A: int,B: int] :
% 0.29/0.51        ( ( A != zero_zero_int )
% 0.29/0.51       => ( ( B != zero_zero_int )
% 0.29/0.51         => ( ( times_times_int @ A @ B )
% 0.29/0.51           != zero_zero_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % no_zero_divisors
% 0.29/0.51  thf(fact_1752_divisors__zero,axiom,
% 0.29/0.51      ! [A: code_integer,B: code_integer] :
% 0.29/0.51        ( ( ( times_3573771949741848930nteger @ A @ B )
% 0.29/0.51          = zero_z3403309356797280102nteger )
% 0.29/0.51       => ( ( A = zero_z3403309356797280102nteger )
% 0.29/0.51          | ( B = zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % divisors_zero
% 0.29/0.51  thf(fact_1753_divisors__zero,axiom,
% 0.29/0.51      ! [A: rat,B: rat] :
% 0.29/0.51        ( ( ( times_times_rat @ A @ B )
% 0.29/0.51          = zero_zero_rat )
% 0.29/0.51       => ( ( A = zero_zero_rat )
% 0.29/0.51          | ( B = zero_zero_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % divisors_zero
% 0.29/0.51  thf(fact_1754_divisors__zero,axiom,
% 0.29/0.51      ! [A: nat,B: nat] :
% 0.29/0.51        ( ( ( times_times_nat @ A @ B )
% 0.29/0.51          = zero_zero_nat )
% 0.29/0.51       => ( ( A = zero_zero_nat )
% 0.29/0.51          | ( B = zero_zero_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % divisors_zero
% 0.29/0.51  thf(fact_1755_divisors__zero,axiom,
% 0.29/0.51      ! [A: int,B: int] :
% 0.29/0.51        ( ( ( times_times_int @ A @ B )
% 0.29/0.51          = zero_zero_int )
% 0.29/0.51       => ( ( A = zero_zero_int )
% 0.29/0.51          | ( B = zero_zero_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % divisors_zero
% 0.29/0.51  thf(fact_1756_mult__not__zero,axiom,
% 0.29/0.51      ! [A: code_integer,B: code_integer] :
% 0.29/0.51        ( ( ( times_3573771949741848930nteger @ A @ B )
% 0.29/0.51         != zero_z3403309356797280102nteger )
% 0.29/0.51       => ( ( A != zero_z3403309356797280102nteger )
% 0.29/0.51          & ( B != zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_not_zero
% 0.29/0.51  thf(fact_1757_mult__not__zero,axiom,
% 0.29/0.51      ! [A: rat,B: rat] :
% 0.29/0.51        ( ( ( times_times_rat @ A @ B )
% 0.29/0.51         != zero_zero_rat )
% 0.29/0.51       => ( ( A != zero_zero_rat )
% 0.29/0.51          & ( B != zero_zero_rat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_not_zero
% 0.29/0.51  thf(fact_1758_mult__not__zero,axiom,
% 0.29/0.51      ! [A: nat,B: nat] :
% 0.29/0.51        ( ( ( times_times_nat @ A @ B )
% 0.29/0.51         != zero_zero_nat )
% 0.29/0.51       => ( ( A != zero_zero_nat )
% 0.29/0.51          & ( B != zero_zero_nat ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_not_zero
% 0.29/0.51  thf(fact_1759_mult__not__zero,axiom,
% 0.29/0.51      ! [A: int,B: int] :
% 0.29/0.51        ( ( ( times_times_int @ A @ B )
% 0.29/0.51         != zero_zero_int )
% 0.29/0.51       => ( ( A != zero_zero_int )
% 0.29/0.51          & ( B != zero_zero_int ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % mult_not_zero
% 0.29/0.51  thf(fact_1760_zero__neq__one,axiom,
% 0.29/0.51      zero_z3403309356797280102nteger != one_one_Code_integer ).
% 0.29/0.51  
% 0.29/0.51  % zero_neq_one
% 0.29/0.51  thf(fact_1761_zero__neq__one,axiom,
% 0.29/0.51      zero_zero_rat != one_one_rat ).
% 0.29/0.51  
% 0.29/0.51  % zero_neq_one
% 0.29/0.51  thf(fact_1762_zero__neq__one,axiom,
% 0.29/0.51      zero_zero_nat != one_one_nat ).
% 0.29/0.51  
% 0.29/0.51  % zero_neq_one
% 0.29/0.51  thf(fact_1763_zero__neq__one,axiom,
% 0.29/0.51      zero_zero_int != one_one_int ).
% 0.29/0.51  
% 0.29/0.51  % zero_neq_one
% 0.29/0.51  thf(fact_1764_rel__restrictI,axiom,
% 0.29/0.51      ! [X: set_Pr958786334691620121nt_int,R: set_se6260736226359567993nt_int,Y: set_Pr958786334691620121nt_int,E: set_Pr8057934254988874055nt_int] :
% 0.29/0.51        ( ~ ( member2340774599025711042nt_int @ X @ R )
% 0.29/0.51       => ( ~ ( member2340774599025711042nt_int @ Y @ R )
% 0.29/0.51         => ( ( member5325734588016868240nt_int @ ( produc782388162306416855nt_int @ X @ Y ) @ E )
% 0.29/0.51           => ( member5325734588016868240nt_int @ ( produc782388162306416855nt_int @ X @ Y ) @ ( rel_re4349003428253852667nt_int @ E @ R ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrictI
% 0.29/0.51  thf(fact_1765_rel__restrictI,axiom,
% 0.29/0.51      ! [X: set_nat,R: set_set_nat,Y: set_nat,E: set_Pr5488025237498180813et_nat] :
% 0.29/0.51        ( ~ ( member_set_nat @ X @ R )
% 0.29/0.51       => ( ~ ( member_set_nat @ Y @ R )
% 0.29/0.51         => ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ X @ Y ) @ E )
% 0.29/0.51           => ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ X @ Y ) @ ( rel_restrict_set_nat @ E @ R ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrictI
% 0.29/0.51  thf(fact_1766_rel__restrictI,axiom,
% 0.29/0.51      ! [X: nat,R: set_nat,Y: nat,E: set_Pr1261947904930325089at_nat] :
% 0.29/0.51        ( ~ ( member_nat @ X @ R )
% 0.29/0.51       => ( ~ ( member_nat @ Y @ R )
% 0.29/0.51         => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ E )
% 0.29/0.51           => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( rel_restrict_nat @ E @ R ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrictI
% 0.29/0.51  thf(fact_1767_rel__restrictI,axiom,
% 0.29/0.51      ! [X: int,R: set_int,Y: int,E: set_Pr958786334691620121nt_int] :
% 0.29/0.51        ( ~ ( member_int @ X @ R )
% 0.29/0.51       => ( ~ ( member_int @ Y @ R )
% 0.29/0.51         => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ E )
% 0.29/0.51           => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( rel_restrict_int @ E @ R ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrictI
% 0.29/0.51  thf(fact_1768_rel__restrictI,axiom,
% 0.29/0.51      ! [X: produc3658429121746597890et_nat > $o,R: set_Pr4532377907799695533_nat_o,Y: produc3658429121746597890et_nat > $o,E: set_Pr2161125870931222855_nat_o] :
% 0.29/0.51        ( ~ ( member6576561426505652726_nat_o @ X @ R )
% 0.29/0.51       => ( ~ ( member6576561426505652726_nat_o @ Y @ R )
% 0.29/0.51         => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ E )
% 0.29/0.51           => ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ ( rel_re3331361160397388719_nat_o @ E @ R ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrictI
% 0.29/0.51  thf(fact_1769_rel__restrict__notR_I1_J,axiom,
% 0.29/0.51      ! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,A2: set_Pr8057934254988874055nt_int,R: set_se6260736226359567993nt_int] :
% 0.29/0.51        ( ( member5325734588016868240nt_int @ ( produc782388162306416855nt_int @ X @ Y ) @ ( rel_re4349003428253852667nt_int @ A2 @ R ) )
% 0.29/0.51       => ~ ( member2340774599025711042nt_int @ X @ R ) ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrict_notR(1)
% 0.29/0.51  thf(fact_1770_rel__restrict__notR_I1_J,axiom,
% 0.29/0.51      ! [X: set_nat,Y: set_nat,A2: set_Pr5488025237498180813et_nat,R: set_set_nat] :
% 0.29/0.51        ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ X @ Y ) @ ( rel_restrict_set_nat @ A2 @ R ) )
% 0.29/0.51       => ~ ( member_set_nat @ X @ R ) ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrict_notR(1)
% 0.29/0.51  thf(fact_1771_rel__restrict__notR_I1_J,axiom,
% 0.29/0.51      ! [X: nat,Y: nat,A2: set_Pr1261947904930325089at_nat,R: set_nat] :
% 0.29/0.51        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( rel_restrict_nat @ A2 @ R ) )
% 0.29/0.51       => ~ ( member_nat @ X @ R ) ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrict_notR(1)
% 0.29/0.51  thf(fact_1772_rel__restrict__notR_I1_J,axiom,
% 0.29/0.51      ! [X: int,Y: int,A2: set_Pr958786334691620121nt_int,R: set_int] :
% 0.29/0.51        ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( rel_restrict_int @ A2 @ R ) )
% 0.29/0.51       => ~ ( member_int @ X @ R ) ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrict_notR(1)
% 0.29/0.51  thf(fact_1773_rel__restrict__notR_I1_J,axiom,
% 0.29/0.51      ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o,A2: set_Pr2161125870931222855_nat_o,R: set_Pr4532377907799695533_nat_o] :
% 0.29/0.51        ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ ( rel_re3331361160397388719_nat_o @ A2 @ R ) )
% 0.29/0.51       => ~ ( member6576561426505652726_nat_o @ X @ R ) ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrict_notR(1)
% 0.29/0.51  thf(fact_1774_rel__restrict__notR_I2_J,axiom,
% 0.29/0.51      ! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,A2: set_Pr8057934254988874055nt_int,R: set_se6260736226359567993nt_int] :
% 0.29/0.51        ( ( member5325734588016868240nt_int @ ( produc782388162306416855nt_int @ X @ Y ) @ ( rel_re4349003428253852667nt_int @ A2 @ R ) )
% 0.29/0.51       => ~ ( member2340774599025711042nt_int @ Y @ R ) ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrict_notR(2)
% 0.29/0.51  thf(fact_1775_rel__restrict__notR_I2_J,axiom,
% 0.29/0.51      ! [X: set_nat,Y: set_nat,A2: set_Pr5488025237498180813et_nat,R: set_set_nat] :
% 0.29/0.51        ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ X @ Y ) @ ( rel_restrict_set_nat @ A2 @ R ) )
% 0.29/0.51       => ~ ( member_set_nat @ Y @ R ) ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrict_notR(2)
% 0.29/0.51  thf(fact_1776_rel__restrict__notR_I2_J,axiom,
% 0.29/0.51      ! [X: nat,Y: nat,A2: set_Pr1261947904930325089at_nat,R: set_nat] :
% 0.29/0.51        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( rel_restrict_nat @ A2 @ R ) )
% 0.29/0.51       => ~ ( member_nat @ Y @ R ) ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrict_notR(2)
% 0.29/0.51  thf(fact_1777_rel__restrict__notR_I2_J,axiom,
% 0.29/0.51      ! [X: int,Y: int,A2: set_Pr958786334691620121nt_int,R: set_int] :
% 0.29/0.51        ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( rel_restrict_int @ A2 @ R ) )
% 0.29/0.51       => ~ ( member_int @ Y @ R ) ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrict_notR(2)
% 0.29/0.51  thf(fact_1778_rel__restrict__notR_I2_J,axiom,
% 0.29/0.51      ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o,A2: set_Pr2161125870931222855_nat_o,R: set_Pr4532377907799695533_nat_o] :
% 0.29/0.51        ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ ( rel_re3331361160397388719_nat_o @ A2 @ R ) )
% 0.29/0.51       => ~ ( member6576561426505652726_nat_o @ Y @ R ) ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrict_notR(2)
% 0.29/0.51  thf(fact_1779_rel__restrict__union,axiom,
% 0.29/0.51      ! [R: set_Pr4759807026041935047at_nat,A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 0.29/0.51        ( ( rel_re2197483123211154633at_nat @ R @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 0.29/0.51        = ( rel_re2197483123211154633at_nat @ ( rel_re2197483123211154633at_nat @ R @ A2 ) @ B2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrict_union
% 0.29/0.51  thf(fact_1780_rel__restrict__union,axiom,
% 0.29/0.51      ! [R: set_Pr5564308138774400199at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.29/0.51        ( ( rel_re2767227651283840073at_nat @ R @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 0.29/0.51        = ( rel_re2767227651283840073at_nat @ ( rel_re2767227651283840073at_nat @ R @ A2 ) @ B2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrict_union
% 0.29/0.51  thf(fact_1781_rel__restrict__union,axiom,
% 0.29/0.51      ! [R: set_Pr1261947904930325089at_nat,A2: set_nat,B2: set_nat] :
% 0.29/0.51        ( ( rel_restrict_nat @ R @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.29/0.51        = ( rel_restrict_nat @ ( rel_restrict_nat @ R @ A2 ) @ B2 ) ) ).
% 0.29/0.51  
% 0.29/0.51  % rel_restrict_union
% 0.29/0.51  thf(fact_1782_Id__on__iff,axiom,
% 0.29/0.51      ! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int] :
% 0.29/0.51        ( ( member5325734588016868240nt_int @ ( produc782388162306416855nt_int @ X @ Y ) @ ( id_on_6410342593070439734nt_int @ A2 ) )
% 0.29/0.51        = ( ( X = Y )
% 0.29/0.51          & ( member2340774599025711042nt_int @ X @ A2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_on_iff
% 0.29/0.51  thf(fact_1783_Id__on__iff,axiom,
% 0.29/0.51      ! [X: set_nat,Y: set_nat,A2: set_set_nat] :
% 0.29/0.51        ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ X @ Y ) @ ( id_on_set_nat @ A2 ) )
% 0.29/0.51        = ( ( X = Y )
% 0.29/0.51          & ( member_set_nat @ X @ A2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_on_iff
% 0.29/0.51  thf(fact_1784_Id__on__iff,axiom,
% 0.29/0.51      ! [X: nat,Y: nat,A2: set_nat] :
% 0.29/0.51        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( id_on_nat @ A2 ) )
% 0.29/0.51        = ( ( X = Y )
% 0.29/0.51          & ( member_nat @ X @ A2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_on_iff
% 0.29/0.51  thf(fact_1785_Id__on__iff,axiom,
% 0.29/0.51      ! [X: int,Y: int,A2: set_int] :
% 0.29/0.51        ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( id_on_int @ A2 ) )
% 0.29/0.51        = ( ( X = Y )
% 0.29/0.51          & ( member_int @ X @ A2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_on_iff
% 0.29/0.51  thf(fact_1786_Id__on__iff,axiom,
% 0.29/0.51      ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.51        ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ ( id_on_7438695062414216554_nat_o @ A2 ) )
% 0.29/0.51        = ( ( X = Y )
% 0.29/0.51          & ( member6576561426505652726_nat_o @ X @ A2 ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_on_iff
% 0.29/0.51  thf(fact_1787_Id__on__eqI,axiom,
% 0.29/0.51      ! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int] :
% 0.29/0.51        ( ( A = B )
% 0.29/0.51       => ( ( member2340774599025711042nt_int @ A @ A2 )
% 0.29/0.51         => ( member5325734588016868240nt_int @ ( produc782388162306416855nt_int @ A @ B ) @ ( id_on_6410342593070439734nt_int @ A2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_on_eqI
% 0.29/0.51  thf(fact_1788_Id__on__eqI,axiom,
% 0.29/0.51      ! [A: set_nat,B: set_nat,A2: set_set_nat] :
% 0.29/0.51        ( ( A = B )
% 0.29/0.51       => ( ( member_set_nat @ A @ A2 )
% 0.29/0.51         => ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A @ B ) @ ( id_on_set_nat @ A2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_on_eqI
% 0.29/0.51  thf(fact_1789_Id__on__eqI,axiom,
% 0.29/0.51      ! [A: nat,B: nat,A2: set_nat] :
% 0.29/0.51        ( ( A = B )
% 0.29/0.51       => ( ( member_nat @ A @ A2 )
% 0.29/0.51         => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( id_on_nat @ A2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_on_eqI
% 0.29/0.51  thf(fact_1790_Id__on__eqI,axiom,
% 0.29/0.51      ! [A: int,B: int,A2: set_int] :
% 0.29/0.51        ( ( A = B )
% 0.29/0.51       => ( ( member_int @ A @ A2 )
% 0.29/0.51         => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( id_on_int @ A2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_on_eqI
% 0.29/0.51  thf(fact_1791_Id__on__eqI,axiom,
% 0.29/0.51      ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.51        ( ( A = B )
% 0.29/0.51       => ( ( member6576561426505652726_nat_o @ A @ A2 )
% 0.29/0.51         => ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A @ B ) @ ( id_on_7438695062414216554_nat_o @ A2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_on_eqI
% 0.29/0.51  thf(fact_1792_Id__onE,axiom,
% 0.29/0.51      ! [C: produc412284730452459111nt_int,A2: set_se6260736226359567993nt_int] :
% 0.29/0.51        ( ( member5325734588016868240nt_int @ C @ ( id_on_6410342593070439734nt_int @ A2 ) )
% 0.29/0.51       => ~ ! [X2: set_Pr958786334691620121nt_int] :
% 0.29/0.51              ( ( member2340774599025711042nt_int @ X2 @ A2 )
% 0.29/0.51             => ( C
% 0.29/0.51               != ( produc782388162306416855nt_int @ X2 @ X2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_onE
% 0.29/0.51  thf(fact_1793_Id__onE,axiom,
% 0.29/0.51      ! [C: produc7819656566062154093et_nat,A2: set_set_nat] :
% 0.29/0.51        ( ( member8277197624267554838et_nat @ C @ ( id_on_set_nat @ A2 ) )
% 0.29/0.51       => ~ ! [X2: set_nat] :
% 0.29/0.51              ( ( member_set_nat @ X2 @ A2 )
% 0.29/0.51             => ( C
% 0.29/0.51               != ( produc4532415448927165861et_nat @ X2 @ X2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_onE
% 0.29/0.51  thf(fact_1794_Id__onE,axiom,
% 0.29/0.51      ! [C: product_prod_nat_nat,A2: set_nat] :
% 0.29/0.51        ( ( member8440522571783428010at_nat @ C @ ( id_on_nat @ A2 ) )
% 0.29/0.51       => ~ ! [X2: nat] :
% 0.29/0.51              ( ( member_nat @ X2 @ A2 )
% 0.29/0.51             => ( C
% 0.29/0.51               != ( product_Pair_nat_nat @ X2 @ X2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_onE
% 0.29/0.51  thf(fact_1795_Id__onE,axiom,
% 0.29/0.51      ! [C: product_prod_int_int,A2: set_int] :
% 0.29/0.51        ( ( member5262025264175285858nt_int @ C @ ( id_on_int @ A2 ) )
% 0.29/0.51       => ~ ! [X2: int] :
% 0.29/0.51              ( ( member_int @ X2 @ A2 )
% 0.29/0.51             => ( C
% 0.29/0.51               != ( product_Pair_int_int @ X2 @ X2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_onE
% 0.29/0.51  thf(fact_1796_Id__onE,axiom,
% 0.29/0.51      ! [C: produc4928098042776334183_nat_o,A2: set_Pr4532377907799695533_nat_o] :
% 0.29/0.51        ( ( member8781333585448626064_nat_o @ C @ ( id_on_7438695062414216554_nat_o @ A2 ) )
% 0.29/0.51       => ~ ! [X2: produc3658429121746597890et_nat > $o] :
% 0.29/0.51              ( ( member6576561426505652726_nat_o @ X2 @ A2 )
% 0.29/0.51             => ( C
% 0.29/0.51               != ( produc7368190662567826135_nat_o @ X2 @ X2 ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % Id_onE
% 0.29/0.51  thf(fact_1797_lambda__zero,axiom,
% 0.29/0.51      ( ( ^ [H2: code_integer] : zero_z3403309356797280102nteger )
% 0.29/0.51      = ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.51  
% 0.29/0.51  % lambda_zero
% 0.29/0.51  thf(fact_1798_lambda__zero,axiom,
% 0.29/0.51      ( ( ^ [H2: rat] : zero_zero_rat )
% 0.29/0.51      = ( times_times_rat @ zero_zero_rat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % lambda_zero
% 0.29/0.51  thf(fact_1799_lambda__zero,axiom,
% 0.29/0.51      ( ( ^ [H2: nat] : zero_zero_nat )
% 0.29/0.51      = ( times_times_nat @ zero_zero_nat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % lambda_zero
% 0.29/0.51  thf(fact_1800_lambda__zero,axiom,
% 0.29/0.51      ( ( ^ [H2: int] : zero_zero_int )
% 0.29/0.51      = ( times_times_int @ zero_zero_int ) ) ).
% 0.29/0.51  
% 0.29/0.51  % lambda_zero
% 0.29/0.51  thf(fact_1801_one__neq__neg__numeral,axiom,
% 0.29/0.51      ! [N: num] :
% 0.29/0.51        ( one_one_int
% 0.29/0.51       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % one_neq_neg_numeral
% 0.29/0.51  thf(fact_1802_one__neq__neg__numeral,axiom,
% 0.29/0.51      ! [N: num] :
% 0.29/0.51        ( one_one_Code_integer
% 0.29/0.51       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % one_neq_neg_numeral
% 0.29/0.51  thf(fact_1803_one__neq__neg__numeral,axiom,
% 0.29/0.51      ! [N: num] :
% 0.29/0.51        ( one_one_rat
% 0.29/0.51       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % one_neq_neg_numeral
% 0.29/0.51  thf(fact_1804_numeral__neq__neg__one,axiom,
% 0.29/0.51      ! [N: num] :
% 0.29/0.51        ( ( numeral_numeral_int @ N )
% 0.29/0.51       != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.51  
% 0.29/0.51  % numeral_neq_neg_one
% 0.29/0.51  thf(fact_1805_numeral__neq__neg__one,axiom,
% 0.29/0.51      ! [N: num] :
% 0.29/0.51        ( ( numera6620942414471956472nteger @ N )
% 0.29/0.51       != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.51  
% 0.29/0.51  % numeral_neq_neg_one
% 0.29/0.51  thf(fact_1806_numeral__neq__neg__one,axiom,
% 0.29/0.51      ! [N: num] :
% 0.29/0.51        ( ( numeral_numeral_rat @ N )
% 0.29/0.51       != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % numeral_neq_neg_one
% 0.29/0.51  thf(fact_1807_zero__neq__neg__one,axiom,
% 0.29/0.51      ( zero_zero_int
% 0.29/0.51     != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_neq_neg_one
% 0.29/0.51  thf(fact_1808_zero__neq__neg__one,axiom,
% 0.29/0.51      ( zero_z3403309356797280102nteger
% 0.29/0.51     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_neq_neg_one
% 0.29/0.51  thf(fact_1809_zero__neq__neg__one,axiom,
% 0.29/0.51      ( zero_zero_rat
% 0.29/0.51     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.51  
% 0.29/0.51  % zero_neq_neg_one
% 0.29/0.51  thf(fact_1810_bijective__def,axiom,
% 0.29/0.51      ( biject9051520373387432658nteger
% 0.29/0.51      = ( ^ [R2: set_Pr1281608226676607948nteger] :
% 0.29/0.51            ( ! [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger,Z3: produc8923325533196201883nteger] :
% 0.29/0.51                ( ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ R2 )
% 0.29/0.51                  & ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Z3 ) @ R2 ) )
% 0.29/0.51               => ( Y3 = Z3 ) )
% 0.29/0.51            & ! [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc6241069584506657477e_term > option6357759511663192854e_term,Z3: produc8923325533196201883nteger] :
% 0.29/0.51                ( ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Z3 ) @ R2 )
% 0.29/0.51                  & ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ Y3 @ Z3 ) @ R2 ) )
% 0.29/0.51               => ( X3 = Y3 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % bijective_def
% 0.29/0.51  thf(fact_1811_bijective__def,axiom,
% 0.29/0.51      ( biject2615096655818420098et_nat
% 0.29/0.51      = ( ^ [R2: set_Pr3286484037609594932et_nat] :
% 0.29/0.51            ( ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat,Z3: produc3658429121746597890et_nat] :
% 0.29/0.51                ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R2 )
% 0.29/0.51                  & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Z3 ) @ R2 ) )
% 0.29/0.51               => ( Y3 = Z3 ) )
% 0.29/0.51            & ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat > $o,Z3: produc3658429121746597890et_nat] :
% 0.29/0.51                ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Z3 ) @ R2 )
% 0.29/0.51                  & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ Y3 @ Z3 ) @ R2 ) )
% 0.29/0.51               => ( X3 = Y3 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % bijective_def
% 0.29/0.51  thf(fact_1812_bijective__def,axiom,
% 0.29/0.51      ( biject1468766312547416318et_nat
% 0.29/0.51      = ( ^ [R2: set_Pr8536935166611901872et_nat] :
% 0.29/0.51            ( ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat,Z3: produc3925858234332021118et_nat] :
% 0.29/0.51                ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R2 )
% 0.29/0.51                  & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Z3 ) @ R2 ) )
% 0.29/0.51               => ( Y3 = Z3 ) )
% 0.29/0.51            & ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat > $o,Z3: produc3925858234332021118et_nat] :
% 0.29/0.51                ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Z3 ) @ R2 )
% 0.29/0.51                  & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ Y3 @ Z3 ) @ R2 ) )
% 0.29/0.51               => ( X3 = Y3 ) ) ) ) ) ).
% 0.29/0.51  
% 0.29/0.51  % bijective_def
% 0.29/0.51  thf(fact_1813_bijective__def,axiom,
% 0.29/0.51      ( biject383251550997737151nt_int
% 0.29/0.51      = ( ^ [R2: set_Pr9222295170931077689nt_int] :
% 0.29/0.51            ( ! [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int,Z3: product_prod_int_int] :
% 0.29/0.51                ( ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ R2 )
% 0.29/0.52                  & ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Z3 ) @ R2 ) )
% 0.29/0.52               => ( Y3 = Z3 ) )
% 0.29/0.52            & ! [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: produc8551481072490612790e_term > option6357759511663192854e_term,Z3: product_prod_int_int] :
% 0.29/0.52                ( ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Z3 ) @ R2 )
% 0.29/0.52                  & ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ Y3 @ Z3 ) @ R2 ) )
% 0.29/0.52               => ( X3 = Y3 ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % bijective_def
% 0.29/0.52  thf(fact_1814_bijective__def,axiom,
% 0.29/0.52      ( biject576505603616484041nt_int
% 0.29/0.52      = ( ^ [R2: set_Pr1872883991513573699nt_int] :
% 0.29/0.52            ( ! [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int,Z3: product_prod_int_int] :
% 0.29/0.52                ( ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ R2 )
% 0.29/0.52                  & ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Z3 ) @ R2 ) )
% 0.29/0.52               => ( Y3 = Z3 ) )
% 0.29/0.52            & ! [X3: int > option6357759511663192854e_term,Y3: int > option6357759511663192854e_term,Z3: product_prod_int_int] :
% 0.29/0.52                ( ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Z3 ) @ R2 )
% 0.29/0.52                  & ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ Y3 @ Z3 ) @ R2 ) )
% 0.29/0.52               => ( X3 = Y3 ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % bijective_def
% 0.29/0.52  thf(fact_1815_semiring__norm_I170_J,axiom,
% 0.29/0.52      ! [V: num,W: num,Y: int] :
% 0.29/0.52        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y ) )
% 0.29/0.52        = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.29/0.52  
% 0.29/0.52  % semiring_norm(170)
% 0.29/0.52  thf(fact_1816_semiring__norm_I170_J,axiom,
% 0.29/0.52      ! [V: num,W: num,Y: code_integer] :
% 0.29/0.52        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y ) )
% 0.29/0.52        = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.29/0.52  
% 0.29/0.52  % semiring_norm(170)
% 0.29/0.52  thf(fact_1817_semiring__norm_I170_J,axiom,
% 0.29/0.52      ! [V: num,W: num,Y: rat] :
% 0.29/0.52        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y ) )
% 0.29/0.52        = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.29/0.52  
% 0.29/0.52  % semiring_norm(170)
% 0.29/0.52  thf(fact_1818_semiring__norm_I171_J,axiom,
% 0.29/0.52      ! [V: num,W: num,Y: int] :
% 0.29/0.52        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 0.29/0.52        = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.29/0.52  
% 0.29/0.52  % semiring_norm(171)
% 0.29/0.52  thf(fact_1819_semiring__norm_I171_J,axiom,
% 0.29/0.52      ! [V: num,W: num,Y: code_integer] :
% 0.29/0.52        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 0.29/0.52        = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.29/0.52  
% 0.29/0.52  % semiring_norm(171)
% 0.29/0.52  thf(fact_1820_semiring__norm_I171_J,axiom,
% 0.29/0.52      ! [V: num,W: num,Y: rat] :
% 0.29/0.52        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 0.29/0.52        = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 0.29/0.52  
% 0.29/0.52  % semiring_norm(171)
% 0.29/0.52  thf(fact_1821_semiring__norm_I172_J,axiom,
% 0.29/0.52      ! [V: num,W: num,Y: int] :
% 0.29/0.52        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 0.29/0.52        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 0.29/0.52  
% 0.29/0.52  % semiring_norm(172)
% 0.29/0.52  thf(fact_1822_semiring__norm_I172_J,axiom,
% 0.29/0.52      ! [V: num,W: num,Y: code_integer] :
% 0.29/0.52        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 0.29/0.52        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 0.29/0.52  
% 0.29/0.52  % semiring_norm(172)
% 0.29/0.52  thf(fact_1823_semiring__norm_I172_J,axiom,
% 0.29/0.52      ! [V: num,W: num,Y: rat] :
% 0.29/0.52        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 0.29/0.52        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 0.29/0.52  
% 0.29/0.52  % semiring_norm(172)
% 0.29/0.52  thf(fact_1824_numeral__times__minus__swap,axiom,
% 0.29/0.52      ! [W: num,X: int] :
% 0.29/0.52        ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X ) )
% 0.29/0.52        = ( times_times_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % numeral_times_minus_swap
% 0.29/0.52  thf(fact_1825_numeral__times__minus__swap,axiom,
% 0.29/0.52      ! [W: num,X: code_integer] :
% 0.29/0.52        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X ) )
% 0.29/0.52        = ( times_3573771949741848930nteger @ X @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % numeral_times_minus_swap
% 0.29/0.52  thf(fact_1826_numeral__times__minus__swap,axiom,
% 0.29/0.52      ! [W: num,X: rat] :
% 0.29/0.52        ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X ) )
% 0.29/0.52        = ( times_times_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % numeral_times_minus_swap
% 0.29/0.52  thf(fact_1827_dbl__simps_I1_J,axiom,
% 0.29/0.52      ! [K: num] :
% 0.29/0.52        ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.29/0.52        = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dbl_simps(1)
% 0.29/0.52  thf(fact_1828_dbl__simps_I1_J,axiom,
% 0.29/0.52      ! [K: num] :
% 0.29/0.52        ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.29/0.52        = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dbl_simps(1)
% 0.29/0.52  thf(fact_1829_dbl__simps_I1_J,axiom,
% 0.29/0.52      ! [K: num] :
% 0.29/0.52        ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.29/0.52        = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % dbl_simps(1)
% 0.29/0.52  thf(fact_1830_eq__divide__eq__numeral1_I2_J,axiom,
% 0.29/0.52      ! [A: rat,B: rat,W: num] :
% 0.29/0.52        ( ( A
% 0.29/0.52          = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 0.29/0.52        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.29/0.52             != zero_zero_rat )
% 0.29/0.52           => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.29/0.52              = B ) )
% 0.29/0.52          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.29/0.52              = zero_zero_rat )
% 0.29/0.52           => ( A = zero_zero_rat ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % eq_divide_eq_numeral1(2)
% 0.29/0.52  thf(fact_1831_divide__eq__eq__numeral1_I2_J,axiom,
% 0.29/0.52      ! [B: rat,W: num,A: rat] :
% 0.29/0.52        ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.29/0.52          = A )
% 0.29/0.52        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.29/0.52             != zero_zero_rat )
% 0.29/0.52           => ( B
% 0.29/0.52              = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 0.29/0.52          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.29/0.52              = zero_zero_rat )
% 0.29/0.52           => ( A = zero_zero_rat ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_eq_eq_numeral1(2)
% 0.29/0.52  thf(fact_1832_eq__numeral__iff__iszero_I12_J,axiom,
% 0.29/0.52      ! [Y: num] :
% 0.29/0.52        ( ( zero_zero_int
% 0.29/0.52          = ( uminus_uminus_int @ ( numeral_numeral_int @ Y ) ) )
% 0.29/0.52        = ( ring_1_iszero_int @ ( numeral_numeral_int @ Y ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % eq_numeral_iff_iszero(12)
% 0.29/0.52  thf(fact_1833_eq__numeral__iff__iszero_I12_J,axiom,
% 0.29/0.52      ! [Y: num] :
% 0.29/0.52        ( ( zero_z3403309356797280102nteger
% 0.29/0.52          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ Y ) ) )
% 0.29/0.52        = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ Y ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % eq_numeral_iff_iszero(12)
% 0.29/0.52  thf(fact_1834_eq__numeral__iff__iszero_I12_J,axiom,
% 0.29/0.52      ! [Y: num] :
% 0.29/0.52        ( ( zero_zero_rat
% 0.29/0.52          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ Y ) ) )
% 0.29/0.52        = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ Y ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % eq_numeral_iff_iszero(12)
% 0.29/0.52  thf(fact_1835_eq__numeral__iff__iszero_I11_J,axiom,
% 0.29/0.52      ! [X: num] :
% 0.29/0.52        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ X ) )
% 0.29/0.52          = zero_zero_int )
% 0.29/0.52        = ( ring_1_iszero_int @ ( numeral_numeral_int @ X ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % eq_numeral_iff_iszero(11)
% 0.29/0.52  thf(fact_1836_eq__numeral__iff__iszero_I11_J,axiom,
% 0.29/0.52      ! [X: num] :
% 0.29/0.52        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) )
% 0.29/0.52          = zero_z3403309356797280102nteger )
% 0.29/0.52        = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ X ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % eq_numeral_iff_iszero(11)
% 0.29/0.52  thf(fact_1837_eq__numeral__iff__iszero_I11_J,axiom,
% 0.29/0.52      ! [X: num] :
% 0.29/0.52        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) )
% 0.29/0.52          = zero_zero_rat )
% 0.29/0.52        = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ X ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % eq_numeral_iff_iszero(11)
% 0.29/0.52  thf(fact_1838_divides__aux__eq,axiom,
% 0.29/0.52      ! [Q4: code_integer,R3: code_integer] :
% 0.29/0.52        ( ( unique5706413561485394159nteger @ ( produc1086072967326762835nteger @ Q4 @ R3 ) )
% 0.29/0.52        = ( R3 = zero_z3403309356797280102nteger ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divides_aux_eq
% 0.29/0.52  thf(fact_1839_divides__aux__eq,axiom,
% 0.29/0.52      ! [Q4: nat,R3: nat] :
% 0.29/0.52        ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q4 @ R3 ) )
% 0.29/0.52        = ( R3 = zero_zero_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divides_aux_eq
% 0.29/0.52  thf(fact_1840_divides__aux__eq,axiom,
% 0.29/0.52      ! [Q4: int,R3: int] :
% 0.29/0.52        ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 0.29/0.52        = ( R3 = zero_zero_int ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divides_aux_eq
% 0.29/0.52  thf(fact_1841_minus__assn__def,axiom,
% 0.29/0.52      ( minus_minus_assn
% 0.29/0.52      = ( ^ [A3: assn,B3: assn] : ( inf_inf_assn @ A3 @ ( uminus_uminus_assn @ B3 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % minus_assn_def
% 0.29/0.52  thf(fact_1842_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( minus_8373710615458151222nteger @ A @ A )
% 0.29/0.52        = zero_z3403309356797280102nteger ) ).
% 0.29/0.52  
% 0.29/0.52  % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.52  thf(fact_1843_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.52      ! [A: multis2468970476368604999at_nat] :
% 0.29/0.52        ( ( minus_4286766774447292334at_nat @ A @ A )
% 0.29/0.52        = zero_z1048942125864253310at_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.52  thf(fact_1844_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( minus_minus_rat @ A @ A )
% 0.29/0.52        = zero_zero_rat ) ).
% 0.29/0.52  
% 0.29/0.52  % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.52  thf(fact_1845_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.52      ! [A: nat] :
% 0.29/0.52        ( ( minus_minus_nat @ A @ A )
% 0.29/0.52        = zero_zero_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.52  thf(fact_1846_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( minus_minus_int @ A @ A )
% 0.29/0.52        = zero_zero_int ) ).
% 0.29/0.52  
% 0.29/0.52  % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.52  thf(fact_1847_diff__zero,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( minus_8373710615458151222nteger @ A @ zero_z3403309356797280102nteger )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_zero
% 0.29/0.52  thf(fact_1848_diff__zero,axiom,
% 0.29/0.52      ! [A: multis2468970476368604999at_nat] :
% 0.29/0.52        ( ( minus_4286766774447292334at_nat @ A @ zero_z1048942125864253310at_nat )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_zero
% 0.29/0.52  thf(fact_1849_diff__zero,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_zero
% 0.29/0.52  thf(fact_1850_diff__zero,axiom,
% 0.29/0.52      ! [A: nat] :
% 0.29/0.52        ( ( minus_minus_nat @ A @ zero_zero_nat )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_zero
% 0.29/0.52  thf(fact_1851_diff__zero,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( minus_minus_int @ A @ zero_zero_int )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_zero
% 0.29/0.52  thf(fact_1852_zero__diff,axiom,
% 0.29/0.52      ! [A: multis2468970476368604999at_nat] :
% 0.29/0.52        ( ( minus_4286766774447292334at_nat @ zero_z1048942125864253310at_nat @ A )
% 0.29/0.52        = zero_z1048942125864253310at_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % zero_diff
% 0.29/0.52  thf(fact_1853_zero__diff,axiom,
% 0.29/0.52      ! [A: nat] :
% 0.29/0.52        ( ( minus_minus_nat @ zero_zero_nat @ A )
% 0.29/0.52        = zero_zero_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % zero_diff
% 0.29/0.52  thf(fact_1854_diff__0__right,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( minus_8373710615458151222nteger @ A @ zero_z3403309356797280102nteger )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_0_right
% 0.29/0.52  thf(fact_1855_diff__0__right,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_0_right
% 0.29/0.52  thf(fact_1856_diff__0__right,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( minus_minus_int @ A @ zero_zero_int )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_0_right
% 0.29/0.52  thf(fact_1857_diff__self,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( minus_8373710615458151222nteger @ A @ A )
% 0.29/0.52        = zero_z3403309356797280102nteger ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_self
% 0.29/0.52  thf(fact_1858_diff__self,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( minus_minus_rat @ A @ A )
% 0.29/0.52        = zero_zero_rat ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_self
% 0.29/0.52  thf(fact_1859_diff__self,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( minus_minus_int @ A @ A )
% 0.29/0.52        = zero_zero_int ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_self
% 0.29/0.52  thf(fact_1860_minus__diff__eq,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 0.29/0.52        = ( minus_minus_int @ B @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % minus_diff_eq
% 0.29/0.52  thf(fact_1861_minus__diff__eq,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.29/0.52        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % minus_diff_eq
% 0.29/0.52  thf(fact_1862_minus__diff__eq,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.52        = ( minus_minus_rat @ B @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % minus_diff_eq
% 0.29/0.52  thf(fact_1863_div__by__1,axiom,
% 0.29/0.52      ! [A: nat] :
% 0.29/0.52        ( ( divide_divide_nat @ A @ one_one_nat )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % div_by_1
% 0.29/0.52  thf(fact_1864_div__by__1,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( divide_divide_int @ A @ one_one_int )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % div_by_1
% 0.29/0.52  thf(fact_1865_div__by__1,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % div_by_1
% 0.29/0.52  thf(fact_1866_div__by__1,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( divide_divide_rat @ A @ one_one_rat )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % div_by_1
% 0.29/0.52  thf(fact_1867_div__by__1,axiom,
% 0.29/0.52      ! [A: code_natural] :
% 0.29/0.52        ( ( divide5121882707175180666atural @ A @ one_one_Code_natural )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % div_by_1
% 0.29/0.52  thf(fact_1868_diff__numeral__special_I9_J,axiom,
% 0.29/0.52      ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ one_one_Code_integer )
% 0.29/0.52      = zero_z3403309356797280102nteger ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_numeral_special(9)
% 0.29/0.52  thf(fact_1869_diff__numeral__special_I9_J,axiom,
% 0.29/0.52      ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 0.29/0.52      = zero_zero_rat ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_numeral_special(9)
% 0.29/0.52  thf(fact_1870_diff__numeral__special_I9_J,axiom,
% 0.29/0.52      ( ( minus_minus_int @ one_one_int @ one_one_int )
% 0.29/0.52      = zero_zero_int ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_numeral_special(9)
% 0.29/0.52  thf(fact_1871_left__diff__distrib__numeral,axiom,
% 0.29/0.52      ! [A: int,B: int,V: num] :
% 0.29/0.52        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 0.29/0.52        = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % left_diff_distrib_numeral
% 0.29/0.52  thf(fact_1872_left__diff__distrib__numeral,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer,V: num] :
% 0.29/0.52        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V ) )
% 0.29/0.52        = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % left_diff_distrib_numeral
% 0.29/0.52  thf(fact_1873_left__diff__distrib__numeral,axiom,
% 0.29/0.52      ! [A: rat,B: rat,V: num] :
% 0.29/0.52        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 0.29/0.52        = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % left_diff_distrib_numeral
% 0.29/0.52  thf(fact_1874_right__diff__distrib__numeral,axiom,
% 0.29/0.52      ! [V: num,B: int,C: int] :
% 0.29/0.52        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 0.29/0.52        = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % right_diff_distrib_numeral
% 0.29/0.52  thf(fact_1875_right__diff__distrib__numeral,axiom,
% 0.29/0.52      ! [V: num,B: code_integer,C: code_integer] :
% 0.29/0.52        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( minus_8373710615458151222nteger @ B @ C ) )
% 0.29/0.52        = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % right_diff_distrib_numeral
% 0.29/0.52  thf(fact_1876_right__diff__distrib__numeral,axiom,
% 0.29/0.52      ! [V: num,B: rat,C: rat] :
% 0.29/0.52        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 0.29/0.52        = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % right_diff_distrib_numeral
% 0.29/0.52  thf(fact_1877_verit__minus__simplify_I3_J,axiom,
% 0.29/0.52      ! [B: int] :
% 0.29/0.52        ( ( minus_minus_int @ zero_zero_int @ B )
% 0.29/0.52        = ( uminus_uminus_int @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % verit_minus_simplify(3)
% 0.29/0.52  thf(fact_1878_verit__minus__simplify_I3_J,axiom,
% 0.29/0.52      ! [B: code_integer] :
% 0.29/0.52        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 0.29/0.52        = ( uminus1351360451143612070nteger @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % verit_minus_simplify(3)
% 0.29/0.52  thf(fact_1879_verit__minus__simplify_I3_J,axiom,
% 0.29/0.52      ! [B: rat] :
% 0.29/0.52        ( ( minus_minus_rat @ zero_zero_rat @ B )
% 0.29/0.52        = ( uminus_uminus_rat @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % verit_minus_simplify(3)
% 0.29/0.52  thf(fact_1880_diff__0,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( minus_minus_int @ zero_zero_int @ A )
% 0.29/0.52        = ( uminus_uminus_int @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_0
% 0.29/0.52  thf(fact_1881_diff__0,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.52        = ( uminus1351360451143612070nteger @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_0
% 0.29/0.52  thf(fact_1882_diff__0,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( minus_minus_rat @ zero_zero_rat @ A )
% 0.29/0.52        = ( uminus_uminus_rat @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_0
% 0.29/0.52  thf(fact_1883_nonzero__mult__div__cancel__left,axiom,
% 0.29/0.52      ! [A: nat,B: nat] :
% 0.29/0.52        ( ( A != zero_zero_nat )
% 0.29/0.52       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_left
% 0.29/0.52  thf(fact_1884_nonzero__mult__div__cancel__left,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( A != zero_zero_int )
% 0.29/0.52       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_left
% 0.29/0.52  thf(fact_1885_nonzero__mult__div__cancel__left,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( A != zero_z3403309356797280102nteger )
% 0.29/0.52       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ A )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_left
% 0.29/0.52  thf(fact_1886_nonzero__mult__div__cancel__left,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( A != zero_zero_rat )
% 0.29/0.52       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_left
% 0.29/0.52  thf(fact_1887_nonzero__mult__div__cancel__left,axiom,
% 0.29/0.52      ! [A: code_natural,B: code_natural] :
% 0.29/0.52        ( ( A != zero_z2226904508553997617atural )
% 0.29/0.52       => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ A )
% 0.29/0.52          = B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_left
% 0.29/0.52  thf(fact_1888_nonzero__mult__div__cancel__right,axiom,
% 0.29/0.52      ! [B: nat,A: nat] :
% 0.29/0.52        ( ( B != zero_zero_nat )
% 0.29/0.52       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_right
% 0.29/0.52  thf(fact_1889_nonzero__mult__div__cancel__right,axiom,
% 0.29/0.52      ! [B: int,A: int] :
% 0.29/0.52        ( ( B != zero_zero_int )
% 0.29/0.52       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_right
% 0.29/0.52  thf(fact_1890_nonzero__mult__div__cancel__right,axiom,
% 0.29/0.52      ! [B: code_integer,A: code_integer] :
% 0.29/0.52        ( ( B != zero_z3403309356797280102nteger )
% 0.29/0.52       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_right
% 0.29/0.52  thf(fact_1891_nonzero__mult__div__cancel__right,axiom,
% 0.29/0.52      ! [B: rat,A: rat] :
% 0.29/0.52        ( ( B != zero_zero_rat )
% 0.29/0.52       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_right
% 0.29/0.52  thf(fact_1892_nonzero__mult__div__cancel__right,axiom,
% 0.29/0.52      ! [B: code_natural,A: code_natural] :
% 0.29/0.52        ( ( B != zero_z2226904508553997617atural )
% 0.29/0.52       => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ B )
% 0.29/0.52          = A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_div_cancel_right
% 0.29/0.52  thf(fact_1893_div__self,axiom,
% 0.29/0.52      ! [A: nat] :
% 0.29/0.52        ( ( A != zero_zero_nat )
% 0.29/0.52       => ( ( divide_divide_nat @ A @ A )
% 0.29/0.52          = one_one_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_self
% 0.29/0.52  thf(fact_1894_div__self,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( A != zero_zero_int )
% 0.29/0.52       => ( ( divide_divide_int @ A @ A )
% 0.29/0.52          = one_one_int ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_self
% 0.29/0.52  thf(fact_1895_div__self,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( A != zero_z3403309356797280102nteger )
% 0.29/0.52       => ( ( divide6298287555418463151nteger @ A @ A )
% 0.29/0.52          = one_one_Code_integer ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_self
% 0.29/0.52  thf(fact_1896_div__self,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( A != zero_zero_rat )
% 0.29/0.52       => ( ( divide_divide_rat @ A @ A )
% 0.29/0.52          = one_one_rat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_self
% 0.29/0.52  thf(fact_1897_div__self,axiom,
% 0.29/0.52      ! [A: code_natural] :
% 0.29/0.52        ( ( A != zero_z2226904508553997617atural )
% 0.29/0.52       => ( ( divide5121882707175180666atural @ A @ A )
% 0.29/0.52          = one_one_Code_natural ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_self
% 0.29/0.52  thf(fact_1898_iszero__neg__numeral,axiom,
% 0.29/0.52      ! [W: num] :
% 0.29/0.52        ( ( ring_1_iszero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) )
% 0.29/0.52        = ( ring_1_iszero_int @ ( numeral_numeral_int @ W ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % iszero_neg_numeral
% 0.29/0.52  thf(fact_1899_iszero__neg__numeral,axiom,
% 0.29/0.52      ! [W: num] :
% 0.29/0.52        ( ( ring_16219924574208605041nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) )
% 0.29/0.52        = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ W ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % iszero_neg_numeral
% 0.29/0.52  thf(fact_1900_iszero__neg__numeral,axiom,
% 0.29/0.52      ! [W: num] :
% 0.29/0.52        ( ( ring_1_iszero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.29/0.52        = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % iszero_neg_numeral
% 0.29/0.52  thf(fact_1901_eq__divide__eq__numeral1_I1_J,axiom,
% 0.29/0.52      ! [A: rat,B: rat,W: num] :
% 0.29/0.52        ( ( A
% 0.29/0.52          = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 0.29/0.52        = ( ( ( ( numeral_numeral_rat @ W )
% 0.29/0.52             != zero_zero_rat )
% 0.29/0.52           => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 0.29/0.52              = B ) )
% 0.29/0.52          & ( ( ( numeral_numeral_rat @ W )
% 0.29/0.52              = zero_zero_rat )
% 0.29/0.52           => ( A = zero_zero_rat ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % eq_divide_eq_numeral1(1)
% 0.29/0.52  thf(fact_1902_divide__eq__eq__numeral1_I1_J,axiom,
% 0.29/0.52      ! [B: rat,W: num,A: rat] :
% 0.29/0.52        ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 0.29/0.52          = A )
% 0.29/0.52        = ( ( ( ( numeral_numeral_rat @ W )
% 0.29/0.52             != zero_zero_rat )
% 0.29/0.52           => ( B
% 0.29/0.52              = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 0.29/0.52          & ( ( ( numeral_numeral_rat @ W )
% 0.29/0.52              = zero_zero_rat )
% 0.29/0.52           => ( A = zero_zero_rat ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_eq_eq_numeral1(1)
% 0.29/0.52  thf(fact_1903_diff__numeral__special_I12_J,axiom,
% 0.29/0.52      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.52      = zero_zero_int ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_numeral_special(12)
% 0.29/0.52  thf(fact_1904_diff__numeral__special_I12_J,axiom,
% 0.29/0.52      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.52      = zero_z3403309356797280102nteger ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_numeral_special(12)
% 0.29/0.52  thf(fact_1905_diff__numeral__special_I12_J,axiom,
% 0.29/0.52      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.52      = zero_zero_rat ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_numeral_special(12)
% 0.29/0.52  thf(fact_1906_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 0.29/0.52      ! [A: rat,C: rat,B: rat] :
% 0.29/0.52        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 0.29/0.52        = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % cancel_ab_semigroup_add_class.diff_right_commute
% 0.29/0.52  thf(fact_1907_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 0.29/0.52      ! [A: nat,C: nat,B: nat] :
% 0.29/0.52        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 0.29/0.52        = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % cancel_ab_semigroup_add_class.diff_right_commute
% 0.29/0.52  thf(fact_1908_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 0.29/0.52      ! [A: int,C: int,B: int] :
% 0.29/0.52        ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 0.29/0.52        = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % cancel_ab_semigroup_add_class.diff_right_commute
% 0.29/0.52  thf(fact_1909_diff__eq__diff__eq,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.52        ( ( ( minus_minus_rat @ A @ B )
% 0.29/0.52          = ( minus_minus_rat @ C @ D2 ) )
% 0.29/0.52       => ( ( A = B )
% 0.29/0.52          = ( C = D2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_eq_diff_eq
% 0.29/0.52  thf(fact_1910_diff__eq__diff__eq,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.52        ( ( ( minus_minus_int @ A @ B )
% 0.29/0.52          = ( minus_minus_int @ C @ D2 ) )
% 0.29/0.52       => ( ( A = B )
% 0.29/0.52          = ( C = D2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_eq_diff_eq
% 0.29/0.52  thf(fact_1911_eq__iff__diff__eq__0,axiom,
% 0.29/0.52      ( ( ^ [Y4: code_integer,Z4: code_integer] : ( Y4 = Z4 ) )
% 0.29/0.52      = ( ^ [A3: code_integer,B3: code_integer] :
% 0.29/0.52            ( ( minus_8373710615458151222nteger @ A3 @ B3 )
% 0.29/0.52            = zero_z3403309356797280102nteger ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % eq_iff_diff_eq_0
% 0.29/0.52  thf(fact_1912_eq__iff__diff__eq__0,axiom,
% 0.29/0.52      ( ( ^ [Y4: rat,Z4: rat] : ( Y4 = Z4 ) )
% 0.29/0.52      = ( ^ [A3: rat,B3: rat] :
% 0.29/0.52            ( ( minus_minus_rat @ A3 @ B3 )
% 0.29/0.52            = zero_zero_rat ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % eq_iff_diff_eq_0
% 0.29/0.52  thf(fact_1913_eq__iff__diff__eq__0,axiom,
% 0.29/0.52      ( ( ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 0.29/0.52      = ( ^ [A3: int,B3: int] :
% 0.29/0.52            ( ( minus_minus_int @ A3 @ B3 )
% 0.29/0.52            = zero_zero_int ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % eq_iff_diff_eq_0
% 0.29/0.52  thf(fact_1914_left__diff__distrib,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.52        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 0.29/0.52        = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % left_diff_distrib
% 0.29/0.52  thf(fact_1915_left__diff__distrib,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.29/0.52        = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % left_diff_distrib
% 0.29/0.52  thf(fact_1916_left__diff__distrib,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.29/0.52        = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % left_diff_distrib
% 0.29/0.52  thf(fact_1917_right__diff__distrib,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.52        ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 0.29/0.52        = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % right_diff_distrib
% 0.29/0.52  thf(fact_1918_right__diff__distrib,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.29/0.52        = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % right_diff_distrib
% 0.29/0.52  thf(fact_1919_right__diff__distrib,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.29/0.52        = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % right_diff_distrib
% 0.29/0.52  thf(fact_1920_left__diff__distrib_H,axiom,
% 0.29/0.52      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.29/0.52        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ C ) @ A )
% 0.29/0.52        = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % left_diff_distrib'
% 0.29/0.52  thf(fact_1921_left__diff__distrib_H,axiom,
% 0.29/0.52      ! [B: rat,C: rat,A: rat] :
% 0.29/0.52        ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 0.29/0.52        = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % left_diff_distrib'
% 0.29/0.52  thf(fact_1922_left__diff__distrib_H,axiom,
% 0.29/0.52      ! [B: nat,C: nat,A: nat] :
% 0.29/0.52        ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 0.29/0.52        = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % left_diff_distrib'
% 0.29/0.52  thf(fact_1923_left__diff__distrib_H,axiom,
% 0.29/0.52      ! [B: int,C: int,A: int] :
% 0.29/0.52        ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 0.29/0.52        = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % left_diff_distrib'
% 0.29/0.52  thf(fact_1924_right__diff__distrib_H,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.52        ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 0.29/0.52        = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % right_diff_distrib'
% 0.29/0.52  thf(fact_1925_right__diff__distrib_H,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.29/0.52        = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % right_diff_distrib'
% 0.29/0.52  thf(fact_1926_right__diff__distrib_H,axiom,
% 0.29/0.52      ! [A: nat,B: nat,C: nat] :
% 0.29/0.52        ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 0.29/0.52        = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % right_diff_distrib'
% 0.29/0.52  thf(fact_1927_right__diff__distrib_H,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.29/0.52        = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % right_diff_distrib'
% 0.29/0.52  thf(fact_1928_minus__diff__commute,axiom,
% 0.29/0.52      ! [B: int,A: int] :
% 0.29/0.52        ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 0.29/0.52        = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % minus_diff_commute
% 0.29/0.52  thf(fact_1929_minus__diff__commute,axiom,
% 0.29/0.52      ! [B: code_integer,A: code_integer] :
% 0.29/0.52        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 0.29/0.52        = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % minus_diff_commute
% 0.29/0.52  thf(fact_1930_minus__diff__commute,axiom,
% 0.29/0.52      ! [B: rat,A: rat] :
% 0.29/0.52        ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 0.29/0.52        = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % minus_diff_commute
% 0.29/0.52  thf(fact_1931_not__iszero__1,axiom,
% 0.29/0.52      ~ ( ring_16219924574208605041nteger @ one_one_Code_integer ) ).
% 0.29/0.52  
% 0.29/0.52  % not_iszero_1
% 0.29/0.52  thf(fact_1932_not__iszero__1,axiom,
% 0.29/0.52      ~ ( ring_1_iszero_rat @ one_one_rat ) ).
% 0.29/0.52  
% 0.29/0.52  % not_iszero_1
% 0.29/0.52  thf(fact_1933_not__iszero__1,axiom,
% 0.29/0.52      ~ ( ring_1_iszero_int @ one_one_int ) ).
% 0.29/0.52  
% 0.29/0.52  % not_iszero_1
% 0.29/0.52  thf(fact_1934_diff__eq,axiom,
% 0.29/0.52      ( minus_1356011639430497352at_nat
% 0.29/0.52      = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ X3 @ ( uminus6524753893492686040at_nat @ Y3 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_eq
% 0.29/0.52  thf(fact_1935_diff__eq,axiom,
% 0.29/0.52      ( minus_711738161318947805_int_o
% 0.29/0.52      = ( ^ [X3: product_prod_int_int > $o,Y3: product_prod_int_int > $o] : ( inf_in3604695632404883862_int_o @ X3 @ ( uminus7117520113953359693_int_o @ Y3 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_eq
% 0.29/0.52  thf(fact_1936_diff__eq,axiom,
% 0.29/0.52      ( minus_6821098565838606101char_o
% 0.29/0.52      = ( ^ [X3: list_char > $o,Y3: list_char > $o] : ( inf_inf_list_char_o @ X3 @ ( uminus7154032370948614053char_o @ Y3 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_eq
% 0.29/0.52  thf(fact_1937_diff__eq,axiom,
% 0.29/0.52      ( minus_minus_set_nat
% 0.29/0.52      = ( ^ [X3: set_nat,Y3: set_nat] : ( inf_inf_set_nat @ X3 @ ( uminus5710092332889474511et_nat @ Y3 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_eq
% 0.29/0.52  thf(fact_1938_diff__eq,axiom,
% 0.29/0.52      ( minus_3524152463667985524t_unit
% 0.29/0.52      = ( ^ [X3: product_unit,Y3: product_unit] : ( inf_inf_Product_unit @ X3 @ ( uminus2952777764628376836t_unit @ Y3 ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_eq
% 0.29/0.52  thf(fact_1939_not__iszero__neg__1,axiom,
% 0.29/0.52      ~ ( ring_1_iszero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.29/0.52  
% 0.29/0.52  % not_iszero_neg_1
% 0.29/0.52  thf(fact_1940_not__iszero__neg__1,axiom,
% 0.29/0.52      ~ ( ring_16219924574208605041nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.29/0.52  
% 0.29/0.52  % not_iszero_neg_1
% 0.29/0.52  thf(fact_1941_not__iszero__neg__1,axiom,
% 0.29/0.52      ~ ( ring_1_iszero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % not_iszero_neg_1
% 0.29/0.52  thf(fact_1942_eq__divide__eq__numeral_I1_J,axiom,
% 0.29/0.52      ! [W: num,B: rat,C: rat] :
% 0.29/0.52        ( ( ( numeral_numeral_rat @ W )
% 0.29/0.52          = ( divide_divide_rat @ B @ C ) )
% 0.29/0.52        = ( ( ( C != zero_zero_rat )
% 0.29/0.52           => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 0.29/0.52              = B ) )
% 0.29/0.52          & ( ( C = zero_zero_rat )
% 0.29/0.52           => ( ( numeral_numeral_rat @ W )
% 0.29/0.52              = zero_zero_rat ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % eq_divide_eq_numeral(1)
% 0.29/0.52  thf(fact_1943_divide__eq__eq__numeral_I1_J,axiom,
% 0.29/0.52      ! [B: rat,C: rat,W: num] :
% 0.29/0.52        ( ( ( divide_divide_rat @ B @ C )
% 0.29/0.52          = ( numeral_numeral_rat @ W ) )
% 0.29/0.52        = ( ( ( C != zero_zero_rat )
% 0.29/0.52           => ( B
% 0.29/0.52              = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.29/0.52          & ( ( C = zero_zero_rat )
% 0.29/0.52           => ( ( numeral_numeral_rat @ W )
% 0.29/0.52              = zero_zero_rat ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_eq_eq_numeral(1)
% 0.29/0.52  thf(fact_1944_divide__eq__eq__numeral_I2_J,axiom,
% 0.29/0.52      ! [B: rat,C: rat,W: num] :
% 0.29/0.52        ( ( ( divide_divide_rat @ B @ C )
% 0.29/0.52          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.29/0.52        = ( ( ( C != zero_zero_rat )
% 0.29/0.52           => ( B
% 0.29/0.52              = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.29/0.52          & ( ( C = zero_zero_rat )
% 0.29/0.52           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.29/0.52              = zero_zero_rat ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_eq_eq_numeral(2)
% 0.29/0.52  thf(fact_1945_eq__divide__eq__numeral_I2_J,axiom,
% 0.29/0.52      ! [W: num,B: rat,C: rat] :
% 0.29/0.52        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.29/0.52          = ( divide_divide_rat @ B @ C ) )
% 0.29/0.52        = ( ( ( C != zero_zero_rat )
% 0.29/0.52           => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 0.29/0.52              = B ) )
% 0.29/0.52          & ( ( C = zero_zero_rat )
% 0.29/0.52           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 0.29/0.52              = zero_zero_rat ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % eq_divide_eq_numeral(2)
% 0.29/0.52  thf(fact_1946_nonzero__divide__mult__cancel__left,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( A != zero_zero_rat )
% 0.29/0.52       => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 0.29/0.52          = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_divide_mult_cancel_left
% 0.29/0.52  thf(fact_1947_nonzero__divide__mult__cancel__right,axiom,
% 0.29/0.52      ! [B: rat,A: rat] :
% 0.29/0.52        ( ( B != zero_zero_rat )
% 0.29/0.52       => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 0.29/0.52          = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_divide_mult_cancel_right
% 0.29/0.52  thf(fact_1948_divide__minus1,axiom,
% 0.29/0.52      ! [X: rat] :
% 0.29/0.52        ( ( divide_divide_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.52        = ( uminus_uminus_rat @ X ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_minus1
% 0.29/0.52  thf(fact_1949_div__minus1__right,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.52        = ( uminus_uminus_int @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_minus1_right
% 0.29/0.52  thf(fact_1950_div__minus1__right,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.52        = ( uminus1351360451143612070nteger @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_minus1_right
% 0.29/0.52  thf(fact_1951_divide__eq__1__iff,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( ( divide_divide_rat @ A @ B )
% 0.29/0.52          = one_one_rat )
% 0.29/0.52        = ( ( B != zero_zero_rat )
% 0.29/0.52          & ( A = B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_eq_1_iff
% 0.29/0.52  thf(fact_1952_one__eq__divide__iff,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( one_one_rat
% 0.29/0.52          = ( divide_divide_rat @ A @ B ) )
% 0.29/0.52        = ( ( B != zero_zero_rat )
% 0.29/0.52          & ( A = B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % one_eq_divide_iff
% 0.29/0.52  thf(fact_1953_divide__self,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( A != zero_zero_rat )
% 0.29/0.52       => ( ( divide_divide_rat @ A @ A )
% 0.29/0.52          = one_one_rat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_self
% 0.29/0.52  thf(fact_1954_divide__self__if,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( ( A = zero_zero_rat )
% 0.29/0.52         => ( ( divide_divide_rat @ A @ A )
% 0.29/0.52            = zero_zero_rat ) )
% 0.29/0.52        & ( ( A != zero_zero_rat )
% 0.29/0.52         => ( ( divide_divide_rat @ A @ A )
% 0.29/0.52            = one_one_rat ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_self_if
% 0.29/0.52  thf(fact_1955_divide__eq__eq__1,axiom,
% 0.29/0.52      ! [B: rat,A: rat] :
% 0.29/0.52        ( ( ( divide_divide_rat @ B @ A )
% 0.29/0.52          = one_one_rat )
% 0.29/0.52        = ( ( A != zero_zero_rat )
% 0.29/0.52          & ( A = B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_eq_eq_1
% 0.29/0.52  thf(fact_1956_eq__divide__eq__1,axiom,
% 0.29/0.52      ! [B: rat,A: rat] :
% 0.29/0.52        ( ( one_one_rat
% 0.29/0.52          = ( divide_divide_rat @ B @ A ) )
% 0.29/0.52        = ( ( A != zero_zero_rat )
% 0.29/0.52          & ( A = B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % eq_divide_eq_1
% 0.29/0.52  thf(fact_1957_Diff__empty,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( minus_1356011639430497352at_nat @ A2 @ bot_bo2099793752762293965at_nat )
% 0.29/0.52        = A2 ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_empty
% 0.29/0.52  thf(fact_1958_Diff__empty,axiom,
% 0.29/0.52      ! [A2: set_o] :
% 0.29/0.52        ( ( minus_minus_set_o @ A2 @ bot_bot_set_o )
% 0.29/0.52        = A2 ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_empty
% 0.29/0.52  thf(fact_1959_Diff__empty,axiom,
% 0.29/0.52      ! [A2: set_int] :
% 0.29/0.52        ( ( minus_minus_set_int @ A2 @ bot_bot_set_int )
% 0.29/0.52        = A2 ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_empty
% 0.29/0.52  thf(fact_1960_Diff__empty,axiom,
% 0.29/0.52      ! [A2: set_nat] :
% 0.29/0.52        ( ( minus_minus_set_nat @ A2 @ bot_bot_set_nat )
% 0.29/0.52        = A2 ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_empty
% 0.29/0.52  thf(fact_1961_empty__Diff,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( minus_1356011639430497352at_nat @ bot_bo2099793752762293965at_nat @ A2 )
% 0.29/0.52        = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % empty_Diff
% 0.29/0.52  thf(fact_1962_empty__Diff,axiom,
% 0.29/0.52      ! [A2: set_o] :
% 0.29/0.52        ( ( minus_minus_set_o @ bot_bot_set_o @ A2 )
% 0.29/0.52        = bot_bot_set_o ) ).
% 0.29/0.52  
% 0.29/0.52  % empty_Diff
% 0.29/0.52  thf(fact_1963_empty__Diff,axiom,
% 0.29/0.52      ! [A2: set_int] :
% 0.29/0.52        ( ( minus_minus_set_int @ bot_bot_set_int @ A2 )
% 0.29/0.52        = bot_bot_set_int ) ).
% 0.29/0.52  
% 0.29/0.52  % empty_Diff
% 0.29/0.52  thf(fact_1964_empty__Diff,axiom,
% 0.29/0.52      ! [A2: set_nat] :
% 0.29/0.52        ( ( minus_minus_set_nat @ bot_bot_set_nat @ A2 )
% 0.29/0.52        = bot_bot_set_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % empty_Diff
% 0.29/0.52  thf(fact_1965_Diff__cancel,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( minus_1356011639430497352at_nat @ A2 @ A2 )
% 0.29/0.52        = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_cancel
% 0.29/0.52  thf(fact_1966_Diff__cancel,axiom,
% 0.29/0.52      ! [A2: set_o] :
% 0.29/0.52        ( ( minus_minus_set_o @ A2 @ A2 )
% 0.29/0.52        = bot_bot_set_o ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_cancel
% 0.29/0.52  thf(fact_1967_Diff__cancel,axiom,
% 0.29/0.52      ! [A2: set_int] :
% 0.29/0.52        ( ( minus_minus_set_int @ A2 @ A2 )
% 0.29/0.52        = bot_bot_set_int ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_cancel
% 0.29/0.52  thf(fact_1968_Diff__cancel,axiom,
% 0.29/0.52      ! [A2: set_nat] :
% 0.29/0.52        ( ( minus_minus_set_nat @ A2 @ A2 )
% 0.29/0.52        = bot_bot_set_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_cancel
% 0.29/0.52  thf(fact_1969_Un__Diff__cancel,axiom,
% 0.29/0.52      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 0.29/0.52        ( ( sup_su3035147773818789531at_nat @ A2 @ ( minus_5060654252129873198at_nat @ B2 @ A2 ) )
% 0.29/0.52        = ( sup_su3035147773818789531at_nat @ A2 @ B2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Un_Diff_cancel
% 0.29/0.52  thf(fact_1970_Un__Diff__cancel,axiom,
% 0.29/0.52      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.29/0.52        ( ( sup_su5525570899277871387at_nat @ A2 @ ( minus_3314409938677909166at_nat @ B2 @ A2 ) )
% 0.29/0.52        = ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Un_Diff_cancel
% 0.29/0.52  thf(fact_1971_Un__Diff__cancel,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.52        ( ( sup_sup_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 0.29/0.52        = ( sup_sup_set_nat @ A2 @ B2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Un_Diff_cancel
% 0.29/0.52  thf(fact_1972_Un__Diff__cancel2,axiom,
% 0.29/0.52      ! [B2: set_Pr8551490117392284871at_nat,A2: set_Pr8551490117392284871at_nat] :
% 0.29/0.52        ( ( sup_su3035147773818789531at_nat @ ( minus_5060654252129873198at_nat @ B2 @ A2 ) @ A2 )
% 0.29/0.52        = ( sup_su3035147773818789531at_nat @ B2 @ A2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Un_Diff_cancel2
% 0.29/0.52  thf(fact_1973_Un__Diff__cancel2,axiom,
% 0.29/0.52      ! [B2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.29/0.52        ( ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ B2 @ A2 ) @ A2 )
% 0.29/0.52        = ( sup_su5525570899277871387at_nat @ B2 @ A2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Un_Diff_cancel2
% 0.29/0.52  thf(fact_1974_Un__Diff__cancel2,axiom,
% 0.29/0.52      ! [B2: set_nat,A2: set_nat] :
% 0.29/0.52        ( ( sup_sup_set_nat @ ( minus_minus_set_nat @ B2 @ A2 ) @ A2 )
% 0.29/0.52        = ( sup_sup_set_nat @ B2 @ A2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Un_Diff_cancel2
% 0.29/0.52  thf(fact_1975_times__divide__eq__right,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.52        = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % times_divide_eq_right
% 0.29/0.52  thf(fact_1976_divide__divide__eq__right,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.52        = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_divide_eq_right
% 0.29/0.52  thf(fact_1977_divide__divide__eq__left,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 0.29/0.52        = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_divide_eq_left
% 0.29/0.52  thf(fact_1978_times__divide__eq__left,axiom,
% 0.29/0.52      ! [B: rat,C: rat,A: rat] :
% 0.29/0.52        ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.29/0.52        = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 0.29/0.52  
% 0.29/0.52  % times_divide_eq_left
% 0.29/0.52  thf(fact_1979_Diff__UNIV,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( minus_1356011639430497352at_nat @ A2 @ top_to4669805908274784177at_nat )
% 0.29/0.52        = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_UNIV
% 0.29/0.52  thf(fact_1980_Diff__UNIV,axiom,
% 0.29/0.52      ! [A2: set_list_nat] :
% 0.29/0.52        ( ( minus_7954133019191499631st_nat @ A2 @ top_top_set_list_nat )
% 0.29/0.52        = bot_bot_set_list_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_UNIV
% 0.29/0.52  thf(fact_1981_Diff__UNIV,axiom,
% 0.29/0.52      ! [A2: set_o] :
% 0.29/0.52        ( ( minus_minus_set_o @ A2 @ top_top_set_o )
% 0.29/0.52        = bot_bot_set_o ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_UNIV
% 0.29/0.52  thf(fact_1982_Diff__UNIV,axiom,
% 0.29/0.52      ! [A2: set_rat] :
% 0.29/0.52        ( ( minus_minus_set_rat @ A2 @ top_top_set_rat )
% 0.29/0.52        = bot_bot_set_rat ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_UNIV
% 0.29/0.52  thf(fact_1983_Diff__UNIV,axiom,
% 0.29/0.52      ! [A2: set_int] :
% 0.29/0.52        ( ( minus_minus_set_int @ A2 @ top_top_set_int )
% 0.29/0.52        = bot_bot_set_int ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_UNIV
% 0.29/0.52  thf(fact_1984_Diff__UNIV,axiom,
% 0.29/0.52      ! [A2: set_nat] :
% 0.29/0.52        ( ( minus_minus_set_nat @ A2 @ top_top_set_nat )
% 0.29/0.52        = bot_bot_set_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_UNIV
% 0.29/0.52  thf(fact_1985_div__minus__minus,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 0.29/0.52        = ( divide_divide_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_minus_minus
% 0.29/0.52  thf(fact_1986_div__minus__minus,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.52        = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_minus_minus
% 0.29/0.52  thf(fact_1987_Diff__disjoint,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( inf_in2572325071724192079at_nat @ A2 @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) )
% 0.29/0.52        = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_disjoint
% 0.29/0.52  thf(fact_1988_Diff__disjoint,axiom,
% 0.29/0.52      ! [A2: set_o,B2: set_o] :
% 0.29/0.52        ( ( inf_inf_set_o @ A2 @ ( minus_minus_set_o @ B2 @ A2 ) )
% 0.29/0.52        = bot_bot_set_o ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_disjoint
% 0.29/0.52  thf(fact_1989_Diff__disjoint,axiom,
% 0.29/0.52      ! [A2: set_int,B2: set_int] :
% 0.29/0.52        ( ( inf_inf_set_int @ A2 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 0.29/0.52        = bot_bot_set_int ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_disjoint
% 0.29/0.52  thf(fact_1990_Diff__disjoint,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.52        ( ( inf_inf_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 0.29/0.52        = bot_bot_set_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_disjoint
% 0.29/0.52  thf(fact_1991_Diff__Compl,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( minus_1356011639430497352at_nat @ A2 @ ( uminus6524753893492686040at_nat @ B2 ) )
% 0.29/0.52        = ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_Compl
% 0.29/0.52  thf(fact_1992_Diff__Compl,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.52        ( ( minus_minus_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ B2 ) )
% 0.29/0.52        = ( inf_inf_set_nat @ A2 @ B2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_Compl
% 0.29/0.52  thf(fact_1993_inter__compl__diff__conv,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( inf_in2572325071724192079at_nat @ A2 @ ( uminus6524753893492686040at_nat @ B2 ) )
% 0.29/0.52        = ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % inter_compl_diff_conv
% 0.29/0.52  thf(fact_1994_inter__compl__diff__conv,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.52        ( ( inf_inf_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ B2 ) )
% 0.29/0.52        = ( minus_minus_set_nat @ A2 @ B2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % inter_compl_diff_conv
% 0.29/0.52  thf(fact_1995_Compl__Diff__eq,axiom,
% 0.29/0.52      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 0.29/0.52        ( ( uminus2330091110623919550at_nat @ ( minus_5060654252129873198at_nat @ A2 @ B2 ) )
% 0.29/0.52        = ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ A2 ) @ B2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Compl_Diff_eq
% 0.29/0.52  thf(fact_1996_Compl__Diff__eq,axiom,
% 0.29/0.52      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.29/0.52        ( ( uminus935396558254630718at_nat @ ( minus_3314409938677909166at_nat @ A2 @ B2 ) )
% 0.29/0.52        = ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ A2 ) @ B2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Compl_Diff_eq
% 0.29/0.52  thf(fact_1997_Compl__Diff__eq,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.52        ( ( uminus5710092332889474511et_nat @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.29/0.52        = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ B2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Compl_Diff_eq
% 0.29/0.52  thf(fact_1998_div__mult__mult1__if,axiom,
% 0.29/0.52      ! [C: nat,A: nat,B: nat] :
% 0.29/0.52        ( ( ( C = zero_zero_nat )
% 0.29/0.52         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.29/0.52            = zero_zero_nat ) )
% 0.29/0.52        & ( ( C != zero_zero_nat )
% 0.29/0.52         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.29/0.52            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_mult1_if
% 0.29/0.52  thf(fact_1999_div__mult__mult1__if,axiom,
% 0.29/0.52      ! [C: int,A: int,B: int] :
% 0.29/0.52        ( ( ( C = zero_zero_int )
% 0.29/0.52         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.52            = zero_zero_int ) )
% 0.29/0.52        & ( ( C != zero_zero_int )
% 0.29/0.52         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.52            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_mult1_if
% 0.29/0.52  thf(fact_2000_div__mult__mult1__if,axiom,
% 0.29/0.52      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( ( C = zero_z3403309356797280102nteger )
% 0.29/0.52         => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.29/0.52            = zero_z3403309356797280102nteger ) )
% 0.29/0.52        & ( ( C != zero_z3403309356797280102nteger )
% 0.29/0.52         => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.29/0.52            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_mult1_if
% 0.29/0.52  thf(fact_2001_div__mult__mult1__if,axiom,
% 0.29/0.52      ! [C: code_natural,A: code_natural,B: code_natural] :
% 0.29/0.52        ( ( ( C = zero_z2226904508553997617atural )
% 0.29/0.52         => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 0.29/0.52            = zero_z2226904508553997617atural ) )
% 0.29/0.52        & ( ( C != zero_z2226904508553997617atural )
% 0.29/0.52         => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 0.29/0.52            = ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_mult1_if
% 0.29/0.52  thf(fact_2002_div__mult__mult2,axiom,
% 0.29/0.52      ! [C: nat,A: nat,B: nat] :
% 0.29/0.52        ( ( C != zero_zero_nat )
% 0.29/0.52       => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.29/0.52          = ( divide_divide_nat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_mult2
% 0.29/0.52  thf(fact_2003_div__mult__mult2,axiom,
% 0.29/0.52      ! [C: int,A: int,B: int] :
% 0.29/0.52        ( ( C != zero_zero_int )
% 0.29/0.52       => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.29/0.52          = ( divide_divide_int @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_mult2
% 0.29/0.52  thf(fact_2004_div__mult__mult2,axiom,
% 0.29/0.52      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( C != zero_z3403309356797280102nteger )
% 0.29/0.52       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.29/0.52          = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_mult2
% 0.29/0.52  thf(fact_2005_div__mult__mult2,axiom,
% 0.29/0.52      ! [C: code_natural,A: code_natural,B: code_natural] :
% 0.29/0.52        ( ( C != zero_z2226904508553997617atural )
% 0.29/0.52       => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) )
% 0.29/0.52          = ( divide5121882707175180666atural @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_mult2
% 0.29/0.52  thf(fact_2006_div__mult__mult1,axiom,
% 0.29/0.52      ! [C: nat,A: nat,B: nat] :
% 0.29/0.52        ( ( C != zero_zero_nat )
% 0.29/0.52       => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.29/0.52          = ( divide_divide_nat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_mult1
% 0.29/0.52  thf(fact_2007_div__mult__mult1,axiom,
% 0.29/0.52      ! [C: int,A: int,B: int] :
% 0.29/0.52        ( ( C != zero_zero_int )
% 0.29/0.52       => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.52          = ( divide_divide_int @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_mult1
% 0.29/0.52  thf(fact_2008_div__mult__mult1,axiom,
% 0.29/0.52      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( C != zero_z3403309356797280102nteger )
% 0.29/0.52       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.29/0.52          = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_mult1
% 0.29/0.52  thf(fact_2009_div__mult__mult1,axiom,
% 0.29/0.52      ! [C: code_natural,A: code_natural,B: code_natural] :
% 0.29/0.52        ( ( C != zero_z2226904508553997617atural )
% 0.29/0.52       => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 0.29/0.52          = ( divide5121882707175180666atural @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_mult_mult1
% 0.29/0.52  thf(fact_2010_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.29/0.52      ! [C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( C != zero_zero_rat )
% 0.29/0.52       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.52          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_divide_mult_cancel_right2
% 0.29/0.52  thf(fact_2011_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.29/0.52      ! [C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( C != zero_zero_rat )
% 0.29/0.52       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.29/0.52          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_divide_mult_cancel_right
% 0.29/0.52  thf(fact_2012_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.29/0.52      ! [C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( C != zero_zero_rat )
% 0.29/0.52       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 0.29/0.52          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_divide_mult_cancel_left2
% 0.29/0.52  thf(fact_2013_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.29/0.52      ! [C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( C != zero_zero_rat )
% 0.29/0.52       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.52          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_mult_divide_mult_cancel_left
% 0.29/0.52  thf(fact_2014_mult__divide__mult__cancel__left__if,axiom,
% 0.29/0.52      ! [C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( ( C = zero_zero_rat )
% 0.29/0.52         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.52            = zero_zero_rat ) )
% 0.29/0.52        & ( ( C != zero_zero_rat )
% 0.29/0.52         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.52            = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % mult_divide_mult_cancel_left_if
% 0.29/0.52  thf(fact_2015_zero__eq__1__divide__iff,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( zero_zero_rat
% 0.29/0.52          = ( divide_divide_rat @ one_one_rat @ A ) )
% 0.29/0.52        = ( A = zero_zero_rat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % zero_eq_1_divide_iff
% 0.29/0.52  thf(fact_2016_one__divide__eq__0__iff,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( ( divide_divide_rat @ one_one_rat @ A )
% 0.29/0.52          = zero_zero_rat )
% 0.29/0.52        = ( A = zero_zero_rat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % one_divide_eq_0_iff
% 0.29/0.52  thf(fact_2017_Int__Diff,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ C2 )
% 0.29/0.52        = ( inf_in2572325071724192079at_nat @ A2 @ ( minus_1356011639430497352at_nat @ B2 @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Int_Diff
% 0.29/0.52  thf(fact_2018_Int__Diff,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 0.29/0.52        ( ( minus_minus_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ C2 )
% 0.29/0.52        = ( inf_inf_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Int_Diff
% 0.29/0.52  thf(fact_2019_Diff__Int2,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ C2 ) @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) )
% 0.29/0.52        = ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ C2 ) @ B2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_Int2
% 0.29/0.52  thf(fact_2020_Diff__Int2,axiom,
% 0.29/0.52      ! [A2: set_nat,C2: set_nat,B2: set_nat] :
% 0.29/0.52        ( ( minus_minus_set_nat @ ( inf_inf_set_nat @ A2 @ C2 ) @ ( inf_inf_set_nat @ B2 @ C2 ) )
% 0.29/0.52        = ( minus_minus_set_nat @ ( inf_inf_set_nat @ A2 @ C2 ) @ B2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_Int2
% 0.29/0.52  thf(fact_2021_Diff__Diff__Int,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( minus_1356011639430497352at_nat @ A2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 0.29/0.52        = ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_Diff_Int
% 0.29/0.52  thf(fact_2022_Diff__Diff__Int,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.52        ( ( minus_minus_set_nat @ A2 @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.29/0.52        = ( inf_inf_set_nat @ A2 @ B2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_Diff_Int
% 0.29/0.52  thf(fact_2023_Diff__Int__distrib,axiom,
% 0.29/0.52      ! [C2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( inf_in2572325071724192079at_nat @ C2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 0.29/0.52        = ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ C2 @ A2 ) @ ( inf_in2572325071724192079at_nat @ C2 @ B2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_Int_distrib
% 0.29/0.52  thf(fact_2024_Diff__Int__distrib,axiom,
% 0.29/0.52      ! [C2: set_nat,A2: set_nat,B2: set_nat] :
% 0.29/0.52        ( ( inf_inf_set_nat @ C2 @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.29/0.52        = ( minus_minus_set_nat @ ( inf_inf_set_nat @ C2 @ A2 ) @ ( inf_inf_set_nat @ C2 @ B2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_Int_distrib
% 0.29/0.52  thf(fact_2025_Diff__Int__distrib2,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( inf_in2572325071724192079at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) @ C2 )
% 0.29/0.52        = ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ C2 ) @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_Int_distrib2
% 0.29/0.52  thf(fact_2026_Diff__Int__distrib2,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 0.29/0.52        ( ( inf_inf_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ C2 )
% 0.29/0.52        = ( minus_minus_set_nat @ ( inf_inf_set_nat @ A2 @ C2 ) @ ( inf_inf_set_nat @ B2 @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_Int_distrib2
% 0.29/0.52  thf(fact_2027_Un__Diff,axiom,
% 0.29/0.52      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 0.29/0.52        ( ( minus_5060654252129873198at_nat @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) @ C2 )
% 0.29/0.52        = ( sup_su3035147773818789531at_nat @ ( minus_5060654252129873198at_nat @ A2 @ C2 ) @ ( minus_5060654252129873198at_nat @ B2 @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Un_Diff
% 0.29/0.52  thf(fact_2028_Un__Diff,axiom,
% 0.29/0.52      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 0.29/0.52        ( ( minus_3314409938677909166at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) @ C2 )
% 0.29/0.52        = ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ A2 @ C2 ) @ ( minus_3314409938677909166at_nat @ B2 @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Un_Diff
% 0.29/0.52  thf(fact_2029_Un__Diff,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 0.29/0.52        ( ( minus_minus_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ C2 )
% 0.29/0.52        = ( sup_sup_set_nat @ ( minus_minus_set_nat @ A2 @ C2 ) @ ( minus_minus_set_nat @ B2 @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Un_Diff
% 0.29/0.52  thf(fact_2030_set__diff__diff__left,axiom,
% 0.29/0.52      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 0.29/0.52        ( ( minus_5060654252129873198at_nat @ ( minus_5060654252129873198at_nat @ A2 @ B2 ) @ C2 )
% 0.29/0.52        = ( minus_5060654252129873198at_nat @ A2 @ ( sup_su3035147773818789531at_nat @ B2 @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % set_diff_diff_left
% 0.29/0.52  thf(fact_2031_set__diff__diff__left,axiom,
% 0.29/0.52      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 0.29/0.52        ( ( minus_3314409938677909166at_nat @ ( minus_3314409938677909166at_nat @ A2 @ B2 ) @ C2 )
% 0.29/0.52        = ( minus_3314409938677909166at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % set_diff_diff_left
% 0.29/0.52  thf(fact_2032_set__diff__diff__left,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 0.29/0.52        ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ C2 )
% 0.29/0.52        = ( minus_minus_set_nat @ A2 @ ( sup_sup_set_nat @ B2 @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % set_diff_diff_left
% 0.29/0.52  thf(fact_2033_Diff__triv,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 0.29/0.52          = bot_bo2099793752762293965at_nat )
% 0.29/0.52       => ( ( minus_1356011639430497352at_nat @ A2 @ B2 )
% 0.29/0.52          = A2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_triv
% 0.29/0.52  thf(fact_2034_Diff__triv,axiom,
% 0.29/0.52      ! [A2: set_o,B2: set_o] :
% 0.29/0.52        ( ( ( inf_inf_set_o @ A2 @ B2 )
% 0.29/0.52          = bot_bot_set_o )
% 0.29/0.52       => ( ( minus_minus_set_o @ A2 @ B2 )
% 0.29/0.52          = A2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_triv
% 0.29/0.52  thf(fact_2035_Diff__triv,axiom,
% 0.29/0.52      ! [A2: set_int,B2: set_int] :
% 0.29/0.52        ( ( ( inf_inf_set_int @ A2 @ B2 )
% 0.29/0.52          = bot_bot_set_int )
% 0.29/0.52       => ( ( minus_minus_set_int @ A2 @ B2 )
% 0.29/0.52          = A2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_triv
% 0.29/0.52  thf(fact_2036_Diff__triv,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.52        ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 0.29/0.52          = bot_bot_set_nat )
% 0.29/0.52       => ( ( minus_minus_set_nat @ A2 @ B2 )
% 0.29/0.52          = A2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_triv
% 0.29/0.52  thf(fact_2037_Int__Diff__disjoint,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 0.29/0.52        = bot_bo2099793752762293965at_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % Int_Diff_disjoint
% 0.29/0.52  thf(fact_2038_Int__Diff__disjoint,axiom,
% 0.29/0.52      ! [A2: set_o,B2: set_o] :
% 0.29/0.52        ( ( inf_inf_set_o @ ( inf_inf_set_o @ A2 @ B2 ) @ ( minus_minus_set_o @ A2 @ B2 ) )
% 0.29/0.52        = bot_bot_set_o ) ).
% 0.29/0.52  
% 0.29/0.52  % Int_Diff_disjoint
% 0.29/0.52  thf(fact_2039_Int__Diff__disjoint,axiom,
% 0.29/0.52      ! [A2: set_int,B2: set_int] :
% 0.29/0.52        ( ( inf_inf_set_int @ ( inf_inf_set_int @ A2 @ B2 ) @ ( minus_minus_set_int @ A2 @ B2 ) )
% 0.29/0.52        = bot_bot_set_int ) ).
% 0.29/0.52  
% 0.29/0.52  % Int_Diff_disjoint
% 0.29/0.52  thf(fact_2040_Int__Diff__disjoint,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.52        ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.29/0.52        = bot_bot_set_nat ) ).
% 0.29/0.52  
% 0.29/0.52  % Int_Diff_disjoint
% 0.29/0.52  thf(fact_2041_disjoint__alt__simp1,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( ( minus_1356011639430497352at_nat @ A2 @ B2 )
% 0.29/0.52          = A2 )
% 0.29/0.52        = ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 0.29/0.52          = bot_bo2099793752762293965at_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % disjoint_alt_simp1
% 0.29/0.52  thf(fact_2042_disjoint__alt__simp1,axiom,
% 0.29/0.52      ! [A2: set_o,B2: set_o] :
% 0.29/0.52        ( ( ( minus_minus_set_o @ A2 @ B2 )
% 0.29/0.52          = A2 )
% 0.29/0.52        = ( ( inf_inf_set_o @ A2 @ B2 )
% 0.29/0.52          = bot_bot_set_o ) ) ).
% 0.29/0.52  
% 0.29/0.52  % disjoint_alt_simp1
% 0.29/0.52  thf(fact_2043_disjoint__alt__simp1,axiom,
% 0.29/0.52      ! [A2: set_int,B2: set_int] :
% 0.29/0.52        ( ( ( minus_minus_set_int @ A2 @ B2 )
% 0.29/0.52          = A2 )
% 0.29/0.52        = ( ( inf_inf_set_int @ A2 @ B2 )
% 0.29/0.52          = bot_bot_set_int ) ) ).
% 0.29/0.52  
% 0.29/0.52  % disjoint_alt_simp1
% 0.29/0.52  thf(fact_2044_disjoint__alt__simp1,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.52        ( ( ( minus_minus_set_nat @ A2 @ B2 )
% 0.29/0.52          = A2 )
% 0.29/0.52        = ( ( inf_inf_set_nat @ A2 @ B2 )
% 0.29/0.52          = bot_bot_set_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % disjoint_alt_simp1
% 0.29/0.52  thf(fact_2045_disjoint__alt__simp2,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( ( minus_1356011639430497352at_nat @ A2 @ B2 )
% 0.29/0.52         != A2 )
% 0.29/0.52        = ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 0.29/0.52         != bot_bo2099793752762293965at_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % disjoint_alt_simp2
% 0.29/0.52  thf(fact_2046_disjoint__alt__simp2,axiom,
% 0.29/0.52      ! [A2: set_o,B2: set_o] :
% 0.29/0.52        ( ( ( minus_minus_set_o @ A2 @ B2 )
% 0.29/0.52         != A2 )
% 0.29/0.52        = ( ( inf_inf_set_o @ A2 @ B2 )
% 0.29/0.52         != bot_bot_set_o ) ) ).
% 0.29/0.52  
% 0.29/0.52  % disjoint_alt_simp2
% 0.29/0.52  thf(fact_2047_disjoint__alt__simp2,axiom,
% 0.29/0.52      ! [A2: set_int,B2: set_int] :
% 0.29/0.52        ( ( ( minus_minus_set_int @ A2 @ B2 )
% 0.29/0.52         != A2 )
% 0.29/0.52        = ( ( inf_inf_set_int @ A2 @ B2 )
% 0.29/0.52         != bot_bot_set_int ) ) ).
% 0.29/0.52  
% 0.29/0.52  % disjoint_alt_simp2
% 0.29/0.52  thf(fact_2048_disjoint__alt__simp2,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.52        ( ( ( minus_minus_set_nat @ A2 @ B2 )
% 0.29/0.52         != A2 )
% 0.29/0.52        = ( ( inf_inf_set_nat @ A2 @ B2 )
% 0.29/0.52         != bot_bot_set_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % disjoint_alt_simp2
% 0.29/0.52  thf(fact_2049_Diff__Un,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( minus_1356011639430497352at_nat @ A2 @ ( sup_su6327502436637775413at_nat @ B2 @ C2 ) )
% 0.29/0.52        = ( inf_in2572325071724192079at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) @ ( minus_1356011639430497352at_nat @ A2 @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_Un
% 0.29/0.52  thf(fact_2050_Diff__Un,axiom,
% 0.29/0.52      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 0.29/0.52        ( ( minus_5060654252129873198at_nat @ A2 @ ( sup_su3035147773818789531at_nat @ B2 @ C2 ) )
% 0.29/0.52        = ( inf_in1697001100524423349at_nat @ ( minus_5060654252129873198at_nat @ A2 @ B2 ) @ ( minus_5060654252129873198at_nat @ A2 @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_Un
% 0.29/0.52  thf(fact_2051_Diff__Un,axiom,
% 0.29/0.52      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 0.29/0.52        ( ( minus_3314409938677909166at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) )
% 0.29/0.52        = ( inf_in7913087082777306421at_nat @ ( minus_3314409938677909166at_nat @ A2 @ B2 ) @ ( minus_3314409938677909166at_nat @ A2 @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_Un
% 0.29/0.52  thf(fact_2052_Diff__Un,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 0.29/0.52        ( ( minus_minus_set_nat @ A2 @ ( sup_sup_set_nat @ B2 @ C2 ) )
% 0.29/0.52        = ( inf_inf_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ ( minus_minus_set_nat @ A2 @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_Un
% 0.29/0.52  thf(fact_2053_Diff__Int,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( minus_1356011639430497352at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) )
% 0.29/0.52        = ( sup_su6327502436637775413at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) @ ( minus_1356011639430497352at_nat @ A2 @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_Int
% 0.29/0.52  thf(fact_2054_Diff__Int,axiom,
% 0.29/0.52      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 0.29/0.52        ( ( minus_5060654252129873198at_nat @ A2 @ ( inf_in1697001100524423349at_nat @ B2 @ C2 ) )
% 0.29/0.52        = ( sup_su3035147773818789531at_nat @ ( minus_5060654252129873198at_nat @ A2 @ B2 ) @ ( minus_5060654252129873198at_nat @ A2 @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_Int
% 0.29/0.52  thf(fact_2055_Diff__Int,axiom,
% 0.29/0.52      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 0.29/0.52        ( ( minus_3314409938677909166at_nat @ A2 @ ( inf_in7913087082777306421at_nat @ B2 @ C2 ) )
% 0.29/0.52        = ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ A2 @ B2 ) @ ( minus_3314409938677909166at_nat @ A2 @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_Int
% 0.29/0.52  thf(fact_2056_Diff__Int,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 0.29/0.52        ( ( minus_minus_set_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C2 ) )
% 0.29/0.52        = ( sup_sup_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ ( minus_minus_set_nat @ A2 @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_Int
% 0.29/0.52  thf(fact_2057_Int__Diff__Un,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 0.29/0.52        = A2 ) ).
% 0.29/0.52  
% 0.29/0.52  % Int_Diff_Un
% 0.29/0.52  thf(fact_2058_Int__Diff__Un,axiom,
% 0.29/0.52      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 0.29/0.52        ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) @ ( minus_5060654252129873198at_nat @ A2 @ B2 ) )
% 0.29/0.52        = A2 ) ).
% 0.29/0.52  
% 0.29/0.52  % Int_Diff_Un
% 0.29/0.52  thf(fact_2059_Int__Diff__Un,axiom,
% 0.29/0.52      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.29/0.52        ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) @ ( minus_3314409938677909166at_nat @ A2 @ B2 ) )
% 0.29/0.52        = A2 ) ).
% 0.29/0.52  
% 0.29/0.52  % Int_Diff_Un
% 0.29/0.52  thf(fact_2060_Int__Diff__Un,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.52        ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 0.29/0.52        = A2 ) ).
% 0.29/0.52  
% 0.29/0.52  % Int_Diff_Un
% 0.29/0.52  thf(fact_2061_Un__Diff__Int,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( sup_su6327502436637775413at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 0.29/0.52        = A2 ) ).
% 0.29/0.52  
% 0.29/0.52  % Un_Diff_Int
% 0.29/0.52  thf(fact_2062_Un__Diff__Int,axiom,
% 0.29/0.52      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 0.29/0.52        ( ( sup_su3035147773818789531at_nat @ ( minus_5060654252129873198at_nat @ A2 @ B2 ) @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) )
% 0.29/0.52        = A2 ) ).
% 0.29/0.52  
% 0.29/0.52  % Un_Diff_Int
% 0.29/0.52  thf(fact_2063_Un__Diff__Int,axiom,
% 0.29/0.52      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.29/0.52        ( ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ A2 @ B2 ) @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) )
% 0.29/0.52        = A2 ) ).
% 0.29/0.52  
% 0.29/0.52  % Un_Diff_Int
% 0.29/0.52  thf(fact_2064_Un__Diff__Int,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.52        ( ( sup_sup_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.29/0.52        = A2 ) ).
% 0.29/0.52  
% 0.29/0.52  % Un_Diff_Int
% 0.29/0.52  thf(fact_2065_Compl__eq__Diff__UNIV,axiom,
% 0.29/0.52      ( uminus3195874150345416415st_nat
% 0.29/0.52      = ( minus_7954133019191499631st_nat @ top_top_set_list_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Compl_eq_Diff_UNIV
% 0.29/0.52  thf(fact_2066_Compl__eq__Diff__UNIV,axiom,
% 0.29/0.52      ( uminus_uminus_set_o
% 0.29/0.52      = ( minus_minus_set_o @ top_top_set_o ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Compl_eq_Diff_UNIV
% 0.29/0.52  thf(fact_2067_Compl__eq__Diff__UNIV,axiom,
% 0.29/0.52      ( uminus2201863774496077783et_rat
% 0.29/0.52      = ( minus_minus_set_rat @ top_top_set_rat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Compl_eq_Diff_UNIV
% 0.29/0.52  thf(fact_2068_Compl__eq__Diff__UNIV,axiom,
% 0.29/0.52      ( uminus1532241313380277803et_int
% 0.29/0.52      = ( minus_minus_set_int @ top_top_set_int ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Compl_eq_Diff_UNIV
% 0.29/0.52  thf(fact_2069_Compl__eq__Diff__UNIV,axiom,
% 0.29/0.52      ( uminus5710092332889474511et_nat
% 0.29/0.52      = ( minus_minus_set_nat @ top_top_set_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Compl_eq_Diff_UNIV
% 0.29/0.52  thf(fact_2070_divide__divide__eq__left_H,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 0.29/0.52        = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_divide_eq_left'
% 0.29/0.52  thf(fact_2071_divide__divide__times__eq,axiom,
% 0.29/0.52      ! [X: rat,Y: rat,Z: rat,W: rat] :
% 0.29/0.52        ( ( divide_divide_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 0.29/0.52        = ( divide_divide_rat @ ( times_times_rat @ X @ W ) @ ( times_times_rat @ Y @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_divide_times_eq
% 0.29/0.52  thf(fact_2072_times__divide__times__eq,axiom,
% 0.29/0.52      ! [X: rat,Y: rat,Z: rat,W: rat] :
% 0.29/0.52        ( ( times_times_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 0.29/0.52        = ( divide_divide_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ W ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % times_divide_times_eq
% 0.29/0.52  thf(fact_2073_div__minus__right,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.29/0.52        = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_minus_right
% 0.29/0.52  thf(fact_2074_div__minus__right,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.52        = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % div_minus_right
% 0.29/0.52  thf(fact_2075_minus__divide__left,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.29/0.52        = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % minus_divide_left
% 0.29/0.52  thf(fact_2076_minus__divide__divide,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.29/0.52        = ( divide_divide_rat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % minus_divide_divide
% 0.29/0.52  thf(fact_2077_minus__divide__right,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.29/0.52        = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % minus_divide_right
% 0.29/0.52  thf(fact_2078_nonzero__eq__divide__eq,axiom,
% 0.29/0.52      ! [C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( C != zero_zero_rat )
% 0.29/0.52       => ( ( A
% 0.29/0.52            = ( divide_divide_rat @ B @ C ) )
% 0.29/0.52          = ( ( times_times_rat @ A @ C )
% 0.29/0.52            = B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_eq_divide_eq
% 0.29/0.52  thf(fact_2079_nonzero__divide__eq__eq,axiom,
% 0.29/0.52      ! [C: rat,B: rat,A: rat] :
% 0.29/0.52        ( ( C != zero_zero_rat )
% 0.29/0.52       => ( ( ( divide_divide_rat @ B @ C )
% 0.29/0.52            = A )
% 0.29/0.52          = ( B
% 0.29/0.52            = ( times_times_rat @ A @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_divide_eq_eq
% 0.29/0.52  thf(fact_2080_eq__divide__imp,axiom,
% 0.29/0.52      ! [C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( C != zero_zero_rat )
% 0.29/0.52       => ( ( ( times_times_rat @ A @ C )
% 0.29/0.52            = B )
% 0.29/0.52         => ( A
% 0.29/0.52            = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % eq_divide_imp
% 0.29/0.52  thf(fact_2081_divide__eq__imp,axiom,
% 0.29/0.52      ! [C: rat,B: rat,A: rat] :
% 0.29/0.52        ( ( C != zero_zero_rat )
% 0.29/0.52       => ( ( B
% 0.29/0.52            = ( times_times_rat @ A @ C ) )
% 0.29/0.52         => ( ( divide_divide_rat @ B @ C )
% 0.29/0.52            = A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_eq_imp
% 0.29/0.52  thf(fact_2082_eq__divide__eq,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( A
% 0.29/0.52          = ( divide_divide_rat @ B @ C ) )
% 0.29/0.52        = ( ( ( C != zero_zero_rat )
% 0.29/0.52           => ( ( times_times_rat @ A @ C )
% 0.29/0.52              = B ) )
% 0.29/0.52          & ( ( C = zero_zero_rat )
% 0.29/0.52           => ( A = zero_zero_rat ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % eq_divide_eq
% 0.29/0.52  thf(fact_2083_divide__eq__eq,axiom,
% 0.29/0.52      ! [B: rat,C: rat,A: rat] :
% 0.29/0.52        ( ( ( divide_divide_rat @ B @ C )
% 0.29/0.52          = A )
% 0.29/0.52        = ( ( ( C != zero_zero_rat )
% 0.29/0.52           => ( B
% 0.29/0.52              = ( times_times_rat @ A @ C ) ) )
% 0.29/0.52          & ( ( C = zero_zero_rat )
% 0.29/0.52           => ( A = zero_zero_rat ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_eq_eq
% 0.29/0.52  thf(fact_2084_frac__eq__eq,axiom,
% 0.29/0.52      ! [Y: rat,Z: rat,X: rat,W: rat] :
% 0.29/0.52        ( ( Y != zero_zero_rat )
% 0.29/0.52       => ( ( Z != zero_zero_rat )
% 0.29/0.52         => ( ( ( divide_divide_rat @ X @ Y )
% 0.29/0.52              = ( divide_divide_rat @ W @ Z ) )
% 0.29/0.52            = ( ( times_times_rat @ X @ Z )
% 0.29/0.52              = ( times_times_rat @ W @ Y ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % frac_eq_eq
% 0.29/0.52  thf(fact_2085_right__inverse__eq,axiom,
% 0.29/0.52      ! [B: rat,A: rat] :
% 0.29/0.52        ( ( B != zero_zero_rat )
% 0.29/0.52       => ( ( ( divide_divide_rat @ A @ B )
% 0.29/0.52            = one_one_rat )
% 0.29/0.52          = ( A = B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % right_inverse_eq
% 0.29/0.52  thf(fact_2086_nonzero__minus__divide__right,axiom,
% 0.29/0.52      ! [B: rat,A: rat] :
% 0.29/0.52        ( ( B != zero_zero_rat )
% 0.29/0.52       => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.29/0.52          = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_minus_divide_right
% 0.29/0.52  thf(fact_2087_nonzero__minus__divide__divide,axiom,
% 0.29/0.52      ! [B: rat,A: rat] :
% 0.29/0.52        ( ( B != zero_zero_rat )
% 0.29/0.52       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.29/0.52          = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_minus_divide_divide
% 0.29/0.52  thf(fact_2088_divide__diff__eq__iff,axiom,
% 0.29/0.52      ! [Z: rat,X: rat,Y: rat] :
% 0.29/0.52        ( ( Z != zero_zero_rat )
% 0.29/0.52       => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 0.29/0.52          = ( divide_divide_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_diff_eq_iff
% 0.29/0.52  thf(fact_2089_diff__divide__eq__iff,axiom,
% 0.29/0.52      ! [Z: rat,X: rat,Y: rat] :
% 0.29/0.52        ( ( Z != zero_zero_rat )
% 0.29/0.52       => ( ( minus_minus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 0.29/0.52          = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_divide_eq_iff
% 0.29/0.52  thf(fact_2090_diff__frac__eq,axiom,
% 0.29/0.52      ! [Y: rat,Z: rat,X: rat,W: rat] :
% 0.29/0.52        ( ( Y != zero_zero_rat )
% 0.29/0.52       => ( ( Z != zero_zero_rat )
% 0.29/0.52         => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 0.29/0.52            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_frac_eq
% 0.29/0.52  thf(fact_2091_add__divide__eq__if__simps_I4_J,axiom,
% 0.29/0.52      ! [Z: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( ( Z = zero_zero_rat )
% 0.29/0.52         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.29/0.52            = A ) )
% 0.29/0.52        & ( ( Z != zero_zero_rat )
% 0.29/0.52         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.29/0.52            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_divide_eq_if_simps(4)
% 0.29/0.52  thf(fact_2092_nonzero__neg__divide__eq__eq2,axiom,
% 0.29/0.52      ! [B: rat,C: rat,A: rat] :
% 0.29/0.52        ( ( B != zero_zero_rat )
% 0.29/0.52       => ( ( C
% 0.29/0.52            = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 0.29/0.52          = ( ( times_times_rat @ C @ B )
% 0.29/0.52            = ( uminus_uminus_rat @ A ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_neg_divide_eq_eq2
% 0.29/0.52  thf(fact_2093_nonzero__neg__divide__eq__eq,axiom,
% 0.29/0.52      ! [B: rat,A: rat,C: rat] :
% 0.29/0.52        ( ( B != zero_zero_rat )
% 0.29/0.52       => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.29/0.52            = C )
% 0.29/0.52          = ( ( uminus_uminus_rat @ A )
% 0.29/0.52            = ( times_times_rat @ C @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % nonzero_neg_divide_eq_eq
% 0.29/0.52  thf(fact_2094_minus__divide__eq__eq,axiom,
% 0.29/0.52      ! [B: rat,C: rat,A: rat] :
% 0.29/0.52        ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.52          = A )
% 0.29/0.52        = ( ( ( C != zero_zero_rat )
% 0.29/0.52           => ( ( uminus_uminus_rat @ B )
% 0.29/0.52              = ( times_times_rat @ A @ C ) ) )
% 0.29/0.52          & ( ( C = zero_zero_rat )
% 0.29/0.52           => ( A = zero_zero_rat ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % minus_divide_eq_eq
% 0.29/0.52  thf(fact_2095_eq__minus__divide__eq,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( A
% 0.29/0.52          = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.29/0.52        = ( ( ( C != zero_zero_rat )
% 0.29/0.52           => ( ( times_times_rat @ A @ C )
% 0.29/0.52              = ( uminus_uminus_rat @ B ) ) )
% 0.29/0.52          & ( ( C = zero_zero_rat )
% 0.29/0.52           => ( A = zero_zero_rat ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % eq_minus_divide_eq
% 0.29/0.52  thf(fact_2096_divide__eq__minus__1__iff,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( ( divide_divide_rat @ A @ B )
% 0.29/0.52          = ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.52        = ( ( B != zero_zero_rat )
% 0.29/0.52          & ( A
% 0.29/0.52            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_eq_minus_1_iff
% 0.29/0.52  thf(fact_2097_minus__divide__diff__eq__iff,axiom,
% 0.29/0.52      ! [Z: rat,X: rat,Y: rat] :
% 0.29/0.52        ( ( Z != zero_zero_rat )
% 0.29/0.52       => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 0.29/0.52          = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % minus_divide_diff_eq_iff
% 0.29/0.52  thf(fact_2098_add__divide__eq__if__simps_I5_J,axiom,
% 0.29/0.52      ! [Z: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( ( Z = zero_zero_rat )
% 0.29/0.52         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.29/0.52            = ( uminus_uminus_rat @ B ) ) )
% 0.29/0.52        & ( ( Z != zero_zero_rat )
% 0.29/0.52         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.29/0.52            = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_divide_eq_if_simps(5)
% 0.29/0.52  thf(fact_2099_add__divide__eq__if__simps_I6_J,axiom,
% 0.29/0.52      ! [Z: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( ( Z = zero_zero_rat )
% 0.29/0.52         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.29/0.52            = ( uminus_uminus_rat @ B ) ) )
% 0.29/0.52        & ( ( Z != zero_zero_rat )
% 0.29/0.52         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.29/0.52            = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % add_divide_eq_if_simps(6)
% 0.29/0.52  thf(fact_2100_bits__div__by__1,axiom,
% 0.29/0.52      ! [A: nat] :
% 0.29/0.52        ( ( divide_divide_nat @ A @ one_one_nat )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % bits_div_by_1
% 0.29/0.52  thf(fact_2101_bits__div__by__1,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( divide_divide_int @ A @ one_one_int )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % bits_div_by_1
% 0.29/0.52  thf(fact_2102_bits__div__by__1,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % bits_div_by_1
% 0.29/0.52  thf(fact_2103_bits__div__by__1,axiom,
% 0.29/0.52      ! [A: code_natural] :
% 0.29/0.52        ( ( divide5121882707175180666atural @ A @ one_one_Code_natural )
% 0.29/0.52        = A ) ).
% 0.29/0.52  
% 0.29/0.52  % bits_div_by_1
% 0.29/0.52  thf(fact_2104_inf__period_I1_J,axiom,
% 0.29/0.52      ! [P: code_integer > $o,D3: code_integer,Q2: code_integer > $o] :
% 0.29/0.52        ( ! [X2: code_integer,K2: code_integer] :
% 0.29/0.52            ( ( P @ X2 )
% 0.29/0.52            = ( P @ ( minus_8373710615458151222nteger @ X2 @ ( times_3573771949741848930nteger @ K2 @ D3 ) ) ) )
% 0.29/0.52       => ( ! [X2: code_integer,K2: code_integer] :
% 0.29/0.52              ( ( Q2 @ X2 )
% 0.29/0.52              = ( Q2 @ ( minus_8373710615458151222nteger @ X2 @ ( times_3573771949741848930nteger @ K2 @ D3 ) ) ) )
% 0.29/0.52         => ! [X5: code_integer,K3: code_integer] :
% 0.29/0.52              ( ( ( P @ X5 )
% 0.29/0.52                & ( Q2 @ X5 ) )
% 0.29/0.52              = ( ( P @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K3 @ D3 ) ) )
% 0.29/0.52                & ( Q2 @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K3 @ D3 ) ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % inf_period(1)
% 0.29/0.52  thf(fact_2105_inf__period_I1_J,axiom,
% 0.29/0.52      ! [P: rat > $o,D3: rat,Q2: rat > $o] :
% 0.29/0.52        ( ! [X2: rat,K2: rat] :
% 0.29/0.52            ( ( P @ X2 )
% 0.29/0.52            = ( P @ ( minus_minus_rat @ X2 @ ( times_times_rat @ K2 @ D3 ) ) ) )
% 0.29/0.52       => ( ! [X2: rat,K2: rat] :
% 0.29/0.52              ( ( Q2 @ X2 )
% 0.29/0.52              = ( Q2 @ ( minus_minus_rat @ X2 @ ( times_times_rat @ K2 @ D3 ) ) ) )
% 0.29/0.52         => ! [X5: rat,K3: rat] :
% 0.29/0.52              ( ( ( P @ X5 )
% 0.29/0.52                & ( Q2 @ X5 ) )
% 0.29/0.52              = ( ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K3 @ D3 ) ) )
% 0.29/0.52                & ( Q2 @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K3 @ D3 ) ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % inf_period(1)
% 0.29/0.52  thf(fact_2106_inf__period_I1_J,axiom,
% 0.29/0.52      ! [P: int > $o,D3: int,Q2: int > $o] :
% 0.29/0.52        ( ! [X2: int,K2: int] :
% 0.29/0.52            ( ( P @ X2 )
% 0.29/0.52            = ( P @ ( minus_minus_int @ X2 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 0.29/0.52       => ( ! [X2: int,K2: int] :
% 0.29/0.52              ( ( Q2 @ X2 )
% 0.29/0.52              = ( Q2 @ ( minus_minus_int @ X2 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 0.29/0.52         => ! [X5: int,K3: int] :
% 0.29/0.52              ( ( ( P @ X5 )
% 0.29/0.52                & ( Q2 @ X5 ) )
% 0.29/0.52              = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K3 @ D3 ) ) )
% 0.29/0.52                & ( Q2 @ ( minus_minus_int @ X5 @ ( times_times_int @ K3 @ D3 ) ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % inf_period(1)
% 0.29/0.52  thf(fact_2107_inf__period_I2_J,axiom,
% 0.29/0.52      ! [P: code_integer > $o,D3: code_integer,Q2: code_integer > $o] :
% 0.29/0.52        ( ! [X2: code_integer,K2: code_integer] :
% 0.29/0.52            ( ( P @ X2 )
% 0.29/0.52            = ( P @ ( minus_8373710615458151222nteger @ X2 @ ( times_3573771949741848930nteger @ K2 @ D3 ) ) ) )
% 0.29/0.52       => ( ! [X2: code_integer,K2: code_integer] :
% 0.29/0.52              ( ( Q2 @ X2 )
% 0.29/0.52              = ( Q2 @ ( minus_8373710615458151222nteger @ X2 @ ( times_3573771949741848930nteger @ K2 @ D3 ) ) ) )
% 0.29/0.52         => ! [X5: code_integer,K3: code_integer] :
% 0.29/0.52              ( ( ( P @ X5 )
% 0.29/0.52                | ( Q2 @ X5 ) )
% 0.29/0.52              = ( ( P @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K3 @ D3 ) ) )
% 0.29/0.52                | ( Q2 @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K3 @ D3 ) ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % inf_period(2)
% 0.29/0.52  thf(fact_2108_inf__period_I2_J,axiom,
% 0.29/0.52      ! [P: rat > $o,D3: rat,Q2: rat > $o] :
% 0.29/0.52        ( ! [X2: rat,K2: rat] :
% 0.29/0.52            ( ( P @ X2 )
% 0.29/0.52            = ( P @ ( minus_minus_rat @ X2 @ ( times_times_rat @ K2 @ D3 ) ) ) )
% 0.29/0.52       => ( ! [X2: rat,K2: rat] :
% 0.29/0.52              ( ( Q2 @ X2 )
% 0.29/0.52              = ( Q2 @ ( minus_minus_rat @ X2 @ ( times_times_rat @ K2 @ D3 ) ) ) )
% 0.29/0.52         => ! [X5: rat,K3: rat] :
% 0.29/0.52              ( ( ( P @ X5 )
% 0.29/0.52                | ( Q2 @ X5 ) )
% 0.29/0.52              = ( ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K3 @ D3 ) ) )
% 0.29/0.52                | ( Q2 @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K3 @ D3 ) ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % inf_period(2)
% 0.29/0.52  thf(fact_2109_inf__period_I2_J,axiom,
% 0.29/0.52      ! [P: int > $o,D3: int,Q2: int > $o] :
% 0.29/0.52        ( ! [X2: int,K2: int] :
% 0.29/0.52            ( ( P @ X2 )
% 0.29/0.52            = ( P @ ( minus_minus_int @ X2 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 0.29/0.52       => ( ! [X2: int,K2: int] :
% 0.29/0.52              ( ( Q2 @ X2 )
% 0.29/0.52              = ( Q2 @ ( minus_minus_int @ X2 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 0.29/0.52         => ! [X5: int,K3: int] :
% 0.29/0.52              ( ( ( P @ X5 )
% 0.29/0.52                | ( Q2 @ X5 ) )
% 0.29/0.52              = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K3 @ D3 ) ) )
% 0.29/0.52                | ( Q2 @ ( minus_minus_int @ X5 @ ( times_times_int @ K3 @ D3 ) ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % inf_period(2)
% 0.29/0.52  thf(fact_2110_diff__numeral__special_I5_J,axiom,
% 0.29/0.52      ! [N: num] :
% 0.29/0.52        ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 0.29/0.52        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_numeral_special(5)
% 0.29/0.52  thf(fact_2111_diff__numeral__special_I5_J,axiom,
% 0.29/0.52      ! [N: num] :
% 0.29/0.52        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 0.29/0.52        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_numeral_special(5)
% 0.29/0.52  thf(fact_2112_diff__numeral__special_I5_J,axiom,
% 0.29/0.52      ! [N: num] :
% 0.29/0.52        ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 0.29/0.52        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_numeral_special(5)
% 0.29/0.52  thf(fact_2113_diff__numeral__special_I6_J,axiom,
% 0.29/0.52      ! [M: num] :
% 0.29/0.52        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.29/0.52        = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_numeral_special(6)
% 0.29/0.52  thf(fact_2114_diff__numeral__special_I6_J,axiom,
% 0.29/0.52      ! [M: num] :
% 0.29/0.52        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.29/0.52        = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_numeral_special(6)
% 0.29/0.52  thf(fact_2115_diff__numeral__special_I6_J,axiom,
% 0.29/0.52      ! [M: num] :
% 0.29/0.52        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.29/0.52        = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_numeral_special(6)
% 0.29/0.52  thf(fact_2116_left__diff__distrib__NO__MATCH,axiom,
% 0.29/0.52      ! [X: nat,Y: nat,C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( nO_MAT8694959213317031834nteger @ ( divide_divide_nat @ X @ Y ) @ C )
% 0.29/0.52       => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 0.29/0.52          = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % left_diff_distrib_NO_MATCH
% 0.29/0.52  thf(fact_2117_left__diff__distrib__NO__MATCH,axiom,
% 0.29/0.52      ! [X: nat,Y: nat,C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X @ Y ) @ C )
% 0.29/0.52       => ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.29/0.52          = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % left_diff_distrib_NO_MATCH
% 0.29/0.52  thf(fact_2118_left__diff__distrib__NO__MATCH,axiom,
% 0.29/0.52      ! [X: nat,Y: nat,C: int,A: int,B: int] :
% 0.29/0.52        ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ C )
% 0.29/0.52       => ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.29/0.52          = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % left_diff_distrib_NO_MATCH
% 0.29/0.52  thf(fact_2119_left__diff__distrib__NO__MATCH,axiom,
% 0.29/0.52      ! [X: int,Y: int,C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( nO_MAT9066612773553876470nteger @ ( divide_divide_int @ X @ Y ) @ C )
% 0.29/0.52       => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 0.29/0.52          = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % left_diff_distrib_NO_MATCH
% 0.29/0.52  thf(fact_2120_left__diff__distrib__NO__MATCH,axiom,
% 0.29/0.52      ! [X: int,Y: int,C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X @ Y ) @ C )
% 0.29/0.52       => ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.29/0.52          = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % left_diff_distrib_NO_MATCH
% 0.29/0.52  thf(fact_2121_left__diff__distrib__NO__MATCH,axiom,
% 0.29/0.52      ! [X: int,Y: int,C: int,A: int,B: int] :
% 0.29/0.52        ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ C )
% 0.29/0.52       => ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.29/0.52          = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % left_diff_distrib_NO_MATCH
% 0.29/0.52  thf(fact_2122_left__diff__distrib__NO__MATCH,axiom,
% 0.29/0.52      ! [X: code_integer,Y: code_integer,C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( nO_MAT8252062027627875367nteger @ ( divide6298287555418463151nteger @ X @ Y ) @ C )
% 0.29/0.52       => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 0.29/0.52          = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % left_diff_distrib_NO_MATCH
% 0.29/0.52  thf(fact_2123_left__diff__distrib__NO__MATCH,axiom,
% 0.29/0.52      ! [X: code_integer,Y: code_integer,C: rat,A: rat,B: rat] :
% 0.29/0.52        ( ( nO_MAT7795273704451493282er_rat @ ( divide6298287555418463151nteger @ X @ Y ) @ C )
% 0.29/0.52       => ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.29/0.52          = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % left_diff_distrib_NO_MATCH
% 0.29/0.52  thf(fact_2124_left__diff__distrib__NO__MATCH,axiom,
% 0.29/0.52      ! [X: code_integer,Y: code_integer,C: int,A: int,B: int] :
% 0.29/0.52        ( ( nO_MAT8427913294028938742er_int @ ( divide6298287555418463151nteger @ X @ Y ) @ C )
% 0.29/0.52       => ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.29/0.52          = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % left_diff_distrib_NO_MATCH
% 0.29/0.52  thf(fact_2125_left__diff__distrib__NO__MATCH,axiom,
% 0.29/0.52      ! [X: rat,Y: rat,C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( nO_MAT243659986023775650nteger @ ( divide_divide_rat @ X @ Y ) @ C )
% 0.29/0.52       => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 0.29/0.52          = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % left_diff_distrib_NO_MATCH
% 0.29/0.52  thf(fact_2126_right__diff__distrib__NO__MATCH,axiom,
% 0.29/0.52      ! [X: nat,Y: nat,A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.52        ( ( nO_MAT8694959213317031834nteger @ ( divide_divide_nat @ X @ Y ) @ A )
% 0.29/0.52       => ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 0.29/0.52          = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % right_diff_distrib_NO_MATCH
% 0.29/0.52  thf(fact_2127_right__diff__distrib__NO__MATCH,axiom,
% 0.29/0.52      ! [X: nat,Y: nat,A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X @ Y ) @ A )
% 0.29/0.52       => ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.29/0.52          = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % right_diff_distrib_NO_MATCH
% 0.29/0.52  thf(fact_2128_right__diff__distrib__NO__MATCH,axiom,
% 0.29/0.52      ! [X: nat,Y: nat,A: int,B: int,C: int] :
% 0.29/0.52        ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ A )
% 0.29/0.52       => ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.29/0.52          = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % right_diff_distrib_NO_MATCH
% 0.29/0.52  thf(fact_2129_right__diff__distrib__NO__MATCH,axiom,
% 0.29/0.52      ! [X: int,Y: int,A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.52        ( ( nO_MAT9066612773553876470nteger @ ( divide_divide_int @ X @ Y ) @ A )
% 0.29/0.52       => ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 0.29/0.52          = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % right_diff_distrib_NO_MATCH
% 0.29/0.52  thf(fact_2130_right__diff__distrib__NO__MATCH,axiom,
% 0.29/0.52      ! [X: int,Y: int,A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X @ Y ) @ A )
% 0.29/0.52       => ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.29/0.52          = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % right_diff_distrib_NO_MATCH
% 0.29/0.52  thf(fact_2131_right__diff__distrib__NO__MATCH,axiom,
% 0.29/0.52      ! [X: int,Y: int,A: int,B: int,C: int] :
% 0.29/0.52        ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ A )
% 0.29/0.52       => ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.29/0.52          = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % right_diff_distrib_NO_MATCH
% 0.29/0.52  thf(fact_2132_right__diff__distrib__NO__MATCH,axiom,
% 0.29/0.52      ! [X: code_integer,Y: code_integer,A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.52        ( ( nO_MAT8252062027627875367nteger @ ( divide6298287555418463151nteger @ X @ Y ) @ A )
% 0.29/0.52       => ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 0.29/0.52          = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % right_diff_distrib_NO_MATCH
% 0.29/0.52  thf(fact_2133_right__diff__distrib__NO__MATCH,axiom,
% 0.29/0.52      ! [X: code_integer,Y: code_integer,A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( nO_MAT7795273704451493282er_rat @ ( divide6298287555418463151nteger @ X @ Y ) @ A )
% 0.29/0.52       => ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.29/0.52          = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % right_diff_distrib_NO_MATCH
% 0.29/0.52  thf(fact_2134_right__diff__distrib__NO__MATCH,axiom,
% 0.29/0.52      ! [X: code_integer,Y: code_integer,A: int,B: int,C: int] :
% 0.29/0.52        ( ( nO_MAT8427913294028938742er_int @ ( divide6298287555418463151nteger @ X @ Y ) @ A )
% 0.29/0.52       => ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.29/0.52          = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % right_diff_distrib_NO_MATCH
% 0.29/0.52  thf(fact_2135_right__diff__distrib__NO__MATCH,axiom,
% 0.29/0.52      ! [X: rat,Y: rat,A: code_integer,B: code_integer,C: code_integer] :
% 0.29/0.52        ( ( nO_MAT243659986023775650nteger @ ( divide_divide_rat @ X @ Y ) @ A )
% 0.29/0.52       => ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 0.29/0.52          = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % right_diff_distrib_NO_MATCH
% 0.29/0.52  thf(fact_2136_divide__less__eq__numeral_I2_J,axiom,
% 0.29/0.52      ! [B: rat,C: rat,W: num] :
% 0.29/0.52        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.29/0.52        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.52           => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.29/0.52          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.52           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.52               => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 0.29/0.52              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.52               => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_less_eq_numeral(2)
% 0.29/0.52  thf(fact_2137_less__divide__eq__numeral_I2_J,axiom,
% 0.29/0.52      ! [W: num,B: rat,C: rat] :
% 0.29/0.52        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 0.29/0.52        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.52           => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 0.29/0.52          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.52           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.52               => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.29/0.52              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.52               => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % less_divide_eq_numeral(2)
% 0.29/0.52  thf(fact_2138_le__divide__eq__numeral1_I2_J,axiom,
% 0.29/0.52      ! [A: rat,B: rat,W: num] :
% 0.29/0.52        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 0.29/0.52        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_divide_eq_numeral1(2)
% 0.29/0.52  thf(fact_2139_dual__order_Orefl,axiom,
% 0.29/0.52      ! [A: filter_nat] : ( ord_le2510731241096832064er_nat @ A @ A ) ).
% 0.29/0.52  
% 0.29/0.52  % dual_order.refl
% 0.29/0.52  thf(fact_2140_dual__order_Orefl,axiom,
% 0.29/0.52      ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 0.29/0.52  
% 0.29/0.52  % dual_order.refl
% 0.29/0.52  thf(fact_2141_dual__order_Orefl,axiom,
% 0.29/0.52      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 0.29/0.52  
% 0.29/0.52  % dual_order.refl
% 0.29/0.52  thf(fact_2142_dual__order_Orefl,axiom,
% 0.29/0.52      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.29/0.52  
% 0.29/0.52  % dual_order.refl
% 0.29/0.52  thf(fact_2143_dual__order_Orefl,axiom,
% 0.29/0.52      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 0.29/0.52  
% 0.29/0.52  % dual_order.refl
% 0.29/0.52  thf(fact_2144_order__refl,axiom,
% 0.29/0.52      ! [X: filter_nat] : ( ord_le2510731241096832064er_nat @ X @ X ) ).
% 0.29/0.52  
% 0.29/0.52  % order_refl
% 0.29/0.52  thf(fact_2145_order__refl,axiom,
% 0.29/0.52      ! [X: set_nat] : ( ord_less_eq_set_nat @ X @ X ) ).
% 0.29/0.52  
% 0.29/0.52  % order_refl
% 0.29/0.52  thf(fact_2146_order__refl,axiom,
% 0.29/0.52      ! [X: rat] : ( ord_less_eq_rat @ X @ X ) ).
% 0.29/0.52  
% 0.29/0.52  % order_refl
% 0.29/0.52  thf(fact_2147_order__refl,axiom,
% 0.29/0.52      ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 0.29/0.52  
% 0.29/0.52  % order_refl
% 0.29/0.52  thf(fact_2148_order__refl,axiom,
% 0.29/0.52      ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 0.29/0.52  
% 0.29/0.52  % order_refl
% 0.29/0.52  thf(fact_2149_empty__subsetI,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ bot_bo2099793752762293965at_nat @ A2 ) ).
% 0.29/0.52  
% 0.29/0.52  % empty_subsetI
% 0.29/0.52  thf(fact_2150_empty__subsetI,axiom,
% 0.29/0.52      ! [A2: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A2 ) ).
% 0.29/0.52  
% 0.29/0.52  % empty_subsetI
% 0.29/0.52  thf(fact_2151_empty__subsetI,axiom,
% 0.29/0.52      ! [A2: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A2 ) ).
% 0.29/0.52  
% 0.29/0.52  % empty_subsetI
% 0.29/0.52  thf(fact_2152_empty__subsetI,axiom,
% 0.29/0.52      ! [A2: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A2 ) ).
% 0.29/0.52  
% 0.29/0.52  % empty_subsetI
% 0.29/0.52  thf(fact_2153_subset__empty,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( ord_le3146513528884898305at_nat @ A2 @ bot_bo2099793752762293965at_nat )
% 0.29/0.52        = ( A2 = bot_bo2099793752762293965at_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % subset_empty
% 0.29/0.52  thf(fact_2154_subset__empty,axiom,
% 0.29/0.52      ! [A2: set_o] :
% 0.29/0.52        ( ( ord_less_eq_set_o @ A2 @ bot_bot_set_o )
% 0.29/0.52        = ( A2 = bot_bot_set_o ) ) ).
% 0.29/0.52  
% 0.29/0.52  % subset_empty
% 0.29/0.52  thf(fact_2155_subset__empty,axiom,
% 0.29/0.52      ! [A2: set_int] :
% 0.29/0.52        ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 0.29/0.52        = ( A2 = bot_bot_set_int ) ) ).
% 0.29/0.52  
% 0.29/0.52  % subset_empty
% 0.29/0.52  thf(fact_2156_subset__empty,axiom,
% 0.29/0.52      ! [A2: set_nat] :
% 0.29/0.52        ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 0.29/0.52        = ( A2 = bot_bot_set_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % subset_empty
% 0.29/0.52  thf(fact_2157_Int__subset__iff,axiom,
% 0.29/0.52      ! [C2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( ord_le3146513528884898305at_nat @ C2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 0.29/0.52        = ( ( ord_le3146513528884898305at_nat @ C2 @ A2 )
% 0.29/0.52          & ( ord_le3146513528884898305at_nat @ C2 @ B2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Int_subset_iff
% 0.29/0.52  thf(fact_2158_Int__subset__iff,axiom,
% 0.29/0.52      ! [C2: set_nat,A2: set_nat,B2: set_nat] :
% 0.29/0.52        ( ( ord_less_eq_set_nat @ C2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.29/0.52        = ( ( ord_less_eq_set_nat @ C2 @ A2 )
% 0.29/0.52          & ( ord_less_eq_set_nat @ C2 @ B2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Int_subset_iff
% 0.29/0.52  thf(fact_2159_Un__subset__iff,axiom,
% 0.29/0.52      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 0.29/0.52        ( ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) @ C2 )
% 0.29/0.52        = ( ( ord_le8081472938463900775at_nat @ A2 @ C2 )
% 0.29/0.52          & ( ord_le8081472938463900775at_nat @ B2 @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Un_subset_iff
% 0.29/0.52  thf(fact_2160_Un__subset__iff,axiom,
% 0.29/0.52      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 0.29/0.52        ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) @ C2 )
% 0.29/0.52        = ( ( ord_le1268244103169919719at_nat @ A2 @ C2 )
% 0.29/0.52          & ( ord_le1268244103169919719at_nat @ B2 @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Un_subset_iff
% 0.29/0.52  thf(fact_2161_Un__subset__iff,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 0.29/0.52        ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ C2 )
% 0.29/0.52        = ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 0.29/0.52          & ( ord_less_eq_set_nat @ B2 @ C2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Un_subset_iff
% 0.29/0.52  thf(fact_2162_Compl__subset__Compl__iff,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.52        ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( uminus5710092332889474511et_nat @ B2 ) )
% 0.29/0.52        = ( ord_less_eq_set_nat @ B2 @ A2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Compl_subset_Compl_iff
% 0.29/0.52  thf(fact_2163_Compl__anti__mono,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.52        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.29/0.52       => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ B2 ) @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Compl_anti_mono
% 0.29/0.52  thf(fact_2164_le__zero__eq,axiom,
% 0.29/0.52      ! [N: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.29/0.52        = ( N = zero_zero_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_zero_eq
% 0.29/0.52  thf(fact_2165_not__gr__zero,axiom,
% 0.29/0.52      ! [N: nat] :
% 0.29/0.52        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.29/0.52        = ( N = zero_zero_nat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % not_gr_zero
% 0.29/0.52  thf(fact_2166_neg__le__iff__le,axiom,
% 0.29/0.52      ! [B: code_integer,A: code_integer] :
% 0.29/0.52        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.52        = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_le_iff_le
% 0.29/0.52  thf(fact_2167_neg__le__iff__le,axiom,
% 0.29/0.52      ! [B: rat,A: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 0.29/0.52        = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_le_iff_le
% 0.29/0.52  thf(fact_2168_neg__le__iff__le,axiom,
% 0.29/0.52      ! [B: int,A: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 0.29/0.52        = ( ord_less_eq_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_le_iff_le
% 0.29/0.52  thf(fact_2169_compl__le__compl__iff,axiom,
% 0.29/0.52      ! [X: product_unit,Y: product_unit] :
% 0.29/0.52        ( ( ord_le3221252021190050221t_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( uminus2952777764628376836t_unit @ Y ) )
% 0.29/0.52        = ( ord_le3221252021190050221t_unit @ Y @ X ) ) ).
% 0.29/0.52  
% 0.29/0.52  % compl_le_compl_iff
% 0.29/0.52  thf(fact_2170_compl__le__compl__iff,axiom,
% 0.29/0.52      ! [X: set_nat,Y: set_nat] :
% 0.29/0.52        ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y ) )
% 0.29/0.52        = ( ord_less_eq_set_nat @ Y @ X ) ) ).
% 0.29/0.52  
% 0.29/0.52  % compl_le_compl_iff
% 0.29/0.52  thf(fact_2171_neg__less__iff__less,axiom,
% 0.29/0.52      ! [B: int,A: int] :
% 0.29/0.52        ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 0.29/0.52        = ( ord_less_int @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_less_iff_less
% 0.29/0.52  thf(fact_2172_neg__less__iff__less,axiom,
% 0.29/0.52      ! [B: code_integer,A: code_integer] :
% 0.29/0.52        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.52        = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_less_iff_less
% 0.29/0.52  thf(fact_2173_neg__less__iff__less,axiom,
% 0.29/0.52      ! [B: rat,A: rat] :
% 0.29/0.52        ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 0.29/0.52        = ( ord_less_rat @ A @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_less_iff_less
% 0.29/0.52  thf(fact_2174_compl__less__compl__iff,axiom,
% 0.29/0.52      ! [X: product_unit,Y: product_unit] :
% 0.29/0.52        ( ( ord_le361264281704409273t_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( uminus2952777764628376836t_unit @ Y ) )
% 0.29/0.52        = ( ord_le361264281704409273t_unit @ Y @ X ) ) ).
% 0.29/0.52  
% 0.29/0.52  % compl_less_compl_iff
% 0.29/0.52  thf(fact_2175_le__inf__iff,axiom,
% 0.29/0.52      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 0.29/0.52        = ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 0.29/0.52          & ( ord_le3146513528884898305at_nat @ X @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_inf_iff
% 0.29/0.52  thf(fact_2176_le__inf__iff,axiom,
% 0.29/0.52      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 0.29/0.52        ( ( ord_le8369615600986905444_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) )
% 0.29/0.52        = ( ( ord_le8369615600986905444_int_o @ X @ Y )
% 0.29/0.52          & ( ord_le8369615600986905444_int_o @ X @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_inf_iff
% 0.29/0.52  thf(fact_2177_le__inf__iff,axiom,
% 0.29/0.52      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 0.29/0.52        ( ( ord_le4796328588573674190char_o @ X @ ( inf_inf_list_char_o @ Y @ Z ) )
% 0.29/0.52        = ( ( ord_le4796328588573674190char_o @ X @ Y )
% 0.29/0.52          & ( ord_le4796328588573674190char_o @ X @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_inf_iff
% 0.29/0.52  thf(fact_2178_le__inf__iff,axiom,
% 0.29/0.52      ! [X: filter_nat,Y: filter_nat,Z: filter_nat] :
% 0.29/0.52        ( ( ord_le2510731241096832064er_nat @ X @ ( inf_inf_filter_nat @ Y @ Z ) )
% 0.29/0.52        = ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 0.29/0.52          & ( ord_le2510731241096832064er_nat @ X @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_inf_iff
% 0.29/0.52  thf(fact_2179_le__inf__iff,axiom,
% 0.29/0.52      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.29/0.52        ( ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 0.29/0.52        = ( ( ord_less_eq_set_nat @ X @ Y )
% 0.29/0.52          & ( ord_less_eq_set_nat @ X @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_inf_iff
% 0.29/0.52  thf(fact_2180_le__inf__iff,axiom,
% 0.29/0.52      ! [X: rat,Y: rat,Z: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ X @ ( inf_inf_rat @ Y @ Z ) )
% 0.29/0.52        = ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.52          & ( ord_less_eq_rat @ X @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_inf_iff
% 0.29/0.52  thf(fact_2181_le__inf__iff,axiom,
% 0.29/0.52      ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 0.29/0.52        = ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.52          & ( ord_less_eq_nat @ X @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_inf_iff
% 0.29/0.52  thf(fact_2182_le__inf__iff,axiom,
% 0.29/0.52      ! [X: int,Y: int,Z: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ X @ ( inf_inf_int @ Y @ Z ) )
% 0.29/0.52        = ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.52          & ( ord_less_eq_int @ X @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_inf_iff
% 0.29/0.52  thf(fact_2183_inf_Obounded__iff,axiom,
% 0.29/0.52      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) )
% 0.29/0.52        = ( ( ord_le3146513528884898305at_nat @ A @ B )
% 0.29/0.52          & ( ord_le3146513528884898305at_nat @ A @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % inf.bounded_iff
% 0.29/0.52  thf(fact_2184_inf_Obounded__iff,axiom,
% 0.29/0.52      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o,C: product_prod_int_int > $o] :
% 0.29/0.52        ( ( ord_le8369615600986905444_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C ) )
% 0.29/0.52        = ( ( ord_le8369615600986905444_int_o @ A @ B )
% 0.29/0.52          & ( ord_le8369615600986905444_int_o @ A @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % inf.bounded_iff
% 0.29/0.52  thf(fact_2185_inf_Obounded__iff,axiom,
% 0.29/0.52      ! [A: list_char > $o,B: list_char > $o,C: list_char > $o] :
% 0.29/0.52        ( ( ord_le4796328588573674190char_o @ A @ ( inf_inf_list_char_o @ B @ C ) )
% 0.29/0.52        = ( ( ord_le4796328588573674190char_o @ A @ B )
% 0.29/0.52          & ( ord_le4796328588573674190char_o @ A @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % inf.bounded_iff
% 0.29/0.52  thf(fact_2186_inf_Obounded__iff,axiom,
% 0.29/0.52      ! [A: filter_nat,B: filter_nat,C: filter_nat] :
% 0.29/0.52        ( ( ord_le2510731241096832064er_nat @ A @ ( inf_inf_filter_nat @ B @ C ) )
% 0.29/0.52        = ( ( ord_le2510731241096832064er_nat @ A @ B )
% 0.29/0.52          & ( ord_le2510731241096832064er_nat @ A @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % inf.bounded_iff
% 0.29/0.52  thf(fact_2187_inf_Obounded__iff,axiom,
% 0.29/0.52      ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.29/0.52        ( ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) )
% 0.29/0.52        = ( ( ord_less_eq_set_nat @ A @ B )
% 0.29/0.52          & ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % inf.bounded_iff
% 0.29/0.52  thf(fact_2188_inf_Obounded__iff,axiom,
% 0.29/0.52      ! [A: rat,B: rat,C: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C ) )
% 0.29/0.52        = ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.52          & ( ord_less_eq_rat @ A @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % inf.bounded_iff
% 0.29/0.52  thf(fact_2189_inf_Obounded__iff,axiom,
% 0.29/0.52      ! [A: nat,B: nat,C: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C ) )
% 0.29/0.52        = ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.52          & ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % inf.bounded_iff
% 0.29/0.52  thf(fact_2190_inf_Obounded__iff,axiom,
% 0.29/0.52      ! [A: int,B: int,C: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C ) )
% 0.29/0.52        = ( ( ord_less_eq_int @ A @ B )
% 0.29/0.52          & ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % inf.bounded_iff
% 0.29/0.52  thf(fact_2191_le__sup__iff,axiom,
% 0.29/0.52      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 0.29/0.52        ( ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ Z )
% 0.29/0.52        = ( ( ord_le8081472938463900775at_nat @ X @ Z )
% 0.29/0.52          & ( ord_le8081472938463900775at_nat @ Y @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_sup_iff
% 0.29/0.52  thf(fact_2192_le__sup__iff,axiom,
% 0.29/0.52      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 0.29/0.52        ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ Z )
% 0.29/0.52        = ( ( ord_le1268244103169919719at_nat @ X @ Z )
% 0.29/0.52          & ( ord_le1268244103169919719at_nat @ Y @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_sup_iff
% 0.29/0.52  thf(fact_2193_le__sup__iff,axiom,
% 0.29/0.52      ! [X: filter_nat,Y: filter_nat,Z: filter_nat] :
% 0.29/0.52        ( ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ X @ Y ) @ Z )
% 0.29/0.52        = ( ( ord_le2510731241096832064er_nat @ X @ Z )
% 0.29/0.52          & ( ord_le2510731241096832064er_nat @ Y @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_sup_iff
% 0.29/0.52  thf(fact_2194_le__sup__iff,axiom,
% 0.29/0.52      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.29/0.52        ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z )
% 0.29/0.52        = ( ( ord_less_eq_set_nat @ X @ Z )
% 0.29/0.52          & ( ord_less_eq_set_nat @ Y @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_sup_iff
% 0.29/0.52  thf(fact_2195_le__sup__iff,axiom,
% 0.29/0.52      ! [X: rat,Y: rat,Z: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ ( sup_sup_rat @ X @ Y ) @ Z )
% 0.29/0.52        = ( ( ord_less_eq_rat @ X @ Z )
% 0.29/0.52          & ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_sup_iff
% 0.29/0.52  thf(fact_2196_le__sup__iff,axiom,
% 0.29/0.52      ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ ( sup_sup_nat @ X @ Y ) @ Z )
% 0.29/0.52        = ( ( ord_less_eq_nat @ X @ Z )
% 0.29/0.52          & ( ord_less_eq_nat @ Y @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_sup_iff
% 0.29/0.52  thf(fact_2197_le__sup__iff,axiom,
% 0.29/0.52      ! [X: int,Y: int,Z: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ ( sup_sup_int @ X @ Y ) @ Z )
% 0.29/0.52        = ( ( ord_less_eq_int @ X @ Z )
% 0.29/0.52          & ( ord_less_eq_int @ Y @ Z ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_sup_iff
% 0.29/0.52  thf(fact_2198_sup_Obounded__iff,axiom,
% 0.29/0.52      ! [B: set_Pr8551490117392284871at_nat,C: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 0.29/0.52        ( ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ B @ C ) @ A )
% 0.29/0.52        = ( ( ord_le8081472938463900775at_nat @ B @ A )
% 0.29/0.52          & ( ord_le8081472938463900775at_nat @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % sup.bounded_iff
% 0.29/0.52  thf(fact_2199_sup_Obounded__iff,axiom,
% 0.29/0.52      ! [B: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 0.29/0.52        ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ B @ C ) @ A )
% 0.29/0.52        = ( ( ord_le1268244103169919719at_nat @ B @ A )
% 0.29/0.52          & ( ord_le1268244103169919719at_nat @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % sup.bounded_iff
% 0.29/0.52  thf(fact_2200_sup_Obounded__iff,axiom,
% 0.29/0.52      ! [B: filter_nat,C: filter_nat,A: filter_nat] :
% 0.29/0.52        ( ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ B @ C ) @ A )
% 0.29/0.52        = ( ( ord_le2510731241096832064er_nat @ B @ A )
% 0.29/0.52          & ( ord_le2510731241096832064er_nat @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % sup.bounded_iff
% 0.29/0.52  thf(fact_2201_sup_Obounded__iff,axiom,
% 0.29/0.52      ! [B: set_nat,C: set_nat,A: set_nat] :
% 0.29/0.52        ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C ) @ A )
% 0.29/0.52        = ( ( ord_less_eq_set_nat @ B @ A )
% 0.29/0.52          & ( ord_less_eq_set_nat @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % sup.bounded_iff
% 0.29/0.52  thf(fact_2202_sup_Obounded__iff,axiom,
% 0.29/0.52      ! [B: rat,C: rat,A: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C ) @ A )
% 0.29/0.52        = ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.52          & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % sup.bounded_iff
% 0.29/0.52  thf(fact_2203_sup_Obounded__iff,axiom,
% 0.29/0.52      ! [B: nat,C: nat,A: nat] :
% 0.29/0.52        ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C ) @ A )
% 0.29/0.52        = ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.52          & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % sup.bounded_iff
% 0.29/0.52  thf(fact_2204_sup_Obounded__iff,axiom,
% 0.29/0.52      ! [B: int,C: int,A: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ ( sup_sup_int @ B @ C ) @ A )
% 0.29/0.52        = ( ( ord_less_eq_int @ B @ A )
% 0.29/0.52          & ( ord_less_eq_int @ C @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % sup.bounded_iff
% 0.29/0.52  thf(fact_2205_Diff__eq__empty__iff,axiom,
% 0.29/0.52      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.52        ( ( ( minus_1356011639430497352at_nat @ A2 @ B2 )
% 0.29/0.52          = bot_bo2099793752762293965at_nat )
% 0.29/0.52        = ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_eq_empty_iff
% 0.29/0.52  thf(fact_2206_Diff__eq__empty__iff,axiom,
% 0.29/0.52      ! [A2: set_o,B2: set_o] :
% 0.29/0.52        ( ( ( minus_minus_set_o @ A2 @ B2 )
% 0.29/0.52          = bot_bot_set_o )
% 0.29/0.52        = ( ord_less_eq_set_o @ A2 @ B2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_eq_empty_iff
% 0.29/0.52  thf(fact_2207_Diff__eq__empty__iff,axiom,
% 0.29/0.52      ! [A2: set_int,B2: set_int] :
% 0.29/0.52        ( ( ( minus_minus_set_int @ A2 @ B2 )
% 0.29/0.52          = bot_bot_set_int )
% 0.29/0.52        = ( ord_less_eq_set_int @ A2 @ B2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_eq_empty_iff
% 0.29/0.52  thf(fact_2208_Diff__eq__empty__iff,axiom,
% 0.29/0.52      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.52        ( ( ( minus_minus_set_nat @ A2 @ B2 )
% 0.29/0.52          = bot_bot_set_nat )
% 0.29/0.52        = ( ord_less_eq_set_nat @ A2 @ B2 ) ) ).
% 0.29/0.52  
% 0.29/0.52  % Diff_eq_empty_iff
% 0.29/0.52  thf(fact_2209_diff__ge__0__iff__ge,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.29/0.52        = ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_ge_0_iff_ge
% 0.29/0.52  thf(fact_2210_diff__ge__0__iff__ge,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.52        = ( ord_less_eq_rat @ B @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_ge_0_iff_ge
% 0.29/0.52  thf(fact_2211_diff__ge__0__iff__ge,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.29/0.52        = ( ord_less_eq_int @ B @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_ge_0_iff_ge
% 0.29/0.52  thf(fact_2212_diff__gt__0__iff__gt,axiom,
% 0.29/0.52      ! [A: code_integer,B: code_integer] :
% 0.29/0.52        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.29/0.52        = ( ord_le6747313008572928689nteger @ B @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_gt_0_iff_gt
% 0.29/0.52  thf(fact_2213_diff__gt__0__iff__gt,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.29/0.52        = ( ord_less_rat @ B @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_gt_0_iff_gt
% 0.29/0.52  thf(fact_2214_diff__gt__0__iff__gt,axiom,
% 0.29/0.52      ! [A: int,B: int] :
% 0.29/0.52        ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.29/0.52        = ( ord_less_int @ B @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % diff_gt_0_iff_gt
% 0.29/0.52  thf(fact_2215_neg__0__le__iff__le,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.52        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_0_le_iff_le
% 0.29/0.52  thf(fact_2216_neg__0__le__iff__le,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 0.29/0.52        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_0_le_iff_le
% 0.29/0.52  thf(fact_2217_neg__0__le__iff__le,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.29/0.52        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_0_le_iff_le
% 0.29/0.52  thf(fact_2218_neg__le__0__iff__le,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 0.29/0.52        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_le_0_iff_le
% 0.29/0.52  thf(fact_2219_neg__le__0__iff__le,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 0.29/0.52        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_le_0_iff_le
% 0.29/0.52  thf(fact_2220_neg__le__0__iff__le,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.29/0.52        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_le_0_iff_le
% 0.29/0.52  thf(fact_2221_less__eq__neg__nonpos,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.52        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.52  
% 0.29/0.52  % less_eq_neg_nonpos
% 0.29/0.52  thf(fact_2222_less__eq__neg__nonpos,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.29/0.52        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % less_eq_neg_nonpos
% 0.29/0.52  thf(fact_2223_less__eq__neg__nonpos,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 0.29/0.52        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.29/0.52  
% 0.29/0.52  % less_eq_neg_nonpos
% 0.29/0.52  thf(fact_2224_neg__less__eq__nonneg,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.29/0.52        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_less_eq_nonneg
% 0.29/0.52  thf(fact_2225_neg__less__eq__nonneg,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.29/0.52        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_less_eq_nonneg
% 0.29/0.52  thf(fact_2226_neg__less__eq__nonneg,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 0.29/0.52        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_less_eq_nonneg
% 0.29/0.52  thf(fact_2227_less__neg__neg,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 0.29/0.52        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.29/0.52  
% 0.29/0.52  % less_neg_neg
% 0.29/0.52  thf(fact_2228_less__neg__neg,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.52        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.52  
% 0.29/0.52  % less_neg_neg
% 0.29/0.52  thf(fact_2229_less__neg__neg,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.29/0.52        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % less_neg_neg
% 0.29/0.52  thf(fact_2230_neg__less__pos,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 0.29/0.52        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_less_pos
% 0.29/0.52  thf(fact_2231_neg__less__pos,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.29/0.52        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_less_pos
% 0.29/0.52  thf(fact_2232_neg__less__pos,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.29/0.52        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_less_pos
% 0.29/0.52  thf(fact_2233_neg__0__less__iff__less,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.29/0.52        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_0_less_iff_less
% 0.29/0.52  thf(fact_2234_neg__0__less__iff__less,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.29/0.52        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_0_less_iff_less
% 0.29/0.52  thf(fact_2235_neg__0__less__iff__less,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 0.29/0.52        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_0_less_iff_less
% 0.29/0.52  thf(fact_2236_neg__less__0__iff__less,axiom,
% 0.29/0.52      ! [A: int] :
% 0.29/0.52        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.29/0.52        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_less_0_iff_less
% 0.29/0.52  thf(fact_2237_neg__less__0__iff__less,axiom,
% 0.29/0.52      ! [A: code_integer] :
% 0.29/0.52        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 0.29/0.52        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_less_0_iff_less
% 0.29/0.52  thf(fact_2238_neg__less__0__iff__less,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 0.29/0.52        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_less_0_iff_less
% 0.29/0.52  thf(fact_2239_neg__numeral__le__iff,axiom,
% 0.29/0.52      ! [M: num,N: num] :
% 0.29/0.52        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.29/0.52        = ( ord_less_eq_num @ N @ M ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_numeral_le_iff
% 0.29/0.52  thf(fact_2240_neg__numeral__le__iff,axiom,
% 0.29/0.52      ! [M: num,N: num] :
% 0.29/0.52        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.29/0.52        = ( ord_less_eq_num @ N @ M ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_numeral_le_iff
% 0.29/0.52  thf(fact_2241_neg__numeral__le__iff,axiom,
% 0.29/0.52      ! [M: num,N: num] :
% 0.29/0.52        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.29/0.52        = ( ord_less_eq_num @ N @ M ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_numeral_le_iff
% 0.29/0.52  thf(fact_2242_neg__numeral__less__iff,axiom,
% 0.29/0.52      ! [M: num,N: num] :
% 0.29/0.52        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.29/0.52        = ( ord_less_num @ N @ M ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_numeral_less_iff
% 0.29/0.52  thf(fact_2243_neg__numeral__less__iff,axiom,
% 0.29/0.52      ! [M: num,N: num] :
% 0.29/0.52        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.29/0.52        = ( ord_less_num @ N @ M ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_numeral_less_iff
% 0.29/0.52  thf(fact_2244_neg__numeral__less__iff,axiom,
% 0.29/0.52      ! [M: num,N: num] :
% 0.29/0.52        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.29/0.52        = ( ord_less_num @ N @ M ) ) ).
% 0.29/0.52  
% 0.29/0.52  % neg_numeral_less_iff
% 0.29/0.52  thf(fact_2245_divide__le__0__1__iff,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 0.29/0.52        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_le_0_1_iff
% 0.29/0.52  thf(fact_2246_zero__le__divide__1__iff,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 0.29/0.52        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % zero_le_divide_1_iff
% 0.29/0.52  thf(fact_2247_divide__less__0__1__iff,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 0.29/0.52        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_less_0_1_iff
% 0.29/0.52  thf(fact_2248_divide__less__eq__1__neg,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.52       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.29/0.52          = ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_less_eq_1_neg
% 0.29/0.52  thf(fact_2249_divide__less__eq__1__pos,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.52       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.29/0.52          = ( ord_less_rat @ B @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_less_eq_1_pos
% 0.29/0.52  thf(fact_2250_less__divide__eq__1__neg,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.52       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.29/0.52          = ( ord_less_rat @ B @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % less_divide_eq_1_neg
% 0.29/0.52  thf(fact_2251_less__divide__eq__1__pos,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.52       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.29/0.52          = ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % less_divide_eq_1_pos
% 0.29/0.52  thf(fact_2252_zero__less__divide__1__iff,axiom,
% 0.29/0.52      ! [A: rat] :
% 0.29/0.52        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 0.29/0.52        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.29/0.52  
% 0.29/0.52  % zero_less_divide_1_iff
% 0.29/0.52  thf(fact_2253_le__divide__eq__numeral1_I1_J,axiom,
% 0.29/0.52      ! [A: rat,B: rat,W: num] :
% 0.29/0.52        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 0.29/0.52        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_divide_eq_numeral1(1)
% 0.29/0.52  thf(fact_2254_divide__le__eq__numeral1_I1_J,axiom,
% 0.29/0.52      ! [B: rat,W: num,A: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 0.29/0.52        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_le_eq_numeral1(1)
% 0.29/0.52  thf(fact_2255_less__divide__eq__numeral1_I1_J,axiom,
% 0.29/0.52      ! [A: rat,B: rat,W: num] :
% 0.29/0.52        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 0.29/0.52        = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % less_divide_eq_numeral1(1)
% 0.29/0.52  thf(fact_2256_divide__less__eq__numeral1_I1_J,axiom,
% 0.29/0.52      ! [B: rat,W: num,A: rat] :
% 0.29/0.52        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 0.29/0.52        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_less_eq_numeral1(1)
% 0.29/0.52  thf(fact_2257_le__divide__eq__1__pos,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.52       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.29/0.52          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_divide_eq_1_pos
% 0.29/0.52  thf(fact_2258_le__divide__eq__1__neg,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.52       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.29/0.52          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % le_divide_eq_1_neg
% 0.29/0.52  thf(fact_2259_divide__le__eq__1__pos,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.52       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.29/0.52          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_le_eq_1_pos
% 0.29/0.52  thf(fact_2260_divide__le__eq__1__neg,axiom,
% 0.29/0.52      ! [A: rat,B: rat] :
% 0.29/0.52        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.29/0.52       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.29/0.52          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_le_eq_1_neg
% 0.29/0.52  thf(fact_2261_divide__le__eq__numeral1_I2_J,axiom,
% 0.29/0.52      ! [B: rat,W: num,A: rat] :
% 0.29/0.52        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 0.29/0.52        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_le_eq_numeral1(2)
% 0.29/0.52  thf(fact_2262_divide__less__eq__numeral1_I2_J,axiom,
% 0.29/0.52      ! [B: rat,W: num,A: rat] :
% 0.29/0.52        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 0.29/0.52        = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 0.29/0.52  
% 0.29/0.52  % divide_less_eq_numeral1(2)
% 0.29/0.52  thf(fact_2263_less__divide__eq__numeral1_I2_J,axiom,
% 0.29/0.52      ! [A: rat,B: rat,W: num] :
% 0.29/0.52        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 0.29/0.52        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % less_divide_eq_numeral1(2)
% 0.29/0.52  thf(fact_2264_minus__set__def,axiom,
% 0.29/0.52      ( minus_2612819937483484256nt_int
% 0.29/0.52      = ( ^ [A4: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
% 0.29/0.52            ( collec5210948495886036740nt_int
% 0.29/0.52            @ ( minus_357216186751819389_int_o
% 0.29/0.52              @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ A4 )
% 0.29/0.52              @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % minus_set_def
% 0.29/0.52  thf(fact_2265_minus__set__def,axiom,
% 0.29/0.52      ( minus_2163939370556025621et_nat
% 0.29/0.52      = ( ^ [A4: set_set_nat,B4: set_set_nat] :
% 0.29/0.52            ( collect_set_nat
% 0.29/0.52            @ ( minus_6910147592129066416_nat_o
% 0.29/0.52              @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A4 )
% 0.29/0.52              @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % minus_set_def
% 0.29/0.52  thf(fact_2266_minus__set__def,axiom,
% 0.29/0.52      ( minus_minus_set_int
% 0.29/0.52      = ( ^ [A4: set_int,B4: set_int] :
% 0.29/0.52            ( collect_int
% 0.29/0.52            @ ( minus_minus_int_o
% 0.29/0.52              @ ^ [X3: int] : ( member_int @ X3 @ A4 )
% 0.29/0.52              @ ^ [X3: int] : ( member_int @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % minus_set_def
% 0.29/0.52  thf(fact_2267_minus__set__def,axiom,
% 0.29/0.52      ( minus_1801376950450012436_nat_o
% 0.29/0.52      = ( ^ [A4: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 0.29/0.52            ( collec939566748876313656_nat_o
% 0.29/0.52            @ ( minus_2803741817741520073at_o_o
% 0.29/0.52              @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ A4 )
% 0.29/0.52              @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % minus_set_def
% 0.29/0.52  thf(fact_2268_minus__set__def,axiom,
% 0.29/0.52      ( minus_minus_set_nat
% 0.29/0.52      = ( ^ [A4: set_nat,B4: set_nat] :
% 0.29/0.52            ( collect_nat
% 0.29/0.52            @ ( minus_minus_nat_o
% 0.29/0.52              @ ^ [X3: nat] : ( member_nat @ X3 @ A4 )
% 0.29/0.52              @ ^ [X3: nat] : ( member_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % minus_set_def
% 0.29/0.52  thf(fact_2269_set__diff__eq,axiom,
% 0.29/0.52      ( minus_2612819937483484256nt_int
% 0.29/0.52      = ( ^ [A4: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
% 0.29/0.52            ( collec5210948495886036740nt_int
% 0.29/0.52            @ ^ [X3: set_Pr958786334691620121nt_int] :
% 0.29/0.52                ( ( member2340774599025711042nt_int @ X3 @ A4 )
% 0.29/0.52                & ~ ( member2340774599025711042nt_int @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % set_diff_eq
% 0.29/0.52  thf(fact_2270_set__diff__eq,axiom,
% 0.29/0.52      ( minus_2163939370556025621et_nat
% 0.29/0.52      = ( ^ [A4: set_set_nat,B4: set_set_nat] :
% 0.29/0.52            ( collect_set_nat
% 0.29/0.52            @ ^ [X3: set_nat] :
% 0.29/0.52                ( ( member_set_nat @ X3 @ A4 )
% 0.29/0.52                & ~ ( member_set_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % set_diff_eq
% 0.29/0.52  thf(fact_2271_set__diff__eq,axiom,
% 0.29/0.52      ( minus_minus_set_int
% 0.29/0.52      = ( ^ [A4: set_int,B4: set_int] :
% 0.29/0.52            ( collect_int
% 0.29/0.52            @ ^ [X3: int] :
% 0.29/0.52                ( ( member_int @ X3 @ A4 )
% 0.29/0.52                & ~ ( member_int @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % set_diff_eq
% 0.29/0.52  thf(fact_2272_set__diff__eq,axiom,
% 0.29/0.52      ( minus_1801376950450012436_nat_o
% 0.29/0.52      = ( ^ [A4: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 0.29/0.52            ( collec939566748876313656_nat_o
% 0.29/0.52            @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.29/0.52                ( ( member6576561426505652726_nat_o @ X3 @ A4 )
% 0.29/0.52                & ~ ( member6576561426505652726_nat_o @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % set_diff_eq
% 0.29/0.52  thf(fact_2273_set__diff__eq,axiom,
% 0.29/0.52      ( minus_minus_set_nat
% 0.29/0.52      = ( ^ [A4: set_nat,B4: set_nat] :
% 0.29/0.52            ( collect_nat
% 0.29/0.52            @ ^ [X3: nat] :
% 0.29/0.52                ( ( member_nat @ X3 @ A4 )
% 0.29/0.52                & ~ ( member_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.29/0.52  
% 0.29/0.52  % set_diff_eq
% 0.29/0.52  thf(fact_2274_order__less__imp__not__less,axiom,
% 0.29/0.52      ! [X: literal,Y: literal] :
% 0.29/0.52        ( ( ord_less_literal @ X @ Y )
% 0.29/0.53       => ~ ( ord_less_literal @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_not_less
% 0.29/0.53  thf(fact_2275_order__less__imp__not__less,axiom,
% 0.29/0.53      ! [X: rat,Y: rat] :
% 0.29/0.53        ( ( ord_less_rat @ X @ Y )
% 0.29/0.53       => ~ ( ord_less_rat @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_not_less
% 0.29/0.53  thf(fact_2276_order__less__imp__not__less,axiom,
% 0.29/0.53      ! [X: nat,Y: nat] :
% 0.29/0.53        ( ( ord_less_nat @ X @ Y )
% 0.29/0.53       => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_not_less
% 0.29/0.53  thf(fact_2277_order__less__imp__not__less,axiom,
% 0.29/0.53      ! [X: int,Y: int] :
% 0.29/0.53        ( ( ord_less_int @ X @ Y )
% 0.29/0.53       => ~ ( ord_less_int @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_not_less
% 0.29/0.53  thf(fact_2278_order__le__imp__less__or__eq,axiom,
% 0.29/0.53      ! [X: literal,Y: literal] :
% 0.29/0.53        ( ( ord_less_eq_literal @ X @ Y )
% 0.29/0.53       => ( ( ord_less_literal @ X @ Y )
% 0.29/0.53          | ( X = Y ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_imp_less_or_eq
% 0.29/0.53  thf(fact_2279_order__le__imp__less__or__eq,axiom,
% 0.29/0.53      ! [X: filter_nat,Y: filter_nat] :
% 0.29/0.53        ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 0.29/0.53       => ( ( ord_less_filter_nat @ X @ Y )
% 0.29/0.53          | ( X = Y ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_imp_less_or_eq
% 0.29/0.53  thf(fact_2280_order__le__imp__less__or__eq,axiom,
% 0.29/0.53      ! [X: set_nat,Y: set_nat] :
% 0.29/0.53        ( ( ord_less_eq_set_nat @ X @ Y )
% 0.29/0.53       => ( ( ord_less_set_nat @ X @ Y )
% 0.29/0.53          | ( X = Y ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_imp_less_or_eq
% 0.29/0.53  thf(fact_2281_order__le__imp__less__or__eq,axiom,
% 0.29/0.53      ! [X: rat,Y: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.53       => ( ( ord_less_rat @ X @ Y )
% 0.29/0.53          | ( X = Y ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_imp_less_or_eq
% 0.29/0.53  thf(fact_2282_order__le__imp__less__or__eq,axiom,
% 0.29/0.53      ! [X: nat,Y: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.53       => ( ( ord_less_nat @ X @ Y )
% 0.29/0.53          | ( X = Y ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_imp_less_or_eq
% 0.29/0.53  thf(fact_2283_order__le__imp__less__or__eq,axiom,
% 0.29/0.53      ! [X: int,Y: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.53       => ( ( ord_less_int @ X @ Y )
% 0.29/0.53          | ( X = Y ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_imp_less_or_eq
% 0.29/0.53  thf(fact_2284_linorder__le__less__linear,axiom,
% 0.29/0.53      ! [X: literal,Y: literal] :
% 0.29/0.53        ( ( ord_less_eq_literal @ X @ Y )
% 0.29/0.53        | ( ord_less_literal @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_le_less_linear
% 0.29/0.53  thf(fact_2285_linorder__le__less__linear,axiom,
% 0.29/0.53      ! [X: rat,Y: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.53        | ( ord_less_rat @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_le_less_linear
% 0.29/0.53  thf(fact_2286_linorder__le__less__linear,axiom,
% 0.29/0.53      ! [X: nat,Y: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.53        | ( ord_less_nat @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_le_less_linear
% 0.29/0.53  thf(fact_2287_linorder__le__less__linear,axiom,
% 0.29/0.53      ! [X: int,Y: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.53        | ( ord_less_int @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_le_less_linear
% 0.29/0.53  thf(fact_2288_order__less__imp__not__eq2,axiom,
% 0.29/0.53      ! [X: literal,Y: literal] :
% 0.29/0.53        ( ( ord_less_literal @ X @ Y )
% 0.29/0.53       => ( Y != X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_not_eq2
% 0.29/0.53  thf(fact_2289_order__less__imp__not__eq2,axiom,
% 0.29/0.53      ! [X: rat,Y: rat] :
% 0.29/0.53        ( ( ord_less_rat @ X @ Y )
% 0.29/0.53       => ( Y != X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_not_eq2
% 0.29/0.53  thf(fact_2290_order__less__imp__not__eq2,axiom,
% 0.29/0.53      ! [X: nat,Y: nat] :
% 0.29/0.53        ( ( ord_less_nat @ X @ Y )
% 0.29/0.53       => ( Y != X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_not_eq2
% 0.29/0.53  thf(fact_2291_order__less__imp__not__eq2,axiom,
% 0.29/0.53      ! [X: int,Y: int] :
% 0.29/0.53        ( ( ord_less_int @ X @ Y )
% 0.29/0.53       => ( Y != X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_not_eq2
% 0.29/0.53  thf(fact_2292_order__less__imp__not__eq,axiom,
% 0.29/0.53      ! [X: literal,Y: literal] :
% 0.29/0.53        ( ( ord_less_literal @ X @ Y )
% 0.29/0.53       => ( X != Y ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_not_eq
% 0.29/0.53  thf(fact_2293_order__less__imp__not__eq,axiom,
% 0.29/0.53      ! [X: rat,Y: rat] :
% 0.29/0.53        ( ( ord_less_rat @ X @ Y )
% 0.29/0.53       => ( X != Y ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_not_eq
% 0.29/0.53  thf(fact_2294_order__less__imp__not__eq,axiom,
% 0.29/0.53      ! [X: nat,Y: nat] :
% 0.29/0.53        ( ( ord_less_nat @ X @ Y )
% 0.29/0.53       => ( X != Y ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_not_eq
% 0.29/0.53  thf(fact_2295_order__less__imp__not__eq,axiom,
% 0.29/0.53      ! [X: int,Y: int] :
% 0.29/0.53        ( ( ord_less_int @ X @ Y )
% 0.29/0.53       => ( X != Y ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_not_eq
% 0.29/0.53  thf(fact_2296_order__less__le__subst2,axiom,
% 0.29/0.53      ! [A: literal,B: literal,F2: literal > literal,C: literal] :
% 0.29/0.53        ( ( ord_less_literal @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_literal @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: literal,Y2: literal] :
% 0.29/0.53                ( ( ord_less_literal @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_subst2
% 0.29/0.53  thf(fact_2297_order__less__le__subst2,axiom,
% 0.29/0.53      ! [A: rat,B: rat,F2: rat > literal,C: literal] :
% 0.29/0.53        ( ( ord_less_rat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_literal @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_subst2
% 0.29/0.53  thf(fact_2298_order__less__le__subst2,axiom,
% 0.29/0.53      ! [A: nat,B: nat,F2: nat > literal,C: literal] :
% 0.29/0.53        ( ( ord_less_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_literal @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_subst2
% 0.29/0.53  thf(fact_2299_order__less__le__subst2,axiom,
% 0.29/0.53      ! [A: int,B: int,F2: int > literal,C: literal] :
% 0.29/0.53        ( ( ord_less_int @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_literal @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_subst2
% 0.29/0.53  thf(fact_2300_order__less__le__subst2,axiom,
% 0.29/0.53      ! [A: literal,B: literal,F2: literal > rat,C: rat] :
% 0.29/0.53        ( ( ord_less_literal @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: literal,Y2: literal] :
% 0.29/0.53                ( ( ord_less_literal @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_subst2
% 0.29/0.53  thf(fact_2301_order__less__le__subst2,axiom,
% 0.29/0.53      ! [A: rat,B: rat,F2: rat > rat,C: rat] :
% 0.29/0.53        ( ( ord_less_rat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_subst2
% 0.29/0.53  thf(fact_2302_order__less__le__subst2,axiom,
% 0.29/0.53      ! [A: nat,B: nat,F2: nat > rat,C: rat] :
% 0.29/0.53        ( ( ord_less_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_subst2
% 0.29/0.53  thf(fact_2303_order__less__le__subst2,axiom,
% 0.29/0.53      ! [A: int,B: int,F2: int > rat,C: rat] :
% 0.29/0.53        ( ( ord_less_int @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_subst2
% 0.29/0.53  thf(fact_2304_order__less__le__subst2,axiom,
% 0.29/0.53      ! [A: literal,B: literal,F2: literal > nat,C: nat] :
% 0.29/0.53        ( ( ord_less_literal @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: literal,Y2: literal] :
% 0.29/0.53                ( ( ord_less_literal @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_subst2
% 0.29/0.53  thf(fact_2305_order__less__le__subst2,axiom,
% 0.29/0.53      ! [A: rat,B: rat,F2: rat > nat,C: nat] :
% 0.29/0.53        ( ( ord_less_rat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_subst2
% 0.29/0.53  thf(fact_2306_order__less__le__subst1,axiom,
% 0.29/0.53      ! [A: literal,F2: rat > literal,B: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_literal @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_subst1
% 0.29/0.53  thf(fact_2307_order__less__le__subst1,axiom,
% 0.29/0.53      ! [A: rat,F2: rat > rat,B: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_subst1
% 0.29/0.53  thf(fact_2308_order__less__le__subst1,axiom,
% 0.29/0.53      ! [A: nat,F2: rat > nat,B: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_nat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_subst1
% 0.29/0.53  thf(fact_2309_order__less__le__subst1,axiom,
% 0.29/0.53      ! [A: int,F2: rat > int,B: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_int @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_subst1
% 0.29/0.53  thf(fact_2310_order__less__le__subst1,axiom,
% 0.29/0.53      ! [A: literal,F2: nat > literal,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_literal @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_subst1
% 0.29/0.53  thf(fact_2311_order__less__le__subst1,axiom,
% 0.29/0.53      ! [A: rat,F2: nat > rat,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_subst1
% 0.29/0.53  thf(fact_2312_order__less__le__subst1,axiom,
% 0.29/0.53      ! [A: nat,F2: nat > nat,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_nat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_subst1
% 0.29/0.53  thf(fact_2313_order__less__le__subst1,axiom,
% 0.29/0.53      ! [A: int,F2: nat > int,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_int @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_subst1
% 0.29/0.53  thf(fact_2314_order__less__le__subst1,axiom,
% 0.29/0.53      ! [A: literal,F2: int > literal,B: int,C: int] :
% 0.29/0.53        ( ( ord_less_literal @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_subst1
% 0.29/0.53  thf(fact_2315_order__less__le__subst1,axiom,
% 0.29/0.53      ! [A: rat,F2: int > rat,B: int,C: int] :
% 0.29/0.53        ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_subst1
% 0.29/0.53  thf(fact_2316_order__le__less__subst2,axiom,
% 0.29/0.53      ! [A: rat,B: rat,F2: rat > literal,C: literal] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.53       => ( ( ord_less_literal @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_subst2
% 0.29/0.53  thf(fact_2317_order__le__less__subst2,axiom,
% 0.29/0.53      ! [A: rat,B: rat,F2: rat > rat,C: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.53       => ( ( ord_less_rat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_subst2
% 0.29/0.53  thf(fact_2318_order__le__less__subst2,axiom,
% 0.29/0.53      ! [A: rat,B: rat,F2: rat > nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.53       => ( ( ord_less_nat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_subst2
% 0.29/0.53  thf(fact_2319_order__le__less__subst2,axiom,
% 0.29/0.53      ! [A: rat,B: rat,F2: rat > int,C: int] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.53       => ( ( ord_less_int @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_subst2
% 0.29/0.53  thf(fact_2320_order__le__less__subst2,axiom,
% 0.29/0.53      ! [A: nat,B: nat,F2: nat > literal,C: literal] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_literal @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_subst2
% 0.29/0.53  thf(fact_2321_order__le__less__subst2,axiom,
% 0.29/0.53      ! [A: nat,B: nat,F2: nat > rat,C: rat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_rat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_subst2
% 0.29/0.53  thf(fact_2322_order__le__less__subst2,axiom,
% 0.29/0.53      ! [A: nat,B: nat,F2: nat > nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_nat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_subst2
% 0.29/0.53  thf(fact_2323_order__le__less__subst2,axiom,
% 0.29/0.53      ! [A: nat,B: nat,F2: nat > int,C: int] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_int @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_subst2
% 0.29/0.53  thf(fact_2324_order__le__less__subst2,axiom,
% 0.29/0.53      ! [A: int,B: int,F2: int > literal,C: literal] :
% 0.29/0.53        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.53       => ( ( ord_less_literal @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_subst2
% 0.29/0.53  thf(fact_2325_order__le__less__subst2,axiom,
% 0.29/0.53      ! [A: int,B: int,F2: int > rat,C: rat] :
% 0.29/0.53        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.53       => ( ( ord_less_rat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_subst2
% 0.29/0.53  thf(fact_2326_order__le__less__subst1,axiom,
% 0.29/0.53      ! [A: literal,F2: literal > literal,B: literal,C: literal] :
% 0.29/0.53        ( ( ord_less_eq_literal @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_literal @ B @ C )
% 0.29/0.53         => ( ! [X2: literal,Y2: literal] :
% 0.29/0.53                ( ( ord_less_literal @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_subst1
% 0.29/0.53  thf(fact_2327_order__le__less__subst1,axiom,
% 0.29/0.53      ! [A: literal,F2: rat > literal,B: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_eq_literal @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_rat @ B @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_subst1
% 0.29/0.53  thf(fact_2328_order__le__less__subst1,axiom,
% 0.29/0.53      ! [A: literal,F2: nat > literal,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_literal @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_nat @ B @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_subst1
% 0.29/0.53  thf(fact_2329_order__le__less__subst1,axiom,
% 0.29/0.53      ! [A: literal,F2: int > literal,B: int,C: int] :
% 0.29/0.53        ( ( ord_less_eq_literal @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_int @ B @ C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_subst1
% 0.29/0.53  thf(fact_2330_order__le__less__subst1,axiom,
% 0.29/0.53      ! [A: rat,F2: literal > rat,B: literal,C: literal] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_literal @ B @ C )
% 0.29/0.53         => ( ! [X2: literal,Y2: literal] :
% 0.29/0.53                ( ( ord_less_literal @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_subst1
% 0.29/0.53  thf(fact_2331_order__le__less__subst1,axiom,
% 0.29/0.53      ! [A: rat,F2: rat > rat,B: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_rat @ B @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_subst1
% 0.29/0.53  thf(fact_2332_order__le__less__subst1,axiom,
% 0.29/0.53      ! [A: rat,F2: nat > rat,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_nat @ B @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_subst1
% 0.29/0.53  thf(fact_2333_order__le__less__subst1,axiom,
% 0.29/0.53      ! [A: rat,F2: int > rat,B: int,C: int] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_int @ B @ C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_subst1
% 0.29/0.53  thf(fact_2334_order__le__less__subst1,axiom,
% 0.29/0.53      ! [A: nat,F2: literal > nat,B: literal,C: literal] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_literal @ B @ C )
% 0.29/0.53         => ( ! [X2: literal,Y2: literal] :
% 0.29/0.53                ( ( ord_less_literal @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_subst1
% 0.29/0.53  thf(fact_2335_order__le__less__subst1,axiom,
% 0.29/0.53      ! [A: nat,F2: rat > nat,B: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_rat @ B @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_subst1
% 0.29/0.53  thf(fact_2336_linorder__less__linear,axiom,
% 0.29/0.53      ! [X: literal,Y: literal] :
% 0.29/0.53        ( ( ord_less_literal @ X @ Y )
% 0.29/0.53        | ( X = Y )
% 0.29/0.53        | ( ord_less_literal @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_less_linear
% 0.29/0.53  thf(fact_2337_linorder__less__linear,axiom,
% 0.29/0.53      ! [X: rat,Y: rat] :
% 0.29/0.53        ( ( ord_less_rat @ X @ Y )
% 0.29/0.53        | ( X = Y )
% 0.29/0.53        | ( ord_less_rat @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_less_linear
% 0.29/0.53  thf(fact_2338_linorder__less__linear,axiom,
% 0.29/0.53      ! [X: nat,Y: nat] :
% 0.29/0.53        ( ( ord_less_nat @ X @ Y )
% 0.29/0.53        | ( X = Y )
% 0.29/0.53        | ( ord_less_nat @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_less_linear
% 0.29/0.53  thf(fact_2339_linorder__less__linear,axiom,
% 0.29/0.53      ! [X: int,Y: int] :
% 0.29/0.53        ( ( ord_less_int @ X @ Y )
% 0.29/0.53        | ( X = Y )
% 0.29/0.53        | ( ord_less_int @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_less_linear
% 0.29/0.53  thf(fact_2340_order__less__le__trans,axiom,
% 0.29/0.53      ! [X: literal,Y: literal,Z: literal] :
% 0.29/0.53        ( ( ord_less_literal @ X @ Y )
% 0.29/0.53       => ( ( ord_less_eq_literal @ Y @ Z )
% 0.29/0.53         => ( ord_less_literal @ X @ Z ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_trans
% 0.29/0.53  thf(fact_2341_order__less__le__trans,axiom,
% 0.29/0.53      ! [X: filter_nat,Y: filter_nat,Z: filter_nat] :
% 0.29/0.53        ( ( ord_less_filter_nat @ X @ Y )
% 0.29/0.53       => ( ( ord_le2510731241096832064er_nat @ Y @ Z )
% 0.29/0.53         => ( ord_less_filter_nat @ X @ Z ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_trans
% 0.29/0.53  thf(fact_2342_order__less__le__trans,axiom,
% 0.29/0.53      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.29/0.53        ( ( ord_less_set_nat @ X @ Y )
% 0.29/0.53       => ( ( ord_less_eq_set_nat @ Y @ Z )
% 0.29/0.53         => ( ord_less_set_nat @ X @ Z ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_trans
% 0.29/0.53  thf(fact_2343_order__less__le__trans,axiom,
% 0.29/0.53      ! [X: rat,Y: rat,Z: rat] :
% 0.29/0.53        ( ( ord_less_rat @ X @ Y )
% 0.29/0.53       => ( ( ord_less_eq_rat @ Y @ Z )
% 0.29/0.53         => ( ord_less_rat @ X @ Z ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_trans
% 0.29/0.53  thf(fact_2344_order__less__le__trans,axiom,
% 0.29/0.53      ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.53        ( ( ord_less_nat @ X @ Y )
% 0.29/0.53       => ( ( ord_less_eq_nat @ Y @ Z )
% 0.29/0.53         => ( ord_less_nat @ X @ Z ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_trans
% 0.29/0.53  thf(fact_2345_order__less__le__trans,axiom,
% 0.29/0.53      ! [X: int,Y: int,Z: int] :
% 0.29/0.53        ( ( ord_less_int @ X @ Y )
% 0.29/0.53       => ( ( ord_less_eq_int @ Y @ Z )
% 0.29/0.53         => ( ord_less_int @ X @ Z ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le_trans
% 0.29/0.53  thf(fact_2346_order__less__imp__triv,axiom,
% 0.29/0.53      ! [X: literal,Y: literal,P: $o] :
% 0.29/0.53        ( ( ord_less_literal @ X @ Y )
% 0.29/0.53       => ( ( ord_less_literal @ Y @ X )
% 0.29/0.53         => P ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_triv
% 0.29/0.53  thf(fact_2347_order__less__imp__triv,axiom,
% 0.29/0.53      ! [X: rat,Y: rat,P: $o] :
% 0.29/0.53        ( ( ord_less_rat @ X @ Y )
% 0.29/0.53       => ( ( ord_less_rat @ Y @ X )
% 0.29/0.53         => P ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_triv
% 0.29/0.53  thf(fact_2348_order__less__imp__triv,axiom,
% 0.29/0.53      ! [X: nat,Y: nat,P: $o] :
% 0.29/0.53        ( ( ord_less_nat @ X @ Y )
% 0.29/0.53       => ( ( ord_less_nat @ Y @ X )
% 0.29/0.53         => P ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_triv
% 0.29/0.53  thf(fact_2349_order__less__imp__triv,axiom,
% 0.29/0.53      ! [X: int,Y: int,P: $o] :
% 0.29/0.53        ( ( ord_less_int @ X @ Y )
% 0.29/0.53       => ( ( ord_less_int @ Y @ X )
% 0.29/0.53         => P ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_triv
% 0.29/0.53  thf(fact_2350_order__le__less__trans,axiom,
% 0.29/0.53      ! [X: literal,Y: literal,Z: literal] :
% 0.29/0.53        ( ( ord_less_eq_literal @ X @ Y )
% 0.29/0.53       => ( ( ord_less_literal @ Y @ Z )
% 0.29/0.53         => ( ord_less_literal @ X @ Z ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_trans
% 0.29/0.53  thf(fact_2351_order__le__less__trans,axiom,
% 0.29/0.53      ! [X: filter_nat,Y: filter_nat,Z: filter_nat] :
% 0.29/0.53        ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 0.29/0.53       => ( ( ord_less_filter_nat @ Y @ Z )
% 0.29/0.53         => ( ord_less_filter_nat @ X @ Z ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_trans
% 0.29/0.53  thf(fact_2352_order__le__less__trans,axiom,
% 0.29/0.53      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.29/0.53        ( ( ord_less_eq_set_nat @ X @ Y )
% 0.29/0.53       => ( ( ord_less_set_nat @ Y @ Z )
% 0.29/0.53         => ( ord_less_set_nat @ X @ Z ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_trans
% 0.29/0.53  thf(fact_2353_order__le__less__trans,axiom,
% 0.29/0.53      ! [X: rat,Y: rat,Z: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.53       => ( ( ord_less_rat @ Y @ Z )
% 0.29/0.53         => ( ord_less_rat @ X @ Z ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_trans
% 0.29/0.53  thf(fact_2354_order__le__less__trans,axiom,
% 0.29/0.53      ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.53       => ( ( ord_less_nat @ Y @ Z )
% 0.29/0.53         => ( ord_less_nat @ X @ Z ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_trans
% 0.29/0.53  thf(fact_2355_order__le__less__trans,axiom,
% 0.29/0.53      ! [X: int,Y: int,Z: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.53       => ( ( ord_less_int @ Y @ Z )
% 0.29/0.53         => ( ord_less_int @ X @ Z ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less_trans
% 0.29/0.53  thf(fact_2356_order__neq__le__trans,axiom,
% 0.29/0.53      ! [A: literal,B: literal] :
% 0.29/0.53        ( ( A != B )
% 0.29/0.53       => ( ( ord_less_eq_literal @ A @ B )
% 0.29/0.53         => ( ord_less_literal @ A @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_neq_le_trans
% 0.29/0.53  thf(fact_2357_order__neq__le__trans,axiom,
% 0.29/0.53      ! [A: filter_nat,B: filter_nat] :
% 0.29/0.53        ( ( A != B )
% 0.29/0.53       => ( ( ord_le2510731241096832064er_nat @ A @ B )
% 0.29/0.53         => ( ord_less_filter_nat @ A @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_neq_le_trans
% 0.29/0.53  thf(fact_2358_order__neq__le__trans,axiom,
% 0.29/0.53      ! [A: set_nat,B: set_nat] :
% 0.29/0.53        ( ( A != B )
% 0.29/0.53       => ( ( ord_less_eq_set_nat @ A @ B )
% 0.29/0.53         => ( ord_less_set_nat @ A @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_neq_le_trans
% 0.29/0.53  thf(fact_2359_order__neq__le__trans,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( A != B )
% 0.29/0.53       => ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.53         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_neq_le_trans
% 0.29/0.53  thf(fact_2360_order__neq__le__trans,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( A != B )
% 0.29/0.53       => ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_neq_le_trans
% 0.29/0.53  thf(fact_2361_order__neq__le__trans,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( A != B )
% 0.29/0.53       => ( ( ord_less_eq_int @ A @ B )
% 0.29/0.53         => ( ord_less_int @ A @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_neq_le_trans
% 0.29/0.53  thf(fact_2362_order__less__not__sym,axiom,
% 0.29/0.53      ! [X: literal,Y: literal] :
% 0.29/0.53        ( ( ord_less_literal @ X @ Y )
% 0.29/0.53       => ~ ( ord_less_literal @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_not_sym
% 0.29/0.53  thf(fact_2363_order__less__not__sym,axiom,
% 0.29/0.53      ! [X: rat,Y: rat] :
% 0.29/0.53        ( ( ord_less_rat @ X @ Y )
% 0.29/0.53       => ~ ( ord_less_rat @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_not_sym
% 0.29/0.53  thf(fact_2364_order__less__not__sym,axiom,
% 0.29/0.53      ! [X: nat,Y: nat] :
% 0.29/0.53        ( ( ord_less_nat @ X @ Y )
% 0.29/0.53       => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_not_sym
% 0.29/0.53  thf(fact_2365_order__less__not__sym,axiom,
% 0.29/0.53      ! [X: int,Y: int] :
% 0.29/0.53        ( ( ord_less_int @ X @ Y )
% 0.29/0.53       => ~ ( ord_less_int @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_not_sym
% 0.29/0.53  thf(fact_2366_order__le__neq__trans,axiom,
% 0.29/0.53      ! [A: literal,B: literal] :
% 0.29/0.53        ( ( ord_less_eq_literal @ A @ B )
% 0.29/0.53       => ( ( A != B )
% 0.29/0.53         => ( ord_less_literal @ A @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_neq_trans
% 0.29/0.53  thf(fact_2367_order__le__neq__trans,axiom,
% 0.29/0.53      ! [A: filter_nat,B: filter_nat] :
% 0.29/0.53        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 0.29/0.53       => ( ( A != B )
% 0.29/0.53         => ( ord_less_filter_nat @ A @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_neq_trans
% 0.29/0.53  thf(fact_2368_order__le__neq__trans,axiom,
% 0.29/0.53      ! [A: set_nat,B: set_nat] :
% 0.29/0.53        ( ( ord_less_eq_set_nat @ A @ B )
% 0.29/0.53       => ( ( A != B )
% 0.29/0.53         => ( ord_less_set_nat @ A @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_neq_trans
% 0.29/0.53  thf(fact_2369_order__le__neq__trans,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.53       => ( ( A != B )
% 0.29/0.53         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_neq_trans
% 0.29/0.53  thf(fact_2370_order__le__neq__trans,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( A != B )
% 0.29/0.53         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_neq_trans
% 0.29/0.53  thf(fact_2371_order__le__neq__trans,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.53       => ( ( A != B )
% 0.29/0.53         => ( ord_less_int @ A @ B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_neq_trans
% 0.29/0.53  thf(fact_2372_order__antisym__conv,axiom,
% 0.29/0.53      ! [Y: filter_nat,X: filter_nat] :
% 0.29/0.53        ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 0.29/0.53       => ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 0.29/0.53          = ( X = Y ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_antisym_conv
% 0.29/0.53  thf(fact_2373_order__antisym__conv,axiom,
% 0.29/0.53      ! [Y: set_nat,X: set_nat] :
% 0.29/0.53        ( ( ord_less_eq_set_nat @ Y @ X )
% 0.29/0.53       => ( ( ord_less_eq_set_nat @ X @ Y )
% 0.29/0.53          = ( X = Y ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_antisym_conv
% 0.29/0.53  thf(fact_2374_order__antisym__conv,axiom,
% 0.29/0.53      ! [Y: rat,X: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ Y @ X )
% 0.29/0.53       => ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.53          = ( X = Y ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_antisym_conv
% 0.29/0.53  thf(fact_2375_order__antisym__conv,axiom,
% 0.29/0.53      ! [Y: nat,X: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ Y @ X )
% 0.29/0.53       => ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.53          = ( X = Y ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_antisym_conv
% 0.29/0.53  thf(fact_2376_order__antisym__conv,axiom,
% 0.29/0.53      ! [Y: int,X: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ Y @ X )
% 0.29/0.53       => ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.53          = ( X = Y ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_antisym_conv
% 0.29/0.53  thf(fact_2377_order__less__subst2,axiom,
% 0.29/0.53      ! [A: literal,B: literal,F2: literal > literal,C: literal] :
% 0.29/0.53        ( ( ord_less_literal @ A @ B )
% 0.29/0.53       => ( ( ord_less_literal @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: literal,Y2: literal] :
% 0.29/0.53                ( ( ord_less_literal @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_subst2
% 0.29/0.53  thf(fact_2378_order__less__subst2,axiom,
% 0.29/0.53      ! [A: literal,B: literal,F2: literal > rat,C: rat] :
% 0.29/0.53        ( ( ord_less_literal @ A @ B )
% 0.29/0.53       => ( ( ord_less_rat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: literal,Y2: literal] :
% 0.29/0.53                ( ( ord_less_literal @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_subst2
% 0.29/0.53  thf(fact_2379_order__less__subst2,axiom,
% 0.29/0.53      ! [A: literal,B: literal,F2: literal > nat,C: nat] :
% 0.29/0.53        ( ( ord_less_literal @ A @ B )
% 0.29/0.53       => ( ( ord_less_nat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: literal,Y2: literal] :
% 0.29/0.53                ( ( ord_less_literal @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_subst2
% 0.29/0.53  thf(fact_2380_order__less__subst2,axiom,
% 0.29/0.53      ! [A: literal,B: literal,F2: literal > int,C: int] :
% 0.29/0.53        ( ( ord_less_literal @ A @ B )
% 0.29/0.53       => ( ( ord_less_int @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: literal,Y2: literal] :
% 0.29/0.53                ( ( ord_less_literal @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_subst2
% 0.29/0.53  thf(fact_2381_order__less__subst2,axiom,
% 0.29/0.53      ! [A: rat,B: rat,F2: rat > literal,C: literal] :
% 0.29/0.53        ( ( ord_less_rat @ A @ B )
% 0.29/0.53       => ( ( ord_less_literal @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_subst2
% 0.29/0.53  thf(fact_2382_order__less__subst2,axiom,
% 0.29/0.53      ! [A: rat,B: rat,F2: rat > rat,C: rat] :
% 0.29/0.53        ( ( ord_less_rat @ A @ B )
% 0.29/0.53       => ( ( ord_less_rat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_subst2
% 0.29/0.53  thf(fact_2383_order__less__subst2,axiom,
% 0.29/0.53      ! [A: rat,B: rat,F2: rat > nat,C: nat] :
% 0.29/0.53        ( ( ord_less_rat @ A @ B )
% 0.29/0.53       => ( ( ord_less_nat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_subst2
% 0.29/0.53  thf(fact_2384_order__less__subst2,axiom,
% 0.29/0.53      ! [A: rat,B: rat,F2: rat > int,C: int] :
% 0.29/0.53        ( ( ord_less_rat @ A @ B )
% 0.29/0.53       => ( ( ord_less_int @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_subst2
% 0.29/0.53  thf(fact_2385_order__less__subst2,axiom,
% 0.29/0.53      ! [A: nat,B: nat,F2: nat > literal,C: literal] :
% 0.29/0.53        ( ( ord_less_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_literal @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_subst2
% 0.29/0.53  thf(fact_2386_order__less__subst2,axiom,
% 0.29/0.53      ! [A: nat,B: nat,F2: nat > rat,C: rat] :
% 0.29/0.53        ( ( ord_less_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_rat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_subst2
% 0.29/0.53  thf(fact_2387_order__less__subst1,axiom,
% 0.29/0.53      ! [A: literal,F2: literal > literal,B: literal,C: literal] :
% 0.29/0.53        ( ( ord_less_literal @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_literal @ B @ C )
% 0.29/0.53         => ( ! [X2: literal,Y2: literal] :
% 0.29/0.53                ( ( ord_less_literal @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_subst1
% 0.29/0.53  thf(fact_2388_order__less__subst1,axiom,
% 0.29/0.53      ! [A: literal,F2: rat > literal,B: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_literal @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_rat @ B @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_subst1
% 0.29/0.53  thf(fact_2389_order__less__subst1,axiom,
% 0.29/0.53      ! [A: literal,F2: nat > literal,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_literal @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_nat @ B @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_subst1
% 0.29/0.53  thf(fact_2390_order__less__subst1,axiom,
% 0.29/0.53      ! [A: literal,F2: int > literal,B: int,C: int] :
% 0.29/0.53        ( ( ord_less_literal @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_int @ B @ C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_subst1
% 0.29/0.53  thf(fact_2391_order__less__subst1,axiom,
% 0.29/0.53      ! [A: rat,F2: literal > rat,B: literal,C: literal] :
% 0.29/0.53        ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_literal @ B @ C )
% 0.29/0.53         => ( ! [X2: literal,Y2: literal] :
% 0.29/0.53                ( ( ord_less_literal @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_subst1
% 0.29/0.53  thf(fact_2392_order__less__subst1,axiom,
% 0.29/0.53      ! [A: rat,F2: rat > rat,B: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_rat @ B @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_subst1
% 0.29/0.53  thf(fact_2393_order__less__subst1,axiom,
% 0.29/0.53      ! [A: rat,F2: nat > rat,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_nat @ B @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_subst1
% 0.29/0.53  thf(fact_2394_order__less__subst1,axiom,
% 0.29/0.53      ! [A: rat,F2: int > rat,B: int,C: int] :
% 0.29/0.53        ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_int @ B @ C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_subst1
% 0.29/0.53  thf(fact_2395_order__less__subst1,axiom,
% 0.29/0.53      ! [A: nat,F2: literal > nat,B: literal,C: literal] :
% 0.29/0.53        ( ( ord_less_nat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_literal @ B @ C )
% 0.29/0.53         => ( ! [X2: literal,Y2: literal] :
% 0.29/0.53                ( ( ord_less_literal @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_subst1
% 0.29/0.53  thf(fact_2396_order__less__subst1,axiom,
% 0.29/0.53      ! [A: nat,F2: rat > nat,B: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_nat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_rat @ B @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_subst1
% 0.29/0.53  thf(fact_2397_order__less__irrefl,axiom,
% 0.29/0.53      ! [X: literal] :
% 0.29/0.53        ~ ( ord_less_literal @ X @ X ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_irrefl
% 0.29/0.53  thf(fact_2398_order__less__irrefl,axiom,
% 0.29/0.53      ! [X: rat] :
% 0.29/0.53        ~ ( ord_less_rat @ X @ X ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_irrefl
% 0.29/0.53  thf(fact_2399_order__less__irrefl,axiom,
% 0.29/0.53      ! [X: nat] :
% 0.29/0.53        ~ ( ord_less_nat @ X @ X ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_irrefl
% 0.29/0.53  thf(fact_2400_order__less__irrefl,axiom,
% 0.29/0.53      ! [X: int] :
% 0.29/0.53        ~ ( ord_less_int @ X @ X ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_irrefl
% 0.29/0.53  thf(fact_2401_order__less__imp__le,axiom,
% 0.29/0.53      ! [X: literal,Y: literal] :
% 0.29/0.53        ( ( ord_less_literal @ X @ Y )
% 0.29/0.53       => ( ord_less_eq_literal @ X @ Y ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_le
% 0.29/0.53  thf(fact_2402_order__less__imp__le,axiom,
% 0.29/0.53      ! [X: filter_nat,Y: filter_nat] :
% 0.29/0.53        ( ( ord_less_filter_nat @ X @ Y )
% 0.29/0.53       => ( ord_le2510731241096832064er_nat @ X @ Y ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_le
% 0.29/0.53  thf(fact_2403_order__less__imp__le,axiom,
% 0.29/0.53      ! [X: set_nat,Y: set_nat] :
% 0.29/0.53        ( ( ord_less_set_nat @ X @ Y )
% 0.29/0.53       => ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_le
% 0.29/0.53  thf(fact_2404_order__less__imp__le,axiom,
% 0.29/0.53      ! [X: rat,Y: rat] :
% 0.29/0.53        ( ( ord_less_rat @ X @ Y )
% 0.29/0.53       => ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_le
% 0.29/0.53  thf(fact_2405_order__less__imp__le,axiom,
% 0.29/0.53      ! [X: nat,Y: nat] :
% 0.29/0.53        ( ( ord_less_nat @ X @ Y )
% 0.29/0.53       => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_le
% 0.29/0.53  thf(fact_2406_order__less__imp__le,axiom,
% 0.29/0.53      ! [X: int,Y: int] :
% 0.29/0.53        ( ( ord_less_int @ X @ Y )
% 0.29/0.53       => ( ord_less_eq_int @ X @ Y ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_imp_le
% 0.29/0.53  thf(fact_2407_ord__less__eq__subst,axiom,
% 0.29/0.53      ! [A: literal,B: literal,F2: literal > literal,C: literal] :
% 0.29/0.53        ( ( ord_less_literal @ A @ B )
% 0.29/0.53       => ( ( ( F2 @ B )
% 0.29/0.53            = C )
% 0.29/0.53         => ( ! [X2: literal,Y2: literal] :
% 0.29/0.53                ( ( ord_less_literal @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_less_eq_subst
% 0.29/0.53  thf(fact_2408_ord__less__eq__subst,axiom,
% 0.29/0.53      ! [A: literal,B: literal,F2: literal > rat,C: rat] :
% 0.29/0.53        ( ( ord_less_literal @ A @ B )
% 0.29/0.53       => ( ( ( F2 @ B )
% 0.29/0.53            = C )
% 0.29/0.53         => ( ! [X2: literal,Y2: literal] :
% 0.29/0.53                ( ( ord_less_literal @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_less_eq_subst
% 0.29/0.53  thf(fact_2409_ord__less__eq__subst,axiom,
% 0.29/0.53      ! [A: literal,B: literal,F2: literal > nat,C: nat] :
% 0.29/0.53        ( ( ord_less_literal @ A @ B )
% 0.29/0.53       => ( ( ( F2 @ B )
% 0.29/0.53            = C )
% 0.29/0.53         => ( ! [X2: literal,Y2: literal] :
% 0.29/0.53                ( ( ord_less_literal @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_less_eq_subst
% 0.29/0.53  thf(fact_2410_ord__less__eq__subst,axiom,
% 0.29/0.53      ! [A: literal,B: literal,F2: literal > int,C: int] :
% 0.29/0.53        ( ( ord_less_literal @ A @ B )
% 0.29/0.53       => ( ( ( F2 @ B )
% 0.29/0.53            = C )
% 0.29/0.53         => ( ! [X2: literal,Y2: literal] :
% 0.29/0.53                ( ( ord_less_literal @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_less_eq_subst
% 0.29/0.53  thf(fact_2411_ord__less__eq__subst,axiom,
% 0.29/0.53      ! [A: rat,B: rat,F2: rat > literal,C: literal] :
% 0.29/0.53        ( ( ord_less_rat @ A @ B )
% 0.29/0.53       => ( ( ( F2 @ B )
% 0.29/0.53            = C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_less_eq_subst
% 0.29/0.53  thf(fact_2412_ord__less__eq__subst,axiom,
% 0.29/0.53      ! [A: rat,B: rat,F2: rat > rat,C: rat] :
% 0.29/0.53        ( ( ord_less_rat @ A @ B )
% 0.29/0.53       => ( ( ( F2 @ B )
% 0.29/0.53            = C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_less_eq_subst
% 0.29/0.53  thf(fact_2413_ord__less__eq__subst,axiom,
% 0.29/0.53      ! [A: rat,B: rat,F2: rat > nat,C: nat] :
% 0.29/0.53        ( ( ord_less_rat @ A @ B )
% 0.29/0.53       => ( ( ( F2 @ B )
% 0.29/0.53            = C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_less_eq_subst
% 0.29/0.53  thf(fact_2414_ord__less__eq__subst,axiom,
% 0.29/0.53      ! [A: rat,B: rat,F2: rat > int,C: int] :
% 0.29/0.53        ( ( ord_less_rat @ A @ B )
% 0.29/0.53       => ( ( ( F2 @ B )
% 0.29/0.53            = C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_less_eq_subst
% 0.29/0.53  thf(fact_2415_ord__less__eq__subst,axiom,
% 0.29/0.53      ! [A: nat,B: nat,F2: nat > literal,C: literal] :
% 0.29/0.53        ( ( ord_less_nat @ A @ B )
% 0.29/0.53       => ( ( ( F2 @ B )
% 0.29/0.53            = C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_less_eq_subst
% 0.29/0.53  thf(fact_2416_ord__less__eq__subst,axiom,
% 0.29/0.53      ! [A: nat,B: nat,F2: nat > rat,C: rat] :
% 0.29/0.53        ( ( ord_less_nat @ A @ B )
% 0.29/0.53       => ( ( ( F2 @ B )
% 0.29/0.53            = C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_less_eq_subst
% 0.29/0.53  thf(fact_2417_ord__eq__less__subst,axiom,
% 0.29/0.53      ! [A: literal,F2: literal > literal,B: literal,C: literal] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_literal @ B @ C )
% 0.29/0.53         => ( ! [X2: literal,Y2: literal] :
% 0.29/0.53                ( ( ord_less_literal @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_eq_less_subst
% 0.29/0.53  thf(fact_2418_ord__eq__less__subst,axiom,
% 0.29/0.53      ! [A: rat,F2: literal > rat,B: literal,C: literal] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_literal @ B @ C )
% 0.29/0.53         => ( ! [X2: literal,Y2: literal] :
% 0.29/0.53                ( ( ord_less_literal @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_eq_less_subst
% 0.29/0.53  thf(fact_2419_ord__eq__less__subst,axiom,
% 0.29/0.53      ! [A: nat,F2: literal > nat,B: literal,C: literal] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_literal @ B @ C )
% 0.29/0.53         => ( ! [X2: literal,Y2: literal] :
% 0.29/0.53                ( ( ord_less_literal @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_eq_less_subst
% 0.29/0.53  thf(fact_2420_ord__eq__less__subst,axiom,
% 0.29/0.53      ! [A: int,F2: literal > int,B: literal,C: literal] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_literal @ B @ C )
% 0.29/0.53         => ( ! [X2: literal,Y2: literal] :
% 0.29/0.53                ( ( ord_less_literal @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_eq_less_subst
% 0.29/0.53  thf(fact_2421_ord__eq__less__subst,axiom,
% 0.29/0.53      ! [A: literal,F2: rat > literal,B: rat,C: rat] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_rat @ B @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_eq_less_subst
% 0.29/0.53  thf(fact_2422_ord__eq__less__subst,axiom,
% 0.29/0.53      ! [A: rat,F2: rat > rat,B: rat,C: rat] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_rat @ B @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_eq_less_subst
% 0.29/0.53  thf(fact_2423_ord__eq__less__subst,axiom,
% 0.29/0.53      ! [A: nat,F2: rat > nat,B: rat,C: rat] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_rat @ B @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_eq_less_subst
% 0.29/0.53  thf(fact_2424_ord__eq__less__subst,axiom,
% 0.29/0.53      ! [A: int,F2: rat > int,B: rat,C: rat] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_rat @ B @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_eq_less_subst
% 0.29/0.53  thf(fact_2425_ord__eq__less__subst,axiom,
% 0.29/0.53      ! [A: literal,F2: nat > literal,B: nat,C: nat] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_nat @ B @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_eq_less_subst
% 0.29/0.53  thf(fact_2426_ord__eq__less__subst,axiom,
% 0.29/0.53      ! [A: rat,F2: nat > rat,B: nat,C: nat] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_nat @ B @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_eq_less_subst
% 0.29/0.53  thf(fact_2427_linorder__not__less,axiom,
% 0.29/0.53      ! [X: literal,Y: literal] :
% 0.29/0.53        ( ( ~ ( ord_less_literal @ X @ Y ) )
% 0.29/0.53        = ( ord_less_eq_literal @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_not_less
% 0.29/0.53  thf(fact_2428_linorder__not__less,axiom,
% 0.29/0.53      ! [X: rat,Y: rat] :
% 0.29/0.53        ( ( ~ ( ord_less_rat @ X @ Y ) )
% 0.29/0.53        = ( ord_less_eq_rat @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_not_less
% 0.29/0.53  thf(fact_2429_linorder__not__less,axiom,
% 0.29/0.53      ! [X: nat,Y: nat] :
% 0.29/0.53        ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.29/0.53        = ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_not_less
% 0.29/0.53  thf(fact_2430_linorder__not__less,axiom,
% 0.29/0.53      ! [X: int,Y: int] :
% 0.29/0.53        ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.29/0.53        = ( ord_less_eq_int @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_not_less
% 0.29/0.53  thf(fact_2431_linorder__le__cases,axiom,
% 0.29/0.53      ! [X: rat,Y: rat] :
% 0.29/0.53        ( ~ ( ord_less_eq_rat @ X @ Y )
% 0.29/0.53       => ( ord_less_eq_rat @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_le_cases
% 0.29/0.53  thf(fact_2432_linorder__le__cases,axiom,
% 0.29/0.53      ! [X: nat,Y: nat] :
% 0.29/0.53        ( ~ ( ord_less_eq_nat @ X @ Y )
% 0.29/0.53       => ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_le_cases
% 0.29/0.53  thf(fact_2433_linorder__le__cases,axiom,
% 0.29/0.53      ! [X: int,Y: int] :
% 0.29/0.53        ( ~ ( ord_less_eq_int @ X @ Y )
% 0.29/0.53       => ( ord_less_eq_int @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_le_cases
% 0.29/0.53  thf(fact_2434_order__less__trans,axiom,
% 0.29/0.53      ! [X: literal,Y: literal,Z: literal] :
% 0.29/0.53        ( ( ord_less_literal @ X @ Y )
% 0.29/0.53       => ( ( ord_less_literal @ Y @ Z )
% 0.29/0.53         => ( ord_less_literal @ X @ Z ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_trans
% 0.29/0.53  thf(fact_2435_order__less__trans,axiom,
% 0.29/0.53      ! [X: rat,Y: rat,Z: rat] :
% 0.29/0.53        ( ( ord_less_rat @ X @ Y )
% 0.29/0.53       => ( ( ord_less_rat @ Y @ Z )
% 0.29/0.53         => ( ord_less_rat @ X @ Z ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_trans
% 0.29/0.53  thf(fact_2436_order__less__trans,axiom,
% 0.29/0.53      ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.53        ( ( ord_less_nat @ X @ Y )
% 0.29/0.53       => ( ( ord_less_nat @ Y @ Z )
% 0.29/0.53         => ( ord_less_nat @ X @ Z ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_trans
% 0.29/0.53  thf(fact_2437_order__less__trans,axiom,
% 0.29/0.53      ! [X: int,Y: int,Z: int] :
% 0.29/0.53        ( ( ord_less_int @ X @ Y )
% 0.29/0.53       => ( ( ord_less_int @ Y @ Z )
% 0.29/0.53         => ( ord_less_int @ X @ Z ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_trans
% 0.29/0.53  thf(fact_2438_order__less__asym_H,axiom,
% 0.29/0.53      ! [A: literal,B: literal] :
% 0.29/0.53        ( ( ord_less_literal @ A @ B )
% 0.29/0.53       => ~ ( ord_less_literal @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_asym'
% 0.29/0.53  thf(fact_2439_order__less__asym_H,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( ord_less_rat @ A @ B )
% 0.29/0.53       => ~ ( ord_less_rat @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_asym'
% 0.29/0.53  thf(fact_2440_order__less__asym_H,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( ord_less_nat @ A @ B )
% 0.29/0.53       => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_asym'
% 0.29/0.53  thf(fact_2441_order__less__asym_H,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( ord_less_int @ A @ B )
% 0.29/0.53       => ~ ( ord_less_int @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_asym'
% 0.29/0.53  thf(fact_2442_linorder__neq__iff,axiom,
% 0.29/0.53      ! [X: literal,Y: literal] :
% 0.29/0.53        ( ( X != Y )
% 0.29/0.53        = ( ( ord_less_literal @ X @ Y )
% 0.29/0.53          | ( ord_less_literal @ Y @ X ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_neq_iff
% 0.29/0.53  thf(fact_2443_linorder__neq__iff,axiom,
% 0.29/0.53      ! [X: rat,Y: rat] :
% 0.29/0.53        ( ( X != Y )
% 0.29/0.53        = ( ( ord_less_rat @ X @ Y )
% 0.29/0.53          | ( ord_less_rat @ Y @ X ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_neq_iff
% 0.29/0.53  thf(fact_2444_linorder__neq__iff,axiom,
% 0.29/0.53      ! [X: nat,Y: nat] :
% 0.29/0.53        ( ( X != Y )
% 0.29/0.53        = ( ( ord_less_nat @ X @ Y )
% 0.29/0.53          | ( ord_less_nat @ Y @ X ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_neq_iff
% 0.29/0.53  thf(fact_2445_linorder__neq__iff,axiom,
% 0.29/0.53      ! [X: int,Y: int] :
% 0.29/0.53        ( ( X != Y )
% 0.29/0.53        = ( ( ord_less_int @ X @ Y )
% 0.29/0.53          | ( ord_less_int @ Y @ X ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_neq_iff
% 0.29/0.53  thf(fact_2446_order__less__asym,axiom,
% 0.29/0.53      ! [X: literal,Y: literal] :
% 0.29/0.53        ( ( ord_less_literal @ X @ Y )
% 0.29/0.53       => ~ ( ord_less_literal @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_asym
% 0.29/0.53  thf(fact_2447_order__less__asym,axiom,
% 0.29/0.53      ! [X: rat,Y: rat] :
% 0.29/0.53        ( ( ord_less_rat @ X @ Y )
% 0.29/0.53       => ~ ( ord_less_rat @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_asym
% 0.29/0.53  thf(fact_2448_order__less__asym,axiom,
% 0.29/0.53      ! [X: nat,Y: nat] :
% 0.29/0.53        ( ( ord_less_nat @ X @ Y )
% 0.29/0.53       => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_asym
% 0.29/0.53  thf(fact_2449_order__less__asym,axiom,
% 0.29/0.53      ! [X: int,Y: int] :
% 0.29/0.53        ( ( ord_less_int @ X @ Y )
% 0.29/0.53       => ~ ( ord_less_int @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_asym
% 0.29/0.53  thf(fact_2450_ord__le__eq__subst,axiom,
% 0.29/0.53      ! [A: rat,B: rat,F2: rat > rat,C: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.53       => ( ( ( F2 @ B )
% 0.29/0.53            = C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_le_eq_subst
% 0.29/0.53  thf(fact_2451_ord__le__eq__subst,axiom,
% 0.29/0.53      ! [A: rat,B: rat,F2: rat > nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.53       => ( ( ( F2 @ B )
% 0.29/0.53            = C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_le_eq_subst
% 0.29/0.53  thf(fact_2452_ord__le__eq__subst,axiom,
% 0.29/0.53      ! [A: rat,B: rat,F2: rat > int,C: int] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.53       => ( ( ( F2 @ B )
% 0.29/0.53            = C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_le_eq_subst
% 0.29/0.53  thf(fact_2453_ord__le__eq__subst,axiom,
% 0.29/0.53      ! [A: nat,B: nat,F2: nat > rat,C: rat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( ( F2 @ B )
% 0.29/0.53            = C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_le_eq_subst
% 0.29/0.53  thf(fact_2454_ord__le__eq__subst,axiom,
% 0.29/0.53      ! [A: nat,B: nat,F2: nat > nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( ( F2 @ B )
% 0.29/0.53            = C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_le_eq_subst
% 0.29/0.53  thf(fact_2455_ord__le__eq__subst,axiom,
% 0.29/0.53      ! [A: nat,B: nat,F2: nat > int,C: int] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( ( F2 @ B )
% 0.29/0.53            = C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_le_eq_subst
% 0.29/0.53  thf(fact_2456_ord__le__eq__subst,axiom,
% 0.29/0.53      ! [A: int,B: int,F2: int > rat,C: rat] :
% 0.29/0.53        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.53       => ( ( ( F2 @ B )
% 0.29/0.53            = C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_le_eq_subst
% 0.29/0.53  thf(fact_2457_ord__le__eq__subst,axiom,
% 0.29/0.53      ! [A: int,B: int,F2: int > nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.53       => ( ( ( F2 @ B )
% 0.29/0.53            = C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_le_eq_subst
% 0.29/0.53  thf(fact_2458_ord__le__eq__subst,axiom,
% 0.29/0.53      ! [A: int,B: int,F2: int > int,C: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.53       => ( ( ( F2 @ B )
% 0.29/0.53            = C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_le_eq_subst
% 0.29/0.53  thf(fact_2459_ord__le__eq__subst,axiom,
% 0.29/0.53      ! [A: filter_nat,B: filter_nat,F2: filter_nat > rat,C: rat] :
% 0.29/0.53        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 0.29/0.53       => ( ( ( F2 @ B )
% 0.29/0.53            = C )
% 0.29/0.53         => ( ! [X2: filter_nat,Y2: filter_nat] :
% 0.29/0.53                ( ( ord_le2510731241096832064er_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_le_eq_subst
% 0.29/0.53  thf(fact_2460_ord__eq__le__subst,axiom,
% 0.29/0.53      ! [A: rat,F2: rat > rat,B: rat,C: rat] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_eq_le_subst
% 0.29/0.53  thf(fact_2461_ord__eq__le__subst,axiom,
% 0.29/0.53      ! [A: nat,F2: rat > nat,B: rat,C: rat] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_eq_le_subst
% 0.29/0.53  thf(fact_2462_ord__eq__le__subst,axiom,
% 0.29/0.53      ! [A: int,F2: rat > int,B: rat,C: rat] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_eq_le_subst
% 0.29/0.53  thf(fact_2463_ord__eq__le__subst,axiom,
% 0.29/0.53      ! [A: rat,F2: nat > rat,B: nat,C: nat] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_eq_le_subst
% 0.29/0.53  thf(fact_2464_ord__eq__le__subst,axiom,
% 0.29/0.53      ! [A: nat,F2: nat > nat,B: nat,C: nat] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_eq_le_subst
% 0.29/0.53  thf(fact_2465_ord__eq__le__subst,axiom,
% 0.29/0.53      ! [A: int,F2: nat > int,B: nat,C: nat] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_eq_le_subst
% 0.29/0.53  thf(fact_2466_ord__eq__le__subst,axiom,
% 0.29/0.53      ! [A: rat,F2: int > rat,B: int,C: int] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_eq_le_subst
% 0.29/0.53  thf(fact_2467_ord__eq__le__subst,axiom,
% 0.29/0.53      ! [A: nat,F2: int > nat,B: int,C: int] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_eq_le_subst
% 0.29/0.53  thf(fact_2468_ord__eq__le__subst,axiom,
% 0.29/0.53      ! [A: int,F2: int > int,B: int,C: int] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_eq_le_subst
% 0.29/0.53  thf(fact_2469_ord__eq__le__subst,axiom,
% 0.29/0.53      ! [A: rat,F2: filter_nat > rat,B: filter_nat,C: filter_nat] :
% 0.29/0.53        ( ( A
% 0.29/0.53          = ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_le2510731241096832064er_nat @ B @ C )
% 0.29/0.53         => ( ! [X2: filter_nat,Y2: filter_nat] :
% 0.29/0.53                ( ( ord_le2510731241096832064er_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % ord_eq_le_subst
% 0.29/0.53  thf(fact_2470_linorder__not__le,axiom,
% 0.29/0.53      ! [X: literal,Y: literal] :
% 0.29/0.53        ( ( ~ ( ord_less_eq_literal @ X @ Y ) )
% 0.29/0.53        = ( ord_less_literal @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_not_le
% 0.29/0.53  thf(fact_2471_linorder__not__le,axiom,
% 0.29/0.53      ! [X: rat,Y: rat] :
% 0.29/0.53        ( ( ~ ( ord_less_eq_rat @ X @ Y ) )
% 0.29/0.53        = ( ord_less_rat @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_not_le
% 0.29/0.53  thf(fact_2472_linorder__not__le,axiom,
% 0.29/0.53      ! [X: nat,Y: nat] :
% 0.29/0.53        ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 0.29/0.53        = ( ord_less_nat @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_not_le
% 0.29/0.53  thf(fact_2473_linorder__not__le,axiom,
% 0.29/0.53      ! [X: int,Y: int] :
% 0.29/0.53        ( ( ~ ( ord_less_eq_int @ X @ Y ) )
% 0.29/0.53        = ( ord_less_int @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_not_le
% 0.29/0.53  thf(fact_2474_linorder__linear,axiom,
% 0.29/0.53      ! [X: rat,Y: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.53        | ( ord_less_eq_rat @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_linear
% 0.29/0.53  thf(fact_2475_linorder__linear,axiom,
% 0.29/0.53      ! [X: nat,Y: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.53        | ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_linear
% 0.29/0.53  thf(fact_2476_linorder__linear,axiom,
% 0.29/0.53      ! [X: int,Y: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.53        | ( ord_less_eq_int @ Y @ X ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_linear
% 0.29/0.53  thf(fact_2477_order__less__le,axiom,
% 0.29/0.53      ( ord_less_literal
% 0.29/0.53      = ( ^ [X3: literal,Y3: literal] :
% 0.29/0.53            ( ( ord_less_eq_literal @ X3 @ Y3 )
% 0.29/0.53            & ( X3 != Y3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le
% 0.29/0.53  thf(fact_2478_order__less__le,axiom,
% 0.29/0.53      ( ord_less_filter_nat
% 0.29/0.53      = ( ^ [X3: filter_nat,Y3: filter_nat] :
% 0.29/0.53            ( ( ord_le2510731241096832064er_nat @ X3 @ Y3 )
% 0.29/0.53            & ( X3 != Y3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le
% 0.29/0.53  thf(fact_2479_order__less__le,axiom,
% 0.29/0.53      ( ord_less_set_nat
% 0.29/0.53      = ( ^ [X3: set_nat,Y3: set_nat] :
% 0.29/0.53            ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 0.29/0.53            & ( X3 != Y3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le
% 0.29/0.53  thf(fact_2480_order__less__le,axiom,
% 0.29/0.53      ( ord_less_rat
% 0.29/0.53      = ( ^ [X3: rat,Y3: rat] :
% 0.29/0.53            ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.53            & ( X3 != Y3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le
% 0.29/0.53  thf(fact_2481_order__less__le,axiom,
% 0.29/0.53      ( ord_less_nat
% 0.29/0.53      = ( ^ [X3: nat,Y3: nat] :
% 0.29/0.53            ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.53            & ( X3 != Y3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le
% 0.29/0.53  thf(fact_2482_order__less__le,axiom,
% 0.29/0.53      ( ord_less_int
% 0.29/0.53      = ( ^ [X3: int,Y3: int] :
% 0.29/0.53            ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.29/0.53            & ( X3 != Y3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_less_le
% 0.29/0.53  thf(fact_2483_order__le__less,axiom,
% 0.29/0.53      ( ord_less_eq_literal
% 0.29/0.53      = ( ^ [X3: literal,Y3: literal] :
% 0.29/0.53            ( ( ord_less_literal @ X3 @ Y3 )
% 0.29/0.53            | ( X3 = Y3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less
% 0.29/0.53  thf(fact_2484_order__le__less,axiom,
% 0.29/0.53      ( ord_le2510731241096832064er_nat
% 0.29/0.53      = ( ^ [X3: filter_nat,Y3: filter_nat] :
% 0.29/0.53            ( ( ord_less_filter_nat @ X3 @ Y3 )
% 0.29/0.53            | ( X3 = Y3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less
% 0.29/0.53  thf(fact_2485_order__le__less,axiom,
% 0.29/0.53      ( ord_less_eq_set_nat
% 0.29/0.53      = ( ^ [X3: set_nat,Y3: set_nat] :
% 0.29/0.53            ( ( ord_less_set_nat @ X3 @ Y3 )
% 0.29/0.53            | ( X3 = Y3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less
% 0.29/0.53  thf(fact_2486_order__le__less,axiom,
% 0.29/0.53      ( ord_less_eq_rat
% 0.29/0.53      = ( ^ [X3: rat,Y3: rat] :
% 0.29/0.53            ( ( ord_less_rat @ X3 @ Y3 )
% 0.29/0.53            | ( X3 = Y3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less
% 0.29/0.53  thf(fact_2487_order__le__less,axiom,
% 0.29/0.53      ( ord_less_eq_nat
% 0.29/0.53      = ( ^ [X3: nat,Y3: nat] :
% 0.29/0.53            ( ( ord_less_nat @ X3 @ Y3 )
% 0.29/0.53            | ( X3 = Y3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less
% 0.29/0.53  thf(fact_2488_order__le__less,axiom,
% 0.29/0.53      ( ord_less_eq_int
% 0.29/0.53      = ( ^ [X3: int,Y3: int] :
% 0.29/0.53            ( ( ord_less_int @ X3 @ Y3 )
% 0.29/0.53            | ( X3 = Y3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_le_less
% 0.29/0.53  thf(fact_2489_order__eq__refl,axiom,
% 0.29/0.53      ! [X: filter_nat,Y: filter_nat] :
% 0.29/0.53        ( ( X = Y )
% 0.29/0.53       => ( ord_le2510731241096832064er_nat @ X @ Y ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_eq_refl
% 0.29/0.53  thf(fact_2490_order__eq__refl,axiom,
% 0.29/0.53      ! [X: set_nat,Y: set_nat] :
% 0.29/0.53        ( ( X = Y )
% 0.29/0.53       => ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_eq_refl
% 0.29/0.53  thf(fact_2491_order__eq__refl,axiom,
% 0.29/0.53      ! [X: rat,Y: rat] :
% 0.29/0.53        ( ( X = Y )
% 0.29/0.53       => ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_eq_refl
% 0.29/0.53  thf(fact_2492_order__eq__refl,axiom,
% 0.29/0.53      ! [X: nat,Y: nat] :
% 0.29/0.53        ( ( X = Y )
% 0.29/0.53       => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_eq_refl
% 0.29/0.53  thf(fact_2493_order__eq__refl,axiom,
% 0.29/0.53      ! [X: int,Y: int] :
% 0.29/0.53        ( ( X = Y )
% 0.29/0.53       => ( ord_less_eq_int @ X @ Y ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_eq_refl
% 0.29/0.53  thf(fact_2494_linorder__neqE,axiom,
% 0.29/0.53      ! [X: literal,Y: literal] :
% 0.29/0.53        ( ( X != Y )
% 0.29/0.53       => ( ~ ( ord_less_literal @ X @ Y )
% 0.29/0.53         => ( ord_less_literal @ Y @ X ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_neqE
% 0.29/0.53  thf(fact_2495_linorder__neqE,axiom,
% 0.29/0.53      ! [X: rat,Y: rat] :
% 0.29/0.53        ( ( X != Y )
% 0.29/0.53       => ( ~ ( ord_less_rat @ X @ Y )
% 0.29/0.53         => ( ord_less_rat @ Y @ X ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_neqE
% 0.29/0.53  thf(fact_2496_linorder__neqE,axiom,
% 0.29/0.53      ! [X: nat,Y: nat] :
% 0.29/0.53        ( ( X != Y )
% 0.29/0.53       => ( ~ ( ord_less_nat @ X @ Y )
% 0.29/0.53         => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_neqE
% 0.29/0.53  thf(fact_2497_linorder__neqE,axiom,
% 0.29/0.53      ! [X: int,Y: int] :
% 0.29/0.53        ( ( X != Y )
% 0.29/0.53       => ( ~ ( ord_less_int @ X @ Y )
% 0.29/0.53         => ( ord_less_int @ Y @ X ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_neqE
% 0.29/0.53  thf(fact_2498_order__subst2,axiom,
% 0.29/0.53      ! [A: rat,B: rat,F2: rat > rat,C: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_subst2
% 0.29/0.53  thf(fact_2499_order__subst2,axiom,
% 0.29/0.53      ! [A: rat,B: rat,F2: rat > nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_subst2
% 0.29/0.53  thf(fact_2500_order__subst2,axiom,
% 0.29/0.53      ! [A: rat,B: rat,F2: rat > int,C: int] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_int @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_subst2
% 0.29/0.53  thf(fact_2501_order__subst2,axiom,
% 0.29/0.53      ! [A: nat,B: nat,F2: nat > rat,C: rat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_subst2
% 0.29/0.53  thf(fact_2502_order__subst2,axiom,
% 0.29/0.53      ! [A: nat,B: nat,F2: nat > nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_subst2
% 0.29/0.53  thf(fact_2503_order__subst2,axiom,
% 0.29/0.53      ! [A: nat,B: nat,F2: nat > int,C: int] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_int @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_subst2
% 0.29/0.53  thf(fact_2504_order__subst2,axiom,
% 0.29/0.53      ! [A: int,B: int,F2: int > rat,C: rat] :
% 0.29/0.53        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_subst2
% 0.29/0.53  thf(fact_2505_order__subst2,axiom,
% 0.29/0.53      ! [A: int,B: int,F2: int > nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_subst2
% 0.29/0.53  thf(fact_2506_order__subst2,axiom,
% 0.29/0.53      ! [A: int,B: int,F2: int > int,C: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_int @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_subst2
% 0.29/0.53  thf(fact_2507_order__subst2,axiom,
% 0.29/0.53      ! [A: filter_nat,B: filter_nat,F2: filter_nat > rat,C: rat] :
% 0.29/0.53        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C )
% 0.29/0.53         => ( ! [X2: filter_nat,Y2: filter_nat] :
% 0.29/0.53                ( ( ord_le2510731241096832064er_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_subst2
% 0.29/0.53  thf(fact_2508_order__subst1,axiom,
% 0.29/0.53      ! [A: rat,F2: rat > rat,B: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_subst1
% 0.29/0.53  thf(fact_2509_order__subst1,axiom,
% 0.29/0.53      ! [A: rat,F2: nat > rat,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_subst1
% 0.29/0.53  thf(fact_2510_order__subst1,axiom,
% 0.29/0.53      ! [A: rat,F2: int > rat,B: int,C: int] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_subst1
% 0.29/0.53  thf(fact_2511_order__subst1,axiom,
% 0.29/0.53      ! [A: nat,F2: rat > nat,B: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_subst1
% 0.29/0.53  thf(fact_2512_order__subst1,axiom,
% 0.29/0.53      ! [A: nat,F2: nat > nat,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_subst1
% 0.29/0.53  thf(fact_2513_order__subst1,axiom,
% 0.29/0.53      ! [A: nat,F2: int > nat,B: int,C: int] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_subst1
% 0.29/0.53  thf(fact_2514_order__subst1,axiom,
% 0.29/0.53      ! [A: int,F2: rat > int,B: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_eq_int @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_subst1
% 0.29/0.53  thf(fact_2515_order__subst1,axiom,
% 0.29/0.53      ! [A: int,F2: nat > int,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_int @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.53         => ( ! [X2: nat,Y2: nat] :
% 0.29/0.53                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_subst1
% 0.29/0.53  thf(fact_2516_order__subst1,axiom,
% 0.29/0.53      ! [A: int,F2: int > int,B: int,C: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.53         => ( ! [X2: int,Y2: int] :
% 0.29/0.53                ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.29/0.53               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_less_eq_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_subst1
% 0.29/0.53  thf(fact_2517_order__subst1,axiom,
% 0.29/0.53      ! [A: filter_nat,F2: rat > filter_nat,B: rat,C: rat] :
% 0.29/0.53        ( ( ord_le2510731241096832064er_nat @ A @ ( F2 @ B ) )
% 0.29/0.53       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.53         => ( ! [X2: rat,Y2: rat] :
% 0.29/0.53                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.53               => ( ord_le2510731241096832064er_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.29/0.53           => ( ord_le2510731241096832064er_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order_subst1
% 0.29/0.53  thf(fact_2518_Orderings_Oorder__eq__iff,axiom,
% 0.29/0.53      ( ( ^ [Y4: filter_nat,Z4: filter_nat] : ( Y4 = Z4 ) )
% 0.29/0.53      = ( ^ [A3: filter_nat,B3: filter_nat] :
% 0.29/0.53            ( ( ord_le2510731241096832064er_nat @ A3 @ B3 )
% 0.29/0.53            & ( ord_le2510731241096832064er_nat @ B3 @ A3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % Orderings.order_eq_iff
% 0.29/0.53  thf(fact_2519_Orderings_Oorder__eq__iff,axiom,
% 0.29/0.53      ( ( ^ [Y4: set_nat,Z4: set_nat] : ( Y4 = Z4 ) )
% 0.29/0.53      = ( ^ [A3: set_nat,B3: set_nat] :
% 0.29/0.53            ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 0.29/0.53            & ( ord_less_eq_set_nat @ B3 @ A3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % Orderings.order_eq_iff
% 0.29/0.53  thf(fact_2520_Orderings_Oorder__eq__iff,axiom,
% 0.29/0.53      ( ( ^ [Y4: rat,Z4: rat] : ( Y4 = Z4 ) )
% 0.29/0.53      = ( ^ [A3: rat,B3: rat] :
% 0.29/0.53            ( ( ord_less_eq_rat @ A3 @ B3 )
% 0.29/0.53            & ( ord_less_eq_rat @ B3 @ A3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % Orderings.order_eq_iff
% 0.29/0.53  thf(fact_2521_Orderings_Oorder__eq__iff,axiom,
% 0.29/0.53      ( ( ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 ) )
% 0.29/0.53      = ( ^ [A3: nat,B3: nat] :
% 0.29/0.53            ( ( ord_less_eq_nat @ A3 @ B3 )
% 0.29/0.53            & ( ord_less_eq_nat @ B3 @ A3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % Orderings.order_eq_iff
% 0.29/0.53  thf(fact_2522_Orderings_Oorder__eq__iff,axiom,
% 0.29/0.53      ( ( ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 0.29/0.53      = ( ^ [A3: int,B3: int] :
% 0.29/0.53            ( ( ord_less_eq_int @ A3 @ B3 )
% 0.29/0.53            & ( ord_less_eq_int @ B3 @ A3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % Orderings.order_eq_iff
% 0.29/0.53  thf(fact_2523_antisym,axiom,
% 0.29/0.53      ! [A: filter_nat,B: filter_nat] :
% 0.29/0.53        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 0.29/0.53       => ( ( ord_le2510731241096832064er_nat @ B @ A )
% 0.29/0.53         => ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % antisym
% 0.29/0.53  thf(fact_2524_antisym,axiom,
% 0.29/0.53      ! [A: set_nat,B: set_nat] :
% 0.29/0.53        ( ( ord_less_eq_set_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_set_nat @ B @ A )
% 0.29/0.53         => ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % antisym
% 0.29/0.53  thf(fact_2525_antisym,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.53         => ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % antisym
% 0.29/0.53  thf(fact_2526_antisym,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.53         => ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % antisym
% 0.29/0.53  thf(fact_2527_antisym,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_int @ B @ A )
% 0.29/0.53         => ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % antisym
% 0.29/0.53  thf(fact_2528_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.53      ! [B: literal,A: literal] :
% 0.29/0.53        ( ( ord_less_literal @ B @ A )
% 0.29/0.53       => ( ord_less_eq_literal @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_implies_order
% 0.29/0.53  thf(fact_2529_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.53      ! [B: filter_nat,A: filter_nat] :
% 0.29/0.53        ( ( ord_less_filter_nat @ B @ A )
% 0.29/0.53       => ( ord_le2510731241096832064er_nat @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_implies_order
% 0.29/0.53  thf(fact_2530_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.53      ! [B: set_nat,A: set_nat] :
% 0.29/0.53        ( ( ord_less_set_nat @ B @ A )
% 0.29/0.53       => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_implies_order
% 0.29/0.53  thf(fact_2531_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.53      ! [B: rat,A: rat] :
% 0.29/0.53        ( ( ord_less_rat @ B @ A )
% 0.29/0.53       => ( ord_less_eq_rat @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_implies_order
% 0.29/0.53  thf(fact_2532_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.53      ! [B: nat,A: nat] :
% 0.29/0.53        ( ( ord_less_nat @ B @ A )
% 0.29/0.53       => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_implies_order
% 0.29/0.53  thf(fact_2533_dual__order_Ostrict__implies__order,axiom,
% 0.29/0.53      ! [B: int,A: int] :
% 0.29/0.53        ( ( ord_less_int @ B @ A )
% 0.29/0.53       => ( ord_less_eq_int @ B @ A ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_implies_order
% 0.29/0.53  thf(fact_2534_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.53      ! [B: literal,A: literal] :
% 0.29/0.53        ( ( ord_less_literal @ B @ A )
% 0.29/0.53       => ( A != B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_implies_not_eq
% 0.29/0.53  thf(fact_2535_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.53      ! [B: rat,A: rat] :
% 0.29/0.53        ( ( ord_less_rat @ B @ A )
% 0.29/0.53       => ( A != B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_implies_not_eq
% 0.29/0.53  thf(fact_2536_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.53      ! [B: nat,A: nat] :
% 0.29/0.53        ( ( ord_less_nat @ B @ A )
% 0.29/0.53       => ( A != B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_implies_not_eq
% 0.29/0.53  thf(fact_2537_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/0.53      ! [B: int,A: int] :
% 0.29/0.53        ( ( ord_less_int @ B @ A )
% 0.29/0.53       => ( A != B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_implies_not_eq
% 0.29/0.53  thf(fact_2538_order_Ostrict__implies__order,axiom,
% 0.29/0.53      ! [A: literal,B: literal] :
% 0.29/0.53        ( ( ord_less_literal @ A @ B )
% 0.29/0.53       => ( ord_less_eq_literal @ A @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_implies_order
% 0.29/0.53  thf(fact_2539_order_Ostrict__implies__order,axiom,
% 0.29/0.53      ! [A: filter_nat,B: filter_nat] :
% 0.29/0.53        ( ( ord_less_filter_nat @ A @ B )
% 0.29/0.53       => ( ord_le2510731241096832064er_nat @ A @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_implies_order
% 0.29/0.53  thf(fact_2540_order_Ostrict__implies__order,axiom,
% 0.29/0.53      ! [A: set_nat,B: set_nat] :
% 0.29/0.53        ( ( ord_less_set_nat @ A @ B )
% 0.29/0.53       => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_implies_order
% 0.29/0.53  thf(fact_2541_order_Ostrict__implies__order,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( ord_less_rat @ A @ B )
% 0.29/0.53       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_implies_order
% 0.29/0.53  thf(fact_2542_order_Ostrict__implies__order,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( ord_less_nat @ A @ B )
% 0.29/0.53       => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_implies_order
% 0.29/0.53  thf(fact_2543_order_Ostrict__implies__order,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( ord_less_int @ A @ B )
% 0.29/0.53       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_implies_order
% 0.29/0.53  thf(fact_2544_dual__order_Ostrict__iff__not,axiom,
% 0.29/0.53      ( ord_less_literal
% 0.29/0.53      = ( ^ [B3: literal,A3: literal] :
% 0.29/0.53            ( ( ord_less_eq_literal @ B3 @ A3 )
% 0.29/0.53            & ~ ( ord_less_eq_literal @ A3 @ B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_iff_not
% 0.29/0.53  thf(fact_2545_dual__order_Ostrict__iff__not,axiom,
% 0.29/0.53      ( ord_less_filter_nat
% 0.29/0.53      = ( ^ [B3: filter_nat,A3: filter_nat] :
% 0.29/0.53            ( ( ord_le2510731241096832064er_nat @ B3 @ A3 )
% 0.29/0.53            & ~ ( ord_le2510731241096832064er_nat @ A3 @ B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_iff_not
% 0.29/0.53  thf(fact_2546_dual__order_Ostrict__iff__not,axiom,
% 0.29/0.53      ( ord_less_set_nat
% 0.29/0.53      = ( ^ [B3: set_nat,A3: set_nat] :
% 0.29/0.53            ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 0.29/0.53            & ~ ( ord_less_eq_set_nat @ A3 @ B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_iff_not
% 0.29/0.53  thf(fact_2547_dual__order_Ostrict__iff__not,axiom,
% 0.29/0.53      ( ord_less_rat
% 0.29/0.53      = ( ^ [B3: rat,A3: rat] :
% 0.29/0.53            ( ( ord_less_eq_rat @ B3 @ A3 )
% 0.29/0.53            & ~ ( ord_less_eq_rat @ A3 @ B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_iff_not
% 0.29/0.53  thf(fact_2548_dual__order_Ostrict__iff__not,axiom,
% 0.29/0.53      ( ord_less_nat
% 0.29/0.53      = ( ^ [B3: nat,A3: nat] :
% 0.29/0.53            ( ( ord_less_eq_nat @ B3 @ A3 )
% 0.29/0.53            & ~ ( ord_less_eq_nat @ A3 @ B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_iff_not
% 0.29/0.53  thf(fact_2549_dual__order_Ostrict__iff__not,axiom,
% 0.29/0.53      ( ord_less_int
% 0.29/0.53      = ( ^ [B3: int,A3: int] :
% 0.29/0.53            ( ( ord_less_eq_int @ B3 @ A3 )
% 0.29/0.53            & ~ ( ord_less_eq_int @ A3 @ B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_iff_not
% 0.29/0.53  thf(fact_2550_dual__order_Ostrict__trans2,axiom,
% 0.29/0.53      ! [B: literal,A: literal,C: literal] :
% 0.29/0.53        ( ( ord_less_literal @ B @ A )
% 0.29/0.53       => ( ( ord_less_eq_literal @ C @ B )
% 0.29/0.53         => ( ord_less_literal @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_trans2
% 0.29/0.53  thf(fact_2551_dual__order_Ostrict__trans2,axiom,
% 0.29/0.53      ! [B: filter_nat,A: filter_nat,C: filter_nat] :
% 0.29/0.53        ( ( ord_less_filter_nat @ B @ A )
% 0.29/0.53       => ( ( ord_le2510731241096832064er_nat @ C @ B )
% 0.29/0.53         => ( ord_less_filter_nat @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_trans2
% 0.29/0.53  thf(fact_2552_dual__order_Ostrict__trans2,axiom,
% 0.29/0.53      ! [B: set_nat,A: set_nat,C: set_nat] :
% 0.29/0.53        ( ( ord_less_set_nat @ B @ A )
% 0.29/0.53       => ( ( ord_less_eq_set_nat @ C @ B )
% 0.29/0.53         => ( ord_less_set_nat @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_trans2
% 0.29/0.53  thf(fact_2553_dual__order_Ostrict__trans2,axiom,
% 0.29/0.53      ! [B: rat,A: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_rat @ B @ A )
% 0.29/0.53       => ( ( ord_less_eq_rat @ C @ B )
% 0.29/0.53         => ( ord_less_rat @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_trans2
% 0.29/0.53  thf(fact_2554_dual__order_Ostrict__trans2,axiom,
% 0.29/0.53      ! [B: nat,A: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_nat @ B @ A )
% 0.29/0.53       => ( ( ord_less_eq_nat @ C @ B )
% 0.29/0.53         => ( ord_less_nat @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_trans2
% 0.29/0.53  thf(fact_2555_dual__order_Ostrict__trans2,axiom,
% 0.29/0.53      ! [B: int,A: int,C: int] :
% 0.29/0.53        ( ( ord_less_int @ B @ A )
% 0.29/0.53       => ( ( ord_less_eq_int @ C @ B )
% 0.29/0.53         => ( ord_less_int @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_trans2
% 0.29/0.53  thf(fact_2556_dual__order_Ostrict__trans1,axiom,
% 0.29/0.53      ! [B: literal,A: literal,C: literal] :
% 0.29/0.53        ( ( ord_less_eq_literal @ B @ A )
% 0.29/0.53       => ( ( ord_less_literal @ C @ B )
% 0.29/0.53         => ( ord_less_literal @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_trans1
% 0.29/0.53  thf(fact_2557_dual__order_Ostrict__trans1,axiom,
% 0.29/0.53      ! [B: filter_nat,A: filter_nat,C: filter_nat] :
% 0.29/0.53        ( ( ord_le2510731241096832064er_nat @ B @ A )
% 0.29/0.53       => ( ( ord_less_filter_nat @ C @ B )
% 0.29/0.53         => ( ord_less_filter_nat @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_trans1
% 0.29/0.53  thf(fact_2558_dual__order_Ostrict__trans1,axiom,
% 0.29/0.53      ! [B: set_nat,A: set_nat,C: set_nat] :
% 0.29/0.53        ( ( ord_less_eq_set_nat @ B @ A )
% 0.29/0.53       => ( ( ord_less_set_nat @ C @ B )
% 0.29/0.53         => ( ord_less_set_nat @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_trans1
% 0.29/0.53  thf(fact_2559_dual__order_Ostrict__trans1,axiom,
% 0.29/0.53      ! [B: rat,A: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.53       => ( ( ord_less_rat @ C @ B )
% 0.29/0.53         => ( ord_less_rat @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_trans1
% 0.29/0.53  thf(fact_2560_dual__order_Ostrict__trans1,axiom,
% 0.29/0.53      ! [B: nat,A: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.53       => ( ( ord_less_nat @ C @ B )
% 0.29/0.53         => ( ord_less_nat @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_trans1
% 0.29/0.53  thf(fact_2561_dual__order_Ostrict__trans1,axiom,
% 0.29/0.53      ! [B: int,A: int,C: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.53       => ( ( ord_less_int @ C @ B )
% 0.29/0.53         => ( ord_less_int @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_trans1
% 0.29/0.53  thf(fact_2562_order_Ostrict__implies__not__eq,axiom,
% 0.29/0.53      ! [A: literal,B: literal] :
% 0.29/0.53        ( ( ord_less_literal @ A @ B )
% 0.29/0.53       => ( A != B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_implies_not_eq
% 0.29/0.53  thf(fact_2563_order_Ostrict__implies__not__eq,axiom,
% 0.29/0.53      ! [A: rat,B: rat] :
% 0.29/0.53        ( ( ord_less_rat @ A @ B )
% 0.29/0.53       => ( A != B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_implies_not_eq
% 0.29/0.53  thf(fact_2564_order_Ostrict__implies__not__eq,axiom,
% 0.29/0.53      ! [A: nat,B: nat] :
% 0.29/0.53        ( ( ord_less_nat @ A @ B )
% 0.29/0.53       => ( A != B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_implies_not_eq
% 0.29/0.53  thf(fact_2565_order_Ostrict__implies__not__eq,axiom,
% 0.29/0.53      ! [A: int,B: int] :
% 0.29/0.53        ( ( ord_less_int @ A @ B )
% 0.29/0.53       => ( A != B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_implies_not_eq
% 0.29/0.53  thf(fact_2566_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.53      ( ord_less_literal
% 0.29/0.53      = ( ^ [B3: literal,A3: literal] :
% 0.29/0.53            ( ( ord_less_eq_literal @ B3 @ A3 )
% 0.29/0.53            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_iff_order
% 0.29/0.53  thf(fact_2567_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.53      ( ord_less_filter_nat
% 0.29/0.53      = ( ^ [B3: filter_nat,A3: filter_nat] :
% 0.29/0.53            ( ( ord_le2510731241096832064er_nat @ B3 @ A3 )
% 0.29/0.53            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_iff_order
% 0.29/0.53  thf(fact_2568_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.53      ( ord_less_set_nat
% 0.29/0.53      = ( ^ [B3: set_nat,A3: set_nat] :
% 0.29/0.53            ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 0.29/0.53            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_iff_order
% 0.29/0.53  thf(fact_2569_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.53      ( ord_less_rat
% 0.29/0.53      = ( ^ [B3: rat,A3: rat] :
% 0.29/0.53            ( ( ord_less_eq_rat @ B3 @ A3 )
% 0.29/0.53            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_iff_order
% 0.29/0.53  thf(fact_2570_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.53      ( ord_less_nat
% 0.29/0.53      = ( ^ [B3: nat,A3: nat] :
% 0.29/0.53            ( ( ord_less_eq_nat @ B3 @ A3 )
% 0.29/0.53            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_iff_order
% 0.29/0.53  thf(fact_2571_dual__order_Ostrict__iff__order,axiom,
% 0.29/0.53      ( ord_less_int
% 0.29/0.53      = ( ^ [B3: int,A3: int] :
% 0.29/0.53            ( ( ord_less_eq_int @ B3 @ A3 )
% 0.29/0.53            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_iff_order
% 0.29/0.53  thf(fact_2572_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.53      ( ord_less_eq_literal
% 0.29/0.53      = ( ^ [B3: literal,A3: literal] :
% 0.29/0.53            ( ( ord_less_literal @ B3 @ A3 )
% 0.29/0.53            | ( A3 = B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.order_iff_strict
% 0.29/0.53  thf(fact_2573_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.53      ( ord_le2510731241096832064er_nat
% 0.29/0.53      = ( ^ [B3: filter_nat,A3: filter_nat] :
% 0.29/0.53            ( ( ord_less_filter_nat @ B3 @ A3 )
% 0.29/0.53            | ( A3 = B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.order_iff_strict
% 0.29/0.53  thf(fact_2574_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.53      ( ord_less_eq_set_nat
% 0.29/0.53      = ( ^ [B3: set_nat,A3: set_nat] :
% 0.29/0.53            ( ( ord_less_set_nat @ B3 @ A3 )
% 0.29/0.53            | ( A3 = B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.order_iff_strict
% 0.29/0.53  thf(fact_2575_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.53      ( ord_less_eq_rat
% 0.29/0.53      = ( ^ [B3: rat,A3: rat] :
% 0.29/0.53            ( ( ord_less_rat @ B3 @ A3 )
% 0.29/0.53            | ( A3 = B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.order_iff_strict
% 0.29/0.53  thf(fact_2576_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.53      ( ord_less_eq_nat
% 0.29/0.53      = ( ^ [B3: nat,A3: nat] :
% 0.29/0.53            ( ( ord_less_nat @ B3 @ A3 )
% 0.29/0.53            | ( A3 = B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.order_iff_strict
% 0.29/0.53  thf(fact_2577_dual__order_Oorder__iff__strict,axiom,
% 0.29/0.53      ( ord_less_eq_int
% 0.29/0.53      = ( ^ [B3: int,A3: int] :
% 0.29/0.53            ( ( ord_less_int @ B3 @ A3 )
% 0.29/0.53            | ( A3 = B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.order_iff_strict
% 0.29/0.53  thf(fact_2578_dual__order_Ostrict__trans,axiom,
% 0.29/0.53      ! [B: literal,A: literal,C: literal] :
% 0.29/0.53        ( ( ord_less_literal @ B @ A )
% 0.29/0.53       => ( ( ord_less_literal @ C @ B )
% 0.29/0.53         => ( ord_less_literal @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_trans
% 0.29/0.53  thf(fact_2579_dual__order_Ostrict__trans,axiom,
% 0.29/0.53      ! [B: rat,A: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_rat @ B @ A )
% 0.29/0.53       => ( ( ord_less_rat @ C @ B )
% 0.29/0.53         => ( ord_less_rat @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_trans
% 0.29/0.53  thf(fact_2580_dual__order_Ostrict__trans,axiom,
% 0.29/0.53      ! [B: nat,A: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_nat @ B @ A )
% 0.29/0.53       => ( ( ord_less_nat @ C @ B )
% 0.29/0.53         => ( ord_less_nat @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_trans
% 0.29/0.53  thf(fact_2581_dual__order_Ostrict__trans,axiom,
% 0.29/0.53      ! [B: int,A: int,C: int] :
% 0.29/0.53        ( ( ord_less_int @ B @ A )
% 0.29/0.53       => ( ( ord_less_int @ C @ B )
% 0.29/0.53         => ( ord_less_int @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.strict_trans
% 0.29/0.53  thf(fact_2582_dense__le__bounded,axiom,
% 0.29/0.53      ! [X: rat,Y: rat,Z: rat] :
% 0.29/0.53        ( ( ord_less_rat @ X @ Y )
% 0.29/0.53       => ( ! [W2: rat] :
% 0.29/0.53              ( ( ord_less_rat @ X @ W2 )
% 0.29/0.53             => ( ( ord_less_rat @ W2 @ Y )
% 0.29/0.53               => ( ord_less_eq_rat @ W2 @ Z ) ) )
% 0.29/0.53         => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dense_le_bounded
% 0.29/0.53  thf(fact_2583_dense__ge__bounded,axiom,
% 0.29/0.53      ! [Z: rat,X: rat,Y: rat] :
% 0.29/0.53        ( ( ord_less_rat @ Z @ X )
% 0.29/0.53       => ( ! [W2: rat] :
% 0.29/0.53              ( ( ord_less_rat @ Z @ W2 )
% 0.29/0.53             => ( ( ord_less_rat @ W2 @ X )
% 0.29/0.53               => ( ord_less_eq_rat @ Y @ W2 ) ) )
% 0.29/0.53         => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dense_ge_bounded
% 0.29/0.53  thf(fact_2584_not__less__iff__gr__or__eq,axiom,
% 0.29/0.53      ! [X: literal,Y: literal] :
% 0.29/0.53        ( ( ~ ( ord_less_literal @ X @ Y ) )
% 0.29/0.53        = ( ( ord_less_literal @ Y @ X )
% 0.29/0.53          | ( X = Y ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % not_less_iff_gr_or_eq
% 0.29/0.53  thf(fact_2585_not__less__iff__gr__or__eq,axiom,
% 0.29/0.53      ! [X: rat,Y: rat] :
% 0.29/0.53        ( ( ~ ( ord_less_rat @ X @ Y ) )
% 0.29/0.53        = ( ( ord_less_rat @ Y @ X )
% 0.29/0.53          | ( X = Y ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % not_less_iff_gr_or_eq
% 0.29/0.53  thf(fact_2586_not__less__iff__gr__or__eq,axiom,
% 0.29/0.53      ! [X: nat,Y: nat] :
% 0.29/0.53        ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.29/0.53        = ( ( ord_less_nat @ Y @ X )
% 0.29/0.53          | ( X = Y ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % not_less_iff_gr_or_eq
% 0.29/0.53  thf(fact_2587_not__less__iff__gr__or__eq,axiom,
% 0.29/0.53      ! [X: int,Y: int] :
% 0.29/0.53        ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.29/0.53        = ( ( ord_less_int @ Y @ X )
% 0.29/0.53          | ( X = Y ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % not_less_iff_gr_or_eq
% 0.29/0.53  thf(fact_2588_order_Ostrict__iff__not,axiom,
% 0.29/0.53      ( ord_less_literal
% 0.29/0.53      = ( ^ [A3: literal,B3: literal] :
% 0.29/0.53            ( ( ord_less_eq_literal @ A3 @ B3 )
% 0.29/0.53            & ~ ( ord_less_eq_literal @ B3 @ A3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_iff_not
% 0.29/0.53  thf(fact_2589_order_Ostrict__iff__not,axiom,
% 0.29/0.53      ( ord_less_filter_nat
% 0.29/0.53      = ( ^ [A3: filter_nat,B3: filter_nat] :
% 0.29/0.53            ( ( ord_le2510731241096832064er_nat @ A3 @ B3 )
% 0.29/0.53            & ~ ( ord_le2510731241096832064er_nat @ B3 @ A3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_iff_not
% 0.29/0.53  thf(fact_2590_order_Ostrict__iff__not,axiom,
% 0.29/0.53      ( ord_less_set_nat
% 0.29/0.53      = ( ^ [A3: set_nat,B3: set_nat] :
% 0.29/0.53            ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 0.29/0.53            & ~ ( ord_less_eq_set_nat @ B3 @ A3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_iff_not
% 0.29/0.53  thf(fact_2591_order_Ostrict__iff__not,axiom,
% 0.29/0.53      ( ord_less_rat
% 0.29/0.53      = ( ^ [A3: rat,B3: rat] :
% 0.29/0.53            ( ( ord_less_eq_rat @ A3 @ B3 )
% 0.29/0.53            & ~ ( ord_less_eq_rat @ B3 @ A3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_iff_not
% 0.29/0.53  thf(fact_2592_order_Ostrict__iff__not,axiom,
% 0.29/0.53      ( ord_less_nat
% 0.29/0.53      = ( ^ [A3: nat,B3: nat] :
% 0.29/0.53            ( ( ord_less_eq_nat @ A3 @ B3 )
% 0.29/0.53            & ~ ( ord_less_eq_nat @ B3 @ A3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_iff_not
% 0.29/0.53  thf(fact_2593_order_Ostrict__iff__not,axiom,
% 0.29/0.53      ( ord_less_int
% 0.29/0.53      = ( ^ [A3: int,B3: int] :
% 0.29/0.53            ( ( ord_less_eq_int @ A3 @ B3 )
% 0.29/0.53            & ~ ( ord_less_eq_int @ B3 @ A3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_iff_not
% 0.29/0.53  thf(fact_2594_order_Ostrict__trans2,axiom,
% 0.29/0.53      ! [A: literal,B: literal,C: literal] :
% 0.29/0.53        ( ( ord_less_literal @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_literal @ B @ C )
% 0.29/0.53         => ( ord_less_literal @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_trans2
% 0.29/0.53  thf(fact_2595_order_Ostrict__trans2,axiom,
% 0.29/0.53      ! [A: filter_nat,B: filter_nat,C: filter_nat] :
% 0.29/0.53        ( ( ord_less_filter_nat @ A @ B )
% 0.29/0.53       => ( ( ord_le2510731241096832064er_nat @ B @ C )
% 0.29/0.53         => ( ord_less_filter_nat @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_trans2
% 0.29/0.53  thf(fact_2596_order_Ostrict__trans2,axiom,
% 0.29/0.53      ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.29/0.53        ( ( ord_less_set_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_set_nat @ B @ C )
% 0.29/0.53         => ( ord_less_set_nat @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_trans2
% 0.29/0.53  thf(fact_2597_order_Ostrict__trans2,axiom,
% 0.29/0.53      ! [A: rat,B: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_rat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.53         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_trans2
% 0.29/0.53  thf(fact_2598_order_Ostrict__trans2,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.53         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_trans2
% 0.29/0.53  thf(fact_2599_order_Ostrict__trans2,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( ord_less_int @ A @ B )
% 0.29/0.53       => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.53         => ( ord_less_int @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_trans2
% 0.29/0.53  thf(fact_2600_order_Ostrict__trans1,axiom,
% 0.29/0.53      ! [A: literal,B: literal,C: literal] :
% 0.29/0.53        ( ( ord_less_eq_literal @ A @ B )
% 0.29/0.53       => ( ( ord_less_literal @ B @ C )
% 0.29/0.53         => ( ord_less_literal @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_trans1
% 0.29/0.53  thf(fact_2601_order_Ostrict__trans1,axiom,
% 0.29/0.53      ! [A: filter_nat,B: filter_nat,C: filter_nat] :
% 0.29/0.53        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_filter_nat @ B @ C )
% 0.29/0.53         => ( ord_less_filter_nat @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_trans1
% 0.29/0.53  thf(fact_2602_order_Ostrict__trans1,axiom,
% 0.29/0.53      ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.29/0.53        ( ( ord_less_eq_set_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_set_nat @ B @ C )
% 0.29/0.53         => ( ord_less_set_nat @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_trans1
% 0.29/0.53  thf(fact_2603_order_Ostrict__trans1,axiom,
% 0.29/0.53      ! [A: rat,B: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.53       => ( ( ord_less_rat @ B @ C )
% 0.29/0.53         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_trans1
% 0.29/0.53  thf(fact_2604_order_Ostrict__trans1,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_nat @ B @ C )
% 0.29/0.53         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_trans1
% 0.29/0.53  thf(fact_2605_order_Ostrict__trans1,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.53       => ( ( ord_less_int @ B @ C )
% 0.29/0.53         => ( ord_less_int @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_trans1
% 0.29/0.53  thf(fact_2606_order_Ostrict__iff__order,axiom,
% 0.29/0.53      ( ord_less_literal
% 0.29/0.53      = ( ^ [A3: literal,B3: literal] :
% 0.29/0.53            ( ( ord_less_eq_literal @ A3 @ B3 )
% 0.29/0.53            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_iff_order
% 0.29/0.53  thf(fact_2607_order_Ostrict__iff__order,axiom,
% 0.29/0.53      ( ord_less_filter_nat
% 0.29/0.53      = ( ^ [A3: filter_nat,B3: filter_nat] :
% 0.29/0.53            ( ( ord_le2510731241096832064er_nat @ A3 @ B3 )
% 0.29/0.53            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_iff_order
% 0.29/0.53  thf(fact_2608_order_Ostrict__iff__order,axiom,
% 0.29/0.53      ( ord_less_set_nat
% 0.29/0.53      = ( ^ [A3: set_nat,B3: set_nat] :
% 0.29/0.53            ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 0.29/0.53            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_iff_order
% 0.29/0.53  thf(fact_2609_order_Ostrict__iff__order,axiom,
% 0.29/0.53      ( ord_less_rat
% 0.29/0.53      = ( ^ [A3: rat,B3: rat] :
% 0.29/0.53            ( ( ord_less_eq_rat @ A3 @ B3 )
% 0.29/0.53            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_iff_order
% 0.29/0.53  thf(fact_2610_order_Ostrict__iff__order,axiom,
% 0.29/0.53      ( ord_less_nat
% 0.29/0.53      = ( ^ [A3: nat,B3: nat] :
% 0.29/0.53            ( ( ord_less_eq_nat @ A3 @ B3 )
% 0.29/0.53            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_iff_order
% 0.29/0.53  thf(fact_2611_order_Ostrict__iff__order,axiom,
% 0.29/0.53      ( ord_less_int
% 0.29/0.53      = ( ^ [A3: int,B3: int] :
% 0.29/0.53            ( ( ord_less_eq_int @ A3 @ B3 )
% 0.29/0.53            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_iff_order
% 0.29/0.53  thf(fact_2612_order_Oorder__iff__strict,axiom,
% 0.29/0.53      ( ord_less_eq_literal
% 0.29/0.53      = ( ^ [A3: literal,B3: literal] :
% 0.29/0.53            ( ( ord_less_literal @ A3 @ B3 )
% 0.29/0.53            | ( A3 = B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.order_iff_strict
% 0.29/0.53  thf(fact_2613_order_Oorder__iff__strict,axiom,
% 0.29/0.53      ( ord_le2510731241096832064er_nat
% 0.29/0.53      = ( ^ [A3: filter_nat,B3: filter_nat] :
% 0.29/0.53            ( ( ord_less_filter_nat @ A3 @ B3 )
% 0.29/0.53            | ( A3 = B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.order_iff_strict
% 0.29/0.53  thf(fact_2614_order_Oorder__iff__strict,axiom,
% 0.29/0.53      ( ord_less_eq_set_nat
% 0.29/0.53      = ( ^ [A3: set_nat,B3: set_nat] :
% 0.29/0.53            ( ( ord_less_set_nat @ A3 @ B3 )
% 0.29/0.53            | ( A3 = B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.order_iff_strict
% 0.29/0.53  thf(fact_2615_order_Oorder__iff__strict,axiom,
% 0.29/0.53      ( ord_less_eq_rat
% 0.29/0.53      = ( ^ [A3: rat,B3: rat] :
% 0.29/0.53            ( ( ord_less_rat @ A3 @ B3 )
% 0.29/0.53            | ( A3 = B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.order_iff_strict
% 0.29/0.53  thf(fact_2616_order_Oorder__iff__strict,axiom,
% 0.29/0.53      ( ord_less_eq_nat
% 0.29/0.53      = ( ^ [A3: nat,B3: nat] :
% 0.29/0.53            ( ( ord_less_nat @ A3 @ B3 )
% 0.29/0.53            | ( A3 = B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.order_iff_strict
% 0.29/0.53  thf(fact_2617_order_Oorder__iff__strict,axiom,
% 0.29/0.53      ( ord_less_eq_int
% 0.29/0.53      = ( ^ [A3: int,B3: int] :
% 0.29/0.53            ( ( ord_less_int @ A3 @ B3 )
% 0.29/0.53            | ( A3 = B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.order_iff_strict
% 0.29/0.53  thf(fact_2618_order_Ostrict__trans,axiom,
% 0.29/0.53      ! [A: literal,B: literal,C: literal] :
% 0.29/0.53        ( ( ord_less_literal @ A @ B )
% 0.29/0.53       => ( ( ord_less_literal @ B @ C )
% 0.29/0.53         => ( ord_less_literal @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_trans
% 0.29/0.53  thf(fact_2619_order_Ostrict__trans,axiom,
% 0.29/0.53      ! [A: rat,B: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_rat @ A @ B )
% 0.29/0.53       => ( ( ord_less_rat @ B @ C )
% 0.29/0.53         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_trans
% 0.29/0.53  thf(fact_2620_order_Ostrict__trans,axiom,
% 0.29/0.53      ! [A: nat,B: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_nat @ A @ B )
% 0.29/0.53       => ( ( ord_less_nat @ B @ C )
% 0.29/0.53         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_trans
% 0.29/0.53  thf(fact_2621_order_Ostrict__trans,axiom,
% 0.29/0.53      ! [A: int,B: int,C: int] :
% 0.29/0.53        ( ( ord_less_int @ A @ B )
% 0.29/0.53       => ( ( ord_less_int @ B @ C )
% 0.29/0.53         => ( ord_less_int @ A @ C ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % order.strict_trans
% 0.29/0.53  thf(fact_2622_linorder__less__wlog,axiom,
% 0.29/0.53      ! [P: literal > literal > $o,A: literal,B: literal] :
% 0.29/0.53        ( ! [A6: literal,B6: literal] :
% 0.29/0.53            ( ( ord_less_literal @ A6 @ B6 )
% 0.29/0.53           => ( P @ A6 @ B6 ) )
% 0.29/0.53       => ( ! [A6: literal] : ( P @ A6 @ A6 )
% 0.29/0.53         => ( ! [A6: literal,B6: literal] :
% 0.29/0.53                ( ( P @ B6 @ A6 )
% 0.29/0.53               => ( P @ A6 @ B6 ) )
% 0.29/0.53           => ( P @ A @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_less_wlog
% 0.29/0.53  thf(fact_2623_linorder__less__wlog,axiom,
% 0.29/0.53      ! [P: rat > rat > $o,A: rat,B: rat] :
% 0.29/0.53        ( ! [A6: rat,B6: rat] :
% 0.29/0.53            ( ( ord_less_rat @ A6 @ B6 )
% 0.29/0.53           => ( P @ A6 @ B6 ) )
% 0.29/0.53       => ( ! [A6: rat] : ( P @ A6 @ A6 )
% 0.29/0.53         => ( ! [A6: rat,B6: rat] :
% 0.29/0.53                ( ( P @ B6 @ A6 )
% 0.29/0.53               => ( P @ A6 @ B6 ) )
% 0.29/0.53           => ( P @ A @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_less_wlog
% 0.29/0.53  thf(fact_2624_linorder__less__wlog,axiom,
% 0.29/0.53      ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.29/0.53        ( ! [A6: nat,B6: nat] :
% 0.29/0.53            ( ( ord_less_nat @ A6 @ B6 )
% 0.29/0.53           => ( P @ A6 @ B6 ) )
% 0.29/0.53       => ( ! [A6: nat] : ( P @ A6 @ A6 )
% 0.29/0.53         => ( ! [A6: nat,B6: nat] :
% 0.29/0.53                ( ( P @ B6 @ A6 )
% 0.29/0.53               => ( P @ A6 @ B6 ) )
% 0.29/0.53           => ( P @ A @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_less_wlog
% 0.29/0.53  thf(fact_2625_linorder__less__wlog,axiom,
% 0.29/0.53      ! [P: int > int > $o,A: int,B: int] :
% 0.29/0.53        ( ! [A6: int,B6: int] :
% 0.29/0.53            ( ( ord_less_int @ A6 @ B6 )
% 0.29/0.53           => ( P @ A6 @ B6 ) )
% 0.29/0.53       => ( ! [A6: int] : ( P @ A6 @ A6 )
% 0.29/0.53         => ( ! [A6: int,B6: int] :
% 0.29/0.53                ( ( P @ B6 @ A6 )
% 0.29/0.53               => ( P @ A6 @ B6 ) )
% 0.29/0.53           => ( P @ A @ B ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % linorder_less_wlog
% 0.29/0.53  thf(fact_2626_exists__least__iff,axiom,
% 0.29/0.53      ( ( ^ [P5: nat > $o] :
% 0.29/0.53          ? [X6: nat] : ( P5 @ X6 ) )
% 0.29/0.53      = ( ^ [P2: nat > $o] :
% 0.29/0.53          ? [N2: nat] :
% 0.29/0.53            ( ( P2 @ N2 )
% 0.29/0.53            & ! [M2: nat] :
% 0.29/0.53                ( ( ord_less_nat @ M2 @ N2 )
% 0.29/0.53               => ~ ( P2 @ M2 ) ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % exists_least_iff
% 0.29/0.53  thf(fact_2627_dual__order_Oirrefl,axiom,
% 0.29/0.53      ! [A: literal] :
% 0.29/0.53        ~ ( ord_less_literal @ A @ A ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.irrefl
% 0.29/0.53  thf(fact_2628_dual__order_Oirrefl,axiom,
% 0.29/0.53      ! [A: rat] :
% 0.29/0.53        ~ ( ord_less_rat @ A @ A ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.irrefl
% 0.29/0.53  thf(fact_2629_dual__order_Oirrefl,axiom,
% 0.29/0.53      ! [A: nat] :
% 0.29/0.53        ~ ( ord_less_nat @ A @ A ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.irrefl
% 0.29/0.53  thf(fact_2630_dual__order_Oirrefl,axiom,
% 0.29/0.53      ! [A: int] :
% 0.29/0.53        ~ ( ord_less_int @ A @ A ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.irrefl
% 0.29/0.53  thf(fact_2631_dual__order_Otrans,axiom,
% 0.29/0.53      ! [B: filter_nat,A: filter_nat,C: filter_nat] :
% 0.29/0.53        ( ( ord_le2510731241096832064er_nat @ B @ A )
% 0.29/0.53       => ( ( ord_le2510731241096832064er_nat @ C @ B )
% 0.29/0.53         => ( ord_le2510731241096832064er_nat @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.trans
% 0.29/0.53  thf(fact_2632_dual__order_Otrans,axiom,
% 0.29/0.53      ! [B: set_nat,A: set_nat,C: set_nat] :
% 0.29/0.53        ( ( ord_less_eq_set_nat @ B @ A )
% 0.29/0.53       => ( ( ord_less_eq_set_nat @ C @ B )
% 0.29/0.53         => ( ord_less_eq_set_nat @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.trans
% 0.29/0.53  thf(fact_2633_dual__order_Otrans,axiom,
% 0.29/0.53      ! [B: rat,A: rat,C: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.53       => ( ( ord_less_eq_rat @ C @ B )
% 0.29/0.53         => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.trans
% 0.29/0.53  thf(fact_2634_dual__order_Otrans,axiom,
% 0.29/0.53      ! [B: nat,A: nat,C: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.53       => ( ( ord_less_eq_nat @ C @ B )
% 0.29/0.53         => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.trans
% 0.29/0.53  thf(fact_2635_dual__order_Otrans,axiom,
% 0.29/0.53      ! [B: int,A: int,C: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.53       => ( ( ord_less_eq_int @ C @ B )
% 0.29/0.53         => ( ord_less_eq_int @ C @ A ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.trans
% 0.29/0.53  thf(fact_2636_dual__order_Oasym,axiom,
% 0.29/0.53      ! [B: literal,A: literal] :
% 0.29/0.53        ( ( ord_less_literal @ B @ A )
% 0.29/0.53       => ~ ( ord_less_literal @ A @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.asym
% 0.29/0.53  thf(fact_2637_dual__order_Oasym,axiom,
% 0.29/0.53      ! [B: rat,A: rat] :
% 0.29/0.53        ( ( ord_less_rat @ B @ A )
% 0.29/0.53       => ~ ( ord_less_rat @ A @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.asym
% 0.29/0.53  thf(fact_2638_dual__order_Oasym,axiom,
% 0.29/0.53      ! [B: nat,A: nat] :
% 0.29/0.53        ( ( ord_less_nat @ B @ A )
% 0.29/0.53       => ~ ( ord_less_nat @ A @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.asym
% 0.29/0.53  thf(fact_2639_dual__order_Oasym,axiom,
% 0.29/0.53      ! [B: int,A: int] :
% 0.29/0.53        ( ( ord_less_int @ B @ A )
% 0.29/0.53       => ~ ( ord_less_int @ A @ B ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.asym
% 0.29/0.53  thf(fact_2640_dual__order_Oantisym,axiom,
% 0.29/0.53      ! [B: filter_nat,A: filter_nat] :
% 0.29/0.53        ( ( ord_le2510731241096832064er_nat @ B @ A )
% 0.29/0.53       => ( ( ord_le2510731241096832064er_nat @ A @ B )
% 0.29/0.53         => ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.antisym
% 0.29/0.53  thf(fact_2641_dual__order_Oantisym,axiom,
% 0.29/0.53      ! [B: set_nat,A: set_nat] :
% 0.29/0.53        ( ( ord_less_eq_set_nat @ B @ A )
% 0.29/0.53       => ( ( ord_less_eq_set_nat @ A @ B )
% 0.29/0.53         => ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.antisym
% 0.29/0.53  thf(fact_2642_dual__order_Oantisym,axiom,
% 0.29/0.53      ! [B: rat,A: rat] :
% 0.29/0.53        ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.53       => ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.53         => ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.antisym
% 0.29/0.53  thf(fact_2643_dual__order_Oantisym,axiom,
% 0.29/0.53      ! [B: nat,A: nat] :
% 0.29/0.53        ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.53       => ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.53         => ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.antisym
% 0.29/0.53  thf(fact_2644_dual__order_Oantisym,axiom,
% 0.29/0.53      ! [B: int,A: int] :
% 0.29/0.53        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.53       => ( ( ord_less_eq_int @ A @ B )
% 0.29/0.53         => ( A = B ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.antisym
% 0.29/0.53  thf(fact_2645_not__le__imp__less,axiom,
% 0.29/0.53      ! [Y: literal,X: literal] :
% 0.29/0.53        ( ~ ( ord_less_eq_literal @ Y @ X )
% 0.29/0.53       => ( ord_less_literal @ X @ Y ) ) ).
% 0.29/0.53  
% 0.29/0.53  % not_le_imp_less
% 0.29/0.53  thf(fact_2646_not__le__imp__less,axiom,
% 0.29/0.53      ! [Y: rat,X: rat] :
% 0.29/0.53        ( ~ ( ord_less_eq_rat @ Y @ X )
% 0.29/0.53       => ( ord_less_rat @ X @ Y ) ) ).
% 0.29/0.53  
% 0.29/0.53  % not_le_imp_less
% 0.29/0.53  thf(fact_2647_not__le__imp__less,axiom,
% 0.29/0.53      ! [Y: nat,X: nat] :
% 0.29/0.53        ( ~ ( ord_less_eq_nat @ Y @ X )
% 0.29/0.53       => ( ord_less_nat @ X @ Y ) ) ).
% 0.29/0.53  
% 0.29/0.53  % not_le_imp_less
% 0.29/0.53  thf(fact_2648_not__le__imp__less,axiom,
% 0.29/0.53      ! [Y: int,X: int] :
% 0.29/0.53        ( ~ ( ord_less_eq_int @ Y @ X )
% 0.29/0.53       => ( ord_less_int @ X @ Y ) ) ).
% 0.29/0.53  
% 0.29/0.53  % not_le_imp_less
% 0.29/0.53  thf(fact_2649_less__le__not__le,axiom,
% 0.29/0.53      ( ord_less_literal
% 0.29/0.53      = ( ^ [X3: literal,Y3: literal] :
% 0.29/0.53            ( ( ord_less_eq_literal @ X3 @ Y3 )
% 0.29/0.53            & ~ ( ord_less_eq_literal @ Y3 @ X3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_le_not_le
% 0.29/0.53  thf(fact_2650_less__le__not__le,axiom,
% 0.29/0.53      ( ord_less_filter_nat
% 0.29/0.53      = ( ^ [X3: filter_nat,Y3: filter_nat] :
% 0.29/0.53            ( ( ord_le2510731241096832064er_nat @ X3 @ Y3 )
% 0.29/0.53            & ~ ( ord_le2510731241096832064er_nat @ Y3 @ X3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_le_not_le
% 0.29/0.53  thf(fact_2651_less__le__not__le,axiom,
% 0.29/0.53      ( ord_less_set_nat
% 0.29/0.53      = ( ^ [X3: set_nat,Y3: set_nat] :
% 0.29/0.53            ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 0.29/0.53            & ~ ( ord_less_eq_set_nat @ Y3 @ X3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_le_not_le
% 0.29/0.53  thf(fact_2652_less__le__not__le,axiom,
% 0.29/0.53      ( ord_less_rat
% 0.29/0.53      = ( ^ [X3: rat,Y3: rat] :
% 0.29/0.53            ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.53            & ~ ( ord_less_eq_rat @ Y3 @ X3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_le_not_le
% 0.29/0.53  thf(fact_2653_less__le__not__le,axiom,
% 0.29/0.53      ( ord_less_nat
% 0.29/0.53      = ( ^ [X3: nat,Y3: nat] :
% 0.29/0.53            ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.53            & ~ ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_le_not_le
% 0.29/0.53  thf(fact_2654_less__le__not__le,axiom,
% 0.29/0.53      ( ord_less_int
% 0.29/0.53      = ( ^ [X3: int,Y3: int] :
% 0.29/0.53            ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.29/0.53            & ~ ( ord_less_eq_int @ Y3 @ X3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % less_le_not_le
% 0.29/0.53  thf(fact_2655_dual__order_Oeq__iff,axiom,
% 0.29/0.53      ( ( ^ [Y4: filter_nat,Z4: filter_nat] : ( Y4 = Z4 ) )
% 0.29/0.53      = ( ^ [A3: filter_nat,B3: filter_nat] :
% 0.29/0.53            ( ( ord_le2510731241096832064er_nat @ B3 @ A3 )
% 0.29/0.53            & ( ord_le2510731241096832064er_nat @ A3 @ B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.eq_iff
% 0.29/0.53  thf(fact_2656_dual__order_Oeq__iff,axiom,
% 0.29/0.53      ( ( ^ [Y4: set_nat,Z4: set_nat] : ( Y4 = Z4 ) )
% 0.29/0.53      = ( ^ [A3: set_nat,B3: set_nat] :
% 0.29/0.53            ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 0.29/0.53            & ( ord_less_eq_set_nat @ A3 @ B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.eq_iff
% 0.29/0.53  thf(fact_2657_dual__order_Oeq__iff,axiom,
% 0.29/0.53      ( ( ^ [Y4: rat,Z4: rat] : ( Y4 = Z4 ) )
% 0.29/0.53      = ( ^ [A3: rat,B3: rat] :
% 0.29/0.53            ( ( ord_less_eq_rat @ B3 @ A3 )
% 0.29/0.53            & ( ord_less_eq_rat @ A3 @ B3 ) ) ) ) ).
% 0.29/0.53  
% 0.29/0.53  % dual_order.eq_iff
% 0.29/0.54  thf(fact_2658_dual__order_Oeq__iff,axiom,
% 0.29/0.54      ( ( ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 ) )
% 0.29/0.54      = ( ^ [A3: nat,B3: nat] :
% 0.29/0.54            ( ( ord_less_eq_nat @ B3 @ A3 )
% 0.29/0.54            & ( ord_less_eq_nat @ A3 @ B3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dual_order.eq_iff
% 0.29/0.54  thf(fact_2659_dual__order_Oeq__iff,axiom,
% 0.29/0.54      ( ( ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 0.29/0.54      = ( ^ [A3: int,B3: int] :
% 0.29/0.54            ( ( ord_less_eq_int @ B3 @ A3 )
% 0.29/0.54            & ( ord_less_eq_int @ A3 @ B3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dual_order.eq_iff
% 0.29/0.54  thf(fact_2660_linorder__cases,axiom,
% 0.29/0.54      ! [X: literal,Y: literal] :
% 0.29/0.54        ( ~ ( ord_less_literal @ X @ Y )
% 0.29/0.54       => ( ( X != Y )
% 0.29/0.54         => ( ord_less_literal @ Y @ X ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % linorder_cases
% 0.29/0.54  thf(fact_2661_linorder__cases,axiom,
% 0.29/0.54      ! [X: rat,Y: rat] :
% 0.29/0.54        ( ~ ( ord_less_rat @ X @ Y )
% 0.29/0.54       => ( ( X != Y )
% 0.29/0.54         => ( ord_less_rat @ Y @ X ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % linorder_cases
% 0.29/0.54  thf(fact_2662_linorder__cases,axiom,
% 0.29/0.54      ! [X: nat,Y: nat] :
% 0.29/0.54        ( ~ ( ord_less_nat @ X @ Y )
% 0.29/0.54       => ( ( X != Y )
% 0.29/0.54         => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % linorder_cases
% 0.29/0.54  thf(fact_2663_linorder__cases,axiom,
% 0.29/0.54      ! [X: int,Y: int] :
% 0.29/0.54        ( ~ ( ord_less_int @ X @ Y )
% 0.29/0.54       => ( ( X != Y )
% 0.29/0.54         => ( ord_less_int @ Y @ X ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % linorder_cases
% 0.29/0.54  thf(fact_2664_dense__le,axiom,
% 0.29/0.54      ! [Y: rat,Z: rat] :
% 0.29/0.54        ( ! [X2: rat] :
% 0.29/0.54            ( ( ord_less_rat @ X2 @ Y )
% 0.29/0.54           => ( ord_less_eq_rat @ X2 @ Z ) )
% 0.29/0.54       => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dense_le
% 0.29/0.54  thf(fact_2665_dense__ge,axiom,
% 0.29/0.54      ! [Z: rat,Y: rat] :
% 0.29/0.54        ( ! [X2: rat] :
% 0.29/0.54            ( ( ord_less_rat @ Z @ X2 )
% 0.29/0.54           => ( ord_less_eq_rat @ Y @ X2 ) )
% 0.29/0.54       => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dense_ge
% 0.29/0.54  thf(fact_2666_linorder__wlog,axiom,
% 0.29/0.54      ! [P: rat > rat > $o,A: rat,B: rat] :
% 0.29/0.54        ( ! [A6: rat,B6: rat] :
% 0.29/0.54            ( ( ord_less_eq_rat @ A6 @ B6 )
% 0.29/0.54           => ( P @ A6 @ B6 ) )
% 0.29/0.54       => ( ! [A6: rat,B6: rat] :
% 0.29/0.54              ( ( P @ B6 @ A6 )
% 0.29/0.54             => ( P @ A6 @ B6 ) )
% 0.29/0.54         => ( P @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % linorder_wlog
% 0.29/0.54  thf(fact_2667_linorder__wlog,axiom,
% 0.29/0.54      ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.29/0.54        ( ! [A6: nat,B6: nat] :
% 0.29/0.54            ( ( ord_less_eq_nat @ A6 @ B6 )
% 0.29/0.54           => ( P @ A6 @ B6 ) )
% 0.29/0.54       => ( ! [A6: nat,B6: nat] :
% 0.29/0.54              ( ( P @ B6 @ A6 )
% 0.29/0.54             => ( P @ A6 @ B6 ) )
% 0.29/0.54         => ( P @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % linorder_wlog
% 0.29/0.54  thf(fact_2668_linorder__wlog,axiom,
% 0.29/0.54      ! [P: int > int > $o,A: int,B: int] :
% 0.29/0.54        ( ! [A6: int,B6: int] :
% 0.29/0.54            ( ( ord_less_eq_int @ A6 @ B6 )
% 0.29/0.54           => ( P @ A6 @ B6 ) )
% 0.29/0.54       => ( ! [A6: int,B6: int] :
% 0.29/0.54              ( ( P @ B6 @ A6 )
% 0.29/0.54             => ( P @ A6 @ B6 ) )
% 0.29/0.54         => ( P @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % linorder_wlog
% 0.29/0.54  thf(fact_2669_antisym__conv3,axiom,
% 0.29/0.54      ! [Y: literal,X: literal] :
% 0.29/0.54        ( ~ ( ord_less_literal @ Y @ X )
% 0.29/0.54       => ( ( ~ ( ord_less_literal @ X @ Y ) )
% 0.29/0.54          = ( X = Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % antisym_conv3
% 0.29/0.54  thf(fact_2670_antisym__conv3,axiom,
% 0.29/0.54      ! [Y: rat,X: rat] :
% 0.29/0.54        ( ~ ( ord_less_rat @ Y @ X )
% 0.29/0.54       => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 0.29/0.54          = ( X = Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % antisym_conv3
% 0.29/0.54  thf(fact_2671_antisym__conv3,axiom,
% 0.29/0.54      ! [Y: nat,X: nat] :
% 0.29/0.54        ( ~ ( ord_less_nat @ Y @ X )
% 0.29/0.54       => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.29/0.54          = ( X = Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % antisym_conv3
% 0.29/0.54  thf(fact_2672_antisym__conv3,axiom,
% 0.29/0.54      ! [Y: int,X: int] :
% 0.29/0.54        ( ~ ( ord_less_int @ Y @ X )
% 0.29/0.54       => ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.29/0.54          = ( X = Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % antisym_conv3
% 0.29/0.54  thf(fact_2673_less__induct,axiom,
% 0.29/0.54      ! [P: nat > $o,A: nat] :
% 0.29/0.54        ( ! [X2: nat] :
% 0.29/0.54            ( ! [Y5: nat] :
% 0.29/0.54                ( ( ord_less_nat @ Y5 @ X2 )
% 0.29/0.54               => ( P @ Y5 ) )
% 0.29/0.54           => ( P @ X2 ) )
% 0.29/0.54       => ( P @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_induct
% 0.29/0.54  thf(fact_2674_ord__less__eq__trans,axiom,
% 0.29/0.54      ! [A: literal,B: literal,C: literal] :
% 0.29/0.54        ( ( ord_less_literal @ A @ B )
% 0.29/0.54       => ( ( B = C )
% 0.29/0.54         => ( ord_less_literal @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ord_less_eq_trans
% 0.29/0.54  thf(fact_2675_ord__less__eq__trans,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ B )
% 0.29/0.54       => ( ( B = C )
% 0.29/0.54         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ord_less_eq_trans
% 0.29/0.54  thf(fact_2676_ord__less__eq__trans,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat] :
% 0.29/0.54        ( ( ord_less_nat @ A @ B )
% 0.29/0.54       => ( ( B = C )
% 0.29/0.54         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ord_less_eq_trans
% 0.29/0.54  thf(fact_2677_ord__less__eq__trans,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int] :
% 0.29/0.54        ( ( ord_less_int @ A @ B )
% 0.29/0.54       => ( ( B = C )
% 0.29/0.54         => ( ord_less_int @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ord_less_eq_trans
% 0.29/0.54  thf(fact_2678_ord__eq__less__trans,axiom,
% 0.29/0.54      ! [A: literal,B: literal,C: literal] :
% 0.29/0.54        ( ( A = B )
% 0.29/0.54       => ( ( ord_less_literal @ B @ C )
% 0.29/0.54         => ( ord_less_literal @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ord_eq_less_trans
% 0.29/0.54  thf(fact_2679_ord__eq__less__trans,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat] :
% 0.29/0.54        ( ( A = B )
% 0.29/0.54       => ( ( ord_less_rat @ B @ C )
% 0.29/0.54         => ( ord_less_rat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ord_eq_less_trans
% 0.29/0.54  thf(fact_2680_ord__eq__less__trans,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat] :
% 0.29/0.54        ( ( A = B )
% 0.29/0.54       => ( ( ord_less_nat @ B @ C )
% 0.29/0.54         => ( ord_less_nat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ord_eq_less_trans
% 0.29/0.54  thf(fact_2681_ord__eq__less__trans,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int] :
% 0.29/0.54        ( ( A = B )
% 0.29/0.54       => ( ( ord_less_int @ B @ C )
% 0.29/0.54         => ( ord_less_int @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ord_eq_less_trans
% 0.29/0.54  thf(fact_2682_order__trans,axiom,
% 0.29/0.54      ! [X: filter_nat,Y: filter_nat,Z: filter_nat] :
% 0.29/0.54        ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 0.29/0.54       => ( ( ord_le2510731241096832064er_nat @ Y @ Z )
% 0.29/0.54         => ( ord_le2510731241096832064er_nat @ X @ Z ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order_trans
% 0.29/0.54  thf(fact_2683_order__trans,axiom,
% 0.29/0.54      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.29/0.54        ( ( ord_less_eq_set_nat @ X @ Y )
% 0.29/0.54       => ( ( ord_less_eq_set_nat @ Y @ Z )
% 0.29/0.54         => ( ord_less_eq_set_nat @ X @ Z ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order_trans
% 0.29/0.54  thf(fact_2684_order__trans,axiom,
% 0.29/0.54      ! [X: rat,Y: rat,Z: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.54       => ( ( ord_less_eq_rat @ Y @ Z )
% 0.29/0.54         => ( ord_less_eq_rat @ X @ Z ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order_trans
% 0.29/0.54  thf(fact_2685_order__trans,axiom,
% 0.29/0.54      ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.54       => ( ( ord_less_eq_nat @ Y @ Z )
% 0.29/0.54         => ( ord_less_eq_nat @ X @ Z ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order_trans
% 0.29/0.54  thf(fact_2686_order__trans,axiom,
% 0.29/0.54      ! [X: int,Y: int,Z: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.54       => ( ( ord_less_eq_int @ Y @ Z )
% 0.29/0.54         => ( ord_less_eq_int @ X @ Z ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order_trans
% 0.29/0.54  thf(fact_2687_order_Otrans,axiom,
% 0.29/0.54      ! [A: filter_nat,B: filter_nat,C: filter_nat] :
% 0.29/0.54        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 0.29/0.54       => ( ( ord_le2510731241096832064er_nat @ B @ C )
% 0.29/0.54         => ( ord_le2510731241096832064er_nat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order.trans
% 0.29/0.54  thf(fact_2688_order_Otrans,axiom,
% 0.29/0.54      ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.29/0.54        ( ( ord_less_eq_set_nat @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_set_nat @ B @ C )
% 0.29/0.54         => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order.trans
% 0.29/0.54  thf(fact_2689_order_Otrans,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.54         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order.trans
% 0.29/0.54  thf(fact_2690_order_Otrans,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.54         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order.trans
% 0.29/0.54  thf(fact_2691_order_Otrans,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.54         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order.trans
% 0.29/0.54  thf(fact_2692_order_Oasym,axiom,
% 0.29/0.54      ! [A: literal,B: literal] :
% 0.29/0.54        ( ( ord_less_literal @ A @ B )
% 0.29/0.54       => ~ ( ord_less_literal @ B @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order.asym
% 0.29/0.54  thf(fact_2693_order_Oasym,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ B )
% 0.29/0.54       => ~ ( ord_less_rat @ B @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order.asym
% 0.29/0.54  thf(fact_2694_order_Oasym,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_nat @ A @ B )
% 0.29/0.54       => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order.asym
% 0.29/0.54  thf(fact_2695_order_Oasym,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ A @ B )
% 0.29/0.54       => ~ ( ord_less_int @ B @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order.asym
% 0.29/0.54  thf(fact_2696_order__antisym,axiom,
% 0.29/0.54      ! [X: filter_nat,Y: filter_nat] :
% 0.29/0.54        ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 0.29/0.54       => ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 0.29/0.54         => ( X = Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order_antisym
% 0.29/0.54  thf(fact_2697_order__antisym,axiom,
% 0.29/0.54      ! [X: set_nat,Y: set_nat] :
% 0.29/0.54        ( ( ord_less_eq_set_nat @ X @ Y )
% 0.29/0.54       => ( ( ord_less_eq_set_nat @ Y @ X )
% 0.29/0.54         => ( X = Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order_antisym
% 0.29/0.54  thf(fact_2698_order__antisym,axiom,
% 0.29/0.54      ! [X: rat,Y: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.54       => ( ( ord_less_eq_rat @ Y @ X )
% 0.29/0.54         => ( X = Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order_antisym
% 0.29/0.54  thf(fact_2699_order__antisym,axiom,
% 0.29/0.54      ! [X: nat,Y: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.54       => ( ( ord_less_eq_nat @ Y @ X )
% 0.29/0.54         => ( X = Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order_antisym
% 0.29/0.54  thf(fact_2700_order__antisym,axiom,
% 0.29/0.54      ! [X: int,Y: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.54       => ( ( ord_less_eq_int @ Y @ X )
% 0.29/0.54         => ( X = Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order_antisym
% 0.29/0.54  thf(fact_2701_antisym__conv2,axiom,
% 0.29/0.54      ! [X: literal,Y: literal] :
% 0.29/0.54        ( ( ord_less_eq_literal @ X @ Y )
% 0.29/0.54       => ( ( ~ ( ord_less_literal @ X @ Y ) )
% 0.29/0.54          = ( X = Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % antisym_conv2
% 0.29/0.54  thf(fact_2702_antisym__conv2,axiom,
% 0.29/0.54      ! [X: filter_nat,Y: filter_nat] :
% 0.29/0.54        ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 0.29/0.54       => ( ( ~ ( ord_less_filter_nat @ X @ Y ) )
% 0.29/0.54          = ( X = Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % antisym_conv2
% 0.29/0.54  thf(fact_2703_antisym__conv2,axiom,
% 0.29/0.54      ! [X: set_nat,Y: set_nat] :
% 0.29/0.54        ( ( ord_less_eq_set_nat @ X @ Y )
% 0.29/0.54       => ( ( ~ ( ord_less_set_nat @ X @ Y ) )
% 0.29/0.54          = ( X = Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % antisym_conv2
% 0.29/0.54  thf(fact_2704_antisym__conv2,axiom,
% 0.29/0.54      ! [X: rat,Y: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.54       => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 0.29/0.54          = ( X = Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % antisym_conv2
% 0.29/0.54  thf(fact_2705_antisym__conv2,axiom,
% 0.29/0.54      ! [X: nat,Y: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.54       => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.29/0.54          = ( X = Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % antisym_conv2
% 0.29/0.54  thf(fact_2706_antisym__conv2,axiom,
% 0.29/0.54      ! [X: int,Y: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.54       => ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.29/0.54          = ( X = Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % antisym_conv2
% 0.29/0.54  thf(fact_2707_antisym__conv1,axiom,
% 0.29/0.54      ! [X: literal,Y: literal] :
% 0.29/0.54        ( ~ ( ord_less_literal @ X @ Y )
% 0.29/0.54       => ( ( ord_less_eq_literal @ X @ Y )
% 0.29/0.54          = ( X = Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % antisym_conv1
% 0.29/0.54  thf(fact_2708_antisym__conv1,axiom,
% 0.29/0.54      ! [X: filter_nat,Y: filter_nat] :
% 0.29/0.54        ( ~ ( ord_less_filter_nat @ X @ Y )
% 0.29/0.54       => ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 0.29/0.54          = ( X = Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % antisym_conv1
% 0.29/0.54  thf(fact_2709_antisym__conv1,axiom,
% 0.29/0.54      ! [X: set_nat,Y: set_nat] :
% 0.29/0.54        ( ~ ( ord_less_set_nat @ X @ Y )
% 0.29/0.54       => ( ( ord_less_eq_set_nat @ X @ Y )
% 0.29/0.54          = ( X = Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % antisym_conv1
% 0.29/0.54  thf(fact_2710_antisym__conv1,axiom,
% 0.29/0.54      ! [X: rat,Y: rat] :
% 0.29/0.54        ( ~ ( ord_less_rat @ X @ Y )
% 0.29/0.54       => ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.54          = ( X = Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % antisym_conv1
% 0.29/0.54  thf(fact_2711_antisym__conv1,axiom,
% 0.29/0.54      ! [X: nat,Y: nat] :
% 0.29/0.54        ( ~ ( ord_less_nat @ X @ Y )
% 0.29/0.54       => ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.54          = ( X = Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % antisym_conv1
% 0.29/0.54  thf(fact_2712_antisym__conv1,axiom,
% 0.29/0.54      ! [X: int,Y: int] :
% 0.29/0.54        ( ~ ( ord_less_int @ X @ Y )
% 0.29/0.54       => ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.54          = ( X = Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % antisym_conv1
% 0.29/0.54  thf(fact_2713_ord__le__eq__trans,axiom,
% 0.29/0.54      ! [A: filter_nat,B: filter_nat,C: filter_nat] :
% 0.29/0.54        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 0.29/0.54       => ( ( B = C )
% 0.29/0.54         => ( ord_le2510731241096832064er_nat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ord_le_eq_trans
% 0.29/0.54  thf(fact_2714_ord__le__eq__trans,axiom,
% 0.29/0.54      ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.29/0.54        ( ( ord_less_eq_set_nat @ A @ B )
% 0.29/0.54       => ( ( B = C )
% 0.29/0.54         => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ord_le_eq_trans
% 0.29/0.54  thf(fact_2715_ord__le__eq__trans,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54       => ( ( B = C )
% 0.29/0.54         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ord_le_eq_trans
% 0.29/0.54  thf(fact_2716_ord__le__eq__trans,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54       => ( ( B = C )
% 0.29/0.54         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ord_le_eq_trans
% 0.29/0.54  thf(fact_2717_ord__le__eq__trans,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54       => ( ( B = C )
% 0.29/0.54         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ord_le_eq_trans
% 0.29/0.54  thf(fact_2718_ord__eq__le__trans,axiom,
% 0.29/0.54      ! [A: filter_nat,B: filter_nat,C: filter_nat] :
% 0.29/0.54        ( ( A = B )
% 0.29/0.54       => ( ( ord_le2510731241096832064er_nat @ B @ C )
% 0.29/0.54         => ( ord_le2510731241096832064er_nat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ord_eq_le_trans
% 0.29/0.54  thf(fact_2719_ord__eq__le__trans,axiom,
% 0.29/0.54      ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.29/0.54        ( ( A = B )
% 0.29/0.54       => ( ( ord_less_eq_set_nat @ B @ C )
% 0.29/0.54         => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ord_eq_le_trans
% 0.29/0.54  thf(fact_2720_ord__eq__le__trans,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat] :
% 0.29/0.54        ( ( A = B )
% 0.29/0.54       => ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.54         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ord_eq_le_trans
% 0.29/0.54  thf(fact_2721_ord__eq__le__trans,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat] :
% 0.29/0.54        ( ( A = B )
% 0.29/0.54       => ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.54         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ord_eq_le_trans
% 0.29/0.54  thf(fact_2722_ord__eq__le__trans,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int] :
% 0.29/0.54        ( ( A = B )
% 0.29/0.54       => ( ( ord_less_eq_int @ B @ C )
% 0.29/0.54         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % ord_eq_le_trans
% 0.29/0.54  thf(fact_2723_order__class_Oorder__eq__iff,axiom,
% 0.29/0.54      ( ( ^ [Y4: filter_nat,Z4: filter_nat] : ( Y4 = Z4 ) )
% 0.29/0.54      = ( ^ [X3: filter_nat,Y3: filter_nat] :
% 0.29/0.54            ( ( ord_le2510731241096832064er_nat @ X3 @ Y3 )
% 0.29/0.54            & ( ord_le2510731241096832064er_nat @ Y3 @ X3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order_class.order_eq_iff
% 0.29/0.54  thf(fact_2724_order__class_Oorder__eq__iff,axiom,
% 0.29/0.54      ( ( ^ [Y4: set_nat,Z4: set_nat] : ( Y4 = Z4 ) )
% 0.29/0.54      = ( ^ [X3: set_nat,Y3: set_nat] :
% 0.29/0.54            ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 0.29/0.54            & ( ord_less_eq_set_nat @ Y3 @ X3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order_class.order_eq_iff
% 0.29/0.54  thf(fact_2725_order__class_Oorder__eq__iff,axiom,
% 0.29/0.54      ( ( ^ [Y4: rat,Z4: rat] : ( Y4 = Z4 ) )
% 0.29/0.54      = ( ^ [X3: rat,Y3: rat] :
% 0.29/0.54            ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.29/0.54            & ( ord_less_eq_rat @ Y3 @ X3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order_class.order_eq_iff
% 0.29/0.54  thf(fact_2726_order__class_Oorder__eq__iff,axiom,
% 0.29/0.54      ( ( ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 ) )
% 0.29/0.54      = ( ^ [X3: nat,Y3: nat] :
% 0.29/0.54            ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.29/0.54            & ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order_class.order_eq_iff
% 0.29/0.54  thf(fact_2727_order__class_Oorder__eq__iff,axiom,
% 0.29/0.54      ( ( ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 0.29/0.54      = ( ^ [X3: int,Y3: int] :
% 0.29/0.54            ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.29/0.54            & ( ord_less_eq_int @ Y3 @ X3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % order_class.order_eq_iff
% 0.29/0.54  thf(fact_2728_less__imp__neq,axiom,
% 0.29/0.54      ! [X: literal,Y: literal] :
% 0.29/0.54        ( ( ord_less_literal @ X @ Y )
% 0.29/0.54       => ( X != Y ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_imp_neq
% 0.29/0.54  thf(fact_2729_less__imp__neq,axiom,
% 0.29/0.54      ! [X: rat,Y: rat] :
% 0.29/0.54        ( ( ord_less_rat @ X @ Y )
% 0.29/0.54       => ( X != Y ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_imp_neq
% 0.29/0.54  thf(fact_2730_less__imp__neq,axiom,
% 0.29/0.54      ! [X: nat,Y: nat] :
% 0.29/0.54        ( ( ord_less_nat @ X @ Y )
% 0.29/0.54       => ( X != Y ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_imp_neq
% 0.29/0.54  thf(fact_2731_less__imp__neq,axiom,
% 0.29/0.54      ! [X: int,Y: int] :
% 0.29/0.54        ( ( ord_less_int @ X @ Y )
% 0.29/0.54       => ( X != Y ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_imp_neq
% 0.29/0.54  thf(fact_2732_le__cases3,axiom,
% 0.29/0.54      ! [X: rat,Y: rat,Z: rat] :
% 0.29/0.54        ( ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.54         => ~ ( ord_less_eq_rat @ Y @ Z ) )
% 0.29/0.54       => ( ( ( ord_less_eq_rat @ Y @ X )
% 0.29/0.54           => ~ ( ord_less_eq_rat @ X @ Z ) )
% 0.29/0.54         => ( ( ( ord_less_eq_rat @ X @ Z )
% 0.29/0.54             => ~ ( ord_less_eq_rat @ Z @ Y ) )
% 0.29/0.54           => ( ( ( ord_less_eq_rat @ Z @ Y )
% 0.29/0.54               => ~ ( ord_less_eq_rat @ Y @ X ) )
% 0.29/0.54             => ( ( ( ord_less_eq_rat @ Y @ Z )
% 0.29/0.54                 => ~ ( ord_less_eq_rat @ Z @ X ) )
% 0.29/0.54               => ~ ( ( ord_less_eq_rat @ Z @ X )
% 0.29/0.54                   => ~ ( ord_less_eq_rat @ X @ Y ) ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_cases3
% 0.29/0.54  thf(fact_2733_le__cases3,axiom,
% 0.29/0.54      ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.54        ( ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.54         => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 0.29/0.54       => ( ( ( ord_less_eq_nat @ Y @ X )
% 0.29/0.54           => ~ ( ord_less_eq_nat @ X @ Z ) )
% 0.29/0.54         => ( ( ( ord_less_eq_nat @ X @ Z )
% 0.29/0.54             => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 0.29/0.54           => ( ( ( ord_less_eq_nat @ Z @ Y )
% 0.29/0.54               => ~ ( ord_less_eq_nat @ Y @ X ) )
% 0.29/0.54             => ( ( ( ord_less_eq_nat @ Y @ Z )
% 0.29/0.54                 => ~ ( ord_less_eq_nat @ Z @ X ) )
% 0.29/0.54               => ~ ( ( ord_less_eq_nat @ Z @ X )
% 0.29/0.54                   => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_cases3
% 0.29/0.54  thf(fact_2734_le__cases3,axiom,
% 0.29/0.54      ! [X: int,Y: int,Z: int] :
% 0.29/0.54        ( ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.54         => ~ ( ord_less_eq_int @ Y @ Z ) )
% 0.29/0.54       => ( ( ( ord_less_eq_int @ Y @ X )
% 0.29/0.54           => ~ ( ord_less_eq_int @ X @ Z ) )
% 0.29/0.54         => ( ( ( ord_less_eq_int @ X @ Z )
% 0.29/0.54             => ~ ( ord_less_eq_int @ Z @ Y ) )
% 0.29/0.54           => ( ( ( ord_less_eq_int @ Z @ Y )
% 0.29/0.54               => ~ ( ord_less_eq_int @ Y @ X ) )
% 0.29/0.54             => ( ( ( ord_less_eq_int @ Y @ Z )
% 0.29/0.54                 => ~ ( ord_less_eq_int @ Z @ X ) )
% 0.29/0.54               => ~ ( ( ord_less_eq_int @ Z @ X )
% 0.29/0.54                   => ~ ( ord_less_eq_int @ X @ Y ) ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_cases3
% 0.29/0.54  thf(fact_2735_dense,axiom,
% 0.29/0.54      ! [X: rat,Y: rat] :
% 0.29/0.54        ( ( ord_less_rat @ X @ Y )
% 0.29/0.54       => ? [Z2: rat] :
% 0.29/0.54            ( ( ord_less_rat @ X @ Z2 )
% 0.29/0.54            & ( ord_less_rat @ Z2 @ Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % dense
% 0.29/0.54  thf(fact_2736_nle__le,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 0.29/0.54        = ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.54          & ( B != A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nle_le
% 0.29/0.54  thf(fact_2737_nle__le,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 0.29/0.54        = ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.54          & ( B != A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nle_le
% 0.29/0.54  thf(fact_2738_nle__le,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 0.29/0.54        = ( ( ord_less_eq_int @ B @ A )
% 0.29/0.54          & ( B != A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nle_le
% 0.29/0.54  thf(fact_2739_nless__le,axiom,
% 0.29/0.54      ! [A: literal,B: literal] :
% 0.29/0.54        ( ( ~ ( ord_less_literal @ A @ B ) )
% 0.29/0.54        = ( ~ ( ord_less_eq_literal @ A @ B )
% 0.29/0.54          | ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nless_le
% 0.29/0.54  thf(fact_2740_nless__le,axiom,
% 0.29/0.54      ! [A: filter_nat,B: filter_nat] :
% 0.29/0.54        ( ( ~ ( ord_less_filter_nat @ A @ B ) )
% 0.29/0.54        = ( ~ ( ord_le2510731241096832064er_nat @ A @ B )
% 0.29/0.54          | ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nless_le
% 0.29/0.54  thf(fact_2741_nless__le,axiom,
% 0.29/0.54      ! [A: set_nat,B: set_nat] :
% 0.29/0.54        ( ( ~ ( ord_less_set_nat @ A @ B ) )
% 0.29/0.54        = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 0.29/0.54          | ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nless_le
% 0.29/0.54  thf(fact_2742_nless__le,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ~ ( ord_less_rat @ A @ B ) )
% 0.29/0.54        = ( ~ ( ord_less_eq_rat @ A @ B )
% 0.29/0.54          | ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nless_le
% 0.29/0.54  thf(fact_2743_nless__le,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( ~ ( ord_less_nat @ A @ B ) )
% 0.29/0.54        = ( ~ ( ord_less_eq_nat @ A @ B )
% 0.29/0.54          | ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nless_le
% 0.29/0.54  thf(fact_2744_nless__le,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ~ ( ord_less_int @ A @ B ) )
% 0.29/0.54        = ( ~ ( ord_less_eq_int @ A @ B )
% 0.29/0.54          | ( A = B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % nless_le
% 0.29/0.54  thf(fact_2745_gt__ex,axiom,
% 0.29/0.54      ! [X: rat] :
% 0.29/0.54      ? [X_1: rat] : ( ord_less_rat @ X @ X_1 ) ).
% 0.29/0.54  
% 0.29/0.54  % gt_ex
% 0.29/0.54  thf(fact_2746_gt__ex,axiom,
% 0.29/0.54      ! [X: nat] :
% 0.29/0.54      ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 0.29/0.54  
% 0.29/0.54  % gt_ex
% 0.29/0.54  thf(fact_2747_gt__ex,axiom,
% 0.29/0.54      ! [X: int] :
% 0.29/0.54      ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 0.29/0.54  
% 0.29/0.54  % gt_ex
% 0.29/0.54  thf(fact_2748_lt__ex,axiom,
% 0.29/0.54      ! [X: rat] :
% 0.29/0.54      ? [Y2: rat] : ( ord_less_rat @ Y2 @ X ) ).
% 0.29/0.54  
% 0.29/0.54  % lt_ex
% 0.29/0.54  thf(fact_2749_lt__ex,axiom,
% 0.29/0.54      ! [X: int] :
% 0.29/0.54      ? [Y2: int] : ( ord_less_int @ Y2 @ X ) ).
% 0.29/0.54  
% 0.29/0.54  % lt_ex
% 0.29/0.54  thf(fact_2750_leI,axiom,
% 0.29/0.54      ! [X: literal,Y: literal] :
% 0.29/0.54        ( ~ ( ord_less_literal @ X @ Y )
% 0.29/0.54       => ( ord_less_eq_literal @ Y @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % leI
% 0.29/0.54  thf(fact_2751_leI,axiom,
% 0.29/0.54      ! [X: rat,Y: rat] :
% 0.29/0.54        ( ~ ( ord_less_rat @ X @ Y )
% 0.29/0.54       => ( ord_less_eq_rat @ Y @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % leI
% 0.29/0.54  thf(fact_2752_leI,axiom,
% 0.29/0.54      ! [X: nat,Y: nat] :
% 0.29/0.54        ( ~ ( ord_less_nat @ X @ Y )
% 0.29/0.54       => ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % leI
% 0.29/0.54  thf(fact_2753_leI,axiom,
% 0.29/0.54      ! [X: int,Y: int] :
% 0.29/0.54        ( ~ ( ord_less_int @ X @ Y )
% 0.29/0.54       => ( ord_less_eq_int @ Y @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % leI
% 0.29/0.54  thf(fact_2754_leD,axiom,
% 0.29/0.54      ! [Y: literal,X: literal] :
% 0.29/0.54        ( ( ord_less_eq_literal @ Y @ X )
% 0.29/0.54       => ~ ( ord_less_literal @ X @ Y ) ) ).
% 0.29/0.54  
% 0.29/0.54  % leD
% 0.29/0.54  thf(fact_2755_leD,axiom,
% 0.29/0.54      ! [Y: filter_nat,X: filter_nat] :
% 0.29/0.54        ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 0.29/0.54       => ~ ( ord_less_filter_nat @ X @ Y ) ) ).
% 0.29/0.54  
% 0.29/0.54  % leD
% 0.29/0.54  thf(fact_2756_leD,axiom,
% 0.29/0.54      ! [Y: set_nat,X: set_nat] :
% 0.29/0.54        ( ( ord_less_eq_set_nat @ Y @ X )
% 0.29/0.54       => ~ ( ord_less_set_nat @ X @ Y ) ) ).
% 0.29/0.54  
% 0.29/0.54  % leD
% 0.29/0.54  thf(fact_2757_leD,axiom,
% 0.29/0.54      ! [Y: rat,X: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ Y @ X )
% 0.29/0.54       => ~ ( ord_less_rat @ X @ Y ) ) ).
% 0.29/0.54  
% 0.29/0.54  % leD
% 0.29/0.54  thf(fact_2758_leD,axiom,
% 0.29/0.54      ! [Y: nat,X: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ Y @ X )
% 0.29/0.54       => ~ ( ord_less_nat @ X @ Y ) ) ).
% 0.29/0.54  
% 0.29/0.54  % leD
% 0.29/0.54  thf(fact_2759_leD,axiom,
% 0.29/0.54      ! [Y: int,X: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ Y @ X )
% 0.29/0.54       => ~ ( ord_less_int @ X @ Y ) ) ).
% 0.29/0.54  
% 0.29/0.54  % leD
% 0.29/0.54  thf(fact_2760_pred__subset__eq2,axiom,
% 0.29/0.54      ! [R: set_Pr1281608226676607948nteger,S: set_Pr1281608226676607948nteger] :
% 0.29/0.54        ( ( ord_le4340812435750786203eger_o
% 0.29/0.54          @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ R )
% 0.29/0.54          @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ S ) )
% 0.29/0.54        = ( ord_le653643898420964396nteger @ R @ S ) ) ).
% 0.29/0.54  
% 0.29/0.54  % pred_subset_eq2
% 0.29/0.54  thf(fact_2761_pred__subset__eq2,axiom,
% 0.29/0.54      ! [R: set_Pr3286484037609594932et_nat,S: set_Pr3286484037609594932et_nat] :
% 0.29/0.54        ( ( ord_le8000401564054156549_nat_o
% 0.29/0.54          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R )
% 0.29/0.54          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ S ) )
% 0.29/0.54        = ( ord_le5966269811547037844et_nat @ R @ S ) ) ).
% 0.29/0.54  
% 0.29/0.54  % pred_subset_eq2
% 0.29/0.54  thf(fact_2762_pred__subset__eq2,axiom,
% 0.29/0.54      ! [R: set_Pr8536935166611901872et_nat,S: set_Pr8536935166611901872et_nat] :
% 0.29/0.54        ( ( ord_le6753239538765779593_nat_o
% 0.29/0.54          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R )
% 0.29/0.54          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ S ) )
% 0.29/0.54        = ( ord_le4763372923235995152et_nat @ R @ S ) ) ).
% 0.29/0.54  
% 0.29/0.54  % pred_subset_eq2
% 0.29/0.54  thf(fact_2763_pred__subset__eq2,axiom,
% 0.29/0.54      ! [R: set_Pr9222295170931077689nt_int,S: set_Pr9222295170931077689nt_int] :
% 0.29/0.54        ( ( ord_le5643404153117327598_int_o
% 0.29/0.54          @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ R )
% 0.29/0.54          @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ S ) )
% 0.29/0.54        = ( ord_le8725513860283290265nt_int @ R @ S ) ) ).
% 0.29/0.54  
% 0.29/0.54  % pred_subset_eq2
% 0.29/0.54  thf(fact_2764_pred__subset__eq2,axiom,
% 0.29/0.54      ! [R: set_Pr1872883991513573699nt_int,S: set_Pr1872883991513573699nt_int] :
% 0.29/0.54        ( ( ord_le2124322318746777828_int_o
% 0.29/0.54          @ ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ R )
% 0.29/0.54          @ ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ S ) )
% 0.29/0.54        = ( ord_le135402666524580259nt_int @ R @ S ) ) ).
% 0.29/0.54  
% 0.29/0.54  % pred_subset_eq2
% 0.29/0.54  thf(fact_2765_mult__less__le__imp__less,axiom,
% 0.29/0.54      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.29/0.54        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.29/0.54       => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 0.29/0.54         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.54           => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.29/0.54             => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_le_imp_less
% 0.29/0.54  thf(fact_2766_mult__less__le__imp__less,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_rat @ C @ D2 )
% 0.29/0.54         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.54           => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.54             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_le_imp_less
% 0.29/0.54  thf(fact_2767_mult__less__le__imp__less,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.29/0.54        ( ( ord_less_nat @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_nat @ C @ D2 )
% 0.29/0.54         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.54           => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.29/0.54             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_le_imp_less
% 0.29/0.54  thf(fact_2768_mult__less__le__imp__less,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.54        ( ( ord_less_int @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_int @ C @ D2 )
% 0.29/0.54         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.54           => ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.54             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_le_imp_less
% 0.29/0.54  thf(fact_2769_mult__le__less__imp__less,axiom,
% 0.29/0.54      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.29/0.54        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.29/0.54       => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 0.29/0.54         => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.54           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.29/0.54             => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_less_imp_less
% 0.29/0.54  thf(fact_2770_mult__le__less__imp__less,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54       => ( ( ord_less_rat @ C @ D2 )
% 0.29/0.54         => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.29/0.54           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.54             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_less_imp_less
% 0.29/0.54  thf(fact_2771_mult__le__less__imp__less,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.54       => ( ( ord_less_nat @ C @ D2 )
% 0.29/0.54         => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.29/0.54           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.54             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_less_imp_less
% 0.29/0.54  thf(fact_2772_mult__le__less__imp__less,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54       => ( ( ord_less_int @ C @ D2 )
% 0.29/0.54         => ( ( ord_less_int @ zero_zero_int @ A )
% 0.29/0.54           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.54             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_less_imp_less
% 0.29/0.54  thf(fact_2773_mult__right__le__imp__le,axiom,
% 0.29/0.54      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.54        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.29/0.54       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.29/0.54         => ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_le_imp_le
% 0.29/0.54  thf(fact_2774_mult__right__le__imp__le,axiom,
% 0.29/0.54      ! [A: rat,C: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.29/0.54       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.54         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_le_imp_le
% 0.29/0.54  thf(fact_2775_mult__right__le__imp__le,axiom,
% 0.29/0.54      ! [A: nat,C: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.29/0.54       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.29/0.54         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_le_imp_le
% 0.29/0.54  thf(fact_2776_mult__right__le__imp__le,axiom,
% 0.29/0.54      ! [A: int,C: int,B: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.29/0.54       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.54         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_le_imp_le
% 0.29/0.54  thf(fact_2777_mult__left__le__imp__le,axiom,
% 0.29/0.54      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.54        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.29/0.54       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.29/0.54         => ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_le_imp_le
% 0.29/0.54  thf(fact_2778_mult__left__le__imp__le,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.54       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.54         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_le_imp_le
% 0.29/0.54  thf(fact_2779_mult__left__le__imp__le,axiom,
% 0.29/0.54      ! [C: nat,A: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.29/0.54       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.29/0.54         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_le_imp_le
% 0.29/0.54  thf(fact_2780_mult__left__le__imp__le,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.54       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.54         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_le_imp_le
% 0.29/0.54  thf(fact_2781_mult__le__cancel__left__pos,axiom,
% 0.29/0.54      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.54        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.29/0.54       => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.29/0.54          = ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_cancel_left_pos
% 0.29/0.54  thf(fact_2782_mult__le__cancel__left__pos,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.54       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.54          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_cancel_left_pos
% 0.29/0.54  thf(fact_2783_mult__le__cancel__left__pos,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.54       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.54          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_cancel_left_pos
% 0.29/0.54  thf(fact_2784_mult__le__cancel__left__neg,axiom,
% 0.29/0.54      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.54        ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.29/0.54       => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.29/0.54          = ( ord_le3102999989581377725nteger @ B @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_cancel_left_neg
% 0.29/0.54  thf(fact_2785_mult__le__cancel__left__neg,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.54       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.54          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_cancel_left_neg
% 0.29/0.54  thf(fact_2786_mult__le__cancel__left__neg,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.54       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.54          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_cancel_left_neg
% 0.29/0.54  thf(fact_2787_mult__less__cancel__right,axiom,
% 0.29/0.54      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.54        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.29/0.54        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.29/0.54           => ( ord_le6747313008572928689nteger @ A @ B ) )
% 0.29/0.54          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.29/0.54           => ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_right
% 0.29/0.54  thf(fact_2788_mult__less__cancel__right,axiom,
% 0.29/0.54      ! [A: rat,C: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.29/0.54        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.54           => ( ord_less_rat @ A @ B ) )
% 0.29/0.54          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.29/0.54           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_right
% 0.29/0.54  thf(fact_2789_mult__less__cancel__right,axiom,
% 0.29/0.54      ! [A: int,C: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.29/0.54        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.54           => ( ord_less_int @ A @ B ) )
% 0.29/0.54          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.29/0.54           => ( ord_less_int @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_right
% 0.29/0.54  thf(fact_2790_mult__strict__mono_H,axiom,
% 0.29/0.54      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.29/0.54        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.29/0.54       => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 0.29/0.54         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.29/0.54           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.29/0.54             => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_mono'
% 0.29/0.54  thf(fact_2791_mult__strict__mono_H,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ B )
% 0.29/0.54       => ( ( ord_less_rat @ C @ D2 )
% 0.29/0.54         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.29/0.54           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.54             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_mono'
% 0.29/0.54  thf(fact_2792_mult__strict__mono_H,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.29/0.54        ( ( ord_less_nat @ A @ B )
% 0.29/0.54       => ( ( ord_less_nat @ C @ D2 )
% 0.29/0.54         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.29/0.54           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.54             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_mono'
% 0.29/0.54  thf(fact_2793_mult__strict__mono_H,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.54        ( ( ord_less_int @ A @ B )
% 0.29/0.54       => ( ( ord_less_int @ C @ D2 )
% 0.29/0.54         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.29/0.54           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.54             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_mono'
% 0.29/0.54  thf(fact_2794_mult__right__less__imp__less,axiom,
% 0.29/0.54      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.54        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.29/0.54       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.29/0.54         => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_less_imp_less
% 0.29/0.54  thf(fact_2795_mult__right__less__imp__less,axiom,
% 0.29/0.54      ! [A: rat,C: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.29/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.54         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_less_imp_less
% 0.29/0.54  thf(fact_2796_mult__right__less__imp__less,axiom,
% 0.29/0.54      ! [A: nat,C: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.29/0.54       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.54         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_less_imp_less
% 0.29/0.54  thf(fact_2797_mult__right__less__imp__less,axiom,
% 0.29/0.54      ! [A: int,C: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.29/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.54         => ( ord_less_int @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_right_less_imp_less
% 0.29/0.54  thf(fact_2798_mult__less__cancel__left,axiom,
% 0.29/0.54      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.54        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.29/0.54        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.29/0.54           => ( ord_le6747313008572928689nteger @ A @ B ) )
% 0.29/0.54          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.29/0.54           => ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_left
% 0.29/0.54  thf(fact_2799_mult__less__cancel__left,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.54        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.54           => ( ord_less_rat @ A @ B ) )
% 0.29/0.54          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.29/0.54           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_left
% 0.29/0.54  thf(fact_2800_mult__less__cancel__left,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.54        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.54           => ( ord_less_int @ A @ B ) )
% 0.29/0.54          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.29/0.54           => ( ord_less_int @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_less_cancel_left
% 0.29/0.54  thf(fact_2801_mult__strict__mono,axiom,
% 0.29/0.54      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.29/0.54        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.29/0.54       => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 0.29/0.54         => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.29/0.54           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.29/0.54             => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_mono
% 0.29/0.54  thf(fact_2802_mult__strict__mono,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ B )
% 0.29/0.54       => ( ( ord_less_rat @ C @ D2 )
% 0.29/0.54         => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.29/0.54           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.54             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_mono
% 0.29/0.54  thf(fact_2803_mult__strict__mono,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.29/0.54        ( ( ord_less_nat @ A @ B )
% 0.29/0.54       => ( ( ord_less_nat @ C @ D2 )
% 0.29/0.54         => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.29/0.54           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.54             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_mono
% 0.29/0.54  thf(fact_2804_mult__strict__mono,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.54        ( ( ord_less_int @ A @ B )
% 0.29/0.54       => ( ( ord_less_int @ C @ D2 )
% 0.29/0.54         => ( ( ord_less_int @ zero_zero_int @ B )
% 0.29/0.54           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.54             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_strict_mono
% 0.29/0.54  thf(fact_2805_mult__left__less__imp__less,axiom,
% 0.29/0.54      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.54        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.29/0.54       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.29/0.54         => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_less_imp_less
% 0.29/0.54  thf(fact_2806_mult__left__less__imp__less,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.54       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.29/0.54         => ( ord_less_rat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_less_imp_less
% 0.29/0.54  thf(fact_2807_mult__left__less__imp__less,axiom,
% 0.29/0.54      ! [C: nat,A: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 0.29/0.54       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.29/0.54         => ( ord_less_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_less_imp_less
% 0.29/0.54  thf(fact_2808_mult__left__less__imp__less,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.54       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.29/0.54         => ( ord_less_int @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_left_less_imp_less
% 0.29/0.54  thf(fact_2809_mult__le__cancel__right,axiom,
% 0.29/0.54      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.29/0.54        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.29/0.54        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.29/0.54           => ( ord_le3102999989581377725nteger @ A @ B ) )
% 0.29/0.54          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.29/0.54           => ( ord_le3102999989581377725nteger @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_cancel_right
% 0.29/0.54  thf(fact_2810_mult__le__cancel__right,axiom,
% 0.29/0.54      ! [A: rat,C: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.29/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.54           => ( ord_less_eq_rat @ A @ B ) )
% 0.29/0.54          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.54           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_cancel_right
% 0.29/0.54  thf(fact_2811_mult__le__cancel__right,axiom,
% 0.29/0.54      ! [A: int,C: int,B: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.29/0.54        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.54           => ( ord_less_eq_int @ A @ B ) )
% 0.29/0.54          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.54           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_cancel_right
% 0.29/0.54  thf(fact_2812_mult__le__cancel__left,axiom,
% 0.29/0.54      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.29/0.54        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.29/0.54        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.29/0.54           => ( ord_le3102999989581377725nteger @ A @ B ) )
% 0.29/0.54          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.29/0.54           => ( ord_le3102999989581377725nteger @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_cancel_left
% 0.29/0.54  thf(fact_2813_mult__le__cancel__left,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.29/0.54        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.29/0.54           => ( ord_less_eq_rat @ A @ B ) )
% 0.29/0.54          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.29/0.54           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_cancel_left
% 0.29/0.54  thf(fact_2814_mult__le__cancel__left,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.29/0.54        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.29/0.54           => ( ord_less_eq_int @ A @ B ) )
% 0.29/0.54          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.29/0.54           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % mult_le_cancel_left
% 0.29/0.54  thf(fact_2815_zero__less__iff__neq__zero,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.29/0.54        = ( N != zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_less_iff_neq_zero
% 0.29/0.54  thf(fact_2816_gr__implies__not__zero,axiom,
% 0.29/0.54      ! [M: nat,N: nat] :
% 0.29/0.54        ( ( ord_less_nat @ M @ N )
% 0.29/0.54       => ( N != zero_zero_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % gr_implies_not_zero
% 0.29/0.54  thf(fact_2817_not__less__zero,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % not_less_zero
% 0.29/0.54  thf(fact_2818_gr__zeroI,axiom,
% 0.29/0.54      ! [N: nat] :
% 0.29/0.54        ( ( N != zero_zero_nat )
% 0.29/0.54       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.29/0.54  
% 0.29/0.54  % gr_zeroI
% 0.29/0.54  thf(fact_2819_zero__le,axiom,
% 0.29/0.54      ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 0.29/0.54  
% 0.29/0.54  % zero_le
% 0.29/0.54  thf(fact_2820_less__numeral__extra_I4_J,axiom,
% 0.29/0.54      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 0.29/0.54  
% 0.29/0.54  % less_numeral_extra(4)
% 0.29/0.54  thf(fact_2821_less__numeral__extra_I4_J,axiom,
% 0.29/0.54      ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 0.29/0.54  
% 0.29/0.54  % less_numeral_extra(4)
% 0.29/0.54  thf(fact_2822_less__numeral__extra_I4_J,axiom,
% 0.29/0.54      ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % less_numeral_extra(4)
% 0.29/0.54  thf(fact_2823_less__numeral__extra_I4_J,axiom,
% 0.29/0.54      ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 0.29/0.54  
% 0.29/0.54  % less_numeral_extra(4)
% 0.29/0.54  thf(fact_2824_diff__strict__right__mono,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ B )
% 0.29/0.54       => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_strict_right_mono
% 0.29/0.54  thf(fact_2825_diff__strict__right__mono,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int] :
% 0.29/0.54        ( ( ord_less_int @ A @ B )
% 0.29/0.54       => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_strict_right_mono
% 0.29/0.54  thf(fact_2826_diff__strict__left__mono,axiom,
% 0.29/0.54      ! [B: rat,A: rat,C: rat] :
% 0.29/0.54        ( ( ord_less_rat @ B @ A )
% 0.29/0.54       => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_strict_left_mono
% 0.29/0.54  thf(fact_2827_diff__strict__left__mono,axiom,
% 0.29/0.54      ! [B: int,A: int,C: int] :
% 0.29/0.54        ( ( ord_less_int @ B @ A )
% 0.29/0.54       => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_strict_left_mono
% 0.29/0.54  thf(fact_2828_diff__eq__diff__less,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.54        ( ( ( minus_minus_rat @ A @ B )
% 0.29/0.54          = ( minus_minus_rat @ C @ D2 ) )
% 0.29/0.54       => ( ( ord_less_rat @ A @ B )
% 0.29/0.54          = ( ord_less_rat @ C @ D2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_eq_diff_less
% 0.29/0.54  thf(fact_2829_diff__eq__diff__less,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.54        ( ( ( minus_minus_int @ A @ B )
% 0.29/0.54          = ( minus_minus_int @ C @ D2 ) )
% 0.29/0.54       => ( ( ord_less_int @ A @ B )
% 0.29/0.54          = ( ord_less_int @ C @ D2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_eq_diff_less
% 0.29/0.54  thf(fact_2830_diff__strict__mono,axiom,
% 0.29/0.54      ! [A: rat,B: rat,D2: rat,C: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ B )
% 0.29/0.54       => ( ( ord_less_rat @ D2 @ C )
% 0.29/0.54         => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_strict_mono
% 0.29/0.54  thf(fact_2831_diff__strict__mono,axiom,
% 0.29/0.54      ! [A: int,B: int,D2: int,C: int] :
% 0.29/0.54        ( ( ord_less_int @ A @ B )
% 0.29/0.54       => ( ( ord_less_int @ D2 @ C )
% 0.29/0.54         => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_strict_mono
% 0.29/0.54  thf(fact_2832_bot_Oextremum__strict,axiom,
% 0.29/0.54      ! [A: set_Pr1261947904930325089at_nat] :
% 0.29/0.54        ~ ( ord_le7866589430770878221at_nat @ A @ bot_bo2099793752762293965at_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum_strict
% 0.29/0.54  thf(fact_2833_bot_Oextremum__strict,axiom,
% 0.29/0.54      ! [A: set_o] :
% 0.29/0.54        ~ ( ord_less_set_o @ A @ bot_bot_set_o ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum_strict
% 0.29/0.54  thf(fact_2834_bot_Oextremum__strict,axiom,
% 0.29/0.54      ! [A: set_nat] :
% 0.29/0.54        ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum_strict
% 0.29/0.54  thf(fact_2835_bot_Oextremum__strict,axiom,
% 0.29/0.54      ! [A: set_int] :
% 0.29/0.54        ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum_strict
% 0.29/0.54  thf(fact_2836_bot_Oextremum__strict,axiom,
% 0.29/0.54      ! [A: nat] :
% 0.29/0.54        ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum_strict
% 0.29/0.54  thf(fact_2837_bot_Onot__eq__extremum,axiom,
% 0.29/0.54      ! [A: set_Pr1261947904930325089at_nat] :
% 0.29/0.54        ( ( A != bot_bo2099793752762293965at_nat )
% 0.29/0.54        = ( ord_le7866589430770878221at_nat @ bot_bo2099793752762293965at_nat @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.not_eq_extremum
% 0.29/0.54  thf(fact_2838_bot_Onot__eq__extremum,axiom,
% 0.29/0.54      ! [A: set_o] :
% 0.29/0.54        ( ( A != bot_bot_set_o )
% 0.29/0.54        = ( ord_less_set_o @ bot_bot_set_o @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.not_eq_extremum
% 0.29/0.54  thf(fact_2839_bot_Onot__eq__extremum,axiom,
% 0.29/0.54      ! [A: set_nat] :
% 0.29/0.54        ( ( A != bot_bot_set_nat )
% 0.29/0.54        = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.not_eq_extremum
% 0.29/0.54  thf(fact_2840_bot_Onot__eq__extremum,axiom,
% 0.29/0.54      ! [A: set_int] :
% 0.29/0.54        ( ( A != bot_bot_set_int )
% 0.29/0.54        = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.not_eq_extremum
% 0.29/0.54  thf(fact_2841_bot_Onot__eq__extremum,axiom,
% 0.29/0.54      ! [A: nat] :
% 0.29/0.54        ( ( A != bot_bot_nat )
% 0.29/0.54        = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.not_eq_extremum
% 0.29/0.54  thf(fact_2842_not__psubset__empty,axiom,
% 0.29/0.54      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.29/0.54        ~ ( ord_le7866589430770878221at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % not_psubset_empty
% 0.29/0.54  thf(fact_2843_not__psubset__empty,axiom,
% 0.29/0.54      ! [A2: set_o] :
% 0.29/0.54        ~ ( ord_less_set_o @ A2 @ bot_bot_set_o ) ).
% 0.29/0.54  
% 0.29/0.54  % not_psubset_empty
% 0.29/0.54  thf(fact_2844_not__psubset__empty,axiom,
% 0.29/0.54      ! [A2: set_nat] :
% 0.29/0.54        ~ ( ord_less_set_nat @ A2 @ bot_bot_set_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % not_psubset_empty
% 0.29/0.54  thf(fact_2845_not__psubset__empty,axiom,
% 0.29/0.54      ! [A2: set_int] :
% 0.29/0.54        ~ ( ord_less_set_int @ A2 @ bot_bot_set_int ) ).
% 0.29/0.54  
% 0.29/0.54  % not_psubset_empty
% 0.29/0.54  thf(fact_2846_verit__negate__coefficient_I2_J,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ A @ B )
% 0.29/0.54       => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % verit_negate_coefficient(2)
% 0.29/0.54  thf(fact_2847_verit__negate__coefficient_I2_J,axiom,
% 0.29/0.54      ! [A: code_integer,B: code_integer] :
% 0.29/0.54        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.29/0.54       => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % verit_negate_coefficient(2)
% 0.29/0.54  thf(fact_2848_verit__negate__coefficient_I2_J,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ B )
% 0.29/0.54       => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % verit_negate_coefficient(2)
% 0.29/0.54  thf(fact_2849_less__minus__iff,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 0.29/0.54        = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_minus_iff
% 0.29/0.54  thf(fact_2850_less__minus__iff,axiom,
% 0.29/0.54      ! [A: code_integer,B: code_integer] :
% 0.29/0.54        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.54        = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_minus_iff
% 0.29/0.54  thf(fact_2851_less__minus__iff,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.29/0.54        = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_minus_iff
% 0.29/0.54  thf(fact_2852_minus__less__iff,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 0.29/0.54        = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % minus_less_iff
% 0.29/0.54  thf(fact_2853_minus__less__iff,axiom,
% 0.29/0.54      ! [A: code_integer,B: code_integer] :
% 0.29/0.54        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.29/0.54        = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % minus_less_iff
% 0.29/0.54  thf(fact_2854_minus__less__iff,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.29/0.54        = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % minus_less_iff
% 0.29/0.54  thf(fact_2855_compl__less__swap2,axiom,
% 0.29/0.54      ! [Y: product_unit,X: product_unit] :
% 0.29/0.54        ( ( ord_le361264281704409273t_unit @ ( uminus2952777764628376836t_unit @ Y ) @ X )
% 0.29/0.54       => ( ord_le361264281704409273t_unit @ ( uminus2952777764628376836t_unit @ X ) @ Y ) ) ).
% 0.29/0.54  
% 0.29/0.54  % compl_less_swap2
% 0.29/0.54  thf(fact_2856_compl__less__swap1,axiom,
% 0.29/0.54      ! [Y: product_unit,X: product_unit] :
% 0.29/0.54        ( ( ord_le361264281704409273t_unit @ Y @ ( uminus2952777764628376836t_unit @ X ) )
% 0.29/0.54       => ( ord_le361264281704409273t_unit @ X @ ( uminus2952777764628376836t_unit @ Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % compl_less_swap1
% 0.29/0.54  thf(fact_2857_le__numeral__extra_I4_J,axiom,
% 0.29/0.54      ord_le3102999989581377725nteger @ one_one_Code_integer @ one_one_Code_integer ).
% 0.29/0.54  
% 0.29/0.54  % le_numeral_extra(4)
% 0.29/0.54  thf(fact_2858_le__numeral__extra_I4_J,axiom,
% 0.29/0.54      ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 0.29/0.54  
% 0.29/0.54  % le_numeral_extra(4)
% 0.29/0.54  thf(fact_2859_le__numeral__extra_I4_J,axiom,
% 0.29/0.54      ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 0.29/0.54  
% 0.29/0.54  % le_numeral_extra(4)
% 0.29/0.54  thf(fact_2860_le__numeral__extra_I4_J,axiom,
% 0.29/0.54      ord_less_eq_int @ one_one_int @ one_one_int ).
% 0.29/0.54  
% 0.29/0.54  % le_numeral_extra(4)
% 0.29/0.54  thf(fact_2861_diff__eq__diff__less__eq,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.29/0.54        ( ( ( minus_minus_rat @ A @ B )
% 0.29/0.54          = ( minus_minus_rat @ C @ D2 ) )
% 0.29/0.54       => ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54          = ( ord_less_eq_rat @ C @ D2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_eq_diff_less_eq
% 0.29/0.54  thf(fact_2862_diff__eq__diff__less__eq,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int,D2: int] :
% 0.29/0.54        ( ( ( minus_minus_int @ A @ B )
% 0.29/0.54          = ( minus_minus_int @ C @ D2 ) )
% 0.29/0.54       => ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54          = ( ord_less_eq_int @ C @ D2 ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_eq_diff_less_eq
% 0.29/0.54  thf(fact_2863_diff__right__mono,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54       => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_right_mono
% 0.29/0.54  thf(fact_2864_diff__right__mono,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54       => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_right_mono
% 0.29/0.54  thf(fact_2865_diff__left__mono,axiom,
% 0.29/0.54      ! [B: rat,A: rat,C: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.54       => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_left_mono
% 0.29/0.54  thf(fact_2866_diff__left__mono,axiom,
% 0.29/0.54      ! [B: int,A: int,C: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.54       => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_left_mono
% 0.29/0.54  thf(fact_2867_diff__mono,axiom,
% 0.29/0.54      ! [A: rat,B: rat,D2: rat,C: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_rat @ D2 @ C )
% 0.29/0.54         => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_mono
% 0.29/0.54  thf(fact_2868_diff__mono,axiom,
% 0.29/0.54      ! [A: int,B: int,D2: int,C: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54       => ( ( ord_less_eq_int @ D2 @ C )
% 0.29/0.54         => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % diff_mono
% 0.29/0.54  thf(fact_2869_subrelI,axiom,
% 0.29/0.54      ! [R3: set_Pr1281608226676607948nteger,S3: set_Pr1281608226676607948nteger] :
% 0.29/0.54        ( ! [X2: produc6241069584506657477e_term > option6357759511663192854e_term,Y2: produc8923325533196201883nteger] :
% 0.29/0.54            ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X2 @ Y2 ) @ R3 )
% 0.29/0.54           => ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X2 @ Y2 ) @ S3 ) )
% 0.29/0.54       => ( ord_le653643898420964396nteger @ R3 @ S3 ) ) ).
% 0.29/0.54  
% 0.29/0.54  % subrelI
% 0.29/0.54  thf(fact_2870_subrelI,axiom,
% 0.29/0.54      ! [R3: set_Pr3286484037609594932et_nat,S3: set_Pr3286484037609594932et_nat] :
% 0.29/0.54        ( ! [X2: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 0.29/0.54            ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X2 @ Y2 ) @ R3 )
% 0.29/0.54           => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X2 @ Y2 ) @ S3 ) )
% 0.29/0.54       => ( ord_le5966269811547037844et_nat @ R3 @ S3 ) ) ).
% 0.29/0.54  
% 0.29/0.54  % subrelI
% 0.29/0.54  thf(fact_2871_subrelI,axiom,
% 0.29/0.54      ! [R3: set_Pr8536935166611901872et_nat,S3: set_Pr8536935166611901872et_nat] :
% 0.29/0.54        ( ! [X2: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat] :
% 0.29/0.54            ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X2 @ Y2 ) @ R3 )
% 0.29/0.54           => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X2 @ Y2 ) @ S3 ) )
% 0.29/0.54       => ( ord_le4763372923235995152et_nat @ R3 @ S3 ) ) ).
% 0.29/0.54  
% 0.29/0.54  % subrelI
% 0.29/0.54  thf(fact_2872_subrelI,axiom,
% 0.29/0.54      ! [R3: set_Pr9222295170931077689nt_int,S3: set_Pr9222295170931077689nt_int] :
% 0.29/0.54        ( ! [X2: produc8551481072490612790e_term > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 0.29/0.54            ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X2 @ Y2 ) @ R3 )
% 0.29/0.54           => ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X2 @ Y2 ) @ S3 ) )
% 0.29/0.54       => ( ord_le8725513860283290265nt_int @ R3 @ S3 ) ) ).
% 0.29/0.54  
% 0.29/0.54  % subrelI
% 0.29/0.54  thf(fact_2873_subrelI,axiom,
% 0.29/0.54      ! [R3: set_Pr1872883991513573699nt_int,S3: set_Pr1872883991513573699nt_int] :
% 0.29/0.54        ( ! [X2: int > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 0.29/0.54            ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X2 @ Y2 ) @ R3 )
% 0.29/0.54           => ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X2 @ Y2 ) @ S3 ) )
% 0.29/0.54       => ( ord_le135402666524580259nt_int @ R3 @ S3 ) ) ).
% 0.29/0.54  
% 0.29/0.54  % subrelI
% 0.29/0.54  thf(fact_2874_bot_Oextremum,axiom,
% 0.29/0.54      ! [A: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ bot_bo2099793752762293965at_nat @ A ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum
% 0.29/0.54  thf(fact_2875_bot_Oextremum,axiom,
% 0.29/0.54      ! [A: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum
% 0.29/0.54  thf(fact_2876_bot_Oextremum,axiom,
% 0.29/0.54      ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum
% 0.29/0.54  thf(fact_2877_bot_Oextremum,axiom,
% 0.29/0.54      ! [A: filter_nat] : ( ord_le2510731241096832064er_nat @ bot_bot_filter_nat @ A ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum
% 0.29/0.54  thf(fact_2878_bot_Oextremum,axiom,
% 0.29/0.54      ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum
% 0.29/0.54  thf(fact_2879_bot_Oextremum,axiom,
% 0.29/0.54      ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum
% 0.29/0.54  thf(fact_2880_bot_Oextremum__unique,axiom,
% 0.29/0.54      ! [A: set_Pr1261947904930325089at_nat] :
% 0.29/0.54        ( ( ord_le3146513528884898305at_nat @ A @ bot_bo2099793752762293965at_nat )
% 0.29/0.54        = ( A = bot_bo2099793752762293965at_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum_unique
% 0.29/0.54  thf(fact_2881_bot_Oextremum__unique,axiom,
% 0.29/0.54      ! [A: set_o] :
% 0.29/0.54        ( ( ord_less_eq_set_o @ A @ bot_bot_set_o )
% 0.29/0.54        = ( A = bot_bot_set_o ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum_unique
% 0.29/0.54  thf(fact_2882_bot_Oextremum__unique,axiom,
% 0.29/0.54      ! [A: set_int] :
% 0.29/0.54        ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 0.29/0.54        = ( A = bot_bot_set_int ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum_unique
% 0.29/0.54  thf(fact_2883_bot_Oextremum__unique,axiom,
% 0.29/0.54      ! [A: filter_nat] :
% 0.29/0.54        ( ( ord_le2510731241096832064er_nat @ A @ bot_bot_filter_nat )
% 0.29/0.54        = ( A = bot_bot_filter_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum_unique
% 0.29/0.54  thf(fact_2884_bot_Oextremum__unique,axiom,
% 0.29/0.54      ! [A: set_nat] :
% 0.29/0.54        ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 0.29/0.54        = ( A = bot_bot_set_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum_unique
% 0.29/0.54  thf(fact_2885_bot_Oextremum__unique,axiom,
% 0.29/0.54      ! [A: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 0.29/0.54        = ( A = bot_bot_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum_unique
% 0.29/0.54  thf(fact_2886_bot_Oextremum__uniqueI,axiom,
% 0.29/0.54      ! [A: set_Pr1261947904930325089at_nat] :
% 0.29/0.54        ( ( ord_le3146513528884898305at_nat @ A @ bot_bo2099793752762293965at_nat )
% 0.29/0.54       => ( A = bot_bo2099793752762293965at_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum_uniqueI
% 0.29/0.54  thf(fact_2887_bot_Oextremum__uniqueI,axiom,
% 0.29/0.54      ! [A: set_o] :
% 0.29/0.54        ( ( ord_less_eq_set_o @ A @ bot_bot_set_o )
% 0.29/0.54       => ( A = bot_bot_set_o ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum_uniqueI
% 0.29/0.54  thf(fact_2888_bot_Oextremum__uniqueI,axiom,
% 0.29/0.54      ! [A: set_int] :
% 0.29/0.54        ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 0.29/0.54       => ( A = bot_bot_set_int ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum_uniqueI
% 0.29/0.54  thf(fact_2889_bot_Oextremum__uniqueI,axiom,
% 0.29/0.54      ! [A: filter_nat] :
% 0.29/0.54        ( ( ord_le2510731241096832064er_nat @ A @ bot_bot_filter_nat )
% 0.29/0.54       => ( A = bot_bot_filter_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum_uniqueI
% 0.29/0.54  thf(fact_2890_bot_Oextremum__uniqueI,axiom,
% 0.29/0.54      ! [A: set_nat] :
% 0.29/0.54        ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 0.29/0.54       => ( A = bot_bot_set_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum_uniqueI
% 0.29/0.54  thf(fact_2891_bot_Oextremum__uniqueI,axiom,
% 0.29/0.54      ! [A: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 0.29/0.54       => ( A = bot_bot_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % bot.extremum_uniqueI
% 0.29/0.54  thf(fact_2892_top_Onot__eq__extremum,axiom,
% 0.29/0.54      ! [A: set_list_nat] :
% 0.29/0.54        ( ( A != top_top_set_list_nat )
% 0.29/0.54        = ( ord_le1190675801316882794st_nat @ A @ top_top_set_list_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % top.not_eq_extremum
% 0.29/0.54  thf(fact_2893_top_Onot__eq__extremum,axiom,
% 0.29/0.54      ! [A: set_o] :
% 0.29/0.54        ( ( A != top_top_set_o )
% 0.29/0.54        = ( ord_less_set_o @ A @ top_top_set_o ) ) ).
% 0.29/0.54  
% 0.29/0.54  % top.not_eq_extremum
% 0.29/0.54  thf(fact_2894_top_Onot__eq__extremum,axiom,
% 0.29/0.54      ! [A: set_rat] :
% 0.29/0.54        ( ( A != top_top_set_rat )
% 0.29/0.54        = ( ord_less_set_rat @ A @ top_top_set_rat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % top.not_eq_extremum
% 0.29/0.54  thf(fact_2895_top_Onot__eq__extremum,axiom,
% 0.29/0.54      ! [A: set_nat] :
% 0.29/0.54        ( ( A != top_top_set_nat )
% 0.29/0.54        = ( ord_less_set_nat @ A @ top_top_set_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % top.not_eq_extremum
% 0.29/0.54  thf(fact_2896_top_Onot__eq__extremum,axiom,
% 0.29/0.54      ! [A: set_int] :
% 0.29/0.54        ( ( A != top_top_set_int )
% 0.29/0.54        = ( ord_less_set_int @ A @ top_top_set_int ) ) ).
% 0.29/0.54  
% 0.29/0.54  % top.not_eq_extremum
% 0.29/0.54  thf(fact_2897_top_Oextremum__strict,axiom,
% 0.29/0.54      ! [A: set_list_nat] :
% 0.29/0.54        ~ ( ord_le1190675801316882794st_nat @ top_top_set_list_nat @ A ) ).
% 0.29/0.54  
% 0.29/0.54  % top.extremum_strict
% 0.29/0.54  thf(fact_2898_top_Oextremum__strict,axiom,
% 0.29/0.54      ! [A: set_o] :
% 0.29/0.54        ~ ( ord_less_set_o @ top_top_set_o @ A ) ).
% 0.29/0.54  
% 0.29/0.54  % top.extremum_strict
% 0.29/0.54  thf(fact_2899_top_Oextremum__strict,axiom,
% 0.29/0.54      ! [A: set_rat] :
% 0.29/0.54        ~ ( ord_less_set_rat @ top_top_set_rat @ A ) ).
% 0.29/0.54  
% 0.29/0.54  % top.extremum_strict
% 0.29/0.54  thf(fact_2900_top_Oextremum__strict,axiom,
% 0.29/0.54      ! [A: set_nat] :
% 0.29/0.54        ~ ( ord_less_set_nat @ top_top_set_nat @ A ) ).
% 0.29/0.54  
% 0.29/0.54  % top.extremum_strict
% 0.29/0.54  thf(fact_2901_top_Oextremum__strict,axiom,
% 0.29/0.54      ! [A: set_int] :
% 0.29/0.54        ~ ( ord_less_set_int @ top_top_set_int @ A ) ).
% 0.29/0.54  
% 0.29/0.54  % top.extremum_strict
% 0.29/0.54  thf(fact_2902_less__infI1,axiom,
% 0.29/0.54      ! [A: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.29/0.54        ( ( ord_le7866589430770878221at_nat @ A @ X )
% 0.29/0.54       => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_infI1
% 0.29/0.54  thf(fact_2903_less__infI1,axiom,
% 0.29/0.54      ! [A: set_nat,X: set_nat,B: set_nat] :
% 0.29/0.54        ( ( ord_less_set_nat @ A @ X )
% 0.29/0.54       => ( ord_less_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_infI1
% 0.29/0.54  thf(fact_2904_less__infI1,axiom,
% 0.29/0.54      ! [A: product_prod_int_int > $o,X: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 0.29/0.54        ( ( ord_le8213806771718485336_int_o @ A @ X )
% 0.29/0.54       => ( ord_le8213806771718485336_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_infI1
% 0.29/0.54  thf(fact_2905_less__infI1,axiom,
% 0.29/0.54      ! [A: list_char > $o,X: list_char > $o,B: list_char > $o] :
% 0.29/0.54        ( ( ord_less_list_char_o @ A @ X )
% 0.29/0.54       => ( ord_less_list_char_o @ ( inf_inf_list_char_o @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_infI1
% 0.29/0.54  thf(fact_2906_less__infI1,axiom,
% 0.29/0.54      ! [A: rat,X: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ X )
% 0.29/0.54       => ( ord_less_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_infI1
% 0.29/0.54  thf(fact_2907_less__infI1,axiom,
% 0.29/0.54      ! [A: nat,X: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_nat @ A @ X )
% 0.29/0.54       => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_infI1
% 0.29/0.54  thf(fact_2908_less__infI1,axiom,
% 0.29/0.54      ! [A: int,X: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ A @ X )
% 0.29/0.54       => ( ord_less_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_infI1
% 0.29/0.54  thf(fact_2909_less__infI2,axiom,
% 0.29/0.54      ! [B: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 0.29/0.54        ( ( ord_le7866589430770878221at_nat @ B @ X )
% 0.29/0.54       => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_infI2
% 0.29/0.54  thf(fact_2910_less__infI2,axiom,
% 0.29/0.54      ! [B: set_nat,X: set_nat,A: set_nat] :
% 0.29/0.54        ( ( ord_less_set_nat @ B @ X )
% 0.29/0.54       => ( ord_less_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_infI2
% 0.29/0.54  thf(fact_2911_less__infI2,axiom,
% 0.29/0.54      ! [B: product_prod_int_int > $o,X: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 0.29/0.54        ( ( ord_le8213806771718485336_int_o @ B @ X )
% 0.29/0.54       => ( ord_le8213806771718485336_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_infI2
% 0.29/0.54  thf(fact_2912_less__infI2,axiom,
% 0.29/0.54      ! [B: list_char > $o,X: list_char > $o,A: list_char > $o] :
% 0.29/0.54        ( ( ord_less_list_char_o @ B @ X )
% 0.29/0.54       => ( ord_less_list_char_o @ ( inf_inf_list_char_o @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_infI2
% 0.29/0.54  thf(fact_2913_less__infI2,axiom,
% 0.29/0.54      ! [B: rat,X: rat,A: rat] :
% 0.29/0.54        ( ( ord_less_rat @ B @ X )
% 0.29/0.54       => ( ord_less_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_infI2
% 0.29/0.54  thf(fact_2914_less__infI2,axiom,
% 0.29/0.54      ! [B: nat,X: nat,A: nat] :
% 0.29/0.54        ( ( ord_less_nat @ B @ X )
% 0.29/0.54       => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_infI2
% 0.29/0.54  thf(fact_2915_less__infI2,axiom,
% 0.29/0.54      ! [B: int,X: int,A: int] :
% 0.29/0.54        ( ( ord_less_int @ B @ X )
% 0.29/0.54       => ( ord_less_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_infI2
% 0.29/0.54  thf(fact_2916_inf_Oabsorb3,axiom,
% 0.29/0.54      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.29/0.54        ( ( ord_le7866589430770878221at_nat @ A @ B )
% 0.29/0.54       => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 0.29/0.54          = A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.absorb3
% 0.29/0.54  thf(fact_2917_inf_Oabsorb3,axiom,
% 0.29/0.54      ! [A: set_nat,B: set_nat] :
% 0.29/0.54        ( ( ord_less_set_nat @ A @ B )
% 0.29/0.54       => ( ( inf_inf_set_nat @ A @ B )
% 0.29/0.54          = A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.absorb3
% 0.29/0.54  thf(fact_2918_inf_Oabsorb3,axiom,
% 0.29/0.54      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 0.29/0.54        ( ( ord_le8213806771718485336_int_o @ A @ B )
% 0.29/0.54       => ( ( inf_in3604695632404883862_int_o @ A @ B )
% 0.29/0.54          = A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.absorb3
% 0.29/0.54  thf(fact_2919_inf_Oabsorb3,axiom,
% 0.29/0.54      ! [A: list_char > $o,B: list_char > $o] :
% 0.29/0.54        ( ( ord_less_list_char_o @ A @ B )
% 0.29/0.54       => ( ( inf_inf_list_char_o @ A @ B )
% 0.29/0.54          = A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.absorb3
% 0.29/0.54  thf(fact_2920_inf_Oabsorb3,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ B )
% 0.29/0.54       => ( ( inf_inf_rat @ A @ B )
% 0.29/0.54          = A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.absorb3
% 0.29/0.54  thf(fact_2921_inf_Oabsorb3,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_nat @ A @ B )
% 0.29/0.54       => ( ( inf_inf_nat @ A @ B )
% 0.29/0.54          = A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.absorb3
% 0.29/0.54  thf(fact_2922_inf_Oabsorb3,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ A @ B )
% 0.29/0.54       => ( ( inf_inf_int @ A @ B )
% 0.29/0.54          = A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.absorb3
% 0.29/0.54  thf(fact_2923_inf_Oabsorb4,axiom,
% 0.29/0.54      ! [B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 0.29/0.54        ( ( ord_le7866589430770878221at_nat @ B @ A )
% 0.29/0.54       => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 0.29/0.54          = B ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.absorb4
% 0.29/0.54  thf(fact_2924_inf_Oabsorb4,axiom,
% 0.29/0.54      ! [B: set_nat,A: set_nat] :
% 0.29/0.54        ( ( ord_less_set_nat @ B @ A )
% 0.29/0.54       => ( ( inf_inf_set_nat @ A @ B )
% 0.29/0.54          = B ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.absorb4
% 0.29/0.54  thf(fact_2925_inf_Oabsorb4,axiom,
% 0.29/0.54      ! [B: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 0.29/0.54        ( ( ord_le8213806771718485336_int_o @ B @ A )
% 0.29/0.54       => ( ( inf_in3604695632404883862_int_o @ A @ B )
% 0.29/0.54          = B ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.absorb4
% 0.29/0.54  thf(fact_2926_inf_Oabsorb4,axiom,
% 0.29/0.54      ! [B: list_char > $o,A: list_char > $o] :
% 0.29/0.54        ( ( ord_less_list_char_o @ B @ A )
% 0.29/0.54       => ( ( inf_inf_list_char_o @ A @ B )
% 0.29/0.54          = B ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.absorb4
% 0.29/0.54  thf(fact_2927_inf_Oabsorb4,axiom,
% 0.29/0.54      ! [B: rat,A: rat] :
% 0.29/0.54        ( ( ord_less_rat @ B @ A )
% 0.29/0.54       => ( ( inf_inf_rat @ A @ B )
% 0.29/0.54          = B ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.absorb4
% 0.29/0.54  thf(fact_2928_inf_Oabsorb4,axiom,
% 0.29/0.54      ! [B: nat,A: nat] :
% 0.29/0.54        ( ( ord_less_nat @ B @ A )
% 0.29/0.54       => ( ( inf_inf_nat @ A @ B )
% 0.29/0.54          = B ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.absorb4
% 0.29/0.54  thf(fact_2929_inf_Oabsorb4,axiom,
% 0.29/0.54      ! [B: int,A: int] :
% 0.29/0.54        ( ( ord_less_int @ B @ A )
% 0.29/0.54       => ( ( inf_inf_int @ A @ B )
% 0.29/0.54          = B ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.absorb4
% 0.29/0.54  thf(fact_2930_inf_Ostrict__boundedE,axiom,
% 0.29/0.54      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 0.29/0.54        ( ( ord_le7866589430770878221at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) )
% 0.29/0.54       => ~ ( ( ord_le7866589430770878221at_nat @ A @ B )
% 0.29/0.54           => ~ ( ord_le7866589430770878221at_nat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_boundedE
% 0.29/0.54  thf(fact_2931_inf_Ostrict__boundedE,axiom,
% 0.29/0.54      ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.29/0.54        ( ( ord_less_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) )
% 0.29/0.54       => ~ ( ( ord_less_set_nat @ A @ B )
% 0.29/0.54           => ~ ( ord_less_set_nat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_boundedE
% 0.29/0.54  thf(fact_2932_inf_Ostrict__boundedE,axiom,
% 0.29/0.54      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o,C: product_prod_int_int > $o] :
% 0.29/0.54        ( ( ord_le8213806771718485336_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C ) )
% 0.29/0.54       => ~ ( ( ord_le8213806771718485336_int_o @ A @ B )
% 0.29/0.54           => ~ ( ord_le8213806771718485336_int_o @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_boundedE
% 0.29/0.54  thf(fact_2933_inf_Ostrict__boundedE,axiom,
% 0.29/0.54      ! [A: list_char > $o,B: list_char > $o,C: list_char > $o] :
% 0.29/0.54        ( ( ord_less_list_char_o @ A @ ( inf_inf_list_char_o @ B @ C ) )
% 0.29/0.54       => ~ ( ( ord_less_list_char_o @ A @ B )
% 0.29/0.54           => ~ ( ord_less_list_char_o @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_boundedE
% 0.29/0.54  thf(fact_2934_inf_Ostrict__boundedE,axiom,
% 0.29/0.54      ! [A: rat,B: rat,C: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ ( inf_inf_rat @ B @ C ) )
% 0.29/0.54       => ~ ( ( ord_less_rat @ A @ B )
% 0.29/0.54           => ~ ( ord_less_rat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_boundedE
% 0.29/0.54  thf(fact_2935_inf_Ostrict__boundedE,axiom,
% 0.29/0.54      ! [A: nat,B: nat,C: nat] :
% 0.29/0.54        ( ( ord_less_nat @ A @ ( inf_inf_nat @ B @ C ) )
% 0.29/0.54       => ~ ( ( ord_less_nat @ A @ B )
% 0.29/0.54           => ~ ( ord_less_nat @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_boundedE
% 0.29/0.54  thf(fact_2936_inf_Ostrict__boundedE,axiom,
% 0.29/0.54      ! [A: int,B: int,C: int] :
% 0.29/0.54        ( ( ord_less_int @ A @ ( inf_inf_int @ B @ C ) )
% 0.29/0.54       => ~ ( ( ord_less_int @ A @ B )
% 0.29/0.54           => ~ ( ord_less_int @ A @ C ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_boundedE
% 0.29/0.54  thf(fact_2937_inf_Ostrict__order__iff,axiom,
% 0.29/0.54      ( ord_le7866589430770878221at_nat
% 0.29/0.54      = ( ^ [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 0.29/0.54            ( ( A3
% 0.29/0.54              = ( inf_in2572325071724192079at_nat @ A3 @ B3 ) )
% 0.29/0.54            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_order_iff
% 0.29/0.54  thf(fact_2938_inf_Ostrict__order__iff,axiom,
% 0.29/0.54      ( ord_less_set_nat
% 0.29/0.54      = ( ^ [A3: set_nat,B3: set_nat] :
% 0.29/0.54            ( ( A3
% 0.29/0.54              = ( inf_inf_set_nat @ A3 @ B3 ) )
% 0.29/0.54            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_order_iff
% 0.29/0.54  thf(fact_2939_inf_Ostrict__order__iff,axiom,
% 0.29/0.54      ( ord_le8213806771718485336_int_o
% 0.29/0.54      = ( ^ [A3: product_prod_int_int > $o,B3: product_prod_int_int > $o] :
% 0.29/0.54            ( ( A3
% 0.29/0.54              = ( inf_in3604695632404883862_int_o @ A3 @ B3 ) )
% 0.29/0.54            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_order_iff
% 0.29/0.54  thf(fact_2940_inf_Ostrict__order__iff,axiom,
% 0.29/0.54      ( ord_less_list_char_o
% 0.29/0.54      = ( ^ [A3: list_char > $o,B3: list_char > $o] :
% 0.29/0.54            ( ( A3
% 0.29/0.54              = ( inf_inf_list_char_o @ A3 @ B3 ) )
% 0.29/0.54            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_order_iff
% 0.29/0.54  thf(fact_2941_inf_Ostrict__order__iff,axiom,
% 0.29/0.54      ( ord_less_rat
% 0.29/0.54      = ( ^ [A3: rat,B3: rat] :
% 0.29/0.54            ( ( A3
% 0.29/0.54              = ( inf_inf_rat @ A3 @ B3 ) )
% 0.29/0.54            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_order_iff
% 0.29/0.54  thf(fact_2942_inf_Ostrict__order__iff,axiom,
% 0.29/0.54      ( ord_less_nat
% 0.29/0.54      = ( ^ [A3: nat,B3: nat] :
% 0.29/0.54            ( ( A3
% 0.29/0.54              = ( inf_inf_nat @ A3 @ B3 ) )
% 0.29/0.54            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_order_iff
% 0.29/0.54  thf(fact_2943_inf_Ostrict__order__iff,axiom,
% 0.29/0.54      ( ord_less_int
% 0.29/0.54      = ( ^ [A3: int,B3: int] :
% 0.29/0.54            ( ( A3
% 0.29/0.54              = ( inf_inf_int @ A3 @ B3 ) )
% 0.29/0.54            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_order_iff
% 0.29/0.54  thf(fact_2944_inf_Ostrict__coboundedI1,axiom,
% 0.29/0.54      ! [A: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.29/0.54        ( ( ord_le7866589430770878221at_nat @ A @ C )
% 0.29/0.54       => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_coboundedI1
% 0.29/0.54  thf(fact_2945_inf_Ostrict__coboundedI1,axiom,
% 0.29/0.54      ! [A: set_nat,C: set_nat,B: set_nat] :
% 0.29/0.54        ( ( ord_less_set_nat @ A @ C )
% 0.29/0.54       => ( ord_less_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_coboundedI1
% 0.29/0.54  thf(fact_2946_inf_Ostrict__coboundedI1,axiom,
% 0.29/0.54      ! [A: product_prod_int_int > $o,C: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 0.29/0.54        ( ( ord_le8213806771718485336_int_o @ A @ C )
% 0.29/0.54       => ( ord_le8213806771718485336_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_coboundedI1
% 0.29/0.54  thf(fact_2947_inf_Ostrict__coboundedI1,axiom,
% 0.29/0.54      ! [A: list_char > $o,C: list_char > $o,B: list_char > $o] :
% 0.29/0.54        ( ( ord_less_list_char_o @ A @ C )
% 0.29/0.54       => ( ord_less_list_char_o @ ( inf_inf_list_char_o @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_coboundedI1
% 0.29/0.54  thf(fact_2948_inf_Ostrict__coboundedI1,axiom,
% 0.29/0.54      ! [A: rat,C: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ C )
% 0.29/0.54       => ( ord_less_rat @ ( inf_inf_rat @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_coboundedI1
% 0.29/0.54  thf(fact_2949_inf_Ostrict__coboundedI1,axiom,
% 0.29/0.54      ! [A: nat,C: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_nat @ A @ C )
% 0.29/0.54       => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_coboundedI1
% 0.29/0.54  thf(fact_2950_inf_Ostrict__coboundedI1,axiom,
% 0.29/0.54      ! [A: int,C: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ A @ C )
% 0.29/0.54       => ( ord_less_int @ ( inf_inf_int @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_coboundedI1
% 0.29/0.54  thf(fact_2951_inf_Ostrict__coboundedI2,axiom,
% 0.29/0.54      ! [B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 0.29/0.54        ( ( ord_le7866589430770878221at_nat @ B @ C )
% 0.29/0.54       => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_coboundedI2
% 0.29/0.54  thf(fact_2952_inf_Ostrict__coboundedI2,axiom,
% 0.29/0.54      ! [B: set_nat,C: set_nat,A: set_nat] :
% 0.29/0.54        ( ( ord_less_set_nat @ B @ C )
% 0.29/0.54       => ( ord_less_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_coboundedI2
% 0.29/0.54  thf(fact_2953_inf_Ostrict__coboundedI2,axiom,
% 0.29/0.54      ! [B: product_prod_int_int > $o,C: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 0.29/0.54        ( ( ord_le8213806771718485336_int_o @ B @ C )
% 0.29/0.54       => ( ord_le8213806771718485336_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_coboundedI2
% 0.29/0.54  thf(fact_2954_inf_Ostrict__coboundedI2,axiom,
% 0.29/0.54      ! [B: list_char > $o,C: list_char > $o,A: list_char > $o] :
% 0.29/0.54        ( ( ord_less_list_char_o @ B @ C )
% 0.29/0.54       => ( ord_less_list_char_o @ ( inf_inf_list_char_o @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_coboundedI2
% 0.29/0.54  thf(fact_2955_inf_Ostrict__coboundedI2,axiom,
% 0.29/0.54      ! [B: rat,C: rat,A: rat] :
% 0.29/0.54        ( ( ord_less_rat @ B @ C )
% 0.29/0.54       => ( ord_less_rat @ ( inf_inf_rat @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_coboundedI2
% 0.29/0.54  thf(fact_2956_inf_Ostrict__coboundedI2,axiom,
% 0.29/0.54      ! [B: nat,C: nat,A: nat] :
% 0.29/0.54        ( ( ord_less_nat @ B @ C )
% 0.29/0.54       => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_coboundedI2
% 0.29/0.54  thf(fact_2957_inf_Ostrict__coboundedI2,axiom,
% 0.29/0.54      ! [B: int,C: int,A: int] :
% 0.29/0.54        ( ( ord_less_int @ B @ C )
% 0.29/0.54       => ( ord_less_int @ ( inf_inf_int @ A @ B ) @ C ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.strict_coboundedI2
% 0.29/0.54  thf(fact_2958_less__supI1,axiom,
% 0.29/0.54      ! [X: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 0.29/0.54        ( ( ord_le7642048601412989811at_nat @ X @ A )
% 0.29/0.54       => ( ord_le7642048601412989811at_nat @ X @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_supI1
% 0.29/0.54  thf(fact_2959_less__supI1,axiom,
% 0.29/0.54      ! [X: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.29/0.54        ( ( ord_le2604355607129572851at_nat @ X @ A )
% 0.29/0.54       => ( ord_le2604355607129572851at_nat @ X @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_supI1
% 0.29/0.54  thf(fact_2960_less__supI1,axiom,
% 0.29/0.54      ! [X: set_nat,A: set_nat,B: set_nat] :
% 0.29/0.54        ( ( ord_less_set_nat @ X @ A )
% 0.29/0.54       => ( ord_less_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_supI1
% 0.29/0.54  thf(fact_2961_less__supI1,axiom,
% 0.29/0.54      ! [X: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ X @ A )
% 0.29/0.54       => ( ord_less_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_supI1
% 0.29/0.54  thf(fact_2962_less__supI1,axiom,
% 0.29/0.54      ! [X: nat,A: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_nat @ X @ A )
% 0.29/0.54       => ( ord_less_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_supI1
% 0.29/0.54  thf(fact_2963_less__supI1,axiom,
% 0.29/0.54      ! [X: int,A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ X @ A )
% 0.29/0.54       => ( ord_less_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_supI1
% 0.29/0.54  thf(fact_2964_less__supI2,axiom,
% 0.29/0.54      ! [X: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 0.29/0.54        ( ( ord_le7642048601412989811at_nat @ X @ B )
% 0.29/0.54       => ( ord_le7642048601412989811at_nat @ X @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_supI2
% 0.29/0.54  thf(fact_2965_less__supI2,axiom,
% 0.29/0.54      ! [X: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 0.29/0.54        ( ( ord_le2604355607129572851at_nat @ X @ B )
% 0.29/0.54       => ( ord_le2604355607129572851at_nat @ X @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_supI2
% 0.29/0.54  thf(fact_2966_less__supI2,axiom,
% 0.29/0.54      ! [X: set_nat,B: set_nat,A: set_nat] :
% 0.29/0.54        ( ( ord_less_set_nat @ X @ B )
% 0.29/0.54       => ( ord_less_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_supI2
% 0.29/0.54  thf(fact_2967_less__supI2,axiom,
% 0.29/0.54      ! [X: rat,B: rat,A: rat] :
% 0.29/0.54        ( ( ord_less_rat @ X @ B )
% 0.29/0.54       => ( ord_less_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_supI2
% 0.29/0.54  thf(fact_2968_less__supI2,axiom,
% 0.29/0.54      ! [X: nat,B: nat,A: nat] :
% 0.29/0.54        ( ( ord_less_nat @ X @ B )
% 0.29/0.54       => ( ord_less_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_supI2
% 0.29/0.54  thf(fact_2969_less__supI2,axiom,
% 0.29/0.54      ! [X: int,B: int,A: int] :
% 0.29/0.54        ( ( ord_less_int @ X @ B )
% 0.29/0.54       => ( ord_less_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % less_supI2
% 0.29/0.54  thf(fact_2970_sup_Oabsorb3,axiom,
% 0.29/0.54      ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 0.29/0.54        ( ( ord_le7642048601412989811at_nat @ B @ A )
% 0.29/0.54       => ( ( sup_su3035147773818789531at_nat @ A @ B )
% 0.29/0.54          = A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.absorb3
% 0.29/0.54  thf(fact_2971_sup_Oabsorb3,axiom,
% 0.29/0.54      ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 0.29/0.54        ( ( ord_le2604355607129572851at_nat @ B @ A )
% 0.29/0.54       => ( ( sup_su5525570899277871387at_nat @ A @ B )
% 0.29/0.54          = A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.absorb3
% 0.29/0.54  thf(fact_2972_sup_Oabsorb3,axiom,
% 0.29/0.54      ! [B: set_nat,A: set_nat] :
% 0.29/0.54        ( ( ord_less_set_nat @ B @ A )
% 0.29/0.54       => ( ( sup_sup_set_nat @ A @ B )
% 0.29/0.54          = A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.absorb3
% 0.29/0.54  thf(fact_2973_sup_Oabsorb3,axiom,
% 0.29/0.54      ! [B: rat,A: rat] :
% 0.29/0.54        ( ( ord_less_rat @ B @ A )
% 0.29/0.54       => ( ( sup_sup_rat @ A @ B )
% 0.29/0.54          = A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.absorb3
% 0.29/0.54  thf(fact_2974_sup_Oabsorb3,axiom,
% 0.29/0.54      ! [B: nat,A: nat] :
% 0.29/0.54        ( ( ord_less_nat @ B @ A )
% 0.29/0.54       => ( ( sup_sup_nat @ A @ B )
% 0.29/0.54          = A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.absorb3
% 0.29/0.54  thf(fact_2975_sup_Oabsorb3,axiom,
% 0.29/0.54      ! [B: int,A: int] :
% 0.29/0.54        ( ( ord_less_int @ B @ A )
% 0.29/0.54       => ( ( sup_sup_int @ A @ B )
% 0.29/0.54          = A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.absorb3
% 0.29/0.54  thf(fact_2976_sup_Oabsorb4,axiom,
% 0.29/0.54      ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 0.29/0.54        ( ( ord_le7642048601412989811at_nat @ A @ B )
% 0.29/0.54       => ( ( sup_su3035147773818789531at_nat @ A @ B )
% 0.29/0.54          = B ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.absorb4
% 0.29/0.54  thf(fact_2977_sup_Oabsorb4,axiom,
% 0.29/0.54      ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.29/0.54        ( ( ord_le2604355607129572851at_nat @ A @ B )
% 0.29/0.54       => ( ( sup_su5525570899277871387at_nat @ A @ B )
% 0.29/0.54          = B ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.absorb4
% 0.29/0.54  thf(fact_2978_sup_Oabsorb4,axiom,
% 0.29/0.54      ! [A: set_nat,B: set_nat] :
% 0.29/0.54        ( ( ord_less_set_nat @ A @ B )
% 0.29/0.54       => ( ( sup_sup_set_nat @ A @ B )
% 0.29/0.54          = B ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.absorb4
% 0.29/0.54  thf(fact_2979_sup_Oabsorb4,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ A @ B )
% 0.29/0.54       => ( ( sup_sup_rat @ A @ B )
% 0.29/0.54          = B ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.absorb4
% 0.29/0.54  thf(fact_2980_sup_Oabsorb4,axiom,
% 0.29/0.54      ! [A: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_nat @ A @ B )
% 0.29/0.54       => ( ( sup_sup_nat @ A @ B )
% 0.29/0.54          = B ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.absorb4
% 0.29/0.54  thf(fact_2981_sup_Oabsorb4,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ A @ B )
% 0.29/0.54       => ( ( sup_sup_int @ A @ B )
% 0.29/0.54          = B ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.absorb4
% 0.29/0.54  thf(fact_2982_sup_Ostrict__boundedE,axiom,
% 0.29/0.54      ! [B: set_Pr8551490117392284871at_nat,C: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 0.29/0.54        ( ( ord_le7642048601412989811at_nat @ ( sup_su3035147773818789531at_nat @ B @ C ) @ A )
% 0.29/0.54       => ~ ( ( ord_le7642048601412989811at_nat @ B @ A )
% 0.29/0.54           => ~ ( ord_le7642048601412989811at_nat @ C @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_boundedE
% 0.29/0.54  thf(fact_2983_sup_Ostrict__boundedE,axiom,
% 0.29/0.54      ! [B: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 0.29/0.54        ( ( ord_le2604355607129572851at_nat @ ( sup_su5525570899277871387at_nat @ B @ C ) @ A )
% 0.29/0.54       => ~ ( ( ord_le2604355607129572851at_nat @ B @ A )
% 0.29/0.54           => ~ ( ord_le2604355607129572851at_nat @ C @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_boundedE
% 0.29/0.54  thf(fact_2984_sup_Ostrict__boundedE,axiom,
% 0.29/0.54      ! [B: set_nat,C: set_nat,A: set_nat] :
% 0.29/0.54        ( ( ord_less_set_nat @ ( sup_sup_set_nat @ B @ C ) @ A )
% 0.29/0.54       => ~ ( ( ord_less_set_nat @ B @ A )
% 0.29/0.54           => ~ ( ord_less_set_nat @ C @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_boundedE
% 0.29/0.54  thf(fact_2985_sup_Ostrict__boundedE,axiom,
% 0.29/0.54      ! [B: rat,C: rat,A: rat] :
% 0.29/0.54        ( ( ord_less_rat @ ( sup_sup_rat @ B @ C ) @ A )
% 0.29/0.54       => ~ ( ( ord_less_rat @ B @ A )
% 0.29/0.54           => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_boundedE
% 0.29/0.54  thf(fact_2986_sup_Ostrict__boundedE,axiom,
% 0.29/0.54      ! [B: nat,C: nat,A: nat] :
% 0.29/0.54        ( ( ord_less_nat @ ( sup_sup_nat @ B @ C ) @ A )
% 0.29/0.54       => ~ ( ( ord_less_nat @ B @ A )
% 0.29/0.54           => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_boundedE
% 0.29/0.54  thf(fact_2987_sup_Ostrict__boundedE,axiom,
% 0.29/0.54      ! [B: int,C: int,A: int] :
% 0.29/0.54        ( ( ord_less_int @ ( sup_sup_int @ B @ C ) @ A )
% 0.29/0.54       => ~ ( ( ord_less_int @ B @ A )
% 0.29/0.54           => ~ ( ord_less_int @ C @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_boundedE
% 0.29/0.54  thf(fact_2988_sup_Ostrict__order__iff,axiom,
% 0.29/0.54      ( ord_le7642048601412989811at_nat
% 0.29/0.54      = ( ^ [B3: set_Pr8551490117392284871at_nat,A3: set_Pr8551490117392284871at_nat] :
% 0.29/0.54            ( ( A3
% 0.29/0.54              = ( sup_su3035147773818789531at_nat @ A3 @ B3 ) )
% 0.29/0.54            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_order_iff
% 0.29/0.54  thf(fact_2989_sup_Ostrict__order__iff,axiom,
% 0.29/0.54      ( ord_le2604355607129572851at_nat
% 0.29/0.54      = ( ^ [B3: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] :
% 0.29/0.54            ( ( A3
% 0.29/0.54              = ( sup_su5525570899277871387at_nat @ A3 @ B3 ) )
% 0.29/0.54            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_order_iff
% 0.29/0.54  thf(fact_2990_sup_Ostrict__order__iff,axiom,
% 0.29/0.54      ( ord_less_set_nat
% 0.29/0.54      = ( ^ [B3: set_nat,A3: set_nat] :
% 0.29/0.54            ( ( A3
% 0.29/0.54              = ( sup_sup_set_nat @ A3 @ B3 ) )
% 0.29/0.54            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_order_iff
% 0.29/0.54  thf(fact_2991_sup_Ostrict__order__iff,axiom,
% 0.29/0.54      ( ord_less_rat
% 0.29/0.54      = ( ^ [B3: rat,A3: rat] :
% 0.29/0.54            ( ( A3
% 0.29/0.54              = ( sup_sup_rat @ A3 @ B3 ) )
% 0.29/0.54            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_order_iff
% 0.29/0.54  thf(fact_2992_sup_Ostrict__order__iff,axiom,
% 0.29/0.54      ( ord_less_nat
% 0.29/0.54      = ( ^ [B3: nat,A3: nat] :
% 0.29/0.54            ( ( A3
% 0.29/0.54              = ( sup_sup_nat @ A3 @ B3 ) )
% 0.29/0.54            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_order_iff
% 0.29/0.54  thf(fact_2993_sup_Ostrict__order__iff,axiom,
% 0.29/0.54      ( ord_less_int
% 0.29/0.54      = ( ^ [B3: int,A3: int] :
% 0.29/0.54            ( ( A3
% 0.29/0.54              = ( sup_sup_int @ A3 @ B3 ) )
% 0.29/0.54            & ( A3 != B3 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_order_iff
% 0.29/0.54  thf(fact_2994_sup_Ostrict__coboundedI1,axiom,
% 0.29/0.54      ! [C: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 0.29/0.54        ( ( ord_le7642048601412989811at_nat @ C @ A )
% 0.29/0.54       => ( ord_le7642048601412989811at_nat @ C @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_coboundedI1
% 0.29/0.54  thf(fact_2995_sup_Ostrict__coboundedI1,axiom,
% 0.29/0.54      ! [C: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.29/0.54        ( ( ord_le2604355607129572851at_nat @ C @ A )
% 0.29/0.54       => ( ord_le2604355607129572851at_nat @ C @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_coboundedI1
% 0.29/0.54  thf(fact_2996_sup_Ostrict__coboundedI1,axiom,
% 0.29/0.54      ! [C: set_nat,A: set_nat,B: set_nat] :
% 0.29/0.54        ( ( ord_less_set_nat @ C @ A )
% 0.29/0.54       => ( ord_less_set_nat @ C @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_coboundedI1
% 0.29/0.54  thf(fact_2997_sup_Ostrict__coboundedI1,axiom,
% 0.29/0.54      ! [C: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_rat @ C @ A )
% 0.29/0.54       => ( ord_less_rat @ C @ ( sup_sup_rat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_coboundedI1
% 0.29/0.54  thf(fact_2998_sup_Ostrict__coboundedI1,axiom,
% 0.29/0.54      ! [C: nat,A: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_nat @ C @ A )
% 0.29/0.54       => ( ord_less_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_coboundedI1
% 0.29/0.54  thf(fact_2999_sup_Ostrict__coboundedI1,axiom,
% 0.29/0.54      ! [C: int,A: int,B: int] :
% 0.29/0.54        ( ( ord_less_int @ C @ A )
% 0.29/0.54       => ( ord_less_int @ C @ ( sup_sup_int @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_coboundedI1
% 0.29/0.54  thf(fact_3000_sup_Ostrict__coboundedI2,axiom,
% 0.29/0.54      ! [C: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 0.29/0.54        ( ( ord_le7642048601412989811at_nat @ C @ B )
% 0.29/0.54       => ( ord_le7642048601412989811at_nat @ C @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_coboundedI2
% 0.29/0.54  thf(fact_3001_sup_Ostrict__coboundedI2,axiom,
% 0.29/0.54      ! [C: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 0.29/0.54        ( ( ord_le2604355607129572851at_nat @ C @ B )
% 0.29/0.54       => ( ord_le2604355607129572851at_nat @ C @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_coboundedI2
% 0.29/0.54  thf(fact_3002_sup_Ostrict__coboundedI2,axiom,
% 0.29/0.54      ! [C: set_nat,B: set_nat,A: set_nat] :
% 0.29/0.54        ( ( ord_less_set_nat @ C @ B )
% 0.29/0.54       => ( ord_less_set_nat @ C @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_coboundedI2
% 0.29/0.54  thf(fact_3003_sup_Ostrict__coboundedI2,axiom,
% 0.29/0.54      ! [C: rat,B: rat,A: rat] :
% 0.29/0.54        ( ( ord_less_rat @ C @ B )
% 0.29/0.54       => ( ord_less_rat @ C @ ( sup_sup_rat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_coboundedI2
% 0.29/0.54  thf(fact_3004_sup_Ostrict__coboundedI2,axiom,
% 0.29/0.54      ! [C: nat,B: nat,A: nat] :
% 0.29/0.54        ( ( ord_less_nat @ C @ B )
% 0.29/0.54       => ( ord_less_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_coboundedI2
% 0.29/0.54  thf(fact_3005_sup_Ostrict__coboundedI2,axiom,
% 0.29/0.54      ! [C: int,B: int,A: int] :
% 0.29/0.54        ( ( ord_less_int @ C @ B )
% 0.29/0.54       => ( ord_less_int @ C @ ( sup_sup_int @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % sup.strict_coboundedI2
% 0.29/0.54  thf(fact_3006_le__minus__iff,axiom,
% 0.29/0.54      ! [A: code_integer,B: code_integer] :
% 0.29/0.54        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.29/0.54        = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_minus_iff
% 0.29/0.54  thf(fact_3007_le__minus__iff,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.29/0.54        = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_minus_iff
% 0.29/0.54  thf(fact_3008_le__minus__iff,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 0.29/0.54        = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_minus_iff
% 0.29/0.54  thf(fact_3009_minus__le__iff,axiom,
% 0.29/0.54      ! [A: code_integer,B: code_integer] :
% 0.29/0.54        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.29/0.54        = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % minus_le_iff
% 0.29/0.54  thf(fact_3010_minus__le__iff,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.29/0.54        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % minus_le_iff
% 0.29/0.54  thf(fact_3011_minus__le__iff,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 0.29/0.54        = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 0.29/0.54  
% 0.29/0.54  % minus_le_iff
% 0.29/0.54  thf(fact_3012_le__imp__neg__le,axiom,
% 0.29/0.54      ! [A: code_integer,B: code_integer] :
% 0.29/0.54        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.29/0.54       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_imp_neg_le
% 0.29/0.54  thf(fact_3013_le__imp__neg__le,axiom,
% 0.29/0.54      ! [A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.54       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_imp_neg_le
% 0.29/0.54  thf(fact_3014_le__imp__neg__le,axiom,
% 0.29/0.54      ! [A: int,B: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.54       => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_imp_neg_le
% 0.29/0.54  thf(fact_3015_compl__le__swap2,axiom,
% 0.29/0.54      ! [Y: product_unit,X: product_unit] :
% 0.29/0.54        ( ( ord_le3221252021190050221t_unit @ ( uminus2952777764628376836t_unit @ Y ) @ X )
% 0.29/0.54       => ( ord_le3221252021190050221t_unit @ ( uminus2952777764628376836t_unit @ X ) @ Y ) ) ).
% 0.29/0.54  
% 0.29/0.54  % compl_le_swap2
% 0.29/0.54  thf(fact_3016_compl__le__swap2,axiom,
% 0.29/0.54      ! [Y: set_nat,X: set_nat] :
% 0.29/0.54        ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ X )
% 0.29/0.54       => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ Y ) ) ).
% 0.29/0.54  
% 0.29/0.54  % compl_le_swap2
% 0.29/0.54  thf(fact_3017_compl__le__swap1,axiom,
% 0.29/0.54      ! [Y: product_unit,X: product_unit] :
% 0.29/0.54        ( ( ord_le3221252021190050221t_unit @ Y @ ( uminus2952777764628376836t_unit @ X ) )
% 0.29/0.54       => ( ord_le3221252021190050221t_unit @ X @ ( uminus2952777764628376836t_unit @ Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % compl_le_swap1
% 0.29/0.54  thf(fact_3018_compl__le__swap1,axiom,
% 0.29/0.54      ! [Y: set_nat,X: set_nat] :
% 0.29/0.54        ( ( ord_less_eq_set_nat @ Y @ ( uminus5710092332889474511et_nat @ X ) )
% 0.29/0.54       => ( ord_less_eq_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % compl_le_swap1
% 0.29/0.54  thf(fact_3019_compl__mono,axiom,
% 0.29/0.54      ! [X: product_unit,Y: product_unit] :
% 0.29/0.54        ( ( ord_le3221252021190050221t_unit @ X @ Y )
% 0.29/0.54       => ( ord_le3221252021190050221t_unit @ ( uminus2952777764628376836t_unit @ Y ) @ ( uminus2952777764628376836t_unit @ X ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % compl_mono
% 0.29/0.54  thf(fact_3020_compl__mono,axiom,
% 0.29/0.54      ! [X: set_nat,Y: set_nat] :
% 0.29/0.54        ( ( ord_less_eq_set_nat @ X @ Y )
% 0.29/0.54       => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ ( uminus5710092332889474511et_nat @ X ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % compl_mono
% 0.29/0.54  thf(fact_3021_subset__minus__empty,axiom,
% 0.29/0.54      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.29/0.54        ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 0.29/0.54       => ( ( minus_1356011639430497352at_nat @ A2 @ B2 )
% 0.29/0.54          = bot_bo2099793752762293965at_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % subset_minus_empty
% 0.29/0.54  thf(fact_3022_subset__minus__empty,axiom,
% 0.29/0.54      ! [A2: set_o,B2: set_o] :
% 0.29/0.54        ( ( ord_less_eq_set_o @ A2 @ B2 )
% 0.29/0.54       => ( ( minus_minus_set_o @ A2 @ B2 )
% 0.29/0.54          = bot_bot_set_o ) ) ).
% 0.29/0.54  
% 0.29/0.54  % subset_minus_empty
% 0.29/0.54  thf(fact_3023_subset__minus__empty,axiom,
% 0.29/0.54      ! [A2: set_int,B2: set_int] :
% 0.29/0.54        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.29/0.54       => ( ( minus_minus_set_int @ A2 @ B2 )
% 0.29/0.54          = bot_bot_set_int ) ) ).
% 0.29/0.54  
% 0.29/0.54  % subset_minus_empty
% 0.29/0.54  thf(fact_3024_subset__minus__empty,axiom,
% 0.29/0.54      ! [A2: set_nat,B2: set_nat] :
% 0.29/0.54        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.29/0.54       => ( ( minus_minus_set_nat @ A2 @ B2 )
% 0.29/0.54          = bot_bot_set_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % subset_minus_empty
% 0.29/0.54  thf(fact_3025_top_Oextremum__uniqueI,axiom,
% 0.29/0.54      ! [A: set_list_nat] :
% 0.29/0.54        ( ( ord_le6045566169113846134st_nat @ top_top_set_list_nat @ A )
% 0.29/0.54       => ( A = top_top_set_list_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % top.extremum_uniqueI
% 0.29/0.54  thf(fact_3026_top_Oextremum__uniqueI,axiom,
% 0.29/0.54      ! [A: set_o] :
% 0.29/0.54        ( ( ord_less_eq_set_o @ top_top_set_o @ A )
% 0.29/0.54       => ( A = top_top_set_o ) ) ).
% 0.29/0.54  
% 0.29/0.54  % top.extremum_uniqueI
% 0.29/0.54  thf(fact_3027_top_Oextremum__uniqueI,axiom,
% 0.29/0.54      ! [A: set_rat] :
% 0.29/0.54        ( ( ord_less_eq_set_rat @ top_top_set_rat @ A )
% 0.29/0.54       => ( A = top_top_set_rat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % top.extremum_uniqueI
% 0.29/0.54  thf(fact_3028_top_Oextremum__uniqueI,axiom,
% 0.29/0.54      ! [A: set_int] :
% 0.29/0.54        ( ( ord_less_eq_set_int @ top_top_set_int @ A )
% 0.29/0.54       => ( A = top_top_set_int ) ) ).
% 0.29/0.54  
% 0.29/0.54  % top.extremum_uniqueI
% 0.29/0.54  thf(fact_3029_top_Oextremum__uniqueI,axiom,
% 0.29/0.54      ! [A: filter_nat] :
% 0.29/0.54        ( ( ord_le2510731241096832064er_nat @ top_top_filter_nat @ A )
% 0.29/0.54       => ( A = top_top_filter_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % top.extremum_uniqueI
% 0.29/0.54  thf(fact_3030_top_Oextremum__uniqueI,axiom,
% 0.29/0.54      ! [A: set_nat] :
% 0.29/0.54        ( ( ord_less_eq_set_nat @ top_top_set_nat @ A )
% 0.29/0.54       => ( A = top_top_set_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % top.extremum_uniqueI
% 0.29/0.54  thf(fact_3031_top_Oextremum__unique,axiom,
% 0.29/0.54      ! [A: set_list_nat] :
% 0.29/0.54        ( ( ord_le6045566169113846134st_nat @ top_top_set_list_nat @ A )
% 0.29/0.54        = ( A = top_top_set_list_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % top.extremum_unique
% 0.29/0.54  thf(fact_3032_top_Oextremum__unique,axiom,
% 0.29/0.54      ! [A: set_o] :
% 0.29/0.54        ( ( ord_less_eq_set_o @ top_top_set_o @ A )
% 0.29/0.54        = ( A = top_top_set_o ) ) ).
% 0.29/0.54  
% 0.29/0.54  % top.extremum_unique
% 0.29/0.54  thf(fact_3033_top_Oextremum__unique,axiom,
% 0.29/0.54      ! [A: set_rat] :
% 0.29/0.54        ( ( ord_less_eq_set_rat @ top_top_set_rat @ A )
% 0.29/0.54        = ( A = top_top_set_rat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % top.extremum_unique
% 0.29/0.54  thf(fact_3034_top_Oextremum__unique,axiom,
% 0.29/0.54      ! [A: set_int] :
% 0.29/0.54        ( ( ord_less_eq_set_int @ top_top_set_int @ A )
% 0.29/0.54        = ( A = top_top_set_int ) ) ).
% 0.29/0.54  
% 0.29/0.54  % top.extremum_unique
% 0.29/0.54  thf(fact_3035_top_Oextremum__unique,axiom,
% 0.29/0.54      ! [A: filter_nat] :
% 0.29/0.54        ( ( ord_le2510731241096832064er_nat @ top_top_filter_nat @ A )
% 0.29/0.54        = ( A = top_top_filter_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % top.extremum_unique
% 0.29/0.54  thf(fact_3036_top_Oextremum__unique,axiom,
% 0.29/0.54      ! [A: set_nat] :
% 0.29/0.54        ( ( ord_less_eq_set_nat @ top_top_set_nat @ A )
% 0.29/0.54        = ( A = top_top_set_nat ) ) ).
% 0.29/0.54  
% 0.29/0.54  % top.extremum_unique
% 0.29/0.54  thf(fact_3037_top__greatest,axiom,
% 0.29/0.54      ! [A: set_list_nat] : ( ord_le6045566169113846134st_nat @ A @ top_top_set_list_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % top_greatest
% 0.29/0.54  thf(fact_3038_top__greatest,axiom,
% 0.29/0.54      ! [A: set_o] : ( ord_less_eq_set_o @ A @ top_top_set_o ) ).
% 0.29/0.54  
% 0.29/0.54  % top_greatest
% 0.29/0.54  thf(fact_3039_top__greatest,axiom,
% 0.29/0.54      ! [A: set_rat] : ( ord_less_eq_set_rat @ A @ top_top_set_rat ) ).
% 0.29/0.54  
% 0.29/0.54  % top_greatest
% 0.29/0.54  thf(fact_3040_top__greatest,axiom,
% 0.29/0.54      ! [A: set_int] : ( ord_less_eq_set_int @ A @ top_top_set_int ) ).
% 0.29/0.54  
% 0.29/0.54  % top_greatest
% 0.29/0.54  thf(fact_3041_top__greatest,axiom,
% 0.29/0.54      ! [A: filter_nat] : ( ord_le2510731241096832064er_nat @ A @ top_top_filter_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % top_greatest
% 0.29/0.54  thf(fact_3042_top__greatest,axiom,
% 0.29/0.54      ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ top_top_set_nat ) ).
% 0.29/0.54  
% 0.29/0.54  % top_greatest
% 0.29/0.54  thf(fact_3043_inf__sup__ord_I2_J,axiom,
% 0.29/0.54      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_sup_ord(2)
% 0.29/0.54  thf(fact_3044_inf__sup__ord_I2_J,axiom,
% 0.29/0.54      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ Y ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_sup_ord(2)
% 0.29/0.54  thf(fact_3045_inf__sup__ord_I2_J,axiom,
% 0.29/0.54      ! [X: list_char > $o,Y: list_char > $o] : ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ X @ Y ) @ Y ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_sup_ord(2)
% 0.29/0.54  thf(fact_3046_inf__sup__ord_I2_J,axiom,
% 0.29/0.54      ! [X: filter_nat,Y: filter_nat] : ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ X @ Y ) @ Y ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_sup_ord(2)
% 0.29/0.54  thf(fact_3047_inf__sup__ord_I2_J,axiom,
% 0.29/0.54      ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_sup_ord(2)
% 0.29/0.54  thf(fact_3048_inf__sup__ord_I2_J,axiom,
% 0.29/0.54      ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ Y ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_sup_ord(2)
% 0.29/0.54  thf(fact_3049_inf__sup__ord_I2_J,axiom,
% 0.29/0.54      ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_sup_ord(2)
% 0.29/0.54  thf(fact_3050_inf__sup__ord_I2_J,axiom,
% 0.29/0.54      ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ Y ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_sup_ord(2)
% 0.29/0.54  thf(fact_3051_inf__sup__ord_I1_J,axiom,
% 0.29/0.54      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ X ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_sup_ord(1)
% 0.29/0.54  thf(fact_3052_inf__sup__ord_I1_J,axiom,
% 0.29/0.54      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ X ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_sup_ord(1)
% 0.29/0.54  thf(fact_3053_inf__sup__ord_I1_J,axiom,
% 0.29/0.54      ! [X: list_char > $o,Y: list_char > $o] : ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ X @ Y ) @ X ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_sup_ord(1)
% 0.29/0.54  thf(fact_3054_inf__sup__ord_I1_J,axiom,
% 0.29/0.54      ! [X: filter_nat,Y: filter_nat] : ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ X @ Y ) @ X ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_sup_ord(1)
% 0.29/0.54  thf(fact_3055_inf__sup__ord_I1_J,axiom,
% 0.29/0.54      ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ X ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_sup_ord(1)
% 0.29/0.54  thf(fact_3056_inf__sup__ord_I1_J,axiom,
% 0.29/0.54      ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ X ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_sup_ord(1)
% 0.29/0.54  thf(fact_3057_inf__sup__ord_I1_J,axiom,
% 0.29/0.54      ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_sup_ord(1)
% 0.29/0.54  thf(fact_3058_inf__sup__ord_I1_J,axiom,
% 0.29/0.54      ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ X ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_sup_ord(1)
% 0.29/0.54  thf(fact_3059_inf__le1,axiom,
% 0.29/0.54      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ X ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_le1
% 0.29/0.54  thf(fact_3060_inf__le1,axiom,
% 0.29/0.54      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ X ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_le1
% 0.29/0.54  thf(fact_3061_inf__le1,axiom,
% 0.29/0.54      ! [X: list_char > $o,Y: list_char > $o] : ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ X @ Y ) @ X ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_le1
% 0.29/0.54  thf(fact_3062_inf__le1,axiom,
% 0.29/0.54      ! [X: filter_nat,Y: filter_nat] : ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ X @ Y ) @ X ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_le1
% 0.29/0.54  thf(fact_3063_inf__le1,axiom,
% 0.29/0.54      ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ X ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_le1
% 0.29/0.54  thf(fact_3064_inf__le1,axiom,
% 0.29/0.54      ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ X ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_le1
% 0.29/0.54  thf(fact_3065_inf__le1,axiom,
% 0.29/0.54      ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_le1
% 0.29/0.54  thf(fact_3066_inf__le1,axiom,
% 0.29/0.54      ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ X ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_le1
% 0.29/0.54  thf(fact_3067_inf__le2,axiom,
% 0.29/0.54      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_le2
% 0.29/0.54  thf(fact_3068_inf__le2,axiom,
% 0.29/0.54      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ Y ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_le2
% 0.29/0.54  thf(fact_3069_inf__le2,axiom,
% 0.29/0.54      ! [X: list_char > $o,Y: list_char > $o] : ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ X @ Y ) @ Y ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_le2
% 0.29/0.54  thf(fact_3070_inf__le2,axiom,
% 0.29/0.54      ! [X: filter_nat,Y: filter_nat] : ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ X @ Y ) @ Y ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_le2
% 0.29/0.54  thf(fact_3071_inf__le2,axiom,
% 0.29/0.54      ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_le2
% 0.29/0.54  thf(fact_3072_inf__le2,axiom,
% 0.29/0.54      ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ Y ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_le2
% 0.29/0.54  thf(fact_3073_inf__le2,axiom,
% 0.29/0.54      ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_le2
% 0.29/0.54  thf(fact_3074_inf__le2,axiom,
% 0.29/0.54      ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ Y ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_le2
% 0.29/0.54  thf(fact_3075_le__infE,axiom,
% 0.29/0.54      ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.29/0.54        ( ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ A @ B ) )
% 0.29/0.54       => ~ ( ( ord_le3146513528884898305at_nat @ X @ A )
% 0.29/0.54           => ~ ( ord_le3146513528884898305at_nat @ X @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infE
% 0.29/0.54  thf(fact_3076_le__infE,axiom,
% 0.29/0.54      ! [X: product_prod_int_int > $o,A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 0.29/0.54        ( ( ord_le8369615600986905444_int_o @ X @ ( inf_in3604695632404883862_int_o @ A @ B ) )
% 0.29/0.54       => ~ ( ( ord_le8369615600986905444_int_o @ X @ A )
% 0.29/0.54           => ~ ( ord_le8369615600986905444_int_o @ X @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infE
% 0.29/0.54  thf(fact_3077_le__infE,axiom,
% 0.29/0.54      ! [X: list_char > $o,A: list_char > $o,B: list_char > $o] :
% 0.29/0.54        ( ( ord_le4796328588573674190char_o @ X @ ( inf_inf_list_char_o @ A @ B ) )
% 0.29/0.54       => ~ ( ( ord_le4796328588573674190char_o @ X @ A )
% 0.29/0.54           => ~ ( ord_le4796328588573674190char_o @ X @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infE
% 0.29/0.54  thf(fact_3078_le__infE,axiom,
% 0.29/0.54      ! [X: filter_nat,A: filter_nat,B: filter_nat] :
% 0.29/0.54        ( ( ord_le2510731241096832064er_nat @ X @ ( inf_inf_filter_nat @ A @ B ) )
% 0.29/0.54       => ~ ( ( ord_le2510731241096832064er_nat @ X @ A )
% 0.29/0.54           => ~ ( ord_le2510731241096832064er_nat @ X @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infE
% 0.29/0.54  thf(fact_3079_le__infE,axiom,
% 0.29/0.54      ! [X: set_nat,A: set_nat,B: set_nat] :
% 0.29/0.54        ( ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ A @ B ) )
% 0.29/0.54       => ~ ( ( ord_less_eq_set_nat @ X @ A )
% 0.29/0.54           => ~ ( ord_less_eq_set_nat @ X @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infE
% 0.29/0.54  thf(fact_3080_le__infE,axiom,
% 0.29/0.54      ! [X: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ X @ ( inf_inf_rat @ A @ B ) )
% 0.29/0.54       => ~ ( ( ord_less_eq_rat @ X @ A )
% 0.29/0.54           => ~ ( ord_less_eq_rat @ X @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infE
% 0.29/0.54  thf(fact_3081_le__infE,axiom,
% 0.29/0.54      ! [X: nat,A: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A @ B ) )
% 0.29/0.54       => ~ ( ( ord_less_eq_nat @ X @ A )
% 0.29/0.54           => ~ ( ord_less_eq_nat @ X @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infE
% 0.29/0.54  thf(fact_3082_le__infE,axiom,
% 0.29/0.54      ! [X: int,A: int,B: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ X @ ( inf_inf_int @ A @ B ) )
% 0.29/0.54       => ~ ( ( ord_less_eq_int @ X @ A )
% 0.29/0.54           => ~ ( ord_less_eq_int @ X @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infE
% 0.29/0.54  thf(fact_3083_le__infI,axiom,
% 0.29/0.54      ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.29/0.54        ( ( ord_le3146513528884898305at_nat @ X @ A )
% 0.29/0.54       => ( ( ord_le3146513528884898305at_nat @ X @ B )
% 0.29/0.54         => ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI
% 0.29/0.54  thf(fact_3084_le__infI,axiom,
% 0.29/0.54      ! [X: product_prod_int_int > $o,A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 0.29/0.54        ( ( ord_le8369615600986905444_int_o @ X @ A )
% 0.29/0.54       => ( ( ord_le8369615600986905444_int_o @ X @ B )
% 0.29/0.54         => ( ord_le8369615600986905444_int_o @ X @ ( inf_in3604695632404883862_int_o @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI
% 0.29/0.54  thf(fact_3085_le__infI,axiom,
% 0.29/0.54      ! [X: list_char > $o,A: list_char > $o,B: list_char > $o] :
% 0.29/0.54        ( ( ord_le4796328588573674190char_o @ X @ A )
% 0.29/0.54       => ( ( ord_le4796328588573674190char_o @ X @ B )
% 0.29/0.54         => ( ord_le4796328588573674190char_o @ X @ ( inf_inf_list_char_o @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI
% 0.29/0.54  thf(fact_3086_le__infI,axiom,
% 0.29/0.54      ! [X: filter_nat,A: filter_nat,B: filter_nat] :
% 0.29/0.54        ( ( ord_le2510731241096832064er_nat @ X @ A )
% 0.29/0.54       => ( ( ord_le2510731241096832064er_nat @ X @ B )
% 0.29/0.54         => ( ord_le2510731241096832064er_nat @ X @ ( inf_inf_filter_nat @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI
% 0.29/0.54  thf(fact_3087_le__infI,axiom,
% 0.29/0.54      ! [X: set_nat,A: set_nat,B: set_nat] :
% 0.29/0.54        ( ( ord_less_eq_set_nat @ X @ A )
% 0.29/0.54       => ( ( ord_less_eq_set_nat @ X @ B )
% 0.29/0.54         => ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI
% 0.29/0.54  thf(fact_3088_le__infI,axiom,
% 0.29/0.54      ! [X: rat,A: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ X @ A )
% 0.29/0.54       => ( ( ord_less_eq_rat @ X @ B )
% 0.29/0.54         => ( ord_less_eq_rat @ X @ ( inf_inf_rat @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI
% 0.29/0.54  thf(fact_3089_le__infI,axiom,
% 0.29/0.54      ! [X: nat,A: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ X @ A )
% 0.29/0.54       => ( ( ord_less_eq_nat @ X @ B )
% 0.29/0.54         => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI
% 0.29/0.54  thf(fact_3090_le__infI,axiom,
% 0.29/0.54      ! [X: int,A: int,B: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ X @ A )
% 0.29/0.54       => ( ( ord_less_eq_int @ X @ B )
% 0.29/0.54         => ( ord_less_eq_int @ X @ ( inf_inf_int @ A @ B ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI
% 0.29/0.54  thf(fact_3091_inf__mono,axiom,
% 0.29/0.54      ! [A: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,D2: set_Pr1261947904930325089at_nat] :
% 0.29/0.54        ( ( ord_le3146513528884898305at_nat @ A @ C )
% 0.29/0.54       => ( ( ord_le3146513528884898305at_nat @ B @ D2 )
% 0.29/0.54         => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ ( inf_in2572325071724192079at_nat @ C @ D2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_mono
% 0.29/0.54  thf(fact_3092_inf__mono,axiom,
% 0.29/0.54      ! [A: product_prod_int_int > $o,C: product_prod_int_int > $o,B: product_prod_int_int > $o,D2: product_prod_int_int > $o] :
% 0.29/0.54        ( ( ord_le8369615600986905444_int_o @ A @ C )
% 0.29/0.54       => ( ( ord_le8369615600986905444_int_o @ B @ D2 )
% 0.29/0.54         => ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ ( inf_in3604695632404883862_int_o @ C @ D2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_mono
% 0.29/0.54  thf(fact_3093_inf__mono,axiom,
% 0.29/0.54      ! [A: list_char > $o,C: list_char > $o,B: list_char > $o,D2: list_char > $o] :
% 0.29/0.54        ( ( ord_le4796328588573674190char_o @ A @ C )
% 0.29/0.54       => ( ( ord_le4796328588573674190char_o @ B @ D2 )
% 0.29/0.54         => ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ A @ B ) @ ( inf_inf_list_char_o @ C @ D2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_mono
% 0.29/0.54  thf(fact_3094_inf__mono,axiom,
% 0.29/0.54      ! [A: filter_nat,C: filter_nat,B: filter_nat,D2: filter_nat] :
% 0.29/0.54        ( ( ord_le2510731241096832064er_nat @ A @ C )
% 0.29/0.54       => ( ( ord_le2510731241096832064er_nat @ B @ D2 )
% 0.29/0.54         => ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ A @ B ) @ ( inf_inf_filter_nat @ C @ D2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_mono
% 0.29/0.54  thf(fact_3095_inf__mono,axiom,
% 0.29/0.54      ! [A: set_nat,C: set_nat,B: set_nat,D2: set_nat] :
% 0.29/0.54        ( ( ord_less_eq_set_nat @ A @ C )
% 0.29/0.54       => ( ( ord_less_eq_set_nat @ B @ D2 )
% 0.29/0.54         => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ ( inf_inf_set_nat @ C @ D2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_mono
% 0.29/0.54  thf(fact_3096_inf__mono,axiom,
% 0.29/0.54      ! [A: rat,C: rat,B: rat,D2: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ A @ C )
% 0.29/0.54       => ( ( ord_less_eq_rat @ B @ D2 )
% 0.29/0.54         => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ ( inf_inf_rat @ C @ D2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_mono
% 0.29/0.54  thf(fact_3097_inf__mono,axiom,
% 0.29/0.54      ! [A: nat,C: nat,B: nat,D2: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ A @ C )
% 0.29/0.54       => ( ( ord_less_eq_nat @ B @ D2 )
% 0.29/0.54         => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ ( inf_inf_nat @ C @ D2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_mono
% 0.29/0.54  thf(fact_3098_inf__mono,axiom,
% 0.29/0.54      ! [A: int,C: int,B: int,D2: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ A @ C )
% 0.29/0.54       => ( ( ord_less_eq_int @ B @ D2 )
% 0.29/0.54         => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ ( inf_inf_int @ C @ D2 ) ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf_mono
% 0.29/0.54  thf(fact_3099_le__infI1,axiom,
% 0.29/0.54      ! [A: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.29/0.54        ( ( ord_le3146513528884898305at_nat @ A @ X )
% 0.29/0.54       => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI1
% 0.29/0.54  thf(fact_3100_le__infI1,axiom,
% 0.29/0.54      ! [A: product_prod_int_int > $o,X: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 0.29/0.54        ( ( ord_le8369615600986905444_int_o @ A @ X )
% 0.29/0.54       => ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI1
% 0.29/0.54  thf(fact_3101_le__infI1,axiom,
% 0.29/0.54      ! [A: list_char > $o,X: list_char > $o,B: list_char > $o] :
% 0.29/0.54        ( ( ord_le4796328588573674190char_o @ A @ X )
% 0.29/0.54       => ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI1
% 0.29/0.54  thf(fact_3102_le__infI1,axiom,
% 0.29/0.54      ! [A: filter_nat,X: filter_nat,B: filter_nat] :
% 0.29/0.54        ( ( ord_le2510731241096832064er_nat @ A @ X )
% 0.29/0.54       => ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI1
% 0.29/0.54  thf(fact_3103_le__infI1,axiom,
% 0.29/0.54      ! [A: set_nat,X: set_nat,B: set_nat] :
% 0.29/0.54        ( ( ord_less_eq_set_nat @ A @ X )
% 0.29/0.54       => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI1
% 0.29/0.54  thf(fact_3104_le__infI1,axiom,
% 0.29/0.54      ! [A: rat,X: rat,B: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ A @ X )
% 0.29/0.54       => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI1
% 0.29/0.54  thf(fact_3105_le__infI1,axiom,
% 0.29/0.54      ! [A: nat,X: nat,B: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ A @ X )
% 0.29/0.54       => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI1
% 0.29/0.54  thf(fact_3106_le__infI1,axiom,
% 0.29/0.54      ! [A: int,X: int,B: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ A @ X )
% 0.29/0.54       => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI1
% 0.29/0.54  thf(fact_3107_le__infI2,axiom,
% 0.29/0.54      ! [B: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 0.29/0.54        ( ( ord_le3146513528884898305at_nat @ B @ X )
% 0.29/0.54       => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI2
% 0.29/0.54  thf(fact_3108_le__infI2,axiom,
% 0.29/0.54      ! [B: product_prod_int_int > $o,X: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 0.29/0.54        ( ( ord_le8369615600986905444_int_o @ B @ X )
% 0.29/0.54       => ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI2
% 0.29/0.54  thf(fact_3109_le__infI2,axiom,
% 0.29/0.54      ! [B: list_char > $o,X: list_char > $o,A: list_char > $o] :
% 0.29/0.54        ( ( ord_le4796328588573674190char_o @ B @ X )
% 0.29/0.54       => ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI2
% 0.29/0.54  thf(fact_3110_le__infI2,axiom,
% 0.29/0.54      ! [B: filter_nat,X: filter_nat,A: filter_nat] :
% 0.29/0.54        ( ( ord_le2510731241096832064er_nat @ B @ X )
% 0.29/0.54       => ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI2
% 0.29/0.54  thf(fact_3111_le__infI2,axiom,
% 0.29/0.54      ! [B: set_nat,X: set_nat,A: set_nat] :
% 0.29/0.54        ( ( ord_less_eq_set_nat @ B @ X )
% 0.29/0.54       => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI2
% 0.29/0.54  thf(fact_3112_le__infI2,axiom,
% 0.29/0.54      ! [B: rat,X: rat,A: rat] :
% 0.29/0.54        ( ( ord_less_eq_rat @ B @ X )
% 0.29/0.54       => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI2
% 0.29/0.54  thf(fact_3113_le__infI2,axiom,
% 0.29/0.54      ! [B: nat,X: nat,A: nat] :
% 0.29/0.54        ( ( ord_less_eq_nat @ B @ X )
% 0.29/0.54       => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI2
% 0.29/0.54  thf(fact_3114_le__infI2,axiom,
% 0.29/0.54      ! [B: int,X: int,A: int] :
% 0.29/0.54        ( ( ord_less_eq_int @ B @ X )
% 0.29/0.54       => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 0.29/0.54  
% 0.29/0.54  % le_infI2
% 0.29/0.54  thf(fact_3115_inf_OorderE,axiom,
% 0.29/0.54      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.29/0.54        ( ( ord_le3146513528884898305at_nat @ A @ B )
% 0.29/0.54       => ( A
% 0.29/0.54          = ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.orderE
% 0.29/0.54  thf(fact_3116_inf_OorderE,axiom,
% 0.29/0.54      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 0.29/0.54        ( ( ord_le8369615600986905444_int_o @ A @ B )
% 0.29/0.54       => ( A
% 0.29/0.54          = ( inf_in3604695632404883862_int_o @ A @ B ) ) ) ).
% 0.29/0.54  
% 0.29/0.54  % inf.orderE
% 0.29/0.54  thf(fact_3117_inf_OorderE,axiom,
% 0.29/0.55      ! [A: list_char > $o,B: list_char > $o] :
% 0.29/0.55        ( ( ord_le4796328588573674190char_o @ A @ B )
% 0.29/0.55       => ( A
% 0.29/0.55          = ( inf_inf_list_char_o @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.orderE
% 0.29/0.55  thf(fact_3118_inf_OorderE,axiom,
% 0.29/0.55      ! [A: filter_nat,B: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 0.29/0.55       => ( A
% 0.29/0.55          = ( inf_inf_filter_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.orderE
% 0.29/0.55  thf(fact_3119_inf_OorderE,axiom,
% 0.29/0.55      ! [A: set_nat,B: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ A @ B )
% 0.29/0.55       => ( A
% 0.29/0.55          = ( inf_inf_set_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.orderE
% 0.29/0.55  thf(fact_3120_inf_OorderE,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.55       => ( A
% 0.29/0.55          = ( inf_inf_rat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.orderE
% 0.29/0.55  thf(fact_3121_inf_OorderE,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.55       => ( A
% 0.29/0.55          = ( inf_inf_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.orderE
% 0.29/0.55  thf(fact_3122_inf_OorderE,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.55       => ( A
% 0.29/0.55          = ( inf_inf_int @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.orderE
% 0.29/0.55  thf(fact_3123_inf_OorderI,axiom,
% 0.29/0.55      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.29/0.55        ( ( A
% 0.29/0.55          = ( inf_in2572325071724192079at_nat @ A @ B ) )
% 0.29/0.55       => ( ord_le3146513528884898305at_nat @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.orderI
% 0.29/0.55  thf(fact_3124_inf_OorderI,axiom,
% 0.29/0.55      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 0.29/0.55        ( ( A
% 0.29/0.55          = ( inf_in3604695632404883862_int_o @ A @ B ) )
% 0.29/0.55       => ( ord_le8369615600986905444_int_o @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.orderI
% 0.29/0.55  thf(fact_3125_inf_OorderI,axiom,
% 0.29/0.55      ! [A: list_char > $o,B: list_char > $o] :
% 0.29/0.55        ( ( A
% 0.29/0.55          = ( inf_inf_list_char_o @ A @ B ) )
% 0.29/0.55       => ( ord_le4796328588573674190char_o @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.orderI
% 0.29/0.55  thf(fact_3126_inf_OorderI,axiom,
% 0.29/0.55      ! [A: filter_nat,B: filter_nat] :
% 0.29/0.55        ( ( A
% 0.29/0.55          = ( inf_inf_filter_nat @ A @ B ) )
% 0.29/0.55       => ( ord_le2510731241096832064er_nat @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.orderI
% 0.29/0.55  thf(fact_3127_inf_OorderI,axiom,
% 0.29/0.55      ! [A: set_nat,B: set_nat] :
% 0.29/0.55        ( ( A
% 0.29/0.55          = ( inf_inf_set_nat @ A @ B ) )
% 0.29/0.55       => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.orderI
% 0.29/0.55  thf(fact_3128_inf_OorderI,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( A
% 0.29/0.55          = ( inf_inf_rat @ A @ B ) )
% 0.29/0.55       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.orderI
% 0.29/0.55  thf(fact_3129_inf_OorderI,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( A
% 0.29/0.55          = ( inf_inf_nat @ A @ B ) )
% 0.29/0.55       => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.orderI
% 0.29/0.55  thf(fact_3130_inf_OorderI,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( A
% 0.29/0.55          = ( inf_inf_int @ A @ B ) )
% 0.29/0.55       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.orderI
% 0.29/0.55  thf(fact_3131_inf__unique,axiom,
% 0.29/0.55      ! [F2: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.29/0.55        ( ! [X2: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( F2 @ X2 @ Y2 ) @ X2 )
% 0.29/0.55       => ( ! [X2: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( F2 @ X2 @ Y2 ) @ Y2 )
% 0.29/0.55         => ( ! [X2: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
% 0.29/0.55                ( ( ord_le3146513528884898305at_nat @ X2 @ Y2 )
% 0.29/0.55               => ( ( ord_le3146513528884898305at_nat @ X2 @ Z2 )
% 0.29/0.55                 => ( ord_le3146513528884898305at_nat @ X2 @ ( F2 @ Y2 @ Z2 ) ) ) )
% 0.29/0.55           => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 0.29/0.55              = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_unique
% 0.29/0.55  thf(fact_3132_inf__unique,axiom,
% 0.29/0.55      ! [F2: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o,X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 0.29/0.55        ( ! [X2: product_prod_int_int > $o,Y2: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( F2 @ X2 @ Y2 ) @ X2 )
% 0.29/0.55       => ( ! [X2: product_prod_int_int > $o,Y2: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( F2 @ X2 @ Y2 ) @ Y2 )
% 0.29/0.55         => ( ! [X2: product_prod_int_int > $o,Y2: product_prod_int_int > $o,Z2: product_prod_int_int > $o] :
% 0.29/0.55                ( ( ord_le8369615600986905444_int_o @ X2 @ Y2 )
% 0.29/0.55               => ( ( ord_le8369615600986905444_int_o @ X2 @ Z2 )
% 0.29/0.55                 => ( ord_le8369615600986905444_int_o @ X2 @ ( F2 @ Y2 @ Z2 ) ) ) )
% 0.29/0.55           => ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 0.29/0.55              = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_unique
% 0.29/0.55  thf(fact_3133_inf__unique,axiom,
% 0.29/0.55      ! [F2: ( list_char > $o ) > ( list_char > $o ) > list_char > $o,X: list_char > $o,Y: list_char > $o] :
% 0.29/0.55        ( ! [X2: list_char > $o,Y2: list_char > $o] : ( ord_le4796328588573674190char_o @ ( F2 @ X2 @ Y2 ) @ X2 )
% 0.29/0.55       => ( ! [X2: list_char > $o,Y2: list_char > $o] : ( ord_le4796328588573674190char_o @ ( F2 @ X2 @ Y2 ) @ Y2 )
% 0.29/0.55         => ( ! [X2: list_char > $o,Y2: list_char > $o,Z2: list_char > $o] :
% 0.29/0.55                ( ( ord_le4796328588573674190char_o @ X2 @ Y2 )
% 0.29/0.55               => ( ( ord_le4796328588573674190char_o @ X2 @ Z2 )
% 0.29/0.55                 => ( ord_le4796328588573674190char_o @ X2 @ ( F2 @ Y2 @ Z2 ) ) ) )
% 0.29/0.55           => ( ( inf_inf_list_char_o @ X @ Y )
% 0.29/0.55              = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_unique
% 0.29/0.55  thf(fact_3134_inf__unique,axiom,
% 0.29/0.55      ! [F2: filter_nat > filter_nat > filter_nat,X: filter_nat,Y: filter_nat] :
% 0.29/0.55        ( ! [X2: filter_nat,Y2: filter_nat] : ( ord_le2510731241096832064er_nat @ ( F2 @ X2 @ Y2 ) @ X2 )
% 0.29/0.55       => ( ! [X2: filter_nat,Y2: filter_nat] : ( ord_le2510731241096832064er_nat @ ( F2 @ X2 @ Y2 ) @ Y2 )
% 0.29/0.55         => ( ! [X2: filter_nat,Y2: filter_nat,Z2: filter_nat] :
% 0.29/0.55                ( ( ord_le2510731241096832064er_nat @ X2 @ Y2 )
% 0.29/0.55               => ( ( ord_le2510731241096832064er_nat @ X2 @ Z2 )
% 0.29/0.55                 => ( ord_le2510731241096832064er_nat @ X2 @ ( F2 @ Y2 @ Z2 ) ) ) )
% 0.29/0.55           => ( ( inf_inf_filter_nat @ X @ Y )
% 0.29/0.55              = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_unique
% 0.29/0.55  thf(fact_3135_inf__unique,axiom,
% 0.29/0.55      ! [F2: set_nat > set_nat > set_nat,X: set_nat,Y: set_nat] :
% 0.29/0.55        ( ! [X2: set_nat,Y2: set_nat] : ( ord_less_eq_set_nat @ ( F2 @ X2 @ Y2 ) @ X2 )
% 0.29/0.55       => ( ! [X2: set_nat,Y2: set_nat] : ( ord_less_eq_set_nat @ ( F2 @ X2 @ Y2 ) @ Y2 )
% 0.29/0.55         => ( ! [X2: set_nat,Y2: set_nat,Z2: set_nat] :
% 0.29/0.55                ( ( ord_less_eq_set_nat @ X2 @ Y2 )
% 0.29/0.55               => ( ( ord_less_eq_set_nat @ X2 @ Z2 )
% 0.29/0.55                 => ( ord_less_eq_set_nat @ X2 @ ( F2 @ Y2 @ Z2 ) ) ) )
% 0.29/0.55           => ( ( inf_inf_set_nat @ X @ Y )
% 0.29/0.55              = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_unique
% 0.29/0.55  thf(fact_3136_inf__unique,axiom,
% 0.29/0.55      ! [F2: rat > rat > rat,X: rat,Y: rat] :
% 0.29/0.55        ( ! [X2: rat,Y2: rat] : ( ord_less_eq_rat @ ( F2 @ X2 @ Y2 ) @ X2 )
% 0.29/0.55       => ( ! [X2: rat,Y2: rat] : ( ord_less_eq_rat @ ( F2 @ X2 @ Y2 ) @ Y2 )
% 0.29/0.55         => ( ! [X2: rat,Y2: rat,Z2: rat] :
% 0.29/0.55                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 0.29/0.55               => ( ( ord_less_eq_rat @ X2 @ Z2 )
% 0.29/0.55                 => ( ord_less_eq_rat @ X2 @ ( F2 @ Y2 @ Z2 ) ) ) )
% 0.29/0.55           => ( ( inf_inf_rat @ X @ Y )
% 0.29/0.55              = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_unique
% 0.29/0.55  thf(fact_3137_inf__unique,axiom,
% 0.29/0.55      ! [F2: nat > nat > nat,X: nat,Y: nat] :
% 0.29/0.55        ( ! [X2: nat,Y2: nat] : ( ord_less_eq_nat @ ( F2 @ X2 @ Y2 ) @ X2 )
% 0.29/0.55       => ( ! [X2: nat,Y2: nat] : ( ord_less_eq_nat @ ( F2 @ X2 @ Y2 ) @ Y2 )
% 0.29/0.55         => ( ! [X2: nat,Y2: nat,Z2: nat] :
% 0.29/0.55                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 0.29/0.55               => ( ( ord_less_eq_nat @ X2 @ Z2 )
% 0.29/0.55                 => ( ord_less_eq_nat @ X2 @ ( F2 @ Y2 @ Z2 ) ) ) )
% 0.29/0.55           => ( ( inf_inf_nat @ X @ Y )
% 0.29/0.55              = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_unique
% 0.29/0.55  thf(fact_3138_inf__unique,axiom,
% 0.29/0.55      ! [F2: int > int > int,X: int,Y: int] :
% 0.29/0.55        ( ! [X2: int,Y2: int] : ( ord_less_eq_int @ ( F2 @ X2 @ Y2 ) @ X2 )
% 0.29/0.55       => ( ! [X2: int,Y2: int] : ( ord_less_eq_int @ ( F2 @ X2 @ Y2 ) @ Y2 )
% 0.29/0.55         => ( ! [X2: int,Y2: int,Z2: int] :
% 0.29/0.55                ( ( ord_less_eq_int @ X2 @ Y2 )
% 0.29/0.55               => ( ( ord_less_eq_int @ X2 @ Z2 )
% 0.29/0.55                 => ( ord_less_eq_int @ X2 @ ( F2 @ Y2 @ Z2 ) ) ) )
% 0.29/0.55           => ( ( inf_inf_int @ X @ Y )
% 0.29/0.55              = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_unique
% 0.29/0.55  thf(fact_3139_le__iff__inf,axiom,
% 0.29/0.55      ( ord_le3146513528884898305at_nat
% 0.29/0.55      = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 0.29/0.55            ( ( inf_in2572325071724192079at_nat @ X3 @ Y3 )
% 0.29/0.55            = X3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_iff_inf
% 0.29/0.55  thf(fact_3140_le__iff__inf,axiom,
% 0.29/0.55      ( ord_le8369615600986905444_int_o
% 0.29/0.55      = ( ^ [X3: product_prod_int_int > $o,Y3: product_prod_int_int > $o] :
% 0.29/0.55            ( ( inf_in3604695632404883862_int_o @ X3 @ Y3 )
% 0.29/0.55            = X3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_iff_inf
% 0.29/0.55  thf(fact_3141_le__iff__inf,axiom,
% 0.29/0.55      ( ord_le4796328588573674190char_o
% 0.29/0.55      = ( ^ [X3: list_char > $o,Y3: list_char > $o] :
% 0.29/0.55            ( ( inf_inf_list_char_o @ X3 @ Y3 )
% 0.29/0.55            = X3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_iff_inf
% 0.29/0.55  thf(fact_3142_le__iff__inf,axiom,
% 0.29/0.55      ( ord_le2510731241096832064er_nat
% 0.29/0.55      = ( ^ [X3: filter_nat,Y3: filter_nat] :
% 0.29/0.55            ( ( inf_inf_filter_nat @ X3 @ Y3 )
% 0.29/0.55            = X3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_iff_inf
% 0.29/0.55  thf(fact_3143_le__iff__inf,axiom,
% 0.29/0.55      ( ord_less_eq_set_nat
% 0.29/0.55      = ( ^ [X3: set_nat,Y3: set_nat] :
% 0.29/0.55            ( ( inf_inf_set_nat @ X3 @ Y3 )
% 0.29/0.55            = X3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_iff_inf
% 0.29/0.55  thf(fact_3144_le__iff__inf,axiom,
% 0.29/0.55      ( ord_less_eq_rat
% 0.29/0.55      = ( ^ [X3: rat,Y3: rat] :
% 0.29/0.55            ( ( inf_inf_rat @ X3 @ Y3 )
% 0.29/0.55            = X3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_iff_inf
% 0.29/0.55  thf(fact_3145_le__iff__inf,axiom,
% 0.29/0.55      ( ord_less_eq_nat
% 0.29/0.55      = ( ^ [X3: nat,Y3: nat] :
% 0.29/0.55            ( ( inf_inf_nat @ X3 @ Y3 )
% 0.29/0.55            = X3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_iff_inf
% 0.29/0.55  thf(fact_3146_le__iff__inf,axiom,
% 0.29/0.55      ( ord_less_eq_int
% 0.29/0.55      = ( ^ [X3: int,Y3: int] :
% 0.29/0.55            ( ( inf_inf_int @ X3 @ Y3 )
% 0.29/0.55            = X3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_iff_inf
% 0.29/0.55  thf(fact_3147_inf_Oabsorb1,axiom,
% 0.29/0.55      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.29/0.55        ( ( ord_le3146513528884898305at_nat @ A @ B )
% 0.29/0.55       => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 0.29/0.55          = A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb1
% 0.29/0.55  thf(fact_3148_inf_Oabsorb1,axiom,
% 0.29/0.55      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 0.29/0.55        ( ( ord_le8369615600986905444_int_o @ A @ B )
% 0.29/0.55       => ( ( inf_in3604695632404883862_int_o @ A @ B )
% 0.29/0.55          = A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb1
% 0.29/0.55  thf(fact_3149_inf_Oabsorb1,axiom,
% 0.29/0.55      ! [A: list_char > $o,B: list_char > $o] :
% 0.29/0.55        ( ( ord_le4796328588573674190char_o @ A @ B )
% 0.29/0.55       => ( ( inf_inf_list_char_o @ A @ B )
% 0.29/0.55          = A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb1
% 0.29/0.55  thf(fact_3150_inf_Oabsorb1,axiom,
% 0.29/0.55      ! [A: filter_nat,B: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 0.29/0.55       => ( ( inf_inf_filter_nat @ A @ B )
% 0.29/0.55          = A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb1
% 0.29/0.55  thf(fact_3151_inf_Oabsorb1,axiom,
% 0.29/0.55      ! [A: set_nat,B: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ A @ B )
% 0.29/0.55       => ( ( inf_inf_set_nat @ A @ B )
% 0.29/0.55          = A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb1
% 0.29/0.55  thf(fact_3152_inf_Oabsorb1,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.55       => ( ( inf_inf_rat @ A @ B )
% 0.29/0.55          = A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb1
% 0.29/0.55  thf(fact_3153_inf_Oabsorb1,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.55       => ( ( inf_inf_nat @ A @ B )
% 0.29/0.55          = A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb1
% 0.29/0.55  thf(fact_3154_inf_Oabsorb1,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.55       => ( ( inf_inf_int @ A @ B )
% 0.29/0.55          = A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb1
% 0.29/0.55  thf(fact_3155_inf_Oabsorb2,axiom,
% 0.29/0.55      ! [B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 0.29/0.55        ( ( ord_le3146513528884898305at_nat @ B @ A )
% 0.29/0.55       => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 0.29/0.55          = B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb2
% 0.29/0.55  thf(fact_3156_inf_Oabsorb2,axiom,
% 0.29/0.55      ! [B: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 0.29/0.55        ( ( ord_le8369615600986905444_int_o @ B @ A )
% 0.29/0.55       => ( ( inf_in3604695632404883862_int_o @ A @ B )
% 0.29/0.55          = B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb2
% 0.29/0.55  thf(fact_3157_inf_Oabsorb2,axiom,
% 0.29/0.55      ! [B: list_char > $o,A: list_char > $o] :
% 0.29/0.55        ( ( ord_le4796328588573674190char_o @ B @ A )
% 0.29/0.55       => ( ( inf_inf_list_char_o @ A @ B )
% 0.29/0.55          = B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb2
% 0.29/0.55  thf(fact_3158_inf_Oabsorb2,axiom,
% 0.29/0.55      ! [B: filter_nat,A: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ B @ A )
% 0.29/0.55       => ( ( inf_inf_filter_nat @ A @ B )
% 0.29/0.55          = B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb2
% 0.29/0.55  thf(fact_3159_inf_Oabsorb2,axiom,
% 0.29/0.55      ! [B: set_nat,A: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ B @ A )
% 0.29/0.55       => ( ( inf_inf_set_nat @ A @ B )
% 0.29/0.55          = B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb2
% 0.29/0.55  thf(fact_3160_inf_Oabsorb2,axiom,
% 0.29/0.55      ! [B: rat,A: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.55       => ( ( inf_inf_rat @ A @ B )
% 0.29/0.55          = B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb2
% 0.29/0.55  thf(fact_3161_inf_Oabsorb2,axiom,
% 0.29/0.55      ! [B: nat,A: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.55       => ( ( inf_inf_nat @ A @ B )
% 0.29/0.55          = B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb2
% 0.29/0.55  thf(fact_3162_inf_Oabsorb2,axiom,
% 0.29/0.55      ! [B: int,A: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.55       => ( ( inf_inf_int @ A @ B )
% 0.29/0.55          = B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb2
% 0.29/0.55  thf(fact_3163_inf__absorb1,axiom,
% 0.29/0.55      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.29/0.55        ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 0.29/0.55       => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 0.29/0.55          = X ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_absorb1
% 0.29/0.55  thf(fact_3164_inf__absorb1,axiom,
% 0.29/0.55      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 0.29/0.55        ( ( ord_le8369615600986905444_int_o @ X @ Y )
% 0.29/0.55       => ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 0.29/0.55          = X ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_absorb1
% 0.29/0.55  thf(fact_3165_inf__absorb1,axiom,
% 0.29/0.55      ! [X: list_char > $o,Y: list_char > $o] :
% 0.29/0.55        ( ( ord_le4796328588573674190char_o @ X @ Y )
% 0.29/0.55       => ( ( inf_inf_list_char_o @ X @ Y )
% 0.29/0.55          = X ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_absorb1
% 0.29/0.55  thf(fact_3166_inf__absorb1,axiom,
% 0.29/0.55      ! [X: filter_nat,Y: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 0.29/0.55       => ( ( inf_inf_filter_nat @ X @ Y )
% 0.29/0.55          = X ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_absorb1
% 0.29/0.55  thf(fact_3167_inf__absorb1,axiom,
% 0.29/0.55      ! [X: set_nat,Y: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ X @ Y )
% 0.29/0.55       => ( ( inf_inf_set_nat @ X @ Y )
% 0.29/0.55          = X ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_absorb1
% 0.29/0.55  thf(fact_3168_inf__absorb1,axiom,
% 0.29/0.55      ! [X: rat,Y: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.55       => ( ( inf_inf_rat @ X @ Y )
% 0.29/0.55          = X ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_absorb1
% 0.29/0.55  thf(fact_3169_inf__absorb1,axiom,
% 0.29/0.55      ! [X: nat,Y: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.55       => ( ( inf_inf_nat @ X @ Y )
% 0.29/0.55          = X ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_absorb1
% 0.29/0.55  thf(fact_3170_inf__absorb1,axiom,
% 0.29/0.55      ! [X: int,Y: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.55       => ( ( inf_inf_int @ X @ Y )
% 0.29/0.55          = X ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_absorb1
% 0.29/0.55  thf(fact_3171_inf__absorb2,axiom,
% 0.29/0.55      ! [Y: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 0.29/0.55        ( ( ord_le3146513528884898305at_nat @ Y @ X )
% 0.29/0.55       => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 0.29/0.55          = Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_absorb2
% 0.29/0.55  thf(fact_3172_inf__absorb2,axiom,
% 0.29/0.55      ! [Y: product_prod_int_int > $o,X: product_prod_int_int > $o] :
% 0.29/0.55        ( ( ord_le8369615600986905444_int_o @ Y @ X )
% 0.29/0.55       => ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 0.29/0.55          = Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_absorb2
% 0.29/0.55  thf(fact_3173_inf__absorb2,axiom,
% 0.29/0.55      ! [Y: list_char > $o,X: list_char > $o] :
% 0.29/0.55        ( ( ord_le4796328588573674190char_o @ Y @ X )
% 0.29/0.55       => ( ( inf_inf_list_char_o @ X @ Y )
% 0.29/0.55          = Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_absorb2
% 0.29/0.55  thf(fact_3174_inf__absorb2,axiom,
% 0.29/0.55      ! [Y: filter_nat,X: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 0.29/0.55       => ( ( inf_inf_filter_nat @ X @ Y )
% 0.29/0.55          = Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_absorb2
% 0.29/0.55  thf(fact_3175_inf__absorb2,axiom,
% 0.29/0.55      ! [Y: set_nat,X: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ Y @ X )
% 0.29/0.55       => ( ( inf_inf_set_nat @ X @ Y )
% 0.29/0.55          = Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_absorb2
% 0.29/0.55  thf(fact_3176_inf__absorb2,axiom,
% 0.29/0.55      ! [Y: rat,X: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ Y @ X )
% 0.29/0.55       => ( ( inf_inf_rat @ X @ Y )
% 0.29/0.55          = Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_absorb2
% 0.29/0.55  thf(fact_3177_inf__absorb2,axiom,
% 0.29/0.55      ! [Y: nat,X: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ Y @ X )
% 0.29/0.55       => ( ( inf_inf_nat @ X @ Y )
% 0.29/0.55          = Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_absorb2
% 0.29/0.55  thf(fact_3178_inf__absorb2,axiom,
% 0.29/0.55      ! [Y: int,X: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ Y @ X )
% 0.29/0.55       => ( ( inf_inf_int @ X @ Y )
% 0.29/0.55          = Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_absorb2
% 0.29/0.55  thf(fact_3179_inf_OboundedE,axiom,
% 0.29/0.55      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 0.29/0.55        ( ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) )
% 0.29/0.55       => ~ ( ( ord_le3146513528884898305at_nat @ A @ B )
% 0.29/0.55           => ~ ( ord_le3146513528884898305at_nat @ A @ C ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.boundedE
% 0.29/0.55  thf(fact_3180_inf_OboundedE,axiom,
% 0.29/0.55      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o,C: product_prod_int_int > $o] :
% 0.29/0.55        ( ( ord_le8369615600986905444_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C ) )
% 0.29/0.55       => ~ ( ( ord_le8369615600986905444_int_o @ A @ B )
% 0.29/0.55           => ~ ( ord_le8369615600986905444_int_o @ A @ C ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.boundedE
% 0.29/0.55  thf(fact_3181_inf_OboundedE,axiom,
% 0.29/0.55      ! [A: list_char > $o,B: list_char > $o,C: list_char > $o] :
% 0.29/0.55        ( ( ord_le4796328588573674190char_o @ A @ ( inf_inf_list_char_o @ B @ C ) )
% 0.29/0.55       => ~ ( ( ord_le4796328588573674190char_o @ A @ B )
% 0.29/0.55           => ~ ( ord_le4796328588573674190char_o @ A @ C ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.boundedE
% 0.29/0.55  thf(fact_3182_inf_OboundedE,axiom,
% 0.29/0.55      ! [A: filter_nat,B: filter_nat,C: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ A @ ( inf_inf_filter_nat @ B @ C ) )
% 0.29/0.55       => ~ ( ( ord_le2510731241096832064er_nat @ A @ B )
% 0.29/0.55           => ~ ( ord_le2510731241096832064er_nat @ A @ C ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.boundedE
% 0.29/0.55  thf(fact_3183_inf_OboundedE,axiom,
% 0.29/0.55      ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) )
% 0.29/0.55       => ~ ( ( ord_less_eq_set_nat @ A @ B )
% 0.29/0.55           => ~ ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.boundedE
% 0.29/0.55  thf(fact_3184_inf_OboundedE,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C ) )
% 0.29/0.55       => ~ ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.55           => ~ ( ord_less_eq_rat @ A @ C ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.boundedE
% 0.29/0.55  thf(fact_3185_inf_OboundedE,axiom,
% 0.29/0.55      ! [A: nat,B: nat,C: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C ) )
% 0.29/0.55       => ~ ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.55           => ~ ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.boundedE
% 0.29/0.55  thf(fact_3186_inf_OboundedE,axiom,
% 0.29/0.55      ! [A: int,B: int,C: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C ) )
% 0.29/0.55       => ~ ( ( ord_less_eq_int @ A @ B )
% 0.29/0.55           => ~ ( ord_less_eq_int @ A @ C ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.boundedE
% 0.29/0.55  thf(fact_3187_inf_OboundedI,axiom,
% 0.29/0.55      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 0.29/0.55        ( ( ord_le3146513528884898305at_nat @ A @ B )
% 0.29/0.55       => ( ( ord_le3146513528884898305at_nat @ A @ C )
% 0.29/0.55         => ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.boundedI
% 0.29/0.55  thf(fact_3188_inf_OboundedI,axiom,
% 0.29/0.55      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o,C: product_prod_int_int > $o] :
% 0.29/0.55        ( ( ord_le8369615600986905444_int_o @ A @ B )
% 0.29/0.55       => ( ( ord_le8369615600986905444_int_o @ A @ C )
% 0.29/0.55         => ( ord_le8369615600986905444_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.boundedI
% 0.29/0.55  thf(fact_3189_inf_OboundedI,axiom,
% 0.29/0.55      ! [A: list_char > $o,B: list_char > $o,C: list_char > $o] :
% 0.29/0.55        ( ( ord_le4796328588573674190char_o @ A @ B )
% 0.29/0.55       => ( ( ord_le4796328588573674190char_o @ A @ C )
% 0.29/0.55         => ( ord_le4796328588573674190char_o @ A @ ( inf_inf_list_char_o @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.boundedI
% 0.29/0.55  thf(fact_3190_inf_OboundedI,axiom,
% 0.29/0.55      ! [A: filter_nat,B: filter_nat,C: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 0.29/0.55       => ( ( ord_le2510731241096832064er_nat @ A @ C )
% 0.29/0.55         => ( ord_le2510731241096832064er_nat @ A @ ( inf_inf_filter_nat @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.boundedI
% 0.29/0.55  thf(fact_3191_inf_OboundedI,axiom,
% 0.29/0.55      ! [A: set_nat,B: set_nat,C: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_set_nat @ A @ C )
% 0.29/0.55         => ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.boundedI
% 0.29/0.55  thf(fact_3192_inf_OboundedI,axiom,
% 0.29/0.55      ! [A: rat,B: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_rat @ A @ C )
% 0.29/0.55         => ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.boundedI
% 0.29/0.55  thf(fact_3193_inf_OboundedI,axiom,
% 0.29/0.55      ! [A: nat,B: nat,C: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_nat @ A @ C )
% 0.29/0.55         => ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.boundedI
% 0.29/0.55  thf(fact_3194_inf_OboundedI,axiom,
% 0.29/0.55      ! [A: int,B: int,C: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.55       => ( ( ord_less_eq_int @ A @ C )
% 0.29/0.55         => ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.boundedI
% 0.29/0.55  thf(fact_3195_inf__greatest,axiom,
% 0.29/0.55      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 0.29/0.55        ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 0.29/0.55       => ( ( ord_le3146513528884898305at_nat @ X @ Z )
% 0.29/0.55         => ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_greatest
% 0.29/0.55  thf(fact_3196_inf__greatest,axiom,
% 0.29/0.55      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 0.29/0.55        ( ( ord_le8369615600986905444_int_o @ X @ Y )
% 0.29/0.55       => ( ( ord_le8369615600986905444_int_o @ X @ Z )
% 0.29/0.55         => ( ord_le8369615600986905444_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_greatest
% 0.29/0.55  thf(fact_3197_inf__greatest,axiom,
% 0.29/0.55      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 0.29/0.55        ( ( ord_le4796328588573674190char_o @ X @ Y )
% 0.29/0.55       => ( ( ord_le4796328588573674190char_o @ X @ Z )
% 0.29/0.55         => ( ord_le4796328588573674190char_o @ X @ ( inf_inf_list_char_o @ Y @ Z ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_greatest
% 0.29/0.55  thf(fact_3198_inf__greatest,axiom,
% 0.29/0.55      ! [X: filter_nat,Y: filter_nat,Z: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 0.29/0.55       => ( ( ord_le2510731241096832064er_nat @ X @ Z )
% 0.29/0.55         => ( ord_le2510731241096832064er_nat @ X @ ( inf_inf_filter_nat @ Y @ Z ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_greatest
% 0.29/0.55  thf(fact_3199_inf__greatest,axiom,
% 0.29/0.55      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ X @ Y )
% 0.29/0.55       => ( ( ord_less_eq_set_nat @ X @ Z )
% 0.29/0.55         => ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_greatest
% 0.29/0.55  thf(fact_3200_inf__greatest,axiom,
% 0.29/0.55      ! [X: rat,Y: rat,Z: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.55       => ( ( ord_less_eq_rat @ X @ Z )
% 0.29/0.55         => ( ord_less_eq_rat @ X @ ( inf_inf_rat @ Y @ Z ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_greatest
% 0.29/0.55  thf(fact_3201_inf__greatest,axiom,
% 0.29/0.55      ! [X: nat,Y: nat,Z: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.55       => ( ( ord_less_eq_nat @ X @ Z )
% 0.29/0.55         => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_greatest
% 0.29/0.55  thf(fact_3202_inf__greatest,axiom,
% 0.29/0.55      ! [X: int,Y: int,Z: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.55       => ( ( ord_less_eq_int @ X @ Z )
% 0.29/0.55         => ( ord_less_eq_int @ X @ ( inf_inf_int @ Y @ Z ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_greatest
% 0.29/0.55  thf(fact_3203_inf_Oorder__iff,axiom,
% 0.29/0.55      ( ord_le3146513528884898305at_nat
% 0.29/0.55      = ( ^ [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 0.29/0.55            ( A3
% 0.29/0.55            = ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.order_iff
% 0.29/0.55  thf(fact_3204_inf_Oorder__iff,axiom,
% 0.29/0.55      ( ord_le8369615600986905444_int_o
% 0.29/0.55      = ( ^ [A3: product_prod_int_int > $o,B3: product_prod_int_int > $o] :
% 0.29/0.55            ( A3
% 0.29/0.55            = ( inf_in3604695632404883862_int_o @ A3 @ B3 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.order_iff
% 0.29/0.55  thf(fact_3205_inf_Oorder__iff,axiom,
% 0.29/0.55      ( ord_le4796328588573674190char_o
% 0.29/0.55      = ( ^ [A3: list_char > $o,B3: list_char > $o] :
% 0.29/0.55            ( A3
% 0.29/0.55            = ( inf_inf_list_char_o @ A3 @ B3 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.order_iff
% 0.29/0.55  thf(fact_3206_inf_Oorder__iff,axiom,
% 0.29/0.55      ( ord_le2510731241096832064er_nat
% 0.29/0.55      = ( ^ [A3: filter_nat,B3: filter_nat] :
% 0.29/0.55            ( A3
% 0.29/0.55            = ( inf_inf_filter_nat @ A3 @ B3 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.order_iff
% 0.29/0.55  thf(fact_3207_inf_Oorder__iff,axiom,
% 0.29/0.55      ( ord_less_eq_set_nat
% 0.29/0.55      = ( ^ [A3: set_nat,B3: set_nat] :
% 0.29/0.55            ( A3
% 0.29/0.55            = ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.order_iff
% 0.29/0.55  thf(fact_3208_inf_Oorder__iff,axiom,
% 0.29/0.55      ( ord_less_eq_rat
% 0.29/0.55      = ( ^ [A3: rat,B3: rat] :
% 0.29/0.55            ( A3
% 0.29/0.55            = ( inf_inf_rat @ A3 @ B3 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.order_iff
% 0.29/0.55  thf(fact_3209_inf_Oorder__iff,axiom,
% 0.29/0.55      ( ord_less_eq_nat
% 0.29/0.55      = ( ^ [A3: nat,B3: nat] :
% 0.29/0.55            ( A3
% 0.29/0.55            = ( inf_inf_nat @ A3 @ B3 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.order_iff
% 0.29/0.55  thf(fact_3210_inf_Oorder__iff,axiom,
% 0.29/0.55      ( ord_less_eq_int
% 0.29/0.55      = ( ^ [A3: int,B3: int] :
% 0.29/0.55            ( A3
% 0.29/0.55            = ( inf_inf_int @ A3 @ B3 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.order_iff
% 0.29/0.55  thf(fact_3211_inf_Ocobounded1,axiom,
% 0.29/0.55      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ A ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.cobounded1
% 0.29/0.55  thf(fact_3212_inf_Ocobounded1,axiom,
% 0.29/0.55      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ A ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.cobounded1
% 0.29/0.55  thf(fact_3213_inf_Ocobounded1,axiom,
% 0.29/0.55      ! [A: list_char > $o,B: list_char > $o] : ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ A @ B ) @ A ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.cobounded1
% 0.29/0.55  thf(fact_3214_inf_Ocobounded1,axiom,
% 0.29/0.55      ! [A: filter_nat,B: filter_nat] : ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ A @ B ) @ A ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.cobounded1
% 0.29/0.55  thf(fact_3215_inf_Ocobounded1,axiom,
% 0.29/0.55      ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ A ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.cobounded1
% 0.29/0.55  thf(fact_3216_inf_Ocobounded1,axiom,
% 0.29/0.55      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ A ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.cobounded1
% 0.29/0.55  thf(fact_3217_inf_Ocobounded1,axiom,
% 0.29/0.55      ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ A ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.cobounded1
% 0.29/0.55  thf(fact_3218_inf_Ocobounded1,axiom,
% 0.29/0.55      ! [A: int,B: int] : ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ A ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.cobounded1
% 0.29/0.55  thf(fact_3219_inf_Ocobounded2,axiom,
% 0.29/0.55      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ B ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.cobounded2
% 0.29/0.55  thf(fact_3220_inf_Ocobounded2,axiom,
% 0.29/0.55      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ B ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.cobounded2
% 0.29/0.55  thf(fact_3221_inf_Ocobounded2,axiom,
% 0.29/0.55      ! [A: list_char > $o,B: list_char > $o] : ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ A @ B ) @ B ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.cobounded2
% 0.29/0.55  thf(fact_3222_inf_Ocobounded2,axiom,
% 0.29/0.55      ! [A: filter_nat,B: filter_nat] : ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ A @ B ) @ B ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.cobounded2
% 0.29/0.55  thf(fact_3223_inf_Ocobounded2,axiom,
% 0.29/0.55      ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ B ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.cobounded2
% 0.29/0.55  thf(fact_3224_inf_Ocobounded2,axiom,
% 0.29/0.55      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ B ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.cobounded2
% 0.29/0.55  thf(fact_3225_inf_Ocobounded2,axiom,
% 0.29/0.55      ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ B ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.cobounded2
% 0.29/0.55  thf(fact_3226_inf_Ocobounded2,axiom,
% 0.29/0.55      ! [A: int,B: int] : ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ B ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.cobounded2
% 0.29/0.55  thf(fact_3227_inf_Oabsorb__iff1,axiom,
% 0.29/0.55      ( ord_le3146513528884898305at_nat
% 0.29/0.55      = ( ^ [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 0.29/0.55            ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 0.29/0.55            = A3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb_iff1
% 0.29/0.55  thf(fact_3228_inf_Oabsorb__iff1,axiom,
% 0.29/0.55      ( ord_le8369615600986905444_int_o
% 0.29/0.55      = ( ^ [A3: product_prod_int_int > $o,B3: product_prod_int_int > $o] :
% 0.29/0.55            ( ( inf_in3604695632404883862_int_o @ A3 @ B3 )
% 0.29/0.55            = A3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb_iff1
% 0.29/0.55  thf(fact_3229_inf_Oabsorb__iff1,axiom,
% 0.29/0.55      ( ord_le4796328588573674190char_o
% 0.29/0.55      = ( ^ [A3: list_char > $o,B3: list_char > $o] :
% 0.29/0.55            ( ( inf_inf_list_char_o @ A3 @ B3 )
% 0.29/0.55            = A3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb_iff1
% 0.29/0.55  thf(fact_3230_inf_Oabsorb__iff1,axiom,
% 0.29/0.55      ( ord_le2510731241096832064er_nat
% 0.29/0.55      = ( ^ [A3: filter_nat,B3: filter_nat] :
% 0.29/0.55            ( ( inf_inf_filter_nat @ A3 @ B3 )
% 0.29/0.55            = A3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb_iff1
% 0.29/0.55  thf(fact_3231_inf_Oabsorb__iff1,axiom,
% 0.29/0.55      ( ord_less_eq_set_nat
% 0.29/0.55      = ( ^ [A3: set_nat,B3: set_nat] :
% 0.29/0.55            ( ( inf_inf_set_nat @ A3 @ B3 )
% 0.29/0.55            = A3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb_iff1
% 0.29/0.55  thf(fact_3232_inf_Oabsorb__iff1,axiom,
% 0.29/0.55      ( ord_less_eq_rat
% 0.29/0.55      = ( ^ [A3: rat,B3: rat] :
% 0.29/0.55            ( ( inf_inf_rat @ A3 @ B3 )
% 0.29/0.55            = A3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb_iff1
% 0.29/0.55  thf(fact_3233_inf_Oabsorb__iff1,axiom,
% 0.29/0.55      ( ord_less_eq_nat
% 0.29/0.55      = ( ^ [A3: nat,B3: nat] :
% 0.29/0.55            ( ( inf_inf_nat @ A3 @ B3 )
% 0.29/0.55            = A3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb_iff1
% 0.29/0.55  thf(fact_3234_inf_Oabsorb__iff1,axiom,
% 0.29/0.55      ( ord_less_eq_int
% 0.29/0.55      = ( ^ [A3: int,B3: int] :
% 0.29/0.55            ( ( inf_inf_int @ A3 @ B3 )
% 0.29/0.55            = A3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb_iff1
% 0.29/0.55  thf(fact_3235_inf_Oabsorb__iff2,axiom,
% 0.29/0.55      ( ord_le3146513528884898305at_nat
% 0.29/0.55      = ( ^ [B3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 0.29/0.55            ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 0.29/0.55            = B3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb_iff2
% 0.29/0.55  thf(fact_3236_inf_Oabsorb__iff2,axiom,
% 0.29/0.55      ( ord_le8369615600986905444_int_o
% 0.29/0.55      = ( ^ [B3: product_prod_int_int > $o,A3: product_prod_int_int > $o] :
% 0.29/0.55            ( ( inf_in3604695632404883862_int_o @ A3 @ B3 )
% 0.29/0.55            = B3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb_iff2
% 0.29/0.55  thf(fact_3237_inf_Oabsorb__iff2,axiom,
% 0.29/0.55      ( ord_le4796328588573674190char_o
% 0.29/0.55      = ( ^ [B3: list_char > $o,A3: list_char > $o] :
% 0.29/0.55            ( ( inf_inf_list_char_o @ A3 @ B3 )
% 0.29/0.55            = B3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb_iff2
% 0.29/0.55  thf(fact_3238_inf_Oabsorb__iff2,axiom,
% 0.29/0.55      ( ord_le2510731241096832064er_nat
% 0.29/0.55      = ( ^ [B3: filter_nat,A3: filter_nat] :
% 0.29/0.55            ( ( inf_inf_filter_nat @ A3 @ B3 )
% 0.29/0.55            = B3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb_iff2
% 0.29/0.55  thf(fact_3239_inf_Oabsorb__iff2,axiom,
% 0.29/0.55      ( ord_less_eq_set_nat
% 0.29/0.55      = ( ^ [B3: set_nat,A3: set_nat] :
% 0.29/0.55            ( ( inf_inf_set_nat @ A3 @ B3 )
% 0.29/0.55            = B3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb_iff2
% 0.29/0.55  thf(fact_3240_inf_Oabsorb__iff2,axiom,
% 0.29/0.55      ( ord_less_eq_rat
% 0.29/0.55      = ( ^ [B3: rat,A3: rat] :
% 0.29/0.55            ( ( inf_inf_rat @ A3 @ B3 )
% 0.29/0.55            = B3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb_iff2
% 0.29/0.55  thf(fact_3241_inf_Oabsorb__iff2,axiom,
% 0.29/0.55      ( ord_less_eq_nat
% 0.29/0.55      = ( ^ [B3: nat,A3: nat] :
% 0.29/0.55            ( ( inf_inf_nat @ A3 @ B3 )
% 0.29/0.55            = B3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb_iff2
% 0.29/0.55  thf(fact_3242_inf_Oabsorb__iff2,axiom,
% 0.29/0.55      ( ord_less_eq_int
% 0.29/0.55      = ( ^ [B3: int,A3: int] :
% 0.29/0.55            ( ( inf_inf_int @ A3 @ B3 )
% 0.29/0.55            = B3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.absorb_iff2
% 0.29/0.55  thf(fact_3243_inf_OcoboundedI1,axiom,
% 0.29/0.55      ! [A: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.29/0.55        ( ( ord_le3146513528884898305at_nat @ A @ C )
% 0.29/0.55       => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.coboundedI1
% 0.29/0.55  thf(fact_3244_inf_OcoboundedI1,axiom,
% 0.29/0.55      ! [A: product_prod_int_int > $o,C: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 0.29/0.55        ( ( ord_le8369615600986905444_int_o @ A @ C )
% 0.29/0.55       => ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.coboundedI1
% 0.29/0.55  thf(fact_3245_inf_OcoboundedI1,axiom,
% 0.29/0.55      ! [A: list_char > $o,C: list_char > $o,B: list_char > $o] :
% 0.29/0.55        ( ( ord_le4796328588573674190char_o @ A @ C )
% 0.29/0.55       => ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ A @ B ) @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.coboundedI1
% 0.29/0.55  thf(fact_3246_inf_OcoboundedI1,axiom,
% 0.29/0.55      ! [A: filter_nat,C: filter_nat,B: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ A @ C )
% 0.29/0.55       => ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ A @ B ) @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.coboundedI1
% 0.29/0.55  thf(fact_3247_inf_OcoboundedI1,axiom,
% 0.29/0.55      ! [A: set_nat,C: set_nat,B: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ A @ C )
% 0.29/0.55       => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.coboundedI1
% 0.29/0.55  thf(fact_3248_inf_OcoboundedI1,axiom,
% 0.29/0.55      ! [A: rat,C: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ C )
% 0.29/0.55       => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.coboundedI1
% 0.29/0.55  thf(fact_3249_inf_OcoboundedI1,axiom,
% 0.29/0.55      ! [A: nat,C: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ A @ C )
% 0.29/0.55       => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.coboundedI1
% 0.29/0.55  thf(fact_3250_inf_OcoboundedI1,axiom,
% 0.29/0.55      ! [A: int,C: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ A @ C )
% 0.29/0.55       => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.coboundedI1
% 0.29/0.55  thf(fact_3251_inf_OcoboundedI2,axiom,
% 0.29/0.55      ! [B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 0.29/0.55        ( ( ord_le3146513528884898305at_nat @ B @ C )
% 0.29/0.55       => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.coboundedI2
% 0.29/0.55  thf(fact_3252_inf_OcoboundedI2,axiom,
% 0.29/0.55      ! [B: product_prod_int_int > $o,C: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 0.29/0.55        ( ( ord_le8369615600986905444_int_o @ B @ C )
% 0.29/0.55       => ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.coboundedI2
% 0.29/0.55  thf(fact_3253_inf_OcoboundedI2,axiom,
% 0.29/0.55      ! [B: list_char > $o,C: list_char > $o,A: list_char > $o] :
% 0.29/0.55        ( ( ord_le4796328588573674190char_o @ B @ C )
% 0.29/0.55       => ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ A @ B ) @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.coboundedI2
% 0.29/0.55  thf(fact_3254_inf_OcoboundedI2,axiom,
% 0.29/0.55      ! [B: filter_nat,C: filter_nat,A: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ B @ C )
% 0.29/0.55       => ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ A @ B ) @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.coboundedI2
% 0.29/0.55  thf(fact_3255_inf_OcoboundedI2,axiom,
% 0.29/0.55      ! [B: set_nat,C: set_nat,A: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ B @ C )
% 0.29/0.55       => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.coboundedI2
% 0.29/0.55  thf(fact_3256_inf_OcoboundedI2,axiom,
% 0.29/0.55      ! [B: rat,C: rat,A: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ B @ C )
% 0.29/0.55       => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.coboundedI2
% 0.29/0.55  thf(fact_3257_inf_OcoboundedI2,axiom,
% 0.29/0.55      ! [B: nat,C: nat,A: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ B @ C )
% 0.29/0.55       => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.coboundedI2
% 0.29/0.55  thf(fact_3258_inf_OcoboundedI2,axiom,
% 0.29/0.55      ! [B: int,C: int,A: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ B @ C )
% 0.29/0.55       => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ C ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf.coboundedI2
% 0.29/0.55  thf(fact_3259_inf__sup__ord_I4_J,axiom,
% 0.29/0.55      ! [Y: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ Y @ ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_sup_ord(4)
% 0.29/0.55  thf(fact_3260_inf__sup__ord_I4_J,axiom,
% 0.29/0.55      ! [Y: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_sup_ord(4)
% 0.29/0.55  thf(fact_3261_inf__sup__ord_I4_J,axiom,
% 0.29/0.55      ! [Y: filter_nat,X: filter_nat] : ( ord_le2510731241096832064er_nat @ Y @ ( sup_sup_filter_nat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_sup_ord(4)
% 0.29/0.55  thf(fact_3262_inf__sup__ord_I4_J,axiom,
% 0.29/0.55      ! [Y: set_nat,X: set_nat] : ( ord_less_eq_set_nat @ Y @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_sup_ord(4)
% 0.29/0.55  thf(fact_3263_inf__sup__ord_I4_J,axiom,
% 0.29/0.55      ! [Y: rat,X: rat] : ( ord_less_eq_rat @ Y @ ( sup_sup_rat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_sup_ord(4)
% 0.29/0.55  thf(fact_3264_inf__sup__ord_I4_J,axiom,
% 0.29/0.55      ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_sup_ord(4)
% 0.29/0.55  thf(fact_3265_inf__sup__ord_I4_J,axiom,
% 0.29/0.55      ! [Y: int,X: int] : ( ord_less_eq_int @ Y @ ( sup_sup_int @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_sup_ord(4)
% 0.29/0.55  thf(fact_3266_inf__sup__ord_I3_J,axiom,
% 0.29/0.55      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_sup_ord(3)
% 0.29/0.55  thf(fact_3267_inf__sup__ord_I3_J,axiom,
% 0.29/0.55      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_sup_ord(3)
% 0.29/0.55  thf(fact_3268_inf__sup__ord_I3_J,axiom,
% 0.29/0.55      ! [X: filter_nat,Y: filter_nat] : ( ord_le2510731241096832064er_nat @ X @ ( sup_sup_filter_nat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_sup_ord(3)
% 0.29/0.55  thf(fact_3269_inf__sup__ord_I3_J,axiom,
% 0.29/0.55      ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_sup_ord(3)
% 0.29/0.55  thf(fact_3270_inf__sup__ord_I3_J,axiom,
% 0.29/0.55      ! [X: rat,Y: rat] : ( ord_less_eq_rat @ X @ ( sup_sup_rat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_sup_ord(3)
% 0.29/0.55  thf(fact_3271_inf__sup__ord_I3_J,axiom,
% 0.29/0.55      ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_sup_ord(3)
% 0.29/0.55  thf(fact_3272_inf__sup__ord_I3_J,axiom,
% 0.29/0.55      ! [X: int,Y: int] : ( ord_less_eq_int @ X @ ( sup_sup_int @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % inf_sup_ord(3)
% 0.29/0.55  thf(fact_3273_le__supE,axiom,
% 0.29/0.55      ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 0.29/0.55        ( ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A @ B ) @ X )
% 0.29/0.55       => ~ ( ( ord_le8081472938463900775at_nat @ A @ X )
% 0.29/0.55           => ~ ( ord_le8081472938463900775at_nat @ B @ X ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supE
% 0.29/0.55  thf(fact_3274_le__supE,axiom,
% 0.29/0.55      ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 0.29/0.55        ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ X )
% 0.29/0.55       => ~ ( ( ord_le1268244103169919719at_nat @ A @ X )
% 0.29/0.55           => ~ ( ord_le1268244103169919719at_nat @ B @ X ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supE
% 0.29/0.55  thf(fact_3275_le__supE,axiom,
% 0.29/0.55      ! [A: filter_nat,B: filter_nat,X: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ A @ B ) @ X )
% 0.29/0.55       => ~ ( ( ord_le2510731241096832064er_nat @ A @ X )
% 0.29/0.55           => ~ ( ord_le2510731241096832064er_nat @ B @ X ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supE
% 0.29/0.55  thf(fact_3276_le__supE,axiom,
% 0.29/0.55      ! [A: set_nat,B: set_nat,X: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ X )
% 0.29/0.55       => ~ ( ( ord_less_eq_set_nat @ A @ X )
% 0.29/0.55           => ~ ( ord_less_eq_set_nat @ B @ X ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supE
% 0.29/0.55  thf(fact_3277_le__supE,axiom,
% 0.29/0.55      ! [A: rat,B: rat,X: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ X )
% 0.29/0.55       => ~ ( ( ord_less_eq_rat @ A @ X )
% 0.29/0.55           => ~ ( ord_less_eq_rat @ B @ X ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supE
% 0.29/0.55  thf(fact_3278_le__supE,axiom,
% 0.29/0.55      ! [A: nat,B: nat,X: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X )
% 0.29/0.55       => ~ ( ( ord_less_eq_nat @ A @ X )
% 0.29/0.55           => ~ ( ord_less_eq_nat @ B @ X ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supE
% 0.29/0.55  thf(fact_3279_le__supE,axiom,
% 0.29/0.55      ! [A: int,B: int,X: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ X )
% 0.29/0.55       => ~ ( ( ord_less_eq_int @ A @ X )
% 0.29/0.55           => ~ ( ord_less_eq_int @ B @ X ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supE
% 0.29/0.55  thf(fact_3280_le__supI,axiom,
% 0.29/0.55      ! [A: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 0.29/0.55        ( ( ord_le8081472938463900775at_nat @ A @ X )
% 0.29/0.55       => ( ( ord_le8081472938463900775at_nat @ B @ X )
% 0.29/0.55         => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A @ B ) @ X ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supI
% 0.29/0.55  thf(fact_3281_le__supI,axiom,
% 0.29/0.55      ! [A: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.29/0.55        ( ( ord_le1268244103169919719at_nat @ A @ X )
% 0.29/0.55       => ( ( ord_le1268244103169919719at_nat @ B @ X )
% 0.29/0.55         => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ X ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supI
% 0.29/0.55  thf(fact_3282_le__supI,axiom,
% 0.29/0.55      ! [A: filter_nat,X: filter_nat,B: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ A @ X )
% 0.29/0.55       => ( ( ord_le2510731241096832064er_nat @ B @ X )
% 0.29/0.55         => ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ A @ B ) @ X ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supI
% 0.29/0.55  thf(fact_3283_le__supI,axiom,
% 0.29/0.55      ! [A: set_nat,X: set_nat,B: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ A @ X )
% 0.29/0.55       => ( ( ord_less_eq_set_nat @ B @ X )
% 0.29/0.55         => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ X ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supI
% 0.29/0.55  thf(fact_3284_le__supI,axiom,
% 0.29/0.55      ! [A: rat,X: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ X )
% 0.29/0.55       => ( ( ord_less_eq_rat @ B @ X )
% 0.29/0.55         => ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ X ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supI
% 0.29/0.55  thf(fact_3285_le__supI,axiom,
% 0.29/0.55      ! [A: nat,X: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ A @ X )
% 0.29/0.55       => ( ( ord_less_eq_nat @ B @ X )
% 0.29/0.55         => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supI
% 0.29/0.55  thf(fact_3286_le__supI,axiom,
% 0.29/0.55      ! [A: int,X: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ A @ X )
% 0.29/0.55       => ( ( ord_less_eq_int @ B @ X )
% 0.29/0.55         => ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ X ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supI
% 0.29/0.55  thf(fact_3287_sup__ge1,axiom,
% 0.29/0.55      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_ge1
% 0.29/0.55  thf(fact_3288_sup__ge1,axiom,
% 0.29/0.55      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_ge1
% 0.29/0.55  thf(fact_3289_sup__ge1,axiom,
% 0.29/0.55      ! [X: filter_nat,Y: filter_nat] : ( ord_le2510731241096832064er_nat @ X @ ( sup_sup_filter_nat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_ge1
% 0.29/0.55  thf(fact_3290_sup__ge1,axiom,
% 0.29/0.55      ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_ge1
% 0.29/0.55  thf(fact_3291_sup__ge1,axiom,
% 0.29/0.55      ! [X: rat,Y: rat] : ( ord_less_eq_rat @ X @ ( sup_sup_rat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_ge1
% 0.29/0.55  thf(fact_3292_sup__ge1,axiom,
% 0.29/0.55      ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_ge1
% 0.29/0.55  thf(fact_3293_sup__ge1,axiom,
% 0.29/0.55      ! [X: int,Y: int] : ( ord_less_eq_int @ X @ ( sup_sup_int @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_ge1
% 0.29/0.55  thf(fact_3294_sup__ge2,axiom,
% 0.29/0.55      ! [Y: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ Y @ ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_ge2
% 0.29/0.55  thf(fact_3295_sup__ge2,axiom,
% 0.29/0.55      ! [Y: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_ge2
% 0.29/0.55  thf(fact_3296_sup__ge2,axiom,
% 0.29/0.55      ! [Y: filter_nat,X: filter_nat] : ( ord_le2510731241096832064er_nat @ Y @ ( sup_sup_filter_nat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_ge2
% 0.29/0.55  thf(fact_3297_sup__ge2,axiom,
% 0.29/0.55      ! [Y: set_nat,X: set_nat] : ( ord_less_eq_set_nat @ Y @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_ge2
% 0.29/0.55  thf(fact_3298_sup__ge2,axiom,
% 0.29/0.55      ! [Y: rat,X: rat] : ( ord_less_eq_rat @ Y @ ( sup_sup_rat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_ge2
% 0.29/0.55  thf(fact_3299_sup__ge2,axiom,
% 0.29/0.55      ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_ge2
% 0.29/0.55  thf(fact_3300_sup__ge2,axiom,
% 0.29/0.55      ! [Y: int,X: int] : ( ord_less_eq_int @ Y @ ( sup_sup_int @ X @ Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_ge2
% 0.29/0.55  thf(fact_3301_le__supI1,axiom,
% 0.29/0.55      ! [X: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 0.29/0.55        ( ( ord_le8081472938463900775at_nat @ X @ A )
% 0.29/0.55       => ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supI1
% 0.29/0.55  thf(fact_3302_le__supI1,axiom,
% 0.29/0.55      ! [X: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.29/0.55        ( ( ord_le1268244103169919719at_nat @ X @ A )
% 0.29/0.55       => ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supI1
% 0.29/0.55  thf(fact_3303_le__supI1,axiom,
% 0.29/0.55      ! [X: filter_nat,A: filter_nat,B: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ X @ A )
% 0.29/0.55       => ( ord_le2510731241096832064er_nat @ X @ ( sup_sup_filter_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supI1
% 0.29/0.55  thf(fact_3304_le__supI1,axiom,
% 0.29/0.55      ! [X: set_nat,A: set_nat,B: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ X @ A )
% 0.29/0.55       => ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supI1
% 0.29/0.55  thf(fact_3305_le__supI1,axiom,
% 0.29/0.55      ! [X: rat,A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ X @ A )
% 0.29/0.55       => ( ord_less_eq_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supI1
% 0.29/0.55  thf(fact_3306_le__supI1,axiom,
% 0.29/0.55      ! [X: nat,A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ X @ A )
% 0.29/0.55       => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supI1
% 0.29/0.55  thf(fact_3307_le__supI1,axiom,
% 0.29/0.55      ! [X: int,A: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ X @ A )
% 0.29/0.55       => ( ord_less_eq_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supI1
% 0.29/0.55  thf(fact_3308_le__supI2,axiom,
% 0.29/0.55      ! [X: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 0.29/0.55        ( ( ord_le8081472938463900775at_nat @ X @ B )
% 0.29/0.55       => ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supI2
% 0.29/0.55  thf(fact_3309_le__supI2,axiom,
% 0.29/0.55      ! [X: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 0.29/0.55        ( ( ord_le1268244103169919719at_nat @ X @ B )
% 0.29/0.55       => ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supI2
% 0.29/0.55  thf(fact_3310_le__supI2,axiom,
% 0.29/0.55      ! [X: filter_nat,B: filter_nat,A: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ X @ B )
% 0.29/0.55       => ( ord_le2510731241096832064er_nat @ X @ ( sup_sup_filter_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supI2
% 0.29/0.55  thf(fact_3311_le__supI2,axiom,
% 0.29/0.55      ! [X: set_nat,B: set_nat,A: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ X @ B )
% 0.29/0.55       => ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supI2
% 0.29/0.55  thf(fact_3312_le__supI2,axiom,
% 0.29/0.55      ! [X: rat,B: rat,A: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ X @ B )
% 0.29/0.55       => ( ord_less_eq_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supI2
% 0.29/0.55  thf(fact_3313_le__supI2,axiom,
% 0.29/0.55      ! [X: nat,B: nat,A: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ X @ B )
% 0.29/0.55       => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supI2
% 0.29/0.55  thf(fact_3314_le__supI2,axiom,
% 0.29/0.55      ! [X: int,B: int,A: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ X @ B )
% 0.29/0.55       => ( ord_less_eq_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_supI2
% 0.29/0.55  thf(fact_3315_sup_Omono,axiom,
% 0.29/0.55      ! [C: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,D2: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 0.29/0.55        ( ( ord_le8081472938463900775at_nat @ C @ A )
% 0.29/0.55       => ( ( ord_le8081472938463900775at_nat @ D2 @ B )
% 0.29/0.55         => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ C @ D2 ) @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.mono
% 0.29/0.55  thf(fact_3316_sup_Omono,axiom,
% 0.29/0.55      ! [C: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,D2: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.29/0.55        ( ( ord_le1268244103169919719at_nat @ C @ A )
% 0.29/0.55       => ( ( ord_le1268244103169919719at_nat @ D2 @ B )
% 0.29/0.55         => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ C @ D2 ) @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.mono
% 0.29/0.55  thf(fact_3317_sup_Omono,axiom,
% 0.29/0.55      ! [C: filter_nat,A: filter_nat,D2: filter_nat,B: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ C @ A )
% 0.29/0.55       => ( ( ord_le2510731241096832064er_nat @ D2 @ B )
% 0.29/0.55         => ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ C @ D2 ) @ ( sup_sup_filter_nat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.mono
% 0.29/0.55  thf(fact_3318_sup_Omono,axiom,
% 0.29/0.55      ! [C: set_nat,A: set_nat,D2: set_nat,B: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ C @ A )
% 0.29/0.55       => ( ( ord_less_eq_set_nat @ D2 @ B )
% 0.29/0.55         => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ C @ D2 ) @ ( sup_sup_set_nat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.mono
% 0.29/0.55  thf(fact_3319_sup_Omono,axiom,
% 0.29/0.55      ! [C: rat,A: rat,D2: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ C @ A )
% 0.29/0.55       => ( ( ord_less_eq_rat @ D2 @ B )
% 0.29/0.55         => ( ord_less_eq_rat @ ( sup_sup_rat @ C @ D2 ) @ ( sup_sup_rat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.mono
% 0.29/0.55  thf(fact_3320_sup_Omono,axiom,
% 0.29/0.55      ! [C: nat,A: nat,D2: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ C @ A )
% 0.29/0.55       => ( ( ord_less_eq_nat @ D2 @ B )
% 0.29/0.55         => ( ord_less_eq_nat @ ( sup_sup_nat @ C @ D2 ) @ ( sup_sup_nat @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.mono
% 0.29/0.55  thf(fact_3321_sup_Omono,axiom,
% 0.29/0.55      ! [C: int,A: int,D2: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ C @ A )
% 0.29/0.55       => ( ( ord_less_eq_int @ D2 @ B )
% 0.29/0.55         => ( ord_less_eq_int @ ( sup_sup_int @ C @ D2 ) @ ( sup_sup_int @ A @ B ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.mono
% 0.29/0.55  thf(fact_3322_sup__mono,axiom,
% 0.29/0.55      ! [A: set_Pr8551490117392284871at_nat,C: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,D2: set_Pr8551490117392284871at_nat] :
% 0.29/0.55        ( ( ord_le8081472938463900775at_nat @ A @ C )
% 0.29/0.55       => ( ( ord_le8081472938463900775at_nat @ B @ D2 )
% 0.29/0.55         => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A @ B ) @ ( sup_su3035147773818789531at_nat @ C @ D2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_mono
% 0.29/0.55  thf(fact_3323_sup__mono,axiom,
% 0.29/0.55      ! [A: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,D2: set_Pr4329608150637261639at_nat] :
% 0.29/0.55        ( ( ord_le1268244103169919719at_nat @ A @ C )
% 0.29/0.55       => ( ( ord_le1268244103169919719at_nat @ B @ D2 )
% 0.29/0.55         => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ ( sup_su5525570899277871387at_nat @ C @ D2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_mono
% 0.29/0.55  thf(fact_3324_sup__mono,axiom,
% 0.29/0.55      ! [A: filter_nat,C: filter_nat,B: filter_nat,D2: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ A @ C )
% 0.29/0.55       => ( ( ord_le2510731241096832064er_nat @ B @ D2 )
% 0.29/0.55         => ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ A @ B ) @ ( sup_sup_filter_nat @ C @ D2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_mono
% 0.29/0.55  thf(fact_3325_sup__mono,axiom,
% 0.29/0.55      ! [A: set_nat,C: set_nat,B: set_nat,D2: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ A @ C )
% 0.29/0.55       => ( ( ord_less_eq_set_nat @ B @ D2 )
% 0.29/0.55         => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ ( sup_sup_set_nat @ C @ D2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_mono
% 0.29/0.55  thf(fact_3326_sup__mono,axiom,
% 0.29/0.55      ! [A: rat,C: rat,B: rat,D2: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ C )
% 0.29/0.55       => ( ( ord_less_eq_rat @ B @ D2 )
% 0.29/0.55         => ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ ( sup_sup_rat @ C @ D2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_mono
% 0.29/0.55  thf(fact_3327_sup__mono,axiom,
% 0.29/0.55      ! [A: nat,C: nat,B: nat,D2: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ A @ C )
% 0.29/0.55       => ( ( ord_less_eq_nat @ B @ D2 )
% 0.29/0.55         => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ ( sup_sup_nat @ C @ D2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_mono
% 0.29/0.55  thf(fact_3328_sup__mono,axiom,
% 0.29/0.55      ! [A: int,C: int,B: int,D2: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ A @ C )
% 0.29/0.55       => ( ( ord_less_eq_int @ B @ D2 )
% 0.29/0.55         => ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ ( sup_sup_int @ C @ D2 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_mono
% 0.29/0.55  thf(fact_3329_sup__least,axiom,
% 0.29/0.55      ! [Y: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 0.29/0.55        ( ( ord_le8081472938463900775at_nat @ Y @ X )
% 0.29/0.55       => ( ( ord_le8081472938463900775at_nat @ Z @ X )
% 0.29/0.55         => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ Y @ Z ) @ X ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_least
% 0.29/0.55  thf(fact_3330_sup__least,axiom,
% 0.29/0.55      ! [Y: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 0.29/0.55        ( ( ord_le1268244103169919719at_nat @ Y @ X )
% 0.29/0.55       => ( ( ord_le1268244103169919719at_nat @ Z @ X )
% 0.29/0.55         => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ Y @ Z ) @ X ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_least
% 0.29/0.55  thf(fact_3331_sup__least,axiom,
% 0.29/0.55      ! [Y: filter_nat,X: filter_nat,Z: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 0.29/0.55       => ( ( ord_le2510731241096832064er_nat @ Z @ X )
% 0.29/0.55         => ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ Y @ Z ) @ X ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_least
% 0.29/0.55  thf(fact_3332_sup__least,axiom,
% 0.29/0.55      ! [Y: set_nat,X: set_nat,Z: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ Y @ X )
% 0.29/0.55       => ( ( ord_less_eq_set_nat @ Z @ X )
% 0.29/0.55         => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ Y @ Z ) @ X ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_least
% 0.29/0.55  thf(fact_3333_sup__least,axiom,
% 0.29/0.55      ! [Y: rat,X: rat,Z: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ Y @ X )
% 0.29/0.55       => ( ( ord_less_eq_rat @ Z @ X )
% 0.29/0.55         => ( ord_less_eq_rat @ ( sup_sup_rat @ Y @ Z ) @ X ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_least
% 0.29/0.55  thf(fact_3334_sup__least,axiom,
% 0.29/0.55      ! [Y: nat,X: nat,Z: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ Y @ X )
% 0.29/0.55       => ( ( ord_less_eq_nat @ Z @ X )
% 0.29/0.55         => ( ord_less_eq_nat @ ( sup_sup_nat @ Y @ Z ) @ X ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_least
% 0.29/0.55  thf(fact_3335_sup__least,axiom,
% 0.29/0.55      ! [Y: int,X: int,Z: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ Y @ X )
% 0.29/0.55       => ( ( ord_less_eq_int @ Z @ X )
% 0.29/0.55         => ( ord_less_eq_int @ ( sup_sup_int @ Y @ Z ) @ X ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_least
% 0.29/0.55  thf(fact_3336_le__iff__sup,axiom,
% 0.29/0.55      ( ord_le8081472938463900775at_nat
% 0.29/0.55      = ( ^ [X3: set_Pr8551490117392284871at_nat,Y3: set_Pr8551490117392284871at_nat] :
% 0.29/0.55            ( ( sup_su3035147773818789531at_nat @ X3 @ Y3 )
% 0.29/0.55            = Y3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_iff_sup
% 0.29/0.55  thf(fact_3337_le__iff__sup,axiom,
% 0.29/0.55      ( ord_le1268244103169919719at_nat
% 0.29/0.55      = ( ^ [X3: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 0.29/0.55            ( ( sup_su5525570899277871387at_nat @ X3 @ Y3 )
% 0.29/0.55            = Y3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_iff_sup
% 0.29/0.55  thf(fact_3338_le__iff__sup,axiom,
% 0.29/0.55      ( ord_le2510731241096832064er_nat
% 0.29/0.55      = ( ^ [X3: filter_nat,Y3: filter_nat] :
% 0.29/0.55            ( ( sup_sup_filter_nat @ X3 @ Y3 )
% 0.29/0.55            = Y3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_iff_sup
% 0.29/0.55  thf(fact_3339_le__iff__sup,axiom,
% 0.29/0.55      ( ord_less_eq_set_nat
% 0.29/0.55      = ( ^ [X3: set_nat,Y3: set_nat] :
% 0.29/0.55            ( ( sup_sup_set_nat @ X3 @ Y3 )
% 0.29/0.55            = Y3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_iff_sup
% 0.29/0.55  thf(fact_3340_le__iff__sup,axiom,
% 0.29/0.55      ( ord_less_eq_rat
% 0.29/0.55      = ( ^ [X3: rat,Y3: rat] :
% 0.29/0.55            ( ( sup_sup_rat @ X3 @ Y3 )
% 0.29/0.55            = Y3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_iff_sup
% 0.29/0.55  thf(fact_3341_le__iff__sup,axiom,
% 0.29/0.55      ( ord_less_eq_nat
% 0.29/0.55      = ( ^ [X3: nat,Y3: nat] :
% 0.29/0.55            ( ( sup_sup_nat @ X3 @ Y3 )
% 0.29/0.55            = Y3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_iff_sup
% 0.29/0.55  thf(fact_3342_le__iff__sup,axiom,
% 0.29/0.55      ( ord_less_eq_int
% 0.29/0.55      = ( ^ [X3: int,Y3: int] :
% 0.29/0.55            ( ( sup_sup_int @ X3 @ Y3 )
% 0.29/0.55            = Y3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % le_iff_sup
% 0.29/0.55  thf(fact_3343_sup_OorderE,axiom,
% 0.29/0.55      ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 0.29/0.55        ( ( ord_le8081472938463900775at_nat @ B @ A )
% 0.29/0.55       => ( A
% 0.29/0.55          = ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.orderE
% 0.29/0.55  thf(fact_3344_sup_OorderE,axiom,
% 0.29/0.55      ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 0.29/0.55        ( ( ord_le1268244103169919719at_nat @ B @ A )
% 0.29/0.55       => ( A
% 0.29/0.55          = ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.orderE
% 0.29/0.55  thf(fact_3345_sup_OorderE,axiom,
% 0.29/0.55      ! [B: filter_nat,A: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ B @ A )
% 0.29/0.55       => ( A
% 0.29/0.55          = ( sup_sup_filter_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.orderE
% 0.29/0.55  thf(fact_3346_sup_OorderE,axiom,
% 0.29/0.55      ! [B: set_nat,A: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ B @ A )
% 0.29/0.55       => ( A
% 0.29/0.55          = ( sup_sup_set_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.orderE
% 0.29/0.55  thf(fact_3347_sup_OorderE,axiom,
% 0.29/0.55      ! [B: rat,A: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.55       => ( A
% 0.29/0.55          = ( sup_sup_rat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.orderE
% 0.29/0.55  thf(fact_3348_sup_OorderE,axiom,
% 0.29/0.55      ! [B: nat,A: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.55       => ( A
% 0.29/0.55          = ( sup_sup_nat @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.orderE
% 0.29/0.55  thf(fact_3349_sup_OorderE,axiom,
% 0.29/0.55      ! [B: int,A: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.55       => ( A
% 0.29/0.55          = ( sup_sup_int @ A @ B ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.orderE
% 0.29/0.55  thf(fact_3350_sup_OorderI,axiom,
% 0.29/0.55      ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 0.29/0.55        ( ( A
% 0.29/0.55          = ( sup_su3035147773818789531at_nat @ A @ B ) )
% 0.29/0.55       => ( ord_le8081472938463900775at_nat @ B @ A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.orderI
% 0.29/0.55  thf(fact_3351_sup_OorderI,axiom,
% 0.29/0.55      ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.29/0.55        ( ( A
% 0.29/0.55          = ( sup_su5525570899277871387at_nat @ A @ B ) )
% 0.29/0.55       => ( ord_le1268244103169919719at_nat @ B @ A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.orderI
% 0.29/0.55  thf(fact_3352_sup_OorderI,axiom,
% 0.29/0.55      ! [A: filter_nat,B: filter_nat] :
% 0.29/0.55        ( ( A
% 0.29/0.55          = ( sup_sup_filter_nat @ A @ B ) )
% 0.29/0.55       => ( ord_le2510731241096832064er_nat @ B @ A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.orderI
% 0.29/0.55  thf(fact_3353_sup_OorderI,axiom,
% 0.29/0.55      ! [A: set_nat,B: set_nat] :
% 0.29/0.55        ( ( A
% 0.29/0.55          = ( sup_sup_set_nat @ A @ B ) )
% 0.29/0.55       => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.orderI
% 0.29/0.55  thf(fact_3354_sup_OorderI,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( A
% 0.29/0.55          = ( sup_sup_rat @ A @ B ) )
% 0.29/0.55       => ( ord_less_eq_rat @ B @ A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.orderI
% 0.29/0.55  thf(fact_3355_sup_OorderI,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( A
% 0.29/0.55          = ( sup_sup_nat @ A @ B ) )
% 0.29/0.55       => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.orderI
% 0.29/0.55  thf(fact_3356_sup_OorderI,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( A
% 0.29/0.55          = ( sup_sup_int @ A @ B ) )
% 0.29/0.55       => ( ord_less_eq_int @ B @ A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.orderI
% 0.29/0.55  thf(fact_3357_sup__unique,axiom,
% 0.29/0.55      ! [F2: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 0.29/0.55        ( ! [X2: set_Pr8551490117392284871at_nat,Y2: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ X2 @ ( F2 @ X2 @ Y2 ) )
% 0.29/0.55       => ( ! [X2: set_Pr8551490117392284871at_nat,Y2: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ Y2 @ ( F2 @ X2 @ Y2 ) )
% 0.29/0.55         => ( ! [X2: set_Pr8551490117392284871at_nat,Y2: set_Pr8551490117392284871at_nat,Z2: set_Pr8551490117392284871at_nat] :
% 0.29/0.55                ( ( ord_le8081472938463900775at_nat @ Y2 @ X2 )
% 0.29/0.55               => ( ( ord_le8081472938463900775at_nat @ Z2 @ X2 )
% 0.29/0.55                 => ( ord_le8081472938463900775at_nat @ ( F2 @ Y2 @ Z2 ) @ X2 ) ) )
% 0.29/0.55           => ( ( sup_su3035147773818789531at_nat @ X @ Y )
% 0.29/0.55              = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_unique
% 0.29/0.55  thf(fact_3358_sup__unique,axiom,
% 0.29/0.55      ! [F2: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 0.29/0.55        ( ! [X2: set_Pr4329608150637261639at_nat,Y2: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ X2 @ ( F2 @ X2 @ Y2 ) )
% 0.29/0.55       => ( ! [X2: set_Pr4329608150637261639at_nat,Y2: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y2 @ ( F2 @ X2 @ Y2 ) )
% 0.29/0.55         => ( ! [X2: set_Pr4329608150637261639at_nat,Y2: set_Pr4329608150637261639at_nat,Z2: set_Pr4329608150637261639at_nat] :
% 0.29/0.55                ( ( ord_le1268244103169919719at_nat @ Y2 @ X2 )
% 0.29/0.55               => ( ( ord_le1268244103169919719at_nat @ Z2 @ X2 )
% 0.29/0.55                 => ( ord_le1268244103169919719at_nat @ ( F2 @ Y2 @ Z2 ) @ X2 ) ) )
% 0.29/0.55           => ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 0.29/0.55              = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_unique
% 0.29/0.55  thf(fact_3359_sup__unique,axiom,
% 0.29/0.55      ! [F2: filter_nat > filter_nat > filter_nat,X: filter_nat,Y: filter_nat] :
% 0.29/0.55        ( ! [X2: filter_nat,Y2: filter_nat] : ( ord_le2510731241096832064er_nat @ X2 @ ( F2 @ X2 @ Y2 ) )
% 0.29/0.55       => ( ! [X2: filter_nat,Y2: filter_nat] : ( ord_le2510731241096832064er_nat @ Y2 @ ( F2 @ X2 @ Y2 ) )
% 0.29/0.55         => ( ! [X2: filter_nat,Y2: filter_nat,Z2: filter_nat] :
% 0.29/0.55                ( ( ord_le2510731241096832064er_nat @ Y2 @ X2 )
% 0.29/0.55               => ( ( ord_le2510731241096832064er_nat @ Z2 @ X2 )
% 0.29/0.55                 => ( ord_le2510731241096832064er_nat @ ( F2 @ Y2 @ Z2 ) @ X2 ) ) )
% 0.29/0.55           => ( ( sup_sup_filter_nat @ X @ Y )
% 0.29/0.55              = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_unique
% 0.29/0.55  thf(fact_3360_sup__unique,axiom,
% 0.29/0.55      ! [F2: set_nat > set_nat > set_nat,X: set_nat,Y: set_nat] :
% 0.29/0.55        ( ! [X2: set_nat,Y2: set_nat] : ( ord_less_eq_set_nat @ X2 @ ( F2 @ X2 @ Y2 ) )
% 0.29/0.55       => ( ! [X2: set_nat,Y2: set_nat] : ( ord_less_eq_set_nat @ Y2 @ ( F2 @ X2 @ Y2 ) )
% 0.29/0.55         => ( ! [X2: set_nat,Y2: set_nat,Z2: set_nat] :
% 0.29/0.55                ( ( ord_less_eq_set_nat @ Y2 @ X2 )
% 0.29/0.55               => ( ( ord_less_eq_set_nat @ Z2 @ X2 )
% 0.29/0.55                 => ( ord_less_eq_set_nat @ ( F2 @ Y2 @ Z2 ) @ X2 ) ) )
% 0.29/0.55           => ( ( sup_sup_set_nat @ X @ Y )
% 0.29/0.55              = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_unique
% 0.29/0.55  thf(fact_3361_sup__unique,axiom,
% 0.29/0.55      ! [F2: rat > rat > rat,X: rat,Y: rat] :
% 0.29/0.55        ( ! [X2: rat,Y2: rat] : ( ord_less_eq_rat @ X2 @ ( F2 @ X2 @ Y2 ) )
% 0.29/0.55       => ( ! [X2: rat,Y2: rat] : ( ord_less_eq_rat @ Y2 @ ( F2 @ X2 @ Y2 ) )
% 0.29/0.55         => ( ! [X2: rat,Y2: rat,Z2: rat] :
% 0.29/0.55                ( ( ord_less_eq_rat @ Y2 @ X2 )
% 0.29/0.55               => ( ( ord_less_eq_rat @ Z2 @ X2 )
% 0.29/0.55                 => ( ord_less_eq_rat @ ( F2 @ Y2 @ Z2 ) @ X2 ) ) )
% 0.29/0.55           => ( ( sup_sup_rat @ X @ Y )
% 0.29/0.55              = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_unique
% 0.29/0.55  thf(fact_3362_sup__unique,axiom,
% 0.29/0.55      ! [F2: nat > nat > nat,X: nat,Y: nat] :
% 0.29/0.55        ( ! [X2: nat,Y2: nat] : ( ord_less_eq_nat @ X2 @ ( F2 @ X2 @ Y2 ) )
% 0.29/0.55       => ( ! [X2: nat,Y2: nat] : ( ord_less_eq_nat @ Y2 @ ( F2 @ X2 @ Y2 ) )
% 0.29/0.55         => ( ! [X2: nat,Y2: nat,Z2: nat] :
% 0.29/0.55                ( ( ord_less_eq_nat @ Y2 @ X2 )
% 0.29/0.55               => ( ( ord_less_eq_nat @ Z2 @ X2 )
% 0.29/0.55                 => ( ord_less_eq_nat @ ( F2 @ Y2 @ Z2 ) @ X2 ) ) )
% 0.29/0.55           => ( ( sup_sup_nat @ X @ Y )
% 0.29/0.55              = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_unique
% 0.29/0.55  thf(fact_3363_sup__unique,axiom,
% 0.29/0.55      ! [F2: int > int > int,X: int,Y: int] :
% 0.29/0.55        ( ! [X2: int,Y2: int] : ( ord_less_eq_int @ X2 @ ( F2 @ X2 @ Y2 ) )
% 0.29/0.55       => ( ! [X2: int,Y2: int] : ( ord_less_eq_int @ Y2 @ ( F2 @ X2 @ Y2 ) )
% 0.29/0.55         => ( ! [X2: int,Y2: int,Z2: int] :
% 0.29/0.55                ( ( ord_less_eq_int @ Y2 @ X2 )
% 0.29/0.55               => ( ( ord_less_eq_int @ Z2 @ X2 )
% 0.29/0.55                 => ( ord_less_eq_int @ ( F2 @ Y2 @ Z2 ) @ X2 ) ) )
% 0.29/0.55           => ( ( sup_sup_int @ X @ Y )
% 0.29/0.55              = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_unique
% 0.29/0.55  thf(fact_3364_sup_Oabsorb1,axiom,
% 0.29/0.55      ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 0.29/0.55        ( ( ord_le8081472938463900775at_nat @ B @ A )
% 0.29/0.55       => ( ( sup_su3035147773818789531at_nat @ A @ B )
% 0.29/0.55          = A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb1
% 0.29/0.55  thf(fact_3365_sup_Oabsorb1,axiom,
% 0.29/0.55      ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 0.29/0.55        ( ( ord_le1268244103169919719at_nat @ B @ A )
% 0.29/0.55       => ( ( sup_su5525570899277871387at_nat @ A @ B )
% 0.29/0.55          = A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb1
% 0.29/0.55  thf(fact_3366_sup_Oabsorb1,axiom,
% 0.29/0.55      ! [B: filter_nat,A: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ B @ A )
% 0.29/0.55       => ( ( sup_sup_filter_nat @ A @ B )
% 0.29/0.55          = A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb1
% 0.29/0.55  thf(fact_3367_sup_Oabsorb1,axiom,
% 0.29/0.55      ! [B: set_nat,A: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ B @ A )
% 0.29/0.55       => ( ( sup_sup_set_nat @ A @ B )
% 0.29/0.55          = A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb1
% 0.29/0.55  thf(fact_3368_sup_Oabsorb1,axiom,
% 0.29/0.55      ! [B: rat,A: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.55       => ( ( sup_sup_rat @ A @ B )
% 0.29/0.55          = A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb1
% 0.29/0.55  thf(fact_3369_sup_Oabsorb1,axiom,
% 0.29/0.55      ! [B: nat,A: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.55       => ( ( sup_sup_nat @ A @ B )
% 0.29/0.55          = A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb1
% 0.29/0.55  thf(fact_3370_sup_Oabsorb1,axiom,
% 0.29/0.55      ! [B: int,A: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.55       => ( ( sup_sup_int @ A @ B )
% 0.29/0.55          = A ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb1
% 0.29/0.55  thf(fact_3371_sup_Oabsorb2,axiom,
% 0.29/0.55      ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 0.29/0.55        ( ( ord_le8081472938463900775at_nat @ A @ B )
% 0.29/0.55       => ( ( sup_su3035147773818789531at_nat @ A @ B )
% 0.29/0.55          = B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb2
% 0.29/0.55  thf(fact_3372_sup_Oabsorb2,axiom,
% 0.29/0.55      ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.29/0.55        ( ( ord_le1268244103169919719at_nat @ A @ B )
% 0.29/0.55       => ( ( sup_su5525570899277871387at_nat @ A @ B )
% 0.29/0.55          = B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb2
% 0.29/0.55  thf(fact_3373_sup_Oabsorb2,axiom,
% 0.29/0.55      ! [A: filter_nat,B: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 0.29/0.55       => ( ( sup_sup_filter_nat @ A @ B )
% 0.29/0.55          = B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb2
% 0.29/0.55  thf(fact_3374_sup_Oabsorb2,axiom,
% 0.29/0.55      ! [A: set_nat,B: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ A @ B )
% 0.29/0.55       => ( ( sup_sup_set_nat @ A @ B )
% 0.29/0.55          = B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb2
% 0.29/0.55  thf(fact_3375_sup_Oabsorb2,axiom,
% 0.29/0.55      ! [A: rat,B: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ A @ B )
% 0.29/0.55       => ( ( sup_sup_rat @ A @ B )
% 0.29/0.55          = B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb2
% 0.29/0.55  thf(fact_3376_sup_Oabsorb2,axiom,
% 0.29/0.55      ! [A: nat,B: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ A @ B )
% 0.29/0.55       => ( ( sup_sup_nat @ A @ B )
% 0.29/0.55          = B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb2
% 0.29/0.55  thf(fact_3377_sup_Oabsorb2,axiom,
% 0.29/0.55      ! [A: int,B: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ A @ B )
% 0.29/0.55       => ( ( sup_sup_int @ A @ B )
% 0.29/0.55          = B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb2
% 0.29/0.55  thf(fact_3378_sup__absorb1,axiom,
% 0.29/0.55      ! [Y: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 0.29/0.55        ( ( ord_le8081472938463900775at_nat @ Y @ X )
% 0.29/0.55       => ( ( sup_su3035147773818789531at_nat @ X @ Y )
% 0.29/0.55          = X ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_absorb1
% 0.29/0.55  thf(fact_3379_sup__absorb1,axiom,
% 0.29/0.55      ! [Y: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 0.29/0.55        ( ( ord_le1268244103169919719at_nat @ Y @ X )
% 0.29/0.55       => ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 0.29/0.55          = X ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_absorb1
% 0.29/0.55  thf(fact_3380_sup__absorb1,axiom,
% 0.29/0.55      ! [Y: filter_nat,X: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 0.29/0.55       => ( ( sup_sup_filter_nat @ X @ Y )
% 0.29/0.55          = X ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_absorb1
% 0.29/0.55  thf(fact_3381_sup__absorb1,axiom,
% 0.29/0.55      ! [Y: set_nat,X: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ Y @ X )
% 0.29/0.55       => ( ( sup_sup_set_nat @ X @ Y )
% 0.29/0.55          = X ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_absorb1
% 0.29/0.55  thf(fact_3382_sup__absorb1,axiom,
% 0.29/0.55      ! [Y: rat,X: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ Y @ X )
% 0.29/0.55       => ( ( sup_sup_rat @ X @ Y )
% 0.29/0.55          = X ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_absorb1
% 0.29/0.55  thf(fact_3383_sup__absorb1,axiom,
% 0.29/0.55      ! [Y: nat,X: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ Y @ X )
% 0.29/0.55       => ( ( sup_sup_nat @ X @ Y )
% 0.29/0.55          = X ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_absorb1
% 0.29/0.55  thf(fact_3384_sup__absorb1,axiom,
% 0.29/0.55      ! [Y: int,X: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ Y @ X )
% 0.29/0.55       => ( ( sup_sup_int @ X @ Y )
% 0.29/0.55          = X ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_absorb1
% 0.29/0.55  thf(fact_3385_sup__absorb2,axiom,
% 0.29/0.55      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 0.29/0.55        ( ( ord_le8081472938463900775at_nat @ X @ Y )
% 0.29/0.55       => ( ( sup_su3035147773818789531at_nat @ X @ Y )
% 0.29/0.55          = Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_absorb2
% 0.29/0.55  thf(fact_3386_sup__absorb2,axiom,
% 0.29/0.55      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 0.29/0.55        ( ( ord_le1268244103169919719at_nat @ X @ Y )
% 0.29/0.55       => ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 0.29/0.55          = Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_absorb2
% 0.29/0.55  thf(fact_3387_sup__absorb2,axiom,
% 0.29/0.55      ! [X: filter_nat,Y: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 0.29/0.55       => ( ( sup_sup_filter_nat @ X @ Y )
% 0.29/0.55          = Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_absorb2
% 0.29/0.55  thf(fact_3388_sup__absorb2,axiom,
% 0.29/0.55      ! [X: set_nat,Y: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ X @ Y )
% 0.29/0.55       => ( ( sup_sup_set_nat @ X @ Y )
% 0.29/0.55          = Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_absorb2
% 0.29/0.55  thf(fact_3389_sup__absorb2,axiom,
% 0.29/0.55      ! [X: rat,Y: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ X @ Y )
% 0.29/0.55       => ( ( sup_sup_rat @ X @ Y )
% 0.29/0.55          = Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_absorb2
% 0.29/0.55  thf(fact_3390_sup__absorb2,axiom,
% 0.29/0.55      ! [X: nat,Y: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ X @ Y )
% 0.29/0.55       => ( ( sup_sup_nat @ X @ Y )
% 0.29/0.55          = Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_absorb2
% 0.29/0.55  thf(fact_3391_sup__absorb2,axiom,
% 0.29/0.55      ! [X: int,Y: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ X @ Y )
% 0.29/0.55       => ( ( sup_sup_int @ X @ Y )
% 0.29/0.55          = Y ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup_absorb2
% 0.29/0.55  thf(fact_3392_sup_OboundedE,axiom,
% 0.29/0.55      ! [B: set_Pr8551490117392284871at_nat,C: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 0.29/0.55        ( ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ B @ C ) @ A )
% 0.29/0.55       => ~ ( ( ord_le8081472938463900775at_nat @ B @ A )
% 0.29/0.55           => ~ ( ord_le8081472938463900775at_nat @ C @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.boundedE
% 0.29/0.55  thf(fact_3393_sup_OboundedE,axiom,
% 0.29/0.55      ! [B: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 0.29/0.55        ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ B @ C ) @ A )
% 0.29/0.55       => ~ ( ( ord_le1268244103169919719at_nat @ B @ A )
% 0.29/0.55           => ~ ( ord_le1268244103169919719at_nat @ C @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.boundedE
% 0.29/0.55  thf(fact_3394_sup_OboundedE,axiom,
% 0.29/0.55      ! [B: filter_nat,C: filter_nat,A: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ B @ C ) @ A )
% 0.29/0.55       => ~ ( ( ord_le2510731241096832064er_nat @ B @ A )
% 0.29/0.55           => ~ ( ord_le2510731241096832064er_nat @ C @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.boundedE
% 0.29/0.55  thf(fact_3395_sup_OboundedE,axiom,
% 0.29/0.55      ! [B: set_nat,C: set_nat,A: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C ) @ A )
% 0.29/0.55       => ~ ( ( ord_less_eq_set_nat @ B @ A )
% 0.29/0.55           => ~ ( ord_less_eq_set_nat @ C @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.boundedE
% 0.29/0.55  thf(fact_3396_sup_OboundedE,axiom,
% 0.29/0.55      ! [B: rat,C: rat,A: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C ) @ A )
% 0.29/0.55       => ~ ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.55           => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.boundedE
% 0.29/0.55  thf(fact_3397_sup_OboundedE,axiom,
% 0.29/0.55      ! [B: nat,C: nat,A: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C ) @ A )
% 0.29/0.55       => ~ ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.55           => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.boundedE
% 0.29/0.55  thf(fact_3398_sup_OboundedE,axiom,
% 0.29/0.55      ! [B: int,C: int,A: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ ( sup_sup_int @ B @ C ) @ A )
% 0.29/0.55       => ~ ( ( ord_less_eq_int @ B @ A )
% 0.29/0.55           => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.boundedE
% 0.29/0.55  thf(fact_3399_sup_OboundedI,axiom,
% 0.29/0.55      ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,C: set_Pr8551490117392284871at_nat] :
% 0.29/0.55        ( ( ord_le8081472938463900775at_nat @ B @ A )
% 0.29/0.55       => ( ( ord_le8081472938463900775at_nat @ C @ A )
% 0.29/0.55         => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ B @ C ) @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.boundedI
% 0.29/0.55  thf(fact_3400_sup_OboundedI,axiom,
% 0.29/0.55      ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat] :
% 0.29/0.55        ( ( ord_le1268244103169919719at_nat @ B @ A )
% 0.29/0.55       => ( ( ord_le1268244103169919719at_nat @ C @ A )
% 0.29/0.55         => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ B @ C ) @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.boundedI
% 0.29/0.55  thf(fact_3401_sup_OboundedI,axiom,
% 0.29/0.55      ! [B: filter_nat,A: filter_nat,C: filter_nat] :
% 0.29/0.55        ( ( ord_le2510731241096832064er_nat @ B @ A )
% 0.29/0.55       => ( ( ord_le2510731241096832064er_nat @ C @ A )
% 0.29/0.55         => ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ B @ C ) @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.boundedI
% 0.29/0.55  thf(fact_3402_sup_OboundedI,axiom,
% 0.29/0.55      ! [B: set_nat,A: set_nat,C: set_nat] :
% 0.29/0.55        ( ( ord_less_eq_set_nat @ B @ A )
% 0.29/0.55       => ( ( ord_less_eq_set_nat @ C @ A )
% 0.29/0.55         => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C ) @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.boundedI
% 0.29/0.55  thf(fact_3403_sup_OboundedI,axiom,
% 0.29/0.55      ! [B: rat,A: rat,C: rat] :
% 0.29/0.55        ( ( ord_less_eq_rat @ B @ A )
% 0.29/0.55       => ( ( ord_less_eq_rat @ C @ A )
% 0.29/0.55         => ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C ) @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.boundedI
% 0.29/0.55  thf(fact_3404_sup_OboundedI,axiom,
% 0.29/0.55      ! [B: nat,A: nat,C: nat] :
% 0.29/0.55        ( ( ord_less_eq_nat @ B @ A )
% 0.29/0.55       => ( ( ord_less_eq_nat @ C @ A )
% 0.29/0.55         => ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C ) @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.boundedI
% 0.29/0.55  thf(fact_3405_sup_OboundedI,axiom,
% 0.29/0.55      ! [B: int,A: int,C: int] :
% 0.29/0.55        ( ( ord_less_eq_int @ B @ A )
% 0.29/0.55       => ( ( ord_less_eq_int @ C @ A )
% 0.29/0.55         => ( ord_less_eq_int @ ( sup_sup_int @ B @ C ) @ A ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.boundedI
% 0.29/0.55  thf(fact_3406_sup_Oorder__iff,axiom,
% 0.29/0.55      ( ord_le8081472938463900775at_nat
% 0.29/0.55      = ( ^ [B3: set_Pr8551490117392284871at_nat,A3: set_Pr8551490117392284871at_nat] :
% 0.29/0.55            ( A3
% 0.29/0.55            = ( sup_su3035147773818789531at_nat @ A3 @ B3 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.order_iff
% 0.29/0.55  thf(fact_3407_sup_Oorder__iff,axiom,
% 0.29/0.55      ( ord_le1268244103169919719at_nat
% 0.29/0.55      = ( ^ [B3: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] :
% 0.29/0.55            ( A3
% 0.29/0.55            = ( sup_su5525570899277871387at_nat @ A3 @ B3 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.order_iff
% 0.29/0.55  thf(fact_3408_sup_Oorder__iff,axiom,
% 0.29/0.55      ( ord_le2510731241096832064er_nat
% 0.29/0.55      = ( ^ [B3: filter_nat,A3: filter_nat] :
% 0.29/0.55            ( A3
% 0.29/0.55            = ( sup_sup_filter_nat @ A3 @ B3 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.order_iff
% 0.29/0.55  thf(fact_3409_sup_Oorder__iff,axiom,
% 0.29/0.55      ( ord_less_eq_set_nat
% 0.29/0.55      = ( ^ [B3: set_nat,A3: set_nat] :
% 0.29/0.55            ( A3
% 0.29/0.55            = ( sup_sup_set_nat @ A3 @ B3 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.order_iff
% 0.29/0.55  thf(fact_3410_sup_Oorder__iff,axiom,
% 0.29/0.55      ( ord_less_eq_rat
% 0.29/0.55      = ( ^ [B3: rat,A3: rat] :
% 0.29/0.55            ( A3
% 0.29/0.55            = ( sup_sup_rat @ A3 @ B3 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.order_iff
% 0.29/0.55  thf(fact_3411_sup_Oorder__iff,axiom,
% 0.29/0.55      ( ord_less_eq_nat
% 0.29/0.55      = ( ^ [B3: nat,A3: nat] :
% 0.29/0.55            ( A3
% 0.29/0.55            = ( sup_sup_nat @ A3 @ B3 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.order_iff
% 0.29/0.55  thf(fact_3412_sup_Oorder__iff,axiom,
% 0.29/0.55      ( ord_less_eq_int
% 0.29/0.55      = ( ^ [B3: int,A3: int] :
% 0.29/0.55            ( A3
% 0.29/0.55            = ( sup_sup_int @ A3 @ B3 ) ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.order_iff
% 0.29/0.55  thf(fact_3413_sup_Ocobounded1,axiom,
% 0.29/0.55      ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ A @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.cobounded1
% 0.29/0.55  thf(fact_3414_sup_Ocobounded1,axiom,
% 0.29/0.55      ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ A @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.cobounded1
% 0.29/0.55  thf(fact_3415_sup_Ocobounded1,axiom,
% 0.29/0.55      ! [A: filter_nat,B: filter_nat] : ( ord_le2510731241096832064er_nat @ A @ ( sup_sup_filter_nat @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.cobounded1
% 0.29/0.55  thf(fact_3416_sup_Ocobounded1,axiom,
% 0.29/0.55      ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ A @ ( sup_sup_set_nat @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.cobounded1
% 0.29/0.55  thf(fact_3417_sup_Ocobounded1,axiom,
% 0.29/0.55      ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( sup_sup_rat @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.cobounded1
% 0.29/0.55  thf(fact_3418_sup_Ocobounded1,axiom,
% 0.29/0.55      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( sup_sup_nat @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.cobounded1
% 0.29/0.55  thf(fact_3419_sup_Ocobounded1,axiom,
% 0.29/0.55      ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( sup_sup_int @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.cobounded1
% 0.29/0.55  thf(fact_3420_sup_Ocobounded2,axiom,
% 0.29/0.55      ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ B @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.cobounded2
% 0.29/0.55  thf(fact_3421_sup_Ocobounded2,axiom,
% 0.29/0.55      ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ B @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.cobounded2
% 0.29/0.55  thf(fact_3422_sup_Ocobounded2,axiom,
% 0.29/0.55      ! [B: filter_nat,A: filter_nat] : ( ord_le2510731241096832064er_nat @ B @ ( sup_sup_filter_nat @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.cobounded2
% 0.29/0.55  thf(fact_3423_sup_Ocobounded2,axiom,
% 0.29/0.55      ! [B: set_nat,A: set_nat] : ( ord_less_eq_set_nat @ B @ ( sup_sup_set_nat @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.cobounded2
% 0.29/0.55  thf(fact_3424_sup_Ocobounded2,axiom,
% 0.29/0.55      ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( sup_sup_rat @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.cobounded2
% 0.29/0.55  thf(fact_3425_sup_Ocobounded2,axiom,
% 0.29/0.55      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( sup_sup_nat @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.cobounded2
% 0.29/0.55  thf(fact_3426_sup_Ocobounded2,axiom,
% 0.29/0.55      ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( sup_sup_int @ A @ B ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.cobounded2
% 0.29/0.55  thf(fact_3427_sup_Oabsorb__iff1,axiom,
% 0.29/0.55      ( ord_le8081472938463900775at_nat
% 0.29/0.55      = ( ^ [B3: set_Pr8551490117392284871at_nat,A3: set_Pr8551490117392284871at_nat] :
% 0.29/0.55            ( ( sup_su3035147773818789531at_nat @ A3 @ B3 )
% 0.29/0.55            = A3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb_iff1
% 0.29/0.55  thf(fact_3428_sup_Oabsorb__iff1,axiom,
% 0.29/0.55      ( ord_le1268244103169919719at_nat
% 0.29/0.55      = ( ^ [B3: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] :
% 0.29/0.55            ( ( sup_su5525570899277871387at_nat @ A3 @ B3 )
% 0.29/0.55            = A3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb_iff1
% 0.29/0.55  thf(fact_3429_sup_Oabsorb__iff1,axiom,
% 0.29/0.55      ( ord_le2510731241096832064er_nat
% 0.29/0.55      = ( ^ [B3: filter_nat,A3: filter_nat] :
% 0.29/0.55            ( ( sup_sup_filter_nat @ A3 @ B3 )
% 0.29/0.55            = A3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb_iff1
% 0.29/0.55  thf(fact_3430_sup_Oabsorb__iff1,axiom,
% 0.29/0.55      ( ord_less_eq_set_nat
% 0.29/0.55      = ( ^ [B3: set_nat,A3: set_nat] :
% 0.29/0.55            ( ( sup_sup_set_nat @ A3 @ B3 )
% 0.29/0.55            = A3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb_iff1
% 0.29/0.55  thf(fact_3431_sup_Oabsorb__iff1,axiom,
% 0.29/0.55      ( ord_less_eq_rat
% 0.29/0.55      = ( ^ [B3: rat,A3: rat] :
% 0.29/0.55            ( ( sup_sup_rat @ A3 @ B3 )
% 0.29/0.55            = A3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb_iff1
% 0.29/0.55  thf(fact_3432_sup_Oabsorb__iff1,axiom,
% 0.29/0.55      ( ord_less_eq_nat
% 0.29/0.55      = ( ^ [B3: nat,A3: nat] :
% 0.29/0.55            ( ( sup_sup_nat @ A3 @ B3 )
% 0.29/0.55            = A3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb_iff1
% 0.29/0.55  thf(fact_3433_sup_Oabsorb__iff1,axiom,
% 0.29/0.55      ( ord_less_eq_int
% 0.29/0.55      = ( ^ [B3: int,A3: int] :
% 0.29/0.55            ( ( sup_sup_int @ A3 @ B3 )
% 0.29/0.55            = A3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb_iff1
% 0.29/0.55  thf(fact_3434_sup_Oabsorb__iff2,axiom,
% 0.29/0.55      ( ord_le8081472938463900775at_nat
% 0.29/0.55      = ( ^ [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] :
% 0.29/0.55            ( ( sup_su3035147773818789531at_nat @ A3 @ B3 )
% 0.29/0.55            = B3 ) ) ) ).
% 0.29/0.55  
% 0.29/0.55  % sup.absorb_iff2
% 0.29/0.55  thf(fact_3435_sup_Oabsorb__iff2,axiom,
% 0.30/0.55      ( ord_le1268244103169919719at_nat
% 0.30/0.55      = ( ^ [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 0.30/0.55            ( ( sup_su5525570899277871387at_nat @ A3 @ B3 )
% 0.30/0.55            = B3 ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % sup.absorb_iff2
% 0.30/0.55  thf(fact_3436_sup_Oabsorb__iff2,axiom,
% 0.30/0.55      ( ord_le2510731241096832064er_nat
% 0.30/0.55      = ( ^ [A3: filter_nat,B3: filter_nat] :
% 0.30/0.55            ( ( sup_sup_filter_nat @ A3 @ B3 )
% 0.30/0.55            = B3 ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % sup.absorb_iff2
% 0.30/0.55  thf(fact_3437_sup_Oabsorb__iff2,axiom,
% 0.30/0.55      ( ord_less_eq_set_nat
% 0.30/0.55      = ( ^ [A3: set_nat,B3: set_nat] :
% 0.30/0.55            ( ( sup_sup_set_nat @ A3 @ B3 )
% 0.30/0.55            = B3 ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % sup.absorb_iff2
% 0.30/0.55  thf(fact_3438_sup_Oabsorb__iff2,axiom,
% 0.30/0.55      ( ord_less_eq_rat
% 0.30/0.55      = ( ^ [A3: rat,B3: rat] :
% 0.30/0.55            ( ( sup_sup_rat @ A3 @ B3 )
% 0.30/0.55            = B3 ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % sup.absorb_iff2
% 0.30/0.55  thf(fact_3439_sup_Oabsorb__iff2,axiom,
% 0.30/0.55      ( ord_less_eq_nat
% 0.30/0.55      = ( ^ [A3: nat,B3: nat] :
% 0.30/0.55            ( ( sup_sup_nat @ A3 @ B3 )
% 0.30/0.55            = B3 ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % sup.absorb_iff2
% 0.30/0.55  thf(fact_3440_sup_Oabsorb__iff2,axiom,
% 0.30/0.55      ( ord_less_eq_int
% 0.30/0.55      = ( ^ [A3: int,B3: int] :
% 0.30/0.55            ( ( sup_sup_int @ A3 @ B3 )
% 0.30/0.55            = B3 ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % sup.absorb_iff2
% 0.30/0.55  thf(fact_3441_sup_OcoboundedI1,axiom,
% 0.30/0.55      ! [C: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 0.30/0.55        ( ( ord_le8081472938463900775at_nat @ C @ A )
% 0.30/0.55       => ( ord_le8081472938463900775at_nat @ C @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % sup.coboundedI1
% 0.30/0.55  thf(fact_3442_sup_OcoboundedI1,axiom,
% 0.30/0.55      ! [C: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 0.30/0.55        ( ( ord_le1268244103169919719at_nat @ C @ A )
% 0.30/0.55       => ( ord_le1268244103169919719at_nat @ C @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % sup.coboundedI1
% 0.30/0.55  thf(fact_3443_sup_OcoboundedI1,axiom,
% 0.30/0.55      ! [C: filter_nat,A: filter_nat,B: filter_nat] :
% 0.30/0.55        ( ( ord_le2510731241096832064er_nat @ C @ A )
% 0.30/0.55       => ( ord_le2510731241096832064er_nat @ C @ ( sup_sup_filter_nat @ A @ B ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % sup.coboundedI1
% 0.30/0.55  thf(fact_3444_sup_OcoboundedI1,axiom,
% 0.30/0.55      ! [C: set_nat,A: set_nat,B: set_nat] :
% 0.30/0.55        ( ( ord_less_eq_set_nat @ C @ A )
% 0.30/0.55       => ( ord_less_eq_set_nat @ C @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % sup.coboundedI1
% 0.30/0.55  thf(fact_3445_sup_OcoboundedI1,axiom,
% 0.30/0.55      ! [C: rat,A: rat,B: rat] :
% 0.30/0.55        ( ( ord_less_eq_rat @ C @ A )
% 0.30/0.55       => ( ord_less_eq_rat @ C @ ( sup_sup_rat @ A @ B ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % sup.coboundedI1
% 0.30/0.55  thf(fact_3446_sup_OcoboundedI1,axiom,
% 0.30/0.55      ! [C: nat,A: nat,B: nat] :
% 0.30/0.55        ( ( ord_less_eq_nat @ C @ A )
% 0.30/0.55       => ( ord_less_eq_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % sup.coboundedI1
% 0.30/0.55  thf(fact_3447_sup_OcoboundedI1,axiom,
% 0.30/0.55      ! [C: int,A: int,B: int] :
% 0.30/0.55        ( ( ord_less_eq_int @ C @ A )
% 0.30/0.55       => ( ord_less_eq_int @ C @ ( sup_sup_int @ A @ B ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % sup.coboundedI1
% 0.30/0.55  thf(fact_3448_sup_OcoboundedI2,axiom,
% 0.30/0.55      ! [C: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 0.30/0.55        ( ( ord_le8081472938463900775at_nat @ C @ B )
% 0.30/0.55       => ( ord_le8081472938463900775at_nat @ C @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % sup.coboundedI2
% 0.30/0.55  thf(fact_3449_sup_OcoboundedI2,axiom,
% 0.30/0.55      ! [C: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 0.30/0.55        ( ( ord_le1268244103169919719at_nat @ C @ B )
% 0.30/0.55       => ( ord_le1268244103169919719at_nat @ C @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % sup.coboundedI2
% 0.30/0.55  thf(fact_3450_sup_OcoboundedI2,axiom,
% 0.30/0.55      ! [C: filter_nat,B: filter_nat,A: filter_nat] :
% 0.30/0.55        ( ( ord_le2510731241096832064er_nat @ C @ B )
% 0.30/0.55       => ( ord_le2510731241096832064er_nat @ C @ ( sup_sup_filter_nat @ A @ B ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % sup.coboundedI2
% 0.30/0.55  thf(fact_3451_sup_OcoboundedI2,axiom,
% 0.30/0.55      ! [C: set_nat,B: set_nat,A: set_nat] :
% 0.30/0.55        ( ( ord_less_eq_set_nat @ C @ B )
% 0.30/0.55       => ( ord_less_eq_set_nat @ C @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % sup.coboundedI2
% 0.30/0.55  thf(fact_3452_sup_OcoboundedI2,axiom,
% 0.30/0.55      ! [C: rat,B: rat,A: rat] :
% 0.30/0.55        ( ( ord_less_eq_rat @ C @ B )
% 0.30/0.55       => ( ord_less_eq_rat @ C @ ( sup_sup_rat @ A @ B ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % sup.coboundedI2
% 0.30/0.55  thf(fact_3453_sup_OcoboundedI2,axiom,
% 0.30/0.55      ! [C: nat,B: nat,A: nat] :
% 0.30/0.55        ( ( ord_less_eq_nat @ C @ B )
% 0.30/0.55       => ( ord_less_eq_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % sup.coboundedI2
% 0.30/0.55  thf(fact_3454_sup_OcoboundedI2,axiom,
% 0.30/0.55      ! [C: int,B: int,A: int] :
% 0.30/0.55        ( ( ord_less_eq_int @ C @ B )
% 0.30/0.55       => ( ord_less_eq_int @ C @ ( sup_sup_int @ A @ B ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % sup.coboundedI2
% 0.30/0.55  thf(fact_3455_subset__UNIV,axiom,
% 0.30/0.55      ! [A2: set_list_nat] : ( ord_le6045566169113846134st_nat @ A2 @ top_top_set_list_nat ) ).
% 0.30/0.55  
% 0.30/0.55  % subset_UNIV
% 0.30/0.55  thf(fact_3456_subset__UNIV,axiom,
% 0.30/0.55      ! [A2: set_o] : ( ord_less_eq_set_o @ A2 @ top_top_set_o ) ).
% 0.30/0.55  
% 0.30/0.55  % subset_UNIV
% 0.30/0.55  thf(fact_3457_subset__UNIV,axiom,
% 0.30/0.55      ! [A2: set_rat] : ( ord_less_eq_set_rat @ A2 @ top_top_set_rat ) ).
% 0.30/0.55  
% 0.30/0.55  % subset_UNIV
% 0.30/0.55  thf(fact_3458_subset__UNIV,axiom,
% 0.30/0.55      ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ top_top_set_int ) ).
% 0.30/0.55  
% 0.30/0.55  % subset_UNIV
% 0.30/0.55  thf(fact_3459_subset__UNIV,axiom,
% 0.30/0.55      ! [A2: set_nat] : ( ord_less_eq_set_nat @ A2 @ top_top_set_nat ) ).
% 0.30/0.55  
% 0.30/0.55  % subset_UNIV
% 0.30/0.55  thf(fact_3460_inter__eq__subsetI,axiom,
% 0.30/0.55      ! [S: set_Pr1261947904930325089at_nat,S4: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.55        ( ( ord_le3146513528884898305at_nat @ S @ S4 )
% 0.30/0.55       => ( ( ( inf_in2572325071724192079at_nat @ A2 @ S4 )
% 0.30/0.55            = ( inf_in2572325071724192079at_nat @ B2 @ S4 ) )
% 0.30/0.55         => ( ( inf_in2572325071724192079at_nat @ A2 @ S )
% 0.30/0.55            = ( inf_in2572325071724192079at_nat @ B2 @ S ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % inter_eq_subsetI
% 0.30/0.55  thf(fact_3461_inter__eq__subsetI,axiom,
% 0.30/0.55      ! [S: set_nat,S4: set_nat,A2: set_nat,B2: set_nat] :
% 0.30/0.55        ( ( ord_less_eq_set_nat @ S @ S4 )
% 0.30/0.55       => ( ( ( inf_inf_set_nat @ A2 @ S4 )
% 0.30/0.55            = ( inf_inf_set_nat @ B2 @ S4 ) )
% 0.30/0.55         => ( ( inf_inf_set_nat @ A2 @ S )
% 0.30/0.55            = ( inf_inf_set_nat @ B2 @ S ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % inter_eq_subsetI
% 0.30/0.55  thf(fact_3462_Int__Collect__mono,axiom,
% 0.30/0.55      ! [A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int,P: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 0.30/0.55        ( ( ord_le483042692224249369nt_int @ A2 @ B2 )
% 0.30/0.55       => ( ! [X2: set_Pr958786334691620121nt_int] :
% 0.30/0.55              ( ( member2340774599025711042nt_int @ X2 @ A2 )
% 0.30/0.55             => ( ( P @ X2 )
% 0.30/0.55               => ( Q2 @ X2 ) ) )
% 0.30/0.55         => ( ord_le483042692224249369nt_int @ ( inf_in8396524679539076455nt_int @ A2 @ ( collec5210948495886036740nt_int @ P ) ) @ ( inf_in8396524679539076455nt_int @ B2 @ ( collec5210948495886036740nt_int @ Q2 ) ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Int_Collect_mono
% 0.30/0.55  thf(fact_3463_Int__Collect__mono,axiom,
% 0.30/0.55      ! [A2: set_set_nat,B2: set_set_nat,P: set_nat > $o,Q2: set_nat > $o] :
% 0.30/0.55        ( ( ord_le6893508408891458716et_nat @ A2 @ B2 )
% 0.30/0.55       => ( ! [X2: set_nat] :
% 0.30/0.55              ( ( member_set_nat @ X2 @ A2 )
% 0.30/0.55             => ( ( P @ X2 )
% 0.30/0.55               => ( Q2 @ X2 ) ) )
% 0.30/0.55         => ( ord_le6893508408891458716et_nat @ ( inf_inf_set_set_nat @ A2 @ ( collect_set_nat @ P ) ) @ ( inf_inf_set_set_nat @ B2 @ ( collect_set_nat @ Q2 ) ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Int_Collect_mono
% 0.30/0.55  thf(fact_3464_Int__Collect__mono,axiom,
% 0.30/0.55      ! [A2: set_int,B2: set_int,P: int > $o,Q2: int > $o] :
% 0.30/0.55        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.30/0.55       => ( ! [X2: int] :
% 0.30/0.55              ( ( member_int @ X2 @ A2 )
% 0.30/0.55             => ( ( P @ X2 )
% 0.30/0.55               => ( Q2 @ X2 ) ) )
% 0.30/0.55         => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) @ ( inf_inf_set_int @ B2 @ ( collect_int @ Q2 ) ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Int_Collect_mono
% 0.30/0.55  thf(fact_3465_Int__Collect__mono,axiom,
% 0.30/0.55      ! [A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o,P: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.30/0.55        ( ( ord_le2965882846123202637_nat_o @ A2 @ B2 )
% 0.30/0.55       => ( ! [X2: produc3658429121746597890et_nat > $o] :
% 0.30/0.55              ( ( member6576561426505652726_nat_o @ X2 @ A2 )
% 0.30/0.55             => ( ( P @ X2 )
% 0.30/0.55               => ( Q2 @ X2 ) ) )
% 0.30/0.55         => ( ord_le2965882846123202637_nat_o @ ( inf_in1906310914598751387_nat_o @ A2 @ ( collec939566748876313656_nat_o @ P ) ) @ ( inf_in1906310914598751387_nat_o @ B2 @ ( collec939566748876313656_nat_o @ Q2 ) ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Int_Collect_mono
% 0.30/0.55  thf(fact_3466_Int__Collect__mono,axiom,
% 0.30/0.55      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > $o] :
% 0.30/0.55        ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 0.30/0.55       => ( ! [X2: product_prod_nat_nat] :
% 0.30/0.55              ( ( member8440522571783428010at_nat @ X2 @ A2 )
% 0.30/0.55             => ( ( P @ X2 )
% 0.30/0.55               => ( Q2 @ X2 ) ) )
% 0.30/0.55         => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ ( collec3392354462482085612at_nat @ P ) ) @ ( inf_in2572325071724192079at_nat @ B2 @ ( collec3392354462482085612at_nat @ Q2 ) ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Int_Collect_mono
% 0.30/0.55  thf(fact_3467_Int__Collect__mono,axiom,
% 0.30/0.55      ! [A2: set_nat,B2: set_nat,P: nat > $o,Q2: nat > $o] :
% 0.30/0.55        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.30/0.55       => ( ! [X2: nat] :
% 0.30/0.55              ( ( member_nat @ X2 @ A2 )
% 0.30/0.55             => ( ( P @ X2 )
% 0.30/0.55               => ( Q2 @ X2 ) ) )
% 0.30/0.55         => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) @ ( inf_inf_set_nat @ B2 @ ( collect_nat @ Q2 ) ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Int_Collect_mono
% 0.30/0.55  thf(fact_3468_Int__greatest,axiom,
% 0.30/0.55      ! [C2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.55        ( ( ord_le3146513528884898305at_nat @ C2 @ A2 )
% 0.30/0.55       => ( ( ord_le3146513528884898305at_nat @ C2 @ B2 )
% 0.30/0.55         => ( ord_le3146513528884898305at_nat @ C2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Int_greatest
% 0.30/0.55  thf(fact_3469_Int__greatest,axiom,
% 0.30/0.55      ! [C2: set_nat,A2: set_nat,B2: set_nat] :
% 0.30/0.55        ( ( ord_less_eq_set_nat @ C2 @ A2 )
% 0.30/0.55       => ( ( ord_less_eq_set_nat @ C2 @ B2 )
% 0.30/0.55         => ( ord_less_eq_set_nat @ C2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Int_greatest
% 0.30/0.55  thf(fact_3470_Int__absorb2,axiom,
% 0.30/0.55      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.55        ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 0.30/0.55       => ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 0.30/0.55          = A2 ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Int_absorb2
% 0.30/0.55  thf(fact_3471_Int__absorb2,axiom,
% 0.30/0.55      ! [A2: set_nat,B2: set_nat] :
% 0.30/0.55        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.30/0.55       => ( ( inf_inf_set_nat @ A2 @ B2 )
% 0.30/0.55          = A2 ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Int_absorb2
% 0.30/0.55  thf(fact_3472_Int__absorb1,axiom,
% 0.30/0.55      ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.30/0.55        ( ( ord_le3146513528884898305at_nat @ B2 @ A2 )
% 0.30/0.55       => ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 0.30/0.55          = B2 ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Int_absorb1
% 0.30/0.55  thf(fact_3473_Int__absorb1,axiom,
% 0.30/0.55      ! [B2: set_nat,A2: set_nat] :
% 0.30/0.55        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.30/0.55       => ( ( inf_inf_set_nat @ A2 @ B2 )
% 0.30/0.55          = B2 ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Int_absorb1
% 0.30/0.55  thf(fact_3474_Int__lower2,axiom,
% 0.30/0.55      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ B2 ) ).
% 0.30/0.55  
% 0.30/0.55  % Int_lower2
% 0.30/0.55  thf(fact_3475_Int__lower2,axiom,
% 0.30/0.55      ! [A2: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ B2 ) ).
% 0.30/0.55  
% 0.30/0.55  % Int_lower2
% 0.30/0.55  thf(fact_3476_Int__lower1,axiom,
% 0.30/0.55      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ A2 ) ).
% 0.30/0.55  
% 0.30/0.55  % Int_lower1
% 0.30/0.55  thf(fact_3477_Int__lower1,axiom,
% 0.30/0.55      ! [A2: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ A2 ) ).
% 0.30/0.55  
% 0.30/0.55  % Int_lower1
% 0.30/0.55  thf(fact_3478_Int__mono,axiom,
% 0.30/0.55      ! [A2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,D3: set_Pr1261947904930325089at_nat] :
% 0.30/0.55        ( ( ord_le3146513528884898305at_nat @ A2 @ C2 )
% 0.30/0.55       => ( ( ord_le3146513528884898305at_nat @ B2 @ D3 )
% 0.30/0.55         => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ ( inf_in2572325071724192079at_nat @ C2 @ D3 ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Int_mono
% 0.30/0.55  thf(fact_3479_Int__mono,axiom,
% 0.30/0.55      ! [A2: set_nat,C2: set_nat,B2: set_nat,D3: set_nat] :
% 0.30/0.55        ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 0.30/0.55       => ( ( ord_less_eq_set_nat @ B2 @ D3 )
% 0.30/0.55         => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ ( inf_inf_set_nat @ C2 @ D3 ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Int_mono
% 0.30/0.55  thf(fact_3480_subset__Un__eq,axiom,
% 0.30/0.55      ( ord_le8081472938463900775at_nat
% 0.30/0.55      = ( ^ [A4: set_Pr8551490117392284871at_nat,B4: set_Pr8551490117392284871at_nat] :
% 0.30/0.55            ( ( sup_su3035147773818789531at_nat @ A4 @ B4 )
% 0.30/0.55            = B4 ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % subset_Un_eq
% 0.30/0.55  thf(fact_3481_subset__Un__eq,axiom,
% 0.30/0.55      ( ord_le1268244103169919719at_nat
% 0.30/0.55      = ( ^ [A4: set_Pr4329608150637261639at_nat,B4: set_Pr4329608150637261639at_nat] :
% 0.30/0.55            ( ( sup_su5525570899277871387at_nat @ A4 @ B4 )
% 0.30/0.55            = B4 ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % subset_Un_eq
% 0.30/0.55  thf(fact_3482_subset__Un__eq,axiom,
% 0.30/0.55      ( ord_less_eq_set_nat
% 0.30/0.55      = ( ^ [A4: set_nat,B4: set_nat] :
% 0.30/0.55            ( ( sup_sup_set_nat @ A4 @ B4 )
% 0.30/0.55            = B4 ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % subset_Un_eq
% 0.30/0.55  thf(fact_3483_subset__UnE,axiom,
% 0.30/0.55      ! [C2: set_Pr8551490117392284871at_nat,A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 0.30/0.55        ( ( ord_le8081472938463900775at_nat @ C2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 0.30/0.55       => ~ ! [A7: set_Pr8551490117392284871at_nat] :
% 0.30/0.55              ( ( ord_le8081472938463900775at_nat @ A7 @ A2 )
% 0.30/0.55             => ! [B7: set_Pr8551490117392284871at_nat] :
% 0.30/0.55                  ( ( ord_le8081472938463900775at_nat @ B7 @ B2 )
% 0.30/0.55                 => ( C2
% 0.30/0.55                   != ( sup_su3035147773818789531at_nat @ A7 @ B7 ) ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % subset_UnE
% 0.30/0.55  thf(fact_3484_subset__UnE,axiom,
% 0.30/0.55      ! [C2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.55        ( ( ord_le1268244103169919719at_nat @ C2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 0.30/0.55       => ~ ! [A7: set_Pr4329608150637261639at_nat] :
% 0.30/0.55              ( ( ord_le1268244103169919719at_nat @ A7 @ A2 )
% 0.30/0.55             => ! [B7: set_Pr4329608150637261639at_nat] :
% 0.30/0.55                  ( ( ord_le1268244103169919719at_nat @ B7 @ B2 )
% 0.30/0.55                 => ( C2
% 0.30/0.55                   != ( sup_su5525570899277871387at_nat @ A7 @ B7 ) ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % subset_UnE
% 0.30/0.55  thf(fact_3485_subset__UnE,axiom,
% 0.30/0.55      ! [C2: set_nat,A2: set_nat,B2: set_nat] :
% 0.30/0.55        ( ( ord_less_eq_set_nat @ C2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.55       => ~ ! [A7: set_nat] :
% 0.30/0.55              ( ( ord_less_eq_set_nat @ A7 @ A2 )
% 0.30/0.55             => ! [B7: set_nat] :
% 0.30/0.55                  ( ( ord_less_eq_set_nat @ B7 @ B2 )
% 0.30/0.55                 => ( C2
% 0.30/0.55                   != ( sup_sup_set_nat @ A7 @ B7 ) ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % subset_UnE
% 0.30/0.55  thf(fact_3486_Un__absorb2,axiom,
% 0.30/0.55      ! [B2: set_Pr8551490117392284871at_nat,A2: set_Pr8551490117392284871at_nat] :
% 0.30/0.55        ( ( ord_le8081472938463900775at_nat @ B2 @ A2 )
% 0.30/0.55       => ( ( sup_su3035147773818789531at_nat @ A2 @ B2 )
% 0.30/0.55          = A2 ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Un_absorb2
% 0.30/0.55  thf(fact_3487_Un__absorb2,axiom,
% 0.30/0.55      ! [B2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.30/0.55        ( ( ord_le1268244103169919719at_nat @ B2 @ A2 )
% 0.30/0.55       => ( ( sup_su5525570899277871387at_nat @ A2 @ B2 )
% 0.30/0.55          = A2 ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Un_absorb2
% 0.30/0.55  thf(fact_3488_Un__absorb2,axiom,
% 0.30/0.55      ! [B2: set_nat,A2: set_nat] :
% 0.30/0.55        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.30/0.55       => ( ( sup_sup_set_nat @ A2 @ B2 )
% 0.30/0.55          = A2 ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Un_absorb2
% 0.30/0.55  thf(fact_3489_Un__absorb1,axiom,
% 0.30/0.55      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 0.30/0.55        ( ( ord_le8081472938463900775at_nat @ A2 @ B2 )
% 0.30/0.55       => ( ( sup_su3035147773818789531at_nat @ A2 @ B2 )
% 0.30/0.55          = B2 ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Un_absorb1
% 0.30/0.55  thf(fact_3490_Un__absorb1,axiom,
% 0.30/0.55      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.55        ( ( ord_le1268244103169919719at_nat @ A2 @ B2 )
% 0.30/0.55       => ( ( sup_su5525570899277871387at_nat @ A2 @ B2 )
% 0.30/0.55          = B2 ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Un_absorb1
% 0.30/0.55  thf(fact_3491_Un__absorb1,axiom,
% 0.30/0.55      ! [A2: set_nat,B2: set_nat] :
% 0.30/0.55        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.30/0.55       => ( ( sup_sup_set_nat @ A2 @ B2 )
% 0.30/0.55          = B2 ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Un_absorb1
% 0.30/0.55  thf(fact_3492_Un__upper2,axiom,
% 0.30/0.55      ! [B2: set_Pr8551490117392284871at_nat,A2: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ B2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Un_upper2
% 0.30/0.55  thf(fact_3493_Un__upper2,axiom,
% 0.30/0.55      ! [B2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ B2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Un_upper2
% 0.30/0.55  thf(fact_3494_Un__upper2,axiom,
% 0.30/0.55      ! [B2: set_nat,A2: set_nat] : ( ord_less_eq_set_nat @ B2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Un_upper2
% 0.30/0.55  thf(fact_3495_Un__upper1,axiom,
% 0.30/0.55      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ A2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Un_upper1
% 0.30/0.55  thf(fact_3496_Un__upper1,axiom,
% 0.30/0.55      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Un_upper1
% 0.30/0.55  thf(fact_3497_Un__upper1,axiom,
% 0.30/0.55      ! [A2: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ A2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Un_upper1
% 0.30/0.55  thf(fact_3498_Un__least,axiom,
% 0.30/0.55      ! [A2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 0.30/0.55        ( ( ord_le8081472938463900775at_nat @ A2 @ C2 )
% 0.30/0.55       => ( ( ord_le8081472938463900775at_nat @ B2 @ C2 )
% 0.30/0.55         => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) @ C2 ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Un_least
% 0.30/0.55  thf(fact_3499_Un__least,axiom,
% 0.30/0.55      ! [A2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.55        ( ( ord_le1268244103169919719at_nat @ A2 @ C2 )
% 0.30/0.55       => ( ( ord_le1268244103169919719at_nat @ B2 @ C2 )
% 0.30/0.55         => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) @ C2 ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Un_least
% 0.30/0.55  thf(fact_3500_Un__least,axiom,
% 0.30/0.55      ! [A2: set_nat,C2: set_nat,B2: set_nat] :
% 0.30/0.55        ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 0.30/0.55       => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 0.30/0.55         => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ C2 ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Un_least
% 0.30/0.55  thf(fact_3501_Un__mono,axiom,
% 0.30/0.55      ! [A2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,D3: set_Pr8551490117392284871at_nat] :
% 0.30/0.55        ( ( ord_le8081472938463900775at_nat @ A2 @ C2 )
% 0.30/0.55       => ( ( ord_le8081472938463900775at_nat @ B2 @ D3 )
% 0.30/0.55         => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) @ ( sup_su3035147773818789531at_nat @ C2 @ D3 ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Un_mono
% 0.30/0.55  thf(fact_3502_Un__mono,axiom,
% 0.30/0.55      ! [A2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,D3: set_Pr4329608150637261639at_nat] :
% 0.30/0.55        ( ( ord_le1268244103169919719at_nat @ A2 @ C2 )
% 0.30/0.55       => ( ( ord_le1268244103169919719at_nat @ B2 @ D3 )
% 0.30/0.55         => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) @ ( sup_su5525570899277871387at_nat @ C2 @ D3 ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Un_mono
% 0.30/0.55  thf(fact_3503_Un__mono,axiom,
% 0.30/0.55      ! [A2: set_nat,C2: set_nat,B2: set_nat,D3: set_nat] :
% 0.30/0.55        ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 0.30/0.55       => ( ( ord_less_eq_set_nat @ B2 @ D3 )
% 0.30/0.55         => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ ( sup_sup_set_nat @ C2 @ D3 ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Un_mono
% 0.30/0.55  thf(fact_3504_Diff__partition,axiom,
% 0.30/0.55      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 0.30/0.55        ( ( ord_le8081472938463900775at_nat @ A2 @ B2 )
% 0.30/0.55       => ( ( sup_su3035147773818789531at_nat @ A2 @ ( minus_5060654252129873198at_nat @ B2 @ A2 ) )
% 0.30/0.55          = B2 ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Diff_partition
% 0.30/0.55  thf(fact_3505_Diff__partition,axiom,
% 0.30/0.55      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.55        ( ( ord_le1268244103169919719at_nat @ A2 @ B2 )
% 0.30/0.55       => ( ( sup_su5525570899277871387at_nat @ A2 @ ( minus_3314409938677909166at_nat @ B2 @ A2 ) )
% 0.30/0.55          = B2 ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Diff_partition
% 0.30/0.55  thf(fact_3506_Diff__partition,axiom,
% 0.30/0.55      ! [A2: set_nat,B2: set_nat] :
% 0.30/0.55        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.30/0.55       => ( ( sup_sup_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 0.30/0.55          = B2 ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Diff_partition
% 0.30/0.55  thf(fact_3507_Diff__subset__conv,axiom,
% 0.30/0.55      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 0.30/0.55        ( ( ord_le8081472938463900775at_nat @ ( minus_5060654252129873198at_nat @ A2 @ B2 ) @ C2 )
% 0.30/0.55        = ( ord_le8081472938463900775at_nat @ A2 @ ( sup_su3035147773818789531at_nat @ B2 @ C2 ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Diff_subset_conv
% 0.30/0.55  thf(fact_3508_Diff__subset__conv,axiom,
% 0.30/0.55      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 0.30/0.55        ( ( ord_le1268244103169919719at_nat @ ( minus_3314409938677909166at_nat @ A2 @ B2 ) @ C2 )
% 0.30/0.55        = ( ord_le1268244103169919719at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Diff_subset_conv
% 0.30/0.55  thf(fact_3509_Diff__subset__conv,axiom,
% 0.30/0.55      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 0.30/0.55        ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ C2 )
% 0.30/0.55        = ( ord_less_eq_set_nat @ A2 @ ( sup_sup_set_nat @ B2 @ C2 ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % Diff_subset_conv
% 0.30/0.55  thf(fact_3510_relH__subset,axiom,
% 0.30/0.55      ! [Bs: set_nat,H3: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.30/0.55        ( ( relH @ Bs @ H3 @ H4 )
% 0.30/0.55       => ( ( ord_less_eq_set_nat @ As @ Bs )
% 0.30/0.55         => ( relH @ As @ H3 @ H4 ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % relH_subset
% 0.30/0.55  thf(fact_3511_mult__le__cancel__left1,axiom,
% 0.30/0.55      ! [C: code_integer,B: code_integer] :
% 0.30/0.55        ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.30/0.55        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.55           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 0.30/0.55          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.30/0.55           => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_le_cancel_left1
% 0.30/0.55  thf(fact_3512_mult__le__cancel__left1,axiom,
% 0.30/0.55      ! [C: rat,B: rat] :
% 0.30/0.55        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 0.30/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.55           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 0.30/0.55          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.55           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_le_cancel_left1
% 0.30/0.55  thf(fact_3513_mult__le__cancel__left1,axiom,
% 0.30/0.55      ! [C: int,B: int] :
% 0.30/0.55        ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 0.30/0.55        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.30/0.55           => ( ord_less_eq_int @ one_one_int @ B ) )
% 0.30/0.55          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.30/0.55           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_le_cancel_left1
% 0.30/0.55  thf(fact_3514_mult__le__cancel__left2,axiom,
% 0.30/0.55      ! [C: code_integer,A: code_integer] :
% 0.30/0.55        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ C )
% 0.30/0.55        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.55           => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 0.30/0.55          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.30/0.55           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_le_cancel_left2
% 0.30/0.55  thf(fact_3515_mult__le__cancel__left2,axiom,
% 0.30/0.55      ! [C: rat,A: rat] :
% 0.30/0.55        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 0.30/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.55           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 0.30/0.55          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.55           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_le_cancel_left2
% 0.30/0.55  thf(fact_3516_mult__le__cancel__left2,axiom,
% 0.30/0.55      ! [C: int,A: int] :
% 0.30/0.55        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 0.30/0.55        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.30/0.55           => ( ord_less_eq_int @ A @ one_one_int ) )
% 0.30/0.55          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.30/0.55           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_le_cancel_left2
% 0.30/0.55  thf(fact_3517_mult__le__cancel__right1,axiom,
% 0.30/0.55      ! [C: code_integer,B: code_integer] :
% 0.30/0.55        ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.30/0.55        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.55           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 0.30/0.55          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.30/0.55           => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_le_cancel_right1
% 0.30/0.55  thf(fact_3518_mult__le__cancel__right1,axiom,
% 0.30/0.55      ! [C: rat,B: rat] :
% 0.30/0.55        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 0.30/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.55           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 0.30/0.55          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.55           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_le_cancel_right1
% 0.30/0.55  thf(fact_3519_mult__le__cancel__right1,axiom,
% 0.30/0.55      ! [C: int,B: int] :
% 0.30/0.55        ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 0.30/0.55        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.30/0.55           => ( ord_less_eq_int @ one_one_int @ B ) )
% 0.30/0.55          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.30/0.55           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_le_cancel_right1
% 0.30/0.55  thf(fact_3520_mult__le__cancel__right2,axiom,
% 0.30/0.55      ! [A: code_integer,C: code_integer] :
% 0.30/0.55        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ C )
% 0.30/0.55        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.55           => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 0.30/0.55          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.30/0.55           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_le_cancel_right2
% 0.30/0.55  thf(fact_3521_mult__le__cancel__right2,axiom,
% 0.30/0.55      ! [A: rat,C: rat] :
% 0.30/0.55        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 0.30/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.55           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 0.30/0.55          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.55           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_le_cancel_right2
% 0.30/0.55  thf(fact_3522_mult__le__cancel__right2,axiom,
% 0.30/0.55      ! [A: int,C: int] :
% 0.30/0.55        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 0.30/0.55        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.30/0.55           => ( ord_less_eq_int @ A @ one_one_int ) )
% 0.30/0.55          & ( ( ord_less_int @ C @ zero_zero_int )
% 0.30/0.55           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_le_cancel_right2
% 0.30/0.55  thf(fact_3523_mult__less__cancel__left1,axiom,
% 0.30/0.55      ! [C: code_integer,B: code_integer] :
% 0.30/0.55        ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.30/0.55        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.55           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 0.30/0.55          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.30/0.55           => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_less_cancel_left1
% 0.30/0.55  thf(fact_3524_mult__less__cancel__left1,axiom,
% 0.30/0.55      ! [C: rat,B: rat] :
% 0.30/0.55        ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 0.30/0.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.30/0.55           => ( ord_less_rat @ one_one_rat @ B ) )
% 0.30/0.55          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.30/0.55           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_less_cancel_left1
% 0.30/0.55  thf(fact_3525_mult__less__cancel__left1,axiom,
% 0.30/0.55      ! [C: int,B: int] :
% 0.30/0.55        ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 0.30/0.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.30/0.55           => ( ord_less_int @ one_one_int @ B ) )
% 0.30/0.55          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.30/0.55           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_less_cancel_left1
% 0.30/0.55  thf(fact_3526_mult__less__cancel__left2,axiom,
% 0.30/0.55      ! [C: code_integer,A: code_integer] :
% 0.30/0.55        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ C )
% 0.30/0.55        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.55           => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 0.30/0.55          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.30/0.55           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_less_cancel_left2
% 0.30/0.55  thf(fact_3527_mult__less__cancel__left2,axiom,
% 0.30/0.55      ! [C: rat,A: rat] :
% 0.30/0.55        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 0.30/0.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.30/0.55           => ( ord_less_rat @ A @ one_one_rat ) )
% 0.30/0.55          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.30/0.55           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_less_cancel_left2
% 0.30/0.55  thf(fact_3528_mult__less__cancel__left2,axiom,
% 0.30/0.55      ! [C: int,A: int] :
% 0.30/0.55        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 0.30/0.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.30/0.55           => ( ord_less_int @ A @ one_one_int ) )
% 0.30/0.55          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.30/0.55           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_less_cancel_left2
% 0.30/0.55  thf(fact_3529_mult__less__cancel__right1,axiom,
% 0.30/0.55      ! [C: code_integer,B: code_integer] :
% 0.30/0.55        ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.30/0.55        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.55           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 0.30/0.55          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.30/0.55           => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_less_cancel_right1
% 0.30/0.55  thf(fact_3530_mult__less__cancel__right1,axiom,
% 0.30/0.55      ! [C: rat,B: rat] :
% 0.30/0.55        ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 0.30/0.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.30/0.55           => ( ord_less_rat @ one_one_rat @ B ) )
% 0.30/0.55          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.30/0.55           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_less_cancel_right1
% 0.30/0.55  thf(fact_3531_mult__less__cancel__right1,axiom,
% 0.30/0.55      ! [C: int,B: int] :
% 0.30/0.55        ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 0.30/0.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.30/0.55           => ( ord_less_int @ one_one_int @ B ) )
% 0.30/0.55          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.30/0.55           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_less_cancel_right1
% 0.30/0.55  thf(fact_3532_mult__less__cancel__right2,axiom,
% 0.30/0.55      ! [A: code_integer,C: code_integer] :
% 0.30/0.55        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ C )
% 0.30/0.55        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.55           => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 0.30/0.55          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.30/0.55           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_less_cancel_right2
% 0.30/0.55  thf(fact_3533_mult__less__cancel__right2,axiom,
% 0.30/0.55      ! [A: rat,C: rat] :
% 0.30/0.55        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 0.30/0.55        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.30/0.55           => ( ord_less_rat @ A @ one_one_rat ) )
% 0.30/0.55          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.30/0.55           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_less_cancel_right2
% 0.30/0.55  thf(fact_3534_mult__less__cancel__right2,axiom,
% 0.30/0.55      ! [A: int,C: int] :
% 0.30/0.55        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 0.30/0.55        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.30/0.55           => ( ord_less_int @ A @ one_one_int ) )
% 0.30/0.55          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.30/0.55           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_less_cancel_right2
% 0.30/0.55  thf(fact_3535_field__le__mult__one__interval,axiom,
% 0.30/0.55      ! [X: rat,Y: rat] :
% 0.30/0.55        ( ! [Z2: rat] :
% 0.30/0.55            ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 0.30/0.55           => ( ( ord_less_rat @ Z2 @ one_one_rat )
% 0.30/0.55             => ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ X ) @ Y ) ) )
% 0.30/0.55       => ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.30/0.55  
% 0.30/0.55  % field_le_mult_one_interval
% 0.30/0.55  thf(fact_3536_divide__left__mono__neg,axiom,
% 0.30/0.55      ! [A: rat,B: rat,C: rat] :
% 0.30/0.55        ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.55       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.30/0.55         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.30/0.55           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % divide_left_mono_neg
% 0.30/0.55  thf(fact_3537_mult__imp__le__div__pos,axiom,
% 0.30/0.55      ! [Y: rat,Z: rat,X: rat] :
% 0.30/0.55        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.30/0.55       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 0.30/0.55         => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_imp_le_div_pos
% 0.30/0.55  thf(fact_3538_mult__imp__div__pos__le,axiom,
% 0.30/0.55      ! [Y: rat,X: rat,Z: rat] :
% 0.30/0.55        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.30/0.55       => ( ( ord_less_eq_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 0.30/0.55         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_imp_div_pos_le
% 0.30/0.55  thf(fact_3539_pos__le__divide__eq,axiom,
% 0.30/0.55      ! [C: rat,A: rat,B: rat] :
% 0.30/0.55        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.55       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.30/0.55          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % pos_le_divide_eq
% 0.30/0.55  thf(fact_3540_pos__divide__le__eq,axiom,
% 0.30/0.55      ! [C: rat,B: rat,A: rat] :
% 0.30/0.55        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.55       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.30/0.55          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % pos_divide_le_eq
% 0.30/0.55  thf(fact_3541_neg__le__divide__eq,axiom,
% 0.30/0.55      ! [C: rat,A: rat,B: rat] :
% 0.30/0.55        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.55       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.30/0.55          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % neg_le_divide_eq
% 0.30/0.55  thf(fact_3542_neg__divide__le__eq,axiom,
% 0.30/0.55      ! [C: rat,B: rat,A: rat] :
% 0.30/0.55        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.55       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.30/0.55          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % neg_divide_le_eq
% 0.30/0.55  thf(fact_3543_divide__left__mono,axiom,
% 0.30/0.55      ! [B: rat,A: rat,C: rat] :
% 0.30/0.55        ( ( ord_less_eq_rat @ B @ A )
% 0.30/0.55       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.30/0.55         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.30/0.55           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % divide_left_mono
% 0.30/0.55  thf(fact_3544_le__divide__eq,axiom,
% 0.30/0.55      ! [A: rat,B: rat,C: rat] :
% 0.30/0.55        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.30/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.55           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.30/0.55          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.55           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.55               => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.30/0.55              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.55               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % le_divide_eq
% 0.30/0.55  thf(fact_3545_divide__le__eq,axiom,
% 0.30/0.55      ! [B: rat,C: rat,A: rat] :
% 0.30/0.55        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.30/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.55           => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.30/0.55          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.55           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.55               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.30/0.55              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.55               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % divide_le_eq
% 0.30/0.55  thf(fact_3546_le__divide__eq__1,axiom,
% 0.30/0.55      ! [B: rat,A: rat] :
% 0.30/0.55        ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.30/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.55            & ( ord_less_eq_rat @ A @ B ) )
% 0.30/0.55          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.30/0.55            & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % le_divide_eq_1
% 0.30/0.55  thf(fact_3547_divide__le__eq__1,axiom,
% 0.30/0.55      ! [B: rat,A: rat] :
% 0.30/0.55        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.30/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.55            & ( ord_less_eq_rat @ B @ A ) )
% 0.30/0.55          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.30/0.55            & ( ord_less_eq_rat @ A @ B ) )
% 0.30/0.55          | ( A = zero_zero_rat ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % divide_le_eq_1
% 0.30/0.55  thf(fact_3548_le__divide__eq__numeral_I1_J,axiom,
% 0.30/0.55      ! [W: num,B: rat,C: rat] :
% 0.30/0.55        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 0.30/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.55           => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 0.30/0.55          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.55           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.55               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.30/0.55              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.55               => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % le_divide_eq_numeral(1)
% 0.30/0.55  thf(fact_3549_divide__le__eq__numeral_I1_J,axiom,
% 0.30/0.55      ! [B: rat,C: rat,W: num] :
% 0.30/0.55        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 0.30/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.55           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.30/0.55          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.55           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.55               => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 0.30/0.55              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.55               => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % divide_le_eq_numeral(1)
% 0.30/0.55  thf(fact_3550_pos__minus__divide__le__eq,axiom,
% 0.30/0.55      ! [C: rat,B: rat,A: rat] :
% 0.30/0.55        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.55       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.30/0.55          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % pos_minus_divide_le_eq
% 0.30/0.55  thf(fact_3551_pos__le__minus__divide__eq,axiom,
% 0.30/0.55      ! [C: rat,A: rat,B: rat] :
% 0.30/0.55        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.55       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.30/0.55          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % pos_le_minus_divide_eq
% 0.30/0.55  thf(fact_3552_neg__minus__divide__le__eq,axiom,
% 0.30/0.55      ! [C: rat,B: rat,A: rat] :
% 0.30/0.55        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.55       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.30/0.55          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % neg_minus_divide_le_eq
% 0.30/0.55  thf(fact_3553_neg__le__minus__divide__eq,axiom,
% 0.30/0.55      ! [C: rat,A: rat,B: rat] :
% 0.30/0.55        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.55       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.30/0.55          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % neg_le_minus_divide_eq
% 0.30/0.55  thf(fact_3554_minus__divide__le__eq,axiom,
% 0.30/0.55      ! [B: rat,C: rat,A: rat] :
% 0.30/0.55        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.30/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.55           => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.30/0.55          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.55           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.55               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.30/0.55              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.55               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % minus_divide_le_eq
% 0.30/0.55  thf(fact_3555_le__minus__divide__eq,axiom,
% 0.30/0.55      ! [A: rat,B: rat,C: rat] :
% 0.30/0.55        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.30/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.55           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.30/0.55          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.55           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.55               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.30/0.55              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.55               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % le_minus_divide_eq
% 0.30/0.55  thf(fact_3556_less__eq__assn__def,axiom,
% 0.30/0.55      ( ord_less_eq_assn
% 0.30/0.55      = ( ^ [A3: assn,B3: assn] :
% 0.30/0.55            ( A3
% 0.30/0.55            = ( inf_inf_assn @ A3 @ B3 ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % less_eq_assn_def
% 0.30/0.55  thf(fact_3557_mult__neg__neg,axiom,
% 0.30/0.55      ! [A: code_integer,B: code_integer] :
% 0.30/0.55        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.30/0.55       => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 0.30/0.55         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_neg_neg
% 0.30/0.55  thf(fact_3558_mult__neg__neg,axiom,
% 0.30/0.55      ! [A: rat,B: rat] :
% 0.30/0.55        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.30/0.55       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.30/0.55         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_neg_neg
% 0.30/0.55  thf(fact_3559_mult__neg__neg,axiom,
% 0.30/0.55      ! [A: int,B: int] :
% 0.30/0.55        ( ( ord_less_int @ A @ zero_zero_int )
% 0.30/0.55       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.30/0.55         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_neg_neg
% 0.30/0.55  thf(fact_3560_not__square__less__zero,axiom,
% 0.30/0.55      ! [A: code_integer] :
% 0.30/0.55        ~ ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ A ) @ zero_z3403309356797280102nteger ) ).
% 0.30/0.55  
% 0.30/0.55  % not_square_less_zero
% 0.30/0.55  thf(fact_3561_not__square__less__zero,axiom,
% 0.30/0.55      ! [A: rat] :
% 0.30/0.55        ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 0.30/0.55  
% 0.30/0.55  % not_square_less_zero
% 0.30/0.55  thf(fact_3562_not__square__less__zero,axiom,
% 0.30/0.55      ! [A: int] :
% 0.30/0.55        ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 0.30/0.55  
% 0.30/0.55  % not_square_less_zero
% 0.30/0.55  thf(fact_3563_mult__less__0__iff,axiom,
% 0.30/0.55      ! [A: code_integer,B: code_integer] :
% 0.30/0.55        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger )
% 0.30/0.55        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.55            & ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger ) )
% 0.30/0.55          | ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.30/0.55            & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_less_0_iff
% 0.30/0.55  thf(fact_3564_mult__less__0__iff,axiom,
% 0.30/0.55      ! [A: rat,B: rat] :
% 0.30/0.55        ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 0.30/0.55        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.55            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 0.30/0.55          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.30/0.55            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_less_0_iff
% 0.30/0.55  thf(fact_3565_mult__less__0__iff,axiom,
% 0.30/0.55      ! [A: int,B: int] :
% 0.30/0.55        ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 0.30/0.55        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.55            & ( ord_less_int @ B @ zero_zero_int ) )
% 0.30/0.55          | ( ( ord_less_int @ A @ zero_zero_int )
% 0.30/0.55            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_less_0_iff
% 0.30/0.55  thf(fact_3566_mult__neg__pos,axiom,
% 0.30/0.55      ! [A: code_integer,B: code_integer] :
% 0.30/0.55        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.30/0.55       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.30/0.55         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_neg_pos
% 0.30/0.55  thf(fact_3567_mult__neg__pos,axiom,
% 0.30/0.55      ! [A: rat,B: rat] :
% 0.30/0.55        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.30/0.55       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.30/0.55         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_neg_pos
% 0.30/0.55  thf(fact_3568_mult__neg__pos,axiom,
% 0.30/0.55      ! [A: nat,B: nat] :
% 0.30/0.55        ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.30/0.55       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.30/0.55         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_neg_pos
% 0.30/0.55  thf(fact_3569_mult__neg__pos,axiom,
% 0.30/0.55      ! [A: int,B: int] :
% 0.30/0.55        ( ( ord_less_int @ A @ zero_zero_int )
% 0.30/0.55       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.55         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_neg_pos
% 0.30/0.55  thf(fact_3570_mult__pos__neg,axiom,
% 0.30/0.55      ! [A: code_integer,B: code_integer] :
% 0.30/0.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.55       => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 0.30/0.55         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_pos_neg
% 0.30/0.55  thf(fact_3571_mult__pos__neg,axiom,
% 0.30/0.55      ! [A: rat,B: rat] :
% 0.30/0.55        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.55       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.30/0.55         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_pos_neg
% 0.30/0.55  thf(fact_3572_mult__pos__neg,axiom,
% 0.30/0.55      ! [A: nat,B: nat] :
% 0.30/0.55        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.55       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.30/0.55         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_pos_neg
% 0.30/0.55  thf(fact_3573_mult__pos__neg,axiom,
% 0.30/0.55      ! [A: int,B: int] :
% 0.30/0.55        ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.55       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.30/0.55         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_pos_neg
% 0.30/0.55  thf(fact_3574_mult__pos__pos,axiom,
% 0.30/0.55      ! [A: code_integer,B: code_integer] :
% 0.30/0.55        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.55       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.30/0.55         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_pos_pos
% 0.30/0.55  thf(fact_3575_mult__pos__pos,axiom,
% 0.30/0.55      ! [A: rat,B: rat] :
% 0.30/0.55        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.55       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.30/0.55         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.30/0.55  
% 0.30/0.55  % mult_pos_pos
% 0.30/0.55  thf(fact_3576_mult__pos__pos,axiom,
% 0.30/0.56      ! [A: nat,B: nat] :
% 0.30/0.56        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.56       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.30/0.56         => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_pos_pos
% 0.30/0.56  thf(fact_3577_mult__pos__pos,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.56       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.56         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_pos_pos
% 0.30/0.56  thf(fact_3578_mult__pos__neg2,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.56       => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 0.30/0.56         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ B @ A ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_pos_neg2
% 0.30/0.56  thf(fact_3579_mult__pos__neg2,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.56       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.30/0.56         => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_pos_neg2
% 0.30/0.56  thf(fact_3580_mult__pos__neg2,axiom,
% 0.30/0.56      ! [A: nat,B: nat] :
% 0.30/0.56        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.56       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.30/0.56         => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_pos_neg2
% 0.30/0.56  thf(fact_3581_mult__pos__neg2,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.56       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.30/0.56         => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_pos_neg2
% 0.30/0.56  thf(fact_3582_zero__less__mult__iff,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.30/0.56        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.56            & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) )
% 0.30/0.56          | ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.30/0.56            & ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_mult_iff
% 0.30/0.56  thf(fact_3583_zero__less__mult__iff,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.30/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.56            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 0.30/0.56          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.30/0.56            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_mult_iff
% 0.30/0.56  thf(fact_3584_zero__less__mult__iff,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.30/0.56        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.56            & ( ord_less_int @ zero_zero_int @ B ) )
% 0.30/0.56          | ( ( ord_less_int @ A @ zero_zero_int )
% 0.30/0.56            & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_mult_iff
% 0.30/0.56  thf(fact_3585_zero__less__mult__pos,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.30/0.56       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.56         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_mult_pos
% 0.30/0.56  thf(fact_3586_zero__less__mult__pos,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.30/0.56       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.56         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_mult_pos
% 0.30/0.56  thf(fact_3587_zero__less__mult__pos,axiom,
% 0.30/0.56      ! [A: nat,B: nat] :
% 0.30/0.56        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 0.30/0.56       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.56         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_mult_pos
% 0.30/0.56  thf(fact_3588_zero__less__mult__pos,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.30/0.56       => ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.56         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_mult_pos
% 0.30/0.56  thf(fact_3589_zero__less__mult__pos2,axiom,
% 0.30/0.56      ! [B: code_integer,A: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ B @ A ) )
% 0.30/0.56       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.56         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_mult_pos2
% 0.30/0.56  thf(fact_3590_zero__less__mult__pos2,axiom,
% 0.30/0.56      ! [B: rat,A: rat] :
% 0.30/0.56        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 0.30/0.56       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.56         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_mult_pos2
% 0.30/0.56  thf(fact_3591_zero__less__mult__pos2,axiom,
% 0.30/0.56      ! [B: nat,A: nat] :
% 0.30/0.56        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 0.30/0.56       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.56         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_mult_pos2
% 0.30/0.56  thf(fact_3592_zero__less__mult__pos2,axiom,
% 0.30/0.56      ! [B: int,A: int] :
% 0.30/0.56        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 0.30/0.56       => ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.56         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_mult_pos2
% 0.30/0.56  thf(fact_3593_mult__less__cancel__left__neg,axiom,
% 0.30/0.56      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.30/0.56       => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.30/0.56          = ( ord_le6747313008572928689nteger @ B @ A ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_less_cancel_left_neg
% 0.30/0.56  thf(fact_3594_mult__less__cancel__left__neg,axiom,
% 0.30/0.56      ! [C: rat,A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.30/0.56          = ( ord_less_rat @ B @ A ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_less_cancel_left_neg
% 0.30/0.56  thf(fact_3595_mult__less__cancel__left__neg,axiom,
% 0.30/0.56      ! [C: int,A: int,B: int] :
% 0.30/0.56        ( ( ord_less_int @ C @ zero_zero_int )
% 0.30/0.56       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.30/0.56          = ( ord_less_int @ B @ A ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_less_cancel_left_neg
% 0.30/0.56  thf(fact_3596_mult__less__cancel__left__pos,axiom,
% 0.30/0.56      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.56       => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.30/0.56          = ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_less_cancel_left_pos
% 0.30/0.56  thf(fact_3597_mult__less__cancel__left__pos,axiom,
% 0.30/0.56      ! [C: rat,A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.30/0.56          = ( ord_less_rat @ A @ B ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_less_cancel_left_pos
% 0.30/0.56  thf(fact_3598_mult__less__cancel__left__pos,axiom,
% 0.30/0.56      ! [C: int,A: int,B: int] :
% 0.30/0.56        ( ( ord_less_int @ zero_zero_int @ C )
% 0.30/0.56       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.30/0.56          = ( ord_less_int @ A @ B ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_less_cancel_left_pos
% 0.30/0.56  thf(fact_3599_mult__strict__left__mono__neg,axiom,
% 0.30/0.56      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ B @ A )
% 0.30/0.56       => ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.30/0.56         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_strict_left_mono_neg
% 0.30/0.56  thf(fact_3600_mult__strict__left__mono__neg,axiom,
% 0.30/0.56      ! [B: rat,A: rat,C: rat] :
% 0.30/0.56        ( ( ord_less_rat @ B @ A )
% 0.30/0.56       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_strict_left_mono_neg
% 0.30/0.56  thf(fact_3601_mult__strict__left__mono__neg,axiom,
% 0.30/0.56      ! [B: int,A: int,C: int] :
% 0.30/0.56        ( ( ord_less_int @ B @ A )
% 0.30/0.56       => ( ( ord_less_int @ C @ zero_zero_int )
% 0.30/0.56         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_strict_left_mono_neg
% 0.30/0.56  thf(fact_3602_mult__strict__left__mono,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.30/0.56       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.56         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_strict_left_mono
% 0.30/0.56  thf(fact_3603_mult__strict__left__mono,axiom,
% 0.30/0.56      ! [A: rat,B: rat,C: rat] :
% 0.30/0.56        ( ( ord_less_rat @ A @ B )
% 0.30/0.56       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_strict_left_mono
% 0.30/0.56  thf(fact_3604_mult__strict__left__mono,axiom,
% 0.30/0.56      ! [A: nat,B: nat,C: nat] :
% 0.30/0.56        ( ( ord_less_nat @ A @ B )
% 0.30/0.56       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.30/0.56         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_strict_left_mono
% 0.30/0.56  thf(fact_3605_mult__strict__left__mono,axiom,
% 0.30/0.56      ! [A: int,B: int,C: int] :
% 0.30/0.56        ( ( ord_less_int @ A @ B )
% 0.30/0.56       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.30/0.56         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_strict_left_mono
% 0.30/0.56  thf(fact_3606_mult__less__cancel__left__disj,axiom,
% 0.30/0.56      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.30/0.56        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.56            & ( ord_le6747313008572928689nteger @ A @ B ) )
% 0.30/0.56          | ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.30/0.56            & ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_less_cancel_left_disj
% 0.30/0.56  thf(fact_3607_mult__less__cancel__left__disj,axiom,
% 0.30/0.56      ! [C: rat,A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.30/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56            & ( ord_less_rat @ A @ B ) )
% 0.30/0.56          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_less_cancel_left_disj
% 0.30/0.56  thf(fact_3608_mult__less__cancel__left__disj,axiom,
% 0.30/0.56      ! [C: int,A: int,B: int] :
% 0.30/0.56        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.30/0.56        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.30/0.56            & ( ord_less_int @ A @ B ) )
% 0.30/0.56          | ( ( ord_less_int @ C @ zero_zero_int )
% 0.30/0.56            & ( ord_less_int @ B @ A ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_less_cancel_left_disj
% 0.30/0.56  thf(fact_3609_mult__strict__right__mono__neg,axiom,
% 0.30/0.56      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ B @ A )
% 0.30/0.56       => ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.30/0.56         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_strict_right_mono_neg
% 0.30/0.56  thf(fact_3610_mult__strict__right__mono__neg,axiom,
% 0.30/0.56      ! [B: rat,A: rat,C: rat] :
% 0.30/0.56        ( ( ord_less_rat @ B @ A )
% 0.30/0.56       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_strict_right_mono_neg
% 0.30/0.56  thf(fact_3611_mult__strict__right__mono__neg,axiom,
% 0.30/0.56      ! [B: int,A: int,C: int] :
% 0.30/0.56        ( ( ord_less_int @ B @ A )
% 0.30/0.56       => ( ( ord_less_int @ C @ zero_zero_int )
% 0.30/0.56         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_strict_right_mono_neg
% 0.30/0.56  thf(fact_3612_mult__strict__right__mono,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.30/0.56       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.56         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_strict_right_mono
% 0.30/0.56  thf(fact_3613_mult__strict__right__mono,axiom,
% 0.30/0.56      ! [A: rat,B: rat,C: rat] :
% 0.30/0.56        ( ( ord_less_rat @ A @ B )
% 0.30/0.56       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_strict_right_mono
% 0.30/0.56  thf(fact_3614_mult__strict__right__mono,axiom,
% 0.30/0.56      ! [A: nat,B: nat,C: nat] :
% 0.30/0.56        ( ( ord_less_nat @ A @ B )
% 0.30/0.56       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.30/0.56         => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_strict_right_mono
% 0.30/0.56  thf(fact_3615_mult__strict__right__mono,axiom,
% 0.30/0.56      ! [A: int,B: int,C: int] :
% 0.30/0.56        ( ( ord_less_int @ A @ B )
% 0.30/0.56       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.30/0.56         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_strict_right_mono
% 0.30/0.56  thf(fact_3616_mult__less__cancel__right__disj,axiom,
% 0.30/0.56      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.30/0.56        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.56            & ( ord_le6747313008572928689nteger @ A @ B ) )
% 0.30/0.56          | ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 0.30/0.56            & ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_less_cancel_right_disj
% 0.30/0.56  thf(fact_3617_mult__less__cancel__right__disj,axiom,
% 0.30/0.56      ! [A: rat,C: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.30/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56            & ( ord_less_rat @ A @ B ) )
% 0.30/0.56          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_less_cancel_right_disj
% 0.30/0.56  thf(fact_3618_mult__less__cancel__right__disj,axiom,
% 0.30/0.56      ! [A: int,C: int,B: int] :
% 0.30/0.56        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.30/0.56        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 0.30/0.56            & ( ord_less_int @ A @ B ) )
% 0.30/0.56          | ( ( ord_less_int @ C @ zero_zero_int )
% 0.30/0.56            & ( ord_less_int @ B @ A ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_less_cancel_right_disj
% 0.30/0.56  thf(fact_3619_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.30/0.56       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.56         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.30/0.56  thf(fact_3620_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.30/0.56      ! [A: rat,B: rat,C: rat] :
% 0.30/0.56        ( ( ord_less_rat @ A @ B )
% 0.30/0.56       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.30/0.56  thf(fact_3621_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.30/0.56      ! [A: nat,B: nat,C: nat] :
% 0.30/0.56        ( ( ord_less_nat @ A @ B )
% 0.30/0.56       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.30/0.56         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.30/0.56  thf(fact_3622_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.30/0.56      ! [A: int,B: int,C: int] :
% 0.30/0.56        ( ( ord_less_int @ A @ B )
% 0.30/0.56       => ( ( ord_less_int @ zero_zero_int @ C )
% 0.30/0.56         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.30/0.56  thf(fact_3623_zero__less__one,axiom,
% 0.30/0.56      ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_one
% 0.30/0.56  thf(fact_3624_zero__less__one,axiom,
% 0.30/0.56      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_one
% 0.30/0.56  thf(fact_3625_zero__less__one,axiom,
% 0.30/0.56      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_one
% 0.30/0.56  thf(fact_3626_zero__less__one,axiom,
% 0.30/0.56      ord_less_int @ zero_zero_int @ one_one_int ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_one
% 0.30/0.56  thf(fact_3627_not__one__less__zero,axiom,
% 0.30/0.56      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 0.30/0.56  
% 0.30/0.56  % not_one_less_zero
% 0.30/0.56  thf(fact_3628_not__one__less__zero,axiom,
% 0.30/0.56      ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 0.30/0.56  
% 0.30/0.56  % not_one_less_zero
% 0.30/0.56  thf(fact_3629_not__one__less__zero,axiom,
% 0.30/0.56      ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.30/0.56  
% 0.30/0.56  % not_one_less_zero
% 0.30/0.56  thf(fact_3630_not__one__less__zero,axiom,
% 0.30/0.56      ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 0.30/0.56  
% 0.30/0.56  % not_one_less_zero
% 0.30/0.56  thf(fact_3631_less__numeral__extra_I1_J,axiom,
% 0.30/0.56      ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 0.30/0.56  
% 0.30/0.56  % less_numeral_extra(1)
% 0.30/0.56  thf(fact_3632_less__numeral__extra_I1_J,axiom,
% 0.30/0.56      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 0.30/0.56  
% 0.30/0.56  % less_numeral_extra(1)
% 0.30/0.56  thf(fact_3633_less__numeral__extra_I1_J,axiom,
% 0.30/0.56      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.30/0.56  
% 0.30/0.56  % less_numeral_extra(1)
% 0.30/0.56  thf(fact_3634_less__numeral__extra_I1_J,axiom,
% 0.30/0.56      ord_less_int @ zero_zero_int @ one_one_int ).
% 0.30/0.56  
% 0.30/0.56  % less_numeral_extra(1)
% 0.30/0.56  thf(fact_3635_less__iff__diff__less__0,axiom,
% 0.30/0.56      ( ord_le6747313008572928689nteger
% 0.30/0.56      = ( ^ [A3: code_integer,B3: code_integer] : ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A3 @ B3 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_iff_diff_less_0
% 0.30/0.56  thf(fact_3636_less__iff__diff__less__0,axiom,
% 0.30/0.56      ( ord_less_rat
% 0.30/0.56      = ( ^ [A3: rat,B3: rat] : ( ord_less_rat @ ( minus_minus_rat @ A3 @ B3 ) @ zero_zero_rat ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_iff_diff_less_0
% 0.30/0.56  thf(fact_3637_less__iff__diff__less__0,axiom,
% 0.30/0.56      ( ord_less_int
% 0.30/0.56      = ( ^ [A3: int,B3: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B3 ) @ zero_zero_int ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_iff_diff_less_0
% 0.30/0.56  thf(fact_3638_not__numeral__less__one,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 0.30/0.56  
% 0.30/0.56  % not_numeral_less_one
% 0.30/0.56  thf(fact_3639_not__numeral__less__one,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 0.30/0.56  
% 0.30/0.56  % not_numeral_less_one
% 0.30/0.56  thf(fact_3640_not__numeral__less__one,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer ) ).
% 0.30/0.56  
% 0.30/0.56  % not_numeral_less_one
% 0.30/0.56  thf(fact_3641_not__numeral__less__one,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 0.30/0.56  
% 0.30/0.56  % not_numeral_less_one
% 0.30/0.56  thf(fact_3642_not__numeral__less__one,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ~ ( ord_le5570908160329646204atural @ ( numera5444537566228673987atural @ N ) @ one_one_Code_natural ) ).
% 0.30/0.56  
% 0.30/0.56  % not_numeral_less_one
% 0.30/0.56  thf(fact_3643_less__1__mult,axiom,
% 0.30/0.56      ! [M: code_integer,N: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ M )
% 0.30/0.56       => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ N )
% 0.30/0.56         => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ M @ N ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_1_mult
% 0.30/0.56  thf(fact_3644_less__1__mult,axiom,
% 0.30/0.56      ! [M: rat,N: rat] :
% 0.30/0.56        ( ( ord_less_rat @ one_one_rat @ M )
% 0.30/0.56       => ( ( ord_less_rat @ one_one_rat @ N )
% 0.30/0.56         => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_1_mult
% 0.30/0.56  thf(fact_3645_less__1__mult,axiom,
% 0.30/0.56      ! [M: nat,N: nat] :
% 0.30/0.56        ( ( ord_less_nat @ one_one_nat @ M )
% 0.30/0.56       => ( ( ord_less_nat @ one_one_nat @ N )
% 0.30/0.56         => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_1_mult
% 0.30/0.56  thf(fact_3646_less__1__mult,axiom,
% 0.30/0.56      ! [M: int,N: int] :
% 0.30/0.56        ( ( ord_less_int @ one_one_int @ M )
% 0.30/0.56       => ( ( ord_less_int @ one_one_int @ N )
% 0.30/0.56         => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_1_mult
% 0.30/0.56  thf(fact_3647_mult__mono,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.30/0.56       => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 0.30/0.56         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.30/0.56           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.56             => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_mono
% 0.30/0.56  thf(fact_3648_mult__mono,axiom,
% 0.30/0.56      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.56       => ( ( ord_less_eq_rat @ C @ D2 )
% 0.30/0.56         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.56           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.30/0.56             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_mono
% 0.30/0.56  thf(fact_3649_mult__mono,axiom,
% 0.30/0.56      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.30/0.56        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.56       => ( ( ord_less_eq_nat @ C @ D2 )
% 0.30/0.56         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.30/0.56           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.30/0.56             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_mono
% 0.30/0.56  thf(fact_3650_mult__mono,axiom,
% 0.30/0.56      ! [A: int,B: int,C: int,D2: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ A @ B )
% 0.30/0.56       => ( ( ord_less_eq_int @ C @ D2 )
% 0.30/0.56         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.30/0.56           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.30/0.56             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_mono
% 0.30/0.56  thf(fact_3651_mult__mono_H,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.30/0.56       => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 0.30/0.56         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.56           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.56             => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_mono'
% 0.30/0.56  thf(fact_3652_mult__mono_H,axiom,
% 0.30/0.56      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.56       => ( ( ord_less_eq_rat @ C @ D2 )
% 0.30/0.56         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.56           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.30/0.56             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_mono'
% 0.30/0.56  thf(fact_3653_mult__mono_H,axiom,
% 0.30/0.56      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.30/0.56        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.56       => ( ( ord_less_eq_nat @ C @ D2 )
% 0.30/0.56         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.56           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.30/0.56             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_mono'
% 0.30/0.56  thf(fact_3654_mult__mono_H,axiom,
% 0.30/0.56      ! [A: int,B: int,C: int,D2: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ A @ B )
% 0.30/0.56       => ( ( ord_less_eq_int @ C @ D2 )
% 0.30/0.56         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.56           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.30/0.56             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_mono'
% 0.30/0.56  thf(fact_3655_zero__le__square,axiom,
% 0.30/0.56      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ A ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_le_square
% 0.30/0.56  thf(fact_3656_zero__le__square,axiom,
% 0.30/0.56      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_le_square
% 0.30/0.56  thf(fact_3657_zero__le__square,axiom,
% 0.30/0.56      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_le_square
% 0.30/0.56  thf(fact_3658_split__mult__pos__le,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.56            & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) )
% 0.30/0.56          | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.30/0.56            & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 0.30/0.56       => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % split_mult_pos_le
% 0.30/0.56  thf(fact_3659_split__mult__pos__le,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.56            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.30/0.56          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.30/0.56            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 0.30/0.56       => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % split_mult_pos_le
% 0.30/0.56  thf(fact_3660_split__mult__pos__le,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.56            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 0.30/0.56          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.30/0.56            & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 0.30/0.56       => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % split_mult_pos_le
% 0.30/0.56  thf(fact_3661_mult__left__mono__neg,axiom,
% 0.30/0.56      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.30/0.56       => ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.30/0.56         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_left_mono_neg
% 0.30/0.56  thf(fact_3662_mult__left__mono__neg,axiom,
% 0.30/0.56      ! [B: rat,A: rat,C: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ B @ A )
% 0.30/0.56       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.30/0.56         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_left_mono_neg
% 0.30/0.56  thf(fact_3663_mult__left__mono__neg,axiom,
% 0.30/0.56      ! [B: int,A: int,C: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ B @ A )
% 0.30/0.56       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.30/0.56         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_left_mono_neg
% 0.30/0.56  thf(fact_3664_mult__nonpos__nonpos,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.30/0.56       => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 0.30/0.56         => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_nonpos_nonpos
% 0.30/0.56  thf(fact_3665_mult__nonpos__nonpos,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.30/0.56       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.30/0.56         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_nonpos_nonpos
% 0.30/0.56  thf(fact_3666_mult__nonpos__nonpos,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.30/0.56       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.30/0.56         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_nonpos_nonpos
% 0.30/0.56  thf(fact_3667_mult__left__mono,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.30/0.56       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.56         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_left_mono
% 0.30/0.56  thf(fact_3668_mult__left__mono,axiom,
% 0.30/0.56      ! [A: rat,B: rat,C: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.30/0.56         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_left_mono
% 0.30/0.56  thf(fact_3669_mult__left__mono,axiom,
% 0.30/0.56      ! [A: nat,B: nat,C: nat] :
% 0.30/0.56        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.56       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.30/0.56         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_left_mono
% 0.30/0.56  thf(fact_3670_mult__left__mono,axiom,
% 0.30/0.56      ! [A: int,B: int,C: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ A @ B )
% 0.30/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.30/0.56         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_left_mono
% 0.30/0.56  thf(fact_3671_mult__right__mono__neg,axiom,
% 0.30/0.56      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.30/0.56       => ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.30/0.56         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_right_mono_neg
% 0.30/0.56  thf(fact_3672_mult__right__mono__neg,axiom,
% 0.30/0.56      ! [B: rat,A: rat,C: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ B @ A )
% 0.30/0.56       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.30/0.56         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_right_mono_neg
% 0.30/0.56  thf(fact_3673_mult__right__mono__neg,axiom,
% 0.30/0.56      ! [B: int,A: int,C: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ B @ A )
% 0.30/0.56       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.30/0.56         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_right_mono_neg
% 0.30/0.56  thf(fact_3674_mult__right__mono,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.30/0.56       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.56         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_right_mono
% 0.30/0.56  thf(fact_3675_mult__right__mono,axiom,
% 0.30/0.56      ! [A: rat,B: rat,C: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.30/0.56         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_right_mono
% 0.30/0.56  thf(fact_3676_mult__right__mono,axiom,
% 0.30/0.56      ! [A: nat,B: nat,C: nat] :
% 0.30/0.56        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.56       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.30/0.56         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_right_mono
% 0.30/0.56  thf(fact_3677_mult__right__mono,axiom,
% 0.30/0.56      ! [A: int,B: int,C: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ A @ B )
% 0.30/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.30/0.56         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_right_mono
% 0.30/0.56  thf(fact_3678_mult__le__0__iff,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger )
% 0.30/0.56        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.56            & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) )
% 0.30/0.56          | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.30/0.56            & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_le_0_iff
% 0.30/0.56  thf(fact_3679_mult__le__0__iff,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 0.30/0.56        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.56            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.30/0.56          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.30/0.56            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_le_0_iff
% 0.30/0.56  thf(fact_3680_mult__le__0__iff,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 0.30/0.56        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.56            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 0.30/0.56          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.30/0.56            & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_le_0_iff
% 0.30/0.56  thf(fact_3681_split__mult__neg__le,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.56            & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) )
% 0.30/0.56          | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.30/0.56            & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) )
% 0.30/0.56       => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ).
% 0.30/0.56  
% 0.30/0.56  % split_mult_neg_le
% 0.30/0.56  thf(fact_3682_split__mult__neg__le,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.56            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.30/0.56          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.30/0.56            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 0.30/0.56       => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % split_mult_neg_le
% 0.30/0.56  thf(fact_3683_split__mult__neg__le,axiom,
% 0.30/0.56      ! [A: nat,B: nat] :
% 0.30/0.56        ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.56            & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 0.30/0.56          | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.30/0.56            & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 0.30/0.56       => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % split_mult_neg_le
% 0.30/0.56  thf(fact_3684_split__mult__neg__le,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.56            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 0.30/0.56          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.30/0.56            & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 0.30/0.56       => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 0.30/0.56  
% 0.30/0.56  % split_mult_neg_le
% 0.30/0.56  thf(fact_3685_mult__nonneg__nonneg,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.56       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.30/0.56         => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_nonneg_nonneg
% 0.30/0.56  thf(fact_3686_mult__nonneg__nonneg,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.56         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_nonneg_nonneg
% 0.30/0.56  thf(fact_3687_mult__nonneg__nonneg,axiom,
% 0.30/0.56      ! [A: nat,B: nat] :
% 0.30/0.56        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.56       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.30/0.56         => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_nonneg_nonneg
% 0.30/0.56  thf(fact_3688_mult__nonneg__nonneg,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.30/0.56         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_nonneg_nonneg
% 0.30/0.56  thf(fact_3689_mult__nonneg__nonpos,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.56       => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 0.30/0.56         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_nonneg_nonpos
% 0.30/0.56  thf(fact_3690_mult__nonneg__nonpos,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.56       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.30/0.56         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_nonneg_nonpos
% 0.30/0.56  thf(fact_3691_mult__nonneg__nonpos,axiom,
% 0.30/0.56      ! [A: nat,B: nat] :
% 0.30/0.56        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.56       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.30/0.56         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_nonneg_nonpos
% 0.30/0.56  thf(fact_3692_mult__nonneg__nonpos,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.56       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.30/0.56         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_nonneg_nonpos
% 0.30/0.56  thf(fact_3693_mult__nonpos__nonneg,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.30/0.56       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.30/0.56         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_nonpos_nonneg
% 0.30/0.56  thf(fact_3694_mult__nonpos__nonneg,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.30/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.56         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_nonpos_nonneg
% 0.30/0.56  thf(fact_3695_mult__nonpos__nonneg,axiom,
% 0.30/0.56      ! [A: nat,B: nat] :
% 0.30/0.56        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.30/0.56       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.30/0.56         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_nonpos_nonneg
% 0.30/0.56  thf(fact_3696_mult__nonpos__nonneg,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.30/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.30/0.56         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_nonpos_nonneg
% 0.30/0.56  thf(fact_3697_mult__nonneg__nonpos2,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.56       => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 0.30/0.56         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ B @ A ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_nonneg_nonpos2
% 0.30/0.56  thf(fact_3698_mult__nonneg__nonpos2,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.56       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.30/0.56         => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_nonneg_nonpos2
% 0.30/0.56  thf(fact_3699_mult__nonneg__nonpos2,axiom,
% 0.30/0.56      ! [A: nat,B: nat] :
% 0.30/0.56        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.56       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.30/0.56         => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_nonneg_nonpos2
% 0.30/0.56  thf(fact_3700_mult__nonneg__nonpos2,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.56       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.30/0.56         => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_nonneg_nonpos2
% 0.30/0.56  thf(fact_3701_zero__le__mult__iff,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.30/0.56        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.56            & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) )
% 0.30/0.56          | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.30/0.56            & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_le_mult_iff
% 0.30/0.56  thf(fact_3702_zero__le__mult__iff,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.30/0.56        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.56            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.30/0.56          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.30/0.56            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_le_mult_iff
% 0.30/0.56  thf(fact_3703_zero__le__mult__iff,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.30/0.56        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.56            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 0.30/0.56          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.30/0.56            & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_le_mult_iff
% 0.30/0.56  thf(fact_3704_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.30/0.56       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.56         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.30/0.56  thf(fact_3705_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.30/0.56      ! [A: rat,B: rat,C: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.30/0.56         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.30/0.56  thf(fact_3706_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.30/0.56      ! [A: nat,B: nat,C: nat] :
% 0.30/0.56        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.56       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.30/0.56         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.30/0.56  thf(fact_3707_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.30/0.56      ! [A: int,B: int,C: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ A @ B )
% 0.30/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.30/0.56         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % ordered_comm_semiring_class.comm_mult_left_mono
% 0.30/0.56  thf(fact_3708_zero__less__one__class_Ozero__le__one,axiom,
% 0.30/0.56      ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_one_class.zero_le_one
% 0.30/0.56  thf(fact_3709_zero__less__one__class_Ozero__le__one,axiom,
% 0.30/0.56      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_one_class.zero_le_one
% 0.30/0.56  thf(fact_3710_zero__less__one__class_Ozero__le__one,axiom,
% 0.30/0.56      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_one_class.zero_le_one
% 0.30/0.56  thf(fact_3711_zero__less__one__class_Ozero__le__one,axiom,
% 0.30/0.56      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_one_class.zero_le_one
% 0.30/0.56  thf(fact_3712_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.30/0.56      ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 0.30/0.56  
% 0.30/0.56  % linordered_nonzero_semiring_class.zero_le_one
% 0.30/0.56  thf(fact_3713_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.30/0.56      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 0.30/0.56  
% 0.30/0.56  % linordered_nonzero_semiring_class.zero_le_one
% 0.30/0.56  thf(fact_3714_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.30/0.56      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 0.30/0.56  
% 0.30/0.56  % linordered_nonzero_semiring_class.zero_le_one
% 0.30/0.56  thf(fact_3715_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.30/0.56      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.30/0.56  
% 0.30/0.56  % linordered_nonzero_semiring_class.zero_le_one
% 0.30/0.56  thf(fact_3716_not__one__le__zero,axiom,
% 0.30/0.56      ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 0.30/0.56  
% 0.30/0.56  % not_one_le_zero
% 0.30/0.56  thf(fact_3717_not__one__le__zero,axiom,
% 0.30/0.56      ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 0.30/0.56  
% 0.30/0.56  % not_one_le_zero
% 0.30/0.56  thf(fact_3718_not__one__le__zero,axiom,
% 0.30/0.56      ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.30/0.56  
% 0.30/0.56  % not_one_le_zero
% 0.30/0.56  thf(fact_3719_not__one__le__zero,axiom,
% 0.30/0.56      ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 0.30/0.56  
% 0.30/0.56  % not_one_le_zero
% 0.30/0.56  thf(fact_3720_le__iff__diff__le__0,axiom,
% 0.30/0.56      ( ord_le3102999989581377725nteger
% 0.30/0.56      = ( ^ [A3: code_integer,B3: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A3 @ B3 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % le_iff_diff_le_0
% 0.30/0.56  thf(fact_3721_le__iff__diff__le__0,axiom,
% 0.30/0.56      ( ord_less_eq_rat
% 0.30/0.56      = ( ^ [A3: rat,B3: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A3 @ B3 ) @ zero_zero_rat ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % le_iff_diff_le_0
% 0.30/0.56  thf(fact_3722_le__iff__diff__le__0,axiom,
% 0.30/0.56      ( ord_less_eq_int
% 0.30/0.56      = ( ^ [A3: int,B3: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B3 ) @ zero_zero_int ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % le_iff_diff_le_0
% 0.30/0.56  thf(fact_3723_not__numeral__less__neg__numeral,axiom,
% 0.30/0.56      ! [M: num,N: num] :
% 0.30/0.56        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_numeral_less_neg_numeral
% 0.30/0.56  thf(fact_3724_not__numeral__less__neg__numeral,axiom,
% 0.30/0.56      ! [M: num,N: num] :
% 0.30/0.56        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_numeral_less_neg_numeral
% 0.30/0.56  thf(fact_3725_not__numeral__less__neg__numeral,axiom,
% 0.30/0.56      ! [M: num,N: num] :
% 0.30/0.56        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_numeral_less_neg_numeral
% 0.30/0.56  thf(fact_3726_neg__numeral__less__numeral,axiom,
% 0.30/0.56      ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_less_numeral
% 0.30/0.56  thf(fact_3727_neg__numeral__less__numeral,axiom,
% 0.30/0.56      ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_less_numeral
% 0.30/0.56  thf(fact_3728_neg__numeral__less__numeral,axiom,
% 0.30/0.56      ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_less_numeral
% 0.30/0.56  thf(fact_3729_less__minus__one__simps_I4_J,axiom,
% 0.30/0.56      ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_minus_one_simps(4)
% 0.30/0.56  thf(fact_3730_less__minus__one__simps_I4_J,axiom,
% 0.30/0.56      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_minus_one_simps(4)
% 0.30/0.56  thf(fact_3731_less__minus__one__simps_I4_J,axiom,
% 0.30/0.56      ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_minus_one_simps(4)
% 0.30/0.56  thf(fact_3732_less__minus__one__simps_I2_J,axiom,
% 0.30/0.56      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.30/0.56  
% 0.30/0.56  % less_minus_one_simps(2)
% 0.30/0.56  thf(fact_3733_less__minus__one__simps_I2_J,axiom,
% 0.30/0.56      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 0.30/0.56  
% 0.30/0.56  % less_minus_one_simps(2)
% 0.30/0.56  thf(fact_3734_less__minus__one__simps_I2_J,axiom,
% 0.30/0.56      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 0.30/0.56  
% 0.30/0.56  % less_minus_one_simps(2)
% 0.30/0.56  thf(fact_3735_one__le__numeral,axiom,
% 0.30/0.56      ! [N: num] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) ) ).
% 0.30/0.56  
% 0.30/0.56  % one_le_numeral
% 0.30/0.56  thf(fact_3736_one__le__numeral,axiom,
% 0.30/0.56      ! [N: num] : ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N ) ) ).
% 0.30/0.56  
% 0.30/0.56  % one_le_numeral
% 0.30/0.56  thf(fact_3737_one__le__numeral,axiom,
% 0.30/0.56      ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 0.30/0.56  
% 0.30/0.56  % one_le_numeral
% 0.30/0.56  thf(fact_3738_one__le__numeral,axiom,
% 0.30/0.56      ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 0.30/0.56  
% 0.30/0.56  % one_le_numeral
% 0.30/0.56  thf(fact_3739_one__le__numeral,axiom,
% 0.30/0.56      ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 0.30/0.56  
% 0.30/0.56  % one_le_numeral
% 0.30/0.56  thf(fact_3740_diff__shunt__var,axiom,
% 0.30/0.56      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.30/0.56        ( ( ( minus_1356011639430497352at_nat @ X @ Y )
% 0.30/0.56          = bot_bo2099793752762293965at_nat )
% 0.30/0.56        = ( ord_le3146513528884898305at_nat @ X @ Y ) ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_shunt_var
% 0.30/0.56  thf(fact_3741_diff__shunt__var,axiom,
% 0.30/0.56      ! [X: set_o,Y: set_o] :
% 0.30/0.56        ( ( ( minus_minus_set_o @ X @ Y )
% 0.30/0.56          = bot_bot_set_o )
% 0.30/0.56        = ( ord_less_eq_set_o @ X @ Y ) ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_shunt_var
% 0.30/0.56  thf(fact_3742_diff__shunt__var,axiom,
% 0.30/0.56      ! [X: set_int,Y: set_int] :
% 0.30/0.56        ( ( ( minus_minus_set_int @ X @ Y )
% 0.30/0.56          = bot_bot_set_int )
% 0.30/0.56        = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_shunt_var
% 0.30/0.56  thf(fact_3743_diff__shunt__var,axiom,
% 0.30/0.56      ! [X: set_nat,Y: set_nat] :
% 0.30/0.56        ( ( ( minus_minus_set_nat @ X @ Y )
% 0.30/0.56          = bot_bot_set_nat )
% 0.30/0.56        = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_shunt_var
% 0.30/0.56  thf(fact_3744_not__numeral__le__neg__numeral,axiom,
% 0.30/0.56      ! [M: num,N: num] :
% 0.30/0.56        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_numeral_le_neg_numeral
% 0.30/0.56  thf(fact_3745_not__numeral__le__neg__numeral,axiom,
% 0.30/0.56      ! [M: num,N: num] :
% 0.30/0.56        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_numeral_le_neg_numeral
% 0.30/0.56  thf(fact_3746_not__numeral__le__neg__numeral,axiom,
% 0.30/0.56      ! [M: num,N: num] :
% 0.30/0.56        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_numeral_le_neg_numeral
% 0.30/0.56  thf(fact_3747_neg__numeral__le__numeral,axiom,
% 0.30/0.56      ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_le_numeral
% 0.30/0.56  thf(fact_3748_neg__numeral__le__numeral,axiom,
% 0.30/0.56      ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_le_numeral
% 0.30/0.56  thf(fact_3749_neg__numeral__le__numeral,axiom,
% 0.30/0.56      ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_le_numeral
% 0.30/0.56  thf(fact_3750_le__minus__one__simps_I4_J,axiom,
% 0.30/0.56      ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.30/0.56  
% 0.30/0.56  % le_minus_one_simps(4)
% 0.30/0.56  thf(fact_3751_le__minus__one__simps_I4_J,axiom,
% 0.30/0.56      ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % le_minus_one_simps(4)
% 0.30/0.56  thf(fact_3752_le__minus__one__simps_I4_J,axiom,
% 0.30/0.56      ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.30/0.56  
% 0.30/0.56  % le_minus_one_simps(4)
% 0.30/0.56  thf(fact_3753_le__minus__one__simps_I2_J,axiom,
% 0.30/0.56      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 0.30/0.56  
% 0.30/0.56  % le_minus_one_simps(2)
% 0.30/0.56  thf(fact_3754_le__minus__one__simps_I2_J,axiom,
% 0.30/0.56      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 0.30/0.56  
% 0.30/0.56  % le_minus_one_simps(2)
% 0.30/0.56  thf(fact_3755_le__minus__one__simps_I2_J,axiom,
% 0.30/0.56      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.30/0.56  
% 0.30/0.56  % le_minus_one_simps(2)
% 0.30/0.56  thf(fact_3756_disjoint__alt__simp3,axiom,
% 0.30/0.56      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.56        ( ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) @ A2 )
% 0.30/0.56        = ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 0.30/0.56         != bot_bo2099793752762293965at_nat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % disjoint_alt_simp3
% 0.30/0.56  thf(fact_3757_disjoint__alt__simp3,axiom,
% 0.30/0.56      ! [A2: set_o,B2: set_o] :
% 0.30/0.56        ( ( ord_less_set_o @ ( minus_minus_set_o @ A2 @ B2 ) @ A2 )
% 0.30/0.56        = ( ( inf_inf_set_o @ A2 @ B2 )
% 0.30/0.56         != bot_bot_set_o ) ) ).
% 0.30/0.56  
% 0.30/0.56  % disjoint_alt_simp3
% 0.30/0.56  thf(fact_3758_disjoint__alt__simp3,axiom,
% 0.30/0.56      ! [A2: set_int,B2: set_int] :
% 0.30/0.56        ( ( ord_less_set_int @ ( minus_minus_set_int @ A2 @ B2 ) @ A2 )
% 0.30/0.56        = ( ( inf_inf_set_int @ A2 @ B2 )
% 0.30/0.56         != bot_bot_set_int ) ) ).
% 0.30/0.56  
% 0.30/0.56  % disjoint_alt_simp3
% 0.30/0.56  thf(fact_3759_disjoint__alt__simp3,axiom,
% 0.30/0.56      ! [A2: set_nat,B2: set_nat] :
% 0.30/0.56        ( ( ord_less_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ A2 )
% 0.30/0.56        = ( ( inf_inf_set_nat @ A2 @ B2 )
% 0.30/0.56         != bot_bot_set_nat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % disjoint_alt_simp3
% 0.30/0.56  thf(fact_3760_distrib__inf__le,axiom,
% 0.30/0.56      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) @ ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_inf_le
% 0.30/0.56  thf(fact_3761_distrib__inf__le,axiom,
% 0.30/0.56      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ ( inf_in3604695632404883862_int_o @ X @ Z ) ) @ ( inf_in3604695632404883862_int_o @ X @ ( sup_su8463660629351352368_int_o @ Y @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_inf_le
% 0.30/0.56  thf(fact_3762_distrib__inf__le,axiom,
% 0.30/0.56      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] : ( ord_le4796328588573674190char_o @ ( sup_sup_list_char_o @ ( inf_inf_list_char_o @ X @ Y ) @ ( inf_inf_list_char_o @ X @ Z ) ) @ ( inf_inf_list_char_o @ X @ ( sup_sup_list_char_o @ Y @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_inf_le
% 0.30/0.56  thf(fact_3763_distrib__inf__le,axiom,
% 0.30/0.56      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) @ ( inf_in1697001100524423349at_nat @ X @ Z ) ) @ ( inf_in1697001100524423349at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_inf_le
% 0.30/0.56  thf(fact_3764_distrib__inf__le,axiom,
% 0.30/0.56      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ ( inf_in7913087082777306421at_nat @ X @ Z ) ) @ ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_inf_le
% 0.30/0.56  thf(fact_3765_distrib__inf__le,axiom,
% 0.30/0.56      ! [X: filter_nat,Y: filter_nat,Z: filter_nat] : ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ ( inf_inf_filter_nat @ X @ Y ) @ ( inf_inf_filter_nat @ X @ Z ) ) @ ( inf_inf_filter_nat @ X @ ( sup_sup_filter_nat @ Y @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_inf_le
% 0.30/0.56  thf(fact_3766_distrib__inf__le,axiom,
% 0.30/0.56      ! [X: set_nat,Y: set_nat,Z: set_nat] : ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z ) ) @ ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_inf_le
% 0.30/0.56  thf(fact_3767_distrib__inf__le,axiom,
% 0.30/0.56      ! [X: rat,Y: rat,Z: rat] : ( ord_less_eq_rat @ ( sup_sup_rat @ ( inf_inf_rat @ X @ Y ) @ ( inf_inf_rat @ X @ Z ) ) @ ( inf_inf_rat @ X @ ( sup_sup_rat @ Y @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_inf_le
% 0.30/0.56  thf(fact_3768_distrib__inf__le,axiom,
% 0.30/0.56      ! [X: nat,Y: nat,Z: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z ) ) @ ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_inf_le
% 0.30/0.56  thf(fact_3769_distrib__inf__le,axiom,
% 0.30/0.56      ! [X: int,Y: int,Z: int] : ( ord_less_eq_int @ ( sup_sup_int @ ( inf_inf_int @ X @ Y ) @ ( inf_inf_int @ X @ Z ) ) @ ( inf_inf_int @ X @ ( sup_sup_int @ Y @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_inf_le
% 0.30/0.56  thf(fact_3770_distrib__sup__le,axiom,
% 0.30/0.56      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) ) @ ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_sup_le
% 0.30/0.56  thf(fact_3771_distrib__sup__le,axiom,
% 0.30/0.56      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( sup_su8463660629351352368_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) ) @ ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ X @ Y ) @ ( sup_su8463660629351352368_int_o @ X @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_sup_le
% 0.30/0.56  thf(fact_3772_distrib__sup__le,axiom,
% 0.30/0.56      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] : ( ord_le4796328588573674190char_o @ ( sup_sup_list_char_o @ X @ ( inf_inf_list_char_o @ Y @ Z ) ) @ ( inf_inf_list_char_o @ ( sup_sup_list_char_o @ X @ Y ) @ ( sup_sup_list_char_o @ X @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_sup_le
% 0.30/0.56  thf(fact_3773_distrib__sup__le,axiom,
% 0.30/0.56      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ X @ ( inf_in1697001100524423349at_nat @ Y @ Z ) ) @ ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ ( sup_su3035147773818789531at_nat @ X @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_sup_le
% 0.30/0.56  thf(fact_3774_distrib__sup__le,axiom,
% 0.30/0.56      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ Y @ Z ) ) @ ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_sup_le
% 0.30/0.56  thf(fact_3775_distrib__sup__le,axiom,
% 0.30/0.56      ! [X: filter_nat,Y: filter_nat,Z: filter_nat] : ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ X @ ( inf_inf_filter_nat @ Y @ Z ) ) @ ( inf_inf_filter_nat @ ( sup_sup_filter_nat @ X @ Y ) @ ( sup_sup_filter_nat @ X @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_sup_le
% 0.30/0.56  thf(fact_3776_distrib__sup__le,axiom,
% 0.30/0.56      ! [X: set_nat,Y: set_nat,Z: set_nat] : ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) ) @ ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_sup_le
% 0.30/0.56  thf(fact_3777_distrib__sup__le,axiom,
% 0.30/0.56      ! [X: rat,Y: rat,Z: rat] : ( ord_less_eq_rat @ ( sup_sup_rat @ X @ ( inf_inf_rat @ Y @ Z ) ) @ ( inf_inf_rat @ ( sup_sup_rat @ X @ Y ) @ ( sup_sup_rat @ X @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_sup_le
% 0.30/0.56  thf(fact_3778_distrib__sup__le,axiom,
% 0.30/0.56      ! [X: nat,Y: nat,Z: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) @ ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_sup_le
% 0.30/0.56  thf(fact_3779_distrib__sup__le,axiom,
% 0.30/0.56      ! [X: int,Y: int,Z: int] : ( ord_less_eq_int @ ( sup_sup_int @ X @ ( inf_inf_int @ Y @ Z ) ) @ ( inf_inf_int @ ( sup_sup_int @ X @ Y ) @ ( sup_sup_int @ X @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_sup_le
% 0.30/0.56  thf(fact_3780_disjoint__mono,axiom,
% 0.30/0.56      ! [A: set_Pr1261947904930325089at_nat,A5: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.30/0.56        ( ( ord_le3146513528884898305at_nat @ A @ A5 )
% 0.30/0.56       => ( ( ord_le3146513528884898305at_nat @ B @ B5 )
% 0.30/0.56         => ( ( ( inf_in2572325071724192079at_nat @ A5 @ B5 )
% 0.30/0.56              = bot_bo2099793752762293965at_nat )
% 0.30/0.56           => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 0.30/0.56              = bot_bo2099793752762293965at_nat ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % disjoint_mono
% 0.30/0.56  thf(fact_3781_disjoint__mono,axiom,
% 0.30/0.56      ! [A: set_o,A5: set_o,B: set_o,B5: set_o] :
% 0.30/0.56        ( ( ord_less_eq_set_o @ A @ A5 )
% 0.30/0.56       => ( ( ord_less_eq_set_o @ B @ B5 )
% 0.30/0.56         => ( ( ( inf_inf_set_o @ A5 @ B5 )
% 0.30/0.56              = bot_bot_set_o )
% 0.30/0.56           => ( ( inf_inf_set_o @ A @ B )
% 0.30/0.56              = bot_bot_set_o ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % disjoint_mono
% 0.30/0.56  thf(fact_3782_disjoint__mono,axiom,
% 0.30/0.56      ! [A: set_int,A5: set_int,B: set_int,B5: set_int] :
% 0.30/0.56        ( ( ord_less_eq_set_int @ A @ A5 )
% 0.30/0.56       => ( ( ord_less_eq_set_int @ B @ B5 )
% 0.30/0.56         => ( ( ( inf_inf_set_int @ A5 @ B5 )
% 0.30/0.56              = bot_bot_set_int )
% 0.30/0.56           => ( ( inf_inf_set_int @ A @ B )
% 0.30/0.56              = bot_bot_set_int ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % disjoint_mono
% 0.30/0.56  thf(fact_3783_disjoint__mono,axiom,
% 0.30/0.56      ! [A: set_nat,A5: set_nat,B: set_nat,B5: set_nat] :
% 0.30/0.56        ( ( ord_less_eq_set_nat @ A @ A5 )
% 0.30/0.56       => ( ( ord_less_eq_set_nat @ B @ B5 )
% 0.30/0.56         => ( ( ( inf_inf_set_nat @ A5 @ B5 )
% 0.30/0.56              = bot_bot_set_nat )
% 0.30/0.56           => ( ( inf_inf_set_nat @ A @ B )
% 0.30/0.56              = bot_bot_set_nat ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % disjoint_mono
% 0.30/0.56  thf(fact_3784_Un__Int__assoc__eq,axiom,
% 0.30/0.56      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 0.30/0.56        ( ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ C2 )
% 0.30/0.56          = ( inf_in2572325071724192079at_nat @ A2 @ ( sup_su6327502436637775413at_nat @ B2 @ C2 ) ) )
% 0.30/0.56        = ( ord_le3146513528884898305at_nat @ C2 @ A2 ) ) ).
% 0.30/0.56  
% 0.30/0.56  % Un_Int_assoc_eq
% 0.30/0.56  thf(fact_3785_Un__Int__assoc__eq,axiom,
% 0.30/0.56      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 0.30/0.56        ( ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) @ C2 )
% 0.30/0.56          = ( inf_in1697001100524423349at_nat @ A2 @ ( sup_su3035147773818789531at_nat @ B2 @ C2 ) ) )
% 0.30/0.56        = ( ord_le8081472938463900775at_nat @ C2 @ A2 ) ) ).
% 0.30/0.56  
% 0.30/0.56  % Un_Int_assoc_eq
% 0.30/0.56  thf(fact_3786_Un__Int__assoc__eq,axiom,
% 0.30/0.56      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 0.30/0.56        ( ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) @ C2 )
% 0.30/0.56          = ( inf_in7913087082777306421at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) ) )
% 0.30/0.56        = ( ord_le1268244103169919719at_nat @ C2 @ A2 ) ) ).
% 0.30/0.56  
% 0.30/0.56  % Un_Int_assoc_eq
% 0.30/0.56  thf(fact_3787_Un__Int__assoc__eq,axiom,
% 0.30/0.56      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 0.30/0.56        ( ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ C2 )
% 0.30/0.56          = ( inf_inf_set_nat @ A2 @ ( sup_sup_set_nat @ B2 @ C2 ) ) )
% 0.30/0.56        = ( ord_less_eq_set_nat @ C2 @ A2 ) ) ).
% 0.30/0.56  
% 0.30/0.56  % Un_Int_assoc_eq
% 0.30/0.56  thf(fact_3788_subset__Compl__self__eq,axiom,
% 0.30/0.56      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.30/0.56        ( ( ord_le3146513528884898305at_nat @ A2 @ ( uminus6524753893492686040at_nat @ A2 ) )
% 0.30/0.56        = ( A2 = bot_bo2099793752762293965at_nat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % subset_Compl_self_eq
% 0.30/0.56  thf(fact_3789_subset__Compl__self__eq,axiom,
% 0.30/0.56      ! [A2: set_o] :
% 0.30/0.56        ( ( ord_less_eq_set_o @ A2 @ ( uminus_uminus_set_o @ A2 ) )
% 0.30/0.56        = ( A2 = bot_bot_set_o ) ) ).
% 0.30/0.56  
% 0.30/0.56  % subset_Compl_self_eq
% 0.30/0.56  thf(fact_3790_subset__Compl__self__eq,axiom,
% 0.30/0.56      ! [A2: set_int] :
% 0.30/0.56        ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ A2 ) )
% 0.30/0.56        = ( A2 = bot_bot_set_int ) ) ).
% 0.30/0.56  
% 0.30/0.56  % subset_Compl_self_eq
% 0.30/0.56  thf(fact_3791_subset__Compl__self__eq,axiom,
% 0.30/0.56      ! [A2: set_nat] :
% 0.30/0.56        ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ A2 ) )
% 0.30/0.56        = ( A2 = bot_bot_set_nat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % subset_Compl_self_eq
% 0.30/0.56  thf(fact_3792_le__divide__eq__numeral_I2_J,axiom,
% 0.30/0.56      ! [W: num,B: rat,C: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 0.30/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56           => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 0.30/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.30/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % le_divide_eq_numeral(2)
% 0.30/0.56  thf(fact_3793_divide__le__eq__numeral_I2_J,axiom,
% 0.30/0.56      ! [B: rat,C: rat,W: num] :
% 0.30/0.56        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 0.30/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 0.30/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56               => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 0.30/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56               => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % divide_le_eq_numeral(2)
% 0.30/0.56  thf(fact_3794_in__range__subset,axiom,
% 0.30/0.56      ! [As: set_nat,As3: set_nat,H3: heap_e7401611519738050253t_unit] :
% 0.30/0.56        ( ( ord_less_eq_set_nat @ As @ As3 )
% 0.30/0.56       => ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 0.30/0.56         => ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % in_range_subset
% 0.30/0.56  thf(fact_3795_not__zero__less__neg__numeral,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_zero_less_neg_numeral
% 0.30/0.56  thf(fact_3796_not__zero__less__neg__numeral,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_zero_less_neg_numeral
% 0.30/0.56  thf(fact_3797_not__zero__less__neg__numeral,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_zero_less_neg_numeral
% 0.30/0.56  thf(fact_3798_neg__numeral__less__zero,axiom,
% 0.30/0.56      ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_less_zero
% 0.30/0.56  thf(fact_3799_neg__numeral__less__zero,axiom,
% 0.30/0.56      ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_less_zero
% 0.30/0.56  thf(fact_3800_neg__numeral__less__zero,axiom,
% 0.30/0.56      ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_less_zero
% 0.30/0.56  thf(fact_3801_less__minus__one__simps_I3_J,axiom,
% 0.30/0.56      ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_minus_one_simps(3)
% 0.30/0.56  thf(fact_3802_less__minus__one__simps_I3_J,axiom,
% 0.30/0.56      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_minus_one_simps(3)
% 0.30/0.56  thf(fact_3803_less__minus__one__simps_I3_J,axiom,
% 0.30/0.56      ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_minus_one_simps(3)
% 0.30/0.56  thf(fact_3804_less__minus__one__simps_I1_J,axiom,
% 0.30/0.56      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 0.30/0.56  
% 0.30/0.56  % less_minus_one_simps(1)
% 0.30/0.56  thf(fact_3805_less__minus__one__simps_I1_J,axiom,
% 0.30/0.56      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 0.30/0.56  
% 0.30/0.56  % less_minus_one_simps(1)
% 0.30/0.56  thf(fact_3806_less__minus__one__simps_I1_J,axiom,
% 0.30/0.56      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 0.30/0.56  
% 0.30/0.56  % less_minus_one_simps(1)
% 0.30/0.56  thf(fact_3807_divide__less__eq,axiom,
% 0.30/0.56      ! [B: rat,C: rat,A: rat] :
% 0.30/0.56        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.30/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56           => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.30/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.30/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % divide_less_eq
% 0.30/0.56  thf(fact_3808_less__divide__eq,axiom,
% 0.30/0.56      ! [A: rat,B: rat,C: rat] :
% 0.30/0.56        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.30/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 0.30/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56               => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 0.30/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_divide_eq
% 0.30/0.56  thf(fact_3809_neg__divide__less__eq,axiom,
% 0.30/0.56      ! [C: rat,B: rat,A: rat] :
% 0.30/0.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.30/0.56          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_divide_less_eq
% 0.30/0.56  thf(fact_3810_neg__less__divide__eq,axiom,
% 0.30/0.56      ! [C: rat,A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.30/0.56          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_less_divide_eq
% 0.30/0.56  thf(fact_3811_pos__divide__less__eq,axiom,
% 0.30/0.56      ! [C: rat,B: rat,A: rat] :
% 0.30/0.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 0.30/0.56          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % pos_divide_less_eq
% 0.30/0.56  thf(fact_3812_pos__less__divide__eq,axiom,
% 0.30/0.56      ! [C: rat,A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 0.30/0.56          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % pos_less_divide_eq
% 0.30/0.56  thf(fact_3813_mult__imp__div__pos__less,axiom,
% 0.30/0.56      ! [Y: rat,X: rat,Z: rat] :
% 0.30/0.56        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.30/0.56       => ( ( ord_less_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 0.30/0.56         => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_imp_div_pos_less
% 0.30/0.56  thf(fact_3814_mult__imp__less__div__pos,axiom,
% 0.30/0.56      ! [Y: rat,Z: rat,X: rat] :
% 0.30/0.56        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.30/0.56       => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 0.30/0.56         => ( ord_less_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_imp_less_div_pos
% 0.30/0.56  thf(fact_3815_divide__strict__left__mono,axiom,
% 0.30/0.56      ! [B: rat,A: rat,C: rat] :
% 0.30/0.56        ( ( ord_less_rat @ B @ A )
% 0.30/0.56       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.30/0.56           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % divide_strict_left_mono
% 0.30/0.56  thf(fact_3816_divide__strict__left__mono__neg,axiom,
% 0.30/0.56      ! [A: rat,B: rat,C: rat] :
% 0.30/0.56        ( ( ord_less_rat @ A @ B )
% 0.30/0.56       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.30/0.56           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % divide_strict_left_mono_neg
% 0.30/0.56  thf(fact_3817_divide__less__eq__1,axiom,
% 0.30/0.56      ! [B: rat,A: rat] :
% 0.30/0.56        ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.30/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.56            & ( ord_less_rat @ B @ A ) )
% 0.30/0.56          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.30/0.56            & ( ord_less_rat @ A @ B ) )
% 0.30/0.56          | ( A = zero_zero_rat ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % divide_less_eq_1
% 0.30/0.56  thf(fact_3818_less__divide__eq__1,axiom,
% 0.30/0.56      ! [B: rat,A: rat] :
% 0.30/0.56        ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.30/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.56            & ( ord_less_rat @ A @ B ) )
% 0.30/0.56          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.30/0.56            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_divide_eq_1
% 0.30/0.56  thf(fact_3819_neg__numeral__less__one,axiom,
% 0.30/0.56      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_less_one
% 0.30/0.56  thf(fact_3820_neg__numeral__less__one,axiom,
% 0.30/0.56      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_less_one
% 0.30/0.56  thf(fact_3821_neg__numeral__less__one,axiom,
% 0.30/0.56      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_less_one
% 0.30/0.56  thf(fact_3822_neg__one__less__numeral,axiom,
% 0.30/0.56      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_one_less_numeral
% 0.30/0.56  thf(fact_3823_neg__one__less__numeral,axiom,
% 0.30/0.56      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_one_less_numeral
% 0.30/0.56  thf(fact_3824_neg__one__less__numeral,axiom,
% 0.30/0.56      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_one_less_numeral
% 0.30/0.56  thf(fact_3825_not__numeral__less__neg__one,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_numeral_less_neg_one
% 0.30/0.56  thf(fact_3826_not__numeral__less__neg__one,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_numeral_less_neg_one
% 0.30/0.56  thf(fact_3827_not__numeral__less__neg__one,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_numeral_less_neg_one
% 0.30/0.56  thf(fact_3828_not__one__less__neg__numeral,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_one_less_neg_numeral
% 0.30/0.56  thf(fact_3829_not__one__less__neg__numeral,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_one_less_neg_numeral
% 0.30/0.56  thf(fact_3830_not__one__less__neg__numeral,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_one_less_neg_numeral
% 0.30/0.56  thf(fact_3831_not__neg__one__less__neg__numeral,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_neg_one_less_neg_numeral
% 0.30/0.56  thf(fact_3832_not__neg__one__less__neg__numeral,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_neg_one_less_neg_numeral
% 0.30/0.56  thf(fact_3833_not__neg__one__less__neg__numeral,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_neg_one_less_neg_numeral
% 0.30/0.56  thf(fact_3834_mult__left__le__one__le,axiom,
% 0.30/0.56      ! [X: code_integer,Y: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 0.30/0.56       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 0.30/0.56         => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 0.30/0.56           => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Y @ X ) @ X ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_left_le_one_le
% 0.30/0.56  thf(fact_3835_mult__left__le__one__le,axiom,
% 0.30/0.56      ! [X: rat,Y: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.30/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.30/0.56         => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 0.30/0.56           => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_left_le_one_le
% 0.30/0.56  thf(fact_3836_mult__left__le__one__le,axiom,
% 0.30/0.56      ! [X: int,Y: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.30/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.30/0.56         => ( ( ord_less_eq_int @ Y @ one_one_int )
% 0.30/0.56           => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_left_le_one_le
% 0.30/0.56  thf(fact_3837_mult__right__le__one__le,axiom,
% 0.30/0.56      ! [X: code_integer,Y: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 0.30/0.56       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 0.30/0.56         => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 0.30/0.56           => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X @ Y ) @ X ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_right_le_one_le
% 0.30/0.56  thf(fact_3838_mult__right__le__one__le,axiom,
% 0.30/0.56      ! [X: rat,Y: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.30/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.30/0.56         => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 0.30/0.56           => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_right_le_one_le
% 0.30/0.56  thf(fact_3839_mult__right__le__one__le,axiom,
% 0.30/0.56      ! [X: int,Y: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.30/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.30/0.56         => ( ( ord_less_eq_int @ Y @ one_one_int )
% 0.30/0.56           => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_right_le_one_le
% 0.30/0.56  thf(fact_3840_mult__le__one,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 0.30/0.56       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.30/0.56         => ( ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer )
% 0.30/0.56           => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_le_one
% 0.30/0.56  thf(fact_3841_mult__le__one,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.30/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.56         => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 0.30/0.56           => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_le_one
% 0.30/0.56  thf(fact_3842_mult__le__one,axiom,
% 0.30/0.56      ! [A: nat,B: nat] :
% 0.30/0.56        ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.30/0.56       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.30/0.56         => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 0.30/0.56           => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_le_one
% 0.30/0.56  thf(fact_3843_mult__le__one,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ A @ one_one_int )
% 0.30/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.30/0.56         => ( ( ord_less_eq_int @ B @ one_one_int )
% 0.30/0.56           => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_le_one
% 0.30/0.56  thf(fact_3844_mult__left__le,axiom,
% 0.30/0.56      ! [C: code_integer,A: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ C @ one_one_Code_integer )
% 0.30/0.56       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.56         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ A ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_left_le
% 0.30/0.56  thf(fact_3845_mult__left__le,axiom,
% 0.30/0.56      ! [C: rat,A: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ C @ one_one_rat )
% 0.30/0.56       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.56         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_left_le
% 0.30/0.56  thf(fact_3846_mult__left__le,axiom,
% 0.30/0.56      ! [C: nat,A: nat] :
% 0.30/0.56        ( ( ord_less_eq_nat @ C @ one_one_nat )
% 0.30/0.56       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.56         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_left_le
% 0.30/0.56  thf(fact_3847_mult__left__le,axiom,
% 0.30/0.56      ! [C: int,A: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ C @ one_one_int )
% 0.30/0.56       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.56         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_left_le
% 0.30/0.56  thf(fact_3848_not__zero__le__neg__numeral,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_zero_le_neg_numeral
% 0.30/0.56  thf(fact_3849_not__zero__le__neg__numeral,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_zero_le_neg_numeral
% 0.30/0.56  thf(fact_3850_not__zero__le__neg__numeral,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_zero_le_neg_numeral
% 0.30/0.56  thf(fact_3851_neg__numeral__le__zero,axiom,
% 0.30/0.56      ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_le_zero
% 0.30/0.56  thf(fact_3852_neg__numeral__le__zero,axiom,
% 0.30/0.56      ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_le_zero
% 0.30/0.56  thf(fact_3853_neg__numeral__le__zero,axiom,
% 0.30/0.56      ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_le_zero
% 0.30/0.56  thf(fact_3854_le__minus__one__simps_I3_J,axiom,
% 0.30/0.56      ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.30/0.56  
% 0.30/0.56  % le_minus_one_simps(3)
% 0.30/0.56  thf(fact_3855_le__minus__one__simps_I3_J,axiom,
% 0.30/0.56      ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % le_minus_one_simps(3)
% 0.30/0.56  thf(fact_3856_le__minus__one__simps_I3_J,axiom,
% 0.30/0.56      ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.30/0.56  
% 0.30/0.56  % le_minus_one_simps(3)
% 0.30/0.56  thf(fact_3857_le__minus__one__simps_I1_J,axiom,
% 0.30/0.56      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 0.30/0.56  
% 0.30/0.56  % le_minus_one_simps(1)
% 0.30/0.56  thf(fact_3858_le__minus__one__simps_I1_J,axiom,
% 0.30/0.56      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 0.30/0.56  
% 0.30/0.56  % le_minus_one_simps(1)
% 0.30/0.56  thf(fact_3859_le__minus__one__simps_I1_J,axiom,
% 0.30/0.56      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 0.30/0.56  
% 0.30/0.56  % le_minus_one_simps(1)
% 0.30/0.56  thf(fact_3860_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 0.30/0.56      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.56       => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.30/0.56          = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 0.30/0.56  thf(fact_3861_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 0.30/0.56      ! [C: nat,A: nat,B: nat] :
% 0.30/0.56        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.30/0.56       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.30/0.56          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 0.30/0.56  thf(fact_3862_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 0.30/0.56      ! [C: int,A: int,B: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.30/0.56       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.30/0.56          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 0.30/0.56  thf(fact_3863_neg__numeral__le__one,axiom,
% 0.30/0.56      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_le_one
% 0.30/0.56  thf(fact_3864_neg__numeral__le__one,axiom,
% 0.30/0.56      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_le_one
% 0.30/0.56  thf(fact_3865_neg__numeral__le__one,axiom,
% 0.30/0.56      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_le_one
% 0.30/0.56  thf(fact_3866_neg__one__le__numeral,axiom,
% 0.30/0.56      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_one_le_numeral
% 0.30/0.56  thf(fact_3867_neg__one__le__numeral,axiom,
% 0.30/0.56      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_one_le_numeral
% 0.30/0.56  thf(fact_3868_neg__one__le__numeral,axiom,
% 0.30/0.56      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_one_le_numeral
% 0.30/0.56  thf(fact_3869_neg__numeral__le__neg__one,axiom,
% 0.30/0.56      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_le_neg_one
% 0.30/0.56  thf(fact_3870_neg__numeral__le__neg__one,axiom,
% 0.30/0.56      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_le_neg_one
% 0.30/0.56  thf(fact_3871_neg__numeral__le__neg__one,axiom,
% 0.30/0.56      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_le_neg_one
% 0.30/0.56  thf(fact_3872_not__numeral__le__neg__one,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_numeral_le_neg_one
% 0.30/0.56  thf(fact_3873_not__numeral__le__neg__one,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_numeral_le_neg_one
% 0.30/0.56  thf(fact_3874_not__numeral__le__neg__one,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_numeral_le_neg_one
% 0.30/0.56  thf(fact_3875_not__one__le__neg__numeral,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_one_le_neg_numeral
% 0.30/0.56  thf(fact_3876_not__one__le__neg__numeral,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_one_le_neg_numeral
% 0.30/0.56  thf(fact_3877_not__one__le__neg__numeral,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_one_le_neg_numeral
% 0.30/0.56  thf(fact_3878_inf__shunt,axiom,
% 0.30/0.56      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 0.30/0.56        ( ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 0.30/0.56          = bot_bo8147686125503663512_int_o )
% 0.30/0.56        = ( ord_le8369615600986905444_int_o @ X @ ( uminus7117520113953359693_int_o @ Y ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % inf_shunt
% 0.30/0.56  thf(fact_3879_inf__shunt,axiom,
% 0.30/0.56      ! [X: list_char > $o,Y: list_char > $o] :
% 0.30/0.56        ( ( ( inf_inf_list_char_o @ X @ Y )
% 0.30/0.56          = bot_bot_list_char_o )
% 0.30/0.56        = ( ord_le4796328588573674190char_o @ X @ ( uminus7154032370948614053char_o @ Y ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % inf_shunt
% 0.30/0.56  thf(fact_3880_inf__shunt,axiom,
% 0.30/0.56      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.30/0.56        ( ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 0.30/0.56          = bot_bo2099793752762293965at_nat )
% 0.30/0.56        = ( ord_le3146513528884898305at_nat @ X @ ( uminus6524753893492686040at_nat @ Y ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % inf_shunt
% 0.30/0.56  thf(fact_3881_inf__shunt,axiom,
% 0.30/0.56      ! [X: set_o,Y: set_o] :
% 0.30/0.56        ( ( ( inf_inf_set_o @ X @ Y )
% 0.30/0.56          = bot_bot_set_o )
% 0.30/0.56        = ( ord_less_eq_set_o @ X @ ( uminus_uminus_set_o @ Y ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % inf_shunt
% 0.30/0.56  thf(fact_3882_inf__shunt,axiom,
% 0.30/0.56      ! [X: set_int,Y: set_int] :
% 0.30/0.56        ( ( ( inf_inf_set_int @ X @ Y )
% 0.30/0.56          = bot_bot_set_int )
% 0.30/0.56        = ( ord_less_eq_set_int @ X @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % inf_shunt
% 0.30/0.56  thf(fact_3883_inf__shunt,axiom,
% 0.30/0.56      ! [X: product_unit,Y: product_unit] :
% 0.30/0.56        ( ( ( inf_inf_Product_unit @ X @ Y )
% 0.30/0.56          = bot_bot_Product_unit )
% 0.30/0.56        = ( ord_le3221252021190050221t_unit @ X @ ( uminus2952777764628376836t_unit @ Y ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % inf_shunt
% 0.30/0.56  thf(fact_3884_inf__shunt,axiom,
% 0.30/0.56      ! [X: set_nat,Y: set_nat] :
% 0.30/0.56        ( ( ( inf_inf_set_nat @ X @ Y )
% 0.30/0.56          = bot_bot_set_nat )
% 0.30/0.56        = ( ord_less_eq_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % inf_shunt
% 0.30/0.56  thf(fact_3885_sup__shunt,axiom,
% 0.30/0.56      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 0.30/0.56        ( ( ( sup_su3035147773818789531at_nat @ X @ Y )
% 0.30/0.56          = top_to8764741339697478167at_nat )
% 0.30/0.56        = ( ord_le8081472938463900775at_nat @ ( uminus2330091110623919550at_nat @ X ) @ Y ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_shunt
% 0.30/0.56  thf(fact_3886_sup__shunt,axiom,
% 0.30/0.56      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 0.30/0.56        ( ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 0.30/0.56          = top_to6833984726390702231at_nat )
% 0.30/0.56        = ( ord_le1268244103169919719at_nat @ ( uminus935396558254630718at_nat @ X ) @ Y ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_shunt
% 0.30/0.56  thf(fact_3887_sup__shunt,axiom,
% 0.30/0.56      ! [X: set_list_nat,Y: set_list_nat] :
% 0.30/0.56        ( ( ( sup_sup_set_list_nat @ X @ Y )
% 0.30/0.56          = top_top_set_list_nat )
% 0.30/0.56        = ( ord_le6045566169113846134st_nat @ ( uminus3195874150345416415st_nat @ X ) @ Y ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_shunt
% 0.30/0.56  thf(fact_3888_sup__shunt,axiom,
% 0.30/0.56      ! [X: set_o,Y: set_o] :
% 0.30/0.56        ( ( ( sup_sup_set_o @ X @ Y )
% 0.30/0.56          = top_top_set_o )
% 0.30/0.56        = ( ord_less_eq_set_o @ ( uminus_uminus_set_o @ X ) @ Y ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_shunt
% 0.30/0.56  thf(fact_3889_sup__shunt,axiom,
% 0.30/0.56      ! [X: set_rat,Y: set_rat] :
% 0.30/0.56        ( ( ( sup_sup_set_rat @ X @ Y )
% 0.30/0.56          = top_top_set_rat )
% 0.30/0.56        = ( ord_less_eq_set_rat @ ( uminus2201863774496077783et_rat @ X ) @ Y ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_shunt
% 0.30/0.56  thf(fact_3890_sup__shunt,axiom,
% 0.30/0.56      ! [X: set_int,Y: set_int] :
% 0.30/0.56        ( ( ( sup_sup_set_int @ X @ Y )
% 0.30/0.56          = top_top_set_int )
% 0.30/0.56        = ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ Y ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_shunt
% 0.30/0.56  thf(fact_3891_sup__shunt,axiom,
% 0.30/0.56      ! [X: product_unit,Y: product_unit] :
% 0.30/0.56        ( ( ( sup_sup_Product_unit @ X @ Y )
% 0.30/0.56          = top_top_Product_unit )
% 0.30/0.56        = ( ord_le3221252021190050221t_unit @ ( uminus2952777764628376836t_unit @ X ) @ Y ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_shunt
% 0.30/0.56  thf(fact_3892_sup__shunt,axiom,
% 0.30/0.56      ! [X: set_nat,Y: set_nat] :
% 0.30/0.56        ( ( ( sup_sup_set_nat @ X @ Y )
% 0.30/0.56          = top_top_set_nat )
% 0.30/0.56        = ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ Y ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_shunt
% 0.30/0.56  thf(fact_3893_shunt1,axiom,
% 0.30/0.56      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 0.30/0.56        ( ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Z )
% 0.30/0.56        = ( ord_le3146513528884898305at_nat @ X @ ( sup_su6327502436637775413at_nat @ ( uminus6524753893492686040at_nat @ Y ) @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % shunt1
% 0.30/0.56  thf(fact_3894_shunt1,axiom,
% 0.30/0.56      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 0.30/0.56        ( ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ Z )
% 0.30/0.56        = ( ord_le8369615600986905444_int_o @ X @ ( sup_su8463660629351352368_int_o @ ( uminus7117520113953359693_int_o @ Y ) @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % shunt1
% 0.30/0.56  thf(fact_3895_shunt1,axiom,
% 0.30/0.56      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 0.30/0.56        ( ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ X @ Y ) @ Z )
% 0.30/0.56        = ( ord_le4796328588573674190char_o @ X @ ( sup_sup_list_char_o @ ( uminus7154032370948614053char_o @ Y ) @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % shunt1
% 0.30/0.56  thf(fact_3896_shunt1,axiom,
% 0.30/0.56      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 0.30/0.56        ( ( ord_le8081472938463900775at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) @ Z )
% 0.30/0.56        = ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ Y ) @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % shunt1
% 0.30/0.56  thf(fact_3897_shunt1,axiom,
% 0.30/0.56      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 0.30/0.56        ( ( ord_le1268244103169919719at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ Z )
% 0.30/0.56        = ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ Y ) @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % shunt1
% 0.30/0.56  thf(fact_3898_shunt1,axiom,
% 0.30/0.56      ! [X: product_unit,Y: product_unit,Z: product_unit] :
% 0.30/0.56        ( ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ X @ Y ) @ Z )
% 0.30/0.56        = ( ord_le3221252021190050221t_unit @ X @ ( sup_sup_Product_unit @ ( uminus2952777764628376836t_unit @ Y ) @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % shunt1
% 0.30/0.56  thf(fact_3899_shunt1,axiom,
% 0.30/0.56      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.30/0.56        ( ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Z )
% 0.30/0.56        = ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % shunt1
% 0.30/0.56  thf(fact_3900_shunt2,axiom,
% 0.30/0.56      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 0.30/0.56        ( ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ ( uminus6524753893492686040at_nat @ Y ) ) @ Z )
% 0.30/0.56        = ( ord_le3146513528884898305at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % shunt2
% 0.30/0.56  thf(fact_3901_shunt2,axiom,
% 0.30/0.56      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 0.30/0.56        ( ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ ( uminus7117520113953359693_int_o @ Y ) ) @ Z )
% 0.30/0.56        = ( ord_le8369615600986905444_int_o @ X @ ( sup_su8463660629351352368_int_o @ Y @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % shunt2
% 0.30/0.56  thf(fact_3902_shunt2,axiom,
% 0.30/0.56      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 0.30/0.56        ( ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ X @ ( uminus7154032370948614053char_o @ Y ) ) @ Z )
% 0.30/0.56        = ( ord_le4796328588573674190char_o @ X @ ( sup_sup_list_char_o @ Y @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % shunt2
% 0.30/0.56  thf(fact_3903_shunt2,axiom,
% 0.30/0.56      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 0.30/0.56        ( ( ord_le8081472938463900775at_nat @ ( inf_in1697001100524423349at_nat @ X @ ( uminus2330091110623919550at_nat @ Y ) ) @ Z )
% 0.30/0.56        = ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % shunt2
% 0.30/0.56  thf(fact_3904_shunt2,axiom,
% 0.30/0.56      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 0.30/0.56        ( ( ord_le1268244103169919719at_nat @ ( inf_in7913087082777306421at_nat @ X @ ( uminus935396558254630718at_nat @ Y ) ) @ Z )
% 0.30/0.56        = ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % shunt2
% 0.30/0.56  thf(fact_3905_shunt2,axiom,
% 0.30/0.56      ! [X: product_unit,Y: product_unit,Z: product_unit] :
% 0.30/0.56        ( ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ X @ ( uminus2952777764628376836t_unit @ Y ) ) @ Z )
% 0.30/0.56        = ( ord_le3221252021190050221t_unit @ X @ ( sup_sup_Product_unit @ Y @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % shunt2
% 0.30/0.56  thf(fact_3906_shunt2,axiom,
% 0.30/0.56      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 0.30/0.56        ( ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) @ Z )
% 0.30/0.56        = ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % shunt2
% 0.30/0.56  thf(fact_3907_sup__neg__inf,axiom,
% 0.30/0.56      ! [P4: set_Pr1261947904930325089at_nat,Q4: set_Pr1261947904930325089at_nat,R3: set_Pr1261947904930325089at_nat] :
% 0.30/0.56        ( ( ord_le3146513528884898305at_nat @ P4 @ ( sup_su6327502436637775413at_nat @ Q4 @ R3 ) )
% 0.30/0.56        = ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ P4 @ ( uminus6524753893492686040at_nat @ Q4 ) ) @ R3 ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_neg_inf
% 0.30/0.56  thf(fact_3908_sup__neg__inf,axiom,
% 0.30/0.56      ! [P4: product_prod_int_int > $o,Q4: product_prod_int_int > $o,R3: product_prod_int_int > $o] :
% 0.30/0.56        ( ( ord_le8369615600986905444_int_o @ P4 @ ( sup_su8463660629351352368_int_o @ Q4 @ R3 ) )
% 0.30/0.56        = ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ P4 @ ( uminus7117520113953359693_int_o @ Q4 ) ) @ R3 ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_neg_inf
% 0.30/0.56  thf(fact_3909_sup__neg__inf,axiom,
% 0.30/0.56      ! [P4: list_char > $o,Q4: list_char > $o,R3: list_char > $o] :
% 0.30/0.56        ( ( ord_le4796328588573674190char_o @ P4 @ ( sup_sup_list_char_o @ Q4 @ R3 ) )
% 0.30/0.56        = ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ P4 @ ( uminus7154032370948614053char_o @ Q4 ) ) @ R3 ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_neg_inf
% 0.30/0.56  thf(fact_3910_sup__neg__inf,axiom,
% 0.30/0.56      ! [P4: set_Pr8551490117392284871at_nat,Q4: set_Pr8551490117392284871at_nat,R3: set_Pr8551490117392284871at_nat] :
% 0.30/0.56        ( ( ord_le8081472938463900775at_nat @ P4 @ ( sup_su3035147773818789531at_nat @ Q4 @ R3 ) )
% 0.30/0.56        = ( ord_le8081472938463900775at_nat @ ( inf_in1697001100524423349at_nat @ P4 @ ( uminus2330091110623919550at_nat @ Q4 ) ) @ R3 ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_neg_inf
% 0.30/0.56  thf(fact_3911_sup__neg__inf,axiom,
% 0.30/0.56      ! [P4: set_Pr4329608150637261639at_nat,Q4: set_Pr4329608150637261639at_nat,R3: set_Pr4329608150637261639at_nat] :
% 0.30/0.56        ( ( ord_le1268244103169919719at_nat @ P4 @ ( sup_su5525570899277871387at_nat @ Q4 @ R3 ) )
% 0.30/0.56        = ( ord_le1268244103169919719at_nat @ ( inf_in7913087082777306421at_nat @ P4 @ ( uminus935396558254630718at_nat @ Q4 ) ) @ R3 ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_neg_inf
% 0.30/0.56  thf(fact_3912_sup__neg__inf,axiom,
% 0.30/0.56      ! [P4: product_unit,Q4: product_unit,R3: product_unit] :
% 0.30/0.56        ( ( ord_le3221252021190050221t_unit @ P4 @ ( sup_sup_Product_unit @ Q4 @ R3 ) )
% 0.30/0.56        = ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ P4 @ ( uminus2952777764628376836t_unit @ Q4 ) ) @ R3 ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_neg_inf
% 0.30/0.56  thf(fact_3913_sup__neg__inf,axiom,
% 0.30/0.56      ! [P4: set_nat,Q4: set_nat,R3: set_nat] :
% 0.30/0.56        ( ( ord_less_eq_set_nat @ P4 @ ( sup_sup_set_nat @ Q4 @ R3 ) )
% 0.30/0.56        = ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ P4 @ ( uminus5710092332889474511et_nat @ Q4 ) ) @ R3 ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_neg_inf
% 0.30/0.56  thf(fact_3914_disjoint__eq__subset__Compl,axiom,
% 0.30/0.56      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.56        ( ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 0.30/0.56          = bot_bo2099793752762293965at_nat )
% 0.30/0.56        = ( ord_le3146513528884898305at_nat @ A2 @ ( uminus6524753893492686040at_nat @ B2 ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % disjoint_eq_subset_Compl
% 0.30/0.56  thf(fact_3915_disjoint__eq__subset__Compl,axiom,
% 0.30/0.56      ! [A2: set_o,B2: set_o] :
% 0.30/0.56        ( ( ( inf_inf_set_o @ A2 @ B2 )
% 0.30/0.56          = bot_bot_set_o )
% 0.30/0.56        = ( ord_less_eq_set_o @ A2 @ ( uminus_uminus_set_o @ B2 ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % disjoint_eq_subset_Compl
% 0.30/0.56  thf(fact_3916_disjoint__eq__subset__Compl,axiom,
% 0.30/0.56      ! [A2: set_int,B2: set_int] :
% 0.30/0.56        ( ( ( inf_inf_set_int @ A2 @ B2 )
% 0.30/0.56          = bot_bot_set_int )
% 0.30/0.56        = ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ B2 ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % disjoint_eq_subset_Compl
% 0.30/0.56  thf(fact_3917_disjoint__eq__subset__Compl,axiom,
% 0.30/0.56      ! [A2: set_nat,B2: set_nat] :
% 0.30/0.56        ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 0.30/0.56          = bot_bot_set_nat )
% 0.30/0.56        = ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ B2 ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % disjoint_eq_subset_Compl
% 0.30/0.56  thf(fact_3918_less__divide__eq__numeral_I1_J,axiom,
% 0.30/0.56      ! [W: num,B: rat,C: rat] :
% 0.30/0.56        ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 0.30/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56           => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 0.30/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56               => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.30/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56               => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_divide_eq_numeral(1)
% 0.30/0.56  thf(fact_3919_divide__less__eq__numeral_I1_J,axiom,
% 0.30/0.56      ! [B: rat,C: rat,W: num] :
% 0.30/0.56        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 0.30/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56           => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 0.30/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56               => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 0.30/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56               => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % divide_less_eq_numeral(1)
% 0.30/0.56  thf(fact_3920_frac__less__eq,axiom,
% 0.30/0.56      ! [Y: rat,Z: rat,X: rat,W: rat] :
% 0.30/0.56        ( ( Y != zero_zero_rat )
% 0.30/0.56       => ( ( Z != zero_zero_rat )
% 0.30/0.56         => ( ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 0.30/0.56            = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % frac_less_eq
% 0.30/0.56  thf(fact_3921_pos__minus__divide__less__eq,axiom,
% 0.30/0.56      ! [C: rat,B: rat,A: rat] :
% 0.30/0.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.30/0.56          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % pos_minus_divide_less_eq
% 0.30/0.56  thf(fact_3922_pos__less__minus__divide__eq,axiom,
% 0.30/0.56      ! [C: rat,A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.30/0.56          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % pos_less_minus_divide_eq
% 0.30/0.56  thf(fact_3923_neg__minus__divide__less__eq,axiom,
% 0.30/0.56      ! [C: rat,B: rat,A: rat] :
% 0.30/0.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.30/0.56          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_minus_divide_less_eq
% 0.30/0.56  thf(fact_3924_neg__less__minus__divide__eq,axiom,
% 0.30/0.56      ! [C: rat,A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.30/0.56          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_less_minus_divide_eq
% 0.30/0.56  thf(fact_3925_minus__divide__less__eq,axiom,
% 0.30/0.56      ! [B: rat,C: rat,A: rat] :
% 0.30/0.56        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 0.30/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56           => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.30/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.30/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % minus_divide_less_eq
% 0.30/0.56  thf(fact_3926_less__minus__divide__eq,axiom,
% 0.30/0.56      ! [A: rat,B: rat,C: rat] :
% 0.30/0.56        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 0.30/0.56        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 0.30/0.56          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 0.30/0.56           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56               => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 0.30/0.56              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 0.30/0.56               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_minus_divide_eq
% 0.30/0.56  thf(fact_3927_frac__le__eq,axiom,
% 0.30/0.56      ! [Y: rat,Z: rat,X: rat,W: rat] :
% 0.30/0.56        ( ( Y != zero_zero_rat )
% 0.30/0.56       => ( ( Z != zero_zero_rat )
% 0.30/0.56         => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 0.30/0.56            = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % frac_le_eq
% 0.30/0.56  thf(fact_3928_mult__le__cancel__iff1,axiom,
% 0.30/0.56      ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z )
% 0.30/0.56       => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X @ Z ) @ ( times_3573771949741848930nteger @ Y @ Z ) )
% 0.30/0.56          = ( ord_le3102999989581377725nteger @ X @ Y ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_le_cancel_iff1
% 0.30/0.56  thf(fact_3929_mult__le__cancel__iff1,axiom,
% 0.30/0.56      ! [Z: rat,X: rat,Y: rat] :
% 0.30/0.56        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 0.30/0.56       => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 0.30/0.56          = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_le_cancel_iff1
% 0.30/0.56  thf(fact_3930_mult__le__cancel__iff1,axiom,
% 0.30/0.56      ! [Z: int,X: int,Y: int] :
% 0.30/0.56        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.30/0.56       => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 0.30/0.56          = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_le_cancel_iff1
% 0.30/0.56  thf(fact_3931_mult__le__cancel__iff2,axiom,
% 0.30/0.56      ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z )
% 0.30/0.56       => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Z @ X ) @ ( times_3573771949741848930nteger @ Z @ Y ) )
% 0.30/0.56          = ( ord_le3102999989581377725nteger @ X @ Y ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_le_cancel_iff2
% 0.30/0.56  thf(fact_3932_mult__le__cancel__iff2,axiom,
% 0.30/0.56      ! [Z: rat,X: rat,Y: rat] :
% 0.30/0.56        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 0.30/0.56       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ ( times_times_rat @ Z @ Y ) )
% 0.30/0.56          = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_le_cancel_iff2
% 0.30/0.56  thf(fact_3933_mult__le__cancel__iff2,axiom,
% 0.30/0.56      ! [Z: int,X: int,Y: int] :
% 0.30/0.56        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.30/0.56       => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X ) @ ( times_times_int @ Z @ Y ) )
% 0.30/0.56          = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_le_cancel_iff2
% 0.30/0.56  thf(fact_3934_mult__less__iff1,axiom,
% 0.30/0.56      ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z )
% 0.30/0.56       => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ X @ Z ) @ ( times_3573771949741848930nteger @ Y @ Z ) )
% 0.30/0.56          = ( ord_le6747313008572928689nteger @ X @ Y ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_less_iff1
% 0.30/0.56  thf(fact_3935_mult__less__iff1,axiom,
% 0.30/0.56      ! [Z: rat,X: rat,Y: rat] :
% 0.30/0.56        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 0.30/0.56       => ( ( ord_less_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 0.30/0.56          = ( ord_less_rat @ X @ Y ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_less_iff1
% 0.30/0.56  thf(fact_3936_mult__less__iff1,axiom,
% 0.30/0.56      ! [Z: int,X: int,Y: int] :
% 0.30/0.56        ( ( ord_less_int @ zero_zero_int @ Z )
% 0.30/0.56       => ( ( ord_less_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 0.30/0.56          = ( ord_less_int @ X @ Y ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % mult_less_iff1
% 0.30/0.56  thf(fact_3937_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 0.30/0.56      ( semila5207306265035627125at_nat @ sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat
% 0.30/0.56      @ ^ [X3: set_Pr8551490117392284871at_nat,Y3: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ Y3 @ X3 )
% 0.30/0.56      @ ^ [X3: set_Pr8551490117392284871at_nat,Y3: set_Pr8551490117392284871at_nat] : ( ord_le7642048601412989811at_nat @ Y3 @ X3 ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_bot.semilattice_neutr_order_axioms
% 0.30/0.56  thf(fact_3938_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 0.30/0.56      ( semila6534579987270727413at_nat @ sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat
% 0.30/0.56      @ ^ [X3: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y3 @ X3 )
% 0.30/0.56      @ ^ [X3: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] : ( ord_le2604355607129572851at_nat @ Y3 @ X3 ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_bot.semilattice_neutr_order_axioms
% 0.30/0.56  thf(fact_3939_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 0.30/0.56      ( semila4918476307565957903at_nat @ sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat
% 0.30/0.56      @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ Y3 @ X3 )
% 0.30/0.56      @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le7866589430770878221at_nat @ Y3 @ X3 ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_bot.semilattice_neutr_order_axioms
% 0.30/0.56  thf(fact_3940_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 0.30/0.56      ( semila2554085542299052326_set_o @ sup_sup_set_o @ bot_bot_set_o
% 0.30/0.56      @ ^ [X3: set_o,Y3: set_o] : ( ord_less_eq_set_o @ Y3 @ X3 )
% 0.30/0.56      @ ^ [X3: set_o,Y3: set_o] : ( ord_less_set_o @ Y3 @ X3 ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_bot.semilattice_neutr_order_axioms
% 0.30/0.56  thf(fact_3941_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 0.30/0.56      ( semila6712789903965657268et_int @ sup_sup_set_int @ bot_bot_set_int
% 0.30/0.56      @ ^ [X3: set_int,Y3: set_int] : ( ord_less_eq_set_int @ Y3 @ X3 )
% 0.30/0.56      @ ^ [X3: set_int,Y3: set_int] : ( ord_less_set_int @ Y3 @ X3 ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_bot.semilattice_neutr_order_axioms
% 0.30/0.56  thf(fact_3942_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 0.30/0.56      ( semila5926144314033625522er_nat @ sup_sup_filter_nat @ bot_bot_filter_nat
% 0.30/0.56      @ ^ [X3: filter_nat,Y3: filter_nat] : ( ord_le2510731241096832064er_nat @ Y3 @ X3 )
% 0.30/0.56      @ ^ [X3: filter_nat,Y3: filter_nat] : ( ord_less_filter_nat @ Y3 @ X3 ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_bot.semilattice_neutr_order_axioms
% 0.30/0.56  thf(fact_3943_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 0.30/0.56      ( semila1667268886620078168et_nat @ sup_sup_set_nat @ bot_bot_set_nat
% 0.30/0.56      @ ^ [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ Y3 @ X3 )
% 0.30/0.56      @ ^ [X3: set_nat,Y3: set_nat] : ( ord_less_set_nat @ Y3 @ X3 ) ) ).
% 0.30/0.56  
% 0.30/0.56  % sup_bot.semilattice_neutr_order_axioms
% 0.30/0.56  thf(fact_3944_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 0.30/0.56      semila4918476307565957903at_nat @ inf_in2572325071724192079at_nat @ top_to4669805908274784177at_nat @ ord_le3146513528884898305at_nat @ ord_le7866589430770878221at_nat ).
% 0.30/0.56  
% 0.30/0.56  % inf_top.semilattice_neutr_order_axioms
% 0.30/0.56  thf(fact_3945_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 0.30/0.56      semila8052717425514686422_int_o @ inf_in3604695632404883862_int_o @ top_to1578927101902068148_int_o @ ord_le8369615600986905444_int_o @ ord_le8213806771718485336_int_o ).
% 0.30/0.56  
% 0.30/0.56  % inf_top.semilattice_neutr_order_axioms
% 0.30/0.56  thf(fact_3946_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 0.30/0.56      semila3134969884451571676char_o @ inf_inf_list_char_o @ top_top_list_char_o @ ord_le4796328588573674190char_o @ ord_less_list_char_o ).
% 0.30/0.56  
% 0.30/0.56  % inf_top.semilattice_neutr_order_axioms
% 0.30/0.56  thf(fact_3947_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 0.30/0.56      semila2613578647866687720st_nat @ inf_inf_set_list_nat @ top_top_set_list_nat @ ord_le6045566169113846134st_nat @ ord_le1190675801316882794st_nat ).
% 0.30/0.56  
% 0.30/0.56  % inf_top.semilattice_neutr_order_axioms
% 0.30/0.56  thf(fact_3948_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 0.30/0.56      semila2554085542299052326_set_o @ inf_inf_set_o @ top_top_set_o @ ord_less_eq_set_o @ ord_less_set_o ).
% 0.30/0.56  
% 0.30/0.56  % inf_top.semilattice_neutr_order_axioms
% 0.30/0.56  thf(fact_3949_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 0.30/0.56      semila7382412365081457248et_rat @ inf_inf_set_rat @ top_top_set_rat @ ord_less_eq_set_rat @ ord_less_set_rat ).
% 0.30/0.56  
% 0.30/0.56  % inf_top.semilattice_neutr_order_axioms
% 0.30/0.56  thf(fact_3950_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 0.30/0.56      semila6712789903965657268et_int @ inf_inf_set_int @ top_top_set_int @ ord_less_eq_set_int @ ord_less_set_int ).
% 0.30/0.56  
% 0.30/0.56  % inf_top.semilattice_neutr_order_axioms
% 0.30/0.56  thf(fact_3951_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 0.30/0.56      semila5926144314033625522er_nat @ inf_inf_filter_nat @ top_top_filter_nat @ ord_le2510731241096832064er_nat @ ord_less_filter_nat ).
% 0.30/0.56  
% 0.30/0.56  % inf_top.semilattice_neutr_order_axioms
% 0.30/0.56  thf(fact_3952_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 0.30/0.56      semila1667268886620078168et_nat @ inf_inf_set_nat @ top_top_set_nat @ ord_less_eq_set_nat @ ord_less_set_nat ).
% 0.30/0.56  
% 0.30/0.56  % inf_top.semilattice_neutr_order_axioms
% 0.30/0.56  thf(fact_3953_bot_Oordering__top__axioms,axiom,
% 0.30/0.56      ( orderi2172309028950807442at_nat
% 0.30/0.56      @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ Y3 @ X3 )
% 0.30/0.56      @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le7866589430770878221at_nat @ Y3 @ X3 )
% 0.30/0.56      @ bot_bo2099793752762293965at_nat ) ).
% 0.30/0.56  
% 0.30/0.56  % bot.ordering_top_axioms
% 0.30/0.56  thf(fact_3954_bot_Oordering__top__axioms,axiom,
% 0.30/0.56      ( ordering_top_set_o
% 0.30/0.56      @ ^ [X3: set_o,Y3: set_o] : ( ord_less_eq_set_o @ Y3 @ X3 )
% 0.30/0.56      @ ^ [X3: set_o,Y3: set_o] : ( ord_less_set_o @ Y3 @ X3 )
% 0.30/0.56      @ bot_bot_set_o ) ).
% 0.30/0.56  
% 0.30/0.56  % bot.ordering_top_axioms
% 0.30/0.56  thf(fact_3955_bot_Oordering__top__axioms,axiom,
% 0.30/0.56      ( ordering_top_set_int
% 0.30/0.56      @ ^ [X3: set_int,Y3: set_int] : ( ord_less_eq_set_int @ Y3 @ X3 )
% 0.30/0.56      @ ^ [X3: set_int,Y3: set_int] : ( ord_less_set_int @ Y3 @ X3 )
% 0.30/0.56      @ bot_bot_set_int ) ).
% 0.30/0.56  
% 0.30/0.56  % bot.ordering_top_axioms
% 0.30/0.56  thf(fact_3956_bot_Oordering__top__axioms,axiom,
% 0.30/0.56      ( orderi2807725203697798511er_nat
% 0.30/0.56      @ ^ [X3: filter_nat,Y3: filter_nat] : ( ord_le2510731241096832064er_nat @ Y3 @ X3 )
% 0.30/0.56      @ ^ [X3: filter_nat,Y3: filter_nat] : ( ord_less_filter_nat @ Y3 @ X3 )
% 0.30/0.56      @ bot_bot_filter_nat ) ).
% 0.30/0.56  
% 0.30/0.56  % bot.ordering_top_axioms
% 0.30/0.56  thf(fact_3957_bot_Oordering__top__axioms,axiom,
% 0.30/0.56      ( ordering_top_set_nat
% 0.30/0.56      @ ^ [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ Y3 @ X3 )
% 0.30/0.56      @ ^ [X3: set_nat,Y3: set_nat] : ( ord_less_set_nat @ Y3 @ X3 )
% 0.30/0.56      @ bot_bot_set_nat ) ).
% 0.30/0.56  
% 0.30/0.56  % bot.ordering_top_axioms
% 0.30/0.56  thf(fact_3958_bot_Oordering__top__axioms,axiom,
% 0.30/0.56      ( ordering_top_nat
% 0.30/0.56      @ ^ [X3: nat,Y3: nat] : ( ord_less_eq_nat @ Y3 @ X3 )
% 0.30/0.56      @ ^ [X3: nat,Y3: nat] : ( ord_less_nat @ Y3 @ X3 )
% 0.30/0.56      @ bot_bot_nat ) ).
% 0.30/0.56  
% 0.30/0.56  % bot.ordering_top_axioms
% 0.30/0.56  thf(fact_3959_neg__numeral__less__neg__one__iff,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.56        = ( M != one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_less_neg_one_iff
% 0.30/0.56  thf(fact_3960_neg__numeral__less__neg__one__iff,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.56        = ( M != one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_less_neg_one_iff
% 0.30/0.56  thf(fact_3961_neg__numeral__less__neg__one__iff,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.30/0.56        = ( M != one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_numeral_less_neg_one_iff
% 0.30/0.56  thf(fact_3962_not__neg__one__le__neg__numeral__iff,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 0.30/0.56        = ( M != one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_neg_one_le_neg_numeral_iff
% 0.30/0.56  thf(fact_3963_not__neg__one__le__neg__numeral__iff,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 0.30/0.56        = ( M != one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_neg_one_le_neg_numeral_iff
% 0.30/0.56  thf(fact_3964_not__neg__one__le__neg__numeral__iff,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 0.30/0.56        = ( M != one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % not_neg_one_le_neg_numeral_iff
% 0.30/0.56  thf(fact_3965_add__neg__numeral__special_I6_J,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.56        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_neg_numeral_special(6)
% 0.30/0.56  thf(fact_3966_add__neg__numeral__special_I6_J,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.56        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_neg_numeral_special(6)
% 0.30/0.56  thf(fact_3967_add__neg__numeral__special_I6_J,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.30/0.56        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_neg_numeral_special(6)
% 0.30/0.56  thf(fact_3968_add__neg__numeral__special_I5_J,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.56        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_neg_numeral_special(5)
% 0.30/0.56  thf(fact_3969_add__neg__numeral__special_I5_J,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.30/0.56        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_neg_numeral_special(5)
% 0.30/0.56  thf(fact_3970_add__neg__numeral__special_I5_J,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.30/0.56        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_neg_numeral_special(5)
% 0.30/0.56  thf(fact_3971_add__left__cancel,axiom,
% 0.30/0.56      ! [A: rat,B: rat,C: rat] :
% 0.30/0.56        ( ( ( plus_plus_rat @ A @ B )
% 0.30/0.56          = ( plus_plus_rat @ A @ C ) )
% 0.30/0.56        = ( B = C ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_left_cancel
% 0.30/0.56  thf(fact_3972_add__left__cancel,axiom,
% 0.30/0.56      ! [A: nat,B: nat,C: nat] :
% 0.30/0.56        ( ( ( plus_plus_nat @ A @ B )
% 0.30/0.56          = ( plus_plus_nat @ A @ C ) )
% 0.30/0.56        = ( B = C ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_left_cancel
% 0.30/0.56  thf(fact_3973_add__left__cancel,axiom,
% 0.30/0.56      ! [A: int,B: int,C: int] :
% 0.30/0.56        ( ( ( plus_plus_int @ A @ B )
% 0.30/0.56          = ( plus_plus_int @ A @ C ) )
% 0.30/0.56        = ( B = C ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_left_cancel
% 0.30/0.56  thf(fact_3974_add__right__cancel,axiom,
% 0.30/0.56      ! [B: rat,A: rat,C: rat] :
% 0.30/0.56        ( ( ( plus_plus_rat @ B @ A )
% 0.30/0.56          = ( plus_plus_rat @ C @ A ) )
% 0.30/0.56        = ( B = C ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_right_cancel
% 0.30/0.56  thf(fact_3975_add__right__cancel,axiom,
% 0.30/0.56      ! [B: nat,A: nat,C: nat] :
% 0.30/0.56        ( ( ( plus_plus_nat @ B @ A )
% 0.30/0.56          = ( plus_plus_nat @ C @ A ) )
% 0.30/0.56        = ( B = C ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_right_cancel
% 0.30/0.56  thf(fact_3976_add__right__cancel,axiom,
% 0.30/0.56      ! [B: int,A: int,C: int] :
% 0.30/0.56        ( ( ( plus_plus_int @ B @ A )
% 0.30/0.56          = ( plus_plus_int @ C @ A ) )
% 0.30/0.56        = ( B = C ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_right_cancel
% 0.30/0.56  thf(fact_3977_add__le__cancel__left,axiom,
% 0.30/0.56      ! [C: rat,A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.30/0.56        = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_le_cancel_left
% 0.30/0.56  thf(fact_3978_add__le__cancel__left,axiom,
% 0.30/0.56      ! [C: nat,A: nat,B: nat] :
% 0.30/0.56        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.30/0.56        = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_le_cancel_left
% 0.30/0.56  thf(fact_3979_add__le__cancel__left,axiom,
% 0.30/0.56      ! [C: int,A: int,B: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.30/0.56        = ( ord_less_eq_int @ A @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_le_cancel_left
% 0.30/0.56  thf(fact_3980_add__le__cancel__right,axiom,
% 0.30/0.56      ! [A: rat,C: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.30/0.56        = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_le_cancel_right
% 0.30/0.56  thf(fact_3981_add__le__cancel__right,axiom,
% 0.30/0.56      ! [A: nat,C: nat,B: nat] :
% 0.30/0.56        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.30/0.56        = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_le_cancel_right
% 0.30/0.56  thf(fact_3982_add__le__cancel__right,axiom,
% 0.30/0.56      ! [A: int,C: int,B: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.30/0.56        = ( ord_less_eq_int @ A @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_le_cancel_right
% 0.30/0.56  thf(fact_3983_add_Oright__neutral,axiom,
% 0.30/0.56      ! [A: literal] :
% 0.30/0.56        ( ( plus_plus_literal @ A @ zero_zero_literal )
% 0.30/0.56        = A ) ).
% 0.30/0.56  
% 0.30/0.56  % add.right_neutral
% 0.30/0.56  thf(fact_3984_add_Oright__neutral,axiom,
% 0.30/0.56      ! [A: code_integer] :
% 0.30/0.56        ( ( plus_p5714425477246183910nteger @ A @ zero_z3403309356797280102nteger )
% 0.30/0.56        = A ) ).
% 0.30/0.56  
% 0.30/0.56  % add.right_neutral
% 0.30/0.56  thf(fact_3985_add_Oright__neutral,axiom,
% 0.30/0.56      ! [A: multis2468970476368604999at_nat] :
% 0.30/0.56        ( ( plus_p7104986032573967614at_nat @ A @ zero_z1048942125864253310at_nat )
% 0.30/0.56        = A ) ).
% 0.30/0.56  
% 0.30/0.56  % add.right_neutral
% 0.30/0.56  thf(fact_3986_add_Oright__neutral,axiom,
% 0.30/0.56      ! [A: rat] :
% 0.30/0.56        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.30/0.56        = A ) ).
% 0.30/0.56  
% 0.30/0.56  % add.right_neutral
% 0.30/0.56  thf(fact_3987_add_Oright__neutral,axiom,
% 0.30/0.56      ! [A: nat] :
% 0.30/0.56        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.30/0.56        = A ) ).
% 0.30/0.56  
% 0.30/0.56  % add.right_neutral
% 0.30/0.56  thf(fact_3988_add_Oright__neutral,axiom,
% 0.30/0.56      ! [A: int] :
% 0.30/0.56        ( ( plus_plus_int @ A @ zero_zero_int )
% 0.30/0.56        = A ) ).
% 0.30/0.56  
% 0.30/0.56  % add.right_neutral
% 0.30/0.56  thf(fact_3989_double__zero__sym,axiom,
% 0.30/0.56      ! [A: code_integer] :
% 0.30/0.56        ( ( zero_z3403309356797280102nteger
% 0.30/0.56          = ( plus_p5714425477246183910nteger @ A @ A ) )
% 0.30/0.56        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.30/0.56  
% 0.30/0.56  % double_zero_sym
% 0.30/0.56  thf(fact_3990_double__zero__sym,axiom,
% 0.30/0.56      ! [A: rat] :
% 0.30/0.56        ( ( zero_zero_rat
% 0.30/0.56          = ( plus_plus_rat @ A @ A ) )
% 0.30/0.56        = ( A = zero_zero_rat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % double_zero_sym
% 0.30/0.56  thf(fact_3991_double__zero__sym,axiom,
% 0.30/0.56      ! [A: int] :
% 0.30/0.56        ( ( zero_zero_int
% 0.30/0.56          = ( plus_plus_int @ A @ A ) )
% 0.30/0.56        = ( A = zero_zero_int ) ) ).
% 0.30/0.56  
% 0.30/0.56  % double_zero_sym
% 0.30/0.56  thf(fact_3992_add__cancel__left__left,axiom,
% 0.30/0.56      ! [B: code_integer,A: code_integer] :
% 0.30/0.56        ( ( ( plus_p5714425477246183910nteger @ B @ A )
% 0.30/0.56          = A )
% 0.30/0.56        = ( B = zero_z3403309356797280102nteger ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_cancel_left_left
% 0.30/0.56  thf(fact_3993_add__cancel__left__left,axiom,
% 0.30/0.56      ! [B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat] :
% 0.30/0.56        ( ( ( plus_p7104986032573967614at_nat @ B @ A )
% 0.30/0.56          = A )
% 0.30/0.56        = ( B = zero_z1048942125864253310at_nat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_cancel_left_left
% 0.30/0.56  thf(fact_3994_add__cancel__left__left,axiom,
% 0.30/0.56      ! [B: rat,A: rat] :
% 0.30/0.56        ( ( ( plus_plus_rat @ B @ A )
% 0.30/0.56          = A )
% 0.30/0.56        = ( B = zero_zero_rat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_cancel_left_left
% 0.30/0.56  thf(fact_3995_add__cancel__left__left,axiom,
% 0.30/0.56      ! [B: nat,A: nat] :
% 0.30/0.56        ( ( ( plus_plus_nat @ B @ A )
% 0.30/0.56          = A )
% 0.30/0.56        = ( B = zero_zero_nat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_cancel_left_left
% 0.30/0.56  thf(fact_3996_add__cancel__left__left,axiom,
% 0.30/0.56      ! [B: int,A: int] :
% 0.30/0.56        ( ( ( plus_plus_int @ B @ A )
% 0.30/0.56          = A )
% 0.30/0.56        = ( B = zero_zero_int ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_cancel_left_left
% 0.30/0.56  thf(fact_3997_add__cancel__left__right,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.30/0.56          = A )
% 0.30/0.56        = ( B = zero_z3403309356797280102nteger ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_cancel_left_right
% 0.30/0.56  thf(fact_3998_add__cancel__left__right,axiom,
% 0.30/0.56      ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 0.30/0.56        ( ( ( plus_p7104986032573967614at_nat @ A @ B )
% 0.30/0.56          = A )
% 0.30/0.56        = ( B = zero_z1048942125864253310at_nat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_cancel_left_right
% 0.30/0.56  thf(fact_3999_add__cancel__left__right,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( ( plus_plus_rat @ A @ B )
% 0.30/0.56          = A )
% 0.30/0.56        = ( B = zero_zero_rat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_cancel_left_right
% 0.30/0.56  thf(fact_4000_add__cancel__left__right,axiom,
% 0.30/0.56      ! [A: nat,B: nat] :
% 0.30/0.56        ( ( ( plus_plus_nat @ A @ B )
% 0.30/0.56          = A )
% 0.30/0.56        = ( B = zero_zero_nat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_cancel_left_right
% 0.30/0.56  thf(fact_4001_add__cancel__left__right,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( ( plus_plus_int @ A @ B )
% 0.30/0.56          = A )
% 0.30/0.56        = ( B = zero_zero_int ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_cancel_left_right
% 0.30/0.56  thf(fact_4002_add__cancel__right__left,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( A
% 0.30/0.56          = ( plus_p5714425477246183910nteger @ B @ A ) )
% 0.30/0.56        = ( B = zero_z3403309356797280102nteger ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_cancel_right_left
% 0.30/0.56  thf(fact_4003_add__cancel__right__left,axiom,
% 0.30/0.56      ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 0.30/0.56        ( ( A
% 0.30/0.56          = ( plus_p7104986032573967614at_nat @ B @ A ) )
% 0.30/0.56        = ( B = zero_z1048942125864253310at_nat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_cancel_right_left
% 0.30/0.56  thf(fact_4004_add__cancel__right__left,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( A
% 0.30/0.56          = ( plus_plus_rat @ B @ A ) )
% 0.30/0.56        = ( B = zero_zero_rat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_cancel_right_left
% 0.30/0.56  thf(fact_4005_add__cancel__right__left,axiom,
% 0.30/0.56      ! [A: nat,B: nat] :
% 0.30/0.56        ( ( A
% 0.30/0.56          = ( plus_plus_nat @ B @ A ) )
% 0.30/0.56        = ( B = zero_zero_nat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_cancel_right_left
% 0.30/0.56  thf(fact_4006_add__cancel__right__left,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( A
% 0.30/0.56          = ( plus_plus_int @ B @ A ) )
% 0.30/0.56        = ( B = zero_zero_int ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_cancel_right_left
% 0.30/0.56  thf(fact_4007_add__cancel__right__right,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( A
% 0.30/0.56          = ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.30/0.56        = ( B = zero_z3403309356797280102nteger ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_cancel_right_right
% 0.30/0.56  thf(fact_4008_add__cancel__right__right,axiom,
% 0.30/0.56      ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 0.30/0.56        ( ( A
% 0.30/0.56          = ( plus_p7104986032573967614at_nat @ A @ B ) )
% 0.30/0.56        = ( B = zero_z1048942125864253310at_nat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_cancel_right_right
% 0.30/0.56  thf(fact_4009_add__cancel__right__right,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( A
% 0.30/0.56          = ( plus_plus_rat @ A @ B ) )
% 0.30/0.56        = ( B = zero_zero_rat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_cancel_right_right
% 0.30/0.56  thf(fact_4010_add__cancel__right__right,axiom,
% 0.30/0.56      ! [A: nat,B: nat] :
% 0.30/0.56        ( ( A
% 0.30/0.56          = ( plus_plus_nat @ A @ B ) )
% 0.30/0.56        = ( B = zero_zero_nat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_cancel_right_right
% 0.30/0.56  thf(fact_4011_add__cancel__right__right,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( A
% 0.30/0.56          = ( plus_plus_int @ A @ B ) )
% 0.30/0.56        = ( B = zero_zero_int ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_cancel_right_right
% 0.30/0.56  thf(fact_4012_add__eq__0__iff__both__eq__0,axiom,
% 0.30/0.56      ! [X: nat,Y: nat] :
% 0.30/0.56        ( ( ( plus_plus_nat @ X @ Y )
% 0.30/0.56          = zero_zero_nat )
% 0.30/0.56        = ( ( X = zero_zero_nat )
% 0.30/0.56          & ( Y = zero_zero_nat ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_eq_0_iff_both_eq_0
% 0.30/0.56  thf(fact_4013_zero__eq__add__iff__both__eq__0,axiom,
% 0.30/0.56      ! [X: nat,Y: nat] :
% 0.30/0.56        ( ( zero_zero_nat
% 0.30/0.56          = ( plus_plus_nat @ X @ Y ) )
% 0.30/0.56        = ( ( X = zero_zero_nat )
% 0.30/0.56          & ( Y = zero_zero_nat ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_eq_add_iff_both_eq_0
% 0.30/0.56  thf(fact_4014_add__0,axiom,
% 0.30/0.56      ! [A: literal] :
% 0.30/0.56        ( ( plus_plus_literal @ zero_zero_literal @ A )
% 0.30/0.56        = A ) ).
% 0.30/0.56  
% 0.30/0.56  % add_0
% 0.30/0.56  thf(fact_4015_add__0,axiom,
% 0.30/0.56      ! [A: code_integer] :
% 0.30/0.56        ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.56        = A ) ).
% 0.30/0.56  
% 0.30/0.56  % add_0
% 0.30/0.56  thf(fact_4016_add__0,axiom,
% 0.30/0.56      ! [A: multis2468970476368604999at_nat] :
% 0.30/0.56        ( ( plus_p7104986032573967614at_nat @ zero_z1048942125864253310at_nat @ A )
% 0.30/0.56        = A ) ).
% 0.30/0.56  
% 0.30/0.56  % add_0
% 0.30/0.56  thf(fact_4017_add__0,axiom,
% 0.30/0.56      ! [A: rat] :
% 0.30/0.56        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.30/0.56        = A ) ).
% 0.30/0.56  
% 0.30/0.56  % add_0
% 0.30/0.56  thf(fact_4018_add__0,axiom,
% 0.30/0.56      ! [A: nat] :
% 0.30/0.56        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.30/0.56        = A ) ).
% 0.30/0.56  
% 0.30/0.56  % add_0
% 0.30/0.56  thf(fact_4019_add__0,axiom,
% 0.30/0.56      ! [A: int] :
% 0.30/0.56        ( ( plus_plus_int @ zero_zero_int @ A )
% 0.30/0.56        = A ) ).
% 0.30/0.56  
% 0.30/0.56  % add_0
% 0.30/0.56  thf(fact_4020_add__less__cancel__left,axiom,
% 0.30/0.56      ! [C: rat,A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.30/0.56        = ( ord_less_rat @ A @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_less_cancel_left
% 0.30/0.56  thf(fact_4021_add__less__cancel__left,axiom,
% 0.30/0.56      ! [C: nat,A: nat,B: nat] :
% 0.30/0.56        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.30/0.56        = ( ord_less_nat @ A @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_less_cancel_left
% 0.30/0.56  thf(fact_4022_add__less__cancel__left,axiom,
% 0.30/0.56      ! [C: int,A: int,B: int] :
% 0.30/0.56        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.30/0.56        = ( ord_less_int @ A @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_less_cancel_left
% 0.30/0.56  thf(fact_4023_add__less__cancel__right,axiom,
% 0.30/0.56      ! [A: rat,C: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.30/0.56        = ( ord_less_rat @ A @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_less_cancel_right
% 0.30/0.56  thf(fact_4024_add__less__cancel__right,axiom,
% 0.30/0.56      ! [A: nat,C: nat,B: nat] :
% 0.30/0.56        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.30/0.56        = ( ord_less_nat @ A @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_less_cancel_right
% 0.30/0.56  thf(fact_4025_add__less__cancel__right,axiom,
% 0.30/0.56      ! [A: int,C: int,B: int] :
% 0.30/0.56        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.30/0.56        = ( ord_less_int @ A @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_less_cancel_right
% 0.30/0.56  thf(fact_4026_add__diff__cancel,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.30/0.56        = A ) ).
% 0.30/0.56  
% 0.30/0.56  % add_diff_cancel
% 0.30/0.56  thf(fact_4027_add__diff__cancel,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.30/0.56        = A ) ).
% 0.30/0.56  
% 0.30/0.56  % add_diff_cancel
% 0.30/0.56  thf(fact_4028_diff__add__cancel,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 0.30/0.56        = A ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_add_cancel
% 0.30/0.56  thf(fact_4029_diff__add__cancel,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.30/0.56        = A ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_add_cancel
% 0.30/0.56  thf(fact_4030_add__diff__cancel__left,axiom,
% 0.30/0.56      ! [C: rat,A: rat,B: rat] :
% 0.30/0.56        ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.30/0.56        = ( minus_minus_rat @ A @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_diff_cancel_left
% 0.30/0.56  thf(fact_4031_add__diff__cancel__left,axiom,
% 0.30/0.56      ! [C: nat,A: nat,B: nat] :
% 0.30/0.56        ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.30/0.56        = ( minus_minus_nat @ A @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_diff_cancel_left
% 0.30/0.56  thf(fact_4032_add__diff__cancel__left,axiom,
% 0.30/0.56      ! [C: int,A: int,B: int] :
% 0.30/0.56        ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.30/0.56        = ( minus_minus_int @ A @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_diff_cancel_left
% 0.30/0.56  thf(fact_4033_add__diff__cancel__left_H,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 0.30/0.56        = B ) ).
% 0.30/0.56  
% 0.30/0.56  % add_diff_cancel_left'
% 0.30/0.56  thf(fact_4034_add__diff__cancel__left_H,axiom,
% 0.30/0.56      ! [A: nat,B: nat] :
% 0.30/0.56        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 0.30/0.56        = B ) ).
% 0.30/0.56  
% 0.30/0.56  % add_diff_cancel_left'
% 0.30/0.56  thf(fact_4035_add__diff__cancel__left_H,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 0.30/0.56        = B ) ).
% 0.30/0.56  
% 0.30/0.56  % add_diff_cancel_left'
% 0.30/0.56  thf(fact_4036_add__diff__cancel__right,axiom,
% 0.30/0.56      ! [A: rat,C: rat,B: rat] :
% 0.30/0.56        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.30/0.56        = ( minus_minus_rat @ A @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_diff_cancel_right
% 0.30/0.56  thf(fact_4037_add__diff__cancel__right,axiom,
% 0.30/0.56      ! [A: nat,C: nat,B: nat] :
% 0.30/0.56        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.30/0.56        = ( minus_minus_nat @ A @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_diff_cancel_right
% 0.30/0.56  thf(fact_4038_add__diff__cancel__right,axiom,
% 0.30/0.56      ! [A: int,C: int,B: int] :
% 0.30/0.56        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.30/0.56        = ( minus_minus_int @ A @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_diff_cancel_right
% 0.30/0.56  thf(fact_4039_add__diff__cancel__right_H,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.30/0.56        = A ) ).
% 0.30/0.56  
% 0.30/0.56  % add_diff_cancel_right'
% 0.30/0.56  thf(fact_4040_add__diff__cancel__right_H,axiom,
% 0.30/0.56      ! [A: nat,B: nat] :
% 0.30/0.56        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.30/0.56        = A ) ).
% 0.30/0.56  
% 0.30/0.56  % add_diff_cancel_right'
% 0.30/0.56  thf(fact_4041_add__diff__cancel__right_H,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.30/0.56        = A ) ).
% 0.30/0.56  
% 0.30/0.56  % add_diff_cancel_right'
% 0.30/0.56  thf(fact_4042_minus__add__distrib,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.30/0.56        = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % minus_add_distrib
% 0.30/0.56  thf(fact_4043_minus__add__distrib,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.30/0.56        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % minus_add_distrib
% 0.30/0.56  thf(fact_4044_minus__add__distrib,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.30/0.56        = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % minus_add_distrib
% 0.30/0.56  thf(fact_4045_minus__add__cancel,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 0.30/0.56        = B ) ).
% 0.30/0.56  
% 0.30/0.56  % minus_add_cancel
% 0.30/0.56  thf(fact_4046_minus__add__cancel,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.30/0.56        = B ) ).
% 0.30/0.56  
% 0.30/0.56  % minus_add_cancel
% 0.30/0.56  thf(fact_4047_minus__add__cancel,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 0.30/0.56        = B ) ).
% 0.30/0.56  
% 0.30/0.56  % minus_add_cancel
% 0.30/0.56  thf(fact_4048_add__minus__cancel,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 0.30/0.56        = B ) ).
% 0.30/0.56  
% 0.30/0.56  % add_minus_cancel
% 0.30/0.56  thf(fact_4049_add__minus__cancel,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 0.30/0.56        = B ) ).
% 0.30/0.56  
% 0.30/0.56  % add_minus_cancel
% 0.30/0.56  thf(fact_4050_add__minus__cancel,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 0.30/0.56        = B ) ).
% 0.30/0.56  
% 0.30/0.56  % add_minus_cancel
% 0.30/0.56  thf(fact_4051_add__le__same__cancel1,axiom,
% 0.30/0.56      ! [B: code_integer,A: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 0.30/0.56        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_le_same_cancel1
% 0.30/0.56  thf(fact_4052_add__le__same__cancel1,axiom,
% 0.30/0.56      ! [B: rat,A: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 0.30/0.56        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_le_same_cancel1
% 0.30/0.56  thf(fact_4053_add__le__same__cancel1,axiom,
% 0.30/0.56      ! [B: nat,A: nat] :
% 0.30/0.56        ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.30/0.56        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_le_same_cancel1
% 0.30/0.56  thf(fact_4054_add__le__same__cancel1,axiom,
% 0.30/0.56      ! [B: int,A: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.30/0.56        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_le_same_cancel1
% 0.30/0.56  thf(fact_4055_add__le__same__cancel2,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 0.30/0.56        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_le_same_cancel2
% 0.30/0.56  thf(fact_4056_add__le__same__cancel2,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.30/0.56        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_le_same_cancel2
% 0.30/0.56  thf(fact_4057_add__le__same__cancel2,axiom,
% 0.30/0.56      ! [A: nat,B: nat] :
% 0.30/0.56        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.30/0.56        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_le_same_cancel2
% 0.30/0.56  thf(fact_4058_add__le__same__cancel2,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.30/0.56        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_le_same_cancel2
% 0.30/0.56  thf(fact_4059_le__add__same__cancel1,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.30/0.56        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % le_add_same_cancel1
% 0.30/0.56  thf(fact_4060_le__add__same__cancel1,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.30/0.56        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % le_add_same_cancel1
% 0.30/0.56  thf(fact_4061_le__add__same__cancel1,axiom,
% 0.30/0.56      ! [A: nat,B: nat] :
% 0.30/0.56        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.30/0.56        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % le_add_same_cancel1
% 0.30/0.56  thf(fact_4062_le__add__same__cancel1,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.30/0.56        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % le_add_same_cancel1
% 0.30/0.56  thf(fact_4063_le__add__same__cancel2,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 0.30/0.56        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % le_add_same_cancel2
% 0.30/0.56  thf(fact_4064_le__add__same__cancel2,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.30/0.56        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % le_add_same_cancel2
% 0.30/0.56  thf(fact_4065_le__add__same__cancel2,axiom,
% 0.30/0.56      ! [A: nat,B: nat] :
% 0.30/0.56        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.30/0.56        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % le_add_same_cancel2
% 0.30/0.56  thf(fact_4066_le__add__same__cancel2,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.30/0.56        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % le_add_same_cancel2
% 0.30/0.56  thf(fact_4067_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.30/0.56      ! [A: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ A ) @ zero_z3403309356797280102nteger )
% 0.30/0.56        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.30/0.56  
% 0.30/0.56  % double_add_le_zero_iff_single_add_le_zero
% 0.30/0.56  thf(fact_4068_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.30/0.56      ! [A: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 0.30/0.56        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % double_add_le_zero_iff_single_add_le_zero
% 0.30/0.56  thf(fact_4069_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.30/0.56      ! [A: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.30/0.56        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.30/0.56  
% 0.30/0.56  % double_add_le_zero_iff_single_add_le_zero
% 0.30/0.56  thf(fact_4070_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.30/0.56      ! [A: code_integer] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ A ) )
% 0.30/0.56        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_le_double_add_iff_zero_le_single_add
% 0.30/0.56  thf(fact_4071_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.30/0.56      ! [A: rat] :
% 0.30/0.56        ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 0.30/0.56        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_le_double_add_iff_zero_le_single_add
% 0.30/0.56  thf(fact_4072_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.30/0.56      ! [A: int] :
% 0.30/0.56        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.30/0.56        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_le_double_add_iff_zero_le_single_add
% 0.30/0.56  thf(fact_4073_add__less__same__cancel1,axiom,
% 0.30/0.56      ! [B: code_integer,A: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 0.30/0.56        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_less_same_cancel1
% 0.30/0.56  thf(fact_4074_add__less__same__cancel1,axiom,
% 0.30/0.56      ! [B: rat,A: rat] :
% 0.30/0.56        ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 0.30/0.56        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_less_same_cancel1
% 0.30/0.56  thf(fact_4075_add__less__same__cancel1,axiom,
% 0.30/0.56      ! [B: nat,A: nat] :
% 0.30/0.56        ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.30/0.56        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_less_same_cancel1
% 0.30/0.56  thf(fact_4076_add__less__same__cancel1,axiom,
% 0.30/0.56      ! [B: int,A: int] :
% 0.30/0.56        ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.30/0.56        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_less_same_cancel1
% 0.30/0.56  thf(fact_4077_add__less__same__cancel2,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 0.30/0.56        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_less_same_cancel2
% 0.30/0.56  thf(fact_4078_add__less__same__cancel2,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.30/0.56        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_less_same_cancel2
% 0.30/0.56  thf(fact_4079_add__less__same__cancel2,axiom,
% 0.30/0.56      ! [A: nat,B: nat] :
% 0.30/0.56        ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.30/0.56        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_less_same_cancel2
% 0.30/0.56  thf(fact_4080_add__less__same__cancel2,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.30/0.56        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_less_same_cancel2
% 0.30/0.56  thf(fact_4081_less__add__same__cancel1,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.30/0.56        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_add_same_cancel1
% 0.30/0.56  thf(fact_4082_less__add__same__cancel1,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.30/0.56        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_add_same_cancel1
% 0.30/0.56  thf(fact_4083_less__add__same__cancel1,axiom,
% 0.30/0.56      ! [A: nat,B: nat] :
% 0.30/0.56        ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.30/0.56        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_add_same_cancel1
% 0.30/0.56  thf(fact_4084_less__add__same__cancel1,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.30/0.56        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_add_same_cancel1
% 0.30/0.56  thf(fact_4085_less__add__same__cancel2,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 0.30/0.56        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_add_same_cancel2
% 0.30/0.56  thf(fact_4086_less__add__same__cancel2,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.30/0.56        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_add_same_cancel2
% 0.30/0.56  thf(fact_4087_less__add__same__cancel2,axiom,
% 0.30/0.56      ! [A: nat,B: nat] :
% 0.30/0.56        ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.30/0.56        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_add_same_cancel2
% 0.30/0.56  thf(fact_4088_less__add__same__cancel2,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.30/0.56        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_add_same_cancel2
% 0.30/0.56  thf(fact_4089_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.30/0.56      ! [A: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ A ) @ zero_z3403309356797280102nteger )
% 0.30/0.56        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.30/0.56  
% 0.30/0.56  % double_add_less_zero_iff_single_add_less_zero
% 0.30/0.56  thf(fact_4090_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.30/0.56      ! [A: rat] :
% 0.30/0.56        ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 0.30/0.56        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.30/0.56  
% 0.30/0.56  % double_add_less_zero_iff_single_add_less_zero
% 0.30/0.56  thf(fact_4091_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.30/0.56      ! [A: int] :
% 0.30/0.56        ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.30/0.56        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.30/0.56  
% 0.30/0.56  % double_add_less_zero_iff_single_add_less_zero
% 0.30/0.56  thf(fact_4092_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.30/0.56      ! [A: code_integer] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ A ) )
% 0.30/0.56        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_double_add_iff_zero_less_single_add
% 0.30/0.56  thf(fact_4093_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.30/0.56      ! [A: rat] :
% 0.30/0.56        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 0.30/0.56        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_double_add_iff_zero_less_single_add
% 0.30/0.56  thf(fact_4094_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.30/0.56      ! [A: int] :
% 0.30/0.56        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.30/0.56        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.30/0.56  
% 0.30/0.56  % zero_less_double_add_iff_zero_less_single_add
% 0.30/0.56  thf(fact_4095_diff__add__zero,axiom,
% 0.30/0.56      ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 0.30/0.56        ( ( minus_4286766774447292334at_nat @ A @ ( plus_p7104986032573967614at_nat @ A @ B ) )
% 0.30/0.56        = zero_z1048942125864253310at_nat ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_add_zero
% 0.30/0.56  thf(fact_4096_diff__add__zero,axiom,
% 0.30/0.56      ! [A: nat,B: nat] :
% 0.30/0.56        ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.30/0.56        = zero_zero_nat ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_add_zero
% 0.30/0.56  thf(fact_4097_distrib__right__numeral,axiom,
% 0.30/0.56      ! [A: nat,B: nat,V: num] :
% 0.30/0.56        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 0.30/0.56        = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_right_numeral
% 0.30/0.56  thf(fact_4098_distrib__right__numeral,axiom,
% 0.30/0.56      ! [A: int,B: int,V: num] :
% 0.30/0.56        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 0.30/0.56        = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_right_numeral
% 0.30/0.56  thf(fact_4099_distrib__right__numeral,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer,V: num] :
% 0.30/0.56        ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V ) )
% 0.30/0.56        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_right_numeral
% 0.30/0.56  thf(fact_4100_distrib__right__numeral,axiom,
% 0.30/0.56      ! [A: rat,B: rat,V: num] :
% 0.30/0.56        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 0.30/0.56        = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_right_numeral
% 0.30/0.56  thf(fact_4101_distrib__right__numeral,axiom,
% 0.30/0.56      ! [A: code_natural,B: code_natural,V: num] :
% 0.30/0.56        ( ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ A @ B ) @ ( numera5444537566228673987atural @ V ) )
% 0.30/0.56        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( numera5444537566228673987atural @ V ) ) @ ( times_2397367101498566445atural @ B @ ( numera5444537566228673987atural @ V ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_right_numeral
% 0.30/0.56  thf(fact_4102_distrib__left__numeral,axiom,
% 0.30/0.56      ! [V: num,B: nat,C: nat] :
% 0.30/0.56        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 0.30/0.56        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_left_numeral
% 0.30/0.56  thf(fact_4103_distrib__left__numeral,axiom,
% 0.30/0.56      ! [V: num,B: int,C: int] :
% 0.30/0.56        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 0.30/0.56        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_left_numeral
% 0.30/0.56  thf(fact_4104_distrib__left__numeral,axiom,
% 0.30/0.56      ! [V: num,B: code_integer,C: code_integer] :
% 0.30/0.56        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.30/0.56        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ C ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_left_numeral
% 0.30/0.56  thf(fact_4105_distrib__left__numeral,axiom,
% 0.30/0.56      ! [V: num,B: rat,C: rat] :
% 0.30/0.56        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 0.30/0.56        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_left_numeral
% 0.30/0.56  thf(fact_4106_distrib__left__numeral,axiom,
% 0.30/0.56      ! [V: num,B: code_natural,C: code_natural] :
% 0.30/0.56        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ ( plus_p4538020629002901425atural @ B @ C ) )
% 0.30/0.56        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ B ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ C ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % distrib_left_numeral
% 0.30/0.56  thf(fact_4107_ab__left__minus,axiom,
% 0.30/0.56      ! [A: int] :
% 0.30/0.56        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 0.30/0.56        = zero_zero_int ) ).
% 0.30/0.56  
% 0.30/0.56  % ab_left_minus
% 0.30/0.56  thf(fact_4108_ab__left__minus,axiom,
% 0.30/0.56      ! [A: code_integer] :
% 0.30/0.56        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.30/0.56        = zero_z3403309356797280102nteger ) ).
% 0.30/0.56  
% 0.30/0.56  % ab_left_minus
% 0.30/0.56  thf(fact_4109_ab__left__minus,axiom,
% 0.30/0.56      ! [A: rat] :
% 0.30/0.56        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.30/0.56        = zero_zero_rat ) ).
% 0.30/0.56  
% 0.30/0.56  % ab_left_minus
% 0.30/0.56  thf(fact_4110_add_Oright__inverse,axiom,
% 0.30/0.56      ! [A: int] :
% 0.30/0.56        ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 0.30/0.56        = zero_zero_int ) ).
% 0.30/0.56  
% 0.30/0.56  % add.right_inverse
% 0.30/0.56  thf(fact_4111_add_Oright__inverse,axiom,
% 0.30/0.56      ! [A: code_integer] :
% 0.30/0.56        ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.30/0.56        = zero_z3403309356797280102nteger ) ).
% 0.30/0.56  
% 0.30/0.56  % add.right_inverse
% 0.30/0.56  thf(fact_4112_add_Oright__inverse,axiom,
% 0.30/0.56      ! [A: rat] :
% 0.30/0.56        ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.30/0.56        = zero_zero_rat ) ).
% 0.30/0.56  
% 0.30/0.56  % add.right_inverse
% 0.30/0.56  thf(fact_4113_semiring__norm_I168_J,axiom,
% 0.30/0.56      ! [V: num,W: num,Y: int] :
% 0.30/0.56        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 0.30/0.56        = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 0.30/0.56  
% 0.30/0.56  % semiring_norm(168)
% 0.30/0.56  thf(fact_4114_semiring__norm_I168_J,axiom,
% 0.30/0.56      ! [V: num,W: num,Y: code_integer] :
% 0.30/0.56        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 0.30/0.56        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 0.30/0.56  
% 0.30/0.56  % semiring_norm(168)
% 0.30/0.56  thf(fact_4115_semiring__norm_I168_J,axiom,
% 0.30/0.56      ! [V: num,W: num,Y: rat] :
% 0.30/0.56        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 0.30/0.56        = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 0.30/0.56  
% 0.30/0.56  % semiring_norm(168)
% 0.30/0.56  thf(fact_4116_add__neg__numeral__simps_I3_J,axiom,
% 0.30/0.56      ! [M: num,N: num] :
% 0.30/0.56        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.56        = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_neg_numeral_simps(3)
% 0.30/0.56  thf(fact_4117_add__neg__numeral__simps_I3_J,axiom,
% 0.30/0.56      ! [M: num,N: num] :
% 0.30/0.56        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.30/0.56        = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_neg_numeral_simps(3)
% 0.30/0.56  thf(fact_4118_add__neg__numeral__simps_I3_J,axiom,
% 0.30/0.56      ! [M: num,N: num] :
% 0.30/0.56        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.30/0.56        = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % add_neg_numeral_simps(3)
% 0.30/0.56  thf(fact_4119_numeral__eq__one__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( ( numeral_numeral_nat @ N )
% 0.30/0.56          = one_one_nat )
% 0.30/0.56        = ( N = one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % numeral_eq_one_iff
% 0.30/0.56  thf(fact_4120_numeral__eq__one__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( ( numeral_numeral_int @ N )
% 0.30/0.56          = one_one_int )
% 0.30/0.56        = ( N = one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % numeral_eq_one_iff
% 0.30/0.56  thf(fact_4121_numeral__eq__one__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( ( numera6620942414471956472nteger @ N )
% 0.30/0.56          = one_one_Code_integer )
% 0.30/0.56        = ( N = one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % numeral_eq_one_iff
% 0.30/0.56  thf(fact_4122_numeral__eq__one__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( ( numeral_numeral_rat @ N )
% 0.30/0.56          = one_one_rat )
% 0.30/0.56        = ( N = one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % numeral_eq_one_iff
% 0.30/0.56  thf(fact_4123_numeral__eq__one__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( ( numera5444537566228673987atural @ N )
% 0.30/0.56          = one_one_Code_natural )
% 0.30/0.56        = ( N = one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % numeral_eq_one_iff
% 0.30/0.56  thf(fact_4124_one__eq__numeral__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( one_one_nat
% 0.30/0.56          = ( numeral_numeral_nat @ N ) )
% 0.30/0.56        = ( one = N ) ) ).
% 0.30/0.56  
% 0.30/0.56  % one_eq_numeral_iff
% 0.30/0.56  thf(fact_4125_one__eq__numeral__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( one_one_int
% 0.30/0.56          = ( numeral_numeral_int @ N ) )
% 0.30/0.56        = ( one = N ) ) ).
% 0.30/0.56  
% 0.30/0.56  % one_eq_numeral_iff
% 0.30/0.56  thf(fact_4126_one__eq__numeral__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( one_one_Code_integer
% 0.30/0.56          = ( numera6620942414471956472nteger @ N ) )
% 0.30/0.56        = ( one = N ) ) ).
% 0.30/0.56  
% 0.30/0.56  % one_eq_numeral_iff
% 0.30/0.56  thf(fact_4127_one__eq__numeral__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( one_one_rat
% 0.30/0.56          = ( numeral_numeral_rat @ N ) )
% 0.30/0.56        = ( one = N ) ) ).
% 0.30/0.56  
% 0.30/0.56  % one_eq_numeral_iff
% 0.30/0.56  thf(fact_4128_one__eq__numeral__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( one_one_Code_natural
% 0.30/0.56          = ( numera5444537566228673987atural @ N ) )
% 0.30/0.56        = ( one = N ) ) ).
% 0.30/0.56  
% 0.30/0.56  % one_eq_numeral_iff
% 0.30/0.56  thf(fact_4129_diff__numeral__simps_I3_J,axiom,
% 0.30/0.56      ! [M: num,N: num] :
% 0.30/0.56        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.30/0.56        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_numeral_simps(3)
% 0.30/0.56  thf(fact_4130_diff__numeral__simps_I3_J,axiom,
% 0.30/0.56      ! [M: num,N: num] :
% 0.30/0.56        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 0.30/0.56        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_numeral_simps(3)
% 0.30/0.56  thf(fact_4131_diff__numeral__simps_I3_J,axiom,
% 0.30/0.56      ! [M: num,N: num] :
% 0.30/0.56        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 0.30/0.56        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_numeral_simps(3)
% 0.30/0.56  thf(fact_4132_diff__numeral__simps_I2_J,axiom,
% 0.30/0.56      ! [M: num,N: num] :
% 0.30/0.56        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.56        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_numeral_simps(2)
% 0.30/0.56  thf(fact_4133_diff__numeral__simps_I2_J,axiom,
% 0.30/0.56      ! [M: num,N: num] :
% 0.30/0.56        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.30/0.56        = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_numeral_simps(2)
% 0.30/0.56  thf(fact_4134_diff__numeral__simps_I2_J,axiom,
% 0.30/0.56      ! [M: num,N: num] :
% 0.30/0.56        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.30/0.56        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_numeral_simps(2)
% 0.30/0.56  thf(fact_4135_uminus__add__conv__diff,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 0.30/0.56        = ( minus_minus_int @ B @ A ) ) ).
% 0.30/0.56  
% 0.30/0.56  % uminus_add_conv_diff
% 0.30/0.56  thf(fact_4136_uminus__add__conv__diff,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.30/0.56        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 0.30/0.56  
% 0.30/0.56  % uminus_add_conv_diff
% 0.30/0.56  thf(fact_4137_uminus__add__conv__diff,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.30/0.56        = ( minus_minus_rat @ B @ A ) ) ).
% 0.30/0.56  
% 0.30/0.56  % uminus_add_conv_diff
% 0.30/0.56  thf(fact_4138_diff__minus__eq__add,axiom,
% 0.30/0.56      ! [A: int,B: int] :
% 0.30/0.56        ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 0.30/0.56        = ( plus_plus_int @ A @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_minus_eq_add
% 0.30/0.56  thf(fact_4139_diff__minus__eq__add,axiom,
% 0.30/0.56      ! [A: code_integer,B: code_integer] :
% 0.30/0.56        ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.30/0.56        = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_minus_eq_add
% 0.30/0.56  thf(fact_4140_diff__minus__eq__add,axiom,
% 0.30/0.56      ! [A: rat,B: rat] :
% 0.30/0.56        ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.30/0.56        = ( plus_plus_rat @ A @ B ) ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_minus_eq_add
% 0.30/0.56  thf(fact_4141_add__neg__numeral__special_I7_J,axiom,
% 0.30/0.56      ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.56      = zero_zero_int ) ).
% 0.30/0.56  
% 0.30/0.56  % add_neg_numeral_special(7)
% 0.30/0.56  thf(fact_4142_add__neg__numeral__special_I7_J,axiom,
% 0.30/0.56      ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.56      = zero_z3403309356797280102nteger ) ).
% 0.30/0.56  
% 0.30/0.56  % add_neg_numeral_special(7)
% 0.30/0.56  thf(fact_4143_add__neg__numeral__special_I7_J,axiom,
% 0.30/0.56      ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.30/0.56      = zero_zero_rat ) ).
% 0.30/0.56  
% 0.30/0.56  % add_neg_numeral_special(7)
% 0.30/0.56  thf(fact_4144_add__neg__numeral__special_I8_J,axiom,
% 0.30/0.56      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 0.30/0.56      = zero_zero_int ) ).
% 0.30/0.56  
% 0.30/0.56  % add_neg_numeral_special(8)
% 0.30/0.56  thf(fact_4145_add__neg__numeral__special_I8_J,axiom,
% 0.30/0.56      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 0.30/0.56      = zero_z3403309356797280102nteger ) ).
% 0.30/0.56  
% 0.30/0.56  % add_neg_numeral_special(8)
% 0.30/0.56  thf(fact_4146_add__neg__numeral__special_I8_J,axiom,
% 0.30/0.56      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 0.30/0.56      = zero_zero_rat ) ).
% 0.30/0.56  
% 0.30/0.56  % add_neg_numeral_special(8)
% 0.30/0.56  thf(fact_4147_div__mult__self4,axiom,
% 0.30/0.56      ! [B: nat,C: nat,A: nat] :
% 0.30/0.56        ( ( B != zero_zero_nat )
% 0.30/0.56       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 0.30/0.56          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % div_mult_self4
% 0.30/0.56  thf(fact_4148_div__mult__self4,axiom,
% 0.30/0.56      ! [B: int,C: int,A: int] :
% 0.30/0.56        ( ( B != zero_zero_int )
% 0.30/0.56       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 0.30/0.56          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % div_mult_self4
% 0.30/0.56  thf(fact_4149_div__mult__self4,axiom,
% 0.30/0.56      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.30/0.56        ( ( B != zero_z3403309356797280102nteger )
% 0.30/0.56       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 0.30/0.56          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % div_mult_self4
% 0.30/0.56  thf(fact_4150_div__mult__self4,axiom,
% 0.30/0.56      ! [B: code_natural,C: code_natural,A: code_natural] :
% 0.30/0.56        ( ( B != zero_z2226904508553997617atural )
% 0.30/0.56       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ C ) @ A ) @ B )
% 0.30/0.56          = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % div_mult_self4
% 0.30/0.56  thf(fact_4151_div__mult__self3,axiom,
% 0.30/0.56      ! [B: nat,C: nat,A: nat] :
% 0.30/0.56        ( ( B != zero_zero_nat )
% 0.30/0.56       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 0.30/0.56          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % div_mult_self3
% 0.30/0.56  thf(fact_4152_div__mult__self3,axiom,
% 0.30/0.56      ! [B: int,C: int,A: int] :
% 0.30/0.56        ( ( B != zero_zero_int )
% 0.30/0.56       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 0.30/0.56          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % div_mult_self3
% 0.30/0.56  thf(fact_4153_div__mult__self3,axiom,
% 0.30/0.56      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.30/0.56        ( ( B != zero_z3403309356797280102nteger )
% 0.30/0.56       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 0.30/0.56          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % div_mult_self3
% 0.30/0.56  thf(fact_4154_div__mult__self3,axiom,
% 0.30/0.56      ! [B: code_natural,C: code_natural,A: code_natural] :
% 0.30/0.56        ( ( B != zero_z2226904508553997617atural )
% 0.30/0.56       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C @ B ) @ A ) @ B )
% 0.30/0.56          = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % div_mult_self3
% 0.30/0.56  thf(fact_4155_div__mult__self2,axiom,
% 0.30/0.56      ! [B: nat,A: nat,C: nat] :
% 0.30/0.56        ( ( B != zero_zero_nat )
% 0.30/0.56       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 0.30/0.56          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % div_mult_self2
% 0.30/0.56  thf(fact_4156_div__mult__self2,axiom,
% 0.30/0.56      ! [B: int,A: int,C: int] :
% 0.30/0.56        ( ( B != zero_zero_int )
% 0.30/0.56       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 0.30/0.56          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % div_mult_self2
% 0.30/0.56  thf(fact_4157_div__mult__self2,axiom,
% 0.30/0.56      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.30/0.56        ( ( B != zero_z3403309356797280102nteger )
% 0.30/0.56       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 0.30/0.56          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % div_mult_self2
% 0.30/0.56  thf(fact_4158_div__mult__self2,axiom,
% 0.30/0.56      ! [B: code_natural,A: code_natural,C: code_natural] :
% 0.30/0.56        ( ( B != zero_z2226904508553997617atural )
% 0.30/0.56       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ B @ C ) ) @ B )
% 0.30/0.56          = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % div_mult_self2
% 0.30/0.56  thf(fact_4159_div__mult__self1,axiom,
% 0.30/0.56      ! [B: nat,A: nat,C: nat] :
% 0.30/0.56        ( ( B != zero_zero_nat )
% 0.30/0.56       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 0.30/0.56          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % div_mult_self1
% 0.30/0.56  thf(fact_4160_div__mult__self1,axiom,
% 0.30/0.56      ! [B: int,A: int,C: int] :
% 0.30/0.56        ( ( B != zero_zero_int )
% 0.30/0.56       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 0.30/0.56          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % div_mult_self1
% 0.30/0.56  thf(fact_4161_div__mult__self1,axiom,
% 0.30/0.56      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.30/0.56        ( ( B != zero_z3403309356797280102nteger )
% 0.30/0.56       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 0.30/0.56          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % div_mult_self1
% 0.30/0.56  thf(fact_4162_div__mult__self1,axiom,
% 0.30/0.56      ! [B: code_natural,A: code_natural,C: code_natural] :
% 0.30/0.56        ( ( B != zero_z2226904508553997617atural )
% 0.30/0.56       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ C @ B ) ) @ B )
% 0.30/0.56          = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % div_mult_self1
% 0.30/0.56  thf(fact_4163_one__plus__numeral,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 0.30/0.56        = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % one_plus_numeral
% 0.30/0.56  thf(fact_4164_one__plus__numeral,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 0.30/0.56        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % one_plus_numeral
% 0.30/0.56  thf(fact_4165_one__plus__numeral,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 0.30/0.56        = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % one_plus_numeral
% 0.30/0.56  thf(fact_4166_one__plus__numeral,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 0.30/0.56        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % one_plus_numeral
% 0.30/0.56  thf(fact_4167_one__plus__numeral,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N ) )
% 0.30/0.56        = ( numera5444537566228673987atural @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % one_plus_numeral
% 0.30/0.56  thf(fact_4168_numeral__plus__one,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 0.30/0.56        = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % numeral_plus_one
% 0.30/0.56  thf(fact_4169_numeral__plus__one,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 0.30/0.56        = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % numeral_plus_one
% 0.30/0.56  thf(fact_4170_numeral__plus__one,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer )
% 0.30/0.56        = ( numera6620942414471956472nteger @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % numeral_plus_one
% 0.30/0.56  thf(fact_4171_numeral__plus__one,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 0.30/0.56        = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % numeral_plus_one
% 0.30/0.56  thf(fact_4172_numeral__plus__one,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N ) @ one_one_Code_natural )
% 0.30/0.56        = ( numera5444537566228673987atural @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % numeral_plus_one
% 0.30/0.56  thf(fact_4173_numeral__eq__neg__one__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 0.30/0.56          = ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.56        = ( N = one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % numeral_eq_neg_one_iff
% 0.30/0.56  thf(fact_4174_numeral__eq__neg__one__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 0.30/0.56          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.56        = ( N = one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % numeral_eq_neg_one_iff
% 0.30/0.56  thf(fact_4175_numeral__eq__neg__one__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 0.30/0.56          = ( uminus_uminus_rat @ one_one_rat ) )
% 0.30/0.56        = ( N = one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % numeral_eq_neg_one_iff
% 0.30/0.56  thf(fact_4176_neg__one__eq__numeral__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( ( uminus_uminus_int @ one_one_int )
% 0.30/0.56          = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.56        = ( N = one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_one_eq_numeral_iff
% 0.30/0.56  thf(fact_4177_neg__one__eq__numeral__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 0.30/0.56          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.30/0.56        = ( N = one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_one_eq_numeral_iff
% 0.30/0.56  thf(fact_4178_neg__one__eq__numeral__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( ( uminus_uminus_rat @ one_one_rat )
% 0.30/0.56          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.30/0.56        = ( N = one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % neg_one_eq_numeral_iff
% 0.30/0.56  thf(fact_4179_diff__numeral__special_I3_J,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.56        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_numeral_special(3)
% 0.30/0.56  thf(fact_4180_diff__numeral__special_I3_J,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.30/0.56        = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_numeral_special(3)
% 0.30/0.56  thf(fact_4181_diff__numeral__special_I3_J,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.30/0.56        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_numeral_special(3)
% 0.30/0.56  thf(fact_4182_diff__numeral__special_I4_J,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 0.30/0.56        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_numeral_special(4)
% 0.30/0.56  thf(fact_4183_diff__numeral__special_I4_J,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 0.30/0.56        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_numeral_special(4)
% 0.30/0.56  thf(fact_4184_diff__numeral__special_I4_J,axiom,
% 0.30/0.56      ! [M: num] :
% 0.30/0.56        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 0.30/0.56        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % diff_numeral_special(4)
% 0.30/0.56  thf(fact_4185_numeral__le__one__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer )
% 0.30/0.56        = ( ord_less_eq_num @ N @ one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % numeral_le_one_iff
% 0.30/0.56  thf(fact_4186_numeral__le__one__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( ord_le1926595141338095240atural @ ( numera5444537566228673987atural @ N ) @ one_one_Code_natural )
% 0.30/0.56        = ( ord_less_eq_num @ N @ one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % numeral_le_one_iff
% 0.30/0.56  thf(fact_4187_numeral__le__one__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 0.30/0.56        = ( ord_less_eq_num @ N @ one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % numeral_le_one_iff
% 0.30/0.56  thf(fact_4188_numeral__le__one__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 0.30/0.56        = ( ord_less_eq_num @ N @ one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % numeral_le_one_iff
% 0.30/0.56  thf(fact_4189_numeral__le__one__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 0.30/0.56        = ( ord_less_eq_num @ N @ one ) ) ).
% 0.30/0.56  
% 0.30/0.56  % numeral_le_one_iff
% 0.30/0.56  thf(fact_4190_one__less__numeral__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 0.30/0.56        = ( ord_less_num @ one @ N ) ) ).
% 0.30/0.56  
% 0.30/0.56  % one_less_numeral_iff
% 0.30/0.56  thf(fact_4191_one__less__numeral__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 0.30/0.56        = ( ord_less_num @ one @ N ) ) ).
% 0.30/0.56  
% 0.30/0.56  % one_less_numeral_iff
% 0.30/0.56  thf(fact_4192_one__less__numeral__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 0.30/0.56        = ( ord_less_num @ one @ N ) ) ).
% 0.30/0.56  
% 0.30/0.56  % one_less_numeral_iff
% 0.30/0.56  thf(fact_4193_one__less__numeral__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 0.30/0.56        = ( ord_less_num @ one @ N ) ) ).
% 0.30/0.56  
% 0.30/0.56  % one_less_numeral_iff
% 0.30/0.56  thf(fact_4194_one__less__numeral__iff,axiom,
% 0.30/0.56      ! [N: num] :
% 0.30/0.56        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N ) )
% 0.30/0.56        = ( ord_less_num @ one @ N ) ) ).
% 0.30/0.56  
% 0.30/0.56  % one_less_numeral_iff
% 0.30/0.56  thf(fact_4195_pred__subset__eq,axiom,
% 0.30/0.56      ! [R: set_se6260736226359567993nt_int,S: set_se6260736226359567993nt_int] :
% 0.30/0.56        ( ( ord_le8334417538754933252_int_o
% 0.30/0.56          @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ R )
% 0.30/0.56          @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ S ) )
% 0.30/0.56        = ( ord_le483042692224249369nt_int @ R @ S ) ) ).
% 0.30/0.56  
% 0.30/0.56  % pred_subset_eq
% 0.30/0.56  thf(fact_4196_pred__subset__eq,axiom,
% 0.30/0.56      ! [R: set_set_nat,S: set_set_nat] :
% 0.30/0.56        ( ( ord_le3964352015994296041_nat_o
% 0.30/0.56          @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ R )
% 0.30/0.56          @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ S ) )
% 0.30/0.56        = ( ord_le6893508408891458716et_nat @ R @ S ) ) ).
% 0.30/0.56  
% 0.30/0.56  % pred_subset_eq
% 0.30/0.56  thf(fact_4197_pred__subset__eq,axiom,
% 0.30/0.56      ! [R: set_int,S: set_int] :
% 0.30/0.56        ( ( ord_less_eq_int_o
% 0.30/0.56          @ ^ [X3: int] : ( member_int @ X3 @ R )
% 0.30/0.56          @ ^ [X3: int] : ( member_int @ X3 @ S ) )
% 0.30/0.56        = ( ord_less_eq_set_int @ R @ S ) ) ).
% 0.30/0.56  
% 0.30/0.56  % pred_subset_eq
% 0.30/0.56  thf(fact_4198_pred__subset__eq,axiom,
% 0.30/0.56      ! [R: set_Pr4532377907799695533_nat_o,S: set_Pr4532377907799695533_nat_o] :
% 0.30/0.56        ( ( ord_le1304494283415849680at_o_o
% 0.30/0.56          @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ R )
% 0.30/0.56          @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ S ) )
% 0.30/0.56        = ( ord_le2965882846123202637_nat_o @ R @ S ) ) ).
% 0.30/0.56  
% 0.30/0.56  % pred_subset_eq
% 0.30/0.56  thf(fact_4199_pred__subset__eq,axiom,
% 0.30/0.56      ! [R: set_nat,S: set_nat] :
% 0.30/0.56        ( ( ord_less_eq_nat_o
% 0.30/0.56          @ ^ [X3: nat] : ( member_nat @ X3 @ R )
% 0.30/0.56          @ ^ [X3: nat] : ( member_nat @ X3 @ S ) )
% 0.30/0.56        = ( ord_less_eq_set_nat @ R @ S ) ) ).
% 0.30/0.56  
% 0.30/0.56  % pred_subset_eq
% 0.30/0.56  thf(fact_4200_less__eq__set__def,axiom,
% 0.30/0.56      ( ord_le483042692224249369nt_int
% 0.30/0.56      = ( ^ [A4: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
% 0.30/0.56            ( ord_le8334417538754933252_int_o
% 0.30/0.56            @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ A4 )
% 0.30/0.56            @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ B4 ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_eq_set_def
% 0.30/0.56  thf(fact_4201_less__eq__set__def,axiom,
% 0.30/0.56      ( ord_le6893508408891458716et_nat
% 0.30/0.56      = ( ^ [A4: set_set_nat,B4: set_set_nat] :
% 0.30/0.56            ( ord_le3964352015994296041_nat_o
% 0.30/0.56            @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A4 )
% 0.30/0.56            @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ B4 ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_eq_set_def
% 0.30/0.56  thf(fact_4202_less__eq__set__def,axiom,
% 0.30/0.56      ( ord_less_eq_set_int
% 0.30/0.56      = ( ^ [A4: set_int,B4: set_int] :
% 0.30/0.56            ( ord_less_eq_int_o
% 0.30/0.56            @ ^ [X3: int] : ( member_int @ X3 @ A4 )
% 0.30/0.56            @ ^ [X3: int] : ( member_int @ X3 @ B4 ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_eq_set_def
% 0.30/0.56  thf(fact_4203_less__eq__set__def,axiom,
% 0.30/0.56      ( ord_le2965882846123202637_nat_o
% 0.30/0.56      = ( ^ [A4: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 0.30/0.56            ( ord_le1304494283415849680at_o_o
% 0.30/0.56            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ A4 )
% 0.30/0.56            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ B4 ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_eq_set_def
% 0.30/0.56  thf(fact_4204_less__eq__set__def,axiom,
% 0.30/0.56      ( ord_less_eq_set_nat
% 0.30/0.56      = ( ^ [A4: set_nat,B4: set_nat] :
% 0.30/0.56            ( ord_less_eq_nat_o
% 0.30/0.56            @ ^ [X3: nat] : ( member_nat @ X3 @ A4 )
% 0.30/0.56            @ ^ [X3: nat] : ( member_nat @ X3 @ B4 ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_eq_set_def
% 0.30/0.56  thf(fact_4205_less__set__def,axiom,
% 0.30/0.56      ( ord_le1924305788584680229nt_int
% 0.30/0.56      = ( ^ [A4: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
% 0.30/0.56            ( ord_le2688692977766382584_int_o
% 0.30/0.56            @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ A4 )
% 0.30/0.56            @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ B4 ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_set_def
% 0.30/0.56  thf(fact_4206_less__set__def,axiom,
% 0.30/0.56      ( ord_less_set_set_nat
% 0.30/0.56      = ( ^ [A4: set_set_nat,B4: set_set_nat] :
% 0.30/0.56            ( ord_less_set_nat_o
% 0.30/0.56            @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A4 )
% 0.30/0.56            @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ B4 ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_set_def
% 0.30/0.56  thf(fact_4207_less__set__def,axiom,
% 0.30/0.56      ( ord_less_set_nat
% 0.30/0.56      = ( ^ [A4: set_nat,B4: set_nat] :
% 0.30/0.56            ( ord_less_nat_o
% 0.30/0.56            @ ^ [X3: nat] : ( member_nat @ X3 @ A4 )
% 0.30/0.56            @ ^ [X3: nat] : ( member_nat @ X3 @ B4 ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_set_def
% 0.30/0.56  thf(fact_4208_less__set__def,axiom,
% 0.30/0.56      ( ord_less_set_int
% 0.30/0.56      = ( ^ [A4: set_int,B4: set_int] :
% 0.30/0.56            ( ord_less_int_o
% 0.30/0.56            @ ^ [X3: int] : ( member_int @ X3 @ A4 )
% 0.30/0.56            @ ^ [X3: int] : ( member_int @ X3 @ B4 ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_set_def
% 0.30/0.56  thf(fact_4209_less__set__def,axiom,
% 0.30/0.56      ( ord_le2453136405763929_nat_o
% 0.30/0.56      = ( ^ [A4: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 0.30/0.56            ( ord_le5728734702541193924at_o_o
% 0.30/0.56            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ A4 )
% 0.30/0.56            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ B4 ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_set_def
% 0.30/0.56  thf(fact_4210_less__assn__def,axiom,
% 0.30/0.56      ( ord_less_assn
% 0.30/0.56      = ( ^ [A3: assn,B3: assn] :
% 0.30/0.56            ( ( ord_less_eq_assn @ A3 @ B3 )
% 0.30/0.56            & ( A3 != B3 ) ) ) ) ).
% 0.30/0.56  
% 0.30/0.56  % less_assn_def
% 0.30/0.56  thf(fact_4211_Collect__subset,axiom,
% 0.30/0.56      ! [A2: set_se6260736226359567993nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 0.30/0.56        ( ord_le483042692224249369nt_int
% 0.30/0.56        @ ( collec5210948495886036740nt_int
% 0.30/0.56          @ ^ [X3: set_Pr958786334691620121nt_int] :
% 0.30/0.56              ( ( member2340774599025711042nt_int @ X3 @ A2 )
% 0.30/0.56              & ( P @ X3 ) ) )
% 0.30/0.56        @ A2 ) ).
% 0.30/0.56  
% 0.30/0.56  % Collect_subset
% 0.30/0.56  thf(fact_4212_Collect__subset,axiom,
% 0.30/0.56      ! [A2: set_set_nat,P: set_nat > $o] :
% 0.30/0.56        ( ord_le6893508408891458716et_nat
% 0.30/0.56        @ ( collect_set_nat
% 0.30/0.56          @ ^ [X3: set_nat] :
% 0.30/0.56              ( ( member_set_nat @ X3 @ A2 )
% 0.30/0.56              & ( P @ X3 ) ) )
% 0.30/0.56        @ A2 ) ).
% 0.30/0.56  
% 0.30/0.56  % Collect_subset
% 0.30/0.56  thf(fact_4213_Collect__subset,axiom,
% 0.30/0.56      ! [A2: set_int,P: int > $o] :
% 0.30/0.56        ( ord_less_eq_set_int
% 0.30/0.56        @ ( collect_int
% 0.30/0.56          @ ^ [X3: int] :
% 0.30/0.56              ( ( member_int @ X3 @ A2 )
% 0.30/0.56              & ( P @ X3 ) ) )
% 0.30/0.56        @ A2 ) ).
% 0.30/0.56  
% 0.30/0.56  % Collect_subset
% 0.30/0.56  thf(fact_4214_Collect__subset,axiom,
% 0.30/0.56      ! [A2: set_Pr4532377907799695533_nat_o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.30/0.56        ( ord_le2965882846123202637_nat_o
% 0.30/0.56        @ ( collec939566748876313656_nat_o
% 0.30/0.56          @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.30/0.56              ( ( member6576561426505652726_nat_o @ X3 @ A2 )
% 0.30/0.56              & ( P @ X3 ) ) )
% 0.30/0.56        @ A2 ) ).
% 0.30/0.56  
% 0.30/0.56  % Collect_subset
% 0.30/0.56  thf(fact_4215_Collect__subset,axiom,
% 0.30/0.56      ! [A2: set_nat,P: nat > $o] :
% 0.30/0.57        ( ord_less_eq_set_nat
% 0.30/0.57        @ ( collect_nat
% 0.30/0.57          @ ^ [X3: nat] :
% 0.30/0.57              ( ( member_nat @ X3 @ A2 )
% 0.30/0.57              & ( P @ X3 ) ) )
% 0.30/0.57        @ A2 ) ).
% 0.30/0.57  
% 0.30/0.57  % Collect_subset
% 0.30/0.57  thf(fact_4216_conj__subset__def,axiom,
% 0.30/0.57      ! [A2: set_se6260736226359567993nt_int,P: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 0.30/0.57        ( ( ord_le483042692224249369nt_int @ A2
% 0.30/0.57          @ ( collec5210948495886036740nt_int
% 0.30/0.57            @ ^ [X3: set_Pr958786334691620121nt_int] :
% 0.30/0.57                ( ( P @ X3 )
% 0.30/0.57                & ( Q2 @ X3 ) ) ) )
% 0.30/0.57        = ( ( ord_le483042692224249369nt_int @ A2 @ ( collec5210948495886036740nt_int @ P ) )
% 0.30/0.57          & ( ord_le483042692224249369nt_int @ A2 @ ( collec5210948495886036740nt_int @ Q2 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % conj_subset_def
% 0.30/0.57  thf(fact_4217_conj__subset__def,axiom,
% 0.30/0.57      ! [A2: set_set_nat,P: set_nat > $o,Q2: set_nat > $o] :
% 0.30/0.57        ( ( ord_le6893508408891458716et_nat @ A2
% 0.30/0.57          @ ( collect_set_nat
% 0.30/0.57            @ ^ [X3: set_nat] :
% 0.30/0.57                ( ( P @ X3 )
% 0.30/0.57                & ( Q2 @ X3 ) ) ) )
% 0.30/0.57        = ( ( ord_le6893508408891458716et_nat @ A2 @ ( collect_set_nat @ P ) )
% 0.30/0.57          & ( ord_le6893508408891458716et_nat @ A2 @ ( collect_set_nat @ Q2 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % conj_subset_def
% 0.30/0.57  thf(fact_4218_conj__subset__def,axiom,
% 0.30/0.57      ! [A2: set_int,P: int > $o,Q2: int > $o] :
% 0.30/0.57        ( ( ord_less_eq_set_int @ A2
% 0.30/0.57          @ ( collect_int
% 0.30/0.57            @ ^ [X3: int] :
% 0.30/0.57                ( ( P @ X3 )
% 0.30/0.57                & ( Q2 @ X3 ) ) ) )
% 0.30/0.57        = ( ( ord_less_eq_set_int @ A2 @ ( collect_int @ P ) )
% 0.30/0.57          & ( ord_less_eq_set_int @ A2 @ ( collect_int @ Q2 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % conj_subset_def
% 0.30/0.57  thf(fact_4219_conj__subset__def,axiom,
% 0.30/0.57      ! [A2: set_Pr4532377907799695533_nat_o,P: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.30/0.57        ( ( ord_le2965882846123202637_nat_o @ A2
% 0.30/0.57          @ ( collec939566748876313656_nat_o
% 0.30/0.57            @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.30/0.57                ( ( P @ X3 )
% 0.30/0.57                & ( Q2 @ X3 ) ) ) )
% 0.30/0.57        = ( ( ord_le2965882846123202637_nat_o @ A2 @ ( collec939566748876313656_nat_o @ P ) )
% 0.30/0.57          & ( ord_le2965882846123202637_nat_o @ A2 @ ( collec939566748876313656_nat_o @ Q2 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % conj_subset_def
% 0.30/0.57  thf(fact_4220_conj__subset__def,axiom,
% 0.30/0.57      ! [A2: set_nat,P: nat > $o,Q2: nat > $o] :
% 0.30/0.57        ( ( ord_less_eq_set_nat @ A2
% 0.30/0.57          @ ( collect_nat
% 0.30/0.57            @ ^ [X3: nat] :
% 0.30/0.57                ( ( P @ X3 )
% 0.30/0.57                & ( Q2 @ X3 ) ) ) )
% 0.30/0.57        = ( ( ord_less_eq_set_nat @ A2 @ ( collect_nat @ P ) )
% 0.30/0.57          & ( ord_less_eq_set_nat @ A2 @ ( collect_nat @ Q2 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % conj_subset_def
% 0.30/0.57  thf(fact_4221_ordering__top_Oextremum,axiom,
% 0.30/0.57      ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 0.30/0.57        ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 0.30/0.57       => ( Less_eq @ A @ Top ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ordering_top.extremum
% 0.30/0.57  thf(fact_4222_ordering__top_Oextremum__strict,axiom,
% 0.30/0.57      ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 0.30/0.57        ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 0.30/0.57       => ~ ( Less @ Top @ A ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ordering_top.extremum_strict
% 0.30/0.57  thf(fact_4223_ordering__top_Oextremum__unique,axiom,
% 0.30/0.57      ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 0.30/0.57        ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 0.30/0.57       => ( ( Less_eq @ Top @ A )
% 0.30/0.57          = ( A = Top ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ordering_top.extremum_unique
% 0.30/0.57  thf(fact_4224_ordering__top_Onot__eq__extremum,axiom,
% 0.30/0.57      ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 0.30/0.57        ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 0.30/0.57       => ( ( A != Top )
% 0.30/0.57          = ( Less @ A @ Top ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ordering_top.not_eq_extremum
% 0.30/0.57  thf(fact_4225_ordering__top_Oextremum__uniqueI,axiom,
% 0.30/0.57      ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 0.30/0.57        ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 0.30/0.57       => ( ( Less_eq @ Top @ A )
% 0.30/0.57         => ( A = Top ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ordering_top.extremum_uniqueI
% 0.30/0.57  thf(fact_4226_semilattice__neutr__order_Oeq__neutr__iff,axiom,
% 0.30/0.57      ! [F2: nat > nat > nat,Z: nat,Less_eq: nat > nat > $o,Less: nat > nat > $o,A: nat,B: nat] :
% 0.30/0.57        ( ( semila1623282765462674594er_nat @ F2 @ Z @ Less_eq @ Less )
% 0.30/0.57       => ( ( ( F2 @ A @ B )
% 0.30/0.57            = Z )
% 0.30/0.57          = ( ( A = Z )
% 0.30/0.57            & ( B = Z ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % semilattice_neutr_order.eq_neutr_iff
% 0.30/0.57  thf(fact_4227_semilattice__neutr__order_Oneutr__eq__iff,axiom,
% 0.30/0.57      ! [F2: nat > nat > nat,Z: nat,Less_eq: nat > nat > $o,Less: nat > nat > $o,A: nat,B: nat] :
% 0.30/0.57        ( ( semila1623282765462674594er_nat @ F2 @ Z @ Less_eq @ Less )
% 0.30/0.57       => ( ( Z
% 0.30/0.57            = ( F2 @ A @ B ) )
% 0.30/0.57          = ( ( A = Z )
% 0.30/0.57            & ( B = Z ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % semilattice_neutr_order.neutr_eq_iff
% 0.30/0.57  thf(fact_4228_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.30/0.57      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.30/0.57        ( ( ( I = J )
% 0.30/0.57          & ( K = L ) )
% 0.30/0.57       => ( ( plus_plus_rat @ I @ K )
% 0.30/0.57          = ( plus_plus_rat @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_semiring(4)
% 0.30/0.57  thf(fact_4229_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.30/0.57      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.30/0.57        ( ( ( I = J )
% 0.30/0.57          & ( K = L ) )
% 0.30/0.57       => ( ( plus_plus_nat @ I @ K )
% 0.30/0.57          = ( plus_plus_nat @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_semiring(4)
% 0.30/0.57  thf(fact_4230_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.30/0.57      ! [I: int,J: int,K: int,L: int] :
% 0.30/0.57        ( ( ( I = J )
% 0.30/0.57          & ( K = L ) )
% 0.30/0.57       => ( ( plus_plus_int @ I @ K )
% 0.30/0.57          = ( plus_plus_int @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_semiring(4)
% 0.30/0.57  thf(fact_4231_group__cancel_Oadd1,axiom,
% 0.30/0.57      ! [A2: rat,K: rat,A: rat,B: rat] :
% 0.30/0.57        ( ( A2
% 0.30/0.57          = ( plus_plus_rat @ K @ A ) )
% 0.30/0.57       => ( ( plus_plus_rat @ A2 @ B )
% 0.30/0.57          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % group_cancel.add1
% 0.30/0.57  thf(fact_4232_group__cancel_Oadd1,axiom,
% 0.30/0.57      ! [A2: nat,K: nat,A: nat,B: nat] :
% 0.30/0.57        ( ( A2
% 0.30/0.57          = ( plus_plus_nat @ K @ A ) )
% 0.30/0.57       => ( ( plus_plus_nat @ A2 @ B )
% 0.30/0.57          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % group_cancel.add1
% 0.30/0.57  thf(fact_4233_group__cancel_Oadd1,axiom,
% 0.30/0.57      ! [A2: int,K: int,A: int,B: int] :
% 0.30/0.57        ( ( A2
% 0.30/0.57          = ( plus_plus_int @ K @ A ) )
% 0.30/0.57       => ( ( plus_plus_int @ A2 @ B )
% 0.30/0.57          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % group_cancel.add1
% 0.30/0.57  thf(fact_4234_group__cancel_Oadd2,axiom,
% 0.30/0.57      ! [B2: rat,K: rat,B: rat,A: rat] :
% 0.30/0.57        ( ( B2
% 0.30/0.57          = ( plus_plus_rat @ K @ B ) )
% 0.30/0.57       => ( ( plus_plus_rat @ A @ B2 )
% 0.30/0.57          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % group_cancel.add2
% 0.30/0.57  thf(fact_4235_group__cancel_Oadd2,axiom,
% 0.30/0.57      ! [B2: nat,K: nat,B: nat,A: nat] :
% 0.30/0.57        ( ( B2
% 0.30/0.57          = ( plus_plus_nat @ K @ B ) )
% 0.30/0.57       => ( ( plus_plus_nat @ A @ B2 )
% 0.30/0.57          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % group_cancel.add2
% 0.30/0.57  thf(fact_4236_group__cancel_Oadd2,axiom,
% 0.30/0.57      ! [B2: int,K: int,B: int,A: int] :
% 0.30/0.57        ( ( B2
% 0.30/0.57          = ( plus_plus_int @ K @ B ) )
% 0.30/0.57       => ( ( plus_plus_int @ A @ B2 )
% 0.30/0.57          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % group_cancel.add2
% 0.30/0.57  thf(fact_4237_add_Oassoc,axiom,
% 0.30/0.57      ! [A: literal,B: literal,C: literal] :
% 0.30/0.57        ( ( plus_plus_literal @ ( plus_plus_literal @ A @ B ) @ C )
% 0.30/0.57        = ( plus_plus_literal @ A @ ( plus_plus_literal @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.assoc
% 0.30/0.57  thf(fact_4238_add_Oassoc,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.30/0.57        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.assoc
% 0.30/0.57  thf(fact_4239_add_Oassoc,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.30/0.57        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.assoc
% 0.30/0.57  thf(fact_4240_add_Oassoc,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.30/0.57        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.assoc
% 0.30/0.57  thf(fact_4241_add_Oleft__cancel,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( ( plus_plus_rat @ A @ B )
% 0.30/0.57          = ( plus_plus_rat @ A @ C ) )
% 0.30/0.57        = ( B = C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.left_cancel
% 0.30/0.57  thf(fact_4242_add_Oleft__cancel,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( ( plus_plus_int @ A @ B )
% 0.30/0.57          = ( plus_plus_int @ A @ C ) )
% 0.30/0.57        = ( B = C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.left_cancel
% 0.30/0.57  thf(fact_4243_add_Oright__cancel,axiom,
% 0.30/0.57      ! [B: rat,A: rat,C: rat] :
% 0.30/0.57        ( ( ( plus_plus_rat @ B @ A )
% 0.30/0.57          = ( plus_plus_rat @ C @ A ) )
% 0.30/0.57        = ( B = C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.right_cancel
% 0.30/0.57  thf(fact_4244_add_Oright__cancel,axiom,
% 0.30/0.57      ! [B: int,A: int,C: int] :
% 0.30/0.57        ( ( ( plus_plus_int @ B @ A )
% 0.30/0.57          = ( plus_plus_int @ C @ A ) )
% 0.30/0.57        = ( B = C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.right_cancel
% 0.30/0.57  thf(fact_4245_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 0.30/0.57      ( plus_plus_rat
% 0.30/0.57      = ( ^ [A3: rat,B3: rat] : ( plus_plus_rat @ B3 @ A3 ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ab_semigroup_add_class.add.commute
% 0.30/0.57  thf(fact_4246_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 0.30/0.57      ( plus_plus_nat
% 0.30/0.57      = ( ^ [A3: nat,B3: nat] : ( plus_plus_nat @ B3 @ A3 ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ab_semigroup_add_class.add.commute
% 0.30/0.57  thf(fact_4247_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 0.30/0.57      ( plus_plus_int
% 0.30/0.57      = ( ^ [A3: int,B3: int] : ( plus_plus_int @ B3 @ A3 ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ab_semigroup_add_class.add.commute
% 0.30/0.57  thf(fact_4248_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 0.30/0.57      ! [B: rat,A: rat,C: rat] :
% 0.30/0.57        ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 0.30/0.57        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ab_semigroup_add_class.add.left_commute
% 0.30/0.57  thf(fact_4249_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 0.30/0.57      ! [B: nat,A: nat,C: nat] :
% 0.30/0.57        ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 0.30/0.57        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ab_semigroup_add_class.add.left_commute
% 0.30/0.57  thf(fact_4250_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 0.30/0.57      ! [B: int,A: int,C: int] :
% 0.30/0.57        ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 0.30/0.57        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ab_semigroup_add_class.add.left_commute
% 0.30/0.57  thf(fact_4251_add__left__imp__eq,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( ( plus_plus_rat @ A @ B )
% 0.30/0.57          = ( plus_plus_rat @ A @ C ) )
% 0.30/0.57       => ( B = C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_left_imp_eq
% 0.30/0.57  thf(fact_4252_add__left__imp__eq,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( ( plus_plus_nat @ A @ B )
% 0.30/0.57          = ( plus_plus_nat @ A @ C ) )
% 0.30/0.57       => ( B = C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_left_imp_eq
% 0.30/0.57  thf(fact_4253_add__left__imp__eq,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( ( plus_plus_int @ A @ B )
% 0.30/0.57          = ( plus_plus_int @ A @ C ) )
% 0.30/0.57       => ( B = C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_left_imp_eq
% 0.30/0.57  thf(fact_4254_add__right__imp__eq,axiom,
% 0.30/0.57      ! [B: rat,A: rat,C: rat] :
% 0.30/0.57        ( ( ( plus_plus_rat @ B @ A )
% 0.30/0.57          = ( plus_plus_rat @ C @ A ) )
% 0.30/0.57       => ( B = C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_right_imp_eq
% 0.30/0.57  thf(fact_4255_add__right__imp__eq,axiom,
% 0.30/0.57      ! [B: nat,A: nat,C: nat] :
% 0.30/0.57        ( ( ( plus_plus_nat @ B @ A )
% 0.30/0.57          = ( plus_plus_nat @ C @ A ) )
% 0.30/0.57       => ( B = C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_right_imp_eq
% 0.30/0.57  thf(fact_4256_add__right__imp__eq,axiom,
% 0.30/0.57      ! [B: int,A: int,C: int] :
% 0.30/0.57        ( ( ( plus_plus_int @ B @ A )
% 0.30/0.57          = ( plus_plus_int @ C @ A ) )
% 0.30/0.57       => ( B = C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_right_imp_eq
% 0.30/0.57  thf(fact_4257_add_Oright__assoc,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.30/0.57        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.right_assoc
% 0.30/0.57  thf(fact_4258_add_Oright__assoc,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.30/0.57        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.right_assoc
% 0.30/0.57  thf(fact_4259_add_Oright__assoc,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.30/0.57        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.right_assoc
% 0.30/0.57  thf(fact_4260_add_Oright__commute,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.30/0.57        = ( plus_plus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.right_commute
% 0.30/0.57  thf(fact_4261_add_Oright__commute,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.30/0.57        = ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.right_commute
% 0.30/0.57  thf(fact_4262_add_Oright__commute,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.30/0.57        = ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.right_commute
% 0.30/0.57  thf(fact_4263_numerals_I1_J,axiom,
% 0.30/0.57      ( ( numeral_numeral_nat @ one )
% 0.30/0.57      = one_one_nat ) ).
% 0.30/0.57  
% 0.30/0.57  % numerals(1)
% 0.30/0.57  thf(fact_4264_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.30/0.57      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.30/0.57        ( ( ( ord_less_eq_rat @ I @ J )
% 0.30/0.57          & ( K = L ) )
% 0.30/0.57       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_semiring(3)
% 0.30/0.57  thf(fact_4265_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.30/0.57      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.30/0.57        ( ( ( ord_less_eq_nat @ I @ J )
% 0.30/0.57          & ( K = L ) )
% 0.30/0.57       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_semiring(3)
% 0.30/0.57  thf(fact_4266_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.30/0.57      ! [I: int,J: int,K: int,L: int] :
% 0.30/0.57        ( ( ( ord_less_eq_int @ I @ J )
% 0.30/0.57          & ( K = L ) )
% 0.30/0.57       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_semiring(3)
% 0.30/0.57  thf(fact_4267_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.30/0.57      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.30/0.57        ( ( ( I = J )
% 0.30/0.57          & ( ord_less_eq_rat @ K @ L ) )
% 0.30/0.57       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_semiring(2)
% 0.30/0.57  thf(fact_4268_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.30/0.57      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.30/0.57        ( ( ( I = J )
% 0.30/0.57          & ( ord_less_eq_nat @ K @ L ) )
% 0.30/0.57       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_semiring(2)
% 0.30/0.57  thf(fact_4269_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.30/0.57      ! [I: int,J: int,K: int,L: int] :
% 0.30/0.57        ( ( ( I = J )
% 0.30/0.57          & ( ord_less_eq_int @ K @ L ) )
% 0.30/0.57       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_semiring(2)
% 0.30/0.57  thf(fact_4270_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.30/0.57      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.30/0.57        ( ( ( ord_less_eq_rat @ I @ J )
% 0.30/0.57          & ( ord_less_eq_rat @ K @ L ) )
% 0.30/0.57       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_semiring(1)
% 0.30/0.57  thf(fact_4271_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.30/0.57      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.30/0.57        ( ( ( ord_less_eq_nat @ I @ J )
% 0.30/0.57          & ( ord_less_eq_nat @ K @ L ) )
% 0.30/0.57       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_semiring(1)
% 0.30/0.57  thf(fact_4272_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.30/0.57      ! [I: int,J: int,K: int,L: int] :
% 0.30/0.57        ( ( ( ord_less_eq_int @ I @ J )
% 0.30/0.57          & ( ord_less_eq_int @ K @ L ) )
% 0.30/0.57       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_semiring(1)
% 0.30/0.57  thf(fact_4273_add__mono,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.57       => ( ( ord_less_eq_rat @ C @ D2 )
% 0.30/0.57         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono
% 0.30/0.57  thf(fact_4274_add__mono,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.57       => ( ( ord_less_eq_nat @ C @ D2 )
% 0.30/0.57         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono
% 0.30/0.57  thf(fact_4275_add__mono,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int,D2: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ A @ B )
% 0.30/0.57       => ( ( ord_less_eq_int @ C @ D2 )
% 0.30/0.57         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono
% 0.30/0.57  thf(fact_4276_add__left__mono,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.57       => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_left_mono
% 0.30/0.57  thf(fact_4277_add__left__mono,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.57       => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_left_mono
% 0.30/0.57  thf(fact_4278_add__left__mono,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ A @ B )
% 0.30/0.57       => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_left_mono
% 0.30/0.57  thf(fact_4279_less__eqE,axiom,
% 0.30/0.57      ! [A: nat,B: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.57       => ~ ! [C3: nat] :
% 0.30/0.57              ( B
% 0.30/0.57             != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % less_eqE
% 0.30/0.57  thf(fact_4280_add__right__mono,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.57       => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_right_mono
% 0.30/0.57  thf(fact_4281_add__right__mono,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.57       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_right_mono
% 0.30/0.57  thf(fact_4282_add__right__mono,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ A @ B )
% 0.30/0.57       => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_right_mono
% 0.30/0.57  thf(fact_4283_le__iff__add,axiom,
% 0.30/0.57      ( ord_less_eq_nat
% 0.30/0.57      = ( ^ [A3: nat,B3: nat] :
% 0.30/0.57          ? [C4: nat] :
% 0.30/0.57            ( B3
% 0.30/0.57            = ( plus_plus_nat @ A3 @ C4 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % le_iff_add
% 0.30/0.57  thf(fact_4284_add__le__imp__le__left,axiom,
% 0.30/0.57      ! [C: rat,A: rat,B: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.30/0.57       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_le_imp_le_left
% 0.30/0.57  thf(fact_4285_add__le__imp__le__left,axiom,
% 0.30/0.57      ! [C: nat,A: nat,B: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.30/0.57       => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_le_imp_le_left
% 0.30/0.57  thf(fact_4286_add__le__imp__le__left,axiom,
% 0.30/0.57      ! [C: int,A: int,B: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.30/0.57       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_le_imp_le_left
% 0.30/0.57  thf(fact_4287_add__le__imp__le__right,axiom,
% 0.30/0.57      ! [A: rat,C: rat,B: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.30/0.57       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_le_imp_le_right
% 0.30/0.57  thf(fact_4288_add__le__imp__le__right,axiom,
% 0.30/0.57      ! [A: nat,C: nat,B: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.30/0.57       => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_le_imp_le_right
% 0.30/0.57  thf(fact_4289_add__le__imp__le__right,axiom,
% 0.30/0.57      ! [A: int,C: int,B: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.30/0.57       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_le_imp_le_right
% 0.30/0.57  thf(fact_4290_comm__monoid__add__class_Oadd__0,axiom,
% 0.30/0.57      ! [A: code_integer] :
% 0.30/0.57        ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % comm_monoid_add_class.add_0
% 0.30/0.57  thf(fact_4291_comm__monoid__add__class_Oadd__0,axiom,
% 0.30/0.57      ! [A: multis2468970476368604999at_nat] :
% 0.30/0.57        ( ( plus_p7104986032573967614at_nat @ zero_z1048942125864253310at_nat @ A )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % comm_monoid_add_class.add_0
% 0.30/0.57  thf(fact_4292_comm__monoid__add__class_Oadd__0,axiom,
% 0.30/0.57      ! [A: rat] :
% 0.30/0.57        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % comm_monoid_add_class.add_0
% 0.30/0.57  thf(fact_4293_comm__monoid__add__class_Oadd__0,axiom,
% 0.30/0.57      ! [A: nat] :
% 0.30/0.57        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % comm_monoid_add_class.add_0
% 0.30/0.57  thf(fact_4294_comm__monoid__add__class_Oadd__0,axiom,
% 0.30/0.57      ! [A: int] :
% 0.30/0.57        ( ( plus_plus_int @ zero_zero_int @ A )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % comm_monoid_add_class.add_0
% 0.30/0.57  thf(fact_4295_add_Ocomm__neutral,axiom,
% 0.30/0.57      ! [A: code_integer] :
% 0.30/0.57        ( ( plus_p5714425477246183910nteger @ A @ zero_z3403309356797280102nteger )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % add.comm_neutral
% 0.30/0.57  thf(fact_4296_add_Ocomm__neutral,axiom,
% 0.30/0.57      ! [A: multis2468970476368604999at_nat] :
% 0.30/0.57        ( ( plus_p7104986032573967614at_nat @ A @ zero_z1048942125864253310at_nat )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % add.comm_neutral
% 0.30/0.57  thf(fact_4297_add_Ocomm__neutral,axiom,
% 0.30/0.57      ! [A: rat] :
% 0.30/0.57        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % add.comm_neutral
% 0.30/0.57  thf(fact_4298_add_Ocomm__neutral,axiom,
% 0.30/0.57      ! [A: nat] :
% 0.30/0.57        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % add.comm_neutral
% 0.30/0.57  thf(fact_4299_add_Ocomm__neutral,axiom,
% 0.30/0.57      ! [A: int] :
% 0.30/0.57        ( ( plus_plus_int @ A @ zero_zero_int )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % add.comm_neutral
% 0.30/0.57  thf(fact_4300_add_Ogroup__left__neutral,axiom,
% 0.30/0.57      ! [A: code_integer] :
% 0.30/0.57        ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % add.group_left_neutral
% 0.30/0.57  thf(fact_4301_add_Ogroup__left__neutral,axiom,
% 0.30/0.57      ! [A: rat] :
% 0.30/0.57        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % add.group_left_neutral
% 0.30/0.57  thf(fact_4302_add_Ogroup__left__neutral,axiom,
% 0.30/0.57      ! [A: int] :
% 0.30/0.57        ( ( plus_plus_int @ zero_zero_int @ A )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % add.group_left_neutral
% 0.30/0.57  thf(fact_4303_add__mono__thms__linordered__field_I5_J,axiom,
% 0.30/0.57      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.30/0.57        ( ( ( ord_less_rat @ I @ J )
% 0.30/0.57          & ( ord_less_rat @ K @ L ) )
% 0.30/0.57       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_field(5)
% 0.30/0.57  thf(fact_4304_add__mono__thms__linordered__field_I5_J,axiom,
% 0.30/0.57      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.30/0.57        ( ( ( ord_less_nat @ I @ J )
% 0.30/0.57          & ( ord_less_nat @ K @ L ) )
% 0.30/0.57       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_field(5)
% 0.30/0.57  thf(fact_4305_add__mono__thms__linordered__field_I5_J,axiom,
% 0.30/0.57      ! [I: int,J: int,K: int,L: int] :
% 0.30/0.57        ( ( ( ord_less_int @ I @ J )
% 0.30/0.57          & ( ord_less_int @ K @ L ) )
% 0.30/0.57       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_field(5)
% 0.30/0.57  thf(fact_4306_add__mono__thms__linordered__field_I2_J,axiom,
% 0.30/0.57      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.30/0.57        ( ( ( I = J )
% 0.30/0.57          & ( ord_less_rat @ K @ L ) )
% 0.30/0.57       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_field(2)
% 0.30/0.57  thf(fact_4307_add__mono__thms__linordered__field_I2_J,axiom,
% 0.30/0.57      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.30/0.57        ( ( ( I = J )
% 0.30/0.57          & ( ord_less_nat @ K @ L ) )
% 0.30/0.57       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_field(2)
% 0.30/0.57  thf(fact_4308_add__mono__thms__linordered__field_I2_J,axiom,
% 0.30/0.57      ! [I: int,J: int,K: int,L: int] :
% 0.30/0.57        ( ( ( I = J )
% 0.30/0.57          & ( ord_less_int @ K @ L ) )
% 0.30/0.57       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_field(2)
% 0.30/0.57  thf(fact_4309_add__mono__thms__linordered__field_I1_J,axiom,
% 0.30/0.57      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.30/0.57        ( ( ( ord_less_rat @ I @ J )
% 0.30/0.57          & ( K = L ) )
% 0.30/0.57       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_field(1)
% 0.30/0.57  thf(fact_4310_add__mono__thms__linordered__field_I1_J,axiom,
% 0.30/0.57      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.30/0.57        ( ( ( ord_less_nat @ I @ J )
% 0.30/0.57          & ( K = L ) )
% 0.30/0.57       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_field(1)
% 0.30/0.57  thf(fact_4311_add__mono__thms__linordered__field_I1_J,axiom,
% 0.30/0.57      ! [I: int,J: int,K: int,L: int] :
% 0.30/0.57        ( ( ( ord_less_int @ I @ J )
% 0.30/0.57          & ( K = L ) )
% 0.30/0.57       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_field(1)
% 0.30/0.57  thf(fact_4312_add__strict__mono,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.30/0.57        ( ( ord_less_rat @ A @ B )
% 0.30/0.57       => ( ( ord_less_rat @ C @ D2 )
% 0.30/0.57         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_strict_mono
% 0.30/0.57  thf(fact_4313_add__strict__mono,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.30/0.57        ( ( ord_less_nat @ A @ B )
% 0.30/0.57       => ( ( ord_less_nat @ C @ D2 )
% 0.30/0.57         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_strict_mono
% 0.30/0.57  thf(fact_4314_add__strict__mono,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int,D2: int] :
% 0.30/0.57        ( ( ord_less_int @ A @ B )
% 0.30/0.57       => ( ( ord_less_int @ C @ D2 )
% 0.30/0.57         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_strict_mono
% 0.30/0.57  thf(fact_4315_add__strict__left__mono,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( ord_less_rat @ A @ B )
% 0.30/0.57       => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_strict_left_mono
% 0.30/0.57  thf(fact_4316_add__strict__left__mono,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( ord_less_nat @ A @ B )
% 0.30/0.57       => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_strict_left_mono
% 0.30/0.57  thf(fact_4317_add__strict__left__mono,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( ord_less_int @ A @ B )
% 0.30/0.57       => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_strict_left_mono
% 0.30/0.57  thf(fact_4318_add__strict__right__mono,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( ord_less_rat @ A @ B )
% 0.30/0.57       => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_strict_right_mono
% 0.30/0.57  thf(fact_4319_add__strict__right__mono,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( ord_less_nat @ A @ B )
% 0.30/0.57       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_strict_right_mono
% 0.30/0.57  thf(fact_4320_add__strict__right__mono,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( ord_less_int @ A @ B )
% 0.30/0.57       => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_strict_right_mono
% 0.30/0.57  thf(fact_4321_add__less__imp__less__left,axiom,
% 0.30/0.57      ! [C: rat,A: rat,B: rat] :
% 0.30/0.57        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 0.30/0.57       => ( ord_less_rat @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_less_imp_less_left
% 0.30/0.57  thf(fact_4322_add__less__imp__less__left,axiom,
% 0.30/0.57      ! [C: nat,A: nat,B: nat] :
% 0.30/0.57        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 0.30/0.57       => ( ord_less_nat @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_less_imp_less_left
% 0.30/0.57  thf(fact_4323_add__less__imp__less__left,axiom,
% 0.30/0.57      ! [C: int,A: int,B: int] :
% 0.30/0.57        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 0.30/0.57       => ( ord_less_int @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_less_imp_less_left
% 0.30/0.57  thf(fact_4324_add__less__imp__less__right,axiom,
% 0.30/0.57      ! [A: rat,C: rat,B: rat] :
% 0.30/0.57        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 0.30/0.57       => ( ord_less_rat @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_less_imp_less_right
% 0.30/0.57  thf(fact_4325_add__less__imp__less__right,axiom,
% 0.30/0.57      ! [A: nat,C: nat,B: nat] :
% 0.30/0.57        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 0.30/0.57       => ( ord_less_nat @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_less_imp_less_right
% 0.30/0.57  thf(fact_4326_add__less__imp__less__right,axiom,
% 0.30/0.57      ! [A: int,C: int,B: int] :
% 0.30/0.57        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 0.30/0.57       => ( ord_less_int @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_less_imp_less_right
% 0.30/0.57  thf(fact_4327_combine__common__factor,axiom,
% 0.30/0.57      ! [A: code_integer,E2: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.57        ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E2 ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ C ) )
% 0.30/0.57        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ E2 ) @ C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % combine_common_factor
% 0.30/0.57  thf(fact_4328_combine__common__factor,axiom,
% 0.30/0.57      ! [A: rat,E2: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ C ) )
% 0.30/0.57        = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E2 ) @ C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % combine_common_factor
% 0.30/0.57  thf(fact_4329_combine__common__factor,axiom,
% 0.30/0.57      ! [A: nat,E2: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( plus_plus_nat @ ( times_times_nat @ A @ E2 ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E2 ) @ C ) )
% 0.30/0.57        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E2 ) @ C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % combine_common_factor
% 0.30/0.57  thf(fact_4330_combine__common__factor,axiom,
% 0.30/0.57      ! [A: int,E2: int,B: int,C: int] :
% 0.30/0.57        ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ C ) )
% 0.30/0.57        = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E2 ) @ C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % combine_common_factor
% 0.30/0.57  thf(fact_4331_distrib__right,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.57        ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.30/0.57        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_right
% 0.30/0.57  thf(fact_4332_distrib__right,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.30/0.57        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_right
% 0.30/0.57  thf(fact_4333_distrib__right,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.30/0.57        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_right
% 0.30/0.57  thf(fact_4334_distrib__right,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.30/0.57        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_right
% 0.30/0.57  thf(fact_4335_distrib__left,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.57        ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.30/0.57        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_left
% 0.30/0.57  thf(fact_4336_distrib__left,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.30/0.57        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_left
% 0.30/0.57  thf(fact_4337_distrib__left,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.30/0.57        = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_left
% 0.30/0.57  thf(fact_4338_distrib__left,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.30/0.57        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_left
% 0.30/0.57  thf(fact_4339_comm__semiring__class_Odistrib,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.57        ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.30/0.57        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % comm_semiring_class.distrib
% 0.30/0.57  thf(fact_4340_comm__semiring__class_Odistrib,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.30/0.57        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % comm_semiring_class.distrib
% 0.30/0.57  thf(fact_4341_comm__semiring__class_Odistrib,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.30/0.57        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % comm_semiring_class.distrib
% 0.30/0.57  thf(fact_4342_comm__semiring__class_Odistrib,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.30/0.57        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % comm_semiring_class.distrib
% 0.30/0.57  thf(fact_4343_ring__class_Oring__distribs_I1_J,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.57        ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.30/0.57        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ring_class.ring_distribs(1)
% 0.30/0.57  thf(fact_4344_ring__class_Oring__distribs_I1_J,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.30/0.57        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ring_class.ring_distribs(1)
% 0.30/0.57  thf(fact_4345_ring__class_Oring__distribs_I1_J,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.30/0.57        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ring_class.ring_distribs(1)
% 0.30/0.57  thf(fact_4346_ring__class_Oring__distribs_I2_J,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.57        ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.30/0.57        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ring_class.ring_distribs(2)
% 0.30/0.57  thf(fact_4347_ring__class_Oring__distribs_I2_J,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.30/0.57        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ring_class.ring_distribs(2)
% 0.30/0.57  thf(fact_4348_ring__class_Oring__distribs_I2_J,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.30/0.57        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ring_class.ring_distribs(2)
% 0.30/0.57  thf(fact_4349_group__cancel_Osub1,axiom,
% 0.30/0.57      ! [A2: rat,K: rat,A: rat,B: rat] :
% 0.30/0.57        ( ( A2
% 0.30/0.57          = ( plus_plus_rat @ K @ A ) )
% 0.30/0.57       => ( ( minus_minus_rat @ A2 @ B )
% 0.30/0.57          = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % group_cancel.sub1
% 0.30/0.57  thf(fact_4350_group__cancel_Osub1,axiom,
% 0.30/0.57      ! [A2: int,K: int,A: int,B: int] :
% 0.30/0.57        ( ( A2
% 0.30/0.57          = ( plus_plus_int @ K @ A ) )
% 0.30/0.57       => ( ( minus_minus_int @ A2 @ B )
% 0.30/0.57          = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % group_cancel.sub1
% 0.30/0.57  thf(fact_4351_diff__eq__eq,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( ( minus_minus_rat @ A @ B )
% 0.30/0.57          = C )
% 0.30/0.57        = ( A
% 0.30/0.57          = ( plus_plus_rat @ C @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_eq_eq
% 0.30/0.57  thf(fact_4352_diff__eq__eq,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( ( minus_minus_int @ A @ B )
% 0.30/0.57          = C )
% 0.30/0.57        = ( A
% 0.30/0.57          = ( plus_plus_int @ C @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_eq_eq
% 0.30/0.57  thf(fact_4353_eq__diff__eq,axiom,
% 0.30/0.57      ! [A: rat,C: rat,B: rat] :
% 0.30/0.57        ( ( A
% 0.30/0.57          = ( minus_minus_rat @ C @ B ) )
% 0.30/0.57        = ( ( plus_plus_rat @ A @ B )
% 0.30/0.57          = C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_diff_eq
% 0.30/0.57  thf(fact_4354_eq__diff__eq,axiom,
% 0.30/0.57      ! [A: int,C: int,B: int] :
% 0.30/0.57        ( ( A
% 0.30/0.57          = ( minus_minus_int @ C @ B ) )
% 0.30/0.57        = ( ( plus_plus_int @ A @ B )
% 0.30/0.57          = C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_diff_eq
% 0.30/0.57  thf(fact_4355_add__diff__eq,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.30/0.57        = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_diff_eq
% 0.30/0.57  thf(fact_4356_add__diff__eq,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.30/0.57        = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_diff_eq
% 0.30/0.57  thf(fact_4357_diff__diff__eq2,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 0.30/0.57        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_diff_eq2
% 0.30/0.57  thf(fact_4358_diff__diff__eq2,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 0.30/0.57        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_diff_eq2
% 0.30/0.57  thf(fact_4359_diff__add__eq,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.30/0.57        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_add_eq
% 0.30/0.57  thf(fact_4360_diff__add__eq,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.30/0.57        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_add_eq
% 0.30/0.57  thf(fact_4361_diff__add__eq__diff__diff__swap,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.30/0.57        = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_add_eq_diff_diff_swap
% 0.30/0.57  thf(fact_4362_diff__add__eq__diff__diff__swap,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.30/0.57        = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_add_eq_diff_diff_swap
% 0.30/0.57  thf(fact_4363_add__implies__diff,axiom,
% 0.30/0.57      ! [C: rat,B: rat,A: rat] :
% 0.30/0.57        ( ( ( plus_plus_rat @ C @ B )
% 0.30/0.57          = A )
% 0.30/0.57       => ( C
% 0.30/0.57          = ( minus_minus_rat @ A @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_implies_diff
% 0.30/0.57  thf(fact_4364_add__implies__diff,axiom,
% 0.30/0.57      ! [C: nat,B: nat,A: nat] :
% 0.30/0.57        ( ( ( plus_plus_nat @ C @ B )
% 0.30/0.57          = A )
% 0.30/0.57       => ( C
% 0.30/0.57          = ( minus_minus_nat @ A @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_implies_diff
% 0.30/0.57  thf(fact_4365_add__implies__diff,axiom,
% 0.30/0.57      ! [C: int,B: int,A: int] :
% 0.30/0.57        ( ( ( plus_plus_int @ C @ B )
% 0.30/0.57          = A )
% 0.30/0.57       => ( C
% 0.30/0.57          = ( minus_minus_int @ A @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_implies_diff
% 0.30/0.57  thf(fact_4366_diff__diff__eq,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.30/0.57        = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_diff_eq
% 0.30/0.57  thf(fact_4367_diff__diff__eq,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 0.30/0.57        = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_diff_eq
% 0.30/0.57  thf(fact_4368_diff__diff__eq,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.30/0.57        = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_diff_eq
% 0.30/0.57  thf(fact_4369_is__num__normalize_I8_J,axiom,
% 0.30/0.57      ! [A: int,B: int] :
% 0.30/0.57        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.30/0.57        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % is_num_normalize(8)
% 0.30/0.57  thf(fact_4370_is__num__normalize_I8_J,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.30/0.57        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % is_num_normalize(8)
% 0.30/0.57  thf(fact_4371_is__num__normalize_I8_J,axiom,
% 0.30/0.57      ! [A: rat,B: rat] :
% 0.30/0.57        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.30/0.57        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % is_num_normalize(8)
% 0.30/0.57  thf(fact_4372_add_Oinverse__distrib__swap,axiom,
% 0.30/0.57      ! [A: int,B: int] :
% 0.30/0.57        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.30/0.57        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.inverse_distrib_swap
% 0.30/0.57  thf(fact_4373_add_Oinverse__distrib__swap,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.30/0.57        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.inverse_distrib_swap
% 0.30/0.57  thf(fact_4374_add_Oinverse__distrib__swap,axiom,
% 0.30/0.57      ! [A: rat,B: rat] :
% 0.30/0.57        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.30/0.57        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.inverse_distrib_swap
% 0.30/0.57  thf(fact_4375_group__cancel_Oneg1,axiom,
% 0.30/0.57      ! [A2: int,K: int,A: int] :
% 0.30/0.57        ( ( A2
% 0.30/0.57          = ( plus_plus_int @ K @ A ) )
% 0.30/0.57       => ( ( uminus_uminus_int @ A2 )
% 0.30/0.57          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % group_cancel.neg1
% 0.30/0.57  thf(fact_4376_group__cancel_Oneg1,axiom,
% 0.30/0.57      ! [A2: code_integer,K: code_integer,A: code_integer] :
% 0.30/0.57        ( ( A2
% 0.30/0.57          = ( plus_p5714425477246183910nteger @ K @ A ) )
% 0.30/0.57       => ( ( uminus1351360451143612070nteger @ A2 )
% 0.30/0.57          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % group_cancel.neg1
% 0.30/0.57  thf(fact_4377_group__cancel_Oneg1,axiom,
% 0.30/0.57      ! [A2: rat,K: rat,A: rat] :
% 0.30/0.57        ( ( A2
% 0.30/0.57          = ( plus_plus_rat @ K @ A ) )
% 0.30/0.57       => ( ( uminus_uminus_rat @ A2 )
% 0.30/0.57          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % group_cancel.neg1
% 0.30/0.57  thf(fact_4378_add_Osafe__commute,axiom,
% 0.30/0.57      ! [X: rat,Y: rat,A: rat,B: rat] :
% 0.30/0.57        ( ( syntax3730441303064801268at_rat @ ( plus_plus_rat @ X @ Y ) @ A )
% 0.30/0.57       => ( ( plus_plus_rat @ A @ B )
% 0.30/0.57          = ( plus_plus_rat @ B @ A ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.safe_commute
% 0.30/0.57  thf(fact_4379_add_Osafe__commute,axiom,
% 0.30/0.57      ! [X: nat,Y: nat,A: nat,B: nat] :
% 0.30/0.57        ( ( syntax4682126007086162916at_nat @ ( plus_plus_nat @ X @ Y ) @ A )
% 0.30/0.57       => ( ( plus_plus_nat @ A @ B )
% 0.30/0.57          = ( plus_plus_nat @ B @ A ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.safe_commute
% 0.30/0.57  thf(fact_4380_add_Osafe__commute,axiom,
% 0.30/0.57      ! [X: int,Y: int,A: int,B: int] :
% 0.30/0.57        ( ( syntax5678989248478167196nt_int @ ( plus_plus_int @ X @ Y ) @ A )
% 0.30/0.57       => ( ( plus_plus_int @ A @ B )
% 0.30/0.57          = ( plus_plus_int @ B @ A ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.safe_commute
% 0.30/0.57  thf(fact_4381_add__nonpos__eq__0__iff,axiom,
% 0.30/0.57      ! [X: code_integer,Y: code_integer] :
% 0.30/0.57        ( ( ord_le3102999989581377725nteger @ X @ zero_z3403309356797280102nteger )
% 0.30/0.57       => ( ( ord_le3102999989581377725nteger @ Y @ zero_z3403309356797280102nteger )
% 0.30/0.57         => ( ( ( plus_p5714425477246183910nteger @ X @ Y )
% 0.30/0.57              = zero_z3403309356797280102nteger )
% 0.30/0.57            = ( ( X = zero_z3403309356797280102nteger )
% 0.30/0.57              & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonpos_eq_0_iff
% 0.30/0.57  thf(fact_4382_add__nonpos__eq__0__iff,axiom,
% 0.30/0.57      ! [X: rat,Y: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 0.30/0.57       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 0.30/0.57         => ( ( ( plus_plus_rat @ X @ Y )
% 0.30/0.57              = zero_zero_rat )
% 0.30/0.57            = ( ( X = zero_zero_rat )
% 0.30/0.57              & ( Y = zero_zero_rat ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonpos_eq_0_iff
% 0.30/0.57  thf(fact_4383_add__nonpos__eq__0__iff,axiom,
% 0.30/0.57      ! [X: nat,Y: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 0.30/0.57       => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 0.30/0.57         => ( ( ( plus_plus_nat @ X @ Y )
% 0.30/0.57              = zero_zero_nat )
% 0.30/0.57            = ( ( X = zero_zero_nat )
% 0.30/0.57              & ( Y = zero_zero_nat ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonpos_eq_0_iff
% 0.30/0.57  thf(fact_4384_add__nonpos__eq__0__iff,axiom,
% 0.30/0.57      ! [X: int,Y: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ X @ zero_zero_int )
% 0.30/0.57       => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 0.30/0.57         => ( ( ( plus_plus_int @ X @ Y )
% 0.30/0.57              = zero_zero_int )
% 0.30/0.57            = ( ( X = zero_zero_int )
% 0.30/0.57              & ( Y = zero_zero_int ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonpos_eq_0_iff
% 0.30/0.57  thf(fact_4385_add__nonneg__eq__0__iff,axiom,
% 0.30/0.57      ! [X: code_integer,Y: code_integer] :
% 0.30/0.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 0.30/0.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 0.30/0.57         => ( ( ( plus_p5714425477246183910nteger @ X @ Y )
% 0.30/0.57              = zero_z3403309356797280102nteger )
% 0.30/0.57            = ( ( X = zero_z3403309356797280102nteger )
% 0.30/0.57              & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonneg_eq_0_iff
% 0.30/0.57  thf(fact_4386_add__nonneg__eq__0__iff,axiom,
% 0.30/0.57      ! [X: rat,Y: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.30/0.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.30/0.57         => ( ( ( plus_plus_rat @ X @ Y )
% 0.30/0.57              = zero_zero_rat )
% 0.30/0.57            = ( ( X = zero_zero_rat )
% 0.30/0.57              & ( Y = zero_zero_rat ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonneg_eq_0_iff
% 0.30/0.57  thf(fact_4387_add__nonneg__eq__0__iff,axiom,
% 0.30/0.57      ! [X: nat,Y: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 0.30/0.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.30/0.57         => ( ( ( plus_plus_nat @ X @ Y )
% 0.30/0.57              = zero_zero_nat )
% 0.30/0.57            = ( ( X = zero_zero_nat )
% 0.30/0.57              & ( Y = zero_zero_nat ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonneg_eq_0_iff
% 0.30/0.57  thf(fact_4388_add__nonneg__eq__0__iff,axiom,
% 0.30/0.57      ! [X: int,Y: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.30/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.30/0.57         => ( ( ( plus_plus_int @ X @ Y )
% 0.30/0.57              = zero_zero_int )
% 0.30/0.57            = ( ( X = zero_zero_int )
% 0.30/0.57              & ( Y = zero_zero_int ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonneg_eq_0_iff
% 0.30/0.57  thf(fact_4389_add__nonpos__nonpos,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.30/0.57       => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 0.30/0.57         => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonpos_nonpos
% 0.30/0.57  thf(fact_4390_add__nonpos__nonpos,axiom,
% 0.30/0.57      ! [A: rat,B: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.30/0.57       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.30/0.57         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonpos_nonpos
% 0.30/0.57  thf(fact_4391_add__nonpos__nonpos,axiom,
% 0.30/0.57      ! [A: nat,B: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.30/0.57       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.30/0.57         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonpos_nonpos
% 0.30/0.57  thf(fact_4392_add__nonpos__nonpos,axiom,
% 0.30/0.57      ! [A: int,B: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.30/0.57       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.30/0.57         => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonpos_nonpos
% 0.30/0.57  thf(fact_4393_add__nonneg__nonneg,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.30/0.57         => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonneg_nonneg
% 0.30/0.57  thf(fact_4394_add__nonneg__nonneg,axiom,
% 0.30/0.57      ! [A: rat,B: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.57         => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonneg_nonneg
% 0.30/0.57  thf(fact_4395_add__nonneg__nonneg,axiom,
% 0.30/0.57      ! [A: nat,B: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.30/0.57         => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonneg_nonneg
% 0.30/0.57  thf(fact_4396_add__nonneg__nonneg,axiom,
% 0.30/0.57      ! [A: int,B: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.30/0.57         => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonneg_nonneg
% 0.30/0.57  thf(fact_4397_add__increasing2,axiom,
% 0.30/0.57      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.30/0.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.57       => ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.30/0.57         => ( ord_le3102999989581377725nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_increasing2
% 0.30/0.57  thf(fact_4398_add__increasing2,axiom,
% 0.30/0.57      ! [C: rat,B: rat,A: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 0.30/0.57       => ( ( ord_less_eq_rat @ B @ A )
% 0.30/0.57         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_increasing2
% 0.30/0.57  thf(fact_4399_add__increasing2,axiom,
% 0.30/0.57      ! [C: nat,B: nat,A: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.30/0.57       => ( ( ord_less_eq_nat @ B @ A )
% 0.30/0.57         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_increasing2
% 0.30/0.57  thf(fact_4400_add__increasing2,axiom,
% 0.30/0.57      ! [C: int,B: int,A: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.30/0.57       => ( ( ord_less_eq_int @ B @ A )
% 0.30/0.57         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_increasing2
% 0.30/0.57  thf(fact_4401_add__decreasing2,axiom,
% 0.30/0.57      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 0.30/0.57       => ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.30/0.57         => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_decreasing2
% 0.30/0.57  thf(fact_4402_add__decreasing2,axiom,
% 0.30/0.57      ! [C: rat,A: rat,B: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 0.30/0.57       => ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.57         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_decreasing2
% 0.30/0.57  thf(fact_4403_add__decreasing2,axiom,
% 0.30/0.57      ! [C: nat,A: nat,B: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 0.30/0.57       => ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.57         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_decreasing2
% 0.30/0.57  thf(fact_4404_add__decreasing2,axiom,
% 0.30/0.57      ! [C: int,A: int,B: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ C @ zero_zero_int )
% 0.30/0.57       => ( ( ord_less_eq_int @ A @ B )
% 0.30/0.57         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_decreasing2
% 0.30/0.57  thf(fact_4405_add__increasing,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.57       => ( ( ord_le3102999989581377725nteger @ B @ C )
% 0.30/0.57         => ( ord_le3102999989581377725nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_increasing
% 0.30/0.57  thf(fact_4406_add__increasing,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.57       => ( ( ord_less_eq_rat @ B @ C )
% 0.30/0.57         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_increasing
% 0.30/0.57  thf(fact_4407_add__increasing,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.57       => ( ( ord_less_eq_nat @ B @ C )
% 0.30/0.57         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_increasing
% 0.30/0.57  thf(fact_4408_add__increasing,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.57       => ( ( ord_less_eq_int @ B @ C )
% 0.30/0.57         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_increasing
% 0.30/0.57  thf(fact_4409_add__decreasing,axiom,
% 0.30/0.57      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.30/0.57        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.30/0.57       => ( ( ord_le3102999989581377725nteger @ C @ B )
% 0.30/0.57         => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_decreasing
% 0.30/0.57  thf(fact_4410_add__decreasing,axiom,
% 0.30/0.57      ! [A: rat,C: rat,B: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.30/0.57       => ( ( ord_less_eq_rat @ C @ B )
% 0.30/0.57         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_decreasing
% 0.30/0.57  thf(fact_4411_add__decreasing,axiom,
% 0.30/0.57      ! [A: nat,C: nat,B: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.30/0.57       => ( ( ord_less_eq_nat @ C @ B )
% 0.30/0.57         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_decreasing
% 0.30/0.57  thf(fact_4412_add__decreasing,axiom,
% 0.30/0.57      ! [A: int,C: int,B: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.30/0.57       => ( ( ord_less_eq_int @ C @ B )
% 0.30/0.57         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_decreasing
% 0.30/0.57  thf(fact_4413_add__mono__thms__linordered__field_I4_J,axiom,
% 0.30/0.57      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.30/0.57        ( ( ( ord_less_eq_rat @ I @ J )
% 0.30/0.57          & ( ord_less_rat @ K @ L ) )
% 0.30/0.57       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_field(4)
% 0.30/0.57  thf(fact_4414_add__mono__thms__linordered__field_I4_J,axiom,
% 0.30/0.57      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.30/0.57        ( ( ( ord_less_eq_nat @ I @ J )
% 0.30/0.57          & ( ord_less_nat @ K @ L ) )
% 0.30/0.57       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_field(4)
% 0.30/0.57  thf(fact_4415_add__mono__thms__linordered__field_I4_J,axiom,
% 0.30/0.57      ! [I: int,J: int,K: int,L: int] :
% 0.30/0.57        ( ( ( ord_less_eq_int @ I @ J )
% 0.30/0.57          & ( ord_less_int @ K @ L ) )
% 0.30/0.57       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_field(4)
% 0.30/0.57  thf(fact_4416_add__mono__thms__linordered__field_I3_J,axiom,
% 0.30/0.57      ! [I: rat,J: rat,K: rat,L: rat] :
% 0.30/0.57        ( ( ( ord_less_rat @ I @ J )
% 0.30/0.57          & ( ord_less_eq_rat @ K @ L ) )
% 0.30/0.57       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_field(3)
% 0.30/0.57  thf(fact_4417_add__mono__thms__linordered__field_I3_J,axiom,
% 0.30/0.57      ! [I: nat,J: nat,K: nat,L: nat] :
% 0.30/0.57        ( ( ( ord_less_nat @ I @ J )
% 0.30/0.57          & ( ord_less_eq_nat @ K @ L ) )
% 0.30/0.57       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_field(3)
% 0.30/0.57  thf(fact_4418_add__mono__thms__linordered__field_I3_J,axiom,
% 0.30/0.57      ! [I: int,J: int,K: int,L: int] :
% 0.30/0.57        ( ( ( ord_less_int @ I @ J )
% 0.30/0.57          & ( ord_less_eq_int @ K @ L ) )
% 0.30/0.57       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono_thms_linordered_field(3)
% 0.30/0.57  thf(fact_4419_add__le__less__mono,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.57       => ( ( ord_less_rat @ C @ D2 )
% 0.30/0.57         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_le_less_mono
% 0.30/0.57  thf(fact_4420_add__le__less__mono,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.57       => ( ( ord_less_nat @ C @ D2 )
% 0.30/0.57         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_le_less_mono
% 0.30/0.57  thf(fact_4421_add__le__less__mono,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int,D2: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ A @ B )
% 0.30/0.57       => ( ( ord_less_int @ C @ D2 )
% 0.30/0.57         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_le_less_mono
% 0.30/0.57  thf(fact_4422_add__less__le__mono,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.30/0.57        ( ( ord_less_rat @ A @ B )
% 0.30/0.57       => ( ( ord_less_eq_rat @ C @ D2 )
% 0.30/0.57         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_less_le_mono
% 0.30/0.57  thf(fact_4423_add__less__le__mono,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.30/0.57        ( ( ord_less_nat @ A @ B )
% 0.30/0.57       => ( ( ord_less_eq_nat @ C @ D2 )
% 0.30/0.57         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_less_le_mono
% 0.30/0.57  thf(fact_4424_add__less__le__mono,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int,D2: int] :
% 0.30/0.57        ( ( ord_less_int @ A @ B )
% 0.30/0.57       => ( ( ord_less_eq_int @ C @ D2 )
% 0.30/0.57         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_less_le_mono
% 0.30/0.57  thf(fact_4425_pos__add__strict,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.57       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 0.30/0.57         => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % pos_add_strict
% 0.30/0.57  thf(fact_4426_pos__add__strict,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.57       => ( ( ord_less_rat @ B @ C )
% 0.30/0.57         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % pos_add_strict
% 0.30/0.57  thf(fact_4427_pos__add__strict,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.57       => ( ( ord_less_nat @ B @ C )
% 0.30/0.57         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % pos_add_strict
% 0.30/0.57  thf(fact_4428_pos__add__strict,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.57       => ( ( ord_less_int @ B @ C )
% 0.30/0.57         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % pos_add_strict
% 0.30/0.57  thf(fact_4429_canonically__ordered__monoid__add__class_OlessE,axiom,
% 0.30/0.57      ! [A: nat,B: nat] :
% 0.30/0.57        ( ( ord_less_nat @ A @ B )
% 0.30/0.57       => ~ ! [C3: nat] :
% 0.30/0.57              ( ( B
% 0.30/0.57                = ( plus_plus_nat @ A @ C3 ) )
% 0.30/0.57             => ( C3 = zero_zero_nat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % canonically_ordered_monoid_add_class.lessE
% 0.30/0.57  thf(fact_4430_add__pos__pos,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.57       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.30/0.57         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_pos_pos
% 0.30/0.57  thf(fact_4431_add__pos__pos,axiom,
% 0.30/0.57      ! [A: rat,B: rat] :
% 0.30/0.57        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.57       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.30/0.57         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_pos_pos
% 0.30/0.57  thf(fact_4432_add__pos__pos,axiom,
% 0.30/0.57      ! [A: nat,B: nat] :
% 0.30/0.57        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.57       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.30/0.57         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_pos_pos
% 0.30/0.57  thf(fact_4433_add__pos__pos,axiom,
% 0.30/0.57      ! [A: int,B: int] :
% 0.30/0.57        ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.57       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.57         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_pos_pos
% 0.30/0.57  thf(fact_4434_add__neg__neg,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.30/0.57       => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 0.30/0.57         => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_neg
% 0.30/0.57  thf(fact_4435_add__neg__neg,axiom,
% 0.30/0.57      ! [A: rat,B: rat] :
% 0.30/0.57        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.30/0.57       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.30/0.57         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_neg
% 0.30/0.57  thf(fact_4436_add__neg__neg,axiom,
% 0.30/0.57      ! [A: nat,B: nat] :
% 0.30/0.57        ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.30/0.57       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.30/0.57         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_neg
% 0.30/0.57  thf(fact_4437_add__neg__neg,axiom,
% 0.30/0.57      ! [A: int,B: int] :
% 0.30/0.57        ( ( ord_less_int @ A @ zero_zero_int )
% 0.30/0.57       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.30/0.57         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_neg
% 0.30/0.57  thf(fact_4438_diff__le__eq,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.30/0.57        = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_le_eq
% 0.30/0.57  thf(fact_4439_diff__le__eq,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.30/0.57        = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_le_eq
% 0.30/0.57  thf(fact_4440_le__diff__eq,axiom,
% 0.30/0.57      ! [A: rat,C: rat,B: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 0.30/0.57        = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % le_diff_eq
% 0.30/0.57  thf(fact_4441_le__diff__eq,axiom,
% 0.30/0.57      ! [A: int,C: int,B: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 0.30/0.57        = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % le_diff_eq
% 0.30/0.57  thf(fact_4442_ordered__cancel__comm__monoid__diff__class_Odiff__add,axiom,
% 0.30/0.57      ! [A: nat,B: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.57       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 0.30/0.57          = B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ordered_cancel_comm_monoid_diff_class.diff_add
% 0.30/0.57  thf(fact_4443_le__add__diff,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.57       => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % le_add_diff
% 0.30/0.57  thf(fact_4444_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.57       => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.30/0.57          = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 0.30/0.57  thf(fact_4445_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.57       => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.30/0.57          = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 0.30/0.57  thf(fact_4446_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.57       => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 0.30/0.57          = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 0.30/0.57  thf(fact_4447_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.57       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 0.30/0.57          = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 0.30/0.57  thf(fact_4448_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.57       => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 0.30/0.57          = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 0.30/0.57  thf(fact_4449_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.57       => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 0.30/0.57          = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 0.30/0.57  thf(fact_4450_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 0.30/0.57      ! [A: nat,B: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.57       => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 0.30/0.57          = B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 0.30/0.57  thf(fact_4451_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.57       => ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.57         => ( ( ( minus_minus_nat @ B @ A )
% 0.30/0.57              = C )
% 0.30/0.57            = ( B
% 0.30/0.57              = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 0.30/0.57  thf(fact_4452_add__mono1,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.30/0.57       => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ B @ one_one_Code_integer ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono1
% 0.30/0.57  thf(fact_4453_add__mono1,axiom,
% 0.30/0.57      ! [A: rat,B: rat] :
% 0.30/0.57        ( ( ord_less_rat @ A @ B )
% 0.30/0.57       => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono1
% 0.30/0.57  thf(fact_4454_add__mono1,axiom,
% 0.30/0.57      ! [A: nat,B: nat] :
% 0.30/0.57        ( ( ord_less_nat @ A @ B )
% 0.30/0.57       => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono1
% 0.30/0.57  thf(fact_4455_add__mono1,axiom,
% 0.30/0.57      ! [A: int,B: int] :
% 0.30/0.57        ( ( ord_less_int @ A @ B )
% 0.30/0.57       => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_mono1
% 0.30/0.57  thf(fact_4456_less__add__one,axiom,
% 0.30/0.57      ! [A: code_integer] : ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) ) ).
% 0.30/0.57  
% 0.30/0.57  % less_add_one
% 0.30/0.57  thf(fact_4457_less__add__one,axiom,
% 0.30/0.57      ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % less_add_one
% 0.30/0.57  thf(fact_4458_less__add__one,axiom,
% 0.30/0.57      ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % less_add_one
% 0.30/0.57  thf(fact_4459_less__add__one,axiom,
% 0.30/0.57      ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 0.30/0.57  
% 0.30/0.57  % less_add_one
% 0.30/0.57  thf(fact_4460_diff__less__eq,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 0.30/0.57        = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_less_eq
% 0.30/0.57  thf(fact_4461_diff__less__eq,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 0.30/0.57        = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_less_eq
% 0.30/0.57  thf(fact_4462_less__diff__eq,axiom,
% 0.30/0.57      ! [A: rat,C: rat,B: rat] :
% 0.30/0.57        ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 0.30/0.57        = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % less_diff_eq
% 0.30/0.57  thf(fact_4463_less__diff__eq,axiom,
% 0.30/0.57      ! [A: int,C: int,B: int] :
% 0.30/0.57        ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 0.30/0.57        = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 0.30/0.57  
% 0.30/0.57  % less_diff_eq
% 0.30/0.57  thf(fact_4464_neg__eq__iff__add__eq__0,axiom,
% 0.30/0.57      ! [A: int,B: int] :
% 0.30/0.57        ( ( ( uminus_uminus_int @ A )
% 0.30/0.57          = B )
% 0.30/0.57        = ( ( plus_plus_int @ A @ B )
% 0.30/0.57          = zero_zero_int ) ) ).
% 0.30/0.57  
% 0.30/0.57  % neg_eq_iff_add_eq_0
% 0.30/0.57  thf(fact_4465_neg__eq__iff__add__eq__0,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( ( uminus1351360451143612070nteger @ A )
% 0.30/0.57          = B )
% 0.30/0.57        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.30/0.57          = zero_z3403309356797280102nteger ) ) ).
% 0.30/0.57  
% 0.30/0.57  % neg_eq_iff_add_eq_0
% 0.30/0.57  thf(fact_4466_neg__eq__iff__add__eq__0,axiom,
% 0.30/0.57      ! [A: rat,B: rat] :
% 0.30/0.57        ( ( ( uminus_uminus_rat @ A )
% 0.30/0.57          = B )
% 0.30/0.57        = ( ( plus_plus_rat @ A @ B )
% 0.30/0.57          = zero_zero_rat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % neg_eq_iff_add_eq_0
% 0.30/0.57  thf(fact_4467_eq__neg__iff__add__eq__0,axiom,
% 0.30/0.57      ! [A: int,B: int] :
% 0.30/0.57        ( ( A
% 0.30/0.57          = ( uminus_uminus_int @ B ) )
% 0.30/0.57        = ( ( plus_plus_int @ A @ B )
% 0.30/0.57          = zero_zero_int ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_neg_iff_add_eq_0
% 0.30/0.57  thf(fact_4468_eq__neg__iff__add__eq__0,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( A
% 0.30/0.57          = ( uminus1351360451143612070nteger @ B ) )
% 0.30/0.57        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.30/0.57          = zero_z3403309356797280102nteger ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_neg_iff_add_eq_0
% 0.30/0.57  thf(fact_4469_eq__neg__iff__add__eq__0,axiom,
% 0.30/0.57      ! [A: rat,B: rat] :
% 0.30/0.57        ( ( A
% 0.30/0.57          = ( uminus_uminus_rat @ B ) )
% 0.30/0.57        = ( ( plus_plus_rat @ A @ B )
% 0.30/0.57          = zero_zero_rat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_neg_iff_add_eq_0
% 0.30/0.57  thf(fact_4470_add_Oinverse__unique,axiom,
% 0.30/0.57      ! [A: int,B: int] :
% 0.30/0.57        ( ( ( plus_plus_int @ A @ B )
% 0.30/0.57          = zero_zero_int )
% 0.30/0.57       => ( ( uminus_uminus_int @ A )
% 0.30/0.57          = B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.inverse_unique
% 0.30/0.57  thf(fact_4471_add_Oinverse__unique,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.30/0.57          = zero_z3403309356797280102nteger )
% 0.30/0.57       => ( ( uminus1351360451143612070nteger @ A )
% 0.30/0.57          = B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.inverse_unique
% 0.30/0.57  thf(fact_4472_add_Oinverse__unique,axiom,
% 0.30/0.57      ! [A: rat,B: rat] :
% 0.30/0.57        ( ( ( plus_plus_rat @ A @ B )
% 0.30/0.57          = zero_zero_rat )
% 0.30/0.57       => ( ( uminus_uminus_rat @ A )
% 0.30/0.57          = B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add.inverse_unique
% 0.30/0.57  thf(fact_4473_ab__group__add__class_Oab__left__minus,axiom,
% 0.30/0.57      ! [A: int] :
% 0.30/0.57        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 0.30/0.57        = zero_zero_int ) ).
% 0.30/0.57  
% 0.30/0.57  % ab_group_add_class.ab_left_minus
% 0.30/0.57  thf(fact_4474_ab__group__add__class_Oab__left__minus,axiom,
% 0.30/0.57      ! [A: code_integer] :
% 0.30/0.57        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.30/0.57        = zero_z3403309356797280102nteger ) ).
% 0.30/0.57  
% 0.30/0.57  % ab_group_add_class.ab_left_minus
% 0.30/0.57  thf(fact_4475_ab__group__add__class_Oab__left__minus,axiom,
% 0.30/0.57      ! [A: rat] :
% 0.30/0.57        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.30/0.57        = zero_zero_rat ) ).
% 0.30/0.57  
% 0.30/0.57  % ab_group_add_class.ab_left_minus
% 0.30/0.57  thf(fact_4476_add__eq__0__iff,axiom,
% 0.30/0.57      ! [A: int,B: int] :
% 0.30/0.57        ( ( ( plus_plus_int @ A @ B )
% 0.30/0.57          = zero_zero_int )
% 0.30/0.57        = ( B
% 0.30/0.57          = ( uminus_uminus_int @ A ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_eq_0_iff
% 0.30/0.57  thf(fact_4477_add__eq__0__iff,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.30/0.57          = zero_z3403309356797280102nteger )
% 0.30/0.57        = ( B
% 0.30/0.57          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_eq_0_iff
% 0.30/0.57  thf(fact_4478_add__eq__0__iff,axiom,
% 0.30/0.57      ! [A: rat,B: rat] :
% 0.30/0.57        ( ( ( plus_plus_rat @ A @ B )
% 0.30/0.57          = zero_zero_rat )
% 0.30/0.57        = ( B
% 0.30/0.57          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_eq_0_iff
% 0.30/0.57  thf(fact_4479_one__plus__numeral__commute,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 0.30/0.57        = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % one_plus_numeral_commute
% 0.30/0.57  thf(fact_4480_one__plus__numeral__commute,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 0.30/0.57        = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 0.30/0.57  
% 0.30/0.57  % one_plus_numeral_commute
% 0.30/0.57  thf(fact_4481_one__plus__numeral__commute,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 0.30/0.57        = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer ) ) ).
% 0.30/0.57  
% 0.30/0.57  % one_plus_numeral_commute
% 0.30/0.57  thf(fact_4482_one__plus__numeral__commute,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 0.30/0.57        = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % one_plus_numeral_commute
% 0.30/0.57  thf(fact_4483_one__plus__numeral__commute,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ X ) )
% 0.30/0.57        = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ X ) @ one_one_Code_natural ) ) ).
% 0.30/0.57  
% 0.30/0.57  % one_plus_numeral_commute
% 0.30/0.57  thf(fact_4484_square__diff__square__factored,axiom,
% 0.30/0.57      ! [X: code_integer,Y: code_integer] :
% 0.30/0.57        ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 0.30/0.57        = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( minus_8373710615458151222nteger @ X @ Y ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % square_diff_square_factored
% 0.30/0.57  thf(fact_4485_square__diff__square__factored,axiom,
% 0.30/0.57      ! [X: rat,Y: rat] :
% 0.30/0.57        ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 0.30/0.57        = ( times_times_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_rat @ X @ Y ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % square_diff_square_factored
% 0.30/0.57  thf(fact_4486_square__diff__square__factored,axiom,
% 0.30/0.57      ! [X: int,Y: int] :
% 0.30/0.57        ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 0.30/0.57        = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % square_diff_square_factored
% 0.30/0.57  thf(fact_4487_eq__add__iff2,axiom,
% 0.30/0.57      ! [A: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 0.30/0.57        ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E2 ) @ C )
% 0.30/0.57          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 0.30/0.57        = ( C
% 0.30/0.57          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_add_iff2
% 0.30/0.57  thf(fact_4488_eq__add__iff2,axiom,
% 0.30/0.57      ! [A: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 0.30/0.57        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 0.30/0.57          = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 0.30/0.57        = ( C
% 0.30/0.57          = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_add_iff2
% 0.30/0.57  thf(fact_4489_eq__add__iff2,axiom,
% 0.30/0.57      ! [A: int,E2: int,C: int,B: int,D2: int] :
% 0.30/0.57        ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 0.30/0.57          = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 0.30/0.57        = ( C
% 0.30/0.57          = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_add_iff2
% 0.30/0.57  thf(fact_4490_eq__add__iff1,axiom,
% 0.30/0.57      ! [A: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 0.30/0.57        ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E2 ) @ C )
% 0.30/0.57          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 0.30/0.57        = ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E2 ) @ C )
% 0.30/0.57          = D2 ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_add_iff1
% 0.30/0.57  thf(fact_4491_eq__add__iff1,axiom,
% 0.30/0.57      ! [A: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 0.30/0.57        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 0.30/0.57          = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 0.30/0.57        = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C )
% 0.30/0.57          = D2 ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_add_iff1
% 0.30/0.57  thf(fact_4492_eq__add__iff1,axiom,
% 0.30/0.57      ! [A: int,E2: int,C: int,B: int,D2: int] :
% 0.30/0.57        ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 0.30/0.57          = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 0.30/0.57        = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C )
% 0.30/0.57          = D2 ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_add_iff1
% 0.30/0.57  thf(fact_4493_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.30/0.57      ( minus_minus_int
% 0.30/0.57      = ( ^ [A3: int,B3: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.30/0.57  thf(fact_4494_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.30/0.57      ( minus_8373710615458151222nteger
% 0.30/0.57      = ( ^ [A3: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.30/0.57  thf(fact_4495_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.30/0.57      ( minus_minus_rat
% 0.30/0.57      = ( ^ [A3: rat,B3: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ab_group_add_class.ab_diff_conv_add_uminus
% 0.30/0.57  thf(fact_4496_diff__conv__add__uminus,axiom,
% 0.30/0.57      ( minus_minus_int
% 0.30/0.57      = ( ^ [A3: int,B3: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_conv_add_uminus
% 0.30/0.57  thf(fact_4497_diff__conv__add__uminus,axiom,
% 0.30/0.57      ( minus_8373710615458151222nteger
% 0.30/0.57      = ( ^ [A3: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_conv_add_uminus
% 0.30/0.57  thf(fact_4498_diff__conv__add__uminus,axiom,
% 0.30/0.57      ( minus_minus_rat
% 0.30/0.57      = ( ^ [A3: rat,B3: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_conv_add_uminus
% 0.30/0.57  thf(fact_4499_group__cancel_Osub2,axiom,
% 0.30/0.57      ! [B2: int,K: int,B: int,A: int] :
% 0.30/0.57        ( ( B2
% 0.30/0.57          = ( plus_plus_int @ K @ B ) )
% 0.30/0.57       => ( ( minus_minus_int @ A @ B2 )
% 0.30/0.57          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % group_cancel.sub2
% 0.30/0.57  thf(fact_4500_group__cancel_Osub2,axiom,
% 0.30/0.57      ! [B2: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 0.30/0.57        ( ( B2
% 0.30/0.57          = ( plus_p5714425477246183910nteger @ K @ B ) )
% 0.30/0.57       => ( ( minus_8373710615458151222nteger @ A @ B2 )
% 0.30/0.57          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % group_cancel.sub2
% 0.30/0.57  thf(fact_4501_group__cancel_Osub2,axiom,
% 0.30/0.57      ! [B2: rat,K: rat,B: rat,A: rat] :
% 0.30/0.57        ( ( B2
% 0.30/0.57          = ( plus_plus_rat @ K @ B ) )
% 0.30/0.57       => ( ( minus_minus_rat @ A @ B2 )
% 0.30/0.57          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % group_cancel.sub2
% 0.30/0.57  thf(fact_4502_eq__numeral__iff__iszero_I7_J,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ X ) )
% 0.30/0.57          = one_one_int )
% 0.30/0.57        = ( ring_1_iszero_int @ ( numeral_numeral_int @ ( plus_plus_num @ X @ one ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_numeral_iff_iszero(7)
% 0.30/0.57  thf(fact_4503_eq__numeral__iff__iszero_I7_J,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) )
% 0.30/0.57          = one_one_Code_integer )
% 0.30/0.57        = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ X @ one ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_numeral_iff_iszero(7)
% 0.30/0.57  thf(fact_4504_eq__numeral__iff__iszero_I7_J,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) )
% 0.30/0.57          = one_one_rat )
% 0.30/0.57        = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ X @ one ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_numeral_iff_iszero(7)
% 0.30/0.57  thf(fact_4505_eq__numeral__iff__iszero_I8_J,axiom,
% 0.30/0.57      ! [Y: num] :
% 0.30/0.57        ( ( one_one_int
% 0.30/0.57          = ( uminus_uminus_int @ ( numeral_numeral_int @ Y ) ) )
% 0.30/0.57        = ( ring_1_iszero_int @ ( numeral_numeral_int @ ( plus_plus_num @ one @ Y ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_numeral_iff_iszero(8)
% 0.30/0.57  thf(fact_4506_eq__numeral__iff__iszero_I8_J,axiom,
% 0.30/0.57      ! [Y: num] :
% 0.30/0.57        ( ( one_one_Code_integer
% 0.30/0.57          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ Y ) ) )
% 0.30/0.57        = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ Y ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_numeral_iff_iszero(8)
% 0.30/0.57  thf(fact_4507_eq__numeral__iff__iszero_I8_J,axiom,
% 0.30/0.57      ! [Y: num] :
% 0.30/0.57        ( ( one_one_rat
% 0.30/0.57          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ Y ) ) )
% 0.30/0.57        = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ one @ Y ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_numeral_iff_iszero(8)
% 0.30/0.57  thf(fact_4508_mult__numeral__1__right,axiom,
% 0.30/0.57      ! [A: nat] :
% 0.30/0.57        ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_numeral_1_right
% 0.30/0.57  thf(fact_4509_mult__numeral__1__right,axiom,
% 0.30/0.57      ! [A: int] :
% 0.30/0.57        ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_numeral_1_right
% 0.30/0.57  thf(fact_4510_mult__numeral__1__right,axiom,
% 0.30/0.57      ! [A: code_integer] :
% 0.30/0.57        ( ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ one ) )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_numeral_1_right
% 0.30/0.57  thf(fact_4511_mult__numeral__1__right,axiom,
% 0.30/0.57      ! [A: rat] :
% 0.30/0.57        ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_numeral_1_right
% 0.30/0.57  thf(fact_4512_mult__numeral__1__right,axiom,
% 0.30/0.57      ! [A: code_natural] :
% 0.30/0.57        ( ( times_2397367101498566445atural @ A @ ( numera5444537566228673987atural @ one ) )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_numeral_1_right
% 0.30/0.57  thf(fact_4513_mult__numeral__1,axiom,
% 0.30/0.57      ! [A: nat] :
% 0.30/0.57        ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_numeral_1
% 0.30/0.57  thf(fact_4514_mult__numeral__1,axiom,
% 0.30/0.57      ! [A: int] :
% 0.30/0.57        ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_numeral_1
% 0.30/0.57  thf(fact_4515_mult__numeral__1,axiom,
% 0.30/0.57      ! [A: code_integer] :
% 0.30/0.57        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ one ) @ A )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_numeral_1
% 0.30/0.57  thf(fact_4516_mult__numeral__1,axiom,
% 0.30/0.57      ! [A: rat] :
% 0.30/0.57        ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_numeral_1
% 0.30/0.57  thf(fact_4517_mult__numeral__1,axiom,
% 0.30/0.57      ! [A: code_natural] :
% 0.30/0.57        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ one ) @ A )
% 0.30/0.57        = A ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_numeral_1
% 0.30/0.57  thf(fact_4518_numeral__One,axiom,
% 0.30/0.57      ( ( numeral_numeral_nat @ one )
% 0.30/0.57      = one_one_nat ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_One
% 0.30/0.57  thf(fact_4519_numeral__One,axiom,
% 0.30/0.57      ( ( numeral_numeral_int @ one )
% 0.30/0.57      = one_one_int ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_One
% 0.30/0.57  thf(fact_4520_numeral__One,axiom,
% 0.30/0.57      ( ( numera6620942414471956472nteger @ one )
% 0.30/0.57      = one_one_Code_integer ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_One
% 0.30/0.57  thf(fact_4521_numeral__One,axiom,
% 0.30/0.57      ( ( numeral_numeral_rat @ one )
% 0.30/0.57      = one_one_rat ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_One
% 0.30/0.57  thf(fact_4522_numeral__One,axiom,
% 0.30/0.57      ( ( numera5444537566228673987atural @ one )
% 0.30/0.57      = one_one_Code_natural ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_One
% 0.30/0.57  thf(fact_4523_add_Ocomm__monoid__axioms,axiom,
% 0.30/0.57      comm_m1654649897431166824nteger @ plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger ).
% 0.30/0.57  
% 0.30/0.57  % add.comm_monoid_axioms
% 0.30/0.57  thf(fact_4524_add_Ocomm__monoid__axioms,axiom,
% 0.30/0.57      comm_m1862543879040115196at_nat @ plus_p7104986032573967614at_nat @ zero_z1048942125864253310at_nat ).
% 0.30/0.57  
% 0.30/0.57  % add.comm_monoid_axioms
% 0.30/0.57  thf(fact_4525_add_Ocomm__monoid__axioms,axiom,
% 0.30/0.57      comm_monoid_rat @ plus_plus_rat @ zero_zero_rat ).
% 0.30/0.57  
% 0.30/0.57  % add.comm_monoid_axioms
% 0.30/0.57  thf(fact_4526_add_Ocomm__monoid__axioms,axiom,
% 0.30/0.57      comm_monoid_nat @ plus_plus_nat @ zero_zero_nat ).
% 0.30/0.57  
% 0.30/0.57  % add.comm_monoid_axioms
% 0.30/0.57  thf(fact_4527_add_Ocomm__monoid__axioms,axiom,
% 0.30/0.57      comm_monoid_int @ plus_plus_int @ zero_zero_int ).
% 0.30/0.57  
% 0.30/0.57  % add.comm_monoid_axioms
% 0.30/0.57  thf(fact_4528_add_Omonoid__axioms,axiom,
% 0.30/0.57      monoid_literal @ plus_plus_literal @ zero_zero_literal ).
% 0.30/0.57  
% 0.30/0.57  % add.monoid_axioms
% 0.30/0.57  thf(fact_4529_add_Omonoid__axioms,axiom,
% 0.30/0.57      monoid_Code_integer @ plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger ).
% 0.30/0.57  
% 0.30/0.57  % add.monoid_axioms
% 0.30/0.57  thf(fact_4530_add_Omonoid__axioms,axiom,
% 0.30/0.57      monoid66256789251010760at_nat @ plus_p7104986032573967614at_nat @ zero_z1048942125864253310at_nat ).
% 0.30/0.57  
% 0.30/0.57  % add.monoid_axioms
% 0.30/0.57  thf(fact_4531_add_Omonoid__axioms,axiom,
% 0.30/0.57      monoid_rat @ plus_plus_rat @ zero_zero_rat ).
% 0.30/0.57  
% 0.30/0.57  % add.monoid_axioms
% 0.30/0.57  thf(fact_4532_add_Omonoid__axioms,axiom,
% 0.30/0.57      monoid_nat @ plus_plus_nat @ zero_zero_nat ).
% 0.30/0.57  
% 0.30/0.57  % add.monoid_axioms
% 0.30/0.57  thf(fact_4533_add_Omonoid__axioms,axiom,
% 0.30/0.57      monoid_int @ plus_plus_int @ zero_zero_int ).
% 0.30/0.57  
% 0.30/0.57  % add.monoid_axioms
% 0.30/0.57  thf(fact_4534_semilattice__neutr__order_Oaxioms_I1_J,axiom,
% 0.30/0.57      ! [F2: nat > nat > nat,Z: nat,Less_eq: nat > nat > $o,Less: nat > nat > $o] :
% 0.30/0.57        ( ( semila1623282765462674594er_nat @ F2 @ Z @ Less_eq @ Less )
% 0.30/0.57       => ( semila9081495762789891438tr_nat @ F2 @ Z ) ) ).
% 0.30/0.57  
% 0.30/0.57  % semilattice_neutr_order.axioms(1)
% 0.30/0.57  thf(fact_4535_dbl__inc__def,axiom,
% 0.30/0.57      ( neg_nu5831290666863070958nteger
% 0.30/0.57      = ( ^ [X3: code_integer] : ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ X3 @ X3 ) @ one_one_Code_integer ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % dbl_inc_def
% 0.30/0.57  thf(fact_4536_dbl__inc__def,axiom,
% 0.30/0.57      ( neg_nu5219082963157363817nc_rat
% 0.30/0.57      = ( ^ [X3: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X3 @ X3 ) @ one_one_rat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % dbl_inc_def
% 0.30/0.57  thf(fact_4537_dbl__inc__def,axiom,
% 0.30/0.57      ( neg_nu5851722552734809277nc_int
% 0.30/0.57      = ( ^ [X3: int] : ( plus_plus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % dbl_inc_def
% 0.30/0.57  thf(fact_4538_add__strict__increasing2,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.57       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 0.30/0.57         => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_strict_increasing2
% 0.30/0.57  thf(fact_4539_add__strict__increasing2,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.57       => ( ( ord_less_rat @ B @ C )
% 0.30/0.57         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_strict_increasing2
% 0.30/0.57  thf(fact_4540_add__strict__increasing2,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.57       => ( ( ord_less_nat @ B @ C )
% 0.30/0.57         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_strict_increasing2
% 0.30/0.57  thf(fact_4541_add__strict__increasing2,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.57       => ( ( ord_less_int @ B @ C )
% 0.30/0.57         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_strict_increasing2
% 0.30/0.57  thf(fact_4542_add__strict__increasing,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.57       => ( ( ord_le3102999989581377725nteger @ B @ C )
% 0.30/0.57         => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_strict_increasing
% 0.30/0.57  thf(fact_4543_add__strict__increasing,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.57       => ( ( ord_less_eq_rat @ B @ C )
% 0.30/0.57         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_strict_increasing
% 0.30/0.57  thf(fact_4544_add__strict__increasing,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.57       => ( ( ord_less_eq_nat @ B @ C )
% 0.30/0.57         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_strict_increasing
% 0.30/0.57  thf(fact_4545_add__strict__increasing,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.57       => ( ( ord_less_eq_int @ B @ C )
% 0.30/0.57         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_strict_increasing
% 0.30/0.57  thf(fact_4546_add__pos__nonneg,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.57       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.30/0.57         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_pos_nonneg
% 0.30/0.57  thf(fact_4547_add__pos__nonneg,axiom,
% 0.30/0.57      ! [A: rat,B: rat] :
% 0.30/0.57        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.57         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_pos_nonneg
% 0.30/0.57  thf(fact_4548_add__pos__nonneg,axiom,
% 0.30/0.57      ! [A: nat,B: nat] :
% 0.30/0.57        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.57       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.30/0.57         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_pos_nonneg
% 0.30/0.57  thf(fact_4549_add__pos__nonneg,axiom,
% 0.30/0.57      ! [A: int,B: int] :
% 0.30/0.57        ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.57       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.30/0.57         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_pos_nonneg
% 0.30/0.57  thf(fact_4550_add__nonpos__neg,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.30/0.57       => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 0.30/0.57         => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonpos_neg
% 0.30/0.57  thf(fact_4551_add__nonpos__neg,axiom,
% 0.30/0.57      ! [A: rat,B: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.30/0.57       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.30/0.57         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonpos_neg
% 0.30/0.57  thf(fact_4552_add__nonpos__neg,axiom,
% 0.30/0.57      ! [A: nat,B: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.30/0.57       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.30/0.57         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonpos_neg
% 0.30/0.57  thf(fact_4553_add__nonpos__neg,axiom,
% 0.30/0.57      ! [A: int,B: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.30/0.57       => ( ( ord_less_int @ B @ zero_zero_int )
% 0.30/0.57         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonpos_neg
% 0.30/0.57  thf(fact_4554_add__nonneg__pos,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.57       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.30/0.57         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonneg_pos
% 0.30/0.57  thf(fact_4555_add__nonneg__pos,axiom,
% 0.30/0.57      ! [A: rat,B: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.57       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.30/0.57         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonneg_pos
% 0.30/0.57  thf(fact_4556_add__nonneg__pos,axiom,
% 0.30/0.57      ! [A: nat,B: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.57       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.30/0.57         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonneg_pos
% 0.30/0.57  thf(fact_4557_add__nonneg__pos,axiom,
% 0.30/0.57      ! [A: int,B: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.57       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.57         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_nonneg_pos
% 0.30/0.57  thf(fact_4558_add__neg__nonpos,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.30/0.57       => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 0.30/0.57         => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_nonpos
% 0.30/0.57  thf(fact_4559_add__neg__nonpos,axiom,
% 0.30/0.57      ! [A: rat,B: rat] :
% 0.30/0.57        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.30/0.57       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.30/0.57         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_nonpos
% 0.30/0.57  thf(fact_4560_add__neg__nonpos,axiom,
% 0.30/0.57      ! [A: nat,B: nat] :
% 0.30/0.57        ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.30/0.57       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.30/0.57         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_nonpos
% 0.30/0.57  thf(fact_4561_add__neg__nonpos,axiom,
% 0.30/0.57      ! [A: int,B: int] :
% 0.30/0.57        ( ( ord_less_int @ A @ zero_zero_int )
% 0.30/0.57       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.30/0.57         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_nonpos
% 0.30/0.57  thf(fact_4562_sum__squares__ge__zero,axiom,
% 0.30/0.57      ! [X: code_integer,Y: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % sum_squares_ge_zero
% 0.30/0.57  thf(fact_4563_sum__squares__ge__zero,axiom,
% 0.30/0.57      ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % sum_squares_ge_zero
% 0.30/0.57  thf(fact_4564_sum__squares__ge__zero,axiom,
% 0.30/0.57      ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % sum_squares_ge_zero
% 0.30/0.57  thf(fact_4565_not__sum__squares__lt__zero,axiom,
% 0.30/0.57      ! [X: code_integer,Y: code_integer] :
% 0.30/0.57        ~ ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger ) ).
% 0.30/0.57  
% 0.30/0.57  % not_sum_squares_lt_zero
% 0.30/0.57  thf(fact_4566_not__sum__squares__lt__zero,axiom,
% 0.30/0.57      ! [X: rat,Y: rat] :
% 0.30/0.57        ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 0.30/0.57  
% 0.30/0.57  % not_sum_squares_lt_zero
% 0.30/0.57  thf(fact_4567_not__sum__squares__lt__zero,axiom,
% 0.30/0.57      ! [X: int,Y: int] :
% 0.30/0.57        ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 0.30/0.57  
% 0.30/0.57  % not_sum_squares_lt_zero
% 0.30/0.57  thf(fact_4568_discrete,axiom,
% 0.30/0.57      ( ord_le6747313008572928689nteger
% 0.30/0.57      = ( ^ [A3: code_integer] : ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A3 @ one_one_Code_integer ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % discrete
% 0.30/0.57  thf(fact_4569_discrete,axiom,
% 0.30/0.57      ( ord_less_nat
% 0.30/0.57      = ( ^ [A3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A3 @ one_one_nat ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % discrete
% 0.30/0.57  thf(fact_4570_discrete,axiom,
% 0.30/0.57      ( ord_less_int
% 0.30/0.57      = ( ^ [A3: int] : ( ord_less_eq_int @ ( plus_plus_int @ A3 @ one_one_int ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % discrete
% 0.30/0.57  thf(fact_4571_zero__less__two,axiom,
% 0.30/0.57      ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 0.30/0.57  
% 0.30/0.57  % zero_less_two
% 0.30/0.57  thf(fact_4572_zero__less__two,axiom,
% 0.30/0.57      ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 0.30/0.57  
% 0.30/0.57  % zero_less_two
% 0.30/0.57  thf(fact_4573_zero__less__two,axiom,
% 0.30/0.57      ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 0.30/0.57  
% 0.30/0.57  % zero_less_two
% 0.30/0.57  thf(fact_4574_zero__less__two,axiom,
% 0.30/0.57      ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 0.30/0.57  
% 0.30/0.57  % zero_less_two
% 0.30/0.57  thf(fact_4575_le__add__iff1,axiom,
% 0.30/0.57      ! [A: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 0.30/0.57        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E2 ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 0.30/0.57        = ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 0.30/0.57  
% 0.30/0.57  % le_add_iff1
% 0.30/0.57  thf(fact_4576_le__add__iff1,axiom,
% 0.30/0.57      ! [A: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 0.30/0.57        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 0.30/0.57  
% 0.30/0.57  % le_add_iff1
% 0.30/0.57  thf(fact_4577_le__add__iff1,axiom,
% 0.30/0.57      ! [A: int,E2: int,C: int,B: int,D2: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 0.30/0.57        = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 0.30/0.57  
% 0.30/0.57  % le_add_iff1
% 0.30/0.57  thf(fact_4578_le__add__iff2,axiom,
% 0.30/0.57      ! [A: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 0.30/0.57        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E2 ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 0.30/0.57        = ( ord_le3102999989581377725nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % le_add_iff2
% 0.30/0.57  thf(fact_4579_le__add__iff2,axiom,
% 0.30/0.57      ! [A: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 0.30/0.57        = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % le_add_iff2
% 0.30/0.57  thf(fact_4580_le__add__iff2,axiom,
% 0.30/0.57      ! [A: int,E2: int,C: int,B: int,D2: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 0.30/0.57        = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % le_add_iff2
% 0.30/0.57  thf(fact_4581_less__add__iff1,axiom,
% 0.30/0.57      ! [A: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 0.30/0.57        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E2 ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 0.30/0.57        = ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 0.30/0.57  
% 0.30/0.57  % less_add_iff1
% 0.30/0.57  thf(fact_4582_less__add__iff1,axiom,
% 0.30/0.57      ! [A: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 0.30/0.57        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 0.30/0.57        = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 0.30/0.57  
% 0.30/0.57  % less_add_iff1
% 0.30/0.57  thf(fact_4583_less__add__iff1,axiom,
% 0.30/0.57      ! [A: int,E2: int,C: int,B: int,D2: int] :
% 0.30/0.57        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 0.30/0.57        = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 0.30/0.57  
% 0.30/0.57  % less_add_iff1
% 0.30/0.57  thf(fact_4584_less__add__iff2,axiom,
% 0.30/0.57      ! [A: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 0.30/0.57        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E2 ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 0.30/0.57        = ( ord_le6747313008572928689nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % less_add_iff2
% 0.30/0.57  thf(fact_4585_less__add__iff2,axiom,
% 0.30/0.57      ! [A: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 0.30/0.57        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 0.30/0.57        = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % less_add_iff2
% 0.30/0.57  thf(fact_4586_less__add__iff2,axiom,
% 0.30/0.57      ! [A: int,E2: int,C: int,B: int,D2: int] :
% 0.30/0.57        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 0.30/0.57        = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % less_add_iff2
% 0.30/0.57  thf(fact_4587_divide__add__eq__iff,axiom,
% 0.30/0.57      ! [Z: rat,X: rat,Y: rat] :
% 0.30/0.57        ( ( Z != zero_zero_rat )
% 0.30/0.57       => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 0.30/0.57          = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divide_add_eq_iff
% 0.30/0.57  thf(fact_4588_add__divide__eq__iff,axiom,
% 0.30/0.57      ! [Z: rat,X: rat,Y: rat] :
% 0.30/0.57        ( ( Z != zero_zero_rat )
% 0.30/0.57       => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 0.30/0.57          = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_divide_eq_iff
% 0.30/0.57  thf(fact_4589_add__num__frac,axiom,
% 0.30/0.57      ! [Y: rat,Z: rat,X: rat] :
% 0.30/0.57        ( ( Y != zero_zero_rat )
% 0.30/0.57       => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X @ Y ) )
% 0.30/0.57          = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_num_frac
% 0.30/0.57  thf(fact_4590_add__frac__num,axiom,
% 0.30/0.57      ! [Y: rat,X: rat,Z: rat] :
% 0.30/0.57        ( ( Y != zero_zero_rat )
% 0.30/0.57       => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ Z )
% 0.30/0.57          = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_frac_num
% 0.30/0.57  thf(fact_4591_add__frac__eq,axiom,
% 0.30/0.57      ! [Y: rat,Z: rat,X: rat,W: rat] :
% 0.30/0.57        ( ( Y != zero_zero_rat )
% 0.30/0.57       => ( ( Z != zero_zero_rat )
% 0.30/0.57         => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 0.30/0.57            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_frac_eq
% 0.30/0.57  thf(fact_4592_add__divide__eq__if__simps_I1_J,axiom,
% 0.30/0.57      ! [Z: rat,A: rat,B: rat] :
% 0.30/0.57        ( ( ( Z = zero_zero_rat )
% 0.30/0.57         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.30/0.57            = A ) )
% 0.30/0.57        & ( ( Z != zero_zero_rat )
% 0.30/0.57         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 0.30/0.57            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_divide_eq_if_simps(1)
% 0.30/0.57  thf(fact_4593_add__divide__eq__if__simps_I2_J,axiom,
% 0.30/0.57      ! [Z: rat,A: rat,B: rat] :
% 0.30/0.57        ( ( ( Z = zero_zero_rat )
% 0.30/0.57         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.30/0.57            = B ) )
% 0.30/0.57        & ( ( Z != zero_zero_rat )
% 0.30/0.57         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 0.30/0.57            = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_divide_eq_if_simps(2)
% 0.30/0.57  thf(fact_4594_square__diff__one__factored,axiom,
% 0.30/0.57      ! [X: code_integer] :
% 0.30/0.57        ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ one_one_Code_integer )
% 0.30/0.57        = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % square_diff_one_factored
% 0.30/0.57  thf(fact_4595_square__diff__one__factored,axiom,
% 0.30/0.57      ! [X: rat] :
% 0.30/0.57        ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 0.30/0.57        = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % square_diff_one_factored
% 0.30/0.57  thf(fact_4596_square__diff__one__factored,axiom,
% 0.30/0.57      ! [X: int] :
% 0.30/0.57        ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 0.30/0.57        = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % square_diff_one_factored
% 0.30/0.57  thf(fact_4597_div__add__self2,axiom,
% 0.30/0.57      ! [B: nat,A: nat] :
% 0.30/0.57        ( ( B != zero_zero_nat )
% 0.30/0.57       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.30/0.57          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % div_add_self2
% 0.30/0.57  thf(fact_4598_div__add__self2,axiom,
% 0.30/0.57      ! [B: int,A: int] :
% 0.30/0.57        ( ( B != zero_zero_int )
% 0.30/0.57       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.30/0.57          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % div_add_self2
% 0.30/0.57  thf(fact_4599_div__add__self2,axiom,
% 0.30/0.57      ! [B: code_integer,A: code_integer] :
% 0.30/0.57        ( ( B != zero_z3403309356797280102nteger )
% 0.30/0.57       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 0.30/0.57          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % div_add_self2
% 0.30/0.57  thf(fact_4600_div__add__self2,axiom,
% 0.30/0.57      ! [B: code_natural,A: code_natural] :
% 0.30/0.57        ( ( B != zero_z2226904508553997617atural )
% 0.30/0.57       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ B )
% 0.30/0.57          = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % div_add_self2
% 0.30/0.57  thf(fact_4601_div__add__self1,axiom,
% 0.30/0.57      ! [B: nat,A: nat] :
% 0.30/0.57        ( ( B != zero_zero_nat )
% 0.30/0.57       => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.30/0.57          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % div_add_self1
% 0.30/0.57  thf(fact_4602_div__add__self1,axiom,
% 0.30/0.57      ! [B: int,A: int] :
% 0.30/0.57        ( ( B != zero_zero_int )
% 0.30/0.57       => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.30/0.57          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % div_add_self1
% 0.30/0.57  thf(fact_4603_div__add__self1,axiom,
% 0.30/0.57      ! [B: code_integer,A: code_integer] :
% 0.30/0.57        ( ( B != zero_z3403309356797280102nteger )
% 0.30/0.57       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 0.30/0.57          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % div_add_self1
% 0.30/0.57  thf(fact_4604_div__add__self1,axiom,
% 0.30/0.57      ! [B: code_natural,A: code_natural] :
% 0.30/0.57        ( ( B != zero_z2226904508553997617atural )
% 0.30/0.57       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ B @ A ) @ B )
% 0.30/0.57          = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % div_add_self1
% 0.30/0.57  thf(fact_4605_less__half__sum,axiom,
% 0.30/0.57      ! [A: rat,B: rat] :
% 0.30/0.57        ( ( ord_less_rat @ A @ B )
% 0.30/0.57       => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % less_half_sum
% 0.30/0.57  thf(fact_4606_gt__half__sum,axiom,
% 0.30/0.57      ! [A: rat,B: rat] :
% 0.30/0.57        ( ( ord_less_rat @ A @ B )
% 0.30/0.57       => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % gt_half_sum
% 0.30/0.57  thf(fact_4607_mult__1s__ring__1_I1_J,axiom,
% 0.30/0.57      ! [B: int] :
% 0.30/0.57        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 0.30/0.57        = ( uminus_uminus_int @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_1s_ring_1(1)
% 0.30/0.57  thf(fact_4608_mult__1s__ring__1_I1_J,axiom,
% 0.30/0.57      ! [B: code_integer] :
% 0.30/0.57        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 0.30/0.57        = ( uminus1351360451143612070nteger @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_1s_ring_1(1)
% 0.30/0.57  thf(fact_4609_mult__1s__ring__1_I1_J,axiom,
% 0.30/0.57      ! [B: rat] :
% 0.30/0.57        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 0.30/0.57        = ( uminus_uminus_rat @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_1s_ring_1(1)
% 0.30/0.57  thf(fact_4610_mult__1s__ring__1_I2_J,axiom,
% 0.30/0.57      ! [B: int] :
% 0.30/0.57        ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 0.30/0.57        = ( uminus_uminus_int @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_1s_ring_1(2)
% 0.30/0.57  thf(fact_4611_mult__1s__ring__1_I2_J,axiom,
% 0.30/0.57      ! [B: code_integer] :
% 0.30/0.57        ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 0.30/0.57        = ( uminus1351360451143612070nteger @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_1s_ring_1(2)
% 0.30/0.57  thf(fact_4612_mult__1s__ring__1_I2_J,axiom,
% 0.30/0.57      ! [B: rat] :
% 0.30/0.57        ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 0.30/0.57        = ( uminus_uminus_rat @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_1s_ring_1(2)
% 0.30/0.57  thf(fact_4613_uminus__numeral__One,axiom,
% 0.30/0.57      ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 0.30/0.57      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.30/0.57  
% 0.30/0.57  % uminus_numeral_One
% 0.30/0.57  thf(fact_4614_uminus__numeral__One,axiom,
% 0.30/0.57      ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 0.30/0.57      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.30/0.57  
% 0.30/0.57  % uminus_numeral_One
% 0.30/0.57  thf(fact_4615_uminus__numeral__One,axiom,
% 0.30/0.57      ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 0.30/0.57      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % uminus_numeral_One
% 0.30/0.57  thf(fact_4616_numeral__inc,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( numeral_numeral_nat @ ( inc @ X ) )
% 0.30/0.57        = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_inc
% 0.30/0.57  thf(fact_4617_numeral__inc,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( numeral_numeral_int @ ( inc @ X ) )
% 0.30/0.57        = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_inc
% 0.30/0.57  thf(fact_4618_numeral__inc,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( numera6620942414471956472nteger @ ( inc @ X ) )
% 0.30/0.57        = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer ) ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_inc
% 0.30/0.57  thf(fact_4619_numeral__inc,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( numeral_numeral_rat @ ( inc @ X ) )
% 0.30/0.57        = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_inc
% 0.30/0.57  thf(fact_4620_numeral__inc,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( numera5444537566228673987atural @ ( inc @ X ) )
% 0.30/0.57        = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ X ) @ one_one_Code_natural ) ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_inc
% 0.30/0.57  thf(fact_4621_eq__numeral__iff__iszero_I3_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ X ) )
% 0.30/0.57          = ( numeral_numeral_int @ Y ) )
% 0.30/0.57        = ( ring_1_iszero_int @ ( numeral_numeral_int @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_numeral_iff_iszero(3)
% 0.30/0.57  thf(fact_4622_eq__numeral__iff__iszero_I3_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) )
% 0.30/0.57          = ( numera6620942414471956472nteger @ Y ) )
% 0.30/0.57        = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_numeral_iff_iszero(3)
% 0.30/0.57  thf(fact_4623_eq__numeral__iff__iszero_I3_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) )
% 0.30/0.57          = ( numeral_numeral_rat @ Y ) )
% 0.30/0.57        = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_numeral_iff_iszero(3)
% 0.30/0.57  thf(fact_4624_eq__numeral__iff__iszero_I2_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( ( numeral_numeral_int @ X )
% 0.30/0.57          = ( uminus_uminus_int @ ( numeral_numeral_int @ Y ) ) )
% 0.30/0.57        = ( ring_1_iszero_int @ ( numeral_numeral_int @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_numeral_iff_iszero(2)
% 0.30/0.57  thf(fact_4625_eq__numeral__iff__iszero_I2_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( ( numera6620942414471956472nteger @ X )
% 0.30/0.57          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ Y ) ) )
% 0.30/0.57        = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_numeral_iff_iszero(2)
% 0.30/0.57  thf(fact_4626_eq__numeral__iff__iszero_I2_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( ( numeral_numeral_rat @ X )
% 0.30/0.57          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ Y ) ) )
% 0.30/0.57        = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_numeral_iff_iszero(2)
% 0.30/0.57  thf(fact_4627_distrib__left__NO__MATCH,axiom,
% 0.30/0.57      ! [X: nat,Y: nat,A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.57        ( ( nO_MAT8694959213317031834nteger @ ( divide_divide_nat @ X @ Y ) @ A )
% 0.30/0.57       => ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.30/0.57          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_left_NO_MATCH
% 0.30/0.57  thf(fact_4628_distrib__left__NO__MATCH,axiom,
% 0.30/0.57      ! [X: nat,Y: nat,A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X @ Y ) @ A )
% 0.30/0.57       => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.30/0.57          = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_left_NO_MATCH
% 0.30/0.57  thf(fact_4629_distrib__left__NO__MATCH,axiom,
% 0.30/0.57      ! [X: nat,Y: nat,A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X @ Y ) @ A )
% 0.30/0.57       => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.30/0.57          = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_left_NO_MATCH
% 0.30/0.57  thf(fact_4630_distrib__left__NO__MATCH,axiom,
% 0.30/0.57      ! [X: nat,Y: nat,A: int,B: int,C: int] :
% 0.30/0.57        ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ A )
% 0.30/0.57       => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.30/0.57          = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_left_NO_MATCH
% 0.30/0.57  thf(fact_4631_distrib__left__NO__MATCH,axiom,
% 0.30/0.57      ! [X: int,Y: int,A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.57        ( ( nO_MAT9066612773553876470nteger @ ( divide_divide_int @ X @ Y ) @ A )
% 0.30/0.57       => ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.30/0.57          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_left_NO_MATCH
% 0.30/0.57  thf(fact_4632_distrib__left__NO__MATCH,axiom,
% 0.30/0.57      ! [X: int,Y: int,A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X @ Y ) @ A )
% 0.30/0.57       => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.30/0.57          = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_left_NO_MATCH
% 0.30/0.57  thf(fact_4633_distrib__left__NO__MATCH,axiom,
% 0.30/0.57      ! [X: int,Y: int,A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X @ Y ) @ A )
% 0.30/0.57       => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 0.30/0.57          = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_left_NO_MATCH
% 0.30/0.57  thf(fact_4634_distrib__left__NO__MATCH,axiom,
% 0.30/0.57      ! [X: int,Y: int,A: int,B: int,C: int] :
% 0.30/0.57        ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ A )
% 0.30/0.57       => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 0.30/0.57          = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_left_NO_MATCH
% 0.30/0.57  thf(fact_4635_distrib__left__NO__MATCH,axiom,
% 0.30/0.57      ! [X: code_integer,Y: code_integer,A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.57        ( ( nO_MAT8252062027627875367nteger @ ( divide6298287555418463151nteger @ X @ Y ) @ A )
% 0.30/0.57       => ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 0.30/0.57          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_left_NO_MATCH
% 0.30/0.57  thf(fact_4636_distrib__left__NO__MATCH,axiom,
% 0.30/0.57      ! [X: code_integer,Y: code_integer,A: rat,B: rat,C: rat] :
% 0.30/0.57        ( ( nO_MAT7795273704451493282er_rat @ ( divide6298287555418463151nteger @ X @ Y ) @ A )
% 0.30/0.57       => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 0.30/0.57          = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_left_NO_MATCH
% 0.30/0.57  thf(fact_4637_distrib__right__NO__MATCH,axiom,
% 0.30/0.57      ! [X: nat,Y: nat,C: code_integer,A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( nO_MAT8694959213317031834nteger @ ( divide_divide_nat @ X @ Y ) @ C )
% 0.30/0.57       => ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.30/0.57          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_right_NO_MATCH
% 0.30/0.57  thf(fact_4638_distrib__right__NO__MATCH,axiom,
% 0.30/0.57      ! [X: nat,Y: nat,C: rat,A: rat,B: rat] :
% 0.30/0.57        ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X @ Y ) @ C )
% 0.30/0.57       => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.30/0.57          = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_right_NO_MATCH
% 0.30/0.57  thf(fact_4639_distrib__right__NO__MATCH,axiom,
% 0.30/0.57      ! [X: nat,Y: nat,C: nat,A: nat,B: nat] :
% 0.30/0.57        ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X @ Y ) @ C )
% 0.30/0.57       => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.30/0.57          = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_right_NO_MATCH
% 0.30/0.57  thf(fact_4640_distrib__right__NO__MATCH,axiom,
% 0.30/0.57      ! [X: nat,Y: nat,C: int,A: int,B: int] :
% 0.30/0.57        ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ C )
% 0.30/0.57       => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.30/0.57          = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_right_NO_MATCH
% 0.30/0.57  thf(fact_4641_distrib__right__NO__MATCH,axiom,
% 0.30/0.57      ! [X: int,Y: int,C: code_integer,A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( nO_MAT9066612773553876470nteger @ ( divide_divide_int @ X @ Y ) @ C )
% 0.30/0.57       => ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.30/0.57          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_right_NO_MATCH
% 0.30/0.57  thf(fact_4642_distrib__right__NO__MATCH,axiom,
% 0.30/0.57      ! [X: int,Y: int,C: rat,A: rat,B: rat] :
% 0.30/0.57        ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X @ Y ) @ C )
% 0.30/0.57       => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.30/0.57          = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_right_NO_MATCH
% 0.30/0.57  thf(fact_4643_distrib__right__NO__MATCH,axiom,
% 0.30/0.57      ! [X: int,Y: int,C: nat,A: nat,B: nat] :
% 0.30/0.57        ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X @ Y ) @ C )
% 0.30/0.57       => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 0.30/0.57          = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_right_NO_MATCH
% 0.30/0.57  thf(fact_4644_distrib__right__NO__MATCH,axiom,
% 0.30/0.57      ! [X: int,Y: int,C: int,A: int,B: int] :
% 0.30/0.57        ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ C )
% 0.30/0.57       => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 0.30/0.57          = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_right_NO_MATCH
% 0.30/0.57  thf(fact_4645_distrib__right__NO__MATCH,axiom,
% 0.30/0.57      ! [X: code_integer,Y: code_integer,C: code_integer,A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( nO_MAT8252062027627875367nteger @ ( divide6298287555418463151nteger @ X @ Y ) @ C )
% 0.30/0.57       => ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 0.30/0.57          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_right_NO_MATCH
% 0.30/0.57  thf(fact_4646_distrib__right__NO__MATCH,axiom,
% 0.30/0.57      ! [X: code_integer,Y: code_integer,C: rat,A: rat,B: rat] :
% 0.30/0.57        ( ( nO_MAT7795273704451493282er_rat @ ( divide6298287555418463151nteger @ X @ Y ) @ C )
% 0.30/0.57       => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 0.30/0.57          = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % distrib_right_NO_MATCH
% 0.30/0.57  thf(fact_4647_dbl__dec__def,axiom,
% 0.30/0.57      ( neg_nu7757733837767384882nteger
% 0.30/0.57      = ( ^ [X3: code_integer] : ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ X3 @ X3 ) @ one_one_Code_integer ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % dbl_dec_def
% 0.30/0.57  thf(fact_4648_dbl__dec__def,axiom,
% 0.30/0.57      ( neg_nu3179335615603231917ec_rat
% 0.30/0.57      = ( ^ [X3: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X3 @ X3 ) @ one_one_rat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % dbl_dec_def
% 0.30/0.57  thf(fact_4649_dbl__dec__def,axiom,
% 0.30/0.57      ( neg_nu3811975205180677377ec_int
% 0.30/0.57      = ( ^ [X3: int] : ( minus_minus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % dbl_dec_def
% 0.30/0.57  thf(fact_4650_not__iszero__neg__Numeral1,axiom,
% 0.30/0.57      ~ ( ring_1_iszero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % not_iszero_neg_Numeral1
% 0.30/0.57  thf(fact_4651_not__iszero__neg__Numeral1,axiom,
% 0.30/0.57      ~ ( ring_16219924574208605041nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % not_iszero_neg_Numeral1
% 0.30/0.57  thf(fact_4652_not__iszero__neg__Numeral1,axiom,
% 0.30/0.57      ~ ( ring_1_iszero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % not_iszero_neg_Numeral1
% 0.30/0.57  thf(fact_4653_convex__bound__le,axiom,
% 0.30/0.57      ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
% 0.30/0.57        ( ( ord_le3102999989581377725nteger @ X @ A )
% 0.30/0.57       => ( ( ord_le3102999989581377725nteger @ Y @ A )
% 0.30/0.57         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 0.30/0.57           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V )
% 0.30/0.57             => ( ( ( plus_p5714425477246183910nteger @ U @ V )
% 0.30/0.57                  = one_one_Code_integer )
% 0.30/0.57               => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % convex_bound_le
% 0.30/0.57  thf(fact_4654_convex__bound__le,axiom,
% 0.30/0.57      ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ X @ A )
% 0.30/0.57       => ( ( ord_less_eq_rat @ Y @ A )
% 0.30/0.57         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 0.30/0.57           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 0.30/0.57             => ( ( ( plus_plus_rat @ U @ V )
% 0.30/0.57                  = one_one_rat )
% 0.30/0.57               => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % convex_bound_le
% 0.30/0.57  thf(fact_4655_convex__bound__le,axiom,
% 0.30/0.57      ! [X: int,A: int,Y: int,U: int,V: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ X @ A )
% 0.30/0.57       => ( ( ord_less_eq_int @ Y @ A )
% 0.30/0.57         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.30/0.57           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 0.30/0.57             => ( ( ( plus_plus_int @ U @ V )
% 0.30/0.57                  = one_one_int )
% 0.30/0.57               => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % convex_bound_le
% 0.30/0.57  thf(fact_4656_minus__divide__add__eq__iff,axiom,
% 0.30/0.57      ! [Z: rat,X: rat,Y: rat] :
% 0.30/0.57        ( ( Z != zero_zero_rat )
% 0.30/0.57       => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 0.30/0.57          = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % minus_divide_add_eq_iff
% 0.30/0.57  thf(fact_4657_add__divide__eq__if__simps_I3_J,axiom,
% 0.30/0.57      ! [Z: rat,A: rat,B: rat] :
% 0.30/0.57        ( ( ( Z = zero_zero_rat )
% 0.30/0.57         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.30/0.57            = B ) )
% 0.30/0.57        & ( ( Z != zero_zero_rat )
% 0.30/0.57         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 0.30/0.57            = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_divide_eq_if_simps(3)
% 0.30/0.57  thf(fact_4658_convex__bound__lt,axiom,
% 0.30/0.57      ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
% 0.30/0.57        ( ( ord_le6747313008572928689nteger @ X @ A )
% 0.30/0.57       => ( ( ord_le6747313008572928689nteger @ Y @ A )
% 0.30/0.57         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 0.30/0.57           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V )
% 0.30/0.57             => ( ( ( plus_p5714425477246183910nteger @ U @ V )
% 0.30/0.57                  = one_one_Code_integer )
% 0.30/0.57               => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % convex_bound_lt
% 0.30/0.57  thf(fact_4659_convex__bound__lt,axiom,
% 0.30/0.57      ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 0.30/0.57        ( ( ord_less_rat @ X @ A )
% 0.30/0.57       => ( ( ord_less_rat @ Y @ A )
% 0.30/0.57         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 0.30/0.57           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 0.30/0.57             => ( ( ( plus_plus_rat @ U @ V )
% 0.30/0.57                  = one_one_rat )
% 0.30/0.57               => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % convex_bound_lt
% 0.30/0.57  thf(fact_4660_convex__bound__lt,axiom,
% 0.30/0.57      ! [X: int,A: int,Y: int,U: int,V: int] :
% 0.30/0.57        ( ( ord_less_int @ X @ A )
% 0.30/0.57       => ( ( ord_less_int @ Y @ A )
% 0.30/0.57         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.30/0.57           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 0.30/0.57             => ( ( ( plus_plus_int @ U @ V )
% 0.30/0.57                  = one_one_int )
% 0.30/0.57               => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % convex_bound_lt
% 0.30/0.57  thf(fact_4661_scaling__mono,axiom,
% 0.30/0.57      ! [U: rat,V: rat,R3: rat,S3: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ U @ V )
% 0.30/0.57       => ( ( ord_less_eq_rat @ zero_zero_rat @ R3 )
% 0.30/0.57         => ( ( ord_less_eq_rat @ R3 @ S3 )
% 0.30/0.57           => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R3 @ ( minus_minus_rat @ V @ U ) ) @ S3 ) ) @ V ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % scaling_mono
% 0.30/0.57  thf(fact_4662_top_Oordering__top__axioms,axiom,
% 0.30/0.57      orderi7613023277850353061st_nat @ ord_le6045566169113846134st_nat @ ord_le1190675801316882794st_nat @ top_top_set_list_nat ).
% 0.30/0.57  
% 0.30/0.57  % top.ordering_top_axioms
% 0.30/0.57  thf(fact_4663_top_Oordering__top__axioms,axiom,
% 0.30/0.57      ordering_top_set_o @ ord_less_eq_set_o @ ord_less_set_o @ top_top_set_o ).
% 0.30/0.57  
% 0.30/0.57  % top.ordering_top_axioms
% 0.30/0.57  thf(fact_4664_top_Oordering__top__axioms,axiom,
% 0.30/0.57      ordering_top_set_rat @ ord_less_eq_set_rat @ ord_less_set_rat @ top_top_set_rat ).
% 0.30/0.57  
% 0.30/0.57  % top.ordering_top_axioms
% 0.30/0.57  thf(fact_4665_top_Oordering__top__axioms,axiom,
% 0.30/0.57      ordering_top_set_int @ ord_less_eq_set_int @ ord_less_set_int @ top_top_set_int ).
% 0.30/0.57  
% 0.30/0.57  % top.ordering_top_axioms
% 0.30/0.57  thf(fact_4666_top_Oordering__top__axioms,axiom,
% 0.30/0.57      orderi2807725203697798511er_nat @ ord_le2510731241096832064er_nat @ ord_less_filter_nat @ top_top_filter_nat ).
% 0.30/0.57  
% 0.30/0.57  % top.ordering_top_axioms
% 0.30/0.57  thf(fact_4667_top_Oordering__top__axioms,axiom,
% 0.30/0.57      ordering_top_set_nat @ ord_less_eq_set_nat @ ord_less_set_nat @ top_top_set_nat ).
% 0.30/0.57  
% 0.30/0.57  % top.ordering_top_axioms
% 0.30/0.57  thf(fact_4668_sum__squares__gt__zero__iff,axiom,
% 0.30/0.57      ! [X: code_integer,Y: code_integer] :
% 0.30/0.57        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) )
% 0.30/0.57        = ( ( X != zero_z3403309356797280102nteger )
% 0.30/0.57          | ( Y != zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % sum_squares_gt_zero_iff
% 0.30/0.57  thf(fact_4669_sum__squares__gt__zero__iff,axiom,
% 0.30/0.57      ! [X: rat,Y: rat] :
% 0.30/0.57        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 0.30/0.57        = ( ( X != zero_zero_rat )
% 0.30/0.57          | ( Y != zero_zero_rat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % sum_squares_gt_zero_iff
% 0.30/0.57  thf(fact_4670_sum__squares__gt__zero__iff,axiom,
% 0.30/0.57      ! [X: int,Y: int] :
% 0.30/0.57        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 0.30/0.57        = ( ( X != zero_zero_int )
% 0.30/0.57          | ( Y != zero_zero_int ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % sum_squares_gt_zero_iff
% 0.30/0.57  thf(fact_4671_sum__squares__le__zero__iff,axiom,
% 0.30/0.57      ! [X: code_integer,Y: code_integer] :
% 0.30/0.57        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger )
% 0.30/0.57        = ( ( X = zero_z3403309356797280102nteger )
% 0.30/0.57          & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % sum_squares_le_zero_iff
% 0.30/0.57  thf(fact_4672_sum__squares__le__zero__iff,axiom,
% 0.30/0.57      ! [X: rat,Y: rat] :
% 0.30/0.57        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 0.30/0.57        = ( ( X = zero_zero_rat )
% 0.30/0.57          & ( Y = zero_zero_rat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % sum_squares_le_zero_iff
% 0.30/0.57  thf(fact_4673_sum__squares__le__zero__iff,axiom,
% 0.30/0.57      ! [X: int,Y: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 0.30/0.57        = ( ( X = zero_zero_int )
% 0.30/0.57          & ( Y = zero_zero_int ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % sum_squares_le_zero_iff
% 0.30/0.57  thf(fact_4674_add__scale__eq__noteq,axiom,
% 0.30/0.57      ! [R3: code_integer,A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.30/0.57        ( ( R3 != zero_z3403309356797280102nteger )
% 0.30/0.57       => ( ( ( A = B )
% 0.30/0.57            & ( C != D2 ) )
% 0.30/0.57         => ( ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ R3 @ C ) )
% 0.30/0.57           != ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ R3 @ D2 ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_scale_eq_noteq
% 0.30/0.57  thf(fact_4675_add__scale__eq__noteq,axiom,
% 0.30/0.57      ! [R3: rat,A: rat,B: rat,C: rat,D2: rat] :
% 0.30/0.57        ( ( R3 != zero_zero_rat )
% 0.30/0.57       => ( ( ( A = B )
% 0.30/0.57            & ( C != D2 ) )
% 0.30/0.57         => ( ( plus_plus_rat @ A @ ( times_times_rat @ R3 @ C ) )
% 0.30/0.57           != ( plus_plus_rat @ B @ ( times_times_rat @ R3 @ D2 ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_scale_eq_noteq
% 0.30/0.57  thf(fact_4676_add__scale__eq__noteq,axiom,
% 0.30/0.57      ! [R3: nat,A: nat,B: nat,C: nat,D2: nat] :
% 0.30/0.57        ( ( R3 != zero_zero_nat )
% 0.30/0.57       => ( ( ( A = B )
% 0.30/0.57            & ( C != D2 ) )
% 0.30/0.57         => ( ( plus_plus_nat @ A @ ( times_times_nat @ R3 @ C ) )
% 0.30/0.57           != ( plus_plus_nat @ B @ ( times_times_nat @ R3 @ D2 ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_scale_eq_noteq
% 0.30/0.57  thf(fact_4677_add__scale__eq__noteq,axiom,
% 0.30/0.57      ! [R3: int,A: int,B: int,C: int,D2: int] :
% 0.30/0.57        ( ( R3 != zero_zero_int )
% 0.30/0.57       => ( ( ( A = B )
% 0.30/0.57            & ( C != D2 ) )
% 0.30/0.57         => ( ( plus_plus_int @ A @ ( times_times_int @ R3 @ C ) )
% 0.30/0.57           != ( plus_plus_int @ B @ ( times_times_int @ R3 @ D2 ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_scale_eq_noteq
% 0.30/0.57  thf(fact_4678_sum__squares__eq__zero__iff,axiom,
% 0.30/0.57      ! [X: code_integer,Y: code_integer] :
% 0.30/0.57        ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 0.30/0.57          = zero_z3403309356797280102nteger )
% 0.30/0.57        = ( ( X = zero_z3403309356797280102nteger )
% 0.30/0.57          & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % sum_squares_eq_zero_iff
% 0.30/0.57  thf(fact_4679_sum__squares__eq__zero__iff,axiom,
% 0.30/0.57      ! [X: rat,Y: rat] :
% 0.30/0.57        ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 0.30/0.57          = zero_zero_rat )
% 0.30/0.57        = ( ( X = zero_zero_rat )
% 0.30/0.57          & ( Y = zero_zero_rat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % sum_squares_eq_zero_iff
% 0.30/0.57  thf(fact_4680_sum__squares__eq__zero__iff,axiom,
% 0.30/0.57      ! [X: int,Y: int] :
% 0.30/0.57        ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 0.30/0.57          = zero_zero_int )
% 0.30/0.57        = ( ( X = zero_zero_int )
% 0.30/0.57          & ( Y = zero_zero_int ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % sum_squares_eq_zero_iff
% 0.30/0.57  thf(fact_4681_less__by__empty,axiom,
% 0.30/0.57      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.57        ( ( A2 = bot_bo2099793752762293965at_nat )
% 0.30/0.57       => ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ).
% 0.30/0.57  
% 0.30/0.57  % less_by_empty
% 0.30/0.57  thf(fact_4682_divmod__algorithm__code_I2_J,axiom,
% 0.30/0.57      ! [M: num] :
% 0.30/0.57        ( ( unique5052692396658037445od_int @ M @ one )
% 0.30/0.57        = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_algorithm_code(2)
% 0.30/0.57  thf(fact_4683_divmod__algorithm__code_I2_J,axiom,
% 0.30/0.57      ! [M: num] :
% 0.30/0.57        ( ( unique5055182867167087721od_nat @ M @ one )
% 0.30/0.57        = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_algorithm_code(2)
% 0.30/0.57  thf(fact_4684_divmod__algorithm__code_I2_J,axiom,
% 0.30/0.57      ! [M: num] :
% 0.30/0.57        ( ( unique3479559517661332726nteger @ M @ one )
% 0.30/0.57        = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_algorithm_code(2)
% 0.30/0.57  thf(fact_4685_minus__sub__one__diff__one,axiom,
% 0.30/0.57      ! [M: num] :
% 0.30/0.57        ( ( minus_minus_int @ ( uminus_uminus_int @ ( neg_numeral_sub_int @ M @ one ) ) @ one_one_int )
% 0.30/0.57        = ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % minus_sub_one_diff_one
% 0.30/0.57  thf(fact_4686_minus__sub__one__diff__one,axiom,
% 0.30/0.57      ! [M: num] :
% 0.30/0.57        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( neg_nu5755505904847501662nteger @ M @ one ) ) @ one_one_Code_integer )
% 0.30/0.57        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % minus_sub_one_diff_one
% 0.30/0.57  thf(fact_4687_minus__sub__one__diff__one,axiom,
% 0.30/0.57      ! [M: num] :
% 0.30/0.57        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( neg_numeral_sub_rat @ M @ one ) ) @ one_one_rat )
% 0.30/0.57        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % minus_sub_one_diff_one
% 0.30/0.57  thf(fact_4688_semiring__norm_I166_J,axiom,
% 0.30/0.57      ! [V: num,W: num,Y: int] :
% 0.30/0.57        ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 0.30/0.57        = ( plus_plus_int @ ( neg_numeral_sub_int @ V @ W ) @ Y ) ) ).
% 0.30/0.57  
% 0.30/0.57  % semiring_norm(166)
% 0.30/0.57  thf(fact_4689_semiring__norm_I166_J,axiom,
% 0.30/0.57      ! [V: num,W: num,Y: code_integer] :
% 0.30/0.57        ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 0.30/0.57        = ( plus_p5714425477246183910nteger @ ( neg_nu5755505904847501662nteger @ V @ W ) @ Y ) ) ).
% 0.30/0.57  
% 0.30/0.57  % semiring_norm(166)
% 0.30/0.57  thf(fact_4690_semiring__norm_I166_J,axiom,
% 0.30/0.57      ! [V: num,W: num,Y: rat] :
% 0.30/0.57        ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 0.30/0.57        = ( plus_plus_rat @ ( neg_numeral_sub_rat @ V @ W ) @ Y ) ) ).
% 0.30/0.57  
% 0.30/0.57  % semiring_norm(166)
% 0.30/0.57  thf(fact_4691_semiring__norm_I167_J,axiom,
% 0.30/0.57      ! [V: num,W: num,Y: int] :
% 0.30/0.57        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Y ) )
% 0.30/0.57        = ( plus_plus_int @ ( neg_numeral_sub_int @ W @ V ) @ Y ) ) ).
% 0.30/0.57  
% 0.30/0.57  % semiring_norm(167)
% 0.30/0.57  thf(fact_4692_semiring__norm_I167_J,axiom,
% 0.30/0.57      ! [V: num,W: num,Y: code_integer] :
% 0.30/0.57        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ W ) @ Y ) )
% 0.30/0.57        = ( plus_p5714425477246183910nteger @ ( neg_nu5755505904847501662nteger @ W @ V ) @ Y ) ) ).
% 0.30/0.57  
% 0.30/0.57  % semiring_norm(167)
% 0.30/0.57  thf(fact_4693_semiring__norm_I167_J,axiom,
% 0.30/0.57      ! [V: num,W: num,Y: rat] :
% 0.30/0.57        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Y ) )
% 0.30/0.57        = ( plus_plus_rat @ ( neg_numeral_sub_rat @ W @ V ) @ Y ) ) ).
% 0.30/0.57  
% 0.30/0.57  % semiring_norm(167)
% 0.30/0.57  thf(fact_4694_add__neg__numeral__simps_I1_J,axiom,
% 0.30/0.57      ! [M: num,N: num] :
% 0.30/0.57        ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.57        = ( neg_numeral_sub_int @ M @ N ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_numeral_simps(1)
% 0.30/0.57  thf(fact_4695_add__neg__numeral__simps_I1_J,axiom,
% 0.30/0.57      ! [M: num,N: num] :
% 0.30/0.57        ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.30/0.57        = ( neg_nu5755505904847501662nteger @ M @ N ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_numeral_simps(1)
% 0.30/0.57  thf(fact_4696_add__neg__numeral__simps_I1_J,axiom,
% 0.30/0.57      ! [M: num,N: num] :
% 0.30/0.57        ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.30/0.57        = ( neg_numeral_sub_rat @ M @ N ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_numeral_simps(1)
% 0.30/0.57  thf(fact_4697_add__neg__numeral__simps_I2_J,axiom,
% 0.30/0.57      ! [M: num,N: num] :
% 0.30/0.57        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.30/0.57        = ( neg_numeral_sub_int @ N @ M ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_numeral_simps(2)
% 0.30/0.57  thf(fact_4698_add__neg__numeral__simps_I2_J,axiom,
% 0.30/0.57      ! [M: num,N: num] :
% 0.30/0.57        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 0.30/0.57        = ( neg_nu5755505904847501662nteger @ N @ M ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_numeral_simps(2)
% 0.30/0.57  thf(fact_4699_add__neg__numeral__simps_I2_J,axiom,
% 0.30/0.57      ! [M: num,N: num] :
% 0.30/0.57        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 0.30/0.57        = ( neg_numeral_sub_rat @ N @ M ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_numeral_simps(2)
% 0.30/0.57  thf(fact_4700_diff__numeral__simps_I4_J,axiom,
% 0.30/0.57      ! [M: num,N: num] :
% 0.30/0.57        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.57        = ( neg_numeral_sub_int @ N @ M ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_numeral_simps(4)
% 0.30/0.57  thf(fact_4701_diff__numeral__simps_I4_J,axiom,
% 0.30/0.57      ! [M: num,N: num] :
% 0.30/0.57        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.30/0.57        = ( neg_nu5755505904847501662nteger @ N @ M ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_numeral_simps(4)
% 0.30/0.57  thf(fact_4702_diff__numeral__simps_I4_J,axiom,
% 0.30/0.57      ! [M: num,N: num] :
% 0.30/0.57        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.30/0.57        = ( neg_numeral_sub_rat @ N @ M ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_numeral_simps(4)
% 0.30/0.57  thf(fact_4703_diff__numeral__special_I2_J,axiom,
% 0.30/0.57      ! [M: num] :
% 0.30/0.57        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int )
% 0.30/0.57        = ( neg_numeral_sub_int @ M @ one ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_numeral_special(2)
% 0.30/0.57  thf(fact_4704_diff__numeral__special_I2_J,axiom,
% 0.30/0.57      ! [M: num] :
% 0.30/0.57        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ one_one_Code_integer )
% 0.30/0.57        = ( neg_nu5755505904847501662nteger @ M @ one ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_numeral_special(2)
% 0.30/0.57  thf(fact_4705_diff__numeral__special_I2_J,axiom,
% 0.30/0.57      ! [M: num] :
% 0.30/0.57        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ one_one_rat )
% 0.30/0.57        = ( neg_numeral_sub_rat @ M @ one ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_numeral_special(2)
% 0.30/0.57  thf(fact_4706_diff__numeral__special_I1_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( minus_minus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 0.30/0.57        = ( neg_numeral_sub_int @ one @ N ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_numeral_special(1)
% 0.30/0.57  thf(fact_4707_diff__numeral__special_I1_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 0.30/0.57        = ( neg_nu5755505904847501662nteger @ one @ N ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_numeral_special(1)
% 0.30/0.57  thf(fact_4708_diff__numeral__special_I1_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( minus_minus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 0.30/0.57        = ( neg_numeral_sub_rat @ one @ N ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_numeral_special(1)
% 0.30/0.57  thf(fact_4709_add__neg__numeral__special_I4_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 0.30/0.57        = ( neg_numeral_sub_int @ N @ one ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_numeral_special(4)
% 0.30/0.57  thf(fact_4710_add__neg__numeral__special_I4_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 0.30/0.57        = ( neg_nu5755505904847501662nteger @ N @ one ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_numeral_special(4)
% 0.30/0.57  thf(fact_4711_add__neg__numeral__special_I4_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 0.30/0.57        = ( neg_numeral_sub_rat @ N @ one ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_numeral_special(4)
% 0.30/0.57  thf(fact_4712_add__neg__numeral__special_I3_J,axiom,
% 0.30/0.57      ! [M: num] :
% 0.30/0.57        ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.57        = ( neg_numeral_sub_int @ M @ one ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_numeral_special(3)
% 0.30/0.57  thf(fact_4713_add__neg__numeral__special_I3_J,axiom,
% 0.30/0.57      ! [M: num] :
% 0.30/0.57        ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.57        = ( neg_nu5755505904847501662nteger @ M @ one ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_numeral_special(3)
% 0.30/0.57  thf(fact_4714_add__neg__numeral__special_I3_J,axiom,
% 0.30/0.57      ! [M: num] :
% 0.30/0.57        ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.30/0.57        = ( neg_numeral_sub_rat @ M @ one ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_numeral_special(3)
% 0.30/0.57  thf(fact_4715_add__neg__numeral__special_I2_J,axiom,
% 0.30/0.57      ! [M: num] :
% 0.30/0.57        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 0.30/0.57        = ( neg_numeral_sub_int @ one @ M ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_numeral_special(2)
% 0.30/0.57  thf(fact_4716_add__neg__numeral__special_I2_J,axiom,
% 0.30/0.57      ! [M: num] :
% 0.30/0.57        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 0.30/0.57        = ( neg_nu5755505904847501662nteger @ one @ M ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_numeral_special(2)
% 0.30/0.57  thf(fact_4717_add__neg__numeral__special_I2_J,axiom,
% 0.30/0.57      ! [M: num] :
% 0.30/0.57        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 0.30/0.57        = ( neg_numeral_sub_rat @ one @ M ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_numeral_special(2)
% 0.30/0.57  thf(fact_4718_add__neg__numeral__special_I1_J,axiom,
% 0.30/0.57      ! [M: num] :
% 0.30/0.57        ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) )
% 0.30/0.57        = ( neg_numeral_sub_int @ one @ M ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_numeral_special(1)
% 0.30/0.57  thf(fact_4719_add__neg__numeral__special_I1_J,axiom,
% 0.30/0.57      ! [M: num] :
% 0.30/0.57        ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) )
% 0.30/0.57        = ( neg_nu5755505904847501662nteger @ one @ M ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_numeral_special(1)
% 0.30/0.57  thf(fact_4720_add__neg__numeral__special_I1_J,axiom,
% 0.30/0.57      ! [M: num] :
% 0.30/0.57        ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) )
% 0.30/0.57        = ( neg_numeral_sub_rat @ one @ M ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_numeral_special(1)
% 0.30/0.57  thf(fact_4721_diff__numeral__special_I8_J,axiom,
% 0.30/0.57      ! [M: num] :
% 0.30/0.57        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.57        = ( neg_numeral_sub_int @ one @ M ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_numeral_special(8)
% 0.30/0.57  thf(fact_4722_diff__numeral__special_I8_J,axiom,
% 0.30/0.57      ! [M: num] :
% 0.30/0.57        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.57        = ( neg_nu5755505904847501662nteger @ one @ M ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_numeral_special(8)
% 0.30/0.57  thf(fact_4723_diff__numeral__special_I8_J,axiom,
% 0.30/0.57      ! [M: num] :
% 0.30/0.57        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.30/0.57        = ( neg_numeral_sub_rat @ one @ M ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_numeral_special(8)
% 0.30/0.57  thf(fact_4724_diff__numeral__special_I7_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.57        = ( neg_numeral_sub_int @ N @ one ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_numeral_special(7)
% 0.30/0.57  thf(fact_4725_diff__numeral__special_I7_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.30/0.57        = ( neg_nu5755505904847501662nteger @ N @ one ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_numeral_special(7)
% 0.30/0.57  thf(fact_4726_diff__numeral__special_I7_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.30/0.57        = ( neg_numeral_sub_rat @ N @ one ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_numeral_special(7)
% 0.30/0.57  thf(fact_4727_div__eq__dividend__iff,axiom,
% 0.30/0.57      ! [M: nat,N: nat] :
% 0.30/0.57        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.30/0.57       => ( ( ( divide_divide_nat @ M @ N )
% 0.30/0.57            = M )
% 0.30/0.57          = ( N = one_one_nat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % div_eq_dividend_iff
% 0.30/0.57  thf(fact_4728_div__less__dividend,axiom,
% 0.30/0.57      ! [N: nat,M: nat] :
% 0.30/0.57        ( ( ord_less_nat @ one_one_nat @ N )
% 0.30/0.57       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.30/0.57         => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % div_less_dividend
% 0.30/0.57  thf(fact_4729_nat__geq__1__eq__neqz,axiom,
% 0.30/0.57      ! [X: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ one_one_nat @ X )
% 0.30/0.57        = ( X != zero_zero_nat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % nat_geq_1_eq_neqz
% 0.30/0.57  thf(fact_4730_eq__numeral__iff__iszero_I4_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ X ) )
% 0.30/0.57          = ( uminus_uminus_int @ ( numeral_numeral_int @ Y ) ) )
% 0.30/0.57        = ( ring_1_iszero_int @ ( neg_numeral_sub_int @ Y @ X ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_numeral_iff_iszero(4)
% 0.30/0.57  thf(fact_4731_eq__numeral__iff__iszero_I4_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) )
% 0.30/0.57          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ Y ) ) )
% 0.30/0.57        = ( ring_16219924574208605041nteger @ ( neg_nu5755505904847501662nteger @ Y @ X ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_numeral_iff_iszero(4)
% 0.30/0.57  thf(fact_4732_eq__numeral__iff__iszero_I4_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) )
% 0.30/0.57          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ Y ) ) )
% 0.30/0.57        = ( ring_1_iszero_rat @ ( neg_numeral_sub_rat @ Y @ X ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_numeral_iff_iszero(4)
% 0.30/0.57  thf(fact_4733_eq__numeral__iff__iszero_I6_J,axiom,
% 0.30/0.57      ! [Y: num] :
% 0.30/0.57        ( ( one_one_int
% 0.30/0.57          = ( numeral_numeral_int @ Y ) )
% 0.30/0.57        = ( ring_1_iszero_int @ ( neg_numeral_sub_int @ one @ Y ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_numeral_iff_iszero(6)
% 0.30/0.57  thf(fact_4734_eq__numeral__iff__iszero_I6_J,axiom,
% 0.30/0.57      ! [Y: num] :
% 0.30/0.57        ( ( one_one_Code_integer
% 0.30/0.57          = ( numera6620942414471956472nteger @ Y ) )
% 0.30/0.57        = ( ring_16219924574208605041nteger @ ( neg_nu5755505904847501662nteger @ one @ Y ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_numeral_iff_iszero(6)
% 0.30/0.57  thf(fact_4735_eq__numeral__iff__iszero_I6_J,axiom,
% 0.30/0.57      ! [Y: num] :
% 0.30/0.57        ( ( one_one_rat
% 0.30/0.57          = ( numeral_numeral_rat @ Y ) )
% 0.30/0.57        = ( ring_1_iszero_rat @ ( neg_numeral_sub_rat @ one @ Y ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_numeral_iff_iszero(6)
% 0.30/0.57  thf(fact_4736_eq__numeral__iff__iszero_I5_J,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( ( numeral_numeral_int @ X )
% 0.30/0.57          = one_one_int )
% 0.30/0.57        = ( ring_1_iszero_int @ ( neg_numeral_sub_int @ X @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_numeral_iff_iszero(5)
% 0.30/0.57  thf(fact_4737_eq__numeral__iff__iszero_I5_J,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( ( numera6620942414471956472nteger @ X )
% 0.30/0.57          = one_one_Code_integer )
% 0.30/0.57        = ( ring_16219924574208605041nteger @ ( neg_nu5755505904847501662nteger @ X @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_numeral_iff_iszero(5)
% 0.30/0.57  thf(fact_4738_eq__numeral__iff__iszero_I5_J,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( ( numeral_numeral_rat @ X )
% 0.30/0.57          = one_one_rat )
% 0.30/0.57        = ( ring_1_iszero_rat @ ( neg_numeral_sub_rat @ X @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % eq_numeral_iff_iszero(5)
% 0.30/0.57  thf(fact_4739_crossproduct__eq,axiom,
% 0.30/0.57      ! [W: code_integer,Y: code_integer,X: code_integer,Z: code_integer] :
% 0.30/0.57        ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ W @ Y ) @ ( times_3573771949741848930nteger @ X @ Z ) )
% 0.30/0.57          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ W @ Z ) @ ( times_3573771949741848930nteger @ X @ Y ) ) )
% 0.30/0.57        = ( ( W = X )
% 0.30/0.57          | ( Y = Z ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % crossproduct_eq
% 0.30/0.57  thf(fact_4740_crossproduct__eq,axiom,
% 0.30/0.57      ! [W: rat,Y: rat,X: rat,Z: rat] :
% 0.30/0.57        ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y ) @ ( times_times_rat @ X @ Z ) )
% 0.30/0.57          = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X @ Y ) ) )
% 0.30/0.57        = ( ( W = X )
% 0.30/0.57          | ( Y = Z ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % crossproduct_eq
% 0.30/0.57  thf(fact_4741_crossproduct__eq,axiom,
% 0.30/0.57      ! [W: nat,Y: nat,X: nat,Z: nat] :
% 0.30/0.57        ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z ) )
% 0.30/0.57          = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y ) ) )
% 0.30/0.57        = ( ( W = X )
% 0.30/0.57          | ( Y = Z ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % crossproduct_eq
% 0.30/0.57  thf(fact_4742_crossproduct__eq,axiom,
% 0.30/0.57      ! [W: int,Y: int,X: int,Z: int] :
% 0.30/0.57        ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X @ Z ) )
% 0.30/0.57          = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X @ Y ) ) )
% 0.30/0.57        = ( ( W = X )
% 0.30/0.57          | ( Y = Z ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % crossproduct_eq
% 0.30/0.57  thf(fact_4743_crossproduct__noteq,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.30/0.57        ( ( ( A != B )
% 0.30/0.57          & ( C != D2 ) )
% 0.30/0.57        = ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) )
% 0.30/0.57         != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ D2 ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % crossproduct_noteq
% 0.30/0.57  thf(fact_4744_crossproduct__noteq,axiom,
% 0.30/0.57      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.30/0.57        ( ( ( A != B )
% 0.30/0.57          & ( C != D2 ) )
% 0.30/0.57        = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) )
% 0.30/0.57         != ( plus_plus_rat @ ( times_times_rat @ A @ D2 ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % crossproduct_noteq
% 0.30/0.57  thf(fact_4745_crossproduct__noteq,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.30/0.57        ( ( ( A != B )
% 0.30/0.57          & ( C != D2 ) )
% 0.30/0.57        = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) )
% 0.30/0.57         != ( plus_plus_nat @ ( times_times_nat @ A @ D2 ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % crossproduct_noteq
% 0.30/0.57  thf(fact_4746_crossproduct__noteq,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int,D2: int] :
% 0.30/0.57        ( ( ( A != B )
% 0.30/0.57          & ( C != D2 ) )
% 0.30/0.57        = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) )
% 0.30/0.57         != ( plus_plus_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % crossproduct_noteq
% 0.30/0.57  thf(fact_4747_less__one,axiom,
% 0.30/0.57      ! [N: nat] :
% 0.30/0.57        ( ( ord_less_nat @ N @ one_one_nat )
% 0.30/0.57        = ( N = zero_zero_nat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % less_one
% 0.30/0.57  thf(fact_4748_nat__mult__eq__1__iff,axiom,
% 0.30/0.57      ! [M: nat,N: nat] :
% 0.30/0.57        ( ( ( times_times_nat @ M @ N )
% 0.30/0.57          = one_one_nat )
% 0.30/0.57        = ( ( M = one_one_nat )
% 0.30/0.57          & ( N = one_one_nat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % nat_mult_eq_1_iff
% 0.30/0.57  thf(fact_4749_nat__1__eq__mult__iff,axiom,
% 0.30/0.57      ! [M: nat,N: nat] :
% 0.30/0.57        ( ( one_one_nat
% 0.30/0.57          = ( times_times_nat @ M @ N ) )
% 0.30/0.57        = ( ( M = one_one_nat )
% 0.30/0.57          & ( N = one_one_nat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % nat_1_eq_mult_iff
% 0.30/0.57  thf(fact_4750_subset__emptyI,axiom,
% 0.30/0.57      ! [A2: set_se6260736226359567993nt_int] :
% 0.30/0.57        ( ! [X2: set_Pr958786334691620121nt_int] :
% 0.30/0.57            ~ ( member2340774599025711042nt_int @ X2 @ A2 )
% 0.30/0.57       => ( ord_le483042692224249369nt_int @ A2 @ bot_bo1488462491386950373nt_int ) ) ).
% 0.30/0.57  
% 0.30/0.57  % subset_emptyI
% 0.30/0.57  thf(fact_4751_subset__emptyI,axiom,
% 0.30/0.57      ! [A2: set_set_nat] :
% 0.30/0.57        ( ! [X2: set_nat] :
% 0.30/0.57            ~ ( member_set_nat @ X2 @ A2 )
% 0.30/0.57       => ( ord_le6893508408891458716et_nat @ A2 @ bot_bot_set_set_nat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % subset_emptyI
% 0.30/0.57  thf(fact_4752_subset__emptyI,axiom,
% 0.30/0.57      ! [A2: set_Pr4532377907799695533_nat_o] :
% 0.30/0.57        ( ! [X2: produc3658429121746597890et_nat > $o] :
% 0.30/0.57            ~ ( member6576561426505652726_nat_o @ X2 @ A2 )
% 0.30/0.57       => ( ord_le2965882846123202637_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) ).
% 0.30/0.57  
% 0.30/0.57  % subset_emptyI
% 0.30/0.57  thf(fact_4753_subset__emptyI,axiom,
% 0.30/0.57      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.30/0.57        ( ! [X2: product_prod_nat_nat] :
% 0.30/0.57            ~ ( member8440522571783428010at_nat @ X2 @ A2 )
% 0.30/0.57       => ( ord_le3146513528884898305at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % subset_emptyI
% 0.30/0.57  thf(fact_4754_subset__emptyI,axiom,
% 0.30/0.57      ! [A2: set_o] :
% 0.30/0.57        ( ! [X2: $o] :
% 0.30/0.57            ~ ( member_o @ X2 @ A2 )
% 0.30/0.57       => ( ord_less_eq_set_o @ A2 @ bot_bot_set_o ) ) ).
% 0.30/0.57  
% 0.30/0.57  % subset_emptyI
% 0.30/0.57  thf(fact_4755_subset__emptyI,axiom,
% 0.30/0.57      ! [A2: set_int] :
% 0.30/0.57        ( ! [X2: int] :
% 0.30/0.57            ~ ( member_int @ X2 @ A2 )
% 0.30/0.57       => ( ord_less_eq_set_int @ A2 @ bot_bot_set_int ) ) ).
% 0.30/0.57  
% 0.30/0.57  % subset_emptyI
% 0.30/0.57  thf(fact_4756_subset__emptyI,axiom,
% 0.30/0.57      ! [A2: set_nat] :
% 0.30/0.57        ( ! [X2: nat] :
% 0.30/0.57            ~ ( member_nat @ X2 @ A2 )
% 0.30/0.57       => ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % subset_emptyI
% 0.30/0.57  thf(fact_4757_dbl__simps_I4_J,axiom,
% 0.30/0.57      ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.57      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % dbl_simps(4)
% 0.30/0.57  thf(fact_4758_dbl__simps_I4_J,axiom,
% 0.30/0.57      ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.57      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % dbl_simps(4)
% 0.30/0.57  thf(fact_4759_dbl__simps_I4_J,axiom,
% 0.30/0.57      ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.30/0.57      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % dbl_simps(4)
% 0.30/0.57  thf(fact_4760_dbl__dec__simps_I4_J,axiom,
% 0.30/0.57      ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.57      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % dbl_dec_simps(4)
% 0.30/0.57  thf(fact_4761_dbl__dec__simps_I4_J,axiom,
% 0.30/0.57      ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.57      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % dbl_dec_simps(4)
% 0.30/0.57  thf(fact_4762_dbl__dec__simps_I4_J,axiom,
% 0.30/0.57      ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.30/0.57      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % dbl_dec_simps(4)
% 0.30/0.57  thf(fact_4763_divmod__algorithm__code_I3_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 0.30/0.57        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_algorithm_code(3)
% 0.30/0.57  thf(fact_4764_divmod__algorithm__code_I3_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 0.30/0.57        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_algorithm_code(3)
% 0.30/0.57  thf(fact_4765_divmod__algorithm__code_I3_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N ) )
% 0.30/0.57        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_algorithm_code(3)
% 0.30/0.57  thf(fact_4766_divmod__step__eq,axiom,
% 0.30/0.57      ! [L: num,R3: int,Q4: int] :
% 0.30/0.57        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R3 )
% 0.30/0.57         => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 0.30/0.57            = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R3 @ ( numeral_numeral_int @ L ) ) ) ) )
% 0.30/0.57        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R3 )
% 0.30/0.57         => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 0.30/0.57            = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R3 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_step_eq
% 0.30/0.57  thf(fact_4767_divmod__step__eq,axiom,
% 0.30/0.57      ! [L: num,R3: nat,Q4: nat] :
% 0.30/0.57        ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R3 )
% 0.30/0.57         => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q4 @ R3 ) )
% 0.30/0.57            = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R3 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 0.30/0.57        & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R3 )
% 0.30/0.57         => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q4 @ R3 ) )
% 0.30/0.57            = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R3 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_step_eq
% 0.30/0.57  thf(fact_4768_divmod__step__eq,axiom,
% 0.30/0.57      ! [L: num,R3: code_integer,Q4: code_integer] :
% 0.30/0.57        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R3 )
% 0.30/0.57         => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q4 @ R3 ) )
% 0.30/0.57            = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R3 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 0.30/0.57        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R3 )
% 0.30/0.57         => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q4 @ R3 ) )
% 0.30/0.57            = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R3 ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_step_eq
% 0.30/0.57  thf(fact_4769_one__add__one,axiom,
% 0.30/0.57      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.30/0.57      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % one_add_one
% 0.30/0.57  thf(fact_4770_one__add__one,axiom,
% 0.30/0.57      ( ( plus_plus_int @ one_one_int @ one_one_int )
% 0.30/0.57      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % one_add_one
% 0.30/0.57  thf(fact_4771_one__add__one,axiom,
% 0.30/0.57      ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer )
% 0.30/0.57      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % one_add_one
% 0.30/0.57  thf(fact_4772_one__add__one,axiom,
% 0.30/0.57      ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 0.30/0.57      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % one_add_one
% 0.30/0.57  thf(fact_4773_one__add__one,axiom,
% 0.30/0.57      ( ( plus_p4538020629002901425atural @ one_one_Code_natural @ one_one_Code_natural )
% 0.30/0.57      = ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % one_add_one
% 0.30/0.57  thf(fact_4774_dbl__simps_I3_J,axiom,
% 0.30/0.57      ( ( neg_numeral_dbl_int @ one_one_int )
% 0.30/0.57      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % dbl_simps(3)
% 0.30/0.57  thf(fact_4775_dbl__simps_I3_J,axiom,
% 0.30/0.57      ( ( neg_nu8804712462038260780nteger @ one_one_Code_integer )
% 0.30/0.57      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % dbl_simps(3)
% 0.30/0.57  thf(fact_4776_dbl__simps_I3_J,axiom,
% 0.30/0.57      ( ( neg_numeral_dbl_rat @ one_one_rat )
% 0.30/0.57      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % dbl_simps(3)
% 0.30/0.57  thf(fact_4777_dbl__inc__simps_I3_J,axiom,
% 0.30/0.57      ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 0.30/0.57      = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % dbl_inc_simps(3)
% 0.30/0.57  thf(fact_4778_dbl__inc__simps_I3_J,axiom,
% 0.30/0.57      ( ( neg_nu5831290666863070958nteger @ one_one_Code_integer )
% 0.30/0.57      = ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % dbl_inc_simps(3)
% 0.30/0.57  thf(fact_4779_dbl__inc__simps_I3_J,axiom,
% 0.30/0.57      ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 0.30/0.57      = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % dbl_inc_simps(3)
% 0.30/0.57  thf(fact_4780_one__div__two__eq__zero,axiom,
% 0.30/0.57      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.57      = zero_zero_nat ) ).
% 0.30/0.57  
% 0.30/0.57  % one_div_two_eq_zero
% 0.30/0.57  thf(fact_4781_one__div__two__eq__zero,axiom,
% 0.30/0.57      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.57      = zero_zero_int ) ).
% 0.30/0.57  
% 0.30/0.57  % one_div_two_eq_zero
% 0.30/0.57  thf(fact_4782_one__div__two__eq__zero,axiom,
% 0.30/0.57      ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.57      = zero_z3403309356797280102nteger ) ).
% 0.30/0.57  
% 0.30/0.57  % one_div_two_eq_zero
% 0.30/0.57  thf(fact_4783_one__div__two__eq__zero,axiom,
% 0.30/0.57      ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.57      = zero_z2226904508553997617atural ) ).
% 0.30/0.57  
% 0.30/0.57  % one_div_two_eq_zero
% 0.30/0.57  thf(fact_4784_bits__1__div__2,axiom,
% 0.30/0.57      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.57      = zero_zero_nat ) ).
% 0.30/0.57  
% 0.30/0.57  % bits_1_div_2
% 0.30/0.57  thf(fact_4785_bits__1__div__2,axiom,
% 0.30/0.57      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.57      = zero_zero_int ) ).
% 0.30/0.57  
% 0.30/0.57  % bits_1_div_2
% 0.30/0.57  thf(fact_4786_bits__1__div__2,axiom,
% 0.30/0.57      ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.57      = zero_z3403309356797280102nteger ) ).
% 0.30/0.57  
% 0.30/0.57  % bits_1_div_2
% 0.30/0.57  thf(fact_4787_bits__1__div__2,axiom,
% 0.30/0.57      ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.57      = zero_z2226904508553997617atural ) ).
% 0.30/0.57  
% 0.30/0.57  % bits_1_div_2
% 0.30/0.57  thf(fact_4788_add__neg__numeral__special_I9_J,axiom,
% 0.30/0.57      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.57      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_numeral_special(9)
% 0.30/0.57  thf(fact_4789_add__neg__numeral__special_I9_J,axiom,
% 0.30/0.57      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.57      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_numeral_special(9)
% 0.30/0.57  thf(fact_4790_add__neg__numeral__special_I9_J,axiom,
% 0.30/0.57      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.30/0.57      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % add_neg_numeral_special(9)
% 0.30/0.57  thf(fact_4791_diff__numeral__special_I10_J,axiom,
% 0.30/0.57      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 0.30/0.57      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_numeral_special(10)
% 0.30/0.57  thf(fact_4792_diff__numeral__special_I10_J,axiom,
% 0.30/0.57      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 0.30/0.57      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_numeral_special(10)
% 0.30/0.57  thf(fact_4793_diff__numeral__special_I10_J,axiom,
% 0.30/0.57      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 0.30/0.57      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_numeral_special(10)
% 0.30/0.57  thf(fact_4794_diff__numeral__special_I11_J,axiom,
% 0.30/0.57      ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.57      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_numeral_special(11)
% 0.30/0.57  thf(fact_4795_diff__numeral__special_I11_J,axiom,
% 0.30/0.57      ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.57      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_numeral_special(11)
% 0.30/0.57  thf(fact_4796_diff__numeral__special_I11_J,axiom,
% 0.30/0.57      ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.30/0.57      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % diff_numeral_special(11)
% 0.30/0.57  thf(fact_4797_divmod__algorithm__code_I4_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 0.30/0.57        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_algorithm_code(4)
% 0.30/0.57  thf(fact_4798_divmod__algorithm__code_I4_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 0.30/0.57        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_algorithm_code(4)
% 0.30/0.57  thf(fact_4799_divmod__algorithm__code_I4_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N ) )
% 0.30/0.57        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_algorithm_code(4)
% 0.30/0.57  thf(fact_4800_sub__num__simps_I3_J,axiom,
% 0.30/0.57      ! [L: num] :
% 0.30/0.57        ( ( neg_numeral_sub_int @ one @ ( bit1 @ L ) )
% 0.30/0.57        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ L ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % sub_num_simps(3)
% 0.30/0.57  thf(fact_4801_sub__num__simps_I3_J,axiom,
% 0.30/0.57      ! [L: num] :
% 0.30/0.57        ( ( neg_nu5755505904847501662nteger @ one @ ( bit1 @ L ) )
% 0.30/0.57        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ L ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % sub_num_simps(3)
% 0.30/0.57  thf(fact_4802_sub__num__simps_I3_J,axiom,
% 0.30/0.57      ! [L: num] :
% 0.30/0.57        ( ( neg_numeral_sub_rat @ one @ ( bit1 @ L ) )
% 0.30/0.57        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ L ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % sub_num_simps(3)
% 0.30/0.57  thf(fact_4803_divmod__algorithm__code_I7_J,axiom,
% 0.30/0.57      ! [M: num,N: num] :
% 0.30/0.57        ( ( ( ord_less_eq_num @ M @ N )
% 0.30/0.57         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.30/0.57            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 0.30/0.57        & ( ~ ( ord_less_eq_num @ M @ N )
% 0.30/0.57         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.30/0.57            = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_algorithm_code(7)
% 0.30/0.57  thf(fact_4804_divmod__algorithm__code_I7_J,axiom,
% 0.30/0.57      ! [M: num,N: num] :
% 0.30/0.57        ( ( ( ord_less_eq_num @ M @ N )
% 0.30/0.57         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.30/0.57            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 0.30/0.57        & ( ~ ( ord_less_eq_num @ M @ N )
% 0.30/0.57         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.30/0.57            = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_algorithm_code(7)
% 0.30/0.57  thf(fact_4805_divmod__algorithm__code_I7_J,axiom,
% 0.30/0.57      ! [M: num,N: num] :
% 0.30/0.57        ( ( ( ord_less_eq_num @ M @ N )
% 0.30/0.57         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.30/0.57            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 0.30/0.57        & ( ~ ( ord_less_eq_num @ M @ N )
% 0.30/0.57         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.30/0.57            = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_algorithm_code(7)
% 0.30/0.57  thf(fact_4806_divmod__algorithm__code_I8_J,axiom,
% 0.30/0.57      ! [M: num,N: num] :
% 0.30/0.57        ( ( ( ord_less_num @ M @ N )
% 0.30/0.57         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.30/0.57            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 0.30/0.57        & ( ~ ( ord_less_num @ M @ N )
% 0.30/0.57         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.30/0.57            = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_algorithm_code(8)
% 0.30/0.57  thf(fact_4807_divmod__algorithm__code_I8_J,axiom,
% 0.30/0.57      ! [M: num,N: num] :
% 0.30/0.57        ( ( ( ord_less_num @ M @ N )
% 0.30/0.57         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.30/0.57            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 0.30/0.57        & ( ~ ( ord_less_num @ M @ N )
% 0.30/0.57         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.30/0.57            = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_algorithm_code(8)
% 0.30/0.57  thf(fact_4808_divmod__algorithm__code_I8_J,axiom,
% 0.30/0.57      ! [M: num,N: num] :
% 0.30/0.57        ( ( ( ord_less_num @ M @ N )
% 0.30/0.57         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.30/0.57            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 0.30/0.57        & ( ~ ( ord_less_num @ M @ N )
% 0.30/0.57         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.30/0.57            = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_algorithm_code(8)
% 0.30/0.57  thf(fact_4809_bot__nat__0_Oordering__top__axioms,axiom,
% 0.30/0.57      ( ordering_top_nat
% 0.30/0.57      @ ^ [X3: nat,Y3: nat] : ( ord_less_eq_nat @ Y3 @ X3 )
% 0.30/0.57      @ ^ [X3: nat,Y3: nat] : ( ord_less_nat @ Y3 @ X3 )
% 0.30/0.57      @ zero_zero_nat ) ).
% 0.30/0.57  
% 0.30/0.57  % bot_nat_0.ordering_top_axioms
% 0.30/0.57  thf(fact_4810_bot__nat__def,axiom,
% 0.30/0.57      bot_bot_nat = zero_zero_nat ).
% 0.30/0.57  
% 0.30/0.57  % bot_nat_def
% 0.30/0.57  thf(fact_4811_xor__num_Ocases,axiom,
% 0.30/0.57      ! [X: product_prod_num_num] :
% 0.30/0.57        ( ( X
% 0.30/0.57         != ( product_Pair_num_num @ one @ one ) )
% 0.30/0.57       => ( ! [N3: num] :
% 0.30/0.57              ( X
% 0.30/0.57             != ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) )
% 0.30/0.57         => ( ! [N3: num] :
% 0.30/0.57                ( X
% 0.30/0.57               != ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) )
% 0.30/0.57           => ( ! [M3: num] :
% 0.30/0.57                  ( X
% 0.30/0.57                 != ( product_Pair_num_num @ ( bit0 @ M3 ) @ one ) )
% 0.30/0.57             => ( ! [M3: num,N3: num] :
% 0.30/0.57                    ( X
% 0.30/0.57                   != ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit0 @ N3 ) ) )
% 0.30/0.57               => ( ! [M3: num,N3: num] :
% 0.30/0.57                      ( X
% 0.30/0.57                     != ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit1 @ N3 ) ) )
% 0.30/0.57                 => ( ! [M3: num] :
% 0.30/0.57                        ( X
% 0.30/0.57                       != ( product_Pair_num_num @ ( bit1 @ M3 ) @ one ) )
% 0.30/0.57                   => ( ! [M3: num,N3: num] :
% 0.30/0.57                          ( X
% 0.30/0.57                         != ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit0 @ N3 ) ) )
% 0.30/0.57                     => ~ ! [M3: num,N3: num] :
% 0.30/0.57                            ( X
% 0.30/0.57                           != ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_num.cases
% 0.30/0.57  thf(fact_4812_neg__zdiv__mult__2,axiom,
% 0.30/0.57      ! [A: int,B: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.30/0.57       => ( ( 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 ) )
% 0.30/0.57          = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % neg_zdiv_mult_2
% 0.30/0.57  thf(fact_4813_pos__zdiv__mult__2,axiom,
% 0.30/0.57      ! [A: int,B: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.57       => ( ( 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 ) )
% 0.30/0.57          = ( divide_divide_int @ B @ A ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % pos_zdiv_mult_2
% 0.30/0.57  thf(fact_4814_int__bit__induct,axiom,
% 0.30/0.57      ! [P: int > $o,K: int] :
% 0.30/0.57        ( ( P @ zero_zero_int )
% 0.30/0.57       => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.57         => ( ! [K2: int] :
% 0.30/0.57                ( ( P @ K2 )
% 0.30/0.57               => ( ( K2 != zero_zero_int )
% 0.30/0.57                 => ( P @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 0.30/0.57           => ( ! [K2: int] :
% 0.30/0.57                  ( ( P @ K2 )
% 0.30/0.57                 => ( ( K2
% 0.30/0.57                     != ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.57                   => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 0.30/0.57             => ( P @ K ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % int_bit_induct
% 0.30/0.57  thf(fact_4815_numeral__code_I2_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 0.30/0.57        = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_code(2)
% 0.30/0.57  thf(fact_4816_numeral__code_I2_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 0.30/0.57        = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_code(2)
% 0.30/0.57  thf(fact_4817_numeral__code_I2_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( numera6620942414471956472nteger @ ( bit0 @ N ) )
% 0.30/0.57        = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_code(2)
% 0.30/0.57  thf(fact_4818_numeral__code_I2_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 0.30/0.57        = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_code(2)
% 0.30/0.57  thf(fact_4819_numeral__code_I2_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( numera5444537566228673987atural @ ( bit0 @ N ) )
% 0.30/0.57        = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N ) @ ( numera5444537566228673987atural @ N ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_code(2)
% 0.30/0.57  thf(fact_4820_numeral__Bit1,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 0.30/0.57        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_Bit1
% 0.30/0.57  thf(fact_4821_numeral__Bit1,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 0.30/0.57        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_Bit1
% 0.30/0.57  thf(fact_4822_numeral__Bit1,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( numera6620942414471956472nteger @ ( bit1 @ N ) )
% 0.30/0.57        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ N ) ) @ one_one_Code_integer ) ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_Bit1
% 0.30/0.57  thf(fact_4823_numeral__Bit1,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 0.30/0.57        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_Bit1
% 0.30/0.57  thf(fact_4824_numeral__Bit1,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( numera5444537566228673987atural @ ( bit1 @ N ) )
% 0.30/0.57        = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N ) @ ( numera5444537566228673987atural @ N ) ) @ one_one_Code_natural ) ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_Bit1
% 0.30/0.57  thf(fact_4825_nat__1__add__1,axiom,
% 0.30/0.57      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.30/0.57      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % nat_1_add_1
% 0.30/0.57  thf(fact_4826_ssubst__Pair__rhs,axiom,
% 0.30/0.57      ! [R3: produc6241069584506657477e_term > option6357759511663192854e_term,S3: produc8923325533196201883nteger,R: set_Pr1281608226676607948nteger,S5: produc8923325533196201883nteger] :
% 0.30/0.57        ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ R3 @ S3 ) @ R )
% 0.30/0.57       => ( ( S5 = S3 )
% 0.30/0.57         => ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ R3 @ S5 ) @ R ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ssubst_Pair_rhs
% 0.30/0.57  thf(fact_4827_ssubst__Pair__rhs,axiom,
% 0.30/0.57      ! [R3: produc3658429121746597890et_nat > $o,S3: produc3658429121746597890et_nat,R: set_Pr3286484037609594932et_nat,S5: produc3658429121746597890et_nat] :
% 0.30/0.57        ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R3 @ S3 ) @ R )
% 0.30/0.57       => ( ( S5 = S3 )
% 0.30/0.57         => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R3 @ S5 ) @ R ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ssubst_Pair_rhs
% 0.30/0.57  thf(fact_4828_ssubst__Pair__rhs,axiom,
% 0.30/0.57      ! [R3: produc3658429121746597890et_nat > $o,S3: produc3925858234332021118et_nat,R: set_Pr8536935166611901872et_nat,S5: produc3925858234332021118et_nat] :
% 0.30/0.57        ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R3 @ S3 ) @ R )
% 0.30/0.57       => ( ( S5 = S3 )
% 0.30/0.57         => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R3 @ S5 ) @ R ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ssubst_Pair_rhs
% 0.30/0.57  thf(fact_4829_ssubst__Pair__rhs,axiom,
% 0.30/0.57      ! [R3: produc8551481072490612790e_term > option6357759511663192854e_term,S3: product_prod_int_int,R: set_Pr9222295170931077689nt_int,S5: product_prod_int_int] :
% 0.30/0.57        ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ R3 @ S3 ) @ R )
% 0.30/0.57       => ( ( S5 = S3 )
% 0.30/0.57         => ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ R3 @ S5 ) @ R ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ssubst_Pair_rhs
% 0.30/0.57  thf(fact_4830_ssubst__Pair__rhs,axiom,
% 0.30/0.57      ! [R3: int > option6357759511663192854e_term,S3: product_prod_int_int,R: set_Pr1872883991513573699nt_int,S5: product_prod_int_int] :
% 0.30/0.57        ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ R3 @ S3 ) @ R )
% 0.30/0.57       => ( ( S5 = S3 )
% 0.30/0.57         => ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ R3 @ S5 ) @ R ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % ssubst_Pair_rhs
% 0.30/0.57  thf(fact_4831_numeral__code_I3_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 0.30/0.57        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_code(3)
% 0.30/0.57  thf(fact_4832_numeral__code_I3_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 0.30/0.57        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_code(3)
% 0.30/0.57  thf(fact_4833_numeral__code_I3_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( numera6620942414471956472nteger @ ( bit1 @ N ) )
% 0.30/0.57        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ N ) ) @ one_one_Code_integer ) ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_code(3)
% 0.30/0.57  thf(fact_4834_numeral__code_I3_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 0.30/0.57        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_code(3)
% 0.30/0.57  thf(fact_4835_numeral__code_I3_J,axiom,
% 0.30/0.57      ! [N: num] :
% 0.30/0.57        ( ( numera5444537566228673987atural @ ( bit1 @ N ) )
% 0.30/0.57        = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N ) @ ( numera5444537566228673987atural @ N ) ) @ one_one_Code_natural ) ) ).
% 0.30/0.57  
% 0.30/0.57  % numeral_code(3)
% 0.30/0.57  thf(fact_4836_mult__eq__self__implies__10,axiom,
% 0.30/0.57      ! [M: nat,N: nat] :
% 0.30/0.57        ( ( M
% 0.30/0.57          = ( times_times_nat @ M @ N ) )
% 0.30/0.57       => ( ( N = one_one_nat )
% 0.30/0.57          | ( M = zero_zero_nat ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_eq_self_implies_10
% 0.30/0.57  thf(fact_4837_nat__mult__1,axiom,
% 0.30/0.57      ! [N: nat] :
% 0.30/0.57        ( ( times_times_nat @ one_one_nat @ N )
% 0.30/0.57        = N ) ).
% 0.30/0.57  
% 0.30/0.57  % nat_mult_1
% 0.30/0.57  thf(fact_4838_nat__mult__1__right,axiom,
% 0.30/0.57      ! [N: nat] :
% 0.30/0.57        ( ( times_times_nat @ N @ one_one_nat )
% 0.30/0.57        = N ) ).
% 0.30/0.57  
% 0.30/0.57  % nat_mult_1_right
% 0.30/0.57  thf(fact_4839_mult__eq__if,axiom,
% 0.30/0.57      ( times_times_nat
% 0.30/0.57      = ( ^ [M2: nat,N2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_eq_if
% 0.30/0.57  thf(fact_4840_divmod__divmod__step,axiom,
% 0.30/0.57      ( unique5052692396658037445od_int
% 0.30/0.57      = ( ^ [M2: num,N2: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M2 @ N2 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M2 ) ) @ ( unique5024387138958732305ep_int @ N2 @ ( unique5052692396658037445od_int @ M2 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_divmod_step
% 0.30/0.57  thf(fact_4841_divmod__divmod__step,axiom,
% 0.30/0.57      ( unique5055182867167087721od_nat
% 0.30/0.57      = ( ^ [M2: num,N2: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M2 @ N2 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M2 ) ) @ ( unique5026877609467782581ep_nat @ N2 @ ( unique5055182867167087721od_nat @ M2 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_divmod_step
% 0.30/0.57  thf(fact_4842_divmod__divmod__step,axiom,
% 0.30/0.57      ( unique3479559517661332726nteger
% 0.30/0.57      = ( ^ [M2: num,N2: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M2 @ N2 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( unique4921790084139445826nteger @ N2 @ ( unique3479559517661332726nteger @ M2 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_divmod_step
% 0.30/0.57  thf(fact_4843_mult__2,axiom,
% 0.30/0.57      ! [Z: nat] :
% 0.30/0.57        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 0.30/0.57        = ( plus_plus_nat @ Z @ Z ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_2
% 0.30/0.57  thf(fact_4844_mult__2,axiom,
% 0.30/0.57      ! [Z: int] :
% 0.30/0.57        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 0.30/0.57        = ( plus_plus_int @ Z @ Z ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_2
% 0.30/0.57  thf(fact_4845_mult__2,axiom,
% 0.30/0.57      ! [Z: code_integer] :
% 0.30/0.57        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Z )
% 0.30/0.57        = ( plus_p5714425477246183910nteger @ Z @ Z ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_2
% 0.30/0.57  thf(fact_4846_mult__2,axiom,
% 0.30/0.57      ! [Z: rat] :
% 0.30/0.57        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 0.30/0.57        = ( plus_plus_rat @ Z @ Z ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_2
% 0.30/0.57  thf(fact_4847_mult__2,axiom,
% 0.30/0.57      ! [Z: code_natural] :
% 0.30/0.57        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ Z )
% 0.30/0.57        = ( plus_p4538020629002901425atural @ Z @ Z ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_2
% 0.30/0.57  thf(fact_4848_mult__2__right,axiom,
% 0.30/0.57      ! [Z: nat] :
% 0.30/0.57        ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.57        = ( plus_plus_nat @ Z @ Z ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_2_right
% 0.30/0.57  thf(fact_4849_mult__2__right,axiom,
% 0.30/0.57      ! [Z: int] :
% 0.30/0.57        ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.57        = ( plus_plus_int @ Z @ Z ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_2_right
% 0.30/0.57  thf(fact_4850_mult__2__right,axiom,
% 0.30/0.57      ! [Z: code_integer] :
% 0.30/0.57        ( ( times_3573771949741848930nteger @ Z @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.57        = ( plus_p5714425477246183910nteger @ Z @ Z ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_2_right
% 0.30/0.57  thf(fact_4851_mult__2__right,axiom,
% 0.30/0.57      ! [Z: rat] :
% 0.30/0.57        ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 0.30/0.57        = ( plus_plus_rat @ Z @ Z ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_2_right
% 0.30/0.57  thf(fact_4852_mult__2__right,axiom,
% 0.30/0.57      ! [Z: code_natural] :
% 0.30/0.57        ( ( times_2397367101498566445atural @ Z @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.57        = ( plus_p4538020629002901425atural @ Z @ Z ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mult_2_right
% 0.30/0.57  thf(fact_4853_left__add__twice,axiom,
% 0.30/0.57      ! [A: nat,B: nat] :
% 0.30/0.57        ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.30/0.57        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % left_add_twice
% 0.30/0.57  thf(fact_4854_left__add__twice,axiom,
% 0.30/0.57      ! [A: int,B: int] :
% 0.30/0.57        ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.30/0.57        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % left_add_twice
% 0.30/0.57  thf(fact_4855_left__add__twice,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.30/0.57        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % left_add_twice
% 0.30/0.57  thf(fact_4856_left__add__twice,axiom,
% 0.30/0.57      ! [A: rat,B: rat] :
% 0.30/0.57        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.30/0.57        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % left_add_twice
% 0.30/0.57  thf(fact_4857_left__add__twice,axiom,
% 0.30/0.57      ! [A: code_natural,B: code_natural] :
% 0.30/0.57        ( ( plus_p4538020629002901425atural @ A @ ( plus_p4538020629002901425atural @ A @ B ) )
% 0.30/0.57        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % left_add_twice
% 0.30/0.57  thf(fact_4858_prop__restrict,axiom,
% 0.30/0.57      ! [X: set_Pr958786334691620121nt_int,Z5: set_se6260736226359567993nt_int,X7: set_se6260736226359567993nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 0.30/0.57        ( ( member2340774599025711042nt_int @ X @ Z5 )
% 0.30/0.57       => ( ( ord_le483042692224249369nt_int @ Z5
% 0.30/0.57            @ ( collec5210948495886036740nt_int
% 0.30/0.57              @ ^ [X3: set_Pr958786334691620121nt_int] :
% 0.30/0.57                  ( ( member2340774599025711042nt_int @ X3 @ X7 )
% 0.30/0.57                  & ( P @ X3 ) ) ) )
% 0.30/0.57         => ( P @ X ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % prop_restrict
% 0.30/0.57  thf(fact_4859_prop__restrict,axiom,
% 0.30/0.57      ! [X: set_nat,Z5: set_set_nat,X7: set_set_nat,P: set_nat > $o] :
% 0.30/0.57        ( ( member_set_nat @ X @ Z5 )
% 0.30/0.57       => ( ( ord_le6893508408891458716et_nat @ Z5
% 0.30/0.57            @ ( collect_set_nat
% 0.30/0.57              @ ^ [X3: set_nat] :
% 0.30/0.57                  ( ( member_set_nat @ X3 @ X7 )
% 0.30/0.57                  & ( P @ X3 ) ) ) )
% 0.30/0.57         => ( P @ X ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % prop_restrict
% 0.30/0.57  thf(fact_4860_prop__restrict,axiom,
% 0.30/0.57      ! [X: int,Z5: set_int,X7: set_int,P: int > $o] :
% 0.30/0.57        ( ( member_int @ X @ Z5 )
% 0.30/0.57       => ( ( ord_less_eq_set_int @ Z5
% 0.30/0.57            @ ( collect_int
% 0.30/0.57              @ ^ [X3: int] :
% 0.30/0.57                  ( ( member_int @ X3 @ X7 )
% 0.30/0.57                  & ( P @ X3 ) ) ) )
% 0.30/0.57         => ( P @ X ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % prop_restrict
% 0.30/0.57  thf(fact_4861_prop__restrict,axiom,
% 0.30/0.57      ! [X: produc3658429121746597890et_nat > $o,Z5: set_Pr4532377907799695533_nat_o,X7: set_Pr4532377907799695533_nat_o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.30/0.57        ( ( member6576561426505652726_nat_o @ X @ Z5 )
% 0.30/0.57       => ( ( ord_le2965882846123202637_nat_o @ Z5
% 0.30/0.57            @ ( collec939566748876313656_nat_o
% 0.30/0.57              @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.30/0.57                  ( ( member6576561426505652726_nat_o @ X3 @ X7 )
% 0.30/0.57                  & ( P @ X3 ) ) ) )
% 0.30/0.57         => ( P @ X ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % prop_restrict
% 0.30/0.57  thf(fact_4862_prop__restrict,axiom,
% 0.30/0.57      ! [X: nat,Z5: set_nat,X7: set_nat,P: nat > $o] :
% 0.30/0.57        ( ( member_nat @ X @ Z5 )
% 0.30/0.57       => ( ( ord_less_eq_set_nat @ Z5
% 0.30/0.57            @ ( collect_nat
% 0.30/0.57              @ ^ [X3: nat] :
% 0.30/0.57                  ( ( member_nat @ X3 @ X7 )
% 0.30/0.57                  & ( P @ X3 ) ) ) )
% 0.30/0.57         => ( P @ X ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % prop_restrict
% 0.30/0.57  thf(fact_4863_Collect__restrict,axiom,
% 0.30/0.57      ! [X7: set_se6260736226359567993nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 0.30/0.57        ( ord_le483042692224249369nt_int
% 0.30/0.57        @ ( collec5210948495886036740nt_int
% 0.30/0.57          @ ^ [X3: set_Pr958786334691620121nt_int] :
% 0.30/0.57              ( ( member2340774599025711042nt_int @ X3 @ X7 )
% 0.30/0.57              & ( P @ X3 ) ) )
% 0.30/0.57        @ X7 ) ).
% 0.30/0.57  
% 0.30/0.57  % Collect_restrict
% 0.30/0.57  thf(fact_4864_Collect__restrict,axiom,
% 0.30/0.57      ! [X7: set_set_nat,P: set_nat > $o] :
% 0.30/0.57        ( ord_le6893508408891458716et_nat
% 0.30/0.57        @ ( collect_set_nat
% 0.30/0.57          @ ^ [X3: set_nat] :
% 0.30/0.57              ( ( member_set_nat @ X3 @ X7 )
% 0.30/0.57              & ( P @ X3 ) ) )
% 0.30/0.57        @ X7 ) ).
% 0.30/0.57  
% 0.30/0.57  % Collect_restrict
% 0.30/0.57  thf(fact_4865_Collect__restrict,axiom,
% 0.30/0.57      ! [X7: set_int,P: int > $o] :
% 0.30/0.57        ( ord_less_eq_set_int
% 0.30/0.57        @ ( collect_int
% 0.30/0.57          @ ^ [X3: int] :
% 0.30/0.57              ( ( member_int @ X3 @ X7 )
% 0.30/0.57              & ( P @ X3 ) ) )
% 0.30/0.57        @ X7 ) ).
% 0.30/0.57  
% 0.30/0.57  % Collect_restrict
% 0.30/0.57  thf(fact_4866_Collect__restrict,axiom,
% 0.30/0.57      ! [X7: set_Pr4532377907799695533_nat_o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.30/0.57        ( ord_le2965882846123202637_nat_o
% 0.30/0.57        @ ( collec939566748876313656_nat_o
% 0.30/0.57          @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.30/0.57              ( ( member6576561426505652726_nat_o @ X3 @ X7 )
% 0.30/0.57              & ( P @ X3 ) ) )
% 0.30/0.57        @ X7 ) ).
% 0.30/0.57  
% 0.30/0.57  % Collect_restrict
% 0.30/0.57  thf(fact_4867_Collect__restrict,axiom,
% 0.30/0.57      ! [X7: set_nat,P: nat > $o] :
% 0.30/0.57        ( ord_less_eq_set_nat
% 0.30/0.57        @ ( collect_nat
% 0.30/0.57          @ ^ [X3: nat] :
% 0.30/0.57              ( ( member_nat @ X3 @ X7 )
% 0.30/0.57              & ( P @ X3 ) ) )
% 0.30/0.57        @ X7 ) ).
% 0.30/0.57  
% 0.30/0.57  % Collect_restrict
% 0.30/0.57  thf(fact_4868_minus__1__div__2__eq,axiom,
% 0.30/0.57      ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.57      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.30/0.57  
% 0.30/0.57  % minus_1_div_2_eq
% 0.30/0.57  thf(fact_4869_minus__1__div__2__eq,axiom,
% 0.30/0.57      ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.57      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.30/0.57  
% 0.30/0.57  % minus_1_div_2_eq
% 0.30/0.57  thf(fact_4870_set__bit__0,axiom,
% 0.30/0.57      ! [A: code_integer] :
% 0.30/0.57        ( ( bit_se2793503036327961859nteger @ zero_zero_nat @ A )
% 0.30/0.57        = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % set_bit_0
% 0.30/0.57  thf(fact_4871_set__bit__0,axiom,
% 0.30/0.57      ! [A: code_natural] :
% 0.30/0.57        ( ( bit_se1617098188084679374atural @ zero_zero_nat @ A )
% 0.30/0.57        = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % set_bit_0
% 0.30/0.57  thf(fact_4872_set__bit__0,axiom,
% 0.30/0.57      ! [A: int] :
% 0.30/0.57        ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 0.30/0.57        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % set_bit_0
% 0.30/0.57  thf(fact_4873_set__bit__0,axiom,
% 0.30/0.57      ! [A: nat] :
% 0.30/0.57        ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 0.30/0.57        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % set_bit_0
% 0.30/0.57  thf(fact_4874_nat__induct2,axiom,
% 0.30/0.57      ! [P: nat > $o,N: nat] :
% 0.30/0.57        ( ( P @ zero_zero_nat )
% 0.30/0.57       => ( ( P @ one_one_nat )
% 0.30/0.57         => ( ! [N3: nat] :
% 0.30/0.57                ( ( P @ N3 )
% 0.30/0.57               => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.30/0.57           => ( P @ N ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % nat_induct2
% 0.30/0.57  thf(fact_4875_unset__bit__0,axiom,
% 0.30/0.57      ! [A: nat] :
% 0.30/0.57        ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 0.30/0.57        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % unset_bit_0
% 0.30/0.57  thf(fact_4876_unset__bit__0,axiom,
% 0.30/0.57      ! [A: code_integer] :
% 0.30/0.57        ( ( bit_se8260200283734997820nteger @ zero_zero_nat @ A )
% 0.30/0.57        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % unset_bit_0
% 0.30/0.57  thf(fact_4877_unset__bit__0,axiom,
% 0.30/0.57      ! [A: code_natural] :
% 0.30/0.57        ( ( bit_se7083795435491715335atural @ zero_zero_nat @ A )
% 0.30/0.57        = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % unset_bit_0
% 0.30/0.57  thf(fact_4878_unset__bit__0,axiom,
% 0.30/0.57      ! [A: int] :
% 0.30/0.57        ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 0.30/0.57        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % unset_bit_0
% 0.30/0.57  thf(fact_4879_divmod__algorithm__code_I6_J,axiom,
% 0.30/0.57      ! [M: num,N: num] :
% 0.30/0.57        ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.30/0.57        = ( produc4245557441103728435nt_int
% 0.30/0.57          @ ^ [Q5: int,R4: int] : ( product_Pair_int_int @ Q5 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R4 ) @ one_one_int ) )
% 0.30/0.57          @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_algorithm_code(6)
% 0.30/0.57  thf(fact_4880_divmod__algorithm__code_I6_J,axiom,
% 0.30/0.57      ! [M: num,N: num] :
% 0.30/0.57        ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.30/0.57        = ( produc2626176000494625587at_nat
% 0.30/0.57          @ ^ [Q5: nat,R4: nat] : ( product_Pair_nat_nat @ Q5 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R4 ) @ one_one_nat ) )
% 0.30/0.57          @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_algorithm_code(6)
% 0.30/0.57  thf(fact_4881_divmod__algorithm__code_I6_J,axiom,
% 0.30/0.57      ! [M: num,N: num] :
% 0.30/0.57        ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.30/0.57        = ( produc6916734918728496179nteger
% 0.30/0.57          @ ^ [Q5: code_integer,R4: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R4 ) @ one_one_Code_integer ) )
% 0.30/0.57          @ ( unique3479559517661332726nteger @ M @ N ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_algorithm_code(6)
% 0.30/0.57  thf(fact_4882_divmod__step__def,axiom,
% 0.30/0.57      ( unique5024387138958732305ep_int
% 0.30/0.57      = ( ^ [L2: num] :
% 0.30/0.57            ( produc4245557441103728435nt_int
% 0.30/0.57            @ ^ [Q5: int,R4: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R4 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R4 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R4 ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_step_def
% 0.30/0.57  thf(fact_4883_divmod__step__def,axiom,
% 0.30/0.57      ( unique5026877609467782581ep_nat
% 0.30/0.57      = ( ^ [L2: num] :
% 0.30/0.57            ( produc2626176000494625587at_nat
% 0.30/0.57            @ ^ [Q5: nat,R4: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R4 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R4 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R4 ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_step_def
% 0.30/0.57  thf(fact_4884_divmod__step__def,axiom,
% 0.30/0.57      ( unique4921790084139445826nteger
% 0.30/0.57      = ( ^ [L2: num] :
% 0.30/0.57            ( produc6916734918728496179nteger
% 0.30/0.57            @ ^ [Q5: code_integer,R4: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R4 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R4 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R4 ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_step_def
% 0.30/0.57  thf(fact_4885_divmod__digit__1_I1_J,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.57       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.30/0.57         => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 0.30/0.57           => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 0.30/0.57              = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_digit_1(1)
% 0.30/0.57  thf(fact_4886_divmod__digit__1_I1_J,axiom,
% 0.30/0.57      ! [A: nat,B: nat] :
% 0.30/0.57        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.57       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.30/0.57         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.30/0.57           => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_nat )
% 0.30/0.57              = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_digit_1(1)
% 0.30/0.57  thf(fact_4887_divmod__digit__1_I1_J,axiom,
% 0.30/0.57      ! [A: int,B: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.57       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.57         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.30/0.57           => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_int )
% 0.30/0.57              = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_digit_1(1)
% 0.30/0.57  thf(fact_4888_xor__numerals_I6_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 0.30/0.57        = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(6)
% 0.30/0.57  thf(fact_4889_xor__numerals_I6_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 0.30/0.57        = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(6)
% 0.30/0.57  thf(fact_4890_xor__numerals_I6_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.30/0.57        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(6)
% 0.30/0.57  thf(fact_4891_xor__numerals_I6_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.30/0.57        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(6)
% 0.30/0.57  thf(fact_4892_mod__minus__minus,axiom,
% 0.30/0.57      ! [A: int,B: int] :
% 0.30/0.57        ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 0.30/0.57        = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_minus_minus
% 0.30/0.57  thf(fact_4893_mod__minus__minus,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 0.30/0.57        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_minus_minus
% 0.30/0.57  thf(fact_4894_case__prod__conv,axiom,
% 0.30/0.57      ! [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 0.30/0.57        ( ( produc27273713700761075at_nat @ F2 @ ( product_Pair_nat_nat @ A @ B ) )
% 0.30/0.57        = ( F2 @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % case_prod_conv
% 0.30/0.57  thf(fact_4895_case__prod__conv,axiom,
% 0.30/0.57      ! [F2: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 0.30/0.57        ( ( produc8739625826339149834_nat_o @ F2 @ ( product_Pair_nat_nat @ A @ B ) )
% 0.30/0.57        = ( F2 @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % case_prod_conv
% 0.30/0.57  thf(fact_4896_case__prod__conv,axiom,
% 0.30/0.57      ! [F2: int > int > product_prod_int_int,A: int,B: int] :
% 0.30/0.57        ( ( produc4245557441103728435nt_int @ F2 @ ( product_Pair_int_int @ A @ B ) )
% 0.30/0.57        = ( F2 @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % case_prod_conv
% 0.30/0.57  thf(fact_4897_case__prod__conv,axiom,
% 0.30/0.57      ! [F2: int > int > $o,A: int,B: int] :
% 0.30/0.57        ( ( produc4947309494688390418_int_o @ F2 @ ( product_Pair_int_int @ A @ B ) )
% 0.30/0.57        = ( F2 @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % case_prod_conv
% 0.30/0.57  thf(fact_4898_case__prod__conv,axiom,
% 0.30/0.57      ! [F2: int > int > int,A: int,B: int] :
% 0.30/0.57        ( ( produc8211389475949308722nt_int @ F2 @ ( product_Pair_int_int @ A @ B ) )
% 0.30/0.57        = ( F2 @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % case_prod_conv
% 0.30/0.57  thf(fact_4899_mod__mult__self1__is__0,axiom,
% 0.30/0.57      ! [B: nat,A: nat] :
% 0.30/0.57        ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 0.30/0.57        = zero_zero_nat ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self1_is_0
% 0.30/0.57  thf(fact_4900_mod__mult__self1__is__0,axiom,
% 0.30/0.57      ! [B: int,A: int] :
% 0.30/0.57        ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 0.30/0.57        = zero_zero_int ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self1_is_0
% 0.30/0.57  thf(fact_4901_mod__mult__self1__is__0,axiom,
% 0.30/0.57      ! [B: code_integer,A: code_integer] :
% 0.30/0.57        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 0.30/0.57        = zero_z3403309356797280102nteger ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self1_is_0
% 0.30/0.57  thf(fact_4902_mod__mult__self1__is__0,axiom,
% 0.30/0.57      ! [B: code_natural,A: code_natural] :
% 0.30/0.57        ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ B @ A ) @ B )
% 0.30/0.57        = zero_z2226904508553997617atural ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self1_is_0
% 0.30/0.57  thf(fact_4903_mod__mult__self2__is__0,axiom,
% 0.30/0.57      ! [A: nat,B: nat] :
% 0.30/0.57        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 0.30/0.57        = zero_zero_nat ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self2_is_0
% 0.30/0.57  thf(fact_4904_mod__mult__self2__is__0,axiom,
% 0.30/0.57      ! [A: int,B: int] :
% 0.30/0.57        ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 0.30/0.57        = zero_zero_int ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self2_is_0
% 0.30/0.57  thf(fact_4905_mod__mult__self2__is__0,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer] :
% 0.30/0.57        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 0.30/0.57        = zero_z3403309356797280102nteger ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self2_is_0
% 0.30/0.57  thf(fact_4906_mod__mult__self2__is__0,axiom,
% 0.30/0.57      ! [A: code_natural,B: code_natural] :
% 0.30/0.57        ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ B )
% 0.30/0.57        = zero_z2226904508553997617atural ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self2_is_0
% 0.30/0.57  thf(fact_4907_bits__mod__by__1,axiom,
% 0.30/0.57      ! [A: nat] :
% 0.30/0.57        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 0.30/0.57        = zero_zero_nat ) ).
% 0.30/0.57  
% 0.30/0.57  % bits_mod_by_1
% 0.30/0.57  thf(fact_4908_bits__mod__by__1,axiom,
% 0.30/0.57      ! [A: int] :
% 0.30/0.57        ( ( modulo_modulo_int @ A @ one_one_int )
% 0.30/0.57        = zero_zero_int ) ).
% 0.30/0.57  
% 0.30/0.57  % bits_mod_by_1
% 0.30/0.57  thf(fact_4909_bits__mod__by__1,axiom,
% 0.30/0.57      ! [A: code_integer] :
% 0.30/0.57        ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 0.30/0.57        = zero_z3403309356797280102nteger ) ).
% 0.30/0.57  
% 0.30/0.57  % bits_mod_by_1
% 0.30/0.57  thf(fact_4910_bits__mod__by__1,axiom,
% 0.30/0.57      ! [A: code_natural] :
% 0.30/0.57        ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 0.30/0.57        = zero_z2226904508553997617atural ) ).
% 0.30/0.57  
% 0.30/0.57  % bits_mod_by_1
% 0.30/0.57  thf(fact_4911_mod__by__1,axiom,
% 0.30/0.57      ! [A: nat] :
% 0.30/0.57        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 0.30/0.57        = zero_zero_nat ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_by_1
% 0.30/0.57  thf(fact_4912_mod__by__1,axiom,
% 0.30/0.57      ! [A: int] :
% 0.30/0.57        ( ( modulo_modulo_int @ A @ one_one_int )
% 0.30/0.57        = zero_zero_int ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_by_1
% 0.30/0.57  thf(fact_4913_mod__by__1,axiom,
% 0.30/0.57      ! [A: code_integer] :
% 0.30/0.57        ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 0.30/0.57        = zero_z3403309356797280102nteger ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_by_1
% 0.30/0.57  thf(fact_4914_mod__by__1,axiom,
% 0.30/0.57      ! [A: code_natural] :
% 0.30/0.57        ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 0.30/0.57        = zero_z2226904508553997617atural ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_by_1
% 0.30/0.57  thf(fact_4915_mod__mult__self4,axiom,
% 0.30/0.57      ! [B: nat,C: nat,A: nat] :
% 0.30/0.57        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 0.30/0.57        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self4
% 0.30/0.57  thf(fact_4916_mod__mult__self4,axiom,
% 0.30/0.57      ! [B: int,C: int,A: int] :
% 0.30/0.57        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 0.30/0.57        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self4
% 0.30/0.57  thf(fact_4917_mod__mult__self4,axiom,
% 0.30/0.57      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.30/0.57        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 0.30/0.57        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self4
% 0.30/0.57  thf(fact_4918_mod__mult__self4,axiom,
% 0.30/0.57      ! [B: code_natural,C: code_natural,A: code_natural] :
% 0.30/0.57        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ C ) @ A ) @ B )
% 0.30/0.57        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self4
% 0.30/0.57  thf(fact_4919_mod__mult__self3,axiom,
% 0.30/0.57      ! [C: nat,B: nat,A: nat] :
% 0.30/0.57        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 0.30/0.57        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self3
% 0.30/0.57  thf(fact_4920_mod__mult__self3,axiom,
% 0.30/0.57      ! [C: int,B: int,A: int] :
% 0.30/0.57        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 0.30/0.57        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self3
% 0.30/0.57  thf(fact_4921_mod__mult__self3,axiom,
% 0.30/0.57      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.30/0.57        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 0.30/0.57        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self3
% 0.30/0.57  thf(fact_4922_mod__mult__self3,axiom,
% 0.30/0.57      ! [C: code_natural,B: code_natural,A: code_natural] :
% 0.30/0.57        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C @ B ) @ A ) @ B )
% 0.30/0.57        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self3
% 0.30/0.57  thf(fact_4923_mod__mult__self2,axiom,
% 0.30/0.57      ! [A: nat,B: nat,C: nat] :
% 0.30/0.57        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 0.30/0.57        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self2
% 0.30/0.57  thf(fact_4924_mod__mult__self2,axiom,
% 0.30/0.57      ! [A: int,B: int,C: int] :
% 0.30/0.57        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 0.30/0.57        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self2
% 0.30/0.57  thf(fact_4925_mod__mult__self2,axiom,
% 0.30/0.57      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.57        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 0.30/0.57        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self2
% 0.30/0.57  thf(fact_4926_mod__mult__self2,axiom,
% 0.30/0.57      ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.30/0.57        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ B @ C ) ) @ B )
% 0.30/0.57        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self2
% 0.30/0.57  thf(fact_4927_mod__mult__self1,axiom,
% 0.30/0.57      ! [A: nat,C: nat,B: nat] :
% 0.30/0.57        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 0.30/0.57        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self1
% 0.30/0.57  thf(fact_4928_mod__mult__self1,axiom,
% 0.30/0.57      ! [A: int,C: int,B: int] :
% 0.30/0.57        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 0.30/0.57        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self1
% 0.30/0.57  thf(fact_4929_mod__mult__self1,axiom,
% 0.30/0.57      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.30/0.57        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 0.30/0.57        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self1
% 0.30/0.57  thf(fact_4930_mod__mult__self1,axiom,
% 0.30/0.57      ! [A: code_natural,C: code_natural,B: code_natural] :
% 0.30/0.57        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ C @ B ) ) @ B )
% 0.30/0.57        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_mult_self1
% 0.30/0.57  thf(fact_4931_minus__mod__self1,axiom,
% 0.30/0.57      ! [B: int,A: int] :
% 0.30/0.57        ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 0.30/0.57        = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % minus_mod_self1
% 0.30/0.57  thf(fact_4932_minus__mod__self1,axiom,
% 0.30/0.57      ! [B: code_integer,A: code_integer] :
% 0.30/0.57        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 0.30/0.57        = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.30/0.57  
% 0.30/0.57  % minus_mod_self1
% 0.30/0.57  thf(fact_4933_mod__minus1__right,axiom,
% 0.30/0.57      ! [A: int] :
% 0.30/0.57        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.57        = zero_zero_int ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_minus1_right
% 0.30/0.57  thf(fact_4934_mod__minus1__right,axiom,
% 0.30/0.57      ! [A: code_integer] :
% 0.30/0.57        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.57        = zero_z3403309356797280102nteger ) ).
% 0.30/0.57  
% 0.30/0.57  % mod_minus1_right
% 0.30/0.57  thf(fact_4935_bits__one__mod__two__eq__one,axiom,
% 0.30/0.57      ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.57      = one_one_nat ) ).
% 0.30/0.57  
% 0.30/0.57  % bits_one_mod_two_eq_one
% 0.30/0.57  thf(fact_4936_bits__one__mod__two__eq__one,axiom,
% 0.30/0.57      ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.57      = one_one_int ) ).
% 0.30/0.57  
% 0.30/0.57  % bits_one_mod_two_eq_one
% 0.30/0.57  thf(fact_4937_bits__one__mod__two__eq__one,axiom,
% 0.30/0.57      ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.57      = one_one_Code_integer ) ).
% 0.30/0.57  
% 0.30/0.57  % bits_one_mod_two_eq_one
% 0.30/0.57  thf(fact_4938_bits__one__mod__two__eq__one,axiom,
% 0.30/0.57      ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.57      = one_one_Code_natural ) ).
% 0.30/0.57  
% 0.30/0.57  % bits_one_mod_two_eq_one
% 0.30/0.57  thf(fact_4939_one__mod__two__eq__one,axiom,
% 0.30/0.57      ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.57      = one_one_nat ) ).
% 0.30/0.57  
% 0.30/0.57  % one_mod_two_eq_one
% 0.30/0.57  thf(fact_4940_one__mod__two__eq__one,axiom,
% 0.30/0.57      ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.57      = one_one_int ) ).
% 0.30/0.57  
% 0.30/0.57  % one_mod_two_eq_one
% 0.30/0.57  thf(fact_4941_one__mod__two__eq__one,axiom,
% 0.30/0.57      ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.57      = one_one_Code_integer ) ).
% 0.30/0.57  
% 0.30/0.57  % one_mod_two_eq_one
% 0.30/0.57  thf(fact_4942_one__mod__two__eq__one,axiom,
% 0.30/0.57      ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.57      = one_one_Code_natural ) ).
% 0.30/0.57  
% 0.30/0.57  % one_mod_two_eq_one
% 0.30/0.57  thf(fact_4943_xor__numerals_I3_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 0.30/0.57        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(3)
% 0.30/0.57  thf(fact_4944_xor__numerals_I3_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 0.30/0.57        = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(3)
% 0.30/0.57  thf(fact_4945_xor__numerals_I3_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.30/0.57        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(3)
% 0.30/0.57  thf(fact_4946_xor__numerals_I3_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.30/0.57        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(3)
% 0.30/0.57  thf(fact_4947_xor__numerals_I8_J,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ one_one_Code_integer )
% 0.30/0.57        = ( numera6620942414471956472nteger @ ( bit0 @ X ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(8)
% 0.30/0.57  thf(fact_4948_xor__numerals_I8_J,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ one_one_Code_natural )
% 0.30/0.57        = ( numera5444537566228673987atural @ ( bit0 @ X ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(8)
% 0.30/0.57  thf(fact_4949_xor__numerals_I8_J,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 0.30/0.57        = ( numeral_numeral_int @ ( bit0 @ X ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(8)
% 0.30/0.57  thf(fact_4950_xor__numerals_I8_J,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 0.30/0.57        = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(8)
% 0.30/0.57  thf(fact_4951_xor__numerals_I5_J,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ one_one_Code_integer )
% 0.30/0.57        = ( numera6620942414471956472nteger @ ( bit1 @ X ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(5)
% 0.30/0.57  thf(fact_4952_xor__numerals_I5_J,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ one_one_Code_natural )
% 0.30/0.57        = ( numera5444537566228673987atural @ ( bit1 @ X ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(5)
% 0.30/0.57  thf(fact_4953_xor__numerals_I5_J,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 0.30/0.57        = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(5)
% 0.30/0.57  thf(fact_4954_xor__numerals_I5_J,axiom,
% 0.30/0.57      ! [X: num] :
% 0.30/0.57        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 0.30/0.57        = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(5)
% 0.30/0.57  thf(fact_4955_xor__numerals_I2_J,axiom,
% 0.30/0.57      ! [Y: num] :
% 0.30/0.57        ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 0.30/0.57        = ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(2)
% 0.30/0.57  thf(fact_4956_xor__numerals_I2_J,axiom,
% 0.30/0.57      ! [Y: num] :
% 0.30/0.57        ( ( bit_se2046307713759805098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 0.30/0.57        = ( numera5444537566228673987atural @ ( bit0 @ Y ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(2)
% 0.30/0.57  thf(fact_4957_xor__numerals_I2_J,axiom,
% 0.30/0.57      ! [Y: num] :
% 0.30/0.57        ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.30/0.57        = ( numeral_numeral_int @ ( bit0 @ Y ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(2)
% 0.30/0.57  thf(fact_4958_xor__numerals_I2_J,axiom,
% 0.30/0.57      ! [Y: num] :
% 0.30/0.57        ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.30/0.57        = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(2)
% 0.30/0.57  thf(fact_4959_xor__numerals_I1_J,axiom,
% 0.30/0.57      ! [Y: num] :
% 0.30/0.57        ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 0.30/0.57        = ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(1)
% 0.30/0.57  thf(fact_4960_xor__numerals_I1_J,axiom,
% 0.30/0.57      ! [Y: num] :
% 0.30/0.57        ( ( bit_se2046307713759805098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 0.30/0.57        = ( numera5444537566228673987atural @ ( bit1 @ Y ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(1)
% 0.30/0.57  thf(fact_4961_xor__numerals_I1_J,axiom,
% 0.30/0.57      ! [Y: num] :
% 0.30/0.57        ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.30/0.57        = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(1)
% 0.30/0.57  thf(fact_4962_xor__numerals_I1_J,axiom,
% 0.30/0.57      ! [Y: num] :
% 0.30/0.57        ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.30/0.57        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(1)
% 0.30/0.57  thf(fact_4963_not__mod__2__eq__0__eq__1,axiom,
% 0.30/0.57      ! [A: nat] :
% 0.30/0.57        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.57         != zero_zero_nat )
% 0.30/0.57        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.57          = one_one_nat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % not_mod_2_eq_0_eq_1
% 0.30/0.57  thf(fact_4964_not__mod__2__eq__0__eq__1,axiom,
% 0.30/0.57      ! [A: int] :
% 0.30/0.57        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.57         != zero_zero_int )
% 0.30/0.57        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.57          = one_one_int ) ) ).
% 0.30/0.57  
% 0.30/0.57  % not_mod_2_eq_0_eq_1
% 0.30/0.57  thf(fact_4965_not__mod__2__eq__0__eq__1,axiom,
% 0.30/0.57      ! [A: code_integer] :
% 0.30/0.57        ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.57         != zero_z3403309356797280102nteger )
% 0.30/0.57        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.57          = one_one_Code_integer ) ) ).
% 0.30/0.57  
% 0.30/0.57  % not_mod_2_eq_0_eq_1
% 0.30/0.57  thf(fact_4966_not__mod__2__eq__0__eq__1,axiom,
% 0.30/0.57      ! [A: code_natural] :
% 0.30/0.57        ( ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.57         != zero_z2226904508553997617atural )
% 0.30/0.57        = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.57          = one_one_Code_natural ) ) ).
% 0.30/0.57  
% 0.30/0.57  % not_mod_2_eq_0_eq_1
% 0.30/0.57  thf(fact_4967_not__mod__2__eq__1__eq__0,axiom,
% 0.30/0.57      ! [A: nat] :
% 0.30/0.57        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.57         != one_one_nat )
% 0.30/0.57        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.57          = zero_zero_nat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % not_mod_2_eq_1_eq_0
% 0.30/0.57  thf(fact_4968_not__mod__2__eq__1__eq__0,axiom,
% 0.30/0.57      ! [A: int] :
% 0.30/0.57        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.57         != one_one_int )
% 0.30/0.57        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.57          = zero_zero_int ) ) ).
% 0.30/0.57  
% 0.30/0.57  % not_mod_2_eq_1_eq_0
% 0.30/0.57  thf(fact_4969_not__mod__2__eq__1__eq__0,axiom,
% 0.30/0.57      ! [A: code_integer] :
% 0.30/0.57        ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.57         != one_one_Code_integer )
% 0.30/0.57        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.57          = zero_z3403309356797280102nteger ) ) ).
% 0.30/0.57  
% 0.30/0.57  % not_mod_2_eq_1_eq_0
% 0.30/0.57  thf(fact_4970_not__mod__2__eq__1__eq__0,axiom,
% 0.30/0.57      ! [A: code_natural] :
% 0.30/0.57        ( ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.57         != one_one_Code_natural )
% 0.30/0.57        = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.57          = zero_z2226904508553997617atural ) ) ).
% 0.30/0.57  
% 0.30/0.57  % not_mod_2_eq_1_eq_0
% 0.30/0.57  thf(fact_4971_minus__1__mod__2__eq,axiom,
% 0.30/0.57      ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.57      = one_one_int ) ).
% 0.30/0.57  
% 0.30/0.57  % minus_1_mod_2_eq
% 0.30/0.57  thf(fact_4972_minus__1__mod__2__eq,axiom,
% 0.30/0.57      ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.57      = one_one_Code_integer ) ).
% 0.30/0.57  
% 0.30/0.57  % minus_1_mod_2_eq
% 0.30/0.57  thf(fact_4973_bits__minus__1__mod__2__eq,axiom,
% 0.30/0.57      ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.57      = one_one_int ) ).
% 0.30/0.57  
% 0.30/0.57  % bits_minus_1_mod_2_eq
% 0.30/0.57  thf(fact_4974_bits__minus__1__mod__2__eq,axiom,
% 0.30/0.57      ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.57      = one_one_Code_integer ) ).
% 0.30/0.57  
% 0.30/0.57  % bits_minus_1_mod_2_eq
% 0.30/0.57  thf(fact_4975_mod2__gr__0,axiom,
% 0.30/0.57      ! [M: nat] :
% 0.30/0.57        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.30/0.57        = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.57          = one_one_nat ) ) ).
% 0.30/0.57  
% 0.30/0.57  % mod2_gr_0
% 0.30/0.57  thf(fact_4976_xor__numerals_I7_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 0.30/0.57        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(7)
% 0.30/0.57  thf(fact_4977_xor__numerals_I7_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 0.30/0.57        = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(7)
% 0.30/0.57  thf(fact_4978_xor__numerals_I7_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.30/0.57        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(7)
% 0.30/0.57  thf(fact_4979_xor__numerals_I7_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.30/0.57        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(7)
% 0.30/0.57  thf(fact_4980_zmod__numeral__Bit1,axiom,
% 0.30/0.57      ! [V: num,W: num] :
% 0.30/0.57        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 0.30/0.57        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) @ one_one_int ) ) ).
% 0.30/0.57  
% 0.30/0.57  % zmod_numeral_Bit1
% 0.30/0.57  thf(fact_4981_divmod__algorithm__code_I5_J,axiom,
% 0.30/0.57      ! [M: num,N: num] :
% 0.30/0.57        ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.30/0.57        = ( produc4245557441103728435nt_int
% 0.30/0.57          @ ^ [Q5: int,R4: int] : ( product_Pair_int_int @ Q5 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R4 ) )
% 0.30/0.57          @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_algorithm_code(5)
% 0.30/0.57  thf(fact_4982_divmod__algorithm__code_I5_J,axiom,
% 0.30/0.57      ! [M: num,N: num] :
% 0.30/0.57        ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.30/0.57        = ( produc2626176000494625587at_nat
% 0.30/0.57          @ ^ [Q5: nat,R4: nat] : ( product_Pair_nat_nat @ Q5 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R4 ) )
% 0.30/0.57          @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_algorithm_code(5)
% 0.30/0.57  thf(fact_4983_divmod__algorithm__code_I5_J,axiom,
% 0.30/0.57      ! [M: num,N: num] :
% 0.30/0.57        ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.30/0.57        = ( produc6916734918728496179nteger
% 0.30/0.57          @ ^ [Q5: code_integer,R4: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R4 ) )
% 0.30/0.57          @ ( unique3479559517661332726nteger @ M @ N ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_algorithm_code(5)
% 0.30/0.57  thf(fact_4984_xor__numerals_I4_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 0.30/0.57        = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(4)
% 0.30/0.57  thf(fact_4985_xor__numerals_I4_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 0.30/0.57        = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(4)
% 0.30/0.57  thf(fact_4986_xor__numerals_I4_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.30/0.57        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(4)
% 0.30/0.57  thf(fact_4987_xor__numerals_I4_J,axiom,
% 0.30/0.57      ! [X: num,Y: num] :
% 0.30/0.57        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.30/0.57        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % xor_numerals(4)
% 0.30/0.57  thf(fact_4988_zmod__minus1,axiom,
% 0.30/0.57      ! [B: int] :
% 0.30/0.57        ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.57       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 0.30/0.57          = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % zmod_minus1
% 0.30/0.57  thf(fact_4989_minus__mod__int__eq,axiom,
% 0.30/0.57      ! [L: int,K: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ zero_zero_int @ L )
% 0.30/0.57       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 0.30/0.57          = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % minus_mod_int_eq
% 0.30/0.57  thf(fact_4990_zdiv__zminus1__eq__if,axiom,
% 0.30/0.57      ! [B: int,A: int] :
% 0.30/0.57        ( ( B != zero_zero_int )
% 0.30/0.57       => ( ( ( ( modulo_modulo_int @ A @ B )
% 0.30/0.57              = zero_zero_int )
% 0.30/0.57           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.30/0.57              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 0.30/0.57          & ( ( ( modulo_modulo_int @ A @ B )
% 0.30/0.57             != zero_zero_int )
% 0.30/0.57           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.30/0.57              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % zdiv_zminus1_eq_if
% 0.30/0.57  thf(fact_4991_zdiv__zminus2__eq__if,axiom,
% 0.30/0.57      ! [B: int,A: int] :
% 0.30/0.57        ( ( B != zero_zero_int )
% 0.30/0.57       => ( ( ( ( modulo_modulo_int @ A @ B )
% 0.30/0.57              = zero_zero_int )
% 0.30/0.57           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.30/0.57              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 0.30/0.57          & ( ( ( modulo_modulo_int @ A @ B )
% 0.30/0.57             != zero_zero_int )
% 0.30/0.57           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.30/0.57              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % zdiv_zminus2_eq_if
% 0.30/0.57  thf(fact_4992_div__pos__neg__trivial,axiom,
% 0.30/0.57      ! [K: int,L: int] :
% 0.30/0.57        ( ( ord_less_int @ zero_zero_int @ K )
% 0.30/0.57       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 0.30/0.57         => ( ( divide_divide_int @ K @ L )
% 0.30/0.57            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % div_pos_neg_trivial
% 0.30/0.57  thf(fact_4993_div__pos__geq,axiom,
% 0.30/0.57      ! [L: int,K: int] :
% 0.30/0.57        ( ( ord_less_int @ zero_zero_int @ L )
% 0.30/0.57       => ( ( ord_less_eq_int @ L @ K )
% 0.30/0.57         => ( ( divide_divide_int @ K @ L )
% 0.30/0.57            = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % div_pos_geq
% 0.30/0.57  thf(fact_4994_int__div__less__self,axiom,
% 0.30/0.57      ! [X: int,K: int] :
% 0.30/0.57        ( ( ord_less_int @ zero_zero_int @ X )
% 0.30/0.57       => ( ( ord_less_int @ one_one_int @ K )
% 0.30/0.57         => ( ord_less_int @ ( divide_divide_int @ X @ K ) @ X ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % int_div_less_self
% 0.30/0.57  thf(fact_4995_verit__less__mono__div__int2,axiom,
% 0.30/0.57      ! [A2: int,B2: int,N: int] :
% 0.30/0.57        ( ( ord_less_eq_int @ A2 @ B2 )
% 0.30/0.57       => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 0.30/0.57         => ( ord_less_eq_int @ ( divide_divide_int @ B2 @ N ) @ ( divide_divide_int @ A2 @ N ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % verit_less_mono_div_int2
% 0.30/0.57  thf(fact_4996_verit__le__mono__div__int,axiom,
% 0.30/0.57      ! [A2: int,B2: int,N: int] :
% 0.30/0.57        ( ( ord_less_int @ A2 @ B2 )
% 0.30/0.57       => ( ( ord_less_int @ zero_zero_int @ N )
% 0.30/0.57         => ( ord_less_eq_int
% 0.30/0.57            @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N )
% 0.30/0.57              @ ( if_int
% 0.30/0.57                @ ( ( modulo_modulo_int @ B2 @ N )
% 0.30/0.57                  = zero_zero_int )
% 0.30/0.57                @ one_one_int
% 0.30/0.57                @ zero_zero_int ) )
% 0.30/0.57            @ ( divide_divide_int @ B2 @ N ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % verit_le_mono_div_int
% 0.30/0.57  thf(fact_4997_div__eq__minus1,axiom,
% 0.30/0.57      ! [B: int] :
% 0.30/0.57        ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.57       => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 0.30/0.57          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % div_eq_minus1
% 0.30/0.57  thf(fact_4998_divmod__int__def,axiom,
% 0.30/0.57      ( unique5052692396658037445od_int
% 0.30/0.57      = ( ^ [M2: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 0.30/0.57  
% 0.30/0.57  % divmod_int_def
% 0.30/0.57  thf(fact_4999_zmod__zminus1__not__zero,axiom,
% 0.30/0.57      ! [K: int,L: int] :
% 0.30/0.57        ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 0.30/0.58         != zero_zero_int )
% 0.30/0.58       => ( ( modulo_modulo_int @ K @ L )
% 0.30/0.58         != zero_zero_int ) ) ).
% 0.30/0.58  
% 0.30/0.58  % zmod_zminus1_not_zero
% 0.30/0.58  thf(fact_5000_zmod__zminus2__not__zero,axiom,
% 0.30/0.58      ! [K: int,L: int] :
% 0.30/0.58        ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L ) )
% 0.30/0.58         != zero_zero_int )
% 0.30/0.58       => ( ( modulo_modulo_int @ K @ L )
% 0.30/0.58         != zero_zero_int ) ) ).
% 0.30/0.58  
% 0.30/0.58  % zmod_zminus2_not_zero
% 0.30/0.58  thf(fact_5001_zmod__zminus2__eq__if,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( ( ( modulo_modulo_int @ A @ B )
% 0.30/0.58            = zero_zero_int )
% 0.30/0.58         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 0.30/0.58            = zero_zero_int ) )
% 0.30/0.58        & ( ( ( modulo_modulo_int @ A @ B )
% 0.30/0.58           != zero_zero_int )
% 0.30/0.58         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 0.30/0.58            = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % zmod_zminus2_eq_if
% 0.30/0.58  thf(fact_5002_zmod__zminus1__eq__if,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( ( ( modulo_modulo_int @ A @ B )
% 0.30/0.58            = zero_zero_int )
% 0.30/0.58         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 0.30/0.58            = zero_zero_int ) )
% 0.30/0.58        & ( ( ( modulo_modulo_int @ A @ B )
% 0.30/0.58           != zero_zero_int )
% 0.30/0.58         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 0.30/0.58            = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % zmod_zminus1_eq_if
% 0.30/0.58  thf(fact_5003_prod_Ocase__distrib,axiom,
% 0.30/0.58      ! [H3: $o > $o,F2: int > int > $o,Prod: product_prod_int_int] :
% 0.30/0.58        ( ( H3 @ ( produc4947309494688390418_int_o @ F2 @ Prod ) )
% 0.30/0.58        = ( produc4947309494688390418_int_o
% 0.30/0.58          @ ^ [X12: int,X23: int] : ( H3 @ ( F2 @ X12 @ X23 ) )
% 0.30/0.58          @ Prod ) ) ).
% 0.30/0.58  
% 0.30/0.58  % prod.case_distrib
% 0.30/0.58  thf(fact_5004_prod_Ocase__distrib,axiom,
% 0.30/0.58      ! [H3: $o > int,F2: int > int > $o,Prod: product_prod_int_int] :
% 0.30/0.58        ( ( H3 @ ( produc4947309494688390418_int_o @ F2 @ Prod ) )
% 0.30/0.58        = ( produc8211389475949308722nt_int
% 0.30/0.58          @ ^ [X12: int,X23: int] : ( H3 @ ( F2 @ X12 @ X23 ) )
% 0.30/0.58          @ Prod ) ) ).
% 0.30/0.58  
% 0.30/0.58  % prod.case_distrib
% 0.30/0.58  thf(fact_5005_prod_Ocase__distrib,axiom,
% 0.30/0.58      ! [H3: int > $o,F2: int > int > int,Prod: product_prod_int_int] :
% 0.30/0.58        ( ( H3 @ ( produc8211389475949308722nt_int @ F2 @ Prod ) )
% 0.30/0.58        = ( produc4947309494688390418_int_o
% 0.30/0.58          @ ^ [X12: int,X23: int] : ( H3 @ ( F2 @ X12 @ X23 ) )
% 0.30/0.58          @ Prod ) ) ).
% 0.30/0.58  
% 0.30/0.58  % prod.case_distrib
% 0.30/0.58  thf(fact_5006_prod_Ocase__distrib,axiom,
% 0.30/0.58      ! [H3: int > int,F2: int > int > int,Prod: product_prod_int_int] :
% 0.30/0.58        ( ( H3 @ ( produc8211389475949308722nt_int @ F2 @ Prod ) )
% 0.30/0.58        = ( produc8211389475949308722nt_int
% 0.30/0.58          @ ^ [X12: int,X23: int] : ( H3 @ ( F2 @ X12 @ X23 ) )
% 0.30/0.58          @ Prod ) ) ).
% 0.30/0.58  
% 0.30/0.58  % prod.case_distrib
% 0.30/0.58  thf(fact_5007_prod_Ocase__distrib,axiom,
% 0.30/0.58      ! [H3: product_prod_int_int > $o,F2: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 0.30/0.58        ( ( H3 @ ( produc4245557441103728435nt_int @ F2 @ Prod ) )
% 0.30/0.58        = ( produc4947309494688390418_int_o
% 0.30/0.58          @ ^ [X12: int,X23: int] : ( H3 @ ( F2 @ X12 @ X23 ) )
% 0.30/0.58          @ Prod ) ) ).
% 0.30/0.58  
% 0.30/0.58  % prod.case_distrib
% 0.30/0.58  thf(fact_5008_prod_Ocase__distrib,axiom,
% 0.30/0.58      ! [H3: product_prod_int_int > int,F2: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 0.30/0.58        ( ( H3 @ ( produc4245557441103728435nt_int @ F2 @ Prod ) )
% 0.30/0.58        = ( produc8211389475949308722nt_int
% 0.30/0.58          @ ^ [X12: int,X23: int] : ( H3 @ ( F2 @ X12 @ X23 ) )
% 0.30/0.58          @ Prod ) ) ).
% 0.30/0.58  
% 0.30/0.58  % prod.case_distrib
% 0.30/0.58  thf(fact_5009_prod_Ocase__distrib,axiom,
% 0.30/0.58      ! [H3: $o > product_prod_int_int,F2: int > int > $o,Prod: product_prod_int_int] :
% 0.30/0.58        ( ( H3 @ ( produc4947309494688390418_int_o @ F2 @ Prod ) )
% 0.30/0.58        = ( produc4245557441103728435nt_int
% 0.30/0.58          @ ^ [X12: int,X23: int] : ( H3 @ ( F2 @ X12 @ X23 ) )
% 0.30/0.58          @ Prod ) ) ).
% 0.30/0.58  
% 0.30/0.58  % prod.case_distrib
% 0.30/0.58  thf(fact_5010_prod_Ocase__distrib,axiom,
% 0.30/0.58      ! [H3: int > product_prod_int_int,F2: int > int > int,Prod: product_prod_int_int] :
% 0.30/0.58        ( ( H3 @ ( produc8211389475949308722nt_int @ F2 @ Prod ) )
% 0.30/0.58        = ( produc4245557441103728435nt_int
% 0.30/0.58          @ ^ [X12: int,X23: int] : ( H3 @ ( F2 @ X12 @ X23 ) )
% 0.30/0.58          @ Prod ) ) ).
% 0.30/0.58  
% 0.30/0.58  % prod.case_distrib
% 0.30/0.58  thf(fact_5011_prod_Ocase__distrib,axiom,
% 0.30/0.58      ! [H3: product_prod_int_int > product_prod_int_int,F2: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 0.30/0.58        ( ( H3 @ ( produc4245557441103728435nt_int @ F2 @ Prod ) )
% 0.30/0.58        = ( produc4245557441103728435nt_int
% 0.30/0.58          @ ^ [X12: int,X23: int] : ( H3 @ ( F2 @ X12 @ X23 ) )
% 0.30/0.58          @ Prod ) ) ).
% 0.30/0.58  
% 0.30/0.58  % prod.case_distrib
% 0.30/0.58  thf(fact_5012_prod_Ocase__distrib,axiom,
% 0.30/0.58      ! [H3: ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o,F2: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 0.30/0.58        ( ( H3 @ ( produc8739625826339149834_nat_o @ F2 @ Prod ) )
% 0.30/0.58        = ( produc8739625826339149834_nat_o
% 0.30/0.58          @ ^ [X12: nat,X23: nat] : ( H3 @ ( F2 @ X12 @ X23 ) )
% 0.30/0.58          @ Prod ) ) ).
% 0.30/0.58  
% 0.30/0.58  % prod.case_distrib
% 0.30/0.58  thf(fact_5013_case__prod__app,axiom,
% 0.30/0.58      ( produc27273713700761075at_nat
% 0.30/0.58      = ( ^ [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.30/0.58            ( produc2626176000494625587at_nat
% 0.30/0.58            @ ^ [L2: nat,R4: nat] : ( F @ L2 @ R4 @ Y3 )
% 0.30/0.58            @ X3 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prod_app
% 0.30/0.58  thf(fact_5014_case__prod__app,axiom,
% 0.30/0.58      ( produc8739625826339149834_nat_o
% 0.30/0.58      = ( ^ [F: nat > nat > product_prod_nat_nat > $o,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.30/0.58            ( produc6081775807080527818_nat_o
% 0.30/0.58            @ ^ [L2: nat,R4: nat] : ( F @ L2 @ R4 @ Y3 )
% 0.30/0.58            @ X3 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prod_app
% 0.30/0.58  thf(fact_5015_nested__case__prod__simp,axiom,
% 0.30/0.58      ( produc27273713700761075at_nat
% 0.30/0.58      = ( ^ [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.30/0.58            ( produc2626176000494625587at_nat
% 0.30/0.58            @ ^ [A3: nat,B3: nat] : ( F @ A3 @ B3 @ Y3 )
% 0.30/0.58            @ X3 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % nested_case_prod_simp
% 0.30/0.58  thf(fact_5016_nested__case__prod__simp,axiom,
% 0.30/0.58      ( produc8739625826339149834_nat_o
% 0.30/0.58      = ( ^ [F: nat > nat > product_prod_nat_nat > $o,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.30/0.58            ( produc6081775807080527818_nat_o
% 0.30/0.58            @ ^ [A3: nat,B3: nat] : ( F @ A3 @ B3 @ Y3 )
% 0.30/0.58            @ X3 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % nested_case_prod_simp
% 0.30/0.58  thf(fact_5017_mod__mult__eq,axiom,
% 0.30/0.58      ! [A: nat,C: nat,B: nat] :
% 0.30/0.58        ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 0.30/0.58        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_eq
% 0.30/0.58  thf(fact_5018_mod__mult__eq,axiom,
% 0.30/0.58      ! [A: int,C: int,B: int] :
% 0.30/0.58        ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.30/0.58        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_eq
% 0.30/0.58  thf(fact_5019_mod__mult__eq,axiom,
% 0.30/0.58      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.30/0.58        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 0.30/0.58        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_eq
% 0.30/0.58  thf(fact_5020_mod__mult__eq,axiom,
% 0.30/0.58      ! [A: code_natural,C: code_natural,B: code_natural] :
% 0.30/0.58        ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ C ) @ ( modulo8411746178871703098atural @ B @ C ) ) @ C )
% 0.30/0.58        = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_eq
% 0.30/0.58  thf(fact_5021_mod__mult__cong,axiom,
% 0.30/0.58      ! [A: nat,C: nat,A5: nat,B: nat,B5: nat] :
% 0.30/0.58        ( ( ( modulo_modulo_nat @ A @ C )
% 0.30/0.58          = ( modulo_modulo_nat @ A5 @ C ) )
% 0.30/0.58       => ( ( ( modulo_modulo_nat @ B @ C )
% 0.30/0.58            = ( modulo_modulo_nat @ B5 @ C ) )
% 0.30/0.58         => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.30/0.58            = ( modulo_modulo_nat @ ( times_times_nat @ A5 @ B5 ) @ C ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_cong
% 0.30/0.58  thf(fact_5022_mod__mult__cong,axiom,
% 0.30/0.58      ! [A: int,C: int,A5: int,B: int,B5: int] :
% 0.30/0.58        ( ( ( modulo_modulo_int @ A @ C )
% 0.30/0.58          = ( modulo_modulo_int @ A5 @ C ) )
% 0.30/0.58       => ( ( ( modulo_modulo_int @ B @ C )
% 0.30/0.58            = ( modulo_modulo_int @ B5 @ C ) )
% 0.30/0.58         => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 0.30/0.58            = ( modulo_modulo_int @ ( times_times_int @ A5 @ B5 ) @ C ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_cong
% 0.30/0.58  thf(fact_5023_mod__mult__cong,axiom,
% 0.30/0.58      ! [A: code_integer,C: code_integer,A5: code_integer,B: code_integer,B5: code_integer] :
% 0.30/0.58        ( ( ( modulo364778990260209775nteger @ A @ C )
% 0.30/0.58          = ( modulo364778990260209775nteger @ A5 @ C ) )
% 0.30/0.58       => ( ( ( modulo364778990260209775nteger @ B @ C )
% 0.30/0.58            = ( modulo364778990260209775nteger @ B5 @ C ) )
% 0.30/0.58         => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.30/0.58            = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A5 @ B5 ) @ C ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_cong
% 0.30/0.58  thf(fact_5024_mod__mult__cong,axiom,
% 0.30/0.58      ! [A: code_natural,C: code_natural,A5: code_natural,B: code_natural,B5: code_natural] :
% 0.30/0.58        ( ( ( modulo8411746178871703098atural @ A @ C )
% 0.30/0.58          = ( modulo8411746178871703098atural @ A5 @ C ) )
% 0.30/0.58       => ( ( ( modulo8411746178871703098atural @ B @ C )
% 0.30/0.58            = ( modulo8411746178871703098atural @ B5 @ C ) )
% 0.30/0.58         => ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C )
% 0.30/0.58            = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A5 @ B5 ) @ C ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_cong
% 0.30/0.58  thf(fact_5025_mod__mult__mult2,axiom,
% 0.30/0.58      ! [A: nat,C: nat,B: nat] :
% 0.30/0.58        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 0.30/0.58        = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_mult2
% 0.30/0.58  thf(fact_5026_mod__mult__mult2,axiom,
% 0.30/0.58      ! [A: int,C: int,B: int] :
% 0.30/0.58        ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.30/0.58        = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_mult2
% 0.30/0.58  thf(fact_5027_mod__mult__mult2,axiom,
% 0.30/0.58      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.30/0.58        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.30/0.58        = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_mult2
% 0.30/0.58  thf(fact_5028_mod__mult__mult2,axiom,
% 0.30/0.58      ! [A: code_natural,C: code_natural,B: code_natural] :
% 0.30/0.58        ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) )
% 0.30/0.58        = ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ B ) @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_mult2
% 0.30/0.58  thf(fact_5029_mult__mod__right,axiom,
% 0.30/0.58      ! [C: nat,A: nat,B: nat] :
% 0.30/0.58        ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 0.30/0.58        = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mult_mod_right
% 0.30/0.58  thf(fact_5030_mult__mod__right,axiom,
% 0.30/0.58      ! [C: int,A: int,B: int] :
% 0.30/0.58        ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 0.30/0.58        = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mult_mod_right
% 0.30/0.58  thf(fact_5031_mult__mod__right,axiom,
% 0.30/0.58      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( times_3573771949741848930nteger @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.30/0.58        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mult_mod_right
% 0.30/0.58  thf(fact_5032_mult__mod__right,axiom,
% 0.30/0.58      ! [C: code_natural,A: code_natural,B: code_natural] :
% 0.30/0.58        ( ( times_2397367101498566445atural @ C @ ( modulo8411746178871703098atural @ A @ B ) )
% 0.30/0.58        = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mult_mod_right
% 0.30/0.58  thf(fact_5033_mod__mult__left__eq,axiom,
% 0.30/0.58      ! [A: nat,C: nat,B: nat] :
% 0.30/0.58        ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 0.30/0.58        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_left_eq
% 0.30/0.58  thf(fact_5034_mod__mult__left__eq,axiom,
% 0.30/0.58      ! [A: int,C: int,B: int] :
% 0.30/0.58        ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 0.30/0.58        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_left_eq
% 0.30/0.58  thf(fact_5035_mod__mult__left__eq,axiom,
% 0.30/0.58      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.30/0.58        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 0.30/0.58        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_left_eq
% 0.30/0.58  thf(fact_5036_mod__mult__left__eq,axiom,
% 0.30/0.58      ! [A: code_natural,C: code_natural,B: code_natural] :
% 0.30/0.58        ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ C ) @ B ) @ C )
% 0.30/0.58        = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_left_eq
% 0.30/0.58  thf(fact_5037_mod__mult__right__eq,axiom,
% 0.30/0.58      ! [A: nat,B: nat,C: nat] :
% 0.30/0.58        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 0.30/0.58        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_right_eq
% 0.30/0.58  thf(fact_5038_mod__mult__right__eq,axiom,
% 0.30/0.58      ! [A: int,B: int,C: int] :
% 0.30/0.58        ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 0.30/0.58        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_right_eq
% 0.30/0.58  thf(fact_5039_mod__mult__right__eq,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.58        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 0.30/0.58        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_right_eq
% 0.30/0.58  thf(fact_5040_mod__mult__right__eq,axiom,
% 0.30/0.58      ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.30/0.58        ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ ( modulo8411746178871703098atural @ B @ C ) ) @ C )
% 0.30/0.58        = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_right_eq
% 0.30/0.58  thf(fact_5041_mod__minus__eq,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 0.30/0.58        = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_minus_eq
% 0.30/0.58  thf(fact_5042_mod__minus__eq,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 0.30/0.58        = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_minus_eq
% 0.30/0.58  thf(fact_5043_mod__minus__cong,axiom,
% 0.30/0.58      ! [A: int,B: int,A5: int] :
% 0.30/0.58        ( ( ( modulo_modulo_int @ A @ B )
% 0.30/0.58          = ( modulo_modulo_int @ A5 @ B ) )
% 0.30/0.58       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 0.30/0.58          = ( modulo_modulo_int @ ( uminus_uminus_int @ A5 ) @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_minus_cong
% 0.30/0.58  thf(fact_5044_mod__minus__cong,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer,A5: code_integer] :
% 0.30/0.58        ( ( ( modulo364778990260209775nteger @ A @ B )
% 0.30/0.58          = ( modulo364778990260209775nteger @ A5 @ B ) )
% 0.30/0.58       => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.30/0.58          = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A5 ) @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_minus_cong
% 0.30/0.58  thf(fact_5045_mod__minus__right,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 0.30/0.58        = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_minus_right
% 0.30/0.58  thf(fact_5046_mod__minus__right,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.30/0.58        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_minus_right
% 0.30/0.58  thf(fact_5047_split__cong,axiom,
% 0.30/0.58      ! [Q4: product_prod_nat_nat,F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,P4: product_prod_nat_nat] :
% 0.30/0.58        ( ! [X2: nat,Y2: nat] :
% 0.30/0.58            ( ( ( product_Pair_nat_nat @ X2 @ Y2 )
% 0.30/0.58              = Q4 )
% 0.30/0.58           => ( ( F2 @ X2 @ Y2 )
% 0.30/0.58              = ( G2 @ X2 @ Y2 ) ) )
% 0.30/0.58       => ( ( P4 = Q4 )
% 0.30/0.58         => ( ( produc27273713700761075at_nat @ F2 @ P4 )
% 0.30/0.58            = ( produc27273713700761075at_nat @ G2 @ Q4 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % split_cong
% 0.30/0.58  thf(fact_5048_split__cong,axiom,
% 0.30/0.58      ! [Q4: product_prod_nat_nat,F2: nat > nat > product_prod_nat_nat > $o,G2: nat > nat > product_prod_nat_nat > $o,P4: product_prod_nat_nat] :
% 0.30/0.58        ( ! [X2: nat,Y2: nat] :
% 0.30/0.58            ( ( ( product_Pair_nat_nat @ X2 @ Y2 )
% 0.30/0.58              = Q4 )
% 0.30/0.58           => ( ( F2 @ X2 @ Y2 )
% 0.30/0.58              = ( G2 @ X2 @ Y2 ) ) )
% 0.30/0.58       => ( ( P4 = Q4 )
% 0.30/0.58         => ( ( produc8739625826339149834_nat_o @ F2 @ P4 )
% 0.30/0.58            = ( produc8739625826339149834_nat_o @ G2 @ Q4 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % split_cong
% 0.30/0.58  thf(fact_5049_split__cong,axiom,
% 0.30/0.58      ! [Q4: product_prod_int_int,F2: int > int > product_prod_int_int,G2: int > int > product_prod_int_int,P4: product_prod_int_int] :
% 0.30/0.58        ( ! [X2: int,Y2: int] :
% 0.30/0.58            ( ( ( product_Pair_int_int @ X2 @ Y2 )
% 0.30/0.58              = Q4 )
% 0.30/0.58           => ( ( F2 @ X2 @ Y2 )
% 0.30/0.58              = ( G2 @ X2 @ Y2 ) ) )
% 0.30/0.58       => ( ( P4 = Q4 )
% 0.30/0.58         => ( ( produc4245557441103728435nt_int @ F2 @ P4 )
% 0.30/0.58            = ( produc4245557441103728435nt_int @ G2 @ Q4 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % split_cong
% 0.30/0.58  thf(fact_5050_split__cong,axiom,
% 0.30/0.58      ! [Q4: product_prod_int_int,F2: int > int > $o,G2: int > int > $o,P4: product_prod_int_int] :
% 0.30/0.58        ( ! [X2: int,Y2: int] :
% 0.30/0.58            ( ( ( product_Pair_int_int @ X2 @ Y2 )
% 0.30/0.58              = Q4 )
% 0.30/0.58           => ( ( F2 @ X2 @ Y2 )
% 0.30/0.58              = ( G2 @ X2 @ Y2 ) ) )
% 0.30/0.58       => ( ( P4 = Q4 )
% 0.30/0.58         => ( ( produc4947309494688390418_int_o @ F2 @ P4 )
% 0.30/0.58            = ( produc4947309494688390418_int_o @ G2 @ Q4 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % split_cong
% 0.30/0.58  thf(fact_5051_split__cong,axiom,
% 0.30/0.58      ! [Q4: product_prod_int_int,F2: int > int > int,G2: int > int > int,P4: product_prod_int_int] :
% 0.30/0.58        ( ! [X2: int,Y2: int] :
% 0.30/0.58            ( ( ( product_Pair_int_int @ X2 @ Y2 )
% 0.30/0.58              = Q4 )
% 0.30/0.58           => ( ( F2 @ X2 @ Y2 )
% 0.30/0.58              = ( G2 @ X2 @ Y2 ) ) )
% 0.30/0.58       => ( ( P4 = Q4 )
% 0.30/0.58         => ( ( produc8211389475949308722nt_int @ F2 @ P4 )
% 0.30/0.58            = ( produc8211389475949308722nt_int @ G2 @ Q4 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % split_cong
% 0.30/0.58  thf(fact_5052_old_Oprod_Ocase,axiom,
% 0.30/0.58      ! [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X22: nat] :
% 0.30/0.58        ( ( produc27273713700761075at_nat @ F2 @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 0.30/0.58        = ( F2 @ X1 @ X22 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % old.prod.case
% 0.30/0.58  thf(fact_5053_old_Oprod_Ocase,axiom,
% 0.30/0.58      ! [F2: nat > nat > product_prod_nat_nat > $o,X1: nat,X22: nat] :
% 0.30/0.58        ( ( produc8739625826339149834_nat_o @ F2 @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 0.30/0.58        = ( F2 @ X1 @ X22 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % old.prod.case
% 0.30/0.58  thf(fact_5054_old_Oprod_Ocase,axiom,
% 0.30/0.58      ! [F2: int > int > product_prod_int_int,X1: int,X22: int] :
% 0.30/0.58        ( ( produc4245557441103728435nt_int @ F2 @ ( product_Pair_int_int @ X1 @ X22 ) )
% 0.30/0.58        = ( F2 @ X1 @ X22 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % old.prod.case
% 0.30/0.58  thf(fact_5055_old_Oprod_Ocase,axiom,
% 0.30/0.58      ! [F2: int > int > $o,X1: int,X22: int] :
% 0.30/0.58        ( ( produc4947309494688390418_int_o @ F2 @ ( product_Pair_int_int @ X1 @ X22 ) )
% 0.30/0.58        = ( F2 @ X1 @ X22 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % old.prod.case
% 0.30/0.58  thf(fact_5056_old_Oprod_Ocase,axiom,
% 0.30/0.58      ! [F2: int > int > int,X1: int,X22: int] :
% 0.30/0.58        ( ( produc8211389475949308722nt_int @ F2 @ ( product_Pair_int_int @ X1 @ X22 ) )
% 0.30/0.58        = ( F2 @ X1 @ X22 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % old.prod.case
% 0.30/0.58  thf(fact_5057_case__prod__Pair__iden,axiom,
% 0.30/0.58      ! [P4: produc1908205239877642774nteger] :
% 0.30/0.58        ( ( produc6512950862096126219nteger @ produc8603105652947943368nteger @ P4 )
% 0.30/0.58        = P4 ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prod_Pair_iden
% 0.30/0.58  thf(fact_5058_case__prod__Pair__iden,axiom,
% 0.30/0.58      ! [P4: produc3925858234332021118et_nat] :
% 0.30/0.58        ( ( produc4058941399401191971et_nat @ produc5001842942810119800et_nat @ P4 )
% 0.30/0.58        = P4 ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prod_Pair_iden
% 0.30/0.58  thf(fact_5059_case__prod__Pair__iden,axiom,
% 0.30/0.58      ! [P4: produc2732055786443039994et_nat] :
% 0.30/0.58        ( ( produc2377985495875741467et_nat @ produc2245416461498447860et_nat @ P4 )
% 0.30/0.58        = P4 ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prod_Pair_iden
% 0.30/0.58  thf(fact_5060_case__prod__Pair__iden,axiom,
% 0.30/0.58      ! [P4: produc2285326912895808259nt_int] :
% 0.30/0.58        ( ( produc8492565224438309093nt_int @ produc5700946648718959541nt_int @ P4 )
% 0.30/0.58        = P4 ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prod_Pair_iden
% 0.30/0.58  thf(fact_5061_case__prod__Pair__iden,axiom,
% 0.30/0.58      ! [P4: produc7773217078559923341nt_int] :
% 0.30/0.58        ( ( produc5122537100556696953nt_int @ produc4305682042979456191nt_int @ P4 )
% 0.30/0.58        = P4 ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prod_Pair_iden
% 0.30/0.58  thf(fact_5062_case__prod__Pair__iden,axiom,
% 0.30/0.58      ! [P4: product_prod_int_int] :
% 0.30/0.58        ( ( produc4245557441103728435nt_int @ product_Pair_int_int @ P4 )
% 0.30/0.58        = P4 ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prod_Pair_iden
% 0.30/0.58  thf(fact_5063_case__prodE2,axiom,
% 0.30/0.58      ! [Q2: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,P: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Z: product_prod_nat_nat] :
% 0.30/0.58        ( ( Q2 @ ( produc27273713700761075at_nat @ P @ Z ) )
% 0.30/0.58       => ~ ! [X2: nat,Y2: nat] :
% 0.30/0.58              ( ( Z
% 0.30/0.58                = ( product_Pair_nat_nat @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( Q2 @ ( P @ X2 @ Y2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodE2
% 0.30/0.58  thf(fact_5064_case__prodE2,axiom,
% 0.30/0.58      ! [Q2: ( product_prod_nat_nat > $o ) > $o,P: nat > nat > product_prod_nat_nat > $o,Z: product_prod_nat_nat] :
% 0.30/0.58        ( ( Q2 @ ( produc8739625826339149834_nat_o @ P @ Z ) )
% 0.30/0.58       => ~ ! [X2: nat,Y2: nat] :
% 0.30/0.58              ( ( Z
% 0.30/0.58                = ( product_Pair_nat_nat @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( Q2 @ ( P @ X2 @ Y2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodE2
% 0.30/0.58  thf(fact_5065_case__prodE2,axiom,
% 0.30/0.58      ! [Q2: product_prod_int_int > $o,P: int > int > product_prod_int_int,Z: product_prod_int_int] :
% 0.30/0.58        ( ( Q2 @ ( produc4245557441103728435nt_int @ P @ Z ) )
% 0.30/0.58       => ~ ! [X2: int,Y2: int] :
% 0.30/0.58              ( ( Z
% 0.30/0.58                = ( product_Pair_int_int @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( Q2 @ ( P @ X2 @ Y2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodE2
% 0.30/0.58  thf(fact_5066_case__prodE2,axiom,
% 0.30/0.58      ! [Q2: $o > $o,P: int > int > $o,Z: product_prod_int_int] :
% 0.30/0.58        ( ( Q2 @ ( produc4947309494688390418_int_o @ P @ Z ) )
% 0.30/0.58       => ~ ! [X2: int,Y2: int] :
% 0.30/0.58              ( ( Z
% 0.30/0.58                = ( product_Pair_int_int @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( Q2 @ ( P @ X2 @ Y2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodE2
% 0.30/0.58  thf(fact_5067_case__prodE2,axiom,
% 0.30/0.58      ! [Q2: int > $o,P: int > int > int,Z: product_prod_int_int] :
% 0.30/0.58        ( ( Q2 @ ( produc8211389475949308722nt_int @ P @ Z ) )
% 0.30/0.58       => ~ ! [X2: int,Y2: int] :
% 0.30/0.58              ( ( Z
% 0.30/0.58                = ( product_Pair_int_int @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( Q2 @ ( P @ X2 @ Y2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodE2
% 0.30/0.58  thf(fact_5068_case__prod__eta,axiom,
% 0.30/0.58      ! [F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 0.30/0.58        ( ( produc27273713700761075at_nat
% 0.30/0.58          @ ^ [X3: nat,Y3: nat] : ( F2 @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 0.30/0.58        = F2 ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prod_eta
% 0.30/0.58  thf(fact_5069_case__prod__eta,axiom,
% 0.30/0.58      ! [F2: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.30/0.58        ( ( produc8739625826339149834_nat_o
% 0.30/0.58          @ ^ [X3: nat,Y3: nat] : ( F2 @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 0.30/0.58        = F2 ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prod_eta
% 0.30/0.58  thf(fact_5070_case__prod__eta,axiom,
% 0.30/0.58      ! [F2: product_prod_int_int > product_prod_int_int] :
% 0.30/0.58        ( ( produc4245557441103728435nt_int
% 0.30/0.58          @ ^ [X3: int,Y3: int] : ( F2 @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 0.30/0.58        = F2 ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prod_eta
% 0.30/0.58  thf(fact_5071_case__prod__eta,axiom,
% 0.30/0.58      ! [F2: product_prod_int_int > $o] :
% 0.30/0.58        ( ( produc4947309494688390418_int_o
% 0.30/0.58          @ ^ [X3: int,Y3: int] : ( F2 @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 0.30/0.58        = F2 ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prod_eta
% 0.30/0.58  thf(fact_5072_case__prod__eta,axiom,
% 0.30/0.58      ! [F2: product_prod_int_int > int] :
% 0.30/0.58        ( ( produc8211389475949308722nt_int
% 0.30/0.58          @ ^ [X3: int,Y3: int] : ( F2 @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 0.30/0.58        = F2 ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prod_eta
% 0.30/0.58  thf(fact_5073_cond__case__prod__eta,axiom,
% 0.30/0.58      ! [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 0.30/0.58        ( ! [X2: nat,Y2: nat] :
% 0.30/0.58            ( ( F2 @ X2 @ Y2 )
% 0.30/0.58            = ( G2 @ ( product_Pair_nat_nat @ X2 @ Y2 ) ) )
% 0.30/0.58       => ( ( produc27273713700761075at_nat @ F2 )
% 0.30/0.58          = G2 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % cond_case_prod_eta
% 0.30/0.58  thf(fact_5074_cond__case__prod__eta,axiom,
% 0.30/0.58      ! [F2: nat > nat > product_prod_nat_nat > $o,G2: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.30/0.58        ( ! [X2: nat,Y2: nat] :
% 0.30/0.58            ( ( F2 @ X2 @ Y2 )
% 0.30/0.58            = ( G2 @ ( product_Pair_nat_nat @ X2 @ Y2 ) ) )
% 0.30/0.58       => ( ( produc8739625826339149834_nat_o @ F2 )
% 0.30/0.58          = G2 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % cond_case_prod_eta
% 0.30/0.58  thf(fact_5075_cond__case__prod__eta,axiom,
% 0.30/0.58      ! [F2: int > int > product_prod_int_int,G2: product_prod_int_int > product_prod_int_int] :
% 0.30/0.58        ( ! [X2: int,Y2: int] :
% 0.30/0.58            ( ( F2 @ X2 @ Y2 )
% 0.30/0.58            = ( G2 @ ( product_Pair_int_int @ X2 @ Y2 ) ) )
% 0.30/0.58       => ( ( produc4245557441103728435nt_int @ F2 )
% 0.30/0.58          = G2 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % cond_case_prod_eta
% 0.30/0.58  thf(fact_5076_cond__case__prod__eta,axiom,
% 0.30/0.58      ! [F2: int > int > $o,G2: product_prod_int_int > $o] :
% 0.30/0.58        ( ! [X2: int,Y2: int] :
% 0.30/0.58            ( ( F2 @ X2 @ Y2 )
% 0.30/0.58            = ( G2 @ ( product_Pair_int_int @ X2 @ Y2 ) ) )
% 0.30/0.58       => ( ( produc4947309494688390418_int_o @ F2 )
% 0.30/0.58          = G2 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % cond_case_prod_eta
% 0.30/0.58  thf(fact_5077_cond__case__prod__eta,axiom,
% 0.30/0.58      ! [F2: int > int > int,G2: product_prod_int_int > int] :
% 0.30/0.58        ( ! [X2: int,Y2: int] :
% 0.30/0.58            ( ( F2 @ X2 @ Y2 )
% 0.30/0.58            = ( G2 @ ( product_Pair_int_int @ X2 @ Y2 ) ) )
% 0.30/0.58       => ( ( produc8211389475949308722nt_int @ F2 )
% 0.30/0.58          = G2 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % cond_case_prod_eta
% 0.30/0.58  thf(fact_5078_mod__eqE,axiom,
% 0.30/0.58      ! [A: int,C: int,B: int] :
% 0.30/0.58        ( ( ( modulo_modulo_int @ A @ C )
% 0.30/0.58          = ( modulo_modulo_int @ B @ C ) )
% 0.30/0.58       => ~ ! [D: int] :
% 0.30/0.58              ( B
% 0.30/0.58             != ( plus_plus_int @ A @ ( times_times_int @ C @ D ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_eqE
% 0.30/0.58  thf(fact_5079_mod__eqE,axiom,
% 0.30/0.58      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.30/0.58        ( ( ( modulo364778990260209775nteger @ A @ C )
% 0.30/0.58          = ( modulo364778990260209775nteger @ B @ C ) )
% 0.30/0.58       => ~ ! [D: code_integer] :
% 0.30/0.58              ( B
% 0.30/0.58             != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_eqE
% 0.30/0.58  thf(fact_5080_pos__zmod__mult__2,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.58       => ( ( 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 ) )
% 0.30/0.58          = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % pos_zmod_mult_2
% 0.30/0.58  thf(fact_5081_neg__zmod__mult__2,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.30/0.58       => ( ( 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 ) )
% 0.30/0.58          = ( 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 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % neg_zmod_mult_2
% 0.30/0.58  thf(fact_5082_divmod_H__nat__def,axiom,
% 0.30/0.58      ( unique5055182867167087721od_nat
% 0.30/0.58      = ( ^ [M2: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % divmod'_nat_def
% 0.30/0.58  thf(fact_5083_divmod__step__int__def,axiom,
% 0.30/0.58      ( unique5024387138958732305ep_int
% 0.30/0.58      = ( ^ [L2: num] :
% 0.30/0.58            ( produc4245557441103728435nt_int
% 0.30/0.58            @ ^ [Q5: int,R4: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R4 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R4 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R4 ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % divmod_step_int_def
% 0.30/0.58  thf(fact_5084_uncurry__def,axiom,
% 0.30/0.58      uncurr8011562610307062878at_nat = produc27273713700761075at_nat ).
% 0.30/0.58  
% 0.30/0.58  % uncurry_def
% 0.30/0.58  thf(fact_5085_uncurry__def,axiom,
% 0.30/0.58      uncurr7511940902602773877_nat_o = produc8739625826339149834_nat_o ).
% 0.30/0.58  
% 0.30/0.58  % uncurry_def
% 0.30/0.58  thf(fact_5086_uncurry__def,axiom,
% 0.30/0.58      uncurr7650761721940715016nt_int = produc4245557441103728435nt_int ).
% 0.30/0.58  
% 0.30/0.58  % uncurry_def
% 0.30/0.58  thf(fact_5087_uncurry__def,axiom,
% 0.30/0.58      uncurry_int_int_o = produc4947309494688390418_int_o ).
% 0.30/0.58  
% 0.30/0.58  % uncurry_def
% 0.30/0.58  thf(fact_5088_uncurry__def,axiom,
% 0.30/0.58      uncurry_int_int_int = produc8211389475949308722nt_int ).
% 0.30/0.58  
% 0.30/0.58  % uncurry_def
% 0.30/0.58  thf(fact_5089_xor_Ocomm__monoid__axioms,axiom,
% 0.30/0.58      comm_m1654649897431166824nteger @ bit_se3222712562003087583nteger @ zero_z3403309356797280102nteger ).
% 0.30/0.58  
% 0.30/0.58  % xor.comm_monoid_axioms
% 0.30/0.58  thf(fact_5090_xor_Ocomm__monoid__axioms,axiom,
% 0.30/0.58      comm_monoid_int @ bit_se6526347334894502574or_int @ zero_zero_int ).
% 0.30/0.58  
% 0.30/0.58  % xor.comm_monoid_axioms
% 0.30/0.58  thf(fact_5091_xor_Ocomm__monoid__axioms,axiom,
% 0.30/0.58      comm_monoid_nat @ bit_se6528837805403552850or_nat @ zero_zero_nat ).
% 0.30/0.58  
% 0.30/0.58  % xor.comm_monoid_axioms
% 0.30/0.58  thf(fact_5092_xor_Omonoid__axioms,axiom,
% 0.30/0.58      monoid_Code_integer @ bit_se3222712562003087583nteger @ zero_z3403309356797280102nteger ).
% 0.30/0.58  
% 0.30/0.58  % xor.monoid_axioms
% 0.30/0.58  thf(fact_5093_xor_Omonoid__axioms,axiom,
% 0.30/0.58      monoid_int @ bit_se6526347334894502574or_int @ zero_zero_int ).
% 0.30/0.58  
% 0.30/0.58  % xor.monoid_axioms
% 0.30/0.58  thf(fact_5094_xor_Omonoid__axioms,axiom,
% 0.30/0.58      monoid_nat @ bit_se6528837805403552850or_nat @ zero_zero_nat ).
% 0.30/0.58  
% 0.30/0.58  % xor.monoid_axioms
% 0.30/0.58  thf(fact_5095_mult__div__mod__eq,axiom,
% 0.30/0.58      ! [B: nat,A: nat] :
% 0.30/0.58        ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % mult_div_mod_eq
% 0.30/0.58  thf(fact_5096_mult__div__mod__eq,axiom,
% 0.30/0.58      ! [B: int,A: int] :
% 0.30/0.58        ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % mult_div_mod_eq
% 0.30/0.58  thf(fact_5097_mult__div__mod__eq,axiom,
% 0.30/0.58      ! [B: code_integer,A: code_integer] :
% 0.30/0.58        ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % mult_div_mod_eq
% 0.30/0.58  thf(fact_5098_mult__div__mod__eq,axiom,
% 0.30/0.58      ! [B: code_natural,A: code_natural] :
% 0.30/0.58        ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % mult_div_mod_eq
% 0.30/0.58  thf(fact_5099_mod__mult__div__eq,axiom,
% 0.30/0.58      ! [A: nat,B: nat] :
% 0.30/0.58        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_div_eq
% 0.30/0.58  thf(fact_5100_mod__mult__div__eq,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_div_eq
% 0.30/0.58  thf(fact_5101_mod__mult__div__eq,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_div_eq
% 0.30/0.58  thf(fact_5102_mod__mult__div__eq,axiom,
% 0.30/0.58      ! [A: code_natural,B: code_natural] :
% 0.30/0.58        ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_mult_div_eq
% 0.30/0.58  thf(fact_5103_mod__div__mult__eq,axiom,
% 0.30/0.58      ! [A: nat,B: nat] :
% 0.30/0.58        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_div_mult_eq
% 0.30/0.58  thf(fact_5104_mod__div__mult__eq,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_div_mult_eq
% 0.30/0.58  thf(fact_5105_mod__div__mult__eq,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_div_mult_eq
% 0.30/0.58  thf(fact_5106_mod__div__mult__eq,axiom,
% 0.30/0.58      ! [A: code_natural,B: code_natural] :
% 0.30/0.58        ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_div_mult_eq
% 0.30/0.58  thf(fact_5107_div__mult__mod__eq,axiom,
% 0.30/0.58      ! [A: nat,B: nat] :
% 0.30/0.58        ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % div_mult_mod_eq
% 0.30/0.58  thf(fact_5108_div__mult__mod__eq,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % div_mult_mod_eq
% 0.30/0.58  thf(fact_5109_div__mult__mod__eq,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % div_mult_mod_eq
% 0.30/0.58  thf(fact_5110_div__mult__mod__eq,axiom,
% 0.30/0.58      ! [A: code_natural,B: code_natural] :
% 0.30/0.58        ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % div_mult_mod_eq
% 0.30/0.58  thf(fact_5111_mod__div__decomp,axiom,
% 0.30/0.58      ! [A: nat,B: nat] :
% 0.30/0.58        ( A
% 0.30/0.58        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_div_decomp
% 0.30/0.58  thf(fact_5112_mod__div__decomp,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( A
% 0.30/0.58        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_div_decomp
% 0.30/0.58  thf(fact_5113_mod__div__decomp,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( A
% 0.30/0.58        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_div_decomp
% 0.30/0.58  thf(fact_5114_mod__div__decomp,axiom,
% 0.30/0.58      ! [A: code_natural,B: code_natural] :
% 0.30/0.58        ( A
% 0.30/0.58        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_div_decomp
% 0.30/0.58  thf(fact_5115_cancel__div__mod__rules_I1_J,axiom,
% 0.30/0.58      ! [A: nat,B: nat,C: nat] :
% 0.30/0.58        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 0.30/0.58        = ( plus_plus_nat @ A @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % cancel_div_mod_rules(1)
% 0.30/0.58  thf(fact_5116_cancel__div__mod__rules_I1_J,axiom,
% 0.30/0.58      ! [A: int,B: int,C: int] :
% 0.30/0.58        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 0.30/0.58        = ( plus_plus_int @ A @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % cancel_div_mod_rules(1)
% 0.30/0.58  thf(fact_5117_cancel__div__mod__rules_I1_J,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.58        ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 0.30/0.58        = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % cancel_div_mod_rules(1)
% 0.30/0.58  thf(fact_5118_cancel__div__mod__rules_I1_J,axiom,
% 0.30/0.58      ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.30/0.58        ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C )
% 0.30/0.58        = ( plus_p4538020629002901425atural @ A @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % cancel_div_mod_rules(1)
% 0.30/0.58  thf(fact_5119_cancel__div__mod__rules_I2_J,axiom,
% 0.30/0.58      ! [B: nat,A: nat,C: nat] :
% 0.30/0.58        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 0.30/0.58        = ( plus_plus_nat @ A @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % cancel_div_mod_rules(2)
% 0.30/0.58  thf(fact_5120_cancel__div__mod__rules_I2_J,axiom,
% 0.30/0.58      ! [B: int,A: int,C: int] :
% 0.30/0.58        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 0.30/0.58        = ( plus_plus_int @ A @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % cancel_div_mod_rules(2)
% 0.30/0.58  thf(fact_5121_cancel__div__mod__rules_I2_J,axiom,
% 0.30/0.58      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.30/0.58        ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 0.30/0.58        = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % cancel_div_mod_rules(2)
% 0.30/0.58  thf(fact_5122_cancel__div__mod__rules_I2_J,axiom,
% 0.30/0.58      ! [B: code_natural,A: code_natural,C: code_natural] :
% 0.30/0.58        ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C )
% 0.30/0.58        = ( plus_p4538020629002901425atural @ A @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % cancel_div_mod_rules(2)
% 0.30/0.58  thf(fact_5123_div__mult1__eq,axiom,
% 0.30/0.58      ! [A: nat,B: nat,C: nat] :
% 0.30/0.58        ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.30/0.58        = ( 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 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % div_mult1_eq
% 0.30/0.58  thf(fact_5124_div__mult1__eq,axiom,
% 0.30/0.58      ! [A: int,B: int,C: int] :
% 0.30/0.58        ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 0.30/0.58        = ( 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 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % div_mult1_eq
% 0.30/0.58  thf(fact_5125_div__mult1__eq,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.58        ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.30/0.58        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % div_mult1_eq
% 0.30/0.58  thf(fact_5126_div__mult1__eq,axiom,
% 0.30/0.58      ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.30/0.58        ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C )
% 0.30/0.58        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C ) ) @ ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ ( modulo8411746178871703098atural @ B @ C ) ) @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % div_mult1_eq
% 0.30/0.58  thf(fact_5127_minus__mult__div__eq__mod,axiom,
% 0.30/0.58      ! [A: nat,B: nat] :
% 0.30/0.58        ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 0.30/0.58        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_mult_div_eq_mod
% 0.30/0.58  thf(fact_5128_minus__mult__div__eq__mod,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 0.30/0.58        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_mult_div_eq_mod
% 0.30/0.58  thf(fact_5129_minus__mult__div__eq__mod,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 0.30/0.58        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_mult_div_eq_mod
% 0.30/0.58  thf(fact_5130_minus__mult__div__eq__mod,axiom,
% 0.30/0.58      ! [A: code_natural,B: code_natural] :
% 0.30/0.58        ( ( minus_7197305767214868737atural @ A @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) )
% 0.30/0.58        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_mult_div_eq_mod
% 0.30/0.58  thf(fact_5131_minus__mod__eq__mult__div,axiom,
% 0.30/0.58      ! [A: nat,B: nat] :
% 0.30/0.58        ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 0.30/0.58        = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_mod_eq_mult_div
% 0.30/0.58  thf(fact_5132_minus__mod__eq__mult__div,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 0.30/0.58        = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_mod_eq_mult_div
% 0.30/0.58  thf(fact_5133_minus__mod__eq__mult__div,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.30/0.58        = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_mod_eq_mult_div
% 0.30/0.58  thf(fact_5134_minus__mod__eq__mult__div,axiom,
% 0.30/0.58      ! [A: code_natural,B: code_natural] :
% 0.30/0.58        ( ( minus_7197305767214868737atural @ A @ ( modulo8411746178871703098atural @ A @ B ) )
% 0.30/0.58        = ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_mod_eq_mult_div
% 0.30/0.58  thf(fact_5135_minus__mod__eq__div__mult,axiom,
% 0.30/0.58      ! [A: nat,B: nat] :
% 0.30/0.58        ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 0.30/0.58        = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_mod_eq_div_mult
% 0.30/0.58  thf(fact_5136_minus__mod__eq__div__mult,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 0.30/0.58        = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_mod_eq_div_mult
% 0.30/0.58  thf(fact_5137_minus__mod__eq__div__mult,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 0.30/0.58        = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_mod_eq_div_mult
% 0.30/0.58  thf(fact_5138_minus__mod__eq__div__mult,axiom,
% 0.30/0.58      ! [A: code_natural,B: code_natural] :
% 0.30/0.58        ( ( minus_7197305767214868737atural @ A @ ( modulo8411746178871703098atural @ A @ B ) )
% 0.30/0.58        = ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_mod_eq_div_mult
% 0.30/0.58  thf(fact_5139_minus__div__mult__eq__mod,axiom,
% 0.30/0.58      ! [A: nat,B: nat] :
% 0.30/0.58        ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 0.30/0.58        = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_div_mult_eq_mod
% 0.30/0.58  thf(fact_5140_minus__div__mult__eq__mod,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 0.30/0.58        = ( modulo_modulo_int @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_div_mult_eq_mod
% 0.30/0.58  thf(fact_5141_minus__div__mult__eq__mod,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 0.30/0.58        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_div_mult_eq_mod
% 0.30/0.58  thf(fact_5142_minus__div__mult__eq__mod,axiom,
% 0.30/0.58      ! [A: code_natural,B: code_natural] :
% 0.30/0.58        ( ( minus_7197305767214868737atural @ A @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) )
% 0.30/0.58        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_div_mult_eq_mod
% 0.30/0.58  thf(fact_5143_divmod__def,axiom,
% 0.30/0.58      ( unique5052692396658037445od_int
% 0.30/0.58      = ( ^ [M2: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % divmod_def
% 0.30/0.58  thf(fact_5144_divmod__def,axiom,
% 0.30/0.58      ( unique5055182867167087721od_nat
% 0.30/0.58      = ( ^ [M2: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % divmod_def
% 0.30/0.58  thf(fact_5145_divmod__def,axiom,
% 0.30/0.58      ( unique3479559517661332726nteger
% 0.30/0.58      = ( ^ [M2: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % divmod_def
% 0.30/0.58  thf(fact_5146_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.30/0.58      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 0.30/0.58       => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.30/0.58          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.30/0.58  thf(fact_5147_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.30/0.58      ! [C: nat,A: nat,B: nat] :
% 0.30/0.58        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 0.30/0.58       => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.30/0.58          = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.30/0.58  thf(fact_5148_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.30/0.58      ! [C: int,A: int,B: int] :
% 0.30/0.58        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 0.30/0.58       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 0.30/0.58          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.30/0.58  thf(fact_5149_verit__le__mono__div,axiom,
% 0.30/0.58      ! [A2: nat,B2: nat,N: nat] :
% 0.30/0.58        ( ( ord_less_nat @ A2 @ B2 )
% 0.30/0.58       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58         => ( ord_less_eq_nat
% 0.30/0.58            @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N )
% 0.30/0.58              @ ( if_nat
% 0.30/0.58                @ ( ( modulo_modulo_nat @ B2 @ N )
% 0.30/0.58                  = zero_zero_nat )
% 0.30/0.58                @ one_one_nat
% 0.30/0.58                @ zero_zero_nat ) )
% 0.30/0.58            @ ( divide_divide_nat @ B2 @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % verit_le_mono_div
% 0.30/0.58  thf(fact_5150_divmod__step__nat__def,axiom,
% 0.30/0.58      ( unique5026877609467782581ep_nat
% 0.30/0.58      = ( ^ [L2: num] :
% 0.30/0.58            ( produc2626176000494625587at_nat
% 0.30/0.58            @ ^ [Q5: nat,R4: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R4 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R4 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R4 ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % divmod_step_nat_def
% 0.30/0.58  thf(fact_5151_divmod__digit__0_I2_J,axiom,
% 0.30/0.58      ! [B: nat,A: nat] :
% 0.30/0.58        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.30/0.58       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.30/0.58         => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 0.30/0.58            = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % divmod_digit_0(2)
% 0.30/0.58  thf(fact_5152_divmod__digit__0_I2_J,axiom,
% 0.30/0.58      ! [B: int,A: int] :
% 0.30/0.58        ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.58       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.30/0.58         => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 0.30/0.58            = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % divmod_digit_0(2)
% 0.30/0.58  thf(fact_5153_divmod__digit__0_I2_J,axiom,
% 0.30/0.58      ! [B: code_integer,A: code_integer] :
% 0.30/0.58        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.30/0.58       => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.30/0.58         => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 0.30/0.58            = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % divmod_digit_0(2)
% 0.30/0.58  thf(fact_5154_divmod__digit__0_I1_J,axiom,
% 0.30/0.58      ! [B: nat,A: nat] :
% 0.30/0.58        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.30/0.58       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.30/0.58         => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.30/0.58            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % divmod_digit_0(1)
% 0.30/0.58  thf(fact_5155_divmod__digit__0_I1_J,axiom,
% 0.30/0.58      ! [B: int,A: int] :
% 0.30/0.58        ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.58       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.30/0.58         => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.30/0.58            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % divmod_digit_0(1)
% 0.30/0.58  thf(fact_5156_divmod__digit__0_I1_J,axiom,
% 0.30/0.58      ! [B: code_integer,A: code_integer] :
% 0.30/0.58        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.30/0.58       => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.30/0.58         => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 0.30/0.58            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % divmod_digit_0(1)
% 0.30/0.58  thf(fact_5157_mod__double__modulus,axiom,
% 0.30/0.58      ! [M: code_integer,X: code_integer] :
% 0.30/0.58        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 0.30/0.58       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 0.30/0.58         => ( ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 0.30/0.58              = ( modulo364778990260209775nteger @ X @ M ) )
% 0.30/0.58            | ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 0.30/0.58              = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X @ M ) @ M ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_double_modulus
% 0.30/0.58  thf(fact_5158_mod__double__modulus,axiom,
% 0.30/0.58      ! [M: nat,X: nat] :
% 0.30/0.58        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.30/0.58       => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 0.30/0.58         => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.30/0.58              = ( modulo_modulo_nat @ X @ M ) )
% 0.30/0.58            | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.30/0.58              = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M ) @ M ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_double_modulus
% 0.30/0.58  thf(fact_5159_mod__double__modulus,axiom,
% 0.30/0.58      ! [M: int,X: int] :
% 0.30/0.58        ( ( ord_less_int @ zero_zero_int @ M )
% 0.30/0.58       => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.30/0.58         => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 0.30/0.58              = ( modulo_modulo_int @ X @ M ) )
% 0.30/0.58            | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 0.30/0.58              = ( plus_plus_int @ ( modulo_modulo_int @ X @ M ) @ M ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_double_modulus
% 0.30/0.58  thf(fact_5160_divmod__digit__1_I2_J,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.58       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.30/0.58         => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 0.30/0.58           => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.30/0.58              = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % divmod_digit_1(2)
% 0.30/0.58  thf(fact_5161_divmod__digit__1_I2_J,axiom,
% 0.30/0.58      ! [A: nat,B: nat] :
% 0.30/0.58        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.58       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.30/0.58         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.30/0.58           => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.30/0.58              = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % divmod_digit_1(2)
% 0.30/0.58  thf(fact_5162_divmod__digit__1_I2_J,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.58       => ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.58         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.30/0.58           => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.30/0.58              = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % divmod_digit_1(2)
% 0.30/0.58  thf(fact_5163_zle__add1__eq__le,axiom,
% 0.30/0.58      ! [W: int,Z: int] :
% 0.30/0.58        ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 0.30/0.58        = ( ord_less_eq_int @ W @ Z ) ) ).
% 0.30/0.58  
% 0.30/0.58  % zle_add1_eq_le
% 0.30/0.58  thf(fact_5164_zle__diff1__eq,axiom,
% 0.30/0.58      ! [W: int,Z: int] :
% 0.30/0.58        ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 0.30/0.58        = ( ord_less_int @ W @ Z ) ) ).
% 0.30/0.58  
% 0.30/0.58  % zle_diff1_eq
% 0.30/0.58  thf(fact_5165_one__div__minus__numeral,axiom,
% 0.30/0.58      ! [N: num] :
% 0.30/0.58        ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.58        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % one_div_minus_numeral
% 0.30/0.58  thf(fact_5166_minus__one__div__numeral,axiom,
% 0.30/0.58      ! [N: num] :
% 0.30/0.58        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 0.30/0.58        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_one_div_numeral
% 0.30/0.58  thf(fact_5167_le__imp__0__less,axiom,
% 0.30/0.58      ! [Z: int] :
% 0.30/0.58        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.30/0.58       => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % le_imp_0_less
% 0.30/0.58  thf(fact_5168_signed__take__bit__rec,axiom,
% 0.30/0.58      ( bit_ri6519982836138164636nteger
% 0.30/0.58      = ( ^ [N2: nat,A3: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % signed_take_bit_rec
% 0.30/0.58  thf(fact_5169_signed__take__bit__rec,axiom,
% 0.30/0.58      ( bit_ri631733984087533419it_int
% 0.30/0.58      = ( ^ [N2: nat,A3: int] : ( if_int @ ( N2 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % signed_take_bit_rec
% 0.30/0.58  thf(fact_5170_numeral__div__minus__numeral,axiom,
% 0.30/0.58      ! [M: num,N: num] :
% 0.30/0.58        ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.58        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % numeral_div_minus_numeral
% 0.30/0.58  thf(fact_5171_minus__numeral__div__numeral,axiom,
% 0.30/0.58      ! [M: num,N: num] :
% 0.30/0.58        ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.30/0.58        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_numeral_div_numeral
% 0.30/0.58  thf(fact_5172_case__prodI2,axiom,
% 0.30/0.58      ! [P4: produc1908205239877642774nteger,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o] :
% 0.30/0.58        ( ! [A6: produc6241069584506657477e_term > option6357759511663192854e_term,B6: produc8923325533196201883nteger] :
% 0.30/0.58            ( ( P4
% 0.30/0.58              = ( produc8603105652947943368nteger @ A6 @ B6 ) )
% 0.30/0.58           => ( C @ A6 @ B6 ) )
% 0.30/0.58       => ( produc6253627499356882019eger_o @ C @ P4 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodI2
% 0.30/0.58  thf(fact_5173_case__prodI2,axiom,
% 0.30/0.58      ! [P4: produc3925858234332021118et_nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 0.30/0.58        ( ! [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat] :
% 0.30/0.58            ( ( P4
% 0.30/0.58              = ( produc5001842942810119800et_nat @ A6 @ B6 ) )
% 0.30/0.58           => ( C @ A6 @ B6 ) )
% 0.30/0.58       => ( produc1437786849005270451_nat_o @ C @ P4 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodI2
% 0.30/0.58  thf(fact_5174_case__prodI2,axiom,
% 0.30/0.58      ! [P4: produc2732055786443039994et_nat,C: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 0.30/0.58        ( ! [A6: produc3658429121746597890et_nat > $o,B6: produc3925858234332021118et_nat] :
% 0.30/0.58            ( ( P4
% 0.30/0.58              = ( produc2245416461498447860et_nat @ A6 @ B6 ) )
% 0.30/0.58           => ( C @ A6 @ B6 ) )
% 0.30/0.58       => ( produc838355143741117751_nat_o @ C @ P4 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodI2
% 0.30/0.58  thf(fact_5175_case__prodI2,axiom,
% 0.30/0.58      ! [P4: produc2285326912895808259nt_int,C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 0.30/0.58        ( ! [A6: produc8551481072490612790e_term > option6357759511663192854e_term,B6: product_prod_int_int] :
% 0.30/0.58            ( ( P4
% 0.30/0.58              = ( produc5700946648718959541nt_int @ A6 @ B6 ) )
% 0.30/0.58           => ( C @ A6 @ B6 ) )
% 0.30/0.58       => ( produc1573362020775583542_int_o @ C @ P4 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodI2
% 0.30/0.58  thf(fact_5176_case__prodI2,axiom,
% 0.30/0.58      ! [P4: produc7773217078559923341nt_int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 0.30/0.58        ( ! [A6: int > option6357759511663192854e_term,B6: product_prod_int_int] :
% 0.30/0.58            ( ( P4
% 0.30/0.58              = ( produc4305682042979456191nt_int @ A6 @ B6 ) )
% 0.30/0.58           => ( C @ A6 @ B6 ) )
% 0.30/0.58       => ( produc2558449545302689196_int_o @ C @ P4 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodI2
% 0.30/0.58  thf(fact_5177_case__prodI2,axiom,
% 0.30/0.58      ! [P4: product_prod_int_int,C: int > int > $o] :
% 0.30/0.58        ( ! [A6: int,B6: int] :
% 0.30/0.58            ( ( P4
% 0.30/0.58              = ( product_Pair_int_int @ A6 @ B6 ) )
% 0.30/0.58           => ( C @ A6 @ B6 ) )
% 0.30/0.58       => ( produc4947309494688390418_int_o @ C @ P4 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodI2
% 0.30/0.58  thf(fact_5178_case__prodI,axiom,
% 0.30/0.58      ! [F2: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 0.30/0.58        ( ( F2 @ A @ B )
% 0.30/0.58       => ( produc6253627499356882019eger_o @ F2 @ ( produc8603105652947943368nteger @ A @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodI
% 0.30/0.58  thf(fact_5179_case__prodI,axiom,
% 0.30/0.58      ! [F2: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 0.30/0.58        ( ( F2 @ A @ B )
% 0.30/0.58       => ( produc1437786849005270451_nat_o @ F2 @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodI
% 0.30/0.58  thf(fact_5180_case__prodI,axiom,
% 0.30/0.58      ! [F2: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 0.30/0.58        ( ( F2 @ A @ B )
% 0.30/0.58       => ( produc838355143741117751_nat_o @ F2 @ ( produc2245416461498447860et_nat @ A @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodI
% 0.30/0.58  thf(fact_5181_case__prodI,axiom,
% 0.30/0.58      ! [F2: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.30/0.58        ( ( F2 @ A @ B )
% 0.30/0.58       => ( produc1573362020775583542_int_o @ F2 @ ( produc5700946648718959541nt_int @ A @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodI
% 0.30/0.58  thf(fact_5182_case__prodI,axiom,
% 0.30/0.58      ! [F2: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.30/0.58        ( ( F2 @ A @ B )
% 0.30/0.58       => ( produc2558449545302689196_int_o @ F2 @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodI
% 0.30/0.58  thf(fact_5183_case__prodI,axiom,
% 0.30/0.58      ! [F2: int > int > $o,A: int,B: int] :
% 0.30/0.58        ( ( F2 @ A @ B )
% 0.30/0.58       => ( produc4947309494688390418_int_o @ F2 @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodI
% 0.30/0.58  thf(fact_5184_mem__case__prodI2,axiom,
% 0.30/0.58      ! [P4: produc7773217078559923341nt_int,Z: nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat] :
% 0.30/0.58        ( ! [A6: int > option6357759511663192854e_term,B6: product_prod_int_int] :
% 0.30/0.58            ( ( P4
% 0.30/0.58              = ( produc4305682042979456191nt_int @ A6 @ B6 ) )
% 0.30/0.58           => ( member_nat @ Z @ ( C @ A6 @ B6 ) ) )
% 0.30/0.58       => ( member_nat @ Z @ ( produc8289552606927098482et_nat @ C @ P4 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodI2
% 0.30/0.58  thf(fact_5185_mem__case__prodI2,axiom,
% 0.30/0.58      ! [P4: produc7773217078559923341nt_int,Z: int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_int] :
% 0.30/0.58        ( ! [A6: int > option6357759511663192854e_term,B6: product_prod_int_int] :
% 0.30/0.58            ( ( P4
% 0.30/0.58              = ( produc4305682042979456191nt_int @ A6 @ B6 ) )
% 0.30/0.58           => ( member_int @ Z @ ( C @ A6 @ B6 ) ) )
% 0.30/0.58       => ( member_int @ Z @ ( produc4111701587417901774et_int @ C @ P4 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodI2
% 0.30/0.58  thf(fact_5186_mem__case__prodI2,axiom,
% 0.30/0.58      ! [P4: produc7773217078559923341nt_int,Z: set_nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_set_nat] :
% 0.30/0.58        ( ! [A6: int > option6357759511663192854e_term,B6: product_prod_int_int] :
% 0.30/0.58            ( ( P4
% 0.30/0.58              = ( produc4305682042979456191nt_int @ A6 @ B6 ) )
% 0.30/0.58           => ( member_set_nat @ Z @ ( C @ A6 @ B6 ) ) )
% 0.30/0.58       => ( member_set_nat @ Z @ ( produc3577156405726439208et_nat @ C @ P4 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodI2
% 0.30/0.58  thf(fact_5187_mem__case__prodI2,axiom,
% 0.30/0.58      ! [P4: produc3925858234332021118et_nat,Z: nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_nat] :
% 0.30/0.58        ( ! [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat] :
% 0.30/0.58            ( ( P4
% 0.30/0.58              = ( produc5001842942810119800et_nat @ A6 @ B6 ) )
% 0.30/0.58           => ( member_nat @ Z @ ( C @ A6 @ B6 ) ) )
% 0.30/0.58       => ( member_nat @ Z @ ( produc8805491454895738411et_nat @ C @ P4 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodI2
% 0.30/0.58  thf(fact_5188_mem__case__prodI2,axiom,
% 0.30/0.58      ! [P4: produc3925858234332021118et_nat,Z: int,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_int] :
% 0.30/0.58        ( ! [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat] :
% 0.30/0.58            ( ( P4
% 0.30/0.58              = ( produc5001842942810119800et_nat @ A6 @ B6 ) )
% 0.30/0.58           => ( member_int @ Z @ ( C @ A6 @ B6 ) ) )
% 0.30/0.58       => ( member_int @ Z @ ( produc4627640435386541703et_int @ C @ P4 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodI2
% 0.30/0.58  thf(fact_5189_mem__case__prodI2,axiom,
% 0.30/0.58      ! [P4: produc3925858234332021118et_nat,Z: set_nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_set_nat] :
% 0.30/0.58        ( ! [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat] :
% 0.30/0.58            ( ( P4
% 0.30/0.58              = ( produc5001842942810119800et_nat @ A6 @ B6 ) )
% 0.30/0.58           => ( member_set_nat @ Z @ ( C @ A6 @ B6 ) ) )
% 0.30/0.58       => ( member_set_nat @ Z @ ( produc2333231157791014625et_nat @ C @ P4 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodI2
% 0.30/0.58  thf(fact_5190_mem__case__prodI2,axiom,
% 0.30/0.58      ! [P4: produc7773217078559923341nt_int,Z: set_Pr958786334691620121nt_int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_se6260736226359567993nt_int] :
% 0.30/0.58        ( ! [A6: int > option6357759511663192854e_term,B6: product_prod_int_int] :
% 0.30/0.58            ( ( P4
% 0.30/0.58              = ( produc4305682042979456191nt_int @ A6 @ B6 ) )
% 0.30/0.58           => ( member2340774599025711042nt_int @ Z @ ( C @ A6 @ B6 ) ) )
% 0.30/0.58       => ( member2340774599025711042nt_int @ Z @ ( produc575502675617541261nt_int @ C @ P4 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodI2
% 0.30/0.58  thf(fact_5191_mem__case__prodI2,axiom,
% 0.30/0.58      ! [P4: produc1908205239877642774nteger,Z: nat,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat] :
% 0.30/0.58        ( ! [A6: produc6241069584506657477e_term > option6357759511663192854e_term,B6: produc8923325533196201883nteger] :
% 0.30/0.58            ( ( P4
% 0.30/0.58              = ( produc8603105652947943368nteger @ A6 @ B6 ) )
% 0.30/0.58           => ( member_nat @ Z @ ( C @ A6 @ B6 ) ) )
% 0.30/0.58       => ( member_nat @ Z @ ( produc654622801845291899et_nat @ C @ P4 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodI2
% 0.30/0.58  thf(fact_5192_mem__case__prodI2,axiom,
% 0.30/0.58      ! [P4: produc1908205239877642774nteger,Z: int,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int] :
% 0.30/0.58        ( ! [A6: produc6241069584506657477e_term > option6357759511663192854e_term,B6: produc8923325533196201883nteger] :
% 0.30/0.58            ( ( P4
% 0.30/0.58              = ( produc8603105652947943368nteger @ A6 @ B6 ) )
% 0.30/0.58           => ( member_int @ Z @ ( C @ A6 @ B6 ) ) )
% 0.30/0.58       => ( member_int @ Z @ ( produc5700143819190870999et_int @ C @ P4 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodI2
% 0.30/0.58  thf(fact_5193_mem__case__prodI2,axiom,
% 0.30/0.58      ! [P4: produc2285326912895808259nt_int,Z: nat,C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > set_nat] :
% 0.30/0.58        ( ! [A6: produc8551481072490612790e_term > option6357759511663192854e_term,B6: product_prod_int_int] :
% 0.30/0.58            ( ( P4
% 0.30/0.58              = ( produc5700946648718959541nt_int @ A6 @ B6 ) )
% 0.30/0.58           => ( member_nat @ Z @ ( C @ A6 @ B6 ) ) )
% 0.30/0.58       => ( member_nat @ Z @ ( produc3619988815162578792et_nat @ C @ P4 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodI2
% 0.30/0.58  thf(fact_5194_mem__case__prodI,axiom,
% 0.30/0.58      ! [Z: nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.30/0.58        ( ( member_nat @ Z @ ( C @ A @ B ) )
% 0.30/0.58       => ( member_nat @ Z @ ( produc8289552606927098482et_nat @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodI
% 0.30/0.58  thf(fact_5195_mem__case__prodI,axiom,
% 0.30/0.58      ! [Z: int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_int,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.30/0.58        ( ( member_int @ Z @ ( C @ A @ B ) )
% 0.30/0.58       => ( member_int @ Z @ ( produc4111701587417901774et_int @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodI
% 0.30/0.58  thf(fact_5196_mem__case__prodI,axiom,
% 0.30/0.58      ! [Z: set_nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_set_nat,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.30/0.58        ( ( member_set_nat @ Z @ ( C @ A @ B ) )
% 0.30/0.58       => ( member_set_nat @ Z @ ( produc3577156405726439208et_nat @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodI
% 0.30/0.58  thf(fact_5197_mem__case__prodI,axiom,
% 0.30/0.58      ! [Z: nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_nat,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 0.30/0.58        ( ( member_nat @ Z @ ( C @ A @ B ) )
% 0.30/0.58       => ( member_nat @ Z @ ( produc8805491454895738411et_nat @ C @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodI
% 0.30/0.58  thf(fact_5198_mem__case__prodI,axiom,
% 0.30/0.58      ! [Z: int,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_int,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 0.30/0.58        ( ( member_int @ Z @ ( C @ A @ B ) )
% 0.30/0.58       => ( member_int @ Z @ ( produc4627640435386541703et_int @ C @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodI
% 0.30/0.58  thf(fact_5199_mem__case__prodI,axiom,
% 0.30/0.58      ! [Z: set_nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_set_nat,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 0.30/0.58        ( ( member_set_nat @ Z @ ( C @ A @ B ) )
% 0.30/0.58       => ( member_set_nat @ Z @ ( produc2333231157791014625et_nat @ C @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodI
% 0.30/0.58  thf(fact_5200_mem__case__prodI,axiom,
% 0.30/0.58      ! [Z: set_Pr958786334691620121nt_int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_se6260736226359567993nt_int,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.30/0.58        ( ( member2340774599025711042nt_int @ Z @ ( C @ A @ B ) )
% 0.30/0.58       => ( member2340774599025711042nt_int @ Z @ ( produc575502675617541261nt_int @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodI
% 0.30/0.58  thf(fact_5201_mem__case__prodI,axiom,
% 0.30/0.58      ! [Z: nat,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 0.30/0.58        ( ( member_nat @ Z @ ( C @ A @ B ) )
% 0.30/0.58       => ( member_nat @ Z @ ( produc654622801845291899et_nat @ C @ ( produc8603105652947943368nteger @ A @ B ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodI
% 0.30/0.58  thf(fact_5202_mem__case__prodI,axiom,
% 0.30/0.58      ! [Z: int,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 0.30/0.58        ( ( member_int @ Z @ ( C @ A @ B ) )
% 0.30/0.58       => ( member_int @ Z @ ( produc5700143819190870999et_int @ C @ ( produc8603105652947943368nteger @ A @ B ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodI
% 0.30/0.58  thf(fact_5203_mem__case__prodI,axiom,
% 0.30/0.58      ! [Z: nat,C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > set_nat,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.30/0.58        ( ( member_nat @ Z @ ( C @ A @ B ) )
% 0.30/0.58       => ( member_nat @ Z @ ( produc3619988815162578792et_nat @ C @ ( produc5700946648718959541nt_int @ A @ B ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodI
% 0.30/0.58  thf(fact_5204_case__prodI2_H,axiom,
% 0.30/0.58      ! [P4: product_prod_nat_nat,C: nat > nat > product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 0.30/0.58        ( ! [A6: nat,B6: nat] :
% 0.30/0.58            ( ( ( product_Pair_nat_nat @ A6 @ B6 )
% 0.30/0.58              = P4 )
% 0.30/0.58           => ( C @ A6 @ B6 @ X ) )
% 0.30/0.58       => ( produc8739625826339149834_nat_o @ C @ P4 @ X ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodI2'
% 0.30/0.58  thf(fact_5205_Collect__const__case__prod,axiom,
% 0.30/0.58      ! [P: $o] :
% 0.30/0.58        ( ( P
% 0.30/0.58         => ( ( collec3392354462482085612at_nat
% 0.30/0.58              @ ( produc6081775807080527818_nat_o
% 0.30/0.58                @ ^ [A3: nat,B3: nat] : P ) )
% 0.30/0.58            = top_to4669805908274784177at_nat ) )
% 0.30/0.58        & ( ~ P
% 0.30/0.58         => ( ( collec3392354462482085612at_nat
% 0.30/0.58              @ ( produc6081775807080527818_nat_o
% 0.30/0.58                @ ^ [A3: nat,B3: nat] : P ) )
% 0.30/0.58            = bot_bo2099793752762293965at_nat ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Collect_const_case_prod
% 0.30/0.58  thf(fact_5206_Collect__const__case__prod,axiom,
% 0.30/0.58      ! [P: $o] :
% 0.30/0.58        ( ( P
% 0.30/0.58         => ( ( collec213857154873943460nt_int
% 0.30/0.58              @ ( produc4947309494688390418_int_o
% 0.30/0.58                @ ^ [A3: int,B3: int] : P ) )
% 0.30/0.58            = top_to4366644338036079209nt_int ) )
% 0.30/0.58        & ( ~ P
% 0.30/0.58         => ( ( collec213857154873943460nt_int
% 0.30/0.58              @ ( produc4947309494688390418_int_o
% 0.30/0.58                @ ^ [A3: int,B3: int] : P ) )
% 0.30/0.58            = bot_bo1796632182523588997nt_int ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Collect_const_case_prod
% 0.30/0.58  thf(fact_5207_signed__take__bit__of__minus__1,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( bit_ri6519982836138164636nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.58        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.30/0.58  
% 0.30/0.58  % signed_take_bit_of_minus_1
% 0.30/0.58  thf(fact_5208_signed__take__bit__of__minus__1,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.58        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.30/0.58  
% 0.30/0.58  % signed_take_bit_of_minus_1
% 0.30/0.58  thf(fact_5209_signed__take__bit__numeral__of__1,axiom,
% 0.30/0.58      ! [K: num] :
% 0.30/0.58        ( ( bit_ri6519982836138164636nteger @ ( numeral_numeral_nat @ K ) @ one_one_Code_integer )
% 0.30/0.58        = one_one_Code_integer ) ).
% 0.30/0.58  
% 0.30/0.58  % signed_take_bit_numeral_of_1
% 0.30/0.58  thf(fact_5210_signed__take__bit__numeral__of__1,axiom,
% 0.30/0.58      ! [K: num] :
% 0.30/0.58        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 0.30/0.58        = one_one_int ) ).
% 0.30/0.58  
% 0.30/0.58  % signed_take_bit_numeral_of_1
% 0.30/0.58  thf(fact_5211_signed__take__bit__0,axiom,
% 0.30/0.58      ! [A: code_integer] :
% 0.30/0.58        ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 0.30/0.58        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % signed_take_bit_0
% 0.30/0.58  thf(fact_5212_signed__take__bit__0,axiom,
% 0.30/0.58      ! [A: int] :
% 0.30/0.58        ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 0.30/0.58        = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % signed_take_bit_0
% 0.30/0.58  thf(fact_5213_mem__case__prodE,axiom,
% 0.30/0.58      ! [Z: nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat,P4: produc7773217078559923341nt_int] :
% 0.30/0.58        ( ( member_nat @ Z @ ( produc8289552606927098482et_nat @ C @ P4 ) )
% 0.30/0.58       => ~ ! [X2: int > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 0.30/0.58              ( ( P4
% 0.30/0.58                = ( produc4305682042979456191nt_int @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( member_nat @ Z @ ( C @ X2 @ Y2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodE
% 0.30/0.58  thf(fact_5214_mem__case__prodE,axiom,
% 0.30/0.58      ! [Z: int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_int,P4: produc7773217078559923341nt_int] :
% 0.30/0.58        ( ( member_int @ Z @ ( produc4111701587417901774et_int @ C @ P4 ) )
% 0.30/0.58       => ~ ! [X2: int > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 0.30/0.58              ( ( P4
% 0.30/0.58                = ( produc4305682042979456191nt_int @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( member_int @ Z @ ( C @ X2 @ Y2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodE
% 0.30/0.58  thf(fact_5215_mem__case__prodE,axiom,
% 0.30/0.58      ! [Z: set_nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_set_nat,P4: produc7773217078559923341nt_int] :
% 0.30/0.58        ( ( member_set_nat @ Z @ ( produc3577156405726439208et_nat @ C @ P4 ) )
% 0.30/0.58       => ~ ! [X2: int > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 0.30/0.58              ( ( P4
% 0.30/0.58                = ( produc4305682042979456191nt_int @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( member_set_nat @ Z @ ( C @ X2 @ Y2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodE
% 0.30/0.58  thf(fact_5216_mem__case__prodE,axiom,
% 0.30/0.58      ! [Z: nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_nat,P4: produc3925858234332021118et_nat] :
% 0.30/0.58        ( ( member_nat @ Z @ ( produc8805491454895738411et_nat @ C @ P4 ) )
% 0.30/0.58       => ~ ! [X2: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 0.30/0.58              ( ( P4
% 0.30/0.58                = ( produc5001842942810119800et_nat @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( member_nat @ Z @ ( C @ X2 @ Y2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodE
% 0.30/0.58  thf(fact_5217_mem__case__prodE,axiom,
% 0.30/0.58      ! [Z: int,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_int,P4: produc3925858234332021118et_nat] :
% 0.30/0.58        ( ( member_int @ Z @ ( produc4627640435386541703et_int @ C @ P4 ) )
% 0.30/0.58       => ~ ! [X2: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 0.30/0.58              ( ( P4
% 0.30/0.58                = ( produc5001842942810119800et_nat @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( member_int @ Z @ ( C @ X2 @ Y2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodE
% 0.30/0.58  thf(fact_5218_mem__case__prodE,axiom,
% 0.30/0.58      ! [Z: set_nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_set_nat,P4: produc3925858234332021118et_nat] :
% 0.30/0.58        ( ( member_set_nat @ Z @ ( produc2333231157791014625et_nat @ C @ P4 ) )
% 0.30/0.58       => ~ ! [X2: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 0.30/0.58              ( ( P4
% 0.30/0.58                = ( produc5001842942810119800et_nat @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( member_set_nat @ Z @ ( C @ X2 @ Y2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodE
% 0.30/0.58  thf(fact_5219_mem__case__prodE,axiom,
% 0.30/0.58      ! [Z: set_Pr958786334691620121nt_int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_se6260736226359567993nt_int,P4: produc7773217078559923341nt_int] :
% 0.30/0.58        ( ( member2340774599025711042nt_int @ Z @ ( produc575502675617541261nt_int @ C @ P4 ) )
% 0.30/0.58       => ~ ! [X2: int > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 0.30/0.58              ( ( P4
% 0.30/0.58                = ( produc4305682042979456191nt_int @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( member2340774599025711042nt_int @ Z @ ( C @ X2 @ Y2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodE
% 0.30/0.58  thf(fact_5220_mem__case__prodE,axiom,
% 0.30/0.58      ! [Z: nat,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat,P4: produc1908205239877642774nteger] :
% 0.30/0.58        ( ( member_nat @ Z @ ( produc654622801845291899et_nat @ C @ P4 ) )
% 0.30/0.58       => ~ ! [X2: produc6241069584506657477e_term > option6357759511663192854e_term,Y2: produc8923325533196201883nteger] :
% 0.30/0.58              ( ( P4
% 0.30/0.58                = ( produc8603105652947943368nteger @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( member_nat @ Z @ ( C @ X2 @ Y2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodE
% 0.30/0.58  thf(fact_5221_mem__case__prodE,axiom,
% 0.30/0.58      ! [Z: int,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int,P4: produc1908205239877642774nteger] :
% 0.30/0.58        ( ( member_int @ Z @ ( produc5700143819190870999et_int @ C @ P4 ) )
% 0.30/0.58       => ~ ! [X2: produc6241069584506657477e_term > option6357759511663192854e_term,Y2: produc8923325533196201883nteger] :
% 0.30/0.58              ( ( P4
% 0.30/0.58                = ( produc8603105652947943368nteger @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( member_int @ Z @ ( C @ X2 @ Y2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodE
% 0.30/0.58  thf(fact_5222_mem__case__prodE,axiom,
% 0.30/0.58      ! [Z: nat,C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > set_nat,P4: produc2285326912895808259nt_int] :
% 0.30/0.58        ( ( member_nat @ Z @ ( produc3619988815162578792et_nat @ C @ P4 ) )
% 0.30/0.58       => ~ ! [X2: produc8551481072490612790e_term > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 0.30/0.58              ( ( P4
% 0.30/0.58                = ( produc5700946648718959541nt_int @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( member_nat @ Z @ ( C @ X2 @ Y2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mem_case_prodE
% 0.30/0.58  thf(fact_5223_signed__take__bit__minus,axiom,
% 0.30/0.58      ! [N: nat,K: int] :
% 0.30/0.58        ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N @ K ) ) )
% 0.30/0.58        = ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % signed_take_bit_minus
% 0.30/0.58  thf(fact_5224_case__prodE,axiom,
% 0.30/0.58      ! [C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,P4: produc1908205239877642774nteger] :
% 0.30/0.58        ( ( produc6253627499356882019eger_o @ C @ P4 )
% 0.30/0.58       => ~ ! [X2: produc6241069584506657477e_term > option6357759511663192854e_term,Y2: produc8923325533196201883nteger] :
% 0.30/0.58              ( ( P4
% 0.30/0.58                = ( produc8603105652947943368nteger @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( C @ X2 @ Y2 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodE
% 0.30/0.58  thf(fact_5225_case__prodE,axiom,
% 0.30/0.58      ! [C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,P4: produc3925858234332021118et_nat] :
% 0.30/0.58        ( ( produc1437786849005270451_nat_o @ C @ P4 )
% 0.30/0.58       => ~ ! [X2: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 0.30/0.58              ( ( P4
% 0.30/0.58                = ( produc5001842942810119800et_nat @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( C @ X2 @ Y2 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodE
% 0.30/0.58  thf(fact_5226_case__prodE,axiom,
% 0.30/0.58      ! [C: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o,P4: produc2732055786443039994et_nat] :
% 0.30/0.58        ( ( produc838355143741117751_nat_o @ C @ P4 )
% 0.30/0.58       => ~ ! [X2: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat] :
% 0.30/0.58              ( ( P4
% 0.30/0.58                = ( produc2245416461498447860et_nat @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( C @ X2 @ Y2 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodE
% 0.30/0.58  thf(fact_5227_case__prodE,axiom,
% 0.30/0.58      ! [C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,P4: produc2285326912895808259nt_int] :
% 0.30/0.58        ( ( produc1573362020775583542_int_o @ C @ P4 )
% 0.30/0.58       => ~ ! [X2: produc8551481072490612790e_term > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 0.30/0.58              ( ( P4
% 0.30/0.58                = ( produc5700946648718959541nt_int @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( C @ X2 @ Y2 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodE
% 0.30/0.58  thf(fact_5228_case__prodE,axiom,
% 0.30/0.58      ! [C: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,P4: produc7773217078559923341nt_int] :
% 0.30/0.58        ( ( produc2558449545302689196_int_o @ C @ P4 )
% 0.30/0.58       => ~ ! [X2: int > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 0.30/0.58              ( ( P4
% 0.30/0.58                = ( produc4305682042979456191nt_int @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( C @ X2 @ Y2 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodE
% 0.30/0.58  thf(fact_5229_case__prodE,axiom,
% 0.30/0.58      ! [C: int > int > $o,P4: product_prod_int_int] :
% 0.30/0.58        ( ( produc4947309494688390418_int_o @ C @ P4 )
% 0.30/0.58       => ~ ! [X2: int,Y2: int] :
% 0.30/0.58              ( ( P4
% 0.30/0.58                = ( product_Pair_int_int @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( C @ X2 @ Y2 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodE
% 0.30/0.58  thf(fact_5230_case__prodD,axiom,
% 0.30/0.58      ! [F2: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 0.30/0.58        ( ( produc6253627499356882019eger_o @ F2 @ ( produc8603105652947943368nteger @ A @ B ) )
% 0.30/0.58       => ( F2 @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodD
% 0.30/0.58  thf(fact_5231_case__prodD,axiom,
% 0.30/0.58      ! [F2: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 0.30/0.58        ( ( produc1437786849005270451_nat_o @ F2 @ ( produc5001842942810119800et_nat @ A @ B ) )
% 0.30/0.58       => ( F2 @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodD
% 0.30/0.58  thf(fact_5232_case__prodD,axiom,
% 0.30/0.58      ! [F2: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 0.30/0.58        ( ( produc838355143741117751_nat_o @ F2 @ ( produc2245416461498447860et_nat @ A @ B ) )
% 0.30/0.58       => ( F2 @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodD
% 0.30/0.58  thf(fact_5233_case__prodD,axiom,
% 0.30/0.58      ! [F2: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.30/0.58        ( ( produc1573362020775583542_int_o @ F2 @ ( produc5700946648718959541nt_int @ A @ B ) )
% 0.30/0.58       => ( F2 @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodD
% 0.30/0.58  thf(fact_5234_case__prodD,axiom,
% 0.30/0.58      ! [F2: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 0.30/0.58        ( ( produc2558449545302689196_int_o @ F2 @ ( produc4305682042979456191nt_int @ A @ B ) )
% 0.30/0.58       => ( F2 @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodD
% 0.30/0.58  thf(fact_5235_case__prodD,axiom,
% 0.30/0.58      ! [F2: int > int > $o,A: int,B: int] :
% 0.30/0.58        ( ( produc4947309494688390418_int_o @ F2 @ ( product_Pair_int_int @ A @ B ) )
% 0.30/0.58       => ( F2 @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodD
% 0.30/0.58  thf(fact_5236_case__prodE_H,axiom,
% 0.30/0.58      ! [C: nat > nat > product_prod_nat_nat > $o,P4: product_prod_nat_nat,Z: product_prod_nat_nat] :
% 0.30/0.58        ( ( produc8739625826339149834_nat_o @ C @ P4 @ Z )
% 0.30/0.58       => ~ ! [X2: nat,Y2: nat] :
% 0.30/0.58              ( ( P4
% 0.30/0.58                = ( product_Pair_nat_nat @ X2 @ Y2 ) )
% 0.30/0.58             => ~ ( C @ X2 @ Y2 @ Z ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodE'
% 0.30/0.58  thf(fact_5237_case__prodD_H,axiom,
% 0.30/0.58      ! [R: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C: product_prod_nat_nat] :
% 0.30/0.58        ( ( produc8739625826339149834_nat_o @ R @ ( product_Pair_nat_nat @ A @ B ) @ C )
% 0.30/0.58       => ( R @ A @ B @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % case_prodD'
% 0.30/0.58  thf(fact_5238_Id__on__def_H,axiom,
% 0.30/0.58      ! [A2: set_Pr958786334691620121nt_int > $o] :
% 0.30/0.58        ( ( id_on_6410342593070439734nt_int @ ( collec5210948495886036740nt_int @ A2 ) )
% 0.30/0.58        = ( collec2889756465124990930nt_int
% 0.30/0.58          @ ( produc1547782455048856492_int_o
% 0.30/0.58            @ ^ [X3: set_Pr958786334691620121nt_int,Y3: set_Pr958786334691620121nt_int] :
% 0.30/0.58                ( ( X3 = Y3 )
% 0.30/0.58                & ( A2 @ X3 ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Id_on_def'
% 0.30/0.58  thf(fact_5239_Id__on__def_H,axiom,
% 0.30/0.58      ! [A2: set_nat > $o] :
% 0.30/0.58        ( ( id_on_set_nat @ ( collect_set_nat @ A2 ) )
% 0.30/0.58        = ( collec6662362479098859352et_nat
% 0.30/0.58          @ ( produc6247414631856714078_nat_o
% 0.30/0.58            @ ^ [X3: set_nat,Y3: set_nat] :
% 0.30/0.58                ( ( X3 = Y3 )
% 0.30/0.58                & ( A2 @ X3 ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Id_on_def'
% 0.30/0.58  thf(fact_5240_Id__on__def_H,axiom,
% 0.30/0.58      ! [A2: nat > $o] :
% 0.30/0.58        ( ( id_on_nat @ ( collect_nat @ A2 ) )
% 0.30/0.58        = ( collec3392354462482085612at_nat
% 0.30/0.58          @ ( produc6081775807080527818_nat_o
% 0.30/0.58            @ ^ [X3: nat,Y3: nat] :
% 0.30/0.58                ( ( X3 = Y3 )
% 0.30/0.58                & ( A2 @ X3 ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Id_on_def'
% 0.30/0.58  thf(fact_5241_Id__on__def_H,axiom,
% 0.30/0.58      ! [A2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.30/0.58        ( ( id_on_7438695062414216554_nat_o @ ( collec939566748876313656_nat_o @ A2 ) )
% 0.30/0.58        = ( collec7086185654880424402_nat_o
% 0.30/0.58          @ ( produc5150382289251079596at_o_o
% 0.30/0.58            @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat > $o] :
% 0.30/0.58                ( ( X3 = Y3 )
% 0.30/0.58                & ( A2 @ X3 ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Id_on_def'
% 0.30/0.58  thf(fact_5242_Id__on__def_H,axiom,
% 0.30/0.58      ! [A2: int > $o] :
% 0.30/0.58        ( ( id_on_int @ ( collect_int @ A2 ) )
% 0.30/0.58        = ( collec213857154873943460nt_int
% 0.30/0.58          @ ( produc4947309494688390418_int_o
% 0.30/0.58            @ ^ [X3: int,Y3: int] :
% 0.30/0.58                ( ( X3 = Y3 )
% 0.30/0.58                & ( A2 @ X3 ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Id_on_def'
% 0.30/0.58  thf(fact_5243_rel__restrict__def,axiom,
% 0.30/0.58      ( rel_re4349003428253852667nt_int
% 0.30/0.58      = ( ^ [R2: set_Pr8057934254988874055nt_int,A4: set_se6260736226359567993nt_int] :
% 0.30/0.58            ( collec2889756465124990930nt_int
% 0.30/0.58            @ ( produc1547782455048856492_int_o
% 0.30/0.58              @ ^ [V2: set_Pr958786334691620121nt_int,W3: set_Pr958786334691620121nt_int] :
% 0.30/0.58                  ( ( member5325734588016868240nt_int @ ( produc782388162306416855nt_int @ V2 @ W3 ) @ R2 )
% 0.30/0.58                  & ~ ( member2340774599025711042nt_int @ V2 @ A4 )
% 0.30/0.58                  & ~ ( member2340774599025711042nt_int @ W3 @ A4 ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % rel_restrict_def
% 0.30/0.58  thf(fact_5244_rel__restrict__def,axiom,
% 0.30/0.58      ( rel_restrict_set_nat
% 0.30/0.58      = ( ^ [R2: set_Pr5488025237498180813et_nat,A4: set_set_nat] :
% 0.30/0.58            ( collec6662362479098859352et_nat
% 0.30/0.58            @ ( produc6247414631856714078_nat_o
% 0.30/0.58              @ ^ [V2: set_nat,W3: set_nat] :
% 0.30/0.58                  ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ V2 @ W3 ) @ R2 )
% 0.30/0.58                  & ~ ( member_set_nat @ V2 @ A4 )
% 0.30/0.58                  & ~ ( member_set_nat @ W3 @ A4 ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % rel_restrict_def
% 0.30/0.58  thf(fact_5245_rel__restrict__def,axiom,
% 0.30/0.58      ( rel_restrict_nat
% 0.30/0.58      = ( ^ [R2: set_Pr1261947904930325089at_nat,A4: set_nat] :
% 0.30/0.58            ( collec3392354462482085612at_nat
% 0.30/0.58            @ ( produc6081775807080527818_nat_o
% 0.30/0.58              @ ^ [V2: nat,W3: nat] :
% 0.30/0.58                  ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ V2 @ W3 ) @ R2 )
% 0.30/0.58                  & ~ ( member_nat @ V2 @ A4 )
% 0.30/0.58                  & ~ ( member_nat @ W3 @ A4 ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % rel_restrict_def
% 0.30/0.58  thf(fact_5246_rel__restrict__def,axiom,
% 0.30/0.58      ( rel_re3331361160397388719_nat_o
% 0.30/0.58      = ( ^ [R2: set_Pr2161125870931222855_nat_o,A4: set_Pr4532377907799695533_nat_o] :
% 0.30/0.58            ( collec7086185654880424402_nat_o
% 0.30/0.58            @ ( produc5150382289251079596at_o_o
% 0.30/0.58              @ ^ [V2: produc3658429121746597890et_nat > $o,W3: produc3658429121746597890et_nat > $o] :
% 0.30/0.58                  ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ V2 @ W3 ) @ R2 )
% 0.30/0.58                  & ~ ( member6576561426505652726_nat_o @ V2 @ A4 )
% 0.30/0.58                  & ~ ( member6576561426505652726_nat_o @ W3 @ A4 ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % rel_restrict_def
% 0.30/0.58  thf(fact_5247_rel__restrict__def,axiom,
% 0.30/0.58      ( rel_restrict_int
% 0.30/0.58      = ( ^ [R2: set_Pr958786334691620121nt_int,A4: set_int] :
% 0.30/0.58            ( collec213857154873943460nt_int
% 0.30/0.58            @ ( produc4947309494688390418_int_o
% 0.30/0.58              @ ^ [V2: int,W3: int] :
% 0.30/0.58                  ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ V2 @ W3 ) @ R2 )
% 0.30/0.58                  & ~ ( member_int @ V2 @ A4 )
% 0.30/0.58                  & ~ ( member_int @ W3 @ A4 ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % rel_restrict_def
% 0.30/0.58  thf(fact_5248_int__less__induct,axiom,
% 0.30/0.58      ! [I: int,K: int,P: int > $o] :
% 0.30/0.58        ( ( ord_less_int @ I @ K )
% 0.30/0.58       => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 0.30/0.58         => ( ! [I2: int] :
% 0.30/0.58                ( ( ord_less_int @ I2 @ K )
% 0.30/0.58               => ( ( P @ I2 )
% 0.30/0.58                 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 0.30/0.58           => ( P @ I ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % int_less_induct
% 0.30/0.58  thf(fact_5249_minus__int__code_I2_J,axiom,
% 0.30/0.58      ! [L: int] :
% 0.30/0.58        ( ( minus_minus_int @ zero_zero_int @ L )
% 0.30/0.58        = ( uminus_uminus_int @ L ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_int_code(2)
% 0.30/0.58  thf(fact_5250_uminus__int__code_I1_J,axiom,
% 0.30/0.58      ( ( uminus_uminus_int @ zero_zero_int )
% 0.30/0.58      = zero_zero_int ) ).
% 0.30/0.58  
% 0.30/0.58  % uminus_int_code(1)
% 0.30/0.58  thf(fact_5251_int__le__induct,axiom,
% 0.30/0.58      ! [I: int,K: int,P: int > $o] :
% 0.30/0.58        ( ( ord_less_eq_int @ I @ K )
% 0.30/0.58       => ( ( P @ K )
% 0.30/0.58         => ( ! [I2: int] :
% 0.30/0.58                ( ( ord_less_eq_int @ I2 @ K )
% 0.30/0.58               => ( ( P @ I2 )
% 0.30/0.58                 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 0.30/0.58           => ( P @ I ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % int_le_induct
% 0.30/0.58  thf(fact_5252_zless__add1__eq,axiom,
% 0.30/0.58      ! [W: int,Z: int] :
% 0.30/0.58        ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 0.30/0.58        = ( ( ord_less_int @ W @ Z )
% 0.30/0.58          | ( W = Z ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % zless_add1_eq
% 0.30/0.58  thf(fact_5253_int__gr__induct,axiom,
% 0.30/0.58      ! [K: int,I: int,P: int > $o] :
% 0.30/0.58        ( ( ord_less_int @ K @ I )
% 0.30/0.58       => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 0.30/0.58         => ( ! [I2: int] :
% 0.30/0.58                ( ( ord_less_int @ K @ I2 )
% 0.30/0.58               => ( ( P @ I2 )
% 0.30/0.58                 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 0.30/0.58           => ( P @ I ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % int_gr_induct
% 0.30/0.58  thf(fact_5254_int__one__le__iff__zero__less,axiom,
% 0.30/0.58      ! [Z: int] :
% 0.30/0.58        ( ( ord_less_eq_int @ one_one_int @ Z )
% 0.30/0.58        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.30/0.58  
% 0.30/0.58  % int_one_le_iff_zero_less
% 0.30/0.58  thf(fact_5255_pos__zmult__eq__1__iff,axiom,
% 0.30/0.58      ! [M: int,N: int] :
% 0.30/0.58        ( ( ord_less_int @ zero_zero_int @ M )
% 0.30/0.58       => ( ( ( times_times_int @ M @ N )
% 0.30/0.58            = one_one_int )
% 0.30/0.58          = ( ( M = one_one_int )
% 0.30/0.58            & ( N = one_one_int ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % pos_zmult_eq_1_iff
% 0.30/0.58  thf(fact_5256_odd__nonzero,axiom,
% 0.30/0.58      ! [Z: int] :
% 0.30/0.58        ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 0.30/0.58       != zero_zero_int ) ).
% 0.30/0.58  
% 0.30/0.58  % odd_nonzero
% 0.30/0.58  thf(fact_5257_odd__less__0__iff,axiom,
% 0.30/0.58      ! [Z: int] :
% 0.30/0.58        ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 0.30/0.58        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 0.30/0.58  
% 0.30/0.58  % odd_less_0_iff
% 0.30/0.58  thf(fact_5258_zless__imp__add1__zle,axiom,
% 0.30/0.58      ! [W: int,Z: int] :
% 0.30/0.58        ( ( ord_less_int @ W @ Z )
% 0.30/0.58       => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 0.30/0.58  
% 0.30/0.58  % zless_imp_add1_zle
% 0.30/0.58  thf(fact_5259_int__ge__induct,axiom,
% 0.30/0.58      ! [K: int,I: int,P: int > $o] :
% 0.30/0.58        ( ( ord_less_eq_int @ K @ I )
% 0.30/0.58       => ( ( P @ K )
% 0.30/0.58         => ( ! [I2: int] :
% 0.30/0.58                ( ( ord_less_eq_int @ K @ I2 )
% 0.30/0.58               => ( ( P @ I2 )
% 0.30/0.58                 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 0.30/0.58           => ( P @ I ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % int_ge_induct
% 0.30/0.58  thf(fact_5260_add1__zle__eq,axiom,
% 0.30/0.58      ! [W: int,Z: int] :
% 0.30/0.58        ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 0.30/0.58        = ( ord_less_int @ W @ Z ) ) ).
% 0.30/0.58  
% 0.30/0.58  % add1_zle_eq
% 0.30/0.58  thf(fact_5261_int__induct,axiom,
% 0.30/0.58      ! [P: int > $o,K: int,I: int] :
% 0.30/0.58        ( ( P @ K )
% 0.30/0.58       => ( ! [I2: int] :
% 0.30/0.58              ( ( ord_less_eq_int @ K @ I2 )
% 0.30/0.58             => ( ( P @ I2 )
% 0.30/0.58               => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 0.30/0.58         => ( ! [I2: int] :
% 0.30/0.58                ( ( ord_less_eq_int @ I2 @ K )
% 0.30/0.58               => ( ( P @ I2 )
% 0.30/0.58                 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 0.30/0.58           => ( P @ I ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % int_induct
% 0.30/0.58  thf(fact_5262_zmult__eq__1__iff,axiom,
% 0.30/0.58      ! [M: int,N: int] :
% 0.30/0.58        ( ( ( times_times_int @ M @ N )
% 0.30/0.58          = one_one_int )
% 0.30/0.58        = ( ( ( M = one_one_int )
% 0.30/0.58            & ( N = one_one_int ) )
% 0.30/0.58          | ( ( M
% 0.30/0.58              = ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.58            & ( N
% 0.30/0.58              = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % zmult_eq_1_iff
% 0.30/0.58  thf(fact_5263_pos__zmult__eq__1__iff__lemma,axiom,
% 0.30/0.58      ! [M: int,N: int] :
% 0.30/0.58        ( ( ( times_times_int @ M @ N )
% 0.30/0.58          = one_one_int )
% 0.30/0.58       => ( ( M = one_one_int )
% 0.30/0.58          | ( M
% 0.30/0.58            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % pos_zmult_eq_1_iff_lemma
% 0.30/0.58  thf(fact_5264_neg__eucl__rel__int__mult__2,axiom,
% 0.30/0.58      ! [B: int,A: int,Q4: int,R3: int] :
% 0.30/0.58        ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.30/0.58       => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 0.30/0.58         => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q4 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R3 ) @ one_one_int ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % neg_eucl_rel_int_mult_2
% 0.30/0.58  thf(fact_5265_signed__take__bit__numeral__minus__bit1,axiom,
% 0.30/0.58      ! [L: num,K: num] :
% 0.30/0.58        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.30/0.58        = ( 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 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % signed_take_bit_numeral_minus_bit1
% 0.30/0.58  thf(fact_5266_pos__eucl__rel__int__mult__2,axiom,
% 0.30/0.58      ! [B: int,A: int,Q4: int,R3: int] :
% 0.30/0.58        ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.30/0.58       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 0.30/0.58         => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q4 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R3 ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % pos_eucl_rel_int_mult_2
% 0.30/0.58  thf(fact_5267_signed__take__bit__Suc__minus__bit1,axiom,
% 0.30/0.58      ! [N: nat,K: num] :
% 0.30/0.58        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.30/0.58        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.30/0.58  
% 0.30/0.58  % signed_take_bit_Suc_minus_bit1
% 0.30/0.58  thf(fact_5268_divmod__BitM__2__eq,axiom,
% 0.30/0.58      ! [M: num] :
% 0.30/0.58        ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 0.30/0.58        = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 0.30/0.58  
% 0.30/0.58  % divmod_BitM_2_eq
% 0.30/0.58  thf(fact_5269_split__part,axiom,
% 0.30/0.58      ! [P: $o,Q2: int > int > $o] :
% 0.30/0.58        ( ( produc4947309494688390418_int_o
% 0.30/0.58          @ ^ [A3: int,B3: int] :
% 0.30/0.58              ( P
% 0.30/0.58              & ( Q2 @ A3 @ B3 ) ) )
% 0.30/0.58        = ( ^ [Ab: product_prod_int_int] :
% 0.30/0.58              ( P
% 0.30/0.58              & ( produc4947309494688390418_int_o @ Q2 @ Ab ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % split_part
% 0.30/0.58  thf(fact_5270_diff__Suc__1,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 0.30/0.58        = N ) ).
% 0.30/0.58  
% 0.30/0.58  % diff_Suc_1
% 0.30/0.58  thf(fact_5271_signed__take__bit__Suc__1,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ one_one_Code_integer )
% 0.30/0.58        = one_one_Code_integer ) ).
% 0.30/0.58  
% 0.30/0.58  % signed_take_bit_Suc_1
% 0.30/0.58  thf(fact_5272_signed__take__bit__Suc__1,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 0.30/0.58        = one_one_int ) ).
% 0.30/0.58  
% 0.30/0.58  % signed_take_bit_Suc_1
% 0.30/0.58  thf(fact_5273_Suc__diff,axiom,
% 0.30/0.58      ! [M: nat,N: nat] :
% 0.30/0.58        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.58       => ( ( ord_less_eq_nat @ one_one_nat @ M )
% 0.30/0.58         => ( ( suc @ ( minus_minus_nat @ N @ M ) )
% 0.30/0.58            = ( minus_minus_nat @ N @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Suc_diff
% 0.30/0.58  thf(fact_5274_Suc__1,axiom,
% 0.30/0.58      ( ( suc @ one_one_nat )
% 0.30/0.58      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Suc_1
% 0.30/0.58  thf(fact_5275_Suc__diff__1,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58       => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.30/0.58          = N ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Suc_diff_1
% 0.30/0.58  thf(fact_5276_Suc__times__numeral__mod__eq,axiom,
% 0.30/0.58      ! [K: num,N: nat] :
% 0.30/0.58        ( ( ( numeral_numeral_nat @ K )
% 0.30/0.58         != one_one_nat )
% 0.30/0.58       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 0.30/0.58          = one_one_nat ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Suc_times_numeral_mod_eq
% 0.30/0.58  thf(fact_5277_sub__num__simps_I2_J,axiom,
% 0.30/0.58      ! [L: num] :
% 0.30/0.58        ( ( neg_numeral_sub_int @ one @ ( bit0 @ L ) )
% 0.30/0.58        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bitM @ L ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % sub_num_simps(2)
% 0.30/0.58  thf(fact_5278_sub__num__simps_I2_J,axiom,
% 0.30/0.58      ! [L: num] :
% 0.30/0.58        ( ( neg_nu5755505904847501662nteger @ one @ ( bit0 @ L ) )
% 0.30/0.58        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bitM @ L ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % sub_num_simps(2)
% 0.30/0.58  thf(fact_5279_sub__num__simps_I2_J,axiom,
% 0.30/0.58      ! [L: num] :
% 0.30/0.58        ( ( neg_numeral_sub_rat @ one @ ( bit0 @ L ) )
% 0.30/0.58        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bitM @ L ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % sub_num_simps(2)
% 0.30/0.58  thf(fact_5280_signed__take__bit__Suc__minus__bit0,axiom,
% 0.30/0.58      ! [N: nat,K: num] :
% 0.30/0.58        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.30/0.58        = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % signed_take_bit_Suc_minus_bit0
% 0.30/0.58  thf(fact_5281_signed__take__bit__numeral__minus__bit0,axiom,
% 0.30/0.58      ! [L: num,K: num] :
% 0.30/0.58        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.30/0.58        = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % signed_take_bit_numeral_minus_bit0
% 0.30/0.58  thf(fact_5282_signed__take__bit__Suc__bit1,axiom,
% 0.30/0.58      ! [N: nat,K: num] :
% 0.30/0.58        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.30/0.58        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.30/0.58  
% 0.30/0.58  % signed_take_bit_Suc_bit1
% 0.30/0.58  thf(fact_5283_signed__take__bit__numeral__bit1,axiom,
% 0.30/0.58      ! [L: num,K: num] :
% 0.30/0.58        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.30/0.58        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.30/0.58  
% 0.30/0.58  % signed_take_bit_numeral_bit1
% 0.30/0.58  thf(fact_5284_prod_Odisc__eq__case,axiom,
% 0.30/0.58      ! [Prod: product_prod_int_int] :
% 0.30/0.58        ( produc4947309494688390418_int_o
% 0.30/0.58        @ ^ [Uu: int,Uv: int] : $true
% 0.30/0.58        @ Prod ) ).
% 0.30/0.58  
% 0.30/0.58  % prod.disc_eq_case
% 0.30/0.58  thf(fact_5285_unique__remainder,axiom,
% 0.30/0.58      ! [A: int,B: int,Q4: int,R3: int,Q6: int,R5: int] :
% 0.30/0.58        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 0.30/0.58       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q6 @ R5 ) )
% 0.30/0.58         => ( R3 = R5 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unique_remainder
% 0.30/0.58  thf(fact_5286_unique__quotient,axiom,
% 0.30/0.58      ! [A: int,B: int,Q4: int,R3: int,Q6: int,R5: int] :
% 0.30/0.58        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 0.30/0.58       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q6 @ R5 ) )
% 0.30/0.58         => ( Q4 = Q6 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unique_quotient
% 0.30/0.58  thf(fact_5287_One__nat__def,axiom,
% 0.30/0.58      ( one_one_nat
% 0.30/0.58      = ( suc @ zero_zero_nat ) ) ).
% 0.30/0.58  
% 0.30/0.58  % One_nat_def
% 0.30/0.58  thf(fact_5288_Suc__eq__plus1,axiom,
% 0.30/0.58      ( suc
% 0.30/0.58      = ( ^ [N2: nat] : ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Suc_eq_plus1
% 0.30/0.58  thf(fact_5289_plus__1__eq__Suc,axiom,
% 0.30/0.58      ( ( plus_plus_nat @ one_one_nat )
% 0.30/0.58      = suc ) ).
% 0.30/0.58  
% 0.30/0.58  % plus_1_eq_Suc
% 0.30/0.58  thf(fact_5290_Suc__eq__plus1__left,axiom,
% 0.30/0.58      ( suc
% 0.30/0.58      = ( plus_plus_nat @ one_one_nat ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Suc_eq_plus1_left
% 0.30/0.58  thf(fact_5291_diff__Suc__eq__diff__pred,axiom,
% 0.30/0.58      ! [M: nat,N: nat] :
% 0.30/0.58        ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 0.30/0.58        = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 0.30/0.58  
% 0.30/0.58  % diff_Suc_eq_diff_pred
% 0.30/0.58  thf(fact_5292_eucl__rel__int__by0,axiom,
% 0.30/0.58      ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 0.30/0.58  
% 0.30/0.58  % eucl_rel_int_by0
% 0.30/0.58  thf(fact_5293_nat__induct__non__zero,axiom,
% 0.30/0.58      ! [N: nat,P: nat > $o] :
% 0.30/0.58        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58       => ( ( P @ one_one_nat )
% 0.30/0.58         => ( ! [N3: nat] :
% 0.30/0.58                ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.30/0.58               => ( ( P @ N3 )
% 0.30/0.58                 => ( P @ ( suc @ N3 ) ) ) )
% 0.30/0.58           => ( P @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % nat_induct_non_zero
% 0.30/0.58  thf(fact_5294_div__int__unique,axiom,
% 0.30/0.58      ! [K: int,L: int,Q4: int,R3: int] :
% 0.30/0.58        ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 0.30/0.58       => ( ( divide_divide_int @ K @ L )
% 0.30/0.58          = Q4 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % div_int_unique
% 0.30/0.58  thf(fact_5295_mod__int__unique,axiom,
% 0.30/0.58      ! [K: int,L: int,Q4: int,R3: int] :
% 0.30/0.58        ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 0.30/0.58       => ( ( modulo_modulo_int @ K @ L )
% 0.30/0.58          = R3 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mod_int_unique
% 0.30/0.58  thf(fact_5296_pred__numeral__def,axiom,
% 0.30/0.58      ( pred_numeral
% 0.30/0.58      = ( ^ [K4: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K4 ) @ one_one_nat ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % pred_numeral_def
% 0.30/0.58  thf(fact_5297_small__lazy_H_Ocases,axiom,
% 0.30/0.58      ! [X: product_prod_int_int] :
% 0.30/0.58        ~ ! [D: int,I2: int] :
% 0.30/0.58            ( X
% 0.30/0.58           != ( product_Pair_int_int @ D @ I2 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % small_lazy'.cases
% 0.30/0.58  thf(fact_5298_exhaustive__int_H_Ocases,axiom,
% 0.30/0.58      ! [X: produc7773217078559923341nt_int] :
% 0.30/0.58        ~ ! [F3: int > option6357759511663192854e_term,D: int,I2: int] :
% 0.30/0.58            ( X
% 0.30/0.58           != ( produc4305682042979456191nt_int @ F3 @ ( product_Pair_int_int @ D @ I2 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % exhaustive_int'.cases
% 0.30/0.58  thf(fact_5299_full__exhaustive__int_H_Ocases,axiom,
% 0.30/0.58      ! [X: produc2285326912895808259nt_int] :
% 0.30/0.58        ~ ! [F3: produc8551481072490612790e_term > option6357759511663192854e_term,D: int,I2: int] :
% 0.30/0.58            ( X
% 0.30/0.58           != ( produc5700946648718959541nt_int @ F3 @ ( product_Pair_int_int @ D @ I2 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % full_exhaustive_int'.cases
% 0.30/0.58  thf(fact_5300_Suc__pred_H,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58       => ( N
% 0.30/0.58          = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Suc_pred'
% 0.30/0.58  thf(fact_5301_Suc__diff__eq__diff__pred,axiom,
% 0.30/0.58      ! [N: nat,M: nat] :
% 0.30/0.58        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58       => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 0.30/0.58          = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Suc_diff_eq_diff_pred
% 0.30/0.58  thf(fact_5302_add__eq__if,axiom,
% 0.30/0.58      ( plus_plus_nat
% 0.30/0.58      = ( ^ [M2: nat,N2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ N2 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % add_eq_if
% 0.30/0.58  thf(fact_5303_Suc__n__minus__m__eq,axiom,
% 0.30/0.58      ! [M: nat,N: nat] :
% 0.30/0.58        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.58       => ( ( ord_less_nat @ one_one_nat @ M )
% 0.30/0.58         => ( ( suc @ ( minus_minus_nat @ N @ M ) )
% 0.30/0.58            = ( minus_minus_nat @ N @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Suc_n_minus_m_eq
% 0.30/0.58  thf(fact_5304_eucl__rel__int__dividesI,axiom,
% 0.30/0.58      ! [L: int,K: int,Q4: int] :
% 0.30/0.58        ( ( L != zero_zero_int )
% 0.30/0.58       => ( ( K
% 0.30/0.58            = ( times_times_int @ Q4 @ L ) )
% 0.30/0.58         => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q4 @ zero_zero_int ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % eucl_rel_int_dividesI
% 0.30/0.58  thf(fact_5305_numeral__BitM,axiom,
% 0.30/0.58      ! [N: num] :
% 0.30/0.58        ( ( numeral_numeral_int @ ( bitM @ N ) )
% 0.30/0.58        = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ one_one_int ) ) ).
% 0.30/0.58  
% 0.30/0.58  % numeral_BitM
% 0.30/0.58  thf(fact_5306_numeral__BitM,axiom,
% 0.30/0.58      ! [N: num] :
% 0.30/0.58        ( ( numera6620942414471956472nteger @ ( bitM @ N ) )
% 0.30/0.58        = ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ one_one_Code_integer ) ) ).
% 0.30/0.58  
% 0.30/0.58  % numeral_BitM
% 0.30/0.58  thf(fact_5307_numeral__BitM,axiom,
% 0.30/0.58      ! [N: num] :
% 0.30/0.58        ( ( numeral_numeral_rat @ ( bitM @ N ) )
% 0.30/0.58        = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N ) ) @ one_one_rat ) ) ).
% 0.30/0.58  
% 0.30/0.58  % numeral_BitM
% 0.30/0.58  thf(fact_5308_eucl__rel__int,axiom,
% 0.30/0.58      ! [K: int,L: int] : ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L ) @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % eucl_rel_int
% 0.30/0.58  thf(fact_5309_Suc__times__mod__eq,axiom,
% 0.30/0.58      ! [M: nat,N: nat] :
% 0.30/0.58        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 0.30/0.58       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 0.30/0.58          = one_one_nat ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Suc_times_mod_eq
% 0.30/0.58  thf(fact_5310_zminus1__lemma,axiom,
% 0.30/0.58      ! [A: int,B: int,Q4: int,R3: int] :
% 0.30/0.58        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 0.30/0.58       => ( ( B != zero_zero_int )
% 0.30/0.58         => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R3 = zero_zero_int ) @ ( uminus_uminus_int @ Q4 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q4 ) @ one_one_int ) ) @ ( if_int @ ( R3 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R3 ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % zminus1_lemma
% 0.30/0.58  thf(fact_5311_signed__take__bit__Suc,axiom,
% 0.30/0.58      ! [N: nat,A: code_integer] :
% 0.30/0.58        ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ A )
% 0.30/0.58        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % signed_take_bit_Suc
% 0.30/0.58  thf(fact_5312_signed__take__bit__Suc,axiom,
% 0.30/0.58      ! [N: nat,A: int] :
% 0.30/0.58        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 0.30/0.58        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % signed_take_bit_Suc
% 0.30/0.58  thf(fact_5313_unset__bit__Suc,axiom,
% 0.30/0.58      ! [N: nat,A: nat] :
% 0.30/0.58        ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 0.30/0.58        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unset_bit_Suc
% 0.30/0.58  thf(fact_5314_unset__bit__Suc,axiom,
% 0.30/0.58      ! [N: nat,A: code_integer] :
% 0.30/0.58        ( ( bit_se8260200283734997820nteger @ ( suc @ N ) @ A )
% 0.30/0.58        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unset_bit_Suc
% 0.30/0.58  thf(fact_5315_unset__bit__Suc,axiom,
% 0.30/0.58      ! [N: nat,A: code_natural] :
% 0.30/0.58        ( ( bit_se7083795435491715335atural @ ( suc @ N ) @ A )
% 0.30/0.58        = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se7083795435491715335atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unset_bit_Suc
% 0.30/0.58  thf(fact_5316_unset__bit__Suc,axiom,
% 0.30/0.58      ! [N: nat,A: int] :
% 0.30/0.58        ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 0.30/0.58        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unset_bit_Suc
% 0.30/0.58  thf(fact_5317_set__bit__Suc,axiom,
% 0.30/0.58      ! [N: nat,A: code_integer] :
% 0.30/0.58        ( ( bit_se2793503036327961859nteger @ ( suc @ N ) @ A )
% 0.30/0.58        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % set_bit_Suc
% 0.30/0.58  thf(fact_5318_set__bit__Suc,axiom,
% 0.30/0.58      ! [N: nat,A: code_natural] :
% 0.30/0.58        ( ( bit_se1617098188084679374atural @ ( suc @ N ) @ A )
% 0.30/0.58        = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se1617098188084679374atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % set_bit_Suc
% 0.30/0.58  thf(fact_5319_set__bit__Suc,axiom,
% 0.30/0.58      ! [N: nat,A: int] :
% 0.30/0.58        ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 0.30/0.58        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % set_bit_Suc
% 0.30/0.58  thf(fact_5320_set__bit__Suc,axiom,
% 0.30/0.58      ! [N: nat,A: nat] :
% 0.30/0.58        ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 0.30/0.58        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % set_bit_Suc
% 0.30/0.58  thf(fact_5321_eucl__rel__int__iff,axiom,
% 0.30/0.58      ! [K: int,L: int,Q4: int,R3: int] :
% 0.30/0.58        ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 0.30/0.58        = ( ( K
% 0.30/0.58            = ( plus_plus_int @ ( times_times_int @ L @ Q4 ) @ R3 ) )
% 0.30/0.58          & ( ( ord_less_int @ zero_zero_int @ L )
% 0.30/0.58           => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 0.30/0.58              & ( ord_less_int @ R3 @ L ) ) )
% 0.30/0.58          & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 0.30/0.58           => ( ( ( ord_less_int @ L @ zero_zero_int )
% 0.30/0.58               => ( ( ord_less_int @ L @ R3 )
% 0.30/0.58                  & ( ord_less_eq_int @ R3 @ zero_zero_int ) ) )
% 0.30/0.58              & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 0.30/0.58               => ( Q4 = zero_zero_int ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % eucl_rel_int_iff
% 0.30/0.58  thf(fact_5322_divmod__nat__if,axiom,
% 0.30/0.58      ( divmod_nat
% 0.30/0.58      = ( ^ [M2: nat,N2: nat] :
% 0.30/0.58            ( if_Pro6206227464963214023at_nat
% 0.30/0.58            @ ( ( N2 = zero_zero_nat )
% 0.30/0.58              | ( ord_less_nat @ M2 @ N2 ) )
% 0.30/0.58            @ ( product_Pair_nat_nat @ zero_zero_nat @ M2 )
% 0.30/0.58            @ ( produc2626176000494625587at_nat
% 0.30/0.58              @ ^ [Q5: nat] : ( product_Pair_nat_nat @ ( suc @ Q5 ) )
% 0.30/0.58              @ ( divmod_nat @ ( minus_minus_nat @ M2 @ N2 ) @ N2 ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % divmod_nat_if
% 0.30/0.58  thf(fact_5323_flip__bit__Suc,axiom,
% 0.30/0.58      ! [N: nat,A: code_integer] :
% 0.30/0.58        ( ( bit_se1345352211410354436nteger @ ( suc @ N ) @ A )
% 0.30/0.58        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % flip_bit_Suc
% 0.30/0.58  thf(fact_5324_flip__bit__Suc,axiom,
% 0.30/0.58      ! [N: nat,A: code_natural] :
% 0.30/0.58        ( ( bit_se168947363167071951atural @ ( suc @ N ) @ A )
% 0.30/0.58        = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se168947363167071951atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % flip_bit_Suc
% 0.30/0.58  thf(fact_5325_flip__bit__Suc,axiom,
% 0.30/0.58      ! [N: nat,A: int] :
% 0.30/0.58        ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 0.30/0.58        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % flip_bit_Suc
% 0.30/0.58  thf(fact_5326_flip__bit__Suc,axiom,
% 0.30/0.58      ! [N: nat,A: nat] :
% 0.30/0.58        ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 0.30/0.58        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % flip_bit_Suc
% 0.30/0.58  thf(fact_5327_take__bit__numeral__minus__bit1,axiom,
% 0.30/0.58      ! [L: num,K: num] :
% 0.30/0.58        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.30/0.58        = ( 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 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_numeral_minus_bit1
% 0.30/0.58  thf(fact_5328_int__ge__less__than2__def,axiom,
% 0.30/0.58      ( int_ge_less_than2
% 0.30/0.58      = ( ^ [D4: int] :
% 0.30/0.58            ( collec213857154873943460nt_int
% 0.30/0.58            @ ( produc4947309494688390418_int_o
% 0.30/0.58              @ ^ [Z6: int,Z3: int] :
% 0.30/0.58                  ( ( ord_less_eq_int @ D4 @ Z3 )
% 0.30/0.58                  & ( ord_less_int @ Z6 @ Z3 ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % int_ge_less_than2_def
% 0.30/0.58  thf(fact_5329_int__ge__less__than__def,axiom,
% 0.30/0.58      ( int_ge_less_than
% 0.30/0.58      = ( ^ [D4: int] :
% 0.30/0.58            ( collec213857154873943460nt_int
% 0.30/0.58            @ ( produc4947309494688390418_int_o
% 0.30/0.58              @ ^ [Z6: int,Z3: int] :
% 0.30/0.58                  ( ( ord_less_eq_int @ D4 @ Z6 )
% 0.30/0.58                  & ( ord_less_int @ Z6 @ Z3 ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % int_ge_less_than_def
% 0.30/0.58  thf(fact_5330_take__bit__Suc__1,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ one_one_Code_integer )
% 0.30/0.58        = one_one_Code_integer ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_Suc_1
% 0.30/0.58  thf(fact_5331_take__bit__Suc__1,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ one_one_nat )
% 0.30/0.58        = one_one_nat ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_Suc_1
% 0.30/0.58  thf(fact_5332_take__bit__Suc__1,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ one_one_int )
% 0.30/0.58        = one_one_int ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_Suc_1
% 0.30/0.58  thf(fact_5333_take__bit__numeral__1,axiom,
% 0.30/0.58      ! [L: num] :
% 0.30/0.58        ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ L ) @ one_one_Code_integer )
% 0.30/0.58        = one_one_Code_integer ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_numeral_1
% 0.30/0.58  thf(fact_5334_take__bit__numeral__1,axiom,
% 0.30/0.58      ! [L: num] :
% 0.30/0.58        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ one_one_nat )
% 0.30/0.58        = one_one_nat ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_numeral_1
% 0.30/0.58  thf(fact_5335_take__bit__numeral__1,axiom,
% 0.30/0.58      ! [L: num] :
% 0.30/0.58        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ one_one_int )
% 0.30/0.58        = one_one_int ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_numeral_1
% 0.30/0.58  thf(fact_5336_take__bit__of__1__eq__0__iff,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( ( bit_se1745604003318907178nteger @ N @ one_one_Code_integer )
% 0.30/0.58          = zero_z3403309356797280102nteger )
% 0.30/0.58        = ( N = zero_zero_nat ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_of_1_eq_0_iff
% 0.30/0.58  thf(fact_5337_take__bit__of__1__eq__0__iff,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 0.30/0.58          = zero_zero_nat )
% 0.30/0.58        = ( N = zero_zero_nat ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_of_1_eq_0_iff
% 0.30/0.58  thf(fact_5338_take__bit__of__1__eq__0__iff,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 0.30/0.58          = zero_zero_int )
% 0.30/0.58        = ( N = zero_zero_nat ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_of_1_eq_0_iff
% 0.30/0.58  thf(fact_5339_take__bit__minus,axiom,
% 0.30/0.58      ! [N: nat,K: int] :
% 0.30/0.58        ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 0.30/0.58        = ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_minus
% 0.30/0.58  thf(fact_5340_take__bit__decr__eq,axiom,
% 0.30/0.58      ! [N: nat,K: int] :
% 0.30/0.58        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.30/0.58         != zero_zero_int )
% 0.30/0.58       => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 0.30/0.58          = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_decr_eq
% 0.30/0.58  thf(fact_5341_take__bit__Suc__bit0,axiom,
% 0.30/0.58      ! [N: nat,K: num] :
% 0.30/0.58        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.30/0.58        = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_Suc_bit0
% 0.30/0.58  thf(fact_5342_take__bit__Suc__bit0,axiom,
% 0.30/0.58      ! [N: nat,K: num] :
% 0.30/0.58        ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) )
% 0.30/0.58        = ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_Suc_bit0
% 0.30/0.58  thf(fact_5343_take__bit__Suc__bit0,axiom,
% 0.30/0.58      ! [N: nat,K: num] :
% 0.30/0.58        ( ( bit_se569199155075624693atural @ ( suc @ N ) @ ( numera5444537566228673987atural @ ( bit0 @ K ) ) )
% 0.30/0.58        = ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ N @ ( numera5444537566228673987atural @ K ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_Suc_bit0
% 0.30/0.58  thf(fact_5344_take__bit__Suc__bit0,axiom,
% 0.30/0.58      ! [N: nat,K: num] :
% 0.30/0.58        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 0.30/0.58        = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_Suc_bit0
% 0.30/0.58  thf(fact_5345_take__bit__numeral__bit0,axiom,
% 0.30/0.58      ! [L: num,K: num] :
% 0.30/0.58        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.30/0.58        = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_numeral_bit0
% 0.30/0.58  thf(fact_5346_take__bit__numeral__bit0,axiom,
% 0.30/0.58      ! [L: num,K: num] :
% 0.30/0.58        ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ L ) @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) )
% 0.30/0.58        = ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( pred_numeral @ L ) @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_numeral_bit0
% 0.30/0.58  thf(fact_5347_take__bit__numeral__bit0,axiom,
% 0.30/0.58      ! [L: num,K: num] :
% 0.30/0.58        ( ( bit_se569199155075624693atural @ ( numeral_numeral_nat @ L ) @ ( numera5444537566228673987atural @ ( bit0 @ K ) ) )
% 0.30/0.58        = ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ ( pred_numeral @ L ) @ ( numera5444537566228673987atural @ K ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_numeral_bit0
% 0.30/0.58  thf(fact_5348_take__bit__numeral__bit0,axiom,
% 0.30/0.58      ! [L: num,K: num] :
% 0.30/0.58        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 0.30/0.58        = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_numeral_bit0
% 0.30/0.58  thf(fact_5349_take__bit__Suc__minus__bit0,axiom,
% 0.30/0.58      ! [N: nat,K: num] :
% 0.30/0.58        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.30/0.58        = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_Suc_minus_bit0
% 0.30/0.58  thf(fact_5350_take__bit__numeral__minus__bit0,axiom,
% 0.30/0.58      ! [L: num,K: num] :
% 0.30/0.58        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.30/0.58        = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_numeral_minus_bit0
% 0.30/0.58  thf(fact_5351_take__bit__Suc__bit1,axiom,
% 0.30/0.58      ! [N: nat,K: num] :
% 0.30/0.58        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.30/0.58        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_Suc_bit1
% 0.30/0.58  thf(fact_5352_take__bit__Suc__bit1,axiom,
% 0.30/0.58      ! [N: nat,K: num] :
% 0.30/0.58        ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( numera6620942414471956472nteger @ ( bit1 @ K ) ) )
% 0.30/0.58        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_Suc_bit1
% 0.30/0.58  thf(fact_5353_take__bit__Suc__bit1,axiom,
% 0.30/0.58      ! [N: nat,K: num] :
% 0.30/0.58        ( ( bit_se569199155075624693atural @ ( suc @ N ) @ ( numera5444537566228673987atural @ ( bit1 @ K ) ) )
% 0.30/0.58        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ N @ ( numera5444537566228673987atural @ K ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ one_one_Code_natural ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_Suc_bit1
% 0.30/0.58  thf(fact_5354_take__bit__Suc__bit1,axiom,
% 0.30/0.58      ! [N: nat,K: num] :
% 0.30/0.58        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.30/0.58        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_Suc_bit1
% 0.30/0.58  thf(fact_5355_take__bit__Suc,axiom,
% 0.30/0.58      ! [N: nat,A: nat] :
% 0.30/0.58        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ A )
% 0.30/0.58        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_Suc
% 0.30/0.58  thf(fact_5356_take__bit__Suc,axiom,
% 0.30/0.58      ! [N: nat,A: code_integer] :
% 0.30/0.58        ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A )
% 0.30/0.58        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_Suc
% 0.30/0.58  thf(fact_5357_take__bit__Suc,axiom,
% 0.30/0.58      ! [N: nat,A: code_natural] :
% 0.30/0.58        ( ( bit_se569199155075624693atural @ ( suc @ N ) @ A )
% 0.30/0.58        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_Suc
% 0.30/0.58  thf(fact_5358_take__bit__Suc,axiom,
% 0.30/0.58      ! [N: nat,A: int] :
% 0.30/0.58        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 0.30/0.58        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_Suc
% 0.30/0.58  thf(fact_5359_take__bit__numeral__bit1,axiom,
% 0.30/0.58      ! [L: num,K: num] :
% 0.30/0.58        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.30/0.58        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_numeral_bit1
% 0.30/0.58  thf(fact_5360_take__bit__numeral__bit1,axiom,
% 0.30/0.58      ! [L: num,K: num] :
% 0.30/0.58        ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ L ) @ ( numera6620942414471956472nteger @ ( bit1 @ K ) ) )
% 0.30/0.58        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( pred_numeral @ L ) @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_numeral_bit1
% 0.30/0.58  thf(fact_5361_take__bit__numeral__bit1,axiom,
% 0.30/0.58      ! [L: num,K: num] :
% 0.30/0.58        ( ( bit_se569199155075624693atural @ ( numeral_numeral_nat @ L ) @ ( numera5444537566228673987atural @ ( bit1 @ K ) ) )
% 0.30/0.58        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ ( pred_numeral @ L ) @ ( numera5444537566228673987atural @ K ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ one_one_Code_natural ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_numeral_bit1
% 0.30/0.58  thf(fact_5362_take__bit__numeral__bit1,axiom,
% 0.30/0.58      ! [L: num,K: num] :
% 0.30/0.58        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 0.30/0.58        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_numeral_bit1
% 0.30/0.58  thf(fact_5363_divmod__nat__def,axiom,
% 0.30/0.58      ( divmod_nat
% 0.30/0.58      = ( ^ [M2: nat,N2: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M2 @ N2 ) @ ( modulo_modulo_nat @ M2 @ N2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % divmod_nat_def
% 0.30/0.58  thf(fact_5364_take__bit__Suc__minus__bit1,axiom,
% 0.30/0.58      ! [N: nat,K: num] :
% 0.30/0.58        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.30/0.58        = ( 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 ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_Suc_minus_bit1
% 0.30/0.58  thf(fact_5365_take__bit__rec,axiom,
% 0.30/0.58      ( bit_se2925701944663578781it_nat
% 0.30/0.58      = ( ^ [N2: nat,A3: nat] : ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_rec
% 0.30/0.58  thf(fact_5366_take__bit__rec,axiom,
% 0.30/0.58      ( bit_se1745604003318907178nteger
% 0.30/0.58      = ( ^ [N2: nat,A3: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_rec
% 0.30/0.58  thf(fact_5367_take__bit__rec,axiom,
% 0.30/0.58      ( bit_se569199155075624693atural
% 0.30/0.58      = ( ^ [N2: nat,A3: code_natural] : ( if_Code_natural @ ( N2 = zero_zero_nat ) @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide5121882707175180666atural @ A3 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( modulo8411746178871703098atural @ A3 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_rec
% 0.30/0.58  thf(fact_5368_take__bit__rec,axiom,
% 0.30/0.58      ( bit_se2923211474154528505it_int
% 0.30/0.58      = ( ^ [N2: nat,A3: int] : ( if_int @ ( N2 = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_rec
% 0.30/0.58  thf(fact_5369_mask__numeral,axiom,
% 0.30/0.58      ! [N: num] :
% 0.30/0.58        ( ( bit_se2119862282449309892nteger @ ( numeral_numeral_nat @ N ) )
% 0.30/0.58        = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ ( pred_numeral @ N ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mask_numeral
% 0.30/0.58  thf(fact_5370_mask__numeral,axiom,
% 0.30/0.58      ! [N: num] :
% 0.30/0.58        ( ( bit_se943457434206027407atural @ ( numeral_numeral_nat @ N ) )
% 0.30/0.58        = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se943457434206027407atural @ ( pred_numeral @ N ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mask_numeral
% 0.30/0.58  thf(fact_5371_mask__numeral,axiom,
% 0.30/0.58      ! [N: num] :
% 0.30/0.58        ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N ) )
% 0.30/0.58        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mask_numeral
% 0.30/0.58  thf(fact_5372_mask__numeral,axiom,
% 0.30/0.58      ! [N: num] :
% 0.30/0.58        ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N ) )
% 0.30/0.58        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mask_numeral
% 0.30/0.58  thf(fact_5373_and__int__unfold,axiom,
% 0.30/0.58      ( bit_se725231765392027082nd_int
% 0.30/0.58      = ( ^ [K4: int,L2: int] :
% 0.30/0.58            ( if_int
% 0.30/0.58            @ ( ( K4 = zero_zero_int )
% 0.30/0.58              | ( L2 = zero_zero_int ) )
% 0.30/0.58            @ zero_zero_int
% 0.30/0.58            @ ( if_int
% 0.30/0.58              @ ( K4
% 0.30/0.58                = ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.58              @ L2
% 0.30/0.58              @ ( if_int
% 0.30/0.58                @ ( L2
% 0.30/0.58                  = ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.58                @ K4
% 0.30/0.58                @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K4 @ ( 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 @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % and_int_unfold
% 0.30/0.58  thf(fact_5374_take__bit__minus__small__eq,axiom,
% 0.30/0.58      ! [K: int,N: nat] :
% 0.30/0.58        ( ( ord_less_int @ zero_zero_int @ K )
% 0.30/0.58       => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.58         => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 0.30/0.58            = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_minus_small_eq
% 0.30/0.58  thf(fact_5375_signed__take__bit__int__greater__eq,axiom,
% 0.30/0.58      ! [K: int,N: nat] :
% 0.30/0.58        ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 0.30/0.58       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % signed_take_bit_int_greater_eq
% 0.30/0.58  thf(fact_5376_normalize__negative,axiom,
% 0.30/0.58      ! [Q4: int,P4: int] :
% 0.30/0.58        ( ( ord_less_int @ Q4 @ zero_zero_int )
% 0.30/0.58       => ( ( normalize @ ( product_Pair_int_int @ P4 @ Q4 ) )
% 0.30/0.58          = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P4 ) @ ( uminus_uminus_int @ Q4 ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % normalize_negative
% 0.30/0.58  thf(fact_5377_odd__two__times__div__two__nat,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.58       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.30/0.58          = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % odd_two_times_div_two_nat
% 0.30/0.58  thf(fact_5378_odd__two__times__div__two__succ,axiom,
% 0.30/0.58      ! [A: nat] :
% 0.30/0.58        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 0.30/0.58          = A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % odd_two_times_div_two_succ
% 0.30/0.58  thf(fact_5379_odd__two__times__div__two__succ,axiom,
% 0.30/0.58      ! [A: int] :
% 0.30/0.58        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 0.30/0.58          = A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % odd_two_times_div_two_succ
% 0.30/0.58  thf(fact_5380_odd__two__times__div__two__succ,axiom,
% 0.30/0.58      ! [A: code_integer] :
% 0.30/0.58        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 0.30/0.58          = A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % odd_two_times_div_two_succ
% 0.30/0.58  thf(fact_5381_odd__two__times__div__two__succ,axiom,
% 0.30/0.58      ! [A: code_natural] :
% 0.30/0.58        ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ one_one_Code_natural )
% 0.30/0.58          = A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % odd_two_times_div_two_succ
% 0.30/0.58  thf(fact_5382_dvd__minus__iff,axiom,
% 0.30/0.58      ! [X: int,Y: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ X @ ( uminus_uminus_int @ Y ) )
% 0.30/0.58        = ( dvd_dvd_int @ X @ Y ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_minus_iff
% 0.30/0.58  thf(fact_5383_dvd__minus__iff,axiom,
% 0.30/0.58      ! [X: code_integer,Y: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ X @ ( uminus1351360451143612070nteger @ Y ) )
% 0.30/0.58        = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_minus_iff
% 0.30/0.58  thf(fact_5384_dvd__minus__iff,axiom,
% 0.30/0.58      ! [X: rat,Y: rat] :
% 0.30/0.58        ( ( dvd_dvd_rat @ X @ ( uminus_uminus_rat @ Y ) )
% 0.30/0.58        = ( dvd_dvd_rat @ X @ Y ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_minus_iff
% 0.30/0.58  thf(fact_5385_minus__dvd__iff,axiom,
% 0.30/0.58      ! [X: int,Y: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ ( uminus_uminus_int @ X ) @ Y )
% 0.30/0.58        = ( dvd_dvd_int @ X @ Y ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_dvd_iff
% 0.30/0.58  thf(fact_5386_minus__dvd__iff,axiom,
% 0.30/0.58      ! [X: code_integer,Y: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X ) @ Y )
% 0.30/0.58        = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_dvd_iff
% 0.30/0.58  thf(fact_5387_minus__dvd__iff,axiom,
% 0.30/0.58      ! [X: rat,Y: rat] :
% 0.30/0.58        ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X ) @ Y )
% 0.30/0.58        = ( dvd_dvd_rat @ X @ Y ) ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_dvd_iff
% 0.30/0.58  thf(fact_5388_power__one,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( power_8256067586552552935nteger @ one_one_Code_integer @ N )
% 0.30/0.58        = one_one_Code_integer ) ).
% 0.30/0.58  
% 0.30/0.58  % power_one
% 0.30/0.58  thf(fact_5389_power__one,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( power_power_assn @ one_one_assn @ N )
% 0.30/0.58        = one_one_assn ) ).
% 0.30/0.58  
% 0.30/0.58  % power_one
% 0.30/0.58  thf(fact_5390_power__one,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( power_power_rat @ one_one_rat @ N )
% 0.30/0.58        = one_one_rat ) ).
% 0.30/0.58  
% 0.30/0.58  % power_one
% 0.30/0.58  thf(fact_5391_power__one,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( power_power_int @ one_one_int @ N )
% 0.30/0.58        = one_one_int ) ).
% 0.30/0.58  
% 0.30/0.58  % power_one
% 0.30/0.58  thf(fact_5392_power__one,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( power_power_nat @ one_one_nat @ N )
% 0.30/0.58        = one_one_nat ) ).
% 0.30/0.58  
% 0.30/0.58  % power_one
% 0.30/0.58  thf(fact_5393_power__one__right,axiom,
% 0.30/0.58      ! [A: int] :
% 0.30/0.58        ( ( power_power_int @ A @ one_one_nat )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % power_one_right
% 0.30/0.58  thf(fact_5394_power__one__right,axiom,
% 0.30/0.58      ! [A: nat] :
% 0.30/0.58        ( ( power_power_nat @ A @ one_one_nat )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % power_one_right
% 0.30/0.58  thf(fact_5395_nat__dvd__1__iff__1,axiom,
% 0.30/0.58      ! [M: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ M @ one_one_nat )
% 0.30/0.58        = ( M = one_one_nat ) ) ).
% 0.30/0.58  
% 0.30/0.58  % nat_dvd_1_iff_1
% 0.30/0.58  thf(fact_5396_dvd__mult__cancel__left,axiom,
% 0.30/0.58      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.30/0.58        = ( ( C = zero_z3403309356797280102nteger )
% 0.30/0.58          | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_cancel_left
% 0.30/0.58  thf(fact_5397_dvd__mult__cancel__left,axiom,
% 0.30/0.58      ! [C: rat,A: rat,B: rat] :
% 0.30/0.58        ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 0.30/0.58        = ( ( C = zero_zero_rat )
% 0.30/0.58          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_cancel_left
% 0.30/0.58  thf(fact_5398_dvd__mult__cancel__left,axiom,
% 0.30/0.58      ! [C: int,A: int,B: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 0.30/0.58        = ( ( C = zero_zero_int )
% 0.30/0.58          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_cancel_left
% 0.30/0.58  thf(fact_5399_dvd__mult__cancel__right,axiom,
% 0.30/0.58      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.30/0.58        = ( ( C = zero_z3403309356797280102nteger )
% 0.30/0.58          | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_cancel_right
% 0.30/0.58  thf(fact_5400_dvd__mult__cancel__right,axiom,
% 0.30/0.58      ! [A: rat,C: rat,B: rat] :
% 0.30/0.58        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 0.30/0.58        = ( ( C = zero_zero_rat )
% 0.30/0.58          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_cancel_right
% 0.30/0.58  thf(fact_5401_dvd__mult__cancel__right,axiom,
% 0.30/0.58      ! [A: int,C: int,B: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 0.30/0.58        = ( ( C = zero_zero_int )
% 0.30/0.58          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_cancel_right
% 0.30/0.58  thf(fact_5402_dvd__times__left__cancel__iff,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.58        ( ( A != zero_z3403309356797280102nteger )
% 0.30/0.58       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 0.30/0.58          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_times_left_cancel_iff
% 0.30/0.58  thf(fact_5403_dvd__times__left__cancel__iff,axiom,
% 0.30/0.58      ! [A: nat,B: nat,C: nat] :
% 0.30/0.58        ( ( A != zero_zero_nat )
% 0.30/0.58       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 0.30/0.58          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_times_left_cancel_iff
% 0.30/0.58  thf(fact_5404_dvd__times__left__cancel__iff,axiom,
% 0.30/0.58      ! [A: int,B: int,C: int] :
% 0.30/0.58        ( ( A != zero_zero_int )
% 0.30/0.58       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 0.30/0.58          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_times_left_cancel_iff
% 0.30/0.58  thf(fact_5405_dvd__times__right__cancel__iff,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.58        ( ( A != zero_z3403309356797280102nteger )
% 0.30/0.58       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 0.30/0.58          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_times_right_cancel_iff
% 0.30/0.58  thf(fact_5406_dvd__times__right__cancel__iff,axiom,
% 0.30/0.58      ! [A: nat,B: nat,C: nat] :
% 0.30/0.58        ( ( A != zero_zero_nat )
% 0.30/0.58       => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 0.30/0.58          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_times_right_cancel_iff
% 0.30/0.58  thf(fact_5407_dvd__times__right__cancel__iff,axiom,
% 0.30/0.58      ! [A: int,B: int,C: int] :
% 0.30/0.58        ( ( A != zero_zero_int )
% 0.30/0.58       => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 0.30/0.58          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_times_right_cancel_iff
% 0.30/0.58  thf(fact_5408_dvd__add__times__triv__left__iff,axiom,
% 0.30/0.58      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 0.30/0.58        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_add_times_triv_left_iff
% 0.30/0.58  thf(fact_5409_dvd__add__times__triv__left__iff,axiom,
% 0.30/0.58      ! [A: rat,C: rat,B: rat] :
% 0.30/0.58        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 0.30/0.58        = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_add_times_triv_left_iff
% 0.30/0.58  thf(fact_5410_dvd__add__times__triv__left__iff,axiom,
% 0.30/0.58      ! [A: nat,C: nat,B: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 0.30/0.58        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_add_times_triv_left_iff
% 0.30/0.58  thf(fact_5411_dvd__add__times__triv__left__iff,axiom,
% 0.30/0.58      ! [A: int,C: int,B: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 0.30/0.58        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_add_times_triv_left_iff
% 0.30/0.58  thf(fact_5412_dvd__add__times__triv__right__iff,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 0.30/0.58        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_add_times_triv_right_iff
% 0.30/0.58  thf(fact_5413_dvd__add__times__triv__right__iff,axiom,
% 0.30/0.58      ! [A: rat,B: rat,C: rat] :
% 0.30/0.58        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 0.30/0.58        = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_add_times_triv_right_iff
% 0.30/0.58  thf(fact_5414_dvd__add__times__triv__right__iff,axiom,
% 0.30/0.58      ! [A: nat,B: nat,C: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 0.30/0.58        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_add_times_triv_right_iff
% 0.30/0.58  thf(fact_5415_dvd__add__times__triv__right__iff,axiom,
% 0.30/0.58      ! [A: int,B: int,C: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 0.30/0.58        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_add_times_triv_right_iff
% 0.30/0.58  thf(fact_5416_unit__prod,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.30/0.58       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.30/0.58         => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_prod
% 0.30/0.58  thf(fact_5417_unit__prod,axiom,
% 0.30/0.58      ! [A: nat,B: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.30/0.58       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.30/0.58         => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_prod
% 0.30/0.58  thf(fact_5418_unit__prod,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.30/0.58       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.30/0.58         => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_prod
% 0.30/0.58  thf(fact_5419_power__inject__exp,axiom,
% 0.30/0.58      ! [A: code_integer,M: nat,N: nat] :
% 0.30/0.58        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.30/0.58       => ( ( ( power_8256067586552552935nteger @ A @ M )
% 0.30/0.58            = ( power_8256067586552552935nteger @ A @ N ) )
% 0.30/0.58          = ( M = N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_inject_exp
% 0.30/0.58  thf(fact_5420_power__inject__exp,axiom,
% 0.30/0.58      ! [A: rat,M: nat,N: nat] :
% 0.30/0.58        ( ( ord_less_rat @ one_one_rat @ A )
% 0.30/0.58       => ( ( ( power_power_rat @ A @ M )
% 0.30/0.58            = ( power_power_rat @ A @ N ) )
% 0.30/0.58          = ( M = N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_inject_exp
% 0.30/0.58  thf(fact_5421_power__inject__exp,axiom,
% 0.30/0.58      ! [A: nat,M: nat,N: nat] :
% 0.30/0.58        ( ( ord_less_nat @ one_one_nat @ A )
% 0.30/0.58       => ( ( ( power_power_nat @ A @ M )
% 0.30/0.58            = ( power_power_nat @ A @ N ) )
% 0.30/0.58          = ( M = N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_inject_exp
% 0.30/0.58  thf(fact_5422_power__inject__exp,axiom,
% 0.30/0.58      ! [A: int,M: nat,N: nat] :
% 0.30/0.58        ( ( ord_less_int @ one_one_int @ A )
% 0.30/0.58       => ( ( ( power_power_int @ A @ M )
% 0.30/0.58            = ( power_power_int @ A @ N ) )
% 0.30/0.58          = ( M = N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_inject_exp
% 0.30/0.58  thf(fact_5423_dvd__div__mult__self,axiom,
% 0.30/0.58      ! [A: nat,B: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ A @ B )
% 0.30/0.58       => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 0.30/0.58          = B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_div_mult_self
% 0.30/0.58  thf(fact_5424_dvd__div__mult__self,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ A @ B )
% 0.30/0.58       => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 0.30/0.58          = B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_div_mult_self
% 0.30/0.58  thf(fact_5425_dvd__div__mult__self,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.30/0.58       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 0.30/0.58          = B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_div_mult_self
% 0.30/0.58  thf(fact_5426_dvd__div__mult__self,axiom,
% 0.30/0.58      ! [A: code_natural,B: code_natural] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ A @ B )
% 0.30/0.58       => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ B @ A ) @ A )
% 0.30/0.58          = B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_div_mult_self
% 0.30/0.58  thf(fact_5427_dvd__mult__div__cancel,axiom,
% 0.30/0.58      ! [A: nat,B: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ A @ B )
% 0.30/0.58       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 0.30/0.58          = B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_div_cancel
% 0.30/0.58  thf(fact_5428_dvd__mult__div__cancel,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ A @ B )
% 0.30/0.58       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 0.30/0.58          = B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_div_cancel
% 0.30/0.58  thf(fact_5429_dvd__mult__div__cancel,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.30/0.58       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 0.30/0.58          = B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_div_cancel
% 0.30/0.58  thf(fact_5430_dvd__mult__div__cancel,axiom,
% 0.30/0.58      ! [A: code_natural,B: code_natural] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ A @ B )
% 0.30/0.58       => ( ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ A ) )
% 0.30/0.58          = B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_div_cancel
% 0.30/0.58  thf(fact_5431_unit__div,axiom,
% 0.30/0.58      ! [A: nat,B: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.30/0.58       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.30/0.58         => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_div
% 0.30/0.58  thf(fact_5432_unit__div,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.30/0.58       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.30/0.58         => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_div
% 0.30/0.58  thf(fact_5433_unit__div,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.30/0.58       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.30/0.58         => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_div
% 0.30/0.58  thf(fact_5434_unit__div,axiom,
% 0.30/0.58      ! [A: code_natural,B: code_natural] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 0.30/0.58       => ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.30/0.58         => ( dvd_dvd_Code_natural @ ( divide5121882707175180666atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_div
% 0.30/0.58  thf(fact_5435_unit__div__1__unit,axiom,
% 0.30/0.58      ! [A: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.30/0.58       => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_div_1_unit
% 0.30/0.58  thf(fact_5436_unit__div__1__unit,axiom,
% 0.30/0.58      ! [A: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.30/0.58       => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_div_1_unit
% 0.30/0.58  thf(fact_5437_unit__div__1__unit,axiom,
% 0.30/0.58      ! [A: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.30/0.58       => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_div_1_unit
% 0.30/0.58  thf(fact_5438_unit__div__1__unit,axiom,
% 0.30/0.58      ! [A: code_natural] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 0.30/0.58       => ( dvd_dvd_Code_natural @ ( divide5121882707175180666atural @ one_one_Code_natural @ A ) @ one_one_Code_natural ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_div_1_unit
% 0.30/0.58  thf(fact_5439_unit__div__1__div__1,axiom,
% 0.30/0.58      ! [A: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.30/0.58       => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 0.30/0.58          = A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_div_1_div_1
% 0.30/0.58  thf(fact_5440_unit__div__1__div__1,axiom,
% 0.30/0.58      ! [A: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.30/0.58       => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 0.30/0.58          = A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_div_1_div_1
% 0.30/0.58  thf(fact_5441_unit__div__1__div__1,axiom,
% 0.30/0.58      ! [A: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.30/0.58       => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 0.30/0.58          = A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_div_1_div_1
% 0.30/0.58  thf(fact_5442_unit__div__1__div__1,axiom,
% 0.30/0.58      ! [A: code_natural] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 0.30/0.58       => ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( divide5121882707175180666atural @ one_one_Code_natural @ A ) )
% 0.30/0.58          = A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_div_1_div_1
% 0.30/0.58  thf(fact_5443_and_Oleft__neutral,axiom,
% 0.30/0.58      ! [A: code_integer] :
% 0.30/0.58        ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % and.left_neutral
% 0.30/0.58  thf(fact_5444_and_Oleft__neutral,axiom,
% 0.30/0.58      ! [A: int] :
% 0.30/0.58        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % and.left_neutral
% 0.30/0.58  thf(fact_5445_and_Oright__neutral,axiom,
% 0.30/0.58      ! [A: code_integer] :
% 0.30/0.58        ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % and.right_neutral
% 0.30/0.58  thf(fact_5446_and_Oright__neutral,axiom,
% 0.30/0.58      ! [A: int] :
% 0.30/0.58        ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % and.right_neutral
% 0.30/0.58  thf(fact_5447_bit_Oconj__one__right,axiom,
% 0.30/0.58      ! [X: code_integer] :
% 0.30/0.58        ( ( bit_se3949692690581998587nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.58        = X ) ).
% 0.30/0.58  
% 0.30/0.58  % bit.conj_one_right
% 0.30/0.58  thf(fact_5448_bit_Oconj__one__right,axiom,
% 0.30/0.58      ! [X: int] :
% 0.30/0.58        ( ( bit_se725231765392027082nd_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.58        = X ) ).
% 0.30/0.58  
% 0.30/0.58  % bit.conj_one_right
% 0.30/0.58  thf(fact_5449_unit__mult__div__div,axiom,
% 0.30/0.58      ! [A: nat,B: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.30/0.58       => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 0.30/0.58          = ( divide_divide_nat @ B @ A ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_mult_div_div
% 0.30/0.58  thf(fact_5450_unit__mult__div__div,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.30/0.58       => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 0.30/0.58          = ( divide_divide_int @ B @ A ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_mult_div_div
% 0.30/0.58  thf(fact_5451_unit__mult__div__div,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.30/0.58       => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 0.30/0.58          = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_mult_div_div
% 0.30/0.58  thf(fact_5452_unit__mult__div__div,axiom,
% 0.30/0.58      ! [A: code_natural,B: code_natural] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 0.30/0.58       => ( ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ one_one_Code_natural @ A ) )
% 0.30/0.58          = ( divide5121882707175180666atural @ B @ A ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_mult_div_div
% 0.30/0.58  thf(fact_5453_unit__div__mult__self,axiom,
% 0.30/0.58      ! [A: nat,B: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.30/0.58       => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 0.30/0.58          = B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_div_mult_self
% 0.30/0.58  thf(fact_5454_unit__div__mult__self,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.30/0.58       => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 0.30/0.58          = B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_div_mult_self
% 0.30/0.58  thf(fact_5455_unit__div__mult__self,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.30/0.58       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 0.30/0.58          = B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_div_mult_self
% 0.30/0.58  thf(fact_5456_unit__div__mult__self,axiom,
% 0.30/0.58      ! [A: code_natural,B: code_natural] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 0.30/0.58       => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ B @ A ) @ A )
% 0.30/0.58          = B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_div_mult_self
% 0.30/0.58  thf(fact_5457_power__strict__increasing__iff,axiom,
% 0.30/0.58      ! [B: code_integer,X: nat,Y: nat] :
% 0.30/0.58        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 0.30/0.58       => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ X ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 0.30/0.58          = ( ord_less_nat @ X @ Y ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_strict_increasing_iff
% 0.30/0.58  thf(fact_5458_power__strict__increasing__iff,axiom,
% 0.30/0.58      ! [B: rat,X: nat,Y: nat] :
% 0.30/0.58        ( ( ord_less_rat @ one_one_rat @ B )
% 0.30/0.58       => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 0.30/0.58          = ( ord_less_nat @ X @ Y ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_strict_increasing_iff
% 0.30/0.58  thf(fact_5459_power__strict__increasing__iff,axiom,
% 0.30/0.58      ! [B: nat,X: nat,Y: nat] :
% 0.30/0.58        ( ( ord_less_nat @ one_one_nat @ B )
% 0.30/0.58       => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 0.30/0.58          = ( ord_less_nat @ X @ Y ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_strict_increasing_iff
% 0.30/0.58  thf(fact_5460_power__strict__increasing__iff,axiom,
% 0.30/0.58      ! [B: int,X: nat,Y: nat] :
% 0.30/0.58        ( ( ord_less_int @ one_one_int @ B )
% 0.30/0.58       => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 0.30/0.58          = ( ord_less_nat @ X @ Y ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_strict_increasing_iff
% 0.30/0.58  thf(fact_5461_minus__one__mult__self,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 0.30/0.58        = one_one_int ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_one_mult_self
% 0.30/0.58  thf(fact_5462_minus__one__mult__self,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 0.30/0.58        = one_one_Code_integer ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_one_mult_self
% 0.30/0.58  thf(fact_5463_minus__one__mult__self,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 0.30/0.58        = one_one_rat ) ).
% 0.30/0.58  
% 0.30/0.58  % minus_one_mult_self
% 0.30/0.58  thf(fact_5464_left__minus__one__mult__self,axiom,
% 0.30/0.58      ! [N: nat,A: int] :
% 0.30/0.58        ( ( 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 ) )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % left_minus_one_mult_self
% 0.30/0.58  thf(fact_5465_left__minus__one__mult__self,axiom,
% 0.30/0.58      ! [N: nat,A: code_integer] :
% 0.30/0.58        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % left_minus_one_mult_self
% 0.30/0.58  thf(fact_5466_left__minus__one__mult__self,axiom,
% 0.30/0.58      ! [N: nat,A: rat] :
% 0.30/0.58        ( ( 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 ) )
% 0.30/0.58        = A ) ).
% 0.30/0.58  
% 0.30/0.58  % left_minus_one_mult_self
% 0.30/0.58  thf(fact_5467_and__numerals_I8_J,axiom,
% 0.30/0.58      ! [X: num] :
% 0.30/0.58        ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ one_one_Code_integer )
% 0.30/0.58        = one_one_Code_integer ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(8)
% 0.30/0.58  thf(fact_5468_and__numerals_I8_J,axiom,
% 0.30/0.58      ! [X: num] :
% 0.30/0.58        ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ one_one_Code_natural )
% 0.30/0.58        = one_one_Code_natural ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(8)
% 0.30/0.58  thf(fact_5469_and__numerals_I8_J,axiom,
% 0.30/0.58      ! [X: num] :
% 0.30/0.58        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 0.30/0.58        = one_one_int ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(8)
% 0.30/0.58  thf(fact_5470_and__numerals_I8_J,axiom,
% 0.30/0.58      ! [X: num] :
% 0.30/0.58        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 0.30/0.58        = one_one_nat ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(8)
% 0.30/0.58  thf(fact_5471_and__numerals_I2_J,axiom,
% 0.30/0.58      ! [Y: num] :
% 0.30/0.58        ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 0.30/0.58        = one_one_Code_integer ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(2)
% 0.30/0.58  thf(fact_5472_and__numerals_I2_J,axiom,
% 0.30/0.58      ! [Y: num] :
% 0.30/0.58        ( ( bit_se2773287842338716102atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 0.30/0.58        = one_one_Code_natural ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(2)
% 0.30/0.58  thf(fact_5473_and__numerals_I2_J,axiom,
% 0.30/0.58      ! [Y: num] :
% 0.30/0.58        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.30/0.58        = one_one_int ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(2)
% 0.30/0.58  thf(fact_5474_and__numerals_I2_J,axiom,
% 0.30/0.58      ! [Y: num] :
% 0.30/0.58        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.30/0.58        = one_one_nat ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(2)
% 0.30/0.58  thf(fact_5475_mask__Suc__0,axiom,
% 0.30/0.58      ( ( bit_se2119862282449309892nteger @ ( suc @ zero_zero_nat ) )
% 0.30/0.58      = one_one_Code_integer ) ).
% 0.30/0.58  
% 0.30/0.58  % mask_Suc_0
% 0.30/0.58  thf(fact_5476_mask__Suc__0,axiom,
% 0.30/0.58      ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 0.30/0.58      = one_one_int ) ).
% 0.30/0.58  
% 0.30/0.58  % mask_Suc_0
% 0.30/0.58  thf(fact_5477_mask__Suc__0,axiom,
% 0.30/0.58      ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 0.30/0.58      = one_one_nat ) ).
% 0.30/0.58  
% 0.30/0.58  % mask_Suc_0
% 0.30/0.58  thf(fact_5478_power__add__numeral,axiom,
% 0.30/0.58      ! [A: code_integer,M: num,N: num] :
% 0.30/0.58        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.30/0.58        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_add_numeral
% 0.30/0.58  thf(fact_5479_power__add__numeral,axiom,
% 0.30/0.58      ! [A: assn,M: num,N: num] :
% 0.30/0.58        ( ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_assn @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.30/0.58        = ( power_power_assn @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_add_numeral
% 0.30/0.58  thf(fact_5480_power__add__numeral,axiom,
% 0.30/0.58      ! [A: rat,M: num,N: num] :
% 0.30/0.58        ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.30/0.58        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_add_numeral
% 0.30/0.58  thf(fact_5481_power__add__numeral,axiom,
% 0.30/0.58      ! [A: nat,M: num,N: num] :
% 0.30/0.58        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.30/0.58        = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_add_numeral
% 0.30/0.58  thf(fact_5482_power__add__numeral,axiom,
% 0.30/0.58      ! [A: int,M: num,N: num] :
% 0.30/0.58        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.30/0.58        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_add_numeral
% 0.30/0.58  thf(fact_5483_power__add__numeral2,axiom,
% 0.30/0.58      ! [A: code_integer,M: num,N: num,B: code_integer] :
% 0.30/0.58        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.30/0.58        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_add_numeral2
% 0.30/0.58  thf(fact_5484_power__add__numeral2,axiom,
% 0.30/0.58      ! [A: assn,M: num,N: num,B: assn] :
% 0.30/0.58        ( ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.30/0.58        = ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_add_numeral2
% 0.30/0.58  thf(fact_5485_power__add__numeral2,axiom,
% 0.30/0.58      ! [A: rat,M: num,N: num,B: rat] :
% 0.30/0.58        ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.30/0.58        = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_add_numeral2
% 0.30/0.58  thf(fact_5486_power__add__numeral2,axiom,
% 0.30/0.58      ! [A: nat,M: num,N: num,B: nat] :
% 0.30/0.58        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.30/0.58        = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_add_numeral2
% 0.30/0.58  thf(fact_5487_power__add__numeral2,axiom,
% 0.30/0.58      ! [A: int,M: num,N: num,B: int] :
% 0.30/0.58        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.30/0.58        = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_add_numeral2
% 0.30/0.58  thf(fact_5488_take__bit__minus__one__eq__mask,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( bit_se1745604003318907178nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.58        = ( bit_se2119862282449309892nteger @ N ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_minus_one_eq_mask
% 0.30/0.58  thf(fact_5489_take__bit__minus__one__eq__mask,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.58        = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_minus_one_eq_mask
% 0.30/0.58  thf(fact_5490_normalize__denom__zero,axiom,
% 0.30/0.58      ! [P4: int] :
% 0.30/0.58        ( ( normalize @ ( product_Pair_int_int @ P4 @ zero_zero_int ) )
% 0.30/0.58        = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 0.30/0.58  
% 0.30/0.58  % normalize_denom_zero
% 0.30/0.58  thf(fact_5491_power__strict__decreasing__iff,axiom,
% 0.30/0.58      ! [B: code_integer,M: nat,N: nat] :
% 0.30/0.58        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.30/0.58       => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 0.30/0.58         => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ M ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 0.30/0.58            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_strict_decreasing_iff
% 0.30/0.58  thf(fact_5492_power__strict__decreasing__iff,axiom,
% 0.30/0.58      ! [B: rat,M: nat,N: nat] :
% 0.30/0.58        ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.30/0.58       => ( ( ord_less_rat @ B @ one_one_rat )
% 0.30/0.58         => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 0.30/0.58            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_strict_decreasing_iff
% 0.30/0.58  thf(fact_5493_power__strict__decreasing__iff,axiom,
% 0.30/0.58      ! [B: nat,M: nat,N: nat] :
% 0.30/0.58        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.30/0.58       => ( ( ord_less_nat @ B @ one_one_nat )
% 0.30/0.58         => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 0.30/0.58            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_strict_decreasing_iff
% 0.30/0.58  thf(fact_5494_power__strict__decreasing__iff,axiom,
% 0.30/0.58      ! [B: int,M: nat,N: nat] :
% 0.30/0.58        ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.58       => ( ( ord_less_int @ B @ one_one_int )
% 0.30/0.58         => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 0.30/0.58            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_strict_decreasing_iff
% 0.30/0.58  thf(fact_5495_even__mult__iff,axiom,
% 0.30/0.58      ! [A: nat,B: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 0.30/0.58        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.30/0.58          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_mult_iff
% 0.30/0.58  thf(fact_5496_even__mult__iff,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 0.30/0.58        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.30/0.58          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_mult_iff
% 0.30/0.58  thf(fact_5497_even__mult__iff,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.30/0.58        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.30/0.58          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_mult_iff
% 0.30/0.58  thf(fact_5498_even__mult__iff,axiom,
% 0.30/0.58      ! [A: code_natural,B: code_natural] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( times_2397367101498566445atural @ A @ B ) )
% 0.30/0.58        = ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.30/0.58          | ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_mult_iff
% 0.30/0.58  thf(fact_5499_power__increasing__iff,axiom,
% 0.30/0.58      ! [B: code_integer,X: nat,Y: nat] :
% 0.30/0.58        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 0.30/0.58       => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ X ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 0.30/0.58          = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_increasing_iff
% 0.30/0.58  thf(fact_5500_power__increasing__iff,axiom,
% 0.30/0.58      ! [B: rat,X: nat,Y: nat] :
% 0.30/0.58        ( ( ord_less_rat @ one_one_rat @ B )
% 0.30/0.58       => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 0.30/0.58          = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_increasing_iff
% 0.30/0.58  thf(fact_5501_power__increasing__iff,axiom,
% 0.30/0.58      ! [B: nat,X: nat,Y: nat] :
% 0.30/0.58        ( ( ord_less_nat @ one_one_nat @ B )
% 0.30/0.58       => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 0.30/0.58          = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_increasing_iff
% 0.30/0.58  thf(fact_5502_power__increasing__iff,axiom,
% 0.30/0.58      ! [B: int,X: nat,Y: nat] :
% 0.30/0.58        ( ( ord_less_int @ one_one_int @ B )
% 0.30/0.58       => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 0.30/0.58          = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_increasing_iff
% 0.30/0.58  thf(fact_5503_and__numerals_I5_J,axiom,
% 0.30/0.58      ! [X: num] :
% 0.30/0.58        ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ one_one_Code_integer )
% 0.30/0.58        = zero_z3403309356797280102nteger ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(5)
% 0.30/0.58  thf(fact_5504_and__numerals_I5_J,axiom,
% 0.30/0.58      ! [X: num] :
% 0.30/0.58        ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ one_one_Code_natural )
% 0.30/0.58        = zero_z2226904508553997617atural ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(5)
% 0.30/0.58  thf(fact_5505_and__numerals_I5_J,axiom,
% 0.30/0.58      ! [X: num] :
% 0.30/0.58        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 0.30/0.58        = zero_zero_int ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(5)
% 0.30/0.58  thf(fact_5506_and__numerals_I5_J,axiom,
% 0.30/0.58      ! [X: num] :
% 0.30/0.58        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 0.30/0.58        = zero_zero_nat ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(5)
% 0.30/0.58  thf(fact_5507_and__numerals_I1_J,axiom,
% 0.30/0.58      ! [Y: num] :
% 0.30/0.58        ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 0.30/0.58        = zero_z3403309356797280102nteger ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(1)
% 0.30/0.58  thf(fact_5508_and__numerals_I1_J,axiom,
% 0.30/0.58      ! [Y: num] :
% 0.30/0.58        ( ( bit_se2773287842338716102atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 0.30/0.58        = zero_z2226904508553997617atural ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(1)
% 0.30/0.58  thf(fact_5509_and__numerals_I1_J,axiom,
% 0.30/0.58      ! [Y: num] :
% 0.30/0.58        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.30/0.58        = zero_zero_int ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(1)
% 0.30/0.58  thf(fact_5510_and__numerals_I1_J,axiom,
% 0.30/0.58      ! [Y: num] :
% 0.30/0.58        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.30/0.58        = zero_zero_nat ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(1)
% 0.30/0.58  thf(fact_5511_and__numerals_I3_J,axiom,
% 0.30/0.58      ! [X: num,Y: num] :
% 0.30/0.58        ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 0.30/0.58        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(3)
% 0.30/0.58  thf(fact_5512_and__numerals_I3_J,axiom,
% 0.30/0.58      ! [X: num,Y: num] :
% 0.30/0.58        ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 0.30/0.58        = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(3)
% 0.30/0.58  thf(fact_5513_and__numerals_I3_J,axiom,
% 0.30/0.58      ! [X: num,Y: num] :
% 0.30/0.58        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.30/0.58        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(3)
% 0.30/0.58  thf(fact_5514_and__numerals_I3_J,axiom,
% 0.30/0.58      ! [X: num,Y: num] :
% 0.30/0.58        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.30/0.58        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(3)
% 0.30/0.58  thf(fact_5515_power2__minus,axiom,
% 0.30/0.58      ! [A: int] :
% 0.30/0.58        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.58        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power2_minus
% 0.30/0.58  thf(fact_5516_power2__minus,axiom,
% 0.30/0.58      ! [A: code_integer] :
% 0.30/0.58        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.58        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power2_minus
% 0.30/0.58  thf(fact_5517_power2__minus,axiom,
% 0.30/0.58      ! [A: rat] :
% 0.30/0.58        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.58        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power2_minus
% 0.30/0.58  thf(fact_5518_and__minus__numerals_I6_J,axiom,
% 0.30/0.58      ! [N: num] :
% 0.30/0.58        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 0.30/0.58        = one_one_int ) ).
% 0.30/0.58  
% 0.30/0.58  % and_minus_numerals(6)
% 0.30/0.58  thf(fact_5519_and__minus__numerals_I2_J,axiom,
% 0.30/0.58      ! [N: num] :
% 0.30/0.58        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.30/0.58        = one_one_int ) ).
% 0.30/0.58  
% 0.30/0.58  % and_minus_numerals(2)
% 0.30/0.58  thf(fact_5520_power__decreasing__iff,axiom,
% 0.30/0.58      ! [B: code_integer,M: nat,N: nat] :
% 0.30/0.58        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.30/0.58       => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 0.30/0.58         => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ M ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 0.30/0.58            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_decreasing_iff
% 0.30/0.58  thf(fact_5521_power__decreasing__iff,axiom,
% 0.30/0.58      ! [B: rat,M: nat,N: nat] :
% 0.30/0.58        ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.30/0.58       => ( ( ord_less_rat @ B @ one_one_rat )
% 0.30/0.58         => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 0.30/0.58            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_decreasing_iff
% 0.30/0.58  thf(fact_5522_power__decreasing__iff,axiom,
% 0.30/0.58      ! [B: nat,M: nat,N: nat] :
% 0.30/0.58        ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.30/0.58       => ( ( ord_less_nat @ B @ one_one_nat )
% 0.30/0.58         => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 0.30/0.58            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_decreasing_iff
% 0.30/0.58  thf(fact_5523_power__decreasing__iff,axiom,
% 0.30/0.58      ! [B: int,M: nat,N: nat] :
% 0.30/0.58        ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.58       => ( ( ord_less_int @ B @ one_one_int )
% 0.30/0.58         => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 0.30/0.58            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_decreasing_iff
% 0.30/0.58  thf(fact_5524_even__plus__one__iff,axiom,
% 0.30/0.58      ! [A: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 0.30/0.58        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_plus_one_iff
% 0.30/0.58  thf(fact_5525_even__plus__one__iff,axiom,
% 0.30/0.58      ! [A: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 0.30/0.58        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_plus_one_iff
% 0.30/0.58  thf(fact_5526_even__plus__one__iff,axiom,
% 0.30/0.58      ! [A: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 0.30/0.58        = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_plus_one_iff
% 0.30/0.58  thf(fact_5527_even__plus__one__iff,axiom,
% 0.30/0.58      ! [A: code_natural] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) )
% 0.30/0.58        = ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_plus_one_iff
% 0.30/0.58  thf(fact_5528_and__numerals_I4_J,axiom,
% 0.30/0.58      ! [X: num,Y: num] :
% 0.30/0.58        ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 0.30/0.58        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(4)
% 0.30/0.58  thf(fact_5529_and__numerals_I4_J,axiom,
% 0.30/0.58      ! [X: num,Y: num] :
% 0.30/0.58        ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 0.30/0.58        = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(4)
% 0.30/0.58  thf(fact_5530_and__numerals_I4_J,axiom,
% 0.30/0.58      ! [X: num,Y: num] :
% 0.30/0.58        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.30/0.58        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(4)
% 0.30/0.58  thf(fact_5531_and__numerals_I4_J,axiom,
% 0.30/0.58      ! [X: num,Y: num] :
% 0.30/0.58        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.30/0.58        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(4)
% 0.30/0.58  thf(fact_5532_and__numerals_I6_J,axiom,
% 0.30/0.58      ! [X: num,Y: num] :
% 0.30/0.58        ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 0.30/0.58        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(6)
% 0.30/0.58  thf(fact_5533_and__numerals_I6_J,axiom,
% 0.30/0.58      ! [X: num,Y: num] :
% 0.30/0.58        ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 0.30/0.58        = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(6)
% 0.30/0.58  thf(fact_5534_and__numerals_I6_J,axiom,
% 0.30/0.58      ! [X: num,Y: num] :
% 0.30/0.58        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.30/0.58        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(6)
% 0.30/0.58  thf(fact_5535_and__numerals_I6_J,axiom,
% 0.30/0.58      ! [X: num,Y: num] :
% 0.30/0.58        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.30/0.58        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(6)
% 0.30/0.58  thf(fact_5536_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.30/0.58      ! [A: int,N: nat] :
% 0.30/0.58        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.58        = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Power.ring_1_class.power_minus_even
% 0.30/0.58  thf(fact_5537_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.30/0.58      ! [A: code_integer,N: nat] :
% 0.30/0.58        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.58        = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Power.ring_1_class.power_minus_even
% 0.30/0.58  thf(fact_5538_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.30/0.58      ! [A: rat,N: nat] :
% 0.30/0.58        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.58        = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Power.ring_1_class.power_minus_even
% 0.30/0.58  thf(fact_5539_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.30/0.58      ! [N: nat,A: int] :
% 0.30/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.58       => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.30/0.58          = ( power_power_int @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Parity.ring_1_class.power_minus_even
% 0.30/0.58  thf(fact_5540_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.30/0.58      ! [N: nat,A: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.58       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.30/0.58          = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Parity.ring_1_class.power_minus_even
% 0.30/0.58  thf(fact_5541_Parity_Oring__1__class_Opower__minus__even,axiom,
% 0.30/0.58      ! [N: nat,A: rat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.58       => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.30/0.58          = ( power_power_rat @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % Parity.ring_1_class.power_minus_even
% 0.30/0.58  thf(fact_5542_power__minus__odd,axiom,
% 0.30/0.58      ! [N: nat,A: int] :
% 0.30/0.58        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.58       => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.30/0.58          = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_minus_odd
% 0.30/0.58  thf(fact_5543_power__minus__odd,axiom,
% 0.30/0.58      ! [N: nat,A: code_integer] :
% 0.30/0.58        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.58       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.30/0.58          = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_minus_odd
% 0.30/0.58  thf(fact_5544_power__minus__odd,axiom,
% 0.30/0.58      ! [N: nat,A: rat] :
% 0.30/0.58        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.58       => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.30/0.58          = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_minus_odd
% 0.30/0.58  thf(fact_5545_and__minus__numerals_I5_J,axiom,
% 0.30/0.58      ! [N: num] :
% 0.30/0.58        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 0.30/0.58        = zero_zero_int ) ).
% 0.30/0.58  
% 0.30/0.58  % and_minus_numerals(5)
% 0.30/0.58  thf(fact_5546_and__minus__numerals_I1_J,axiom,
% 0.30/0.58      ! [N: num] :
% 0.30/0.58        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.30/0.58        = zero_zero_int ) ).
% 0.30/0.58  
% 0.30/0.58  % and_minus_numerals(1)
% 0.30/0.58  thf(fact_5547_even__succ__div__two,axiom,
% 0.30/0.58      ! [A: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.58          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_succ_div_two
% 0.30/0.58  thf(fact_5548_even__succ__div__two,axiom,
% 0.30/0.58      ! [A: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.58          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_succ_div_two
% 0.30/0.58  thf(fact_5549_even__succ__div__two,axiom,
% 0.30/0.58      ! [A: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.58          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_succ_div_two
% 0.30/0.58  thf(fact_5550_even__succ__div__two,axiom,
% 0.30/0.58      ! [A: code_natural] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.58          = ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_succ_div_two
% 0.30/0.58  thf(fact_5551_odd__succ__div__two,axiom,
% 0.30/0.58      ! [A: nat] :
% 0.30/0.58        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.58          = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % odd_succ_div_two
% 0.30/0.58  thf(fact_5552_odd__succ__div__two,axiom,
% 0.30/0.58      ! [A: int] :
% 0.30/0.58        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.58          = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % odd_succ_div_two
% 0.30/0.58  thf(fact_5553_odd__succ__div__two,axiom,
% 0.30/0.58      ! [A: code_integer] :
% 0.30/0.58        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.58          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % odd_succ_div_two
% 0.30/0.58  thf(fact_5554_odd__succ__div__two,axiom,
% 0.30/0.58      ! [A: code_natural] :
% 0.30/0.58        ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.58          = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ one_one_Code_natural ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % odd_succ_div_two
% 0.30/0.58  thf(fact_5555_even__succ__div__2,axiom,
% 0.30/0.58      ! [A: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.58          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_succ_div_2
% 0.30/0.58  thf(fact_5556_even__succ__div__2,axiom,
% 0.30/0.58      ! [A: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.58          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_succ_div_2
% 0.30/0.58  thf(fact_5557_even__succ__div__2,axiom,
% 0.30/0.58      ! [A: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.58          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_succ_div_2
% 0.30/0.58  thf(fact_5558_even__succ__div__2,axiom,
% 0.30/0.58      ! [A: code_natural] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.58          = ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_succ_div_2
% 0.30/0.58  thf(fact_5559_power__minus1__even,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.58        = one_one_int ) ).
% 0.30/0.58  
% 0.30/0.58  % power_minus1_even
% 0.30/0.58  thf(fact_5560_power__minus1__even,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.58        = one_one_Code_integer ) ).
% 0.30/0.58  
% 0.30/0.58  % power_minus1_even
% 0.30/0.58  thf(fact_5561_power__minus1__even,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.58        = one_one_rat ) ).
% 0.30/0.58  
% 0.30/0.58  % power_minus1_even
% 0.30/0.58  thf(fact_5562_neg__one__odd__power,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.58       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 0.30/0.58          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % neg_one_odd_power
% 0.30/0.58  thf(fact_5563_neg__one__odd__power,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.58       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 0.30/0.58          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % neg_one_odd_power
% 0.30/0.58  thf(fact_5564_neg__one__odd__power,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.58       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 0.30/0.58          = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % neg_one_odd_power
% 0.30/0.58  thf(fact_5565_neg__one__even__power,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.58       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 0.30/0.58          = one_one_int ) ) ).
% 0.30/0.58  
% 0.30/0.58  % neg_one_even_power
% 0.30/0.58  thf(fact_5566_neg__one__even__power,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.58       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 0.30/0.58          = one_one_Code_integer ) ) ).
% 0.30/0.58  
% 0.30/0.58  % neg_one_even_power
% 0.30/0.58  thf(fact_5567_neg__one__even__power,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.58       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 0.30/0.58          = one_one_rat ) ) ).
% 0.30/0.58  
% 0.30/0.58  % neg_one_even_power
% 0.30/0.58  thf(fact_5568_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 0.30/0.58        = ( N = zero_zero_nat ) ) ).
% 0.30/0.58  
% 0.30/0.58  % semiring_parity_class.even_mask_iff
% 0.30/0.58  thf(fact_5569_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 0.30/0.58        = ( N = zero_zero_nat ) ) ).
% 0.30/0.58  
% 0.30/0.58  % semiring_parity_class.even_mask_iff
% 0.30/0.58  thf(fact_5570_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 0.30/0.58        = ( N = zero_zero_nat ) ) ).
% 0.30/0.58  
% 0.30/0.58  % semiring_parity_class.even_mask_iff
% 0.30/0.58  thf(fact_5571_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.30/0.58      ! [N: nat] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) @ one_one_Code_natural ) )
% 0.30/0.58        = ( N = zero_zero_nat ) ) ).
% 0.30/0.58  
% 0.30/0.58  % semiring_parity_class.even_mask_iff
% 0.30/0.58  thf(fact_5572_and__numerals_I7_J,axiom,
% 0.30/0.58      ! [X: num,Y: num] :
% 0.30/0.58        ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 0.30/0.58        = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(7)
% 0.30/0.58  thf(fact_5573_and__numerals_I7_J,axiom,
% 0.30/0.58      ! [X: num,Y: num] :
% 0.30/0.58        ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 0.30/0.58        = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(7)
% 0.30/0.58  thf(fact_5574_and__numerals_I7_J,axiom,
% 0.30/0.58      ! [X: num,Y: num] :
% 0.30/0.58        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.30/0.58        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(7)
% 0.30/0.58  thf(fact_5575_and__numerals_I7_J,axiom,
% 0.30/0.58      ! [X: num,Y: num] :
% 0.30/0.58        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.30/0.58        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % and_numerals(7)
% 0.30/0.58  thf(fact_5576_even__succ__div__exp,axiom,
% 0.30/0.58      ! [A: nat,N: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58         => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.58            = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_succ_div_exp
% 0.30/0.58  thf(fact_5577_even__succ__div__exp,axiom,
% 0.30/0.58      ! [A: int,N: nat] :
% 0.30/0.58        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58         => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.58            = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_succ_div_exp
% 0.30/0.58  thf(fact_5578_even__succ__div__exp,axiom,
% 0.30/0.58      ! [A: code_integer,N: nat] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58         => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.58            = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_succ_div_exp
% 0.30/0.58  thf(fact_5579_even__succ__div__exp,axiom,
% 0.30/0.58      ! [A: code_natural,N: nat] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58         => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.58            = ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_succ_div_exp
% 0.30/0.58  thf(fact_5580_even__succ__mod__exp,axiom,
% 0.30/0.58      ! [A: nat,N: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.58            = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_succ_mod_exp
% 0.30/0.58  thf(fact_5581_even__succ__mod__exp,axiom,
% 0.30/0.58      ! [A: int,N: nat] :
% 0.30/0.58        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58         => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.58            = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_succ_mod_exp
% 0.30/0.58  thf(fact_5582_even__succ__mod__exp,axiom,
% 0.30/0.58      ! [A: code_integer,N: nat] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58         => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.58            = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_succ_mod_exp
% 0.30/0.58  thf(fact_5583_even__succ__mod__exp,axiom,
% 0.30/0.58      ! [A: code_natural,N: nat] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.30/0.58       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58         => ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.58            = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % even_succ_mod_exp
% 0.30/0.58  thf(fact_5584_is__unit__power__iff,axiom,
% 0.30/0.58      ! [A: code_integer,N: nat] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 0.30/0.58        = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.30/0.58          | ( N = zero_zero_nat ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % is_unit_power_iff
% 0.30/0.58  thf(fact_5585_is__unit__power__iff,axiom,
% 0.30/0.58      ! [A: int,N: nat] :
% 0.30/0.58        ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 0.30/0.58        = ( ( dvd_dvd_int @ A @ one_one_int )
% 0.30/0.58          | ( N = zero_zero_nat ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % is_unit_power_iff
% 0.30/0.58  thf(fact_5586_is__unit__power__iff,axiom,
% 0.30/0.58      ! [A: nat,N: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 0.30/0.58        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.30/0.58          | ( N = zero_zero_nat ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % is_unit_power_iff
% 0.30/0.58  thf(fact_5587_power__commuting__commutes,axiom,
% 0.30/0.58      ! [X: code_integer,Y: code_integer,N: nat] :
% 0.30/0.58        ( ( ( times_3573771949741848930nteger @ X @ Y )
% 0.30/0.58          = ( times_3573771949741848930nteger @ Y @ X ) )
% 0.30/0.58       => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ N ) @ Y )
% 0.30/0.58          = ( times_3573771949741848930nteger @ Y @ ( power_8256067586552552935nteger @ X @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_commuting_commutes
% 0.30/0.58  thf(fact_5588_power__commuting__commutes,axiom,
% 0.30/0.58      ! [X: assn,Y: assn,N: nat] :
% 0.30/0.58        ( ( ( times_times_assn @ X @ Y )
% 0.30/0.58          = ( times_times_assn @ Y @ X ) )
% 0.30/0.58       => ( ( times_times_assn @ ( power_power_assn @ X @ N ) @ Y )
% 0.30/0.58          = ( times_times_assn @ Y @ ( power_power_assn @ X @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_commuting_commutes
% 0.30/0.58  thf(fact_5589_power__commuting__commutes,axiom,
% 0.30/0.58      ! [X: rat,Y: rat,N: nat] :
% 0.30/0.58        ( ( ( times_times_rat @ X @ Y )
% 0.30/0.58          = ( times_times_rat @ Y @ X ) )
% 0.30/0.58       => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ Y )
% 0.30/0.58          = ( times_times_rat @ Y @ ( power_power_rat @ X @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_commuting_commutes
% 0.30/0.58  thf(fact_5590_power__commuting__commutes,axiom,
% 0.30/0.58      ! [X: nat,Y: nat,N: nat] :
% 0.30/0.58        ( ( ( times_times_nat @ X @ Y )
% 0.30/0.58          = ( times_times_nat @ Y @ X ) )
% 0.30/0.58       => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ Y )
% 0.30/0.58          = ( times_times_nat @ Y @ ( power_power_nat @ X @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_commuting_commutes
% 0.30/0.58  thf(fact_5591_power__commuting__commutes,axiom,
% 0.30/0.58      ! [X: int,Y: int,N: nat] :
% 0.30/0.58        ( ( ( times_times_int @ X @ Y )
% 0.30/0.58          = ( times_times_int @ Y @ X ) )
% 0.30/0.58       => ( ( times_times_int @ ( power_power_int @ X @ N ) @ Y )
% 0.30/0.58          = ( times_times_int @ Y @ ( power_power_int @ X @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_commuting_commutes
% 0.30/0.58  thf(fact_5592_power__mult__distrib,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer,N: nat] :
% 0.30/0.58        ( ( power_8256067586552552935nteger @ ( times_3573771949741848930nteger @ A @ B ) @ N )
% 0.30/0.58        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_mult_distrib
% 0.30/0.58  thf(fact_5593_power__mult__distrib,axiom,
% 0.30/0.58      ! [A: assn,B: assn,N: nat] :
% 0.30/0.58        ( ( power_power_assn @ ( times_times_assn @ A @ B ) @ N )
% 0.30/0.58        = ( times_times_assn @ ( power_power_assn @ A @ N ) @ ( power_power_assn @ B @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_mult_distrib
% 0.30/0.58  thf(fact_5594_power__mult__distrib,axiom,
% 0.30/0.58      ! [A: rat,B: rat,N: nat] :
% 0.30/0.58        ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N )
% 0.30/0.58        = ( times_times_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_mult_distrib
% 0.30/0.58  thf(fact_5595_power__mult__distrib,axiom,
% 0.30/0.58      ! [A: nat,B: nat,N: nat] :
% 0.30/0.58        ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 0.30/0.58        = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_mult_distrib
% 0.30/0.58  thf(fact_5596_power__mult__distrib,axiom,
% 0.30/0.58      ! [A: int,B: int,N: nat] :
% 0.30/0.58        ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 0.30/0.58        = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_mult_distrib
% 0.30/0.58  thf(fact_5597_power__commutes,axiom,
% 0.30/0.58      ! [A: code_integer,N: nat] :
% 0.30/0.58        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ N ) @ A )
% 0.30/0.58        = ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_commutes
% 0.30/0.58  thf(fact_5598_power__commutes,axiom,
% 0.30/0.58      ! [A: assn,N: nat] :
% 0.30/0.58        ( ( times_times_assn @ ( power_power_assn @ A @ N ) @ A )
% 0.30/0.58        = ( times_times_assn @ A @ ( power_power_assn @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_commutes
% 0.30/0.58  thf(fact_5599_power__commutes,axiom,
% 0.30/0.58      ! [A: rat,N: nat] :
% 0.30/0.58        ( ( times_times_rat @ ( power_power_rat @ A @ N ) @ A )
% 0.30/0.58        = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_commutes
% 0.30/0.58  thf(fact_5600_power__commutes,axiom,
% 0.30/0.58      ! [A: nat,N: nat] :
% 0.30/0.58        ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 0.30/0.58        = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_commutes
% 0.30/0.58  thf(fact_5601_power__commutes,axiom,
% 0.30/0.58      ! [A: int,N: nat] :
% 0.30/0.58        ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 0.30/0.58        = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_commutes
% 0.30/0.58  thf(fact_5602_dvdE,axiom,
% 0.30/0.58      ! [B: code_integer,A: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.30/0.58       => ~ ! [K2: code_integer] :
% 0.30/0.58              ( A
% 0.30/0.58             != ( times_3573771949741848930nteger @ B @ K2 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvdE
% 0.30/0.58  thf(fact_5603_dvdE,axiom,
% 0.30/0.58      ! [B: assn,A: assn] :
% 0.30/0.58        ( ( dvd_dvd_assn @ B @ A )
% 0.30/0.58       => ~ ! [K2: assn] :
% 0.30/0.58              ( A
% 0.30/0.58             != ( times_times_assn @ B @ K2 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvdE
% 0.30/0.58  thf(fact_5604_dvdE,axiom,
% 0.30/0.58      ! [B: rat,A: rat] :
% 0.30/0.58        ( ( dvd_dvd_rat @ B @ A )
% 0.30/0.58       => ~ ! [K2: rat] :
% 0.30/0.58              ( A
% 0.30/0.58             != ( times_times_rat @ B @ K2 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvdE
% 0.30/0.58  thf(fact_5605_dvdE,axiom,
% 0.30/0.58      ! [B: nat,A: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ B @ A )
% 0.30/0.58       => ~ ! [K2: nat] :
% 0.30/0.58              ( A
% 0.30/0.58             != ( times_times_nat @ B @ K2 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvdE
% 0.30/0.58  thf(fact_5606_dvdE,axiom,
% 0.30/0.58      ! [B: int,A: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ B @ A )
% 0.30/0.58       => ~ ! [K2: int] :
% 0.30/0.58              ( A
% 0.30/0.58             != ( times_times_int @ B @ K2 ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvdE
% 0.30/0.58  thf(fact_5607_dvdI,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer,K: code_integer] :
% 0.30/0.58        ( ( A
% 0.30/0.58          = ( times_3573771949741848930nteger @ B @ K ) )
% 0.30/0.58       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvdI
% 0.30/0.58  thf(fact_5608_dvdI,axiom,
% 0.30/0.58      ! [A: assn,B: assn,K: assn] :
% 0.30/0.58        ( ( A
% 0.30/0.58          = ( times_times_assn @ B @ K ) )
% 0.30/0.58       => ( dvd_dvd_assn @ B @ A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvdI
% 0.30/0.58  thf(fact_5609_dvdI,axiom,
% 0.30/0.58      ! [A: rat,B: rat,K: rat] :
% 0.30/0.58        ( ( A
% 0.30/0.58          = ( times_times_rat @ B @ K ) )
% 0.30/0.58       => ( dvd_dvd_rat @ B @ A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvdI
% 0.30/0.58  thf(fact_5610_dvdI,axiom,
% 0.30/0.58      ! [A: nat,B: nat,K: nat] :
% 0.30/0.58        ( ( A
% 0.30/0.58          = ( times_times_nat @ B @ K ) )
% 0.30/0.58       => ( dvd_dvd_nat @ B @ A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvdI
% 0.30/0.58  thf(fact_5611_dvdI,axiom,
% 0.30/0.58      ! [A: int,B: int,K: int] :
% 0.30/0.58        ( ( A
% 0.30/0.58          = ( times_times_int @ B @ K ) )
% 0.30/0.58       => ( dvd_dvd_int @ B @ A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvdI
% 0.30/0.58  thf(fact_5612_dvd__def,axiom,
% 0.30/0.58      ( dvd_dvd_Code_integer
% 0.30/0.58      = ( ^ [B3: code_integer,A3: code_integer] :
% 0.30/0.58          ? [K4: code_integer] :
% 0.30/0.58            ( A3
% 0.30/0.58            = ( times_3573771949741848930nteger @ B3 @ K4 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_def
% 0.30/0.58  thf(fact_5613_dvd__def,axiom,
% 0.30/0.58      ( dvd_dvd_assn
% 0.30/0.58      = ( ^ [B3: assn,A3: assn] :
% 0.30/0.58          ? [K4: assn] :
% 0.30/0.58            ( A3
% 0.30/0.58            = ( times_times_assn @ B3 @ K4 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_def
% 0.30/0.58  thf(fact_5614_dvd__def,axiom,
% 0.30/0.58      ( dvd_dvd_rat
% 0.30/0.58      = ( ^ [B3: rat,A3: rat] :
% 0.30/0.58          ? [K4: rat] :
% 0.30/0.58            ( A3
% 0.30/0.58            = ( times_times_rat @ B3 @ K4 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_def
% 0.30/0.58  thf(fact_5615_dvd__def,axiom,
% 0.30/0.58      ( dvd_dvd_nat
% 0.30/0.58      = ( ^ [B3: nat,A3: nat] :
% 0.30/0.58          ? [K4: nat] :
% 0.30/0.58            ( A3
% 0.30/0.58            = ( times_times_nat @ B3 @ K4 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_def
% 0.30/0.58  thf(fact_5616_dvd__def,axiom,
% 0.30/0.58      ( dvd_dvd_int
% 0.30/0.58      = ( ^ [B3: int,A3: int] :
% 0.30/0.58          ? [K4: int] :
% 0.30/0.58            ( A3
% 0.30/0.58            = ( times_times_int @ B3 @ K4 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_def
% 0.30/0.58  thf(fact_5617_dvd__mult,axiom,
% 0.30/0.58      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ A @ C )
% 0.30/0.58       => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult
% 0.30/0.58  thf(fact_5618_dvd__mult,axiom,
% 0.30/0.58      ! [A: assn,C: assn,B: assn] :
% 0.30/0.58        ( ( dvd_dvd_assn @ A @ C )
% 0.30/0.58       => ( dvd_dvd_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult
% 0.30/0.58  thf(fact_5619_dvd__mult,axiom,
% 0.30/0.58      ! [A: rat,C: rat,B: rat] :
% 0.30/0.58        ( ( dvd_dvd_rat @ A @ C )
% 0.30/0.58       => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult
% 0.30/0.58  thf(fact_5620_dvd__mult,axiom,
% 0.30/0.58      ! [A: nat,C: nat,B: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ A @ C )
% 0.30/0.58       => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult
% 0.30/0.58  thf(fact_5621_dvd__mult,axiom,
% 0.30/0.58      ! [A: int,C: int,B: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ A @ C )
% 0.30/0.58       => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult
% 0.30/0.58  thf(fact_5622_dvd__mult2,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.30/0.58       => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult2
% 0.30/0.58  thf(fact_5623_dvd__mult2,axiom,
% 0.30/0.58      ! [A: assn,B: assn,C: assn] :
% 0.30/0.58        ( ( dvd_dvd_assn @ A @ B )
% 0.30/0.58       => ( dvd_dvd_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult2
% 0.30/0.58  thf(fact_5624_dvd__mult2,axiom,
% 0.30/0.58      ! [A: rat,B: rat,C: rat] :
% 0.30/0.58        ( ( dvd_dvd_rat @ A @ B )
% 0.30/0.58       => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult2
% 0.30/0.58  thf(fact_5625_dvd__mult2,axiom,
% 0.30/0.58      ! [A: nat,B: nat,C: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ A @ B )
% 0.30/0.58       => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult2
% 0.30/0.58  thf(fact_5626_dvd__mult2,axiom,
% 0.30/0.58      ! [A: int,B: int,C: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ A @ B )
% 0.30/0.58       => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult2
% 0.30/0.58  thf(fact_5627_dvd__mult__left,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.30/0.58       => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_left
% 0.30/0.58  thf(fact_5628_dvd__mult__left,axiom,
% 0.30/0.58      ! [A: assn,B: assn,C: assn] :
% 0.30/0.58        ( ( dvd_dvd_assn @ ( times_times_assn @ A @ B ) @ C )
% 0.30/0.58       => ( dvd_dvd_assn @ A @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_left
% 0.30/0.58  thf(fact_5629_dvd__mult__left,axiom,
% 0.30/0.58      ! [A: rat,B: rat,C: rat] :
% 0.30/0.58        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 0.30/0.58       => ( dvd_dvd_rat @ A @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_left
% 0.30/0.58  thf(fact_5630_dvd__mult__left,axiom,
% 0.30/0.58      ! [A: nat,B: nat,C: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.30/0.58       => ( dvd_dvd_nat @ A @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_left
% 0.30/0.58  thf(fact_5631_dvd__mult__left,axiom,
% 0.30/0.58      ! [A: int,B: int,C: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.30/0.58       => ( dvd_dvd_int @ A @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_left
% 0.30/0.58  thf(fact_5632_dvd__triv__left,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_triv_left
% 0.30/0.58  thf(fact_5633_dvd__triv__left,axiom,
% 0.30/0.58      ! [A: assn,B: assn] : ( dvd_dvd_assn @ A @ ( times_times_assn @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_triv_left
% 0.30/0.58  thf(fact_5634_dvd__triv__left,axiom,
% 0.30/0.58      ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_triv_left
% 0.30/0.58  thf(fact_5635_dvd__triv__left,axiom,
% 0.30/0.58      ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_triv_left
% 0.30/0.58  thf(fact_5636_dvd__triv__left,axiom,
% 0.30/0.58      ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_triv_left
% 0.30/0.58  thf(fact_5637_mult__dvd__mono,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.30/0.58       => ( ( dvd_dvd_Code_integer @ C @ D2 )
% 0.30/0.58         => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mult_dvd_mono
% 0.30/0.58  thf(fact_5638_mult__dvd__mono,axiom,
% 0.30/0.58      ! [A: assn,B: assn,C: assn,D2: assn] :
% 0.30/0.58        ( ( dvd_dvd_assn @ A @ B )
% 0.30/0.58       => ( ( dvd_dvd_assn @ C @ D2 )
% 0.30/0.58         => ( dvd_dvd_assn @ ( times_times_assn @ A @ C ) @ ( times_times_assn @ B @ D2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mult_dvd_mono
% 0.30/0.58  thf(fact_5639_mult__dvd__mono,axiom,
% 0.30/0.58      ! [A: rat,B: rat,C: rat,D2: rat] :
% 0.30/0.58        ( ( dvd_dvd_rat @ A @ B )
% 0.30/0.58       => ( ( dvd_dvd_rat @ C @ D2 )
% 0.30/0.58         => ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mult_dvd_mono
% 0.30/0.58  thf(fact_5640_mult__dvd__mono,axiom,
% 0.30/0.58      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ A @ B )
% 0.30/0.58       => ( ( dvd_dvd_nat @ C @ D2 )
% 0.30/0.58         => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mult_dvd_mono
% 0.30/0.58  thf(fact_5641_mult__dvd__mono,axiom,
% 0.30/0.58      ! [A: int,B: int,C: int,D2: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ A @ B )
% 0.30/0.58       => ( ( dvd_dvd_int @ C @ D2 )
% 0.30/0.58         => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mult_dvd_mono
% 0.30/0.58  thf(fact_5642_dvd__mult__right,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.30/0.58       => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_right
% 0.30/0.58  thf(fact_5643_dvd__mult__right,axiom,
% 0.30/0.58      ! [A: assn,B: assn,C: assn] :
% 0.30/0.58        ( ( dvd_dvd_assn @ ( times_times_assn @ A @ B ) @ C )
% 0.30/0.58       => ( dvd_dvd_assn @ B @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_right
% 0.30/0.58  thf(fact_5644_dvd__mult__right,axiom,
% 0.30/0.58      ! [A: rat,B: rat,C: rat] :
% 0.30/0.58        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 0.30/0.58       => ( dvd_dvd_rat @ B @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_right
% 0.30/0.58  thf(fact_5645_dvd__mult__right,axiom,
% 0.30/0.58      ! [A: nat,B: nat,C: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.30/0.58       => ( dvd_dvd_nat @ B @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_right
% 0.30/0.58  thf(fact_5646_dvd__mult__right,axiom,
% 0.30/0.58      ! [A: int,B: int,C: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.30/0.58       => ( dvd_dvd_int @ B @ C ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_right
% 0.30/0.58  thf(fact_5647_dvd__triv__right,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_triv_right
% 0.30/0.58  thf(fact_5648_dvd__triv__right,axiom,
% 0.30/0.58      ! [A: assn,B: assn] : ( dvd_dvd_assn @ A @ ( times_times_assn @ B @ A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_triv_right
% 0.30/0.58  thf(fact_5649_dvd__triv__right,axiom,
% 0.30/0.58      ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_triv_right
% 0.30/0.58  thf(fact_5650_dvd__triv__right,axiom,
% 0.30/0.58      ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_triv_right
% 0.30/0.58  thf(fact_5651_dvd__triv__right,axiom,
% 0.30/0.58      ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_triv_right
% 0.30/0.58  thf(fact_5652_one__dvd,axiom,
% 0.30/0.58      ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 0.30/0.58  
% 0.30/0.58  % one_dvd
% 0.30/0.58  thf(fact_5653_one__dvd,axiom,
% 0.30/0.58      ! [A: assn] : ( dvd_dvd_assn @ one_one_assn @ A ) ).
% 0.30/0.58  
% 0.30/0.58  % one_dvd
% 0.30/0.58  thf(fact_5654_one__dvd,axiom,
% 0.30/0.58      ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 0.30/0.58  
% 0.30/0.58  % one_dvd
% 0.30/0.58  thf(fact_5655_one__dvd,axiom,
% 0.30/0.58      ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 0.30/0.58  
% 0.30/0.58  % one_dvd
% 0.30/0.58  thf(fact_5656_one__dvd,axiom,
% 0.30/0.58      ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 0.30/0.58  
% 0.30/0.58  % one_dvd
% 0.30/0.58  thf(fact_5657_unit__imp__dvd,axiom,
% 0.30/0.58      ! [B: code_integer,A: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.30/0.58       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_imp_dvd
% 0.30/0.58  thf(fact_5658_unit__imp__dvd,axiom,
% 0.30/0.58      ! [B: nat,A: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.30/0.58       => ( dvd_dvd_nat @ B @ A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_imp_dvd
% 0.30/0.58  thf(fact_5659_unit__imp__dvd,axiom,
% 0.30/0.58      ! [B: int,A: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.30/0.58       => ( dvd_dvd_int @ B @ A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_imp_dvd
% 0.30/0.58  thf(fact_5660_dvd__unit__imp__unit,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ A @ B )
% 0.30/0.58       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.30/0.58         => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_unit_imp_unit
% 0.30/0.58  thf(fact_5661_dvd__unit__imp__unit,axiom,
% 0.30/0.58      ! [A: nat,B: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ A @ B )
% 0.30/0.58       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.30/0.58         => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_unit_imp_unit
% 0.30/0.58  thf(fact_5662_dvd__unit__imp__unit,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ A @ B )
% 0.30/0.58       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.30/0.58         => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_unit_imp_unit
% 0.30/0.58  thf(fact_5663_uminus__dvd__conv_I1_J,axiom,
% 0.30/0.58      ( dvd_dvd_int
% 0.30/0.58      = ( ^ [D4: int] : ( dvd_dvd_int @ ( uminus_uminus_int @ D4 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % uminus_dvd_conv(1)
% 0.30/0.58  thf(fact_5664_uminus__dvd__conv_I2_J,axiom,
% 0.30/0.58      ( dvd_dvd_int
% 0.30/0.58      = ( ^ [D4: int,T2: int] : ( dvd_dvd_int @ D4 @ ( uminus_uminus_int @ T2 ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % uminus_dvd_conv(2)
% 0.30/0.58  thf(fact_5665_dvd__power__iff,axiom,
% 0.30/0.58      ! [X: code_integer,M: nat,N: nat] :
% 0.30/0.58        ( ( X != zero_z3403309356797280102nteger )
% 0.30/0.58       => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M ) @ ( power_8256067586552552935nteger @ X @ N ) )
% 0.30/0.58          = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 0.30/0.58            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_power_iff
% 0.30/0.58  thf(fact_5666_dvd__power__iff,axiom,
% 0.30/0.58      ! [X: int,M: nat,N: nat] :
% 0.30/0.58        ( ( X != zero_zero_int )
% 0.30/0.58       => ( ( dvd_dvd_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ N ) )
% 0.30/0.58          = ( ( dvd_dvd_int @ X @ one_one_int )
% 0.30/0.58            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_power_iff
% 0.30/0.58  thf(fact_5667_dvd__power__iff,axiom,
% 0.30/0.58      ! [X: nat,M: nat,N: nat] :
% 0.30/0.58        ( ( X != zero_zero_nat )
% 0.30/0.58       => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M ) @ ( power_power_nat @ X @ N ) )
% 0.30/0.58          = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 0.30/0.58            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_power_iff
% 0.30/0.58  thf(fact_5668_dvd__power,axiom,
% 0.30/0.58      ! [N: nat,X: code_integer] :
% 0.30/0.58        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58          | ( X = one_one_Code_integer ) )
% 0.30/0.58       => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_power
% 0.30/0.58  thf(fact_5669_dvd__power,axiom,
% 0.30/0.58      ! [N: nat,X: rat] :
% 0.30/0.58        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58          | ( X = one_one_rat ) )
% 0.30/0.58       => ( dvd_dvd_rat @ X @ ( power_power_rat @ X @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_power
% 0.30/0.58  thf(fact_5670_dvd__power,axiom,
% 0.30/0.58      ! [N: nat,X: int] :
% 0.30/0.58        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58          | ( X = one_one_int ) )
% 0.30/0.58       => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_power
% 0.30/0.58  thf(fact_5671_dvd__power,axiom,
% 0.30/0.58      ! [N: nat,X: nat] :
% 0.30/0.58        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58          | ( X = one_one_nat ) )
% 0.30/0.58       => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_power
% 0.30/0.58  thf(fact_5672_subset__divisors__dvd,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( ord_less_eq_set_int
% 0.30/0.58          @ ( collect_int
% 0.30/0.58            @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ A ) )
% 0.30/0.58          @ ( collect_int
% 0.30/0.58            @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ B ) ) )
% 0.30/0.58        = ( dvd_dvd_int @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % subset_divisors_dvd
% 0.30/0.58  thf(fact_5673_subset__divisors__dvd,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( ord_le7084787975880047091nteger
% 0.30/0.58          @ ( collect_Code_integer
% 0.30/0.58            @ ^ [C4: code_integer] : ( dvd_dvd_Code_integer @ C4 @ A ) )
% 0.30/0.58          @ ( collect_Code_integer
% 0.30/0.58            @ ^ [C4: code_integer] : ( dvd_dvd_Code_integer @ C4 @ B ) ) )
% 0.30/0.58        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % subset_divisors_dvd
% 0.30/0.58  thf(fact_5674_subset__divisors__dvd,axiom,
% 0.30/0.58      ! [A: nat,B: nat] :
% 0.30/0.58        ( ( ord_less_eq_set_nat
% 0.30/0.58          @ ( collect_nat
% 0.30/0.58            @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ A ) )
% 0.30/0.58          @ ( collect_nat
% 0.30/0.58            @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ B ) ) )
% 0.30/0.58        = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.30/0.58  
% 0.30/0.58  % subset_divisors_dvd
% 0.30/0.58  thf(fact_5675_strict__subset__divisors__dvd,axiom,
% 0.30/0.58      ! [A: nat,B: nat] :
% 0.30/0.58        ( ( ord_less_set_nat
% 0.30/0.58          @ ( collect_nat
% 0.30/0.58            @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ A ) )
% 0.30/0.58          @ ( collect_nat
% 0.30/0.58            @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ B ) ) )
% 0.30/0.58        = ( ( dvd_dvd_nat @ A @ B )
% 0.30/0.58          & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % strict_subset_divisors_dvd
% 0.30/0.58  thf(fact_5676_strict__subset__divisors__dvd,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( ord_less_set_int
% 0.30/0.58          @ ( collect_int
% 0.30/0.58            @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ A ) )
% 0.30/0.58          @ ( collect_int
% 0.30/0.58            @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ B ) ) )
% 0.30/0.58        = ( ( dvd_dvd_int @ A @ B )
% 0.30/0.58          & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % strict_subset_divisors_dvd
% 0.30/0.58  thf(fact_5677_strict__subset__divisors__dvd,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( ord_le1307284697595431911nteger
% 0.30/0.58          @ ( collect_Code_integer
% 0.30/0.58            @ ^ [C4: code_integer] : ( dvd_dvd_Code_integer @ C4 @ A ) )
% 0.30/0.58          @ ( collect_Code_integer
% 0.30/0.58            @ ^ [C4: code_integer] : ( dvd_dvd_Code_integer @ C4 @ B ) ) )
% 0.30/0.58        = ( ( dvd_dvd_Code_integer @ A @ B )
% 0.30/0.58          & ~ ( dvd_dvd_Code_integer @ B @ A ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % strict_subset_divisors_dvd
% 0.30/0.58  thf(fact_5678_and__eq__minus__1__iff,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 0.30/0.58          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.58        = ( ( A
% 0.30/0.58            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.58          & ( B
% 0.30/0.58            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % and_eq_minus_1_iff
% 0.30/0.58  thf(fact_5679_and__eq__minus__1__iff,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 0.30/0.58          = ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.58        = ( ( A
% 0.30/0.58            = ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.58          & ( B
% 0.30/0.58            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % and_eq_minus_1_iff
% 0.30/0.58  thf(fact_5680_uminus__power__if,axiom,
% 0.30/0.58      ! [N: nat,A: int] :
% 0.30/0.58        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.58         => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.30/0.58            = ( power_power_int @ A @ N ) ) )
% 0.30/0.58        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.58         => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.30/0.58            = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % uminus_power_if
% 0.30/0.58  thf(fact_5681_uminus__power__if,axiom,
% 0.30/0.58      ! [N: nat,A: code_integer] :
% 0.30/0.58        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.58         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.30/0.58            = ( power_8256067586552552935nteger @ A @ N ) ) )
% 0.30/0.58        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.58         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.30/0.58            = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % uminus_power_if
% 0.30/0.58  thf(fact_5682_uminus__power__if,axiom,
% 0.30/0.58      ! [N: nat,A: rat] :
% 0.30/0.58        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.58         => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.30/0.58            = ( power_power_rat @ A @ N ) ) )
% 0.30/0.58        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.58         => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.30/0.58            = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % uminus_power_if
% 0.30/0.58  thf(fact_5683_take__bit__eq__mask__iff__exp__dvd,axiom,
% 0.30/0.58      ! [N: nat,K: int] :
% 0.30/0.58        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.30/0.58          = ( bit_se2000444600071755411sk_int @ N ) )
% 0.30/0.58        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % take_bit_eq_mask_iff_exp_dvd
% 0.30/0.58  thf(fact_5684_one__le__power,axiom,
% 0.30/0.58      ! [A: code_integer,N: nat] :
% 0.30/0.58        ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 0.30/0.58       => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % one_le_power
% 0.30/0.58  thf(fact_5685_one__le__power,axiom,
% 0.30/0.58      ! [A: rat,N: nat] :
% 0.30/0.58        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.30/0.58       => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % one_le_power
% 0.30/0.58  thf(fact_5686_one__le__power,axiom,
% 0.30/0.58      ! [A: nat,N: nat] :
% 0.30/0.58        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.30/0.58       => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % one_le_power
% 0.30/0.58  thf(fact_5687_one__le__power,axiom,
% 0.30/0.58      ! [A: int,N: nat] :
% 0.30/0.58        ( ( ord_less_eq_int @ one_one_int @ A )
% 0.30/0.58       => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % one_le_power
% 0.30/0.58  thf(fact_5688_not__is__unit__0,axiom,
% 0.30/0.58      ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 0.30/0.58  
% 0.30/0.58  % not_is_unit_0
% 0.30/0.58  thf(fact_5689_not__is__unit__0,axiom,
% 0.30/0.58      ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 0.30/0.58  
% 0.30/0.58  % not_is_unit_0
% 0.30/0.58  thf(fact_5690_not__is__unit__0,axiom,
% 0.30/0.58      ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 0.30/0.58  
% 0.30/0.58  % not_is_unit_0
% 0.30/0.58  thf(fact_5691_left__right__inverse__power,axiom,
% 0.30/0.58      ! [X: code_integer,Y: code_integer,N: nat] :
% 0.30/0.58        ( ( ( times_3573771949741848930nteger @ X @ Y )
% 0.30/0.58          = one_one_Code_integer )
% 0.30/0.58       => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y @ N ) )
% 0.30/0.58          = one_one_Code_integer ) ) ).
% 0.30/0.58  
% 0.30/0.58  % left_right_inverse_power
% 0.30/0.58  thf(fact_5692_left__right__inverse__power,axiom,
% 0.30/0.58      ! [X: assn,Y: assn,N: nat] :
% 0.30/0.58        ( ( ( times_times_assn @ X @ Y )
% 0.30/0.58          = one_one_assn )
% 0.30/0.58       => ( ( times_times_assn @ ( power_power_assn @ X @ N ) @ ( power_power_assn @ Y @ N ) )
% 0.30/0.58          = one_one_assn ) ) ).
% 0.30/0.58  
% 0.30/0.58  % left_right_inverse_power
% 0.30/0.58  thf(fact_5693_left__right__inverse__power,axiom,
% 0.30/0.58      ! [X: rat,Y: rat,N: nat] :
% 0.30/0.58        ( ( ( times_times_rat @ X @ Y )
% 0.30/0.58          = one_one_rat )
% 0.30/0.58       => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y @ N ) )
% 0.30/0.58          = one_one_rat ) ) ).
% 0.30/0.58  
% 0.30/0.58  % left_right_inverse_power
% 0.30/0.58  thf(fact_5694_left__right__inverse__power,axiom,
% 0.30/0.58      ! [X: nat,Y: nat,N: nat] :
% 0.30/0.58        ( ( ( times_times_nat @ X @ Y )
% 0.30/0.58          = one_one_nat )
% 0.30/0.58       => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) )
% 0.30/0.58          = one_one_nat ) ) ).
% 0.30/0.58  
% 0.30/0.58  % left_right_inverse_power
% 0.30/0.58  thf(fact_5695_left__right__inverse__power,axiom,
% 0.30/0.58      ! [X: int,Y: int,N: nat] :
% 0.30/0.58        ( ( ( times_times_int @ X @ Y )
% 0.30/0.58          = one_one_int )
% 0.30/0.58       => ( ( times_times_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 0.30/0.58          = one_one_int ) ) ).
% 0.30/0.58  
% 0.30/0.58  % left_right_inverse_power
% 0.30/0.58  thf(fact_5696_power__Suc,axiom,
% 0.30/0.58      ! [A: code_integer,N: nat] :
% 0.30/0.58        ( ( power_8256067586552552935nteger @ A @ ( suc @ N ) )
% 0.30/0.58        = ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_Suc
% 0.30/0.58  thf(fact_5697_power__Suc,axiom,
% 0.30/0.58      ! [A: assn,N: nat] :
% 0.30/0.58        ( ( power_power_assn @ A @ ( suc @ N ) )
% 0.30/0.58        = ( times_times_assn @ A @ ( power_power_assn @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_Suc
% 0.30/0.58  thf(fact_5698_power__Suc,axiom,
% 0.30/0.58      ! [A: rat,N: nat] :
% 0.30/0.58        ( ( power_power_rat @ A @ ( suc @ N ) )
% 0.30/0.58        = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_Suc
% 0.30/0.58  thf(fact_5699_power__Suc,axiom,
% 0.30/0.58      ! [A: nat,N: nat] :
% 0.30/0.58        ( ( power_power_nat @ A @ ( suc @ N ) )
% 0.30/0.58        = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_Suc
% 0.30/0.58  thf(fact_5700_power__Suc,axiom,
% 0.30/0.58      ! [A: int,N: nat] :
% 0.30/0.58        ( ( power_power_int @ A @ ( suc @ N ) )
% 0.30/0.58        = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_Suc
% 0.30/0.58  thf(fact_5701_power__Suc2,axiom,
% 0.30/0.58      ! [A: code_integer,N: nat] :
% 0.30/0.58        ( ( power_8256067586552552935nteger @ A @ ( suc @ N ) )
% 0.30/0.58        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ N ) @ A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_Suc2
% 0.30/0.58  thf(fact_5702_power__Suc2,axiom,
% 0.30/0.58      ! [A: assn,N: nat] :
% 0.30/0.58        ( ( power_power_assn @ A @ ( suc @ N ) )
% 0.30/0.58        = ( times_times_assn @ ( power_power_assn @ A @ N ) @ A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_Suc2
% 0.30/0.58  thf(fact_5703_power__Suc2,axiom,
% 0.30/0.58      ! [A: rat,N: nat] :
% 0.30/0.58        ( ( power_power_rat @ A @ ( suc @ N ) )
% 0.30/0.58        = ( times_times_rat @ ( power_power_rat @ A @ N ) @ A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_Suc2
% 0.30/0.58  thf(fact_5704_power__Suc2,axiom,
% 0.30/0.58      ! [A: nat,N: nat] :
% 0.30/0.58        ( ( power_power_nat @ A @ ( suc @ N ) )
% 0.30/0.58        = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_Suc2
% 0.30/0.58  thf(fact_5705_power__Suc2,axiom,
% 0.30/0.58      ! [A: int,N: nat] :
% 0.30/0.58        ( ( power_power_int @ A @ ( suc @ N ) )
% 0.30/0.58        = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_Suc2
% 0.30/0.58  thf(fact_5706_is__unit__mult__iff,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 0.30/0.58        = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.30/0.58          & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % is_unit_mult_iff
% 0.30/0.58  thf(fact_5707_is__unit__mult__iff,axiom,
% 0.30/0.58      ! [A: nat,B: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 0.30/0.58        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.30/0.58          & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % is_unit_mult_iff
% 0.30/0.58  thf(fact_5708_is__unit__mult__iff,axiom,
% 0.30/0.58      ! [A: int,B: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 0.30/0.58        = ( ( dvd_dvd_int @ A @ one_one_int )
% 0.30/0.58          & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % is_unit_mult_iff
% 0.30/0.58  thf(fact_5709_dvd__mult__unit__iff,axiom,
% 0.30/0.58      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.30/0.58       => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 0.30/0.58          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_unit_iff
% 0.30/0.58  thf(fact_5710_dvd__mult__unit__iff,axiom,
% 0.30/0.58      ! [B: nat,A: nat,C: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.30/0.58       => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 0.30/0.58          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_unit_iff
% 0.30/0.58  thf(fact_5711_dvd__mult__unit__iff,axiom,
% 0.30/0.58      ! [B: int,A: int,C: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.30/0.58       => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 0.30/0.58          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_unit_iff
% 0.30/0.58  thf(fact_5712_mult__unit__dvd__iff,axiom,
% 0.30/0.58      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.30/0.58       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.30/0.58          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mult_unit_dvd_iff
% 0.30/0.58  thf(fact_5713_mult__unit__dvd__iff,axiom,
% 0.30/0.58      ! [B: nat,A: nat,C: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.30/0.58       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.30/0.58          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mult_unit_dvd_iff
% 0.30/0.58  thf(fact_5714_mult__unit__dvd__iff,axiom,
% 0.30/0.58      ! [B: int,A: int,C: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.30/0.58       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.30/0.58          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mult_unit_dvd_iff
% 0.30/0.58  thf(fact_5715_dvd__mult__unit__iff_H,axiom,
% 0.30/0.58      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.30/0.58       => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.30/0.58          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_unit_iff'
% 0.30/0.58  thf(fact_5716_dvd__mult__unit__iff_H,axiom,
% 0.30/0.58      ! [B: nat,A: nat,C: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.30/0.58       => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.30/0.58          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_unit_iff'
% 0.30/0.58  thf(fact_5717_dvd__mult__unit__iff_H,axiom,
% 0.30/0.58      ! [B: int,A: int,C: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.30/0.58       => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 0.30/0.58          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_unit_iff'
% 0.30/0.58  thf(fact_5718_mult__unit__dvd__iff_H,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.30/0.58       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 0.30/0.58          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mult_unit_dvd_iff'
% 0.30/0.58  thf(fact_5719_mult__unit__dvd__iff_H,axiom,
% 0.30/0.58      ! [A: nat,B: nat,C: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.30/0.58       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 0.30/0.58          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mult_unit_dvd_iff'
% 0.30/0.58  thf(fact_5720_mult__unit__dvd__iff_H,axiom,
% 0.30/0.58      ! [A: int,B: int,C: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.30/0.58       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 0.30/0.58          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % mult_unit_dvd_iff'
% 0.30/0.58  thf(fact_5721_unit__mult__left__cancel,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.30/0.58       => ( ( ( times_3573771949741848930nteger @ A @ B )
% 0.30/0.58            = ( times_3573771949741848930nteger @ A @ C ) )
% 0.30/0.58          = ( B = C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_mult_left_cancel
% 0.30/0.58  thf(fact_5722_unit__mult__left__cancel,axiom,
% 0.30/0.58      ! [A: nat,B: nat,C: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.30/0.58       => ( ( ( times_times_nat @ A @ B )
% 0.30/0.58            = ( times_times_nat @ A @ C ) )
% 0.30/0.58          = ( B = C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_mult_left_cancel
% 0.30/0.58  thf(fact_5723_unit__mult__left__cancel,axiom,
% 0.30/0.58      ! [A: int,B: int,C: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.30/0.58       => ( ( ( times_times_int @ A @ B )
% 0.30/0.58            = ( times_times_int @ A @ C ) )
% 0.30/0.58          = ( B = C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_mult_left_cancel
% 0.30/0.58  thf(fact_5724_unit__mult__right__cancel,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.30/0.58       => ( ( ( times_3573771949741848930nteger @ B @ A )
% 0.30/0.58            = ( times_3573771949741848930nteger @ C @ A ) )
% 0.30/0.58          = ( B = C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_mult_right_cancel
% 0.30/0.58  thf(fact_5725_unit__mult__right__cancel,axiom,
% 0.30/0.58      ! [A: nat,B: nat,C: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.30/0.58       => ( ( ( times_times_nat @ B @ A )
% 0.30/0.58            = ( times_times_nat @ C @ A ) )
% 0.30/0.58          = ( B = C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_mult_right_cancel
% 0.30/0.58  thf(fact_5726_unit__mult__right__cancel,axiom,
% 0.30/0.58      ! [A: int,B: int,C: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.30/0.58       => ( ( ( times_times_int @ B @ A )
% 0.30/0.58            = ( times_times_int @ C @ A ) )
% 0.30/0.58          = ( B = C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_mult_right_cancel
% 0.30/0.58  thf(fact_5727_power__0,axiom,
% 0.30/0.58      ! [A: code_integer] :
% 0.30/0.58        ( ( power_8256067586552552935nteger @ A @ zero_zero_nat )
% 0.30/0.58        = one_one_Code_integer ) ).
% 0.30/0.58  
% 0.30/0.58  % power_0
% 0.30/0.58  thf(fact_5728_power__0,axiom,
% 0.30/0.58      ! [A: assn] :
% 0.30/0.58        ( ( power_power_assn @ A @ zero_zero_nat )
% 0.30/0.58        = one_one_assn ) ).
% 0.30/0.58  
% 0.30/0.58  % power_0
% 0.30/0.58  thf(fact_5729_power__0,axiom,
% 0.30/0.58      ! [A: rat] :
% 0.30/0.58        ( ( power_power_rat @ A @ zero_zero_nat )
% 0.30/0.58        = one_one_rat ) ).
% 0.30/0.58  
% 0.30/0.58  % power_0
% 0.30/0.58  thf(fact_5730_power__0,axiom,
% 0.30/0.58      ! [A: int] :
% 0.30/0.58        ( ( power_power_int @ A @ zero_zero_nat )
% 0.30/0.58        = one_one_int ) ).
% 0.30/0.58  
% 0.30/0.58  % power_0
% 0.30/0.58  thf(fact_5731_power__0,axiom,
% 0.30/0.58      ! [A: nat] :
% 0.30/0.58        ( ( power_power_nat @ A @ zero_zero_nat )
% 0.30/0.58        = one_one_nat ) ).
% 0.30/0.58  
% 0.30/0.58  % power_0
% 0.30/0.58  thf(fact_5732_power__one__over,axiom,
% 0.30/0.58      ! [A: rat,N: nat] :
% 0.30/0.58        ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 0.30/0.58        = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_one_over
% 0.30/0.58  thf(fact_5733_dvd__div__mult,axiom,
% 0.30/0.58      ! [C: nat,B: nat,A: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ C @ B )
% 0.30/0.58       => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 0.30/0.58          = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_div_mult
% 0.30/0.58  thf(fact_5734_dvd__div__mult,axiom,
% 0.30/0.58      ! [C: int,B: int,A: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ C @ B )
% 0.30/0.58       => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 0.30/0.58          = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_div_mult
% 0.30/0.58  thf(fact_5735_dvd__div__mult,axiom,
% 0.30/0.58      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ C @ B )
% 0.30/0.58       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 0.30/0.58          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_div_mult
% 0.30/0.58  thf(fact_5736_dvd__div__mult,axiom,
% 0.30/0.58      ! [C: code_natural,B: code_natural,A: code_natural] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ C @ B )
% 0.30/0.58       => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ B @ C ) @ A )
% 0.30/0.58          = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ B @ A ) @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_div_mult
% 0.30/0.58  thf(fact_5737_div__mult__swap,axiom,
% 0.30/0.58      ! [C: nat,B: nat,A: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ C @ B )
% 0.30/0.58       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.30/0.58          = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % div_mult_swap
% 0.30/0.58  thf(fact_5738_div__mult__swap,axiom,
% 0.30/0.58      ! [C: int,B: int,A: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ C @ B )
% 0.30/0.58       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.30/0.58          = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % div_mult_swap
% 0.30/0.58  thf(fact_5739_div__mult__swap,axiom,
% 0.30/0.58      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ C @ B )
% 0.30/0.58       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 0.30/0.58          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % div_mult_swap
% 0.30/0.58  thf(fact_5740_div__mult__swap,axiom,
% 0.30/0.58      ! [C: code_natural,B: code_natural,A: code_natural] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ C @ B )
% 0.30/0.58       => ( ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C ) )
% 0.30/0.58          = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % div_mult_swap
% 0.30/0.58  thf(fact_5741_div__div__eq__right,axiom,
% 0.30/0.58      ! [C: nat,B: nat,A: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ C @ B )
% 0.30/0.58       => ( ( dvd_dvd_nat @ B @ A )
% 0.30/0.58         => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.30/0.58            = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % div_div_eq_right
% 0.30/0.58  thf(fact_5742_div__div__eq__right,axiom,
% 0.30/0.58      ! [C: int,B: int,A: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ C @ B )
% 0.30/0.58       => ( ( dvd_dvd_int @ B @ A )
% 0.30/0.58         => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.30/0.58            = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % div_div_eq_right
% 0.30/0.58  thf(fact_5743_div__div__eq__right,axiom,
% 0.30/0.58      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ C @ B )
% 0.30/0.58       => ( ( dvd_dvd_Code_integer @ B @ A )
% 0.30/0.58         => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 0.30/0.58            = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % div_div_eq_right
% 0.30/0.58  thf(fact_5744_div__div__eq__right,axiom,
% 0.30/0.58      ! [C: code_natural,B: code_natural,A: code_natural] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ C @ B )
% 0.30/0.58       => ( ( dvd_dvd_Code_natural @ B @ A )
% 0.30/0.58         => ( ( divide5121882707175180666atural @ A @ ( divide5121882707175180666atural @ B @ C ) )
% 0.30/0.58            = ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ C ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % div_div_eq_right
% 0.30/0.58  thf(fact_5745_dvd__div__mult2__eq,axiom,
% 0.30/0.58      ! [B: nat,C: nat,A: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 0.30/0.58       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.30/0.58          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_div_mult2_eq
% 0.30/0.58  thf(fact_5746_dvd__div__mult2__eq,axiom,
% 0.30/0.58      ! [B: int,C: int,A: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 0.30/0.58       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.30/0.58          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_div_mult2_eq
% 0.30/0.58  thf(fact_5747_dvd__div__mult2__eq,axiom,
% 0.30/0.58      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 0.30/0.58       => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.30/0.58          = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_div_mult2_eq
% 0.30/0.58  thf(fact_5748_dvd__div__mult2__eq,axiom,
% 0.30/0.58      ! [B: code_natural,C: code_natural,A: code_natural] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ B @ C ) @ A )
% 0.30/0.58       => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ C ) )
% 0.30/0.58          = ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ B ) @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_div_mult2_eq
% 0.30/0.58  thf(fact_5749_dvd__mult__imp__div,axiom,
% 0.30/0.58      ! [A: nat,C: nat,B: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 0.30/0.58       => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_imp_div
% 0.30/0.58  thf(fact_5750_dvd__mult__imp__div,axiom,
% 0.30/0.58      ! [A: int,C: int,B: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 0.30/0.58       => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_imp_div
% 0.30/0.58  thf(fact_5751_dvd__mult__imp__div,axiom,
% 0.30/0.58      ! [A: code_integer,C: code_integer,B: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 0.30/0.58       => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_imp_div
% 0.30/0.58  thf(fact_5752_dvd__mult__imp__div,axiom,
% 0.30/0.58      ! [A: code_natural,C: code_natural,B: code_natural] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ A @ C ) @ B )
% 0.30/0.58       => ( dvd_dvd_Code_natural @ A @ ( divide5121882707175180666atural @ B @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_mult_imp_div
% 0.30/0.58  thf(fact_5753_div__mult__div__if__dvd,axiom,
% 0.30/0.58      ! [B: nat,A: nat,D2: nat,C: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ B @ A )
% 0.30/0.58       => ( ( dvd_dvd_nat @ D2 @ C )
% 0.30/0.58         => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D2 ) )
% 0.30/0.58            = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % div_mult_div_if_dvd
% 0.30/0.58  thf(fact_5754_div__mult__div__if__dvd,axiom,
% 0.30/0.58      ! [B: int,A: int,D2: int,C: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ B @ A )
% 0.30/0.58       => ( ( dvd_dvd_int @ D2 @ C )
% 0.30/0.58         => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D2 ) )
% 0.30/0.58            = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % div_mult_div_if_dvd
% 0.30/0.58  thf(fact_5755_div__mult__div__if__dvd,axiom,
% 0.30/0.58      ! [B: code_integer,A: code_integer,D2: code_integer,C: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.30/0.58       => ( ( dvd_dvd_Code_integer @ D2 @ C )
% 0.30/0.58         => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D2 ) )
% 0.30/0.58            = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % div_mult_div_if_dvd
% 0.30/0.58  thf(fact_5756_div__mult__div__if__dvd,axiom,
% 0.30/0.58      ! [B: code_natural,A: code_natural,D2: code_natural,C: code_natural] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ B @ A )
% 0.30/0.58       => ( ( dvd_dvd_Code_natural @ D2 @ C )
% 0.30/0.58         => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ ( divide5121882707175180666atural @ C @ D2 ) )
% 0.30/0.58            = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D2 ) ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % div_mult_div_if_dvd
% 0.30/0.58  thf(fact_5757_power__add,axiom,
% 0.30/0.58      ! [A: code_integer,M: nat,N: nat] :
% 0.30/0.58        ( ( power_8256067586552552935nteger @ A @ ( plus_plus_nat @ M @ N ) )
% 0.30/0.58        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_add
% 0.30/0.58  thf(fact_5758_power__add,axiom,
% 0.30/0.58      ! [A: assn,M: nat,N: nat] :
% 0.30/0.58        ( ( power_power_assn @ A @ ( plus_plus_nat @ M @ N ) )
% 0.30/0.58        = ( times_times_assn @ ( power_power_assn @ A @ M ) @ ( power_power_assn @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_add
% 0.30/0.58  thf(fact_5759_power__add,axiom,
% 0.30/0.58      ! [A: rat,M: nat,N: nat] :
% 0.30/0.58        ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N ) )
% 0.30/0.58        = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_add
% 0.30/0.58  thf(fact_5760_power__add,axiom,
% 0.30/0.58      ! [A: nat,M: nat,N: nat] :
% 0.30/0.58        ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 0.30/0.58        = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_add
% 0.30/0.58  thf(fact_5761_power__add,axiom,
% 0.30/0.58      ! [A: int,M: nat,N: nat] :
% 0.30/0.58        ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 0.30/0.58        = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % power_add
% 0.30/0.58  thf(fact_5762_unit__div__cancel,axiom,
% 0.30/0.58      ! [A: nat,B: nat,C: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.30/0.58       => ( ( ( divide_divide_nat @ B @ A )
% 0.30/0.58            = ( divide_divide_nat @ C @ A ) )
% 0.30/0.58          = ( B = C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_div_cancel
% 0.30/0.58  thf(fact_5763_unit__div__cancel,axiom,
% 0.30/0.58      ! [A: int,B: int,C: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.30/0.58       => ( ( ( divide_divide_int @ B @ A )
% 0.30/0.58            = ( divide_divide_int @ C @ A ) )
% 0.30/0.58          = ( B = C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_div_cancel
% 0.30/0.58  thf(fact_5764_unit__div__cancel,axiom,
% 0.30/0.58      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.30/0.58       => ( ( ( divide6298287555418463151nteger @ B @ A )
% 0.30/0.58            = ( divide6298287555418463151nteger @ C @ A ) )
% 0.30/0.58          = ( B = C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_div_cancel
% 0.30/0.58  thf(fact_5765_unit__div__cancel,axiom,
% 0.30/0.58      ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 0.30/0.58       => ( ( ( divide5121882707175180666atural @ B @ A )
% 0.30/0.58            = ( divide5121882707175180666atural @ C @ A ) )
% 0.30/0.58          = ( B = C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % unit_div_cancel
% 0.30/0.58  thf(fact_5766_div__unit__dvd__iff,axiom,
% 0.30/0.58      ! [B: nat,A: nat,C: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.30/0.58       => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 0.30/0.58          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % div_unit_dvd_iff
% 0.30/0.58  thf(fact_5767_div__unit__dvd__iff,axiom,
% 0.30/0.58      ! [B: int,A: int,C: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.30/0.58       => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 0.30/0.58          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % div_unit_dvd_iff
% 0.30/0.58  thf(fact_5768_div__unit__dvd__iff,axiom,
% 0.30/0.58      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.30/0.58       => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 0.30/0.58          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % div_unit_dvd_iff
% 0.30/0.58  thf(fact_5769_div__unit__dvd__iff,axiom,
% 0.30/0.58      ! [B: code_natural,A: code_natural,C: code_natural] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.30/0.58       => ( ( dvd_dvd_Code_natural @ ( divide5121882707175180666atural @ A @ B ) @ C )
% 0.30/0.58          = ( dvd_dvd_Code_natural @ A @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % div_unit_dvd_iff
% 0.30/0.58  thf(fact_5770_dvd__div__unit__iff,axiom,
% 0.30/0.58      ! [B: nat,A: nat,C: nat] :
% 0.30/0.58        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.30/0.58       => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 0.30/0.58          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_div_unit_iff
% 0.30/0.58  thf(fact_5771_dvd__div__unit__iff,axiom,
% 0.30/0.58      ! [B: int,A: int,C: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.30/0.58       => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 0.30/0.58          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_div_unit_iff
% 0.30/0.58  thf(fact_5772_dvd__div__unit__iff,axiom,
% 0.30/0.58      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.30/0.58       => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 0.30/0.58          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_div_unit_iff
% 0.30/0.58  thf(fact_5773_dvd__div__unit__iff,axiom,
% 0.30/0.58      ! [B: code_natural,A: code_natural,C: code_natural] :
% 0.30/0.58        ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.30/0.58       => ( ( dvd_dvd_Code_natural @ A @ ( divide5121882707175180666atural @ C @ B ) )
% 0.30/0.58          = ( dvd_dvd_Code_natural @ A @ C ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_div_unit_iff
% 0.30/0.58  thf(fact_5774_dvd__div__neg,axiom,
% 0.30/0.58      ! [B: int,A: int] :
% 0.30/0.58        ( ( dvd_dvd_int @ B @ A )
% 0.30/0.58       => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.30/0.58          = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.30/0.58  
% 0.30/0.58  % dvd_div_neg
% 0.30/0.58  thf(fact_5775_dvd__div__neg,axiom,
% 0.30/0.58      ! [B: code_integer,A: code_integer] :
% 0.30/0.58        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.30/0.58       => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.30/0.58          = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % dvd_div_neg
% 0.30/0.59  thf(fact_5776_dvd__div__neg,axiom,
% 0.30/0.59      ! [B: rat,A: rat] :
% 0.30/0.59        ( ( dvd_dvd_rat @ B @ A )
% 0.30/0.59       => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.30/0.59          = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % dvd_div_neg
% 0.30/0.59  thf(fact_5777_dvd__neg__div,axiom,
% 0.30/0.59      ! [B: int,A: int] :
% 0.30/0.59        ( ( dvd_dvd_int @ B @ A )
% 0.30/0.59       => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.30/0.59          = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % dvd_neg_div
% 0.30/0.59  thf(fact_5778_dvd__neg__div,axiom,
% 0.30/0.59      ! [B: code_integer,A: code_integer] :
% 0.30/0.59        ( ( dvd_dvd_Code_integer @ B @ A )
% 0.30/0.59       => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.30/0.59          = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % dvd_neg_div
% 0.30/0.59  thf(fact_5779_dvd__neg__div,axiom,
% 0.30/0.59      ! [B: rat,A: rat] :
% 0.30/0.59        ( ( dvd_dvd_rat @ B @ A )
% 0.30/0.59       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.30/0.59          = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % dvd_neg_div
% 0.30/0.59  thf(fact_5780_minus__one__power__iff,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.59         => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 0.30/0.59            = one_one_int ) )
% 0.30/0.59        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.59         => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 0.30/0.59            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % minus_one_power_iff
% 0.30/0.59  thf(fact_5781_minus__one__power__iff,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.59         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 0.30/0.59            = one_one_Code_integer ) )
% 0.30/0.59        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.59         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 0.30/0.59            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % minus_one_power_iff
% 0.30/0.59  thf(fact_5782_minus__one__power__iff,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.59         => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 0.30/0.59            = one_one_rat ) )
% 0.30/0.59        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.59         => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 0.30/0.59            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % minus_one_power_iff
% 0.30/0.59  thf(fact_5783_mask__int__def,axiom,
% 0.30/0.59      ( bit_se2000444600071755411sk_int
% 0.30/0.59      = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % mask_int_def
% 0.30/0.59  thf(fact_5784_mask__eq__exp__minus__1,axiom,
% 0.30/0.59      ( bit_se2119862282449309892nteger
% 0.30/0.59      = ( ^ [N2: nat] : ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % mask_eq_exp_minus_1
% 0.30/0.59  thf(fact_5785_mask__eq__exp__minus__1,axiom,
% 0.30/0.59      ( bit_se943457434206027407atural
% 0.30/0.59      = ( ^ [N2: nat] : ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_natural ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % mask_eq_exp_minus_1
% 0.30/0.59  thf(fact_5786_mask__eq__exp__minus__1,axiom,
% 0.30/0.59      ( bit_se2000444600071755411sk_int
% 0.30/0.59      = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % mask_eq_exp_minus_1
% 0.30/0.59  thf(fact_5787_mask__eq__exp__minus__1,axiom,
% 0.30/0.59      ( bit_se2002935070580805687sk_nat
% 0.30/0.59      = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % mask_eq_exp_minus_1
% 0.30/0.59  thf(fact_5788_power__le__one,axiom,
% 0.30/0.59      ! [A: code_integer,N: nat] :
% 0.30/0.59        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.59       => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 0.30/0.59         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_le_one
% 0.30/0.59  thf(fact_5789_power__le__one,axiom,
% 0.30/0.59      ! [A: rat,N: nat] :
% 0.30/0.59        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.59       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.30/0.59         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_le_one
% 0.30/0.59  thf(fact_5790_power__le__one,axiom,
% 0.30/0.59      ! [A: nat,N: nat] :
% 0.30/0.59        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.59       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.30/0.59         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_le_one
% 0.30/0.59  thf(fact_5791_power__le__one,axiom,
% 0.30/0.59      ! [A: int,N: nat] :
% 0.30/0.59        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.59       => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.30/0.59         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_le_one
% 0.30/0.59  thf(fact_5792_power__gt1__lemma,axiom,
% 0.30/0.59      ! [A: code_integer,N: nat] :
% 0.30/0.59        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.30/0.59       => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_gt1_lemma
% 0.30/0.59  thf(fact_5793_power__gt1__lemma,axiom,
% 0.30/0.59      ! [A: rat,N: nat] :
% 0.30/0.59        ( ( ord_less_rat @ one_one_rat @ A )
% 0.30/0.59       => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_gt1_lemma
% 0.30/0.59  thf(fact_5794_power__gt1__lemma,axiom,
% 0.30/0.59      ! [A: nat,N: nat] :
% 0.30/0.59        ( ( ord_less_nat @ one_one_nat @ A )
% 0.30/0.59       => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_gt1_lemma
% 0.30/0.59  thf(fact_5795_power__gt1__lemma,axiom,
% 0.30/0.59      ! [A: int,N: nat] :
% 0.30/0.59        ( ( ord_less_int @ one_one_int @ A )
% 0.30/0.59       => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_gt1_lemma
% 0.30/0.59  thf(fact_5796_power__less__power__Suc,axiom,
% 0.30/0.59      ! [A: code_integer,N: nat] :
% 0.30/0.59        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.30/0.59       => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_less_power_Suc
% 0.30/0.59  thf(fact_5797_power__less__power__Suc,axiom,
% 0.30/0.59      ! [A: rat,N: nat] :
% 0.30/0.59        ( ( ord_less_rat @ one_one_rat @ A )
% 0.30/0.59       => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_less_power_Suc
% 0.30/0.59  thf(fact_5798_power__less__power__Suc,axiom,
% 0.30/0.59      ! [A: nat,N: nat] :
% 0.30/0.59        ( ( ord_less_nat @ one_one_nat @ A )
% 0.30/0.59       => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_less_power_Suc
% 0.30/0.59  thf(fact_5799_power__less__power__Suc,axiom,
% 0.30/0.59      ! [A: int,N: nat] :
% 0.30/0.59        ( ( ord_less_int @ one_one_int @ A )
% 0.30/0.59       => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_less_power_Suc
% 0.30/0.59  thf(fact_5800_unity__coeff__ex,axiom,
% 0.30/0.59      ! [P: code_integer > $o,L: code_integer] :
% 0.30/0.59        ( ( ? [X3: code_integer] : ( P @ ( times_3573771949741848930nteger @ L @ X3 ) ) )
% 0.30/0.59        = ( ? [X3: code_integer] :
% 0.30/0.59              ( ( dvd_dvd_Code_integer @ L @ ( plus_p5714425477246183910nteger @ X3 @ zero_z3403309356797280102nteger ) )
% 0.30/0.59              & ( P @ X3 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unity_coeff_ex
% 0.30/0.59  thf(fact_5801_unity__coeff__ex,axiom,
% 0.30/0.59      ! [P: rat > $o,L: rat] :
% 0.30/0.59        ( ( ? [X3: rat] : ( P @ ( times_times_rat @ L @ X3 ) ) )
% 0.30/0.59        = ( ? [X3: rat] :
% 0.30/0.59              ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X3 @ zero_zero_rat ) )
% 0.30/0.59              & ( P @ X3 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unity_coeff_ex
% 0.30/0.59  thf(fact_5802_unity__coeff__ex,axiom,
% 0.30/0.59      ! [P: nat > $o,L: nat] :
% 0.30/0.59        ( ( ? [X3: nat] : ( P @ ( times_times_nat @ L @ X3 ) ) )
% 0.30/0.59        = ( ? [X3: nat] :
% 0.30/0.59              ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X3 @ zero_zero_nat ) )
% 0.30/0.59              & ( P @ X3 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unity_coeff_ex
% 0.30/0.59  thf(fact_5803_unity__coeff__ex,axiom,
% 0.30/0.59      ! [P: int > $o,L: int] :
% 0.30/0.59        ( ( ? [X3: int] : ( P @ ( times_times_int @ L @ X3 ) ) )
% 0.30/0.59        = ( ? [X3: int] :
% 0.30/0.59              ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X3 @ zero_zero_int ) )
% 0.30/0.59              & ( P @ X3 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unity_coeff_ex
% 0.30/0.59  thf(fact_5804_power__0__left,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( ( N = zero_zero_nat )
% 0.30/0.59         => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 0.30/0.59            = one_one_Code_integer ) )
% 0.30/0.59        & ( ( N != zero_zero_nat )
% 0.30/0.59         => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 0.30/0.59            = zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_0_left
% 0.30/0.59  thf(fact_5805_power__0__left,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( ( N = zero_zero_nat )
% 0.30/0.59         => ( ( power_power_rat @ zero_zero_rat @ N )
% 0.30/0.59            = one_one_rat ) )
% 0.30/0.59        & ( ( N != zero_zero_nat )
% 0.30/0.59         => ( ( power_power_rat @ zero_zero_rat @ N )
% 0.30/0.59            = zero_zero_rat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_0_left
% 0.30/0.59  thf(fact_5806_power__0__left,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( ( N = zero_zero_nat )
% 0.30/0.59         => ( ( power_power_int @ zero_zero_int @ N )
% 0.30/0.59            = one_one_int ) )
% 0.30/0.59        & ( ( N != zero_zero_nat )
% 0.30/0.59         => ( ( power_power_int @ zero_zero_int @ N )
% 0.30/0.59            = zero_zero_int ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_0_left
% 0.30/0.59  thf(fact_5807_power__0__left,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( ( N = zero_zero_nat )
% 0.30/0.59         => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.30/0.59            = one_one_nat ) )
% 0.30/0.59        & ( ( N != zero_zero_nat )
% 0.30/0.59         => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.30/0.59            = zero_zero_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_0_left
% 0.30/0.59  thf(fact_5808_unit__dvdE,axiom,
% 0.30/0.59      ! [A: code_integer,B: code_integer] :
% 0.30/0.59        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.30/0.59       => ~ ( ( A != zero_z3403309356797280102nteger )
% 0.30/0.59           => ! [C3: code_integer] :
% 0.30/0.59                ( B
% 0.30/0.59               != ( times_3573771949741848930nteger @ A @ C3 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_dvdE
% 0.30/0.59  thf(fact_5809_unit__dvdE,axiom,
% 0.30/0.59      ! [A: nat,B: nat] :
% 0.30/0.59        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.30/0.59       => ~ ( ( A != zero_zero_nat )
% 0.30/0.59           => ! [C3: nat] :
% 0.30/0.59                ( B
% 0.30/0.59               != ( times_times_nat @ A @ C3 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_dvdE
% 0.30/0.59  thf(fact_5810_unit__dvdE,axiom,
% 0.30/0.59      ! [A: int,B: int] :
% 0.30/0.59        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.30/0.59       => ~ ( ( A != zero_zero_int )
% 0.30/0.59           => ! [C3: int] :
% 0.30/0.59                ( B
% 0.30/0.59               != ( times_times_int @ A @ C3 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_dvdE
% 0.30/0.59  thf(fact_5811_power__gt1,axiom,
% 0.30/0.59      ! [A: code_integer,N: nat] :
% 0.30/0.59        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.30/0.59       => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_gt1
% 0.30/0.59  thf(fact_5812_power__gt1,axiom,
% 0.30/0.59      ! [A: rat,N: nat] :
% 0.30/0.59        ( ( ord_less_rat @ one_one_rat @ A )
% 0.30/0.59       => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_gt1
% 0.30/0.59  thf(fact_5813_power__gt1,axiom,
% 0.30/0.59      ! [A: nat,N: nat] :
% 0.30/0.59        ( ( ord_less_nat @ one_one_nat @ A )
% 0.30/0.59       => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_gt1
% 0.30/0.59  thf(fact_5814_power__gt1,axiom,
% 0.30/0.59      ! [A: int,N: nat] :
% 0.30/0.59        ( ( ord_less_int @ one_one_int @ A )
% 0.30/0.59       => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_gt1
% 0.30/0.59  thf(fact_5815_and_Ocomm__monoid__axioms,axiom,
% 0.30/0.59      comm_m1654649897431166824nteger @ bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ).
% 0.30/0.59  
% 0.30/0.59  % and.comm_monoid_axioms
% 0.30/0.59  thf(fact_5816_and_Ocomm__monoid__axioms,axiom,
% 0.30/0.59      comm_monoid_int @ bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) ).
% 0.30/0.59  
% 0.30/0.59  % and.comm_monoid_axioms
% 0.30/0.59  thf(fact_5817_power__less__imp__less__exp,axiom,
% 0.30/0.59      ! [A: code_integer,M: nat,N: nat] :
% 0.30/0.59        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.30/0.59       => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 0.30/0.59         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_less_imp_less_exp
% 0.30/0.59  thf(fact_5818_power__less__imp__less__exp,axiom,
% 0.30/0.59      ! [A: rat,M: nat,N: nat] :
% 0.30/0.59        ( ( ord_less_rat @ one_one_rat @ A )
% 0.30/0.59       => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 0.30/0.59         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_less_imp_less_exp
% 0.30/0.59  thf(fact_5819_power__less__imp__less__exp,axiom,
% 0.30/0.59      ! [A: nat,M: nat,N: nat] :
% 0.30/0.59        ( ( ord_less_nat @ one_one_nat @ A )
% 0.30/0.59       => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.30/0.59         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_less_imp_less_exp
% 0.30/0.59  thf(fact_5820_power__less__imp__less__exp,axiom,
% 0.30/0.59      ! [A: int,M: nat,N: nat] :
% 0.30/0.59        ( ( ord_less_int @ one_one_int @ A )
% 0.30/0.59       => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.30/0.59         => ( ord_less_nat @ M @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_less_imp_less_exp
% 0.30/0.59  thf(fact_5821_power__strict__increasing,axiom,
% 0.30/0.59      ! [N: nat,N4: nat,A: code_integer] :
% 0.30/0.59        ( ( ord_less_nat @ N @ N4 )
% 0.30/0.59       => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.30/0.59         => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ A @ N4 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_strict_increasing
% 0.30/0.59  thf(fact_5822_power__strict__increasing,axiom,
% 0.30/0.59      ! [N: nat,N4: nat,A: rat] :
% 0.30/0.59        ( ( ord_less_nat @ N @ N4 )
% 0.30/0.59       => ( ( ord_less_rat @ one_one_rat @ A )
% 0.30/0.59         => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_strict_increasing
% 0.30/0.59  thf(fact_5823_power__strict__increasing,axiom,
% 0.30/0.59      ! [N: nat,N4: nat,A: nat] :
% 0.30/0.59        ( ( ord_less_nat @ N @ N4 )
% 0.30/0.59       => ( ( ord_less_nat @ one_one_nat @ A )
% 0.30/0.59         => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_strict_increasing
% 0.30/0.59  thf(fact_5824_power__strict__increasing,axiom,
% 0.30/0.59      ! [N: nat,N4: nat,A: int] :
% 0.30/0.59        ( ( ord_less_nat @ N @ N4 )
% 0.30/0.59       => ( ( ord_less_int @ one_one_int @ A )
% 0.30/0.59         => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_strict_increasing
% 0.30/0.59  thf(fact_5825_power__increasing,axiom,
% 0.30/0.59      ! [N: nat,N4: nat,A: code_integer] :
% 0.30/0.59        ( ( ord_less_eq_nat @ N @ N4 )
% 0.30/0.59       => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 0.30/0.59         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ A @ N4 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_increasing
% 0.30/0.59  thf(fact_5826_power__increasing,axiom,
% 0.30/0.59      ! [N: nat,N4: nat,A: rat] :
% 0.30/0.59        ( ( ord_less_eq_nat @ N @ N4 )
% 0.30/0.59       => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.30/0.59         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_increasing
% 0.30/0.59  thf(fact_5827_power__increasing,axiom,
% 0.30/0.59      ! [N: nat,N4: nat,A: nat] :
% 0.30/0.59        ( ( ord_less_eq_nat @ N @ N4 )
% 0.30/0.59       => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.30/0.59         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_increasing
% 0.30/0.59  thf(fact_5828_power__increasing,axiom,
% 0.30/0.59      ! [N: nat,N4: nat,A: int] :
% 0.30/0.59        ( ( ord_less_eq_nat @ N @ N4 )
% 0.30/0.59       => ( ( ord_less_eq_int @ one_one_int @ A )
% 0.30/0.59         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_increasing
% 0.30/0.59  thf(fact_5829_power__minus,axiom,
% 0.30/0.59      ! [A: int,N: nat] :
% 0.30/0.59        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.30/0.59        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_minus
% 0.30/0.59  thf(fact_5830_power__minus,axiom,
% 0.30/0.59      ! [A: code_integer,N: nat] :
% 0.30/0.59        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.30/0.59        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_minus
% 0.30/0.59  thf(fact_5831_power__minus,axiom,
% 0.30/0.59      ! [A: rat,N: nat] :
% 0.30/0.59        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.30/0.59        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_minus
% 0.30/0.59  thf(fact_5832_inf__period_I4_J,axiom,
% 0.30/0.59      ! [D2: code_integer,D3: code_integer,T3: code_integer] :
% 0.30/0.59        ( ( dvd_dvd_Code_integer @ D2 @ D3 )
% 0.30/0.59       => ! [X5: code_integer,K3: code_integer] :
% 0.30/0.59            ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ T3 ) ) )
% 0.30/0.59            = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K3 @ D3 ) ) @ T3 ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % inf_period(4)
% 0.30/0.59  thf(fact_5833_inf__period_I4_J,axiom,
% 0.30/0.59      ! [D2: rat,D3: rat,T3: rat] :
% 0.30/0.59        ( ( dvd_dvd_rat @ D2 @ D3 )
% 0.30/0.59       => ! [X5: rat,K3: rat] :
% 0.30/0.59            ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ T3 ) ) )
% 0.30/0.59            = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K3 @ D3 ) ) @ T3 ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % inf_period(4)
% 0.30/0.59  thf(fact_5834_inf__period_I4_J,axiom,
% 0.30/0.59      ! [D2: int,D3: int,T3: int] :
% 0.30/0.59        ( ( dvd_dvd_int @ D2 @ D3 )
% 0.30/0.59       => ! [X5: int,K3: int] :
% 0.30/0.59            ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T3 ) ) )
% 0.30/0.59            = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K3 @ D3 ) ) @ T3 ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % inf_period(4)
% 0.30/0.59  thf(fact_5835_inf__period_I3_J,axiom,
% 0.30/0.59      ! [D2: code_integer,D3: code_integer,T3: code_integer] :
% 0.30/0.59        ( ( dvd_dvd_Code_integer @ D2 @ D3 )
% 0.30/0.59       => ! [X5: code_integer,K3: code_integer] :
% 0.30/0.59            ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ T3 ) )
% 0.30/0.59            = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K3 @ D3 ) ) @ T3 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % inf_period(3)
% 0.30/0.59  thf(fact_5836_inf__period_I3_J,axiom,
% 0.30/0.59      ! [D2: rat,D3: rat,T3: rat] :
% 0.30/0.59        ( ( dvd_dvd_rat @ D2 @ D3 )
% 0.30/0.59       => ! [X5: rat,K3: rat] :
% 0.30/0.59            ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ T3 ) )
% 0.30/0.59            = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K3 @ D3 ) ) @ T3 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % inf_period(3)
% 0.30/0.59  thf(fact_5837_inf__period_I3_J,axiom,
% 0.30/0.59      ! [D2: int,D3: int,T3: int] :
% 0.30/0.59        ( ( dvd_dvd_int @ D2 @ D3 )
% 0.30/0.59       => ! [X5: int,K3: int] :
% 0.30/0.59            ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T3 ) )
% 0.30/0.59            = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K3 @ D3 ) ) @ T3 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % inf_period(3)
% 0.30/0.59  thf(fact_5838_dvd__div__div__eq__mult,axiom,
% 0.30/0.59      ! [A: nat,C: nat,B: nat,D2: nat] :
% 0.30/0.59        ( ( A != zero_zero_nat )
% 0.30/0.59       => ( ( C != zero_zero_nat )
% 0.30/0.59         => ( ( dvd_dvd_nat @ A @ B )
% 0.30/0.59           => ( ( dvd_dvd_nat @ C @ D2 )
% 0.30/0.59             => ( ( ( divide_divide_nat @ B @ A )
% 0.30/0.59                  = ( divide_divide_nat @ D2 @ C ) )
% 0.30/0.59                = ( ( times_times_nat @ B @ C )
% 0.30/0.59                  = ( times_times_nat @ A @ D2 ) ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % dvd_div_div_eq_mult
% 0.30/0.59  thf(fact_5839_dvd__div__div__eq__mult,axiom,
% 0.30/0.59      ! [A: int,C: int,B: int,D2: int] :
% 0.30/0.59        ( ( A != zero_zero_int )
% 0.30/0.59       => ( ( C != zero_zero_int )
% 0.30/0.59         => ( ( dvd_dvd_int @ A @ B )
% 0.30/0.59           => ( ( dvd_dvd_int @ C @ D2 )
% 0.30/0.59             => ( ( ( divide_divide_int @ B @ A )
% 0.30/0.59                  = ( divide_divide_int @ D2 @ C ) )
% 0.30/0.59                = ( ( times_times_int @ B @ C )
% 0.30/0.59                  = ( times_times_int @ A @ D2 ) ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % dvd_div_div_eq_mult
% 0.30/0.59  thf(fact_5840_dvd__div__div__eq__mult,axiom,
% 0.30/0.59      ! [A: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 0.30/0.59        ( ( A != zero_z3403309356797280102nteger )
% 0.30/0.59       => ( ( C != zero_z3403309356797280102nteger )
% 0.30/0.59         => ( ( dvd_dvd_Code_integer @ A @ B )
% 0.30/0.59           => ( ( dvd_dvd_Code_integer @ C @ D2 )
% 0.30/0.59             => ( ( ( divide6298287555418463151nteger @ B @ A )
% 0.30/0.59                  = ( divide6298287555418463151nteger @ D2 @ C ) )
% 0.30/0.59                = ( ( times_3573771949741848930nteger @ B @ C )
% 0.30/0.59                  = ( times_3573771949741848930nteger @ A @ D2 ) ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % dvd_div_div_eq_mult
% 0.30/0.59  thf(fact_5841_dvd__div__div__eq__mult,axiom,
% 0.30/0.59      ! [A: code_natural,C: code_natural,B: code_natural,D2: code_natural] :
% 0.30/0.59        ( ( A != zero_z2226904508553997617atural )
% 0.30/0.59       => ( ( C != zero_z2226904508553997617atural )
% 0.30/0.59         => ( ( dvd_dvd_Code_natural @ A @ B )
% 0.30/0.59           => ( ( dvd_dvd_Code_natural @ C @ D2 )
% 0.30/0.59             => ( ( ( divide5121882707175180666atural @ B @ A )
% 0.30/0.59                  = ( divide5121882707175180666atural @ D2 @ C ) )
% 0.30/0.59                = ( ( times_2397367101498566445atural @ B @ C )
% 0.30/0.59                  = ( times_2397367101498566445atural @ A @ D2 ) ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % dvd_div_div_eq_mult
% 0.30/0.59  thf(fact_5842_dvd__div__iff__mult,axiom,
% 0.30/0.59      ! [C: nat,B: nat,A: nat] :
% 0.30/0.59        ( ( C != zero_zero_nat )
% 0.30/0.59       => ( ( dvd_dvd_nat @ C @ B )
% 0.30/0.59         => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.30/0.59            = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % dvd_div_iff_mult
% 0.30/0.59  thf(fact_5843_dvd__div__iff__mult,axiom,
% 0.30/0.59      ! [C: int,B: int,A: int] :
% 0.30/0.59        ( ( C != zero_zero_int )
% 0.30/0.59       => ( ( dvd_dvd_int @ C @ B )
% 0.30/0.59         => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.30/0.59            = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % dvd_div_iff_mult
% 0.30/0.59  thf(fact_5844_dvd__div__iff__mult,axiom,
% 0.30/0.59      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.30/0.59        ( ( C != zero_z3403309356797280102nteger )
% 0.30/0.59       => ( ( dvd_dvd_Code_integer @ C @ B )
% 0.30/0.59         => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 0.30/0.59            = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % dvd_div_iff_mult
% 0.30/0.59  thf(fact_5845_dvd__div__iff__mult,axiom,
% 0.30/0.59      ! [C: code_natural,B: code_natural,A: code_natural] :
% 0.30/0.59        ( ( C != zero_z2226904508553997617atural )
% 0.30/0.59       => ( ( dvd_dvd_Code_natural @ C @ B )
% 0.30/0.59         => ( ( dvd_dvd_Code_natural @ A @ ( divide5121882707175180666atural @ B @ C ) )
% 0.30/0.59            = ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ A @ C ) @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % dvd_div_iff_mult
% 0.30/0.59  thf(fact_5846_div__dvd__iff__mult,axiom,
% 0.30/0.59      ! [B: nat,A: nat,C: nat] :
% 0.30/0.59        ( ( B != zero_zero_nat )
% 0.30/0.59       => ( ( dvd_dvd_nat @ B @ A )
% 0.30/0.59         => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 0.30/0.59            = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % div_dvd_iff_mult
% 0.30/0.59  thf(fact_5847_div__dvd__iff__mult,axiom,
% 0.30/0.59      ! [B: int,A: int,C: int] :
% 0.30/0.59        ( ( B != zero_zero_int )
% 0.30/0.59       => ( ( dvd_dvd_int @ B @ A )
% 0.30/0.59         => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 0.30/0.59            = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % div_dvd_iff_mult
% 0.30/0.59  thf(fact_5848_div__dvd__iff__mult,axiom,
% 0.30/0.59      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.30/0.59        ( ( B != zero_z3403309356797280102nteger )
% 0.30/0.59       => ( ( dvd_dvd_Code_integer @ B @ A )
% 0.30/0.59         => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 0.30/0.59            = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % div_dvd_iff_mult
% 0.30/0.59  thf(fact_5849_div__dvd__iff__mult,axiom,
% 0.30/0.59      ! [B: code_natural,A: code_natural,C: code_natural] :
% 0.30/0.59        ( ( B != zero_z2226904508553997617atural )
% 0.30/0.59       => ( ( dvd_dvd_Code_natural @ B @ A )
% 0.30/0.59         => ( ( dvd_dvd_Code_natural @ ( divide5121882707175180666atural @ A @ B ) @ C )
% 0.30/0.59            = ( dvd_dvd_Code_natural @ A @ ( times_2397367101498566445atural @ C @ B ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % div_dvd_iff_mult
% 0.30/0.59  thf(fact_5850_dvd__div__eq__mult,axiom,
% 0.30/0.59      ! [A: nat,B: nat,C: nat] :
% 0.30/0.59        ( ( A != zero_zero_nat )
% 0.30/0.59       => ( ( dvd_dvd_nat @ A @ B )
% 0.30/0.59         => ( ( ( divide_divide_nat @ B @ A )
% 0.30/0.59              = C )
% 0.30/0.59            = ( B
% 0.30/0.59              = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % dvd_div_eq_mult
% 0.30/0.59  thf(fact_5851_dvd__div__eq__mult,axiom,
% 0.30/0.59      ! [A: int,B: int,C: int] :
% 0.30/0.59        ( ( A != zero_zero_int )
% 0.30/0.59       => ( ( dvd_dvd_int @ A @ B )
% 0.30/0.59         => ( ( ( divide_divide_int @ B @ A )
% 0.30/0.59              = C )
% 0.30/0.59            = ( B
% 0.30/0.59              = ( times_times_int @ C @ A ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % dvd_div_eq_mult
% 0.30/0.59  thf(fact_5852_dvd__div__eq__mult,axiom,
% 0.30/0.59      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.59        ( ( A != zero_z3403309356797280102nteger )
% 0.30/0.59       => ( ( dvd_dvd_Code_integer @ A @ B )
% 0.30/0.59         => ( ( ( divide6298287555418463151nteger @ B @ A )
% 0.30/0.59              = C )
% 0.30/0.59            = ( B
% 0.30/0.59              = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % dvd_div_eq_mult
% 0.30/0.59  thf(fact_5853_dvd__div__eq__mult,axiom,
% 0.30/0.59      ! [A: code_natural,B: code_natural,C: code_natural] :
% 0.30/0.59        ( ( A != zero_z2226904508553997617atural )
% 0.30/0.59       => ( ( dvd_dvd_Code_natural @ A @ B )
% 0.30/0.59         => ( ( ( divide5121882707175180666atural @ B @ A )
% 0.30/0.59              = C )
% 0.30/0.59            = ( B
% 0.30/0.59              = ( times_2397367101498566445atural @ C @ A ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % dvd_div_eq_mult
% 0.30/0.59  thf(fact_5854_unit__div__eq__0__iff,axiom,
% 0.30/0.59      ! [B: nat,A: nat] :
% 0.30/0.59        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.30/0.59       => ( ( ( divide_divide_nat @ A @ B )
% 0.30/0.59            = zero_zero_nat )
% 0.30/0.59          = ( A = zero_zero_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_div_eq_0_iff
% 0.30/0.59  thf(fact_5855_unit__div__eq__0__iff,axiom,
% 0.30/0.59      ! [B: int,A: int] :
% 0.30/0.59        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.30/0.59       => ( ( ( divide_divide_int @ A @ B )
% 0.30/0.59            = zero_zero_int )
% 0.30/0.59          = ( A = zero_zero_int ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_div_eq_0_iff
% 0.30/0.59  thf(fact_5856_unit__div__eq__0__iff,axiom,
% 0.30/0.59      ! [B: code_integer,A: code_integer] :
% 0.30/0.59        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.30/0.59       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 0.30/0.59            = zero_z3403309356797280102nteger )
% 0.30/0.59          = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_div_eq_0_iff
% 0.30/0.59  thf(fact_5857_unit__div__eq__0__iff,axiom,
% 0.30/0.59      ! [B: code_natural,A: code_natural] :
% 0.30/0.59        ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.30/0.59       => ( ( ( divide5121882707175180666atural @ A @ B )
% 0.30/0.59            = zero_z2226904508553997617atural )
% 0.30/0.59          = ( A = zero_z2226904508553997617atural ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_div_eq_0_iff
% 0.30/0.59  thf(fact_5858_and_Omonoid__axioms,axiom,
% 0.30/0.59      monoid_Code_integer @ bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ).
% 0.30/0.59  
% 0.30/0.59  % and.monoid_axioms
% 0.30/0.59  thf(fact_5859_and_Omonoid__axioms,axiom,
% 0.30/0.59      monoid_int @ bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) ).
% 0.30/0.59  
% 0.30/0.59  % and.monoid_axioms
% 0.30/0.59  thf(fact_5860_unit__eq__div1,axiom,
% 0.30/0.59      ! [B: nat,A: nat,C: nat] :
% 0.30/0.59        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.30/0.59       => ( ( ( divide_divide_nat @ A @ B )
% 0.30/0.59            = C )
% 0.30/0.59          = ( A
% 0.30/0.59            = ( times_times_nat @ C @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_eq_div1
% 0.30/0.59  thf(fact_5861_unit__eq__div1,axiom,
% 0.30/0.59      ! [B: int,A: int,C: int] :
% 0.30/0.59        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.30/0.59       => ( ( ( divide_divide_int @ A @ B )
% 0.30/0.59            = C )
% 0.30/0.59          = ( A
% 0.30/0.59            = ( times_times_int @ C @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_eq_div1
% 0.30/0.59  thf(fact_5862_unit__eq__div1,axiom,
% 0.30/0.59      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.30/0.59        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.30/0.59       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 0.30/0.59            = C )
% 0.30/0.59          = ( A
% 0.30/0.59            = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_eq_div1
% 0.30/0.59  thf(fact_5863_unit__eq__div1,axiom,
% 0.30/0.59      ! [B: code_natural,A: code_natural,C: code_natural] :
% 0.30/0.59        ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.30/0.59       => ( ( ( divide5121882707175180666atural @ A @ B )
% 0.30/0.59            = C )
% 0.30/0.59          = ( A
% 0.30/0.59            = ( times_2397367101498566445atural @ C @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_eq_div1
% 0.30/0.59  thf(fact_5864_unit__eq__div2,axiom,
% 0.30/0.59      ! [B: nat,A: nat,C: nat] :
% 0.30/0.59        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.30/0.59       => ( ( A
% 0.30/0.59            = ( divide_divide_nat @ C @ B ) )
% 0.30/0.59          = ( ( times_times_nat @ A @ B )
% 0.30/0.59            = C ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_eq_div2
% 0.30/0.59  thf(fact_5865_unit__eq__div2,axiom,
% 0.30/0.59      ! [B: int,A: int,C: int] :
% 0.30/0.59        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.30/0.59       => ( ( A
% 0.30/0.59            = ( divide_divide_int @ C @ B ) )
% 0.30/0.59          = ( ( times_times_int @ A @ B )
% 0.30/0.59            = C ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_eq_div2
% 0.30/0.59  thf(fact_5866_unit__eq__div2,axiom,
% 0.30/0.59      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.30/0.59        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.30/0.59       => ( ( A
% 0.30/0.59            = ( divide6298287555418463151nteger @ C @ B ) )
% 0.30/0.59          = ( ( times_3573771949741848930nteger @ A @ B )
% 0.30/0.59            = C ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_eq_div2
% 0.30/0.59  thf(fact_5867_unit__eq__div2,axiom,
% 0.30/0.59      ! [B: code_natural,A: code_natural,C: code_natural] :
% 0.30/0.59        ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.30/0.59       => ( ( A
% 0.30/0.59            = ( divide5121882707175180666atural @ C @ B ) )
% 0.30/0.59          = ( ( times_2397367101498566445atural @ A @ B )
% 0.30/0.59            = C ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_eq_div2
% 0.30/0.59  thf(fact_5868_div__mult__unit2,axiom,
% 0.30/0.59      ! [C: nat,B: nat,A: nat] :
% 0.30/0.59        ( ( dvd_dvd_nat @ C @ one_one_nat )
% 0.30/0.59       => ( ( dvd_dvd_nat @ B @ A )
% 0.30/0.59         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.30/0.59            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % div_mult_unit2
% 0.30/0.59  thf(fact_5869_div__mult__unit2,axiom,
% 0.30/0.59      ! [C: int,B: int,A: int] :
% 0.30/0.59        ( ( dvd_dvd_int @ C @ one_one_int )
% 0.30/0.59       => ( ( dvd_dvd_int @ B @ A )
% 0.30/0.59         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.30/0.59            = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % div_mult_unit2
% 0.30/0.59  thf(fact_5870_div__mult__unit2,axiom,
% 0.30/0.59      ! [C: code_integer,B: code_integer,A: code_integer] :
% 0.30/0.59        ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 0.30/0.59       => ( ( dvd_dvd_Code_integer @ B @ A )
% 0.30/0.59         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.30/0.59            = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % div_mult_unit2
% 0.30/0.59  thf(fact_5871_div__mult__unit2,axiom,
% 0.30/0.59      ! [C: code_natural,B: code_natural,A: code_natural] :
% 0.30/0.59        ( ( dvd_dvd_Code_natural @ C @ one_one_Code_natural )
% 0.30/0.59       => ( ( dvd_dvd_Code_natural @ B @ A )
% 0.30/0.59         => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ C ) )
% 0.30/0.59            = ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ B ) @ C ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % div_mult_unit2
% 0.30/0.59  thf(fact_5872_unit__div__commute,axiom,
% 0.30/0.59      ! [B: nat,A: nat,C: nat] :
% 0.30/0.59        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.30/0.59       => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 0.30/0.59          = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_div_commute
% 0.30/0.59  thf(fact_5873_unit__div__commute,axiom,
% 0.30/0.59      ! [B: int,A: int,C: int] :
% 0.30/0.59        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.30/0.59       => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 0.30/0.59          = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_div_commute
% 0.30/0.59  thf(fact_5874_unit__div__commute,axiom,
% 0.30/0.59      ! [B: code_integer,A: code_integer,C: code_integer] :
% 0.30/0.59        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.30/0.59       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 0.30/0.59          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_div_commute
% 0.30/0.59  thf(fact_5875_unit__div__commute,axiom,
% 0.30/0.59      ! [B: code_natural,A: code_natural,C: code_natural] :
% 0.30/0.59        ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.30/0.59       => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ C )
% 0.30/0.59          = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ C ) @ B ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_div_commute
% 0.30/0.59  thf(fact_5876_unit__div__mult__swap,axiom,
% 0.30/0.59      ! [C: nat,A: nat,B: nat] :
% 0.30/0.59        ( ( dvd_dvd_nat @ C @ one_one_nat )
% 0.30/0.59       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 0.30/0.59          = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_div_mult_swap
% 0.30/0.59  thf(fact_5877_unit__div__mult__swap,axiom,
% 0.30/0.59      ! [C: int,A: int,B: int] :
% 0.30/0.59        ( ( dvd_dvd_int @ C @ one_one_int )
% 0.30/0.59       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 0.30/0.59          = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_div_mult_swap
% 0.30/0.59  thf(fact_5878_unit__div__mult__swap,axiom,
% 0.30/0.59      ! [C: code_integer,A: code_integer,B: code_integer] :
% 0.30/0.59        ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 0.30/0.59       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 0.30/0.59          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_div_mult_swap
% 0.30/0.59  thf(fact_5879_unit__div__mult__swap,axiom,
% 0.30/0.59      ! [C: code_natural,A: code_natural,B: code_natural] :
% 0.30/0.59        ( ( dvd_dvd_Code_natural @ C @ one_one_Code_natural )
% 0.30/0.59       => ( ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C ) )
% 0.30/0.59          = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_div_mult_swap
% 0.30/0.59  thf(fact_5880_is__unit__div__mult2__eq,axiom,
% 0.30/0.59      ! [B: nat,C: nat,A: nat] :
% 0.30/0.59        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.30/0.59       => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 0.30/0.59         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.30/0.59            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % is_unit_div_mult2_eq
% 0.30/0.59  thf(fact_5881_is__unit__div__mult2__eq,axiom,
% 0.30/0.59      ! [B: int,C: int,A: int] :
% 0.30/0.59        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.30/0.59       => ( ( dvd_dvd_int @ C @ one_one_int )
% 0.30/0.59         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 0.30/0.59            = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % is_unit_div_mult2_eq
% 0.30/0.59  thf(fact_5882_is__unit__div__mult2__eq,axiom,
% 0.30/0.59      ! [B: code_integer,C: code_integer,A: code_integer] :
% 0.30/0.59        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.30/0.59       => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 0.30/0.59         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 0.30/0.59            = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % is_unit_div_mult2_eq
% 0.30/0.59  thf(fact_5883_is__unit__div__mult2__eq,axiom,
% 0.30/0.59      ! [B: code_natural,C: code_natural,A: code_natural] :
% 0.30/0.59        ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.30/0.59       => ( ( dvd_dvd_Code_natural @ C @ one_one_Code_natural )
% 0.30/0.59         => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ C ) )
% 0.30/0.59            = ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ B ) @ C ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % is_unit_div_mult2_eq
% 0.30/0.59  thf(fact_5884_unit__imp__mod__eq__0,axiom,
% 0.30/0.59      ! [B: nat,A: nat] :
% 0.30/0.59        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.30/0.59       => ( ( modulo_modulo_nat @ A @ B )
% 0.30/0.59          = zero_zero_nat ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_imp_mod_eq_0
% 0.30/0.59  thf(fact_5885_unit__imp__mod__eq__0,axiom,
% 0.30/0.59      ! [B: int,A: int] :
% 0.30/0.59        ( ( dvd_dvd_int @ B @ one_one_int )
% 0.30/0.59       => ( ( modulo_modulo_int @ A @ B )
% 0.30/0.59          = zero_zero_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_imp_mod_eq_0
% 0.30/0.59  thf(fact_5886_unit__imp__mod__eq__0,axiom,
% 0.30/0.59      ! [B: code_integer,A: code_integer] :
% 0.30/0.59        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.30/0.59       => ( ( modulo364778990260209775nteger @ A @ B )
% 0.30/0.59          = zero_z3403309356797280102nteger ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_imp_mod_eq_0
% 0.30/0.59  thf(fact_5887_unit__imp__mod__eq__0,axiom,
% 0.30/0.59      ! [B: code_natural,A: code_natural] :
% 0.30/0.59        ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.30/0.59       => ( ( modulo8411746178871703098atural @ A @ B )
% 0.30/0.59          = zero_z2226904508553997617atural ) ) ).
% 0.30/0.59  
% 0.30/0.59  % unit_imp_mod_eq_0
% 0.30/0.59  thf(fact_5888_power__minus__Bit0,axiom,
% 0.30/0.59      ! [X: int,K: num] :
% 0.30/0.59        ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.30/0.59        = ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_minus_Bit0
% 0.30/0.59  thf(fact_5889_power__minus__Bit0,axiom,
% 0.30/0.59      ! [X: code_integer,K: num] :
% 0.30/0.59        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.30/0.59        = ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_minus_Bit0
% 0.30/0.59  thf(fact_5890_power__minus__Bit0,axiom,
% 0.30/0.59      ! [X: rat,K: num] :
% 0.30/0.59        ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 0.30/0.59        = ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_minus_Bit0
% 0.30/0.59  thf(fact_5891_and_Osemilattice__neutr__axioms,axiom,
% 0.30/0.59      semila6106414119144251899nteger @ bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ).
% 0.30/0.59  
% 0.30/0.59  % and.semilattice_neutr_axioms
% 0.30/0.59  thf(fact_5892_and_Osemilattice__neutr__axioms,axiom,
% 0.30/0.59      semila9079005292280841162tr_int @ bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) ).
% 0.30/0.59  
% 0.30/0.59  % and.semilattice_neutr_axioms
% 0.30/0.59  thf(fact_5893_power__minus__Bit1,axiom,
% 0.30/0.59      ! [X: int,K: num] :
% 0.30/0.59        ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.30/0.59        = ( uminus_uminus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_minus_Bit1
% 0.30/0.59  thf(fact_5894_power__minus__Bit1,axiom,
% 0.30/0.59      ! [X: code_integer,K: num] :
% 0.30/0.59        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.30/0.59        = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_minus_Bit1
% 0.30/0.59  thf(fact_5895_power__minus__Bit1,axiom,
% 0.30/0.59      ! [X: rat,K: num] :
% 0.30/0.59        ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 0.30/0.59        = ( uminus_uminus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_minus_Bit1
% 0.30/0.59  thf(fact_5896_even__mask__div__iff_H,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.30/0.59        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/0.59  
% 0.30/0.59  % even_mask_div_iff'
% 0.30/0.59  thf(fact_5897_even__mask__div__iff_H,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 0.30/0.59        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/0.59  
% 0.30/0.59  % even_mask_div_iff'
% 0.30/0.59  thf(fact_5898_even__mask__div__iff_H,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 0.30/0.59        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/0.59  
% 0.30/0.59  % even_mask_div_iff'
% 0.30/0.59  thf(fact_5899_even__mask__div__iff_H,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) @ one_one_Code_natural ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) )
% 0.30/0.59        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/0.59  
% 0.30/0.59  % even_mask_div_iff'
% 0.30/0.59  thf(fact_5900_power__numeral__even,axiom,
% 0.30/0.59      ! [Z: code_integer,W: num] :
% 0.30/0.59        ( ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.30/0.59        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_numeral_even
% 0.30/0.59  thf(fact_5901_power__numeral__even,axiom,
% 0.30/0.59      ! [Z: assn,W: num] :
% 0.30/0.59        ( ( power_power_assn @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.30/0.59        = ( times_times_assn @ ( power_power_assn @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_assn @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_numeral_even
% 0.30/0.59  thf(fact_5902_power__numeral__even,axiom,
% 0.30/0.59      ! [Z: rat,W: num] :
% 0.30/0.59        ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.30/0.59        = ( times_times_rat @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_numeral_even
% 0.30/0.59  thf(fact_5903_power__numeral__even,axiom,
% 0.30/0.59      ! [Z: nat,W: num] :
% 0.30/0.59        ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.30/0.59        = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_numeral_even
% 0.30/0.59  thf(fact_5904_power__numeral__even,axiom,
% 0.30/0.59      ! [Z: int,W: num] :
% 0.30/0.59        ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 0.30/0.59        = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_numeral_even
% 0.30/0.59  thf(fact_5905_power__numeral__odd,axiom,
% 0.30/0.59      ! [Z: code_integer,W: num] :
% 0.30/0.59        ( ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.30/0.59        = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ Z @ ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_numeral_odd
% 0.30/0.59  thf(fact_5906_power__numeral__odd,axiom,
% 0.30/0.59      ! [Z: assn,W: num] :
% 0.30/0.59        ( ( power_power_assn @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.30/0.59        = ( times_times_assn @ ( times_times_assn @ Z @ ( power_power_assn @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_assn @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_numeral_odd
% 0.30/0.59  thf(fact_5907_power__numeral__odd,axiom,
% 0.30/0.59      ! [Z: rat,W: num] :
% 0.30/0.59        ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.30/0.59        = ( times_times_rat @ ( times_times_rat @ Z @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_numeral_odd
% 0.30/0.59  thf(fact_5908_power__numeral__odd,axiom,
% 0.30/0.59      ! [Z: nat,W: num] :
% 0.30/0.59        ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.30/0.59        = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_numeral_odd
% 0.30/0.59  thf(fact_5909_power__numeral__odd,axiom,
% 0.30/0.59      ! [Z: int,W: num] :
% 0.30/0.59        ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 0.30/0.59        = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_numeral_odd
% 0.30/0.59  thf(fact_5910_even__mask__div__iff,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.30/0.59        = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.59            = zero_zero_nat )
% 0.30/0.59          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % even_mask_div_iff
% 0.30/0.59  thf(fact_5911_even__mask__div__iff,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 0.30/0.59        = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.30/0.59            = zero_zero_int )
% 0.30/0.59          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % even_mask_div_iff
% 0.30/0.59  thf(fact_5912_even__mask__div__iff,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 0.30/0.59        = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 0.30/0.59            = zero_z3403309356797280102nteger )
% 0.30/0.59          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % even_mask_div_iff
% 0.30/0.59  thf(fact_5913_even__mask__div__iff,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) @ one_one_Code_natural ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) )
% 0.30/0.59        = ( ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N )
% 0.30/0.59            = zero_z2226904508553997617atural )
% 0.30/0.59          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % even_mask_div_iff
% 0.30/0.59  thf(fact_5914_stable__imp__take__bit__eq,axiom,
% 0.30/0.59      ! [A: nat,N: nat] :
% 0.30/0.59        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59          = A )
% 0.30/0.59       => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.30/0.59           => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 0.30/0.59              = zero_zero_nat ) )
% 0.30/0.59          & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.30/0.59           => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 0.30/0.59              = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % stable_imp_take_bit_eq
% 0.30/0.59  thf(fact_5915_stable__imp__take__bit__eq,axiom,
% 0.30/0.59      ! [A: code_integer,N: nat] :
% 0.30/0.59        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.59          = A )
% 0.30/0.59       => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.30/0.59           => ( ( bit_se1745604003318907178nteger @ N @ A )
% 0.30/0.59              = zero_z3403309356797280102nteger ) )
% 0.30/0.59          & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.30/0.59           => ( ( bit_se1745604003318907178nteger @ N @ A )
% 0.30/0.59              = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % stable_imp_take_bit_eq
% 0.30/0.59  thf(fact_5916_stable__imp__take__bit__eq,axiom,
% 0.30/0.59      ! [A: code_natural,N: nat] :
% 0.30/0.59        ( ( ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.59          = A )
% 0.30/0.59       => ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.30/0.59           => ( ( bit_se569199155075624693atural @ N @ A )
% 0.30/0.59              = zero_z2226904508553997617atural ) )
% 0.30/0.59          & ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.30/0.59           => ( ( bit_se569199155075624693atural @ N @ A )
% 0.30/0.59              = ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) @ one_one_Code_natural ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % stable_imp_take_bit_eq
% 0.30/0.59  thf(fact_5917_stable__imp__take__bit__eq,axiom,
% 0.30/0.59      ! [A: int,N: nat] :
% 0.30/0.59        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.59          = A )
% 0.30/0.59       => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.30/0.59           => ( ( bit_se2923211474154528505it_int @ N @ A )
% 0.30/0.59              = zero_zero_int ) )
% 0.30/0.59          & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.30/0.59           => ( ( bit_se2923211474154528505it_int @ N @ A )
% 0.30/0.59              = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % stable_imp_take_bit_eq
% 0.30/0.59  thf(fact_5918_power__Suc__less,axiom,
% 0.30/0.59      ! [A: code_integer,N: nat] :
% 0.30/0.59        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.59       => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 0.30/0.59         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_Suc_less
% 0.30/0.59  thf(fact_5919_power__Suc__less,axiom,
% 0.30/0.59      ! [A: rat,N: nat] :
% 0.30/0.59        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.59       => ( ( ord_less_rat @ A @ one_one_rat )
% 0.30/0.59         => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_Suc_less
% 0.30/0.59  thf(fact_5920_power__Suc__less,axiom,
% 0.30/0.59      ! [A: nat,N: nat] :
% 0.30/0.59        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.59       => ( ( ord_less_nat @ A @ one_one_nat )
% 0.30/0.59         => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_Suc_less
% 0.30/0.59  thf(fact_5921_power__Suc__less,axiom,
% 0.30/0.59      ! [A: int,N: nat] :
% 0.30/0.59        ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.59       => ( ( ord_less_int @ A @ one_one_int )
% 0.30/0.59         => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_Suc_less
% 0.30/0.59  thf(fact_5922_power__Suc__le__self,axiom,
% 0.30/0.59      ! [A: code_integer,N: nat] :
% 0.30/0.59        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.59       => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 0.30/0.59         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_Suc_le_self
% 0.30/0.59  thf(fact_5923_power__Suc__le__self,axiom,
% 0.30/0.59      ! [A: rat,N: nat] :
% 0.30/0.59        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.59       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.30/0.59         => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_Suc_le_self
% 0.30/0.59  thf(fact_5924_power__Suc__le__self,axiom,
% 0.30/0.59      ! [A: nat,N: nat] :
% 0.30/0.59        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.59       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.30/0.59         => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_Suc_le_self
% 0.30/0.59  thf(fact_5925_power__Suc__le__self,axiom,
% 0.30/0.59      ! [A: int,N: nat] :
% 0.30/0.59        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.59       => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.30/0.59         => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_Suc_le_self
% 0.30/0.59  thf(fact_5926_power__Suc__less__one,axiom,
% 0.30/0.59      ! [A: code_integer,N: nat] :
% 0.30/0.59        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.59       => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 0.30/0.59         => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) @ one_one_Code_integer ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_Suc_less_one
% 0.30/0.59  thf(fact_5927_power__Suc__less__one,axiom,
% 0.30/0.59      ! [A: rat,N: nat] :
% 0.30/0.59        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.59       => ( ( ord_less_rat @ A @ one_one_rat )
% 0.30/0.59         => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_Suc_less_one
% 0.30/0.59  thf(fact_5928_power__Suc__less__one,axiom,
% 0.30/0.59      ! [A: nat,N: nat] :
% 0.30/0.59        ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.59       => ( ( ord_less_nat @ A @ one_one_nat )
% 0.30/0.59         => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_Suc_less_one
% 0.30/0.59  thf(fact_5929_power__Suc__less__one,axiom,
% 0.30/0.59      ! [A: int,N: nat] :
% 0.30/0.59        ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.59       => ( ( ord_less_int @ A @ one_one_int )
% 0.30/0.59         => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_Suc_less_one
% 0.30/0.59  thf(fact_5930_power__strict__decreasing,axiom,
% 0.30/0.59      ! [N: nat,N4: nat,A: code_integer] :
% 0.30/0.59        ( ( ord_less_nat @ N @ N4 )
% 0.30/0.59       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.59         => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 0.30/0.59           => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N4 ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_strict_decreasing
% 0.30/0.59  thf(fact_5931_power__strict__decreasing,axiom,
% 0.30/0.59      ! [N: nat,N4: nat,A: rat] :
% 0.30/0.59        ( ( ord_less_nat @ N @ N4 )
% 0.30/0.59       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.59         => ( ( ord_less_rat @ A @ one_one_rat )
% 0.30/0.59           => ( ord_less_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_strict_decreasing
% 0.30/0.59  thf(fact_5932_power__strict__decreasing,axiom,
% 0.30/0.59      ! [N: nat,N4: nat,A: nat] :
% 0.30/0.59        ( ( ord_less_nat @ N @ N4 )
% 0.30/0.59       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.59         => ( ( ord_less_nat @ A @ one_one_nat )
% 0.30/0.59           => ( ord_less_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_strict_decreasing
% 0.30/0.59  thf(fact_5933_power__strict__decreasing,axiom,
% 0.30/0.59      ! [N: nat,N4: nat,A: int] :
% 0.30/0.59        ( ( ord_less_nat @ N @ N4 )
% 0.30/0.59       => ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.59         => ( ( ord_less_int @ A @ one_one_int )
% 0.30/0.59           => ( ord_less_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_strict_decreasing
% 0.30/0.59  thf(fact_5934_power__decreasing,axiom,
% 0.30/0.59      ! [N: nat,N4: nat,A: code_integer] :
% 0.30/0.59        ( ( ord_less_eq_nat @ N @ N4 )
% 0.30/0.59       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.59         => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 0.30/0.59           => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N4 ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_decreasing
% 0.30/0.59  thf(fact_5935_power__decreasing,axiom,
% 0.30/0.59      ! [N: nat,N4: nat,A: rat] :
% 0.30/0.59        ( ( ord_less_eq_nat @ N @ N4 )
% 0.30/0.59       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.59         => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.30/0.59           => ( ord_less_eq_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_decreasing
% 0.30/0.59  thf(fact_5936_power__decreasing,axiom,
% 0.30/0.59      ! [N: nat,N4: nat,A: nat] :
% 0.30/0.59        ( ( ord_less_eq_nat @ N @ N4 )
% 0.30/0.59       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.59         => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.30/0.59           => ( ord_less_eq_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_decreasing
% 0.30/0.59  thf(fact_5937_power__decreasing,axiom,
% 0.30/0.59      ! [N: nat,N4: nat,A: int] :
% 0.30/0.59        ( ( ord_less_eq_nat @ N @ N4 )
% 0.30/0.59       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.59         => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.30/0.59           => ( ord_less_eq_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_decreasing
% 0.30/0.59  thf(fact_5938_power__le__imp__le__exp,axiom,
% 0.30/0.59      ! [A: code_integer,M: nat,N: nat] :
% 0.30/0.59        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.30/0.59       => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 0.30/0.59         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_le_imp_le_exp
% 0.30/0.59  thf(fact_5939_power__le__imp__le__exp,axiom,
% 0.30/0.59      ! [A: rat,M: nat,N: nat] :
% 0.30/0.59        ( ( ord_less_rat @ one_one_rat @ A )
% 0.30/0.59       => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 0.30/0.59         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_le_imp_le_exp
% 0.30/0.59  thf(fact_5940_power__le__imp__le__exp,axiom,
% 0.30/0.59      ! [A: nat,M: nat,N: nat] :
% 0.30/0.59        ( ( ord_less_nat @ one_one_nat @ A )
% 0.30/0.59       => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.30/0.59         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_le_imp_le_exp
% 0.30/0.59  thf(fact_5941_power__le__imp__le__exp,axiom,
% 0.30/0.59      ! [A: int,M: nat,N: nat] :
% 0.30/0.59        ( ( ord_less_int @ one_one_int @ A )
% 0.30/0.59       => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.30/0.59         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_le_imp_le_exp
% 0.30/0.59  thf(fact_5942_self__le__power,axiom,
% 0.30/0.59      ! [A: code_integer,N: nat] :
% 0.30/0.59        ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 0.30/0.59       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.59         => ( ord_le3102999989581377725nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % self_le_power
% 0.30/0.59  thf(fact_5943_self__le__power,axiom,
% 0.30/0.59      ! [A: rat,N: nat] :
% 0.30/0.59        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.30/0.59       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.59         => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % self_le_power
% 0.30/0.59  thf(fact_5944_self__le__power,axiom,
% 0.30/0.59      ! [A: nat,N: nat] :
% 0.30/0.59        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.30/0.59       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.59         => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % self_le_power
% 0.30/0.59  thf(fact_5945_self__le__power,axiom,
% 0.30/0.59      ! [A: int,N: nat] :
% 0.30/0.59        ( ( ord_less_eq_int @ one_one_int @ A )
% 0.30/0.59       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.59         => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % self_le_power
% 0.30/0.59  thf(fact_5946_one__less__power,axiom,
% 0.30/0.59      ! [A: code_integer,N: nat] :
% 0.30/0.59        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.30/0.59       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.59         => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % one_less_power
% 0.30/0.59  thf(fact_5947_one__less__power,axiom,
% 0.30/0.59      ! [A: rat,N: nat] :
% 0.30/0.59        ( ( ord_less_rat @ one_one_rat @ A )
% 0.30/0.59       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.59         => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % one_less_power
% 0.30/0.59  thf(fact_5948_one__less__power,axiom,
% 0.30/0.59      ! [A: nat,N: nat] :
% 0.30/0.59        ( ( ord_less_nat @ one_one_nat @ A )
% 0.30/0.59       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.59         => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % one_less_power
% 0.30/0.59  thf(fact_5949_one__less__power,axiom,
% 0.30/0.59      ! [A: int,N: nat] :
% 0.30/0.59        ( ( ord_less_int @ one_one_int @ A )
% 0.30/0.59       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.59         => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % one_less_power
% 0.30/0.59  thf(fact_5950_is__unit__div__mult__cancel__right,axiom,
% 0.30/0.59      ! [A: nat,B: nat] :
% 0.30/0.59        ( ( A != zero_zero_nat )
% 0.30/0.59       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.30/0.59         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 0.30/0.59            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % is_unit_div_mult_cancel_right
% 0.30/0.59  thf(fact_5951_is__unit__div__mult__cancel__right,axiom,
% 0.30/0.59      ! [A: int,B: int] :
% 0.30/0.59        ( ( A != zero_zero_int )
% 0.30/0.59       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.30/0.59         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 0.30/0.59            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % is_unit_div_mult_cancel_right
% 0.30/0.59  thf(fact_5952_is__unit__div__mult__cancel__right,axiom,
% 0.30/0.59      ! [A: code_integer,B: code_integer] :
% 0.30/0.59        ( ( A != zero_z3403309356797280102nteger )
% 0.30/0.59       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.30/0.59         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 0.30/0.59            = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % is_unit_div_mult_cancel_right
% 0.30/0.59  thf(fact_5953_is__unit__div__mult__cancel__right,axiom,
% 0.30/0.59      ! [A: code_natural,B: code_natural] :
% 0.30/0.59        ( ( A != zero_z2226904508553997617atural )
% 0.30/0.59       => ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.30/0.59         => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ A ) )
% 0.30/0.59            = ( divide5121882707175180666atural @ one_one_Code_natural @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % is_unit_div_mult_cancel_right
% 0.30/0.59  thf(fact_5954_is__unit__div__mult__cancel__left,axiom,
% 0.30/0.59      ! [A: nat,B: nat] :
% 0.30/0.59        ( ( A != zero_zero_nat )
% 0.30/0.59       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.30/0.59         => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 0.30/0.59            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % is_unit_div_mult_cancel_left
% 0.30/0.59  thf(fact_5955_is__unit__div__mult__cancel__left,axiom,
% 0.30/0.59      ! [A: int,B: int] :
% 0.30/0.59        ( ( A != zero_zero_int )
% 0.30/0.59       => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.30/0.59         => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 0.30/0.59            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % is_unit_div_mult_cancel_left
% 0.30/0.59  thf(fact_5956_is__unit__div__mult__cancel__left,axiom,
% 0.30/0.59      ! [A: code_integer,B: code_integer] :
% 0.30/0.59        ( ( A != zero_z3403309356797280102nteger )
% 0.30/0.59       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.30/0.59         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.30/0.59            = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % is_unit_div_mult_cancel_left
% 0.30/0.59  thf(fact_5957_is__unit__div__mult__cancel__left,axiom,
% 0.30/0.59      ! [A: code_natural,B: code_natural] :
% 0.30/0.59        ( ( A != zero_z2226904508553997617atural )
% 0.30/0.59       => ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.30/0.59         => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ A @ B ) )
% 0.30/0.59            = ( divide5121882707175180666atural @ one_one_Code_natural @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % is_unit_div_mult_cancel_left
% 0.30/0.59  thf(fact_5958_is__unitE,axiom,
% 0.30/0.59      ! [A: nat,C: nat] :
% 0.30/0.59        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.30/0.59       => ~ ( ( A != zero_zero_nat )
% 0.30/0.59           => ! [B6: nat] :
% 0.30/0.59                ( ( B6 != zero_zero_nat )
% 0.30/0.59               => ( ( dvd_dvd_nat @ B6 @ one_one_nat )
% 0.30/0.59                 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 0.30/0.59                      = B6 )
% 0.30/0.59                   => ( ( ( divide_divide_nat @ one_one_nat @ B6 )
% 0.30/0.59                        = A )
% 0.30/0.59                     => ( ( ( times_times_nat @ A @ B6 )
% 0.30/0.59                          = one_one_nat )
% 0.30/0.59                       => ( ( divide_divide_nat @ C @ A )
% 0.30/0.59                         != ( times_times_nat @ C @ B6 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % is_unitE
% 0.30/0.59  thf(fact_5959_is__unitE,axiom,
% 0.30/0.59      ! [A: int,C: int] :
% 0.30/0.59        ( ( dvd_dvd_int @ A @ one_one_int )
% 0.30/0.59       => ~ ( ( A != zero_zero_int )
% 0.30/0.59           => ! [B6: int] :
% 0.30/0.59                ( ( B6 != zero_zero_int )
% 0.30/0.59               => ( ( dvd_dvd_int @ B6 @ one_one_int )
% 0.30/0.59                 => ( ( ( divide_divide_int @ one_one_int @ A )
% 0.30/0.59                      = B6 )
% 0.30/0.59                   => ( ( ( divide_divide_int @ one_one_int @ B6 )
% 0.30/0.59                        = A )
% 0.30/0.59                     => ( ( ( times_times_int @ A @ B6 )
% 0.30/0.59                          = one_one_int )
% 0.30/0.59                       => ( ( divide_divide_int @ C @ A )
% 0.30/0.59                         != ( times_times_int @ C @ B6 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % is_unitE
% 0.30/0.59  thf(fact_5960_is__unitE,axiom,
% 0.30/0.59      ! [A: code_integer,C: code_integer] :
% 0.30/0.59        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.30/0.59       => ~ ( ( A != zero_z3403309356797280102nteger )
% 0.30/0.59           => ! [B6: code_integer] :
% 0.30/0.59                ( ( B6 != zero_z3403309356797280102nteger )
% 0.30/0.59               => ( ( dvd_dvd_Code_integer @ B6 @ one_one_Code_integer )
% 0.30/0.59                 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 0.30/0.59                      = B6 )
% 0.30/0.59                   => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B6 )
% 0.30/0.59                        = A )
% 0.30/0.59                     => ( ( ( times_3573771949741848930nteger @ A @ B6 )
% 0.30/0.59                          = one_one_Code_integer )
% 0.30/0.59                       => ( ( divide6298287555418463151nteger @ C @ A )
% 0.30/0.59                         != ( times_3573771949741848930nteger @ C @ B6 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % is_unitE
% 0.30/0.59  thf(fact_5961_is__unitE,axiom,
% 0.30/0.59      ! [A: code_natural,C: code_natural] :
% 0.30/0.59        ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 0.30/0.59       => ~ ( ( A != zero_z2226904508553997617atural )
% 0.30/0.59           => ! [B6: code_natural] :
% 0.30/0.59                ( ( B6 != zero_z2226904508553997617atural )
% 0.30/0.59               => ( ( dvd_dvd_Code_natural @ B6 @ one_one_Code_natural )
% 0.30/0.59                 => ( ( ( divide5121882707175180666atural @ one_one_Code_natural @ A )
% 0.30/0.59                      = B6 )
% 0.30/0.59                   => ( ( ( divide5121882707175180666atural @ one_one_Code_natural @ B6 )
% 0.30/0.59                        = A )
% 0.30/0.59                     => ( ( ( times_2397367101498566445atural @ A @ B6 )
% 0.30/0.59                          = one_one_Code_natural )
% 0.30/0.59                       => ( ( divide5121882707175180666atural @ C @ A )
% 0.30/0.59                         != ( times_2397367101498566445atural @ C @ B6 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % is_unitE
% 0.30/0.59  thf(fact_5962_evenE,axiom,
% 0.30/0.59      ! [A: nat] :
% 0.30/0.59        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.30/0.59       => ~ ! [B6: nat] :
% 0.30/0.59              ( A
% 0.30/0.59             != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B6 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % evenE
% 0.30/0.59  thf(fact_5963_evenE,axiom,
% 0.30/0.59      ! [A: int] :
% 0.30/0.59        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.30/0.59       => ~ ! [B6: int] :
% 0.30/0.59              ( A
% 0.30/0.59             != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B6 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % evenE
% 0.30/0.59  thf(fact_5964_evenE,axiom,
% 0.30/0.59      ! [A: code_integer] :
% 0.30/0.59        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.30/0.59       => ~ ! [B6: code_integer] :
% 0.30/0.59              ( A
% 0.30/0.59             != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B6 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % evenE
% 0.30/0.59  thf(fact_5965_evenE,axiom,
% 0.30/0.59      ! [A: code_natural] :
% 0.30/0.59        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.30/0.59       => ~ ! [B6: code_natural] :
% 0.30/0.59              ( A
% 0.30/0.59             != ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B6 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % evenE
% 0.30/0.59  thf(fact_5966_odd__one,axiom,
% 0.30/0.59      ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 0.30/0.59  
% 0.30/0.59  % odd_one
% 0.30/0.59  thf(fact_5967_odd__one,axiom,
% 0.30/0.59      ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 0.30/0.59  
% 0.30/0.59  % odd_one
% 0.30/0.59  thf(fact_5968_odd__one,axiom,
% 0.30/0.59      ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 0.30/0.59  
% 0.30/0.59  % odd_one
% 0.30/0.59  thf(fact_5969_odd__one,axiom,
% 0.30/0.59      ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ one_one_Code_natural ) ).
% 0.30/0.59  
% 0.30/0.59  % odd_one
% 0.30/0.59  thf(fact_5970_even__minus,axiom,
% 0.30/0.59      ! [A: int] :
% 0.30/0.59        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 0.30/0.59        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % even_minus
% 0.30/0.59  thf(fact_5971_even__minus,axiom,
% 0.30/0.59      ! [A: code_integer] :
% 0.30/0.59        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.30/0.59        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % even_minus
% 0.30/0.59  thf(fact_5972_power4__eq__xxxx,axiom,
% 0.30/0.59      ! [X: code_integer] :
% 0.30/0.59        ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.30/0.59        = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ X @ X ) @ X ) @ X ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power4_eq_xxxx
% 0.30/0.59  thf(fact_5973_power4__eq__xxxx,axiom,
% 0.30/0.59      ! [X: assn] :
% 0.30/0.59        ( ( power_power_assn @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.30/0.59        = ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ X @ X ) @ X ) @ X ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power4_eq_xxxx
% 0.30/0.59  thf(fact_5974_power4__eq__xxxx,axiom,
% 0.30/0.59      ! [X: rat] :
% 0.30/0.59        ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.30/0.59        = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X @ X ) @ X ) @ X ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power4_eq_xxxx
% 0.30/0.59  thf(fact_5975_power4__eq__xxxx,axiom,
% 0.30/0.59      ! [X: nat] :
% 0.30/0.59        ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.30/0.59        = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power4_eq_xxxx
% 0.30/0.59  thf(fact_5976_power4__eq__xxxx,axiom,
% 0.30/0.59      ! [X: int] :
% 0.30/0.59        ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.30/0.59        = ( times_times_int @ ( times_times_int @ ( times_times_int @ X @ X ) @ X ) @ X ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power4_eq_xxxx
% 0.30/0.59  thf(fact_5977_power2__eq__square,axiom,
% 0.30/0.59      ! [A: code_integer] :
% 0.30/0.59        ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59        = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power2_eq_square
% 0.30/0.59  thf(fact_5978_power2__eq__square,axiom,
% 0.30/0.59      ! [A: assn] :
% 0.30/0.59        ( ( power_power_assn @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59        = ( times_times_assn @ A @ A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power2_eq_square
% 0.30/0.59  thf(fact_5979_power2__eq__square,axiom,
% 0.30/0.59      ! [A: rat] :
% 0.30/0.59        ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59        = ( times_times_rat @ A @ A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power2_eq_square
% 0.30/0.59  thf(fact_5980_power2__eq__square,axiom,
% 0.30/0.59      ! [A: nat] :
% 0.30/0.59        ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59        = ( times_times_nat @ A @ A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power2_eq_square
% 0.30/0.59  thf(fact_5981_power2__eq__square,axiom,
% 0.30/0.59      ! [A: int] :
% 0.30/0.59        ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59        = ( times_times_int @ A @ A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power2_eq_square
% 0.30/0.59  thf(fact_5982_one__power2,axiom,
% 0.30/0.59      ( ( power_8256067586552552935nteger @ one_one_Code_integer @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59      = one_one_Code_integer ) ).
% 0.30/0.59  
% 0.30/0.59  % one_power2
% 0.30/0.59  thf(fact_5983_one__power2,axiom,
% 0.30/0.59      ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59      = one_one_rat ) ).
% 0.30/0.59  
% 0.30/0.59  % one_power2
% 0.30/0.59  thf(fact_5984_one__power2,axiom,
% 0.30/0.59      ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59      = one_one_int ) ).
% 0.30/0.59  
% 0.30/0.59  % one_power2
% 0.30/0.59  thf(fact_5985_one__power2,axiom,
% 0.30/0.59      ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59      = one_one_nat ) ).
% 0.30/0.59  
% 0.30/0.59  % one_power2
% 0.30/0.59  thf(fact_5986_power2__eq__iff,axiom,
% 0.30/0.59      ! [X: int,Y: int] :
% 0.30/0.59        ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59          = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.30/0.59        = ( ( X = Y )
% 0.30/0.59          | ( X
% 0.30/0.59            = ( uminus_uminus_int @ Y ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power2_eq_iff
% 0.30/0.59  thf(fact_5987_power2__eq__iff,axiom,
% 0.30/0.59      ! [X: code_integer,Y: code_integer] :
% 0.30/0.59        ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59          = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.30/0.59        = ( ( X = Y )
% 0.30/0.59          | ( X
% 0.30/0.59            = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power2_eq_iff
% 0.30/0.59  thf(fact_5988_power2__eq__iff,axiom,
% 0.30/0.59      ! [X: rat,Y: rat] :
% 0.30/0.59        ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59          = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.30/0.59        = ( ( X = Y )
% 0.30/0.59          | ( X
% 0.30/0.59            = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power2_eq_iff
% 0.30/0.59  thf(fact_5989_power3__eq__cube,axiom,
% 0.30/0.59      ! [A: code_integer] :
% 0.30/0.59        ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.30/0.59        = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A @ A ) @ A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power3_eq_cube
% 0.30/0.59  thf(fact_5990_power3__eq__cube,axiom,
% 0.30/0.59      ! [A: assn] :
% 0.30/0.59        ( ( power_power_assn @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.30/0.59        = ( times_times_assn @ ( times_times_assn @ A @ A ) @ A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power3_eq_cube
% 0.30/0.59  thf(fact_5991_power3__eq__cube,axiom,
% 0.30/0.59      ! [A: rat] :
% 0.30/0.59        ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.30/0.59        = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power3_eq_cube
% 0.30/0.59  thf(fact_5992_power3__eq__cube,axiom,
% 0.30/0.59      ! [A: nat] :
% 0.30/0.59        ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.30/0.59        = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power3_eq_cube
% 0.30/0.59  thf(fact_5993_power3__eq__cube,axiom,
% 0.30/0.59      ! [A: int] :
% 0.30/0.59        ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.30/0.59        = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power3_eq_cube
% 0.30/0.59  thf(fact_5994_dvd__mult__cancel2,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.30/0.59       => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 0.30/0.59          = ( N = one_one_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % dvd_mult_cancel2
% 0.30/0.59  thf(fact_5995_dvd__mult__cancel1,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.30/0.59       => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 0.30/0.59          = ( N = one_one_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % dvd_mult_cancel1
% 0.30/0.59  thf(fact_5996_even__mult__exp__div__exp__iff,axiom,
% 0.30/0.59      ! [A: nat,M: nat,N: nat] :
% 0.30/0.59        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.30/0.59        = ( ( ord_less_nat @ N @ M )
% 0.30/0.59          | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.30/0.59            = zero_zero_nat )
% 0.30/0.59          | ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.59            & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % even_mult_exp_div_exp_iff
% 0.30/0.59  thf(fact_5997_even__mult__exp__div__exp__iff,axiom,
% 0.30/0.59      ! [A: int,M: nat,N: nat] :
% 0.30/0.59        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 0.30/0.59        = ( ( ord_less_nat @ N @ M )
% 0.30/0.59          | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.30/0.59            = zero_zero_int )
% 0.30/0.59          | ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.59            & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % even_mult_exp_div_exp_iff
% 0.30/0.59  thf(fact_5998_even__mult__exp__div__exp__iff,axiom,
% 0.30/0.59      ! [A: code_integer,M: nat,N: nat] :
% 0.30/0.59        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 0.30/0.59        = ( ( ord_less_nat @ N @ M )
% 0.30/0.59          | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 0.30/0.59            = zero_z3403309356797280102nteger )
% 0.30/0.59          | ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.59            & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % even_mult_exp_div_exp_iff
% 0.30/0.59  thf(fact_5999_even__mult__exp__div__exp__iff,axiom,
% 0.30/0.59      ! [A: code_natural,M: nat,N: nat] :
% 0.30/0.59        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) )
% 0.30/0.59        = ( ( ord_less_nat @ N @ M )
% 0.30/0.59          | ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N )
% 0.30/0.59            = zero_z2226904508553997617atural )
% 0.30/0.59          | ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.59            & ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % even_mult_exp_div_exp_iff
% 0.30/0.59  thf(fact_6000_power__minus_H,axiom,
% 0.30/0.59      ! [X: int,N: nat] :
% 0.30/0.59        ( ( nO_MATCH_int_int @ one_one_int @ X )
% 0.30/0.59       => ( ( power_power_int @ ( uminus_uminus_int @ X ) @ N )
% 0.30/0.59          = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ X @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_minus'
% 0.30/0.59  thf(fact_6001_power__minus_H,axiom,
% 0.30/0.59      ! [X: code_integer,N: nat] :
% 0.30/0.59        ( ( nO_MAT8252062027627875367nteger @ one_one_Code_integer @ X )
% 0.30/0.59       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ N )
% 0.30/0.59          = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ X @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_minus'
% 0.30/0.59  thf(fact_6002_power__minus_H,axiom,
% 0.30/0.59      ! [X: rat,N: nat] :
% 0.30/0.59        ( ( nO_MATCH_rat_rat @ one_one_rat @ X )
% 0.30/0.59       => ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ N )
% 0.30/0.59          = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ X @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_minus'
% 0.30/0.59  thf(fact_6003_and__one__eq,axiom,
% 0.30/0.59      ! [A: code_integer] :
% 0.30/0.59        ( ( bit_se3949692690581998587nteger @ A @ one_one_Code_integer )
% 0.30/0.59        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % and_one_eq
% 0.30/0.59  thf(fact_6004_and__one__eq,axiom,
% 0.30/0.59      ! [A: code_natural] :
% 0.30/0.59        ( ( bit_se2773287842338716102atural @ A @ one_one_Code_natural )
% 0.30/0.59        = ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % and_one_eq
% 0.30/0.59  thf(fact_6005_and__one__eq,axiom,
% 0.30/0.59      ! [A: int] :
% 0.30/0.59        ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 0.30/0.59        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % and_one_eq
% 0.30/0.59  thf(fact_6006_and__one__eq,axiom,
% 0.30/0.59      ! [A: nat] :
% 0.30/0.59        ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 0.30/0.59        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % and_one_eq
% 0.30/0.59  thf(fact_6007_one__and__eq,axiom,
% 0.30/0.59      ! [A: code_integer] :
% 0.30/0.59        ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ A )
% 0.30/0.59        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % one_and_eq
% 0.30/0.59  thf(fact_6008_one__and__eq,axiom,
% 0.30/0.59      ! [A: code_natural] :
% 0.30/0.59        ( ( bit_se2773287842338716102atural @ one_one_Code_natural @ A )
% 0.30/0.59        = ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % one_and_eq
% 0.30/0.59  thf(fact_6009_one__and__eq,axiom,
% 0.30/0.59      ! [A: int] :
% 0.30/0.59        ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 0.30/0.59        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % one_and_eq
% 0.30/0.59  thf(fact_6010_one__and__eq,axiom,
% 0.30/0.59      ! [A: nat] :
% 0.30/0.59        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 0.30/0.59        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % one_and_eq
% 0.30/0.59  thf(fact_6011_take__bit__eq__mask__iff,axiom,
% 0.30/0.59      ! [N: nat,K: int] :
% 0.30/0.59        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.30/0.59          = ( bit_se2000444600071755411sk_int @ N ) )
% 0.30/0.59        = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 0.30/0.59          = zero_zero_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % take_bit_eq_mask_iff
% 0.30/0.59  thf(fact_6012_even__two__times__div__two,axiom,
% 0.30/0.59      ! [A: nat] :
% 0.30/0.59        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.30/0.59       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.30/0.59          = A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % even_two_times_div_two
% 0.30/0.59  thf(fact_6013_even__two__times__div__two,axiom,
% 0.30/0.59      ! [A: int] :
% 0.30/0.59        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.30/0.59       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.30/0.59          = A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % even_two_times_div_two
% 0.30/0.59  thf(fact_6014_even__two__times__div__two,axiom,
% 0.30/0.59      ! [A: code_integer] :
% 0.30/0.59        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.30/0.59       => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 0.30/0.59          = A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % even_two_times_div_two
% 0.30/0.59  thf(fact_6015_even__two__times__div__two,axiom,
% 0.30/0.59      ! [A: code_natural] :
% 0.30/0.59        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.30/0.59       => ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) )
% 0.30/0.59          = A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % even_two_times_div_two
% 0.30/0.59  thf(fact_6016_power2__eq__1__iff,axiom,
% 0.30/0.59      ! [A: int] :
% 0.30/0.59        ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59          = one_one_int )
% 0.30/0.59        = ( ( A = one_one_int )
% 0.30/0.59          | ( A
% 0.30/0.59            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power2_eq_1_iff
% 0.30/0.59  thf(fact_6017_power2__eq__1__iff,axiom,
% 0.30/0.59      ! [A: code_integer] :
% 0.30/0.59        ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59          = one_one_Code_integer )
% 0.30/0.59        = ( ( A = one_one_Code_integer )
% 0.30/0.59          | ( A
% 0.30/0.59            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power2_eq_1_iff
% 0.30/0.59  thf(fact_6018_power2__eq__1__iff,axiom,
% 0.30/0.59      ! [A: rat] :
% 0.30/0.59        ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59          = one_one_rat )
% 0.30/0.59        = ( ( A = one_one_rat )
% 0.30/0.59          | ( A
% 0.30/0.59            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power2_eq_1_iff
% 0.30/0.59  thf(fact_6019_power__diff__power__eq,axiom,
% 0.30/0.59      ! [A: nat,N: nat,M: nat] :
% 0.30/0.59        ( ( A != zero_zero_nat )
% 0.30/0.59       => ( ( ( ord_less_eq_nat @ N @ M )
% 0.30/0.59           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.30/0.59              = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 0.30/0.59          & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.30/0.59           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 0.30/0.59              = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_diff_power_eq
% 0.30/0.59  thf(fact_6020_power__diff__power__eq,axiom,
% 0.30/0.59      ! [A: int,N: nat,M: nat] :
% 0.30/0.59        ( ( A != zero_zero_int )
% 0.30/0.59       => ( ( ( ord_less_eq_nat @ N @ M )
% 0.30/0.59           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.30/0.59              = ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 0.30/0.59          & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.30/0.59           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 0.30/0.59              = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_diff_power_eq
% 0.30/0.59  thf(fact_6021_power__diff__power__eq,axiom,
% 0.30/0.59      ! [A: code_integer,N: nat,M: nat] :
% 0.30/0.59        ( ( A != zero_z3403309356797280102nteger )
% 0.30/0.59       => ( ( ( ord_less_eq_nat @ N @ M )
% 0.30/0.59           => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 0.30/0.59              = ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 0.30/0.59          & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.30/0.59           => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 0.30/0.59              = ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_diff_power_eq
% 0.30/0.59  thf(fact_6022_power__diff__power__eq,axiom,
% 0.30/0.59      ! [A: code_natural,N: nat,M: nat] :
% 0.30/0.59        ( ( A != zero_z2226904508553997617atural )
% 0.30/0.59       => ( ( ( ord_less_eq_nat @ N @ M )
% 0.30/0.59           => ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M ) @ ( power_7079662738309270450atural @ A @ N ) )
% 0.30/0.59              = ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 0.30/0.59          & ( ~ ( ord_less_eq_nat @ N @ M )
% 0.30/0.59           => ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M ) @ ( power_7079662738309270450atural @ A @ N ) )
% 0.30/0.59              = ( divide5121882707175180666atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_diff_power_eq
% 0.30/0.59  thf(fact_6023_odd__iff__mod__2__eq__one,axiom,
% 0.30/0.59      ! [A: nat] :
% 0.30/0.59        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 0.30/0.59        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59          = one_one_nat ) ) ).
% 0.30/0.59  
% 0.30/0.59  % odd_iff_mod_2_eq_one
% 0.30/0.59  thf(fact_6024_odd__iff__mod__2__eq__one,axiom,
% 0.30/0.59      ! [A: int] :
% 0.30/0.59        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.30/0.59        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.59          = one_one_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % odd_iff_mod_2_eq_one
% 0.30/0.59  thf(fact_6025_odd__iff__mod__2__eq__one,axiom,
% 0.30/0.59      ! [A: code_integer] :
% 0.30/0.59        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 0.30/0.59        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.59          = one_one_Code_integer ) ) ).
% 0.30/0.59  
% 0.30/0.59  % odd_iff_mod_2_eq_one
% 0.30/0.59  thf(fact_6026_odd__iff__mod__2__eq__one,axiom,
% 0.30/0.59      ! [A: code_natural] :
% 0.30/0.59        ( ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) )
% 0.30/0.59        = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.59          = one_one_Code_natural ) ) ).
% 0.30/0.59  
% 0.30/0.59  % odd_iff_mod_2_eq_one
% 0.30/0.59  thf(fact_6027_normalize__denom__pos,axiom,
% 0.30/0.59      ! [R3: product_prod_int_int,P4: int,Q4: int] :
% 0.30/0.59        ( ( ( normalize @ R3 )
% 0.30/0.59          = ( product_Pair_int_int @ P4 @ Q4 ) )
% 0.30/0.59       => ( ord_less_int @ zero_zero_int @ Q4 ) ) ).
% 0.30/0.59  
% 0.30/0.59  % normalize_denom_pos
% 0.30/0.59  thf(fact_6028_power__eq__if,axiom,
% 0.30/0.59      ( power_8256067586552552935nteger
% 0.30/0.59      = ( ^ [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 ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_eq_if
% 0.30/0.59  thf(fact_6029_power__eq__if,axiom,
% 0.30/0.59      ( power_power_assn
% 0.30/0.59      = ( ^ [P6: assn,M2: nat] : ( if_assn @ ( M2 = zero_zero_nat ) @ one_one_assn @ ( times_times_assn @ P6 @ ( power_power_assn @ P6 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_eq_if
% 0.30/0.59  thf(fact_6030_power__eq__if,axiom,
% 0.30/0.59      ( power_power_rat
% 0.30/0.59      = ( ^ [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 ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_eq_if
% 0.30/0.59  thf(fact_6031_power__eq__if,axiom,
% 0.30/0.59      ( power_power_nat
% 0.30/0.59      = ( ^ [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 ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_eq_if
% 0.30/0.59  thf(fact_6032_power__eq__if,axiom,
% 0.30/0.59      ( power_power_int
% 0.30/0.59      = ( ^ [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 ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_eq_if
% 0.30/0.59  thf(fact_6033_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.30/0.59      ! [K: nat,N: nat] :
% 0.30/0.59        ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.59       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 0.30/0.59          = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % neg_one_power_add_eq_neg_one_power_diff
% 0.30/0.59  thf(fact_6034_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.30/0.59      ! [K: nat,N: nat] :
% 0.30/0.59        ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.59       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 0.30/0.59          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % neg_one_power_add_eq_neg_one_power_diff
% 0.30/0.59  thf(fact_6035_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.30/0.59      ! [K: nat,N: nat] :
% 0.30/0.59        ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.59       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 0.30/0.59          = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % neg_one_power_add_eq_neg_one_power_diff
% 0.30/0.59  thf(fact_6036_normalize__crossproduct,axiom,
% 0.30/0.59      ! [Q4: int,S3: int,P4: int,R3: int] :
% 0.30/0.59        ( ( Q4 != zero_zero_int )
% 0.30/0.59       => ( ( S3 != zero_zero_int )
% 0.30/0.59         => ( ( ( normalize @ ( product_Pair_int_int @ P4 @ Q4 ) )
% 0.30/0.59              = ( normalize @ ( product_Pair_int_int @ R3 @ S3 ) ) )
% 0.30/0.59           => ( ( times_times_int @ P4 @ S3 )
% 0.30/0.59              = ( times_times_int @ R3 @ Q4 ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % normalize_crossproduct
% 0.30/0.59  thf(fact_6037_power__minus__mult,axiom,
% 0.30/0.59      ! [N: nat,A: code_integer] :
% 0.30/0.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.59       => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.30/0.59          = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_minus_mult
% 0.30/0.59  thf(fact_6038_power__minus__mult,axiom,
% 0.30/0.59      ! [N: nat,A: assn] :
% 0.30/0.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.59       => ( ( times_times_assn @ ( power_power_assn @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.30/0.59          = ( power_power_assn @ A @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_minus_mult
% 0.30/0.59  thf(fact_6039_power__minus__mult,axiom,
% 0.30/0.59      ! [N: nat,A: rat] :
% 0.30/0.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.59       => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.30/0.59          = ( power_power_rat @ A @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_minus_mult
% 0.30/0.59  thf(fact_6040_power__minus__mult,axiom,
% 0.30/0.59      ! [N: nat,A: nat] :
% 0.30/0.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.59       => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.30/0.59          = ( power_power_nat @ A @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_minus_mult
% 0.30/0.59  thf(fact_6041_power__minus__mult,axiom,
% 0.30/0.59      ! [N: nat,A: int] :
% 0.30/0.59        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.59       => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.30/0.59          = ( power_power_int @ A @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_minus_mult
% 0.30/0.59  thf(fact_6042_power2__sum,axiom,
% 0.30/0.59      ! [X: nat,Y: nat] :
% 0.30/0.59        ( ( power_power_nat @ ( plus_plus_nat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59        = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power2_sum
% 0.30/0.59  thf(fact_6043_power2__sum,axiom,
% 0.30/0.59      ! [X: int,Y: int] :
% 0.30/0.59        ( ( power_power_int @ ( plus_plus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59        = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power2_sum
% 0.30/0.59  thf(fact_6044_power2__sum,axiom,
% 0.30/0.59      ! [X: code_integer,Y: code_integer] :
% 0.30/0.59        ( ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power2_sum
% 0.30/0.59  thf(fact_6045_power2__sum,axiom,
% 0.30/0.59      ! [X: rat,Y: rat] :
% 0.30/0.59        ( ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59        = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power2_sum
% 0.30/0.59  thf(fact_6046_power2__sum,axiom,
% 0.30/0.59      ! [X: code_natural,Y: code_natural] :
% 0.30/0.59        ( ( power_7079662738309270450atural @ ( plus_p4538020629002901425atural @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59        = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( power_7079662738309270450atural @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_7079662738309270450atural @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_2397367101498566445atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power2_sum
% 0.30/0.59  thf(fact_6047_oddE,axiom,
% 0.30/0.59      ! [A: nat] :
% 0.30/0.59        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.30/0.59       => ~ ! [B6: nat] :
% 0.30/0.59              ( A
% 0.30/0.59             != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B6 ) @ one_one_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % oddE
% 0.30/0.59  thf(fact_6048_oddE,axiom,
% 0.30/0.59      ! [A: int] :
% 0.30/0.59        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.30/0.59       => ~ ! [B6: int] :
% 0.30/0.59              ( A
% 0.30/0.59             != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B6 ) @ one_one_int ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % oddE
% 0.30/0.59  thf(fact_6049_oddE,axiom,
% 0.30/0.59      ! [A: code_integer] :
% 0.30/0.59        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.30/0.59       => ~ ! [B6: code_integer] :
% 0.30/0.59              ( A
% 0.30/0.59             != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B6 ) @ one_one_Code_integer ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % oddE
% 0.30/0.59  thf(fact_6050_oddE,axiom,
% 0.30/0.59      ! [A: code_natural] :
% 0.30/0.59        ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.30/0.59       => ~ ! [B6: code_natural] :
% 0.30/0.59              ( A
% 0.30/0.59             != ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B6 ) @ one_one_Code_natural ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % oddE
% 0.30/0.59  thf(fact_6051_square__le__1,axiom,
% 0.30/0.59      ! [X: code_integer] :
% 0.30/0.59        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 0.30/0.59       => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 0.30/0.59         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % square_le_1
% 0.30/0.59  thf(fact_6052_square__le__1,axiom,
% 0.30/0.59      ! [X: rat] :
% 0.30/0.59        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 0.30/0.59       => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 0.30/0.59         => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % square_le_1
% 0.30/0.59  thf(fact_6053_square__le__1,axiom,
% 0.30/0.59      ! [X: int] :
% 0.30/0.59        ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 0.30/0.59       => ( ( ord_less_eq_int @ X @ one_one_int )
% 0.30/0.59         => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % square_le_1
% 0.30/0.59  thf(fact_6054_parity__cases,axiom,
% 0.30/0.59      ! [A: nat] :
% 0.30/0.59        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.30/0.59         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59           != zero_zero_nat ) )
% 0.30/0.59       => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.30/0.59           => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59             != one_one_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % parity_cases
% 0.30/0.59  thf(fact_6055_parity__cases,axiom,
% 0.30/0.59      ! [A: int] :
% 0.30/0.59        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.30/0.59         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.59           != zero_zero_int ) )
% 0.30/0.59       => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.30/0.59           => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.59             != one_one_int ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % parity_cases
% 0.30/0.59  thf(fact_6056_parity__cases,axiom,
% 0.30/0.59      ! [A: code_integer] :
% 0.30/0.59        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.30/0.59         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.59           != zero_z3403309356797280102nteger ) )
% 0.30/0.59       => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.30/0.59           => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.59             != one_one_Code_integer ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % parity_cases
% 0.30/0.59  thf(fact_6057_parity__cases,axiom,
% 0.30/0.59      ! [A: code_natural] :
% 0.30/0.59        ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.30/0.59         => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.59           != zero_z2226904508553997617atural ) )
% 0.30/0.59       => ~ ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.30/0.59           => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.59             != one_one_Code_natural ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % parity_cases
% 0.30/0.59  thf(fact_6058_mod2__eq__if,axiom,
% 0.30/0.59      ! [A: nat] :
% 0.30/0.59        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.30/0.59         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59            = zero_zero_nat ) )
% 0.30/0.59        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.30/0.59         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59            = one_one_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % mod2_eq_if
% 0.30/0.59  thf(fact_6059_mod2__eq__if,axiom,
% 0.30/0.59      ! [A: int] :
% 0.30/0.59        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.30/0.59         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.59            = zero_zero_int ) )
% 0.30/0.59        & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.30/0.59         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.59            = one_one_int ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % mod2_eq_if
% 0.30/0.59  thf(fact_6060_mod2__eq__if,axiom,
% 0.30/0.59      ! [A: code_integer] :
% 0.30/0.59        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.30/0.59         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.59            = zero_z3403309356797280102nteger ) )
% 0.30/0.59        & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.30/0.59         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.59            = one_one_Code_integer ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % mod2_eq_if
% 0.30/0.59  thf(fact_6061_mod2__eq__if,axiom,
% 0.30/0.59      ! [A: code_natural] :
% 0.30/0.59        ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.30/0.59         => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.59            = zero_z2226904508553997617atural ) )
% 0.30/0.59        & ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.30/0.59         => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.59            = one_one_Code_natural ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % mod2_eq_if
% 0.30/0.59  thf(fact_6062_minus__power__mult__self,axiom,
% 0.30/0.59      ! [A: int,N: nat] :
% 0.30/0.59        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 0.30/0.59        = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % minus_power_mult_self
% 0.30/0.59  thf(fact_6063_minus__power__mult__self,axiom,
% 0.30/0.59      ! [A: code_integer,N: nat] :
% 0.30/0.59        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 0.30/0.59        = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % minus_power_mult_self
% 0.30/0.59  thf(fact_6064_minus__power__mult__self,axiom,
% 0.30/0.59      ! [A: rat,N: nat] :
% 0.30/0.59        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 0.30/0.59        = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % minus_power_mult_self
% 0.30/0.59  thf(fact_6065_power__odd__eq,axiom,
% 0.30/0.59      ! [A: code_integer,N: nat] :
% 0.30/0.59        ( ( power_8256067586552552935nteger @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.30/0.59        = ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_odd_eq
% 0.30/0.59  thf(fact_6066_power__odd__eq,axiom,
% 0.30/0.59      ! [A: assn,N: nat] :
% 0.30/0.59        ( ( power_power_assn @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.30/0.59        = ( times_times_assn @ A @ ( power_power_assn @ ( power_power_assn @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_odd_eq
% 0.30/0.59  thf(fact_6067_power__odd__eq,axiom,
% 0.30/0.59      ! [A: rat,N: nat] :
% 0.30/0.59        ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.30/0.59        = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_odd_eq
% 0.30/0.59  thf(fact_6068_power__odd__eq,axiom,
% 0.30/0.59      ! [A: nat,N: nat] :
% 0.30/0.59        ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.30/0.59        = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_odd_eq
% 0.30/0.59  thf(fact_6069_power__odd__eq,axiom,
% 0.30/0.59      ! [A: int,N: nat] :
% 0.30/0.59        ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.30/0.59        = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_odd_eq
% 0.30/0.59  thf(fact_6070_minus__1__div__exp__eq__int,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % minus_1_div_exp_eq_int
% 0.30/0.59  thf(fact_6071_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 0.30/0.59      ! [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 ) ) ).
% 0.30/0.59  
% 0.30/0.59  % signed_take_bit_int_greater_eq_minus_exp
% 0.30/0.59  thf(fact_6072_signed__take__bit__int__less__eq__self__iff,axiom,
% 0.30/0.59      ! [N: nat,K: int] :
% 0.30/0.59        ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 0.30/0.59        = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 0.30/0.59  
% 0.30/0.59  % signed_take_bit_int_less_eq_self_iff
% 0.30/0.59  thf(fact_6073_signed__take__bit__int__greater__self__iff,axiom,
% 0.30/0.59      ! [K: int,N: nat] :
% 0.30/0.59        ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 0.30/0.59        = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % signed_take_bit_int_greater_self_iff
% 0.30/0.59  thf(fact_6074_power2__diff,axiom,
% 0.30/0.59      ! [X: int,Y: int] :
% 0.30/0.59        ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59        = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power2_diff
% 0.30/0.59  thf(fact_6075_power2__diff,axiom,
% 0.30/0.59      ! [X: code_integer,Y: code_integer] :
% 0.30/0.59        ( ( power_8256067586552552935nteger @ ( minus_8373710615458151222nteger @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59        = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power2_diff
% 0.30/0.59  thf(fact_6076_power2__diff,axiom,
% 0.30/0.59      ! [X: rat,Y: rat] :
% 0.30/0.59        ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59        = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power2_diff
% 0.30/0.59  thf(fact_6077_mask__half__int,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.59        = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % mask_half_int
% 0.30/0.59  thf(fact_6078_mult__exp__mod__exp__eq,axiom,
% 0.30/0.59      ! [M: nat,N: nat,A: nat] :
% 0.30/0.59        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.59       => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59          = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % mult_exp_mod_exp_eq
% 0.30/0.59  thf(fact_6079_mult__exp__mod__exp__eq,axiom,
% 0.30/0.59      ! [M: nat,N: nat,A: int] :
% 0.30/0.59        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.59       => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59          = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % mult_exp_mod_exp_eq
% 0.30/0.59  thf(fact_6080_mult__exp__mod__exp__eq,axiom,
% 0.30/0.59      ! [M: nat,N: nat,A: code_integer] :
% 0.30/0.59        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.59       => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59          = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % mult_exp_mod_exp_eq
% 0.30/0.59  thf(fact_6081_mult__exp__mod__exp__eq,axiom,
% 0.30/0.59      ! [M: nat,N: nat,A: code_natural] :
% 0.30/0.59        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.59       => ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59          = ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % mult_exp_mod_exp_eq
% 0.30/0.59  thf(fact_6082_power__minus1__odd,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.30/0.59        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_minus1_odd
% 0.30/0.59  thf(fact_6083_power__minus1__odd,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.30/0.59        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_minus1_odd
% 0.30/0.59  thf(fact_6084_power__minus1__odd,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.30/0.59        = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_minus1_odd
% 0.30/0.59  thf(fact_6085_signed__take__bit__int__eq__self__iff,axiom,
% 0.30/0.59      ! [N: nat,K: int] :
% 0.30/0.59        ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 0.30/0.59          = K )
% 0.30/0.59        = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 0.30/0.59          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % signed_take_bit_int_eq_self_iff
% 0.30/0.59  thf(fact_6086_signed__take__bit__int__eq__self,axiom,
% 0.30/0.59      ! [N: nat,K: int] :
% 0.30/0.59        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 0.30/0.59       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59         => ( ( bit_ri631733984087533419it_int @ N @ K )
% 0.30/0.59            = K ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % signed_take_bit_int_eq_self
% 0.30/0.59  thf(fact_6087_take__bit__incr__eq,axiom,
% 0.30/0.59      ! [N: nat,K: int] :
% 0.30/0.59        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 0.30/0.59         != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 0.30/0.59       => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 0.30/0.59          = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % take_bit_incr_eq
% 0.30/0.59  thf(fact_6088_take__bit__Suc__minus__1__eq,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.59        = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_Code_integer ) ) ).
% 0.30/0.59  
% 0.30/0.59  % take_bit_Suc_minus_1_eq
% 0.30/0.59  thf(fact_6089_take__bit__Suc__minus__1__eq,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.59        = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % take_bit_Suc_minus_1_eq
% 0.30/0.59  thf(fact_6090_take__bit__numeral__minus__1__eq,axiom,
% 0.30/0.59      ! [K: num] :
% 0.30/0.59        ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.59        = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 0.30/0.59  
% 0.30/0.59  % take_bit_numeral_minus_1_eq
% 0.30/0.59  thf(fact_6091_take__bit__numeral__minus__1__eq,axiom,
% 0.30/0.59      ! [K: num] :
% 0.30/0.59        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.59        = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % take_bit_numeral_minus_1_eq
% 0.30/0.59  thf(fact_6092_gcd__nat_Oordering__top__axioms,axiom,
% 0.30/0.59      ( ordering_top_nat @ dvd_dvd_nat
% 0.30/0.59      @ ^ [M2: nat,N2: nat] :
% 0.30/0.59          ( ( dvd_dvd_nat @ M2 @ N2 )
% 0.30/0.59          & ( M2 != N2 ) )
% 0.30/0.59      @ zero_zero_nat ) ).
% 0.30/0.59  
% 0.30/0.59  % gcd_nat.ordering_top_axioms
% 0.30/0.59  thf(fact_6093_fold__atLeastAtMost__nat_Opsimps,axiom,
% 0.30/0.59      ! [F2: nat > nat > nat,A: nat,B: nat,Acc: nat] :
% 0.30/0.59        ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ F2 @ ( produc487386426758144856at_nat @ A @ ( product_Pair_nat_nat @ B @ Acc ) ) ) )
% 0.30/0.59       => ( ( ( ord_less_nat @ B @ A )
% 0.30/0.59           => ( ( set_fo2584398358068434914at_nat @ F2 @ A @ B @ Acc )
% 0.30/0.59              = Acc ) )
% 0.30/0.59          & ( ~ ( ord_less_nat @ B @ A )
% 0.30/0.59           => ( ( set_fo2584398358068434914at_nat @ F2 @ A @ B @ Acc )
% 0.30/0.59              = ( set_fo2584398358068434914at_nat @ F2 @ ( plus_plus_nat @ A @ one_one_nat ) @ B @ ( F2 @ A @ Acc ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % fold_atLeastAtMost_nat.psimps
% 0.30/0.59  thf(fact_6094_fold__atLeastAtMost__nat_Opelims,axiom,
% 0.30/0.59      ! [X: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y: nat] :
% 0.30/0.59        ( ( ( set_fo2584398358068434914at_nat @ X @ Xa @ Xb @ Xc )
% 0.30/0.59          = Y )
% 0.30/0.59       => ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ X @ ( produc487386426758144856at_nat @ Xa @ ( product_Pair_nat_nat @ Xb @ Xc ) ) ) )
% 0.30/0.59         => ~ ( ( ( ( ord_less_nat @ Xb @ Xa )
% 0.30/0.59                 => ( Y = Xc ) )
% 0.30/0.59                & ( ~ ( ord_less_nat @ Xb @ Xa )
% 0.30/0.59                 => ( Y
% 0.30/0.59                    = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X @ Xa @ Xc ) ) ) ) )
% 0.30/0.59             => ~ ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ X @ ( produc487386426758144856at_nat @ Xa @ ( product_Pair_nat_nat @ Xb @ Xc ) ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % fold_atLeastAtMost_nat.pelims
% 0.30/0.59  thf(fact_6095_flip__bit__0,axiom,
% 0.30/0.59      ! [A: code_integer] :
% 0.30/0.59        ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 0.30/0.59        = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % flip_bit_0
% 0.30/0.59  thf(fact_6096_flip__bit__0,axiom,
% 0.30/0.59      ! [A: code_natural] :
% 0.30/0.59        ( ( bit_se168947363167071951atural @ zero_zero_nat @ A )
% 0.30/0.59        = ( plus_p4538020629002901425atural @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % flip_bit_0
% 0.30/0.59  thf(fact_6097_flip__bit__0,axiom,
% 0.30/0.59      ! [A: int] :
% 0.30/0.59        ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 0.30/0.59        = ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % flip_bit_0
% 0.30/0.59  thf(fact_6098_flip__bit__0,axiom,
% 0.30/0.59      ! [A: nat] :
% 0.30/0.59        ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 0.30/0.59        = ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % flip_bit_0
% 0.30/0.59  thf(fact_6099_one__mod__2__pow__eq,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % one_mod_2_pow_eq
% 0.30/0.59  thf(fact_6100_one__mod__2__pow__eq,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( zero_n8403883297036319079atural @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % one_mod_2_pow_eq
% 0.30/0.59  thf(fact_6101_one__mod__2__pow__eq,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % one_mod_2_pow_eq
% 0.30/0.59  thf(fact_6102_one__mod__2__pow__eq,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % one_mod_2_pow_eq
% 0.30/0.59  thf(fact_6103_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.30/0.59      ! [X: num,N: nat,A: int] :
% 0.30/0.59        ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 0.30/0.59        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % neg_numeral_power_less_of_int_cancel_iff
% 0.30/0.59  thf(fact_6104_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.30/0.59      ! [X: num,N: nat,A: int] :
% 0.30/0.59        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 0.30/0.59        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % neg_numeral_power_less_of_int_cancel_iff
% 0.30/0.59  thf(fact_6105_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 0.30/0.59      ! [X: num,N: nat,A: int] :
% 0.30/0.59        ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 0.30/0.59        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % neg_numeral_power_less_of_int_cancel_iff
% 0.30/0.59  thf(fact_6106_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.30/0.59      ! [A: int,X: num,N: nat] :
% 0.30/0.59        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 0.30/0.59        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_less_neg_numeral_power_cancel_iff
% 0.30/0.59  thf(fact_6107_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.30/0.59      ! [A: int,X: num,N: nat] :
% 0.30/0.59        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 0.30/0.59        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_less_neg_numeral_power_cancel_iff
% 0.30/0.59  thf(fact_6108_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 0.30/0.59      ! [A: int,X: num,N: nat] :
% 0.30/0.59        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 0.30/0.59        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_less_neg_numeral_power_cancel_iff
% 0.30/0.59  thf(fact_6109_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.30/0.59      ! [X: num,N: nat,A: int] :
% 0.30/0.59        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 0.30/0.59        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % neg_numeral_power_le_of_int_cancel_iff
% 0.30/0.59  thf(fact_6110_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.30/0.59      ! [X: num,N: nat,A: int] :
% 0.30/0.59        ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 0.30/0.59        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % neg_numeral_power_le_of_int_cancel_iff
% 0.30/0.59  thf(fact_6111_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 0.30/0.59      ! [X: num,N: nat,A: int] :
% 0.30/0.59        ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 0.30/0.59        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % neg_numeral_power_le_of_int_cancel_iff
% 0.30/0.59  thf(fact_6112_of__bool__eq__1__iff,axiom,
% 0.30/0.59      ! [P: $o] :
% 0.30/0.59        ( ( ( zero_n356916108424825756nteger @ P )
% 0.30/0.59          = one_one_Code_integer )
% 0.30/0.59        = P ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_eq_1_iff
% 0.30/0.59  thf(fact_6113_of__bool__eq__1__iff,axiom,
% 0.30/0.59      ! [P: $o] :
% 0.30/0.59        ( ( ( zero_n2052037380579107095ol_rat @ P )
% 0.30/0.59          = one_one_rat )
% 0.30/0.59        = P ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_eq_1_iff
% 0.30/0.59  thf(fact_6114_of__bool__eq__1__iff,axiom,
% 0.30/0.59      ! [P: $o] :
% 0.30/0.59        ( ( ( zero_n2684676970156552555ol_int @ P )
% 0.30/0.59          = one_one_int )
% 0.30/0.59        = P ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_eq_1_iff
% 0.30/0.59  thf(fact_6115_of__bool__eq__1__iff,axiom,
% 0.30/0.59      ! [P: $o] :
% 0.30/0.59        ( ( ( zero_n2687167440665602831ol_nat @ P )
% 0.30/0.59          = one_one_nat )
% 0.30/0.59        = P ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_eq_1_iff
% 0.30/0.59  thf(fact_6116_of__bool__eq_I2_J,axiom,
% 0.30/0.59      ( ( zero_n356916108424825756nteger @ $true )
% 0.30/0.59      = one_one_Code_integer ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_eq(2)
% 0.30/0.59  thf(fact_6117_of__bool__eq_I2_J,axiom,
% 0.30/0.59      ( ( zero_n2052037380579107095ol_rat @ $true )
% 0.30/0.59      = one_one_rat ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_eq(2)
% 0.30/0.59  thf(fact_6118_of__bool__eq_I2_J,axiom,
% 0.30/0.59      ( ( zero_n2684676970156552555ol_int @ $true )
% 0.30/0.59      = one_one_int ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_eq(2)
% 0.30/0.59  thf(fact_6119_of__bool__eq_I2_J,axiom,
% 0.30/0.59      ( ( zero_n2687167440665602831ol_nat @ $true )
% 0.30/0.59      = one_one_nat ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_eq(2)
% 0.30/0.59  thf(fact_6120_of__bool__less__one__iff,axiom,
% 0.30/0.59      ! [P: $o] :
% 0.30/0.59        ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 0.30/0.59        = ( ~ P ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_less_one_iff
% 0.30/0.59  thf(fact_6121_of__bool__less__one__iff,axiom,
% 0.30/0.59      ! [P: $o] :
% 0.30/0.59        ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 0.30/0.59        = ( ~ P ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_less_one_iff
% 0.30/0.59  thf(fact_6122_of__bool__less__one__iff,axiom,
% 0.30/0.59      ! [P: $o] :
% 0.30/0.59        ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 0.30/0.59        = ( ~ P ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_less_one_iff
% 0.30/0.59  thf(fact_6123_of__bool__less__one__iff,axiom,
% 0.30/0.59      ! [P: $o] :
% 0.30/0.59        ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 0.30/0.59        = ( ~ P ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_less_one_iff
% 0.30/0.59  thf(fact_6124_of__bool__not__iff,axiom,
% 0.30/0.59      ! [P: $o] :
% 0.30/0.59        ( ( zero_n356916108424825756nteger @ ~ P )
% 0.30/0.59        = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_not_iff
% 0.30/0.59  thf(fact_6125_of__bool__not__iff,axiom,
% 0.30/0.59      ! [P: $o] :
% 0.30/0.59        ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 0.30/0.59        = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_not_iff
% 0.30/0.59  thf(fact_6126_of__bool__not__iff,axiom,
% 0.30/0.59      ! [P: $o] :
% 0.30/0.59        ( ( zero_n2684676970156552555ol_int @ ~ P )
% 0.30/0.59        = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_not_iff
% 0.30/0.59  thf(fact_6127_of__int__1,axiom,
% 0.30/0.59      ( ( ring_18347121197199848620nteger @ one_one_int )
% 0.30/0.59      = one_one_Code_integer ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_1
% 0.30/0.59  thf(fact_6128_of__int__1,axiom,
% 0.30/0.59      ( ( ring_1_of_int_int @ one_one_int )
% 0.30/0.59      = one_one_int ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_1
% 0.30/0.59  thf(fact_6129_of__int__1,axiom,
% 0.30/0.59      ( ( ring_1_of_int_rat @ one_one_int )
% 0.30/0.59      = one_one_rat ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_1
% 0.30/0.59  thf(fact_6130_of__int__eq__1__iff,axiom,
% 0.30/0.59      ! [Z: int] :
% 0.30/0.59        ( ( ( ring_18347121197199848620nteger @ Z )
% 0.30/0.59          = one_one_Code_integer )
% 0.30/0.59        = ( Z = one_one_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_eq_1_iff
% 0.30/0.59  thf(fact_6131_of__int__eq__1__iff,axiom,
% 0.30/0.59      ! [Z: int] :
% 0.30/0.59        ( ( ( ring_1_of_int_int @ Z )
% 0.30/0.59          = one_one_int )
% 0.30/0.59        = ( Z = one_one_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_eq_1_iff
% 0.30/0.59  thf(fact_6132_of__int__eq__1__iff,axiom,
% 0.30/0.59      ! [Z: int] :
% 0.30/0.59        ( ( ( ring_1_of_int_rat @ Z )
% 0.30/0.59          = one_one_rat )
% 0.30/0.59        = ( Z = one_one_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_eq_1_iff
% 0.30/0.59  thf(fact_6133_of__int__mult,axiom,
% 0.30/0.59      ! [W: int,Z: int] :
% 0.30/0.59        ( ( ring_18347121197199848620nteger @ ( times_times_int @ W @ Z ) )
% 0.30/0.59        = ( times_3573771949741848930nteger @ ( ring_18347121197199848620nteger @ W ) @ ( ring_18347121197199848620nteger @ Z ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_mult
% 0.30/0.59  thf(fact_6134_of__int__mult,axiom,
% 0.30/0.59      ! [W: int,Z: int] :
% 0.30/0.59        ( ( ring_1_of_int_rat @ ( times_times_int @ W @ Z ) )
% 0.30/0.59        = ( times_times_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_mult
% 0.30/0.59  thf(fact_6135_of__int__mult,axiom,
% 0.30/0.59      ! [W: int,Z: int] :
% 0.30/0.59        ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 0.30/0.59        = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_mult
% 0.30/0.59  thf(fact_6136_of__int__minus,axiom,
% 0.30/0.59      ! [Z: int] :
% 0.30/0.59        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ Z ) )
% 0.30/0.59        = ( uminus_uminus_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_minus
% 0.30/0.59  thf(fact_6137_of__int__minus,axiom,
% 0.30/0.59      ! [Z: int] :
% 0.30/0.59        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ Z ) )
% 0.30/0.59        = ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ Z ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_minus
% 0.30/0.59  thf(fact_6138_of__int__minus,axiom,
% 0.30/0.59      ! [Z: int] :
% 0.30/0.59        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ Z ) )
% 0.30/0.59        = ( uminus_uminus_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_minus
% 0.30/0.59  thf(fact_6139_Divides_Oadjust__div__eq,axiom,
% 0.30/0.59      ! [Q4: int,R3: int] :
% 0.30/0.59        ( ( adjust_div @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 0.30/0.59        = ( plus_plus_int @ Q4 @ ( zero_n2684676970156552555ol_int @ ( R3 != zero_zero_int ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Divides.adjust_div_eq
% 0.30/0.59  thf(fact_6140_and__nat__numerals_I4_J,axiom,
% 0.30/0.59      ! [X: num] :
% 0.30/0.59        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.30/0.59        = one_one_nat ) ).
% 0.30/0.59  
% 0.30/0.59  % and_nat_numerals(4)
% 0.30/0.59  thf(fact_6141_and__nat__numerals_I2_J,axiom,
% 0.30/0.59      ! [Y: num] :
% 0.30/0.59        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.30/0.59        = one_one_nat ) ).
% 0.30/0.59  
% 0.30/0.59  % and_nat_numerals(2)
% 0.30/0.59  thf(fact_6142_of__int__le__1__iff,axiom,
% 0.30/0.59      ! [Z: int] :
% 0.30/0.59        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ Z ) @ one_one_Code_integer )
% 0.30/0.59        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_le_1_iff
% 0.30/0.59  thf(fact_6143_of__int__le__1__iff,axiom,
% 0.30/0.59      ! [Z: int] :
% 0.30/0.59        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 0.30/0.59        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_le_1_iff
% 0.30/0.59  thf(fact_6144_of__int__le__1__iff,axiom,
% 0.30/0.59      ! [Z: int] :
% 0.30/0.59        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 0.30/0.59        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_le_1_iff
% 0.30/0.59  thf(fact_6145_of__int__1__le__iff,axiom,
% 0.30/0.59      ! [Z: int] :
% 0.30/0.59        ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( ring_18347121197199848620nteger @ Z ) )
% 0.30/0.59        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_1_le_iff
% 0.30/0.59  thf(fact_6146_of__int__1__le__iff,axiom,
% 0.30/0.59      ! [Z: int] :
% 0.30/0.59        ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.30/0.59        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_1_le_iff
% 0.30/0.59  thf(fact_6147_of__int__1__le__iff,axiom,
% 0.30/0.59      ! [Z: int] :
% 0.30/0.59        ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 0.30/0.59        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_1_le_iff
% 0.30/0.59  thf(fact_6148_of__int__less__1__iff,axiom,
% 0.30/0.59      ! [Z: int] :
% 0.30/0.59        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ Z ) @ one_one_Code_integer )
% 0.30/0.59        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_less_1_iff
% 0.30/0.59  thf(fact_6149_of__int__less__1__iff,axiom,
% 0.30/0.59      ! [Z: int] :
% 0.30/0.59        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 0.30/0.59        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_less_1_iff
% 0.30/0.59  thf(fact_6150_of__int__less__1__iff,axiom,
% 0.30/0.59      ! [Z: int] :
% 0.30/0.59        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 0.30/0.59        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_less_1_iff
% 0.30/0.59  thf(fact_6151_of__int__1__less__iff,axiom,
% 0.30/0.59      ! [Z: int] :
% 0.30/0.59        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( ring_18347121197199848620nteger @ Z ) )
% 0.30/0.59        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_1_less_iff
% 0.30/0.59  thf(fact_6152_of__int__1__less__iff,axiom,
% 0.30/0.59      ! [Z: int] :
% 0.30/0.59        ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 0.30/0.59        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_1_less_iff
% 0.30/0.59  thf(fact_6153_of__int__1__less__iff,axiom,
% 0.30/0.59      ! [Z: int] :
% 0.30/0.59        ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 0.30/0.59        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_1_less_iff
% 0.30/0.59  thf(fact_6154_take__bit__of__1,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( bit_se1745604003318907178nteger @ N @ one_one_Code_integer )
% 0.30/0.59        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % take_bit_of_1
% 0.30/0.59  thf(fact_6155_take__bit__of__1,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 0.30/0.59        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % take_bit_of_1
% 0.30/0.59  thf(fact_6156_take__bit__of__1,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 0.30/0.59        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % take_bit_of_1
% 0.30/0.59  thf(fact_6157_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.30/0.59      ! [X: num,N: nat,Y: int] :
% 0.30/0.59        ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 0.30/0.59          = ( ring_1_of_int_int @ Y ) )
% 0.30/0.59        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 0.30/0.59          = Y ) ) ).
% 0.30/0.59  
% 0.30/0.59  % neg_numeral_power_eq_of_int_cancel_iff
% 0.30/0.59  thf(fact_6158_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.30/0.59      ! [X: num,N: nat,Y: int] :
% 0.30/0.59        ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N )
% 0.30/0.59          = ( ring_18347121197199848620nteger @ Y ) )
% 0.30/0.59        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 0.30/0.59          = Y ) ) ).
% 0.30/0.59  
% 0.30/0.59  % neg_numeral_power_eq_of_int_cancel_iff
% 0.30/0.59  thf(fact_6159_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 0.30/0.59      ! [X: num,N: nat,Y: int] :
% 0.30/0.59        ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N )
% 0.30/0.59          = ( ring_1_of_int_rat @ Y ) )
% 0.30/0.59        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 0.30/0.59          = Y ) ) ).
% 0.30/0.59  
% 0.30/0.59  % neg_numeral_power_eq_of_int_cancel_iff
% 0.30/0.59  thf(fact_6160_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.30/0.59      ! [Y: int,X: num,N: nat] :
% 0.30/0.59        ( ( ( ring_1_of_int_int @ Y )
% 0.30/0.59          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 0.30/0.59        = ( Y
% 0.30/0.59          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_eq_neg_numeral_power_cancel_iff
% 0.30/0.59  thf(fact_6161_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.30/0.59      ! [Y: int,X: num,N: nat] :
% 0.30/0.59        ( ( ( ring_18347121197199848620nteger @ Y )
% 0.30/0.59          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 0.30/0.59        = ( Y
% 0.30/0.59          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_eq_neg_numeral_power_cancel_iff
% 0.30/0.59  thf(fact_6162_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 0.30/0.59      ! [Y: int,X: num,N: nat] :
% 0.30/0.59        ( ( ( ring_1_of_int_rat @ Y )
% 0.30/0.59          = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 0.30/0.59        = ( Y
% 0.30/0.59          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_eq_neg_numeral_power_cancel_iff
% 0.30/0.59  thf(fact_6163_one__div__2__pow__eq,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % one_div_2_pow_eq
% 0.30/0.59  thf(fact_6164_one__div__2__pow__eq,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( zero_n8403883297036319079atural @ ( N = zero_zero_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % one_div_2_pow_eq
% 0.30/0.59  thf(fact_6165_one__div__2__pow__eq,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % one_div_2_pow_eq
% 0.30/0.59  thf(fact_6166_one__div__2__pow__eq,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % one_div_2_pow_eq
% 0.30/0.59  thf(fact_6167_bits__1__div__exp,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % bits_1_div_exp
% 0.30/0.59  thf(fact_6168_bits__1__div__exp,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( zero_n8403883297036319079atural @ ( N = zero_zero_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % bits_1_div_exp
% 0.30/0.59  thf(fact_6169_bits__1__div__exp,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % bits_1_div_exp
% 0.30/0.59  thf(fact_6170_bits__1__div__exp,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % bits_1_div_exp
% 0.30/0.59  thf(fact_6171_take__bit__of__exp,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % take_bit_of_exp
% 0.30/0.59  thf(fact_6172_take__bit__of__exp,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( bit_se569199155075624693atural @ M @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( times_2397367101498566445atural @ ( zero_n8403883297036319079atural @ ( ord_less_nat @ N @ M ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % take_bit_of_exp
% 0.30/0.59  thf(fact_6173_take__bit__of__exp,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % take_bit_of_exp
% 0.30/0.59  thf(fact_6174_take__bit__of__exp,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % take_bit_of_exp
% 0.30/0.59  thf(fact_6175_take__bit__of__2,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.59        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % take_bit_of_2
% 0.30/0.59  thf(fact_6176_take__bit__of__2,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( bit_se569199155075624693atural @ N @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.59        = ( times_2397367101498566445atural @ ( zero_n8403883297036319079atural @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % take_bit_of_2
% 0.30/0.59  thf(fact_6177_take__bit__of__2,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % take_bit_of_2
% 0.30/0.59  thf(fact_6178_take__bit__of__2,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.59        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % take_bit_of_2
% 0.30/0.59  thf(fact_6179_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.30/0.59      ! [A: int,X: num,N: nat] :
% 0.30/0.59        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 0.30/0.59        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_le_neg_numeral_power_cancel_iff
% 0.30/0.59  thf(fact_6180_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.30/0.59      ! [A: int,X: num,N: nat] :
% 0.30/0.59        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 0.30/0.59        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_le_neg_numeral_power_cancel_iff
% 0.30/0.59  thf(fact_6181_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 0.30/0.59      ! [A: int,X: num,N: nat] :
% 0.30/0.59        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 0.30/0.59        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_le_neg_numeral_power_cancel_iff
% 0.30/0.59  thf(fact_6182_mult__of__int__commute,axiom,
% 0.30/0.59      ! [X: int,Y: code_integer] :
% 0.30/0.59        ( ( times_3573771949741848930nteger @ ( ring_18347121197199848620nteger @ X ) @ Y )
% 0.30/0.59        = ( times_3573771949741848930nteger @ Y @ ( ring_18347121197199848620nteger @ X ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % mult_of_int_commute
% 0.30/0.59  thf(fact_6183_mult__of__int__commute,axiom,
% 0.30/0.59      ! [X: int,Y: rat] :
% 0.30/0.59        ( ( times_times_rat @ ( ring_1_of_int_rat @ X ) @ Y )
% 0.30/0.59        = ( times_times_rat @ Y @ ( ring_1_of_int_rat @ X ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % mult_of_int_commute
% 0.30/0.59  thf(fact_6184_mult__of__int__commute,axiom,
% 0.30/0.59      ! [X: int,Y: int] :
% 0.30/0.59        ( ( times_times_int @ ( ring_1_of_int_int @ X ) @ Y )
% 0.30/0.59        = ( times_times_int @ Y @ ( ring_1_of_int_int @ X ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % mult_of_int_commute
% 0.30/0.59  thf(fact_6185_of__bool__conj,axiom,
% 0.30/0.59      ! [P: $o,Q2: $o] :
% 0.30/0.59        ( ( zero_n356916108424825756nteger
% 0.30/0.59          @ ( P
% 0.30/0.59            & Q2 ) )
% 0.30/0.59        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_conj
% 0.30/0.59  thf(fact_6186_of__bool__conj,axiom,
% 0.30/0.59      ! [P: $o,Q2: $o] :
% 0.30/0.59        ( ( zero_n2052037380579107095ol_rat
% 0.30/0.59          @ ( P
% 0.30/0.59            & Q2 ) )
% 0.30/0.59        = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_conj
% 0.30/0.59  thf(fact_6187_of__bool__conj,axiom,
% 0.30/0.59      ! [P: $o,Q2: $o] :
% 0.30/0.59        ( ( zero_n2684676970156552555ol_int
% 0.30/0.59          @ ( P
% 0.30/0.59            & Q2 ) )
% 0.30/0.59        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_conj
% 0.30/0.59  thf(fact_6188_of__bool__conj,axiom,
% 0.30/0.59      ! [P: $o,Q2: $o] :
% 0.30/0.59        ( ( zero_n2687167440665602831ol_nat
% 0.30/0.59          @ ( P
% 0.30/0.59            & Q2 ) )
% 0.30/0.59        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_conj
% 0.30/0.59  thf(fact_6189_of__bool__less__eq__one,axiom,
% 0.30/0.59      ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_less_eq_one
% 0.30/0.59  thf(fact_6190_of__bool__less__eq__one,axiom,
% 0.30/0.59      ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_less_eq_one
% 0.30/0.59  thf(fact_6191_of__bool__less__eq__one,axiom,
% 0.30/0.59      ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_less_eq_one
% 0.30/0.59  thf(fact_6192_of__bool__less__eq__one,axiom,
% 0.30/0.59      ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_less_eq_one
% 0.30/0.59  thf(fact_6193_split__of__bool__asm,axiom,
% 0.30/0.59      ! [P: code_integer > $o,P4: $o] :
% 0.30/0.59        ( ( P @ ( zero_n356916108424825756nteger @ P4 ) )
% 0.30/0.59        = ( ~ ( ( P4
% 0.30/0.59                & ~ ( P @ one_one_Code_integer ) )
% 0.30/0.59              | ( ~ P4
% 0.30/0.59                & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % split_of_bool_asm
% 0.30/0.59  thf(fact_6194_split__of__bool__asm,axiom,
% 0.30/0.59      ! [P: rat > $o,P4: $o] :
% 0.30/0.59        ( ( P @ ( zero_n2052037380579107095ol_rat @ P4 ) )
% 0.30/0.59        = ( ~ ( ( P4
% 0.30/0.59                & ~ ( P @ one_one_rat ) )
% 0.30/0.59              | ( ~ P4
% 0.30/0.59                & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % split_of_bool_asm
% 0.30/0.59  thf(fact_6195_split__of__bool__asm,axiom,
% 0.30/0.59      ! [P: int > $o,P4: $o] :
% 0.30/0.59        ( ( P @ ( zero_n2684676970156552555ol_int @ P4 ) )
% 0.30/0.59        = ( ~ ( ( P4
% 0.30/0.59                & ~ ( P @ one_one_int ) )
% 0.30/0.59              | ( ~ P4
% 0.30/0.59                & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % split_of_bool_asm
% 0.30/0.59  thf(fact_6196_split__of__bool__asm,axiom,
% 0.30/0.59      ! [P: nat > $o,P4: $o] :
% 0.30/0.59        ( ( P @ ( zero_n2687167440665602831ol_nat @ P4 ) )
% 0.30/0.59        = ( ~ ( ( P4
% 0.30/0.59                & ~ ( P @ one_one_nat ) )
% 0.30/0.59              | ( ~ P4
% 0.30/0.59                & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % split_of_bool_asm
% 0.30/0.59  thf(fact_6197_split__of__bool,axiom,
% 0.30/0.59      ! [P: code_integer > $o,P4: $o] :
% 0.30/0.59        ( ( P @ ( zero_n356916108424825756nteger @ P4 ) )
% 0.30/0.59        = ( ( P4
% 0.30/0.59           => ( P @ one_one_Code_integer ) )
% 0.30/0.59          & ( ~ P4
% 0.30/0.59           => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % split_of_bool
% 0.30/0.59  thf(fact_6198_split__of__bool,axiom,
% 0.30/0.59      ! [P: rat > $o,P4: $o] :
% 0.30/0.59        ( ( P @ ( zero_n2052037380579107095ol_rat @ P4 ) )
% 0.30/0.59        = ( ( P4
% 0.30/0.59           => ( P @ one_one_rat ) )
% 0.30/0.59          & ( ~ P4
% 0.30/0.59           => ( P @ zero_zero_rat ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % split_of_bool
% 0.30/0.59  thf(fact_6199_split__of__bool,axiom,
% 0.30/0.59      ! [P: int > $o,P4: $o] :
% 0.30/0.59        ( ( P @ ( zero_n2684676970156552555ol_int @ P4 ) )
% 0.30/0.59        = ( ( P4
% 0.30/0.59           => ( P @ one_one_int ) )
% 0.30/0.59          & ( ~ P4
% 0.30/0.59           => ( P @ zero_zero_int ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % split_of_bool
% 0.30/0.59  thf(fact_6200_split__of__bool,axiom,
% 0.30/0.59      ! [P: nat > $o,P4: $o] :
% 0.30/0.59        ( ( P @ ( zero_n2687167440665602831ol_nat @ P4 ) )
% 0.30/0.59        = ( ( P4
% 0.30/0.59           => ( P @ one_one_nat ) )
% 0.30/0.59          & ( ~ P4
% 0.30/0.59           => ( P @ zero_zero_nat ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % split_of_bool
% 0.30/0.59  thf(fact_6201_of__bool__def,axiom,
% 0.30/0.59      ( zero_n356916108424825756nteger
% 0.30/0.59      = ( ^ [P6: $o] : ( if_Code_integer @ P6 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_def
% 0.30/0.59  thf(fact_6202_of__bool__def,axiom,
% 0.30/0.59      ( zero_n2052037380579107095ol_rat
% 0.30/0.59      = ( ^ [P6: $o] : ( if_rat @ P6 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_def
% 0.30/0.59  thf(fact_6203_of__bool__def,axiom,
% 0.30/0.59      ( zero_n2684676970156552555ol_int
% 0.30/0.59      = ( ^ [P6: $o] : ( if_int @ P6 @ one_one_int @ zero_zero_int ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_def
% 0.30/0.59  thf(fact_6204_of__bool__def,axiom,
% 0.30/0.59      ( zero_n2687167440665602831ol_nat
% 0.30/0.59      = ( ^ [P6: $o] : ( if_nat @ P6 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_bool_def
% 0.30/0.59  thf(fact_6205_Divides_Oadjust__div__def,axiom,
% 0.30/0.59      ( adjust_div
% 0.30/0.59      = ( produc8211389475949308722nt_int
% 0.30/0.59        @ ^ [Q5: int,R4: int] : ( plus_plus_int @ Q5 @ ( zero_n2684676970156552555ol_int @ ( R4 != zero_zero_int ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Divides.adjust_div_def
% 0.30/0.59  thf(fact_6206_of__int__neg__numeral,axiom,
% 0.30/0.59      ! [K: num] :
% 0.30/0.59        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.30/0.59        = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_neg_numeral
% 0.30/0.59  thf(fact_6207_of__int__neg__numeral,axiom,
% 0.30/0.59      ! [K: num] :
% 0.30/0.59        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.30/0.59        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_neg_numeral
% 0.30/0.59  thf(fact_6208_of__int__neg__numeral,axiom,
% 0.30/0.59      ! [K: num] :
% 0.30/0.59        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.30/0.59        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % of_int_neg_numeral
% 0.30/0.59  thf(fact_6209_power__dvd__imp__le,axiom,
% 0.30/0.59      ! [I: nat,M: nat,N: nat] :
% 0.30/0.59        ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 0.30/0.59       => ( ( ord_less_nat @ one_one_nat @ I )
% 0.30/0.59         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % power_dvd_imp_le
% 0.30/0.59  thf(fact_6210_fold__atLeastAtMost__nat_Osimps,axiom,
% 0.30/0.59      ( set_fo2584398358068434914at_nat
% 0.30/0.59      = ( ^ [F: nat > nat > nat,A3: nat,B3: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B3 @ A3 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F @ ( plus_plus_nat @ A3 @ one_one_nat ) @ B3 @ ( F @ A3 @ Acc2 ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % fold_atLeastAtMost_nat.simps
% 0.30/0.59  thf(fact_6211_fold__atLeastAtMost__nat_Oelims,axiom,
% 0.30/0.59      ! [X: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y: nat] :
% 0.30/0.59        ( ( ( set_fo2584398358068434914at_nat @ X @ Xa @ Xb @ Xc )
% 0.30/0.59          = Y )
% 0.30/0.59       => ( ( ( ord_less_nat @ Xb @ Xa )
% 0.30/0.59           => ( Y = Xc ) )
% 0.30/0.59          & ( ~ ( ord_less_nat @ Xb @ Xa )
% 0.30/0.59           => ( Y
% 0.30/0.59              = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X @ Xa @ Xc ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % fold_atLeastAtMost_nat.elims
% 0.30/0.59  thf(fact_6212_mask__nat__def,axiom,
% 0.30/0.59      ( bit_se2002935070580805687sk_nat
% 0.30/0.59      = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % mask_nat_def
% 0.30/0.59  thf(fact_6213_bits__induct,axiom,
% 0.30/0.59      ! [P: code_integer > $o,A: code_integer] :
% 0.30/0.59        ( ! [A6: code_integer] :
% 0.30/0.59            ( ( ( divide6298287555418463151nteger @ A6 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.59              = A6 )
% 0.30/0.59           => ( P @ A6 ) )
% 0.30/0.59       => ( ! [A6: code_integer,B6: $o] :
% 0.30/0.59              ( ( P @ A6 )
% 0.30/0.59             => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B6 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A6 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.59                  = A6 )
% 0.30/0.59               => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B6 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A6 ) ) ) ) )
% 0.30/0.59         => ( P @ A ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % bits_induct
% 0.30/0.59  thf(fact_6214_bits__induct,axiom,
% 0.30/0.59      ! [P: code_natural > $o,A: code_natural] :
% 0.30/0.59        ( ! [A6: code_natural] :
% 0.30/0.59            ( ( ( divide5121882707175180666atural @ A6 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.59              = A6 )
% 0.30/0.59           => ( P @ A6 ) )
% 0.30/0.59       => ( ! [A6: code_natural,B6: $o] :
% 0.30/0.59              ( ( P @ A6 )
% 0.30/0.59             => ( ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( zero_n8403883297036319079atural @ B6 ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A6 ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.59                  = A6 )
% 0.30/0.59               => ( P @ ( plus_p4538020629002901425atural @ ( zero_n8403883297036319079atural @ B6 ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A6 ) ) ) ) )
% 0.30/0.59         => ( P @ A ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % bits_induct
% 0.30/0.59  thf(fact_6215_bits__induct,axiom,
% 0.30/0.59      ! [P: int > $o,A: int] :
% 0.30/0.59        ( ! [A6: int] :
% 0.30/0.59            ( ( ( divide_divide_int @ A6 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.59              = A6 )
% 0.30/0.59           => ( P @ A6 ) )
% 0.30/0.59       => ( ! [A6: int,B6: $o] :
% 0.30/0.59              ( ( P @ A6 )
% 0.30/0.59             => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B6 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A6 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.59                  = A6 )
% 0.30/0.59               => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B6 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A6 ) ) ) ) )
% 0.30/0.59         => ( P @ A ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % bits_induct
% 0.30/0.59  thf(fact_6216_bits__induct,axiom,
% 0.30/0.59      ! [P: nat > $o,A: nat] :
% 0.30/0.59        ( ! [A6: nat] :
% 0.30/0.59            ( ( ( divide_divide_nat @ A6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59              = A6 )
% 0.30/0.59           => ( P @ A6 ) )
% 0.30/0.59       => ( ! [A6: nat,B6: $o] :
% 0.30/0.59              ( ( P @ A6 )
% 0.30/0.59             => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B6 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A6 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.59                  = A6 )
% 0.30/0.59               => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B6 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A6 ) ) ) ) )
% 0.30/0.59         => ( P @ A ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % bits_induct
% 0.30/0.59  thf(fact_6217_exp__mod__exp,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % exp_mod_exp
% 0.30/0.59  thf(fact_6218_exp__mod__exp,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( modulo8411746178871703098atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( times_2397367101498566445atural @ ( zero_n8403883297036319079atural @ ( ord_less_nat @ M @ N ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % exp_mod_exp
% 0.30/0.59  thf(fact_6219_exp__mod__exp,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % exp_mod_exp
% 0.30/0.59  thf(fact_6220_exp__mod__exp,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % exp_mod_exp
% 0.30/0.59  thf(fact_6221_dvd__productE,axiom,
% 0.30/0.59      ! [P4: nat,A: nat,B: nat] :
% 0.30/0.59        ( ( dvd_dvd_nat @ P4 @ ( times_times_nat @ A @ B ) )
% 0.30/0.59       => ~ ! [X2: nat,Y2: nat] :
% 0.30/0.59              ( ( P4
% 0.30/0.59                = ( times_times_nat @ X2 @ Y2 ) )
% 0.30/0.59             => ( ( dvd_dvd_nat @ X2 @ A )
% 0.30/0.59               => ~ ( dvd_dvd_nat @ Y2 @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % dvd_productE
% 0.30/0.59  thf(fact_6222_dvd__productE,axiom,
% 0.30/0.59      ! [P4: int,A: int,B: int] :
% 0.30/0.59        ( ( dvd_dvd_int @ P4 @ ( times_times_int @ A @ B ) )
% 0.30/0.59       => ~ ! [X2: int,Y2: int] :
% 0.30/0.59              ( ( P4
% 0.30/0.59                = ( times_times_int @ X2 @ Y2 ) )
% 0.30/0.59             => ( ( dvd_dvd_int @ X2 @ A )
% 0.30/0.59               => ~ ( dvd_dvd_int @ Y2 @ B ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % dvd_productE
% 0.30/0.59  thf(fact_6223_division__decomp,axiom,
% 0.30/0.59      ! [A: nat,B: nat,C: nat] :
% 0.30/0.59        ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 0.30/0.59       => ? [B8: nat,C5: nat] :
% 0.30/0.59            ( ( A
% 0.30/0.59              = ( times_times_nat @ B8 @ C5 ) )
% 0.30/0.59            & ( dvd_dvd_nat @ B8 @ B )
% 0.30/0.59            & ( dvd_dvd_nat @ C5 @ C ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % division_decomp
% 0.30/0.59  thf(fact_6224_division__decomp,axiom,
% 0.30/0.59      ! [A: int,B: int,C: int] :
% 0.30/0.59        ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 0.30/0.59       => ? [B8: int,C5: int] :
% 0.30/0.59            ( ( A
% 0.30/0.59              = ( times_times_int @ B8 @ C5 ) )
% 0.30/0.59            & ( dvd_dvd_int @ B8 @ B )
% 0.30/0.59            & ( dvd_dvd_int @ C5 @ C ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % division_decomp
% 0.30/0.59  thf(fact_6225_ex__power__ivl1,axiom,
% 0.30/0.59      ! [B: nat,K: nat] :
% 0.30/0.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.30/0.59       => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 0.30/0.59         => ? [N3: nat] :
% 0.30/0.59              ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 0.30/0.59              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ex_power_ivl1
% 0.30/0.59  thf(fact_6226_ex__power__ivl2,axiom,
% 0.30/0.59      ! [B: nat,K: nat] :
% 0.30/0.59        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.30/0.59       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.30/0.59         => ? [N3: nat] :
% 0.30/0.59              ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 0.30/0.59              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ex_power_ivl2
% 0.30/0.59  thf(fact_6227_xor__one__eq,axiom,
% 0.30/0.59      ! [A: code_integer] :
% 0.30/0.59        ( ( bit_se3222712562003087583nteger @ A @ one_one_Code_integer )
% 0.30/0.59        = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 0.30/0.59          @ ( zero_n356916108424825756nteger
% 0.30/0.59            @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % xor_one_eq
% 0.30/0.59  thf(fact_6228_xor__one__eq,axiom,
% 0.30/0.59      ! [A: code_natural] :
% 0.30/0.59        ( ( bit_se2046307713759805098atural @ A @ one_one_Code_natural )
% 0.30/0.59        = ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ A @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) )
% 0.30/0.59          @ ( zero_n8403883297036319079atural
% 0.30/0.59            @ ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % xor_one_eq
% 0.30/0.59  thf(fact_6229_xor__one__eq,axiom,
% 0.30/0.59      ! [A: int] :
% 0.30/0.59        ( ( bit_se6526347334894502574or_int @ A @ one_one_int )
% 0.30/0.59        = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 0.30/0.59          @ ( zero_n2684676970156552555ol_int
% 0.30/0.59            @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % xor_one_eq
% 0.30/0.59  thf(fact_6230_xor__one__eq,axiom,
% 0.30/0.59      ! [A: nat] :
% 0.30/0.59        ( ( bit_se6528837805403552850or_nat @ A @ one_one_nat )
% 0.30/0.59        = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 0.30/0.59          @ ( zero_n2687167440665602831ol_nat
% 0.30/0.59            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % xor_one_eq
% 0.30/0.59  thf(fact_6231_one__xor__eq,axiom,
% 0.30/0.59      ! [A: code_integer] :
% 0.30/0.59        ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ A )
% 0.30/0.59        = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 0.30/0.59          @ ( zero_n356916108424825756nteger
% 0.30/0.59            @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % one_xor_eq
% 0.30/0.59  thf(fact_6232_one__xor__eq,axiom,
% 0.30/0.59      ! [A: code_natural] :
% 0.30/0.59        ( ( bit_se2046307713759805098atural @ one_one_Code_natural @ A )
% 0.30/0.59        = ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ A @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) )
% 0.30/0.59          @ ( zero_n8403883297036319079atural
% 0.30/0.59            @ ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % one_xor_eq
% 0.30/0.59  thf(fact_6233_one__xor__eq,axiom,
% 0.30/0.59      ! [A: int] :
% 0.30/0.59        ( ( bit_se6526347334894502574or_int @ one_one_int @ A )
% 0.30/0.59        = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 0.30/0.59          @ ( zero_n2684676970156552555ol_int
% 0.30/0.59            @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % one_xor_eq
% 0.30/0.59  thf(fact_6234_one__xor__eq,axiom,
% 0.30/0.59      ! [A: nat] :
% 0.30/0.59        ( ( bit_se6528837805403552850or_nat @ one_one_nat @ A )
% 0.30/0.59        = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 0.30/0.59          @ ( zero_n2687167440665602831ol_nat
% 0.30/0.59            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % one_xor_eq
% 0.30/0.59  thf(fact_6235_exp__div__exp__eq,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( times_3573771949741848930nteger
% 0.30/0.59          @ ( zero_n356916108424825756nteger
% 0.30/0.59            @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 0.30/0.59               != zero_z3403309356797280102nteger )
% 0.30/0.59              & ( ord_less_eq_nat @ N @ M ) ) )
% 0.30/0.59          @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % exp_div_exp_eq
% 0.30/0.59  thf(fact_6236_exp__div__exp__eq,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( times_2397367101498566445atural
% 0.30/0.59          @ ( zero_n8403883297036319079atural
% 0.30/0.59            @ ( ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M )
% 0.30/0.59               != zero_z2226904508553997617atural )
% 0.30/0.59              & ( ord_less_eq_nat @ N @ M ) ) )
% 0.30/0.59          @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % exp_div_exp_eq
% 0.30/0.59  thf(fact_6237_exp__div__exp__eq,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( times_times_int
% 0.30/0.59          @ ( zero_n2684676970156552555ol_int
% 0.30/0.59            @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 0.30/0.59               != zero_zero_int )
% 0.30/0.59              & ( ord_less_eq_nat @ N @ M ) ) )
% 0.30/0.59          @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % exp_div_exp_eq
% 0.30/0.59  thf(fact_6238_exp__div__exp__eq,axiom,
% 0.30/0.59      ! [M: nat,N: nat] :
% 0.30/0.59        ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.59        = ( times_times_nat
% 0.30/0.59          @ ( zero_n2687167440665602831ol_nat
% 0.30/0.59            @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 0.30/0.59               != zero_zero_nat )
% 0.30/0.59              & ( ord_less_eq_nat @ N @ M ) ) )
% 0.30/0.59          @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % exp_div_exp_eq
% 0.30/0.59  thf(fact_6239_floor__exists1,axiom,
% 0.30/0.59      ! [X: rat] :
% 0.30/0.59      ? [X2: int] :
% 0.30/0.59        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X2 ) @ X )
% 0.30/0.59        & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ X2 @ one_one_int ) ) )
% 0.30/0.59        & ! [Y5: int] :
% 0.30/0.59            ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y5 ) @ X )
% 0.30/0.59              & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y5 @ one_one_int ) ) ) )
% 0.30/0.59           => ( Y5 = X2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % floor_exists1
% 0.30/0.59  thf(fact_6240_floor__exists,axiom,
% 0.30/0.59      ! [X: rat] :
% 0.30/0.59      ? [Z2: int] :
% 0.30/0.59        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X )
% 0.30/0.59        & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % floor_exists
% 0.30/0.59  thf(fact_6241_and__int_Osimps,axiom,
% 0.30/0.59      ( bit_se725231765392027082nd_int
% 0.30/0.59      = ( ^ [K4: int,L2: int] :
% 0.30/0.59            ( if_int
% 0.30/0.59            @ ( ( member_int @ K4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.30/0.59              & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.30/0.59            @ ( uminus_uminus_int
% 0.30/0.59              @ ( zero_n2684676970156552555ol_int
% 0.30/0.59                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K4 )
% 0.30/0.59                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 0.30/0.59            @ ( plus_plus_int
% 0.30/0.59              @ ( zero_n2684676970156552555ol_int
% 0.30/0.59                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K4 )
% 0.30/0.59                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 0.30/0.59              @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % and_int.simps
% 0.30/0.59  thf(fact_6242_and__int_Oelims,axiom,
% 0.30/0.59      ! [X: int,Xa: int,Y: int] :
% 0.30/0.59        ( ( ( bit_se725231765392027082nd_int @ X @ Xa )
% 0.30/0.59          = Y )
% 0.30/0.59       => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.30/0.59              & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.30/0.59           => ( Y
% 0.30/0.59              = ( uminus_uminus_int
% 0.30/0.59                @ ( zero_n2684676970156552555ol_int
% 0.30/0.59                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 0.30/0.59                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 0.30/0.59          & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.30/0.59                & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.30/0.59           => ( Y
% 0.30/0.59              = ( plus_plus_int
% 0.30/0.59                @ ( zero_n2684676970156552555ol_int
% 0.30/0.59                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 0.30/0.59                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 0.30/0.59                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % and_int.elims
% 0.30/0.59  thf(fact_6243_round__unique,axiom,
% 0.30/0.59      ! [X: rat,Y: int] :
% 0.30/0.59        ( ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y ) )
% 0.30/0.59       => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 0.30/0.59         => ( ( archim7778729529865785530nd_rat @ X )
% 0.30/0.59            = Y ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % round_unique
% 0.30/0.59  thf(fact_6244_push__bit__numeral__minus__1,axiom,
% 0.30/0.59      ! [N: num] :
% 0.30/0.59        ( ( bit_se7788150548672797655nteger @ ( numeral_numeral_nat @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.59        = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % push_bit_numeral_minus_1
% 0.30/0.59  thf(fact_6245_push__bit__numeral__minus__1,axiom,
% 0.30/0.59      ! [N: num] :
% 0.30/0.59        ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.59        = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % push_bit_numeral_minus_1
% 0.30/0.59  thf(fact_6246_divmod__step__integer__def,axiom,
% 0.30/0.59      ( unique4921790084139445826nteger
% 0.30/0.59      = ( ^ [L2: num] :
% 0.30/0.59            ( produc6916734918728496179nteger
% 0.30/0.59            @ ^ [Q5: code_integer,R4: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R4 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R4 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R4 ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % divmod_step_integer_def
% 0.30/0.59  thf(fact_6247_singletonI,axiom,
% 0.30/0.59      ! [A: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ A @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singletonI
% 0.30/0.59  thf(fact_6248_singletonI,axiom,
% 0.30/0.59      ! [A: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ A @ ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singletonI
% 0.30/0.59  thf(fact_6249_singletonI,axiom,
% 0.30/0.59      ! [A: set_nat] : ( member_set_nat @ A @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singletonI
% 0.30/0.59  thf(fact_6250_singletonI,axiom,
% 0.30/0.59      ! [A: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ A @ ( insert5175938949040314269_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singletonI
% 0.30/0.59  thf(fact_6251_singletonI,axiom,
% 0.30/0.59      ! [A: product_prod_nat_nat] : ( member8440522571783428010at_nat @ A @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singletonI
% 0.30/0.59  thf(fact_6252_singletonI,axiom,
% 0.30/0.59      ! [A: $o] : ( member_o @ A @ ( insert_o @ A @ bot_bot_set_o ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singletonI
% 0.30/0.59  thf(fact_6253_singletonI,axiom,
% 0.30/0.59      ! [A: nat] : ( member_nat @ A @ ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singletonI
% 0.30/0.59  thf(fact_6254_singletonI,axiom,
% 0.30/0.59      ! [A: int] : ( member_int @ A @ ( insert_int @ A @ bot_bot_set_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singletonI
% 0.30/0.59  thf(fact_6255_Int__insert__right__if1,axiom,
% 0.30/0.59      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.59        ( ( member8757157785044589968at_nat @ A @ A2 )
% 0.30/0.59       => ( ( inf_in7913087082777306421at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ B2 ) )
% 0.30/0.59          = ( insert9069300056098147895at_nat @ A @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_right_if1
% 0.30/0.59  thf(fact_6256_Int__insert__right__if1,axiom,
% 0.30/0.59      ! [A: $o,A2: set_o,B2: set_o] :
% 0.30/0.59        ( ( member_o @ A @ A2 )
% 0.30/0.59       => ( ( inf_inf_set_o @ A2 @ ( insert_o @ A @ B2 ) )
% 0.30/0.59          = ( insert_o @ A @ ( inf_inf_set_o @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_right_if1
% 0.30/0.59  thf(fact_6257_Int__insert__right__if1,axiom,
% 0.30/0.59      ! [A: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 0.30/0.59        ( ( member2340774599025711042nt_int @ A @ A2 )
% 0.30/0.59       => ( ( inf_in8396524679539076455nt_int @ A2 @ ( insert8897473484851387113nt_int @ A @ B2 ) )
% 0.30/0.59          = ( insert8897473484851387113nt_int @ A @ ( inf_in8396524679539076455nt_int @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_right_if1
% 0.30/0.59  thf(fact_6258_Int__insert__right__if1,axiom,
% 0.30/0.59      ! [A: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.30/0.59        ( ( member_set_nat @ A @ A2 )
% 0.30/0.59       => ( ( inf_inf_set_set_nat @ A2 @ ( insert_set_nat @ A @ B2 ) )
% 0.30/0.59          = ( insert_set_nat @ A @ ( inf_inf_set_set_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_right_if1
% 0.30/0.59  thf(fact_6259_Int__insert__right__if1,axiom,
% 0.30/0.59      ! [A: int,A2: set_int,B2: set_int] :
% 0.30/0.59        ( ( member_int @ A @ A2 )
% 0.30/0.59       => ( ( inf_inf_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 0.30/0.59          = ( insert_int @ A @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_right_if1
% 0.30/0.59  thf(fact_6260_Int__insert__right__if1,axiom,
% 0.30/0.59      ! [A: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 0.30/0.59        ( ( member6576561426505652726_nat_o @ A @ A2 )
% 0.30/0.59       => ( ( inf_in1906310914598751387_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ A @ B2 ) )
% 0.30/0.59          = ( insert5175938949040314269_nat_o @ A @ ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_right_if1
% 0.30/0.59  thf(fact_6261_Int__insert__right__if1,axiom,
% 0.30/0.59      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.59        ( ( member8440522571783428010at_nat @ A @ A2 )
% 0.30/0.59       => ( ( inf_in2572325071724192079at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 0.30/0.59          = ( insert8211810215607154385at_nat @ A @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_right_if1
% 0.30/0.59  thf(fact_6262_Int__insert__right__if1,axiom,
% 0.30/0.59      ! [A: nat,A2: set_nat,B2: set_nat] :
% 0.30/0.59        ( ( member_nat @ A @ A2 )
% 0.30/0.59       => ( ( inf_inf_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 0.30/0.59          = ( insert_nat @ A @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_right_if1
% 0.30/0.59  thf(fact_6263_Int__insert__right__if0,axiom,
% 0.30/0.59      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.59        ( ~ ( member8757157785044589968at_nat @ A @ A2 )
% 0.30/0.59       => ( ( inf_in7913087082777306421at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ B2 ) )
% 0.30/0.59          = ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_right_if0
% 0.30/0.59  thf(fact_6264_Int__insert__right__if0,axiom,
% 0.30/0.59      ! [A: $o,A2: set_o,B2: set_o] :
% 0.30/0.59        ( ~ ( member_o @ A @ A2 )
% 0.30/0.59       => ( ( inf_inf_set_o @ A2 @ ( insert_o @ A @ B2 ) )
% 0.30/0.59          = ( inf_inf_set_o @ A2 @ B2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_right_if0
% 0.30/0.59  thf(fact_6265_Int__insert__right__if0,axiom,
% 0.30/0.59      ! [A: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 0.30/0.59        ( ~ ( member2340774599025711042nt_int @ A @ A2 )
% 0.30/0.59       => ( ( inf_in8396524679539076455nt_int @ A2 @ ( insert8897473484851387113nt_int @ A @ B2 ) )
% 0.30/0.59          = ( inf_in8396524679539076455nt_int @ A2 @ B2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_right_if0
% 0.30/0.59  thf(fact_6266_Int__insert__right__if0,axiom,
% 0.30/0.59      ! [A: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.30/0.59        ( ~ ( member_set_nat @ A @ A2 )
% 0.30/0.59       => ( ( inf_inf_set_set_nat @ A2 @ ( insert_set_nat @ A @ B2 ) )
% 0.30/0.59          = ( inf_inf_set_set_nat @ A2 @ B2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_right_if0
% 0.30/0.59  thf(fact_6267_Int__insert__right__if0,axiom,
% 0.30/0.59      ! [A: int,A2: set_int,B2: set_int] :
% 0.30/0.59        ( ~ ( member_int @ A @ A2 )
% 0.30/0.59       => ( ( inf_inf_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 0.30/0.59          = ( inf_inf_set_int @ A2 @ B2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_right_if0
% 0.30/0.59  thf(fact_6268_Int__insert__right__if0,axiom,
% 0.30/0.59      ! [A: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 0.30/0.59        ( ~ ( member6576561426505652726_nat_o @ A @ A2 )
% 0.30/0.59       => ( ( inf_in1906310914598751387_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ A @ B2 ) )
% 0.30/0.59          = ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_right_if0
% 0.30/0.59  thf(fact_6269_Int__insert__right__if0,axiom,
% 0.30/0.59      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.59        ( ~ ( member8440522571783428010at_nat @ A @ A2 )
% 0.30/0.59       => ( ( inf_in2572325071724192079at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 0.30/0.59          = ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_right_if0
% 0.30/0.59  thf(fact_6270_Int__insert__right__if0,axiom,
% 0.30/0.59      ! [A: nat,A2: set_nat,B2: set_nat] :
% 0.30/0.59        ( ~ ( member_nat @ A @ A2 )
% 0.30/0.59       => ( ( inf_inf_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 0.30/0.59          = ( inf_inf_set_nat @ A2 @ B2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_right_if0
% 0.30/0.59  thf(fact_6271_insert__inter__insert,axiom,
% 0.30/0.59      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.59        ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A @ A2 ) @ ( insert9069300056098147895at_nat @ A @ B2 ) )
% 0.30/0.59        = ( insert9069300056098147895at_nat @ A @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_inter_insert
% 0.30/0.59  thf(fact_6272_insert__inter__insert,axiom,
% 0.30/0.59      ! [A: $o,A2: set_o,B2: set_o] :
% 0.30/0.59        ( ( inf_inf_set_o @ ( insert_o @ A @ A2 ) @ ( insert_o @ A @ B2 ) )
% 0.30/0.59        = ( insert_o @ A @ ( inf_inf_set_o @ A2 @ B2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_inter_insert
% 0.30/0.59  thf(fact_6273_insert__inter__insert,axiom,
% 0.30/0.59      ! [A: int,A2: set_int,B2: set_int] :
% 0.30/0.59        ( ( inf_inf_set_int @ ( insert_int @ A @ A2 ) @ ( insert_int @ A @ B2 ) )
% 0.30/0.59        = ( insert_int @ A @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_inter_insert
% 0.30/0.59  thf(fact_6274_insert__inter__insert,axiom,
% 0.30/0.59      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.59        ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ A2 ) @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 0.30/0.59        = ( insert8211810215607154385at_nat @ A @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_inter_insert
% 0.30/0.59  thf(fact_6275_insert__inter__insert,axiom,
% 0.30/0.59      ! [A: nat,A2: set_nat,B2: set_nat] :
% 0.30/0.59        ( ( inf_inf_set_nat @ ( insert_nat @ A @ A2 ) @ ( insert_nat @ A @ B2 ) )
% 0.30/0.59        = ( insert_nat @ A @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_inter_insert
% 0.30/0.59  thf(fact_6276_Int__insert__left__if1,axiom,
% 0.30/0.59      ! [A: produc3843707927480180839at_nat,C2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.59        ( ( member8757157785044589968at_nat @ A @ C2 )
% 0.30/0.59       => ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A @ B2 ) @ C2 )
% 0.30/0.59          = ( insert9069300056098147895at_nat @ A @ ( inf_in7913087082777306421at_nat @ B2 @ C2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_left_if1
% 0.30/0.59  thf(fact_6277_Int__insert__left__if1,axiom,
% 0.30/0.59      ! [A: $o,C2: set_o,B2: set_o] :
% 0.30/0.59        ( ( member_o @ A @ C2 )
% 0.30/0.59       => ( ( inf_inf_set_o @ ( insert_o @ A @ B2 ) @ C2 )
% 0.30/0.59          = ( insert_o @ A @ ( inf_inf_set_o @ B2 @ C2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_left_if1
% 0.30/0.59  thf(fact_6278_Int__insert__left__if1,axiom,
% 0.30/0.59      ! [A: set_Pr958786334691620121nt_int,C2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 0.30/0.59        ( ( member2340774599025711042nt_int @ A @ C2 )
% 0.30/0.59       => ( ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ B2 ) @ C2 )
% 0.30/0.59          = ( insert8897473484851387113nt_int @ A @ ( inf_in8396524679539076455nt_int @ B2 @ C2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_left_if1
% 0.30/0.59  thf(fact_6279_Int__insert__left__if1,axiom,
% 0.30/0.59      ! [A: set_nat,C2: set_set_nat,B2: set_set_nat] :
% 0.30/0.59        ( ( member_set_nat @ A @ C2 )
% 0.30/0.59       => ( ( inf_inf_set_set_nat @ ( insert_set_nat @ A @ B2 ) @ C2 )
% 0.30/0.59          = ( insert_set_nat @ A @ ( inf_inf_set_set_nat @ B2 @ C2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_left_if1
% 0.30/0.59  thf(fact_6280_Int__insert__left__if1,axiom,
% 0.30/0.59      ! [A: int,C2: set_int,B2: set_int] :
% 0.30/0.59        ( ( member_int @ A @ C2 )
% 0.30/0.59       => ( ( inf_inf_set_int @ ( insert_int @ A @ B2 ) @ C2 )
% 0.30/0.59          = ( insert_int @ A @ ( inf_inf_set_int @ B2 @ C2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_left_if1
% 0.30/0.59  thf(fact_6281_Int__insert__left__if1,axiom,
% 0.30/0.59      ! [A: produc3658429121746597890et_nat > $o,C2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 0.30/0.59        ( ( member6576561426505652726_nat_o @ A @ C2 )
% 0.30/0.59       => ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A @ B2 ) @ C2 )
% 0.30/0.59          = ( insert5175938949040314269_nat_o @ A @ ( inf_in1906310914598751387_nat_o @ B2 @ C2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_left_if1
% 0.30/0.59  thf(fact_6282_Int__insert__left__if1,axiom,
% 0.30/0.59      ! [A: product_prod_nat_nat,C2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.59        ( ( member8440522571783428010at_nat @ A @ C2 )
% 0.30/0.59       => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ B2 ) @ C2 )
% 0.30/0.59          = ( insert8211810215607154385at_nat @ A @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_left_if1
% 0.30/0.59  thf(fact_6283_Int__insert__left__if1,axiom,
% 0.30/0.59      ! [A: nat,C2: set_nat,B2: set_nat] :
% 0.30/0.59        ( ( member_nat @ A @ C2 )
% 0.30/0.59       => ( ( inf_inf_set_nat @ ( insert_nat @ A @ B2 ) @ C2 )
% 0.30/0.59          = ( insert_nat @ A @ ( inf_inf_set_nat @ B2 @ C2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_left_if1
% 0.30/0.59  thf(fact_6284_Int__insert__left__if0,axiom,
% 0.30/0.59      ! [A: produc3843707927480180839at_nat,C2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.59        ( ~ ( member8757157785044589968at_nat @ A @ C2 )
% 0.30/0.59       => ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A @ B2 ) @ C2 )
% 0.30/0.59          = ( inf_in7913087082777306421at_nat @ B2 @ C2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_left_if0
% 0.30/0.59  thf(fact_6285_Int__insert__left__if0,axiom,
% 0.30/0.59      ! [A: $o,C2: set_o,B2: set_o] :
% 0.30/0.59        ( ~ ( member_o @ A @ C2 )
% 0.30/0.59       => ( ( inf_inf_set_o @ ( insert_o @ A @ B2 ) @ C2 )
% 0.30/0.59          = ( inf_inf_set_o @ B2 @ C2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_left_if0
% 0.30/0.59  thf(fact_6286_Int__insert__left__if0,axiom,
% 0.30/0.59      ! [A: set_Pr958786334691620121nt_int,C2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 0.30/0.59        ( ~ ( member2340774599025711042nt_int @ A @ C2 )
% 0.30/0.59       => ( ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ B2 ) @ C2 )
% 0.30/0.59          = ( inf_in8396524679539076455nt_int @ B2 @ C2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_left_if0
% 0.30/0.59  thf(fact_6287_Int__insert__left__if0,axiom,
% 0.30/0.59      ! [A: set_nat,C2: set_set_nat,B2: set_set_nat] :
% 0.30/0.59        ( ~ ( member_set_nat @ A @ C2 )
% 0.30/0.59       => ( ( inf_inf_set_set_nat @ ( insert_set_nat @ A @ B2 ) @ C2 )
% 0.30/0.59          = ( inf_inf_set_set_nat @ B2 @ C2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_left_if0
% 0.30/0.59  thf(fact_6288_Int__insert__left__if0,axiom,
% 0.30/0.59      ! [A: int,C2: set_int,B2: set_int] :
% 0.30/0.59        ( ~ ( member_int @ A @ C2 )
% 0.30/0.59       => ( ( inf_inf_set_int @ ( insert_int @ A @ B2 ) @ C2 )
% 0.30/0.59          = ( inf_inf_set_int @ B2 @ C2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_left_if0
% 0.30/0.59  thf(fact_6289_Int__insert__left__if0,axiom,
% 0.30/0.59      ! [A: produc3658429121746597890et_nat > $o,C2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 0.30/0.59        ( ~ ( member6576561426505652726_nat_o @ A @ C2 )
% 0.30/0.59       => ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A @ B2 ) @ C2 )
% 0.30/0.59          = ( inf_in1906310914598751387_nat_o @ B2 @ C2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_left_if0
% 0.30/0.59  thf(fact_6290_Int__insert__left__if0,axiom,
% 0.30/0.59      ! [A: product_prod_nat_nat,C2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.59        ( ~ ( member8440522571783428010at_nat @ A @ C2 )
% 0.30/0.59       => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ B2 ) @ C2 )
% 0.30/0.59          = ( inf_in2572325071724192079at_nat @ B2 @ C2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_left_if0
% 0.30/0.59  thf(fact_6291_Int__insert__left__if0,axiom,
% 0.30/0.59      ! [A: nat,C2: set_nat,B2: set_nat] :
% 0.30/0.59        ( ~ ( member_nat @ A @ C2 )
% 0.30/0.59       => ( ( inf_inf_set_nat @ ( insert_nat @ A @ B2 ) @ C2 )
% 0.30/0.59          = ( inf_inf_set_nat @ B2 @ C2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_left_if0
% 0.30/0.59  thf(fact_6292_Un__insert__right,axiom,
% 0.30/0.59      ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.59        ( ( sup_su6327502436637775413at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 0.30/0.59        = ( insert8211810215607154385at_nat @ A @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Un_insert_right
% 0.30/0.59  thf(fact_6293_Un__insert__right,axiom,
% 0.30/0.59      ! [A2: set_o,A: $o,B2: set_o] :
% 0.30/0.59        ( ( sup_sup_set_o @ A2 @ ( insert_o @ A @ B2 ) )
% 0.30/0.59        = ( insert_o @ A @ ( sup_sup_set_o @ A2 @ B2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Un_insert_right
% 0.30/0.59  thf(fact_6294_Un__insert__right,axiom,
% 0.30/0.59      ! [A2: set_int,A: int,B2: set_int] :
% 0.30/0.59        ( ( sup_sup_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 0.30/0.59        = ( insert_int @ A @ ( sup_sup_set_int @ A2 @ B2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Un_insert_right
% 0.30/0.59  thf(fact_6295_Un__insert__right,axiom,
% 0.30/0.59      ! [A2: set_Pr8551490117392284871at_nat,A: produc4166570645942440679at_nat,B2: set_Pr8551490117392284871at_nat] :
% 0.30/0.59        ( ( sup_su3035147773818789531at_nat @ A2 @ ( insert6337962749363155127at_nat @ A @ B2 ) )
% 0.30/0.59        = ( insert6337962749363155127at_nat @ A @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Un_insert_right
% 0.30/0.59  thf(fact_6296_Un__insert__right,axiom,
% 0.30/0.59      ! [A2: set_Pr4329608150637261639at_nat,A: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.59        ( ( sup_su5525570899277871387at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ B2 ) )
% 0.30/0.59        = ( insert9069300056098147895at_nat @ A @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Un_insert_right
% 0.30/0.59  thf(fact_6297_Un__insert__right,axiom,
% 0.30/0.59      ! [A2: set_nat,A: nat,B2: set_nat] :
% 0.30/0.59        ( ( sup_sup_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 0.30/0.59        = ( insert_nat @ A @ ( sup_sup_set_nat @ A2 @ B2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Un_insert_right
% 0.30/0.59  thf(fact_6298_Un__insert__left,axiom,
% 0.30/0.59      ! [A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 0.30/0.59        ( ( sup_su6327502436637775413at_nat @ ( insert8211810215607154385at_nat @ A @ B2 ) @ C2 )
% 0.30/0.59        = ( insert8211810215607154385at_nat @ A @ ( sup_su6327502436637775413at_nat @ B2 @ C2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Un_insert_left
% 0.30/0.59  thf(fact_6299_Un__insert__left,axiom,
% 0.30/0.59      ! [A: $o,B2: set_o,C2: set_o] :
% 0.30/0.59        ( ( sup_sup_set_o @ ( insert_o @ A @ B2 ) @ C2 )
% 0.30/0.59        = ( insert_o @ A @ ( sup_sup_set_o @ B2 @ C2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Un_insert_left
% 0.30/0.59  thf(fact_6300_Un__insert__left,axiom,
% 0.30/0.59      ! [A: int,B2: set_int,C2: set_int] :
% 0.30/0.59        ( ( sup_sup_set_int @ ( insert_int @ A @ B2 ) @ C2 )
% 0.30/0.59        = ( insert_int @ A @ ( sup_sup_set_int @ B2 @ C2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Un_insert_left
% 0.30/0.59  thf(fact_6301_Un__insert__left,axiom,
% 0.30/0.59      ! [A: produc4166570645942440679at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 0.30/0.59        ( ( sup_su3035147773818789531at_nat @ ( insert6337962749363155127at_nat @ A @ B2 ) @ C2 )
% 0.30/0.59        = ( insert6337962749363155127at_nat @ A @ ( sup_su3035147773818789531at_nat @ B2 @ C2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Un_insert_left
% 0.30/0.59  thf(fact_6302_Un__insert__left,axiom,
% 0.30/0.59      ! [A: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 0.30/0.59        ( ( sup_su5525570899277871387at_nat @ ( insert9069300056098147895at_nat @ A @ B2 ) @ C2 )
% 0.30/0.59        = ( insert9069300056098147895at_nat @ A @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Un_insert_left
% 0.30/0.59  thf(fact_6303_Un__insert__left,axiom,
% 0.30/0.59      ! [A: nat,B2: set_nat,C2: set_nat] :
% 0.30/0.59        ( ( sup_sup_set_nat @ ( insert_nat @ A @ B2 ) @ C2 )
% 0.30/0.59        = ( insert_nat @ A @ ( sup_sup_set_nat @ B2 @ C2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Un_insert_left
% 0.30/0.59  thf(fact_6304_singleton__conv2,axiom,
% 0.30/0.59      ! [A: produc3843707927480180839at_nat] :
% 0.30/0.59        ( ( collec6321179662152712658at_nat
% 0.30/0.59          @ ( ^ [Y4: produc3843707927480180839at_nat,Z4: produc3843707927480180839at_nat] : ( Y4 = Z4 )
% 0.30/0.59            @ A ) )
% 0.30/0.59        = ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_conv2
% 0.30/0.59  thf(fact_6305_singleton__conv2,axiom,
% 0.30/0.59      ! [A: set_Pr958786334691620121nt_int] :
% 0.30/0.59        ( ( collec5210948495886036740nt_int
% 0.30/0.59          @ ( ^ [Y4: set_Pr958786334691620121nt_int,Z4: set_Pr958786334691620121nt_int] : ( Y4 = Z4 )
% 0.30/0.59            @ A ) )
% 0.30/0.59        = ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_conv2
% 0.30/0.59  thf(fact_6306_singleton__conv2,axiom,
% 0.30/0.59      ! [A: set_nat] :
% 0.30/0.59        ( ( collect_set_nat
% 0.30/0.59          @ ( ^ [Y4: set_nat,Z4: set_nat] : ( Y4 = Z4 )
% 0.30/0.59            @ A ) )
% 0.30/0.59        = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_conv2
% 0.30/0.59  thf(fact_6307_singleton__conv2,axiom,
% 0.30/0.59      ! [A: produc3658429121746597890et_nat > $o] :
% 0.30/0.59        ( ( collec939566748876313656_nat_o
% 0.30/0.59          @ ( ^ [Y4: produc3658429121746597890et_nat > $o,Z4: produc3658429121746597890et_nat > $o] : ( Y4 = Z4 )
% 0.30/0.59            @ A ) )
% 0.30/0.59        = ( insert5175938949040314269_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_conv2
% 0.30/0.59  thf(fact_6308_singleton__conv2,axiom,
% 0.30/0.59      ! [A: product_prod_nat_nat] :
% 0.30/0.59        ( ( collec3392354462482085612at_nat
% 0.30/0.59          @ ( ^ [Y4: product_prod_nat_nat,Z4: product_prod_nat_nat] : ( Y4 = Z4 )
% 0.30/0.59            @ A ) )
% 0.30/0.59        = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_conv2
% 0.30/0.59  thf(fact_6309_singleton__conv2,axiom,
% 0.30/0.59      ! [A: $o] :
% 0.30/0.59        ( ( collect_o
% 0.30/0.59          @ ( ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 0.30/0.59            @ A ) )
% 0.30/0.59        = ( insert_o @ A @ bot_bot_set_o ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_conv2
% 0.30/0.59  thf(fact_6310_singleton__conv2,axiom,
% 0.30/0.59      ! [A: nat] :
% 0.30/0.59        ( ( collect_nat
% 0.30/0.59          @ ( ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 )
% 0.30/0.59            @ A ) )
% 0.30/0.59        = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_conv2
% 0.30/0.59  thf(fact_6311_singleton__conv2,axiom,
% 0.30/0.59      ! [A: int] :
% 0.30/0.59        ( ( collect_int
% 0.30/0.59          @ ( ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 0.30/0.59            @ A ) )
% 0.30/0.59        = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_conv2
% 0.30/0.59  thf(fact_6312_singleton__conv,axiom,
% 0.30/0.59      ! [A: produc3843707927480180839at_nat] :
% 0.30/0.59        ( ( collec6321179662152712658at_nat
% 0.30/0.59          @ ^ [X3: produc3843707927480180839at_nat] : ( X3 = A ) )
% 0.30/0.59        = ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_conv
% 0.30/0.59  thf(fact_6313_singleton__conv,axiom,
% 0.30/0.59      ! [A: set_Pr958786334691620121nt_int] :
% 0.30/0.59        ( ( collec5210948495886036740nt_int
% 0.30/0.59          @ ^ [X3: set_Pr958786334691620121nt_int] : ( X3 = A ) )
% 0.30/0.59        = ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_conv
% 0.30/0.59  thf(fact_6314_singleton__conv,axiom,
% 0.30/0.59      ! [A: set_nat] :
% 0.30/0.59        ( ( collect_set_nat
% 0.30/0.59          @ ^ [X3: set_nat] : ( X3 = A ) )
% 0.30/0.59        = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_conv
% 0.30/0.59  thf(fact_6315_singleton__conv,axiom,
% 0.30/0.59      ! [A: produc3658429121746597890et_nat > $o] :
% 0.30/0.59        ( ( collec939566748876313656_nat_o
% 0.30/0.59          @ ^ [X3: produc3658429121746597890et_nat > $o] : ( X3 = A ) )
% 0.30/0.59        = ( insert5175938949040314269_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_conv
% 0.30/0.59  thf(fact_6316_singleton__conv,axiom,
% 0.30/0.59      ! [A: product_prod_nat_nat] :
% 0.30/0.59        ( ( collec3392354462482085612at_nat
% 0.30/0.59          @ ^ [X3: product_prod_nat_nat] : ( X3 = A ) )
% 0.30/0.59        = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_conv
% 0.30/0.59  thf(fact_6317_singleton__conv,axiom,
% 0.30/0.59      ! [A: $o] :
% 0.30/0.59        ( ( collect_o
% 0.30/0.59          @ ^ [X3: $o] : ( X3 = A ) )
% 0.30/0.59        = ( insert_o @ A @ bot_bot_set_o ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_conv
% 0.30/0.59  thf(fact_6318_singleton__conv,axiom,
% 0.30/0.59      ! [A: nat] :
% 0.30/0.59        ( ( collect_nat
% 0.30/0.59          @ ^ [X3: nat] : ( X3 = A ) )
% 0.30/0.59        = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_conv
% 0.30/0.59  thf(fact_6319_singleton__conv,axiom,
% 0.30/0.59      ! [A: int] :
% 0.30/0.59        ( ( collect_int
% 0.30/0.59          @ ^ [X3: int] : ( X3 = A ) )
% 0.30/0.59        = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_conv
% 0.30/0.59  thf(fact_6320_singleton__insert__inj__eq,axiom,
% 0.30/0.59      ! [B: produc3843707927480180839at_nat,A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.30/0.59        ( ( ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat )
% 0.30/0.59          = ( insert9069300056098147895at_nat @ A @ A2 ) )
% 0.30/0.59        = ( ( A = B )
% 0.30/0.59          & ( ord_le1268244103169919719at_nat @ A2 @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_insert_inj_eq
% 0.30/0.59  thf(fact_6321_singleton__insert__inj__eq,axiom,
% 0.30/0.59      ! [B: product_prod_nat_nat,A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.30/0.59        ( ( ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat )
% 0.30/0.59          = ( insert8211810215607154385at_nat @ A @ A2 ) )
% 0.30/0.59        = ( ( A = B )
% 0.30/0.59          & ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_insert_inj_eq
% 0.30/0.59  thf(fact_6322_singleton__insert__inj__eq,axiom,
% 0.30/0.59      ! [B: $o,A: $o,A2: set_o] :
% 0.30/0.59        ( ( ( insert_o @ B @ bot_bot_set_o )
% 0.30/0.59          = ( insert_o @ A @ A2 ) )
% 0.30/0.59        = ( ( A = B )
% 0.30/0.59          & ( ord_less_eq_set_o @ A2 @ ( insert_o @ B @ bot_bot_set_o ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_insert_inj_eq
% 0.30/0.59  thf(fact_6323_singleton__insert__inj__eq,axiom,
% 0.30/0.59      ! [B: int,A: int,A2: set_int] :
% 0.30/0.59        ( ( ( insert_int @ B @ bot_bot_set_int )
% 0.30/0.59          = ( insert_int @ A @ A2 ) )
% 0.30/0.59        = ( ( A = B )
% 0.30/0.59          & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_insert_inj_eq
% 0.30/0.59  thf(fact_6324_singleton__insert__inj__eq,axiom,
% 0.30/0.59      ! [B: nat,A: nat,A2: set_nat] :
% 0.30/0.59        ( ( ( insert_nat @ B @ bot_bot_set_nat )
% 0.30/0.59          = ( insert_nat @ A @ A2 ) )
% 0.30/0.59        = ( ( A = B )
% 0.30/0.59          & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_insert_inj_eq
% 0.30/0.59  thf(fact_6325_singleton__insert__inj__eq_H,axiom,
% 0.30/0.59      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B: produc3843707927480180839at_nat] :
% 0.30/0.59        ( ( ( insert9069300056098147895at_nat @ A @ A2 )
% 0.30/0.59          = ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) )
% 0.30/0.59        = ( ( A = B )
% 0.30/0.59          & ( ord_le1268244103169919719at_nat @ A2 @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_insert_inj_eq'
% 0.30/0.59  thf(fact_6326_singleton__insert__inj__eq_H,axiom,
% 0.30/0.59      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat] :
% 0.30/0.59        ( ( ( insert8211810215607154385at_nat @ A @ A2 )
% 0.30/0.59          = ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) )
% 0.30/0.59        = ( ( A = B )
% 0.30/0.59          & ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_insert_inj_eq'
% 0.30/0.59  thf(fact_6327_singleton__insert__inj__eq_H,axiom,
% 0.30/0.59      ! [A: $o,A2: set_o,B: $o] :
% 0.30/0.59        ( ( ( insert_o @ A @ A2 )
% 0.30/0.59          = ( insert_o @ B @ bot_bot_set_o ) )
% 0.30/0.59        = ( ( A = B )
% 0.30/0.59          & ( ord_less_eq_set_o @ A2 @ ( insert_o @ B @ bot_bot_set_o ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_insert_inj_eq'
% 0.30/0.59  thf(fact_6328_singleton__insert__inj__eq_H,axiom,
% 0.30/0.59      ! [A: int,A2: set_int,B: int] :
% 0.30/0.59        ( ( ( insert_int @ A @ A2 )
% 0.30/0.59          = ( insert_int @ B @ bot_bot_set_int ) )
% 0.30/0.59        = ( ( A = B )
% 0.30/0.59          & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_insert_inj_eq'
% 0.30/0.59  thf(fact_6329_singleton__insert__inj__eq_H,axiom,
% 0.30/0.59      ! [A: nat,A2: set_nat,B: nat] :
% 0.30/0.59        ( ( ( insert_nat @ A @ A2 )
% 0.30/0.59          = ( insert_nat @ B @ bot_bot_set_nat ) )
% 0.30/0.59        = ( ( A = B )
% 0.30/0.59          & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_insert_inj_eq'
% 0.30/0.59  thf(fact_6330_insert__disjoint_I1_J,axiom,
% 0.30/0.59      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.59        ( ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A @ A2 ) @ B2 )
% 0.30/0.59          = bot_bo228742789529271731at_nat )
% 0.30/0.59        = ( ~ ( member8757157785044589968at_nat @ A @ B2 )
% 0.30/0.59          & ( ( inf_in7913087082777306421at_nat @ A2 @ B2 )
% 0.30/0.59            = bot_bo228742789529271731at_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_disjoint(1)
% 0.30/0.59  thf(fact_6331_insert__disjoint_I1_J,axiom,
% 0.30/0.59      ! [A: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 0.30/0.59        ( ( ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ A2 ) @ B2 )
% 0.30/0.59          = bot_bo1488462491386950373nt_int )
% 0.30/0.59        = ( ~ ( member2340774599025711042nt_int @ A @ B2 )
% 0.30/0.59          & ( ( inf_in8396524679539076455nt_int @ A2 @ B2 )
% 0.30/0.59            = bot_bo1488462491386950373nt_int ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_disjoint(1)
% 0.30/0.59  thf(fact_6332_insert__disjoint_I1_J,axiom,
% 0.30/0.59      ! [A: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.30/0.59        ( ( ( inf_inf_set_set_nat @ ( insert_set_nat @ A @ A2 ) @ B2 )
% 0.30/0.59          = bot_bot_set_set_nat )
% 0.30/0.59        = ( ~ ( member_set_nat @ A @ B2 )
% 0.30/0.59          & ( ( inf_inf_set_set_nat @ A2 @ B2 )
% 0.30/0.59            = bot_bot_set_set_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_disjoint(1)
% 0.30/0.59  thf(fact_6333_insert__disjoint_I1_J,axiom,
% 0.30/0.59      ! [A: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 0.30/0.59        ( ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A @ A2 ) @ B2 )
% 0.30/0.59          = bot_bo7824918357723582233_nat_o )
% 0.30/0.59        = ( ~ ( member6576561426505652726_nat_o @ A @ B2 )
% 0.30/0.59          & ( ( inf_in1906310914598751387_nat_o @ A2 @ B2 )
% 0.30/0.59            = bot_bo7824918357723582233_nat_o ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_disjoint(1)
% 0.30/0.59  thf(fact_6334_insert__disjoint_I1_J,axiom,
% 0.30/0.59      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.59        ( ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ A2 ) @ B2 )
% 0.30/0.59          = bot_bo2099793752762293965at_nat )
% 0.30/0.59        = ( ~ ( member8440522571783428010at_nat @ A @ B2 )
% 0.30/0.59          & ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 0.30/0.59            = bot_bo2099793752762293965at_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_disjoint(1)
% 0.30/0.59  thf(fact_6335_insert__disjoint_I1_J,axiom,
% 0.30/0.59      ! [A: $o,A2: set_o,B2: set_o] :
% 0.30/0.59        ( ( ( inf_inf_set_o @ ( insert_o @ A @ A2 ) @ B2 )
% 0.30/0.59          = bot_bot_set_o )
% 0.30/0.59        = ( ~ ( member_o @ A @ B2 )
% 0.30/0.59          & ( ( inf_inf_set_o @ A2 @ B2 )
% 0.30/0.59            = bot_bot_set_o ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_disjoint(1)
% 0.30/0.59  thf(fact_6336_insert__disjoint_I1_J,axiom,
% 0.30/0.59      ! [A: nat,A2: set_nat,B2: set_nat] :
% 0.30/0.59        ( ( ( inf_inf_set_nat @ ( insert_nat @ A @ A2 ) @ B2 )
% 0.30/0.59          = bot_bot_set_nat )
% 0.30/0.59        = ( ~ ( member_nat @ A @ B2 )
% 0.30/0.59          & ( ( inf_inf_set_nat @ A2 @ B2 )
% 0.30/0.59            = bot_bot_set_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_disjoint(1)
% 0.30/0.59  thf(fact_6337_insert__disjoint_I1_J,axiom,
% 0.30/0.59      ! [A: int,A2: set_int,B2: set_int] :
% 0.30/0.59        ( ( ( inf_inf_set_int @ ( insert_int @ A @ A2 ) @ B2 )
% 0.30/0.59          = bot_bot_set_int )
% 0.30/0.59        = ( ~ ( member_int @ A @ B2 )
% 0.30/0.59          & ( ( inf_inf_set_int @ A2 @ B2 )
% 0.30/0.59            = bot_bot_set_int ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_disjoint(1)
% 0.30/0.59  thf(fact_6338_insert__disjoint_I2_J,axiom,
% 0.30/0.59      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.59        ( ( bot_bo228742789529271731at_nat
% 0.30/0.59          = ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A @ A2 ) @ B2 ) )
% 0.30/0.59        = ( ~ ( member8757157785044589968at_nat @ A @ B2 )
% 0.30/0.59          & ( bot_bo228742789529271731at_nat
% 0.30/0.59            = ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_disjoint(2)
% 0.30/0.59  thf(fact_6339_insert__disjoint_I2_J,axiom,
% 0.30/0.59      ! [A: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 0.30/0.59        ( ( bot_bo1488462491386950373nt_int
% 0.30/0.59          = ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ A2 ) @ B2 ) )
% 0.30/0.59        = ( ~ ( member2340774599025711042nt_int @ A @ B2 )
% 0.30/0.59          & ( bot_bo1488462491386950373nt_int
% 0.30/0.59            = ( inf_in8396524679539076455nt_int @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_disjoint(2)
% 0.30/0.59  thf(fact_6340_insert__disjoint_I2_J,axiom,
% 0.30/0.59      ! [A: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.30/0.59        ( ( bot_bot_set_set_nat
% 0.30/0.59          = ( inf_inf_set_set_nat @ ( insert_set_nat @ A @ A2 ) @ B2 ) )
% 0.30/0.59        = ( ~ ( member_set_nat @ A @ B2 )
% 0.30/0.59          & ( bot_bot_set_set_nat
% 0.30/0.59            = ( inf_inf_set_set_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_disjoint(2)
% 0.30/0.59  thf(fact_6341_insert__disjoint_I2_J,axiom,
% 0.30/0.59      ! [A: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 0.30/0.59        ( ( bot_bo7824918357723582233_nat_o
% 0.30/0.59          = ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A @ A2 ) @ B2 ) )
% 0.30/0.59        = ( ~ ( member6576561426505652726_nat_o @ A @ B2 )
% 0.30/0.59          & ( bot_bo7824918357723582233_nat_o
% 0.30/0.59            = ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_disjoint(2)
% 0.30/0.59  thf(fact_6342_insert__disjoint_I2_J,axiom,
% 0.30/0.59      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.59        ( ( bot_bo2099793752762293965at_nat
% 0.30/0.59          = ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ A2 ) @ B2 ) )
% 0.30/0.59        = ( ~ ( member8440522571783428010at_nat @ A @ B2 )
% 0.30/0.59          & ( bot_bo2099793752762293965at_nat
% 0.30/0.59            = ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_disjoint(2)
% 0.30/0.59  thf(fact_6343_insert__disjoint_I2_J,axiom,
% 0.30/0.59      ! [A: $o,A2: set_o,B2: set_o] :
% 0.30/0.59        ( ( bot_bot_set_o
% 0.30/0.59          = ( inf_inf_set_o @ ( insert_o @ A @ A2 ) @ B2 ) )
% 0.30/0.59        = ( ~ ( member_o @ A @ B2 )
% 0.30/0.59          & ( bot_bot_set_o
% 0.30/0.59            = ( inf_inf_set_o @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_disjoint(2)
% 0.30/0.59  thf(fact_6344_insert__disjoint_I2_J,axiom,
% 0.30/0.59      ! [A: nat,A2: set_nat,B2: set_nat] :
% 0.30/0.59        ( ( bot_bot_set_nat
% 0.30/0.59          = ( inf_inf_set_nat @ ( insert_nat @ A @ A2 ) @ B2 ) )
% 0.30/0.59        = ( ~ ( member_nat @ A @ B2 )
% 0.30/0.59          & ( bot_bot_set_nat
% 0.30/0.59            = ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_disjoint(2)
% 0.30/0.59  thf(fact_6345_insert__disjoint_I2_J,axiom,
% 0.30/0.59      ! [A: int,A2: set_int,B2: set_int] :
% 0.30/0.59        ( ( bot_bot_set_int
% 0.30/0.59          = ( inf_inf_set_int @ ( insert_int @ A @ A2 ) @ B2 ) )
% 0.30/0.59        = ( ~ ( member_int @ A @ B2 )
% 0.30/0.59          & ( bot_bot_set_int
% 0.30/0.59            = ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_disjoint(2)
% 0.30/0.59  thf(fact_6346_disjoint__insert_I1_J,axiom,
% 0.30/0.59      ! [B2: set_Pr4329608150637261639at_nat,A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.30/0.59        ( ( ( inf_in7913087082777306421at_nat @ B2 @ ( insert9069300056098147895at_nat @ A @ A2 ) )
% 0.30/0.59          = bot_bo228742789529271731at_nat )
% 0.30/0.59        = ( ~ ( member8757157785044589968at_nat @ A @ B2 )
% 0.30/0.59          & ( ( inf_in7913087082777306421at_nat @ B2 @ A2 )
% 0.30/0.59            = bot_bo228742789529271731at_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % disjoint_insert(1)
% 0.30/0.59  thf(fact_6347_disjoint__insert_I1_J,axiom,
% 0.30/0.59      ! [B2: set_se6260736226359567993nt_int,A: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int] :
% 0.30/0.59        ( ( ( inf_in8396524679539076455nt_int @ B2 @ ( insert8897473484851387113nt_int @ A @ A2 ) )
% 0.30/0.59          = bot_bo1488462491386950373nt_int )
% 0.30/0.59        = ( ~ ( member2340774599025711042nt_int @ A @ B2 )
% 0.30/0.59          & ( ( inf_in8396524679539076455nt_int @ B2 @ A2 )
% 0.30/0.59            = bot_bo1488462491386950373nt_int ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % disjoint_insert(1)
% 0.30/0.59  thf(fact_6348_disjoint__insert_I1_J,axiom,
% 0.30/0.59      ! [B2: set_set_nat,A: set_nat,A2: set_set_nat] :
% 0.30/0.59        ( ( ( inf_inf_set_set_nat @ B2 @ ( insert_set_nat @ A @ A2 ) )
% 0.30/0.59          = bot_bot_set_set_nat )
% 0.30/0.59        = ( ~ ( member_set_nat @ A @ B2 )
% 0.30/0.59          & ( ( inf_inf_set_set_nat @ B2 @ A2 )
% 0.30/0.59            = bot_bot_set_set_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % disjoint_insert(1)
% 0.30/0.59  thf(fact_6349_disjoint__insert_I1_J,axiom,
% 0.30/0.59      ! [B2: set_Pr4532377907799695533_nat_o,A: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o] :
% 0.30/0.59        ( ( ( inf_in1906310914598751387_nat_o @ B2 @ ( insert5175938949040314269_nat_o @ A @ A2 ) )
% 0.30/0.59          = bot_bo7824918357723582233_nat_o )
% 0.30/0.59        = ( ~ ( member6576561426505652726_nat_o @ A @ B2 )
% 0.30/0.59          & ( ( inf_in1906310914598751387_nat_o @ B2 @ A2 )
% 0.30/0.59            = bot_bo7824918357723582233_nat_o ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % disjoint_insert(1)
% 0.30/0.59  thf(fact_6350_disjoint__insert_I1_J,axiom,
% 0.30/0.59      ! [B2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.30/0.59        ( ( ( inf_in2572325071724192079at_nat @ B2 @ ( insert8211810215607154385at_nat @ A @ A2 ) )
% 0.30/0.59          = bot_bo2099793752762293965at_nat )
% 0.30/0.59        = ( ~ ( member8440522571783428010at_nat @ A @ B2 )
% 0.30/0.59          & ( ( inf_in2572325071724192079at_nat @ B2 @ A2 )
% 0.30/0.59            = bot_bo2099793752762293965at_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % disjoint_insert(1)
% 0.30/0.59  thf(fact_6351_disjoint__insert_I1_J,axiom,
% 0.30/0.59      ! [B2: set_o,A: $o,A2: set_o] :
% 0.30/0.59        ( ( ( inf_inf_set_o @ B2 @ ( insert_o @ A @ A2 ) )
% 0.30/0.59          = bot_bot_set_o )
% 0.30/0.59        = ( ~ ( member_o @ A @ B2 )
% 0.30/0.59          & ( ( inf_inf_set_o @ B2 @ A2 )
% 0.30/0.59            = bot_bot_set_o ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % disjoint_insert(1)
% 0.30/0.59  thf(fact_6352_disjoint__insert_I1_J,axiom,
% 0.30/0.59      ! [B2: set_nat,A: nat,A2: set_nat] :
% 0.30/0.59        ( ( ( inf_inf_set_nat @ B2 @ ( insert_nat @ A @ A2 ) )
% 0.30/0.59          = bot_bot_set_nat )
% 0.30/0.59        = ( ~ ( member_nat @ A @ B2 )
% 0.30/0.59          & ( ( inf_inf_set_nat @ B2 @ A2 )
% 0.30/0.59            = bot_bot_set_nat ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % disjoint_insert(1)
% 0.30/0.59  thf(fact_6353_disjoint__insert_I1_J,axiom,
% 0.30/0.59      ! [B2: set_int,A: int,A2: set_int] :
% 0.30/0.59        ( ( ( inf_inf_set_int @ B2 @ ( insert_int @ A @ A2 ) )
% 0.30/0.59          = bot_bot_set_int )
% 0.30/0.59        = ( ~ ( member_int @ A @ B2 )
% 0.30/0.59          & ( ( inf_inf_set_int @ B2 @ A2 )
% 0.30/0.59            = bot_bot_set_int ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % disjoint_insert(1)
% 0.30/0.59  thf(fact_6354_disjoint__insert_I2_J,axiom,
% 0.30/0.59      ! [A2: set_Pr4329608150637261639at_nat,B: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.59        ( ( bot_bo228742789529271731at_nat
% 0.30/0.59          = ( inf_in7913087082777306421at_nat @ A2 @ ( insert9069300056098147895at_nat @ B @ B2 ) ) )
% 0.30/0.59        = ( ~ ( member8757157785044589968at_nat @ B @ A2 )
% 0.30/0.59          & ( bot_bo228742789529271731at_nat
% 0.30/0.59            = ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % disjoint_insert(2)
% 0.30/0.59  thf(fact_6355_disjoint__insert_I2_J,axiom,
% 0.30/0.59      ! [A2: set_se6260736226359567993nt_int,B: set_Pr958786334691620121nt_int,B2: set_se6260736226359567993nt_int] :
% 0.30/0.59        ( ( bot_bo1488462491386950373nt_int
% 0.30/0.59          = ( inf_in8396524679539076455nt_int @ A2 @ ( insert8897473484851387113nt_int @ B @ B2 ) ) )
% 0.30/0.59        = ( ~ ( member2340774599025711042nt_int @ B @ A2 )
% 0.30/0.59          & ( bot_bo1488462491386950373nt_int
% 0.30/0.59            = ( inf_in8396524679539076455nt_int @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % disjoint_insert(2)
% 0.30/0.59  thf(fact_6356_disjoint__insert_I2_J,axiom,
% 0.30/0.59      ! [A2: set_set_nat,B: set_nat,B2: set_set_nat] :
% 0.30/0.59        ( ( bot_bot_set_set_nat
% 0.30/0.59          = ( inf_inf_set_set_nat @ A2 @ ( insert_set_nat @ B @ B2 ) ) )
% 0.30/0.59        = ( ~ ( member_set_nat @ B @ A2 )
% 0.30/0.59          & ( bot_bot_set_set_nat
% 0.30/0.59            = ( inf_inf_set_set_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % disjoint_insert(2)
% 0.30/0.59  thf(fact_6357_disjoint__insert_I2_J,axiom,
% 0.30/0.59      ! [A2: set_Pr4532377907799695533_nat_o,B: produc3658429121746597890et_nat > $o,B2: set_Pr4532377907799695533_nat_o] :
% 0.30/0.59        ( ( bot_bo7824918357723582233_nat_o
% 0.30/0.59          = ( inf_in1906310914598751387_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ B @ B2 ) ) )
% 0.30/0.59        = ( ~ ( member6576561426505652726_nat_o @ B @ A2 )
% 0.30/0.59          & ( bot_bo7824918357723582233_nat_o
% 0.30/0.59            = ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % disjoint_insert(2)
% 0.30/0.59  thf(fact_6358_disjoint__insert_I2_J,axiom,
% 0.30/0.59      ! [A2: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.59        ( ( bot_bo2099793752762293965at_nat
% 0.30/0.59          = ( inf_in2572325071724192079at_nat @ A2 @ ( insert8211810215607154385at_nat @ B @ B2 ) ) )
% 0.30/0.59        = ( ~ ( member8440522571783428010at_nat @ B @ A2 )
% 0.30/0.59          & ( bot_bo2099793752762293965at_nat
% 0.30/0.59            = ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % disjoint_insert(2)
% 0.30/0.59  thf(fact_6359_disjoint__insert_I2_J,axiom,
% 0.30/0.59      ! [A2: set_o,B: $o,B2: set_o] :
% 0.30/0.59        ( ( bot_bot_set_o
% 0.30/0.59          = ( inf_inf_set_o @ A2 @ ( insert_o @ B @ B2 ) ) )
% 0.30/0.59        = ( ~ ( member_o @ B @ A2 )
% 0.30/0.59          & ( bot_bot_set_o
% 0.30/0.59            = ( inf_inf_set_o @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % disjoint_insert(2)
% 0.30/0.59  thf(fact_6360_disjoint__insert_I2_J,axiom,
% 0.30/0.59      ! [A2: set_nat,B: nat,B2: set_nat] :
% 0.30/0.59        ( ( bot_bot_set_nat
% 0.30/0.59          = ( inf_inf_set_nat @ A2 @ ( insert_nat @ B @ B2 ) ) )
% 0.30/0.59        = ( ~ ( member_nat @ B @ A2 )
% 0.30/0.59          & ( bot_bot_set_nat
% 0.30/0.59            = ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % disjoint_insert(2)
% 0.30/0.59  thf(fact_6361_disjoint__insert_I2_J,axiom,
% 0.30/0.59      ! [A2: set_int,B: int,B2: set_int] :
% 0.30/0.59        ( ( bot_bot_set_int
% 0.30/0.59          = ( inf_inf_set_int @ A2 @ ( insert_int @ B @ B2 ) ) )
% 0.30/0.59        = ( ~ ( member_int @ B @ A2 )
% 0.30/0.59          & ( bot_bot_set_int
% 0.30/0.59            = ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % disjoint_insert(2)
% 0.30/0.59  thf(fact_6362_insert__Diff__single,axiom,
% 0.30/0.59      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.30/0.59        ( ( insert9069300056098147895at_nat @ A @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) )
% 0.30/0.59        = ( insert9069300056098147895at_nat @ A @ A2 ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_Diff_single
% 0.30/0.59  thf(fact_6363_insert__Diff__single,axiom,
% 0.30/0.59      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.30/0.59        ( ( insert8211810215607154385at_nat @ A @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 0.30/0.59        = ( insert8211810215607154385at_nat @ A @ A2 ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_Diff_single
% 0.30/0.59  thf(fact_6364_insert__Diff__single,axiom,
% 0.30/0.59      ! [A: $o,A2: set_o] :
% 0.30/0.59        ( ( insert_o @ A @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.30/0.59        = ( insert_o @ A @ A2 ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_Diff_single
% 0.30/0.59  thf(fact_6365_insert__Diff__single,axiom,
% 0.30/0.59      ! [A: int,A2: set_int] :
% 0.30/0.59        ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.30/0.59        = ( insert_int @ A @ A2 ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_Diff_single
% 0.30/0.59  thf(fact_6366_insert__Diff__single,axiom,
% 0.30/0.59      ! [A: nat,A2: set_nat] :
% 0.30/0.59        ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.30/0.59        = ( insert_nat @ A @ A2 ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_Diff_single
% 0.30/0.59  thf(fact_6367_round__1,axiom,
% 0.30/0.59      ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 0.30/0.59      = one_one_int ) ).
% 0.30/0.59  
% 0.30/0.59  % round_1
% 0.30/0.59  thf(fact_6368_subset__Compl__singleton,axiom,
% 0.30/0.59      ! [A2: set_Pr4329608150637261639at_nat,B: produc3843707927480180839at_nat] :
% 0.30/0.59        ( ( ord_le1268244103169919719at_nat @ A2 @ ( uminus935396558254630718at_nat @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) )
% 0.30/0.59        = ( ~ ( member8757157785044589968at_nat @ B @ A2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % subset_Compl_singleton
% 0.30/0.59  thf(fact_6369_subset__Compl__singleton,axiom,
% 0.30/0.59      ! [A2: set_se6260736226359567993nt_int,B: set_Pr958786334691620121nt_int] :
% 0.30/0.59        ( ( ord_le483042692224249369nt_int @ A2 @ ( uminus6423885277529793776nt_int @ ( insert8897473484851387113nt_int @ B @ bot_bo1488462491386950373nt_int ) ) )
% 0.30/0.59        = ( ~ ( member2340774599025711042nt_int @ B @ A2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % subset_Compl_singleton
% 0.30/0.59  thf(fact_6370_subset__Compl__singleton,axiom,
% 0.30/0.59      ! [A2: set_set_nat,B: set_nat] :
% 0.30/0.59        ( ( ord_le6893508408891458716et_nat @ A2 @ ( uminus613421341184616069et_nat @ ( insert_set_nat @ B @ bot_bot_set_set_nat ) ) )
% 0.30/0.59        = ( ~ ( member_set_nat @ B @ A2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % subset_Compl_singleton
% 0.30/0.59  thf(fact_6371_subset__Compl__singleton,axiom,
% 0.30/0.59      ! [A2: set_Pr4532377907799695533_nat_o,B: produc3658429121746597890et_nat > $o] :
% 0.30/0.59        ( ( ord_le2965882846123202637_nat_o @ A2 @ ( uminus5254974436814262692_nat_o @ ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) ) )
% 0.30/0.59        = ( ~ ( member6576561426505652726_nat_o @ B @ A2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % subset_Compl_singleton
% 0.30/0.59  thf(fact_6372_subset__Compl__singleton,axiom,
% 0.30/0.59      ! [A2: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat] :
% 0.30/0.59        ( ( ord_le3146513528884898305at_nat @ A2 @ ( uminus6524753893492686040at_nat @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) )
% 0.30/0.59        = ( ~ ( member8440522571783428010at_nat @ B @ A2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % subset_Compl_singleton
% 0.30/0.59  thf(fact_6373_subset__Compl__singleton,axiom,
% 0.30/0.59      ! [A2: set_o,B: $o] :
% 0.30/0.59        ( ( ord_less_eq_set_o @ A2 @ ( uminus_uminus_set_o @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 0.30/0.59        = ( ~ ( member_o @ B @ A2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % subset_Compl_singleton
% 0.30/0.59  thf(fact_6374_subset__Compl__singleton,axiom,
% 0.30/0.59      ! [A2: set_int,B: int] :
% 0.30/0.59        ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 0.30/0.59        = ( ~ ( member_int @ B @ A2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % subset_Compl_singleton
% 0.30/0.59  thf(fact_6375_subset__Compl__singleton,axiom,
% 0.30/0.59      ! [A2: set_nat,B: nat] :
% 0.30/0.59        ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 0.30/0.59        = ( ~ ( member_nat @ B @ A2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % subset_Compl_singleton
% 0.30/0.59  thf(fact_6376_push__bit__Suc__minus__numeral,axiom,
% 0.30/0.59      ! [N: nat,K: num] :
% 0.30/0.59        ( ( bit_se7788150548672797655nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.30/0.59        = ( bit_se7788150548672797655nteger @ N @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % push_bit_Suc_minus_numeral
% 0.30/0.59  thf(fact_6377_push__bit__Suc__minus__numeral,axiom,
% 0.30/0.59      ! [N: nat,K: num] :
% 0.30/0.59        ( ( bit_se545348938243370406it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.30/0.59        = ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % push_bit_Suc_minus_numeral
% 0.30/0.59  thf(fact_6378_round__neg__numeral,axiom,
% 0.30/0.59      ! [N: num] :
% 0.30/0.59        ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.30/0.59        = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % round_neg_numeral
% 0.30/0.59  thf(fact_6379_push__bit__Suc,axiom,
% 0.30/0.59      ! [N: nat,A: code_integer] :
% 0.30/0.59        ( ( bit_se7788150548672797655nteger @ ( suc @ N ) @ A )
% 0.30/0.59        = ( bit_se7788150548672797655nteger @ N @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % push_bit_Suc
% 0.30/0.59  thf(fact_6380_push__bit__Suc,axiom,
% 0.30/0.59      ! [N: nat,A: code_natural] :
% 0.30/0.59        ( ( bit_se6611745700429515170atural @ ( suc @ N ) @ A )
% 0.30/0.59        = ( bit_se6611745700429515170atural @ N @ ( times_2397367101498566445atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % push_bit_Suc
% 0.30/0.59  thf(fact_6381_push__bit__Suc,axiom,
% 0.30/0.59      ! [N: nat,A: int] :
% 0.30/0.59        ( ( bit_se545348938243370406it_int @ ( suc @ N ) @ A )
% 0.30/0.59        = ( bit_se545348938243370406it_int @ N @ ( times_times_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % push_bit_Suc
% 0.30/0.59  thf(fact_6382_push__bit__Suc,axiom,
% 0.30/0.59      ! [N: nat,A: nat] :
% 0.30/0.59        ( ( bit_se547839408752420682it_nat @ ( suc @ N ) @ A )
% 0.30/0.59        = ( bit_se547839408752420682it_nat @ N @ ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % push_bit_Suc
% 0.30/0.59  thf(fact_6383_push__bit__of__1,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( bit_se7788150548672797655nteger @ N @ one_one_Code_integer )
% 0.30/0.59        = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ).
% 0.30/0.59  
% 0.30/0.59  % push_bit_of_1
% 0.30/0.59  thf(fact_6384_push__bit__of__1,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( bit_se6611745700429515170atural @ N @ one_one_Code_natural )
% 0.30/0.59        = ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) ).
% 0.30/0.59  
% 0.30/0.59  % push_bit_of_1
% 0.30/0.59  thf(fact_6385_push__bit__of__1,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( bit_se545348938243370406it_int @ N @ one_one_int )
% 0.30/0.59        = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 0.30/0.59  
% 0.30/0.59  % push_bit_of_1
% 0.30/0.59  thf(fact_6386_push__bit__of__1,axiom,
% 0.30/0.59      ! [N: nat] :
% 0.30/0.59        ( ( bit_se547839408752420682it_nat @ N @ one_one_nat )
% 0.30/0.59        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.30/0.59  
% 0.30/0.59  % push_bit_of_1
% 0.30/0.59  thf(fact_6387_push__bit__minus__numeral,axiom,
% 0.30/0.59      ! [L: num,K: num] :
% 0.30/0.59        ( ( bit_se7788150548672797655nteger @ ( numeral_numeral_nat @ L ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 0.30/0.59        = ( bit_se7788150548672797655nteger @ ( pred_numeral @ L ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % push_bit_minus_numeral
% 0.30/0.59  thf(fact_6388_push__bit__minus__numeral,axiom,
% 0.30/0.59      ! [L: num,K: num] :
% 0.30/0.59        ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.30/0.59        = ( bit_se545348938243370406it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % push_bit_minus_numeral
% 0.30/0.59  thf(fact_6389_minus__integer__code_I2_J,axiom,
% 0.30/0.59      ! [L: code_integer] :
% 0.30/0.59        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L )
% 0.30/0.59        = ( uminus1351360451143612070nteger @ L ) ) ).
% 0.30/0.59  
% 0.30/0.59  % minus_integer_code(2)
% 0.30/0.59  thf(fact_6390_insert__Collect,axiom,
% 0.30/0.59      ! [A: produc3843707927480180839at_nat,P: produc3843707927480180839at_nat > $o] :
% 0.30/0.59        ( ( insert9069300056098147895at_nat @ A @ ( collec6321179662152712658at_nat @ P ) )
% 0.30/0.59        = ( collec6321179662152712658at_nat
% 0.30/0.59          @ ^ [U2: produc3843707927480180839at_nat] :
% 0.30/0.59              ( ( U2 != A )
% 0.30/0.59             => ( P @ U2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_Collect
% 0.30/0.59  thf(fact_6391_insert__Collect,axiom,
% 0.30/0.59      ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 0.30/0.59        ( ( insert8211810215607154385at_nat @ A @ ( collec3392354462482085612at_nat @ P ) )
% 0.30/0.59        = ( collec3392354462482085612at_nat
% 0.30/0.59          @ ^ [U2: product_prod_nat_nat] :
% 0.30/0.59              ( ( U2 != A )
% 0.30/0.59             => ( P @ U2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_Collect
% 0.30/0.59  thf(fact_6392_insert__Collect,axiom,
% 0.30/0.59      ! [A: $o,P: $o > $o] :
% 0.30/0.59        ( ( insert_o @ A @ ( collect_o @ P ) )
% 0.30/0.59        = ( collect_o
% 0.30/0.59          @ ^ [U2: $o] :
% 0.30/0.59              ( ( U2 != A )
% 0.30/0.59             => ( P @ U2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_Collect
% 0.30/0.59  thf(fact_6393_insert__Collect,axiom,
% 0.30/0.59      ! [A: set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 0.30/0.59        ( ( insert8897473484851387113nt_int @ A @ ( collec5210948495886036740nt_int @ P ) )
% 0.30/0.59        = ( collec5210948495886036740nt_int
% 0.30/0.59          @ ^ [U2: set_Pr958786334691620121nt_int] :
% 0.30/0.59              ( ( U2 != A )
% 0.30/0.59             => ( P @ U2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_Collect
% 0.30/0.59  thf(fact_6394_insert__Collect,axiom,
% 0.30/0.59      ! [A: set_nat,P: set_nat > $o] :
% 0.30/0.59        ( ( insert_set_nat @ A @ ( collect_set_nat @ P ) )
% 0.30/0.59        = ( collect_set_nat
% 0.30/0.59          @ ^ [U2: set_nat] :
% 0.30/0.59              ( ( U2 != A )
% 0.30/0.59             => ( P @ U2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_Collect
% 0.30/0.59  thf(fact_6395_insert__Collect,axiom,
% 0.30/0.59      ! [A: nat,P: nat > $o] :
% 0.30/0.59        ( ( insert_nat @ A @ ( collect_nat @ P ) )
% 0.30/0.59        = ( collect_nat
% 0.30/0.59          @ ^ [U2: nat] :
% 0.30/0.59              ( ( U2 != A )
% 0.30/0.59             => ( P @ U2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_Collect
% 0.30/0.59  thf(fact_6396_insert__Collect,axiom,
% 0.30/0.59      ! [A: int,P: int > $o] :
% 0.30/0.59        ( ( insert_int @ A @ ( collect_int @ P ) )
% 0.30/0.59        = ( collect_int
% 0.30/0.59          @ ^ [U2: int] :
% 0.30/0.59              ( ( U2 != A )
% 0.30/0.59             => ( P @ U2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_Collect
% 0.30/0.59  thf(fact_6397_insert__Collect,axiom,
% 0.30/0.59      ! [A: produc3658429121746597890et_nat > $o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.30/0.59        ( ( insert5175938949040314269_nat_o @ A @ ( collec939566748876313656_nat_o @ P ) )
% 0.30/0.59        = ( collec939566748876313656_nat_o
% 0.30/0.59          @ ^ [U2: produc3658429121746597890et_nat > $o] :
% 0.30/0.59              ( ( U2 != A )
% 0.30/0.59             => ( P @ U2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_Collect
% 0.30/0.59  thf(fact_6398_insert__compr,axiom,
% 0.30/0.59      ( insert9069300056098147895at_nat
% 0.30/0.59      = ( ^ [A3: produc3843707927480180839at_nat,B4: set_Pr4329608150637261639at_nat] :
% 0.30/0.59            ( collec6321179662152712658at_nat
% 0.30/0.59            @ ^ [X3: produc3843707927480180839at_nat] :
% 0.30/0.59                ( ( X3 = A3 )
% 0.30/0.59                | ( member8757157785044589968at_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_compr
% 0.30/0.59  thf(fact_6399_insert__compr,axiom,
% 0.30/0.59      ( insert8211810215607154385at_nat
% 0.30/0.59      = ( ^ [A3: product_prod_nat_nat,B4: set_Pr1261947904930325089at_nat] :
% 0.30/0.59            ( collec3392354462482085612at_nat
% 0.30/0.59            @ ^ [X3: product_prod_nat_nat] :
% 0.30/0.59                ( ( X3 = A3 )
% 0.30/0.59                | ( member8440522571783428010at_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_compr
% 0.30/0.59  thf(fact_6400_insert__compr,axiom,
% 0.30/0.59      ( insert_o
% 0.30/0.59      = ( ^ [A3: $o,B4: set_o] :
% 0.30/0.59            ( collect_o
% 0.30/0.59            @ ^ [X3: $o] :
% 0.30/0.59                ( ( X3 = A3 )
% 0.30/0.59                | ( member_o @ X3 @ B4 ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_compr
% 0.30/0.59  thf(fact_6401_insert__compr,axiom,
% 0.30/0.59      ( insert8897473484851387113nt_int
% 0.30/0.59      = ( ^ [A3: set_Pr958786334691620121nt_int,B4: set_se6260736226359567993nt_int] :
% 0.30/0.59            ( collec5210948495886036740nt_int
% 0.30/0.59            @ ^ [X3: set_Pr958786334691620121nt_int] :
% 0.30/0.59                ( ( X3 = A3 )
% 0.30/0.59                | ( member2340774599025711042nt_int @ X3 @ B4 ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_compr
% 0.30/0.59  thf(fact_6402_insert__compr,axiom,
% 0.30/0.59      ( insert_set_nat
% 0.30/0.59      = ( ^ [A3: set_nat,B4: set_set_nat] :
% 0.30/0.59            ( collect_set_nat
% 0.30/0.59            @ ^ [X3: set_nat] :
% 0.30/0.59                ( ( X3 = A3 )
% 0.30/0.59                | ( member_set_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_compr
% 0.30/0.59  thf(fact_6403_insert__compr,axiom,
% 0.30/0.59      ( insert_nat
% 0.30/0.59      = ( ^ [A3: nat,B4: set_nat] :
% 0.30/0.59            ( collect_nat
% 0.30/0.59            @ ^ [X3: nat] :
% 0.30/0.59                ( ( X3 = A3 )
% 0.30/0.59                | ( member_nat @ X3 @ B4 ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_compr
% 0.30/0.59  thf(fact_6404_insert__compr,axiom,
% 0.30/0.59      ( insert_int
% 0.30/0.59      = ( ^ [A3: int,B4: set_int] :
% 0.30/0.59            ( collect_int
% 0.30/0.59            @ ^ [X3: int] :
% 0.30/0.59                ( ( X3 = A3 )
% 0.30/0.59                | ( member_int @ X3 @ B4 ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_compr
% 0.30/0.59  thf(fact_6405_insert__compr,axiom,
% 0.30/0.59      ( insert5175938949040314269_nat_o
% 0.30/0.59      = ( ^ [A3: produc3658429121746597890et_nat > $o,B4: set_Pr4532377907799695533_nat_o] :
% 0.30/0.59            ( collec939566748876313656_nat_o
% 0.30/0.59            @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.30/0.59                ( ( X3 = A3 )
% 0.30/0.59                | ( member6576561426505652726_nat_o @ X3 @ B4 ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_compr
% 0.30/0.59  thf(fact_6406_divmod__integer_H__def,axiom,
% 0.30/0.59      ( unique3479559517661332726nteger
% 0.30/0.59      = ( ^ [M2: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % divmod_integer'_def
% 0.30/0.59  thf(fact_6407_exhaustive__integer_H_Ocases,axiom,
% 0.30/0.59      ! [X: produc8763457246119570046nteger] :
% 0.30/0.59        ~ ! [F3: code_integer > option6357759511663192854e_term,D: code_integer,I2: code_integer] :
% 0.30/0.59            ( X
% 0.30/0.59           != ( produc6137756002093451184nteger @ F3 @ ( produc1086072967326762835nteger @ D @ I2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % exhaustive_integer'.cases
% 0.30/0.59  thf(fact_6408_full__exhaustive__integer_H_Ocases,axiom,
% 0.30/0.59      ! [X: produc1908205239877642774nteger] :
% 0.30/0.59        ~ ! [F3: produc6241069584506657477e_term > option6357759511663192854e_term,D: code_integer,I2: code_integer] :
% 0.30/0.59            ( X
% 0.30/0.59           != ( produc8603105652947943368nteger @ F3 @ ( produc1086072967326762835nteger @ D @ I2 ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % full_exhaustive_integer'.cases
% 0.30/0.59  thf(fact_6409_ID_Opred__cong,axiom,
% 0.30/0.59      ! [X: produc3843707927480180839at_nat,Ya: produc3843707927480180839at_nat,P: produc3843707927480180839at_nat > $o,Pa: produc3843707927480180839at_nat > $o] :
% 0.30/0.59        ( ( X = Ya )
% 0.30/0.59       => ( ! [Z2: produc3843707927480180839at_nat] :
% 0.30/0.59              ( ( member8757157785044589968at_nat @ Z2 @ ( insert9069300056098147895at_nat @ Ya @ bot_bo228742789529271731at_nat ) )
% 0.30/0.59             => ( ( P @ Z2 )
% 0.30/0.59                = ( Pa @ Z2 ) ) )
% 0.30/0.59         => ( ( bNF_id1044457264471098170_nat_o @ P @ X )
% 0.30/0.59            = ( bNF_id1044457264471098170_nat_o @ Pa @ Ya ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.pred_cong
% 0.30/0.59  thf(fact_6410_ID_Opred__cong,axiom,
% 0.30/0.59      ! [X: set_Pr958786334691620121nt_int,Ya: set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o,Pa: set_Pr958786334691620121nt_int > $o] :
% 0.30/0.59        ( ( X = Ya )
% 0.30/0.59       => ( ! [Z2: set_Pr958786334691620121nt_int] :
% 0.30/0.59              ( ( member2340774599025711042nt_int @ Z2 @ ( insert8897473484851387113nt_int @ Ya @ bot_bo1488462491386950373nt_int ) )
% 0.30/0.59             => ( ( P @ Z2 )
% 0.30/0.59                = ( Pa @ Z2 ) ) )
% 0.30/0.59         => ( ( bNF_id9176111459293603464_int_o @ P @ X )
% 0.30/0.59            = ( bNF_id9176111459293603464_int_o @ Pa @ Ya ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.pred_cong
% 0.30/0.59  thf(fact_6411_ID_Opred__cong,axiom,
% 0.30/0.59      ! [X: set_nat,Ya: set_nat,P: set_nat > $o,Pa: set_nat > $o] :
% 0.30/0.59        ( ( X = Ya )
% 0.30/0.59       => ( ! [Z2: set_nat] :
% 0.30/0.59              ( ( member_set_nat @ Z2 @ ( insert_set_nat @ Ya @ bot_bot_set_set_nat ) )
% 0.30/0.59             => ( ( P @ Z2 )
% 0.30/0.59                = ( Pa @ Z2 ) ) )
% 0.30/0.59         => ( ( bNF_id_bnf_set_nat_o @ P @ X )
% 0.30/0.59            = ( bNF_id_bnf_set_nat_o @ Pa @ Ya ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.pred_cong
% 0.30/0.59  thf(fact_6412_ID_Opred__cong,axiom,
% 0.30/0.59      ! [X: produc3658429121746597890et_nat > $o,Ya: produc3658429121746597890et_nat > $o,P: ( produc3658429121746597890et_nat > $o ) > $o,Pa: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.30/0.59        ( ( X = Ya )
% 0.30/0.59       => ( ! [Z2: produc3658429121746597890et_nat > $o] :
% 0.30/0.59              ( ( member6576561426505652726_nat_o @ Z2 @ ( insert5175938949040314269_nat_o @ Ya @ bot_bo7824918357723582233_nat_o ) )
% 0.30/0.59             => ( ( P @ Z2 )
% 0.30/0.59                = ( Pa @ Z2 ) ) )
% 0.30/0.59         => ( ( bNF_id4470576313039291732at_o_o @ P @ X )
% 0.30/0.59            = ( bNF_id4470576313039291732at_o_o @ Pa @ Ya ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.pred_cong
% 0.30/0.59  thf(fact_6413_ID_Opred__cong,axiom,
% 0.30/0.59      ! [X: product_prod_nat_nat,Ya: product_prod_nat_nat,P: product_prod_nat_nat > $o,Pa: product_prod_nat_nat > $o] :
% 0.30/0.59        ( ( X = Ya )
% 0.30/0.59       => ( ! [Z2: product_prod_nat_nat] :
% 0.30/0.59              ( ( member8440522571783428010at_nat @ Z2 @ ( insert8211810215607154385at_nat @ Ya @ bot_bo2099793752762293965at_nat ) )
% 0.30/0.59             => ( ( P @ Z2 )
% 0.30/0.59                = ( Pa @ Z2 ) ) )
% 0.30/0.59         => ( ( bNF_id5045731369644952736_nat_o @ P @ X )
% 0.30/0.59            = ( bNF_id5045731369644952736_nat_o @ Pa @ Ya ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.pred_cong
% 0.30/0.59  thf(fact_6414_ID_Opred__cong,axiom,
% 0.30/0.59      ! [X: $o,Ya: $o,P: $o > $o,Pa: $o > $o] :
% 0.30/0.59        ( ( X = Ya )
% 0.30/0.59       => ( ! [Z2: $o] :
% 0.30/0.59              ( ( member_o @ Z2 @ ( insert_o @ Ya @ bot_bot_set_o ) )
% 0.30/0.59             => ( ( P @ Z2 )
% 0.30/0.59                = ( Pa @ Z2 ) ) )
% 0.30/0.59         => ( ( bNF_id_bnf_o_o @ P @ X )
% 0.30/0.59            = ( bNF_id_bnf_o_o @ Pa @ Ya ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.pred_cong
% 0.30/0.59  thf(fact_6415_ID_Opred__cong,axiom,
% 0.30/0.59      ! [X: nat,Ya: nat,P: nat > $o,Pa: nat > $o] :
% 0.30/0.59        ( ( X = Ya )
% 0.30/0.59       => ( ! [Z2: nat] :
% 0.30/0.59              ( ( member_nat @ Z2 @ ( insert_nat @ Ya @ bot_bot_set_nat ) )
% 0.30/0.59             => ( ( P @ Z2 )
% 0.30/0.59                = ( Pa @ Z2 ) ) )
% 0.30/0.59         => ( ( bNF_id_bnf_nat_o @ P @ X )
% 0.30/0.59            = ( bNF_id_bnf_nat_o @ Pa @ Ya ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.pred_cong
% 0.30/0.59  thf(fact_6416_ID_Opred__cong,axiom,
% 0.30/0.59      ! [X: int,Ya: int,P: int > $o,Pa: int > $o] :
% 0.30/0.59        ( ( X = Ya )
% 0.30/0.59       => ( ! [Z2: int] :
% 0.30/0.59              ( ( member_int @ Z2 @ ( insert_int @ Ya @ bot_bot_set_int ) )
% 0.30/0.59             => ( ( P @ Z2 )
% 0.30/0.59                = ( Pa @ Z2 ) ) )
% 0.30/0.59         => ( ( bNF_id_bnf_int_o @ P @ X )
% 0.30/0.59            = ( bNF_id_bnf_int_o @ Pa @ Ya ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.pred_cong
% 0.30/0.59  thf(fact_6417_ID_Opred__mono__strong,axiom,
% 0.30/0.59      ! [P: produc3843707927480180839at_nat > $o,X: produc3843707927480180839at_nat,Pa: produc3843707927480180839at_nat > $o] :
% 0.30/0.59        ( ( bNF_id1044457264471098170_nat_o @ P @ X )
% 0.30/0.59       => ( ! [Z2: produc3843707927480180839at_nat] :
% 0.30/0.59              ( ( member8757157785044589968at_nat @ Z2 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 0.30/0.59             => ( ( P @ Z2 )
% 0.30/0.59               => ( Pa @ Z2 ) ) )
% 0.30/0.59         => ( bNF_id1044457264471098170_nat_o @ Pa @ X ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.pred_mono_strong
% 0.30/0.59  thf(fact_6418_ID_Opred__mono__strong,axiom,
% 0.30/0.59      ! [P: set_Pr958786334691620121nt_int > $o,X: set_Pr958786334691620121nt_int,Pa: set_Pr958786334691620121nt_int > $o] :
% 0.30/0.59        ( ( bNF_id9176111459293603464_int_o @ P @ X )
% 0.30/0.59       => ( ! [Z2: set_Pr958786334691620121nt_int] :
% 0.30/0.59              ( ( member2340774599025711042nt_int @ Z2 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
% 0.30/0.59             => ( ( P @ Z2 )
% 0.30/0.59               => ( Pa @ Z2 ) ) )
% 0.30/0.59         => ( bNF_id9176111459293603464_int_o @ Pa @ X ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.pred_mono_strong
% 0.30/0.59  thf(fact_6419_ID_Opred__mono__strong,axiom,
% 0.30/0.59      ! [P: set_nat > $o,X: set_nat,Pa: set_nat > $o] :
% 0.30/0.59        ( ( bNF_id_bnf_set_nat_o @ P @ X )
% 0.30/0.59       => ( ! [Z2: set_nat] :
% 0.30/0.59              ( ( member_set_nat @ Z2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 0.30/0.59             => ( ( P @ Z2 )
% 0.30/0.59               => ( Pa @ Z2 ) ) )
% 0.30/0.59         => ( bNF_id_bnf_set_nat_o @ Pa @ X ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.pred_mono_strong
% 0.30/0.59  thf(fact_6420_ID_Opred__mono__strong,axiom,
% 0.30/0.59      ! [P: ( produc3658429121746597890et_nat > $o ) > $o,X: produc3658429121746597890et_nat > $o,Pa: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.30/0.59        ( ( bNF_id4470576313039291732at_o_o @ P @ X )
% 0.30/0.59       => ( ! [Z2: produc3658429121746597890et_nat > $o] :
% 0.30/0.59              ( ( member6576561426505652726_nat_o @ Z2 @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 0.30/0.59             => ( ( P @ Z2 )
% 0.30/0.59               => ( Pa @ Z2 ) ) )
% 0.30/0.59         => ( bNF_id4470576313039291732at_o_o @ Pa @ X ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.pred_mono_strong
% 0.30/0.59  thf(fact_6421_ID_Opred__mono__strong,axiom,
% 0.30/0.59      ! [P: product_prod_nat_nat > $o,X: product_prod_nat_nat,Pa: product_prod_nat_nat > $o] :
% 0.30/0.59        ( ( bNF_id5045731369644952736_nat_o @ P @ X )
% 0.30/0.59       => ( ! [Z2: product_prod_nat_nat] :
% 0.30/0.59              ( ( member8440522571783428010at_nat @ Z2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 0.30/0.59             => ( ( P @ Z2 )
% 0.30/0.59               => ( Pa @ Z2 ) ) )
% 0.30/0.59         => ( bNF_id5045731369644952736_nat_o @ Pa @ X ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.pred_mono_strong
% 0.30/0.59  thf(fact_6422_ID_Opred__mono__strong,axiom,
% 0.30/0.59      ! [P: $o > $o,X: $o,Pa: $o > $o] :
% 0.30/0.59        ( ( bNF_id_bnf_o_o @ P @ X )
% 0.30/0.59       => ( ! [Z2: $o] :
% 0.30/0.59              ( ( member_o @ Z2 @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.30/0.59             => ( ( P @ Z2 )
% 0.30/0.59               => ( Pa @ Z2 ) ) )
% 0.30/0.59         => ( bNF_id_bnf_o_o @ Pa @ X ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.pred_mono_strong
% 0.30/0.59  thf(fact_6423_ID_Opred__mono__strong,axiom,
% 0.30/0.59      ! [P: nat > $o,X: nat,Pa: nat > $o] :
% 0.30/0.59        ( ( bNF_id_bnf_nat_o @ P @ X )
% 0.30/0.59       => ( ! [Z2: nat] :
% 0.30/0.59              ( ( member_nat @ Z2 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.30/0.59             => ( ( P @ Z2 )
% 0.30/0.59               => ( Pa @ Z2 ) ) )
% 0.30/0.59         => ( bNF_id_bnf_nat_o @ Pa @ X ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.pred_mono_strong
% 0.30/0.59  thf(fact_6424_ID_Opred__mono__strong,axiom,
% 0.30/0.59      ! [P: int > $o,X: int,Pa: int > $o] :
% 0.30/0.59        ( ( bNF_id_bnf_int_o @ P @ X )
% 0.30/0.59       => ( ! [Z2: int] :
% 0.30/0.59              ( ( member_int @ Z2 @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.30/0.59             => ( ( P @ Z2 )
% 0.30/0.59               => ( Pa @ Z2 ) ) )
% 0.30/0.59         => ( bNF_id_bnf_int_o @ Pa @ X ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.pred_mono_strong
% 0.30/0.59  thf(fact_6425_ID_Orel__cong,axiom,
% 0.30/0.59      ! [X: $o,Ya: $o,Y: $o,Xa: $o,R: $o > $o > $o,Ra: $o > $o > $o] :
% 0.30/0.59        ( ( X = Ya )
% 0.30/0.59       => ( ( Y = Xa )
% 0.30/0.59         => ( ! [Z2: $o,Yb: $o] :
% 0.30/0.59                ( ( member_o @ Z2 @ ( insert_o @ Ya @ bot_bot_set_o ) )
% 0.30/0.59               => ( ( member_o @ Yb @ ( insert_o @ Xa @ bot_bot_set_o ) )
% 0.30/0.59                 => ( ( R @ Z2 @ Yb )
% 0.30/0.59                    = ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.59           => ( ( bNF_id_bnf_o_o_o @ R @ X @ Y )
% 0.30/0.59              = ( bNF_id_bnf_o_o_o @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_cong
% 0.30/0.59  thf(fact_6426_ID_Orel__cong,axiom,
% 0.30/0.59      ! [X: $o,Ya: $o,Y: nat,Xa: nat,R: $o > nat > $o,Ra: $o > nat > $o] :
% 0.30/0.59        ( ( X = Ya )
% 0.30/0.59       => ( ( Y = Xa )
% 0.30/0.59         => ( ! [Z2: $o,Yb: nat] :
% 0.30/0.59                ( ( member_o @ Z2 @ ( insert_o @ Ya @ bot_bot_set_o ) )
% 0.30/0.59               => ( ( member_nat @ Yb @ ( insert_nat @ Xa @ bot_bot_set_nat ) )
% 0.30/0.59                 => ( ( R @ Z2 @ Yb )
% 0.30/0.59                    = ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.59           => ( ( bNF_id_bnf_o_nat_o @ R @ X @ Y )
% 0.30/0.59              = ( bNF_id_bnf_o_nat_o @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_cong
% 0.30/0.59  thf(fact_6427_ID_Orel__cong,axiom,
% 0.30/0.59      ! [X: $o,Ya: $o,Y: int,Xa: int,R: $o > int > $o,Ra: $o > int > $o] :
% 0.30/0.59        ( ( X = Ya )
% 0.30/0.59       => ( ( Y = Xa )
% 0.30/0.59         => ( ! [Z2: $o,Yb: int] :
% 0.30/0.59                ( ( member_o @ Z2 @ ( insert_o @ Ya @ bot_bot_set_o ) )
% 0.30/0.59               => ( ( member_int @ Yb @ ( insert_int @ Xa @ bot_bot_set_int ) )
% 0.30/0.59                 => ( ( R @ Z2 @ Yb )
% 0.30/0.59                    = ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.59           => ( ( bNF_id_bnf_o_int_o @ R @ X @ Y )
% 0.30/0.59              = ( bNF_id_bnf_o_int_o @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_cong
% 0.30/0.59  thf(fact_6428_ID_Orel__cong,axiom,
% 0.30/0.59      ! [X: nat,Ya: nat,Y: $o,Xa: $o,R: nat > $o > $o,Ra: nat > $o > $o] :
% 0.30/0.59        ( ( X = Ya )
% 0.30/0.59       => ( ( Y = Xa )
% 0.30/0.59         => ( ! [Z2: nat,Yb: $o] :
% 0.30/0.59                ( ( member_nat @ Z2 @ ( insert_nat @ Ya @ bot_bot_set_nat ) )
% 0.30/0.59               => ( ( member_o @ Yb @ ( insert_o @ Xa @ bot_bot_set_o ) )
% 0.30/0.59                 => ( ( R @ Z2 @ Yb )
% 0.30/0.59                    = ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.59           => ( ( bNF_id_bnf_nat_o_o @ R @ X @ Y )
% 0.30/0.59              = ( bNF_id_bnf_nat_o_o @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_cong
% 0.30/0.59  thf(fact_6429_ID_Orel__cong,axiom,
% 0.30/0.59      ! [X: nat,Ya: nat,Y: nat,Xa: nat,R: nat > nat > $o,Ra: nat > nat > $o] :
% 0.30/0.59        ( ( X = Ya )
% 0.30/0.59       => ( ( Y = Xa )
% 0.30/0.59         => ( ! [Z2: nat,Yb: nat] :
% 0.30/0.59                ( ( member_nat @ Z2 @ ( insert_nat @ Ya @ bot_bot_set_nat ) )
% 0.30/0.59               => ( ( member_nat @ Yb @ ( insert_nat @ Xa @ bot_bot_set_nat ) )
% 0.30/0.59                 => ( ( R @ Z2 @ Yb )
% 0.30/0.59                    = ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.59           => ( ( bNF_id_bnf_nat_nat_o @ R @ X @ Y )
% 0.30/0.59              = ( bNF_id_bnf_nat_nat_o @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_cong
% 0.30/0.59  thf(fact_6430_ID_Orel__cong,axiom,
% 0.30/0.59      ! [X: nat,Ya: nat,Y: int,Xa: int,R: nat > int > $o,Ra: nat > int > $o] :
% 0.30/0.59        ( ( X = Ya )
% 0.30/0.59       => ( ( Y = Xa )
% 0.30/0.59         => ( ! [Z2: nat,Yb: int] :
% 0.30/0.59                ( ( member_nat @ Z2 @ ( insert_nat @ Ya @ bot_bot_set_nat ) )
% 0.30/0.59               => ( ( member_int @ Yb @ ( insert_int @ Xa @ bot_bot_set_int ) )
% 0.30/0.59                 => ( ( R @ Z2 @ Yb )
% 0.30/0.59                    = ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.59           => ( ( bNF_id_bnf_nat_int_o @ R @ X @ Y )
% 0.30/0.59              = ( bNF_id_bnf_nat_int_o @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_cong
% 0.30/0.59  thf(fact_6431_ID_Orel__cong,axiom,
% 0.30/0.59      ! [X: int,Ya: int,Y: $o,Xa: $o,R: int > $o > $o,Ra: int > $o > $o] :
% 0.30/0.59        ( ( X = Ya )
% 0.30/0.59       => ( ( Y = Xa )
% 0.30/0.59         => ( ! [Z2: int,Yb: $o] :
% 0.30/0.59                ( ( member_int @ Z2 @ ( insert_int @ Ya @ bot_bot_set_int ) )
% 0.30/0.59               => ( ( member_o @ Yb @ ( insert_o @ Xa @ bot_bot_set_o ) )
% 0.30/0.59                 => ( ( R @ Z2 @ Yb )
% 0.30/0.59                    = ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.59           => ( ( bNF_id_bnf_int_o_o @ R @ X @ Y )
% 0.30/0.59              = ( bNF_id_bnf_int_o_o @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_cong
% 0.30/0.59  thf(fact_6432_ID_Orel__cong,axiom,
% 0.30/0.59      ! [X: int,Ya: int,Y: nat,Xa: nat,R: int > nat > $o,Ra: int > nat > $o] :
% 0.30/0.59        ( ( X = Ya )
% 0.30/0.59       => ( ( Y = Xa )
% 0.30/0.59         => ( ! [Z2: int,Yb: nat] :
% 0.30/0.59                ( ( member_int @ Z2 @ ( insert_int @ Ya @ bot_bot_set_int ) )
% 0.30/0.59               => ( ( member_nat @ Yb @ ( insert_nat @ Xa @ bot_bot_set_nat ) )
% 0.30/0.59                 => ( ( R @ Z2 @ Yb )
% 0.30/0.59                    = ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.59           => ( ( bNF_id_bnf_int_nat_o @ R @ X @ Y )
% 0.30/0.59              = ( bNF_id_bnf_int_nat_o @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_cong
% 0.30/0.59  thf(fact_6433_ID_Orel__cong,axiom,
% 0.30/0.59      ! [X: int,Ya: int,Y: int,Xa: int,R: int > int > $o,Ra: int > int > $o] :
% 0.30/0.59        ( ( X = Ya )
% 0.30/0.59       => ( ( Y = Xa )
% 0.30/0.59         => ( ! [Z2: int,Yb: int] :
% 0.30/0.59                ( ( member_int @ Z2 @ ( insert_int @ Ya @ bot_bot_set_int ) )
% 0.30/0.59               => ( ( member_int @ Yb @ ( insert_int @ Xa @ bot_bot_set_int ) )
% 0.30/0.59                 => ( ( R @ Z2 @ Yb )
% 0.30/0.59                    = ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.59           => ( ( bNF_id_bnf_int_int_o @ R @ X @ Y )
% 0.30/0.59              = ( bNF_id_bnf_int_int_o @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_cong
% 0.30/0.59  thf(fact_6434_ID_Orel__cong,axiom,
% 0.30/0.59      ! [X: set_nat,Ya: set_nat,Y: $o,Xa: $o,R: set_nat > $o > $o,Ra: set_nat > $o > $o] :
% 0.30/0.59        ( ( X = Ya )
% 0.30/0.59       => ( ( Y = Xa )
% 0.30/0.59         => ( ! [Z2: set_nat,Yb: $o] :
% 0.30/0.59                ( ( member_set_nat @ Z2 @ ( insert_set_nat @ Ya @ bot_bot_set_set_nat ) )
% 0.30/0.59               => ( ( member_o @ Yb @ ( insert_o @ Xa @ bot_bot_set_o ) )
% 0.30/0.59                 => ( ( R @ Z2 @ Yb )
% 0.30/0.59                    = ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.59           => ( ( bNF_id1382368747416007662at_o_o @ R @ X @ Y )
% 0.30/0.59              = ( bNF_id1382368747416007662at_o_o @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_cong
% 0.30/0.59  thf(fact_6435_ID_Orel__mono__strong,axiom,
% 0.30/0.59      ! [R: $o > $o > $o,X: $o,Y: $o,Ra: $o > $o > $o] :
% 0.30/0.59        ( ( bNF_id_bnf_o_o_o @ R @ X @ Y )
% 0.30/0.59       => ( ! [Z2: $o,Yb: $o] :
% 0.30/0.59              ( ( member_o @ Z2 @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.30/0.59             => ( ( member_o @ Yb @ ( insert_o @ Y @ bot_bot_set_o ) )
% 0.30/0.59               => ( ( R @ Z2 @ Yb )
% 0.30/0.59                 => ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.59         => ( bNF_id_bnf_o_o_o @ Ra @ X @ Y ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_mono_strong
% 0.30/0.59  thf(fact_6436_ID_Orel__mono__strong,axiom,
% 0.30/0.59      ! [R: $o > nat > $o,X: $o,Y: nat,Ra: $o > nat > $o] :
% 0.30/0.59        ( ( bNF_id_bnf_o_nat_o @ R @ X @ Y )
% 0.30/0.59       => ( ! [Z2: $o,Yb: nat] :
% 0.30/0.59              ( ( member_o @ Z2 @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.30/0.59             => ( ( member_nat @ Yb @ ( insert_nat @ Y @ bot_bot_set_nat ) )
% 0.30/0.59               => ( ( R @ Z2 @ Yb )
% 0.30/0.59                 => ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.59         => ( bNF_id_bnf_o_nat_o @ Ra @ X @ Y ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_mono_strong
% 0.30/0.59  thf(fact_6437_ID_Orel__mono__strong,axiom,
% 0.30/0.59      ! [R: $o > int > $o,X: $o,Y: int,Ra: $o > int > $o] :
% 0.30/0.59        ( ( bNF_id_bnf_o_int_o @ R @ X @ Y )
% 0.30/0.59       => ( ! [Z2: $o,Yb: int] :
% 0.30/0.59              ( ( member_o @ Z2 @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.30/0.59             => ( ( member_int @ Yb @ ( insert_int @ Y @ bot_bot_set_int ) )
% 0.30/0.59               => ( ( R @ Z2 @ Yb )
% 0.30/0.59                 => ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.59         => ( bNF_id_bnf_o_int_o @ Ra @ X @ Y ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_mono_strong
% 0.30/0.59  thf(fact_6438_ID_Orel__mono__strong,axiom,
% 0.30/0.59      ! [R: nat > $o > $o,X: nat,Y: $o,Ra: nat > $o > $o] :
% 0.30/0.59        ( ( bNF_id_bnf_nat_o_o @ R @ X @ Y )
% 0.30/0.59       => ( ! [Z2: nat,Yb: $o] :
% 0.30/0.59              ( ( member_nat @ Z2 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.30/0.59             => ( ( member_o @ Yb @ ( insert_o @ Y @ bot_bot_set_o ) )
% 0.30/0.59               => ( ( R @ Z2 @ Yb )
% 0.30/0.59                 => ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.59         => ( bNF_id_bnf_nat_o_o @ Ra @ X @ Y ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_mono_strong
% 0.30/0.59  thf(fact_6439_ID_Orel__mono__strong,axiom,
% 0.30/0.59      ! [R: nat > nat > $o,X: nat,Y: nat,Ra: nat > nat > $o] :
% 0.30/0.59        ( ( bNF_id_bnf_nat_nat_o @ R @ X @ Y )
% 0.30/0.59       => ( ! [Z2: nat,Yb: nat] :
% 0.30/0.59              ( ( member_nat @ Z2 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.30/0.59             => ( ( member_nat @ Yb @ ( insert_nat @ Y @ bot_bot_set_nat ) )
% 0.30/0.59               => ( ( R @ Z2 @ Yb )
% 0.30/0.59                 => ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.59         => ( bNF_id_bnf_nat_nat_o @ Ra @ X @ Y ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_mono_strong
% 0.30/0.59  thf(fact_6440_ID_Orel__mono__strong,axiom,
% 0.30/0.59      ! [R: nat > int > $o,X: nat,Y: int,Ra: nat > int > $o] :
% 0.30/0.59        ( ( bNF_id_bnf_nat_int_o @ R @ X @ Y )
% 0.30/0.59       => ( ! [Z2: nat,Yb: int] :
% 0.30/0.59              ( ( member_nat @ Z2 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.30/0.59             => ( ( member_int @ Yb @ ( insert_int @ Y @ bot_bot_set_int ) )
% 0.30/0.59               => ( ( R @ Z2 @ Yb )
% 0.30/0.59                 => ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.59         => ( bNF_id_bnf_nat_int_o @ Ra @ X @ Y ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_mono_strong
% 0.30/0.59  thf(fact_6441_ID_Orel__mono__strong,axiom,
% 0.30/0.59      ! [R: int > $o > $o,X: int,Y: $o,Ra: int > $o > $o] :
% 0.30/0.59        ( ( bNF_id_bnf_int_o_o @ R @ X @ Y )
% 0.30/0.59       => ( ! [Z2: int,Yb: $o] :
% 0.30/0.59              ( ( member_int @ Z2 @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.30/0.59             => ( ( member_o @ Yb @ ( insert_o @ Y @ bot_bot_set_o ) )
% 0.30/0.59               => ( ( R @ Z2 @ Yb )
% 0.30/0.59                 => ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.59         => ( bNF_id_bnf_int_o_o @ Ra @ X @ Y ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_mono_strong
% 0.30/0.59  thf(fact_6442_ID_Orel__mono__strong,axiom,
% 0.30/0.59      ! [R: int > nat > $o,X: int,Y: nat,Ra: int > nat > $o] :
% 0.30/0.59        ( ( bNF_id_bnf_int_nat_o @ R @ X @ Y )
% 0.30/0.59       => ( ! [Z2: int,Yb: nat] :
% 0.30/0.59              ( ( member_int @ Z2 @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.30/0.59             => ( ( member_nat @ Yb @ ( insert_nat @ Y @ bot_bot_set_nat ) )
% 0.30/0.59               => ( ( R @ Z2 @ Yb )
% 0.30/0.59                 => ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.59         => ( bNF_id_bnf_int_nat_o @ Ra @ X @ Y ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_mono_strong
% 0.30/0.59  thf(fact_6443_ID_Orel__mono__strong,axiom,
% 0.30/0.59      ! [R: int > int > $o,X: int,Y: int,Ra: int > int > $o] :
% 0.30/0.59        ( ( bNF_id_bnf_int_int_o @ R @ X @ Y )
% 0.30/0.59       => ( ! [Z2: int,Yb: int] :
% 0.30/0.59              ( ( member_int @ Z2 @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.30/0.59             => ( ( member_int @ Yb @ ( insert_int @ Y @ bot_bot_set_int ) )
% 0.30/0.59               => ( ( R @ Z2 @ Yb )
% 0.30/0.59                 => ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.59         => ( bNF_id_bnf_int_int_o @ Ra @ X @ Y ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_mono_strong
% 0.30/0.59  thf(fact_6444_ID_Orel__mono__strong,axiom,
% 0.30/0.59      ! [R: set_nat > $o > $o,X: set_nat,Y: $o,Ra: set_nat > $o > $o] :
% 0.30/0.59        ( ( bNF_id1382368747416007662at_o_o @ R @ X @ Y )
% 0.30/0.59       => ( ! [Z2: set_nat,Yb: $o] :
% 0.30/0.59              ( ( member_set_nat @ Z2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 0.30/0.59             => ( ( member_o @ Yb @ ( insert_o @ Y @ bot_bot_set_o ) )
% 0.30/0.59               => ( ( R @ Z2 @ Yb )
% 0.30/0.59                 => ( Ra @ Z2 @ Yb ) ) ) )
% 0.30/0.59         => ( bNF_id1382368747416007662at_o_o @ Ra @ X @ Y ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_mono_strong
% 0.30/0.59  thf(fact_6445_ID_Orel__refl__strong,axiom,
% 0.30/0.59      ! [X: produc3843707927480180839at_nat,Ra: produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o] :
% 0.30/0.59        ( ! [Z2: produc3843707927480180839at_nat] :
% 0.30/0.59            ( ( member8757157785044589968at_nat @ Z2 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 0.30/0.59           => ( Ra @ Z2 @ Z2 ) )
% 0.30/0.59       => ( bNF_id5557877041440844106_nat_o @ Ra @ X @ X ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_refl_strong
% 0.30/0.59  thf(fact_6446_ID_Orel__refl__strong,axiom,
% 0.30/0.59      ! [X: set_Pr958786334691620121nt_int,Ra: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o] :
% 0.30/0.59        ( ! [Z2: set_Pr958786334691620121nt_int] :
% 0.30/0.59            ( ( member2340774599025711042nt_int @ Z2 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
% 0.30/0.59           => ( Ra @ Z2 @ Z2 ) )
% 0.30/0.59       => ( bNF_id745042670895148362_int_o @ Ra @ X @ X ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_refl_strong
% 0.30/0.59  thf(fact_6447_ID_Orel__refl__strong,axiom,
% 0.30/0.59      ! [X: set_nat,Ra: set_nat > set_nat > $o] :
% 0.30/0.59        ( ! [Z2: set_nat] :
% 0.30/0.59            ( ( member_set_nat @ Z2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 0.30/0.59           => ( Ra @ Z2 @ Z2 ) )
% 0.30/0.59       => ( bNF_id293821497076346774_nat_o @ Ra @ X @ X ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_refl_strong
% 0.30/0.59  thf(fact_6448_ID_Orel__refl__strong,axiom,
% 0.30/0.59      ! [X: produc3658429121746597890et_nat > $o,Ra: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.30/0.59        ( ! [Z2: produc3658429121746597890et_nat > $o] :
% 0.30/0.59            ( ( member6576561426505652726_nat_o @ Z2 @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 0.30/0.59           => ( Ra @ Z2 @ Z2 ) )
% 0.30/0.59       => ( bNF_id2059982186938784458at_o_o @ Ra @ X @ X ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_refl_strong
% 0.30/0.59  thf(fact_6449_ID_Orel__refl__strong,axiom,
% 0.30/0.59      ! [X: product_prod_nat_nat,Ra: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 0.30/0.59        ( ! [Z2: product_prod_nat_nat] :
% 0.30/0.59            ( ( member8440522571783428010at_nat @ Z2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 0.30/0.59           => ( Ra @ Z2 @ Z2 ) )
% 0.30/0.59       => ( bNF_id146787821168362314_nat_o @ Ra @ X @ X ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_refl_strong
% 0.30/0.59  thf(fact_6450_ID_Orel__refl__strong,axiom,
% 0.30/0.59      ! [X: $o,Ra: $o > $o > $o] :
% 0.30/0.59        ( ! [Z2: $o] :
% 0.30/0.59            ( ( member_o @ Z2 @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.30/0.59           => ( Ra @ Z2 @ Z2 ) )
% 0.30/0.59       => ( bNF_id_bnf_o_o_o @ Ra @ X @ X ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_refl_strong
% 0.30/0.59  thf(fact_6451_ID_Orel__refl__strong,axiom,
% 0.30/0.59      ! [X: nat,Ra: nat > nat > $o] :
% 0.30/0.59        ( ! [Z2: nat] :
% 0.30/0.59            ( ( member_nat @ Z2 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.30/0.59           => ( Ra @ Z2 @ Z2 ) )
% 0.30/0.59       => ( bNF_id_bnf_nat_nat_o @ Ra @ X @ X ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_refl_strong
% 0.30/0.59  thf(fact_6452_ID_Orel__refl__strong,axiom,
% 0.30/0.59      ! [X: int,Ra: int > int > $o] :
% 0.30/0.59        ( ! [Z2: int] :
% 0.30/0.59            ( ( member_int @ Z2 @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.30/0.59           => ( Ra @ Z2 @ Z2 ) )
% 0.30/0.59       => ( bNF_id_bnf_int_int_o @ Ra @ X @ X ) ) ).
% 0.30/0.59  
% 0.30/0.59  % ID.rel_refl_strong
% 0.30/0.59  thf(fact_6453_singleton__inject,axiom,
% 0.30/0.59      ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
% 0.30/0.59        ( ( ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat )
% 0.30/0.59          = ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) )
% 0.30/0.59       => ( A = B ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_inject
% 0.30/0.59  thf(fact_6454_singleton__inject,axiom,
% 0.30/0.59      ! [A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 0.30/0.59        ( ( ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat )
% 0.30/0.59          = ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) )
% 0.30/0.59       => ( A = B ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_inject
% 0.30/0.59  thf(fact_6455_singleton__inject,axiom,
% 0.30/0.59      ! [A: $o,B: $o] :
% 0.30/0.59        ( ( ( insert_o @ A @ bot_bot_set_o )
% 0.30/0.59          = ( insert_o @ B @ bot_bot_set_o ) )
% 0.30/0.59       => ( A = B ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_inject
% 0.30/0.59  thf(fact_6456_singleton__inject,axiom,
% 0.30/0.59      ! [A: nat,B: nat] :
% 0.30/0.59        ( ( ( insert_nat @ A @ bot_bot_set_nat )
% 0.30/0.59          = ( insert_nat @ B @ bot_bot_set_nat ) )
% 0.30/0.59       => ( A = B ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_inject
% 0.30/0.59  thf(fact_6457_singleton__inject,axiom,
% 0.30/0.59      ! [A: int,B: int] :
% 0.30/0.59        ( ( ( insert_int @ A @ bot_bot_set_int )
% 0.30/0.59          = ( insert_int @ B @ bot_bot_set_int ) )
% 0.30/0.59       => ( A = B ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_inject
% 0.30/0.59  thf(fact_6458_insert__not__empty,axiom,
% 0.30/0.59      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.30/0.59        ( ( insert9069300056098147895at_nat @ A @ A2 )
% 0.30/0.59       != bot_bo228742789529271731at_nat ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_not_empty
% 0.30/0.59  thf(fact_6459_insert__not__empty,axiom,
% 0.30/0.59      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.30/0.59        ( ( insert8211810215607154385at_nat @ A @ A2 )
% 0.30/0.59       != bot_bo2099793752762293965at_nat ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_not_empty
% 0.30/0.59  thf(fact_6460_insert__not__empty,axiom,
% 0.30/0.59      ! [A: $o,A2: set_o] :
% 0.30/0.59        ( ( insert_o @ A @ A2 )
% 0.30/0.59       != bot_bot_set_o ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_not_empty
% 0.30/0.59  thf(fact_6461_insert__not__empty,axiom,
% 0.30/0.59      ! [A: nat,A2: set_nat] :
% 0.30/0.59        ( ( insert_nat @ A @ A2 )
% 0.30/0.59       != bot_bot_set_nat ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_not_empty
% 0.30/0.59  thf(fact_6462_insert__not__empty,axiom,
% 0.30/0.59      ! [A: int,A2: set_int] :
% 0.30/0.59        ( ( insert_int @ A @ A2 )
% 0.30/0.59       != bot_bot_set_int ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_not_empty
% 0.30/0.59  thf(fact_6463_doubleton__eq__iff,axiom,
% 0.30/0.59      ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat,C: produc3843707927480180839at_nat,D2: produc3843707927480180839at_nat] :
% 0.30/0.59        ( ( ( insert9069300056098147895at_nat @ A @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) )
% 0.30/0.59          = ( insert9069300056098147895at_nat @ C @ ( insert9069300056098147895at_nat @ D2 @ bot_bo228742789529271731at_nat ) ) )
% 0.30/0.59        = ( ( ( A = C )
% 0.30/0.59            & ( B = D2 ) )
% 0.30/0.59          | ( ( A = D2 )
% 0.30/0.59            & ( B = C ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % doubleton_eq_iff
% 0.30/0.59  thf(fact_6464_doubleton__eq__iff,axiom,
% 0.30/0.59      ! [A: product_prod_nat_nat,B: product_prod_nat_nat,C: product_prod_nat_nat,D2: product_prod_nat_nat] :
% 0.30/0.59        ( ( ( insert8211810215607154385at_nat @ A @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) )
% 0.30/0.59          = ( insert8211810215607154385at_nat @ C @ ( insert8211810215607154385at_nat @ D2 @ bot_bo2099793752762293965at_nat ) ) )
% 0.30/0.59        = ( ( ( A = C )
% 0.30/0.59            & ( B = D2 ) )
% 0.30/0.59          | ( ( A = D2 )
% 0.30/0.59            & ( B = C ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % doubleton_eq_iff
% 0.30/0.59  thf(fact_6465_doubleton__eq__iff,axiom,
% 0.30/0.59      ! [A: $o,B: $o,C: $o,D2: $o] :
% 0.30/0.59        ( ( ( insert_o @ A @ ( insert_o @ B @ bot_bot_set_o ) )
% 0.30/0.59          = ( insert_o @ C @ ( insert_o @ D2 @ bot_bot_set_o ) ) )
% 0.30/0.59        = ( ( ( A = C )
% 0.30/0.59            & ( B = D2 ) )
% 0.30/0.59          | ( ( A = D2 )
% 0.30/0.59            & ( B = C ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % doubleton_eq_iff
% 0.30/0.59  thf(fact_6466_doubleton__eq__iff,axiom,
% 0.30/0.59      ! [A: nat,B: nat,C: nat,D2: nat] :
% 0.30/0.59        ( ( ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) )
% 0.30/0.59          = ( insert_nat @ C @ ( insert_nat @ D2 @ bot_bot_set_nat ) ) )
% 0.30/0.59        = ( ( ( A = C )
% 0.30/0.59            & ( B = D2 ) )
% 0.30/0.59          | ( ( A = D2 )
% 0.30/0.59            & ( B = C ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % doubleton_eq_iff
% 0.30/0.59  thf(fact_6467_doubleton__eq__iff,axiom,
% 0.30/0.59      ! [A: int,B: int,C: int,D2: int] :
% 0.30/0.59        ( ( ( insert_int @ A @ ( insert_int @ B @ bot_bot_set_int ) )
% 0.30/0.59          = ( insert_int @ C @ ( insert_int @ D2 @ bot_bot_set_int ) ) )
% 0.30/0.59        = ( ( ( A = C )
% 0.30/0.59            & ( B = D2 ) )
% 0.30/0.59          | ( ( A = D2 )
% 0.30/0.59            & ( B = C ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % doubleton_eq_iff
% 0.30/0.59  thf(fact_6468_singleton__iff,axiom,
% 0.30/0.59      ! [B: produc3843707927480180839at_nat,A: produc3843707927480180839at_nat] :
% 0.30/0.59        ( ( member8757157785044589968at_nat @ B @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) )
% 0.30/0.59        = ( B = A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_iff
% 0.30/0.59  thf(fact_6469_singleton__iff,axiom,
% 0.30/0.59      ! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
% 0.30/0.59        ( ( member2340774599025711042nt_int @ B @ ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) )
% 0.30/0.59        = ( B = A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_iff
% 0.30/0.59  thf(fact_6470_singleton__iff,axiom,
% 0.30/0.59      ! [B: set_nat,A: set_nat] :
% 0.30/0.59        ( ( member_set_nat @ B @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) )
% 0.30/0.59        = ( B = A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_iff
% 0.30/0.59  thf(fact_6471_singleton__iff,axiom,
% 0.30/0.59      ! [B: produc3658429121746597890et_nat > $o,A: produc3658429121746597890et_nat > $o] :
% 0.30/0.59        ( ( member6576561426505652726_nat_o @ B @ ( insert5175938949040314269_nat_o @ A @ bot_bo7824918357723582233_nat_o ) )
% 0.30/0.59        = ( B = A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_iff
% 0.30/0.59  thf(fact_6472_singleton__iff,axiom,
% 0.30/0.59      ! [B: product_prod_nat_nat,A: product_prod_nat_nat] :
% 0.30/0.59        ( ( member8440522571783428010at_nat @ B @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) )
% 0.30/0.59        = ( B = A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_iff
% 0.30/0.59  thf(fact_6473_singleton__iff,axiom,
% 0.30/0.59      ! [B: $o,A: $o] :
% 0.30/0.59        ( ( member_o @ B @ ( insert_o @ A @ bot_bot_set_o ) )
% 0.30/0.59        = ( B = A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_iff
% 0.30/0.59  thf(fact_6474_singleton__iff,axiom,
% 0.30/0.59      ! [B: nat,A: nat] :
% 0.30/0.59        ( ( member_nat @ B @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 0.30/0.59        = ( B = A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_iff
% 0.30/0.59  thf(fact_6475_singleton__iff,axiom,
% 0.30/0.59      ! [B: int,A: int] :
% 0.30/0.59        ( ( member_int @ B @ ( insert_int @ A @ bot_bot_set_int ) )
% 0.30/0.59        = ( B = A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singleton_iff
% 0.30/0.59  thf(fact_6476_singletonD,axiom,
% 0.30/0.59      ! [B: produc3843707927480180839at_nat,A: produc3843707927480180839at_nat] :
% 0.30/0.59        ( ( member8757157785044589968at_nat @ B @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) )
% 0.30/0.59       => ( B = A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singletonD
% 0.30/0.59  thf(fact_6477_singletonD,axiom,
% 0.30/0.59      ! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
% 0.30/0.59        ( ( member2340774599025711042nt_int @ B @ ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) )
% 0.30/0.59       => ( B = A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singletonD
% 0.30/0.59  thf(fact_6478_singletonD,axiom,
% 0.30/0.59      ! [B: set_nat,A: set_nat] :
% 0.30/0.59        ( ( member_set_nat @ B @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) )
% 0.30/0.59       => ( B = A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singletonD
% 0.30/0.59  thf(fact_6479_singletonD,axiom,
% 0.30/0.59      ! [B: produc3658429121746597890et_nat > $o,A: produc3658429121746597890et_nat > $o] :
% 0.30/0.59        ( ( member6576561426505652726_nat_o @ B @ ( insert5175938949040314269_nat_o @ A @ bot_bo7824918357723582233_nat_o ) )
% 0.30/0.59       => ( B = A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singletonD
% 0.30/0.59  thf(fact_6480_singletonD,axiom,
% 0.30/0.59      ! [B: product_prod_nat_nat,A: product_prod_nat_nat] :
% 0.30/0.59        ( ( member8440522571783428010at_nat @ B @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) )
% 0.30/0.59       => ( B = A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singletonD
% 0.30/0.59  thf(fact_6481_singletonD,axiom,
% 0.30/0.59      ! [B: $o,A: $o] :
% 0.30/0.59        ( ( member_o @ B @ ( insert_o @ A @ bot_bot_set_o ) )
% 0.30/0.59       => ( B = A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singletonD
% 0.30/0.59  thf(fact_6482_singletonD,axiom,
% 0.30/0.59      ! [B: nat,A: nat] :
% 0.30/0.59        ( ( member_nat @ B @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 0.30/0.59       => ( B = A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singletonD
% 0.30/0.59  thf(fact_6483_singletonD,axiom,
% 0.30/0.59      ! [B: int,A: int] :
% 0.30/0.59        ( ( member_int @ B @ ( insert_int @ A @ bot_bot_set_int ) )
% 0.30/0.59       => ( B = A ) ) ).
% 0.30/0.59  
% 0.30/0.59  % singletonD
% 0.30/0.59  thf(fact_6484_flip__bit__int__def,axiom,
% 0.30/0.59      ( bit_se2159334234014336723it_int
% 0.30/0.59      = ( ^ [N2: nat,K4: int] : ( bit_se6526347334894502574or_int @ K4 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % flip_bit_int_def
% 0.30/0.59  thf(fact_6485_insert__UNIV,axiom,
% 0.30/0.59      ! [X: produc3843707927480180839at_nat] :
% 0.30/0.59        ( ( insert9069300056098147895at_nat @ X @ top_to6833984726390702231at_nat )
% 0.30/0.59        = top_to6833984726390702231at_nat ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_UNIV
% 0.30/0.59  thf(fact_6486_insert__UNIV,axiom,
% 0.30/0.59      ! [X: product_prod_nat_nat] :
% 0.30/0.59        ( ( insert8211810215607154385at_nat @ X @ top_to4669805908274784177at_nat )
% 0.30/0.59        = top_to4669805908274784177at_nat ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_UNIV
% 0.30/0.59  thf(fact_6487_insert__UNIV,axiom,
% 0.30/0.59      ! [X: list_nat] :
% 0.30/0.59        ( ( insert_list_nat @ X @ top_top_set_list_nat )
% 0.30/0.59        = top_top_set_list_nat ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_UNIV
% 0.30/0.59  thf(fact_6488_insert__UNIV,axiom,
% 0.30/0.59      ! [X: $o] :
% 0.30/0.59        ( ( insert_o @ X @ top_top_set_o )
% 0.30/0.59        = top_top_set_o ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_UNIV
% 0.30/0.59  thf(fact_6489_insert__UNIV,axiom,
% 0.30/0.59      ! [X: rat] :
% 0.30/0.59        ( ( insert_rat @ X @ top_top_set_rat )
% 0.30/0.59        = top_top_set_rat ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_UNIV
% 0.30/0.59  thf(fact_6490_insert__UNIV,axiom,
% 0.30/0.59      ! [X: nat] :
% 0.30/0.59        ( ( insert_nat @ X @ top_top_set_nat )
% 0.30/0.59        = top_top_set_nat ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_UNIV
% 0.30/0.59  thf(fact_6491_insert__UNIV,axiom,
% 0.30/0.59      ! [X: int] :
% 0.30/0.59        ( ( insert_int @ X @ top_top_set_int )
% 0.30/0.59        = top_top_set_int ) ).
% 0.30/0.59  
% 0.30/0.59  % insert_UNIV
% 0.30/0.59  thf(fact_6492_Int__insert__right,axiom,
% 0.30/0.59      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.59        ( ( ( member8757157785044589968at_nat @ A @ A2 )
% 0.30/0.59         => ( ( inf_in7913087082777306421at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ B2 ) )
% 0.30/0.59            = ( insert9069300056098147895at_nat @ A @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) )
% 0.30/0.59        & ( ~ ( member8757157785044589968at_nat @ A @ A2 )
% 0.30/0.59         => ( ( inf_in7913087082777306421at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ B2 ) )
% 0.30/0.59            = ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_right
% 0.30/0.59  thf(fact_6493_Int__insert__right,axiom,
% 0.30/0.59      ! [A: $o,A2: set_o,B2: set_o] :
% 0.30/0.59        ( ( ( member_o @ A @ A2 )
% 0.30/0.59         => ( ( inf_inf_set_o @ A2 @ ( insert_o @ A @ B2 ) )
% 0.30/0.59            = ( insert_o @ A @ ( inf_inf_set_o @ A2 @ B2 ) ) ) )
% 0.30/0.59        & ( ~ ( member_o @ A @ A2 )
% 0.30/0.59         => ( ( inf_inf_set_o @ A2 @ ( insert_o @ A @ B2 ) )
% 0.30/0.59            = ( inf_inf_set_o @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_right
% 0.30/0.59  thf(fact_6494_Int__insert__right,axiom,
% 0.30/0.59      ! [A: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 0.30/0.59        ( ( ( member2340774599025711042nt_int @ A @ A2 )
% 0.30/0.59         => ( ( inf_in8396524679539076455nt_int @ A2 @ ( insert8897473484851387113nt_int @ A @ B2 ) )
% 0.30/0.59            = ( insert8897473484851387113nt_int @ A @ ( inf_in8396524679539076455nt_int @ A2 @ B2 ) ) ) )
% 0.30/0.59        & ( ~ ( member2340774599025711042nt_int @ A @ A2 )
% 0.30/0.59         => ( ( inf_in8396524679539076455nt_int @ A2 @ ( insert8897473484851387113nt_int @ A @ B2 ) )
% 0.30/0.59            = ( inf_in8396524679539076455nt_int @ A2 @ B2 ) ) ) ) ).
% 0.30/0.59  
% 0.30/0.59  % Int_insert_right
% 0.30/0.59  thf(fact_6495_Int__insert__right,axiom,
% 0.30/0.59      ! [A: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.30/0.59        ( ( ( member_set_nat @ A @ A2 )
% 0.30/0.59         => ( ( inf_inf_set_set_nat @ A2 @ ( insert_set_nat @ A @ B2 ) )
% 0.30/0.59            = ( insert_set_nat @ A @ ( inf_inf_set_set_nat @ A2 @ B2 ) ) ) )
% 0.30/0.60        & ( ~ ( member_set_nat @ A @ A2 )
% 0.30/0.60         => ( ( inf_inf_set_set_nat @ A2 @ ( insert_set_nat @ A @ B2 ) )
% 0.30/0.60            = ( inf_inf_set_set_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Int_insert_right
% 0.30/0.60  thf(fact_6496_Int__insert__right,axiom,
% 0.30/0.60      ! [A: int,A2: set_int,B2: set_int] :
% 0.30/0.60        ( ( ( member_int @ A @ A2 )
% 0.30/0.60         => ( ( inf_inf_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 0.30/0.60            = ( insert_int @ A @ ( inf_inf_set_int @ A2 @ B2 ) ) ) )
% 0.30/0.60        & ( ~ ( member_int @ A @ A2 )
% 0.30/0.60         => ( ( inf_inf_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 0.30/0.60            = ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Int_insert_right
% 0.30/0.60  thf(fact_6497_Int__insert__right,axiom,
% 0.30/0.60      ! [A: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 0.30/0.60        ( ( ( member6576561426505652726_nat_o @ A @ A2 )
% 0.30/0.60         => ( ( inf_in1906310914598751387_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ A @ B2 ) )
% 0.30/0.60            = ( insert5175938949040314269_nat_o @ A @ ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) ) ) )
% 0.30/0.60        & ( ~ ( member6576561426505652726_nat_o @ A @ A2 )
% 0.30/0.60         => ( ( inf_in1906310914598751387_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ A @ B2 ) )
% 0.30/0.60            = ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Int_insert_right
% 0.30/0.60  thf(fact_6498_Int__insert__right,axiom,
% 0.30/0.60      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.60        ( ( ( member8440522571783428010at_nat @ A @ A2 )
% 0.30/0.60         => ( ( inf_in2572325071724192079at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 0.30/0.60            = ( insert8211810215607154385at_nat @ A @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) )
% 0.30/0.60        & ( ~ ( member8440522571783428010at_nat @ A @ A2 )
% 0.30/0.60         => ( ( inf_in2572325071724192079at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 0.30/0.60            = ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Int_insert_right
% 0.30/0.60  thf(fact_6499_Int__insert__right,axiom,
% 0.30/0.60      ! [A: nat,A2: set_nat,B2: set_nat] :
% 0.30/0.60        ( ( ( member_nat @ A @ A2 )
% 0.30/0.60         => ( ( inf_inf_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 0.30/0.60            = ( insert_nat @ A @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) )
% 0.30/0.60        & ( ~ ( member_nat @ A @ A2 )
% 0.30/0.60         => ( ( inf_inf_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 0.30/0.60            = ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Int_insert_right
% 0.30/0.60  thf(fact_6500_Int__insert__left,axiom,
% 0.30/0.60      ! [A: produc3843707927480180839at_nat,C2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.60        ( ( ( member8757157785044589968at_nat @ A @ C2 )
% 0.30/0.60         => ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A @ B2 ) @ C2 )
% 0.30/0.60            = ( insert9069300056098147895at_nat @ A @ ( inf_in7913087082777306421at_nat @ B2 @ C2 ) ) ) )
% 0.30/0.60        & ( ~ ( member8757157785044589968at_nat @ A @ C2 )
% 0.30/0.60         => ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A @ B2 ) @ C2 )
% 0.30/0.60            = ( inf_in7913087082777306421at_nat @ B2 @ C2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Int_insert_left
% 0.30/0.60  thf(fact_6501_Int__insert__left,axiom,
% 0.30/0.60      ! [A: $o,C2: set_o,B2: set_o] :
% 0.30/0.60        ( ( ( member_o @ A @ C2 )
% 0.30/0.60         => ( ( inf_inf_set_o @ ( insert_o @ A @ B2 ) @ C2 )
% 0.30/0.60            = ( insert_o @ A @ ( inf_inf_set_o @ B2 @ C2 ) ) ) )
% 0.30/0.60        & ( ~ ( member_o @ A @ C2 )
% 0.30/0.60         => ( ( inf_inf_set_o @ ( insert_o @ A @ B2 ) @ C2 )
% 0.30/0.60            = ( inf_inf_set_o @ B2 @ C2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Int_insert_left
% 0.30/0.60  thf(fact_6502_Int__insert__left,axiom,
% 0.30/0.60      ! [A: set_Pr958786334691620121nt_int,C2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 0.30/0.60        ( ( ( member2340774599025711042nt_int @ A @ C2 )
% 0.30/0.60         => ( ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ B2 ) @ C2 )
% 0.30/0.60            = ( insert8897473484851387113nt_int @ A @ ( inf_in8396524679539076455nt_int @ B2 @ C2 ) ) ) )
% 0.30/0.60        & ( ~ ( member2340774599025711042nt_int @ A @ C2 )
% 0.30/0.60         => ( ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ B2 ) @ C2 )
% 0.30/0.60            = ( inf_in8396524679539076455nt_int @ B2 @ C2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Int_insert_left
% 0.30/0.60  thf(fact_6503_Int__insert__left,axiom,
% 0.30/0.60      ! [A: set_nat,C2: set_set_nat,B2: set_set_nat] :
% 0.30/0.60        ( ( ( member_set_nat @ A @ C2 )
% 0.30/0.60         => ( ( inf_inf_set_set_nat @ ( insert_set_nat @ A @ B2 ) @ C2 )
% 0.30/0.60            = ( insert_set_nat @ A @ ( inf_inf_set_set_nat @ B2 @ C2 ) ) ) )
% 0.30/0.60        & ( ~ ( member_set_nat @ A @ C2 )
% 0.30/0.60         => ( ( inf_inf_set_set_nat @ ( insert_set_nat @ A @ B2 ) @ C2 )
% 0.30/0.60            = ( inf_inf_set_set_nat @ B2 @ C2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Int_insert_left
% 0.30/0.60  thf(fact_6504_Int__insert__left,axiom,
% 0.30/0.60      ! [A: int,C2: set_int,B2: set_int] :
% 0.30/0.60        ( ( ( member_int @ A @ C2 )
% 0.30/0.60         => ( ( inf_inf_set_int @ ( insert_int @ A @ B2 ) @ C2 )
% 0.30/0.60            = ( insert_int @ A @ ( inf_inf_set_int @ B2 @ C2 ) ) ) )
% 0.30/0.60        & ( ~ ( member_int @ A @ C2 )
% 0.30/0.60         => ( ( inf_inf_set_int @ ( insert_int @ A @ B2 ) @ C2 )
% 0.30/0.60            = ( inf_inf_set_int @ B2 @ C2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Int_insert_left
% 0.30/0.60  thf(fact_6505_Int__insert__left,axiom,
% 0.30/0.60      ! [A: produc3658429121746597890et_nat > $o,C2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 0.30/0.60        ( ( ( member6576561426505652726_nat_o @ A @ C2 )
% 0.30/0.60         => ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A @ B2 ) @ C2 )
% 0.30/0.60            = ( insert5175938949040314269_nat_o @ A @ ( inf_in1906310914598751387_nat_o @ B2 @ C2 ) ) ) )
% 0.30/0.60        & ( ~ ( member6576561426505652726_nat_o @ A @ C2 )
% 0.30/0.60         => ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A @ B2 ) @ C2 )
% 0.30/0.60            = ( inf_in1906310914598751387_nat_o @ B2 @ C2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Int_insert_left
% 0.30/0.60  thf(fact_6506_Int__insert__left,axiom,
% 0.30/0.60      ! [A: product_prod_nat_nat,C2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.60        ( ( ( member8440522571783428010at_nat @ A @ C2 )
% 0.30/0.60         => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ B2 ) @ C2 )
% 0.30/0.60            = ( insert8211810215607154385at_nat @ A @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) ) ) )
% 0.30/0.60        & ( ~ ( member8440522571783428010at_nat @ A @ C2 )
% 0.30/0.60         => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ B2 ) @ C2 )
% 0.30/0.60            = ( inf_in2572325071724192079at_nat @ B2 @ C2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Int_insert_left
% 0.30/0.60  thf(fact_6507_Int__insert__left,axiom,
% 0.30/0.60      ! [A: nat,C2: set_nat,B2: set_nat] :
% 0.30/0.60        ( ( ( member_nat @ A @ C2 )
% 0.30/0.60         => ( ( inf_inf_set_nat @ ( insert_nat @ A @ B2 ) @ C2 )
% 0.30/0.60            = ( insert_nat @ A @ ( inf_inf_set_nat @ B2 @ C2 ) ) ) )
% 0.30/0.60        & ( ~ ( member_nat @ A @ C2 )
% 0.30/0.60         => ( ( inf_inf_set_nat @ ( insert_nat @ A @ B2 ) @ C2 )
% 0.30/0.60            = ( inf_inf_set_nat @ B2 @ C2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Int_insert_left
% 0.30/0.60  thf(fact_6508_flip__bit__nat__def,axiom,
% 0.30/0.60      ( bit_se2161824704523386999it_nat
% 0.30/0.60      = ( ^ [M2: nat,N2: nat] : ( bit_se6528837805403552850or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M2 @ one_one_nat ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % flip_bit_nat_def
% 0.30/0.60  thf(fact_6509_push__bit__minus,axiom,
% 0.30/0.60      ! [N: nat,A: code_integer] :
% 0.30/0.60        ( ( bit_se7788150548672797655nteger @ N @ ( uminus1351360451143612070nteger @ A ) )
% 0.30/0.60        = ( uminus1351360451143612070nteger @ ( bit_se7788150548672797655nteger @ N @ A ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % push_bit_minus
% 0.30/0.60  thf(fact_6510_push__bit__minus,axiom,
% 0.30/0.60      ! [N: nat,A: int] :
% 0.30/0.60        ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ A ) )
% 0.30/0.60        = ( uminus_uminus_int @ ( bit_se545348938243370406it_int @ N @ A ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % push_bit_minus
% 0.30/0.60  thf(fact_6511_Collect__conv__if2,axiom,
% 0.30/0.60      ! [P: produc3843707927480180839at_nat > $o,A: produc3843707927480180839at_nat] :
% 0.30/0.60        ( ( ( P @ A )
% 0.30/0.60         => ( ( collec6321179662152712658at_nat
% 0.30/0.60              @ ^ [X3: produc3843707927480180839at_nat] :
% 0.30/0.60                  ( ( A = X3 )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) )
% 0.30/0.60        & ( ~ ( P @ A )
% 0.30/0.60         => ( ( collec6321179662152712658at_nat
% 0.30/0.60              @ ^ [X3: produc3843707927480180839at_nat] :
% 0.30/0.60                  ( ( A = X3 )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = bot_bo228742789529271731at_nat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Collect_conv_if2
% 0.30/0.60  thf(fact_6512_Collect__conv__if2,axiom,
% 0.30/0.60      ! [P: set_Pr958786334691620121nt_int > $o,A: set_Pr958786334691620121nt_int] :
% 0.30/0.60        ( ( ( P @ A )
% 0.30/0.60         => ( ( collec5210948495886036740nt_int
% 0.30/0.60              @ ^ [X3: set_Pr958786334691620121nt_int] :
% 0.30/0.60                  ( ( A = X3 )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) )
% 0.30/0.60        & ( ~ ( P @ A )
% 0.30/0.60         => ( ( collec5210948495886036740nt_int
% 0.30/0.60              @ ^ [X3: set_Pr958786334691620121nt_int] :
% 0.30/0.60                  ( ( A = X3 )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = bot_bo1488462491386950373nt_int ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Collect_conv_if2
% 0.30/0.60  thf(fact_6513_Collect__conv__if2,axiom,
% 0.30/0.60      ! [P: set_nat > $o,A: set_nat] :
% 0.30/0.60        ( ( ( P @ A )
% 0.30/0.60         => ( ( collect_set_nat
% 0.30/0.60              @ ^ [X3: set_nat] :
% 0.30/0.60                  ( ( A = X3 )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.30/0.60        & ( ~ ( P @ A )
% 0.30/0.60         => ( ( collect_set_nat
% 0.30/0.60              @ ^ [X3: set_nat] :
% 0.30/0.60                  ( ( A = X3 )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = bot_bot_set_set_nat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Collect_conv_if2
% 0.30/0.60  thf(fact_6514_Collect__conv__if2,axiom,
% 0.30/0.60      ! [P: ( produc3658429121746597890et_nat > $o ) > $o,A: produc3658429121746597890et_nat > $o] :
% 0.30/0.60        ( ( ( P @ A )
% 0.30/0.60         => ( ( collec939566748876313656_nat_o
% 0.30/0.60              @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.30/0.60                  ( ( A = X3 )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = ( insert5175938949040314269_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ) )
% 0.30/0.60        & ( ~ ( P @ A )
% 0.30/0.60         => ( ( collec939566748876313656_nat_o
% 0.30/0.60              @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.30/0.60                  ( ( A = X3 )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = bot_bo7824918357723582233_nat_o ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Collect_conv_if2
% 0.30/0.60  thf(fact_6515_Collect__conv__if2,axiom,
% 0.30/0.60      ! [P: product_prod_nat_nat > $o,A: product_prod_nat_nat] :
% 0.30/0.60        ( ( ( P @ A )
% 0.30/0.60         => ( ( collec3392354462482085612at_nat
% 0.30/0.60              @ ^ [X3: product_prod_nat_nat] :
% 0.30/0.60                  ( ( A = X3 )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 0.30/0.60        & ( ~ ( P @ A )
% 0.30/0.60         => ( ( collec3392354462482085612at_nat
% 0.30/0.60              @ ^ [X3: product_prod_nat_nat] :
% 0.30/0.60                  ( ( A = X3 )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = bot_bo2099793752762293965at_nat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Collect_conv_if2
% 0.30/0.60  thf(fact_6516_Collect__conv__if2,axiom,
% 0.30/0.60      ! [P: $o > $o,A: $o] :
% 0.30/0.60        ( ( ( P @ A )
% 0.30/0.60         => ( ( collect_o
% 0.30/0.60              @ ^ [X3: $o] :
% 0.30/0.60                  ( ( A = X3 )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.30/0.60        & ( ~ ( P @ A )
% 0.30/0.60         => ( ( collect_o
% 0.30/0.60              @ ^ [X3: $o] :
% 0.30/0.60                  ( ( A = X3 )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = bot_bot_set_o ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Collect_conv_if2
% 0.30/0.60  thf(fact_6517_Collect__conv__if2,axiom,
% 0.30/0.60      ! [P: nat > $o,A: nat] :
% 0.30/0.60        ( ( ( P @ A )
% 0.30/0.60         => ( ( collect_nat
% 0.30/0.60              @ ^ [X3: nat] :
% 0.30/0.60                  ( ( A = X3 )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.30/0.60        & ( ~ ( P @ A )
% 0.30/0.60         => ( ( collect_nat
% 0.30/0.60              @ ^ [X3: nat] :
% 0.30/0.60                  ( ( A = X3 )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = bot_bot_set_nat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Collect_conv_if2
% 0.30/0.60  thf(fact_6518_Collect__conv__if2,axiom,
% 0.30/0.60      ! [P: int > $o,A: int] :
% 0.30/0.60        ( ( ( P @ A )
% 0.30/0.60         => ( ( collect_int
% 0.30/0.60              @ ^ [X3: int] :
% 0.30/0.60                  ( ( A = X3 )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.30/0.60        & ( ~ ( P @ A )
% 0.30/0.60         => ( ( collect_int
% 0.30/0.60              @ ^ [X3: int] :
% 0.30/0.60                  ( ( A = X3 )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = bot_bot_set_int ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Collect_conv_if2
% 0.30/0.60  thf(fact_6519_Collect__conv__if,axiom,
% 0.30/0.60      ! [P: produc3843707927480180839at_nat > $o,A: produc3843707927480180839at_nat] :
% 0.30/0.60        ( ( ( P @ A )
% 0.30/0.60         => ( ( collec6321179662152712658at_nat
% 0.30/0.60              @ ^ [X3: produc3843707927480180839at_nat] :
% 0.30/0.60                  ( ( X3 = A )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) )
% 0.30/0.60        & ( ~ ( P @ A )
% 0.30/0.60         => ( ( collec6321179662152712658at_nat
% 0.30/0.60              @ ^ [X3: produc3843707927480180839at_nat] :
% 0.30/0.60                  ( ( X3 = A )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = bot_bo228742789529271731at_nat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Collect_conv_if
% 0.30/0.60  thf(fact_6520_Collect__conv__if,axiom,
% 0.30/0.60      ! [P: set_Pr958786334691620121nt_int > $o,A: set_Pr958786334691620121nt_int] :
% 0.30/0.60        ( ( ( P @ A )
% 0.30/0.60         => ( ( collec5210948495886036740nt_int
% 0.30/0.60              @ ^ [X3: set_Pr958786334691620121nt_int] :
% 0.30/0.60                  ( ( X3 = A )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) )
% 0.30/0.60        & ( ~ ( P @ A )
% 0.30/0.60         => ( ( collec5210948495886036740nt_int
% 0.30/0.60              @ ^ [X3: set_Pr958786334691620121nt_int] :
% 0.30/0.60                  ( ( X3 = A )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = bot_bo1488462491386950373nt_int ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Collect_conv_if
% 0.30/0.60  thf(fact_6521_Collect__conv__if,axiom,
% 0.30/0.60      ! [P: set_nat > $o,A: set_nat] :
% 0.30/0.60        ( ( ( P @ A )
% 0.30/0.60         => ( ( collect_set_nat
% 0.30/0.60              @ ^ [X3: set_nat] :
% 0.30/0.60                  ( ( X3 = A )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.30/0.60        & ( ~ ( P @ A )
% 0.30/0.60         => ( ( collect_set_nat
% 0.30/0.60              @ ^ [X3: set_nat] :
% 0.30/0.60                  ( ( X3 = A )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = bot_bot_set_set_nat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Collect_conv_if
% 0.30/0.60  thf(fact_6522_Collect__conv__if,axiom,
% 0.30/0.60      ! [P: ( produc3658429121746597890et_nat > $o ) > $o,A: produc3658429121746597890et_nat > $o] :
% 0.30/0.60        ( ( ( P @ A )
% 0.30/0.60         => ( ( collec939566748876313656_nat_o
% 0.30/0.60              @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.30/0.60                  ( ( X3 = A )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = ( insert5175938949040314269_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ) )
% 0.30/0.60        & ( ~ ( P @ A )
% 0.30/0.60         => ( ( collec939566748876313656_nat_o
% 0.30/0.60              @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.30/0.60                  ( ( X3 = A )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = bot_bo7824918357723582233_nat_o ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Collect_conv_if
% 0.30/0.60  thf(fact_6523_Collect__conv__if,axiom,
% 0.30/0.60      ! [P: product_prod_nat_nat > $o,A: product_prod_nat_nat] :
% 0.30/0.60        ( ( ( P @ A )
% 0.30/0.60         => ( ( collec3392354462482085612at_nat
% 0.30/0.60              @ ^ [X3: product_prod_nat_nat] :
% 0.30/0.60                  ( ( X3 = A )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 0.30/0.60        & ( ~ ( P @ A )
% 0.30/0.60         => ( ( collec3392354462482085612at_nat
% 0.30/0.60              @ ^ [X3: product_prod_nat_nat] :
% 0.30/0.60                  ( ( X3 = A )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = bot_bo2099793752762293965at_nat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Collect_conv_if
% 0.30/0.60  thf(fact_6524_Collect__conv__if,axiom,
% 0.30/0.60      ! [P: $o > $o,A: $o] :
% 0.30/0.60        ( ( ( P @ A )
% 0.30/0.60         => ( ( collect_o
% 0.30/0.60              @ ^ [X3: $o] :
% 0.30/0.60                  ( ( X3 = A )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.30/0.60        & ( ~ ( P @ A )
% 0.30/0.60         => ( ( collect_o
% 0.30/0.60              @ ^ [X3: $o] :
% 0.30/0.60                  ( ( X3 = A )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = bot_bot_set_o ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Collect_conv_if
% 0.30/0.60  thf(fact_6525_Collect__conv__if,axiom,
% 0.30/0.60      ! [P: nat > $o,A: nat] :
% 0.30/0.60        ( ( ( P @ A )
% 0.30/0.60         => ( ( collect_nat
% 0.30/0.60              @ ^ [X3: nat] :
% 0.30/0.60                  ( ( X3 = A )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.30/0.60        & ( ~ ( P @ A )
% 0.30/0.60         => ( ( collect_nat
% 0.30/0.60              @ ^ [X3: nat] :
% 0.30/0.60                  ( ( X3 = A )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = bot_bot_set_nat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Collect_conv_if
% 0.30/0.60  thf(fact_6526_Collect__conv__if,axiom,
% 0.30/0.60      ! [P: int > $o,A: int] :
% 0.30/0.60        ( ( ( P @ A )
% 0.30/0.60         => ( ( collect_int
% 0.30/0.60              @ ^ [X3: int] :
% 0.30/0.60                  ( ( X3 = A )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.30/0.60        & ( ~ ( P @ A )
% 0.30/0.60         => ( ( collect_int
% 0.30/0.60              @ ^ [X3: int] :
% 0.30/0.60                  ( ( X3 = A )
% 0.30/0.60                  & ( P @ X3 ) ) )
% 0.30/0.60            = bot_bot_set_int ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Collect_conv_if
% 0.30/0.60  thf(fact_6527_insert__def,axiom,
% 0.30/0.60      ( insert8211810215607154385at_nat
% 0.30/0.60      = ( ^ [A3: product_prod_nat_nat] :
% 0.30/0.60            ( sup_su6327502436637775413at_nat
% 0.30/0.60            @ ( collec3392354462482085612at_nat
% 0.30/0.60              @ ^ [X3: product_prod_nat_nat] : ( X3 = A3 ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_def
% 0.30/0.60  thf(fact_6528_insert__def,axiom,
% 0.30/0.60      ( insert_o
% 0.30/0.60      = ( ^ [A3: $o] :
% 0.30/0.60            ( sup_sup_set_o
% 0.30/0.60            @ ( collect_o
% 0.30/0.60              @ ^ [X3: $o] : ( X3 = A3 ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_def
% 0.30/0.60  thf(fact_6529_insert__def,axiom,
% 0.30/0.60      ( insert8897473484851387113nt_int
% 0.30/0.60      = ( ^ [A3: set_Pr958786334691620121nt_int] :
% 0.30/0.60            ( sup_su2047564715030645325nt_int
% 0.30/0.60            @ ( collec5210948495886036740nt_int
% 0.30/0.60              @ ^ [X3: set_Pr958786334691620121nt_int] : ( X3 = A3 ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_def
% 0.30/0.60  thf(fact_6530_insert__def,axiom,
% 0.30/0.60      ( insert_set_nat
% 0.30/0.60      = ( ^ [A3: set_nat] :
% 0.30/0.60            ( sup_sup_set_set_nat
% 0.30/0.60            @ ( collect_set_nat
% 0.30/0.60              @ ^ [X3: set_nat] : ( X3 = A3 ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_def
% 0.30/0.60  thf(fact_6531_insert__def,axiom,
% 0.30/0.60      ( insert_int
% 0.30/0.60      = ( ^ [A3: int] :
% 0.30/0.60            ( sup_sup_set_int
% 0.30/0.60            @ ( collect_int
% 0.30/0.60              @ ^ [X3: int] : ( X3 = A3 ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_def
% 0.30/0.60  thf(fact_6532_insert__def,axiom,
% 0.30/0.60      ( insert5175938949040314269_nat_o
% 0.30/0.60      = ( ^ [A3: produc3658429121746597890et_nat > $o] :
% 0.30/0.60            ( sup_su5209123915105501825_nat_o
% 0.30/0.60            @ ( collec939566748876313656_nat_o
% 0.30/0.60              @ ^ [X3: produc3658429121746597890et_nat > $o] : ( X3 = A3 ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_def
% 0.30/0.60  thf(fact_6533_insert__def,axiom,
% 0.30/0.60      ( insert6337962749363155127at_nat
% 0.30/0.60      = ( ^ [A3: produc4166570645942440679at_nat] :
% 0.30/0.60            ( sup_su3035147773818789531at_nat
% 0.30/0.60            @ ( collec5204685387357076818at_nat
% 0.30/0.60              @ ^ [X3: produc4166570645942440679at_nat] : ( X3 = A3 ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_def
% 0.30/0.60  thf(fact_6534_insert__def,axiom,
% 0.30/0.60      ( insert9069300056098147895at_nat
% 0.30/0.60      = ( ^ [A3: produc3843707927480180839at_nat] :
% 0.30/0.60            ( sup_su5525570899277871387at_nat
% 0.30/0.60            @ ( collec6321179662152712658at_nat
% 0.30/0.60              @ ^ [X3: produc3843707927480180839at_nat] : ( X3 = A3 ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_def
% 0.30/0.60  thf(fact_6535_insert__def,axiom,
% 0.30/0.60      ( insert_nat
% 0.30/0.60      = ( ^ [A3: nat] :
% 0.30/0.60            ( sup_sup_set_nat
% 0.30/0.60            @ ( collect_nat
% 0.30/0.60              @ ^ [X3: nat] : ( X3 = A3 ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_def
% 0.30/0.60  thf(fact_6536_subset__singletonD,axiom,
% 0.30/0.60      ! [A2: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat] :
% 0.30/0.60        ( ( ord_le1268244103169919719at_nat @ A2 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 0.30/0.60       => ( ( A2 = bot_bo228742789529271731at_nat )
% 0.30/0.60          | ( A2
% 0.30/0.60            = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % subset_singletonD
% 0.30/0.60  thf(fact_6537_subset__singletonD,axiom,
% 0.30/0.60      ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 0.30/0.60        ( ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 0.30/0.60       => ( ( A2 = bot_bo2099793752762293965at_nat )
% 0.30/0.60          | ( A2
% 0.30/0.60            = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % subset_singletonD
% 0.30/0.60  thf(fact_6538_subset__singletonD,axiom,
% 0.30/0.60      ! [A2: set_o,X: $o] :
% 0.30/0.60        ( ( ord_less_eq_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.30/0.60       => ( ( A2 = bot_bot_set_o )
% 0.30/0.60          | ( A2
% 0.30/0.60            = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % subset_singletonD
% 0.30/0.60  thf(fact_6539_subset__singletonD,axiom,
% 0.30/0.60      ! [A2: set_int,X: int] :
% 0.30/0.60        ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.30/0.60       => ( ( A2 = bot_bot_set_int )
% 0.30/0.60          | ( A2
% 0.30/0.60            = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % subset_singletonD
% 0.30/0.60  thf(fact_6540_subset__singletonD,axiom,
% 0.30/0.60      ! [A2: set_nat,X: nat] :
% 0.30/0.60        ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.30/0.60       => ( ( A2 = bot_bot_set_nat )
% 0.30/0.60          | ( A2
% 0.30/0.60            = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % subset_singletonD
% 0.30/0.60  thf(fact_6541_subset__singleton__iff,axiom,
% 0.30/0.60      ! [X7: set_Pr4329608150637261639at_nat,A: produc3843707927480180839at_nat] :
% 0.30/0.60        ( ( ord_le1268244103169919719at_nat @ X7 @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) )
% 0.30/0.60        = ( ( X7 = bot_bo228742789529271731at_nat )
% 0.30/0.60          | ( X7
% 0.30/0.60            = ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % subset_singleton_iff
% 0.30/0.60  thf(fact_6542_subset__singleton__iff,axiom,
% 0.30/0.60      ! [X7: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
% 0.30/0.60        ( ( ord_le3146513528884898305at_nat @ X7 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) )
% 0.30/0.60        = ( ( X7 = bot_bo2099793752762293965at_nat )
% 0.30/0.60          | ( X7
% 0.30/0.60            = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % subset_singleton_iff
% 0.30/0.60  thf(fact_6543_subset__singleton__iff,axiom,
% 0.30/0.60      ! [X7: set_o,A: $o] :
% 0.30/0.60        ( ( ord_less_eq_set_o @ X7 @ ( insert_o @ A @ bot_bot_set_o ) )
% 0.30/0.60        = ( ( X7 = bot_bot_set_o )
% 0.30/0.60          | ( X7
% 0.30/0.60            = ( insert_o @ A @ bot_bot_set_o ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % subset_singleton_iff
% 0.30/0.60  thf(fact_6544_subset__singleton__iff,axiom,
% 0.30/0.60      ! [X7: set_int,A: int] :
% 0.30/0.60        ( ( ord_less_eq_set_int @ X7 @ ( insert_int @ A @ bot_bot_set_int ) )
% 0.30/0.60        = ( ( X7 = bot_bot_set_int )
% 0.30/0.60          | ( X7
% 0.30/0.60            = ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % subset_singleton_iff
% 0.30/0.60  thf(fact_6545_subset__singleton__iff,axiom,
% 0.30/0.60      ! [X7: set_nat,A: nat] :
% 0.30/0.60        ( ( ord_less_eq_set_nat @ X7 @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 0.30/0.60        = ( ( X7 = bot_bot_set_nat )
% 0.30/0.60          | ( X7
% 0.30/0.60            = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % subset_singleton_iff
% 0.30/0.60  thf(fact_6546_singleton__Un__iff,axiom,
% 0.30/0.60      ! [X: produc4166570645942440679at_nat,A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 0.30/0.60        ( ( ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat )
% 0.30/0.60          = ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 0.30/0.60        = ( ( ( A2 = bot_bo8422036546324065075at_nat )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) )
% 0.30/0.60            & ( B2 = bot_bo8422036546324065075at_nat ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % singleton_Un_iff
% 0.30/0.60  thf(fact_6547_singleton__Un__iff,axiom,
% 0.30/0.60      ! [X: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.60        ( ( ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat )
% 0.30/0.60          = ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 0.30/0.60        = ( ( ( A2 = bot_bo228742789529271731at_nat )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 0.30/0.60            & ( B2 = bot_bo228742789529271731at_nat ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % singleton_Un_iff
% 0.30/0.60  thf(fact_6548_singleton__Un__iff,axiom,
% 0.30/0.60      ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.60        ( ( ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat )
% 0.30/0.60          = ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 0.30/0.60        = ( ( ( A2 = bot_bo2099793752762293965at_nat )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 0.30/0.60            & ( B2 = bot_bo2099793752762293965at_nat ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % singleton_Un_iff
% 0.30/0.60  thf(fact_6549_singleton__Un__iff,axiom,
% 0.30/0.60      ! [X: $o,A2: set_o,B2: set_o] :
% 0.30/0.60        ( ( ( insert_o @ X @ bot_bot_set_o )
% 0.30/0.60          = ( sup_sup_set_o @ A2 @ B2 ) )
% 0.30/0.60        = ( ( ( A2 = bot_bot_set_o )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert_o @ X @ bot_bot_set_o ) ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert_o @ X @ bot_bot_set_o ) )
% 0.30/0.60            & ( B2 = bot_bot_set_o ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert_o @ X @ bot_bot_set_o ) )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % singleton_Un_iff
% 0.30/0.60  thf(fact_6550_singleton__Un__iff,axiom,
% 0.30/0.60      ! [X: nat,A2: set_nat,B2: set_nat] :
% 0.30/0.60        ( ( ( insert_nat @ X @ bot_bot_set_nat )
% 0.30/0.60          = ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.60        = ( ( ( A2 = bot_bot_set_nat )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.30/0.60            & ( B2 = bot_bot_set_nat ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % singleton_Un_iff
% 0.30/0.60  thf(fact_6551_singleton__Un__iff,axiom,
% 0.30/0.60      ! [X: int,A2: set_int,B2: set_int] :
% 0.30/0.60        ( ( ( insert_int @ X @ bot_bot_set_int )
% 0.30/0.60          = ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.60        = ( ( ( A2 = bot_bot_set_int )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert_int @ X @ bot_bot_set_int ) ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert_int @ X @ bot_bot_set_int ) )
% 0.30/0.60            & ( B2 = bot_bot_set_int ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert_int @ X @ bot_bot_set_int ) )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % singleton_Un_iff
% 0.30/0.60  thf(fact_6552_Un__singleton__iff,axiom,
% 0.30/0.60      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,X: produc4166570645942440679at_nat] :
% 0.30/0.60        ( ( ( sup_su3035147773818789531at_nat @ A2 @ B2 )
% 0.30/0.60          = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) )
% 0.30/0.60        = ( ( ( A2 = bot_bo8422036546324065075at_nat )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) )
% 0.30/0.60            & ( B2 = bot_bo8422036546324065075at_nat ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Un_singleton_iff
% 0.30/0.60  thf(fact_6553_Un__singleton__iff,axiom,
% 0.30/0.60      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat] :
% 0.30/0.60        ( ( ( sup_su5525570899277871387at_nat @ A2 @ B2 )
% 0.30/0.60          = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 0.30/0.60        = ( ( ( A2 = bot_bo228742789529271731at_nat )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 0.30/0.60            & ( B2 = bot_bo228742789529271731at_nat ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Un_singleton_iff
% 0.30/0.60  thf(fact_6554_Un__singleton__iff,axiom,
% 0.30/0.60      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 0.30/0.60        ( ( ( sup_su6327502436637775413at_nat @ A2 @ B2 )
% 0.30/0.60          = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 0.30/0.60        = ( ( ( A2 = bot_bo2099793752762293965at_nat )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 0.30/0.60            & ( B2 = bot_bo2099793752762293965at_nat ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Un_singleton_iff
% 0.30/0.60  thf(fact_6555_Un__singleton__iff,axiom,
% 0.30/0.60      ! [A2: set_o,B2: set_o,X: $o] :
% 0.30/0.60        ( ( ( sup_sup_set_o @ A2 @ B2 )
% 0.30/0.60          = ( insert_o @ X @ bot_bot_set_o ) )
% 0.30/0.60        = ( ( ( A2 = bot_bot_set_o )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert_o @ X @ bot_bot_set_o ) ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert_o @ X @ bot_bot_set_o ) )
% 0.30/0.60            & ( B2 = bot_bot_set_o ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert_o @ X @ bot_bot_set_o ) )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Un_singleton_iff
% 0.30/0.60  thf(fact_6556_Un__singleton__iff,axiom,
% 0.30/0.60      ! [A2: set_nat,B2: set_nat,X: nat] :
% 0.30/0.60        ( ( ( sup_sup_set_nat @ A2 @ B2 )
% 0.30/0.60          = ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.30/0.60        = ( ( ( A2 = bot_bot_set_nat )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.30/0.60            & ( B2 = bot_bot_set_nat ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Un_singleton_iff
% 0.30/0.60  thf(fact_6557_Un__singleton__iff,axiom,
% 0.30/0.60      ! [A2: set_int,B2: set_int,X: int] :
% 0.30/0.60        ( ( ( sup_sup_set_int @ A2 @ B2 )
% 0.30/0.60          = ( insert_int @ X @ bot_bot_set_int ) )
% 0.30/0.60        = ( ( ( A2 = bot_bot_set_int )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert_int @ X @ bot_bot_set_int ) ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert_int @ X @ bot_bot_set_int ) )
% 0.30/0.60            & ( B2 = bot_bot_set_int ) )
% 0.30/0.60          | ( ( A2
% 0.30/0.60              = ( insert_int @ X @ bot_bot_set_int ) )
% 0.30/0.60            & ( B2
% 0.30/0.60              = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Un_singleton_iff
% 0.30/0.60  thf(fact_6558_insert__is__Un,axiom,
% 0.30/0.60      ( insert6337962749363155127at_nat
% 0.30/0.60      = ( ^ [A3: produc4166570645942440679at_nat] : ( sup_su3035147773818789531at_nat @ ( insert6337962749363155127at_nat @ A3 @ bot_bo8422036546324065075at_nat ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_is_Un
% 0.30/0.60  thf(fact_6559_insert__is__Un,axiom,
% 0.30/0.60      ( insert9069300056098147895at_nat
% 0.30/0.60      = ( ^ [A3: produc3843707927480180839at_nat] : ( sup_su5525570899277871387at_nat @ ( insert9069300056098147895at_nat @ A3 @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_is_Un
% 0.30/0.60  thf(fact_6560_insert__is__Un,axiom,
% 0.30/0.60      ( insert8211810215607154385at_nat
% 0.30/0.60      = ( ^ [A3: product_prod_nat_nat] : ( sup_su6327502436637775413at_nat @ ( insert8211810215607154385at_nat @ A3 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_is_Un
% 0.30/0.60  thf(fact_6561_insert__is__Un,axiom,
% 0.30/0.60      ( insert_o
% 0.30/0.60      = ( ^ [A3: $o] : ( sup_sup_set_o @ ( insert_o @ A3 @ bot_bot_set_o ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_is_Un
% 0.30/0.60  thf(fact_6562_insert__is__Un,axiom,
% 0.30/0.60      ( insert_nat
% 0.30/0.60      = ( ^ [A3: nat] : ( sup_sup_set_nat @ ( insert_nat @ A3 @ bot_bot_set_nat ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_is_Un
% 0.30/0.60  thf(fact_6563_insert__is__Un,axiom,
% 0.30/0.60      ( insert_int
% 0.30/0.60      = ( ^ [A3: int] : ( sup_sup_set_int @ ( insert_int @ A3 @ bot_bot_set_int ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_is_Un
% 0.30/0.60  thf(fact_6564_set__minus__singleton__eq,axiom,
% 0.30/0.60      ! [X: produc3843707927480180839at_nat,X7: set_Pr4329608150637261639at_nat] :
% 0.30/0.60        ( ~ ( member8757157785044589968at_nat @ X @ X7 )
% 0.30/0.60       => ( ( minus_3314409938677909166at_nat @ X7 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 0.30/0.60          = X7 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % set_minus_singleton_eq
% 0.30/0.60  thf(fact_6565_set__minus__singleton__eq,axiom,
% 0.30/0.60      ! [X: set_Pr958786334691620121nt_int,X7: set_se6260736226359567993nt_int] :
% 0.30/0.60        ( ~ ( member2340774599025711042nt_int @ X @ X7 )
% 0.30/0.60       => ( ( minus_2612819937483484256nt_int @ X7 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
% 0.30/0.60          = X7 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % set_minus_singleton_eq
% 0.30/0.60  thf(fact_6566_set__minus__singleton__eq,axiom,
% 0.30/0.60      ! [X: set_nat,X7: set_set_nat] :
% 0.30/0.60        ( ~ ( member_set_nat @ X @ X7 )
% 0.30/0.60       => ( ( minus_2163939370556025621et_nat @ X7 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 0.30/0.60          = X7 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % set_minus_singleton_eq
% 0.30/0.60  thf(fact_6567_set__minus__singleton__eq,axiom,
% 0.30/0.60      ! [X: produc3658429121746597890et_nat > $o,X7: set_Pr4532377907799695533_nat_o] :
% 0.30/0.60        ( ~ ( member6576561426505652726_nat_o @ X @ X7 )
% 0.30/0.60       => ( ( minus_1801376950450012436_nat_o @ X7 @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 0.30/0.60          = X7 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % set_minus_singleton_eq
% 0.30/0.60  thf(fact_6568_set__minus__singleton__eq,axiom,
% 0.30/0.60      ! [X: product_prod_nat_nat,X7: set_Pr1261947904930325089at_nat] :
% 0.30/0.60        ( ~ ( member8440522571783428010at_nat @ X @ X7 )
% 0.30/0.60       => ( ( minus_1356011639430497352at_nat @ X7 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 0.30/0.60          = X7 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % set_minus_singleton_eq
% 0.30/0.60  thf(fact_6569_set__minus__singleton__eq,axiom,
% 0.30/0.60      ! [X: $o,X7: set_o] :
% 0.30/0.60        ( ~ ( member_o @ X @ X7 )
% 0.30/0.60       => ( ( minus_minus_set_o @ X7 @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.30/0.60          = X7 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % set_minus_singleton_eq
% 0.30/0.60  thf(fact_6570_set__minus__singleton__eq,axiom,
% 0.30/0.60      ! [X: int,X7: set_int] :
% 0.30/0.60        ( ~ ( member_int @ X @ X7 )
% 0.30/0.60       => ( ( minus_minus_set_int @ X7 @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.30/0.60          = X7 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % set_minus_singleton_eq
% 0.30/0.60  thf(fact_6571_set__minus__singleton__eq,axiom,
% 0.30/0.60      ! [X: nat,X7: set_nat] :
% 0.30/0.60        ( ~ ( member_nat @ X @ X7 )
% 0.30/0.60       => ( ( minus_minus_set_nat @ X7 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.30/0.60          = X7 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % set_minus_singleton_eq
% 0.30/0.60  thf(fact_6572_insert__minus__eq,axiom,
% 0.30/0.60      ! [X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.30/0.60        ( ( X != Y )
% 0.30/0.60       => ( ( minus_3314409938677909166at_nat @ ( insert9069300056098147895at_nat @ X @ A2 ) @ ( insert9069300056098147895at_nat @ Y @ bot_bo228742789529271731at_nat ) )
% 0.30/0.60          = ( insert9069300056098147895at_nat @ X @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ Y @ bot_bo228742789529271731at_nat ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_minus_eq
% 0.30/0.60  thf(fact_6573_insert__minus__eq,axiom,
% 0.30/0.60      ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.30/0.60        ( ( X != Y )
% 0.30/0.60       => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ ( insert8211810215607154385at_nat @ Y @ bot_bo2099793752762293965at_nat ) )
% 0.30/0.60          = ( insert8211810215607154385at_nat @ X @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ Y @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_minus_eq
% 0.30/0.60  thf(fact_6574_insert__minus__eq,axiom,
% 0.30/0.60      ! [X: $o,Y: $o,A2: set_o] :
% 0.30/0.60        ( ( X != Y )
% 0.30/0.60       => ( ( minus_minus_set_o @ ( insert_o @ X @ A2 ) @ ( insert_o @ Y @ bot_bot_set_o ) )
% 0.30/0.60          = ( insert_o @ X @ ( minus_minus_set_o @ A2 @ ( insert_o @ Y @ bot_bot_set_o ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_minus_eq
% 0.30/0.60  thf(fact_6575_insert__minus__eq,axiom,
% 0.30/0.60      ! [X: int,Y: int,A2: set_int] :
% 0.30/0.60        ( ( X != Y )
% 0.30/0.60       => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ ( insert_int @ Y @ bot_bot_set_int ) )
% 0.30/0.60          = ( insert_int @ X @ ( minus_minus_set_int @ A2 @ ( insert_int @ Y @ bot_bot_set_int ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_minus_eq
% 0.30/0.60  thf(fact_6576_insert__minus__eq,axiom,
% 0.30/0.60      ! [X: nat,Y: nat,A2: set_nat] :
% 0.30/0.60        ( ( X != Y )
% 0.30/0.60       => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ ( insert_nat @ Y @ bot_bot_set_nat ) )
% 0.30/0.60          = ( insert_nat @ X @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ Y @ bot_bot_set_nat ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_minus_eq
% 0.30/0.60  thf(fact_6577_Diff__insert,axiom,
% 0.30/0.60      ! [A2: set_Pr4329608150637261639at_nat,A: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.60        ( ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ B2 ) )
% 0.30/0.60        = ( minus_3314409938677909166at_nat @ ( minus_3314409938677909166at_nat @ A2 @ B2 ) @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_insert
% 0.30/0.60  thf(fact_6578_Diff__insert,axiom,
% 0.30/0.60      ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.60        ( ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 0.30/0.60        = ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_insert
% 0.30/0.60  thf(fact_6579_Diff__insert,axiom,
% 0.30/0.60      ! [A2: set_o,A: $o,B2: set_o] :
% 0.30/0.60        ( ( minus_minus_set_o @ A2 @ ( insert_o @ A @ B2 ) )
% 0.30/0.60        = ( minus_minus_set_o @ ( minus_minus_set_o @ A2 @ B2 ) @ ( insert_o @ A @ bot_bot_set_o ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_insert
% 0.30/0.60  thf(fact_6580_Diff__insert,axiom,
% 0.30/0.60      ! [A2: set_int,A: int,B2: set_int] :
% 0.30/0.60        ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 0.30/0.60        = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ B2 ) @ ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_insert
% 0.30/0.60  thf(fact_6581_Diff__insert,axiom,
% 0.30/0.60      ! [A2: set_nat,A: nat,B2: set_nat] :
% 0.30/0.60        ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 0.30/0.60        = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_insert
% 0.30/0.60  thf(fact_6582_insert__Diff,axiom,
% 0.30/0.60      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.30/0.60        ( ( member8757157785044589968at_nat @ A @ A2 )
% 0.30/0.60       => ( ( insert9069300056098147895at_nat @ A @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) )
% 0.30/0.60          = A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_Diff
% 0.30/0.60  thf(fact_6583_insert__Diff,axiom,
% 0.30/0.60      ! [A: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int] :
% 0.30/0.60        ( ( member2340774599025711042nt_int @ A @ A2 )
% 0.30/0.60       => ( ( insert8897473484851387113nt_int @ A @ ( minus_2612819937483484256nt_int @ A2 @ ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) )
% 0.30/0.60          = A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_Diff
% 0.30/0.60  thf(fact_6584_insert__Diff,axiom,
% 0.30/0.60      ! [A: set_nat,A2: set_set_nat] :
% 0.30/0.60        ( ( member_set_nat @ A @ A2 )
% 0.30/0.60       => ( ( insert_set_nat @ A @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.30/0.60          = A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_Diff
% 0.30/0.60  thf(fact_6585_insert__Diff,axiom,
% 0.30/0.60      ! [A: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o] :
% 0.30/0.60        ( ( member6576561426505652726_nat_o @ A @ A2 )
% 0.30/0.60       => ( ( insert5175938949040314269_nat_o @ A @ ( minus_1801376950450012436_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ) )
% 0.30/0.60          = A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_Diff
% 0.30/0.60  thf(fact_6586_insert__Diff,axiom,
% 0.30/0.60      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.30/0.60        ( ( member8440522571783428010at_nat @ A @ A2 )
% 0.30/0.60       => ( ( insert8211810215607154385at_nat @ A @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 0.30/0.60          = A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_Diff
% 0.30/0.60  thf(fact_6587_insert__Diff,axiom,
% 0.30/0.60      ! [A: $o,A2: set_o] :
% 0.30/0.60        ( ( member_o @ A @ A2 )
% 0.30/0.60       => ( ( insert_o @ A @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.30/0.60          = A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_Diff
% 0.30/0.60  thf(fact_6588_insert__Diff,axiom,
% 0.30/0.60      ! [A: int,A2: set_int] :
% 0.30/0.60        ( ( member_int @ A @ A2 )
% 0.30/0.60       => ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.30/0.60          = A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_Diff
% 0.30/0.60  thf(fact_6589_insert__Diff,axiom,
% 0.30/0.60      ! [A: nat,A2: set_nat] :
% 0.30/0.60        ( ( member_nat @ A @ A2 )
% 0.30/0.60       => ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.30/0.60          = A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % insert_Diff
% 0.30/0.60  thf(fact_6590_Diff__insert2,axiom,
% 0.30/0.60      ! [A2: set_Pr4329608150637261639at_nat,A: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.60        ( ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ B2 ) )
% 0.30/0.60        = ( minus_3314409938677909166at_nat @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) @ B2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_insert2
% 0.30/0.60  thf(fact_6591_Diff__insert2,axiom,
% 0.30/0.60      ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.60        ( ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 0.30/0.60        = ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) @ B2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_insert2
% 0.30/0.60  thf(fact_6592_Diff__insert2,axiom,
% 0.30/0.60      ! [A2: set_o,A: $o,B2: set_o] :
% 0.30/0.60        ( ( minus_minus_set_o @ A2 @ ( insert_o @ A @ B2 ) )
% 0.30/0.60        = ( minus_minus_set_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) @ B2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_insert2
% 0.30/0.60  thf(fact_6593_Diff__insert2,axiom,
% 0.30/0.60      ! [A2: set_int,A: int,B2: set_int] :
% 0.30/0.60        ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 0.30/0.60        = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) @ B2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_insert2
% 0.30/0.60  thf(fact_6594_Diff__insert2,axiom,
% 0.30/0.60      ! [A2: set_nat,A: nat,B2: set_nat] :
% 0.30/0.60        ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 0.30/0.60        = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ B2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_insert2
% 0.30/0.60  thf(fact_6595_Diff__insert__absorb,axiom,
% 0.30/0.60      ! [X: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.30/0.60        ( ~ ( member8757157785044589968at_nat @ X @ A2 )
% 0.30/0.60       => ( ( minus_3314409938677909166at_nat @ ( insert9069300056098147895at_nat @ X @ A2 ) @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 0.30/0.60          = A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_insert_absorb
% 0.30/0.60  thf(fact_6596_Diff__insert__absorb,axiom,
% 0.30/0.60      ! [X: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int] :
% 0.30/0.60        ( ~ ( member2340774599025711042nt_int @ X @ A2 )
% 0.30/0.60       => ( ( minus_2612819937483484256nt_int @ ( insert8897473484851387113nt_int @ X @ A2 ) @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
% 0.30/0.60          = A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_insert_absorb
% 0.30/0.60  thf(fact_6597_Diff__insert__absorb,axiom,
% 0.30/0.60      ! [X: set_nat,A2: set_set_nat] :
% 0.30/0.60        ( ~ ( member_set_nat @ X @ A2 )
% 0.30/0.60       => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 0.30/0.60          = A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_insert_absorb
% 0.30/0.60  thf(fact_6598_Diff__insert__absorb,axiom,
% 0.30/0.60      ! [X: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o] :
% 0.30/0.60        ( ~ ( member6576561426505652726_nat_o @ X @ A2 )
% 0.30/0.60       => ( ( minus_1801376950450012436_nat_o @ ( insert5175938949040314269_nat_o @ X @ A2 ) @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 0.30/0.60          = A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_insert_absorb
% 0.30/0.60  thf(fact_6599_Diff__insert__absorb,axiom,
% 0.30/0.60      ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.30/0.60        ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 0.30/0.60       => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 0.30/0.60          = A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_insert_absorb
% 0.30/0.60  thf(fact_6600_Diff__insert__absorb,axiom,
% 0.30/0.60      ! [X: $o,A2: set_o] :
% 0.30/0.60        ( ~ ( member_o @ X @ A2 )
% 0.30/0.60       => ( ( minus_minus_set_o @ ( insert_o @ X @ A2 ) @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.30/0.60          = A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_insert_absorb
% 0.30/0.60  thf(fact_6601_Diff__insert__absorb,axiom,
% 0.30/0.60      ! [X: int,A2: set_int] :
% 0.30/0.60        ( ~ ( member_int @ X @ A2 )
% 0.30/0.60       => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.30/0.60          = A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_insert_absorb
% 0.30/0.60  thf(fact_6602_Diff__insert__absorb,axiom,
% 0.30/0.60      ! [X: nat,A2: set_nat] :
% 0.30/0.60        ( ~ ( member_nat @ X @ A2 )
% 0.30/0.60       => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.30/0.60          = A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_insert_absorb
% 0.30/0.60  thf(fact_6603_vimage__singleton__eq,axiom,
% 0.30/0.60      ! [A: nat,F2: nat > $o,B: $o] :
% 0.30/0.60        ( ( member_nat @ A @ ( vimage_nat_o @ F2 @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 0.30/0.60        = ( ( F2 @ A )
% 0.30/0.60          = B ) ) ).
% 0.30/0.60  
% 0.30/0.60  % vimage_singleton_eq
% 0.30/0.60  thf(fact_6604_vimage__singleton__eq,axiom,
% 0.30/0.60      ! [A: int,F2: int > $o,B: $o] :
% 0.30/0.60        ( ( member_int @ A @ ( vimage_int_o @ F2 @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 0.30/0.60        = ( ( F2 @ A )
% 0.30/0.60          = B ) ) ).
% 0.30/0.60  
% 0.30/0.60  % vimage_singleton_eq
% 0.30/0.60  thf(fact_6605_vimage__singleton__eq,axiom,
% 0.30/0.60      ! [A: nat,F2: nat > nat,B: nat] :
% 0.30/0.60        ( ( member_nat @ A @ ( vimage_nat_nat @ F2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 0.30/0.60        = ( ( F2 @ A )
% 0.30/0.60          = B ) ) ).
% 0.30/0.60  
% 0.30/0.60  % vimage_singleton_eq
% 0.30/0.60  thf(fact_6606_vimage__singleton__eq,axiom,
% 0.30/0.60      ! [A: int,F2: int > nat,B: nat] :
% 0.30/0.60        ( ( member_int @ A @ ( vimage_int_nat @ F2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 0.30/0.60        = ( ( F2 @ A )
% 0.30/0.60          = B ) ) ).
% 0.30/0.60  
% 0.30/0.60  % vimage_singleton_eq
% 0.30/0.60  thf(fact_6607_vimage__singleton__eq,axiom,
% 0.30/0.60      ! [A: nat,F2: nat > int,B: int] :
% 0.30/0.60        ( ( member_nat @ A @ ( vimage_nat_int @ F2 @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 0.30/0.60        = ( ( F2 @ A )
% 0.30/0.60          = B ) ) ).
% 0.30/0.60  
% 0.30/0.60  % vimage_singleton_eq
% 0.30/0.60  thf(fact_6608_vimage__singleton__eq,axiom,
% 0.30/0.60      ! [A: int,F2: int > int,B: int] :
% 0.30/0.60        ( ( member_int @ A @ ( vimage_int_int @ F2 @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 0.30/0.60        = ( ( F2 @ A )
% 0.30/0.60          = B ) ) ).
% 0.30/0.60  
% 0.30/0.60  % vimage_singleton_eq
% 0.30/0.60  thf(fact_6609_vimage__singleton__eq,axiom,
% 0.30/0.60      ! [A: set_nat,F2: set_nat > $o,B: $o] :
% 0.30/0.60        ( ( member_set_nat @ A @ ( vimage_set_nat_o @ F2 @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 0.30/0.60        = ( ( F2 @ A )
% 0.30/0.60          = B ) ) ).
% 0.30/0.60  
% 0.30/0.60  % vimage_singleton_eq
% 0.30/0.60  thf(fact_6610_vimage__singleton__eq,axiom,
% 0.30/0.60      ! [A: set_nat,F2: set_nat > nat,B: nat] :
% 0.30/0.60        ( ( member_set_nat @ A @ ( vimage_set_nat_nat @ F2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 0.30/0.60        = ( ( F2 @ A )
% 0.30/0.60          = B ) ) ).
% 0.30/0.60  
% 0.30/0.60  % vimage_singleton_eq
% 0.30/0.60  thf(fact_6611_vimage__singleton__eq,axiom,
% 0.30/0.60      ! [A: set_nat,F2: set_nat > int,B: int] :
% 0.30/0.60        ( ( member_set_nat @ A @ ( vimage_set_nat_int @ F2 @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 0.30/0.60        = ( ( F2 @ A )
% 0.30/0.60          = B ) ) ).
% 0.30/0.60  
% 0.30/0.60  % vimage_singleton_eq
% 0.30/0.60  thf(fact_6612_vimage__singleton__eq,axiom,
% 0.30/0.60      ! [A: nat,F2: nat > product_prod_nat_nat,B: product_prod_nat_nat] :
% 0.30/0.60        ( ( member_nat @ A @ ( vimage8013328719654469172at_nat @ F2 @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) )
% 0.30/0.60        = ( ( F2 @ A )
% 0.30/0.60          = B ) ) ).
% 0.30/0.60  
% 0.30/0.60  % vimage_singleton_eq
% 0.30/0.60  thf(fact_6613_subset__insert__iff,axiom,
% 0.30/0.60      ! [A2: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.60        ( ( ord_le1268244103169919719at_nat @ A2 @ ( insert9069300056098147895at_nat @ X @ B2 ) )
% 0.30/0.60        = ( ( ( member8757157785044589968at_nat @ X @ A2 )
% 0.30/0.60           => ( ord_le1268244103169919719at_nat @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) @ B2 ) )
% 0.30/0.60          & ( ~ ( member8757157785044589968at_nat @ X @ A2 )
% 0.30/0.60           => ( ord_le1268244103169919719at_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % subset_insert_iff
% 0.30/0.60  thf(fact_6614_subset__insert__iff,axiom,
% 0.30/0.60      ! [A2: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int,B2: set_se6260736226359567993nt_int] :
% 0.30/0.60        ( ( ord_le483042692224249369nt_int @ A2 @ ( insert8897473484851387113nt_int @ X @ B2 ) )
% 0.30/0.60        = ( ( ( member2340774599025711042nt_int @ X @ A2 )
% 0.30/0.60           => ( ord_le483042692224249369nt_int @ ( minus_2612819937483484256nt_int @ A2 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) ) @ B2 ) )
% 0.30/0.60          & ( ~ ( member2340774599025711042nt_int @ X @ A2 )
% 0.30/0.60           => ( ord_le483042692224249369nt_int @ A2 @ B2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % subset_insert_iff
% 0.30/0.60  thf(fact_6615_subset__insert__iff,axiom,
% 0.30/0.60      ! [A2: set_set_nat,X: set_nat,B2: set_set_nat] :
% 0.30/0.60        ( ( ord_le6893508408891458716et_nat @ A2 @ ( insert_set_nat @ X @ B2 ) )
% 0.30/0.60        = ( ( ( member_set_nat @ X @ A2 )
% 0.30/0.60           => ( ord_le6893508408891458716et_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B2 ) )
% 0.30/0.60          & ( ~ ( member_set_nat @ X @ A2 )
% 0.30/0.60           => ( ord_le6893508408891458716et_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % subset_insert_iff
% 0.30/0.60  thf(fact_6616_subset__insert__iff,axiom,
% 0.30/0.60      ! [A2: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,B2: set_Pr4532377907799695533_nat_o] :
% 0.30/0.60        ( ( ord_le2965882846123202637_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ X @ B2 ) )
% 0.30/0.60        = ( ( ( member6576561426505652726_nat_o @ X @ A2 )
% 0.30/0.60           => ( ord_le2965882846123202637_nat_o @ ( minus_1801376950450012436_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) @ B2 ) )
% 0.30/0.60          & ( ~ ( member6576561426505652726_nat_o @ X @ A2 )
% 0.30/0.60           => ( ord_le2965882846123202637_nat_o @ A2 @ B2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % subset_insert_iff
% 0.30/0.60  thf(fact_6617_subset__insert__iff,axiom,
% 0.30/0.60      ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.60        ( ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) )
% 0.30/0.60        = ( ( ( member8440522571783428010at_nat @ X @ A2 )
% 0.30/0.60           => ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B2 ) )
% 0.30/0.60          & ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 0.30/0.60           => ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % subset_insert_iff
% 0.30/0.60  thf(fact_6618_subset__insert__iff,axiom,
% 0.30/0.60      ! [A2: set_o,X: $o,B2: set_o] :
% 0.30/0.60        ( ( ord_less_eq_set_o @ A2 @ ( insert_o @ X @ B2 ) )
% 0.30/0.60        = ( ( ( member_o @ X @ A2 )
% 0.30/0.60           => ( ord_less_eq_set_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) @ B2 ) )
% 0.30/0.60          & ( ~ ( member_o @ X @ A2 )
% 0.30/0.60           => ( ord_less_eq_set_o @ A2 @ B2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % subset_insert_iff
% 0.30/0.60  thf(fact_6619_subset__insert__iff,axiom,
% 0.30/0.60      ! [A2: set_int,X: int,B2: set_int] :
% 0.30/0.60        ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B2 ) )
% 0.30/0.60        = ( ( ( member_int @ X @ A2 )
% 0.30/0.60           => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B2 ) )
% 0.30/0.60          & ( ~ ( member_int @ X @ A2 )
% 0.30/0.60           => ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % subset_insert_iff
% 0.30/0.60  thf(fact_6620_subset__insert__iff,axiom,
% 0.30/0.60      ! [A2: set_nat,X: nat,B2: set_nat] :
% 0.30/0.60        ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B2 ) )
% 0.30/0.60        = ( ( ( member_nat @ X @ A2 )
% 0.30/0.60           => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B2 ) )
% 0.30/0.60          & ( ~ ( member_nat @ X @ A2 )
% 0.30/0.60           => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % subset_insert_iff
% 0.30/0.60  thf(fact_6621_Diff__single__insert,axiom,
% 0.30/0.60      ! [A2: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.60        ( ( ord_le1268244103169919719at_nat @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) @ B2 )
% 0.30/0.60       => ( ord_le1268244103169919719at_nat @ A2 @ ( insert9069300056098147895at_nat @ X @ B2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_single_insert
% 0.30/0.60  thf(fact_6622_Diff__single__insert,axiom,
% 0.30/0.60      ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.60        ( ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B2 )
% 0.30/0.60       => ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_single_insert
% 0.30/0.60  thf(fact_6623_Diff__single__insert,axiom,
% 0.30/0.60      ! [A2: set_o,X: $o,B2: set_o] :
% 0.30/0.60        ( ( ord_less_eq_set_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) @ B2 )
% 0.30/0.60       => ( ord_less_eq_set_o @ A2 @ ( insert_o @ X @ B2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_single_insert
% 0.30/0.60  thf(fact_6624_Diff__single__insert,axiom,
% 0.30/0.60      ! [A2: set_int,X: int,B2: set_int] :
% 0.30/0.60        ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B2 )
% 0.30/0.60       => ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_single_insert
% 0.30/0.60  thf(fact_6625_Diff__single__insert,axiom,
% 0.30/0.60      ! [A2: set_nat,X: nat,B2: set_nat] :
% 0.30/0.60        ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B2 )
% 0.30/0.60       => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Diff_single_insert
% 0.30/0.60  thf(fact_6626_remove__subset,axiom,
% 0.30/0.60      ! [X: produc3843707927480180839at_nat,S: set_Pr4329608150637261639at_nat] :
% 0.30/0.60        ( ( member8757157785044589968at_nat @ X @ S )
% 0.30/0.60       => ( ord_le2604355607129572851at_nat @ ( minus_3314409938677909166at_nat @ S @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) @ S ) ) ).
% 0.30/0.60  
% 0.30/0.60  % remove_subset
% 0.30/0.60  thf(fact_6627_remove__subset,axiom,
% 0.30/0.60      ! [X: set_Pr958786334691620121nt_int,S: set_se6260736226359567993nt_int] :
% 0.30/0.60        ( ( member2340774599025711042nt_int @ X @ S )
% 0.30/0.60       => ( ord_le1924305788584680229nt_int @ ( minus_2612819937483484256nt_int @ S @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) ) @ S ) ) ).
% 0.30/0.60  
% 0.30/0.60  % remove_subset
% 0.30/0.60  thf(fact_6628_remove__subset,axiom,
% 0.30/0.60      ! [X: set_nat,S: set_set_nat] :
% 0.30/0.60        ( ( member_set_nat @ X @ S )
% 0.30/0.60       => ( ord_less_set_set_nat @ ( minus_2163939370556025621et_nat @ S @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ S ) ) ).
% 0.30/0.60  
% 0.30/0.60  % remove_subset
% 0.30/0.60  thf(fact_6629_remove__subset,axiom,
% 0.30/0.60      ! [X: produc3658429121746597890et_nat > $o,S: set_Pr4532377907799695533_nat_o] :
% 0.30/0.60        ( ( member6576561426505652726_nat_o @ X @ S )
% 0.30/0.60       => ( ord_le2453136405763929_nat_o @ ( minus_1801376950450012436_nat_o @ S @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) @ S ) ) ).
% 0.30/0.60  
% 0.30/0.60  % remove_subset
% 0.30/0.60  thf(fact_6630_remove__subset,axiom,
% 0.30/0.60      ! [X: product_prod_nat_nat,S: set_Pr1261947904930325089at_nat] :
% 0.30/0.60        ( ( member8440522571783428010at_nat @ X @ S )
% 0.30/0.60       => ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ S @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ S ) ) ).
% 0.30/0.60  
% 0.30/0.60  % remove_subset
% 0.30/0.60  thf(fact_6631_remove__subset,axiom,
% 0.30/0.60      ! [X: $o,S: set_o] :
% 0.30/0.60        ( ( member_o @ X @ S )
% 0.30/0.60       => ( ord_less_set_o @ ( minus_minus_set_o @ S @ ( insert_o @ X @ bot_bot_set_o ) ) @ S ) ) ).
% 0.30/0.60  
% 0.30/0.60  % remove_subset
% 0.30/0.60  thf(fact_6632_remove__subset,axiom,
% 0.30/0.60      ! [X: int,S: set_int] :
% 0.30/0.60        ( ( member_int @ X @ S )
% 0.30/0.60       => ( ord_less_set_int @ ( minus_minus_set_int @ S @ ( insert_int @ X @ bot_bot_set_int ) ) @ S ) ) ).
% 0.30/0.60  
% 0.30/0.60  % remove_subset
% 0.30/0.60  thf(fact_6633_remove__subset,axiom,
% 0.30/0.60      ! [X: nat,S: set_nat] :
% 0.30/0.60        ( ( member_nat @ X @ S )
% 0.30/0.60       => ( ord_less_set_nat @ ( minus_minus_set_nat @ S @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ S ) ) ).
% 0.30/0.60  
% 0.30/0.60  % remove_subset
% 0.30/0.60  thf(fact_6634_vimage__insert,axiom,
% 0.30/0.60      ! [F2: nat > $o,A: $o,B2: set_o] :
% 0.30/0.60        ( ( vimage_nat_o @ F2 @ ( insert_o @ A @ B2 ) )
% 0.30/0.60        = ( sup_sup_set_nat @ ( vimage_nat_o @ F2 @ ( insert_o @ A @ bot_bot_set_o ) ) @ ( vimage_nat_o @ F2 @ B2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % vimage_insert
% 0.30/0.60  thf(fact_6635_vimage__insert,axiom,
% 0.30/0.60      ! [F2: nat > nat,A: nat,B2: set_nat] :
% 0.30/0.60        ( ( vimage_nat_nat @ F2 @ ( insert_nat @ A @ B2 ) )
% 0.30/0.60        = ( sup_sup_set_nat @ ( vimage_nat_nat @ F2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ ( vimage_nat_nat @ F2 @ B2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % vimage_insert
% 0.30/0.60  thf(fact_6636_vimage__insert,axiom,
% 0.30/0.60      ! [F2: nat > int,A: int,B2: set_int] :
% 0.30/0.60        ( ( vimage_nat_int @ F2 @ ( insert_int @ A @ B2 ) )
% 0.30/0.60        = ( sup_sup_set_nat @ ( vimage_nat_int @ F2 @ ( insert_int @ A @ bot_bot_set_int ) ) @ ( vimage_nat_int @ F2 @ B2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % vimage_insert
% 0.30/0.60  thf(fact_6637_vimage__insert,axiom,
% 0.30/0.60      ! [F2: nat > product_prod_nat_nat,A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.60        ( ( vimage8013328719654469172at_nat @ F2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 0.30/0.60        = ( sup_sup_set_nat @ ( vimage8013328719654469172at_nat @ F2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) @ ( vimage8013328719654469172at_nat @ F2 @ B2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % vimage_insert
% 0.30/0.60  thf(fact_6638_vimage__insert,axiom,
% 0.30/0.60      ! [F2: nat > produc3843707927480180839at_nat,A: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.60        ( ( vimage6435164912253009178at_nat @ F2 @ ( insert9069300056098147895at_nat @ A @ B2 ) )
% 0.30/0.60        = ( sup_sup_set_nat @ ( vimage6435164912253009178at_nat @ F2 @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) @ ( vimage6435164912253009178at_nat @ F2 @ B2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % vimage_insert
% 0.30/0.60  thf(fact_6639_vimage__insert,axiom,
% 0.30/0.60      ! [F2: produc4166570645942440679at_nat > $o,A: $o,B2: set_o] :
% 0.30/0.60        ( ( vimage2280073292226551852_nat_o @ F2 @ ( insert_o @ A @ B2 ) )
% 0.30/0.60        = ( sup_su3035147773818789531at_nat @ ( vimage2280073292226551852_nat_o @ F2 @ ( insert_o @ A @ bot_bot_set_o ) ) @ ( vimage2280073292226551852_nat_o @ F2 @ B2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % vimage_insert
% 0.30/0.60  thf(fact_6640_vimage__insert,axiom,
% 0.30/0.60      ! [F2: produc3843707927480180839at_nat > $o,A: $o,B2: set_o] :
% 0.30/0.60        ( ( vimage3307185822755684012_nat_o @ F2 @ ( insert_o @ A @ B2 ) )
% 0.30/0.60        = ( sup_su5525570899277871387at_nat @ ( vimage3307185822755684012_nat_o @ F2 @ ( insert_o @ A @ bot_bot_set_o ) ) @ ( vimage3307185822755684012_nat_o @ F2 @ B2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % vimage_insert
% 0.30/0.60  thf(fact_6641_vimage__insert,axiom,
% 0.30/0.60      ! [F2: produc4166570645942440679at_nat > nat,A: nat,B2: set_nat] :
% 0.30/0.60        ( ( vimage7952471809483217980at_nat @ F2 @ ( insert_nat @ A @ B2 ) )
% 0.30/0.60        = ( sup_su3035147773818789531at_nat @ ( vimage7952471809483217980at_nat @ F2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ ( vimage7952471809483217980at_nat @ F2 @ B2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % vimage_insert
% 0.30/0.60  thf(fact_6642_vimage__insert,axiom,
% 0.30/0.60      ! [F2: produc3843707927480180839at_nat > nat,A: nat,B2: set_nat] :
% 0.30/0.60        ( ( vimage7134676753939176892at_nat @ F2 @ ( insert_nat @ A @ B2 ) )
% 0.30/0.60        = ( sup_su5525570899277871387at_nat @ ( vimage7134676753939176892at_nat @ F2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ ( vimage7134676753939176892at_nat @ F2 @ B2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % vimage_insert
% 0.30/0.60  thf(fact_6643_vimage__insert,axiom,
% 0.30/0.60      ! [F2: produc4166570645942440679at_nat > int,A: int,B2: set_int] :
% 0.30/0.60        ( ( vimage7949981338974167704at_int @ F2 @ ( insert_int @ A @ B2 ) )
% 0.30/0.60        = ( sup_su3035147773818789531at_nat @ ( vimage7949981338974167704at_int @ F2 @ ( insert_int @ A @ bot_bot_set_int ) ) @ ( vimage7949981338974167704at_int @ F2 @ B2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % vimage_insert
% 0.30/0.60  thf(fact_6644_Compl__insert,axiom,
% 0.30/0.60      ! [X: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 0.30/0.60        ( ( uminus935396558254630718at_nat @ ( insert9069300056098147895at_nat @ X @ A2 ) )
% 0.30/0.60        = ( minus_3314409938677909166at_nat @ ( uminus935396558254630718at_nat @ A2 ) @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Compl_insert
% 0.30/0.60  thf(fact_6645_Compl__insert,axiom,
% 0.30/0.60      ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 0.30/0.60        ( ( uminus6524753893492686040at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) )
% 0.30/0.60        = ( minus_1356011639430497352at_nat @ ( uminus6524753893492686040at_nat @ A2 ) @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Compl_insert
% 0.30/0.60  thf(fact_6646_Compl__insert,axiom,
% 0.30/0.60      ! [X: $o,A2: set_o] :
% 0.30/0.60        ( ( uminus_uminus_set_o @ ( insert_o @ X @ A2 ) )
% 0.30/0.60        = ( minus_minus_set_o @ ( uminus_uminus_set_o @ A2 ) @ ( insert_o @ X @ bot_bot_set_o ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Compl_insert
% 0.30/0.60  thf(fact_6647_Compl__insert,axiom,
% 0.30/0.60      ! [X: int,A2: set_int] :
% 0.30/0.60        ( ( uminus1532241313380277803et_int @ ( insert_int @ X @ A2 ) )
% 0.30/0.60        = ( minus_minus_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Compl_insert
% 0.30/0.60  thf(fact_6648_Compl__insert,axiom,
% 0.30/0.60      ! [X: nat,A2: set_nat] :
% 0.30/0.60        ( ( uminus5710092332889474511et_nat @ ( insert_nat @ X @ A2 ) )
% 0.30/0.60        = ( minus_minus_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Compl_insert
% 0.30/0.60  thf(fact_6649_one__integer_Orsp,axiom,
% 0.30/0.60      one_one_int = one_one_int ).
% 0.30/0.60  
% 0.30/0.60  % one_integer.rsp
% 0.30/0.60  thf(fact_6650_one__natural_Orsp,axiom,
% 0.30/0.60      one_one_nat = one_one_nat ).
% 0.30/0.60  
% 0.30/0.60  % one_natural.rsp
% 0.30/0.60  thf(fact_6651_flip__bit__eq__xor,axiom,
% 0.30/0.60      ( bit_se1345352211410354436nteger
% 0.30/0.60      = ( ^ [N2: nat,A3: code_integer] : ( bit_se3222712562003087583nteger @ A3 @ ( bit_se7788150548672797655nteger @ N2 @ one_one_Code_integer ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % flip_bit_eq_xor
% 0.30/0.60  thf(fact_6652_flip__bit__eq__xor,axiom,
% 0.30/0.60      ( bit_se2159334234014336723it_int
% 0.30/0.60      = ( ^ [N2: nat,A3: int] : ( bit_se6526347334894502574or_int @ A3 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % flip_bit_eq_xor
% 0.30/0.60  thf(fact_6653_flip__bit__eq__xor,axiom,
% 0.30/0.60      ( bit_se2161824704523386999it_nat
% 0.30/0.60      = ( ^ [N2: nat,A3: nat] : ( bit_se6528837805403552850or_nat @ A3 @ ( bit_se547839408752420682it_nat @ N2 @ one_one_nat ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % flip_bit_eq_xor
% 0.30/0.60  thf(fact_6654_psubset__insert__iff,axiom,
% 0.30/0.60      ! [A2: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.60        ( ( ord_le2604355607129572851at_nat @ A2 @ ( insert9069300056098147895at_nat @ X @ B2 ) )
% 0.30/0.60        = ( ( ( member8757157785044589968at_nat @ X @ B2 )
% 0.30/0.60           => ( ord_le2604355607129572851at_nat @ A2 @ B2 ) )
% 0.30/0.60          & ( ~ ( member8757157785044589968at_nat @ X @ B2 )
% 0.30/0.60           => ( ( ( member8757157785044589968at_nat @ X @ A2 )
% 0.30/0.60               => ( ord_le2604355607129572851at_nat @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) @ B2 ) )
% 0.30/0.60              & ( ~ ( member8757157785044589968at_nat @ X @ A2 )
% 0.30/0.60               => ( ord_le1268244103169919719at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % psubset_insert_iff
% 0.30/0.60  thf(fact_6655_psubset__insert__iff,axiom,
% 0.30/0.60      ! [A2: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int,B2: set_se6260736226359567993nt_int] :
% 0.30/0.60        ( ( ord_le1924305788584680229nt_int @ A2 @ ( insert8897473484851387113nt_int @ X @ B2 ) )
% 0.30/0.60        = ( ( ( member2340774599025711042nt_int @ X @ B2 )
% 0.30/0.60           => ( ord_le1924305788584680229nt_int @ A2 @ B2 ) )
% 0.30/0.60          & ( ~ ( member2340774599025711042nt_int @ X @ B2 )
% 0.30/0.60           => ( ( ( member2340774599025711042nt_int @ X @ A2 )
% 0.30/0.60               => ( ord_le1924305788584680229nt_int @ ( minus_2612819937483484256nt_int @ A2 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) ) @ B2 ) )
% 0.30/0.60              & ( ~ ( member2340774599025711042nt_int @ X @ A2 )
% 0.30/0.60               => ( ord_le483042692224249369nt_int @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % psubset_insert_iff
% 0.30/0.60  thf(fact_6656_psubset__insert__iff,axiom,
% 0.30/0.60      ! [A2: set_set_nat,X: set_nat,B2: set_set_nat] :
% 0.30/0.60        ( ( ord_less_set_set_nat @ A2 @ ( insert_set_nat @ X @ B2 ) )
% 0.30/0.60        = ( ( ( member_set_nat @ X @ B2 )
% 0.30/0.60           => ( ord_less_set_set_nat @ A2 @ B2 ) )
% 0.30/0.60          & ( ~ ( member_set_nat @ X @ B2 )
% 0.30/0.60           => ( ( ( member_set_nat @ X @ A2 )
% 0.30/0.60               => ( ord_less_set_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B2 ) )
% 0.30/0.60              & ( ~ ( member_set_nat @ X @ A2 )
% 0.30/0.60               => ( ord_le6893508408891458716et_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % psubset_insert_iff
% 0.30/0.60  thf(fact_6657_psubset__insert__iff,axiom,
% 0.30/0.60      ! [A2: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,B2: set_Pr4532377907799695533_nat_o] :
% 0.30/0.60        ( ( ord_le2453136405763929_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ X @ B2 ) )
% 0.30/0.60        = ( ( ( member6576561426505652726_nat_o @ X @ B2 )
% 0.30/0.60           => ( ord_le2453136405763929_nat_o @ A2 @ B2 ) )
% 0.30/0.60          & ( ~ ( member6576561426505652726_nat_o @ X @ B2 )
% 0.30/0.60           => ( ( ( member6576561426505652726_nat_o @ X @ A2 )
% 0.30/0.60               => ( ord_le2453136405763929_nat_o @ ( minus_1801376950450012436_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) @ B2 ) )
% 0.30/0.60              & ( ~ ( member6576561426505652726_nat_o @ X @ A2 )
% 0.30/0.60               => ( ord_le2965882846123202637_nat_o @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % psubset_insert_iff
% 0.30/0.60  thf(fact_6658_psubset__insert__iff,axiom,
% 0.30/0.60      ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.60        ( ( ord_le7866589430770878221at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) )
% 0.30/0.60        = ( ( ( member8440522571783428010at_nat @ X @ B2 )
% 0.30/0.60           => ( ord_le7866589430770878221at_nat @ A2 @ B2 ) )
% 0.30/0.60          & ( ~ ( member8440522571783428010at_nat @ X @ B2 )
% 0.30/0.60           => ( ( ( member8440522571783428010at_nat @ X @ A2 )
% 0.30/0.60               => ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B2 ) )
% 0.30/0.60              & ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 0.30/0.60               => ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % psubset_insert_iff
% 0.30/0.60  thf(fact_6659_psubset__insert__iff,axiom,
% 0.30/0.60      ! [A2: set_o,X: $o,B2: set_o] :
% 0.30/0.60        ( ( ord_less_set_o @ A2 @ ( insert_o @ X @ B2 ) )
% 0.30/0.60        = ( ( ( member_o @ X @ B2 )
% 0.30/0.60           => ( ord_less_set_o @ A2 @ B2 ) )
% 0.30/0.60          & ( ~ ( member_o @ X @ B2 )
% 0.30/0.60           => ( ( ( member_o @ X @ A2 )
% 0.30/0.60               => ( ord_less_set_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) @ B2 ) )
% 0.30/0.60              & ( ~ ( member_o @ X @ A2 )
% 0.30/0.60               => ( ord_less_eq_set_o @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % psubset_insert_iff
% 0.30/0.60  thf(fact_6660_psubset__insert__iff,axiom,
% 0.30/0.60      ! [A2: set_int,X: int,B2: set_int] :
% 0.30/0.60        ( ( ord_less_set_int @ A2 @ ( insert_int @ X @ B2 ) )
% 0.30/0.60        = ( ( ( member_int @ X @ B2 )
% 0.30/0.60           => ( ord_less_set_int @ A2 @ B2 ) )
% 0.30/0.60          & ( ~ ( member_int @ X @ B2 )
% 0.30/0.60           => ( ( ( member_int @ X @ A2 )
% 0.30/0.60               => ( ord_less_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B2 ) )
% 0.30/0.60              & ( ~ ( member_int @ X @ A2 )
% 0.30/0.60               => ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % psubset_insert_iff
% 0.30/0.60  thf(fact_6661_psubset__insert__iff,axiom,
% 0.30/0.60      ! [A2: set_nat,X: nat,B2: set_nat] :
% 0.30/0.60        ( ( ord_less_set_nat @ A2 @ ( insert_nat @ X @ B2 ) )
% 0.30/0.60        = ( ( ( member_nat @ X @ B2 )
% 0.30/0.60           => ( ord_less_set_nat @ A2 @ B2 ) )
% 0.30/0.60          & ( ~ ( member_nat @ X @ B2 )
% 0.30/0.60           => ( ( ( member_nat @ X @ A2 )
% 0.30/0.60               => ( ord_less_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B2 ) )
% 0.30/0.60              & ( ~ ( member_nat @ X @ A2 )
% 0.30/0.60               => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % psubset_insert_iff
% 0.30/0.60  thf(fact_6662_push__bit__double,axiom,
% 0.30/0.60      ! [N: nat,A: code_integer] :
% 0.30/0.60        ( ( bit_se7788150548672797655nteger @ N @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 0.30/0.60        = ( times_3573771949741848930nteger @ ( bit_se7788150548672797655nteger @ N @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % push_bit_double
% 0.30/0.60  thf(fact_6663_push__bit__double,axiom,
% 0.30/0.60      ! [N: nat,A: code_natural] :
% 0.30/0.60        ( ( bit_se6611745700429515170atural @ N @ ( times_2397367101498566445atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) )
% 0.30/0.60        = ( times_2397367101498566445atural @ ( bit_se6611745700429515170atural @ N @ A ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % push_bit_double
% 0.30/0.60  thf(fact_6664_push__bit__double,axiom,
% 0.30/0.60      ! [N: nat,A: int] :
% 0.30/0.60        ( ( bit_se545348938243370406it_int @ N @ ( times_times_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.30/0.60        = ( times_times_int @ ( bit_se545348938243370406it_int @ N @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % push_bit_double
% 0.30/0.60  thf(fact_6665_push__bit__double,axiom,
% 0.30/0.60      ! [N: nat,A: nat] :
% 0.30/0.60        ( ( bit_se547839408752420682it_nat @ N @ ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.30/0.60        = ( times_times_nat @ ( bit_se547839408752420682it_nat @ N @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % push_bit_double
% 0.30/0.60  thf(fact_6666_push__bit__eq__mult,axiom,
% 0.30/0.60      ( bit_se7788150548672797655nteger
% 0.30/0.60      = ( ^ [N2: nat,A3: code_integer] : ( times_3573771949741848930nteger @ A3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % push_bit_eq_mult
% 0.30/0.60  thf(fact_6667_push__bit__eq__mult,axiom,
% 0.30/0.60      ( bit_se6611745700429515170atural
% 0.30/0.60      = ( ^ [N2: nat,A3: code_natural] : ( times_2397367101498566445atural @ A3 @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % push_bit_eq_mult
% 0.30/0.60  thf(fact_6668_push__bit__eq__mult,axiom,
% 0.30/0.60      ( bit_se545348938243370406it_int
% 0.30/0.60      = ( ^ [N2: nat,A3: int] : ( times_times_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % push_bit_eq_mult
% 0.30/0.60  thf(fact_6669_push__bit__eq__mult,axiom,
% 0.30/0.60      ( bit_se547839408752420682it_nat
% 0.30/0.60      = ( ^ [N2: nat,A3: nat] : ( times_times_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % push_bit_eq_mult
% 0.30/0.60  thf(fact_6670_push__bit__minus__one,axiom,
% 0.30/0.60      ! [N: nat] :
% 0.30/0.60        ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.60        = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % push_bit_minus_one
% 0.30/0.60  thf(fact_6671_of__int__round__le,axiom,
% 0.30/0.60      ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % of_int_round_le
% 0.30/0.60  thf(fact_6672_of__int__round__ge,axiom,
% 0.30/0.60      ! [X: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % of_int_round_ge
% 0.30/0.60  thf(fact_6673_of__int__round__gt,axiom,
% 0.30/0.60      ! [X: rat] : ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % of_int_round_gt
% 0.30/0.60  thf(fact_6674_integer__of__int__code,axiom,
% 0.30/0.60      ( code_integer_of_int
% 0.30/0.60      = ( ^ [K4: int] :
% 0.30/0.60            ( if_Code_integer @ ( ord_less_int @ K4 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K4 ) ) )
% 0.30/0.60            @ ( if_Code_integer @ ( K4 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 0.30/0.60              @ ( if_Code_integer
% 0.30/0.60                @ ( ( modulo_modulo_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.60                  = zero_zero_int )
% 0.30/0.60                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.30/0.60                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % integer_of_int_code
% 0.30/0.60  thf(fact_6675_and__int_Opsimps,axiom,
% 0.30/0.60      ! [K: int,L: int] :
% 0.30/0.60        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 0.30/0.60       => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.30/0.60              & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.30/0.60           => ( ( bit_se725231765392027082nd_int @ K @ L )
% 0.30/0.60              = ( uminus_uminus_int
% 0.30/0.60                @ ( zero_n2684676970156552555ol_int
% 0.30/0.60                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 0.30/0.60                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 0.30/0.60          & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.30/0.60                & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.30/0.60           => ( ( bit_se725231765392027082nd_int @ K @ L )
% 0.30/0.60              = ( plus_plus_int
% 0.30/0.60                @ ( zero_n2684676970156552555ol_int
% 0.30/0.60                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 0.30/0.60                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 0.30/0.60                @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % and_int.psimps
% 0.30/0.60  thf(fact_6676_and__int_Opelims,axiom,
% 0.30/0.60      ! [X: int,Xa: int,Y: int] :
% 0.30/0.60        ( ( ( bit_se725231765392027082nd_int @ X @ Xa )
% 0.30/0.60          = Y )
% 0.30/0.60       => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) )
% 0.30/0.60         => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.30/0.60                    & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.30/0.60                 => ( Y
% 0.30/0.60                    = ( uminus_uminus_int
% 0.30/0.60                      @ ( zero_n2684676970156552555ol_int
% 0.30/0.60                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 0.30/0.60                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 0.30/0.60                & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.30/0.60                      & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.30/0.60                 => ( Y
% 0.30/0.60                    = ( plus_plus_int
% 0.30/0.60                      @ ( zero_n2684676970156552555ol_int
% 0.30/0.60                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 0.30/0.60                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 0.30/0.60                      @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.30/0.60             => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % and_int.pelims
% 0.30/0.60  thf(fact_6677_neg__numeral__le__ceiling,axiom,
% 0.30/0.60      ! [V: num,X: rat] :
% 0.30/0.60        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 0.30/0.60        = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 0.30/0.60  
% 0.30/0.60  % neg_numeral_le_ceiling
% 0.30/0.60  thf(fact_6678_ceiling__less__neg__numeral,axiom,
% 0.30/0.60      ! [X: rat,V: num] :
% 0.30/0.60        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.30/0.60        = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ceiling_less_neg_numeral
% 0.30/0.60  thf(fact_6679_floor__le__neg__numeral,axiom,
% 0.30/0.60      ! [X: rat,V: num] :
% 0.30/0.60        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.30/0.60        = ( ord_less_rat @ X @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % floor_le_neg_numeral
% 0.30/0.60  thf(fact_6680_neg__numeral__less__floor,axiom,
% 0.30/0.60      ! [V: num,X: rat] :
% 0.30/0.60        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 0.30/0.60        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 0.30/0.60  
% 0.30/0.60  % neg_numeral_less_floor
% 0.30/0.60  thf(fact_6681_floor__one,axiom,
% 0.30/0.60      ( ( archim3151403230148437115or_rat @ one_one_rat )
% 0.30/0.60      = one_one_int ) ).
% 0.30/0.60  
% 0.30/0.60  % floor_one
% 0.30/0.60  thf(fact_6682_ceiling__one,axiom,
% 0.30/0.60      ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 0.30/0.60      = one_one_int ) ).
% 0.30/0.60  
% 0.30/0.60  % ceiling_one
% 0.30/0.60  thf(fact_6683_floor__uminus__of__int,axiom,
% 0.30/0.60      ! [Z: int] :
% 0.30/0.60        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ Z ) ) )
% 0.30/0.60        = ( uminus_uminus_int @ Z ) ) ).
% 0.30/0.60  
% 0.30/0.60  % floor_uminus_of_int
% 0.30/0.60  thf(fact_6684_zero__less__floor,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 0.30/0.60        = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 0.30/0.60  
% 0.30/0.60  % zero_less_floor
% 0.30/0.60  thf(fact_6685_floor__le__zero,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 0.30/0.60        = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % floor_le_zero
% 0.30/0.60  thf(fact_6686_one__le__floor,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 0.30/0.60        = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 0.30/0.60  
% 0.30/0.60  % one_le_floor
% 0.30/0.60  thf(fact_6687_ceiling__less__one,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 0.30/0.60        = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ceiling_less_one
% 0.30/0.60  thf(fact_6688_one__le__ceiling,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 0.30/0.60        = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 0.30/0.60  
% 0.30/0.60  % one_le_ceiling
% 0.30/0.60  thf(fact_6689_floor__less__one,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 0.30/0.60        = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % floor_less_one
% 0.30/0.60  thf(fact_6690_ceiling__le__one,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 0.30/0.60        = ( ord_less_eq_rat @ X @ one_one_rat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ceiling_le_one
% 0.30/0.60  thf(fact_6691_one__less__ceiling,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 0.30/0.60        = ( ord_less_rat @ one_one_rat @ X ) ) ).
% 0.30/0.60  
% 0.30/0.60  % one_less_ceiling
% 0.30/0.60  thf(fact_6692_floor__neg__numeral,axiom,
% 0.30/0.60      ! [V: num] :
% 0.30/0.60        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.30/0.60        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % floor_neg_numeral
% 0.30/0.60  thf(fact_6693_ceiling__neg__numeral,axiom,
% 0.30/0.60      ! [V: num] :
% 0.30/0.60        ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 0.30/0.60        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ceiling_neg_numeral
% 0.30/0.60  thf(fact_6694_ceiling__add__one,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 0.30/0.60        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ceiling_add_one
% 0.30/0.60  thf(fact_6695_floor__diff__one,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 0.30/0.60        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % floor_diff_one
% 0.30/0.60  thf(fact_6696_ceiling__diff__one,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 0.30/0.60        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ceiling_diff_one
% 0.30/0.60  thf(fact_6697_ceiling__less__zero,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 0.30/0.60        = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ceiling_less_zero
% 0.30/0.60  thf(fact_6698_zero__le__ceiling,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 0.30/0.60        = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X ) ) ).
% 0.30/0.60  
% 0.30/0.60  % zero_le_ceiling
% 0.30/0.60  thf(fact_6699_numeral__less__floor,axiom,
% 0.30/0.60      ! [V: num,X: rat] :
% 0.30/0.60        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 0.30/0.60        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 0.30/0.60  
% 0.30/0.60  % numeral_less_floor
% 0.30/0.60  thf(fact_6700_floor__le__numeral,axiom,
% 0.30/0.60      ! [X: rat,V: num] :
% 0.30/0.60        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 0.30/0.60        = ( ord_less_rat @ X @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % floor_le_numeral
% 0.30/0.60  thf(fact_6701_ceiling__less__numeral,axiom,
% 0.30/0.60      ! [X: rat,V: num] :
% 0.30/0.60        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 0.30/0.60        = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ceiling_less_numeral
% 0.30/0.60  thf(fact_6702_numeral__le__ceiling,axiom,
% 0.30/0.60      ! [V: num,X: rat] :
% 0.30/0.60        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 0.30/0.60        = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 0.30/0.60  
% 0.30/0.60  % numeral_le_ceiling
% 0.30/0.60  thf(fact_6703_one__less__floor,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 0.30/0.60        = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) ) ).
% 0.30/0.60  
% 0.30/0.60  % one_less_floor
% 0.30/0.60  thf(fact_6704_floor__le__one,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 0.30/0.60        = ( ord_less_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % floor_le_one
% 0.30/0.60  thf(fact_6705_neg__numeral__le__floor,axiom,
% 0.30/0.60      ! [V: num,X: rat] :
% 0.30/0.60        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 0.30/0.60        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 0.30/0.60  
% 0.30/0.60  % neg_numeral_le_floor
% 0.30/0.60  thf(fact_6706_floor__less__neg__numeral,axiom,
% 0.30/0.60      ! [X: rat,V: num] :
% 0.30/0.60        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.30/0.60        = ( ord_less_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % floor_less_neg_numeral
% 0.30/0.60  thf(fact_6707_ceiling__le__neg__numeral,axiom,
% 0.30/0.60      ! [X: rat,V: num] :
% 0.30/0.60        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 0.30/0.60        = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ceiling_le_neg_numeral
% 0.30/0.60  thf(fact_6708_neg__numeral__less__ceiling,axiom,
% 0.30/0.60      ! [V: num,X: rat] :
% 0.30/0.60        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 0.30/0.60        = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 0.30/0.60  
% 0.30/0.60  % neg_numeral_less_ceiling
% 0.30/0.60  thf(fact_6709_integer__of__int__cases,axiom,
% 0.30/0.60      ! [X: code_integer] :
% 0.30/0.60        ~ ! [Y2: int] :
% 0.30/0.60            ( ( X
% 0.30/0.60              = ( code_integer_of_int @ Y2 ) )
% 0.30/0.60           => ~ ( member_int @ Y2 @ top_top_set_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % integer_of_int_cases
% 0.30/0.60  thf(fact_6710_integer__of__int__induct,axiom,
% 0.30/0.60      ! [P: code_integer > $o,X: code_integer] :
% 0.30/0.60        ( ! [Y2: int] :
% 0.30/0.60            ( ( member_int @ Y2 @ top_top_set_int )
% 0.30/0.60           => ( P @ ( code_integer_of_int @ Y2 ) ) )
% 0.30/0.60       => ( P @ X ) ) ).
% 0.30/0.60  
% 0.30/0.60  % integer_of_int_induct
% 0.30/0.60  thf(fact_6711_integer__of__int__inject,axiom,
% 0.30/0.60      ! [X: int,Y: int] :
% 0.30/0.60        ( ( member_int @ X @ top_top_set_int )
% 0.30/0.60       => ( ( member_int @ Y @ top_top_set_int )
% 0.30/0.60         => ( ( ( code_integer_of_int @ X )
% 0.30/0.60              = ( code_integer_of_int @ Y ) )
% 0.30/0.60            = ( X = Y ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % integer_of_int_inject
% 0.30/0.60  thf(fact_6712_uminus__integer__code_I1_J,axiom,
% 0.30/0.60      ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 0.30/0.60      = zero_z3403309356797280102nteger ) ).
% 0.30/0.60  
% 0.30/0.60  % uminus_integer_code(1)
% 0.30/0.60  thf(fact_6713_ceiling__def,axiom,
% 0.30/0.60      ( archim2889992004027027881ng_rat
% 0.30/0.60      = ( ^ [X3: rat] : ( uminus_uminus_int @ ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ X3 ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ceiling_def
% 0.30/0.60  thf(fact_6714_floor__minus,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ X ) )
% 0.30/0.60        = ( uminus_uminus_int @ ( archim2889992004027027881ng_rat @ X ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % floor_minus
% 0.30/0.60  thf(fact_6715_ceiling__minus,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ X ) )
% 0.30/0.60        = ( uminus_uminus_int @ ( archim3151403230148437115or_rat @ X ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ceiling_minus
% 0.30/0.60  thf(fact_6716_uminus__integer_Oabs__eq,axiom,
% 0.30/0.60      ! [X: int] :
% 0.30/0.60        ( ( uminus1351360451143612070nteger @ ( code_integer_of_int @ X ) )
% 0.30/0.60        = ( code_integer_of_int @ ( uminus_uminus_int @ X ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % uminus_integer.abs_eq
% 0.30/0.60  thf(fact_6717_ceiling__diff__floor__le__1,axiom,
% 0.30/0.60      ! [X: rat] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim3151403230148437115or_rat @ X ) ) @ one_one_int ) ).
% 0.30/0.60  
% 0.30/0.60  % ceiling_diff_floor_le_1
% 0.30/0.60  thf(fact_6718_ceiling__altdef,axiom,
% 0.30/0.60      ( archim2889992004027027881ng_rat
% 0.30/0.60      = ( ^ [X3: rat] :
% 0.30/0.60            ( if_int
% 0.30/0.60            @ ( X3
% 0.30/0.60              = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X3 ) ) )
% 0.30/0.60            @ ( archim3151403230148437115or_rat @ X3 )
% 0.30/0.60            @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X3 ) @ one_one_int ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ceiling_altdef
% 0.30/0.60  thf(fact_6719_one__integer__def,axiom,
% 0.30/0.60      ( one_one_Code_integer
% 0.30/0.60      = ( code_integer_of_int @ one_one_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % one_integer_def
% 0.30/0.60  thf(fact_6720_one__add__floor,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 0.30/0.60        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ one_one_rat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % one_add_floor
% 0.30/0.60  thf(fact_6721_floor__unique,axiom,
% 0.30/0.60      ! [Z: int,X: rat] :
% 0.30/0.60        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X )
% 0.30/0.60       => ( ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 0.30/0.60         => ( ( archim3151403230148437115or_rat @ X )
% 0.30/0.60            = Z ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % floor_unique
% 0.30/0.60  thf(fact_6722_floor__eq__iff,axiom,
% 0.30/0.60      ! [X: rat,A: int] :
% 0.30/0.60        ( ( ( archim3151403230148437115or_rat @ X )
% 0.30/0.60          = A )
% 0.30/0.60        = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X )
% 0.30/0.60          & ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % floor_eq_iff
% 0.30/0.60  thf(fact_6723_floor__split,axiom,
% 0.30/0.60      ! [P: int > $o,T3: rat] :
% 0.30/0.60        ( ( P @ ( archim3151403230148437115or_rat @ T3 ) )
% 0.30/0.60        = ( ! [I3: int] :
% 0.30/0.60              ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I3 ) @ T3 )
% 0.30/0.60                & ( ord_less_rat @ T3 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I3 ) @ one_one_rat ) ) )
% 0.30/0.60             => ( P @ I3 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % floor_split
% 0.30/0.60  thf(fact_6724_le__mult__floor,axiom,
% 0.30/0.60      ! [A: rat,B: rat] :
% 0.30/0.60        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.60       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.60         => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % le_mult_floor
% 0.30/0.60  thf(fact_6725_less__floor__iff,axiom,
% 0.30/0.60      ! [Z: int,X: rat] :
% 0.30/0.60        ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 0.30/0.60        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 0.30/0.60  
% 0.30/0.60  % less_floor_iff
% 0.30/0.60  thf(fact_6726_floor__le__iff,axiom,
% 0.30/0.60      ! [X: rat,Z: int] :
% 0.30/0.60        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 0.30/0.60        = ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % floor_le_iff
% 0.30/0.60  thf(fact_6727_floor__correct,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) @ X )
% 0.30/0.60        & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % floor_correct
% 0.30/0.60  thf(fact_6728_ceiling__correct,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) @ one_one_rat ) @ X )
% 0.30/0.60        & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ceiling_correct
% 0.30/0.60  thf(fact_6729_ceiling__unique,axiom,
% 0.30/0.60      ! [Z: int,X: rat] :
% 0.30/0.60        ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X )
% 0.30/0.60       => ( ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z ) )
% 0.30/0.60         => ( ( archim2889992004027027881ng_rat @ X )
% 0.30/0.60            = Z ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ceiling_unique
% 0.30/0.60  thf(fact_6730_ceiling__eq__iff,axiom,
% 0.30/0.60      ! [X: rat,A: int] :
% 0.30/0.60        ( ( ( archim2889992004027027881ng_rat @ X )
% 0.30/0.60          = A )
% 0.30/0.60        = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X )
% 0.30/0.60          & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ceiling_eq_iff
% 0.30/0.60  thf(fact_6731_ceiling__split,axiom,
% 0.30/0.60      ! [P: int > $o,T3: rat] :
% 0.30/0.60        ( ( P @ ( archim2889992004027027881ng_rat @ T3 ) )
% 0.30/0.60        = ( ! [I3: int] :
% 0.30/0.60              ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I3 ) @ one_one_rat ) @ T3 )
% 0.30/0.60                & ( ord_less_eq_rat @ T3 @ ( ring_1_of_int_rat @ I3 ) ) )
% 0.30/0.60             => ( P @ I3 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ceiling_split
% 0.30/0.60  thf(fact_6732_mult__ceiling__le,axiom,
% 0.30/0.60      ! [A: rat,B: rat] :
% 0.30/0.60        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.60       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.60         => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % mult_ceiling_le
% 0.30/0.60  thf(fact_6733_ceiling__less__iff,axiom,
% 0.30/0.60      ! [X: rat,Z: int] :
% 0.30/0.60        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ Z )
% 0.30/0.60        = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ceiling_less_iff
% 0.30/0.60  thf(fact_6734_le__ceiling__iff,axiom,
% 0.30/0.60      ! [Z: int,X: rat] :
% 0.30/0.60        ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X ) )
% 0.30/0.60        = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 0.30/0.60  
% 0.30/0.60  % le_ceiling_iff
% 0.30/0.60  thf(fact_6735_floor__divide__lower,axiom,
% 0.30/0.60      ! [Q4: rat,P4: rat] :
% 0.30/0.60        ( ( ord_less_rat @ zero_zero_rat @ Q4 )
% 0.30/0.60       => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P4 @ Q4 ) ) ) @ Q4 ) @ P4 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % floor_divide_lower
% 0.30/0.60  thf(fact_6736_ceiling__divide__upper,axiom,
% 0.30/0.60      ! [Q4: rat,P4: rat] :
% 0.30/0.60        ( ( ord_less_rat @ zero_zero_rat @ Q4 )
% 0.30/0.60       => ( ord_less_eq_rat @ P4 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P4 @ Q4 ) ) ) @ Q4 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ceiling_divide_upper
% 0.30/0.60  thf(fact_6737_floor__divide__upper,axiom,
% 0.30/0.60      ! [Q4: rat,P4: rat] :
% 0.30/0.60        ( ( ord_less_rat @ zero_zero_rat @ Q4 )
% 0.30/0.60       => ( ord_less_rat @ P4 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P4 @ Q4 ) ) ) @ one_one_rat ) @ Q4 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % floor_divide_upper
% 0.30/0.60  thf(fact_6738_round__def,axiom,
% 0.30/0.60      ( archim7778729529865785530nd_rat
% 0.30/0.60      = ( ^ [X3: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % round_def
% 0.30/0.60  thf(fact_6739_ceiling__divide__lower,axiom,
% 0.30/0.60      ! [Q4: rat,P4: rat] :
% 0.30/0.60        ( ( ord_less_rat @ zero_zero_rat @ Q4 )
% 0.30/0.60       => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P4 @ Q4 ) ) ) @ one_one_rat ) @ Q4 ) @ P4 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ceiling_divide_lower
% 0.30/0.60  thf(fact_6740_and__int_Opinduct,axiom,
% 0.30/0.60      ! [A0: int,A1: int,P: int > int > $o] :
% 0.30/0.60        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 0.30/0.60       => ( ! [K2: int,L3: int] :
% 0.30/0.60              ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L3 ) )
% 0.30/0.60             => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.30/0.60                      & ( member_int @ L3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.30/0.60                 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.30/0.60               => ( P @ K2 @ L3 ) ) )
% 0.30/0.60         => ( P @ A0 @ A1 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % and_int.pinduct
% 0.30/0.60  thf(fact_6741_upto_Opinduct,axiom,
% 0.30/0.60      ! [A0: int,A1: int,P: int > int > $o] :
% 0.30/0.60        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 0.30/0.60       => ( ! [I2: int,J2: int] :
% 0.30/0.60              ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J2 ) )
% 0.30/0.60             => ( ( ( ord_less_eq_int @ I2 @ J2 )
% 0.30/0.60                 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) @ J2 ) )
% 0.30/0.60               => ( P @ I2 @ J2 ) ) )
% 0.30/0.60         => ( P @ A0 @ A1 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % upto.pinduct
% 0.30/0.60  thf(fact_6742_round__altdef,axiom,
% 0.30/0.60      ( archim7778729529865785530nd_rat
% 0.30/0.60      = ( ^ [X3: rat] : ( if_int @ ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( archimedean_frac_rat @ X3 ) ) @ ( archim2889992004027027881ng_rat @ X3 ) @ ( archim3151403230148437115or_rat @ X3 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % round_altdef
% 0.30/0.60  thf(fact_6743_the__elem__eq,axiom,
% 0.30/0.60      ! [X: produc3843707927480180839at_nat] :
% 0.30/0.60        ( ( the_el221668144340439132at_nat @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 0.30/0.60        = X ) ).
% 0.30/0.60  
% 0.30/0.60  % the_elem_eq
% 0.30/0.60  thf(fact_6744_the__elem__eq,axiom,
% 0.30/0.60      ! [X: product_prod_nat_nat] :
% 0.30/0.60        ( ( the_el2281957884133575798at_nat @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 0.30/0.60        = X ) ).
% 0.30/0.60  
% 0.30/0.60  % the_elem_eq
% 0.30/0.60  thf(fact_6745_the__elem__eq,axiom,
% 0.30/0.60      ! [X: $o] :
% 0.30/0.60        ( ( the_elem_o @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.30/0.60        = X ) ).
% 0.30/0.60  
% 0.30/0.60  % the_elem_eq
% 0.30/0.60  thf(fact_6746_the__elem__eq,axiom,
% 0.30/0.60      ! [X: nat] :
% 0.30/0.60        ( ( the_elem_nat @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.30/0.60        = X ) ).
% 0.30/0.60  
% 0.30/0.60  % the_elem_eq
% 0.30/0.60  thf(fact_6747_the__elem__eq,axiom,
% 0.30/0.60      ! [X: int] :
% 0.30/0.60        ( ( the_elem_int @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.30/0.60        = X ) ).
% 0.30/0.60  
% 0.30/0.60  % the_elem_eq
% 0.30/0.60  thf(fact_6748_round__unique_H,axiom,
% 0.30/0.60      ! [X: rat,N: int] :
% 0.30/0.60        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ N ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.30/0.60       => ( ( archim7778729529865785530nd_rat @ X )
% 0.30/0.60          = N ) ) ).
% 0.30/0.60  
% 0.30/0.60  % round_unique'
% 0.30/0.60  thf(fact_6749_of__int__round__abs__le,axiom,
% 0.30/0.60      ! [X: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ X ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % of_int_round_abs_le
% 0.30/0.60  thf(fact_6750_num__of__integer__code,axiom,
% 0.30/0.60      ( code_num_of_integer
% 0.30/0.60      = ( ^ [K4: code_integer] :
% 0.30/0.60            ( if_num @ ( ord_le3102999989581377725nteger @ K4 @ one_one_Code_integer ) @ one
% 0.30/0.60            @ ( produc7336495610019696514er_num
% 0.30/0.60              @ ^ [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 ) )
% 0.30/0.60              @ ( code_divmod_integer @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % num_of_integer_code
% 0.30/0.60  thf(fact_6751_bit__cut__integer__def,axiom,
% 0.30/0.60      ( code_bit_cut_integer
% 0.30/0.60      = ( ^ [K4: code_integer] :
% 0.30/0.60            ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.60            @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K4 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % bit_cut_integer_def
% 0.30/0.60  thf(fact_6752_abs__idempotent,axiom,
% 0.30/0.60      ! [A: int] :
% 0.30/0.60        ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 0.30/0.60        = ( abs_abs_int @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_idempotent
% 0.30/0.60  thf(fact_6753_abs__idempotent,axiom,
% 0.30/0.60      ! [A: code_integer] :
% 0.30/0.60        ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 0.30/0.60        = ( abs_abs_Code_integer @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_idempotent
% 0.30/0.60  thf(fact_6754_abs__idempotent,axiom,
% 0.30/0.60      ! [A: rat] :
% 0.30/0.60        ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 0.30/0.60        = ( abs_abs_rat @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_idempotent
% 0.30/0.60  thf(fact_6755_abs__zero,axiom,
% 0.30/0.60      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 0.30/0.60      = zero_z3403309356797280102nteger ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_zero
% 0.30/0.60  thf(fact_6756_abs__zero,axiom,
% 0.30/0.60      ( ( abs_abs_rat @ zero_zero_rat )
% 0.30/0.60      = zero_zero_rat ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_zero
% 0.30/0.60  thf(fact_6757_abs__zero,axiom,
% 0.30/0.60      ( ( abs_abs_int @ zero_zero_int )
% 0.30/0.60      = zero_zero_int ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_zero
% 0.30/0.60  thf(fact_6758_abs__eq__0,axiom,
% 0.30/0.60      ! [A: code_integer] :
% 0.30/0.60        ( ( ( abs_abs_Code_integer @ A )
% 0.30/0.60          = zero_z3403309356797280102nteger )
% 0.30/0.60        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_eq_0
% 0.30/0.60  thf(fact_6759_abs__eq__0,axiom,
% 0.30/0.60      ! [A: rat] :
% 0.30/0.60        ( ( ( abs_abs_rat @ A )
% 0.30/0.60          = zero_zero_rat )
% 0.30/0.60        = ( A = zero_zero_rat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_eq_0
% 0.30/0.60  thf(fact_6760_abs__eq__0,axiom,
% 0.30/0.60      ! [A: int] :
% 0.30/0.60        ( ( ( abs_abs_int @ A )
% 0.30/0.60          = zero_zero_int )
% 0.30/0.60        = ( A = zero_zero_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_eq_0
% 0.30/0.60  thf(fact_6761_abs__0__eq,axiom,
% 0.30/0.60      ! [A: code_integer] :
% 0.30/0.60        ( ( zero_z3403309356797280102nteger
% 0.30/0.60          = ( abs_abs_Code_integer @ A ) )
% 0.30/0.60        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_0_eq
% 0.30/0.60  thf(fact_6762_abs__0__eq,axiom,
% 0.30/0.60      ! [A: rat] :
% 0.30/0.60        ( ( zero_zero_rat
% 0.30/0.60          = ( abs_abs_rat @ A ) )
% 0.30/0.60        = ( A = zero_zero_rat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_0_eq
% 0.30/0.60  thf(fact_6763_abs__0__eq,axiom,
% 0.30/0.60      ! [A: int] :
% 0.30/0.60        ( ( zero_zero_int
% 0.30/0.60          = ( abs_abs_int @ A ) )
% 0.30/0.60        = ( A = zero_zero_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_0_eq
% 0.30/0.60  thf(fact_6764_abs__add__abs,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer] :
% 0.30/0.60        ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 0.30/0.60        = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_add_abs
% 0.30/0.60  thf(fact_6765_abs__add__abs,axiom,
% 0.30/0.60      ! [A: rat,B: rat] :
% 0.30/0.60        ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 0.30/0.60        = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_add_abs
% 0.30/0.60  thf(fact_6766_abs__add__abs,axiom,
% 0.30/0.60      ! [A: int,B: int] :
% 0.30/0.60        ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 0.30/0.60        = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_add_abs
% 0.30/0.60  thf(fact_6767_abs__mult__self__eq,axiom,
% 0.30/0.60      ! [A: code_integer] :
% 0.30/0.60        ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 0.30/0.60        = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_mult_self_eq
% 0.30/0.60  thf(fact_6768_abs__mult__self__eq,axiom,
% 0.30/0.60      ! [A: rat] :
% 0.30/0.60        ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 0.30/0.60        = ( times_times_rat @ A @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_mult_self_eq
% 0.30/0.60  thf(fact_6769_abs__mult__self__eq,axiom,
% 0.30/0.60      ! [A: int] :
% 0.30/0.60        ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 0.30/0.60        = ( times_times_int @ A @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_mult_self_eq
% 0.30/0.60  thf(fact_6770_abs__1,axiom,
% 0.30/0.60      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 0.30/0.60      = one_one_Code_integer ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_1
% 0.30/0.60  thf(fact_6771_abs__1,axiom,
% 0.30/0.60      ( ( abs_abs_rat @ one_one_rat )
% 0.30/0.60      = one_one_rat ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_1
% 0.30/0.60  thf(fact_6772_abs__1,axiom,
% 0.30/0.60      ( ( abs_abs_int @ one_one_int )
% 0.30/0.60      = one_one_int ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_1
% 0.30/0.60  thf(fact_6773_abs__minus,axiom,
% 0.30/0.60      ! [A: int] :
% 0.30/0.60        ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 0.30/0.60        = ( abs_abs_int @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_minus
% 0.30/0.60  thf(fact_6774_abs__minus,axiom,
% 0.30/0.60      ! [A: code_integer] :
% 0.30/0.60        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 0.30/0.60        = ( abs_abs_Code_integer @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_minus
% 0.30/0.60  thf(fact_6775_abs__minus,axiom,
% 0.30/0.60      ! [A: rat] :
% 0.30/0.60        ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 0.30/0.60        = ( abs_abs_rat @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_minus
% 0.30/0.60  thf(fact_6776_abs__minus__cancel,axiom,
% 0.30/0.60      ! [A: int] :
% 0.30/0.60        ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 0.30/0.60        = ( abs_abs_int @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_minus_cancel
% 0.30/0.60  thf(fact_6777_abs__minus__cancel,axiom,
% 0.30/0.60      ! [A: code_integer] :
% 0.30/0.60        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 0.30/0.60        = ( abs_abs_Code_integer @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_minus_cancel
% 0.30/0.60  thf(fact_6778_abs__minus__cancel,axiom,
% 0.30/0.60      ! [A: rat] :
% 0.30/0.60        ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 0.30/0.60        = ( abs_abs_rat @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_minus_cancel
% 0.30/0.60  thf(fact_6779_zdvd1__eq,axiom,
% 0.30/0.60      ! [X: int] :
% 0.30/0.60        ( ( dvd_dvd_int @ X @ one_one_int )
% 0.30/0.60        = ( ( abs_abs_int @ X )
% 0.30/0.60          = one_one_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % zdvd1_eq
% 0.30/0.60  thf(fact_6780_abs__le__zero__iff,axiom,
% 0.30/0.60      ! [A: code_integer] :
% 0.30/0.60        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 0.30/0.60        = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_le_zero_iff
% 0.30/0.60  thf(fact_6781_abs__le__zero__iff,axiom,
% 0.30/0.60      ! [A: rat] :
% 0.30/0.60        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 0.30/0.60        = ( A = zero_zero_rat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_le_zero_iff
% 0.30/0.60  thf(fact_6782_abs__le__zero__iff,axiom,
% 0.30/0.60      ! [A: int] :
% 0.30/0.60        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 0.30/0.60        = ( A = zero_zero_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_le_zero_iff
% 0.30/0.60  thf(fact_6783_abs__le__self__iff,axiom,
% 0.30/0.60      ! [A: code_integer] :
% 0.30/0.60        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 0.30/0.60        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_le_self_iff
% 0.30/0.60  thf(fact_6784_abs__le__self__iff,axiom,
% 0.30/0.60      ! [A: rat] :
% 0.30/0.60        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 0.30/0.60        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_le_self_iff
% 0.30/0.60  thf(fact_6785_abs__le__self__iff,axiom,
% 0.30/0.60      ! [A: int] :
% 0.30/0.60        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 0.30/0.60        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_le_self_iff
% 0.30/0.60  thf(fact_6786_abs__of__nonneg,axiom,
% 0.30/0.60      ! [A: code_integer] :
% 0.30/0.60        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.60       => ( ( abs_abs_Code_integer @ A )
% 0.30/0.60          = A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_of_nonneg
% 0.30/0.60  thf(fact_6787_abs__of__nonneg,axiom,
% 0.30/0.60      ! [A: rat] :
% 0.30/0.60        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.60       => ( ( abs_abs_rat @ A )
% 0.30/0.60          = A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_of_nonneg
% 0.30/0.60  thf(fact_6788_abs__of__nonneg,axiom,
% 0.30/0.60      ! [A: int] :
% 0.30/0.60        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.60       => ( ( abs_abs_int @ A )
% 0.30/0.60          = A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_of_nonneg
% 0.30/0.60  thf(fact_6789_zero__less__abs__iff,axiom,
% 0.30/0.60      ! [A: code_integer] :
% 0.30/0.60        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 0.30/0.60        = ( A != zero_z3403309356797280102nteger ) ) ).
% 0.30/0.60  
% 0.30/0.60  % zero_less_abs_iff
% 0.30/0.60  thf(fact_6790_zero__less__abs__iff,axiom,
% 0.30/0.60      ! [A: rat] :
% 0.30/0.60        ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 0.30/0.60        = ( A != zero_zero_rat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % zero_less_abs_iff
% 0.30/0.60  thf(fact_6791_zero__less__abs__iff,axiom,
% 0.30/0.60      ! [A: int] :
% 0.30/0.60        ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 0.30/0.60        = ( A != zero_zero_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % zero_less_abs_iff
% 0.30/0.60  thf(fact_6792_abs__neg__numeral,axiom,
% 0.30/0.60      ! [N: num] :
% 0.30/0.60        ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.60        = ( numeral_numeral_int @ N ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_neg_numeral
% 0.30/0.60  thf(fact_6793_abs__neg__numeral,axiom,
% 0.30/0.60      ! [N: num] :
% 0.30/0.60        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.30/0.60        = ( numera6620942414471956472nteger @ N ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_neg_numeral
% 0.30/0.60  thf(fact_6794_abs__neg__numeral,axiom,
% 0.30/0.60      ! [N: num] :
% 0.30/0.60        ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.30/0.60        = ( numeral_numeral_rat @ N ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_neg_numeral
% 0.30/0.60  thf(fact_6795_abs__neg__one,axiom,
% 0.30/0.60      ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.60      = one_one_int ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_neg_one
% 0.30/0.60  thf(fact_6796_abs__neg__one,axiom,
% 0.30/0.60      ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.60      = one_one_Code_integer ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_neg_one
% 0.30/0.60  thf(fact_6797_abs__neg__one,axiom,
% 0.30/0.60      ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.30/0.60      = one_one_rat ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_neg_one
% 0.30/0.60  thf(fact_6798_abs__power__minus,axiom,
% 0.30/0.60      ! [A: int,N: nat] :
% 0.30/0.60        ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 0.30/0.60        = ( abs_abs_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_power_minus
% 0.30/0.60  thf(fact_6799_abs__power__minus,axiom,
% 0.30/0.60      ! [A: code_integer,N: nat] :
% 0.30/0.60        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 0.30/0.60        = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_power_minus
% 0.30/0.60  thf(fact_6800_abs__power__minus,axiom,
% 0.30/0.60      ! [A: rat,N: nat] :
% 0.30/0.60        ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 0.30/0.60        = ( abs_abs_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_power_minus
% 0.30/0.60  thf(fact_6801_zabs__less__one__iff,axiom,
% 0.30/0.60      ! [Z: int] :
% 0.30/0.60        ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 0.30/0.60        = ( Z = zero_zero_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % zabs_less_one_iff
% 0.30/0.60  thf(fact_6802_abs__of__nonpos,axiom,
% 0.30/0.60      ! [A: code_integer] :
% 0.30/0.60        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.30/0.60       => ( ( abs_abs_Code_integer @ A )
% 0.30/0.60          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_of_nonpos
% 0.30/0.60  thf(fact_6803_abs__of__nonpos,axiom,
% 0.30/0.60      ! [A: rat] :
% 0.30/0.60        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.30/0.60       => ( ( abs_abs_rat @ A )
% 0.30/0.60          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_of_nonpos
% 0.30/0.60  thf(fact_6804_abs__of__nonpos,axiom,
% 0.30/0.60      ! [A: int] :
% 0.30/0.60        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.30/0.60       => ( ( abs_abs_int @ A )
% 0.30/0.60          = ( uminus_uminus_int @ A ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_of_nonpos
% 0.30/0.60  thf(fact_6805_abs__ge__self,axiom,
% 0.30/0.60      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_ge_self
% 0.30/0.60  thf(fact_6806_abs__ge__self,axiom,
% 0.30/0.60      ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_ge_self
% 0.30/0.60  thf(fact_6807_abs__ge__self,axiom,
% 0.30/0.60      ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_ge_self
% 0.30/0.60  thf(fact_6808_abs__le__D1,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer] :
% 0.30/0.60        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.30/0.60       => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_le_D1
% 0.30/0.60  thf(fact_6809_abs__le__D1,axiom,
% 0.30/0.60      ! [A: rat,B: rat] :
% 0.30/0.60        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.30/0.60       => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_le_D1
% 0.30/0.60  thf(fact_6810_abs__le__D1,axiom,
% 0.30/0.60      ! [A: int,B: int] :
% 0.30/0.60        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.30/0.60       => ( ord_less_eq_int @ A @ B ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_le_D1
% 0.30/0.60  thf(fact_6811_abs__mult,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer] :
% 0.30/0.60        ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.30/0.60        = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_mult
% 0.30/0.60  thf(fact_6812_abs__mult,axiom,
% 0.30/0.60      ! [A: rat,B: rat] :
% 0.30/0.60        ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 0.30/0.60        = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_mult
% 0.30/0.60  thf(fact_6813_abs__mult,axiom,
% 0.30/0.60      ! [A: int,B: int] :
% 0.30/0.60        ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 0.30/0.60        = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_mult
% 0.30/0.60  thf(fact_6814_abs__one,axiom,
% 0.30/0.60      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 0.30/0.60      = one_one_Code_integer ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_one
% 0.30/0.60  thf(fact_6815_abs__one,axiom,
% 0.30/0.60      ( ( abs_abs_rat @ one_one_rat )
% 0.30/0.60      = one_one_rat ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_one
% 0.30/0.60  thf(fact_6816_abs__one,axiom,
% 0.30/0.60      ( ( abs_abs_int @ one_one_int )
% 0.30/0.60      = one_one_int ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_one
% 0.30/0.60  thf(fact_6817_abs__minus__commute,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer] :
% 0.30/0.60        ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.30/0.60        = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_minus_commute
% 0.30/0.60  thf(fact_6818_abs__minus__commute,axiom,
% 0.30/0.60      ! [A: rat,B: rat] :
% 0.30/0.60        ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 0.30/0.60        = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_minus_commute
% 0.30/0.60  thf(fact_6819_abs__minus__commute,axiom,
% 0.30/0.60      ! [A: int,B: int] :
% 0.30/0.60        ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 0.30/0.60        = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_minus_commute
% 0.30/0.60  thf(fact_6820_abs__eq__iff,axiom,
% 0.30/0.60      ! [X: int,Y: int] :
% 0.30/0.60        ( ( ( abs_abs_int @ X )
% 0.30/0.60          = ( abs_abs_int @ Y ) )
% 0.30/0.60        = ( ( X = Y )
% 0.30/0.60          | ( X
% 0.30/0.60            = ( uminus_uminus_int @ Y ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_eq_iff
% 0.30/0.60  thf(fact_6821_abs__eq__iff,axiom,
% 0.30/0.60      ! [X: code_integer,Y: code_integer] :
% 0.30/0.60        ( ( ( abs_abs_Code_integer @ X )
% 0.30/0.60          = ( abs_abs_Code_integer @ Y ) )
% 0.30/0.60        = ( ( X = Y )
% 0.30/0.60          | ( X
% 0.30/0.60            = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_eq_iff
% 0.30/0.60  thf(fact_6822_abs__eq__iff,axiom,
% 0.30/0.60      ! [X: rat,Y: rat] :
% 0.30/0.60        ( ( ( abs_abs_rat @ X )
% 0.30/0.60          = ( abs_abs_rat @ Y ) )
% 0.30/0.60        = ( ( X = Y )
% 0.30/0.60          | ( X
% 0.30/0.60            = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_eq_iff
% 0.30/0.60  thf(fact_6823_abs__ge__zero,axiom,
% 0.30/0.60      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_ge_zero
% 0.30/0.60  thf(fact_6824_abs__ge__zero,axiom,
% 0.30/0.60      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_ge_zero
% 0.30/0.60  thf(fact_6825_abs__ge__zero,axiom,
% 0.30/0.60      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_ge_zero
% 0.30/0.60  thf(fact_6826_abs__of__pos,axiom,
% 0.30/0.60      ! [A: code_integer] :
% 0.30/0.60        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.60       => ( ( abs_abs_Code_integer @ A )
% 0.30/0.60          = A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_of_pos
% 0.30/0.60  thf(fact_6827_abs__of__pos,axiom,
% 0.30/0.60      ! [A: rat] :
% 0.30/0.60        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.60       => ( ( abs_abs_rat @ A )
% 0.30/0.60          = A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_of_pos
% 0.30/0.60  thf(fact_6828_abs__of__pos,axiom,
% 0.30/0.60      ! [A: int] :
% 0.30/0.60        ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.60       => ( ( abs_abs_int @ A )
% 0.30/0.60          = A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_of_pos
% 0.30/0.60  thf(fact_6829_abs__not__less__zero,axiom,
% 0.30/0.60      ! [A: code_integer] :
% 0.30/0.60        ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_not_less_zero
% 0.30/0.60  thf(fact_6830_abs__not__less__zero,axiom,
% 0.30/0.60      ! [A: rat] :
% 0.30/0.60        ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_not_less_zero
% 0.30/0.60  thf(fact_6831_abs__not__less__zero,axiom,
% 0.30/0.60      ! [A: int] :
% 0.30/0.60        ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_not_less_zero
% 0.30/0.60  thf(fact_6832_abs__triangle__ineq,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_triangle_ineq
% 0.30/0.60  thf(fact_6833_abs__triangle__ineq,axiom,
% 0.30/0.60      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_triangle_ineq
% 0.30/0.60  thf(fact_6834_abs__triangle__ineq,axiom,
% 0.30/0.60      ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_triangle_ineq
% 0.30/0.60  thf(fact_6835_abs__triangle__ineq2__sym,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_triangle_ineq2_sym
% 0.30/0.60  thf(fact_6836_abs__triangle__ineq2__sym,axiom,
% 0.30/0.60      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_triangle_ineq2_sym
% 0.30/0.60  thf(fact_6837_abs__triangle__ineq2__sym,axiom,
% 0.30/0.60      ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_triangle_ineq2_sym
% 0.30/0.60  thf(fact_6838_abs__triangle__ineq3,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_triangle_ineq3
% 0.30/0.60  thf(fact_6839_abs__triangle__ineq3,axiom,
% 0.30/0.60      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_triangle_ineq3
% 0.30/0.60  thf(fact_6840_abs__triangle__ineq3,axiom,
% 0.30/0.60      ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_triangle_ineq3
% 0.30/0.60  thf(fact_6841_abs__triangle__ineq2,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_triangle_ineq2
% 0.30/0.60  thf(fact_6842_abs__triangle__ineq2,axiom,
% 0.30/0.60      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_triangle_ineq2
% 0.30/0.60  thf(fact_6843_abs__triangle__ineq2,axiom,
% 0.30/0.60      ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_triangle_ineq2
% 0.30/0.60  thf(fact_6844_abs__mult__less,axiom,
% 0.30/0.60      ! [A: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 0.30/0.60        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 0.30/0.60       => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D2 )
% 0.30/0.60         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_mult_less
% 0.30/0.60  thf(fact_6845_abs__mult__less,axiom,
% 0.30/0.60      ! [A: rat,C: rat,B: rat,D2: rat] :
% 0.30/0.60        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 0.30/0.60       => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D2 )
% 0.30/0.60         => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_mult_less
% 0.30/0.60  thf(fact_6846_abs__mult__less,axiom,
% 0.30/0.60      ! [A: int,C: int,B: int,D2: int] :
% 0.30/0.60        ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 0.30/0.60       => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D2 )
% 0.30/0.60         => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_mult_less
% 0.30/0.60  thf(fact_6847_abs__ge__minus__self,axiom,
% 0.30/0.60      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_ge_minus_self
% 0.30/0.60  thf(fact_6848_abs__ge__minus__self,axiom,
% 0.30/0.60      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_ge_minus_self
% 0.30/0.60  thf(fact_6849_abs__ge__minus__self,axiom,
% 0.30/0.60      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_ge_minus_self
% 0.30/0.60  thf(fact_6850_abs__le__iff,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer] :
% 0.30/0.60        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.30/0.60        = ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.30/0.60          & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_le_iff
% 0.30/0.60  thf(fact_6851_abs__le__iff,axiom,
% 0.30/0.60      ! [A: rat,B: rat] :
% 0.30/0.60        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.30/0.60        = ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.60          & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_le_iff
% 0.30/0.60  thf(fact_6852_abs__le__iff,axiom,
% 0.30/0.60      ! [A: int,B: int] :
% 0.30/0.60        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.30/0.60        = ( ( ord_less_eq_int @ A @ B )
% 0.30/0.60          & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_le_iff
% 0.30/0.60  thf(fact_6853_abs__le__D2,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer] :
% 0.30/0.60        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.30/0.60       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_le_D2
% 0.30/0.60  thf(fact_6854_abs__le__D2,axiom,
% 0.30/0.60      ! [A: rat,B: rat] :
% 0.30/0.60        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.30/0.60       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_le_D2
% 0.30/0.60  thf(fact_6855_abs__le__D2,axiom,
% 0.30/0.60      ! [A: int,B: int] :
% 0.30/0.60        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.30/0.60       => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_le_D2
% 0.30/0.60  thf(fact_6856_abs__leI,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer] :
% 0.30/0.60        ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.30/0.60       => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.30/0.60         => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_leI
% 0.30/0.60  thf(fact_6857_abs__leI,axiom,
% 0.30/0.60      ! [A: rat,B: rat] :
% 0.30/0.60        ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.60       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.30/0.60         => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_leI
% 0.30/0.60  thf(fact_6858_abs__leI,axiom,
% 0.30/0.60      ! [A: int,B: int] :
% 0.30/0.60        ( ( ord_less_eq_int @ A @ B )
% 0.30/0.60       => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 0.30/0.60         => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_leI
% 0.30/0.60  thf(fact_6859_abs__less__iff,axiom,
% 0.30/0.60      ! [A: int,B: int] :
% 0.30/0.60        ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 0.30/0.60        = ( ( ord_less_int @ A @ B )
% 0.30/0.60          & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_less_iff
% 0.30/0.60  thf(fact_6860_abs__less__iff,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer] :
% 0.30/0.60        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.30/0.60        = ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.30/0.60          & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_less_iff
% 0.30/0.60  thf(fact_6861_abs__less__iff,axiom,
% 0.30/0.60      ! [A: rat,B: rat] :
% 0.30/0.60        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 0.30/0.60        = ( ( ord_less_rat @ A @ B )
% 0.30/0.60          & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_less_iff
% 0.30/0.60  thf(fact_6862_abs__zmult__eq__1,axiom,
% 0.30/0.60      ! [M: int,N: int] :
% 0.30/0.60        ( ( ( abs_abs_int @ ( times_times_int @ M @ N ) )
% 0.30/0.60          = one_one_int )
% 0.30/0.60       => ( ( abs_abs_int @ M )
% 0.30/0.60          = one_one_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_zmult_eq_1
% 0.30/0.60  thf(fact_6863_frac__lt__1,axiom,
% 0.30/0.60      ! [X: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X ) @ one_one_rat ) ).
% 0.30/0.60  
% 0.30/0.60  % frac_lt_1
% 0.30/0.60  thf(fact_6864_frac__1__eq,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 0.30/0.60        = ( archimedean_frac_rat @ X ) ) ).
% 0.30/0.60  
% 0.30/0.60  % frac_1_eq
% 0.30/0.60  thf(fact_6865_dense__eq0__I,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ! [E3: rat] :
% 0.30/0.60            ( ( ord_less_rat @ zero_zero_rat @ E3 )
% 0.30/0.60           => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E3 ) )
% 0.30/0.60       => ( X = zero_zero_rat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % dense_eq0_I
% 0.30/0.60  thf(fact_6866_abs__eq__mult,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer] :
% 0.30/0.60        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.60            | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 0.30/0.60          & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.30/0.60            | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 0.30/0.60       => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.30/0.60          = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_eq_mult
% 0.30/0.60  thf(fact_6867_abs__eq__mult,axiom,
% 0.30/0.60      ! [A: rat,B: rat] :
% 0.30/0.60        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.60            | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 0.30/0.60          & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.60            | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 0.30/0.60       => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 0.30/0.60          = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_eq_mult
% 0.30/0.60  thf(fact_6868_abs__eq__mult,axiom,
% 0.30/0.60      ! [A: int,B: int] :
% 0.30/0.60        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.60            | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 0.30/0.60          & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.30/0.60            | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 0.30/0.60       => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 0.30/0.60          = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_eq_mult
% 0.30/0.60  thf(fact_6869_abs__mult__pos,axiom,
% 0.30/0.60      ! [X: code_integer,Y: code_integer] :
% 0.30/0.60        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 0.30/0.60       => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X )
% 0.30/0.60          = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_mult_pos
% 0.30/0.60  thf(fact_6870_abs__mult__pos,axiom,
% 0.30/0.60      ! [X: rat,Y: rat] :
% 0.30/0.60        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.30/0.60       => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X )
% 0.30/0.60          = ( abs_abs_rat @ ( times_times_rat @ Y @ X ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_mult_pos
% 0.30/0.60  thf(fact_6871_abs__mult__pos,axiom,
% 0.30/0.60      ! [X: int,Y: int] :
% 0.30/0.60        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.30/0.60       => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X )
% 0.30/0.60          = ( abs_abs_int @ ( times_times_int @ Y @ X ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_mult_pos
% 0.30/0.60  thf(fact_6872_abs__minus__le__zero,axiom,
% 0.30/0.60      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_minus_le_zero
% 0.30/0.60  thf(fact_6873_abs__minus__le__zero,axiom,
% 0.30/0.60      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_minus_le_zero
% 0.30/0.60  thf(fact_6874_abs__minus__le__zero,axiom,
% 0.30/0.60      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_minus_le_zero
% 0.30/0.60  thf(fact_6875_eq__abs__iff_H,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer] :
% 0.30/0.60        ( ( A
% 0.30/0.60          = ( abs_abs_Code_integer @ B ) )
% 0.30/0.60        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.60          & ( ( B = A )
% 0.30/0.60            | ( B
% 0.30/0.60              = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % eq_abs_iff'
% 0.30/0.60  thf(fact_6876_eq__abs__iff_H,axiom,
% 0.30/0.60      ! [A: rat,B: rat] :
% 0.30/0.60        ( ( A
% 0.30/0.60          = ( abs_abs_rat @ B ) )
% 0.30/0.60        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.60          & ( ( B = A )
% 0.30/0.60            | ( B
% 0.30/0.60              = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % eq_abs_iff'
% 0.30/0.60  thf(fact_6877_eq__abs__iff_H,axiom,
% 0.30/0.60      ! [A: int,B: int] :
% 0.30/0.60        ( ( A
% 0.30/0.60          = ( abs_abs_int @ B ) )
% 0.30/0.60        = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.60          & ( ( B = A )
% 0.30/0.60            | ( B
% 0.30/0.60              = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % eq_abs_iff'
% 0.30/0.60  thf(fact_6878_abs__eq__iff_H,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer] :
% 0.30/0.60        ( ( ( abs_abs_Code_integer @ A )
% 0.30/0.60          = B )
% 0.30/0.60        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.30/0.60          & ( ( A = B )
% 0.30/0.60            | ( A
% 0.30/0.60              = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_eq_iff'
% 0.30/0.60  thf(fact_6879_abs__eq__iff_H,axiom,
% 0.30/0.60      ! [A: rat,B: rat] :
% 0.30/0.60        ( ( ( abs_abs_rat @ A )
% 0.30/0.60          = B )
% 0.30/0.60        = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.60          & ( ( A = B )
% 0.30/0.60            | ( A
% 0.30/0.60              = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_eq_iff'
% 0.30/0.60  thf(fact_6880_abs__eq__iff_H,axiom,
% 0.30/0.60      ! [A: int,B: int] :
% 0.30/0.60        ( ( ( abs_abs_int @ A )
% 0.30/0.60          = B )
% 0.30/0.60        = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.30/0.60          & ( ( A = B )
% 0.30/0.60            | ( A
% 0.30/0.60              = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_eq_iff'
% 0.30/0.60  thf(fact_6881_abs__diff__triangle__ineq,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D2 ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_diff_triangle_ineq
% 0.30/0.60  thf(fact_6882_abs__diff__triangle__ineq,axiom,
% 0.30/0.60      ! [A: rat,B: rat,C: rat,D2: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D2 ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_diff_triangle_ineq
% 0.30/0.60  thf(fact_6883_abs__diff__triangle__ineq,axiom,
% 0.30/0.60      ! [A: int,B: int,C: int,D2: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D2 ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_diff_triangle_ineq
% 0.30/0.60  thf(fact_6884_abs__triangle__ineq4,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_triangle_ineq4
% 0.30/0.60  thf(fact_6885_abs__triangle__ineq4,axiom,
% 0.30/0.60      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_triangle_ineq4
% 0.30/0.60  thf(fact_6886_abs__triangle__ineq4,axiom,
% 0.30/0.60      ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_triangle_ineq4
% 0.30/0.60  thf(fact_6887_abs__if__raw,axiom,
% 0.30/0.60      ( abs_abs_int
% 0.30/0.60      = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_if_raw
% 0.30/0.60  thf(fact_6888_abs__if__raw,axiom,
% 0.30/0.60      ( abs_abs_Code_integer
% 0.30/0.60      = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_if_raw
% 0.30/0.60  thf(fact_6889_abs__if__raw,axiom,
% 0.30/0.60      ( abs_abs_rat
% 0.30/0.60      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_if_raw
% 0.30/0.60  thf(fact_6890_abs__of__neg,axiom,
% 0.30/0.60      ! [A: int] :
% 0.30/0.60        ( ( ord_less_int @ A @ zero_zero_int )
% 0.30/0.60       => ( ( abs_abs_int @ A )
% 0.30/0.60          = ( uminus_uminus_int @ A ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_of_neg
% 0.30/0.60  thf(fact_6891_abs__of__neg,axiom,
% 0.30/0.60      ! [A: code_integer] :
% 0.30/0.60        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.30/0.60       => ( ( abs_abs_Code_integer @ A )
% 0.30/0.60          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_of_neg
% 0.30/0.60  thf(fact_6892_abs__of__neg,axiom,
% 0.30/0.60      ! [A: rat] :
% 0.30/0.60        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.30/0.60       => ( ( abs_abs_rat @ A )
% 0.30/0.60          = ( uminus_uminus_rat @ A ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_of_neg
% 0.30/0.60  thf(fact_6893_abs__if,axiom,
% 0.30/0.60      ( abs_abs_int
% 0.30/0.60      = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_if
% 0.30/0.60  thf(fact_6894_abs__if,axiom,
% 0.30/0.60      ( abs_abs_Code_integer
% 0.30/0.60      = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_if
% 0.30/0.60  thf(fact_6895_abs__if,axiom,
% 0.30/0.60      ( abs_abs_rat
% 0.30/0.60      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_if
% 0.30/0.60  thf(fact_6896_zabs__def,axiom,
% 0.30/0.60      ( abs_abs_int
% 0.30/0.60      = ( ^ [I3: int] : ( if_int @ ( ord_less_int @ I3 @ zero_zero_int ) @ ( uminus_uminus_int @ I3 ) @ I3 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % zabs_def
% 0.30/0.60  thf(fact_6897_abs__integer__code,axiom,
% 0.30/0.60      ( abs_abs_Code_integer
% 0.30/0.60      = ( ^ [K4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K4 ) @ K4 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_integer_code
% 0.30/0.60  thf(fact_6898_abs__add__one__gt__zero,axiom,
% 0.30/0.60      ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_add_one_gt_zero
% 0.30/0.60  thf(fact_6899_abs__add__one__gt__zero,axiom,
% 0.30/0.60      ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_add_one_gt_zero
% 0.30/0.60  thf(fact_6900_abs__add__one__gt__zero,axiom,
% 0.30/0.60      ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_add_one_gt_zero
% 0.30/0.60  thf(fact_6901_of__int__leD,axiom,
% 0.30/0.60      ! [N: int,X: code_integer] :
% 0.30/0.60        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 0.30/0.60       => ( ( N = zero_zero_int )
% 0.30/0.60          | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % of_int_leD
% 0.30/0.60  thf(fact_6902_of__int__leD,axiom,
% 0.30/0.60      ! [N: int,X: rat] :
% 0.30/0.60        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 0.30/0.60       => ( ( N = zero_zero_int )
% 0.30/0.60          | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % of_int_leD
% 0.30/0.60  thf(fact_6903_of__int__leD,axiom,
% 0.30/0.60      ! [N: int,X: int] :
% 0.30/0.60        ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 0.30/0.60       => ( ( N = zero_zero_int )
% 0.30/0.60          | ( ord_less_eq_int @ one_one_int @ X ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % of_int_leD
% 0.30/0.60  thf(fact_6904_of__int__lessD,axiom,
% 0.30/0.60      ! [N: int,X: code_integer] :
% 0.30/0.60        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 0.30/0.60       => ( ( N = zero_zero_int )
% 0.30/0.60          | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % of_int_lessD
% 0.30/0.60  thf(fact_6905_of__int__lessD,axiom,
% 0.30/0.60      ! [N: int,X: rat] :
% 0.30/0.60        ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 0.30/0.60       => ( ( N = zero_zero_int )
% 0.30/0.60          | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % of_int_lessD
% 0.30/0.60  thf(fact_6906_of__int__lessD,axiom,
% 0.30/0.60      ! [N: int,X: int] :
% 0.30/0.60        ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 0.30/0.60       => ( ( N = zero_zero_int )
% 0.30/0.60          | ( ord_less_int @ one_one_int @ X ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % of_int_lessD
% 0.30/0.60  thf(fact_6907_zdvd__mult__cancel1,axiom,
% 0.30/0.60      ! [M: int,N: int] :
% 0.30/0.60        ( ( M != zero_zero_int )
% 0.30/0.60       => ( ( dvd_dvd_int @ ( times_times_int @ M @ N ) @ M )
% 0.30/0.60          = ( ( abs_abs_int @ N )
% 0.30/0.60            = one_one_int ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % zdvd_mult_cancel1
% 0.30/0.60  thf(fact_6908_abs__square__eq__1,axiom,
% 0.30/0.60      ! [X: code_integer] :
% 0.30/0.60        ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.60          = one_one_Code_integer )
% 0.30/0.60        = ( ( abs_abs_Code_integer @ X )
% 0.30/0.60          = one_one_Code_integer ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_square_eq_1
% 0.30/0.60  thf(fact_6909_abs__square__eq__1,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.60          = one_one_rat )
% 0.30/0.60        = ( ( abs_abs_rat @ X )
% 0.30/0.60          = one_one_rat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_square_eq_1
% 0.30/0.60  thf(fact_6910_abs__square__eq__1,axiom,
% 0.30/0.60      ! [X: int] :
% 0.30/0.60        ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.60          = one_one_int )
% 0.30/0.60        = ( ( abs_abs_int @ X )
% 0.30/0.60          = one_one_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_square_eq_1
% 0.30/0.60  thf(fact_6911_frac__eq,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( ( archimedean_frac_rat @ X )
% 0.30/0.60          = X )
% 0.30/0.60        = ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.30/0.60          & ( ord_less_rat @ X @ one_one_rat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % frac_eq
% 0.30/0.60  thf(fact_6912_frac__add,axiom,
% 0.30/0.60      ! [X: rat,Y: rat] :
% 0.30/0.60        ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 0.30/0.60         => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 0.30/0.60            = ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) ) )
% 0.30/0.60        & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 0.30/0.60         => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 0.30/0.60            = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % frac_add
% 0.30/0.60  thf(fact_6913_abs__square__le__1,axiom,
% 0.30/0.60      ! [X: code_integer] :
% 0.30/0.60        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 0.30/0.60        = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_square_le_1
% 0.30/0.60  thf(fact_6914_abs__square__le__1,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 0.30/0.60        = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_square_le_1
% 0.30/0.60  thf(fact_6915_abs__square__le__1,axiom,
% 0.30/0.60      ! [X: int] :
% 0.30/0.60        ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 0.30/0.60        = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_square_le_1
% 0.30/0.60  thf(fact_6916_abs__square__less__1,axiom,
% 0.30/0.60      ! [X: code_integer] :
% 0.30/0.60        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 0.30/0.60        = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_square_less_1
% 0.30/0.60  thf(fact_6917_abs__square__less__1,axiom,
% 0.30/0.60      ! [X: rat] :
% 0.30/0.60        ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 0.30/0.60        = ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_square_less_1
% 0.30/0.60  thf(fact_6918_abs__square__less__1,axiom,
% 0.30/0.60      ! [X: int] :
% 0.30/0.60        ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 0.30/0.60        = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_square_less_1
% 0.30/0.60  thf(fact_6919_nat__intermed__int__val,axiom,
% 0.30/0.60      ! [M: nat,N: nat,F2: nat > int,K: int] :
% 0.30/0.60        ( ! [I2: nat] :
% 0.30/0.60            ( ( ( ord_less_eq_nat @ M @ I2 )
% 0.30/0.60              & ( ord_less_nat @ I2 @ N ) )
% 0.30/0.60           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F2 @ ( suc @ I2 ) ) @ ( F2 @ I2 ) ) ) @ one_one_int ) )
% 0.30/0.60       => ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.60         => ( ( ord_less_eq_int @ ( F2 @ M ) @ K )
% 0.30/0.60           => ( ( ord_less_eq_int @ K @ ( F2 @ N ) )
% 0.30/0.60             => ? [I2: nat] :
% 0.30/0.60                  ( ( ord_less_eq_nat @ M @ I2 )
% 0.30/0.60                  & ( ord_less_eq_nat @ I2 @ N )
% 0.30/0.60                  & ( ( F2 @ I2 )
% 0.30/0.60                    = K ) ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % nat_intermed_int_val
% 0.30/0.60  thf(fact_6920_incr__lemma,axiom,
% 0.30/0.60      ! [D2: int,Z: int,X: int] :
% 0.30/0.60        ( ( ord_less_int @ zero_zero_int @ D2 )
% 0.30/0.60       => ( ord_less_int @ Z @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % incr_lemma
% 0.30/0.60  thf(fact_6921_decr__lemma,axiom,
% 0.30/0.60      ! [D2: int,X: int,Z: int] :
% 0.30/0.60        ( ( ord_less_int @ zero_zero_int @ D2 )
% 0.30/0.60       => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D2 ) ) @ Z ) ) ).
% 0.30/0.60  
% 0.30/0.60  % decr_lemma
% 0.30/0.60  thf(fact_6922_nat__ivt__aux,axiom,
% 0.30/0.60      ! [N: nat,F2: nat > int,K: int] :
% 0.30/0.60        ( ! [I2: nat] :
% 0.30/0.60            ( ( ord_less_nat @ I2 @ N )
% 0.30/0.60           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F2 @ ( suc @ I2 ) ) @ ( F2 @ I2 ) ) ) @ one_one_int ) )
% 0.30/0.60       => ( ( ord_less_eq_int @ ( F2 @ zero_zero_nat ) @ K )
% 0.30/0.60         => ( ( ord_less_eq_int @ K @ ( F2 @ N ) )
% 0.30/0.60           => ? [I2: nat] :
% 0.30/0.60                ( ( ord_less_eq_nat @ I2 @ N )
% 0.30/0.60                & ( ( F2 @ I2 )
% 0.30/0.60                  = K ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % nat_ivt_aux
% 0.30/0.60  thf(fact_6923_floor__add,axiom,
% 0.30/0.60      ! [X: rat,Y: rat] :
% 0.30/0.60        ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 0.30/0.60         => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 0.30/0.60            = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) ) )
% 0.30/0.60        & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 0.30/0.60         => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 0.30/0.60            = ( plus_plus_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) @ one_one_int ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % floor_add
% 0.30/0.60  thf(fact_6924_nat0__intermed__int__val,axiom,
% 0.30/0.60      ! [N: nat,F2: nat > int,K: int] :
% 0.30/0.60        ( ! [I2: nat] :
% 0.30/0.60            ( ( ord_less_nat @ I2 @ N )
% 0.30/0.60           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F2 @ ( plus_plus_nat @ I2 @ one_one_nat ) ) @ ( F2 @ I2 ) ) ) @ one_one_int ) )
% 0.30/0.60       => ( ( ord_less_eq_int @ ( F2 @ zero_zero_nat ) @ K )
% 0.30/0.60         => ( ( ord_less_eq_int @ K @ ( F2 @ N ) )
% 0.30/0.60           => ? [I2: nat] :
% 0.30/0.60                ( ( ord_less_eq_nat @ I2 @ N )
% 0.30/0.60                & ( ( F2 @ I2 )
% 0.30/0.60                  = K ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % nat0_intermed_int_val
% 0.30/0.60  thf(fact_6925_divmod__integer__def,axiom,
% 0.30/0.60      ( code_divmod_integer
% 0.30/0.60      = ( ^ [K4: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K4 @ L2 ) @ ( modulo364778990260209775nteger @ K4 @ L2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % divmod_integer_def
% 0.30/0.60  thf(fact_6926_bit__cut__integer__code,axiom,
% 0.30/0.60      ( code_bit_cut_integer
% 0.30/0.60      = ( ^ [K4: code_integer] :
% 0.30/0.60            ( if_Pro5737122678794959658eger_o @ ( K4 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 0.30/0.60            @ ( produc9125791028180074456eger_o
% 0.30/0.60              @ ^ [R4: code_integer,S2: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K4 ) @ R4 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ S2 ) ) @ ( S2 = one_one_Code_integer ) )
% 0.30/0.60              @ ( code_divmod_abs @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % bit_cut_integer_code
% 0.30/0.60  thf(fact_6927_nat__of__integer__code,axiom,
% 0.30/0.60      ( code_nat_of_integer
% 0.30/0.60      = ( ^ [K4: code_integer] :
% 0.30/0.60            ( if_nat @ ( ord_le3102999989581377725nteger @ K4 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 0.30/0.60            @ ( produc1555791787009142072er_nat
% 0.30/0.60              @ ^ [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 ) )
% 0.30/0.60              @ ( code_divmod_integer @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % nat_of_integer_code
% 0.30/0.60  thf(fact_6928_int__of__integer__code,axiom,
% 0.30/0.60      ( code_int_of_integer
% 0.30/0.60      = ( ^ [K4: code_integer] :
% 0.30/0.60            ( if_int @ ( ord_le6747313008572928689nteger @ K4 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K4 ) ) )
% 0.30/0.60            @ ( if_int @ ( K4 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 0.30/0.60              @ ( produc1553301316500091796er_int
% 0.30/0.60                @ ^ [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 ) )
% 0.30/0.60                @ ( code_divmod_integer @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % int_of_integer_code
% 0.30/0.60  thf(fact_6929_xor__int__unfold,axiom,
% 0.30/0.60      ( bit_se6526347334894502574or_int
% 0.30/0.60      = ( ^ [K4: int,L2: int] :
% 0.30/0.60            ( if_int
% 0.30/0.60            @ ( K4
% 0.30/0.60              = ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.60            @ ( bit_ri7919022796975470100ot_int @ L2 )
% 0.30/0.60            @ ( if_int
% 0.30/0.60              @ ( L2
% 0.30/0.60                = ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.60              @ ( bit_ri7919022796975470100ot_int @ K4 )
% 0.30/0.60              @ ( if_int @ ( K4 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K4 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K4 @ ( 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 @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % xor_int_unfold
% 0.30/0.60  thf(fact_6930_is__singleton__the__elem,axiom,
% 0.30/0.60      ( is_sin2937591304547752795at_nat
% 0.30/0.60      = ( ^ [A4: set_Pr4329608150637261639at_nat] :
% 0.30/0.60            ( A4
% 0.30/0.60            = ( insert9069300056098147895at_nat @ ( the_el221668144340439132at_nat @ A4 ) @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singleton_the_elem
% 0.30/0.60  thf(fact_6931_is__singleton__the__elem,axiom,
% 0.30/0.60      ( is_sin2850979758926227957at_nat
% 0.30/0.60      = ( ^ [A4: set_Pr1261947904930325089at_nat] :
% 0.30/0.60            ( A4
% 0.30/0.60            = ( insert8211810215607154385at_nat @ ( the_el2281957884133575798at_nat @ A4 ) @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singleton_the_elem
% 0.30/0.60  thf(fact_6932_is__singleton__the__elem,axiom,
% 0.30/0.60      ( is_singleton_o
% 0.30/0.60      = ( ^ [A4: set_o] :
% 0.30/0.60            ( A4
% 0.30/0.60            = ( insert_o @ ( the_elem_o @ A4 ) @ bot_bot_set_o ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singleton_the_elem
% 0.30/0.60  thf(fact_6933_is__singleton__the__elem,axiom,
% 0.30/0.60      ( is_singleton_nat
% 0.30/0.60      = ( ^ [A4: set_nat] :
% 0.30/0.60            ( A4
% 0.30/0.60            = ( insert_nat @ ( the_elem_nat @ A4 ) @ bot_bot_set_nat ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singleton_the_elem
% 0.30/0.60  thf(fact_6934_is__singleton__the__elem,axiom,
% 0.30/0.60      ( is_singleton_int
% 0.30/0.60      = ( ^ [A4: set_int] :
% 0.30/0.60            ( A4
% 0.30/0.60            = ( insert_int @ ( the_elem_int @ A4 ) @ bot_bot_set_int ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singleton_the_elem
% 0.30/0.60  thf(fact_6935_integer__of__num_I3_J,axiom,
% 0.30/0.60      ! [N: num] :
% 0.30/0.60        ( ( code_integer_of_num @ ( bit1 @ N ) )
% 0.30/0.60        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 0.30/0.60  
% 0.30/0.60  % integer_of_num(3)
% 0.30/0.60  thf(fact_6936_mask__eq__sum__exp__nat,axiom,
% 0.30/0.60      ! [N: nat] :
% 0.30/0.60        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 0.30/0.60        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.60          @ ( collect_nat
% 0.30/0.60            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % mask_eq_sum_exp_nat
% 0.30/0.60  thf(fact_6937_of__int__sum,axiom,
% 0.30/0.60      ! [F2: int > int,A2: set_int] :
% 0.30/0.60        ( ( ring_1_of_int_rat @ ( groups4538972089207619220nt_int @ F2 @ A2 ) )
% 0.30/0.60        = ( groups3906332499630173760nt_rat
% 0.30/0.60          @ ^ [X3: int] : ( ring_1_of_int_rat @ ( F2 @ X3 ) )
% 0.30/0.60          @ A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % of_int_sum
% 0.30/0.60  thf(fact_6938_of__int__sum,axiom,
% 0.30/0.60      ! [F2: int > int,A2: set_int] :
% 0.30/0.60        ( ( ring_1_of_int_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) )
% 0.30/0.60        = ( groups4538972089207619220nt_int
% 0.30/0.60          @ ^ [X3: int] : ( ring_1_of_int_int @ ( F2 @ X3 ) )
% 0.30/0.60          @ A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % of_int_sum
% 0.30/0.60  thf(fact_6939_one__integer_Orep__eq,axiom,
% 0.30/0.60      ( ( code_int_of_integer @ one_one_Code_integer )
% 0.30/0.60      = one_one_int ) ).
% 0.30/0.60  
% 0.30/0.60  % one_integer.rep_eq
% 0.30/0.60  thf(fact_6940_uminus__integer_Orep__eq,axiom,
% 0.30/0.60      ! [X: code_integer] :
% 0.30/0.60        ( ( code_int_of_integer @ ( uminus1351360451143612070nteger @ X ) )
% 0.30/0.60        = ( uminus_uminus_int @ ( code_int_of_integer @ X ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % uminus_integer.rep_eq
% 0.30/0.60  thf(fact_6941_is__singletonI,axiom,
% 0.30/0.60      ! [X: produc3843707927480180839at_nat] : ( is_sin2937591304547752795at_nat @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singletonI
% 0.30/0.60  thf(fact_6942_is__singletonI,axiom,
% 0.30/0.60      ! [X: product_prod_nat_nat] : ( is_sin2850979758926227957at_nat @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singletonI
% 0.30/0.60  thf(fact_6943_is__singletonI,axiom,
% 0.30/0.60      ! [X: $o] : ( is_singleton_o @ ( insert_o @ X @ bot_bot_set_o ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singletonI
% 0.30/0.60  thf(fact_6944_is__singletonI,axiom,
% 0.30/0.60      ! [X: nat] : ( is_singleton_nat @ ( insert_nat @ X @ bot_bot_set_nat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singletonI
% 0.30/0.60  thf(fact_6945_is__singletonI,axiom,
% 0.30/0.60      ! [X: int] : ( is_singleton_int @ ( insert_int @ X @ bot_bot_set_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singletonI
% 0.30/0.60  thf(fact_6946_bit_Ocompl__zero,axiom,
% 0.30/0.60      ( ( bit_ri7632146776885996613nteger @ zero_z3403309356797280102nteger )
% 0.30/0.60      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.30/0.60  
% 0.30/0.60  % bit.compl_zero
% 0.30/0.60  thf(fact_6947_bit_Ocompl__zero,axiom,
% 0.30/0.60      ( ( bit_ri7919022796975470100ot_int @ zero_zero_int )
% 0.30/0.60      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % bit.compl_zero
% 0.30/0.60  thf(fact_6948_bit_Ocompl__one,axiom,
% 0.30/0.60      ( ( bit_ri7632146776885996613nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.60      = zero_z3403309356797280102nteger ) ).
% 0.30/0.60  
% 0.30/0.60  % bit.compl_one
% 0.30/0.60  thf(fact_6949_bit_Ocompl__one,axiom,
% 0.30/0.60      ( ( bit_ri7919022796975470100ot_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.60      = zero_zero_int ) ).
% 0.30/0.60  
% 0.30/0.60  % bit.compl_one
% 0.30/0.60  thf(fact_6950_bit_Oxor__cancel__right,axiom,
% 0.30/0.60      ! [X: code_integer] :
% 0.30/0.60        ( ( bit_se3222712562003087583nteger @ X @ ( bit_ri7632146776885996613nteger @ X ) )
% 0.30/0.60        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.30/0.60  
% 0.30/0.60  % bit.xor_cancel_right
% 0.30/0.60  thf(fact_6951_bit_Oxor__cancel__right,axiom,
% 0.30/0.60      ! [X: int] :
% 0.30/0.60        ( ( bit_se6526347334894502574or_int @ X @ ( bit_ri7919022796975470100ot_int @ X ) )
% 0.30/0.60        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % bit.xor_cancel_right
% 0.30/0.60  thf(fact_6952_bit_Oxor__cancel__left,axiom,
% 0.30/0.60      ! [X: code_integer] :
% 0.30/0.60        ( ( bit_se3222712562003087583nteger @ ( bit_ri7632146776885996613nteger @ X ) @ X )
% 0.30/0.60        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.30/0.60  
% 0.30/0.60  % bit.xor_cancel_left
% 0.30/0.60  thf(fact_6953_bit_Oxor__cancel__left,axiom,
% 0.30/0.60      ! [X: int] :
% 0.30/0.60        ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X ) @ X )
% 0.30/0.60        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % bit.xor_cancel_left
% 0.30/0.60  thf(fact_6954_bit_Oxor__one__right,axiom,
% 0.30/0.60      ! [X: code_integer] :
% 0.30/0.60        ( ( bit_se3222712562003087583nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.60        = ( bit_ri7632146776885996613nteger @ X ) ) ).
% 0.30/0.60  
% 0.30/0.60  % bit.xor_one_right
% 0.30/0.60  thf(fact_6955_bit_Oxor__one__right,axiom,
% 0.30/0.60      ! [X: int] :
% 0.30/0.60        ( ( bit_se6526347334894502574or_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.60        = ( bit_ri7919022796975470100ot_int @ X ) ) ).
% 0.30/0.60  
% 0.30/0.60  % bit.xor_one_right
% 0.30/0.60  thf(fact_6956_bit_Oxor__one__left,axiom,
% 0.30/0.60      ! [X: code_integer] :
% 0.30/0.60        ( ( bit_se3222712562003087583nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 0.30/0.60        = ( bit_ri7632146776885996613nteger @ X ) ) ).
% 0.30/0.60  
% 0.30/0.60  % bit.xor_one_left
% 0.30/0.60  thf(fact_6957_bit_Oxor__one__left,axiom,
% 0.30/0.60      ! [X: int] :
% 0.30/0.60        ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 0.30/0.60        = ( bit_ri7919022796975470100ot_int @ X ) ) ).
% 0.30/0.60  
% 0.30/0.60  % bit.xor_one_left
% 0.30/0.60  thf(fact_6958_minus__not__numeral__eq,axiom,
% 0.30/0.60      ! [N: num] :
% 0.30/0.60        ( ( uminus1351360451143612070nteger @ ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.30/0.60        = ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % minus_not_numeral_eq
% 0.30/0.60  thf(fact_6959_minus__not__numeral__eq,axiom,
% 0.30/0.60      ! [N: num] :
% 0.30/0.60        ( ( uminus_uminus_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.60        = ( numeral_numeral_int @ ( inc @ N ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % minus_not_numeral_eq
% 0.30/0.60  thf(fact_6960_not__minus__numeral__eq,axiom,
% 0.30/0.60      ! [N: num] :
% 0.30/0.60        ( ( bit_ri7632146776885996613nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.30/0.60        = ( neg_nu5755505904847501662nteger @ N @ one ) ) ).
% 0.30/0.60  
% 0.30/0.60  % not_minus_numeral_eq
% 0.30/0.60  thf(fact_6961_not__minus__numeral__eq,axiom,
% 0.30/0.60      ! [N: num] :
% 0.30/0.60        ( ( bit_ri7919022796975470100ot_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.60        = ( neg_numeral_sub_int @ N @ one ) ) ).
% 0.30/0.60  
% 0.30/0.60  % not_minus_numeral_eq
% 0.30/0.60  thf(fact_6962_push__bit__minus__one__eq__not__mask,axiom,
% 0.30/0.60      ! [N: nat] :
% 0.30/0.60        ( ( bit_se7788150548672797655nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.60        = ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % push_bit_minus_one_eq_not_mask
% 0.30/0.60  thf(fact_6963_push__bit__minus__one__eq__not__mask,axiom,
% 0.30/0.60      ! [N: nat] :
% 0.30/0.60        ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.60        = ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % push_bit_minus_one_eq_not_mask
% 0.30/0.60  thf(fact_6964_xor__minus__numerals_I2_J,axiom,
% 0.30/0.60      ! [K: int,N: num] :
% 0.30/0.60        ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.60        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N @ one ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % xor_minus_numerals(2)
% 0.30/0.60  thf(fact_6965_xor__minus__numerals_I1_J,axiom,
% 0.30/0.60      ! [N: num,K: int] :
% 0.30/0.60        ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ K )
% 0.30/0.60        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N @ one ) @ K ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % xor_minus_numerals(1)
% 0.30/0.60  thf(fact_6966_not__one__eq,axiom,
% 0.30/0.60      ( ( bit_ri7632146776885996613nteger @ one_one_Code_integer )
% 0.30/0.60      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % not_one_eq
% 0.30/0.60  thf(fact_6967_not__one__eq,axiom,
% 0.30/0.60      ( ( bit_ri7919022796975470100ot_int @ one_one_int )
% 0.30/0.60      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % not_one_eq
% 0.30/0.60  thf(fact_6968_int__of__integer,axiom,
% 0.30/0.60      ! [X: code_integer] : ( member_int @ ( code_int_of_integer @ X ) @ top_top_set_int ) ).
% 0.30/0.60  
% 0.30/0.60  % int_of_integer
% 0.30/0.60  thf(fact_6969_int__of__integer__cases,axiom,
% 0.30/0.60      ! [Y: int] :
% 0.30/0.60        ( ( member_int @ Y @ top_top_set_int )
% 0.30/0.60       => ~ ! [X2: code_integer] :
% 0.30/0.60              ( Y
% 0.30/0.60             != ( code_int_of_integer @ X2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % int_of_integer_cases
% 0.30/0.60  thf(fact_6970_int__of__integer__induct,axiom,
% 0.30/0.60      ! [Y: int,P: int > $o] :
% 0.30/0.60        ( ( member_int @ Y @ top_top_set_int )
% 0.30/0.60       => ( ! [X2: code_integer] : ( P @ ( code_int_of_integer @ X2 ) )
% 0.30/0.60         => ( P @ Y ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % int_of_integer_induct
% 0.30/0.60  thf(fact_6971_mod__sum__eq,axiom,
% 0.30/0.60      ! [F2: nat > nat,A: nat,A2: set_nat] :
% 0.30/0.60        ( ( modulo_modulo_nat
% 0.30/0.60          @ ( groups3542108847815614940at_nat
% 0.30/0.60            @ ^ [I3: nat] : ( modulo_modulo_nat @ ( F2 @ I3 ) @ A )
% 0.30/0.60            @ A2 )
% 0.30/0.60          @ A )
% 0.30/0.60        = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F2 @ A2 ) @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % mod_sum_eq
% 0.30/0.60  thf(fact_6972_mod__sum__eq,axiom,
% 0.30/0.60      ! [F2: int > int,A: int,A2: set_int] :
% 0.30/0.60        ( ( modulo_modulo_int
% 0.30/0.60          @ ( groups4538972089207619220nt_int
% 0.30/0.60            @ ^ [I3: int] : ( modulo_modulo_int @ ( F2 @ I3 ) @ A )
% 0.30/0.60            @ A2 )
% 0.30/0.60          @ A )
% 0.30/0.60        = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) @ A ) ) ).
% 0.30/0.60  
% 0.30/0.60  % mod_sum_eq
% 0.30/0.60  thf(fact_6973_type__definition__integer,axiom,
% 0.30/0.60      type_d8366093980585677751er_int @ code_int_of_integer @ code_integer_of_int @ top_top_set_int ).
% 0.30/0.60  
% 0.30/0.60  % type_definition_integer
% 0.30/0.60  thf(fact_6974_integer__of__int__inverse,axiom,
% 0.30/0.60      ! [Y: int] :
% 0.30/0.60        ( ( member_int @ Y @ top_top_set_int )
% 0.30/0.60       => ( ( code_int_of_integer @ ( code_integer_of_int @ Y ) )
% 0.30/0.60          = Y ) ) ).
% 0.30/0.60  
% 0.30/0.60  % integer_of_int_inverse
% 0.30/0.60  thf(fact_6975_is__singletonI_H,axiom,
% 0.30/0.60      ! [A2: set_se6260736226359567993nt_int] :
% 0.30/0.60        ( ( A2 != bot_bo1488462491386950373nt_int )
% 0.30/0.60       => ( ! [X2: set_Pr958786334691620121nt_int,Y2: set_Pr958786334691620121nt_int] :
% 0.30/0.60              ( ( member2340774599025711042nt_int @ X2 @ A2 )
% 0.30/0.60             => ( ( member2340774599025711042nt_int @ Y2 @ A2 )
% 0.30/0.60               => ( X2 = Y2 ) ) )
% 0.30/0.60         => ( is_sin6299389887212142093nt_int @ A2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singletonI'
% 0.30/0.60  thf(fact_6976_is__singletonI_H,axiom,
% 0.30/0.60      ! [A2: set_set_nat] :
% 0.30/0.60        ( ( A2 != bot_bot_set_set_nat )
% 0.30/0.60       => ( ! [X2: set_nat,Y2: set_nat] :
% 0.30/0.60              ( ( member_set_nat @ X2 @ A2 )
% 0.30/0.60             => ( ( member_set_nat @ Y2 @ A2 )
% 0.30/0.60               => ( X2 = Y2 ) ) )
% 0.30/0.60         => ( is_singleton_set_nat @ A2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singletonI'
% 0.30/0.60  thf(fact_6977_is__singletonI_H,axiom,
% 0.30/0.60      ! [A2: set_Pr4532377907799695533_nat_o] :
% 0.30/0.60        ( ( A2 != bot_bo7824918357723582233_nat_o )
% 0.30/0.60       => ( ! [X2: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat > $o] :
% 0.30/0.60              ( ( member6576561426505652726_nat_o @ X2 @ A2 )
% 0.30/0.60             => ( ( member6576561426505652726_nat_o @ Y2 @ A2 )
% 0.30/0.60               => ( X2 = Y2 ) ) )
% 0.30/0.60         => ( is_sin5180296473474724033_nat_o @ A2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singletonI'
% 0.30/0.60  thf(fact_6978_is__singletonI_H,axiom,
% 0.30/0.60      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.30/0.60        ( ( A2 != bot_bo2099793752762293965at_nat )
% 0.30/0.60       => ( ! [X2: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 0.30/0.60              ( ( member8440522571783428010at_nat @ X2 @ A2 )
% 0.30/0.60             => ( ( member8440522571783428010at_nat @ Y2 @ A2 )
% 0.30/0.60               => ( X2 = Y2 ) ) )
% 0.30/0.60         => ( is_sin2850979758926227957at_nat @ A2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singletonI'
% 0.30/0.60  thf(fact_6979_is__singletonI_H,axiom,
% 0.30/0.60      ! [A2: set_o] :
% 0.30/0.60        ( ( A2 != bot_bot_set_o )
% 0.30/0.60       => ( ! [X2: $o,Y2: $o] :
% 0.30/0.60              ( ( member_o @ X2 @ A2 )
% 0.30/0.60             => ( ( member_o @ Y2 @ A2 )
% 0.30/0.60               => ( X2 = Y2 ) ) )
% 0.30/0.60         => ( is_singleton_o @ A2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singletonI'
% 0.30/0.60  thf(fact_6980_is__singletonI_H,axiom,
% 0.30/0.60      ! [A2: set_nat] :
% 0.30/0.60        ( ( A2 != bot_bot_set_nat )
% 0.30/0.60       => ( ! [X2: nat,Y2: nat] :
% 0.30/0.60              ( ( member_nat @ X2 @ A2 )
% 0.30/0.60             => ( ( member_nat @ Y2 @ A2 )
% 0.30/0.60               => ( X2 = Y2 ) ) )
% 0.30/0.60         => ( is_singleton_nat @ A2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singletonI'
% 0.30/0.60  thf(fact_6981_is__singletonI_H,axiom,
% 0.30/0.60      ! [A2: set_int] :
% 0.30/0.60        ( ( A2 != bot_bot_set_int )
% 0.30/0.60       => ( ! [X2: int,Y2: int] :
% 0.30/0.60              ( ( member_int @ X2 @ A2 )
% 0.30/0.60             => ( ( member_int @ Y2 @ A2 )
% 0.30/0.60               => ( X2 = Y2 ) ) )
% 0.30/0.60         => ( is_singleton_int @ A2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singletonI'
% 0.30/0.60  thf(fact_6982_minus__eq__not__plus__1,axiom,
% 0.30/0.60      ( uminus1351360451143612070nteger
% 0.30/0.60      = ( ^ [A3: code_integer] : ( plus_p5714425477246183910nteger @ ( bit_ri7632146776885996613nteger @ A3 ) @ one_one_Code_integer ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % minus_eq_not_plus_1
% 0.30/0.60  thf(fact_6983_minus__eq__not__plus__1,axiom,
% 0.30/0.60      ( uminus_uminus_int
% 0.30/0.60      = ( ^ [A3: int] : ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A3 ) @ one_one_int ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % minus_eq_not_plus_1
% 0.30/0.60  thf(fact_6984_minus__eq__not__minus__1,axiom,
% 0.30/0.60      ( uminus1351360451143612070nteger
% 0.30/0.60      = ( ^ [A3: code_integer] : ( bit_ri7632146776885996613nteger @ ( minus_8373710615458151222nteger @ A3 @ one_one_Code_integer ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % minus_eq_not_minus_1
% 0.30/0.60  thf(fact_6985_minus__eq__not__minus__1,axiom,
% 0.30/0.60      ( uminus_uminus_int
% 0.30/0.60      = ( ^ [A3: int] : ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A3 @ one_one_int ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % minus_eq_not_minus_1
% 0.30/0.60  thf(fact_6986_not__eq__complement,axiom,
% 0.30/0.60      ( bit_ri7632146776885996613nteger
% 0.30/0.60      = ( ^ [A3: code_integer] : ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A3 ) @ one_one_Code_integer ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % not_eq_complement
% 0.30/0.60  thf(fact_6987_not__eq__complement,axiom,
% 0.30/0.60      ( bit_ri7919022796975470100ot_int
% 0.30/0.60      = ( ^ [A3: int] : ( minus_minus_int @ ( uminus_uminus_int @ A3 ) @ one_one_int ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % not_eq_complement
% 0.30/0.60  thf(fact_6988_not__int__def,axiom,
% 0.30/0.60      ( bit_ri7919022796975470100ot_int
% 0.30/0.60      = ( ^ [K4: int] : ( minus_minus_int @ ( uminus_uminus_int @ K4 ) @ one_one_int ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % not_int_def
% 0.30/0.60  thf(fact_6989_and__not__numerals_I1_J,axiom,
% 0.30/0.60      ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.30/0.60      = zero_zero_int ) ).
% 0.30/0.60  
% 0.30/0.60  % and_not_numerals(1)
% 0.30/0.60  thf(fact_6990_sum__power__add,axiom,
% 0.30/0.60      ! [X: code_integer,M: nat,I4: set_nat] :
% 0.30/0.60        ( ( groups7501900531339628137nteger
% 0.30/0.60          @ ^ [I3: nat] : ( power_8256067586552552935nteger @ X @ ( plus_plus_nat @ M @ I3 ) )
% 0.30/0.60          @ I4 )
% 0.30/0.60        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ M ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ I4 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_power_add
% 0.30/0.60  thf(fact_6991_sum__power__add,axiom,
% 0.30/0.60      ! [X: rat,M: nat,I4: set_nat] :
% 0.30/0.60        ( ( groups2906978787729119204at_rat
% 0.30/0.60          @ ^ [I3: nat] : ( power_power_rat @ X @ ( plus_plus_nat @ M @ I3 ) )
% 0.30/0.60          @ I4 )
% 0.30/0.60        = ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ I4 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_power_add
% 0.30/0.60  thf(fact_6992_sum__power__add,axiom,
% 0.30/0.60      ! [X: int,M: nat,I4: set_nat] :
% 0.30/0.60        ( ( groups3539618377306564664at_int
% 0.30/0.60          @ ^ [I3: nat] : ( power_power_int @ X @ ( plus_plus_nat @ M @ I3 ) )
% 0.30/0.60          @ I4 )
% 0.30/0.60        = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ I4 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_power_add
% 0.30/0.60  thf(fact_6993_minus__numeral__inc__eq,axiom,
% 0.30/0.60      ! [N: num] :
% 0.30/0.60        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) )
% 0.30/0.60        = ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % minus_numeral_inc_eq
% 0.30/0.60  thf(fact_6994_minus__numeral__inc__eq,axiom,
% 0.30/0.60      ! [N: num] :
% 0.30/0.60        ( ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) )
% 0.30/0.60        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % minus_numeral_inc_eq
% 0.30/0.60  thf(fact_6995_unset__bit__int__def,axiom,
% 0.30/0.60      ( bit_se4203085406695923979it_int
% 0.30/0.60      = ( ^ [N2: nat,K4: int] : ( bit_se725231765392027082nd_int @ K4 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % unset_bit_int_def
% 0.30/0.60  thf(fact_6996_divmod__abs__code_I6_J,axiom,
% 0.30/0.60      ! [J: code_integer] :
% 0.30/0.60        ( ( code_divmod_abs @ zero_z3403309356797280102nteger @ J )
% 0.30/0.60        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ) ).
% 0.30/0.60  
% 0.30/0.60  % divmod_abs_code(6)
% 0.30/0.60  thf(fact_6997_divmod__abs__code_I5_J,axiom,
% 0.30/0.60      ! [J: code_integer] :
% 0.30/0.60        ( ( code_divmod_abs @ J @ zero_z3403309356797280102nteger )
% 0.30/0.60        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ J ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % divmod_abs_code(5)
% 0.30/0.60  thf(fact_6998_and__not__numerals_I2_J,axiom,
% 0.30/0.60      ! [N: num] :
% 0.30/0.60        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.30/0.60        = one_one_int ) ).
% 0.30/0.60  
% 0.30/0.60  % and_not_numerals(2)
% 0.30/0.60  thf(fact_6999_and__not__numerals_I4_J,axiom,
% 0.30/0.60      ! [M: num] :
% 0.30/0.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.30/0.60        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % and_not_numerals(4)
% 0.30/0.60  thf(fact_7000_not__numeral__Bit0__eq,axiom,
% 0.30/0.60      ! [N: num] :
% 0.30/0.60        ( ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) )
% 0.30/0.60        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % not_numeral_Bit0_eq
% 0.30/0.60  thf(fact_7001_not__numeral__Bit0__eq,axiom,
% 0.30/0.60      ! [N: num] :
% 0.30/0.60        ( ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) )
% 0.30/0.60        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % not_numeral_Bit0_eq
% 0.30/0.60  thf(fact_7002_minus__numeral__eq__not__sub__one,axiom,
% 0.30/0.60      ! [N: num] :
% 0.30/0.60        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 0.30/0.60        = ( bit_ri7632146776885996613nteger @ ( neg_nu5755505904847501662nteger @ N @ one ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % minus_numeral_eq_not_sub_one
% 0.30/0.60  thf(fact_7003_minus__numeral__eq__not__sub__one,axiom,
% 0.30/0.60      ! [N: num] :
% 0.30/0.60        ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 0.30/0.60        = ( bit_ri7919022796975470100ot_int @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % minus_numeral_eq_not_sub_one
% 0.30/0.60  thf(fact_7004_not__numeral__BitM__eq,axiom,
% 0.30/0.60      ! [N: num] :
% 0.30/0.60        ( ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ ( bitM @ N ) ) )
% 0.30/0.60        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % not_numeral_BitM_eq
% 0.30/0.60  thf(fact_7005_not__numeral__BitM__eq,axiom,
% 0.30/0.60      ! [N: num] :
% 0.30/0.60        ( ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bitM @ N ) ) )
% 0.30/0.60        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % not_numeral_BitM_eq
% 0.30/0.60  thf(fact_7006_unset__bit__eq__and__not,axiom,
% 0.30/0.60      ( bit_se8260200283734997820nteger
% 0.30/0.60      = ( ^ [N2: nat,A3: code_integer] : ( bit_se3949692690581998587nteger @ A3 @ ( bit_ri7632146776885996613nteger @ ( bit_se7788150548672797655nteger @ N2 @ one_one_Code_integer ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % unset_bit_eq_and_not
% 0.30/0.60  thf(fact_7007_unset__bit__eq__and__not,axiom,
% 0.30/0.60      ( bit_se4203085406695923979it_int
% 0.30/0.60      = ( ^ [N2: nat,A3: int] : ( bit_se725231765392027082nd_int @ A3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % unset_bit_eq_and_not
% 0.30/0.60  thf(fact_7008_is__singletonE,axiom,
% 0.30/0.60      ! [A2: set_Pr4329608150637261639at_nat] :
% 0.30/0.60        ( ( is_sin2937591304547752795at_nat @ A2 )
% 0.30/0.60       => ~ ! [X2: produc3843707927480180839at_nat] :
% 0.30/0.60              ( A2
% 0.30/0.60             != ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singletonE
% 0.30/0.60  thf(fact_7009_is__singletonE,axiom,
% 0.30/0.60      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.30/0.60        ( ( is_sin2850979758926227957at_nat @ A2 )
% 0.30/0.60       => ~ ! [X2: product_prod_nat_nat] :
% 0.30/0.60              ( A2
% 0.30/0.60             != ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singletonE
% 0.30/0.60  thf(fact_7010_is__singletonE,axiom,
% 0.30/0.60      ! [A2: set_o] :
% 0.30/0.60        ( ( is_singleton_o @ A2 )
% 0.30/0.60       => ~ ! [X2: $o] :
% 0.30/0.60              ( A2
% 0.30/0.60             != ( insert_o @ X2 @ bot_bot_set_o ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singletonE
% 0.30/0.60  thf(fact_7011_is__singletonE,axiom,
% 0.30/0.60      ! [A2: set_nat] :
% 0.30/0.60        ( ( is_singleton_nat @ A2 )
% 0.30/0.60       => ~ ! [X2: nat] :
% 0.30/0.60              ( A2
% 0.30/0.60             != ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singletonE
% 0.30/0.60  thf(fact_7012_is__singletonE,axiom,
% 0.30/0.60      ! [A2: set_int] :
% 0.30/0.60        ( ( is_singleton_int @ A2 )
% 0.30/0.60       => ~ ! [X2: int] :
% 0.30/0.60              ( A2
% 0.30/0.60             != ( insert_int @ X2 @ bot_bot_set_int ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singletonE
% 0.30/0.60  thf(fact_7013_is__singleton__def,axiom,
% 0.30/0.60      ( is_sin2937591304547752795at_nat
% 0.30/0.60      = ( ^ [A4: set_Pr4329608150637261639at_nat] :
% 0.30/0.60          ? [X3: produc3843707927480180839at_nat] :
% 0.30/0.60            ( A4
% 0.30/0.60            = ( insert9069300056098147895at_nat @ X3 @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singleton_def
% 0.30/0.60  thf(fact_7014_is__singleton__def,axiom,
% 0.30/0.60      ( is_sin2850979758926227957at_nat
% 0.30/0.60      = ( ^ [A4: set_Pr1261947904930325089at_nat] :
% 0.30/0.60          ? [X3: product_prod_nat_nat] :
% 0.30/0.60            ( A4
% 0.30/0.60            = ( insert8211810215607154385at_nat @ X3 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singleton_def
% 0.30/0.60  thf(fact_7015_is__singleton__def,axiom,
% 0.30/0.60      ( is_singleton_o
% 0.30/0.60      = ( ^ [A4: set_o] :
% 0.30/0.60          ? [X3: $o] :
% 0.30/0.60            ( A4
% 0.30/0.60            = ( insert_o @ X3 @ bot_bot_set_o ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singleton_def
% 0.30/0.60  thf(fact_7016_is__singleton__def,axiom,
% 0.30/0.60      ( is_singleton_nat
% 0.30/0.60      = ( ^ [A4: set_nat] :
% 0.30/0.60          ? [X3: nat] :
% 0.30/0.60            ( A4
% 0.30/0.60            = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singleton_def
% 0.30/0.60  thf(fact_7017_is__singleton__def,axiom,
% 0.30/0.60      ( is_singleton_int
% 0.30/0.60      = ( ^ [A4: set_int] :
% 0.30/0.60          ? [X3: int] :
% 0.30/0.60            ( A4
% 0.30/0.60            = ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % is_singleton_def
% 0.30/0.60  thf(fact_7018_and__not__numerals_I7_J,axiom,
% 0.30/0.60      ! [M: num] :
% 0.30/0.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.30/0.60        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % and_not_numerals(7)
% 0.30/0.60  thf(fact_7019_and__not__numerals_I3_J,axiom,
% 0.30/0.60      ! [N: num] :
% 0.30/0.60        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.30/0.60        = zero_zero_int ) ).
% 0.30/0.60  
% 0.30/0.60  % and_not_numerals(3)
% 0.30/0.60  thf(fact_7020_integer__of__num__triv_I1_J,axiom,
% 0.30/0.60      ( ( code_integer_of_num @ one )
% 0.30/0.60      = one_one_Code_integer ) ).
% 0.30/0.60  
% 0.30/0.60  % integer_of_num_triv(1)
% 0.30/0.60  thf(fact_7021_integer__of__num_I2_J,axiom,
% 0.30/0.60      ! [N: num] :
% 0.30/0.60        ( ( code_integer_of_num @ ( bit0 @ N ) )
% 0.30/0.60        = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % integer_of_num(2)
% 0.30/0.60  thf(fact_7022_minus__exp__eq__not__mask,axiom,
% 0.30/0.60      ! [N: nat] :
% 0.30/0.60        ( ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.60        = ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % minus_exp_eq_not_mask
% 0.30/0.60  thf(fact_7023_minus__exp__eq__not__mask,axiom,
% 0.30/0.60      ! [N: nat] :
% 0.30/0.60        ( ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.60        = ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % minus_exp_eq_not_mask
% 0.30/0.60  thf(fact_7024_divmod__abs__def,axiom,
% 0.30/0.60      ( code_divmod_abs
% 0.30/0.60      = ( ^ [K4: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K4 ) @ ( abs_abs_Code_integer @ L2 ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K4 ) @ ( abs_abs_Code_integer @ L2 ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % divmod_abs_def
% 0.30/0.60  thf(fact_7025_mask__eq__sum__exp,axiom,
% 0.30/0.60      ! [N: nat] :
% 0.30/0.60        ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int )
% 0.30/0.60        = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.30/0.60          @ ( collect_nat
% 0.30/0.60            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % mask_eq_sum_exp
% 0.30/0.60  thf(fact_7026_mask__eq__sum__exp,axiom,
% 0.30/0.60      ! [N: nat] :
% 0.30/0.60        ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer )
% 0.30/0.60        = ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.30/0.60          @ ( collect_nat
% 0.30/0.60            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % mask_eq_sum_exp
% 0.30/0.60  thf(fact_7027_mask__eq__sum__exp,axiom,
% 0.30/0.60      ! [N: nat] :
% 0.30/0.60        ( ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) @ one_one_Code_natural )
% 0.30/0.60        = ( groups6325495683096345652atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.30/0.60          @ ( collect_nat
% 0.30/0.60            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % mask_eq_sum_exp
% 0.30/0.60  thf(fact_7028_mask__eq__sum__exp,axiom,
% 0.30/0.60      ! [N: nat] :
% 0.30/0.60        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat )
% 0.30/0.60        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.60          @ ( collect_nat
% 0.30/0.60            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % mask_eq_sum_exp
% 0.30/0.60  thf(fact_7029_and__not__numerals_I8_J,axiom,
% 0.30/0.60      ! [M: num,N: num] :
% 0.30/0.60        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.30/0.60        = ( 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 ) ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % and_not_numerals(8)
% 0.30/0.60  thf(fact_7030_sum__abs__ge__zero,axiom,
% 0.30/0.60      ! [F2: int > int,A2: set_int] :
% 0.30/0.60        ( ord_less_eq_int @ zero_zero_int
% 0.30/0.60        @ ( groups4538972089207619220nt_int
% 0.30/0.60          @ ^ [I3: int] : ( abs_abs_int @ ( F2 @ I3 ) )
% 0.30/0.60          @ A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_abs_ge_zero
% 0.30/0.60  thf(fact_7031_sum__abs,axiom,
% 0.30/0.60      ! [F2: int > int,A2: set_int] :
% 0.30/0.60        ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) )
% 0.30/0.60        @ ( groups4538972089207619220nt_int
% 0.30/0.60          @ ^ [I3: int] : ( abs_abs_int @ ( F2 @ I3 ) )
% 0.30/0.60          @ A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_abs
% 0.30/0.60  thf(fact_7032_sum_Oempty,axiom,
% 0.30/0.60      ! [G2: $o > code_integer] :
% 0.30/0.60        ( ( groups4406642042086082107nteger @ G2 @ bot_bot_set_o )
% 0.30/0.60        = zero_z3403309356797280102nteger ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.empty
% 0.30/0.60  thf(fact_7033_sum_Oempty,axiom,
% 0.30/0.60      ! [G2: $o > rat] :
% 0.30/0.60        ( ( groups7872700643590313910_o_rat @ G2 @ bot_bot_set_o )
% 0.30/0.60        = zero_zero_rat ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.empty
% 0.30/0.60  thf(fact_7034_sum_Oempty,axiom,
% 0.30/0.60      ! [G2: $o > nat] :
% 0.30/0.60        ( ( groups8507830703676809646_o_nat @ G2 @ bot_bot_set_o )
% 0.30/0.60        = zero_zero_nat ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.empty
% 0.30/0.60  thf(fact_7035_sum_Oempty,axiom,
% 0.30/0.60      ! [G2: $o > int] :
% 0.30/0.60        ( ( groups8505340233167759370_o_int @ G2 @ bot_bot_set_o )
% 0.30/0.60        = zero_zero_int ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.empty
% 0.30/0.60  thf(fact_7036_sum_Oempty,axiom,
% 0.30/0.60      ! [G2: nat > code_integer] :
% 0.30/0.60        ( ( groups7501900531339628137nteger @ G2 @ bot_bot_set_nat )
% 0.30/0.60        = zero_z3403309356797280102nteger ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.empty
% 0.30/0.60  thf(fact_7037_sum_Oempty,axiom,
% 0.30/0.60      ! [G2: nat > rat] :
% 0.30/0.60        ( ( groups2906978787729119204at_rat @ G2 @ bot_bot_set_nat )
% 0.30/0.60        = zero_zero_rat ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.empty
% 0.30/0.60  thf(fact_7038_sum_Oempty,axiom,
% 0.30/0.60      ! [G2: nat > int] :
% 0.30/0.60        ( ( groups3539618377306564664at_int @ G2 @ bot_bot_set_nat )
% 0.30/0.60        = zero_zero_int ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.empty
% 0.30/0.60  thf(fact_7039_sum_Oempty,axiom,
% 0.30/0.60      ! [G2: int > code_integer] :
% 0.30/0.60        ( ( groups7873554091576472773nteger @ G2 @ bot_bot_set_int )
% 0.30/0.60        = zero_z3403309356797280102nteger ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.empty
% 0.30/0.60  thf(fact_7040_sum_Oempty,axiom,
% 0.30/0.60      ! [G2: int > rat] :
% 0.30/0.60        ( ( groups3906332499630173760nt_rat @ G2 @ bot_bot_set_int )
% 0.30/0.60        = zero_zero_rat ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.empty
% 0.30/0.60  thf(fact_7041_sum_Oempty,axiom,
% 0.30/0.60      ! [G2: int > nat] :
% 0.30/0.60        ( ( groups4541462559716669496nt_nat @ G2 @ bot_bot_set_int )
% 0.30/0.60        = zero_zero_nat ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.empty
% 0.30/0.60  thf(fact_7042_convex__sum__bound__le,axiom,
% 0.30/0.60      ! [I4: set_nat,X: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 0.30/0.60        ( ! [I2: nat] :
% 0.30/0.60            ( ( member_nat @ I2 @ I4 )
% 0.30/0.60           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I2 ) ) )
% 0.30/0.60       => ( ( ( groups7501900531339628137nteger @ X @ I4 )
% 0.30/0.60            = one_one_Code_integer )
% 0.30/0.60         => ( ! [I2: nat] :
% 0.30/0.60                ( ( member_nat @ I2 @ I4 )
% 0.30/0.60               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 0.30/0.60           => ( ord_le3102999989581377725nteger
% 0.30/0.60              @ ( abs_abs_Code_integer
% 0.30/0.60                @ ( minus_8373710615458151222nteger
% 0.30/0.60                  @ ( groups7501900531339628137nteger
% 0.30/0.60                    @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.30/0.60                    @ I4 )
% 0.30/0.60                  @ B ) )
% 0.30/0.60              @ Delta ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % convex_sum_bound_le
% 0.30/0.60  thf(fact_7043_convex__sum__bound__le,axiom,
% 0.30/0.60      ! [I4: set_int,X: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 0.30/0.60        ( ! [I2: int] :
% 0.30/0.60            ( ( member_int @ I2 @ I4 )
% 0.30/0.60           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I2 ) ) )
% 0.30/0.60       => ( ( ( groups7873554091576472773nteger @ X @ I4 )
% 0.30/0.60            = one_one_Code_integer )
% 0.30/0.60         => ( ! [I2: int] :
% 0.30/0.60                ( ( member_int @ I2 @ I4 )
% 0.30/0.60               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 0.30/0.60           => ( ord_le3102999989581377725nteger
% 0.30/0.60              @ ( abs_abs_Code_integer
% 0.30/0.60                @ ( minus_8373710615458151222nteger
% 0.30/0.60                  @ ( groups7873554091576472773nteger
% 0.30/0.60                    @ ^ [I3: int] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.30/0.60                    @ I4 )
% 0.30/0.60                  @ B ) )
% 0.30/0.60              @ Delta ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % convex_sum_bound_le
% 0.30/0.60  thf(fact_7044_convex__sum__bound__le,axiom,
% 0.30/0.60      ! [I4: set_nat,X: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 0.30/0.60        ( ! [I2: nat] :
% 0.30/0.60            ( ( member_nat @ I2 @ I4 )
% 0.30/0.60           => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I2 ) ) )
% 0.30/0.60       => ( ( ( groups2906978787729119204at_rat @ X @ I4 )
% 0.30/0.60            = one_one_rat )
% 0.30/0.60         => ( ! [I2: nat] :
% 0.30/0.60                ( ( member_nat @ I2 @ I4 )
% 0.30/0.60               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 0.30/0.60           => ( ord_less_eq_rat
% 0.30/0.60              @ ( abs_abs_rat
% 0.30/0.60                @ ( minus_minus_rat
% 0.30/0.60                  @ ( groups2906978787729119204at_rat
% 0.30/0.60                    @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.30/0.60                    @ I4 )
% 0.30/0.60                  @ B ) )
% 0.30/0.60              @ Delta ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % convex_sum_bound_le
% 0.30/0.60  thf(fact_7045_convex__sum__bound__le,axiom,
% 0.30/0.60      ! [I4: set_int,X: int > rat,A: int > rat,B: rat,Delta: rat] :
% 0.30/0.60        ( ! [I2: int] :
% 0.30/0.60            ( ( member_int @ I2 @ I4 )
% 0.30/0.60           => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I2 ) ) )
% 0.30/0.60       => ( ( ( groups3906332499630173760nt_rat @ X @ I4 )
% 0.30/0.60            = one_one_rat )
% 0.30/0.60         => ( ! [I2: int] :
% 0.30/0.60                ( ( member_int @ I2 @ I4 )
% 0.30/0.60               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 0.30/0.60           => ( ord_less_eq_rat
% 0.30/0.60              @ ( abs_abs_rat
% 0.30/0.60                @ ( minus_minus_rat
% 0.30/0.60                  @ ( groups3906332499630173760nt_rat
% 0.30/0.60                    @ ^ [I3: int] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.30/0.60                    @ I4 )
% 0.30/0.60                  @ B ) )
% 0.30/0.60              @ Delta ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % convex_sum_bound_le
% 0.30/0.60  thf(fact_7046_convex__sum__bound__le,axiom,
% 0.30/0.60      ! [I4: set_nat,X: nat > int,A: nat > int,B: int,Delta: int] :
% 0.30/0.60        ( ! [I2: nat] :
% 0.30/0.60            ( ( member_nat @ I2 @ I4 )
% 0.30/0.60           => ( ord_less_eq_int @ zero_zero_int @ ( X @ I2 ) ) )
% 0.30/0.60       => ( ( ( groups3539618377306564664at_int @ X @ I4 )
% 0.30/0.60            = one_one_int )
% 0.30/0.60         => ( ! [I2: nat] :
% 0.30/0.60                ( ( member_nat @ I2 @ I4 )
% 0.30/0.60               => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 0.30/0.60           => ( ord_less_eq_int
% 0.30/0.60              @ ( abs_abs_int
% 0.30/0.60                @ ( minus_minus_int
% 0.30/0.60                  @ ( groups3539618377306564664at_int
% 0.30/0.60                    @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.30/0.60                    @ I4 )
% 0.30/0.60                  @ B ) )
% 0.30/0.60              @ Delta ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % convex_sum_bound_le
% 0.30/0.60  thf(fact_7047_convex__sum__bound__le,axiom,
% 0.30/0.60      ! [I4: set_int,X: int > int,A: int > int,B: int,Delta: int] :
% 0.30/0.60        ( ! [I2: int] :
% 0.30/0.60            ( ( member_int @ I2 @ I4 )
% 0.30/0.60           => ( ord_less_eq_int @ zero_zero_int @ ( X @ I2 ) ) )
% 0.30/0.60       => ( ( ( groups4538972089207619220nt_int @ X @ I4 )
% 0.30/0.60            = one_one_int )
% 0.30/0.60         => ( ! [I2: int] :
% 0.30/0.60                ( ( member_int @ I2 @ I4 )
% 0.30/0.60               => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 0.30/0.60           => ( ord_less_eq_int
% 0.30/0.60              @ ( abs_abs_int
% 0.30/0.60                @ ( minus_minus_int
% 0.30/0.60                  @ ( groups4538972089207619220nt_int
% 0.30/0.60                    @ ^ [I3: int] : ( times_times_int @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.30/0.60                    @ I4 )
% 0.30/0.60                  @ B ) )
% 0.30/0.60              @ Delta ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % convex_sum_bound_le
% 0.30/0.60  thf(fact_7048_convex__sum__bound__le,axiom,
% 0.30/0.60      ! [I4: set_set_nat,X: set_nat > code_integer,A: set_nat > code_integer,B: code_integer,Delta: code_integer] :
% 0.30/0.60        ( ! [I2: set_nat] :
% 0.30/0.60            ( ( member_set_nat @ I2 @ I4 )
% 0.30/0.60           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I2 ) ) )
% 0.30/0.60       => ( ( ( groups9190459664516455967nteger @ X @ I4 )
% 0.30/0.60            = one_one_Code_integer )
% 0.30/0.60         => ( ! [I2: set_nat] :
% 0.30/0.60                ( ( member_set_nat @ I2 @ I4 )
% 0.30/0.60               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 0.30/0.60           => ( ord_le3102999989581377725nteger
% 0.30/0.60              @ ( abs_abs_Code_integer
% 0.30/0.60                @ ( minus_8373710615458151222nteger
% 0.30/0.60                  @ ( groups9190459664516455967nteger
% 0.30/0.60                    @ ^ [I3: set_nat] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.30/0.60                    @ I4 )
% 0.30/0.60                  @ B ) )
% 0.30/0.60              @ Delta ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % convex_sum_bound_le
% 0.30/0.60  thf(fact_7049_convex__sum__bound__le,axiom,
% 0.30/0.60      ! [I4: set_set_nat,X: set_nat > rat,A: set_nat > rat,B: rat,Delta: rat] :
% 0.30/0.60        ( ! [I2: set_nat] :
% 0.30/0.60            ( ( member_set_nat @ I2 @ I4 )
% 0.30/0.60           => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I2 ) ) )
% 0.30/0.60       => ( ( ( groups7659867448343625626at_rat @ X @ I4 )
% 0.30/0.60            = one_one_rat )
% 0.30/0.60         => ( ! [I2: set_nat] :
% 0.30/0.60                ( ( member_set_nat @ I2 @ I4 )
% 0.30/0.60               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 0.30/0.60           => ( ord_less_eq_rat
% 0.30/0.60              @ ( abs_abs_rat
% 0.30/0.60                @ ( minus_minus_rat
% 0.30/0.60                  @ ( groups7659867448343625626at_rat
% 0.30/0.60                    @ ^ [I3: set_nat] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.30/0.60                    @ I4 )
% 0.30/0.60                  @ B ) )
% 0.30/0.60              @ Delta ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % convex_sum_bound_le
% 0.30/0.60  thf(fact_7050_convex__sum__bound__le,axiom,
% 0.30/0.60      ! [I4: set_set_nat,X: set_nat > int,A: set_nat > int,B: int,Delta: int] :
% 0.30/0.60        ( ! [I2: set_nat] :
% 0.30/0.60            ( ( member_set_nat @ I2 @ I4 )
% 0.30/0.60           => ( ord_less_eq_int @ zero_zero_int @ ( X @ I2 ) ) )
% 0.30/0.60       => ( ( ( groups8292507037921071086at_int @ X @ I4 )
% 0.30/0.60            = one_one_int )
% 0.30/0.60         => ( ! [I2: set_nat] :
% 0.30/0.60                ( ( member_set_nat @ I2 @ I4 )
% 0.30/0.60               => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 0.30/0.60           => ( ord_less_eq_int
% 0.30/0.60              @ ( abs_abs_int
% 0.30/0.60                @ ( minus_minus_int
% 0.30/0.60                  @ ( groups8292507037921071086at_int
% 0.30/0.60                    @ ^ [I3: set_nat] : ( times_times_int @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.30/0.60                    @ I4 )
% 0.30/0.60                  @ B ) )
% 0.30/0.60              @ Delta ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % convex_sum_bound_le
% 0.30/0.60  thf(fact_7051_convex__sum__bound__le,axiom,
% 0.30/0.60      ! [I4: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int > code_integer,A: set_Pr958786334691620121nt_int > code_integer,B: code_integer,Delta: code_integer] :
% 0.30/0.60        ( ! [I2: set_Pr958786334691620121nt_int] :
% 0.30/0.60            ( ( member2340774599025711042nt_int @ I2 @ I4 )
% 0.30/0.60           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I2 ) ) )
% 0.30/0.60       => ( ( ( groups3738144136874984124nteger @ X @ I4 )
% 0.30/0.60            = one_one_Code_integer )
% 0.30/0.60         => ( ! [I2: set_Pr958786334691620121nt_int] :
% 0.30/0.60                ( ( member2340774599025711042nt_int @ I2 @ I4 )
% 0.30/0.60               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 0.30/0.60           => ( ord_le3102999989581377725nteger
% 0.30/0.60              @ ( abs_abs_Code_integer
% 0.30/0.60                @ ( minus_8373710615458151222nteger
% 0.30/0.60                  @ ( groups3738144136874984124nteger
% 0.30/0.60                    @ ^ [I3: set_Pr958786334691620121nt_int] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 0.30/0.60                    @ I4 )
% 0.30/0.60                  @ B ) )
% 0.30/0.60              @ Delta ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % convex_sum_bound_le
% 0.30/0.60  thf(fact_7052_abs__sum__abs,axiom,
% 0.30/0.60      ! [F2: int > int,A2: set_int] :
% 0.30/0.60        ( ( abs_abs_int
% 0.30/0.60          @ ( groups4538972089207619220nt_int
% 0.30/0.60            @ ^ [A3: int] : ( abs_abs_int @ ( F2 @ A3 ) )
% 0.30/0.60            @ A2 ) )
% 0.30/0.60        = ( groups4538972089207619220nt_int
% 0.30/0.60          @ ^ [A3: int] : ( abs_abs_int @ ( F2 @ A3 ) )
% 0.30/0.60          @ A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % abs_sum_abs
% 0.30/0.60  thf(fact_7053_sum_Oneutral__const,axiom,
% 0.30/0.60      ! [A2: set_nat] :
% 0.30/0.60        ( ( groups3542108847815614940at_nat
% 0.30/0.60          @ ^ [Uu: nat] : zero_zero_nat
% 0.30/0.60          @ A2 )
% 0.30/0.60        = zero_zero_nat ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.neutral_const
% 0.30/0.60  thf(fact_7054_sum_Oneutral__const,axiom,
% 0.30/0.60      ! [A2: set_int] :
% 0.30/0.60        ( ( groups4538972089207619220nt_int
% 0.30/0.60          @ ^ [Uu: int] : zero_zero_int
% 0.30/0.60          @ A2 )
% 0.30/0.60        = zero_zero_int ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.neutral_const
% 0.30/0.60  thf(fact_7055_sum__diff1__nat,axiom,
% 0.30/0.60      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,F2: produc3843707927480180839at_nat > nat] :
% 0.30/0.60        ( ( ( member8757157785044589968at_nat @ A @ A2 )
% 0.30/0.60         => ( ( groups3860910324918113789at_nat @ F2 @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) )
% 0.30/0.60            = ( minus_minus_nat @ ( groups3860910324918113789at_nat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.60        & ( ~ ( member8757157785044589968at_nat @ A @ A2 )
% 0.30/0.60         => ( ( groups3860910324918113789at_nat @ F2 @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) )
% 0.30/0.60            = ( groups3860910324918113789at_nat @ F2 @ A2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_diff1_nat
% 0.30/0.60  thf(fact_7056_sum__diff1__nat,axiom,
% 0.30/0.60      ! [A: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,F2: set_Pr958786334691620121nt_int > nat] :
% 0.30/0.60        ( ( ( member2340774599025711042nt_int @ A @ A2 )
% 0.30/0.60         => ( ( groups185207323561075247nt_nat @ F2 @ ( minus_2612819937483484256nt_int @ A2 @ ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) )
% 0.30/0.60            = ( minus_minus_nat @ ( groups185207323561075247nt_nat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.60        & ( ~ ( member2340774599025711042nt_int @ A @ A2 )
% 0.30/0.60         => ( ( groups185207323561075247nt_nat @ F2 @ ( minus_2612819937483484256nt_int @ A2 @ ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) )
% 0.30/0.60            = ( groups185207323561075247nt_nat @ F2 @ A2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_diff1_nat
% 0.30/0.60  thf(fact_7057_sum__diff1__nat,axiom,
% 0.30/0.60      ! [A: set_nat,A2: set_set_nat,F2: set_nat > nat] :
% 0.30/0.60        ( ( ( member_set_nat @ A @ A2 )
% 0.30/0.60         => ( ( groups8294997508430121362at_nat @ F2 @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.30/0.60            = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.60        & ( ~ ( member_set_nat @ A @ A2 )
% 0.30/0.60         => ( ( groups8294997508430121362at_nat @ F2 @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.30/0.60            = ( groups8294997508430121362at_nat @ F2 @ A2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_diff1_nat
% 0.30/0.60  thf(fact_7058_sum__diff1__nat,axiom,
% 0.30/0.60      ! [A: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,F2: ( produc3658429121746597890et_nat > $o ) > nat] :
% 0.30/0.60        ( ( ( member6576561426505652726_nat_o @ A @ A2 )
% 0.30/0.60         => ( ( groups6742167275697360483_o_nat @ F2 @ ( minus_1801376950450012436_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ) )
% 0.30/0.60            = ( minus_minus_nat @ ( groups6742167275697360483_o_nat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.60        & ( ~ ( member6576561426505652726_nat_o @ A @ A2 )
% 0.30/0.60         => ( ( groups6742167275697360483_o_nat @ F2 @ ( minus_1801376950450012436_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ) )
% 0.30/0.60            = ( groups6742167275697360483_o_nat @ F2 @ A2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_diff1_nat
% 0.30/0.60  thf(fact_7059_sum__diff1__nat,axiom,
% 0.30/0.60      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > nat] :
% 0.30/0.60        ( ( ( member8440522571783428010at_nat @ A @ A2 )
% 0.30/0.60         => ( ( groups977919841031483927at_nat @ F2 @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 0.30/0.60            = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.60        & ( ~ ( member8440522571783428010at_nat @ A @ A2 )
% 0.30/0.60         => ( ( groups977919841031483927at_nat @ F2 @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 0.30/0.60            = ( groups977919841031483927at_nat @ F2 @ A2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_diff1_nat
% 0.30/0.60  thf(fact_7060_sum__diff1__nat,axiom,
% 0.30/0.60      ! [A: $o,A2: set_o,F2: $o > nat] :
% 0.30/0.60        ( ( ( member_o @ A @ A2 )
% 0.30/0.60         => ( ( groups8507830703676809646_o_nat @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.30/0.60            = ( minus_minus_nat @ ( groups8507830703676809646_o_nat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.60        & ( ~ ( member_o @ A @ A2 )
% 0.30/0.60         => ( ( groups8507830703676809646_o_nat @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.30/0.60            = ( groups8507830703676809646_o_nat @ F2 @ A2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_diff1_nat
% 0.30/0.60  thf(fact_7061_sum__diff1__nat,axiom,
% 0.30/0.60      ! [A: int,A2: set_int,F2: int > nat] :
% 0.30/0.60        ( ( ( member_int @ A @ A2 )
% 0.30/0.60         => ( ( groups4541462559716669496nt_nat @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.30/0.60            = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.60        & ( ~ ( member_int @ A @ A2 )
% 0.30/0.60         => ( ( groups4541462559716669496nt_nat @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.30/0.60            = ( groups4541462559716669496nt_nat @ F2 @ A2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_diff1_nat
% 0.30/0.60  thf(fact_7062_sum__diff1__nat,axiom,
% 0.30/0.60      ! [A: nat,A2: set_nat,F2: nat > nat] :
% 0.30/0.60        ( ( ( member_nat @ A @ A2 )
% 0.30/0.60         => ( ( groups3542108847815614940at_nat @ F2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.30/0.60            = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.60        & ( ~ ( member_nat @ A @ A2 )
% 0.30/0.60         => ( ( groups3542108847815614940at_nat @ F2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.30/0.60            = ( groups3542108847815614940at_nat @ F2 @ A2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_diff1_nat
% 0.30/0.60  thf(fact_7063_sum_Oswap,axiom,
% 0.30/0.60      ! [G2: nat > nat > nat,B2: set_nat,A2: set_nat] :
% 0.30/0.60        ( ( groups3542108847815614940at_nat
% 0.30/0.60          @ ^ [I3: nat] : ( groups3542108847815614940at_nat @ ( G2 @ I3 ) @ B2 )
% 0.30/0.60          @ A2 )
% 0.30/0.60        = ( groups3542108847815614940at_nat
% 0.30/0.60          @ ^ [J3: nat] :
% 0.30/0.60              ( groups3542108847815614940at_nat
% 0.30/0.60              @ ^ [I3: nat] : ( G2 @ I3 @ J3 )
% 0.30/0.60              @ A2 )
% 0.30/0.60          @ B2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.swap
% 0.30/0.60  thf(fact_7064_sum_Oswap,axiom,
% 0.30/0.60      ! [G2: int > int > int,B2: set_int,A2: set_int] :
% 0.30/0.60        ( ( groups4538972089207619220nt_int
% 0.30/0.60          @ ^ [I3: int] : ( groups4538972089207619220nt_int @ ( G2 @ I3 ) @ B2 )
% 0.30/0.60          @ A2 )
% 0.30/0.60        = ( groups4538972089207619220nt_int
% 0.30/0.60          @ ^ [J3: int] :
% 0.30/0.60              ( groups4538972089207619220nt_int
% 0.30/0.60              @ ^ [I3: int] : ( G2 @ I3 @ J3 )
% 0.30/0.60              @ A2 )
% 0.30/0.60          @ B2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.swap
% 0.30/0.60  thf(fact_7065_sum__mono,axiom,
% 0.30/0.60      ! [K5: set_nat,F2: nat > rat,G2: nat > rat] :
% 0.30/0.60        ( ! [I2: nat] :
% 0.30/0.60            ( ( member_nat @ I2 @ K5 )
% 0.30/0.60           => ( ord_less_eq_rat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) )
% 0.30/0.60       => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ K5 ) @ ( groups2906978787729119204at_rat @ G2 @ K5 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_mono
% 0.30/0.60  thf(fact_7066_sum__mono,axiom,
% 0.30/0.60      ! [K5: set_int,F2: int > rat,G2: int > rat] :
% 0.30/0.60        ( ! [I2: int] :
% 0.30/0.60            ( ( member_int @ I2 @ K5 )
% 0.30/0.60           => ( ord_less_eq_rat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) )
% 0.30/0.60       => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ K5 ) @ ( groups3906332499630173760nt_rat @ G2 @ K5 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_mono
% 0.30/0.60  thf(fact_7067_sum__mono,axiom,
% 0.30/0.60      ! [K5: set_int,F2: int > nat,G2: int > nat] :
% 0.30/0.60        ( ! [I2: int] :
% 0.30/0.60            ( ( member_int @ I2 @ K5 )
% 0.30/0.60           => ( ord_less_eq_nat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) )
% 0.30/0.60       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F2 @ K5 ) @ ( groups4541462559716669496nt_nat @ G2 @ K5 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_mono
% 0.30/0.60  thf(fact_7068_sum__mono,axiom,
% 0.30/0.60      ! [K5: set_nat,F2: nat > int,G2: nat > int] :
% 0.30/0.60        ( ! [I2: nat] :
% 0.30/0.60            ( ( member_nat @ I2 @ K5 )
% 0.30/0.60           => ( ord_less_eq_int @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) )
% 0.30/0.60       => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F2 @ K5 ) @ ( groups3539618377306564664at_int @ G2 @ K5 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_mono
% 0.30/0.60  thf(fact_7069_sum__mono,axiom,
% 0.30/0.60      ! [K5: set_nat,F2: nat > nat,G2: nat > nat] :
% 0.30/0.60        ( ! [I2: nat] :
% 0.30/0.60            ( ( member_nat @ I2 @ K5 )
% 0.30/0.60           => ( ord_less_eq_nat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) )
% 0.30/0.60       => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F2 @ K5 ) @ ( groups3542108847815614940at_nat @ G2 @ K5 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_mono
% 0.30/0.60  thf(fact_7070_sum__mono,axiom,
% 0.30/0.60      ! [K5: set_int,F2: int > int,G2: int > int] :
% 0.30/0.60        ( ! [I2: int] :
% 0.30/0.60            ( ( member_int @ I2 @ K5 )
% 0.30/0.60           => ( ord_less_eq_int @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) )
% 0.30/0.60       => ( ord_less_eq_int @ ( groups4538972089207619220nt_int @ F2 @ K5 ) @ ( groups4538972089207619220nt_int @ G2 @ K5 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_mono
% 0.30/0.60  thf(fact_7071_sum__mono,axiom,
% 0.30/0.60      ! [K5: set_set_nat,F2: set_nat > rat,G2: set_nat > rat] :
% 0.30/0.60        ( ! [I2: set_nat] :
% 0.30/0.60            ( ( member_set_nat @ I2 @ K5 )
% 0.30/0.60           => ( ord_less_eq_rat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) )
% 0.30/0.60       => ( ord_less_eq_rat @ ( groups7659867448343625626at_rat @ F2 @ K5 ) @ ( groups7659867448343625626at_rat @ G2 @ K5 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_mono
% 0.30/0.60  thf(fact_7072_sum__mono,axiom,
% 0.30/0.60      ! [K5: set_set_nat,F2: set_nat > nat,G2: set_nat > nat] :
% 0.30/0.60        ( ! [I2: set_nat] :
% 0.30/0.60            ( ( member_set_nat @ I2 @ K5 )
% 0.30/0.60           => ( ord_less_eq_nat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) )
% 0.30/0.60       => ( ord_less_eq_nat @ ( groups8294997508430121362at_nat @ F2 @ K5 ) @ ( groups8294997508430121362at_nat @ G2 @ K5 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_mono
% 0.30/0.60  thf(fact_7073_sum__mono,axiom,
% 0.30/0.60      ! [K5: set_set_nat,F2: set_nat > int,G2: set_nat > int] :
% 0.30/0.60        ( ! [I2: set_nat] :
% 0.30/0.60            ( ( member_set_nat @ I2 @ K5 )
% 0.30/0.60           => ( ord_less_eq_int @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) )
% 0.30/0.60       => ( ord_less_eq_int @ ( groups8292507037921071086at_int @ F2 @ K5 ) @ ( groups8292507037921071086at_int @ G2 @ K5 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_mono
% 0.30/0.60  thf(fact_7074_sum__mono,axiom,
% 0.30/0.60      ! [K5: set_se6260736226359567993nt_int,F2: set_Pr958786334691620121nt_int > rat,G2: set_Pr958786334691620121nt_int > rat] :
% 0.30/0.60        ( ! [I2: set_Pr958786334691620121nt_int] :
% 0.30/0.60            ( ( member2340774599025711042nt_int @ I2 @ K5 )
% 0.30/0.60           => ( ord_less_eq_rat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) )
% 0.30/0.60       => ( ord_less_eq_rat @ ( groups8773449300329355319nt_rat @ F2 @ K5 ) @ ( groups8773449300329355319nt_rat @ G2 @ K5 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_mono
% 0.30/0.60  thf(fact_7075_sum_Odistrib,axiom,
% 0.30/0.60      ! [G2: nat > nat,H3: nat > nat,A2: set_nat] :
% 0.30/0.60        ( ( groups3542108847815614940at_nat
% 0.30/0.60          @ ^ [X3: nat] : ( plus_plus_nat @ ( G2 @ X3 ) @ ( H3 @ X3 ) )
% 0.30/0.60          @ A2 )
% 0.30/0.60        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ A2 ) @ ( groups3542108847815614940at_nat @ H3 @ A2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.distrib
% 0.30/0.60  thf(fact_7076_sum_Odistrib,axiom,
% 0.30/0.60      ! [G2: int > int,H3: int > int,A2: set_int] :
% 0.30/0.60        ( ( groups4538972089207619220nt_int
% 0.30/0.60          @ ^ [X3: int] : ( plus_plus_int @ ( G2 @ X3 ) @ ( H3 @ X3 ) )
% 0.30/0.60          @ A2 )
% 0.30/0.60        = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G2 @ A2 ) @ ( groups4538972089207619220nt_int @ H3 @ A2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.distrib
% 0.30/0.60  thf(fact_7077_sum__product,axiom,
% 0.30/0.60      ! [F2: nat > nat,A2: set_nat,G2: nat > nat,B2: set_nat] :
% 0.30/0.60        ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F2 @ A2 ) @ ( groups3542108847815614940at_nat @ G2 @ B2 ) )
% 0.30/0.60        = ( groups3542108847815614940at_nat
% 0.30/0.60          @ ^ [I3: nat] :
% 0.30/0.60              ( groups3542108847815614940at_nat
% 0.30/0.60              @ ^ [J3: nat] : ( times_times_nat @ ( F2 @ I3 ) @ ( G2 @ J3 ) )
% 0.30/0.60              @ B2 )
% 0.30/0.60          @ A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_product
% 0.30/0.60  thf(fact_7078_sum__product,axiom,
% 0.30/0.60      ! [F2: int > int,A2: set_int,G2: int > int,B2: set_int] :
% 0.30/0.60        ( ( times_times_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) @ ( groups4538972089207619220nt_int @ G2 @ B2 ) )
% 0.30/0.60        = ( groups4538972089207619220nt_int
% 0.30/0.60          @ ^ [I3: int] :
% 0.30/0.60              ( groups4538972089207619220nt_int
% 0.30/0.60              @ ^ [J3: int] : ( times_times_int @ ( F2 @ I3 ) @ ( G2 @ J3 ) )
% 0.30/0.60              @ B2 )
% 0.30/0.60          @ A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_product
% 0.30/0.60  thf(fact_7079_sum__distrib__right,axiom,
% 0.30/0.60      ! [F2: nat > nat,A2: set_nat,R3: nat] :
% 0.30/0.60        ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F2 @ A2 ) @ R3 )
% 0.30/0.60        = ( groups3542108847815614940at_nat
% 0.30/0.60          @ ^ [N2: nat] : ( times_times_nat @ ( F2 @ N2 ) @ R3 )
% 0.30/0.60          @ A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_distrib_right
% 0.30/0.60  thf(fact_7080_sum__distrib__right,axiom,
% 0.30/0.60      ! [F2: int > int,A2: set_int,R3: int] :
% 0.30/0.60        ( ( times_times_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) @ R3 )
% 0.30/0.60        = ( groups4538972089207619220nt_int
% 0.30/0.60          @ ^ [N2: int] : ( times_times_int @ ( F2 @ N2 ) @ R3 )
% 0.30/0.60          @ A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_distrib_right
% 0.30/0.60  thf(fact_7081_sum__distrib__left,axiom,
% 0.30/0.60      ! [R3: nat,F2: nat > nat,A2: set_nat] :
% 0.30/0.60        ( ( times_times_nat @ R3 @ ( groups3542108847815614940at_nat @ F2 @ A2 ) )
% 0.30/0.60        = ( groups3542108847815614940at_nat
% 0.30/0.60          @ ^ [N2: nat] : ( times_times_nat @ R3 @ ( F2 @ N2 ) )
% 0.30/0.60          @ A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_distrib_left
% 0.30/0.60  thf(fact_7082_sum__distrib__left,axiom,
% 0.30/0.60      ! [R3: int,F2: int > int,A2: set_int] :
% 0.30/0.60        ( ( times_times_int @ R3 @ ( groups4538972089207619220nt_int @ F2 @ A2 ) )
% 0.30/0.60        = ( groups4538972089207619220nt_int
% 0.30/0.60          @ ^ [N2: int] : ( times_times_int @ R3 @ ( F2 @ N2 ) )
% 0.30/0.60          @ A2 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_distrib_left
% 0.30/0.60  thf(fact_7083_sum__subtractf,axiom,
% 0.30/0.60      ! [F2: int > int,G2: int > int,A2: set_int] :
% 0.30/0.60        ( ( groups4538972089207619220nt_int
% 0.30/0.60          @ ^ [X3: int] : ( minus_minus_int @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.60          @ A2 )
% 0.30/0.60        = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) @ ( groups4538972089207619220nt_int @ G2 @ A2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_subtractf
% 0.30/0.60  thf(fact_7084_sum__negf,axiom,
% 0.30/0.60      ! [F2: int > int,A2: set_int] :
% 0.30/0.60        ( ( groups4538972089207619220nt_int
% 0.30/0.60          @ ^ [X3: int] : ( uminus_uminus_int @ ( F2 @ X3 ) )
% 0.30/0.60          @ A2 )
% 0.30/0.60        = ( uminus_uminus_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_negf
% 0.30/0.60  thf(fact_7085_sum__subtractf__nat,axiom,
% 0.30/0.60      ! [A2: set_se6260736226359567993nt_int,G2: set_Pr958786334691620121nt_int > nat,F2: set_Pr958786334691620121nt_int > nat] :
% 0.30/0.60        ( ! [X2: set_Pr958786334691620121nt_int] :
% 0.30/0.60            ( ( member2340774599025711042nt_int @ X2 @ A2 )
% 0.30/0.60           => ( ord_less_eq_nat @ ( G2 @ X2 ) @ ( F2 @ X2 ) ) )
% 0.30/0.60       => ( ( groups185207323561075247nt_nat
% 0.30/0.60            @ ^ [X3: set_Pr958786334691620121nt_int] : ( minus_minus_nat @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.60            @ A2 )
% 0.30/0.60          = ( minus_minus_nat @ ( groups185207323561075247nt_nat @ F2 @ A2 ) @ ( groups185207323561075247nt_nat @ G2 @ A2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_subtractf_nat
% 0.30/0.60  thf(fact_7086_sum__subtractf__nat,axiom,
% 0.30/0.60      ! [A2: set_set_nat,G2: set_nat > nat,F2: set_nat > nat] :
% 0.30/0.60        ( ! [X2: set_nat] :
% 0.30/0.60            ( ( member_set_nat @ X2 @ A2 )
% 0.30/0.60           => ( ord_less_eq_nat @ ( G2 @ X2 ) @ ( F2 @ X2 ) ) )
% 0.30/0.60       => ( ( groups8294997508430121362at_nat
% 0.30/0.60            @ ^ [X3: set_nat] : ( minus_minus_nat @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.60            @ A2 )
% 0.30/0.60          = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F2 @ A2 ) @ ( groups8294997508430121362at_nat @ G2 @ A2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_subtractf_nat
% 0.30/0.60  thf(fact_7087_sum__subtractf__nat,axiom,
% 0.30/0.60      ! [A2: set_int,G2: int > nat,F2: int > nat] :
% 0.30/0.60        ( ! [X2: int] :
% 0.30/0.60            ( ( member_int @ X2 @ A2 )
% 0.30/0.60           => ( ord_less_eq_nat @ ( G2 @ X2 ) @ ( F2 @ X2 ) ) )
% 0.30/0.60       => ( ( groups4541462559716669496nt_nat
% 0.30/0.60            @ ^ [X3: int] : ( minus_minus_nat @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.60            @ A2 )
% 0.30/0.60          = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F2 @ A2 ) @ ( groups4541462559716669496nt_nat @ G2 @ A2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_subtractf_nat
% 0.30/0.60  thf(fact_7088_sum__subtractf__nat,axiom,
% 0.30/0.60      ! [A2: set_Pr4532377907799695533_nat_o,G2: ( produc3658429121746597890et_nat > $o ) > nat,F2: ( produc3658429121746597890et_nat > $o ) > nat] :
% 0.30/0.60        ( ! [X2: produc3658429121746597890et_nat > $o] :
% 0.30/0.60            ( ( member6576561426505652726_nat_o @ X2 @ A2 )
% 0.30/0.60           => ( ord_less_eq_nat @ ( G2 @ X2 ) @ ( F2 @ X2 ) ) )
% 0.30/0.60       => ( ( groups6742167275697360483_o_nat
% 0.30/0.60            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( minus_minus_nat @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.60            @ A2 )
% 0.30/0.60          = ( minus_minus_nat @ ( groups6742167275697360483_o_nat @ F2 @ A2 ) @ ( groups6742167275697360483_o_nat @ G2 @ A2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_subtractf_nat
% 0.30/0.60  thf(fact_7089_sum__subtractf__nat,axiom,
% 0.30/0.60      ! [A2: set_nat,G2: nat > nat,F2: nat > nat] :
% 0.30/0.60        ( ! [X2: nat] :
% 0.30/0.60            ( ( member_nat @ X2 @ A2 )
% 0.30/0.60           => ( ord_less_eq_nat @ ( G2 @ X2 ) @ ( F2 @ X2 ) ) )
% 0.30/0.60       => ( ( groups3542108847815614940at_nat
% 0.30/0.60            @ ^ [X3: nat] : ( minus_minus_nat @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.60            @ A2 )
% 0.30/0.60          = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F2 @ A2 ) @ ( groups3542108847815614940at_nat @ G2 @ A2 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_subtractf_nat
% 0.30/0.60  thf(fact_7090_divmod__integer__code,axiom,
% 0.30/0.60      ( code_divmod_integer
% 0.30/0.60      = ( ^ [K4: code_integer,L2: code_integer] :
% 0.30/0.60            ( if_Pro6119634080678213985nteger @ ( K4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.30/0.60            @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L2 )
% 0.30/0.60              @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K4 ) @ ( code_divmod_abs @ K4 @ L2 )
% 0.30/0.60                @ ( produc6916734918728496179nteger
% 0.30/0.60                  @ ^ [R4: code_integer,S2: code_integer] : ( if_Pro6119634080678213985nteger @ ( S2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R4 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L2 @ S2 ) ) )
% 0.30/0.60                  @ ( code_divmod_abs @ K4 @ L2 ) ) )
% 0.30/0.60              @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K4 )
% 0.30/0.60                @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 0.30/0.60                  @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K4 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K4 @ L2 )
% 0.30/0.60                    @ ( produc6916734918728496179nteger
% 0.30/0.60                      @ ^ [R4: code_integer,S2: code_integer] : ( if_Pro6119634080678213985nteger @ ( S2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R4 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L2 ) @ S2 ) ) )
% 0.30/0.60                      @ ( code_divmod_abs @ K4 @ L2 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % divmod_integer_code
% 0.30/0.60  thf(fact_7091_Sum__Icc__nat,axiom,
% 0.30/0.60      ! [M: nat,N: nat] :
% 0.30/0.60        ( ( groups3542108847815614940at_nat
% 0.30/0.60          @ ^ [X3: nat] : X3
% 0.30/0.60          @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.60        = ( 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 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Sum_Icc_nat
% 0.30/0.60  thf(fact_7092_arith__series__nat,axiom,
% 0.30/0.60      ! [A: nat,D2: nat,N: nat] :
% 0.30/0.60        ( ( groups3542108847815614940at_nat
% 0.30/0.60          @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I3 @ D2 ) )
% 0.30/0.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.30/0.60        = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % arith_series_nat
% 0.30/0.60  thf(fact_7093_Sum__Icc__int,axiom,
% 0.30/0.60      ! [M: int,N: int] :
% 0.30/0.60        ( ( ord_less_eq_int @ M @ N )
% 0.30/0.60       => ( ( groups4538972089207619220nt_int
% 0.30/0.60            @ ^ [X3: int] : X3
% 0.30/0.60            @ ( set_or1266510415728281911st_int @ M @ N ) )
% 0.30/0.60          = ( 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 ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Sum_Icc_int
% 0.30/0.60  thf(fact_7094_Sum__Ico__nat,axiom,
% 0.30/0.60      ! [M: nat,N: nat] :
% 0.30/0.60        ( ( groups3542108847815614940at_nat
% 0.30/0.60          @ ^ [X3: nat] : X3
% 0.30/0.60          @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 0.30/0.60        = ( 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 ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % Sum_Ico_nat
% 0.30/0.60  thf(fact_7095_sum__power2,axiom,
% 0.30/0.60      ! [K: nat] :
% 0.30/0.60        ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 0.30/0.60        = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum_power2
% 0.30/0.60  thf(fact_7096_gauss__sum__nat,axiom,
% 0.30/0.60      ! [N: nat] :
% 0.30/0.60        ( ( groups3542108847815614940at_nat
% 0.30/0.60          @ ^ [X3: nat] : X3
% 0.30/0.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.30/0.60        = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % gauss_sum_nat
% 0.30/0.60  thf(fact_7097_apsnd__conv,axiom,
% 0.30/0.60      ! [F2: produc8923325533196201883nteger > produc8923325533196201883nteger,X: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger] :
% 0.30/0.60        ( ( produc717174245515237944e_term @ F2 @ ( produc8603105652947943368nteger @ X @ Y ) )
% 0.30/0.60        = ( produc8603105652947943368nteger @ X @ ( F2 @ Y ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % apsnd_conv
% 0.30/0.60  thf(fact_7098_apsnd__conv,axiom,
% 0.30/0.60      ! [F2: produc3658429121746597890et_nat > produc3658429121746597890et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 0.30/0.60        ( ( produc8750854537940449737_nat_o @ F2 @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 0.30/0.60        = ( produc5001842942810119800et_nat @ X @ ( F2 @ Y ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % apsnd_conv
% 0.30/0.60  thf(fact_7099_apsnd__conv,axiom,
% 0.30/0.60      ! [F2: produc3658429121746597890et_nat > produc3925858234332021118et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 0.30/0.60        ( ( produc7714581247149323085_nat_o @ F2 @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 0.30/0.60        = ( produc2245416461498447860et_nat @ X @ ( F2 @ Y ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % apsnd_conv
% 0.30/0.60  thf(fact_7100_apsnd__conv,axiom,
% 0.30/0.60      ! [F2: produc3925858234332021118et_nat > produc3658429121746597890et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 0.30/0.60        ( ( produc1515462096303866701_nat_o @ F2 @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 0.30/0.60        = ( produc5001842942810119800et_nat @ X @ ( F2 @ Y ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % apsnd_conv
% 0.30/0.60  thf(fact_7101_apsnd__conv,axiom,
% 0.30/0.60      ! [F2: produc3925858234332021118et_nat > produc3925858234332021118et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 0.30/0.60        ( ( produc969530845752564945_nat_o @ F2 @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 0.30/0.60        = ( produc2245416461498447860et_nat @ X @ ( F2 @ Y ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % apsnd_conv
% 0.30/0.60  thf(fact_7102_apsnd__conv,axiom,
% 0.30/0.60      ! [F2: product_prod_int_int > product_prod_int_int,X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int] :
% 0.30/0.60        ( ( produc4973430039190721449e_term @ F2 @ ( produc5700946648718959541nt_int @ X @ Y ) )
% 0.30/0.60        = ( produc5700946648718959541nt_int @ X @ ( F2 @ Y ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % apsnd_conv
% 0.30/0.60  thf(fact_7103_apsnd__conv,axiom,
% 0.30/0.60      ! [F2: product_prod_int_int > product_prod_int_int,X: int > option6357759511663192854e_term,Y: product_prod_int_int] :
% 0.30/0.60        ( ( produc7011684061226097695e_term @ F2 @ ( produc4305682042979456191nt_int @ X @ Y ) )
% 0.30/0.60        = ( produc4305682042979456191nt_int @ X @ ( F2 @ Y ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % apsnd_conv
% 0.30/0.60  thf(fact_7104_apsnd__conv,axiom,
% 0.30/0.60      ! [F2: code_integer > code_integer,X: code_integer,Y: code_integer] :
% 0.30/0.60        ( ( produc6499014454317279255nteger @ F2 @ ( produc1086072967326762835nteger @ X @ Y ) )
% 0.30/0.60        = ( produc1086072967326762835nteger @ X @ ( F2 @ Y ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % apsnd_conv
% 0.30/0.60  thf(fact_7105_atLeastatMost__empty__iff,axiom,
% 0.30/0.60      ! [A: $o,B: $o] :
% 0.30/0.60        ( ( ( set_or8904488021354931149Most_o @ A @ B )
% 0.30/0.60          = bot_bot_set_o )
% 0.30/0.60        = ( ~ ( ord_less_eq_o @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastatMost_empty_iff
% 0.30/0.60  thf(fact_7106_atLeastatMost__empty__iff,axiom,
% 0.30/0.60      ! [A: filter_nat,B: filter_nat] :
% 0.30/0.60        ( ( ( set_or1955772592623580779er_nat @ A @ B )
% 0.30/0.60          = bot_bo498966703094740906er_nat )
% 0.30/0.60        = ( ~ ( ord_le2510731241096832064er_nat @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastatMost_empty_iff
% 0.30/0.60  thf(fact_7107_atLeastatMost__empty__iff,axiom,
% 0.30/0.60      ! [A: set_nat,B: set_nat] :
% 0.30/0.60        ( ( ( set_or4548717258645045905et_nat @ A @ B )
% 0.30/0.60          = bot_bot_set_set_nat )
% 0.30/0.60        = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastatMost_empty_iff
% 0.30/0.60  thf(fact_7108_atLeastatMost__empty__iff,axiom,
% 0.30/0.60      ! [A: rat,B: rat] :
% 0.30/0.60        ( ( ( set_or633870826150836451st_rat @ A @ B )
% 0.30/0.60          = bot_bot_set_rat )
% 0.30/0.60        = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastatMost_empty_iff
% 0.30/0.60  thf(fact_7109_atLeastatMost__empty__iff,axiom,
% 0.30/0.60      ! [A: nat,B: nat] :
% 0.30/0.60        ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.30/0.60          = bot_bot_set_nat )
% 0.30/0.60        = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastatMost_empty_iff
% 0.30/0.60  thf(fact_7110_atLeastatMost__empty__iff,axiom,
% 0.30/0.60      ! [A: int,B: int] :
% 0.30/0.60        ( ( ( set_or1266510415728281911st_int @ A @ B )
% 0.30/0.60          = bot_bot_set_int )
% 0.30/0.60        = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastatMost_empty_iff
% 0.30/0.60  thf(fact_7111_atLeastatMost__empty__iff,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer] :
% 0.30/0.60        ( ( ( set_or189985376899183464nteger @ A @ B )
% 0.30/0.60          = bot_bo3990330152332043303nteger )
% 0.30/0.60        = ( ~ ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastatMost_empty_iff
% 0.30/0.60  thf(fact_7112_atLeastatMost__empty__iff2,axiom,
% 0.30/0.60      ! [A: $o,B: $o] :
% 0.30/0.60        ( ( bot_bot_set_o
% 0.30/0.60          = ( set_or8904488021354931149Most_o @ A @ B ) )
% 0.30/0.60        = ( ~ ( ord_less_eq_o @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastatMost_empty_iff2
% 0.30/0.60  thf(fact_7113_atLeastatMost__empty__iff2,axiom,
% 0.30/0.60      ! [A: filter_nat,B: filter_nat] :
% 0.30/0.60        ( ( bot_bo498966703094740906er_nat
% 0.30/0.60          = ( set_or1955772592623580779er_nat @ A @ B ) )
% 0.30/0.60        = ( ~ ( ord_le2510731241096832064er_nat @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastatMost_empty_iff2
% 0.30/0.60  thf(fact_7114_atLeastatMost__empty__iff2,axiom,
% 0.30/0.60      ! [A: set_nat,B: set_nat] :
% 0.30/0.60        ( ( bot_bot_set_set_nat
% 0.30/0.60          = ( set_or4548717258645045905et_nat @ A @ B ) )
% 0.30/0.60        = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastatMost_empty_iff2
% 0.30/0.60  thf(fact_7115_atLeastatMost__empty__iff2,axiom,
% 0.30/0.60      ! [A: rat,B: rat] :
% 0.30/0.60        ( ( bot_bot_set_rat
% 0.30/0.60          = ( set_or633870826150836451st_rat @ A @ B ) )
% 0.30/0.60        = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastatMost_empty_iff2
% 0.30/0.60  thf(fact_7116_atLeastatMost__empty__iff2,axiom,
% 0.30/0.60      ! [A: nat,B: nat] :
% 0.30/0.60        ( ( bot_bot_set_nat
% 0.30/0.60          = ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.30/0.60        = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastatMost_empty_iff2
% 0.30/0.60  thf(fact_7117_atLeastatMost__empty__iff2,axiom,
% 0.30/0.60      ! [A: int,B: int] :
% 0.30/0.60        ( ( bot_bot_set_int
% 0.30/0.60          = ( set_or1266510415728281911st_int @ A @ B ) )
% 0.30/0.60        = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastatMost_empty_iff2
% 0.30/0.60  thf(fact_7118_atLeastatMost__empty__iff2,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer] :
% 0.30/0.60        ( ( bot_bo3990330152332043303nteger
% 0.30/0.60          = ( set_or189985376899183464nteger @ A @ B ) )
% 0.30/0.60        = ( ~ ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastatMost_empty_iff2
% 0.30/0.60  thf(fact_7119_atLeastatMost__empty,axiom,
% 0.30/0.60      ! [B: $o,A: $o] :
% 0.30/0.60        ( ( ord_less_o @ B @ A )
% 0.30/0.60       => ( ( set_or8904488021354931149Most_o @ A @ B )
% 0.30/0.60          = bot_bot_set_o ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastatMost_empty
% 0.30/0.60  thf(fact_7120_atLeastatMost__empty,axiom,
% 0.30/0.60      ! [B: literal,A: literal] :
% 0.30/0.60        ( ( ord_less_literal @ B @ A )
% 0.30/0.60       => ( ( set_or8436436507035938825iteral @ A @ B )
% 0.30/0.60          = bot_bot_set_literal ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastatMost_empty
% 0.30/0.60  thf(fact_7121_atLeastatMost__empty,axiom,
% 0.30/0.60      ! [B: rat,A: rat] :
% 0.30/0.60        ( ( ord_less_rat @ B @ A )
% 0.30/0.60       => ( ( set_or633870826150836451st_rat @ A @ B )
% 0.30/0.60          = bot_bot_set_rat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastatMost_empty
% 0.30/0.60  thf(fact_7122_atLeastatMost__empty,axiom,
% 0.30/0.60      ! [B: nat,A: nat] :
% 0.30/0.60        ( ( ord_less_nat @ B @ A )
% 0.30/0.60       => ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.30/0.60          = bot_bot_set_nat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastatMost_empty
% 0.30/0.60  thf(fact_7123_atLeastatMost__empty,axiom,
% 0.30/0.60      ! [B: int,A: int] :
% 0.30/0.60        ( ( ord_less_int @ B @ A )
% 0.30/0.60       => ( ( set_or1266510415728281911st_int @ A @ B )
% 0.30/0.60          = bot_bot_set_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastatMost_empty
% 0.30/0.60  thf(fact_7124_atLeastatMost__empty,axiom,
% 0.30/0.60      ! [B: code_integer,A: code_integer] :
% 0.30/0.60        ( ( ord_le6747313008572928689nteger @ B @ A )
% 0.30/0.60       => ( ( set_or189985376899183464nteger @ A @ B )
% 0.30/0.60          = bot_bo3990330152332043303nteger ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastatMost_empty
% 0.30/0.60  thf(fact_7125_atLeastLessThan__empty,axiom,
% 0.30/0.60      ! [B: $o,A: $o] :
% 0.30/0.60        ( ( ord_less_eq_o @ B @ A )
% 0.30/0.60       => ( ( set_or7139685690850216873Than_o @ A @ B )
% 0.30/0.60          = bot_bot_set_o ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_empty
% 0.30/0.60  thf(fact_7126_atLeastLessThan__empty,axiom,
% 0.30/0.60      ! [B: filter_nat,A: filter_nat] :
% 0.30/0.60        ( ( ord_le2510731241096832064er_nat @ B @ A )
% 0.30/0.60       => ( ( set_or1773934645810362255er_nat @ A @ B )
% 0.30/0.60          = bot_bo498966703094740906er_nat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_empty
% 0.30/0.60  thf(fact_7127_atLeastLessThan__empty,axiom,
% 0.30/0.60      ! [B: set_nat,A: set_nat] :
% 0.30/0.60        ( ( ord_less_eq_set_nat @ B @ A )
% 0.30/0.60       => ( ( set_or3540276404033026485et_nat @ A @ B )
% 0.30/0.60          = bot_bot_set_set_nat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_empty
% 0.30/0.60  thf(fact_7128_atLeastLessThan__empty,axiom,
% 0.30/0.60      ! [B: rat,A: rat] :
% 0.30/0.60        ( ( ord_less_eq_rat @ B @ A )
% 0.30/0.60       => ( ( set_or4029947393144176647an_rat @ A @ B )
% 0.30/0.60          = bot_bot_set_rat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_empty
% 0.30/0.60  thf(fact_7129_atLeastLessThan__empty,axiom,
% 0.30/0.60      ! [B: nat,A: nat] :
% 0.30/0.60        ( ( ord_less_eq_nat @ B @ A )
% 0.30/0.60       => ( ( set_or4665077453230672383an_nat @ A @ B )
% 0.30/0.60          = bot_bot_set_nat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_empty
% 0.30/0.60  thf(fact_7130_atLeastLessThan__empty,axiom,
% 0.30/0.60      ! [B: code_integer,A: code_integer] :
% 0.30/0.60        ( ( ord_le3102999989581377725nteger @ B @ A )
% 0.30/0.60       => ( ( set_or8404916559141939852nteger @ A @ B )
% 0.30/0.60          = bot_bo3990330152332043303nteger ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_empty
% 0.30/0.60  thf(fact_7131_atLeastLessThan__empty,axiom,
% 0.30/0.60      ! [B: int,A: int] :
% 0.30/0.60        ( ( ord_less_eq_int @ B @ A )
% 0.30/0.60       => ( ( set_or4662586982721622107an_int @ A @ B )
% 0.30/0.60          = bot_bot_set_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_empty
% 0.30/0.60  thf(fact_7132_atLeastLessThan__empty__iff,axiom,
% 0.30/0.60      ! [A: $o,B: $o] :
% 0.30/0.60        ( ( ( set_or7139685690850216873Than_o @ A @ B )
% 0.30/0.60          = bot_bot_set_o )
% 0.30/0.60        = ( ~ ( ord_less_o @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_empty_iff
% 0.30/0.60  thf(fact_7133_atLeastLessThan__empty__iff,axiom,
% 0.30/0.60      ! [A: literal,B: literal] :
% 0.30/0.60        ( ( ( set_or4828121863581493221iteral @ A @ B )
% 0.30/0.60          = bot_bot_set_literal )
% 0.30/0.60        = ( ~ ( ord_less_literal @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_empty_iff
% 0.30/0.60  thf(fact_7134_atLeastLessThan__empty__iff,axiom,
% 0.30/0.60      ! [A: rat,B: rat] :
% 0.30/0.60        ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 0.30/0.60          = bot_bot_set_rat )
% 0.30/0.60        = ( ~ ( ord_less_rat @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_empty_iff
% 0.30/0.60  thf(fact_7135_atLeastLessThan__empty__iff,axiom,
% 0.30/0.60      ! [A: nat,B: nat] :
% 0.30/0.60        ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 0.30/0.60          = bot_bot_set_nat )
% 0.30/0.60        = ( ~ ( ord_less_nat @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_empty_iff
% 0.30/0.60  thf(fact_7136_atLeastLessThan__empty__iff,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer] :
% 0.30/0.60        ( ( ( set_or8404916559141939852nteger @ A @ B )
% 0.30/0.60          = bot_bo3990330152332043303nteger )
% 0.30/0.60        = ( ~ ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_empty_iff
% 0.30/0.60  thf(fact_7137_atLeastLessThan__empty__iff,axiom,
% 0.30/0.60      ! [A: int,B: int] :
% 0.30/0.60        ( ( ( set_or4662586982721622107an_int @ A @ B )
% 0.30/0.60          = bot_bot_set_int )
% 0.30/0.60        = ( ~ ( ord_less_int @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_empty_iff
% 0.30/0.60  thf(fact_7138_atLeastLessThan__empty__iff2,axiom,
% 0.30/0.60      ! [A: $o,B: $o] :
% 0.30/0.60        ( ( bot_bot_set_o
% 0.30/0.60          = ( set_or7139685690850216873Than_o @ A @ B ) )
% 0.30/0.60        = ( ~ ( ord_less_o @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_empty_iff2
% 0.30/0.60  thf(fact_7139_atLeastLessThan__empty__iff2,axiom,
% 0.30/0.60      ! [A: literal,B: literal] :
% 0.30/0.60        ( ( bot_bot_set_literal
% 0.30/0.60          = ( set_or4828121863581493221iteral @ A @ B ) )
% 0.30/0.60        = ( ~ ( ord_less_literal @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_empty_iff2
% 0.30/0.60  thf(fact_7140_atLeastLessThan__empty__iff2,axiom,
% 0.30/0.60      ! [A: rat,B: rat] :
% 0.30/0.60        ( ( bot_bot_set_rat
% 0.30/0.60          = ( set_or4029947393144176647an_rat @ A @ B ) )
% 0.30/0.60        = ( ~ ( ord_less_rat @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_empty_iff2
% 0.30/0.60  thf(fact_7141_atLeastLessThan__empty__iff2,axiom,
% 0.30/0.60      ! [A: nat,B: nat] :
% 0.30/0.60        ( ( bot_bot_set_nat
% 0.30/0.60          = ( set_or4665077453230672383an_nat @ A @ B ) )
% 0.30/0.60        = ( ~ ( ord_less_nat @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_empty_iff2
% 0.30/0.60  thf(fact_7142_atLeastLessThan__empty__iff2,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer] :
% 0.30/0.60        ( ( bot_bo3990330152332043303nteger
% 0.30/0.60          = ( set_or8404916559141939852nteger @ A @ B ) )
% 0.30/0.60        = ( ~ ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_empty_iff2
% 0.30/0.60  thf(fact_7143_atLeastLessThan__empty__iff2,axiom,
% 0.30/0.60      ! [A: int,B: int] :
% 0.30/0.60        ( ( bot_bot_set_int
% 0.30/0.60          = ( set_or4662586982721622107an_int @ A @ B ) )
% 0.30/0.60        = ( ~ ( ord_less_int @ A @ B ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_empty_iff2
% 0.30/0.60  thf(fact_7144_atLeastAtMost__singleton,axiom,
% 0.30/0.60      ! [A: $o] :
% 0.30/0.60        ( ( set_or8904488021354931149Most_o @ A @ A )
% 0.30/0.60        = ( insert_o @ A @ bot_bot_set_o ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastAtMost_singleton
% 0.30/0.60  thf(fact_7145_atLeastAtMost__singleton,axiom,
% 0.30/0.60      ! [A: nat] :
% 0.30/0.60        ( ( set_or1269000886237332187st_nat @ A @ A )
% 0.30/0.60        = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastAtMost_singleton
% 0.30/0.60  thf(fact_7146_atLeastAtMost__singleton,axiom,
% 0.30/0.60      ! [A: int] :
% 0.30/0.60        ( ( set_or1266510415728281911st_int @ A @ A )
% 0.30/0.60        = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastAtMost_singleton
% 0.30/0.60  thf(fact_7147_atLeastAtMost__singleton,axiom,
% 0.30/0.60      ! [A: code_integer] :
% 0.30/0.60        ( ( set_or189985376899183464nteger @ A @ A )
% 0.30/0.60        = ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastAtMost_singleton
% 0.30/0.60  thf(fact_7148_atLeastAtMost__singleton__iff,axiom,
% 0.30/0.60      ! [A: $o,B: $o,C: $o] :
% 0.30/0.60        ( ( ( set_or8904488021354931149Most_o @ A @ B )
% 0.30/0.60          = ( insert_o @ C @ bot_bot_set_o ) )
% 0.30/0.60        = ( ( A = B )
% 0.30/0.60          & ( B = C ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastAtMost_singleton_iff
% 0.30/0.60  thf(fact_7149_atLeastAtMost__singleton__iff,axiom,
% 0.30/0.60      ! [A: nat,B: nat,C: nat] :
% 0.30/0.60        ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.30/0.60          = ( insert_nat @ C @ bot_bot_set_nat ) )
% 0.30/0.60        = ( ( A = B )
% 0.30/0.60          & ( B = C ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastAtMost_singleton_iff
% 0.30/0.60  thf(fact_7150_atLeastAtMost__singleton__iff,axiom,
% 0.30/0.60      ! [A: int,B: int,C: int] :
% 0.30/0.60        ( ( ( set_or1266510415728281911st_int @ A @ B )
% 0.30/0.60          = ( insert_int @ C @ bot_bot_set_int ) )
% 0.30/0.60        = ( ( A = B )
% 0.30/0.60          & ( B = C ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastAtMost_singleton_iff
% 0.30/0.60  thf(fact_7151_atLeastAtMost__singleton__iff,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer,C: code_integer] :
% 0.30/0.60        ( ( ( set_or189985376899183464nteger @ A @ B )
% 0.30/0.60          = ( insert_Code_integer @ C @ bot_bo3990330152332043303nteger ) )
% 0.30/0.60        = ( ( A = B )
% 0.30/0.60          & ( B = C ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastAtMost_singleton_iff
% 0.30/0.60  thf(fact_7152_atLeastLessThan__singleton,axiom,
% 0.30/0.60      ! [M: nat] :
% 0.30/0.60        ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 0.30/0.60        = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_singleton
% 0.30/0.60  thf(fact_7153_ivl__disj__un__two_I7_J,axiom,
% 0.30/0.60      ! [L: rat,M: rat,U: rat] :
% 0.30/0.60        ( ( ord_less_eq_rat @ L @ M )
% 0.30/0.60       => ( ( ord_less_eq_rat @ M @ U )
% 0.30/0.60         => ( ( sup_sup_set_rat @ ( set_or4029947393144176647an_rat @ L @ M ) @ ( set_or633870826150836451st_rat @ M @ U ) )
% 0.30/0.60            = ( set_or633870826150836451st_rat @ L @ U ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_two(7)
% 0.30/0.60  thf(fact_7154_ivl__disj__un__two_I7_J,axiom,
% 0.30/0.60      ! [L: nat,M: nat,U: nat] :
% 0.30/0.60        ( ( ord_less_eq_nat @ L @ M )
% 0.30/0.60       => ( ( ord_less_eq_nat @ M @ U )
% 0.30/0.60         => ( ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ L @ M ) @ ( set_or1269000886237332187st_nat @ M @ U ) )
% 0.30/0.60            = ( set_or1269000886237332187st_nat @ L @ U ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_two(7)
% 0.30/0.60  thf(fact_7155_ivl__disj__un__two_I7_J,axiom,
% 0.30/0.60      ! [L: code_integer,M: code_integer,U: code_integer] :
% 0.30/0.60        ( ( ord_le3102999989581377725nteger @ L @ M )
% 0.30/0.60       => ( ( ord_le3102999989581377725nteger @ M @ U )
% 0.30/0.60         => ( ( sup_su848401254843788991nteger @ ( set_or8404916559141939852nteger @ L @ M ) @ ( set_or189985376899183464nteger @ M @ U ) )
% 0.30/0.60            = ( set_or189985376899183464nteger @ L @ U ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_two(7)
% 0.30/0.60  thf(fact_7156_ivl__disj__un__two_I7_J,axiom,
% 0.30/0.60      ! [L: int,M: int,U: int] :
% 0.30/0.60        ( ( ord_less_eq_int @ L @ M )
% 0.30/0.60       => ( ( ord_less_eq_int @ M @ U )
% 0.30/0.60         => ( ( sup_sup_set_int @ ( set_or4662586982721622107an_int @ L @ M ) @ ( set_or1266510415728281911st_int @ M @ U ) )
% 0.30/0.60            = ( set_or1266510415728281911st_int @ L @ U ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_two(7)
% 0.30/0.60  thf(fact_7157_ivl__disj__int__two_I7_J,axiom,
% 0.30/0.60      ! [L: $o,M: $o,U: $o] :
% 0.30/0.60        ( ( inf_inf_set_o @ ( set_or7139685690850216873Than_o @ L @ M ) @ ( set_or8904488021354931149Most_o @ M @ U ) )
% 0.30/0.60        = bot_bot_set_o ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_int_two(7)
% 0.30/0.60  thf(fact_7158_ivl__disj__int__two_I7_J,axiom,
% 0.30/0.60      ! [L: nat,M: nat,U: nat] :
% 0.30/0.60        ( ( inf_inf_set_nat @ ( set_or4665077453230672383an_nat @ L @ M ) @ ( set_or1269000886237332187st_nat @ M @ U ) )
% 0.30/0.60        = bot_bot_set_nat ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_int_two(7)
% 0.30/0.60  thf(fact_7159_ivl__disj__int__two_I7_J,axiom,
% 0.30/0.60      ! [L: code_integer,M: code_integer,U: code_integer] :
% 0.30/0.60        ( ( inf_in1364745209274528805nteger @ ( set_or8404916559141939852nteger @ L @ M ) @ ( set_or189985376899183464nteger @ M @ U ) )
% 0.30/0.60        = bot_bo3990330152332043303nteger ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_int_two(7)
% 0.30/0.60  thf(fact_7160_ivl__disj__int__two_I7_J,axiom,
% 0.30/0.60      ! [L: int,M: int,U: int] :
% 0.30/0.60        ( ( inf_inf_set_int @ ( set_or4662586982721622107an_int @ L @ M ) @ ( set_or1266510415728281911st_int @ M @ U ) )
% 0.30/0.60        = bot_bot_set_int ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_int_two(7)
% 0.30/0.60  thf(fact_7161_not__UNIV__eq__Icc,axiom,
% 0.30/0.60      ! [L4: rat,H4: rat] :
% 0.30/0.60        ( top_top_set_rat
% 0.30/0.60       != ( set_or633870826150836451st_rat @ L4 @ H4 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % not_UNIV_eq_Icc
% 0.30/0.60  thf(fact_7162_not__UNIV__eq__Icc,axiom,
% 0.30/0.60      ! [L4: nat,H4: nat] :
% 0.30/0.60        ( top_top_set_nat
% 0.30/0.60       != ( set_or1269000886237332187st_nat @ L4 @ H4 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % not_UNIV_eq_Icc
% 0.30/0.60  thf(fact_7163_not__UNIV__eq__Icc,axiom,
% 0.30/0.60      ! [L4: int,H4: int] :
% 0.30/0.60        ( top_top_set_int
% 0.30/0.60       != ( set_or1266510415728281911st_int @ L4 @ H4 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % not_UNIV_eq_Icc
% 0.30/0.60  thf(fact_7164_ivl__disj__un__two__touch_I2_J,axiom,
% 0.30/0.60      ! [L: literal,M: literal,U: literal] :
% 0.30/0.60        ( ( ord_less_eq_literal @ L @ M )
% 0.30/0.60       => ( ( ord_less_literal @ M @ U )
% 0.30/0.60         => ( ( sup_sup_set_literal @ ( set_or8436436507035938825iteral @ L @ M ) @ ( set_or4828121863581493221iteral @ M @ U ) )
% 0.30/0.60            = ( set_or4828121863581493221iteral @ L @ U ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_two_touch(2)
% 0.30/0.60  thf(fact_7165_ivl__disj__un__two__touch_I2_J,axiom,
% 0.30/0.60      ! [L: rat,M: rat,U: rat] :
% 0.30/0.60        ( ( ord_less_eq_rat @ L @ M )
% 0.30/0.60       => ( ( ord_less_rat @ M @ U )
% 0.30/0.60         => ( ( sup_sup_set_rat @ ( set_or633870826150836451st_rat @ L @ M ) @ ( set_or4029947393144176647an_rat @ M @ U ) )
% 0.30/0.60            = ( set_or4029947393144176647an_rat @ L @ U ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_two_touch(2)
% 0.30/0.60  thf(fact_7166_ivl__disj__un__two__touch_I2_J,axiom,
% 0.30/0.60      ! [L: nat,M: nat,U: nat] :
% 0.30/0.60        ( ( ord_less_eq_nat @ L @ M )
% 0.30/0.60       => ( ( ord_less_nat @ M @ U )
% 0.30/0.60         => ( ( sup_sup_set_nat @ ( set_or1269000886237332187st_nat @ L @ M ) @ ( set_or4665077453230672383an_nat @ M @ U ) )
% 0.30/0.60            = ( set_or4665077453230672383an_nat @ L @ U ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_two_touch(2)
% 0.30/0.60  thf(fact_7167_ivl__disj__un__two__touch_I2_J,axiom,
% 0.30/0.60      ! [L: code_integer,M: code_integer,U: code_integer] :
% 0.30/0.60        ( ( ord_le3102999989581377725nteger @ L @ M )
% 0.30/0.60       => ( ( ord_le6747313008572928689nteger @ M @ U )
% 0.30/0.60         => ( ( sup_su848401254843788991nteger @ ( set_or189985376899183464nteger @ L @ M ) @ ( set_or8404916559141939852nteger @ M @ U ) )
% 0.30/0.60            = ( set_or8404916559141939852nteger @ L @ U ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_two_touch(2)
% 0.30/0.60  thf(fact_7168_ivl__disj__un__two__touch_I2_J,axiom,
% 0.30/0.60      ! [L: int,M: int,U: int] :
% 0.30/0.60        ( ( ord_less_eq_int @ L @ M )
% 0.30/0.60       => ( ( ord_less_int @ M @ U )
% 0.30/0.60         => ( ( sup_sup_set_int @ ( set_or1266510415728281911st_int @ L @ M ) @ ( set_or4662586982721622107an_int @ M @ U ) )
% 0.30/0.60            = ( set_or4662586982721622107an_int @ L @ U ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_two_touch(2)
% 0.30/0.60  thf(fact_7169_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
% 0.30/0.60      ( set_or7139685690850216873Than_o
% 0.30/0.60      = ( ^ [A3: $o,B3: $o] : ( minus_minus_set_o @ ( set_or8904488021354931149Most_o @ A3 @ B3 ) @ ( insert_o @ B3 @ bot_bot_set_o ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_eq_atLeastAtMost_diff
% 0.30/0.60  thf(fact_7170_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
% 0.30/0.60      ( set_or4665077453230672383an_nat
% 0.30/0.60      = ( ^ [A3: nat,B3: nat] : ( minus_minus_set_nat @ ( set_or1269000886237332187st_nat @ A3 @ B3 ) @ ( insert_nat @ B3 @ bot_bot_set_nat ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_eq_atLeastAtMost_diff
% 0.30/0.60  thf(fact_7171_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
% 0.30/0.60      ( set_or8404916559141939852nteger
% 0.30/0.60      = ( ^ [A3: code_integer,B3: code_integer] : ( minus_2355218937544613996nteger @ ( set_or189985376899183464nteger @ A3 @ B3 ) @ ( insert_Code_integer @ B3 @ bot_bo3990330152332043303nteger ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_eq_atLeastAtMost_diff
% 0.30/0.60  thf(fact_7172_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
% 0.30/0.60      ( set_or4662586982721622107an_int
% 0.30/0.60      = ( ^ [A3: int,B3: int] : ( minus_minus_set_int @ ( set_or1266510415728281911st_int @ A3 @ B3 ) @ ( insert_int @ B3 @ bot_bot_set_int ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan_eq_atLeastAtMost_diff
% 0.30/0.60  thf(fact_7173_sum_Onested__swap,axiom,
% 0.30/0.60      ! [A: nat > nat > nat,N: nat] :
% 0.30/0.60        ( ( groups3542108847815614940at_nat
% 0.30/0.60          @ ^ [I3: nat] : ( groups3542108847815614940at_nat @ ( A @ I3 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I3 ) )
% 0.30/0.60          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.30/0.60        = ( groups3542108847815614940at_nat
% 0.30/0.60          @ ^ [J3: nat] :
% 0.30/0.60              ( groups3542108847815614940at_nat
% 0.30/0.60              @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 0.30/0.60              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 0.30/0.60          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.nested_swap
% 0.30/0.60  thf(fact_7174_ivl__disj__un__singleton_I6_J,axiom,
% 0.30/0.60      ! [L: $o,U: $o] :
% 0.30/0.60        ( ( ord_less_eq_o @ L @ U )
% 0.30/0.60       => ( ( sup_sup_set_o @ ( set_or7139685690850216873Than_o @ L @ U ) @ ( insert_o @ U @ bot_bot_set_o ) )
% 0.30/0.60          = ( set_or8904488021354931149Most_o @ L @ U ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_singleton(6)
% 0.30/0.60  thf(fact_7175_ivl__disj__un__singleton_I6_J,axiom,
% 0.30/0.60      ! [L: rat,U: rat] :
% 0.30/0.60        ( ( ord_less_eq_rat @ L @ U )
% 0.30/0.60       => ( ( sup_sup_set_rat @ ( set_or4029947393144176647an_rat @ L @ U ) @ ( insert_rat @ U @ bot_bot_set_rat ) )
% 0.30/0.60          = ( set_or633870826150836451st_rat @ L @ U ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_singleton(6)
% 0.30/0.60  thf(fact_7176_ivl__disj__un__singleton_I6_J,axiom,
% 0.30/0.60      ! [L: nat,U: nat] :
% 0.30/0.60        ( ( ord_less_eq_nat @ L @ U )
% 0.30/0.60       => ( ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ L @ U ) @ ( insert_nat @ U @ bot_bot_set_nat ) )
% 0.30/0.60          = ( set_or1269000886237332187st_nat @ L @ U ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_singleton(6)
% 0.30/0.60  thf(fact_7177_ivl__disj__un__singleton_I6_J,axiom,
% 0.30/0.60      ! [L: code_integer,U: code_integer] :
% 0.30/0.60        ( ( ord_le3102999989581377725nteger @ L @ U )
% 0.30/0.60       => ( ( sup_su848401254843788991nteger @ ( set_or8404916559141939852nteger @ L @ U ) @ ( insert_Code_integer @ U @ bot_bo3990330152332043303nteger ) )
% 0.30/0.60          = ( set_or189985376899183464nteger @ L @ U ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_singleton(6)
% 0.30/0.60  thf(fact_7178_ivl__disj__un__singleton_I6_J,axiom,
% 0.30/0.60      ! [L: int,U: int] :
% 0.30/0.60        ( ( ord_less_eq_int @ L @ U )
% 0.30/0.60       => ( ( sup_sup_set_int @ ( set_or4662586982721622107an_int @ L @ U ) @ ( insert_int @ U @ bot_bot_set_int ) )
% 0.30/0.60          = ( set_or1266510415728281911st_int @ L @ U ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_singleton(6)
% 0.30/0.60  thf(fact_7179_ivl__disj__un__two__touch_I4_J,axiom,
% 0.30/0.60      ! [L: rat,M: rat,U: rat] :
% 0.30/0.60        ( ( ord_less_eq_rat @ L @ M )
% 0.30/0.60       => ( ( ord_less_eq_rat @ M @ U )
% 0.30/0.60         => ( ( sup_sup_set_rat @ ( set_or633870826150836451st_rat @ L @ M ) @ ( set_or633870826150836451st_rat @ M @ U ) )
% 0.30/0.60            = ( set_or633870826150836451st_rat @ L @ U ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_two_touch(4)
% 0.30/0.60  thf(fact_7180_ivl__disj__un__two__touch_I4_J,axiom,
% 0.30/0.60      ! [L: nat,M: nat,U: nat] :
% 0.30/0.60        ( ( ord_less_eq_nat @ L @ M )
% 0.30/0.60       => ( ( ord_less_eq_nat @ M @ U )
% 0.30/0.60         => ( ( sup_sup_set_nat @ ( set_or1269000886237332187st_nat @ L @ M ) @ ( set_or1269000886237332187st_nat @ M @ U ) )
% 0.30/0.60            = ( set_or1269000886237332187st_nat @ L @ U ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_two_touch(4)
% 0.30/0.60  thf(fact_7181_ivl__disj__un__two__touch_I4_J,axiom,
% 0.30/0.60      ! [L: int,M: int,U: int] :
% 0.30/0.60        ( ( ord_less_eq_int @ L @ M )
% 0.30/0.60       => ( ( ord_less_eq_int @ M @ U )
% 0.30/0.60         => ( ( sup_sup_set_int @ ( set_or1266510415728281911st_int @ L @ M ) @ ( set_or1266510415728281911st_int @ M @ U ) )
% 0.30/0.60            = ( set_or1266510415728281911st_int @ L @ U ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_two_touch(4)
% 0.30/0.60  thf(fact_7182_ivl__disj__un__two__touch_I4_J,axiom,
% 0.30/0.60      ! [L: code_integer,M: code_integer,U: code_integer] :
% 0.30/0.60        ( ( ord_le3102999989581377725nteger @ L @ M )
% 0.30/0.60       => ( ( ord_le3102999989581377725nteger @ M @ U )
% 0.30/0.60         => ( ( sup_su848401254843788991nteger @ ( set_or189985376899183464nteger @ L @ M ) @ ( set_or189985376899183464nteger @ M @ U ) )
% 0.30/0.60            = ( set_or189985376899183464nteger @ L @ U ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_two_touch(4)
% 0.30/0.60  thf(fact_7183_atLeastAtMost__singleton_H,axiom,
% 0.30/0.60      ! [A: $o,B: $o] :
% 0.30/0.60        ( ( A = B )
% 0.30/0.60       => ( ( set_or8904488021354931149Most_o @ A @ B )
% 0.30/0.60          = ( insert_o @ A @ bot_bot_set_o ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastAtMost_singleton'
% 0.30/0.60  thf(fact_7184_atLeastAtMost__singleton_H,axiom,
% 0.30/0.60      ! [A: nat,B: nat] :
% 0.30/0.60        ( ( A = B )
% 0.30/0.60       => ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.30/0.60          = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastAtMost_singleton'
% 0.30/0.60  thf(fact_7185_atLeastAtMost__singleton_H,axiom,
% 0.30/0.60      ! [A: int,B: int] :
% 0.30/0.60        ( ( A = B )
% 0.30/0.60       => ( ( set_or1266510415728281911st_int @ A @ B )
% 0.30/0.60          = ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastAtMost_singleton'
% 0.30/0.60  thf(fact_7186_atLeastAtMost__singleton_H,axiom,
% 0.30/0.60      ! [A: code_integer,B: code_integer] :
% 0.30/0.60        ( ( A = B )
% 0.30/0.60       => ( ( set_or189985376899183464nteger @ A @ B )
% 0.30/0.60          = ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastAtMost_singleton'
% 0.30/0.60  thf(fact_7187_not__UNIV__le__Icc,axiom,
% 0.30/0.60      ! [L: rat,H3: rat] :
% 0.30/0.60        ~ ( ord_less_eq_set_rat @ top_top_set_rat @ ( set_or633870826150836451st_rat @ L @ H3 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % not_UNIV_le_Icc
% 0.30/0.60  thf(fact_7188_not__UNIV__le__Icc,axiom,
% 0.30/0.60      ! [L: nat,H3: nat] :
% 0.30/0.60        ~ ( ord_less_eq_set_nat @ top_top_set_nat @ ( set_or1269000886237332187st_nat @ L @ H3 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % not_UNIV_le_Icc
% 0.30/0.60  thf(fact_7189_not__UNIV__le__Icc,axiom,
% 0.30/0.60      ! [L: int,H3: int] :
% 0.30/0.60        ~ ( ord_less_eq_set_int @ top_top_set_int @ ( set_or1266510415728281911st_int @ L @ H3 ) ) ).
% 0.30/0.60  
% 0.30/0.60  % not_UNIV_le_Icc
% 0.30/0.60  thf(fact_7190_ivl__disj__un__two_I3_J,axiom,
% 0.30/0.60      ! [L: rat,M: rat,U: rat] :
% 0.30/0.60        ( ( ord_less_eq_rat @ L @ M )
% 0.30/0.60       => ( ( ord_less_eq_rat @ M @ U )
% 0.30/0.60         => ( ( sup_sup_set_rat @ ( set_or4029947393144176647an_rat @ L @ M ) @ ( set_or4029947393144176647an_rat @ M @ U ) )
% 0.30/0.60            = ( set_or4029947393144176647an_rat @ L @ U ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_two(3)
% 0.30/0.60  thf(fact_7191_ivl__disj__un__two_I3_J,axiom,
% 0.30/0.60      ! [L: nat,M: nat,U: nat] :
% 0.30/0.60        ( ( ord_less_eq_nat @ L @ M )
% 0.30/0.60       => ( ( ord_less_eq_nat @ M @ U )
% 0.30/0.60         => ( ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ L @ M ) @ ( set_or4665077453230672383an_nat @ M @ U ) )
% 0.30/0.60            = ( set_or4665077453230672383an_nat @ L @ U ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_two(3)
% 0.30/0.60  thf(fact_7192_ivl__disj__un__two_I3_J,axiom,
% 0.30/0.60      ! [L: code_integer,M: code_integer,U: code_integer] :
% 0.30/0.60        ( ( ord_le3102999989581377725nteger @ L @ M )
% 0.30/0.60       => ( ( ord_le3102999989581377725nteger @ M @ U )
% 0.30/0.60         => ( ( sup_su848401254843788991nteger @ ( set_or8404916559141939852nteger @ L @ M ) @ ( set_or8404916559141939852nteger @ M @ U ) )
% 0.30/0.60            = ( set_or8404916559141939852nteger @ L @ U ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_two(3)
% 0.30/0.60  thf(fact_7193_ivl__disj__un__two_I3_J,axiom,
% 0.30/0.60      ! [L: int,M: int,U: int] :
% 0.30/0.60        ( ( ord_less_eq_int @ L @ M )
% 0.30/0.60       => ( ( ord_less_eq_int @ M @ U )
% 0.30/0.60         => ( ( sup_sup_set_int @ ( set_or4662586982721622107an_int @ L @ M ) @ ( set_or4662586982721622107an_int @ M @ U ) )
% 0.30/0.60            = ( set_or4662586982721622107an_int @ L @ U ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_un_two(3)
% 0.30/0.60  thf(fact_7194_ivl__disj__int__two_I3_J,axiom,
% 0.30/0.60      ! [L: $o,M: $o,U: $o] :
% 0.30/0.60        ( ( inf_inf_set_o @ ( set_or7139685690850216873Than_o @ L @ M ) @ ( set_or7139685690850216873Than_o @ M @ U ) )
% 0.30/0.60        = bot_bot_set_o ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_int_two(3)
% 0.30/0.60  thf(fact_7195_ivl__disj__int__two_I3_J,axiom,
% 0.30/0.60      ! [L: nat,M: nat,U: nat] :
% 0.30/0.60        ( ( inf_inf_set_nat @ ( set_or4665077453230672383an_nat @ L @ M ) @ ( set_or4665077453230672383an_nat @ M @ U ) )
% 0.30/0.60        = bot_bot_set_nat ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_int_two(3)
% 0.30/0.60  thf(fact_7196_ivl__disj__int__two_I3_J,axiom,
% 0.30/0.60      ! [L: code_integer,M: code_integer,U: code_integer] :
% 0.30/0.60        ( ( inf_in1364745209274528805nteger @ ( set_or8404916559141939852nteger @ L @ M ) @ ( set_or8404916559141939852nteger @ M @ U ) )
% 0.30/0.60        = bot_bo3990330152332043303nteger ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_int_two(3)
% 0.30/0.60  thf(fact_7197_ivl__disj__int__two_I3_J,axiom,
% 0.30/0.60      ! [L: int,M: int,U: int] :
% 0.30/0.60        ( ( inf_inf_set_int @ ( set_or4662586982721622107an_int @ L @ M ) @ ( set_or4662586982721622107an_int @ M @ U ) )
% 0.30/0.60        = bot_bot_set_int ) ).
% 0.30/0.60  
% 0.30/0.60  % ivl_disj_int_two(3)
% 0.30/0.60  thf(fact_7198_sum_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 0.30/0.60      ! [G2: nat > nat,N: nat,M: nat] :
% 0.30/0.60        ( ( groups3542108847815614940at_nat @ G2 @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 0.30/0.60        = ( groups3542108847815614940at_nat
% 0.30/0.60          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 0.30/0.60          @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.atLeastLessThan_rev_at_least_Suc_atMost
% 0.30/0.60  thf(fact_7199_atLeastLessThan0,axiom,
% 0.30/0.60      ! [M: nat] :
% 0.30/0.60        ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 0.30/0.60        = bot_bot_set_nat ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastLessThan0
% 0.30/0.60  thf(fact_7200_sum_Oshift__bounds__Suc__ivl,axiom,
% 0.30/0.60      ! [G2: nat > nat,M: nat,N: nat] :
% 0.30/0.60        ( ( groups3542108847815614940at_nat @ G2 @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 0.30/0.60        = ( groups3542108847815614940at_nat
% 0.30/0.60          @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.60          @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.shift_bounds_Suc_ivl
% 0.30/0.60  thf(fact_7201_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.30/0.60      ! [G2: nat > nat,M: nat,N: nat] :
% 0.30/0.60        ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 0.30/0.60        = ( groups3542108847815614940at_nat
% 0.30/0.60          @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.60          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.shift_bounds_cl_Suc_ivl
% 0.30/0.60  thf(fact_7202_sum_Oshift__bounds__nat__ivl,axiom,
% 0.30/0.60      ! [G2: nat > nat,M: nat,K: nat,N: nat] :
% 0.30/0.60        ( ( groups3542108847815614940at_nat @ G2 @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 0.30/0.60        = ( groups3542108847815614940at_nat
% 0.30/0.60          @ ^ [I3: nat] : ( G2 @ ( plus_plus_nat @ I3 @ K ) )
% 0.30/0.60          @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.shift_bounds_nat_ivl
% 0.30/0.60  thf(fact_7203_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 0.30/0.60      ! [G2: nat > nat,M: nat,K: nat,N: nat] :
% 0.30/0.60        ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 0.30/0.60        = ( groups3542108847815614940at_nat
% 0.30/0.60          @ ^ [I3: nat] : ( G2 @ ( plus_plus_nat @ I3 @ K ) )
% 0.30/0.60          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % sum.shift_bounds_cl_nat_ivl
% 0.30/0.60  thf(fact_7204_atLeastAtMost__eq__UNIV__iff,axiom,
% 0.30/0.60      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.30/0.60        ( ( ( set_or2784603332384507286at_nat @ X @ Y )
% 0.30/0.60          = top_to7629004291339433233at_nat )
% 0.30/0.60        = ( ( X = bot_bo2099793752762293965at_nat )
% 0.30/0.60          & ( Y = top_to4669805908274784177at_nat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastAtMost_eq_UNIV_iff
% 0.30/0.60  thf(fact_7205_atLeastAtMost__eq__UNIV__iff,axiom,
% 0.30/0.60      ! [X: set_list_nat,Y: set_list_nat] :
% 0.30/0.60        ( ( ( set_or1270514513317581473st_nat @ X @ Y )
% 0.30/0.60          = top_to1619013496918823676st_nat )
% 0.30/0.60        = ( ( X = bot_bot_set_list_nat )
% 0.30/0.60          & ( Y = top_top_set_list_nat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastAtMost_eq_UNIV_iff
% 0.30/0.60  thf(fact_7206_atLeastAtMost__eq__UNIV__iff,axiom,
% 0.30/0.60      ! [X: set_o,Y: set_o] :
% 0.30/0.60        ( ( ( set_or266616469461849773_set_o @ X @ Y )
% 0.30/0.60          = top_top_set_set_o )
% 0.30/0.60        = ( ( X = bot_bot_set_o )
% 0.30/0.60          & ( Y = top_top_set_o ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastAtMost_eq_UNIV_iff
% 0.30/0.60  thf(fact_7207_atLeastAtMost__eq__UNIV__iff,axiom,
% 0.30/0.60      ! [X: set_rat,Y: set_rat] :
% 0.30/0.60        ( ( ( set_or1040488700251649177et_rat @ X @ Y )
% 0.30/0.60          = top_top_set_set_rat )
% 0.30/0.60        = ( ( X = bot_bot_set_rat )
% 0.30/0.60          & ( Y = top_top_set_rat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastAtMost_eq_UNIV_iff
% 0.30/0.60  thf(fact_7208_atLeastAtMost__eq__UNIV__iff,axiom,
% 0.30/0.60      ! [X: set_nat,Y: set_nat] :
% 0.30/0.60        ( ( ( set_or4548717258645045905et_nat @ X @ Y )
% 0.30/0.60          = top_top_set_set_nat )
% 0.30/0.60        = ( ( X = bot_bot_set_nat )
% 0.30/0.60          & ( Y = top_top_set_nat ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastAtMost_eq_UNIV_iff
% 0.30/0.60  thf(fact_7209_atLeastAtMost__eq__UNIV__iff,axiom,
% 0.30/0.60      ! [X: set_int,Y: set_int] :
% 0.30/0.60        ( ( ( set_or370866239135849197et_int @ X @ Y )
% 0.30/0.60          = top_top_set_set_int )
% 0.30/0.60        = ( ( X = bot_bot_set_int )
% 0.30/0.60          & ( Y = top_top_set_int ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastAtMost_eq_UNIV_iff
% 0.30/0.60  thf(fact_7210_atLeastAtMost__eq__UNIV__iff,axiom,
% 0.30/0.60      ! [X: $o,Y: $o] :
% 0.30/0.60        ( ( ( set_or8904488021354931149Most_o @ X @ Y )
% 0.30/0.60          = top_top_set_o )
% 0.30/0.60        = ( ( X = bot_bot_o )
% 0.30/0.60          & ( Y = top_top_o ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % atLeastAtMost_eq_UNIV_iff
% 0.30/0.60  thf(fact_7211_aset_I2_J,axiom,
% 0.30/0.60      ! [D3: int,A2: set_int,P: int > $o,Q2: int > $o] :
% 0.30/0.60        ( ! [X2: int] :
% 0.30/0.60            ( ! [Xa2: int] :
% 0.30/0.60                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.60               => ! [Xb2: int] :
% 0.30/0.60                    ( ( member_int @ Xb2 @ A2 )
% 0.30/0.60                   => ( X2
% 0.30/0.60                     != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.30/0.60           => ( ( P @ X2 )
% 0.30/0.60             => ( P @ ( plus_plus_int @ X2 @ D3 ) ) ) )
% 0.30/0.60       => ( ! [X2: int] :
% 0.30/0.60              ( ! [Xa2: int] :
% 0.30/0.60                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.60                 => ! [Xb2: int] :
% 0.30/0.60                      ( ( member_int @ Xb2 @ A2 )
% 0.30/0.60                     => ( X2
% 0.30/0.60                       != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.30/0.60             => ( ( Q2 @ X2 )
% 0.30/0.60               => ( Q2 @ ( plus_plus_int @ X2 @ D3 ) ) ) )
% 0.30/0.60         => ! [X5: int] :
% 0.30/0.60              ( ! [Xa3: int] :
% 0.30/0.60                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.60                 => ! [Xb3: int] :
% 0.30/0.60                      ( ( member_int @ Xb3 @ A2 )
% 0.30/0.60                     => ( X5
% 0.30/0.60                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.30/0.60             => ( ( ( P @ X5 )
% 0.30/0.60                  | ( Q2 @ X5 ) )
% 0.30/0.60               => ( ( P @ ( plus_plus_int @ X5 @ D3 ) )
% 0.30/0.60                  | ( Q2 @ ( plus_plus_int @ X5 @ D3 ) ) ) ) ) ) ) ).
% 0.30/0.60  
% 0.30/0.60  % aset(2)
% 0.30/0.60  thf(fact_7212_aset_I1_J,axiom,
% 0.30/0.60      ! [D3: int,A2: set_int,P: int > $o,Q2: int > $o] :
% 0.30/0.60        ( ! [X2: int] :
% 0.30/0.60            ( ! [Xa2: int] :
% 0.30/0.60                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.60               => ! [Xb2: int] :
% 0.30/0.60                    ( ( member_int @ Xb2 @ A2 )
% 0.30/0.60                   => ( X2
% 0.30/0.60                     != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.30/0.60           => ( ( P @ X2 )
% 0.30/0.60             => ( P @ ( plus_plus_int @ X2 @ D3 ) ) ) )
% 0.30/0.60       => ( ! [X2: int] :
% 0.30/0.60              ( ! [Xa2: int] :
% 0.30/0.60                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.60                 => ! [Xb2: int] :
% 0.30/0.60                      ( ( member_int @ Xb2 @ A2 )
% 0.30/0.60                     => ( X2
% 0.30/0.60                       != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.30/0.60             => ( ( Q2 @ X2 )
% 0.30/0.60               => ( Q2 @ ( plus_plus_int @ X2 @ D3 ) ) ) )
% 0.30/0.60         => ! [X5: int] :
% 0.30/0.60              ( ! [Xa3: int] :
% 0.30/0.60                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61                 => ! [Xb3: int] :
% 0.30/0.61                      ( ( member_int @ Xb3 @ A2 )
% 0.30/0.61                     => ( X5
% 0.30/0.61                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.30/0.61             => ( ( ( P @ X5 )
% 0.30/0.61                  & ( Q2 @ X5 ) )
% 0.30/0.61               => ( ( P @ ( plus_plus_int @ X5 @ D3 ) )
% 0.30/0.61                  & ( Q2 @ ( plus_plus_int @ X5 @ D3 ) ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % aset(1)
% 0.30/0.61  thf(fact_7213_bset_I2_J,axiom,
% 0.30/0.61      ! [D3: int,B2: set_int,P: int > $o,Q2: int > $o] :
% 0.30/0.61        ( ! [X2: int] :
% 0.30/0.61            ( ! [Xa2: int] :
% 0.30/0.61                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61               => ! [Xb2: int] :
% 0.30/0.61                    ( ( member_int @ Xb2 @ B2 )
% 0.30/0.61                   => ( X2
% 0.30/0.61                     != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.30/0.61           => ( ( P @ X2 )
% 0.30/0.61             => ( P @ ( minus_minus_int @ X2 @ D3 ) ) ) )
% 0.30/0.61       => ( ! [X2: int] :
% 0.30/0.61              ( ! [Xa2: int] :
% 0.30/0.61                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61                 => ! [Xb2: int] :
% 0.30/0.61                      ( ( member_int @ Xb2 @ B2 )
% 0.30/0.61                     => ( X2
% 0.30/0.61                       != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.30/0.61             => ( ( Q2 @ X2 )
% 0.30/0.61               => ( Q2 @ ( minus_minus_int @ X2 @ D3 ) ) ) )
% 0.30/0.61         => ! [X5: int] :
% 0.30/0.61              ( ! [Xa3: int] :
% 0.30/0.61                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61                 => ! [Xb3: int] :
% 0.30/0.61                      ( ( member_int @ Xb3 @ B2 )
% 0.30/0.61                     => ( X5
% 0.30/0.61                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.30/0.61             => ( ( ( P @ X5 )
% 0.30/0.61                  | ( Q2 @ X5 ) )
% 0.30/0.61               => ( ( P @ ( minus_minus_int @ X5 @ D3 ) )
% 0.30/0.61                  | ( Q2 @ ( minus_minus_int @ X5 @ D3 ) ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % bset(2)
% 0.30/0.61  thf(fact_7214_bset_I1_J,axiom,
% 0.30/0.61      ! [D3: int,B2: set_int,P: int > $o,Q2: int > $o] :
% 0.30/0.61        ( ! [X2: int] :
% 0.30/0.61            ( ! [Xa2: int] :
% 0.30/0.61                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61               => ! [Xb2: int] :
% 0.30/0.61                    ( ( member_int @ Xb2 @ B2 )
% 0.30/0.61                   => ( X2
% 0.30/0.61                     != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.30/0.61           => ( ( P @ X2 )
% 0.30/0.61             => ( P @ ( minus_minus_int @ X2 @ D3 ) ) ) )
% 0.30/0.61       => ( ! [X2: int] :
% 0.30/0.61              ( ! [Xa2: int] :
% 0.30/0.61                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61                 => ! [Xb2: int] :
% 0.30/0.61                      ( ( member_int @ Xb2 @ B2 )
% 0.30/0.61                     => ( X2
% 0.30/0.61                       != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.30/0.61             => ( ( Q2 @ X2 )
% 0.30/0.61               => ( Q2 @ ( minus_minus_int @ X2 @ D3 ) ) ) )
% 0.30/0.61         => ! [X5: int] :
% 0.30/0.61              ( ! [Xa3: int] :
% 0.30/0.61                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61                 => ! [Xb3: int] :
% 0.30/0.61                      ( ( member_int @ Xb3 @ B2 )
% 0.30/0.61                     => ( X5
% 0.30/0.61                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.30/0.61             => ( ( ( P @ X5 )
% 0.30/0.61                  & ( Q2 @ X5 ) )
% 0.30/0.61               => ( ( P @ ( minus_minus_int @ X5 @ D3 ) )
% 0.30/0.61                  & ( Q2 @ ( minus_minus_int @ X5 @ D3 ) ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % bset(1)
% 0.30/0.61  thf(fact_7215_atLeastLessThanSuc,axiom,
% 0.30/0.61      ! [M: nat,N: nat] :
% 0.30/0.61        ( ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 0.30/0.61            = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 0.30/0.61        & ( ~ ( ord_less_eq_nat @ M @ N )
% 0.30/0.61         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 0.30/0.61            = bot_bot_set_nat ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % atLeastLessThanSuc
% 0.30/0.61  thf(fact_7216_atLeastLessThan__add__Un,axiom,
% 0.30/0.61      ! [I: nat,J: nat,K: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ I @ J )
% 0.30/0.61       => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 0.30/0.61          = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % atLeastLessThan_add_Un
% 0.30/0.61  thf(fact_7217_sum_OatLeastAtMost__rev,axiom,
% 0.30/0.61      ! [G2: nat > nat,N: nat,M: nat] :
% 0.30/0.61        ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 0.30/0.61        = ( groups3542108847815614940at_nat
% 0.30/0.61          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.atLeastAtMost_rev
% 0.30/0.61  thf(fact_7218_aset_I10_J,axiom,
% 0.30/0.61      ! [D2: int,D3: int,A2: set_int,T3: int] :
% 0.30/0.61        ( ( dvd_dvd_int @ D2 @ D3 )
% 0.30/0.61       => ! [X5: int] :
% 0.30/0.61            ( ! [Xa3: int] :
% 0.30/0.61                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61               => ! [Xb3: int] :
% 0.30/0.61                    ( ( member_int @ Xb3 @ A2 )
% 0.30/0.61                   => ( X5
% 0.30/0.61                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.30/0.61           => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T3 ) )
% 0.30/0.61             => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X5 @ D3 ) @ T3 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % aset(10)
% 0.30/0.61  thf(fact_7219_aset_I9_J,axiom,
% 0.30/0.61      ! [D2: int,D3: int,A2: set_int,T3: int] :
% 0.30/0.61        ( ( dvd_dvd_int @ D2 @ D3 )
% 0.30/0.61       => ! [X5: int] :
% 0.30/0.61            ( ! [Xa3: int] :
% 0.30/0.61                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61               => ! [Xb3: int] :
% 0.30/0.61                    ( ( member_int @ Xb3 @ A2 )
% 0.30/0.61                   => ( X5
% 0.30/0.61                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.30/0.61           => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T3 ) )
% 0.30/0.61             => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X5 @ D3 ) @ T3 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % aset(9)
% 0.30/0.61  thf(fact_7220_bset_I10_J,axiom,
% 0.30/0.61      ! [D2: int,D3: int,B2: set_int,T3: int] :
% 0.30/0.61        ( ( dvd_dvd_int @ D2 @ D3 )
% 0.30/0.61       => ! [X5: int] :
% 0.30/0.61            ( ! [Xa3: int] :
% 0.30/0.61                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61               => ! [Xb3: int] :
% 0.30/0.61                    ( ( member_int @ Xb3 @ B2 )
% 0.30/0.61                   => ( X5
% 0.30/0.61                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.30/0.61           => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T3 ) )
% 0.30/0.61             => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X5 @ D3 ) @ T3 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % bset(10)
% 0.30/0.61  thf(fact_7221_bset_I9_J,axiom,
% 0.30/0.61      ! [D2: int,D3: int,B2: set_int,T3: int] :
% 0.30/0.61        ( ( dvd_dvd_int @ D2 @ D3 )
% 0.30/0.61       => ! [X5: int] :
% 0.30/0.61            ( ! [Xa3: int] :
% 0.30/0.61                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61               => ! [Xb3: int] :
% 0.30/0.61                    ( ( member_int @ Xb3 @ B2 )
% 0.30/0.61                   => ( X5
% 0.30/0.61                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.30/0.61           => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T3 ) )
% 0.30/0.61             => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X5 @ D3 ) @ T3 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % bset(9)
% 0.30/0.61  thf(fact_7222_atLeastAtMostPlus1__int__conv,axiom,
% 0.30/0.61      ! [M: int,N: int] :
% 0.30/0.61        ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 0.30/0.61       => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 0.30/0.61          = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % atLeastAtMostPlus1_int_conv
% 0.30/0.61  thf(fact_7223_atLeastLessThan__nat__numeral,axiom,
% 0.30/0.61      ! [M: nat,K: num] :
% 0.30/0.61        ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 0.30/0.61         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 0.30/0.61            = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 0.30/0.61        & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 0.30/0.61         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 0.30/0.61            = bot_bot_set_nat ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % atLeastLessThan_nat_numeral
% 0.30/0.61  thf(fact_7224_sum__Suc__diff_H,axiom,
% 0.30/0.61      ! [M: nat,N: nat,F2: nat > rat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( groups2906978787729119204at_rat
% 0.30/0.61            @ ^ [I3: nat] : ( minus_minus_rat @ ( F2 @ ( suc @ I3 ) ) @ ( F2 @ I3 ) )
% 0.30/0.61            @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 0.30/0.61          = ( minus_minus_rat @ ( F2 @ N ) @ ( F2 @ M ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_Suc_diff'
% 0.30/0.61  thf(fact_7225_sum__Suc__diff_H,axiom,
% 0.30/0.61      ! [M: nat,N: nat,F2: nat > int] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( groups3539618377306564664at_int
% 0.30/0.61            @ ^ [I3: nat] : ( minus_minus_int @ ( F2 @ ( suc @ I3 ) ) @ ( F2 @ I3 ) )
% 0.30/0.61            @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 0.30/0.61          = ( minus_minus_int @ ( F2 @ N ) @ ( F2 @ M ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_Suc_diff'
% 0.30/0.61  thf(fact_7226_sum_OSuc__reindex__ivl,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > rat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 0.30/0.61          = ( plus_plus_rat @ ( G2 @ M )
% 0.30/0.61            @ ( groups2906978787729119204at_rat
% 0.30/0.61              @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.61              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.Suc_reindex_ivl
% 0.30/0.61  thf(fact_7227_sum_OSuc__reindex__ivl,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > int] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 0.30/0.61          = ( plus_plus_int @ ( G2 @ M )
% 0.30/0.61            @ ( groups3539618377306564664at_int
% 0.30/0.61              @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.61              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.Suc_reindex_ivl
% 0.30/0.61  thf(fact_7228_sum_OSuc__reindex__ivl,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 0.30/0.61          = ( plus_plus_nat @ ( G2 @ M )
% 0.30/0.61            @ ( groups3542108847815614940at_nat
% 0.30/0.61              @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.61              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.Suc_reindex_ivl
% 0.30/0.61  thf(fact_7229_sum__Suc__diff,axiom,
% 0.30/0.61      ! [M: nat,N: nat,F2: nat > rat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.30/0.61       => ( ( groups2906978787729119204at_rat
% 0.30/0.61            @ ^ [I3: nat] : ( minus_minus_rat @ ( F2 @ ( suc @ I3 ) ) @ ( F2 @ I3 ) )
% 0.30/0.61            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61          = ( minus_minus_rat @ ( F2 @ ( suc @ N ) ) @ ( F2 @ M ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_Suc_diff
% 0.30/0.61  thf(fact_7230_sum__Suc__diff,axiom,
% 0.30/0.61      ! [M: nat,N: nat,F2: nat > int] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.30/0.61       => ( ( groups3539618377306564664at_int
% 0.30/0.61            @ ^ [I3: nat] : ( minus_minus_int @ ( F2 @ ( suc @ I3 ) ) @ ( F2 @ I3 ) )
% 0.30/0.61            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61          = ( minus_minus_int @ ( F2 @ ( suc @ N ) ) @ ( F2 @ M ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_Suc_diff
% 0.30/0.61  thf(fact_7231_sum_OatLeastLessThan__rev,axiom,
% 0.30/0.61      ! [G2: nat > nat,N: nat,M: nat] :
% 0.30/0.61        ( ( groups3542108847815614940at_nat @ G2 @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 0.30/0.61        = ( groups3542108847815614940at_nat
% 0.30/0.61          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ ( suc @ I3 ) ) )
% 0.30/0.61          @ ( set_or4665077453230672383an_nat @ N @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.atLeastLessThan_rev
% 0.30/0.61  thf(fact_7232_sum__atLeastAtMost__code,axiom,
% 0.30/0.61      ! [F2: nat > code_integer,A: nat,B: nat] :
% 0.30/0.61        ( ( groups7501900531339628137nteger @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.30/0.61        = ( set_fo1084959871951514735nteger
% 0.30/0.61          @ ^ [A3: nat] : ( plus_p5714425477246183910nteger @ ( F2 @ A3 ) )
% 0.30/0.61          @ A
% 0.30/0.61          @ B
% 0.30/0.61          @ zero_z3403309356797280102nteger ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_atLeastAtMost_code
% 0.30/0.61  thf(fact_7233_sum__atLeastAtMost__code,axiom,
% 0.30/0.61      ! [F2: nat > multis2468970476368604999at_nat,A: nat,B: nat] :
% 0.30/0.61        ( ( groups6857163185585827899at_nat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.30/0.61        = ( set_fo4497565046347964853at_nat
% 0.30/0.61          @ ^ [A3: nat] : ( plus_p7104986032573967614at_nat @ ( F2 @ A3 ) )
% 0.30/0.61          @ A
% 0.30/0.61          @ B
% 0.30/0.61          @ zero_z1048942125864253310at_nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_atLeastAtMost_code
% 0.30/0.61  thf(fact_7234_sum__atLeastAtMost__code,axiom,
% 0.30/0.61      ! [F2: nat > rat,A: nat,B: nat] :
% 0.30/0.61        ( ( groups2906978787729119204at_rat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.30/0.61        = ( set_fo1949268297981939178at_rat
% 0.30/0.61          @ ^ [A3: nat] : ( plus_plus_rat @ ( F2 @ A3 ) )
% 0.30/0.61          @ A
% 0.30/0.61          @ B
% 0.30/0.61          @ zero_zero_rat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_atLeastAtMost_code
% 0.30/0.61  thf(fact_7235_sum__atLeastAtMost__code,axiom,
% 0.30/0.61      ! [F2: nat > int,A: nat,B: nat] :
% 0.30/0.61        ( ( groups3539618377306564664at_int @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.30/0.61        = ( set_fo2581907887559384638at_int
% 0.30/0.61          @ ^ [A3: nat] : ( plus_plus_int @ ( F2 @ A3 ) )
% 0.30/0.61          @ A
% 0.30/0.61          @ B
% 0.30/0.61          @ zero_zero_int ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_atLeastAtMost_code
% 0.30/0.61  thf(fact_7236_sum__atLeastAtMost__code,axiom,
% 0.30/0.61      ! [F2: nat > nat,A: nat,B: nat] :
% 0.30/0.61        ( ( groups3542108847815614940at_nat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.30/0.61        = ( set_fo2584398358068434914at_nat
% 0.30/0.61          @ ^ [A3: nat] : ( plus_plus_nat @ ( F2 @ A3 ) )
% 0.30/0.61          @ A
% 0.30/0.61          @ B
% 0.30/0.61          @ zero_zero_nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_atLeastAtMost_code
% 0.30/0.61  thf(fact_7237_periodic__finite__ex,axiom,
% 0.30/0.61      ! [D2: int,P: int > $o] :
% 0.30/0.61        ( ( ord_less_int @ zero_zero_int @ D2 )
% 0.30/0.61       => ( ! [X2: int,K2: int] :
% 0.30/0.61              ( ( P @ X2 )
% 0.30/0.61              = ( P @ ( minus_minus_int @ X2 @ ( times_times_int @ K2 @ D2 ) ) ) )
% 0.30/0.61         => ( ( ? [X4: int] : ( P @ X4 ) )
% 0.30/0.61            = ( ? [X3: int] :
% 0.30/0.61                  ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D2 ) )
% 0.30/0.61                  & ( P @ X3 ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % periodic_finite_ex
% 0.30/0.61  thf(fact_7238_aset_I7_J,axiom,
% 0.30/0.61      ! [D3: int,A2: set_int,T3: int] :
% 0.30/0.61        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.30/0.61       => ! [X5: int] :
% 0.30/0.61            ( ! [Xa3: int] :
% 0.30/0.61                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61               => ! [Xb3: int] :
% 0.30/0.61                    ( ( member_int @ Xb3 @ A2 )
% 0.30/0.61                   => ( X5
% 0.30/0.61                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.30/0.61           => ( ( ord_less_int @ T3 @ X5 )
% 0.30/0.61             => ( ord_less_int @ T3 @ ( plus_plus_int @ X5 @ D3 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % aset(7)
% 0.30/0.61  thf(fact_7239_aset_I5_J,axiom,
% 0.30/0.61      ! [D3: int,T3: int,A2: set_int] :
% 0.30/0.61        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.30/0.61       => ( ( member_int @ T3 @ A2 )
% 0.30/0.61         => ! [X5: int] :
% 0.30/0.61              ( ! [Xa3: int] :
% 0.30/0.61                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61                 => ! [Xb3: int] :
% 0.30/0.61                      ( ( member_int @ Xb3 @ A2 )
% 0.30/0.61                     => ( X5
% 0.30/0.61                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.30/0.61             => ( ( ord_less_int @ X5 @ T3 )
% 0.30/0.61               => ( ord_less_int @ ( plus_plus_int @ X5 @ D3 ) @ T3 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % aset(5)
% 0.30/0.61  thf(fact_7240_aset_I4_J,axiom,
% 0.30/0.61      ! [D3: int,T3: int,A2: set_int] :
% 0.30/0.61        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.30/0.61       => ( ( member_int @ T3 @ A2 )
% 0.30/0.61         => ! [X5: int] :
% 0.30/0.61              ( ! [Xa3: int] :
% 0.30/0.61                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61                 => ! [Xb3: int] :
% 0.30/0.61                      ( ( member_int @ Xb3 @ A2 )
% 0.30/0.61                     => ( X5
% 0.30/0.61                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.30/0.61             => ( ( X5 != T3 )
% 0.30/0.61               => ( ( plus_plus_int @ X5 @ D3 )
% 0.30/0.61                 != T3 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % aset(4)
% 0.30/0.61  thf(fact_7241_aset_I3_J,axiom,
% 0.30/0.61      ! [D3: int,T3: int,A2: set_int] :
% 0.30/0.61        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.30/0.61       => ( ( member_int @ ( plus_plus_int @ T3 @ one_one_int ) @ A2 )
% 0.30/0.61         => ! [X5: int] :
% 0.30/0.61              ( ! [Xa3: int] :
% 0.30/0.61                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61                 => ! [Xb3: int] :
% 0.30/0.61                      ( ( member_int @ Xb3 @ A2 )
% 0.30/0.61                     => ( X5
% 0.30/0.61                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.30/0.61             => ( ( X5 = T3 )
% 0.30/0.61               => ( ( plus_plus_int @ X5 @ D3 )
% 0.30/0.61                  = T3 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % aset(3)
% 0.30/0.61  thf(fact_7242_bset_I7_J,axiom,
% 0.30/0.61      ! [D3: int,T3: int,B2: set_int] :
% 0.30/0.61        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.30/0.61       => ( ( member_int @ T3 @ B2 )
% 0.30/0.61         => ! [X5: int] :
% 0.30/0.61              ( ! [Xa3: int] :
% 0.30/0.61                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61                 => ! [Xb3: int] :
% 0.30/0.61                      ( ( member_int @ Xb3 @ B2 )
% 0.30/0.61                     => ( X5
% 0.30/0.61                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.30/0.61             => ( ( ord_less_int @ T3 @ X5 )
% 0.30/0.61               => ( ord_less_int @ T3 @ ( minus_minus_int @ X5 @ D3 ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % bset(7)
% 0.30/0.61  thf(fact_7243_bset_I5_J,axiom,
% 0.30/0.61      ! [D3: int,B2: set_int,T3: int] :
% 0.30/0.61        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.30/0.61       => ! [X5: int] :
% 0.30/0.61            ( ! [Xa3: int] :
% 0.30/0.61                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61               => ! [Xb3: int] :
% 0.30/0.61                    ( ( member_int @ Xb3 @ B2 )
% 0.30/0.61                   => ( X5
% 0.30/0.61                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.30/0.61           => ( ( ord_less_int @ X5 @ T3 )
% 0.30/0.61             => ( ord_less_int @ ( minus_minus_int @ X5 @ D3 ) @ T3 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % bset(5)
% 0.30/0.61  thf(fact_7244_bset_I4_J,axiom,
% 0.30/0.61      ! [D3: int,T3: int,B2: set_int] :
% 0.30/0.61        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.30/0.61       => ( ( member_int @ T3 @ B2 )
% 0.30/0.61         => ! [X5: int] :
% 0.30/0.61              ( ! [Xa3: int] :
% 0.30/0.61                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61                 => ! [Xb3: int] :
% 0.30/0.61                      ( ( member_int @ Xb3 @ B2 )
% 0.30/0.61                     => ( X5
% 0.30/0.61                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.30/0.61             => ( ( X5 != T3 )
% 0.30/0.61               => ( ( minus_minus_int @ X5 @ D3 )
% 0.30/0.61                 != T3 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % bset(4)
% 0.30/0.61  thf(fact_7245_bset_I3_J,axiom,
% 0.30/0.61      ! [D3: int,T3: int,B2: set_int] :
% 0.30/0.61        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.30/0.61       => ( ( member_int @ ( minus_minus_int @ T3 @ one_one_int ) @ B2 )
% 0.30/0.61         => ! [X5: int] :
% 0.30/0.61              ( ! [Xa3: int] :
% 0.30/0.61                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61                 => ! [Xb3: int] :
% 0.30/0.61                      ( ( member_int @ Xb3 @ B2 )
% 0.30/0.61                     => ( X5
% 0.30/0.61                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.30/0.61             => ( ( X5 = T3 )
% 0.30/0.61               => ( ( minus_minus_int @ X5 @ D3 )
% 0.30/0.61                  = T3 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % bset(3)
% 0.30/0.61  thf(fact_7246_sum_Oub__add__nat,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > rat,P4: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.30/0.61       => ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 0.30/0.61          = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.ub_add_nat
% 0.30/0.61  thf(fact_7247_sum_Oub__add__nat,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > int,P4: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.30/0.61       => ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 0.30/0.61          = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.ub_add_nat
% 0.30/0.61  thf(fact_7248_sum_Oub__add__nat,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > nat,P4: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.30/0.61       => ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 0.30/0.61          = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.ub_add_nat
% 0.30/0.61  thf(fact_7249_simp__from__to,axiom,
% 0.30/0.61      ( set_or1266510415728281911st_int
% 0.30/0.61      = ( ^ [I3: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I3 ) @ bot_bot_set_int @ ( insert_int @ I3 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % simp_from_to
% 0.30/0.61  thf(fact_7250_aset_I8_J,axiom,
% 0.30/0.61      ! [D3: int,A2: set_int,T3: int] :
% 0.30/0.61        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.30/0.61       => ! [X5: int] :
% 0.30/0.61            ( ! [Xa3: int] :
% 0.30/0.61                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61               => ! [Xb3: int] :
% 0.30/0.61                    ( ( member_int @ Xb3 @ A2 )
% 0.30/0.61                   => ( X5
% 0.30/0.61                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.30/0.61           => ( ( ord_less_eq_int @ T3 @ X5 )
% 0.30/0.61             => ( ord_less_eq_int @ T3 @ ( plus_plus_int @ X5 @ D3 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % aset(8)
% 0.30/0.61  thf(fact_7251_aset_I6_J,axiom,
% 0.30/0.61      ! [D3: int,T3: int,A2: set_int] :
% 0.30/0.61        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.30/0.61       => ( ( member_int @ ( plus_plus_int @ T3 @ one_one_int ) @ A2 )
% 0.30/0.61         => ! [X5: int] :
% 0.30/0.61              ( ! [Xa3: int] :
% 0.30/0.61                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61                 => ! [Xb3: int] :
% 0.30/0.61                      ( ( member_int @ Xb3 @ A2 )
% 0.30/0.61                     => ( X5
% 0.30/0.61                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 0.30/0.61             => ( ( ord_less_eq_int @ X5 @ T3 )
% 0.30/0.61               => ( ord_less_eq_int @ ( plus_plus_int @ X5 @ D3 ) @ T3 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % aset(6)
% 0.30/0.61  thf(fact_7252_bset_I8_J,axiom,
% 0.30/0.61      ! [D3: int,T3: int,B2: set_int] :
% 0.30/0.61        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.30/0.61       => ( ( member_int @ ( minus_minus_int @ T3 @ one_one_int ) @ B2 )
% 0.30/0.61         => ! [X5: int] :
% 0.30/0.61              ( ! [Xa3: int] :
% 0.30/0.61                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61                 => ! [Xb3: int] :
% 0.30/0.61                      ( ( member_int @ Xb3 @ B2 )
% 0.30/0.61                     => ( X5
% 0.30/0.61                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.30/0.61             => ( ( ord_less_eq_int @ T3 @ X5 )
% 0.30/0.61               => ( ord_less_eq_int @ T3 @ ( minus_minus_int @ X5 @ D3 ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % bset(8)
% 0.30/0.61  thf(fact_7253_bset_I6_J,axiom,
% 0.30/0.61      ! [D3: int,B2: set_int,T3: int] :
% 0.30/0.61        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.30/0.61       => ! [X5: int] :
% 0.30/0.61            ( ! [Xa3: int] :
% 0.30/0.61                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61               => ! [Xb3: int] :
% 0.30/0.61                    ( ( member_int @ Xb3 @ B2 )
% 0.30/0.61                   => ( X5
% 0.30/0.61                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 0.30/0.61           => ( ( ord_less_eq_int @ X5 @ T3 )
% 0.30/0.61             => ( ord_less_eq_int @ ( minus_minus_int @ X5 @ D3 ) @ T3 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % bset(6)
% 0.30/0.61  thf(fact_7254_cpmi,axiom,
% 0.30/0.61      ! [D3: int,P: int > $o,P7: int > $o,B2: set_int] :
% 0.30/0.61        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.30/0.61       => ( ? [Z7: int] :
% 0.30/0.61            ! [X2: int] :
% 0.30/0.61              ( ( ord_less_int @ X2 @ Z7 )
% 0.30/0.61             => ( ( P @ X2 )
% 0.30/0.61                = ( P7 @ X2 ) ) )
% 0.30/0.61         => ( ! [X2: int] :
% 0.30/0.61                ( ! [Xa2: int] :
% 0.30/0.61                    ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61                   => ! [Xb2: int] :
% 0.30/0.61                        ( ( member_int @ Xb2 @ B2 )
% 0.30/0.61                       => ( X2
% 0.30/0.61                         != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 0.30/0.61               => ( ( P @ X2 )
% 0.30/0.61                 => ( P @ ( minus_minus_int @ X2 @ D3 ) ) ) )
% 0.30/0.61           => ( ! [X2: int,K2: int] :
% 0.30/0.61                  ( ( P7 @ X2 )
% 0.30/0.61                  = ( P7 @ ( minus_minus_int @ X2 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 0.30/0.61             => ( ( ? [X4: int] : ( P @ X4 ) )
% 0.30/0.61                = ( ? [X3: int] :
% 0.30/0.61                      ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61                      & ( P7 @ X3 ) )
% 0.30/0.61                  | ? [X3: int] :
% 0.30/0.61                      ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61                      & ? [Y3: int] :
% 0.30/0.61                          ( ( member_int @ Y3 @ B2 )
% 0.30/0.61                          & ( P @ ( plus_plus_int @ Y3 @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % cpmi
% 0.30/0.61  thf(fact_7255_cppi,axiom,
% 0.30/0.61      ! [D3: int,P: int > $o,P7: int > $o,A2: set_int] :
% 0.30/0.61        ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.30/0.61       => ( ? [Z7: int] :
% 0.30/0.61            ! [X2: int] :
% 0.30/0.61              ( ( ord_less_int @ Z7 @ X2 )
% 0.30/0.61             => ( ( P @ X2 )
% 0.30/0.61                = ( P7 @ X2 ) ) )
% 0.30/0.61         => ( ! [X2: int] :
% 0.30/0.61                ( ! [Xa2: int] :
% 0.30/0.61                    ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61                   => ! [Xb2: int] :
% 0.30/0.61                        ( ( member_int @ Xb2 @ A2 )
% 0.30/0.61                       => ( X2
% 0.30/0.61                         != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 0.30/0.61               => ( ( P @ X2 )
% 0.30/0.61                 => ( P @ ( plus_plus_int @ X2 @ D3 ) ) ) )
% 0.30/0.61           => ( ! [X2: int,K2: int] :
% 0.30/0.61                  ( ( P7 @ X2 )
% 0.30/0.61                  = ( P7 @ ( minus_minus_int @ X2 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 0.30/0.61             => ( ( ? [X4: int] : ( P @ X4 ) )
% 0.30/0.61                = ( ? [X3: int] :
% 0.30/0.61                      ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61                      & ( P7 @ X3 ) )
% 0.30/0.61                  | ? [X3: int] :
% 0.30/0.61                      ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.30/0.61                      & ? [Y3: int] :
% 0.30/0.61                          ( ( member_int @ Y3 @ A2 )
% 0.30/0.61                          & ( P @ ( minus_minus_int @ Y3 @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % cppi
% 0.30/0.61  thf(fact_7256_sum__natinterval__diff,axiom,
% 0.30/0.61      ! [M: nat,N: nat,F2: nat > code_integer] :
% 0.30/0.61        ( ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61         => ( ( groups7501900531339628137nteger
% 0.30/0.61              @ ^ [K4: nat] : ( minus_8373710615458151222nteger @ ( F2 @ K4 ) @ ( F2 @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 0.30/0.61              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61            = ( minus_8373710615458151222nteger @ ( F2 @ M ) @ ( F2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 0.30/0.61        & ( ~ ( ord_less_eq_nat @ M @ N )
% 0.30/0.61         => ( ( groups7501900531339628137nteger
% 0.30/0.61              @ ^ [K4: nat] : ( minus_8373710615458151222nteger @ ( F2 @ K4 ) @ ( F2 @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 0.30/0.61              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61            = zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_natinterval_diff
% 0.30/0.61  thf(fact_7257_sum__natinterval__diff,axiom,
% 0.30/0.61      ! [M: nat,N: nat,F2: nat > rat] :
% 0.30/0.61        ( ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61         => ( ( groups2906978787729119204at_rat
% 0.30/0.61              @ ^ [K4: nat] : ( minus_minus_rat @ ( F2 @ K4 ) @ ( F2 @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 0.30/0.61              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61            = ( minus_minus_rat @ ( F2 @ M ) @ ( F2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 0.30/0.61        & ( ~ ( ord_less_eq_nat @ M @ N )
% 0.30/0.61         => ( ( groups2906978787729119204at_rat
% 0.30/0.61              @ ^ [K4: nat] : ( minus_minus_rat @ ( F2 @ K4 ) @ ( F2 @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 0.30/0.61              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61            = zero_zero_rat ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_natinterval_diff
% 0.30/0.61  thf(fact_7258_sum__natinterval__diff,axiom,
% 0.30/0.61      ! [M: nat,N: nat,F2: nat > int] :
% 0.30/0.61        ( ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61         => ( ( groups3539618377306564664at_int
% 0.30/0.61              @ ^ [K4: nat] : ( minus_minus_int @ ( F2 @ K4 ) @ ( F2 @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 0.30/0.61              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61            = ( minus_minus_int @ ( F2 @ M ) @ ( F2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 0.30/0.61        & ( ~ ( ord_less_eq_nat @ M @ N )
% 0.30/0.61         => ( ( groups3539618377306564664at_int
% 0.30/0.61              @ ^ [K4: nat] : ( minus_minus_int @ ( F2 @ K4 ) @ ( F2 @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 0.30/0.61              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61            = zero_zero_int ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_natinterval_diff
% 0.30/0.61  thf(fact_7259_sum__telescope_H_H,axiom,
% 0.30/0.61      ! [M: nat,N: nat,F2: nat > rat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( groups2906978787729119204at_rat
% 0.30/0.61            @ ^ [K4: nat] : ( minus_minus_rat @ ( F2 @ K4 ) @ ( F2 @ ( minus_minus_nat @ K4 @ one_one_nat ) ) )
% 0.30/0.61            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 0.30/0.61          = ( minus_minus_rat @ ( F2 @ N ) @ ( F2 @ M ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_telescope''
% 0.30/0.61  thf(fact_7260_sum__telescope_H_H,axiom,
% 0.30/0.61      ! [M: nat,N: nat,F2: nat > int] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( groups3539618377306564664at_int
% 0.30/0.61            @ ^ [K4: nat] : ( minus_minus_int @ ( F2 @ K4 ) @ ( F2 @ ( minus_minus_nat @ K4 @ one_one_nat ) ) )
% 0.30/0.61            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 0.30/0.61          = ( minus_minus_int @ ( F2 @ N ) @ ( F2 @ M ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_telescope''
% 0.30/0.61  thf(fact_7261_sum__gp__multiplied,axiom,
% 0.30/0.61      ! [M: nat,N: nat,X: code_integer] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 0.30/0.61          = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ M ) @ ( power_8256067586552552935nteger @ X @ ( suc @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_gp_multiplied
% 0.30/0.61  thf(fact_7262_sum__gp__multiplied,axiom,
% 0.30/0.61      ! [M: nat,N: nat,X: rat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 0.30/0.61          = ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_gp_multiplied
% 0.30/0.61  thf(fact_7263_sum__gp__multiplied,axiom,
% 0.30/0.61      ! [M: nat,N: nat,X: int] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 0.30/0.61          = ( minus_minus_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ ( suc @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_gp_multiplied
% 0.30/0.61  thf(fact_7264_sum_Oin__pairs,axiom,
% 0.30/0.61      ! [G2: nat > rat,M: nat,N: nat] :
% 0.30/0.61        ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.30/0.61        = ( groups2906978787729119204at_rat
% 0.30/0.61          @ ^ [I3: nat] : ( plus_plus_rat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.in_pairs
% 0.30/0.61  thf(fact_7265_sum_Oin__pairs,axiom,
% 0.30/0.61      ! [G2: nat > int,M: nat,N: nat] :
% 0.30/0.61        ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.30/0.61        = ( groups3539618377306564664at_int
% 0.30/0.61          @ ^ [I3: nat] : ( plus_plus_int @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.in_pairs
% 0.30/0.61  thf(fact_7266_sum_Oin__pairs,axiom,
% 0.30/0.61      ! [G2: nat > nat,M: nat,N: nat] :
% 0.30/0.61        ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.30/0.61        = ( groups3542108847815614940at_nat
% 0.30/0.61          @ ^ [I3: nat] : ( plus_plus_nat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.in_pairs
% 0.30/0.61  thf(fact_7267_sum__gp,axiom,
% 0.30/0.61      ! [N: nat,M: nat,X: rat] :
% 0.30/0.61        ( ( ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61            = zero_zero_rat ) )
% 0.30/0.61        & ( ~ ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( ( X = one_one_rat )
% 0.30/0.61             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61                = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 0.30/0.61            & ( ( X != one_one_rat )
% 0.30/0.61             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61                = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_gp
% 0.30/0.61  thf(fact_7268_gauss__sum__from__Suc__0,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.30/0.61        = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gauss_sum_from_Suc_0
% 0.30/0.61  thf(fact_7269_gauss__sum__from__Suc__0,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.30/0.61        = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N ) @ one_one_Code_natural ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gauss_sum_from_Suc_0
% 0.30/0.61  thf(fact_7270_gauss__sum__from__Suc__0,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.30/0.61        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gauss_sum_from_Suc_0
% 0.30/0.61  thf(fact_7271_gauss__sum__from__Suc__0,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.30/0.61        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gauss_sum_from_Suc_0
% 0.30/0.61  thf(fact_7272_sum__gp__offset,axiom,
% 0.30/0.61      ! [X: rat,M: nat,N: nat] :
% 0.30/0.61        ( ( ( X = one_one_rat )
% 0.30/0.61         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 0.30/0.61            = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) )
% 0.30/0.61        & ( ( X != one_one_rat )
% 0.30/0.61         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 0.30/0.61            = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_gp_offset
% 0.30/0.61  thf(fact_7273_arith__series,axiom,
% 0.30/0.61      ! [A: code_integer,D2: code_integer,N: nat] :
% 0.30/0.61        ( ( groups7501900531339628137nteger
% 0.30/0.61          @ ^ [I3: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I3 ) @ D2 ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.30/0.61        = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ D2 ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % arith_series
% 0.30/0.61  thf(fact_7274_arith__series,axiom,
% 0.30/0.61      ! [A: code_natural,D2: code_natural,N: nat] :
% 0.30/0.61        ( ( groups6325495683096345652atural
% 0.30/0.61          @ ^ [I3: nat] : ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ I3 ) @ D2 ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.30/0.61        = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N ) @ one_one_Code_natural ) @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N ) @ D2 ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % arith_series
% 0.30/0.61  thf(fact_7275_arith__series,axiom,
% 0.30/0.61      ! [A: int,D2: int,N: nat] :
% 0.30/0.61        ( ( groups3539618377306564664at_int
% 0.30/0.61          @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D2 ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.30/0.61        = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % arith_series
% 0.30/0.61  thf(fact_7276_arith__series,axiom,
% 0.30/0.61      ! [A: nat,D2: nat,N: nat] :
% 0.30/0.61        ( ( groups3542108847815614940at_nat
% 0.30/0.61          @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D2 ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.30/0.61        = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % arith_series
% 0.30/0.61  thf(fact_7277_gauss__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.30/0.61        = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gauss_sum
% 0.30/0.61  thf(fact_7278_gauss__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.30/0.61        = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N ) @ one_one_Code_natural ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gauss_sum
% 0.30/0.61  thf(fact_7279_gauss__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.30/0.61        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gauss_sum
% 0.30/0.61  thf(fact_7280_gauss__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.30/0.61        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gauss_sum
% 0.30/0.61  thf(fact_7281_double__gauss__sum__from__Suc__0,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.30/0.61        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % double_gauss_sum_from_Suc_0
% 0.30/0.61  thf(fact_7282_double__gauss__sum__from__Suc__0,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.30/0.61        = ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N ) @ one_one_Code_natural ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % double_gauss_sum_from_Suc_0
% 0.30/0.61  thf(fact_7283_double__gauss__sum__from__Suc__0,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.30/0.61        = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % double_gauss_sum_from_Suc_0
% 0.30/0.61  thf(fact_7284_double__gauss__sum__from__Suc__0,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.30/0.61        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % double_gauss_sum_from_Suc_0
% 0.30/0.61  thf(fact_7285_double__gauss__sum__from__Suc__0,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.30/0.61        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % double_gauss_sum_from_Suc_0
% 0.30/0.61  thf(fact_7286_double__arith__series,axiom,
% 0.30/0.61      ! [A: code_integer,D2: code_integer,N: nat] :
% 0.30/0.61        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 0.30/0.61          @ ( groups7501900531339628137nteger
% 0.30/0.61            @ ^ [I3: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I3 ) @ D2 ) )
% 0.30/0.61            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.30/0.61        = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ D2 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % double_arith_series
% 0.30/0.61  thf(fact_7287_double__arith__series,axiom,
% 0.30/0.61      ! [A: code_natural,D2: code_natural,N: nat] :
% 0.30/0.61        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) )
% 0.30/0.61          @ ( groups6325495683096345652atural
% 0.30/0.61            @ ^ [I3: nat] : ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ I3 ) @ D2 ) )
% 0.30/0.61            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.30/0.61        = ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N ) @ one_one_Code_natural ) @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N ) @ D2 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % double_arith_series
% 0.30/0.61  thf(fact_7288_double__arith__series,axiom,
% 0.30/0.61      ! [A: int,D2: int,N: nat] :
% 0.30/0.61        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 0.30/0.61          @ ( groups3539618377306564664at_int
% 0.30/0.61            @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D2 ) )
% 0.30/0.61            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.30/0.61        = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D2 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % double_arith_series
% 0.30/0.61  thf(fact_7289_double__arith__series,axiom,
% 0.30/0.61      ! [A: rat,D2: rat,N: nat] :
% 0.30/0.61        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 0.30/0.61          @ ( groups2906978787729119204at_rat
% 0.30/0.61            @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I3 ) @ D2 ) )
% 0.30/0.61            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.30/0.61        = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ D2 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % double_arith_series
% 0.30/0.61  thf(fact_7290_double__arith__series,axiom,
% 0.30/0.61      ! [A: nat,D2: nat,N: nat] :
% 0.30/0.61        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.30/0.61          @ ( groups3542108847815614940at_nat
% 0.30/0.61            @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D2 ) )
% 0.30/0.61            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.30/0.61        = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D2 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % double_arith_series
% 0.30/0.61  thf(fact_7291_negative__eq__positive,axiom,
% 0.30/0.61      ! [N: nat,M: nat] :
% 0.30/0.61        ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
% 0.30/0.61          = ( semiri1314217659103216013at_int @ M ) )
% 0.30/0.61        = ( ( N = zero_zero_nat )
% 0.30/0.61          & ( M = zero_zero_nat ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % negative_eq_positive
% 0.30/0.61  thf(fact_7292_negative__zle,axiom,
% 0.30/0.61      ! [N: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 0.30/0.61  
% 0.30/0.61  % negative_zle
% 0.30/0.61  thf(fact_7293_of__nat__mult,axiom,
% 0.30/0.61      ! [M: nat,N: nat] :
% 0.30/0.61        ( ( semiri4939895301339042750nteger @ ( times_times_nat @ M @ N ) )
% 0.30/0.61        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_mult
% 0.30/0.61  thf(fact_7294_of__nat__mult,axiom,
% 0.30/0.61      ! [M: nat,N: nat] :
% 0.30/0.61        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 0.30/0.61        = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_mult
% 0.30/0.61  thf(fact_7295_of__nat__mult,axiom,
% 0.30/0.61      ! [M: nat,N: nat] :
% 0.30/0.61        ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 0.30/0.61        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_mult
% 0.30/0.61  thf(fact_7296_of__nat__mult,axiom,
% 0.30/0.61      ! [M: nat,N: nat] :
% 0.30/0.61        ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N ) )
% 0.30/0.61        = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_mult
% 0.30/0.61  thf(fact_7297_of__nat__1,axiom,
% 0.30/0.61      ( ( semiri4939895301339042750nteger @ one_one_nat )
% 0.30/0.61      = one_one_Code_integer ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_1
% 0.30/0.61  thf(fact_7298_of__nat__1,axiom,
% 0.30/0.61      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 0.30/0.61      = one_one_int ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_1
% 0.30/0.61  thf(fact_7299_of__nat__1,axiom,
% 0.30/0.61      ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 0.30/0.61      = one_one_nat ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_1
% 0.30/0.61  thf(fact_7300_of__nat__1,axiom,
% 0.30/0.61      ( ( semiri681578069525770553at_rat @ one_one_nat )
% 0.30/0.61      = one_one_rat ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_1
% 0.30/0.61  thf(fact_7301_of__nat__1__eq__iff,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( one_one_Code_integer
% 0.30/0.61          = ( semiri4939895301339042750nteger @ N ) )
% 0.30/0.61        = ( N = one_one_nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_1_eq_iff
% 0.30/0.61  thf(fact_7302_of__nat__1__eq__iff,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( one_one_int
% 0.30/0.61          = ( semiri1314217659103216013at_int @ N ) )
% 0.30/0.61        = ( N = one_one_nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_1_eq_iff
% 0.30/0.61  thf(fact_7303_of__nat__1__eq__iff,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( one_one_nat
% 0.30/0.61          = ( semiri1316708129612266289at_nat @ N ) )
% 0.30/0.61        = ( N = one_one_nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_1_eq_iff
% 0.30/0.61  thf(fact_7304_of__nat__1__eq__iff,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( one_one_rat
% 0.30/0.61          = ( semiri681578069525770553at_rat @ N ) )
% 0.30/0.61        = ( N = one_one_nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_1_eq_iff
% 0.30/0.61  thf(fact_7305_of__nat__eq__1__iff,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( ( semiri4939895301339042750nteger @ N )
% 0.30/0.61          = one_one_Code_integer )
% 0.30/0.61        = ( N = one_one_nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_eq_1_iff
% 0.30/0.61  thf(fact_7306_of__nat__eq__1__iff,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( ( semiri1314217659103216013at_int @ N )
% 0.30/0.61          = one_one_int )
% 0.30/0.61        = ( N = one_one_nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_eq_1_iff
% 0.30/0.61  thf(fact_7307_of__nat__eq__1__iff,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( ( semiri1316708129612266289at_nat @ N )
% 0.30/0.61          = one_one_nat )
% 0.30/0.61        = ( N = one_one_nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_eq_1_iff
% 0.30/0.61  thf(fact_7308_of__nat__eq__1__iff,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( ( semiri681578069525770553at_rat @ N )
% 0.30/0.61          = one_one_rat )
% 0.30/0.61        = ( N = one_one_nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_eq_1_iff
% 0.30/0.61  thf(fact_7309_negative__zless,axiom,
% 0.30/0.61      ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 0.30/0.61  
% 0.30/0.61  % negative_zless
% 0.30/0.61  thf(fact_7310_of__nat__sum,axiom,
% 0.30/0.61      ! [F2: int > nat,A2: set_int] :
% 0.30/0.61        ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F2 @ A2 ) )
% 0.30/0.61        = ( groups4538972089207619220nt_int
% 0.30/0.61          @ ^ [X3: int] : ( semiri1314217659103216013at_int @ ( F2 @ X3 ) )
% 0.30/0.61          @ A2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_sum
% 0.30/0.61  thf(fact_7311_of__nat__sum,axiom,
% 0.30/0.61      ! [F2: nat > nat,A2: set_nat] :
% 0.30/0.61        ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F2 @ A2 ) )
% 0.30/0.61        = ( groups3539618377306564664at_int
% 0.30/0.61          @ ^ [X3: nat] : ( semiri1314217659103216013at_int @ ( F2 @ X3 ) )
% 0.30/0.61          @ A2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_sum
% 0.30/0.61  thf(fact_7312_of__nat__sum,axiom,
% 0.30/0.61      ! [F2: nat > nat,A2: set_nat] :
% 0.30/0.61        ( ( semiri681578069525770553at_rat @ ( groups3542108847815614940at_nat @ F2 @ A2 ) )
% 0.30/0.61        = ( groups2906978787729119204at_rat
% 0.30/0.61          @ ^ [X3: nat] : ( semiri681578069525770553at_rat @ ( F2 @ X3 ) )
% 0.30/0.61          @ A2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_sum
% 0.30/0.61  thf(fact_7313_of__nat__sum,axiom,
% 0.30/0.61      ! [F2: nat > nat,A2: set_nat] :
% 0.30/0.61        ( ( semiri1316708129612266289at_nat @ ( groups3542108847815614940at_nat @ F2 @ A2 ) )
% 0.30/0.61        = ( groups3542108847815614940at_nat
% 0.30/0.61          @ ^ [X3: nat] : ( semiri1316708129612266289at_nat @ ( F2 @ X3 ) )
% 0.30/0.61          @ A2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_sum
% 0.30/0.61  thf(fact_7314_of__nat__Suc,axiom,
% 0.30/0.61      ! [M: nat] :
% 0.30/0.61        ( ( semiri4939895301339042750nteger @ ( suc @ M ) )
% 0.30/0.61        = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( semiri4939895301339042750nteger @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_Suc
% 0.30/0.61  thf(fact_7315_of__nat__Suc,axiom,
% 0.30/0.61      ! [M: nat] :
% 0.30/0.61        ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 0.30/0.61        = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_Suc
% 0.30/0.61  thf(fact_7316_of__nat__Suc,axiom,
% 0.30/0.61      ! [M: nat] :
% 0.30/0.61        ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 0.30/0.61        = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_Suc
% 0.30/0.61  thf(fact_7317_of__nat__Suc,axiom,
% 0.30/0.61      ! [M: nat] :
% 0.30/0.61        ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 0.30/0.61        = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_Suc
% 0.30/0.61  thf(fact_7318_mult__of__nat__commute,axiom,
% 0.30/0.61      ! [X: nat,Y: code_integer] :
% 0.30/0.61        ( ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ X ) @ Y )
% 0.30/0.61        = ( times_3573771949741848930nteger @ Y @ ( semiri4939895301339042750nteger @ X ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % mult_of_nat_commute
% 0.30/0.61  thf(fact_7319_mult__of__nat__commute,axiom,
% 0.30/0.61      ! [X: nat,Y: int] :
% 0.30/0.61        ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y )
% 0.30/0.61        = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % mult_of_nat_commute
% 0.30/0.61  thf(fact_7320_mult__of__nat__commute,axiom,
% 0.30/0.61      ! [X: nat,Y: nat] :
% 0.30/0.61        ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
% 0.30/0.61        = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % mult_of_nat_commute
% 0.30/0.61  thf(fact_7321_mult__of__nat__commute,axiom,
% 0.30/0.61      ! [X: nat,Y: rat] :
% 0.30/0.61        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X ) @ Y )
% 0.30/0.61        = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % mult_of_nat_commute
% 0.30/0.61  thf(fact_7322_atLeastLessThanPlusOne__atLeastAtMost__integer,axiom,
% 0.30/0.61      ! [L: code_integer,U: code_integer] :
% 0.30/0.61        ( ( set_or8404916559141939852nteger @ L @ ( plus_p5714425477246183910nteger @ U @ one_one_Code_integer ) )
% 0.30/0.61        = ( set_or189985376899183464nteger @ L @ U ) ) ).
% 0.30/0.61  
% 0.30/0.61  % atLeastLessThanPlusOne_atLeastAtMost_integer
% 0.30/0.61  thf(fact_7323_int__cases2,axiom,
% 0.30/0.61      ! [Z: int] :
% 0.30/0.61        ( ! [N3: nat] :
% 0.30/0.61            ( Z
% 0.30/0.61           != ( semiri1314217659103216013at_int @ N3 ) )
% 0.30/0.61       => ~ ! [N3: nat] :
% 0.30/0.61              ( Z
% 0.30/0.61             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % int_cases2
% 0.30/0.61  thf(fact_7324_div__mult2__eq_H,axiom,
% 0.30/0.61      ! [A: code_integer,M: nat,N: nat] :
% 0.30/0.61        ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 0.30/0.61        = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % div_mult2_eq'
% 0.30/0.61  thf(fact_7325_div__mult2__eq_H,axiom,
% 0.30/0.61      ! [A: code_natural,M: nat,N: nat] :
% 0.30/0.61        ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) ) )
% 0.30/0.61        = ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ ( semiri3763490453095760265atural @ M ) ) @ ( semiri3763490453095760265atural @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % div_mult2_eq'
% 0.30/0.61  thf(fact_7326_div__mult2__eq_H,axiom,
% 0.30/0.61      ! [A: int,M: nat,N: nat] :
% 0.30/0.61        ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.30/0.61        = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % div_mult2_eq'
% 0.30/0.61  thf(fact_7327_div__mult2__eq_H,axiom,
% 0.30/0.61      ! [A: nat,M: nat,N: nat] :
% 0.30/0.61        ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 0.30/0.61        = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % div_mult2_eq'
% 0.30/0.61  thf(fact_7328_int__cases,axiom,
% 0.30/0.61      ! [Z: int] :
% 0.30/0.61        ( ! [N3: nat] :
% 0.30/0.61            ( Z
% 0.30/0.61           != ( semiri1314217659103216013at_int @ N3 ) )
% 0.30/0.61       => ~ ! [N3: nat] :
% 0.30/0.61              ( Z
% 0.30/0.61             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % int_cases
% 0.30/0.61  thf(fact_7329_int__of__nat__induct,axiom,
% 0.30/0.61      ! [P: int > $o,Z: int] :
% 0.30/0.61        ( ! [N3: nat] : ( P @ ( semiri1314217659103216013at_int @ N3 ) )
% 0.30/0.61       => ( ! [N3: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) )
% 0.30/0.61         => ( P @ Z ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % int_of_nat_induct
% 0.30/0.61  thf(fact_7330_int__ops_I2_J,axiom,
% 0.30/0.61      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 0.30/0.61      = one_one_int ) ).
% 0.30/0.61  
% 0.30/0.61  % int_ops(2)
% 0.30/0.61  thf(fact_7331_not__int__zless__negative,axiom,
% 0.30/0.61      ! [N: nat,M: nat] :
% 0.30/0.61        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % not_int_zless_negative
% 0.30/0.61  thf(fact_7332_nat__less__as__int,axiom,
% 0.30/0.61      ( ord_less_nat
% 0.30/0.61      = ( ^ [A3: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % nat_less_as_int
% 0.30/0.61  thf(fact_7333_nat__leq__as__int,axiom,
% 0.30/0.61      ( ord_less_eq_nat
% 0.30/0.61      = ( ^ [A3: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % nat_leq_as_int
% 0.30/0.61  thf(fact_7334_ex__less__of__nat__mult,axiom,
% 0.30/0.61      ! [X: rat,Y: rat] :
% 0.30/0.61        ( ( ord_less_rat @ zero_zero_rat @ X )
% 0.30/0.61       => ? [N3: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % ex_less_of_nat_mult
% 0.30/0.61  thf(fact_7335_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 0.30/0.61      ! [L: int,U: int] :
% 0.30/0.61        ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 0.30/0.61        = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 0.30/0.61  
% 0.30/0.61  % atLeastLessThanPlusOne_atLeastAtMost_int
% 0.30/0.61  thf(fact_7336_int__cases4,axiom,
% 0.30/0.61      ! [M: int] :
% 0.30/0.61        ( ! [N3: nat] :
% 0.30/0.61            ( M
% 0.30/0.61           != ( semiri1314217659103216013at_int @ N3 ) )
% 0.30/0.61       => ~ ! [N3: nat] :
% 0.30/0.61              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.30/0.61             => ( M
% 0.30/0.61               != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % int_cases4
% 0.30/0.61  thf(fact_7337_int__zle__neg,axiom,
% 0.30/0.61      ! [N: nat,M: nat] :
% 0.30/0.61        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 0.30/0.61        = ( ( N = zero_zero_nat )
% 0.30/0.61          & ( M = zero_zero_nat ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % int_zle_neg
% 0.30/0.61  thf(fact_7338_int__Suc,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 0.30/0.61        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 0.30/0.61  
% 0.30/0.61  % int_Suc
% 0.30/0.61  thf(fact_7339_int__ops_I4_J,axiom,
% 0.30/0.61      ! [A: nat] :
% 0.30/0.61        ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 0.30/0.61        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 0.30/0.61  
% 0.30/0.61  % int_ops(4)
% 0.30/0.61  thf(fact_7340_negative__zle__0,axiom,
% 0.30/0.61      ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% 0.30/0.61  
% 0.30/0.61  % negative_zle_0
% 0.30/0.61  thf(fact_7341_nonpos__int__cases,axiom,
% 0.30/0.61      ! [K: int] :
% 0.30/0.61        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 0.30/0.61       => ~ ! [N3: nat] :
% 0.30/0.61              ( K
% 0.30/0.61             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % nonpos_int_cases
% 0.30/0.61  thf(fact_7342_int__sum,axiom,
% 0.30/0.61      ! [F2: int > nat,A2: set_int] :
% 0.30/0.61        ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F2 @ A2 ) )
% 0.30/0.61        = ( groups4538972089207619220nt_int
% 0.30/0.61          @ ^ [X3: int] : ( semiri1314217659103216013at_int @ ( F2 @ X3 ) )
% 0.30/0.61          @ A2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % int_sum
% 0.30/0.61  thf(fact_7343_int__sum,axiom,
% 0.30/0.61      ! [F2: nat > nat,A2: set_nat] :
% 0.30/0.61        ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F2 @ A2 ) )
% 0.30/0.61        = ( groups3539618377306564664at_int
% 0.30/0.61          @ ^ [X3: nat] : ( semiri1314217659103216013at_int @ ( F2 @ X3 ) )
% 0.30/0.61          @ A2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % int_sum
% 0.30/0.61  thf(fact_7344_mod__mult2__eq_H,axiom,
% 0.30/0.61      ! [A: code_integer,M: nat,N: nat] :
% 0.30/0.61        ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 0.30/0.61        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % mod_mult2_eq'
% 0.30/0.61  thf(fact_7345_mod__mult2__eq_H,axiom,
% 0.30/0.61      ! [A: code_natural,M: nat,N: nat] :
% 0.30/0.61        ( ( modulo8411746178871703098atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) ) )
% 0.30/0.61        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M ) @ ( modulo8411746178871703098atural @ ( divide5121882707175180666atural @ A @ ( semiri3763490453095760265atural @ M ) ) @ ( semiri3763490453095760265atural @ N ) ) ) @ ( modulo8411746178871703098atural @ A @ ( semiri3763490453095760265atural @ M ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % mod_mult2_eq'
% 0.30/0.61  thf(fact_7346_mod__mult2__eq_H,axiom,
% 0.30/0.61      ! [A: int,M: nat,N: nat] :
% 0.30/0.61        ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.30/0.61        = ( 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 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % mod_mult2_eq'
% 0.30/0.61  thf(fact_7347_mod__mult2__eq_H,axiom,
% 0.30/0.61      ! [A: nat,M: nat,N: nat] :
% 0.30/0.61        ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 0.30/0.61        = ( 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 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % mod_mult2_eq'
% 0.30/0.61  thf(fact_7348_int__cases3,axiom,
% 0.30/0.61      ! [K: int] :
% 0.30/0.61        ( ( K != zero_zero_int )
% 0.30/0.61       => ( ! [N3: nat] :
% 0.30/0.61              ( ( K
% 0.30/0.61                = ( semiri1314217659103216013at_int @ N3 ) )
% 0.30/0.61             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 0.30/0.61         => ~ ! [N3: nat] :
% 0.30/0.61                ( ( K
% 0.30/0.61                  = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 0.30/0.61               => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % int_cases3
% 0.30/0.61  thf(fact_7349_not__zle__0__negative,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % not_zle_0_negative
% 0.30/0.61  thf(fact_7350_negD,axiom,
% 0.30/0.61      ! [X: int] :
% 0.30/0.61        ( ( ord_less_int @ X @ zero_zero_int )
% 0.30/0.61       => ? [N3: nat] :
% 0.30/0.61            ( X
% 0.30/0.61            = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % negD
% 0.30/0.61  thf(fact_7351_negative__zless__0,axiom,
% 0.30/0.61      ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 0.30/0.61  
% 0.30/0.61  % negative_zless_0
% 0.30/0.61  thf(fact_7352_nat__approx__posE,axiom,
% 0.30/0.61      ! [E2: rat] :
% 0.30/0.61        ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 0.30/0.61       => ~ ! [N3: nat] :
% 0.30/0.61              ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % nat_approx_posE
% 0.30/0.61  thf(fact_7353_neg__int__cases,axiom,
% 0.30/0.61      ! [K: int] :
% 0.30/0.61        ( ( ord_less_int @ K @ zero_zero_int )
% 0.30/0.61       => ~ ! [N3: nat] :
% 0.30/0.61              ( ( K
% 0.30/0.61                = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 0.30/0.61             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % neg_int_cases
% 0.30/0.61  thf(fact_7354_double__gauss__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.30/0.61        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % double_gauss_sum
% 0.30/0.61  thf(fact_7355_double__gauss__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.30/0.61        = ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N ) @ one_one_Code_natural ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % double_gauss_sum
% 0.30/0.61  thf(fact_7356_double__gauss__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.30/0.61        = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % double_gauss_sum
% 0.30/0.61  thf(fact_7357_double__gauss__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.30/0.61        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % double_gauss_sum
% 0.30/0.61  thf(fact_7358_double__gauss__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.30/0.61        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % double_gauss_sum
% 0.30/0.61  thf(fact_7359_pochhammer__double,axiom,
% 0.30/0.61      ! [Z: rat,N: nat] :
% 0.30/0.61        ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.61        = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_double
% 0.30/0.61  thf(fact_7360_of__nat__code,axiom,
% 0.30/0.61      ( semiri4939895301339042750nteger
% 0.30/0.61      = ( ^ [N2: nat] :
% 0.30/0.61            ( semiri4055485073559036834nteger
% 0.30/0.61            @ ^ [I3: code_integer] : ( plus_p5714425477246183910nteger @ I3 @ one_one_Code_integer )
% 0.30/0.61            @ N2
% 0.30/0.61            @ zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_code
% 0.30/0.61  thf(fact_7361_of__nat__code,axiom,
% 0.30/0.61      ( semiri1314217659103216013at_int
% 0.30/0.61      = ( ^ [N2: nat] :
% 0.30/0.61            ( semiri8420488043553186161ux_int
% 0.30/0.61            @ ^ [I3: int] : ( plus_plus_int @ I3 @ one_one_int )
% 0.30/0.61            @ N2
% 0.30/0.61            @ zero_zero_int ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_code
% 0.30/0.61  thf(fact_7362_of__nat__code,axiom,
% 0.30/0.61      ( semiri1316708129612266289at_nat
% 0.30/0.61      = ( ^ [N2: nat] :
% 0.30/0.61            ( semiri8422978514062236437ux_nat
% 0.30/0.61            @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ one_one_nat )
% 0.30/0.61            @ N2
% 0.30/0.61            @ zero_zero_nat ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_code
% 0.30/0.61  thf(fact_7363_of__nat__code,axiom,
% 0.30/0.61      ( semiri681578069525770553at_rat
% 0.30/0.61      = ( ^ [N2: nat] :
% 0.30/0.61            ( semiri7787848453975740701ux_rat
% 0.30/0.61            @ ^ [I3: rat] : ( plus_plus_rat @ I3 @ one_one_rat )
% 0.30/0.61            @ N2
% 0.30/0.61            @ zero_zero_rat ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_code
% 0.30/0.61  thf(fact_7364_pochhammer__code,axiom,
% 0.30/0.61      ( comm_s8582702949713902594nteger
% 0.30/0.61      = ( ^ [A3: code_integer,N2: nat] :
% 0.30/0.61            ( if_Code_integer @ ( N2 = zero_zero_nat ) @ one_one_Code_integer
% 0.30/0.61            @ ( set_fo1084959871951514735nteger
% 0.30/0.61              @ ^ [O: nat] : ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A3 @ ( semiri4939895301339042750nteger @ O ) ) )
% 0.30/0.61              @ zero_zero_nat
% 0.30/0.61              @ ( minus_minus_nat @ N2 @ one_one_nat )
% 0.30/0.61              @ one_one_Code_integer ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_code
% 0.30/0.61  thf(fact_7365_pochhammer__code,axiom,
% 0.30/0.61      ( comm_s4660882817536571857er_int
% 0.30/0.61      = ( ^ [A3: int,N2: nat] :
% 0.30/0.61            ( if_int @ ( N2 = zero_zero_nat ) @ one_one_int
% 0.30/0.61            @ ( set_fo2581907887559384638at_int
% 0.30/0.61              @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ O ) ) )
% 0.30/0.61              @ zero_zero_nat
% 0.30/0.61              @ ( minus_minus_nat @ N2 @ one_one_nat )
% 0.30/0.61              @ one_one_int ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_code
% 0.30/0.61  thf(fact_7366_pochhammer__code,axiom,
% 0.30/0.61      ( comm_s4028243227959126397er_rat
% 0.30/0.61      = ( ^ [A3: rat,N2: nat] :
% 0.30/0.61            ( if_rat @ ( N2 = zero_zero_nat ) @ one_one_rat
% 0.30/0.61            @ ( set_fo1949268297981939178at_rat
% 0.30/0.61              @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ O ) ) )
% 0.30/0.61              @ zero_zero_nat
% 0.30/0.61              @ ( minus_minus_nat @ N2 @ one_one_nat )
% 0.30/0.61              @ one_one_rat ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_code
% 0.30/0.61  thf(fact_7367_pochhammer__code,axiom,
% 0.30/0.61      ( comm_s4663373288045622133er_nat
% 0.30/0.61      = ( ^ [A3: nat,N2: nat] :
% 0.30/0.61            ( if_nat @ ( N2 = zero_zero_nat ) @ one_one_nat
% 0.30/0.61            @ ( set_fo2584398358068434914at_nat
% 0.30/0.61              @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 0.30/0.61              @ zero_zero_nat
% 0.30/0.61              @ ( minus_minus_nat @ N2 @ one_one_nat )
% 0.30/0.61              @ one_one_nat ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_code
% 0.30/0.61  thf(fact_7368_sum__gp0,axiom,
% 0.30/0.61      ! [X: rat,N: nat] :
% 0.30/0.61        ( ( ( X = one_one_rat )
% 0.30/0.61         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.61            = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 0.30/0.61        & ( ( X != one_one_rat )
% 0.30/0.61         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.61            = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_gp0
% 0.30/0.61  thf(fact_7369_gchoose__row__sum__weighted,axiom,
% 0.30/0.61      ! [R3: rat,M: nat] :
% 0.30/0.61        ( ( groups2906978787729119204at_rat
% 0.30/0.61          @ ^ [K4: nat] : ( times_times_rat @ ( gbinomial_rat @ R3 @ K4 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K4 ) ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 0.30/0.61        = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R3 @ ( suc @ M ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gchoose_row_sum_weighted
% 0.30/0.61  thf(fact_7370_case__nat__add__eq__if,axiom,
% 0.30/0.61      ! [A: $o,F2: nat > $o,V: num,N: nat] :
% 0.30/0.61        ( ( case_nat_o @ A @ F2 @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 0.30/0.61        = ( F2 @ ( plus_plus_nat @ ( pred_numeral @ V ) @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % case_nat_add_eq_if
% 0.30/0.61  thf(fact_7371_case__nat__add__eq__if,axiom,
% 0.30/0.61      ! [A: nat,F2: nat > nat,V: num,N: nat] :
% 0.30/0.61        ( ( case_nat_nat @ A @ F2 @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 0.30/0.61        = ( F2 @ ( plus_plus_nat @ ( pred_numeral @ V ) @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % case_nat_add_eq_if
% 0.30/0.61  thf(fact_7372_case__nat__add__eq__if,axiom,
% 0.30/0.61      ! [A: option_num,F2: nat > option_num,V: num,N: nat] :
% 0.30/0.61        ( ( case_nat_option_num @ A @ F2 @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 0.30/0.61        = ( F2 @ ( plus_plus_nat @ ( pred_numeral @ V ) @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % case_nat_add_eq_if
% 0.30/0.61  thf(fact_7373_gbinomial__0_I1_J,axiom,
% 0.30/0.61      ! [A: code_integer] :
% 0.30/0.61        ( ( gbinom8545251970709558553nteger @ A @ zero_zero_nat )
% 0.30/0.61        = one_one_Code_integer ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_0(1)
% 0.30/0.61  thf(fact_7374_gbinomial__0_I1_J,axiom,
% 0.30/0.61      ! [A: rat] :
% 0.30/0.61        ( ( gbinomial_rat @ A @ zero_zero_nat )
% 0.30/0.61        = one_one_rat ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_0(1)
% 0.30/0.61  thf(fact_7375_gbinomial__0_I1_J,axiom,
% 0.30/0.61      ! [A: nat] :
% 0.30/0.61        ( ( gbinomial_nat @ A @ zero_zero_nat )
% 0.30/0.61        = one_one_nat ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_0(1)
% 0.30/0.61  thf(fact_7376_gbinomial__0_I1_J,axiom,
% 0.30/0.61      ! [A: int] :
% 0.30/0.61        ( ( gbinomial_int @ A @ zero_zero_nat )
% 0.30/0.61        = one_one_int ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_0(1)
% 0.30/0.61  thf(fact_7377_pochhammer__0,axiom,
% 0.30/0.61      ! [A: code_integer] :
% 0.30/0.61        ( ( comm_s8582702949713902594nteger @ A @ zero_zero_nat )
% 0.30/0.61        = one_one_Code_integer ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_0
% 0.30/0.61  thf(fact_7378_pochhammer__0,axiom,
% 0.30/0.61      ! [A: rat] :
% 0.30/0.61        ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 0.30/0.61        = one_one_rat ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_0
% 0.30/0.61  thf(fact_7379_pochhammer__0,axiom,
% 0.30/0.61      ! [A: nat] :
% 0.30/0.61        ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 0.30/0.61        = one_one_nat ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_0
% 0.30/0.61  thf(fact_7380_pochhammer__0,axiom,
% 0.30/0.61      ! [A: int] :
% 0.30/0.61        ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 0.30/0.61        = one_one_int ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_0
% 0.30/0.61  thf(fact_7381_case__nat__numeral,axiom,
% 0.30/0.61      ! [A: $o,F2: nat > $o,V: num] :
% 0.30/0.61        ( ( case_nat_o @ A @ F2 @ ( numeral_numeral_nat @ V ) )
% 0.30/0.61        = ( F2 @ ( pred_numeral @ V ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % case_nat_numeral
% 0.30/0.61  thf(fact_7382_case__nat__numeral,axiom,
% 0.30/0.61      ! [A: nat,F2: nat > nat,V: num] :
% 0.30/0.61        ( ( case_nat_nat @ A @ F2 @ ( numeral_numeral_nat @ V ) )
% 0.30/0.61        = ( F2 @ ( pred_numeral @ V ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % case_nat_numeral
% 0.30/0.61  thf(fact_7383_case__nat__numeral,axiom,
% 0.30/0.61      ! [A: option_num,F2: nat > option_num,V: num] :
% 0.30/0.61        ( ( case_nat_option_num @ A @ F2 @ ( numeral_numeral_nat @ V ) )
% 0.30/0.61        = ( F2 @ ( pred_numeral @ V ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % case_nat_numeral
% 0.30/0.61  thf(fact_7384_atMost__0,axiom,
% 0.30/0.61      ( ( set_ord_atMost_nat @ zero_zero_nat )
% 0.30/0.61      = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % atMost_0
% 0.30/0.61  thf(fact_7385_nat_Ocase__distrib,axiom,
% 0.30/0.61      ! [H3: $o > $o,F1: $o,F22: nat > $o,Nat: nat] :
% 0.30/0.61        ( ( H3 @ ( case_nat_o @ F1 @ F22 @ Nat ) )
% 0.30/0.61        = ( case_nat_o @ ( H3 @ F1 )
% 0.30/0.61          @ ^ [X3: nat] : ( H3 @ ( F22 @ X3 ) )
% 0.30/0.61          @ Nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % nat.case_distrib
% 0.30/0.61  thf(fact_7386_nat_Ocase__distrib,axiom,
% 0.30/0.61      ! [H3: $o > nat,F1: $o,F22: nat > $o,Nat: nat] :
% 0.30/0.61        ( ( H3 @ ( case_nat_o @ F1 @ F22 @ Nat ) )
% 0.30/0.61        = ( case_nat_nat @ ( H3 @ F1 )
% 0.30/0.61          @ ^ [X3: nat] : ( H3 @ ( F22 @ X3 ) )
% 0.30/0.61          @ Nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % nat.case_distrib
% 0.30/0.61  thf(fact_7387_nat_Ocase__distrib,axiom,
% 0.30/0.61      ! [H3: $o > option_num,F1: $o,F22: nat > $o,Nat: nat] :
% 0.30/0.61        ( ( H3 @ ( case_nat_o @ F1 @ F22 @ Nat ) )
% 0.30/0.61        = ( case_nat_option_num @ ( H3 @ F1 )
% 0.30/0.61          @ ^ [X3: nat] : ( H3 @ ( F22 @ X3 ) )
% 0.30/0.61          @ Nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % nat.case_distrib
% 0.30/0.61  thf(fact_7388_nat_Ocase__distrib,axiom,
% 0.30/0.61      ! [H3: nat > $o,F1: nat,F22: nat > nat,Nat: nat] :
% 0.30/0.61        ( ( H3 @ ( case_nat_nat @ F1 @ F22 @ Nat ) )
% 0.30/0.61        = ( case_nat_o @ ( H3 @ F1 )
% 0.30/0.61          @ ^ [X3: nat] : ( H3 @ ( F22 @ X3 ) )
% 0.30/0.61          @ Nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % nat.case_distrib
% 0.30/0.61  thf(fact_7389_nat_Ocase__distrib,axiom,
% 0.30/0.61      ! [H3: nat > nat,F1: nat,F22: nat > nat,Nat: nat] :
% 0.30/0.61        ( ( H3 @ ( case_nat_nat @ F1 @ F22 @ Nat ) )
% 0.30/0.61        = ( case_nat_nat @ ( H3 @ F1 )
% 0.30/0.61          @ ^ [X3: nat] : ( H3 @ ( F22 @ X3 ) )
% 0.30/0.61          @ Nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % nat.case_distrib
% 0.30/0.61  thf(fact_7390_nat_Ocase__distrib,axiom,
% 0.30/0.61      ! [H3: nat > option_num,F1: nat,F22: nat > nat,Nat: nat] :
% 0.30/0.61        ( ( H3 @ ( case_nat_nat @ F1 @ F22 @ Nat ) )
% 0.30/0.61        = ( case_nat_option_num @ ( H3 @ F1 )
% 0.30/0.61          @ ^ [X3: nat] : ( H3 @ ( F22 @ X3 ) )
% 0.30/0.61          @ Nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % nat.case_distrib
% 0.30/0.61  thf(fact_7391_nat_Ocase__distrib,axiom,
% 0.30/0.61      ! [H3: option_num > $o,F1: option_num,F22: nat > option_num,Nat: nat] :
% 0.30/0.61        ( ( H3 @ ( case_nat_option_num @ F1 @ F22 @ Nat ) )
% 0.30/0.61        = ( case_nat_o @ ( H3 @ F1 )
% 0.30/0.61          @ ^ [X3: nat] : ( H3 @ ( F22 @ X3 ) )
% 0.30/0.61          @ Nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % nat.case_distrib
% 0.30/0.61  thf(fact_7392_nat_Ocase__distrib,axiom,
% 0.30/0.61      ! [H3: option_num > nat,F1: option_num,F22: nat > option_num,Nat: nat] :
% 0.30/0.61        ( ( H3 @ ( case_nat_option_num @ F1 @ F22 @ Nat ) )
% 0.30/0.61        = ( case_nat_nat @ ( H3 @ F1 )
% 0.30/0.61          @ ^ [X3: nat] : ( H3 @ ( F22 @ X3 ) )
% 0.30/0.61          @ Nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % nat.case_distrib
% 0.30/0.61  thf(fact_7393_nat_Ocase__distrib,axiom,
% 0.30/0.61      ! [H3: option_num > option_num,F1: option_num,F22: nat > option_num,Nat: nat] :
% 0.30/0.61        ( ( H3 @ ( case_nat_option_num @ F1 @ F22 @ Nat ) )
% 0.30/0.61        = ( case_nat_option_num @ ( H3 @ F1 )
% 0.30/0.61          @ ^ [X3: nat] : ( H3 @ ( F22 @ X3 ) )
% 0.30/0.61          @ Nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % nat.case_distrib
% 0.30/0.61  thf(fact_7394_not__empty__eq__Iic__eq__empty,axiom,
% 0.30/0.61      ! [H3: $o] :
% 0.30/0.61        ( bot_bot_set_o
% 0.30/0.61       != ( set_ord_atMost_o @ H3 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % not_empty_eq_Iic_eq_empty
% 0.30/0.61  thf(fact_7395_not__empty__eq__Iic__eq__empty,axiom,
% 0.30/0.61      ! [H3: int] :
% 0.30/0.61        ( bot_bot_set_int
% 0.30/0.61       != ( set_ord_atMost_int @ H3 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % not_empty_eq_Iic_eq_empty
% 0.30/0.61  thf(fact_7396_not__empty__eq__Iic__eq__empty,axiom,
% 0.30/0.61      ! [H3: nat] :
% 0.30/0.61        ( bot_bot_set_nat
% 0.30/0.61       != ( set_ord_atMost_nat @ H3 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % not_empty_eq_Iic_eq_empty
% 0.30/0.61  thf(fact_7397_not__UNIV__eq__Iic,axiom,
% 0.30/0.61      ! [H4: rat] :
% 0.30/0.61        ( top_top_set_rat
% 0.30/0.61       != ( set_ord_atMost_rat @ H4 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % not_UNIV_eq_Iic
% 0.30/0.61  thf(fact_7398_not__UNIV__eq__Iic,axiom,
% 0.30/0.61      ! [H4: int] :
% 0.30/0.61        ( top_top_set_int
% 0.30/0.61       != ( set_ord_atMost_int @ H4 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % not_UNIV_eq_Iic
% 0.30/0.61  thf(fact_7399_not__UNIV__eq__Iic,axiom,
% 0.30/0.61      ! [H4: nat] :
% 0.30/0.61        ( top_top_set_nat
% 0.30/0.61       != ( set_ord_atMost_nat @ H4 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % not_UNIV_eq_Iic
% 0.30/0.61  thf(fact_7400_atMost__def,axiom,
% 0.30/0.61      ( set_or2459421552957432928nt_int
% 0.30/0.61      = ( ^ [U2: set_Pr958786334691620121nt_int] :
% 0.30/0.61            ( collec5210948495886036740nt_int
% 0.30/0.61            @ ^ [X3: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ X3 @ U2 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % atMost_def
% 0.30/0.61  thf(fact_7401_atMost__def,axiom,
% 0.30/0.61      ( set_or1537382583742010260_nat_o
% 0.30/0.61      = ( ^ [U2: produc3658429121746597890et_nat > $o] :
% 0.30/0.61            ( collec939566748876313656_nat_o
% 0.30/0.61            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( ord_le729326519192465773_nat_o @ X3 @ U2 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % atMost_def
% 0.30/0.61  thf(fact_7402_atMost__def,axiom,
% 0.30/0.61      ( set_or9144418160755794905er_nat
% 0.30/0.61      = ( ^ [U2: filter_nat] :
% 0.30/0.61            ( collect_filter_nat
% 0.30/0.61            @ ^ [X3: filter_nat] : ( ord_le2510731241096832064er_nat @ X3 @ U2 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % atMost_def
% 0.30/0.61  thf(fact_7403_atMost__def,axiom,
% 0.30/0.61      ( set_or4236626031148496127et_nat
% 0.30/0.61      = ( ^ [U2: set_nat] :
% 0.30/0.61            ( collect_set_nat
% 0.30/0.61            @ ^ [X3: set_nat] : ( ord_less_eq_set_nat @ X3 @ U2 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % atMost_def
% 0.30/0.61  thf(fact_7404_atMost__def,axiom,
% 0.30/0.61      ( set_ord_atMost_rat
% 0.30/0.61      = ( ^ [U2: rat] :
% 0.30/0.61            ( collect_rat
% 0.30/0.61            @ ^ [X3: rat] : ( ord_less_eq_rat @ X3 @ U2 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % atMost_def
% 0.30/0.61  thf(fact_7405_atMost__def,axiom,
% 0.30/0.61      ( set_ord_atMost_int
% 0.30/0.61      = ( ^ [U2: int] :
% 0.30/0.61            ( collect_int
% 0.30/0.61            @ ^ [X3: int] : ( ord_less_eq_int @ X3 @ U2 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % atMost_def
% 0.30/0.61  thf(fact_7406_atMost__def,axiom,
% 0.30/0.61      ( set_ord_atMost_nat
% 0.30/0.61      = ( ^ [U2: nat] :
% 0.30/0.61            ( collect_nat
% 0.30/0.61            @ ^ [X3: nat] : ( ord_less_eq_nat @ X3 @ U2 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % atMost_def
% 0.30/0.61  thf(fact_7407_gbinomial__parallel__sum,axiom,
% 0.30/0.61      ! [A: rat,N: nat] :
% 0.30/0.61        ( ( groups2906978787729119204at_rat
% 0.30/0.61          @ ^ [K4: nat] : ( gbinomial_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K4 ) ) @ K4 )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.61        = ( gbinomial_rat @ ( plus_plus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ N ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_parallel_sum
% 0.30/0.61  thf(fact_7408_gbinomial__Suc__Suc,axiom,
% 0.30/0.61      ! [A: rat,K: nat] :
% 0.30/0.61        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 0.30/0.61        = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_Suc_Suc
% 0.30/0.61  thf(fact_7409_nat_Odisc__eq__case_I2_J,axiom,
% 0.30/0.61      ! [Nat: nat] :
% 0.30/0.61        ( ( Nat != zero_zero_nat )
% 0.30/0.61        = ( case_nat_o @ $false
% 0.30/0.61          @ ^ [Uu: nat] : $true
% 0.30/0.61          @ Nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % nat.disc_eq_case(2)
% 0.30/0.61  thf(fact_7410_nat_Odisc__eq__case_I1_J,axiom,
% 0.30/0.61      ! [Nat: nat] :
% 0.30/0.61        ( ( Nat = zero_zero_nat )
% 0.30/0.61        = ( case_nat_o @ $true
% 0.30/0.61          @ ^ [Uu: nat] : $false
% 0.30/0.61          @ Nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % nat.disc_eq_case(1)
% 0.30/0.61  thf(fact_7411_not__UNIV__le__Iic,axiom,
% 0.30/0.61      ! [H3: rat] :
% 0.30/0.61        ~ ( ord_less_eq_set_rat @ top_top_set_rat @ ( set_ord_atMost_rat @ H3 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % not_UNIV_le_Iic
% 0.30/0.61  thf(fact_7412_not__UNIV__le__Iic,axiom,
% 0.30/0.61      ! [H3: int] :
% 0.30/0.61        ~ ( ord_less_eq_set_int @ top_top_set_int @ ( set_ord_atMost_int @ H3 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % not_UNIV_le_Iic
% 0.30/0.61  thf(fact_7413_not__UNIV__le__Iic,axiom,
% 0.30/0.61      ! [H3: nat] :
% 0.30/0.61        ~ ( ord_less_eq_set_nat @ top_top_set_nat @ ( set_ord_atMost_nat @ H3 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % not_UNIV_le_Iic
% 0.30/0.61  thf(fact_7414_atMost__eq__UNIV__iff,axiom,
% 0.30/0.61      ! [X: set_list_nat] :
% 0.30/0.61        ( ( ( set_or2492388921469580815st_nat @ X )
% 0.30/0.61          = top_to1619013496918823676st_nat )
% 0.30/0.61        = ( X = top_top_set_list_nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % atMost_eq_UNIV_iff
% 0.30/0.61  thf(fact_7415_atMost__eq__UNIV__iff,axiom,
% 0.30/0.61      ! [X: set_o] :
% 0.30/0.61        ( ( ( set_ord_atMost_set_o @ X )
% 0.30/0.61          = top_top_set_set_o )
% 0.30/0.61        = ( X = top_top_set_o ) ) ).
% 0.30/0.61  
% 0.30/0.61  % atMost_eq_UNIV_iff
% 0.30/0.61  thf(fact_7416_atMost__eq__UNIV__iff,axiom,
% 0.30/0.61      ! [X: set_rat] :
% 0.30/0.61        ( ( ( set_or728397472755099399et_rat @ X )
% 0.30/0.61          = top_top_set_set_rat )
% 0.30/0.61        = ( X = top_top_set_rat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % atMost_eq_UNIV_iff
% 0.30/0.61  thf(fact_7417_atMost__eq__UNIV__iff,axiom,
% 0.30/0.61      ! [X: set_nat] :
% 0.30/0.61        ( ( ( set_or4236626031148496127et_nat @ X )
% 0.30/0.61          = top_top_set_set_nat )
% 0.30/0.61        = ( X = top_top_set_nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % atMost_eq_UNIV_iff
% 0.30/0.61  thf(fact_7418_atMost__eq__UNIV__iff,axiom,
% 0.30/0.61      ! [X: set_int] :
% 0.30/0.61        ( ( ( set_or58775011639299419et_int @ X )
% 0.30/0.61          = top_top_set_set_int )
% 0.30/0.61        = ( X = top_top_set_int ) ) ).
% 0.30/0.61  
% 0.30/0.61  % atMost_eq_UNIV_iff
% 0.30/0.61  thf(fact_7419_atMost__eq__UNIV__iff,axiom,
% 0.30/0.61      ! [X: $o] :
% 0.30/0.61        ( ( ( set_ord_atMost_o @ X )
% 0.30/0.61          = top_top_set_o )
% 0.30/0.61        = ( X = top_top_o ) ) ).
% 0.30/0.61  
% 0.30/0.61  % atMost_eq_UNIV_iff
% 0.30/0.61  thf(fact_7420_gbinomial__sum__lower__neg,axiom,
% 0.30/0.61      ! [A: rat,M: nat] :
% 0.30/0.61        ( ( groups2906978787729119204at_rat
% 0.30/0.61          @ ^ [K4: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K4 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K4 ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ M ) )
% 0.30/0.61        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_sum_lower_neg
% 0.30/0.61  thf(fact_7421_gbinomial__addition__formula,axiom,
% 0.30/0.61      ! [A: rat,K: nat] :
% 0.30/0.61        ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 0.30/0.61        = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_addition_formula
% 0.30/0.61  thf(fact_7422_gbinomial__absorb__comp,axiom,
% 0.30/0.61      ! [A: rat,K: nat] :
% 0.30/0.61        ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 0.30/0.61        = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_absorb_comp
% 0.30/0.61  thf(fact_7423_gbinomial__mult__1,axiom,
% 0.30/0.61      ! [A: rat,K: nat] :
% 0.30/0.61        ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 0.30/0.61        = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_mult_1
% 0.30/0.61  thf(fact_7424_gbinomial__mult__1_H,axiom,
% 0.30/0.61      ! [A: rat,K: nat] :
% 0.30/0.61        ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 0.30/0.61        = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_mult_1'
% 0.30/0.61  thf(fact_7425_gbinomial__partial__sum__poly,axiom,
% 0.30/0.61      ! [M: nat,A: rat,X: rat,Y: rat] :
% 0.30/0.61        ( ( groups2906978787729119204at_rat
% 0.30/0.61          @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K4 ) @ ( power_power_rat @ X @ K4 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M @ K4 ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ M ) )
% 0.30/0.61        = ( groups2906978787729119204at_rat
% 0.30/0.61          @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K4 ) @ ( power_power_rat @ ( uminus_uminus_rat @ X ) @ K4 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_nat @ M @ K4 ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_partial_sum_poly
% 0.30/0.61  thf(fact_7426_pochhammer__0__left,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( ( N = zero_zero_nat )
% 0.30/0.61         => ( ( comm_s8582702949713902594nteger @ zero_z3403309356797280102nteger @ N )
% 0.30/0.61            = one_one_Code_integer ) )
% 0.30/0.61        & ( ( N != zero_zero_nat )
% 0.30/0.61         => ( ( comm_s8582702949713902594nteger @ zero_z3403309356797280102nteger @ N )
% 0.30/0.61            = zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_0_left
% 0.30/0.61  thf(fact_7427_pochhammer__0__left,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( ( N = zero_zero_nat )
% 0.30/0.61         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 0.30/0.61            = one_one_rat ) )
% 0.30/0.61        & ( ( N != zero_zero_nat )
% 0.30/0.61         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 0.30/0.61            = zero_zero_rat ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_0_left
% 0.30/0.61  thf(fact_7428_pochhammer__0__left,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( ( N = zero_zero_nat )
% 0.30/0.61         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 0.30/0.61            = one_one_nat ) )
% 0.30/0.61        & ( ( N != zero_zero_nat )
% 0.30/0.61         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 0.30/0.61            = zero_zero_nat ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_0_left
% 0.30/0.61  thf(fact_7429_pochhammer__0__left,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( ( N = zero_zero_nat )
% 0.30/0.61         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 0.30/0.61            = one_one_int ) )
% 0.30/0.61        & ( ( N != zero_zero_nat )
% 0.30/0.61         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 0.30/0.61            = zero_zero_int ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_0_left
% 0.30/0.61  thf(fact_7430_gbinomial__partial__sum__poly__xpos,axiom,
% 0.30/0.61      ! [M: nat,A: rat,X: rat,Y: rat] :
% 0.30/0.61        ( ( groups2906978787729119204at_rat
% 0.30/0.61          @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K4 ) @ ( power_power_rat @ X @ K4 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M @ K4 ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ M ) )
% 0.30/0.61        = ( groups2906978787729119204at_rat
% 0.30/0.61          @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ K4 ) @ A ) @ one_one_rat ) @ K4 ) @ ( power_power_rat @ X @ K4 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_nat @ M @ K4 ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_partial_sum_poly_xpos
% 0.30/0.61  thf(fact_7431_gbinomial__sum__nat__pow2,axiom,
% 0.30/0.61      ! [M: nat] :
% 0.30/0.61        ( ( groups2906978787729119204at_rat
% 0.30/0.61          @ ^ [K4: nat] : ( divide_divide_rat @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ K4 ) ) @ K4 ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ K4 ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ M ) )
% 0.30/0.61        = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ M ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_sum_nat_pow2
% 0.30/0.61  thf(fact_7432_Suc__times__gbinomial,axiom,
% 0.30/0.61      ! [K: nat,A: rat] :
% 0.30/0.61        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 0.30/0.61        = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % Suc_times_gbinomial
% 0.30/0.61  thf(fact_7433_gbinomial__absorption,axiom,
% 0.30/0.61      ! [K: nat,A: rat] :
% 0.30/0.61        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 0.30/0.61        = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_absorption
% 0.30/0.61  thf(fact_7434_less__eq__nat_Osimps_I2_J,axiom,
% 0.30/0.61      ! [M: nat,N: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.30/0.61        = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 0.30/0.61  
% 0.30/0.61  % less_eq_nat.simps(2)
% 0.30/0.61  thf(fact_7435_gbinomial__trinomial__revision,axiom,
% 0.30/0.61      ! [K: nat,M: nat,A: rat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ K @ M )
% 0.30/0.61       => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 0.30/0.61          = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_trinomial_revision
% 0.30/0.61  thf(fact_7436_sum_OatMost__Suc__shift,axiom,
% 0.30/0.61      ! [G2: nat > rat,N: nat] :
% 0.30/0.61        ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( plus_plus_rat @ ( G2 @ zero_zero_nat )
% 0.30/0.61          @ ( groups2906978787729119204at_rat
% 0.30/0.61            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.61            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.atMost_Suc_shift
% 0.30/0.61  thf(fact_7437_sum_OatMost__Suc__shift,axiom,
% 0.30/0.61      ! [G2: nat > int,N: nat] :
% 0.30/0.61        ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( plus_plus_int @ ( G2 @ zero_zero_nat )
% 0.30/0.61          @ ( groups3539618377306564664at_int
% 0.30/0.61            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.61            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.atMost_Suc_shift
% 0.30/0.61  thf(fact_7438_sum_OatMost__Suc__shift,axiom,
% 0.30/0.61      ! [G2: nat > nat,N: nat] :
% 0.30/0.61        ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( plus_plus_nat @ ( G2 @ zero_zero_nat )
% 0.30/0.61          @ ( groups3542108847815614940at_nat
% 0.30/0.61            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.61            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.atMost_Suc_shift
% 0.30/0.61  thf(fact_7439_sum__telescope,axiom,
% 0.30/0.61      ! [F2: nat > rat,I: nat] :
% 0.30/0.61        ( ( groups2906978787729119204at_rat
% 0.30/0.61          @ ^ [I3: nat] : ( minus_minus_rat @ ( F2 @ I3 ) @ ( F2 @ ( suc @ I3 ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ I ) )
% 0.30/0.61        = ( minus_minus_rat @ ( F2 @ zero_zero_nat ) @ ( F2 @ ( suc @ I ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_telescope
% 0.30/0.61  thf(fact_7440_sum__telescope,axiom,
% 0.30/0.61      ! [F2: nat > int,I: nat] :
% 0.30/0.61        ( ( groups3539618377306564664at_int
% 0.30/0.61          @ ^ [I3: nat] : ( minus_minus_int @ ( F2 @ I3 ) @ ( F2 @ ( suc @ I3 ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ I ) )
% 0.30/0.61        = ( minus_minus_int @ ( F2 @ zero_zero_nat ) @ ( F2 @ ( suc @ I ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_telescope
% 0.30/0.61  thf(fact_7441_pochhammer__rec,axiom,
% 0.30/0.61      ! [A: code_integer,N: nat] :
% 0.30/0.61        ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N ) )
% 0.30/0.61        = ( times_3573771949741848930nteger @ A @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_rec
% 0.30/0.61  thf(fact_7442_pochhammer__rec,axiom,
% 0.30/0.61      ! [A: rat,N: nat] :
% 0.30/0.61        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 0.30/0.61        = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_rec
% 0.30/0.61  thf(fact_7443_pochhammer__rec,axiom,
% 0.30/0.61      ! [A: nat,N: nat] :
% 0.30/0.61        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 0.30/0.61        = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_rec
% 0.30/0.61  thf(fact_7444_pochhammer__rec,axiom,
% 0.30/0.61      ! [A: int,N: nat] :
% 0.30/0.61        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 0.30/0.61        = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_rec
% 0.30/0.61  thf(fact_7445_pochhammer__Suc,axiom,
% 0.30/0.61      ! [A: code_integer,N: nat] :
% 0.30/0.61        ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N ) )
% 0.30/0.61        = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ A @ N ) @ ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_Suc
% 0.30/0.61  thf(fact_7446_pochhammer__Suc,axiom,
% 0.30/0.61      ! [A: int,N: nat] :
% 0.30/0.61        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 0.30/0.61        = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_Suc
% 0.30/0.61  thf(fact_7447_pochhammer__Suc,axiom,
% 0.30/0.61      ! [A: nat,N: nat] :
% 0.30/0.61        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 0.30/0.61        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_Suc
% 0.30/0.61  thf(fact_7448_pochhammer__Suc,axiom,
% 0.30/0.61      ! [A: rat,N: nat] :
% 0.30/0.61        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 0.30/0.61        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_Suc
% 0.30/0.61  thf(fact_7449_pochhammer__rec_H,axiom,
% 0.30/0.61      ! [Z: code_integer,N: nat] :
% 0.30/0.61        ( ( comm_s8582702949713902594nteger @ Z @ ( suc @ N ) )
% 0.30/0.61        = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ N ) ) @ ( comm_s8582702949713902594nteger @ Z @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_rec'
% 0.30/0.61  thf(fact_7450_pochhammer__rec_H,axiom,
% 0.30/0.61      ! [Z: int,N: nat] :
% 0.30/0.61        ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N ) )
% 0.30/0.61        = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_rec'
% 0.30/0.61  thf(fact_7451_pochhammer__rec_H,axiom,
% 0.30/0.61      ! [Z: nat,N: nat] :
% 0.30/0.61        ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N ) )
% 0.30/0.61        = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_rec'
% 0.30/0.61  thf(fact_7452_pochhammer__rec_H,axiom,
% 0.30/0.61      ! [Z: rat,N: nat] :
% 0.30/0.61        ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) )
% 0.30/0.61        = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_rec'
% 0.30/0.61  thf(fact_7453_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.30/0.61      ! [N: nat,K: nat] :
% 0.30/0.61        ( ( ord_less_nat @ N @ K )
% 0.30/0.61       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 0.30/0.61          = zero_z3403309356797280102nteger ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_of_nat_eq_0_lemma
% 0.30/0.61  thf(fact_7454_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.30/0.61      ! [N: nat,K: nat] :
% 0.30/0.61        ( ( ord_less_nat @ N @ K )
% 0.30/0.61       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 0.30/0.61          = zero_zero_int ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_of_nat_eq_0_lemma
% 0.30/0.61  thf(fact_7455_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.30/0.61      ! [N: nat,K: nat] :
% 0.30/0.61        ( ( ord_less_nat @ N @ K )
% 0.30/0.61       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 0.30/0.61          = zero_zero_rat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_of_nat_eq_0_lemma
% 0.30/0.61  thf(fact_7456_pochhammer__of__nat__eq__0__iff,axiom,
% 0.30/0.61      ! [N: nat,K: nat] :
% 0.30/0.61        ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 0.30/0.61          = zero_z3403309356797280102nteger )
% 0.30/0.61        = ( ord_less_nat @ N @ K ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_of_nat_eq_0_iff
% 0.30/0.61  thf(fact_7457_pochhammer__of__nat__eq__0__iff,axiom,
% 0.30/0.61      ! [N: nat,K: nat] :
% 0.30/0.61        ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 0.30/0.61          = zero_zero_int )
% 0.30/0.61        = ( ord_less_nat @ N @ K ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_of_nat_eq_0_iff
% 0.30/0.61  thf(fact_7458_pochhammer__of__nat__eq__0__iff,axiom,
% 0.30/0.61      ! [N: nat,K: nat] :
% 0.30/0.61        ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 0.30/0.61          = zero_zero_rat )
% 0.30/0.61        = ( ord_less_nat @ N @ K ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_of_nat_eq_0_iff
% 0.30/0.61  thf(fact_7459_pochhammer__eq__0__iff,axiom,
% 0.30/0.61      ! [A: rat,N: nat] :
% 0.30/0.61        ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 0.30/0.61          = zero_zero_rat )
% 0.30/0.61        = ( ? [K4: nat] :
% 0.30/0.61              ( ( ord_less_nat @ K4 @ N )
% 0.30/0.61              & ( A
% 0.30/0.61                = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K4 ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_eq_0_iff
% 0.30/0.61  thf(fact_7460_gbinomial__rec,axiom,
% 0.30/0.61      ! [A: rat,K: nat] :
% 0.30/0.61        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 0.30/0.61        = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_rec
% 0.30/0.61  thf(fact_7461_gbinomial__factors,axiom,
% 0.30/0.61      ! [A: rat,K: nat] :
% 0.30/0.61        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 0.30/0.61        = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_factors
% 0.30/0.61  thf(fact_7462_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.30/0.61      ! [K: nat,N: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.61       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 0.30/0.61         != zero_z3403309356797280102nteger ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_of_nat_eq_0_lemma'
% 0.30/0.61  thf(fact_7463_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.30/0.61      ! [K: nat,N: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.61       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 0.30/0.61         != zero_zero_int ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_of_nat_eq_0_lemma'
% 0.30/0.61  thf(fact_7464_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.30/0.61      ! [K: nat,N: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.61       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 0.30/0.61         != zero_zero_rat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_of_nat_eq_0_lemma'
% 0.30/0.61  thf(fact_7465_pochhammer__product_H,axiom,
% 0.30/0.61      ! [Z: code_integer,N: nat,M: nat] :
% 0.30/0.61        ( ( comm_s8582702949713902594nteger @ Z @ ( plus_plus_nat @ N @ M ) )
% 0.30/0.61        = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z @ N ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ N ) ) @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_product'
% 0.30/0.61  thf(fact_7466_pochhammer__product_H,axiom,
% 0.30/0.61      ! [Z: int,N: nat,M: nat] :
% 0.30/0.61        ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N @ M ) )
% 0.30/0.61        = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_product'
% 0.30/0.61  thf(fact_7467_pochhammer__product_H,axiom,
% 0.30/0.61      ! [Z: nat,N: nat,M: nat] :
% 0.30/0.61        ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N @ M ) )
% 0.30/0.61        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_product'
% 0.30/0.61  thf(fact_7468_pochhammer__product_H,axiom,
% 0.30/0.61      ! [Z: rat,N: nat,M: nat] :
% 0.30/0.61        ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N @ M ) )
% 0.30/0.61        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_product'
% 0.30/0.61  thf(fact_7469_gbinomial__negated__upper,axiom,
% 0.30/0.61      ( gbinomial_rat
% 0.30/0.61      = ( ^ [A3: rat,K4: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K4 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K4 ) @ A3 ) @ one_one_rat ) @ K4 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_negated_upper
% 0.30/0.61  thf(fact_7470_gbinomial__index__swap,axiom,
% 0.30/0.61      ! [K: nat,N: nat] :
% 0.30/0.61        ( ( 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 ) )
% 0.30/0.61        = ( 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 ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_index_swap
% 0.30/0.61  thf(fact_7471_gbinomial__r__part__sum,axiom,
% 0.30/0.61      ! [M: nat] :
% 0.30/0.61        ( ( groups2906978787729119204at_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M ) ) @ one_one_rat ) ) @ ( set_ord_atMost_nat @ M ) )
% 0.30/0.61        = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_r_part_sum
% 0.30/0.61  thf(fact_7472_diff__Suc,axiom,
% 0.30/0.61      ! [M: nat,N: nat] :
% 0.30/0.61        ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 0.30/0.61        = ( case_nat_nat @ zero_zero_nat
% 0.30/0.61          @ ^ [K4: nat] : K4
% 0.30/0.61          @ ( minus_minus_nat @ M @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % diff_Suc
% 0.30/0.61  thf(fact_7473_gbinomial__partial__row__sum,axiom,
% 0.30/0.61      ! [A: rat,M: nat] :
% 0.30/0.61        ( ( groups2906978787729119204at_rat
% 0.30/0.61          @ ^ [K4: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K4 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K4 ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ M ) )
% 0.30/0.61        = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ one_one_rat ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_partial_row_sum
% 0.30/0.61  thf(fact_7474_Nitpick_Ocase__nat__unfold,axiom,
% 0.30/0.61      ( case_nat_o
% 0.30/0.61      = ( ^ [X3: $o,F: nat > $o,N2: nat] :
% 0.30/0.61            ( ( ( N2 = zero_zero_nat )
% 0.30/0.61             => X3 )
% 0.30/0.61            & ( ( N2 != zero_zero_nat )
% 0.30/0.61             => ( F @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % Nitpick.case_nat_unfold
% 0.30/0.61  thf(fact_7475_Nitpick_Ocase__nat__unfold,axiom,
% 0.30/0.61      ( case_nat_nat
% 0.30/0.61      = ( ^ [X3: nat,F: nat > nat,N2: nat] : ( if_nat @ ( N2 = zero_zero_nat ) @ X3 @ ( F @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % Nitpick.case_nat_unfold
% 0.30/0.61  thf(fact_7476_Nitpick_Ocase__nat__unfold,axiom,
% 0.30/0.61      ( case_nat_option_num
% 0.30/0.61      = ( ^ [X3: option_num,F: nat > option_num,N2: nat] : ( if_option_num @ ( N2 = zero_zero_nat ) @ X3 @ ( F @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % Nitpick.case_nat_unfold
% 0.30/0.61  thf(fact_7477_gbinomial__minus,axiom,
% 0.30/0.61      ! [A: rat,K: nat] :
% 0.30/0.61        ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 0.30/0.61        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_minus
% 0.30/0.61  thf(fact_7478_atLeast1__atMost__eq__remove0,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.30/0.61        = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % atLeast1_atMost_eq_remove0
% 0.30/0.61  thf(fact_7479_gbinomial__reduce__nat,axiom,
% 0.30/0.61      ! [K: nat,A: rat] :
% 0.30/0.61        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.30/0.61       => ( ( gbinomial_rat @ A @ K )
% 0.30/0.61          = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_reduce_nat
% 0.30/0.61  thf(fact_7480_sum_Otriangle__reindex__eq,axiom,
% 0.30/0.61      ! [G2: nat > nat > nat,N: nat] :
% 0.30/0.61        ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G2 )
% 0.30/0.61          @ ( collec3392354462482085612at_nat
% 0.30/0.61            @ ( produc6081775807080527818_nat_o
% 0.30/0.61              @ ^ [I3: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 0.30/0.61        = ( groups3542108847815614940at_nat
% 0.30/0.61          @ ^ [K4: nat] :
% 0.30/0.61              ( groups3542108847815614940at_nat
% 0.30/0.61              @ ^ [I3: nat] : ( G2 @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ K4 ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.triangle_reindex_eq
% 0.30/0.61  thf(fact_7481_pochhammer__product,axiom,
% 0.30/0.61      ! [M: nat,N: nat,Z: code_integer] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( comm_s8582702949713902594nteger @ Z @ N )
% 0.30/0.61          = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z @ M ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_product
% 0.30/0.61  thf(fact_7482_pochhammer__product,axiom,
% 0.30/0.61      ! [M: nat,N: nat,Z: int] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( comm_s4660882817536571857er_int @ Z @ N )
% 0.30/0.61          = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_product
% 0.30/0.61  thf(fact_7483_pochhammer__product,axiom,
% 0.30/0.61      ! [M: nat,N: nat,Z: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( comm_s4663373288045622133er_nat @ Z @ N )
% 0.30/0.61          = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_product
% 0.30/0.61  thf(fact_7484_pochhammer__product,axiom,
% 0.30/0.61      ! [M: nat,N: nat,Z: rat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( comm_s4028243227959126397er_rat @ Z @ N )
% 0.30/0.61          = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_product
% 0.30/0.61  thf(fact_7485_sum__gp__basic,axiom,
% 0.30/0.61      ! [X: code_integer,N: nat] :
% 0.30/0.61        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 0.30/0.61        = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ ( suc @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_gp_basic
% 0.30/0.61  thf(fact_7486_sum__gp__basic,axiom,
% 0.30/0.61      ! [X: rat,N: nat] :
% 0.30/0.61        ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 0.30/0.61        = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_gp_basic
% 0.30/0.61  thf(fact_7487_sum__gp__basic,axiom,
% 0.30/0.61      ! [X: int,N: nat] :
% 0.30/0.61        ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 0.30/0.61        = ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ ( suc @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_gp_basic
% 0.30/0.61  thf(fact_7488_sum__power__shift,axiom,
% 0.30/0.61      ! [M: nat,N: nat,X: code_integer] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61          = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ M ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_power_shift
% 0.30/0.61  thf(fact_7489_sum__power__shift,axiom,
% 0.30/0.61      ! [M: nat,N: nat,X: rat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61          = ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_power_shift
% 0.30/0.61  thf(fact_7490_sum__power__shift,axiom,
% 0.30/0.61      ! [M: nat,N: nat,X: int] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61          = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_power_shift
% 0.30/0.61  thf(fact_7491_gbinomial__sum__up__index,axiom,
% 0.30/0.61      ! [K: nat,N: nat] :
% 0.30/0.61        ( ( groups2906978787729119204at_rat
% 0.30/0.61          @ ^ [J3: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J3 ) @ K )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.30/0.61        = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_sum_up_index
% 0.30/0.61  thf(fact_7492_pochhammer__absorb__comp,axiom,
% 0.30/0.61      ! [R3: code_integer,K: nat] :
% 0.30/0.61        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R3 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R3 ) @ K ) )
% 0.30/0.61        = ( times_3573771949741848930nteger @ R3 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R3 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_absorb_comp
% 0.30/0.61  thf(fact_7493_pochhammer__absorb__comp,axiom,
% 0.30/0.61      ! [R3: int,K: nat] :
% 0.30/0.61        ( ( times_times_int @ ( minus_minus_int @ R3 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R3 ) @ K ) )
% 0.30/0.61        = ( times_times_int @ R3 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R3 ) @ one_one_int ) @ K ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_absorb_comp
% 0.30/0.61  thf(fact_7494_pochhammer__absorb__comp,axiom,
% 0.30/0.61      ! [R3: rat,K: nat] :
% 0.30/0.61        ( ( times_times_rat @ ( minus_minus_rat @ R3 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R3 ) @ K ) )
% 0.30/0.61        = ( times_times_rat @ R3 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R3 ) @ one_one_rat ) @ K ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_absorb_comp
% 0.30/0.61  thf(fact_7495_gbinomial__absorption_H,axiom,
% 0.30/0.61      ! [K: nat,A: rat] :
% 0.30/0.61        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.30/0.61       => ( ( gbinomial_rat @ A @ K )
% 0.30/0.61          = ( times_times_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_absorption'
% 0.30/0.61  thf(fact_7496_sum_Oin__pairs__0,axiom,
% 0.30/0.61      ! [G2: nat > rat,N: nat] :
% 0.30/0.61        ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.30/0.61        = ( groups2906978787729119204at_rat
% 0.30/0.61          @ ^ [I3: nat] : ( plus_plus_rat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.in_pairs_0
% 0.30/0.61  thf(fact_7497_sum_Oin__pairs__0,axiom,
% 0.30/0.61      ! [G2: nat > int,N: nat] :
% 0.30/0.61        ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.30/0.61        = ( groups3539618377306564664at_int
% 0.30/0.61          @ ^ [I3: nat] : ( plus_plus_int @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.in_pairs_0
% 0.30/0.61  thf(fact_7498_sum_Oin__pairs__0,axiom,
% 0.30/0.61      ! [G2: nat > nat,N: nat] :
% 0.30/0.61        ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.30/0.61        = ( groups3542108847815614940at_nat
% 0.30/0.61          @ ^ [I3: nat] : ( plus_plus_nat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.in_pairs_0
% 0.30/0.61  thf(fact_7499_pochhammer__minus_H,axiom,
% 0.30/0.61      ! [B: code_integer,K: nat] :
% 0.30/0.61        ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 0.30/0.61        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_minus'
% 0.30/0.61  thf(fact_7500_pochhammer__minus_H,axiom,
% 0.30/0.61      ! [B: int,K: nat] :
% 0.30/0.61        ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 0.30/0.61        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_minus'
% 0.30/0.61  thf(fact_7501_pochhammer__minus_H,axiom,
% 0.30/0.61      ! [B: rat,K: nat] :
% 0.30/0.61        ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 0.30/0.61        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_minus'
% 0.30/0.61  thf(fact_7502_pochhammer__minus,axiom,
% 0.30/0.61      ! [B: code_integer,K: nat] :
% 0.30/0.61        ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 0.30/0.61        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_minus
% 0.30/0.61  thf(fact_7503_pochhammer__minus,axiom,
% 0.30/0.61      ! [B: int,K: nat] :
% 0.30/0.61        ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 0.30/0.61        = ( 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 ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_minus
% 0.30/0.61  thf(fact_7504_pochhammer__minus,axiom,
% 0.30/0.61      ! [B: rat,K: nat] :
% 0.30/0.61        ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 0.30/0.61        = ( 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 ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_minus
% 0.30/0.61  thf(fact_7505_sum_Ozero__middle,axiom,
% 0.30/0.61      ! [P4: nat,K: nat,G2: nat > code_integer,H3: nat > code_integer] :
% 0.30/0.61        ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 0.30/0.61       => ( ( ord_less_eq_nat @ K @ P4 )
% 0.30/0.61         => ( ( groups7501900531339628137nteger
% 0.30/0.61              @ ^ [J3: nat] : ( if_Code_integer @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( if_Code_integer @ ( J3 = K ) @ zero_z3403309356797280102nteger @ ( H3 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ P4 ) )
% 0.30/0.61            = ( groups7501900531339628137nteger
% 0.30/0.61              @ ^ [J3: nat] : ( if_Code_integer @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( H3 @ J3 ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.zero_middle
% 0.30/0.61  thf(fact_7506_sum_Ozero__middle,axiom,
% 0.30/0.61      ! [P4: nat,K: nat,G2: nat > multis2468970476368604999at_nat,H3: nat > multis2468970476368604999at_nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 0.30/0.61       => ( ( ord_less_eq_nat @ K @ P4 )
% 0.30/0.61         => ( ( groups6857163185585827899at_nat
% 0.30/0.61              @ ^ [J3: nat] : ( if_mul8430962117462786573at_nat @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( if_mul8430962117462786573at_nat @ ( J3 = K ) @ zero_z1048942125864253310at_nat @ ( H3 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ P4 ) )
% 0.30/0.61            = ( groups6857163185585827899at_nat
% 0.30/0.61              @ ^ [J3: nat] : ( if_mul8430962117462786573at_nat @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( H3 @ J3 ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.zero_middle
% 0.30/0.61  thf(fact_7507_sum_Ozero__middle,axiom,
% 0.30/0.61      ! [P4: nat,K: nat,G2: nat > rat,H3: nat > rat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 0.30/0.61       => ( ( ord_less_eq_nat @ K @ P4 )
% 0.30/0.61         => ( ( groups2906978787729119204at_rat
% 0.30/0.61              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( if_rat @ ( J3 = K ) @ zero_zero_rat @ ( H3 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ P4 ) )
% 0.30/0.61            = ( groups2906978787729119204at_rat
% 0.30/0.61              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( H3 @ J3 ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.zero_middle
% 0.30/0.61  thf(fact_7508_sum_Ozero__middle,axiom,
% 0.30/0.61      ! [P4: nat,K: nat,G2: nat > int,H3: nat > int] :
% 0.30/0.61        ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 0.30/0.61       => ( ( ord_less_eq_nat @ K @ P4 )
% 0.30/0.61         => ( ( groups3539618377306564664at_int
% 0.30/0.61              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( if_int @ ( J3 = K ) @ zero_zero_int @ ( H3 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ P4 ) )
% 0.30/0.61            = ( groups3539618377306564664at_int
% 0.30/0.61              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( H3 @ J3 ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.zero_middle
% 0.30/0.61  thf(fact_7509_sum_Ozero__middle,axiom,
% 0.30/0.61      ! [P4: nat,K: nat,G2: nat > nat,H3: nat > nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 0.30/0.61       => ( ( ord_less_eq_nat @ K @ P4 )
% 0.30/0.61         => ( ( groups3542108847815614940at_nat
% 0.30/0.61              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( if_nat @ ( J3 = K ) @ zero_zero_nat @ ( H3 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ P4 ) )
% 0.30/0.61            = ( groups3542108847815614940at_nat
% 0.30/0.61              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( H3 @ J3 ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.zero_middle
% 0.30/0.61  thf(fact_7510_pochhammer__times__pochhammer__half,axiom,
% 0.30/0.61      ! [Z: rat,N: nat] :
% 0.30/0.61        ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 0.30/0.61        = ( groups73079841787564623at_rat
% 0.30/0.61          @ ^ [K4: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K4 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_times_pochhammer_half
% 0.30/0.61  thf(fact_7511_choose__odd__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.61       => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 0.30/0.61            @ ( groups7501900531339628137nteger
% 0.30/0.61              @ ^ [I3: nat] :
% 0.30/0.61                  ( if_Code_integer
% 0.30/0.61                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 0.30/0.61                  @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I3 ) )
% 0.30/0.61                  @ zero_z3403309356797280102nteger )
% 0.30/0.61              @ ( set_ord_atMost_nat @ N ) ) )
% 0.30/0.61          = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_odd_sum
% 0.30/0.61  thf(fact_7512_choose__odd__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.61       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 0.30/0.61            @ ( groups3539618377306564664at_int
% 0.30/0.61              @ ^ [I3: nat] :
% 0.30/0.61                  ( if_int
% 0.30/0.61                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 0.30/0.61                  @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I3 ) )
% 0.30/0.61                  @ zero_zero_int )
% 0.30/0.61              @ ( set_ord_atMost_nat @ N ) ) )
% 0.30/0.61          = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_odd_sum
% 0.30/0.61  thf(fact_7513_choose__odd__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.61       => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 0.30/0.61            @ ( groups2906978787729119204at_rat
% 0.30/0.61              @ ^ [I3: nat] :
% 0.30/0.61                  ( if_rat
% 0.30/0.61                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 0.30/0.61                  @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I3 ) )
% 0.30/0.61                  @ zero_zero_rat )
% 0.30/0.61              @ ( set_ord_atMost_nat @ N ) ) )
% 0.30/0.61          = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_odd_sum
% 0.30/0.61  thf(fact_7514_choose__even__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.61       => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 0.30/0.61            @ ( groups7501900531339628137nteger
% 0.30/0.61              @ ^ [I3: nat] : ( if_Code_integer @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I3 ) ) @ zero_z3403309356797280102nteger )
% 0.30/0.61              @ ( set_ord_atMost_nat @ N ) ) )
% 0.30/0.61          = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_even_sum
% 0.30/0.61  thf(fact_7515_choose__even__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.61       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 0.30/0.61            @ ( groups3539618377306564664at_int
% 0.30/0.61              @ ^ [I3: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I3 ) ) @ zero_zero_int )
% 0.30/0.61              @ ( set_ord_atMost_nat @ N ) ) )
% 0.30/0.61          = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_even_sum
% 0.30/0.61  thf(fact_7516_choose__even__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.61       => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 0.30/0.61            @ ( groups2906978787729119204at_rat
% 0.30/0.61              @ ^ [I3: nat] : ( if_rat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I3 ) ) @ zero_zero_rat )
% 0.30/0.61              @ ( set_ord_atMost_nat @ N ) ) )
% 0.30/0.61          = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_even_sum
% 0.30/0.61  thf(fact_7517_gbinomial__code,axiom,
% 0.30/0.61      ( gbinomial_rat
% 0.30/0.61      = ( ^ [A3: rat,K4: nat] :
% 0.30/0.61            ( if_rat @ ( K4 = zero_zero_nat ) @ one_one_rat
% 0.30/0.61            @ ( divide_divide_rat
% 0.30/0.61              @ ( set_fo1949268297981939178at_rat
% 0.30/0.61                @ ^ [L2: nat] : ( times_times_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ L2 ) ) )
% 0.30/0.61                @ zero_zero_nat
% 0.30/0.61                @ ( minus_minus_nat @ K4 @ one_one_nat )
% 0.30/0.61                @ one_one_rat )
% 0.30/0.61              @ ( semiri773545260158071498ct_rat @ K4 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_code
% 0.30/0.61  thf(fact_7518_fact__double,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.61        = ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_double
% 0.30/0.61  thf(fact_7519_choose__alternating__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.61       => ( ( groups7501900531339628137nteger
% 0.30/0.61            @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I3 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I3 ) ) )
% 0.30/0.61            @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.61          = zero_z3403309356797280102nteger ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_alternating_sum
% 0.30/0.61  thf(fact_7520_choose__alternating__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.61       => ( ( groups3539618377306564664at_int
% 0.30/0.61            @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I3 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I3 ) ) )
% 0.30/0.61            @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.61          = zero_zero_int ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_alternating_sum
% 0.30/0.61  thf(fact_7521_choose__alternating__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.61       => ( ( groups2906978787729119204at_rat
% 0.30/0.61            @ ^ [I3: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I3 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I3 ) ) )
% 0.30/0.61            @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.61          = zero_zero_rat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_alternating_sum
% 0.30/0.61  thf(fact_7522_atMost__UNIV__triv,axiom,
% 0.30/0.61      ( ( set_or2492388921469580815st_nat @ top_top_set_list_nat )
% 0.30/0.61      = top_to1619013496918823676st_nat ) ).
% 0.30/0.61  
% 0.30/0.61  % atMost_UNIV_triv
% 0.30/0.61  thf(fact_7523_atMost__UNIV__triv,axiom,
% 0.30/0.61      ( ( set_ord_atMost_set_o @ top_top_set_o )
% 0.30/0.61      = top_top_set_set_o ) ).
% 0.30/0.61  
% 0.30/0.61  % atMost_UNIV_triv
% 0.30/0.61  thf(fact_7524_atMost__UNIV__triv,axiom,
% 0.30/0.61      ( ( set_or728397472755099399et_rat @ top_top_set_rat )
% 0.30/0.61      = top_top_set_set_rat ) ).
% 0.30/0.61  
% 0.30/0.61  % atMost_UNIV_triv
% 0.30/0.61  thf(fact_7525_atMost__UNIV__triv,axiom,
% 0.30/0.61      ( ( set_or4236626031148496127et_nat @ top_top_set_nat )
% 0.30/0.61      = top_top_set_set_nat ) ).
% 0.30/0.61  
% 0.30/0.61  % atMost_UNIV_triv
% 0.30/0.61  thf(fact_7526_atMost__UNIV__triv,axiom,
% 0.30/0.61      ( ( set_or58775011639299419et_int @ top_top_set_int )
% 0.30/0.61      = top_top_set_set_int ) ).
% 0.30/0.61  
% 0.30/0.61  % atMost_UNIV_triv
% 0.30/0.61  thf(fact_7527_binomial__n__n,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( binomial @ N @ N )
% 0.30/0.61        = one_one_nat ) ).
% 0.30/0.61  
% 0.30/0.61  % binomial_n_n
% 0.30/0.61  thf(fact_7528_prod_Oneutral__const,axiom,
% 0.30/0.61      ! [A2: set_nat] :
% 0.30/0.61        ( ( groups708209901874060359at_nat
% 0.30/0.61          @ ^ [Uu: nat] : one_one_nat
% 0.30/0.61          @ A2 )
% 0.30/0.61        = one_one_nat ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.neutral_const
% 0.30/0.61  thf(fact_7529_prod_Oneutral__const,axiom,
% 0.30/0.61      ! [A2: set_nat] :
% 0.30/0.61        ( ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [Uu: nat] : one_one_int
% 0.30/0.61          @ A2 )
% 0.30/0.61        = one_one_int ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.neutral_const
% 0.30/0.61  thf(fact_7530_prod_Oneutral__const,axiom,
% 0.30/0.61      ! [A2: set_int] :
% 0.30/0.61        ( ( groups1705073143266064639nt_int
% 0.30/0.61          @ ^ [Uu: int] : one_one_int
% 0.30/0.61          @ A2 )
% 0.30/0.61        = one_one_int ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.neutral_const
% 0.30/0.61  thf(fact_7531_of__nat__prod,axiom,
% 0.30/0.61      ! [F2: int > nat,A2: set_int] :
% 0.30/0.61        ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F2 @ A2 ) )
% 0.30/0.61        = ( groups1705073143266064639nt_int
% 0.30/0.61          @ ^ [X3: int] : ( semiri1314217659103216013at_int @ ( F2 @ X3 ) )
% 0.30/0.61          @ A2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_prod
% 0.30/0.61  thf(fact_7532_of__nat__prod,axiom,
% 0.30/0.61      ! [F2: nat > nat,A2: set_nat] :
% 0.30/0.61        ( ( semiri681578069525770553at_rat @ ( groups708209901874060359at_nat @ F2 @ A2 ) )
% 0.30/0.61        = ( groups73079841787564623at_rat
% 0.30/0.61          @ ^ [X3: nat] : ( semiri681578069525770553at_rat @ ( F2 @ X3 ) )
% 0.30/0.61          @ A2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_prod
% 0.30/0.61  thf(fact_7533_of__nat__prod,axiom,
% 0.30/0.61      ! [F2: nat > nat,A2: set_nat] :
% 0.30/0.61        ( ( semiri1316708129612266289at_nat @ ( groups708209901874060359at_nat @ F2 @ A2 ) )
% 0.30/0.61        = ( groups708209901874060359at_nat
% 0.30/0.61          @ ^ [X3: nat] : ( semiri1316708129612266289at_nat @ ( F2 @ X3 ) )
% 0.30/0.61          @ A2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_prod
% 0.30/0.61  thf(fact_7534_of__nat__prod,axiom,
% 0.30/0.61      ! [F2: nat > nat,A2: set_nat] :
% 0.30/0.61        ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F2 @ A2 ) )
% 0.30/0.61        = ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [X3: nat] : ( semiri1314217659103216013at_int @ ( F2 @ X3 ) )
% 0.30/0.61          @ A2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_nat_prod
% 0.30/0.61  thf(fact_7535_of__int__prod,axiom,
% 0.30/0.61      ! [F2: nat > int,A2: set_nat] :
% 0.30/0.61        ( ( ring_1_of_int_rat @ ( groups705719431365010083at_int @ F2 @ A2 ) )
% 0.30/0.61        = ( groups73079841787564623at_rat
% 0.30/0.61          @ ^ [X3: nat] : ( ring_1_of_int_rat @ ( F2 @ X3 ) )
% 0.30/0.61          @ A2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_int_prod
% 0.30/0.61  thf(fact_7536_of__int__prod,axiom,
% 0.30/0.61      ! [F2: nat > int,A2: set_nat] :
% 0.30/0.61        ( ( ring_1_of_int_int @ ( groups705719431365010083at_int @ F2 @ A2 ) )
% 0.30/0.61        = ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [X3: nat] : ( ring_1_of_int_int @ ( F2 @ X3 ) )
% 0.30/0.61          @ A2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_int_prod
% 0.30/0.61  thf(fact_7537_of__int__prod,axiom,
% 0.30/0.61      ! [F2: int > int,A2: set_int] :
% 0.30/0.61        ( ( ring_1_of_int_rat @ ( groups1705073143266064639nt_int @ F2 @ A2 ) )
% 0.30/0.61        = ( groups1072433553688619179nt_rat
% 0.30/0.61          @ ^ [X3: int] : ( ring_1_of_int_rat @ ( F2 @ X3 ) )
% 0.30/0.61          @ A2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_int_prod
% 0.30/0.61  thf(fact_7538_of__int__prod,axiom,
% 0.30/0.61      ! [F2: int > int,A2: set_int] :
% 0.30/0.61        ( ( ring_1_of_int_int @ ( groups1705073143266064639nt_int @ F2 @ A2 ) )
% 0.30/0.61        = ( groups1705073143266064639nt_int
% 0.30/0.61          @ ^ [X3: int] : ( ring_1_of_int_int @ ( F2 @ X3 ) )
% 0.30/0.61          @ A2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % of_int_prod
% 0.30/0.61  thf(fact_7539_prod_Oempty,axiom,
% 0.30/0.61      ! [G2: $o > code_integer] :
% 0.30/0.61        ( ( groups7694694392188491536nteger @ G2 @ bot_bot_set_o )
% 0.30/0.61        = one_one_Code_integer ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.empty
% 0.30/0.61  thf(fact_7540_prod_Oempty,axiom,
% 0.30/0.61      ! [G2: $o > assn] :
% 0.30/0.61        ( ( groups5301882518646026715o_assn @ G2 @ bot_bot_set_o )
% 0.30/0.61        = one_one_assn ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.empty
% 0.30/0.61  thf(fact_7541_prod_Oempty,axiom,
% 0.30/0.61      ! [G2: $o > rat] :
% 0.30/0.61        ( ( groups2869687844427037835_o_rat @ G2 @ bot_bot_set_o )
% 0.30/0.61        = one_one_rat ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.empty
% 0.30/0.61  thf(fact_7542_prod_Oempty,axiom,
% 0.30/0.61      ! [G2: $o > nat] :
% 0.30/0.61        ( ( groups3504817904513533571_o_nat @ G2 @ bot_bot_set_o )
% 0.30/0.61        = one_one_nat ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.empty
% 0.30/0.61  thf(fact_7543_prod_Oempty,axiom,
% 0.30/0.61      ! [G2: $o > int] :
% 0.30/0.61        ( ( groups3502327434004483295_o_int @ G2 @ bot_bot_set_o )
% 0.30/0.61        = one_one_int ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.empty
% 0.30/0.61  thf(fact_7544_prod_Oempty,axiom,
% 0.30/0.61      ! [G2: nat > code_integer] :
% 0.30/0.61        ( ( groups3455450783089532116nteger @ G2 @ bot_bot_set_nat )
% 0.30/0.61        = one_one_Code_integer ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.empty
% 0.30/0.61  thf(fact_7545_prod_Oempty,axiom,
% 0.30/0.61      ! [G2: nat > assn] :
% 0.30/0.61        ( ( groups6906906614972039071t_assn @ G2 @ bot_bot_set_nat )
% 0.30/0.61        = one_one_assn ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.empty
% 0.30/0.61  thf(fact_7546_prod_Oempty,axiom,
% 0.30/0.61      ! [G2: nat > rat] :
% 0.30/0.61        ( ( groups73079841787564623at_rat @ G2 @ bot_bot_set_nat )
% 0.30/0.61        = one_one_rat ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.empty
% 0.30/0.61  thf(fact_7547_prod_Oempty,axiom,
% 0.30/0.61      ! [G2: int > code_integer] :
% 0.30/0.61        ( ( groups3827104343326376752nteger @ G2 @ bot_bot_set_int )
% 0.30/0.61        = one_one_Code_integer ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.empty
% 0.30/0.61  thf(fact_7548_prod_Oempty,axiom,
% 0.30/0.61      ! [G2: int > assn] :
% 0.30/0.61        ( ( groups7882442080178216443t_assn @ G2 @ bot_bot_set_int )
% 0.30/0.61        = one_one_assn ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.empty
% 0.30/0.61  thf(fact_7549_fact__0,axiom,
% 0.30/0.61      ( ( semiri3624122377584611663nteger @ zero_zero_nat )
% 0.30/0.61      = one_one_Code_integer ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_0
% 0.30/0.61  thf(fact_7550_fact__0,axiom,
% 0.30/0.61      ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 0.30/0.61      = one_one_rat ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_0
% 0.30/0.61  thf(fact_7551_fact__0,axiom,
% 0.30/0.61      ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 0.30/0.61      = one_one_int ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_0
% 0.30/0.61  thf(fact_7552_fact__0,axiom,
% 0.30/0.61      ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 0.30/0.61      = one_one_nat ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_0
% 0.30/0.61  thf(fact_7553_fact__1,axiom,
% 0.30/0.61      ( ( semiri3624122377584611663nteger @ one_one_nat )
% 0.30/0.61      = one_one_Code_integer ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_1
% 0.30/0.61  thf(fact_7554_fact__1,axiom,
% 0.30/0.61      ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 0.30/0.61      = one_one_rat ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_1
% 0.30/0.61  thf(fact_7555_fact__1,axiom,
% 0.30/0.61      ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 0.30/0.61      = one_one_int ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_1
% 0.30/0.61  thf(fact_7556_fact__1,axiom,
% 0.30/0.61      ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 0.30/0.61      = one_one_nat ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_1
% 0.30/0.61  thf(fact_7557_binomial__n__0,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( binomial @ N @ zero_zero_nat )
% 0.30/0.61        = one_one_nat ) ).
% 0.30/0.61  
% 0.30/0.61  % binomial_n_0
% 0.30/0.61  thf(fact_7558_fact__Suc__0,axiom,
% 0.30/0.61      ( ( semiri3624122377584611663nteger @ ( suc @ zero_zero_nat ) )
% 0.30/0.61      = one_one_Code_integer ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_Suc_0
% 0.30/0.61  thf(fact_7559_fact__Suc__0,axiom,
% 0.30/0.61      ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 0.30/0.61      = one_one_rat ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_Suc_0
% 0.30/0.61  thf(fact_7560_fact__Suc__0,axiom,
% 0.30/0.61      ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 0.30/0.61      = one_one_int ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_Suc_0
% 0.30/0.61  thf(fact_7561_fact__Suc__0,axiom,
% 0.30/0.61      ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 0.30/0.61      = one_one_nat ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_Suc_0
% 0.30/0.61  thf(fact_7562_fact__Suc,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( semiri3624122377584611663nteger @ ( suc @ N ) )
% 0.30/0.61        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( suc @ N ) ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_Suc
% 0.30/0.61  thf(fact_7563_fact__Suc,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( semiri1406184849735516958ct_int @ ( suc @ N ) )
% 0.30/0.61        = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_Suc
% 0.30/0.61  thf(fact_7564_fact__Suc,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( semiri773545260158071498ct_rat @ ( suc @ N ) )
% 0.30/0.61        = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_Suc
% 0.30/0.61  thf(fact_7565_fact__Suc,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( semiri1408675320244567234ct_nat @ ( suc @ N ) )
% 0.30/0.61        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_Suc
% 0.30/0.61  thf(fact_7566_prod_OatMost__Suc,axiom,
% 0.30/0.61      ! [G2: nat > code_integer,N: nat] :
% 0.30/0.61        ( ( groups3455450783089532116nteger @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atMost_Suc
% 0.30/0.61  thf(fact_7567_prod_OatMost__Suc,axiom,
% 0.30/0.61      ! [G2: nat > assn,N: nat] :
% 0.30/0.61        ( ( groups6906906614972039071t_assn @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atMost_Suc
% 0.30/0.61  thf(fact_7568_prod_OatMost__Suc,axiom,
% 0.30/0.61      ! [G2: nat > rat,N: nat] :
% 0.30/0.61        ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atMost_Suc
% 0.30/0.61  thf(fact_7569_prod_OatMost__Suc,axiom,
% 0.30/0.61      ! [G2: nat > nat,N: nat] :
% 0.30/0.61        ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atMost_Suc
% 0.30/0.61  thf(fact_7570_prod_OatMost__Suc,axiom,
% 0.30/0.61      ! [G2: nat > int,N: nat] :
% 0.30/0.61        ( ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atMost_Suc
% 0.30/0.61  thf(fact_7571_prod_Ocl__ivl__Suc,axiom,
% 0.30/0.61      ! [N: nat,M: nat,G2: nat > code_integer] :
% 0.30/0.61        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.30/0.61         => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61            = one_one_Code_integer ) )
% 0.30/0.61        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.30/0.61         => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61            = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.cl_ivl_Suc
% 0.30/0.61  thf(fact_7572_prod_Ocl__ivl__Suc,axiom,
% 0.30/0.61      ! [N: nat,M: nat,G2: nat > assn] :
% 0.30/0.61        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.30/0.61         => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61            = one_one_assn ) )
% 0.30/0.61        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.30/0.61         => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61            = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.cl_ivl_Suc
% 0.30/0.61  thf(fact_7573_prod_Ocl__ivl__Suc,axiom,
% 0.30/0.61      ! [N: nat,M: nat,G2: nat > rat] :
% 0.30/0.61        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.30/0.61         => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61            = one_one_rat ) )
% 0.30/0.61        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.30/0.61         => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61            = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.cl_ivl_Suc
% 0.30/0.61  thf(fact_7574_prod_Ocl__ivl__Suc,axiom,
% 0.30/0.61      ! [N: nat,M: nat,G2: nat > nat] :
% 0.30/0.61        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.30/0.61         => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61            = one_one_nat ) )
% 0.30/0.61        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.30/0.61         => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61            = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.cl_ivl_Suc
% 0.30/0.61  thf(fact_7575_prod_Ocl__ivl__Suc,axiom,
% 0.30/0.61      ! [N: nat,M: nat,G2: nat > int] :
% 0.30/0.61        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.30/0.61         => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61            = one_one_int ) )
% 0.30/0.61        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 0.30/0.61         => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61            = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.cl_ivl_Suc
% 0.30/0.61  thf(fact_7576_prod_Oop__ivl__Suc,axiom,
% 0.30/0.61      ! [N: nat,M: nat,G2: nat > code_integer] :
% 0.30/0.61        ( ( ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61            = one_one_Code_integer ) )
% 0.30/0.61        & ( ~ ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61            = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G2 @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.op_ivl_Suc
% 0.30/0.61  thf(fact_7577_prod_Oop__ivl__Suc,axiom,
% 0.30/0.61      ! [N: nat,M: nat,G2: nat > assn] :
% 0.30/0.61        ( ( ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61            = one_one_assn ) )
% 0.30/0.61        & ( ~ ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61            = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G2 @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.op_ivl_Suc
% 0.30/0.61  thf(fact_7578_prod_Oop__ivl__Suc,axiom,
% 0.30/0.61      ! [N: nat,M: nat,G2: nat > rat] :
% 0.30/0.61        ( ( ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61            = one_one_rat ) )
% 0.30/0.61        & ( ~ ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61            = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G2 @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.op_ivl_Suc
% 0.30/0.61  thf(fact_7579_prod_Oop__ivl__Suc,axiom,
% 0.30/0.61      ! [N: nat,M: nat,G2: nat > nat] :
% 0.30/0.61        ( ( ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61            = one_one_nat ) )
% 0.30/0.61        & ( ~ ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61            = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G2 @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.op_ivl_Suc
% 0.30/0.61  thf(fact_7580_prod_Oop__ivl__Suc,axiom,
% 0.30/0.61      ! [N: nat,M: nat,G2: nat > int] :
% 0.30/0.61        ( ( ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61            = one_one_int ) )
% 0.30/0.61        & ( ~ ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61            = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G2 @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.op_ivl_Suc
% 0.30/0.61  thf(fact_7581_prod_Oswap,axiom,
% 0.30/0.61      ! [G2: nat > nat > nat,B2: set_nat,A2: set_nat] :
% 0.30/0.61        ( ( groups708209901874060359at_nat
% 0.30/0.61          @ ^ [I3: nat] : ( groups708209901874060359at_nat @ ( G2 @ I3 ) @ B2 )
% 0.30/0.61          @ A2 )
% 0.30/0.61        = ( groups708209901874060359at_nat
% 0.30/0.61          @ ^ [J3: nat] :
% 0.30/0.61              ( groups708209901874060359at_nat
% 0.30/0.61              @ ^ [I3: nat] : ( G2 @ I3 @ J3 )
% 0.30/0.61              @ A2 )
% 0.30/0.61          @ B2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.swap
% 0.30/0.61  thf(fact_7582_prod_Oswap,axiom,
% 0.30/0.61      ! [G2: nat > nat > int,B2: set_nat,A2: set_nat] :
% 0.30/0.61        ( ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [I3: nat] : ( groups705719431365010083at_int @ ( G2 @ I3 ) @ B2 )
% 0.30/0.61          @ A2 )
% 0.30/0.61        = ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [J3: nat] :
% 0.30/0.61              ( groups705719431365010083at_int
% 0.30/0.61              @ ^ [I3: nat] : ( G2 @ I3 @ J3 )
% 0.30/0.61              @ A2 )
% 0.30/0.61          @ B2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.swap
% 0.30/0.61  thf(fact_7583_prod_Oswap,axiom,
% 0.30/0.61      ! [G2: nat > int > int,B2: set_int,A2: set_nat] :
% 0.30/0.61        ( ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [I3: nat] : ( groups1705073143266064639nt_int @ ( G2 @ I3 ) @ B2 )
% 0.30/0.61          @ A2 )
% 0.30/0.61        = ( groups1705073143266064639nt_int
% 0.30/0.61          @ ^ [J3: int] :
% 0.30/0.61              ( groups705719431365010083at_int
% 0.30/0.61              @ ^ [I3: nat] : ( G2 @ I3 @ J3 )
% 0.30/0.61              @ A2 )
% 0.30/0.61          @ B2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.swap
% 0.30/0.61  thf(fact_7584_prod_Oswap,axiom,
% 0.30/0.61      ! [G2: int > nat > int,B2: set_nat,A2: set_int] :
% 0.30/0.61        ( ( groups1705073143266064639nt_int
% 0.30/0.61          @ ^ [I3: int] : ( groups705719431365010083at_int @ ( G2 @ I3 ) @ B2 )
% 0.30/0.61          @ A2 )
% 0.30/0.61        = ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [J3: nat] :
% 0.30/0.61              ( groups1705073143266064639nt_int
% 0.30/0.61              @ ^ [I3: int] : ( G2 @ I3 @ J3 )
% 0.30/0.61              @ A2 )
% 0.30/0.61          @ B2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.swap
% 0.30/0.61  thf(fact_7585_prod_Oswap,axiom,
% 0.30/0.61      ! [G2: int > int > int,B2: set_int,A2: set_int] :
% 0.30/0.61        ( ( groups1705073143266064639nt_int
% 0.30/0.61          @ ^ [I3: int] : ( groups1705073143266064639nt_int @ ( G2 @ I3 ) @ B2 )
% 0.30/0.61          @ A2 )
% 0.30/0.61        = ( groups1705073143266064639nt_int
% 0.30/0.61          @ ^ [J3: int] :
% 0.30/0.61              ( groups1705073143266064639nt_int
% 0.30/0.61              @ ^ [I3: int] : ( G2 @ I3 @ J3 )
% 0.30/0.61              @ A2 )
% 0.30/0.61          @ B2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.swap
% 0.30/0.61  thf(fact_7586_prod_Oneutral,axiom,
% 0.30/0.61      ! [A2: set_nat,G2: nat > nat] :
% 0.30/0.61        ( ! [X2: nat] :
% 0.30/0.61            ( ( member_nat @ X2 @ A2 )
% 0.30/0.61           => ( ( G2 @ X2 )
% 0.30/0.61              = one_one_nat ) )
% 0.30/0.61       => ( ( groups708209901874060359at_nat @ G2 @ A2 )
% 0.30/0.61          = one_one_nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.neutral
% 0.30/0.61  thf(fact_7587_prod_Oneutral,axiom,
% 0.30/0.61      ! [A2: set_nat,G2: nat > int] :
% 0.30/0.61        ( ! [X2: nat] :
% 0.30/0.61            ( ( member_nat @ X2 @ A2 )
% 0.30/0.61           => ( ( G2 @ X2 )
% 0.30/0.61              = one_one_int ) )
% 0.30/0.61       => ( ( groups705719431365010083at_int @ G2 @ A2 )
% 0.30/0.61          = one_one_int ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.neutral
% 0.30/0.61  thf(fact_7588_prod_Oneutral,axiom,
% 0.30/0.61      ! [A2: set_int,G2: int > int] :
% 0.30/0.61        ( ! [X2: int] :
% 0.30/0.61            ( ( member_int @ X2 @ A2 )
% 0.30/0.61           => ( ( G2 @ X2 )
% 0.30/0.61              = one_one_int ) )
% 0.30/0.61       => ( ( groups1705073143266064639nt_int @ G2 @ A2 )
% 0.30/0.61          = one_one_int ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.neutral
% 0.30/0.61  thf(fact_7589_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.30/0.61      ! [G2: nat > code_integer,A2: set_nat] :
% 0.30/0.61        ( ( ( groups3455450783089532116nteger @ G2 @ A2 )
% 0.30/0.61         != one_one_Code_integer )
% 0.30/0.61       => ~ ! [A6: nat] :
% 0.30/0.61              ( ( member_nat @ A6 @ A2 )
% 0.30/0.61             => ( ( G2 @ A6 )
% 0.30/0.61                = one_one_Code_integer ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.not_neutral_contains_not_neutral
% 0.30/0.61  thf(fact_7590_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.30/0.61      ! [G2: int > code_integer,A2: set_int] :
% 0.30/0.61        ( ( ( groups3827104343326376752nteger @ G2 @ A2 )
% 0.30/0.61         != one_one_Code_integer )
% 0.30/0.61       => ~ ! [A6: int] :
% 0.30/0.61              ( ( member_int @ A6 @ A2 )
% 0.30/0.61             => ( ( G2 @ A6 )
% 0.30/0.61                = one_one_Code_integer ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.not_neutral_contains_not_neutral
% 0.30/0.61  thf(fact_7591_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.30/0.61      ! [G2: nat > assn,A2: set_nat] :
% 0.30/0.61        ( ( ( groups6906906614972039071t_assn @ G2 @ A2 )
% 0.30/0.61         != one_one_assn )
% 0.30/0.61       => ~ ! [A6: nat] :
% 0.30/0.61              ( ( member_nat @ A6 @ A2 )
% 0.30/0.61             => ( ( G2 @ A6 )
% 0.30/0.61                = one_one_assn ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.not_neutral_contains_not_neutral
% 0.30/0.61  thf(fact_7592_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.30/0.61      ! [G2: int > assn,A2: set_int] :
% 0.30/0.61        ( ( ( groups7882442080178216443t_assn @ G2 @ A2 )
% 0.30/0.61         != one_one_assn )
% 0.30/0.61       => ~ ! [A6: int] :
% 0.30/0.61              ( ( member_int @ A6 @ A2 )
% 0.30/0.61             => ( ( G2 @ A6 )
% 0.30/0.61                = one_one_assn ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.not_neutral_contains_not_neutral
% 0.30/0.61  thf(fact_7593_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.30/0.61      ! [G2: nat > rat,A2: set_nat] :
% 0.30/0.61        ( ( ( groups73079841787564623at_rat @ G2 @ A2 )
% 0.30/0.61         != one_one_rat )
% 0.30/0.61       => ~ ! [A6: nat] :
% 0.30/0.61              ( ( member_nat @ A6 @ A2 )
% 0.30/0.61             => ( ( G2 @ A6 )
% 0.30/0.61                = one_one_rat ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.not_neutral_contains_not_neutral
% 0.30/0.61  thf(fact_7594_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.30/0.61      ! [G2: int > rat,A2: set_int] :
% 0.30/0.61        ( ( ( groups1072433553688619179nt_rat @ G2 @ A2 )
% 0.30/0.61         != one_one_rat )
% 0.30/0.61       => ~ ! [A6: int] :
% 0.30/0.61              ( ( member_int @ A6 @ A2 )
% 0.30/0.61             => ( ( G2 @ A6 )
% 0.30/0.61                = one_one_rat ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.not_neutral_contains_not_neutral
% 0.30/0.61  thf(fact_7595_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.30/0.61      ! [G2: int > nat,A2: set_int] :
% 0.30/0.61        ( ( ( groups1707563613775114915nt_nat @ G2 @ A2 )
% 0.30/0.61         != one_one_nat )
% 0.30/0.61       => ~ ! [A6: int] :
% 0.30/0.61              ( ( member_int @ A6 @ A2 )
% 0.30/0.61             => ( ( G2 @ A6 )
% 0.30/0.61                = one_one_nat ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.not_neutral_contains_not_neutral
% 0.30/0.61  thf(fact_7596_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.30/0.61      ! [G2: nat > nat,A2: set_nat] :
% 0.30/0.61        ( ( ( groups708209901874060359at_nat @ G2 @ A2 )
% 0.30/0.61         != one_one_nat )
% 0.30/0.61       => ~ ! [A6: nat] :
% 0.30/0.61              ( ( member_nat @ A6 @ A2 )
% 0.30/0.61             => ( ( G2 @ A6 )
% 0.30/0.61                = one_one_nat ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.not_neutral_contains_not_neutral
% 0.30/0.61  thf(fact_7597_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.30/0.61      ! [G2: nat > int,A2: set_nat] :
% 0.30/0.61        ( ( ( groups705719431365010083at_int @ G2 @ A2 )
% 0.30/0.61         != one_one_int )
% 0.30/0.61       => ~ ! [A6: nat] :
% 0.30/0.61              ( ( member_nat @ A6 @ A2 )
% 0.30/0.61             => ( ( G2 @ A6 )
% 0.30/0.61                = one_one_int ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.not_neutral_contains_not_neutral
% 0.30/0.61  thf(fact_7598_prod_Onot__neutral__contains__not__neutral,axiom,
% 0.30/0.61      ! [G2: int > int,A2: set_int] :
% 0.30/0.61        ( ( ( groups1705073143266064639nt_int @ G2 @ A2 )
% 0.30/0.61         != one_one_int )
% 0.30/0.61       => ~ ! [A6: int] :
% 0.30/0.61              ( ( member_int @ A6 @ A2 )
% 0.30/0.61             => ( ( G2 @ A6 )
% 0.30/0.61                = one_one_int ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.not_neutral_contains_not_neutral
% 0.30/0.61  thf(fact_7599_choose__one,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( binomial @ N @ one_one_nat )
% 0.30/0.61        = N ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_one
% 0.30/0.61  thf(fact_7600_prod_Odistrib,axiom,
% 0.30/0.61      ! [G2: nat > nat,H3: nat > nat,A2: set_nat] :
% 0.30/0.61        ( ( groups708209901874060359at_nat
% 0.30/0.61          @ ^ [X3: nat] : ( times_times_nat @ ( G2 @ X3 ) @ ( H3 @ X3 ) )
% 0.30/0.61          @ A2 )
% 0.30/0.61        = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ A2 ) @ ( groups708209901874060359at_nat @ H3 @ A2 ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.distrib
% 0.30/0.61  thf(fact_7601_prod_Odistrib,axiom,
% 0.30/0.61      ! [G2: nat > int,H3: nat > int,A2: set_nat] :
% 0.30/0.61        ( ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [X3: nat] : ( times_times_int @ ( G2 @ X3 ) @ ( H3 @ X3 ) )
% 0.30/0.61          @ A2 )
% 0.30/0.61        = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ A2 ) @ ( groups705719431365010083at_int @ H3 @ A2 ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.distrib
% 0.30/0.61  thf(fact_7602_prod_Odistrib,axiom,
% 0.30/0.61      ! [G2: int > int,H3: int > int,A2: set_int] :
% 0.30/0.61        ( ( groups1705073143266064639nt_int
% 0.30/0.61          @ ^ [X3: int] : ( times_times_int @ ( G2 @ X3 ) @ ( H3 @ X3 ) )
% 0.30/0.61          @ A2 )
% 0.30/0.61        = ( times_times_int @ ( groups1705073143266064639nt_int @ G2 @ A2 ) @ ( groups1705073143266064639nt_int @ H3 @ A2 ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.distrib
% 0.30/0.61  thf(fact_7603_prod__power__distrib,axiom,
% 0.30/0.61      ! [F2: nat > nat,A2: set_nat,N: nat] :
% 0.30/0.61        ( ( power_power_nat @ ( groups708209901874060359at_nat @ F2 @ A2 ) @ N )
% 0.30/0.61        = ( groups708209901874060359at_nat
% 0.30/0.61          @ ^ [X3: nat] : ( power_power_nat @ ( F2 @ X3 ) @ N )
% 0.30/0.61          @ A2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_power_distrib
% 0.30/0.61  thf(fact_7604_prod__power__distrib,axiom,
% 0.30/0.61      ! [F2: nat > int,A2: set_nat,N: nat] :
% 0.30/0.61        ( ( power_power_int @ ( groups705719431365010083at_int @ F2 @ A2 ) @ N )
% 0.30/0.61        = ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [X3: nat] : ( power_power_int @ ( F2 @ X3 ) @ N )
% 0.30/0.61          @ A2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_power_distrib
% 0.30/0.61  thf(fact_7605_prod__power__distrib,axiom,
% 0.30/0.61      ! [F2: int > int,A2: set_int,N: nat] :
% 0.30/0.61        ( ( power_power_int @ ( groups1705073143266064639nt_int @ F2 @ A2 ) @ N )
% 0.30/0.61        = ( groups1705073143266064639nt_int
% 0.30/0.61          @ ^ [X3: int] : ( power_power_int @ ( F2 @ X3 ) @ N )
% 0.30/0.61          @ A2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_power_distrib
% 0.30/0.61  thf(fact_7606_mod__prod__eq,axiom,
% 0.30/0.61      ! [F2: nat > nat,A: nat,A2: set_nat] :
% 0.30/0.61        ( ( modulo_modulo_nat
% 0.30/0.61          @ ( groups708209901874060359at_nat
% 0.30/0.61            @ ^ [I3: nat] : ( modulo_modulo_nat @ ( F2 @ I3 ) @ A )
% 0.30/0.61            @ A2 )
% 0.30/0.61          @ A )
% 0.30/0.61        = ( modulo_modulo_nat @ ( groups708209901874060359at_nat @ F2 @ A2 ) @ A ) ) ).
% 0.30/0.61  
% 0.30/0.61  % mod_prod_eq
% 0.30/0.61  thf(fact_7607_mod__prod__eq,axiom,
% 0.30/0.61      ! [F2: nat > int,A: int,A2: set_nat] :
% 0.30/0.61        ( ( modulo_modulo_int
% 0.30/0.61          @ ( groups705719431365010083at_int
% 0.30/0.61            @ ^ [I3: nat] : ( modulo_modulo_int @ ( F2 @ I3 ) @ A )
% 0.30/0.61            @ A2 )
% 0.30/0.61          @ A )
% 0.30/0.61        = ( modulo_modulo_int @ ( groups705719431365010083at_int @ F2 @ A2 ) @ A ) ) ).
% 0.30/0.61  
% 0.30/0.61  % mod_prod_eq
% 0.30/0.61  thf(fact_7608_mod__prod__eq,axiom,
% 0.30/0.61      ! [F2: int > int,A: int,A2: set_int] :
% 0.30/0.61        ( ( modulo_modulo_int
% 0.30/0.61          @ ( groups1705073143266064639nt_int
% 0.30/0.61            @ ^ [I3: int] : ( modulo_modulo_int @ ( F2 @ I3 ) @ A )
% 0.30/0.61            @ A2 )
% 0.30/0.61          @ A )
% 0.30/0.61        = ( modulo_modulo_int @ ( groups1705073143266064639nt_int @ F2 @ A2 ) @ A ) ) ).
% 0.30/0.61  
% 0.30/0.61  % mod_prod_eq
% 0.30/0.61  thf(fact_7609_fact__prod,axiom,
% 0.30/0.61      ( semiri1406184849735516958ct_int
% 0.30/0.61      = ( ^ [N2: nat] :
% 0.30/0.61            ( semiri1314217659103216013at_int
% 0.30/0.61            @ ( groups708209901874060359at_nat
% 0.30/0.61              @ ^ [X3: nat] : X3
% 0.30/0.61              @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_prod
% 0.30/0.61  thf(fact_7610_fact__prod,axiom,
% 0.30/0.61      ( semiri773545260158071498ct_rat
% 0.30/0.61      = ( ^ [N2: nat] :
% 0.30/0.61            ( semiri681578069525770553at_rat
% 0.30/0.61            @ ( groups708209901874060359at_nat
% 0.30/0.61              @ ^ [X3: nat] : X3
% 0.30/0.61              @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_prod
% 0.30/0.61  thf(fact_7611_fact__prod,axiom,
% 0.30/0.61      ( semiri1408675320244567234ct_nat
% 0.30/0.61      = ( ^ [N2: nat] :
% 0.30/0.61            ( semiri1316708129612266289at_nat
% 0.30/0.61            @ ( groups708209901874060359at_nat
% 0.30/0.61              @ ^ [X3: nat] : X3
% 0.30/0.61              @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_prod
% 0.30/0.61  thf(fact_7612_prod__ge__1,axiom,
% 0.30/0.61      ! [A2: set_nat,F2: nat > code_integer] :
% 0.30/0.61        ( ! [X2: nat] :
% 0.30/0.61            ( ( member_nat @ X2 @ A2 )
% 0.30/0.61           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ X2 ) ) )
% 0.30/0.61       => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F2 @ A2 ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_ge_1
% 0.30/0.61  thf(fact_7613_prod__ge__1,axiom,
% 0.30/0.61      ! [A2: set_int,F2: int > code_integer] :
% 0.30/0.61        ( ! [X2: int] :
% 0.30/0.61            ( ( member_int @ X2 @ A2 )
% 0.30/0.61           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ X2 ) ) )
% 0.30/0.61       => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F2 @ A2 ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_ge_1
% 0.30/0.61  thf(fact_7614_prod__ge__1,axiom,
% 0.30/0.61      ! [A2: set_nat,F2: nat > rat] :
% 0.30/0.61        ( ! [X2: nat] :
% 0.30/0.61            ( ( member_nat @ X2 @ A2 )
% 0.30/0.61           => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ X2 ) ) )
% 0.30/0.61       => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F2 @ A2 ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_ge_1
% 0.30/0.61  thf(fact_7615_prod__ge__1,axiom,
% 0.30/0.61      ! [A2: set_int,F2: int > rat] :
% 0.30/0.61        ( ! [X2: int] :
% 0.30/0.61            ( ( member_int @ X2 @ A2 )
% 0.30/0.61           => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ X2 ) ) )
% 0.30/0.61       => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F2 @ A2 ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_ge_1
% 0.30/0.61  thf(fact_7616_prod__ge__1,axiom,
% 0.30/0.61      ! [A2: set_int,F2: int > nat] :
% 0.30/0.61        ( ! [X2: int] :
% 0.30/0.61            ( ( member_int @ X2 @ A2 )
% 0.30/0.61           => ( ord_less_eq_nat @ one_one_nat @ ( F2 @ X2 ) ) )
% 0.30/0.61       => ( ord_less_eq_nat @ one_one_nat @ ( groups1707563613775114915nt_nat @ F2 @ A2 ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_ge_1
% 0.30/0.61  thf(fact_7617_prod__ge__1,axiom,
% 0.30/0.61      ! [A2: set_nat,F2: nat > nat] :
% 0.30/0.61        ( ! [X2: nat] :
% 0.30/0.61            ( ( member_nat @ X2 @ A2 )
% 0.30/0.61           => ( ord_less_eq_nat @ one_one_nat @ ( F2 @ X2 ) ) )
% 0.30/0.61       => ( ord_less_eq_nat @ one_one_nat @ ( groups708209901874060359at_nat @ F2 @ A2 ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_ge_1
% 0.30/0.61  thf(fact_7618_prod__ge__1,axiom,
% 0.30/0.61      ! [A2: set_nat,F2: nat > int] :
% 0.30/0.61        ( ! [X2: nat] :
% 0.30/0.61            ( ( member_nat @ X2 @ A2 )
% 0.30/0.61           => ( ord_less_eq_int @ one_one_int @ ( F2 @ X2 ) ) )
% 0.30/0.61       => ( ord_less_eq_int @ one_one_int @ ( groups705719431365010083at_int @ F2 @ A2 ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_ge_1
% 0.30/0.61  thf(fact_7619_prod__ge__1,axiom,
% 0.30/0.61      ! [A2: set_int,F2: int > int] :
% 0.30/0.61        ( ! [X2: int] :
% 0.30/0.61            ( ( member_int @ X2 @ A2 )
% 0.30/0.61           => ( ord_less_eq_int @ one_one_int @ ( F2 @ X2 ) ) )
% 0.30/0.61       => ( ord_less_eq_int @ one_one_int @ ( groups1705073143266064639nt_int @ F2 @ A2 ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_ge_1
% 0.30/0.61  thf(fact_7620_prod__ge__1,axiom,
% 0.30/0.61      ! [A2: set_set_nat,F2: set_nat > code_integer] :
% 0.30/0.61        ( ! [X2: set_nat] :
% 0.30/0.61            ( ( member_set_nat @ X2 @ A2 )
% 0.30/0.61           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ X2 ) ) )
% 0.30/0.61       => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups2761809935038513290nteger @ F2 @ A2 ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_ge_1
% 0.30/0.61  thf(fact_7621_prod__ge__1,axiom,
% 0.30/0.61      ! [A2: set_set_nat,F2: set_nat > rat] :
% 0.30/0.61        ( ! [X2: set_nat] :
% 0.30/0.61            ( ( member_set_nat @ X2 @ A2 )
% 0.30/0.61           => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ X2 ) ) )
% 0.30/0.61       => ( ord_less_eq_rat @ one_one_rat @ ( groups3613417700093529605at_rat @ F2 @ A2 ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_ge_1
% 0.30/0.61  thf(fact_7622_fact__eq__fact__times,axiom,
% 0.30/0.61      ! [N: nat,M: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ N @ M )
% 0.30/0.61       => ( ( semiri1408675320244567234ct_nat @ M )
% 0.30/0.61          = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 0.30/0.61            @ ( groups708209901874060359at_nat
% 0.30/0.61              @ ^ [X3: nat] : X3
% 0.30/0.61              @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_eq_fact_times
% 0.30/0.61  thf(fact_7623_fact__prod__rev,axiom,
% 0.30/0.61      ( semiri1406184849735516958ct_int
% 0.30/0.61      = ( ^ [N2: nat] : ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ ( minus_minus_nat @ N2 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_prod_rev
% 0.30/0.61  thf(fact_7624_fact__prod__rev,axiom,
% 0.30/0.61      ( semiri773545260158071498ct_rat
% 0.30/0.61      = ( ^ [N2: nat] : ( semiri681578069525770553at_rat @ ( groups708209901874060359at_nat @ ( minus_minus_nat @ N2 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_prod_rev
% 0.30/0.61  thf(fact_7625_fact__prod__rev,axiom,
% 0.30/0.61      ( semiri1408675320244567234ct_nat
% 0.30/0.61      = ( ^ [N2: nat] : ( semiri1316708129612266289at_nat @ ( groups708209901874060359at_nat @ ( minus_minus_nat @ N2 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_prod_rev
% 0.30/0.61  thf(fact_7626_fact__ge__1,axiom,
% 0.30/0.61      ! [N: nat] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( semiri3624122377584611663nteger @ N ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_ge_1
% 0.30/0.61  thf(fact_7627_fact__ge__1,axiom,
% 0.30/0.61      ! [N: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_ge_1
% 0.30/0.61  thf(fact_7628_fact__ge__1,axiom,
% 0.30/0.61      ! [N: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_ge_1
% 0.30/0.61  thf(fact_7629_fact__ge__1,axiom,
% 0.30/0.61      ! [N: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_ge_1
% 0.30/0.61  thf(fact_7630_pochhammer__fact,axiom,
% 0.30/0.61      ( semiri3624122377584611663nteger
% 0.30/0.61      = ( comm_s8582702949713902594nteger @ one_one_Code_integer ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_fact
% 0.30/0.61  thf(fact_7631_pochhammer__fact,axiom,
% 0.30/0.61      ( semiri773545260158071498ct_rat
% 0.30/0.61      = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_fact
% 0.30/0.61  thf(fact_7632_pochhammer__fact,axiom,
% 0.30/0.61      ( semiri1406184849735516958ct_int
% 0.30/0.61      = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_fact
% 0.30/0.61  thf(fact_7633_pochhammer__fact,axiom,
% 0.30/0.61      ( semiri1408675320244567234ct_nat
% 0.30/0.61      = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_fact
% 0.30/0.61  thf(fact_7634_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.30/0.61      ! [G2: nat > nat,M: nat,N: nat] :
% 0.30/0.61        ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 0.30/0.61        = ( groups708209901874060359at_nat
% 0.30/0.61          @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.shift_bounds_cl_Suc_ivl
% 0.30/0.61  thf(fact_7635_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.30/0.61      ! [G2: nat > int,M: nat,N: nat] :
% 0.30/0.61        ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 0.30/0.61        = ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.shift_bounds_cl_Suc_ivl
% 0.30/0.61  thf(fact_7636_prod_Oshift__bounds__Suc__ivl,axiom,
% 0.30/0.61      ! [G2: nat > nat,M: nat,N: nat] :
% 0.30/0.61        ( ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 0.30/0.61        = ( groups708209901874060359at_nat
% 0.30/0.61          @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.61          @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.shift_bounds_Suc_ivl
% 0.30/0.61  thf(fact_7637_prod_Oshift__bounds__Suc__ivl,axiom,
% 0.30/0.61      ! [G2: nat > int,M: nat,N: nat] :
% 0.30/0.61        ( ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 0.30/0.61        = ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.61          @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.shift_bounds_Suc_ivl
% 0.30/0.61  thf(fact_7638_power__sum,axiom,
% 0.30/0.61      ! [C: nat,F2: nat > nat,A2: set_nat] :
% 0.30/0.61        ( ( power_power_nat @ C @ ( groups3542108847815614940at_nat @ F2 @ A2 ) )
% 0.30/0.61        = ( groups708209901874060359at_nat
% 0.30/0.61          @ ^ [A3: nat] : ( power_power_nat @ C @ ( F2 @ A3 ) )
% 0.30/0.61          @ A2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % power_sum
% 0.30/0.61  thf(fact_7639_power__sum,axiom,
% 0.30/0.61      ! [C: int,F2: nat > nat,A2: set_nat] :
% 0.30/0.61        ( ( power_power_int @ C @ ( groups3542108847815614940at_nat @ F2 @ A2 ) )
% 0.30/0.61        = ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [A3: nat] : ( power_power_int @ C @ ( F2 @ A3 ) )
% 0.30/0.61          @ A2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % power_sum
% 0.30/0.61  thf(fact_7640_power__sum,axiom,
% 0.30/0.61      ! [C: int,F2: int > nat,A2: set_int] :
% 0.30/0.61        ( ( power_power_int @ C @ ( groups4541462559716669496nt_nat @ F2 @ A2 ) )
% 0.30/0.61        = ( groups1705073143266064639nt_int
% 0.30/0.61          @ ^ [A3: int] : ( power_power_int @ C @ ( F2 @ A3 ) )
% 0.30/0.61          @ A2 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % power_sum
% 0.30/0.61  thf(fact_7641_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 0.30/0.61      ! [G2: nat > nat,M: nat,K: nat,N: nat] :
% 0.30/0.61        ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 0.30/0.61        = ( groups708209901874060359at_nat
% 0.30/0.61          @ ^ [I3: nat] : ( G2 @ ( plus_plus_nat @ I3 @ K ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.shift_bounds_cl_nat_ivl
% 0.30/0.61  thf(fact_7642_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 0.30/0.61      ! [G2: nat > int,M: nat,K: nat,N: nat] :
% 0.30/0.61        ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 0.30/0.61        = ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [I3: nat] : ( G2 @ ( plus_plus_nat @ I3 @ K ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.shift_bounds_cl_nat_ivl
% 0.30/0.61  thf(fact_7643_prod_Oshift__bounds__nat__ivl,axiom,
% 0.30/0.61      ! [G2: nat > nat,M: nat,K: nat,N: nat] :
% 0.30/0.61        ( ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 0.30/0.61        = ( groups708209901874060359at_nat
% 0.30/0.61          @ ^ [I3: nat] : ( G2 @ ( plus_plus_nat @ I3 @ K ) )
% 0.30/0.61          @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.shift_bounds_nat_ivl
% 0.30/0.61  thf(fact_7644_prod_Oshift__bounds__nat__ivl,axiom,
% 0.30/0.61      ! [G2: nat > int,M: nat,K: nat,N: nat] :
% 0.30/0.61        ( ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 0.30/0.61        = ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [I3: nat] : ( G2 @ ( plus_plus_nat @ I3 @ K ) )
% 0.30/0.61          @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.shift_bounds_nat_ivl
% 0.30/0.61  thf(fact_7645_fact__binomial,axiom,
% 0.30/0.61      ! [K: nat,N: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.61       => ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) )
% 0.30/0.61          = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_binomial
% 0.30/0.61  thf(fact_7646_binomial__fact,axiom,
% 0.30/0.61      ! [K: nat,N: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.61       => ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) )
% 0.30/0.61          = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % binomial_fact
% 0.30/0.61  thf(fact_7647_fact__div__fact,axiom,
% 0.30/0.61      ! [N: nat,M: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ N @ M )
% 0.30/0.61       => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 0.30/0.61          = ( groups708209901874060359at_nat
% 0.30/0.61            @ ^ [X3: nat] : X3
% 0.30/0.61            @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_div_fact
% 0.30/0.61  thf(fact_7648_prod__le__1,axiom,
% 0.30/0.61      ! [A2: set_nat,F2: nat > code_integer] :
% 0.30/0.61        ( ! [X2: nat] :
% 0.30/0.61            ( ( member_nat @ X2 @ A2 )
% 0.30/0.61           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X2 ) )
% 0.30/0.61              & ( ord_le3102999989581377725nteger @ ( F2 @ X2 ) @ one_one_Code_integer ) ) )
% 0.30/0.61       => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F2 @ A2 ) @ one_one_Code_integer ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_le_1
% 0.30/0.61  thf(fact_7649_prod__le__1,axiom,
% 0.30/0.61      ! [A2: set_int,F2: int > code_integer] :
% 0.30/0.61        ( ! [X2: int] :
% 0.30/0.61            ( ( member_int @ X2 @ A2 )
% 0.30/0.61           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X2 ) )
% 0.30/0.61              & ( ord_le3102999989581377725nteger @ ( F2 @ X2 ) @ one_one_Code_integer ) ) )
% 0.30/0.61       => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F2 @ A2 ) @ one_one_Code_integer ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_le_1
% 0.30/0.61  thf(fact_7650_prod__le__1,axiom,
% 0.30/0.61      ! [A2: set_nat,F2: nat > rat] :
% 0.30/0.61        ( ! [X2: nat] :
% 0.30/0.61            ( ( member_nat @ X2 @ A2 )
% 0.30/0.61           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X2 ) )
% 0.30/0.61              & ( ord_less_eq_rat @ ( F2 @ X2 ) @ one_one_rat ) ) )
% 0.30/0.61       => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F2 @ A2 ) @ one_one_rat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_le_1
% 0.30/0.61  thf(fact_7651_prod__le__1,axiom,
% 0.30/0.61      ! [A2: set_int,F2: int > rat] :
% 0.30/0.61        ( ! [X2: int] :
% 0.30/0.61            ( ( member_int @ X2 @ A2 )
% 0.30/0.61           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X2 ) )
% 0.30/0.61              & ( ord_less_eq_rat @ ( F2 @ X2 ) @ one_one_rat ) ) )
% 0.30/0.61       => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F2 @ A2 ) @ one_one_rat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_le_1
% 0.30/0.61  thf(fact_7652_prod__le__1,axiom,
% 0.30/0.61      ! [A2: set_int,F2: int > nat] :
% 0.30/0.61        ( ! [X2: int] :
% 0.30/0.61            ( ( member_int @ X2 @ A2 )
% 0.30/0.61           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X2 ) )
% 0.30/0.61              & ( ord_less_eq_nat @ ( F2 @ X2 ) @ one_one_nat ) ) )
% 0.30/0.61       => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F2 @ A2 ) @ one_one_nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_le_1
% 0.30/0.61  thf(fact_7653_prod__le__1,axiom,
% 0.30/0.61      ! [A2: set_nat,F2: nat > nat] :
% 0.30/0.61        ( ! [X2: nat] :
% 0.30/0.61            ( ( member_nat @ X2 @ A2 )
% 0.30/0.61           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X2 ) )
% 0.30/0.61              & ( ord_less_eq_nat @ ( F2 @ X2 ) @ one_one_nat ) ) )
% 0.30/0.61       => ( ord_less_eq_nat @ ( groups708209901874060359at_nat @ F2 @ A2 ) @ one_one_nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_le_1
% 0.30/0.61  thf(fact_7654_prod__le__1,axiom,
% 0.30/0.61      ! [A2: set_nat,F2: nat > int] :
% 0.30/0.61        ( ! [X2: nat] :
% 0.30/0.61            ( ( member_nat @ X2 @ A2 )
% 0.30/0.61           => ( ( ord_less_eq_int @ zero_zero_int @ ( F2 @ X2 ) )
% 0.30/0.61              & ( ord_less_eq_int @ ( F2 @ X2 ) @ one_one_int ) ) )
% 0.30/0.61       => ( ord_less_eq_int @ ( groups705719431365010083at_int @ F2 @ A2 ) @ one_one_int ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_le_1
% 0.30/0.61  thf(fact_7655_prod__le__1,axiom,
% 0.30/0.61      ! [A2: set_int,F2: int > int] :
% 0.30/0.61        ( ! [X2: int] :
% 0.30/0.61            ( ( member_int @ X2 @ A2 )
% 0.30/0.61           => ( ( ord_less_eq_int @ zero_zero_int @ ( F2 @ X2 ) )
% 0.30/0.61              & ( ord_less_eq_int @ ( F2 @ X2 ) @ one_one_int ) ) )
% 0.30/0.61       => ( ord_less_eq_int @ ( groups1705073143266064639nt_int @ F2 @ A2 ) @ one_one_int ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_le_1
% 0.30/0.61  thf(fact_7656_prod__le__1,axiom,
% 0.30/0.61      ! [A2: set_set_nat,F2: set_nat > code_integer] :
% 0.30/0.61        ( ! [X2: set_nat] :
% 0.30/0.61            ( ( member_set_nat @ X2 @ A2 )
% 0.30/0.61           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X2 ) )
% 0.30/0.61              & ( ord_le3102999989581377725nteger @ ( F2 @ X2 ) @ one_one_Code_integer ) ) )
% 0.30/0.61       => ( ord_le3102999989581377725nteger @ ( groups2761809935038513290nteger @ F2 @ A2 ) @ one_one_Code_integer ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_le_1
% 0.30/0.61  thf(fact_7657_prod__le__1,axiom,
% 0.30/0.61      ! [A2: set_set_nat,F2: set_nat > rat] :
% 0.30/0.61        ( ! [X2: set_nat] :
% 0.30/0.61            ( ( member_set_nat @ X2 @ A2 )
% 0.30/0.61           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X2 ) )
% 0.30/0.61              & ( ord_less_eq_rat @ ( F2 @ X2 ) @ one_one_rat ) ) )
% 0.30/0.61       => ( ord_less_eq_rat @ ( groups3613417700093529605at_rat @ F2 @ A2 ) @ one_one_rat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_le_1
% 0.30/0.61  thf(fact_7658_fact__split,axiom,
% 0.30/0.61      ! [K: nat,N: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.61       => ( ( semiri3624122377584611663nteger @ N )
% 0.30/0.61          = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ N @ K ) @ N ) ) ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_split
% 0.30/0.61  thf(fact_7659_fact__split,axiom,
% 0.30/0.61      ! [K: nat,N: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.61       => ( ( semiri1406184849735516958ct_int @ N )
% 0.30/0.61          = ( times_times_int @ ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ N @ K ) @ N ) ) ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_split
% 0.30/0.61  thf(fact_7660_fact__split,axiom,
% 0.30/0.61      ! [K: nat,N: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.61       => ( ( semiri773545260158071498ct_rat @ N )
% 0.30/0.61          = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ N @ K ) @ N ) ) ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_split
% 0.30/0.61  thf(fact_7661_fact__split,axiom,
% 0.30/0.61      ! [K: nat,N: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.61       => ( ( semiri1408675320244567234ct_nat @ N )
% 0.30/0.61          = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ N @ K ) @ N ) ) ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_split
% 0.30/0.61  thf(fact_7662_prod_OatLeastLessThan__concat,axiom,
% 0.30/0.61      ! [M: nat,N: nat,P4: nat,G2: nat > code_integer] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( ord_less_eq_nat @ N @ P4 )
% 0.30/0.61         => ( ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ N @ P4 ) ) )
% 0.30/0.61            = ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ M @ P4 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeastLessThan_concat
% 0.30/0.61  thf(fact_7663_prod_OatLeastLessThan__concat,axiom,
% 0.30/0.61      ! [M: nat,N: nat,P4: nat,G2: nat > assn] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( ord_less_eq_nat @ N @ P4 )
% 0.30/0.61         => ( ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ N @ P4 ) ) )
% 0.30/0.61            = ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ M @ P4 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeastLessThan_concat
% 0.30/0.61  thf(fact_7664_prod_OatLeastLessThan__concat,axiom,
% 0.30/0.61      ! [M: nat,N: nat,P4: nat,G2: nat > rat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( ord_less_eq_nat @ N @ P4 )
% 0.30/0.61         => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ N @ P4 ) ) )
% 0.30/0.61            = ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ M @ P4 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeastLessThan_concat
% 0.30/0.61  thf(fact_7665_prod_OatLeastLessThan__concat,axiom,
% 0.30/0.61      ! [M: nat,N: nat,P4: nat,G2: nat > nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( ord_less_eq_nat @ N @ P4 )
% 0.30/0.61         => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ N @ P4 ) ) )
% 0.30/0.61            = ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ M @ P4 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeastLessThan_concat
% 0.30/0.61  thf(fact_7666_prod_OatLeastLessThan__concat,axiom,
% 0.30/0.61      ! [M: nat,N: nat,P4: nat,G2: nat > int] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( ord_less_eq_nat @ N @ P4 )
% 0.30/0.61         => ( ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ N @ P4 ) ) )
% 0.30/0.61            = ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ M @ P4 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeastLessThan_concat
% 0.30/0.61  thf(fact_7667_binomial__altdef__of__nat,axiom,
% 0.30/0.61      ! [K: nat,N: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.61       => ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) )
% 0.30/0.61          = ( groups73079841787564623at_rat
% 0.30/0.61            @ ^ [I3: nat] : ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I3 ) ) @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ K @ I3 ) ) )
% 0.30/0.61            @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % binomial_altdef_of_nat
% 0.30/0.61  thf(fact_7668_binomial__absorb__comp,axiom,
% 0.30/0.61      ! [N: nat,K: nat] :
% 0.30/0.61        ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 0.30/0.61        = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % binomial_absorb_comp
% 0.30/0.61  thf(fact_7669_dvd__fact,axiom,
% 0.30/0.61      ! [M: nat,N: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 0.30/0.61       => ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61         => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % dvd_fact
% 0.30/0.61  thf(fact_7670_gbinomial__mult__fact_H,axiom,
% 0.30/0.61      ! [A: rat,K: nat] :
% 0.30/0.61        ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( semiri773545260158071498ct_rat @ K ) )
% 0.30/0.61        = ( groups73079841787564623at_rat
% 0.30/0.61          @ ^ [I3: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I3 ) )
% 0.30/0.61          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_mult_fact'
% 0.30/0.61  thf(fact_7671_gbinomial__mult__fact,axiom,
% 0.30/0.61      ! [K: nat,A: rat] :
% 0.30/0.61        ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( gbinomial_rat @ A @ K ) )
% 0.30/0.61        = ( groups73079841787564623at_rat
% 0.30/0.61          @ ^ [I3: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I3 ) )
% 0.30/0.61          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_mult_fact
% 0.30/0.61  thf(fact_7672_gbinomial__prod__rev,axiom,
% 0.30/0.61      ( gbinom8545251970709558553nteger
% 0.30/0.61      = ( ^ [A3: code_integer,K4: nat] :
% 0.30/0.61            ( divide6298287555418463151nteger
% 0.30/0.61            @ ( groups3455450783089532116nteger
% 0.30/0.61              @ ^ [I3: nat] : ( minus_8373710615458151222nteger @ A3 @ ( semiri4939895301339042750nteger @ I3 ) )
% 0.30/0.61              @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K4 ) )
% 0.30/0.61            @ ( semiri3624122377584611663nteger @ K4 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_prod_rev
% 0.30/0.61  thf(fact_7673_gbinomial__prod__rev,axiom,
% 0.30/0.61      ( gbinom7368847122466276068atural
% 0.30/0.61      = ( ^ [A3: code_natural,K4: nat] :
% 0.30/0.61            ( divide5121882707175180666atural
% 0.30/0.61            @ ( groups2279045934846249631atural
% 0.30/0.61              @ ^ [I3: nat] : ( minus_7197305767214868737atural @ A3 @ ( semiri3763490453095760265atural @ I3 ) )
% 0.30/0.61              @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K4 ) )
% 0.30/0.61            @ ( semiri2447717529341329178atural @ K4 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_prod_rev
% 0.30/0.61  thf(fact_7674_gbinomial__prod__rev,axiom,
% 0.30/0.61      ( gbinomial_rat
% 0.30/0.61      = ( ^ [A3: rat,K4: nat] :
% 0.30/0.61            ( divide_divide_rat
% 0.30/0.61            @ ( groups73079841787564623at_rat
% 0.30/0.61              @ ^ [I3: nat] : ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ I3 ) )
% 0.30/0.61              @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K4 ) )
% 0.30/0.61            @ ( semiri773545260158071498ct_rat @ K4 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_prod_rev
% 0.30/0.61  thf(fact_7675_gbinomial__prod__rev,axiom,
% 0.30/0.61      ( gbinomial_nat
% 0.30/0.61      = ( ^ [A3: nat,K4: nat] :
% 0.30/0.61            ( divide_divide_nat
% 0.30/0.61            @ ( groups708209901874060359at_nat
% 0.30/0.61              @ ^ [I3: nat] : ( minus_minus_nat @ A3 @ ( semiri1316708129612266289at_nat @ I3 ) )
% 0.30/0.61              @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K4 ) )
% 0.30/0.61            @ ( semiri1408675320244567234ct_nat @ K4 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_prod_rev
% 0.30/0.61  thf(fact_7676_gbinomial__prod__rev,axiom,
% 0.30/0.61      ( gbinomial_int
% 0.30/0.61      = ( ^ [A3: int,K4: nat] :
% 0.30/0.61            ( divide_divide_int
% 0.30/0.61            @ ( groups705719431365010083at_int
% 0.30/0.61              @ ^ [I3: nat] : ( minus_minus_int @ A3 @ ( semiri1314217659103216013at_int @ I3 ) )
% 0.30/0.61              @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K4 ) )
% 0.30/0.61            @ ( semiri1406184849735516958ct_int @ K4 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_prod_rev
% 0.30/0.61  thf(fact_7677_fact__fact__dvd__fact,axiom,
% 0.30/0.61      ! [K: nat,N: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_fact_dvd_fact
% 0.30/0.61  thf(fact_7678_fact__fact__dvd__fact,axiom,
% 0.30/0.61      ! [K: nat,N: nat] : ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ N ) ) @ ( semiri773545260158071498ct_rat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_fact_dvd_fact
% 0.30/0.61  thf(fact_7679_fact__fact__dvd__fact,axiom,
% 0.30/0.61      ! [K: nat,N: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_fact_dvd_fact
% 0.30/0.61  thf(fact_7680_fact__fact__dvd__fact,axiom,
% 0.30/0.61      ! [K: nat,N: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_fact_dvd_fact
% 0.30/0.61  thf(fact_7681_prod_OatLeastAtMost__rev,axiom,
% 0.30/0.61      ! [G2: nat > nat,N: nat,M: nat] :
% 0.30/0.61        ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 0.30/0.61        = ( groups708209901874060359at_nat
% 0.30/0.61          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeastAtMost_rev
% 0.30/0.61  thf(fact_7682_prod_OatLeastAtMost__rev,axiom,
% 0.30/0.61      ! [G2: nat > int,N: nat,M: nat] :
% 0.30/0.61        ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 0.30/0.61        = ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeastAtMost_rev
% 0.30/0.61  thf(fact_7683_gbinomial__Suc,axiom,
% 0.30/0.61      ! [A: code_integer,K: nat] :
% 0.30/0.61        ( ( gbinom8545251970709558553nteger @ A @ ( suc @ K ) )
% 0.30/0.61        = ( divide6298287555418463151nteger
% 0.30/0.61          @ ( groups3455450783089532116nteger
% 0.30/0.61            @ ^ [I3: nat] : ( minus_8373710615458151222nteger @ A @ ( semiri4939895301339042750nteger @ I3 ) )
% 0.30/0.61            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 0.30/0.61          @ ( semiri3624122377584611663nteger @ ( suc @ K ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_Suc
% 0.30/0.61  thf(fact_7684_gbinomial__Suc,axiom,
% 0.30/0.61      ! [A: code_natural,K: nat] :
% 0.30/0.61        ( ( gbinom7368847122466276068atural @ A @ ( suc @ K ) )
% 0.30/0.61        = ( divide5121882707175180666atural
% 0.30/0.61          @ ( groups2279045934846249631atural
% 0.30/0.61            @ ^ [I3: nat] : ( minus_7197305767214868737atural @ A @ ( semiri3763490453095760265atural @ I3 ) )
% 0.30/0.61            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 0.30/0.61          @ ( semiri2447717529341329178atural @ ( suc @ K ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_Suc
% 0.30/0.61  thf(fact_7685_gbinomial__Suc,axiom,
% 0.30/0.61      ! [A: rat,K: nat] :
% 0.30/0.61        ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 0.30/0.61        = ( divide_divide_rat
% 0.30/0.61          @ ( groups73079841787564623at_rat
% 0.30/0.61            @ ^ [I3: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I3 ) )
% 0.30/0.61            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 0.30/0.61          @ ( semiri773545260158071498ct_rat @ ( suc @ K ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_Suc
% 0.30/0.61  thf(fact_7686_gbinomial__Suc,axiom,
% 0.30/0.61      ! [A: nat,K: nat] :
% 0.30/0.61        ( ( gbinomial_nat @ A @ ( suc @ K ) )
% 0.30/0.61        = ( divide_divide_nat
% 0.30/0.61          @ ( groups708209901874060359at_nat
% 0.30/0.61            @ ^ [I3: nat] : ( minus_minus_nat @ A @ ( semiri1316708129612266289at_nat @ I3 ) )
% 0.30/0.61            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 0.30/0.61          @ ( semiri1408675320244567234ct_nat @ ( suc @ K ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_Suc
% 0.30/0.61  thf(fact_7687_gbinomial__Suc,axiom,
% 0.30/0.61      ! [A: int,K: nat] :
% 0.30/0.61        ( ( gbinomial_int @ A @ ( suc @ K ) )
% 0.30/0.61        = ( divide_divide_int
% 0.30/0.61          @ ( groups705719431365010083at_int
% 0.30/0.61            @ ^ [I3: nat] : ( minus_minus_int @ A @ ( semiri1314217659103216013at_int @ I3 ) )
% 0.30/0.61            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 0.30/0.61          @ ( semiri1406184849735516958ct_int @ ( suc @ K ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_Suc
% 0.30/0.61  thf(fact_7688_sum__choose__upper,axiom,
% 0.30/0.61      ! [M: nat,N: nat] :
% 0.30/0.61        ( ( groups3542108847815614940at_nat
% 0.30/0.61          @ ^ [K4: nat] : ( binomial @ K4 @ M )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.61        = ( binomial @ ( suc @ N ) @ ( suc @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_choose_upper
% 0.30/0.61  thf(fact_7689_prod_OatLeast0__atMost__Suc,axiom,
% 0.30/0.61      ! [G2: nat > code_integer,N: nat] :
% 0.30/0.61        ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeast0_atMost_Suc
% 0.30/0.61  thf(fact_7690_prod_OatLeast0__atMost__Suc,axiom,
% 0.30/0.61      ! [G2: nat > assn,N: nat] :
% 0.30/0.61        ( ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeast0_atMost_Suc
% 0.30/0.61  thf(fact_7691_prod_OatLeast0__atMost__Suc,axiom,
% 0.30/0.61      ! [G2: nat > rat,N: nat] :
% 0.30/0.61        ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeast0_atMost_Suc
% 0.30/0.61  thf(fact_7692_prod_OatLeast0__atMost__Suc,axiom,
% 0.30/0.61      ! [G2: nat > nat,N: nat] :
% 0.30/0.61        ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeast0_atMost_Suc
% 0.30/0.61  thf(fact_7693_prod_OatLeast0__atMost__Suc,axiom,
% 0.30/0.61      ! [G2: nat > int,N: nat] :
% 0.30/0.61        ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeast0_atMost_Suc
% 0.30/0.61  thf(fact_7694_prod_OatLeast0__lessThan__Suc,axiom,
% 0.30/0.61      ! [G2: nat > code_integer,N: nat] :
% 0.30/0.61        ( ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeast0_lessThan_Suc
% 0.30/0.61  thf(fact_7695_prod_OatLeast0__lessThan__Suc,axiom,
% 0.30/0.61      ! [G2: nat > assn,N: nat] :
% 0.30/0.61        ( ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeast0_lessThan_Suc
% 0.30/0.61  thf(fact_7696_prod_OatLeast0__lessThan__Suc,axiom,
% 0.30/0.61      ! [G2: nat > rat,N: nat] :
% 0.30/0.61        ( ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeast0_lessThan_Suc
% 0.30/0.61  thf(fact_7697_prod_OatLeast0__lessThan__Suc,axiom,
% 0.30/0.61      ! [G2: nat > nat,N: nat] :
% 0.30/0.61        ( ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeast0_lessThan_Suc
% 0.30/0.61  thf(fact_7698_prod_OatLeast0__lessThan__Suc,axiom,
% 0.30/0.61      ! [G2: nat > int,N: nat] :
% 0.30/0.61        ( ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeast0_lessThan_Suc
% 0.30/0.61  thf(fact_7699_prod_OatLeast__Suc__lessThan,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > code_integer] :
% 0.30/0.61        ( ( ord_less_nat @ M @ N )
% 0.30/0.61       => ( ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 0.30/0.61          = ( times_3573771949741848930nteger @ ( G2 @ M ) @ ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeast_Suc_lessThan
% 0.30/0.61  thf(fact_7700_prod_OatLeast__Suc__lessThan,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > assn] :
% 0.30/0.61        ( ( ord_less_nat @ M @ N )
% 0.30/0.61       => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 0.30/0.61          = ( times_times_assn @ ( G2 @ M ) @ ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeast_Suc_lessThan
% 0.30/0.61  thf(fact_7701_prod_OatLeast__Suc__lessThan,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > rat] :
% 0.30/0.61        ( ( ord_less_nat @ M @ N )
% 0.30/0.61       => ( ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 0.30/0.61          = ( times_times_rat @ ( G2 @ M ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeast_Suc_lessThan
% 0.30/0.61  thf(fact_7702_prod_OatLeast__Suc__lessThan,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > nat] :
% 0.30/0.61        ( ( ord_less_nat @ M @ N )
% 0.30/0.61       => ( ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 0.30/0.61          = ( times_times_nat @ ( G2 @ M ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeast_Suc_lessThan
% 0.30/0.61  thf(fact_7703_prod_OatLeast__Suc__lessThan,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > int] :
% 0.30/0.61        ( ( ord_less_nat @ M @ N )
% 0.30/0.61       => ( ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 0.30/0.61          = ( times_times_int @ ( G2 @ M ) @ ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeast_Suc_lessThan
% 0.30/0.61  thf(fact_7704_prod_Onat__ivl__Suc_H,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > code_integer] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.30/0.61       => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61          = ( times_3573771949741848930nteger @ ( G2 @ ( suc @ N ) ) @ ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.nat_ivl_Suc'
% 0.30/0.61  thf(fact_7705_prod_Onat__ivl__Suc_H,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > assn] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.30/0.61       => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61          = ( times_times_assn @ ( G2 @ ( suc @ N ) ) @ ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.nat_ivl_Suc'
% 0.30/0.61  thf(fact_7706_prod_Onat__ivl__Suc_H,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > rat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.30/0.61       => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61          = ( times_times_rat @ ( G2 @ ( suc @ N ) ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.nat_ivl_Suc'
% 0.30/0.61  thf(fact_7707_prod_Onat__ivl__Suc_H,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.30/0.61       => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61          = ( times_times_nat @ ( G2 @ ( suc @ N ) ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.nat_ivl_Suc'
% 0.30/0.61  thf(fact_7708_prod_Onat__ivl__Suc_H,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > int] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.30/0.61       => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 0.30/0.61          = ( times_times_int @ ( G2 @ ( suc @ N ) ) @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.nat_ivl_Suc'
% 0.30/0.61  thf(fact_7709_prod_OatLeast__Suc__atMost,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > code_integer] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61          = ( times_3573771949741848930nteger @ ( G2 @ M ) @ ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeast_Suc_atMost
% 0.30/0.61  thf(fact_7710_prod_OatLeast__Suc__atMost,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > assn] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61          = ( times_times_assn @ ( G2 @ M ) @ ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeast_Suc_atMost
% 0.30/0.61  thf(fact_7711_prod_OatLeast__Suc__atMost,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > rat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61          = ( times_times_rat @ ( G2 @ M ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeast_Suc_atMost
% 0.30/0.61  thf(fact_7712_prod_OatLeast__Suc__atMost,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61          = ( times_times_nat @ ( G2 @ M ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeast_Suc_atMost
% 0.30/0.61  thf(fact_7713_prod_OatLeast__Suc__atMost,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > int] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61          = ( times_times_int @ ( G2 @ M ) @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeast_Suc_atMost
% 0.30/0.61  thf(fact_7714_prod_OatLeastLessThan__Suc,axiom,
% 0.30/0.61      ! [A: nat,B: nat,G2: nat > code_integer] :
% 0.30/0.61        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.61       => ( ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 0.30/0.61          = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G2 @ B ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeastLessThan_Suc
% 0.30/0.61  thf(fact_7715_prod_OatLeastLessThan__Suc,axiom,
% 0.30/0.61      ! [A: nat,B: nat,G2: nat > assn] :
% 0.30/0.61        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.61       => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 0.30/0.61          = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G2 @ B ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeastLessThan_Suc
% 0.30/0.61  thf(fact_7716_prod_OatLeastLessThan__Suc,axiom,
% 0.30/0.61      ! [A: nat,B: nat,G2: nat > rat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.61       => ( ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 0.30/0.61          = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G2 @ B ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeastLessThan_Suc
% 0.30/0.61  thf(fact_7717_prod_OatLeastLessThan__Suc,axiom,
% 0.30/0.61      ! [A: nat,B: nat,G2: nat > nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.61       => ( ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 0.30/0.61          = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G2 @ B ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeastLessThan_Suc
% 0.30/0.61  thf(fact_7718_prod_OatLeastLessThan__Suc,axiom,
% 0.30/0.61      ! [A: nat,B: nat,G2: nat > int] :
% 0.30/0.61        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.61       => ( ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 0.30/0.61          = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G2 @ B ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeastLessThan_Suc
% 0.30/0.61  thf(fact_7719_prod_Olast__plus,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > code_integer] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61          = ( times_3573771949741848930nteger @ ( G2 @ N ) @ ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.last_plus
% 0.30/0.61  thf(fact_7720_prod_Olast__plus,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > assn] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61          = ( times_times_assn @ ( G2 @ N ) @ ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.last_plus
% 0.30/0.61  thf(fact_7721_prod_Olast__plus,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > rat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61          = ( times_times_rat @ ( G2 @ N ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.last_plus
% 0.30/0.61  thf(fact_7722_prod_Olast__plus,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61          = ( times_times_nat @ ( G2 @ N ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.last_plus
% 0.30/0.61  thf(fact_7723_prod_Olast__plus,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > int] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61          = ( times_times_int @ ( G2 @ N ) @ ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.last_plus
% 0.30/0.61  thf(fact_7724_binomial__absorption,axiom,
% 0.30/0.61      ! [K: nat,N: nat] :
% 0.30/0.61        ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 0.30/0.61        = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % binomial_absorption
% 0.30/0.61  thf(fact_7725_prod_OSuc__reindex__ivl,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > code_integer] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 0.30/0.61          = ( times_3573771949741848930nteger @ ( G2 @ M )
% 0.30/0.61            @ ( groups3455450783089532116nteger
% 0.30/0.61              @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.61              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.Suc_reindex_ivl
% 0.30/0.61  thf(fact_7726_prod_OSuc__reindex__ivl,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > assn] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 0.30/0.61          = ( times_times_assn @ ( G2 @ M )
% 0.30/0.61            @ ( groups6906906614972039071t_assn
% 0.30/0.61              @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.61              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.Suc_reindex_ivl
% 0.30/0.61  thf(fact_7727_prod_OSuc__reindex__ivl,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > rat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 0.30/0.61          = ( times_times_rat @ ( G2 @ M )
% 0.30/0.61            @ ( groups73079841787564623at_rat
% 0.30/0.61              @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.61              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.Suc_reindex_ivl
% 0.30/0.61  thf(fact_7728_prod_OSuc__reindex__ivl,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 0.30/0.61          = ( times_times_nat @ ( G2 @ M )
% 0.30/0.61            @ ( groups708209901874060359at_nat
% 0.30/0.61              @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.61              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.Suc_reindex_ivl
% 0.30/0.61  thf(fact_7729_prod_OSuc__reindex__ivl,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > int] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 0.30/0.61          = ( times_times_int @ ( G2 @ M )
% 0.30/0.61            @ ( groups705719431365010083at_int
% 0.30/0.61              @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.61              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.Suc_reindex_ivl
% 0.30/0.61  thf(fact_7730_prod_OatMost__Suc__shift,axiom,
% 0.30/0.61      ! [G2: nat > code_integer,N: nat] :
% 0.30/0.61        ( ( groups3455450783089532116nteger @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( times_3573771949741848930nteger @ ( G2 @ zero_zero_nat )
% 0.30/0.61          @ ( groups3455450783089532116nteger
% 0.30/0.61            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.61            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atMost_Suc_shift
% 0.30/0.61  thf(fact_7731_prod_OatMost__Suc__shift,axiom,
% 0.30/0.61      ! [G2: nat > assn,N: nat] :
% 0.30/0.61        ( ( groups6906906614972039071t_assn @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( times_times_assn @ ( G2 @ zero_zero_nat )
% 0.30/0.61          @ ( groups6906906614972039071t_assn
% 0.30/0.61            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.61            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atMost_Suc_shift
% 0.30/0.61  thf(fact_7732_prod_OatMost__Suc__shift,axiom,
% 0.30/0.61      ! [G2: nat > rat,N: nat] :
% 0.30/0.61        ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( times_times_rat @ ( G2 @ zero_zero_nat )
% 0.30/0.61          @ ( groups73079841787564623at_rat
% 0.30/0.61            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.61            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atMost_Suc_shift
% 0.30/0.61  thf(fact_7733_prod_OatMost__Suc__shift,axiom,
% 0.30/0.61      ! [G2: nat > nat,N: nat] :
% 0.30/0.61        ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( times_times_nat @ ( G2 @ zero_zero_nat )
% 0.30/0.61          @ ( groups708209901874060359at_nat
% 0.30/0.61            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.61            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atMost_Suc_shift
% 0.30/0.61  thf(fact_7734_prod_OatMost__Suc__shift,axiom,
% 0.30/0.61      ! [G2: nat > int,N: nat] :
% 0.30/0.61        ( ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.30/0.61        = ( times_times_int @ ( G2 @ zero_zero_nat )
% 0.30/0.61          @ ( groups705719431365010083at_int
% 0.30/0.61            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.61            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atMost_Suc_shift
% 0.30/0.61  thf(fact_7735_prod_OatLeastLessThan__rev,axiom,
% 0.30/0.61      ! [G2: nat > nat,N: nat,M: nat] :
% 0.30/0.61        ( ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 0.30/0.61        = ( groups708209901874060359at_nat
% 0.30/0.61          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ ( suc @ I3 ) ) )
% 0.30/0.61          @ ( set_or4665077453230672383an_nat @ N @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeastLessThan_rev
% 0.30/0.61  thf(fact_7736_prod_OatLeastLessThan__rev,axiom,
% 0.30/0.61      ! [G2: nat > int,N: nat,M: nat] :
% 0.30/0.61        ( ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 0.30/0.61        = ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ ( suc @ I3 ) ) )
% 0.30/0.61          @ ( set_or4665077453230672383an_nat @ N @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeastLessThan_rev
% 0.30/0.61  thf(fact_7737_choose__dvd,axiom,
% 0.30/0.61      ! [K: nat,N: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.61       => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_dvd
% 0.30/0.61  thf(fact_7738_choose__dvd,axiom,
% 0.30/0.61      ! [K: nat,N: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.61       => ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_dvd
% 0.30/0.61  thf(fact_7739_choose__dvd,axiom,
% 0.30/0.61      ! [K: nat,N: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.61       => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_dvd
% 0.30/0.61  thf(fact_7740_choose__dvd,axiom,
% 0.30/0.61      ! [K: nat,N: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.61       => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_dvd
% 0.30/0.61  thf(fact_7741_prod_Onested__swap,axiom,
% 0.30/0.61      ! [A: nat > nat > nat,N: nat] :
% 0.30/0.61        ( ( groups708209901874060359at_nat
% 0.30/0.61          @ ^ [I3: nat] : ( groups708209901874060359at_nat @ ( A @ I3 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I3 ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.30/0.61        = ( groups708209901874060359at_nat
% 0.30/0.61          @ ^ [J3: nat] :
% 0.30/0.61              ( groups708209901874060359at_nat
% 0.30/0.61              @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 0.30/0.61              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 0.30/0.61          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.nested_swap
% 0.30/0.61  thf(fact_7742_prod_Onested__swap,axiom,
% 0.30/0.61      ! [A: nat > nat > int,N: nat] :
% 0.30/0.61        ( ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [I3: nat] : ( groups705719431365010083at_int @ ( A @ I3 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I3 ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.30/0.61        = ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [J3: nat] :
% 0.30/0.61              ( groups705719431365010083at_int
% 0.30/0.61              @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 0.30/0.61              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 0.30/0.61          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.nested_swap
% 0.30/0.61  thf(fact_7743_fact__numeral,axiom,
% 0.30/0.61      ! [K: num] :
% 0.30/0.61        ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 0.30/0.61        = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_numeral
% 0.30/0.61  thf(fact_7744_fact__numeral,axiom,
% 0.30/0.61      ! [K: num] :
% 0.30/0.61        ( ( semiri3624122377584611663nteger @ ( numeral_numeral_nat @ K ) )
% 0.30/0.61        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ K ) @ ( semiri3624122377584611663nteger @ ( pred_numeral @ K ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_numeral
% 0.30/0.61  thf(fact_7745_fact__numeral,axiom,
% 0.30/0.61      ! [K: num] :
% 0.30/0.61        ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ K ) )
% 0.30/0.61        = ( times_times_rat @ ( numeral_numeral_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( pred_numeral @ K ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_numeral
% 0.30/0.61  thf(fact_7746_fact__numeral,axiom,
% 0.30/0.61      ! [K: num] :
% 0.30/0.61        ( ( semiri2447717529341329178atural @ ( numeral_numeral_nat @ K ) )
% 0.30/0.61        = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ K ) @ ( semiri2447717529341329178atural @ ( pred_numeral @ K ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_numeral
% 0.30/0.61  thf(fact_7747_fact__numeral,axiom,
% 0.30/0.61      ! [K: num] :
% 0.30/0.61        ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 0.30/0.61        = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_numeral
% 0.30/0.61  thf(fact_7748_prod__atLeastAtMost__code,axiom,
% 0.30/0.61      ! [F2: nat > code_integer,A: nat,B: nat] :
% 0.30/0.61        ( ( groups3455450783089532116nteger @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.30/0.61        = ( set_fo1084959871951514735nteger
% 0.30/0.61          @ ^ [A3: nat] : ( times_3573771949741848930nteger @ ( F2 @ A3 ) )
% 0.30/0.61          @ A
% 0.30/0.61          @ B
% 0.30/0.61          @ one_one_Code_integer ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_atLeastAtMost_code
% 0.30/0.61  thf(fact_7749_prod__atLeastAtMost__code,axiom,
% 0.30/0.61      ! [F2: nat > assn,A: nat,B: nat] :
% 0.30/0.61        ( ( groups6906906614972039071t_assn @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.30/0.61        = ( set_fo1959793692361082170t_assn
% 0.30/0.61          @ ^ [A3: nat] : ( times_times_assn @ ( F2 @ A3 ) )
% 0.30/0.61          @ A
% 0.30/0.61          @ B
% 0.30/0.61          @ one_one_assn ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_atLeastAtMost_code
% 0.30/0.61  thf(fact_7750_prod__atLeastAtMost__code,axiom,
% 0.30/0.61      ! [F2: nat > rat,A: nat,B: nat] :
% 0.30/0.61        ( ( groups73079841787564623at_rat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.30/0.61        = ( set_fo1949268297981939178at_rat
% 0.30/0.61          @ ^ [A3: nat] : ( times_times_rat @ ( F2 @ A3 ) )
% 0.30/0.61          @ A
% 0.30/0.61          @ B
% 0.30/0.61          @ one_one_rat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_atLeastAtMost_code
% 0.30/0.61  thf(fact_7751_prod__atLeastAtMost__code,axiom,
% 0.30/0.61      ! [F2: nat > nat,A: nat,B: nat] :
% 0.30/0.61        ( ( groups708209901874060359at_nat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.30/0.61        = ( set_fo2584398358068434914at_nat
% 0.30/0.61          @ ^ [A3: nat] : ( times_times_nat @ ( F2 @ A3 ) )
% 0.30/0.61          @ A
% 0.30/0.61          @ B
% 0.30/0.61          @ one_one_nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_atLeastAtMost_code
% 0.30/0.61  thf(fact_7752_prod__atLeastAtMost__code,axiom,
% 0.30/0.61      ! [F2: nat > int,A: nat,B: nat] :
% 0.30/0.61        ( ( groups705719431365010083at_int @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.30/0.61        = ( set_fo2581907887559384638at_int
% 0.30/0.61          @ ^ [A3: nat] : ( times_times_int @ ( F2 @ A3 ) )
% 0.30/0.61          @ A
% 0.30/0.61          @ B
% 0.30/0.61          @ one_one_int ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod_atLeastAtMost_code
% 0.30/0.61  thf(fact_7753_sum__choose__lower,axiom,
% 0.30/0.61      ! [R3: nat,N: nat] :
% 0.30/0.61        ( ( groups3542108847815614940at_nat
% 0.30/0.61          @ ^ [K4: nat] : ( binomial @ ( plus_plus_nat @ R3 @ K4 ) @ K4 )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.61        = ( binomial @ ( suc @ ( plus_plus_nat @ R3 @ N ) ) @ N ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_choose_lower
% 0.30/0.61  thf(fact_7754_choose__rising__sum_I2_J,axiom,
% 0.30/0.61      ! [N: nat,M: nat] :
% 0.30/0.61        ( ( groups3542108847815614940at_nat
% 0.30/0.61          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 0.30/0.61          @ ( set_ord_atMost_nat @ M ) )
% 0.30/0.61        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ M ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_rising_sum(2)
% 0.30/0.61  thf(fact_7755_choose__rising__sum_I1_J,axiom,
% 0.30/0.61      ! [N: nat,M: nat] :
% 0.30/0.61        ( ( groups3542108847815614940at_nat
% 0.30/0.61          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 0.30/0.61          @ ( set_ord_atMost_nat @ M ) )
% 0.30/0.61        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_rising_sum(1)
% 0.30/0.61  thf(fact_7756_binomial__code,axiom,
% 0.30/0.61      ( binomial
% 0.30/0.61      = ( ^ [N2: nat,K4: nat] : ( if_nat @ ( ord_less_nat @ N2 @ K4 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K4 ) ) @ ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K4 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N2 @ K4 ) @ one_one_nat ) @ N2 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K4 ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % binomial_code
% 0.30/0.61  thf(fact_7757_prod_Ohead__if,axiom,
% 0.30/0.61      ! [N: nat,M: nat,G2: nat > code_integer] :
% 0.30/0.61        ( ( ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61            = one_one_Code_integer ) )
% 0.30/0.61        & ( ~ ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61            = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G2 @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.head_if
% 0.30/0.61  thf(fact_7758_prod_Ohead__if,axiom,
% 0.30/0.61      ! [N: nat,M: nat,G2: nat > assn] :
% 0.30/0.61        ( ( ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61            = one_one_assn ) )
% 0.30/0.61        & ( ~ ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61            = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G2 @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.head_if
% 0.30/0.61  thf(fact_7759_prod_Ohead__if,axiom,
% 0.30/0.61      ! [N: nat,M: nat,G2: nat > rat] :
% 0.30/0.61        ( ( ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61            = one_one_rat ) )
% 0.30/0.61        & ( ~ ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61            = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G2 @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.head_if
% 0.30/0.61  thf(fact_7760_prod_Ohead__if,axiom,
% 0.30/0.61      ! [N: nat,M: nat,G2: nat > nat] :
% 0.30/0.61        ( ( ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61            = one_one_nat ) )
% 0.30/0.61        & ( ~ ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61            = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G2 @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.head_if
% 0.30/0.61  thf(fact_7761_prod_Ohead__if,axiom,
% 0.30/0.61      ! [N: nat,M: nat,G2: nat > int] :
% 0.30/0.61        ( ( ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61            = one_one_int ) )
% 0.30/0.61        & ( ~ ( ord_less_nat @ N @ M )
% 0.30/0.61         => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 0.30/0.61            = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G2 @ N ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.head_if
% 0.30/0.61  thf(fact_7762_prod_Oub__add__nat,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > code_integer,P4: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.30/0.61       => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 0.30/0.61          = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.ub_add_nat
% 0.30/0.61  thf(fact_7763_prod_Oub__add__nat,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > assn,P4: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.30/0.61       => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 0.30/0.61          = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.ub_add_nat
% 0.30/0.61  thf(fact_7764_prod_Oub__add__nat,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > rat,P4: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.30/0.61       => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 0.30/0.61          = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.ub_add_nat
% 0.30/0.61  thf(fact_7765_prod_Oub__add__nat,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > nat,P4: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.30/0.61       => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 0.30/0.61          = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.ub_add_nat
% 0.30/0.61  thf(fact_7766_prod_Oub__add__nat,axiom,
% 0.30/0.61      ! [M: nat,N: nat,G2: nat > int,P4: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.30/0.61       => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 0.30/0.61          = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.ub_add_nat
% 0.30/0.61  thf(fact_7767_choose__reduce__nat,axiom,
% 0.30/0.61      ! [N: nat,K: nat] :
% 0.30/0.61        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.61       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.30/0.61         => ( ( binomial @ N @ K )
% 0.30/0.61            = ( 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 ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_reduce_nat
% 0.30/0.61  thf(fact_7768_times__binomial__minus1__eq,axiom,
% 0.30/0.61      ! [K: nat,N: nat] :
% 0.30/0.61        ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.30/0.61       => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 0.30/0.61          = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % times_binomial_minus1_eq
% 0.30/0.61  thf(fact_7769_prod_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 0.30/0.61      ! [G2: nat > nat,N: nat,M: nat] :
% 0.30/0.61        ( ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 0.30/0.61        = ( groups708209901874060359at_nat
% 0.30/0.61          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeastLessThan_rev_at_least_Suc_atMost
% 0.30/0.61  thf(fact_7770_prod_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 0.30/0.61      ! [G2: nat > int,N: nat,M: nat] :
% 0.30/0.61        ( ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 0.30/0.61        = ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.atLeastLessThan_rev_at_least_Suc_atMost
% 0.30/0.61  thf(fact_7771_pochhammer__prod,axiom,
% 0.30/0.61      ( comm_s4028243227959126397er_rat
% 0.30/0.61      = ( ^ [A3: rat,N2: nat] :
% 0.30/0.61            ( groups73079841787564623at_rat
% 0.30/0.61            @ ^ [I3: nat] : ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ I3 ) )
% 0.30/0.61            @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_prod
% 0.30/0.61  thf(fact_7772_pochhammer__prod,axiom,
% 0.30/0.61      ( comm_s4663373288045622133er_nat
% 0.30/0.61      = ( ^ [A3: nat,N2: nat] :
% 0.30/0.61            ( groups708209901874060359at_nat
% 0.30/0.61            @ ^ [I3: nat] : ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ I3 ) )
% 0.30/0.61            @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_prod
% 0.30/0.61  thf(fact_7773_pochhammer__prod,axiom,
% 0.30/0.61      ( comm_s4660882817536571857er_int
% 0.30/0.61      = ( ^ [A3: int,N2: nat] :
% 0.30/0.61            ( groups705719431365010083at_int
% 0.30/0.61            @ ^ [I3: nat] : ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ I3 ) )
% 0.30/0.61            @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_prod
% 0.30/0.61  thf(fact_7774_sum__choose__diagonal,axiom,
% 0.30/0.61      ! [M: nat,N: nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.61       => ( ( groups3542108847815614940at_nat
% 0.30/0.61            @ ^ [K4: nat] : ( binomial @ ( minus_minus_nat @ N @ K4 ) @ ( minus_minus_nat @ M @ K4 ) )
% 0.30/0.61            @ ( set_ord_atMost_nat @ M ) )
% 0.30/0.61          = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_choose_diagonal
% 0.30/0.61  thf(fact_7775_vandermonde,axiom,
% 0.30/0.61      ! [M: nat,N: nat,R3: nat] :
% 0.30/0.61        ( ( groups3542108847815614940at_nat
% 0.30/0.61          @ ^ [K4: nat] : ( times_times_nat @ ( binomial @ M @ K4 ) @ ( binomial @ N @ ( minus_minus_nat @ R3 @ K4 ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ R3 ) )
% 0.30/0.61        = ( binomial @ ( plus_plus_nat @ M @ N ) @ R3 ) ) ).
% 0.30/0.61  
% 0.30/0.61  % vandermonde
% 0.30/0.61  thf(fact_7776_binomial__addition__formula,axiom,
% 0.30/0.61      ! [N: nat,K: nat] :
% 0.30/0.61        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.61       => ( ( binomial @ N @ ( suc @ K ) )
% 0.30/0.61          = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % binomial_addition_formula
% 0.30/0.61  thf(fact_7777_pochhammer__Suc__prod,axiom,
% 0.30/0.61      ! [A: rat,N: nat] :
% 0.30/0.61        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 0.30/0.61        = ( groups73079841787564623at_rat
% 0.30/0.61          @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I3 ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_Suc_prod
% 0.30/0.61  thf(fact_7778_pochhammer__Suc__prod,axiom,
% 0.30/0.61      ! [A: nat,N: nat] :
% 0.30/0.61        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 0.30/0.61        = ( groups708209901874060359at_nat
% 0.30/0.61          @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I3 ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_Suc_prod
% 0.30/0.61  thf(fact_7779_pochhammer__Suc__prod,axiom,
% 0.30/0.61      ! [A: int,N: nat] :
% 0.30/0.61        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 0.30/0.61        = ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [I3: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I3 ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_Suc_prod
% 0.30/0.61  thf(fact_7780_pochhammer__prod__rev,axiom,
% 0.30/0.61      ( comm_s4028243227959126397er_rat
% 0.30/0.61      = ( ^ [A3: rat,N2: nat] :
% 0.30/0.61            ( groups73079841787564623at_rat
% 0.30/0.61            @ ^ [I3: nat] : ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 0.30/0.61            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_prod_rev
% 0.30/0.61  thf(fact_7781_pochhammer__prod__rev,axiom,
% 0.30/0.61      ( comm_s4663373288045622133er_nat
% 0.30/0.61      = ( ^ [A3: nat,N2: nat] :
% 0.30/0.61            ( groups708209901874060359at_nat
% 0.30/0.61            @ ^ [I3: nat] : ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 0.30/0.61            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_prod_rev
% 0.30/0.61  thf(fact_7782_pochhammer__prod__rev,axiom,
% 0.30/0.61      ( comm_s4660882817536571857er_int
% 0.30/0.61      = ( ^ [A3: int,N2: nat] :
% 0.30/0.61            ( groups705719431365010083at_int
% 0.30/0.61            @ ^ [I3: nat] : ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 0.30/0.61            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_prod_rev
% 0.30/0.61  thf(fact_7783_fact__num__eq__if,axiom,
% 0.30/0.61      ( semiri3624122377584611663nteger
% 0.30/0.61      = ( ^ [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 ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_num_eq_if
% 0.30/0.61  thf(fact_7784_fact__num__eq__if,axiom,
% 0.30/0.61      ( semiri1406184849735516958ct_int
% 0.30/0.61      = ( ^ [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 ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_num_eq_if
% 0.30/0.61  thf(fact_7785_fact__num__eq__if,axiom,
% 0.30/0.61      ( semiri773545260158071498ct_rat
% 0.30/0.61      = ( ^ [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 ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_num_eq_if
% 0.30/0.61  thf(fact_7786_fact__num__eq__if,axiom,
% 0.30/0.61      ( semiri1408675320244567234ct_nat
% 0.30/0.61      = ( ^ [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 ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_num_eq_if
% 0.30/0.61  thf(fact_7787_fact__reduce,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.61       => ( ( semiri3624122377584611663nteger @ N )
% 0.30/0.61          = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_reduce
% 0.30/0.61  thf(fact_7788_fact__reduce,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.61       => ( ( semiri1406184849735516958ct_int @ N )
% 0.30/0.61          = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_reduce
% 0.30/0.61  thf(fact_7789_fact__reduce,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.61       => ( ( semiri773545260158071498ct_rat @ N )
% 0.30/0.61          = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_reduce
% 0.30/0.61  thf(fact_7790_fact__reduce,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.61       => ( ( semiri1408675320244567234ct_nat @ N )
% 0.30/0.61          = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_reduce
% 0.30/0.61  thf(fact_7791_fact__code,axiom,
% 0.30/0.61      ( semiri1406184849735516958ct_int
% 0.30/0.61      = ( ^ [N2: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_code
% 0.30/0.61  thf(fact_7792_fact__code,axiom,
% 0.30/0.61      ( semiri773545260158071498ct_rat
% 0.30/0.61      = ( ^ [N2: nat] : ( semiri681578069525770553at_rat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_code
% 0.30/0.61  thf(fact_7793_fact__code,axiom,
% 0.30/0.61      ( semiri1408675320244567234ct_nat
% 0.30/0.61      = ( ^ [N2: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % fact_code
% 0.30/0.61  thf(fact_7794_pochhammer__same,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ N )
% 0.30/0.61        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_same
% 0.30/0.61  thf(fact_7795_pochhammer__same,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ N )
% 0.30/0.61        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_same
% 0.30/0.61  thf(fact_7796_pochhammer__same,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ N )
% 0.30/0.61        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_same
% 0.30/0.61  thf(fact_7797_choose__row__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.61        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_row_sum
% 0.30/0.61  thf(fact_7798_binomial,axiom,
% 0.30/0.61      ! [A: nat,B: nat,N: nat] :
% 0.30/0.61        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 0.30/0.61        = ( groups3542108847815614940at_nat
% 0.30/0.61          @ ^ [K4: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K4 ) ) @ ( power_power_nat @ A @ K4 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K4 ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % binomial
% 0.30/0.61  thf(fact_7799_choose__two,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.61        = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_two
% 0.30/0.61  thf(fact_7800_prod_Oin__pairs,axiom,
% 0.30/0.61      ! [G2: nat > code_integer,M: nat,N: nat] :
% 0.30/0.61        ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.30/0.61        = ( groups3455450783089532116nteger
% 0.30/0.61          @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.in_pairs
% 0.30/0.61  thf(fact_7801_prod_Oin__pairs,axiom,
% 0.30/0.61      ! [G2: nat > assn,M: nat,N: nat] :
% 0.30/0.61        ( ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.30/0.61        = ( groups6906906614972039071t_assn
% 0.30/0.61          @ ^ [I3: nat] : ( times_times_assn @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.in_pairs
% 0.30/0.61  thf(fact_7802_prod_Oin__pairs,axiom,
% 0.30/0.61      ! [G2: nat > rat,M: nat,N: nat] :
% 0.30/0.61        ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.30/0.61        = ( groups73079841787564623at_rat
% 0.30/0.61          @ ^ [I3: nat] : ( times_times_rat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.in_pairs
% 0.30/0.61  thf(fact_7803_prod_Oin__pairs,axiom,
% 0.30/0.61      ! [G2: nat > nat,M: nat,N: nat] :
% 0.30/0.61        ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.30/0.61        = ( groups708209901874060359at_nat
% 0.30/0.61          @ ^ [I3: nat] : ( times_times_nat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.in_pairs
% 0.30/0.61  thf(fact_7804_prod_Oin__pairs,axiom,
% 0.30/0.61      ! [G2: nat > int,M: nat,N: nat] :
% 0.30/0.61        ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.30/0.61        = ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [I3: nat] : ( times_times_int @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.in_pairs
% 0.30/0.61  thf(fact_7805_prod_Oin__pairs__0,axiom,
% 0.30/0.61      ! [G2: nat > code_integer,N: nat] :
% 0.30/0.61        ( ( groups3455450783089532116nteger @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.30/0.61        = ( groups3455450783089532116nteger
% 0.30/0.61          @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.in_pairs_0
% 0.30/0.61  thf(fact_7806_prod_Oin__pairs__0,axiom,
% 0.30/0.61      ! [G2: nat > assn,N: nat] :
% 0.30/0.61        ( ( groups6906906614972039071t_assn @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.30/0.61        = ( groups6906906614972039071t_assn
% 0.30/0.61          @ ^ [I3: nat] : ( times_times_assn @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.in_pairs_0
% 0.30/0.61  thf(fact_7807_prod_Oin__pairs__0,axiom,
% 0.30/0.61      ! [G2: nat > rat,N: nat] :
% 0.30/0.61        ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.30/0.61        = ( groups73079841787564623at_rat
% 0.30/0.61          @ ^ [I3: nat] : ( times_times_rat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.in_pairs_0
% 0.30/0.61  thf(fact_7808_prod_Oin__pairs__0,axiom,
% 0.30/0.61      ! [G2: nat > nat,N: nat] :
% 0.30/0.61        ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.30/0.61        = ( groups708209901874060359at_nat
% 0.30/0.61          @ ^ [I3: nat] : ( times_times_nat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.in_pairs_0
% 0.30/0.61  thf(fact_7809_prod_Oin__pairs__0,axiom,
% 0.30/0.61      ! [G2: nat > int,N: nat] :
% 0.30/0.61        ( ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.30/0.61        = ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [I3: nat] : ( times_times_int @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.in_pairs_0
% 0.30/0.61  thf(fact_7810_gbinomial__altdef__of__nat,axiom,
% 0.30/0.61      ( gbinomial_rat
% 0.30/0.61      = ( ^ [A3: rat,K4: nat] :
% 0.30/0.61            ( groups73079841787564623at_rat
% 0.30/0.61            @ ^ [I3: nat] : ( divide_divide_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ I3 ) ) @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ K4 @ I3 ) ) )
% 0.30/0.61            @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K4 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_altdef_of_nat
% 0.30/0.61  thf(fact_7811_pochhammer__Suc__prod__rev,axiom,
% 0.30/0.61      ! [A: rat,N: nat] :
% 0.30/0.61        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 0.30/0.61        = ( groups73079841787564623at_rat
% 0.30/0.61          @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I3 ) ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_Suc_prod_rev
% 0.30/0.61  thf(fact_7812_pochhammer__Suc__prod__rev,axiom,
% 0.30/0.61      ! [A: nat,N: nat] :
% 0.30/0.61        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 0.30/0.61        = ( groups708209901874060359at_nat
% 0.30/0.61          @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I3 ) ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_Suc_prod_rev
% 0.30/0.61  thf(fact_7813_pochhammer__Suc__prod__rev,axiom,
% 0.30/0.61      ! [A: int,N: nat] :
% 0.30/0.61        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 0.30/0.61        = ( groups705719431365010083at_int
% 0.30/0.61          @ ^ [I3: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I3 ) ) )
% 0.30/0.61          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_Suc_prod_rev
% 0.30/0.61  thf(fact_7814_binomial__ring,axiom,
% 0.30/0.61      ! [A: code_integer,B: code_integer,N: nat] :
% 0.30/0.61        ( ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ N )
% 0.30/0.61        = ( groups7501900531339628137nteger
% 0.30/0.61          @ ^ [K4: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( binomial @ N @ K4 ) ) @ ( power_8256067586552552935nteger @ A @ K4 ) ) @ ( power_8256067586552552935nteger @ B @ ( minus_minus_nat @ N @ K4 ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % binomial_ring
% 0.30/0.61  thf(fact_7815_binomial__ring,axiom,
% 0.30/0.61      ! [A: int,B: int,N: nat] :
% 0.30/0.61        ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N )
% 0.30/0.61        = ( groups3539618377306564664at_int
% 0.30/0.61          @ ^ [K4: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K4 ) ) @ ( power_power_int @ A @ K4 ) ) @ ( power_power_int @ B @ ( minus_minus_nat @ N @ K4 ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % binomial_ring
% 0.30/0.61  thf(fact_7816_binomial__ring,axiom,
% 0.30/0.61      ! [A: rat,B: rat,N: nat] :
% 0.30/0.61        ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 0.30/0.61        = ( groups2906978787729119204at_rat
% 0.30/0.61          @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K4 ) ) @ ( power_power_rat @ A @ K4 ) ) @ ( power_power_rat @ B @ ( minus_minus_nat @ N @ K4 ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % binomial_ring
% 0.30/0.61  thf(fact_7817_binomial__ring,axiom,
% 0.30/0.61      ! [A: nat,B: nat,N: nat] :
% 0.30/0.61        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 0.30/0.61        = ( groups3542108847815614940at_nat
% 0.30/0.61          @ ^ [K4: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K4 ) ) @ ( power_power_nat @ A @ K4 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K4 ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % binomial_ring
% 0.30/0.61  thf(fact_7818_pochhammer__binomial__sum,axiom,
% 0.30/0.61      ! [A: code_integer,B: code_integer,N: nat] :
% 0.30/0.61        ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ N )
% 0.30/0.61        = ( groups7501900531339628137nteger
% 0.30/0.61          @ ^ [K4: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( binomial @ N @ K4 ) ) @ ( comm_s8582702949713902594nteger @ A @ K4 ) ) @ ( comm_s8582702949713902594nteger @ B @ ( minus_minus_nat @ N @ K4 ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_binomial_sum
% 0.30/0.61  thf(fact_7819_pochhammer__binomial__sum,axiom,
% 0.30/0.61      ! [A: int,B: int,N: nat] :
% 0.30/0.61        ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N )
% 0.30/0.61        = ( groups3539618377306564664at_int
% 0.30/0.61          @ ^ [K4: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K4 ) ) @ ( comm_s4660882817536571857er_int @ A @ K4 ) ) @ ( comm_s4660882817536571857er_int @ B @ ( minus_minus_nat @ N @ K4 ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_binomial_sum
% 0.30/0.61  thf(fact_7820_pochhammer__binomial__sum,axiom,
% 0.30/0.61      ! [A: rat,B: rat,N: nat] :
% 0.30/0.61        ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 0.30/0.61        = ( groups2906978787729119204at_rat
% 0.30/0.61          @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K4 ) ) @ ( comm_s4028243227959126397er_rat @ A @ K4 ) ) @ ( comm_s4028243227959126397er_rat @ B @ ( minus_minus_nat @ N @ K4 ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % pochhammer_binomial_sum
% 0.30/0.61  thf(fact_7821_gbinomial__pochhammer_H,axiom,
% 0.30/0.61      ( gbinomial_rat
% 0.30/0.61      = ( ^ [A3: rat,K4: nat] : ( divide_divide_rat @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ K4 ) ) @ one_one_rat ) @ K4 ) @ ( semiri773545260158071498ct_rat @ K4 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_pochhammer'
% 0.30/0.61  thf(fact_7822_choose__square__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( groups3542108847815614940at_nat
% 0.30/0.61          @ ^ [K4: nat] : ( power_power_nat @ ( binomial @ N @ K4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.61        = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_square_sum
% 0.30/0.61  thf(fact_7823_gbinomial__pochhammer,axiom,
% 0.30/0.61      ( gbinomial_rat
% 0.30/0.61      = ( ^ [A3: rat,K4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K4 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ A3 ) @ K4 ) ) @ ( semiri773545260158071498ct_rat @ K4 ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % gbinomial_pochhammer
% 0.30/0.61  thf(fact_7824_prod_Ozero__middle,axiom,
% 0.30/0.61      ! [P4: nat,K: nat,G2: nat > code_integer,H3: nat > code_integer] :
% 0.30/0.61        ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 0.30/0.61       => ( ( ord_less_eq_nat @ K @ P4 )
% 0.30/0.61         => ( ( groups3455450783089532116nteger
% 0.30/0.61              @ ^ [J3: nat] : ( if_Code_integer @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( if_Code_integer @ ( J3 = K ) @ one_one_Code_integer @ ( H3 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ P4 ) )
% 0.30/0.61            = ( groups3455450783089532116nteger
% 0.30/0.61              @ ^ [J3: nat] : ( if_Code_integer @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( H3 @ J3 ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.zero_middle
% 0.30/0.61  thf(fact_7825_prod_Ozero__middle,axiom,
% 0.30/0.61      ! [P4: nat,K: nat,G2: nat > assn,H3: nat > assn] :
% 0.30/0.61        ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 0.30/0.61       => ( ( ord_less_eq_nat @ K @ P4 )
% 0.30/0.61         => ( ( groups6906906614972039071t_assn
% 0.30/0.61              @ ^ [J3: nat] : ( if_assn @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( if_assn @ ( J3 = K ) @ one_one_assn @ ( H3 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ P4 ) )
% 0.30/0.61            = ( groups6906906614972039071t_assn
% 0.30/0.61              @ ^ [J3: nat] : ( if_assn @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( H3 @ J3 ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.zero_middle
% 0.30/0.61  thf(fact_7826_prod_Ozero__middle,axiom,
% 0.30/0.61      ! [P4: nat,K: nat,G2: nat > rat,H3: nat > rat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 0.30/0.61       => ( ( ord_less_eq_nat @ K @ P4 )
% 0.30/0.61         => ( ( groups73079841787564623at_rat
% 0.30/0.61              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( if_rat @ ( J3 = K ) @ one_one_rat @ ( H3 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ P4 ) )
% 0.30/0.61            = ( groups73079841787564623at_rat
% 0.30/0.61              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( H3 @ J3 ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.zero_middle
% 0.30/0.61  thf(fact_7827_prod_Ozero__middle,axiom,
% 0.30/0.61      ! [P4: nat,K: nat,G2: nat > nat,H3: nat > nat] :
% 0.30/0.61        ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 0.30/0.61       => ( ( ord_less_eq_nat @ K @ P4 )
% 0.30/0.61         => ( ( groups708209901874060359at_nat
% 0.30/0.61              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( if_nat @ ( J3 = K ) @ one_one_nat @ ( H3 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ P4 ) )
% 0.30/0.61            = ( groups708209901874060359at_nat
% 0.30/0.61              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( H3 @ J3 ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.zero_middle
% 0.30/0.61  thf(fact_7828_prod_Ozero__middle,axiom,
% 0.30/0.61      ! [P4: nat,K: nat,G2: nat > int,H3: nat > int] :
% 0.30/0.61        ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 0.30/0.61       => ( ( ord_less_eq_nat @ K @ P4 )
% 0.30/0.61         => ( ( groups705719431365010083at_int
% 0.30/0.61              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( if_int @ ( J3 = K ) @ one_one_int @ ( H3 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ P4 ) )
% 0.30/0.61            = ( groups705719431365010083at_int
% 0.30/0.61              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( H3 @ J3 ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.zero_middle
% 0.30/0.61  thf(fact_7829_choose__alternating__linear__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( N != one_one_nat )
% 0.30/0.61       => ( ( groups7501900531339628137nteger
% 0.30/0.61            @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I3 ) @ ( semiri4939895301339042750nteger @ I3 ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I3 ) ) )
% 0.30/0.61            @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.61          = zero_z3403309356797280102nteger ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_alternating_linear_sum
% 0.30/0.61  thf(fact_7830_choose__alternating__linear__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( N != one_one_nat )
% 0.30/0.61       => ( ( groups3539618377306564664at_int
% 0.30/0.61            @ ^ [I3: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I3 ) @ ( semiri1314217659103216013at_int @ I3 ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I3 ) ) )
% 0.30/0.61            @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.61          = zero_zero_int ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_alternating_linear_sum
% 0.30/0.61  thf(fact_7831_choose__alternating__linear__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( N != one_one_nat )
% 0.30/0.61       => ( ( groups2906978787729119204at_rat
% 0.30/0.61            @ ^ [I3: nat] : ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I3 ) @ ( semiri681578069525770553at_rat @ I3 ) ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I3 ) ) )
% 0.30/0.61            @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.61          = zero_zero_rat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_alternating_linear_sum
% 0.30/0.61  thf(fact_7832_binomial__r__part__sum,axiom,
% 0.30/0.61      ! [M: nat] :
% 0.30/0.61        ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 0.30/0.61        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % binomial_r_part_sum
% 0.30/0.61  thf(fact_7833_choose__linear__sum,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( groups3542108847815614940at_nat
% 0.30/0.61          @ ^ [I3: nat] : ( times_times_nat @ I3 @ ( binomial @ N @ I3 ) )
% 0.30/0.61          @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.61        = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % choose_linear_sum
% 0.30/0.61  thf(fact_7834_sum_Otriangle__reindex,axiom,
% 0.30/0.61      ! [G2: nat > nat > nat,N: nat] :
% 0.30/0.61        ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G2 )
% 0.30/0.61          @ ( collec3392354462482085612at_nat
% 0.30/0.61            @ ( produc6081775807080527818_nat_o
% 0.30/0.61              @ ^ [I3: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 0.30/0.61        = ( groups3542108847815614940at_nat
% 0.30/0.61          @ ^ [K4: nat] :
% 0.30/0.61              ( groups3542108847815614940at_nat
% 0.30/0.61              @ ^ [I3: nat] : ( G2 @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 0.30/0.61              @ ( set_ord_atMost_nat @ K4 ) )
% 0.30/0.61          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.triangle_reindex
% 0.30/0.61  thf(fact_7835_divide__int__unfold,axiom,
% 0.30/0.61      ! [L: int,K: int,N: nat,M: nat] :
% 0.30/0.61        ( ( ( ( ( sgn_sgn_int @ L )
% 0.30/0.61              = zero_zero_int )
% 0.30/0.61            | ( ( sgn_sgn_int @ K )
% 0.30/0.61              = zero_zero_int )
% 0.30/0.61            | ( N = zero_zero_nat ) )
% 0.30/0.61         => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.30/0.61            = zero_zero_int ) )
% 0.30/0.61        & ( ~ ( ( ( sgn_sgn_int @ L )
% 0.30/0.61                = zero_zero_int )
% 0.30/0.61              | ( ( sgn_sgn_int @ K )
% 0.30/0.61                = zero_zero_int )
% 0.30/0.61              | ( N = zero_zero_nat ) )
% 0.30/0.61         => ( ( ( ( sgn_sgn_int @ K )
% 0.30/0.61                = ( sgn_sgn_int @ L ) )
% 0.30/0.61             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.30/0.61                = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 0.30/0.61            & ( ( ( sgn_sgn_int @ K )
% 0.30/0.61               != ( sgn_sgn_int @ L ) )
% 0.30/0.61             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.30/0.61                = ( uminus_uminus_int
% 0.30/0.61                  @ ( semiri1314217659103216013at_int
% 0.30/0.61                    @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 0.30/0.61                      @ ( zero_n2687167440665602831ol_nat
% 0.30/0.61                        @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % divide_int_unfold
% 0.30/0.61  thf(fact_7836_sum__zero__power_H,axiom,
% 0.30/0.61      ! [A2: set_nat,C: nat > rat,D2: nat > rat] :
% 0.30/0.61        ( ( ( ( finite_finite_nat @ A2 )
% 0.30/0.61            & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.30/0.61         => ( ( groups2906978787729119204at_rat
% 0.30/0.61              @ ^ [I3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) ) @ ( D2 @ I3 ) )
% 0.30/0.61              @ A2 )
% 0.30/0.61            = ( divide_divide_rat @ ( C @ zero_zero_nat ) @ ( D2 @ zero_zero_nat ) ) ) )
% 0.30/0.61        & ( ~ ( ( finite_finite_nat @ A2 )
% 0.30/0.61              & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.30/0.61         => ( ( groups2906978787729119204at_rat
% 0.30/0.61              @ ^ [I3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) ) @ ( D2 @ I3 ) )
% 0.30/0.61              @ A2 )
% 0.30/0.61            = zero_zero_rat ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum_zero_power'
% 0.30/0.61  thf(fact_7837_bezw__0,axiom,
% 0.30/0.61      ! [X: nat] :
% 0.30/0.61        ( ( bezw @ X @ zero_zero_nat )
% 0.30/0.61        = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 0.30/0.61  
% 0.30/0.61  % bezw_0
% 0.30/0.61  thf(fact_7838_drop__bit__numeral__minus__bit1,axiom,
% 0.30/0.61      ! [L: num,K: num] :
% 0.30/0.61        ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.30/0.61        = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % drop_bit_numeral_minus_bit1
% 0.30/0.61  thf(fact_7839_sgn__1,axiom,
% 0.30/0.61      ( ( sgn_sgn_int @ one_one_int )
% 0.30/0.61      = one_one_int ) ).
% 0.30/0.61  
% 0.30/0.61  % sgn_1
% 0.30/0.61  thf(fact_7840_sgn__1,axiom,
% 0.30/0.61      ( ( sgn_sgn_Code_integer @ one_one_Code_integer )
% 0.30/0.61      = one_one_Code_integer ) ).
% 0.30/0.61  
% 0.30/0.61  % sgn_1
% 0.30/0.61  thf(fact_7841_sgn__1,axiom,
% 0.30/0.61      ( ( sgn_sgn_rat @ one_one_rat )
% 0.30/0.61      = one_one_rat ) ).
% 0.30/0.61  
% 0.30/0.61  % sgn_1
% 0.30/0.61  thf(fact_7842_sgn__minus,axiom,
% 0.30/0.61      ! [A: int] :
% 0.30/0.61        ( ( sgn_sgn_int @ ( uminus_uminus_int @ A ) )
% 0.30/0.61        = ( uminus_uminus_int @ ( sgn_sgn_int @ A ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sgn_minus
% 0.30/0.61  thf(fact_7843_sgn__minus,axiom,
% 0.30/0.61      ! [A: code_integer] :
% 0.30/0.61        ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 0.30/0.61        = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ A ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sgn_minus
% 0.30/0.61  thf(fact_7844_sgn__minus,axiom,
% 0.30/0.61      ! [A: rat] :
% 0.30/0.61        ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ A ) )
% 0.30/0.61        = ( uminus_uminus_rat @ ( sgn_sgn_rat @ A ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sgn_minus
% 0.30/0.61  thf(fact_7845_prod_Oinfinite,axiom,
% 0.30/0.61      ! [A2: set_nat,G2: nat > code_integer] :
% 0.30/0.61        ( ~ ( finite_finite_nat @ A2 )
% 0.30/0.61       => ( ( groups3455450783089532116nteger @ G2 @ A2 )
% 0.30/0.61          = one_one_Code_integer ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.infinite
% 0.30/0.61  thf(fact_7846_prod_Oinfinite,axiom,
% 0.30/0.61      ! [A2: set_int,G2: int > code_integer] :
% 0.30/0.61        ( ~ ( finite_finite_int @ A2 )
% 0.30/0.61       => ( ( groups3827104343326376752nteger @ G2 @ A2 )
% 0.30/0.61          = one_one_Code_integer ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.infinite
% 0.30/0.61  thf(fact_7847_prod_Oinfinite,axiom,
% 0.30/0.61      ! [A2: set_nat,G2: nat > assn] :
% 0.30/0.61        ( ~ ( finite_finite_nat @ A2 )
% 0.30/0.61       => ( ( groups6906906614972039071t_assn @ G2 @ A2 )
% 0.30/0.61          = one_one_assn ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.infinite
% 0.30/0.61  thf(fact_7848_prod_Oinfinite,axiom,
% 0.30/0.61      ! [A2: set_int,G2: int > assn] :
% 0.30/0.61        ( ~ ( finite_finite_int @ A2 )
% 0.30/0.61       => ( ( groups7882442080178216443t_assn @ G2 @ A2 )
% 0.30/0.61          = one_one_assn ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.infinite
% 0.30/0.61  thf(fact_7849_prod_Oinfinite,axiom,
% 0.30/0.61      ! [A2: set_nat,G2: nat > rat] :
% 0.30/0.61        ( ~ ( finite_finite_nat @ A2 )
% 0.30/0.61       => ( ( groups73079841787564623at_rat @ G2 @ A2 )
% 0.30/0.61          = one_one_rat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.infinite
% 0.30/0.61  thf(fact_7850_prod_Oinfinite,axiom,
% 0.30/0.61      ! [A2: set_int,G2: int > rat] :
% 0.30/0.61        ( ~ ( finite_finite_int @ A2 )
% 0.30/0.61       => ( ( groups1072433553688619179nt_rat @ G2 @ A2 )
% 0.30/0.61          = one_one_rat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.infinite
% 0.30/0.61  thf(fact_7851_prod_Oinfinite,axiom,
% 0.30/0.61      ! [A2: set_int,G2: int > nat] :
% 0.30/0.61        ( ~ ( finite_finite_int @ A2 )
% 0.30/0.61       => ( ( groups1707563613775114915nt_nat @ G2 @ A2 )
% 0.30/0.61          = one_one_nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.infinite
% 0.30/0.61  thf(fact_7852_prod_Oinfinite,axiom,
% 0.30/0.61      ! [A2: set_nat,G2: nat > nat] :
% 0.30/0.61        ( ~ ( finite_finite_nat @ A2 )
% 0.30/0.61       => ( ( groups708209901874060359at_nat @ G2 @ A2 )
% 0.30/0.61          = one_one_nat ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.infinite
% 0.30/0.61  thf(fact_7853_prod_Oinfinite,axiom,
% 0.30/0.61      ! [A2: set_nat,G2: nat > int] :
% 0.30/0.61        ( ~ ( finite_finite_nat @ A2 )
% 0.30/0.61       => ( ( groups705719431365010083at_int @ G2 @ A2 )
% 0.30/0.61          = one_one_int ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.infinite
% 0.30/0.61  thf(fact_7854_prod_Oinfinite,axiom,
% 0.30/0.61      ! [A2: set_int,G2: int > int] :
% 0.30/0.61        ( ~ ( finite_finite_int @ A2 )
% 0.30/0.61       => ( ( groups1705073143266064639nt_int @ G2 @ A2 )
% 0.30/0.61          = one_one_int ) ) ).
% 0.30/0.61  
% 0.30/0.61  % prod.infinite
% 0.30/0.61  thf(fact_7855_divide__sgn,axiom,
% 0.30/0.61      ! [A: rat,B: rat] :
% 0.30/0.61        ( ( divide_divide_rat @ A @ ( sgn_sgn_rat @ B ) )
% 0.30/0.61        = ( times_times_rat @ A @ ( sgn_sgn_rat @ B ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % divide_sgn
% 0.30/0.61  thf(fact_7856_lessThan__0,axiom,
% 0.30/0.61      ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 0.30/0.61      = bot_bot_set_nat ) ).
% 0.30/0.61  
% 0.30/0.61  % lessThan_0
% 0.30/0.61  thf(fact_7857_drop__bit__minus__one,axiom,
% 0.30/0.61      ! [N: nat] :
% 0.30/0.61        ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.61        = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.30/0.61  
% 0.30/0.61  % drop_bit_minus_one
% 0.30/0.61  thf(fact_7858_sum_Odelta_H,axiom,
% 0.30/0.61      ! [S: set_nat,A: nat,B: nat > code_integer] :
% 0.30/0.61        ( ( finite_finite_nat @ S )
% 0.30/0.61       => ( ( ( member_nat @ A @ S )
% 0.30/0.61           => ( ( groups7501900531339628137nteger
% 0.30/0.61                @ ^ [K4: nat] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 0.30/0.61                @ S )
% 0.30/0.61              = ( B @ A ) ) )
% 0.30/0.61          & ( ~ ( member_nat @ A @ S )
% 0.30/0.61           => ( ( groups7501900531339628137nteger
% 0.30/0.61                @ ^ [K4: nat] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 0.30/0.61                @ S )
% 0.30/0.61              = zero_z3403309356797280102nteger ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.delta'
% 0.30/0.61  thf(fact_7859_sum_Odelta_H,axiom,
% 0.30/0.61      ! [S: set_int,A: int,B: int > code_integer] :
% 0.30/0.61        ( ( finite_finite_int @ S )
% 0.30/0.61       => ( ( ( member_int @ A @ S )
% 0.30/0.61           => ( ( groups7873554091576472773nteger
% 0.30/0.61                @ ^ [K4: int] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 0.30/0.61                @ S )
% 0.30/0.61              = ( B @ A ) ) )
% 0.30/0.61          & ( ~ ( member_int @ A @ S )
% 0.30/0.61           => ( ( groups7873554091576472773nteger
% 0.30/0.61                @ ^ [K4: int] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 0.30/0.61                @ S )
% 0.30/0.61              = zero_z3403309356797280102nteger ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.delta'
% 0.30/0.61  thf(fact_7860_sum_Odelta_H,axiom,
% 0.30/0.61      ! [S: set_nat,A: nat,B: nat > rat] :
% 0.30/0.61        ( ( finite_finite_nat @ S )
% 0.30/0.61       => ( ( ( member_nat @ A @ S )
% 0.30/0.61           => ( ( groups2906978787729119204at_rat
% 0.30/0.61                @ ^ [K4: nat] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_rat )
% 0.30/0.61                @ S )
% 0.30/0.61              = ( B @ A ) ) )
% 0.30/0.61          & ( ~ ( member_nat @ A @ S )
% 0.30/0.61           => ( ( groups2906978787729119204at_rat
% 0.30/0.61                @ ^ [K4: nat] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_rat )
% 0.30/0.61                @ S )
% 0.30/0.61              = zero_zero_rat ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.delta'
% 0.30/0.61  thf(fact_7861_sum_Odelta_H,axiom,
% 0.30/0.61      ! [S: set_int,A: int,B: int > rat] :
% 0.30/0.61        ( ( finite_finite_int @ S )
% 0.30/0.61       => ( ( ( member_int @ A @ S )
% 0.30/0.61           => ( ( groups3906332499630173760nt_rat
% 0.30/0.61                @ ^ [K4: int] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_rat )
% 0.30/0.61                @ S )
% 0.30/0.61              = ( B @ A ) ) )
% 0.30/0.61          & ( ~ ( member_int @ A @ S )
% 0.30/0.61           => ( ( groups3906332499630173760nt_rat
% 0.30/0.61                @ ^ [K4: int] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_rat )
% 0.30/0.61                @ S )
% 0.30/0.61              = zero_zero_rat ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.delta'
% 0.30/0.61  thf(fact_7862_sum_Odelta_H,axiom,
% 0.30/0.61      ! [S: set_int,A: int,B: int > nat] :
% 0.30/0.61        ( ( finite_finite_int @ S )
% 0.30/0.61       => ( ( ( member_int @ A @ S )
% 0.30/0.61           => ( ( groups4541462559716669496nt_nat
% 0.30/0.61                @ ^ [K4: int] : ( if_nat @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_nat )
% 0.30/0.61                @ S )
% 0.30/0.61              = ( B @ A ) ) )
% 0.30/0.61          & ( ~ ( member_int @ A @ S )
% 0.30/0.61           => ( ( groups4541462559716669496nt_nat
% 0.30/0.61                @ ^ [K4: int] : ( if_nat @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_nat )
% 0.30/0.61                @ S )
% 0.30/0.61              = zero_zero_nat ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.delta'
% 0.30/0.61  thf(fact_7863_sum_Odelta_H,axiom,
% 0.30/0.61      ! [S: set_nat,A: nat,B: nat > int] :
% 0.30/0.61        ( ( finite_finite_nat @ S )
% 0.30/0.61       => ( ( ( member_nat @ A @ S )
% 0.30/0.61           => ( ( groups3539618377306564664at_int
% 0.30/0.61                @ ^ [K4: nat] : ( if_int @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_int )
% 0.30/0.61                @ S )
% 0.30/0.61              = ( B @ A ) ) )
% 0.30/0.61          & ( ~ ( member_nat @ A @ S )
% 0.30/0.61           => ( ( groups3539618377306564664at_int
% 0.30/0.61                @ ^ [K4: nat] : ( if_int @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_int )
% 0.30/0.61                @ S )
% 0.30/0.61              = zero_zero_int ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.delta'
% 0.30/0.61  thf(fact_7864_sum_Odelta_H,axiom,
% 0.30/0.61      ! [S: set_nat,A: nat,B: nat > nat] :
% 0.30/0.61        ( ( finite_finite_nat @ S )
% 0.30/0.61       => ( ( ( member_nat @ A @ S )
% 0.30/0.61           => ( ( groups3542108847815614940at_nat
% 0.30/0.61                @ ^ [K4: nat] : ( if_nat @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_nat )
% 0.30/0.61                @ S )
% 0.30/0.61              = ( B @ A ) ) )
% 0.30/0.61          & ( ~ ( member_nat @ A @ S )
% 0.30/0.61           => ( ( groups3542108847815614940at_nat
% 0.30/0.61                @ ^ [K4: nat] : ( if_nat @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_nat )
% 0.30/0.61                @ S )
% 0.30/0.61              = zero_zero_nat ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.delta'
% 0.30/0.61  thf(fact_7865_sum_Odelta_H,axiom,
% 0.30/0.61      ! [S: set_int,A: int,B: int > int] :
% 0.30/0.61        ( ( finite_finite_int @ S )
% 0.30/0.61       => ( ( ( member_int @ A @ S )
% 0.30/0.61           => ( ( groups4538972089207619220nt_int
% 0.30/0.61                @ ^ [K4: int] : ( if_int @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_int )
% 0.30/0.61                @ S )
% 0.30/0.61              = ( B @ A ) ) )
% 0.30/0.61          & ( ~ ( member_int @ A @ S )
% 0.30/0.61           => ( ( groups4538972089207619220nt_int
% 0.30/0.61                @ ^ [K4: int] : ( if_int @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_int )
% 0.30/0.61                @ S )
% 0.30/0.61              = zero_zero_int ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.delta'
% 0.30/0.61  thf(fact_7866_sum_Odelta_H,axiom,
% 0.30/0.61      ! [S: set_set_nat,A: set_nat,B: set_nat > code_integer] :
% 0.30/0.61        ( ( finite1152437895449049373et_nat @ S )
% 0.30/0.61       => ( ( ( member_set_nat @ A @ S )
% 0.30/0.61           => ( ( groups9190459664516455967nteger
% 0.30/0.61                @ ^ [K4: set_nat] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 0.30/0.61                @ S )
% 0.30/0.61              = ( B @ A ) ) )
% 0.30/0.61          & ( ~ ( member_set_nat @ A @ S )
% 0.30/0.61           => ( ( groups9190459664516455967nteger
% 0.30/0.61                @ ^ [K4: set_nat] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 0.30/0.61                @ S )
% 0.30/0.61              = zero_z3403309356797280102nteger ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.delta'
% 0.30/0.61  thf(fact_7867_sum_Odelta_H,axiom,
% 0.30/0.61      ! [S: set_set_nat,A: set_nat,B: set_nat > rat] :
% 0.30/0.61        ( ( finite1152437895449049373et_nat @ S )
% 0.30/0.61       => ( ( ( member_set_nat @ A @ S )
% 0.30/0.61           => ( ( groups7659867448343625626at_rat
% 0.30/0.61                @ ^ [K4: set_nat] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_rat )
% 0.30/0.61                @ S )
% 0.30/0.61              = ( B @ A ) ) )
% 0.30/0.61          & ( ~ ( member_set_nat @ A @ S )
% 0.30/0.61           => ( ( groups7659867448343625626at_rat
% 0.30/0.61                @ ^ [K4: set_nat] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_rat )
% 0.30/0.61                @ S )
% 0.30/0.61              = zero_zero_rat ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.delta'
% 0.30/0.61  thf(fact_7868_sum_Odelta,axiom,
% 0.30/0.61      ! [S: set_nat,A: nat,B: nat > code_integer] :
% 0.30/0.61        ( ( finite_finite_nat @ S )
% 0.30/0.61       => ( ( ( member_nat @ A @ S )
% 0.30/0.61           => ( ( groups7501900531339628137nteger
% 0.30/0.61                @ ^ [K4: nat] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 0.30/0.61                @ S )
% 0.30/0.61              = ( B @ A ) ) )
% 0.30/0.61          & ( ~ ( member_nat @ A @ S )
% 0.30/0.61           => ( ( groups7501900531339628137nteger
% 0.30/0.61                @ ^ [K4: nat] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 0.30/0.61                @ S )
% 0.30/0.61              = zero_z3403309356797280102nteger ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.delta
% 0.30/0.61  thf(fact_7869_sum_Odelta,axiom,
% 0.30/0.61      ! [S: set_int,A: int,B: int > code_integer] :
% 0.30/0.61        ( ( finite_finite_int @ S )
% 0.30/0.61       => ( ( ( member_int @ A @ S )
% 0.30/0.61           => ( ( groups7873554091576472773nteger
% 0.30/0.61                @ ^ [K4: int] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 0.30/0.61                @ S )
% 0.30/0.61              = ( B @ A ) ) )
% 0.30/0.61          & ( ~ ( member_int @ A @ S )
% 0.30/0.61           => ( ( groups7873554091576472773nteger
% 0.30/0.61                @ ^ [K4: int] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 0.30/0.61                @ S )
% 0.30/0.61              = zero_z3403309356797280102nteger ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.delta
% 0.30/0.61  thf(fact_7870_sum_Odelta,axiom,
% 0.30/0.61      ! [S: set_nat,A: nat,B: nat > rat] :
% 0.30/0.61        ( ( finite_finite_nat @ S )
% 0.30/0.61       => ( ( ( member_nat @ A @ S )
% 0.30/0.61           => ( ( groups2906978787729119204at_rat
% 0.30/0.61                @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_rat )
% 0.30/0.61                @ S )
% 0.30/0.61              = ( B @ A ) ) )
% 0.30/0.61          & ( ~ ( member_nat @ A @ S )
% 0.30/0.61           => ( ( groups2906978787729119204at_rat
% 0.30/0.61                @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_rat )
% 0.30/0.61                @ S )
% 0.30/0.61              = zero_zero_rat ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.delta
% 0.30/0.61  thf(fact_7871_sum_Odelta,axiom,
% 0.30/0.61      ! [S: set_int,A: int,B: int > rat] :
% 0.30/0.61        ( ( finite_finite_int @ S )
% 0.30/0.61       => ( ( ( member_int @ A @ S )
% 0.30/0.61           => ( ( groups3906332499630173760nt_rat
% 0.30/0.61                @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_rat )
% 0.30/0.61                @ S )
% 0.30/0.61              = ( B @ A ) ) )
% 0.30/0.61          & ( ~ ( member_int @ A @ S )
% 0.30/0.61           => ( ( groups3906332499630173760nt_rat
% 0.30/0.61                @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_rat )
% 0.30/0.61                @ S )
% 0.30/0.61              = zero_zero_rat ) ) ) ) ).
% 0.30/0.61  
% 0.30/0.61  % sum.delta
% 0.30/0.61  thf(fact_7872_sum_Odelta,axiom,
% 0.30/0.61      ! [S: set_int,A: int,B: int > nat] :
% 0.30/0.61        ( ( finite_finite_int @ S )
% 0.30/0.61       => ( ( ( member_int @ A @ S )
% 0.30/0.61           => ( ( groups4541462559716669496nt_nat
% 0.30/0.61                @ ^ [K4: int] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_nat )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups4541462559716669496nt_nat
% 0.30/0.62                @ ^ [K4: int] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_nat )
% 0.30/0.62                @ S )
% 0.30/0.62              = zero_zero_nat ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.delta
% 0.30/0.62  thf(fact_7873_sum_Odelta,axiom,
% 0.30/0.62      ! [S: set_nat,A: nat,B: nat > int] :
% 0.30/0.62        ( ( finite_finite_nat @ S )
% 0.30/0.62       => ( ( ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups3539618377306564664at_int
% 0.30/0.62                @ ^ [K4: nat] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_int )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups3539618377306564664at_int
% 0.30/0.62                @ ^ [K4: nat] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_int )
% 0.30/0.62                @ S )
% 0.30/0.62              = zero_zero_int ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.delta
% 0.30/0.62  thf(fact_7874_sum_Odelta,axiom,
% 0.30/0.62      ! [S: set_nat,A: nat,B: nat > nat] :
% 0.30/0.62        ( ( finite_finite_nat @ S )
% 0.30/0.62       => ( ( ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups3542108847815614940at_nat
% 0.30/0.62                @ ^ [K4: nat] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_nat )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups3542108847815614940at_nat
% 0.30/0.62                @ ^ [K4: nat] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_nat )
% 0.30/0.62                @ S )
% 0.30/0.62              = zero_zero_nat ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.delta
% 0.30/0.62  thf(fact_7875_sum_Odelta,axiom,
% 0.30/0.62      ! [S: set_int,A: int,B: int > int] :
% 0.30/0.62        ( ( finite_finite_int @ S )
% 0.30/0.62       => ( ( ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups4538972089207619220nt_int
% 0.30/0.62                @ ^ [K4: int] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_int )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups4538972089207619220nt_int
% 0.30/0.62                @ ^ [K4: int] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_int )
% 0.30/0.62                @ S )
% 0.30/0.62              = zero_zero_int ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.delta
% 0.30/0.62  thf(fact_7876_sum_Odelta,axiom,
% 0.30/0.62      ! [S: set_set_nat,A: set_nat,B: set_nat > code_integer] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ S )
% 0.30/0.62       => ( ( ( member_set_nat @ A @ S )
% 0.30/0.62           => ( ( groups9190459664516455967nteger
% 0.30/0.62                @ ^ [K4: set_nat] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_set_nat @ A @ S )
% 0.30/0.62           => ( ( groups9190459664516455967nteger
% 0.30/0.62                @ ^ [K4: set_nat] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 0.30/0.62                @ S )
% 0.30/0.62              = zero_z3403309356797280102nteger ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.delta
% 0.30/0.62  thf(fact_7877_sum_Odelta,axiom,
% 0.30/0.62      ! [S: set_set_nat,A: set_nat,B: set_nat > rat] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ S )
% 0.30/0.62       => ( ( ( member_set_nat @ A @ S )
% 0.30/0.62           => ( ( groups7659867448343625626at_rat
% 0.30/0.62                @ ^ [K4: set_nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_rat )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_set_nat @ A @ S )
% 0.30/0.62           => ( ( groups7659867448343625626at_rat
% 0.30/0.62                @ ^ [K4: set_nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_rat )
% 0.30/0.62                @ S )
% 0.30/0.62              = zero_zero_rat ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.delta
% 0.30/0.62  thf(fact_7878_prod__eq__1__iff,axiom,
% 0.30/0.62      ! [A2: set_int,F2: int > nat] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( ( groups1707563613775114915nt_nat @ F2 @ A2 )
% 0.30/0.62            = one_one_nat )
% 0.30/0.62          = ( ! [X3: int] :
% 0.30/0.62                ( ( member_int @ X3 @ A2 )
% 0.30/0.62               => ( ( F2 @ X3 )
% 0.30/0.62                  = one_one_nat ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod_eq_1_iff
% 0.30/0.62  thf(fact_7879_prod__eq__1__iff,axiom,
% 0.30/0.62      ! [A2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > nat] :
% 0.30/0.62        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.62       => ( ( ( groups4077766827762148844at_nat @ F2 @ A2 )
% 0.30/0.62            = one_one_nat )
% 0.30/0.62          = ( ! [X3: product_prod_nat_nat] :
% 0.30/0.62                ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 0.30/0.62               => ( ( F2 @ X3 )
% 0.30/0.62                  = one_one_nat ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod_eq_1_iff
% 0.30/0.62  thf(fact_7880_prod__eq__1__iff,axiom,
% 0.30/0.62      ! [A2: set_nat,F2: nat > nat] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( ( groups708209901874060359at_nat @ F2 @ A2 )
% 0.30/0.62            = one_one_nat )
% 0.30/0.62          = ( ! [X3: nat] :
% 0.30/0.62                ( ( member_nat @ X3 @ A2 )
% 0.30/0.62               => ( ( F2 @ X3 )
% 0.30/0.62                  = one_one_nat ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod_eq_1_iff
% 0.30/0.62  thf(fact_7881_prod_Odelta,axiom,
% 0.30/0.62      ! [S: set_nat,A: nat,B: nat > code_integer] :
% 0.30/0.62        ( ( finite_finite_nat @ S )
% 0.30/0.62       => ( ( ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups3455450783089532116nteger
% 0.30/0.62                @ ^ [K4: nat] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups3455450783089532116nteger
% 0.30/0.62                @ ^ [K4: nat] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.30/0.62                @ S )
% 0.30/0.62              = one_one_Code_integer ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.delta
% 0.30/0.62  thf(fact_7882_prod_Odelta,axiom,
% 0.30/0.62      ! [S: set_int,A: int,B: int > code_integer] :
% 0.30/0.62        ( ( finite_finite_int @ S )
% 0.30/0.62       => ( ( ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups3827104343326376752nteger
% 0.30/0.62                @ ^ [K4: int] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups3827104343326376752nteger
% 0.30/0.62                @ ^ [K4: int] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.30/0.62                @ S )
% 0.30/0.62              = one_one_Code_integer ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.delta
% 0.30/0.62  thf(fact_7883_prod_Odelta,axiom,
% 0.30/0.62      ! [S: set_nat,A: nat,B: nat > assn] :
% 0.30/0.62        ( ( finite_finite_nat @ S )
% 0.30/0.62       => ( ( ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups6906906614972039071t_assn
% 0.30/0.62                @ ^ [K4: nat] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups6906906614972039071t_assn
% 0.30/0.62                @ ^ [K4: nat] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 0.30/0.62                @ S )
% 0.30/0.62              = one_one_assn ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.delta
% 0.30/0.62  thf(fact_7884_prod_Odelta,axiom,
% 0.30/0.62      ! [S: set_int,A: int,B: int > assn] :
% 0.30/0.62        ( ( finite_finite_int @ S )
% 0.30/0.62       => ( ( ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups7882442080178216443t_assn
% 0.30/0.62                @ ^ [K4: int] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups7882442080178216443t_assn
% 0.30/0.62                @ ^ [K4: int] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 0.30/0.62                @ S )
% 0.30/0.62              = one_one_assn ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.delta
% 0.30/0.62  thf(fact_7885_prod_Odelta,axiom,
% 0.30/0.62      ! [S: set_nat,A: nat,B: nat > rat] :
% 0.30/0.62        ( ( finite_finite_nat @ S )
% 0.30/0.62       => ( ( ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups73079841787564623at_rat
% 0.30/0.62                @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_rat )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups73079841787564623at_rat
% 0.30/0.62                @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_rat )
% 0.30/0.62                @ S )
% 0.30/0.62              = one_one_rat ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.delta
% 0.30/0.62  thf(fact_7886_prod_Odelta,axiom,
% 0.30/0.62      ! [S: set_int,A: int,B: int > rat] :
% 0.30/0.62        ( ( finite_finite_int @ S )
% 0.30/0.62       => ( ( ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups1072433553688619179nt_rat
% 0.30/0.62                @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_rat )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups1072433553688619179nt_rat
% 0.30/0.62                @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_rat )
% 0.30/0.62                @ S )
% 0.30/0.62              = one_one_rat ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.delta
% 0.30/0.62  thf(fact_7887_prod_Odelta,axiom,
% 0.30/0.62      ! [S: set_int,A: int,B: int > nat] :
% 0.30/0.62        ( ( finite_finite_int @ S )
% 0.30/0.62       => ( ( ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups1707563613775114915nt_nat
% 0.30/0.62                @ ^ [K4: int] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_nat )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups1707563613775114915nt_nat
% 0.30/0.62                @ ^ [K4: int] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_nat )
% 0.30/0.62                @ S )
% 0.30/0.62              = one_one_nat ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.delta
% 0.30/0.62  thf(fact_7888_prod_Odelta,axiom,
% 0.30/0.62      ! [S: set_nat,A: nat,B: nat > nat] :
% 0.30/0.62        ( ( finite_finite_nat @ S )
% 0.30/0.62       => ( ( ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups708209901874060359at_nat
% 0.30/0.62                @ ^ [K4: nat] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_nat )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups708209901874060359at_nat
% 0.30/0.62                @ ^ [K4: nat] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_nat )
% 0.30/0.62                @ S )
% 0.30/0.62              = one_one_nat ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.delta
% 0.30/0.62  thf(fact_7889_prod_Odelta,axiom,
% 0.30/0.62      ! [S: set_nat,A: nat,B: nat > int] :
% 0.30/0.62        ( ( finite_finite_nat @ S )
% 0.30/0.62       => ( ( ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups705719431365010083at_int
% 0.30/0.62                @ ^ [K4: nat] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ one_one_int )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups705719431365010083at_int
% 0.30/0.62                @ ^ [K4: nat] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ one_one_int )
% 0.30/0.62                @ S )
% 0.30/0.62              = one_one_int ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.delta
% 0.30/0.62  thf(fact_7890_prod_Odelta,axiom,
% 0.30/0.62      ! [S: set_int,A: int,B: int > int] :
% 0.30/0.62        ( ( finite_finite_int @ S )
% 0.30/0.62       => ( ( ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups1705073143266064639nt_int
% 0.30/0.62                @ ^ [K4: int] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ one_one_int )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups1705073143266064639nt_int
% 0.30/0.62                @ ^ [K4: int] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ one_one_int )
% 0.30/0.62                @ S )
% 0.30/0.62              = one_one_int ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.delta
% 0.30/0.62  thf(fact_7891_prod_Odelta_H,axiom,
% 0.30/0.62      ! [S: set_nat,A: nat,B: nat > code_integer] :
% 0.30/0.62        ( ( finite_finite_nat @ S )
% 0.30/0.62       => ( ( ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups3455450783089532116nteger
% 0.30/0.62                @ ^ [K4: nat] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups3455450783089532116nteger
% 0.30/0.62                @ ^ [K4: nat] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.30/0.62                @ S )
% 0.30/0.62              = one_one_Code_integer ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.delta'
% 0.30/0.62  thf(fact_7892_prod_Odelta_H,axiom,
% 0.30/0.62      ! [S: set_int,A: int,B: int > code_integer] :
% 0.30/0.62        ( ( finite_finite_int @ S )
% 0.30/0.62       => ( ( ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups3827104343326376752nteger
% 0.30/0.62                @ ^ [K4: int] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups3827104343326376752nteger
% 0.30/0.62                @ ^ [K4: int] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 0.30/0.62                @ S )
% 0.30/0.62              = one_one_Code_integer ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.delta'
% 0.30/0.62  thf(fact_7893_prod_Odelta_H,axiom,
% 0.30/0.62      ! [S: set_nat,A: nat,B: nat > assn] :
% 0.30/0.62        ( ( finite_finite_nat @ S )
% 0.30/0.62       => ( ( ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups6906906614972039071t_assn
% 0.30/0.62                @ ^ [K4: nat] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups6906906614972039071t_assn
% 0.30/0.62                @ ^ [K4: nat] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 0.30/0.62                @ S )
% 0.30/0.62              = one_one_assn ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.delta'
% 0.30/0.62  thf(fact_7894_prod_Odelta_H,axiom,
% 0.30/0.62      ! [S: set_int,A: int,B: int > assn] :
% 0.30/0.62        ( ( finite_finite_int @ S )
% 0.30/0.62       => ( ( ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups7882442080178216443t_assn
% 0.30/0.62                @ ^ [K4: int] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups7882442080178216443t_assn
% 0.30/0.62                @ ^ [K4: int] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 0.30/0.62                @ S )
% 0.30/0.62              = one_one_assn ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.delta'
% 0.30/0.62  thf(fact_7895_prod_Odelta_H,axiom,
% 0.30/0.62      ! [S: set_nat,A: nat,B: nat > rat] :
% 0.30/0.62        ( ( finite_finite_nat @ S )
% 0.30/0.62       => ( ( ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups73079841787564623at_rat
% 0.30/0.62                @ ^ [K4: nat] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_rat )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups73079841787564623at_rat
% 0.30/0.62                @ ^ [K4: nat] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_rat )
% 0.30/0.62                @ S )
% 0.30/0.62              = one_one_rat ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.delta'
% 0.30/0.62  thf(fact_7896_prod_Odelta_H,axiom,
% 0.30/0.62      ! [S: set_int,A: int,B: int > rat] :
% 0.30/0.62        ( ( finite_finite_int @ S )
% 0.30/0.62       => ( ( ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups1072433553688619179nt_rat
% 0.30/0.62                @ ^ [K4: int] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_rat )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups1072433553688619179nt_rat
% 0.30/0.62                @ ^ [K4: int] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_rat )
% 0.30/0.62                @ S )
% 0.30/0.62              = one_one_rat ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.delta'
% 0.30/0.62  thf(fact_7897_prod_Odelta_H,axiom,
% 0.30/0.62      ! [S: set_int,A: int,B: int > nat] :
% 0.30/0.62        ( ( finite_finite_int @ S )
% 0.30/0.62       => ( ( ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups1707563613775114915nt_nat
% 0.30/0.62                @ ^ [K4: int] : ( if_nat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_nat )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups1707563613775114915nt_nat
% 0.30/0.62                @ ^ [K4: int] : ( if_nat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_nat )
% 0.30/0.62                @ S )
% 0.30/0.62              = one_one_nat ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.delta'
% 0.30/0.62  thf(fact_7898_prod_Odelta_H,axiom,
% 0.30/0.62      ! [S: set_nat,A: nat,B: nat > nat] :
% 0.30/0.62        ( ( finite_finite_nat @ S )
% 0.30/0.62       => ( ( ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups708209901874060359at_nat
% 0.30/0.62                @ ^ [K4: nat] : ( if_nat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_nat )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups708209901874060359at_nat
% 0.30/0.62                @ ^ [K4: nat] : ( if_nat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_nat )
% 0.30/0.62                @ S )
% 0.30/0.62              = one_one_nat ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.delta'
% 0.30/0.62  thf(fact_7899_prod_Odelta_H,axiom,
% 0.30/0.62      ! [S: set_nat,A: nat,B: nat > int] :
% 0.30/0.62        ( ( finite_finite_nat @ S )
% 0.30/0.62       => ( ( ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups705719431365010083at_int
% 0.30/0.62                @ ^ [K4: nat] : ( if_int @ ( A = K4 ) @ ( B @ K4 ) @ one_one_int )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_nat @ A @ S )
% 0.30/0.62           => ( ( groups705719431365010083at_int
% 0.30/0.62                @ ^ [K4: nat] : ( if_int @ ( A = K4 ) @ ( B @ K4 ) @ one_one_int )
% 0.30/0.62                @ S )
% 0.30/0.62              = one_one_int ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.delta'
% 0.30/0.62  thf(fact_7900_prod_Odelta_H,axiom,
% 0.30/0.62      ! [S: set_int,A: int,B: int > int] :
% 0.30/0.62        ( ( finite_finite_int @ S )
% 0.30/0.62       => ( ( ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups1705073143266064639nt_int
% 0.30/0.62                @ ^ [K4: int] : ( if_int @ ( A = K4 ) @ ( B @ K4 ) @ one_one_int )
% 0.30/0.62                @ S )
% 0.30/0.62              = ( B @ A ) ) )
% 0.30/0.62          & ( ~ ( member_int @ A @ S )
% 0.30/0.62           => ( ( groups1705073143266064639nt_int
% 0.30/0.62                @ ^ [K4: int] : ( if_int @ ( A = K4 ) @ ( B @ K4 ) @ one_one_int )
% 0.30/0.62                @ S )
% 0.30/0.62              = one_one_int ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.delta'
% 0.30/0.62  thf(fact_7901_sgn__pos,axiom,
% 0.30/0.62      ! [A: code_integer] :
% 0.30/0.62        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.62       => ( ( sgn_sgn_Code_integer @ A )
% 0.30/0.62          = one_one_Code_integer ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_pos
% 0.30/0.62  thf(fact_7902_sgn__pos,axiom,
% 0.30/0.62      ! [A: rat] :
% 0.30/0.62        ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.62       => ( ( sgn_sgn_rat @ A )
% 0.30/0.62          = one_one_rat ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_pos
% 0.30/0.62  thf(fact_7903_sgn__pos,axiom,
% 0.30/0.62      ! [A: int] :
% 0.30/0.62        ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.62       => ( ( sgn_sgn_int @ A )
% 0.30/0.62          = one_one_int ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_pos
% 0.30/0.62  thf(fact_7904_prod_Oinsert,axiom,
% 0.30/0.62      ! [A2: set_o,X: $o,G2: $o > code_integer] :
% 0.30/0.62        ( ( finite_finite_o @ A2 )
% 0.30/0.62       => ( ~ ( member_o @ X @ A2 )
% 0.30/0.62         => ( ( groups7694694392188491536nteger @ G2 @ ( insert_o @ X @ A2 ) )
% 0.30/0.62            = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups7694694392188491536nteger @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.insert
% 0.30/0.62  thf(fact_7905_prod_Oinsert,axiom,
% 0.30/0.62      ! [A2: set_nat,X: nat,G2: nat > code_integer] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ~ ( member_nat @ X @ A2 )
% 0.30/0.62         => ( ( groups3455450783089532116nteger @ G2 @ ( insert_nat @ X @ A2 ) )
% 0.30/0.62            = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups3455450783089532116nteger @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.insert
% 0.30/0.62  thf(fact_7906_prod_Oinsert,axiom,
% 0.30/0.62      ! [A2: set_int,X: int,G2: int > code_integer] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ~ ( member_int @ X @ A2 )
% 0.30/0.62         => ( ( groups3827104343326376752nteger @ G2 @ ( insert_int @ X @ A2 ) )
% 0.30/0.62            = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups3827104343326376752nteger @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.insert
% 0.30/0.62  thf(fact_7907_prod_Oinsert,axiom,
% 0.30/0.62      ! [A2: set_o,X: $o,G2: $o > assn] :
% 0.30/0.62        ( ( finite_finite_o @ A2 )
% 0.30/0.62       => ( ~ ( member_o @ X @ A2 )
% 0.30/0.62         => ( ( groups5301882518646026715o_assn @ G2 @ ( insert_o @ X @ A2 ) )
% 0.30/0.62            = ( times_times_assn @ ( G2 @ X ) @ ( groups5301882518646026715o_assn @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.insert
% 0.30/0.62  thf(fact_7908_prod_Oinsert,axiom,
% 0.30/0.62      ! [A2: set_nat,X: nat,G2: nat > assn] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ~ ( member_nat @ X @ A2 )
% 0.30/0.62         => ( ( groups6906906614972039071t_assn @ G2 @ ( insert_nat @ X @ A2 ) )
% 0.30/0.62            = ( times_times_assn @ ( G2 @ X ) @ ( groups6906906614972039071t_assn @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.insert
% 0.30/0.62  thf(fact_7909_prod_Oinsert,axiom,
% 0.30/0.62      ! [A2: set_int,X: int,G2: int > assn] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ~ ( member_int @ X @ A2 )
% 0.30/0.62         => ( ( groups7882442080178216443t_assn @ G2 @ ( insert_int @ X @ A2 ) )
% 0.30/0.62            = ( times_times_assn @ ( G2 @ X ) @ ( groups7882442080178216443t_assn @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.insert
% 0.30/0.62  thf(fact_7910_prod_Oinsert,axiom,
% 0.30/0.62      ! [A2: set_o,X: $o,G2: $o > rat] :
% 0.30/0.62        ( ( finite_finite_o @ A2 )
% 0.30/0.62       => ( ~ ( member_o @ X @ A2 )
% 0.30/0.62         => ( ( groups2869687844427037835_o_rat @ G2 @ ( insert_o @ X @ A2 ) )
% 0.30/0.62            = ( times_times_rat @ ( G2 @ X ) @ ( groups2869687844427037835_o_rat @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.insert
% 0.30/0.62  thf(fact_7911_prod_Oinsert,axiom,
% 0.30/0.62      ! [A2: set_nat,X: nat,G2: nat > rat] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ~ ( member_nat @ X @ A2 )
% 0.30/0.62         => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A2 ) )
% 0.30/0.62            = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.insert
% 0.30/0.62  thf(fact_7912_prod_Oinsert,axiom,
% 0.30/0.62      ! [A2: set_int,X: int,G2: int > rat] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ~ ( member_int @ X @ A2 )
% 0.30/0.62         => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A2 ) )
% 0.30/0.62            = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.insert
% 0.30/0.62  thf(fact_7913_prod_Oinsert,axiom,
% 0.30/0.62      ! [A2: set_o,X: $o,G2: $o > nat] :
% 0.30/0.62        ( ( finite_finite_o @ A2 )
% 0.30/0.62       => ( ~ ( member_o @ X @ A2 )
% 0.30/0.62         => ( ( groups3504817904513533571_o_nat @ G2 @ ( insert_o @ X @ A2 ) )
% 0.30/0.62            = ( times_times_nat @ ( G2 @ X ) @ ( groups3504817904513533571_o_nat @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.insert
% 0.30/0.62  thf(fact_7914_abs__sgn__eq__1,axiom,
% 0.30/0.62      ! [A: code_integer] :
% 0.30/0.62        ( ( A != zero_z3403309356797280102nteger )
% 0.30/0.62       => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 0.30/0.62          = one_one_Code_integer ) ) ).
% 0.30/0.62  
% 0.30/0.62  % abs_sgn_eq_1
% 0.30/0.62  thf(fact_7915_abs__sgn__eq__1,axiom,
% 0.30/0.62      ! [A: rat] :
% 0.30/0.62        ( ( A != zero_zero_rat )
% 0.30/0.62       => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 0.30/0.62          = one_one_rat ) ) ).
% 0.30/0.62  
% 0.30/0.62  % abs_sgn_eq_1
% 0.30/0.62  thf(fact_7916_abs__sgn__eq__1,axiom,
% 0.30/0.62      ! [A: int] :
% 0.30/0.62        ( ( A != zero_zero_int )
% 0.30/0.62       => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 0.30/0.62          = one_one_int ) ) ).
% 0.30/0.62  
% 0.30/0.62  % abs_sgn_eq_1
% 0.30/0.62  thf(fact_7917_single__Diff__lessThan,axiom,
% 0.30/0.62      ! [K: $o] :
% 0.30/0.62        ( ( minus_minus_set_o @ ( insert_o @ K @ bot_bot_set_o ) @ ( set_ord_lessThan_o @ K ) )
% 0.30/0.62        = ( insert_o @ K @ bot_bot_set_o ) ) ).
% 0.30/0.62  
% 0.30/0.62  % single_Diff_lessThan
% 0.30/0.62  thf(fact_7918_single__Diff__lessThan,axiom,
% 0.30/0.62      ! [K: int] :
% 0.30/0.62        ( ( minus_minus_set_int @ ( insert_int @ K @ bot_bot_set_int ) @ ( set_ord_lessThan_int @ K ) )
% 0.30/0.62        = ( insert_int @ K @ bot_bot_set_int ) ) ).
% 0.30/0.62  
% 0.30/0.62  % single_Diff_lessThan
% 0.30/0.62  thf(fact_7919_single__Diff__lessThan,axiom,
% 0.30/0.62      ! [K: nat] :
% 0.30/0.62        ( ( minus_minus_set_nat @ ( insert_nat @ K @ bot_bot_set_nat ) @ ( set_ord_lessThan_nat @ K ) )
% 0.30/0.62        = ( insert_nat @ K @ bot_bot_set_nat ) ) ).
% 0.30/0.62  
% 0.30/0.62  % single_Diff_lessThan
% 0.30/0.62  thf(fact_7920_sgn__mult__self__eq,axiom,
% 0.30/0.62      ! [A: code_integer] :
% 0.30/0.62        ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 0.30/0.62        = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_mult_self_eq
% 0.30/0.62  thf(fact_7921_sgn__mult__self__eq,axiom,
% 0.30/0.62      ! [A: rat] :
% 0.30/0.62        ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 0.30/0.62        = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_mult_self_eq
% 0.30/0.62  thf(fact_7922_sgn__mult__self__eq,axiom,
% 0.30/0.62      ! [A: int] :
% 0.30/0.62        ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ A ) )
% 0.30/0.62        = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_mult_self_eq
% 0.30/0.62  thf(fact_7923_drop__bit__of__1,axiom,
% 0.30/0.62      ! [N: nat] :
% 0.30/0.62        ( ( bit_se3928097537394005634nteger @ N @ one_one_Code_integer )
% 0.30/0.62        = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % drop_bit_of_1
% 0.30/0.62  thf(fact_7924_drop__bit__of__1,axiom,
% 0.30/0.62      ! [N: nat] :
% 0.30/0.62        ( ( bit_se8570568707652914677it_nat @ N @ one_one_nat )
% 0.30/0.62        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % drop_bit_of_1
% 0.30/0.62  thf(fact_7925_drop__bit__of__1,axiom,
% 0.30/0.62      ! [N: nat] :
% 0.30/0.62        ( ( bit_se8568078237143864401it_int @ N @ one_one_int )
% 0.30/0.62        = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % drop_bit_of_1
% 0.30/0.62  thf(fact_7926_prod_OlessThan__Suc,axiom,
% 0.30/0.62      ! [G2: nat > code_integer,N: nat] :
% 0.30/0.62        ( ( groups3455450783089532116nteger @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.30/0.62        = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.lessThan_Suc
% 0.30/0.62  thf(fact_7927_prod_OlessThan__Suc,axiom,
% 0.30/0.62      ! [G2: nat > assn,N: nat] :
% 0.30/0.62        ( ( groups6906906614972039071t_assn @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.30/0.62        = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.lessThan_Suc
% 0.30/0.62  thf(fact_7928_prod_OlessThan__Suc,axiom,
% 0.30/0.62      ! [G2: nat > rat,N: nat] :
% 0.30/0.62        ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.30/0.62        = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.lessThan_Suc
% 0.30/0.62  thf(fact_7929_prod_OlessThan__Suc,axiom,
% 0.30/0.62      ! [G2: nat > nat,N: nat] :
% 0.30/0.62        ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.30/0.62        = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.lessThan_Suc
% 0.30/0.62  thf(fact_7930_prod_OlessThan__Suc,axiom,
% 0.30/0.62      ! [G2: nat > int,N: nat] :
% 0.30/0.62        ( ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.30/0.62        = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.lessThan_Suc
% 0.30/0.62  thf(fact_7931_sgn__neg,axiom,
% 0.30/0.62      ! [A: int] :
% 0.30/0.62        ( ( ord_less_int @ A @ zero_zero_int )
% 0.30/0.62       => ( ( sgn_sgn_int @ A )
% 0.30/0.62          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_neg
% 0.30/0.62  thf(fact_7932_sgn__neg,axiom,
% 0.30/0.62      ! [A: code_integer] :
% 0.30/0.62        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.30/0.62       => ( ( sgn_sgn_Code_integer @ A )
% 0.30/0.62          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_neg
% 0.30/0.62  thf(fact_7933_sgn__neg,axiom,
% 0.30/0.62      ! [A: rat] :
% 0.30/0.62        ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.30/0.62       => ( ( sgn_sgn_rat @ A )
% 0.30/0.62          = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_neg
% 0.30/0.62  thf(fact_7934_drop__bit__Suc__minus__bit0,axiom,
% 0.30/0.62      ! [N: nat,K: num] :
% 0.30/0.62        ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.30/0.62        = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % drop_bit_Suc_minus_bit0
% 0.30/0.62  thf(fact_7935_sum__mult__of__bool__eq,axiom,
% 0.30/0.62      ! [A2: set_int,F2: int > code_integer,P: int > $o] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups7873554091576472773nteger
% 0.30/0.62            @ ^ [X3: int] : ( times_3573771949741848930nteger @ ( F2 @ X3 ) @ ( zero_n356916108424825756nteger @ ( P @ X3 ) ) )
% 0.30/0.62            @ A2 )
% 0.30/0.62          = ( groups7873554091576472773nteger @ F2 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_mult_of_bool_eq
% 0.30/0.62  thf(fact_7936_sum__mult__of__bool__eq,axiom,
% 0.30/0.62      ! [A2: set_nat,F2: nat > code_integer,P: nat > $o] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups7501900531339628137nteger
% 0.30/0.62            @ ^ [X3: nat] : ( times_3573771949741848930nteger @ ( F2 @ X3 ) @ ( zero_n356916108424825756nteger @ ( P @ X3 ) ) )
% 0.30/0.62            @ A2 )
% 0.30/0.62          = ( groups7501900531339628137nteger @ F2 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_mult_of_bool_eq
% 0.30/0.62  thf(fact_7937_sum__mult__of__bool__eq,axiom,
% 0.30/0.62      ! [A2: set_int,F2: int > rat,P: int > $o] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups3906332499630173760nt_rat
% 0.30/0.62            @ ^ [X3: int] : ( times_times_rat @ ( F2 @ X3 ) @ ( zero_n2052037380579107095ol_rat @ ( P @ X3 ) ) )
% 0.30/0.62            @ A2 )
% 0.30/0.62          = ( groups3906332499630173760nt_rat @ F2 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_mult_of_bool_eq
% 0.30/0.62  thf(fact_7938_sum__mult__of__bool__eq,axiom,
% 0.30/0.62      ! [A2: set_nat,F2: nat > rat,P: nat > $o] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups2906978787729119204at_rat
% 0.30/0.62            @ ^ [X3: nat] : ( times_times_rat @ ( F2 @ X3 ) @ ( zero_n2052037380579107095ol_rat @ ( P @ X3 ) ) )
% 0.30/0.62            @ A2 )
% 0.30/0.62          = ( groups2906978787729119204at_rat @ F2 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_mult_of_bool_eq
% 0.30/0.62  thf(fact_7939_sum__mult__of__bool__eq,axiom,
% 0.30/0.62      ! [A2: set_nat,F2: nat > int,P: nat > $o] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups3539618377306564664at_int
% 0.30/0.62            @ ^ [X3: nat] : ( times_times_int @ ( F2 @ X3 ) @ ( zero_n2684676970156552555ol_int @ ( P @ X3 ) ) )
% 0.30/0.62            @ A2 )
% 0.30/0.62          = ( groups3539618377306564664at_int @ F2 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_mult_of_bool_eq
% 0.30/0.62  thf(fact_7940_sum__mult__of__bool__eq,axiom,
% 0.30/0.62      ! [A2: set_int,F2: int > nat,P: int > $o] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups4541462559716669496nt_nat
% 0.30/0.62            @ ^ [X3: int] : ( times_times_nat @ ( F2 @ X3 ) @ ( zero_n2687167440665602831ol_nat @ ( P @ X3 ) ) )
% 0.30/0.62            @ A2 )
% 0.30/0.62          = ( groups4541462559716669496nt_nat @ F2 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_mult_of_bool_eq
% 0.30/0.62  thf(fact_7941_sum__mult__of__bool__eq,axiom,
% 0.30/0.62      ! [A2: set_nat,F2: nat > nat,P: nat > $o] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups3542108847815614940at_nat
% 0.30/0.62            @ ^ [X3: nat] : ( times_times_nat @ ( F2 @ X3 ) @ ( zero_n2687167440665602831ol_nat @ ( P @ X3 ) ) )
% 0.30/0.62            @ A2 )
% 0.30/0.62          = ( groups3542108847815614940at_nat @ F2 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_mult_of_bool_eq
% 0.30/0.62  thf(fact_7942_sum__mult__of__bool__eq,axiom,
% 0.30/0.62      ! [A2: set_int,F2: int > int,P: int > $o] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups4538972089207619220nt_int
% 0.30/0.62            @ ^ [X3: int] : ( times_times_int @ ( F2 @ X3 ) @ ( zero_n2684676970156552555ol_int @ ( P @ X3 ) ) )
% 0.30/0.62            @ A2 )
% 0.30/0.62          = ( groups4538972089207619220nt_int @ F2 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_mult_of_bool_eq
% 0.30/0.62  thf(fact_7943_sum__mult__of__bool__eq,axiom,
% 0.30/0.62      ! [A2: set_set_nat,F2: set_nat > code_integer,P: set_nat > $o] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.62       => ( ( groups9190459664516455967nteger
% 0.30/0.62            @ ^ [X3: set_nat] : ( times_3573771949741848930nteger @ ( F2 @ X3 ) @ ( zero_n356916108424825756nteger @ ( P @ X3 ) ) )
% 0.30/0.62            @ A2 )
% 0.30/0.62          = ( groups9190459664516455967nteger @ F2 @ ( inf_inf_set_set_nat @ A2 @ ( collect_set_nat @ P ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_mult_of_bool_eq
% 0.30/0.62  thf(fact_7944_sum__mult__of__bool__eq,axiom,
% 0.30/0.62      ! [A2: set_set_nat,F2: set_nat > rat,P: set_nat > $o] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.62       => ( ( groups7659867448343625626at_rat
% 0.30/0.62            @ ^ [X3: set_nat] : ( times_times_rat @ ( F2 @ X3 ) @ ( zero_n2052037380579107095ol_rat @ ( P @ X3 ) ) )
% 0.30/0.62            @ A2 )
% 0.30/0.62          = ( groups7659867448343625626at_rat @ F2 @ ( inf_inf_set_set_nat @ A2 @ ( collect_set_nat @ P ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_mult_of_bool_eq
% 0.30/0.62  thf(fact_7945_sum__of__bool__mult__eq,axiom,
% 0.30/0.62      ! [A2: set_int,P: int > $o,F2: int > code_integer] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups7873554091576472773nteger
% 0.30/0.62            @ ^ [X3: int] : ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( P @ X3 ) ) @ ( F2 @ X3 ) )
% 0.30/0.62            @ A2 )
% 0.30/0.62          = ( groups7873554091576472773nteger @ F2 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_of_bool_mult_eq
% 0.30/0.62  thf(fact_7946_sum__of__bool__mult__eq,axiom,
% 0.30/0.62      ! [A2: set_nat,P: nat > $o,F2: nat > code_integer] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups7501900531339628137nteger
% 0.30/0.62            @ ^ [X3: nat] : ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( P @ X3 ) ) @ ( F2 @ X3 ) )
% 0.30/0.62            @ A2 )
% 0.30/0.62          = ( groups7501900531339628137nteger @ F2 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_of_bool_mult_eq
% 0.30/0.62  thf(fact_7947_sum__of__bool__mult__eq,axiom,
% 0.30/0.62      ! [A2: set_int,P: int > $o,F2: int > rat] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups3906332499630173760nt_rat
% 0.30/0.62            @ ^ [X3: int] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P @ X3 ) ) @ ( F2 @ X3 ) )
% 0.30/0.62            @ A2 )
% 0.30/0.62          = ( groups3906332499630173760nt_rat @ F2 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_of_bool_mult_eq
% 0.30/0.62  thf(fact_7948_sum__of__bool__mult__eq,axiom,
% 0.30/0.62      ! [A2: set_nat,P: nat > $o,F2: nat > rat] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups2906978787729119204at_rat
% 0.30/0.62            @ ^ [X3: nat] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P @ X3 ) ) @ ( F2 @ X3 ) )
% 0.30/0.62            @ A2 )
% 0.30/0.62          = ( groups2906978787729119204at_rat @ F2 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_of_bool_mult_eq
% 0.30/0.62  thf(fact_7949_sum__of__bool__mult__eq,axiom,
% 0.30/0.62      ! [A2: set_nat,P: nat > $o,F2: nat > int] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups3539618377306564664at_int
% 0.30/0.62            @ ^ [X3: nat] : ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( P @ X3 ) ) @ ( F2 @ X3 ) )
% 0.30/0.62            @ A2 )
% 0.30/0.62          = ( groups3539618377306564664at_int @ F2 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_of_bool_mult_eq
% 0.30/0.62  thf(fact_7950_sum__of__bool__mult__eq,axiom,
% 0.30/0.62      ! [A2: set_int,P: int > $o,F2: int > nat] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups4541462559716669496nt_nat
% 0.30/0.62            @ ^ [X3: int] : ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( P @ X3 ) ) @ ( F2 @ X3 ) )
% 0.30/0.62            @ A2 )
% 0.30/0.62          = ( groups4541462559716669496nt_nat @ F2 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_of_bool_mult_eq
% 0.30/0.62  thf(fact_7951_sum__of__bool__mult__eq,axiom,
% 0.30/0.62      ! [A2: set_nat,P: nat > $o,F2: nat > nat] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups3542108847815614940at_nat
% 0.30/0.62            @ ^ [X3: nat] : ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( P @ X3 ) ) @ ( F2 @ X3 ) )
% 0.30/0.62            @ A2 )
% 0.30/0.62          = ( groups3542108847815614940at_nat @ F2 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_of_bool_mult_eq
% 0.30/0.62  thf(fact_7952_sum__of__bool__mult__eq,axiom,
% 0.30/0.62      ! [A2: set_int,P: int > $o,F2: int > int] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups4538972089207619220nt_int
% 0.30/0.62            @ ^ [X3: int] : ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( P @ X3 ) ) @ ( F2 @ X3 ) )
% 0.30/0.62            @ A2 )
% 0.30/0.62          = ( groups4538972089207619220nt_int @ F2 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_of_bool_mult_eq
% 0.30/0.62  thf(fact_7953_sum__of__bool__mult__eq,axiom,
% 0.30/0.62      ! [A2: set_set_nat,P: set_nat > $o,F2: set_nat > code_integer] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.62       => ( ( groups9190459664516455967nteger
% 0.30/0.62            @ ^ [X3: set_nat] : ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( P @ X3 ) ) @ ( F2 @ X3 ) )
% 0.30/0.62            @ A2 )
% 0.30/0.62          = ( groups9190459664516455967nteger @ F2 @ ( inf_inf_set_set_nat @ A2 @ ( collect_set_nat @ P ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_of_bool_mult_eq
% 0.30/0.62  thf(fact_7954_sum__of__bool__mult__eq,axiom,
% 0.30/0.62      ! [A2: set_set_nat,P: set_nat > $o,F2: set_nat > rat] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.62       => ( ( groups7659867448343625626at_rat
% 0.30/0.62            @ ^ [X3: set_nat] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P @ X3 ) ) @ ( F2 @ X3 ) )
% 0.30/0.62            @ A2 )
% 0.30/0.62          = ( groups7659867448343625626at_rat @ F2 @ ( inf_inf_set_set_nat @ A2 @ ( collect_set_nat @ P ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_of_bool_mult_eq
% 0.30/0.62  thf(fact_7955_drop__bit__numeral__minus__bit0,axiom,
% 0.30/0.62      ! [L: num,K: num] :
% 0.30/0.62        ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 0.30/0.62        = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % drop_bit_numeral_minus_bit0
% 0.30/0.62  thf(fact_7956_sum__zero__power,axiom,
% 0.30/0.62      ! [A2: set_nat,C: nat > rat] :
% 0.30/0.62        ( ( ( ( finite_finite_nat @ A2 )
% 0.30/0.62            & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.30/0.62         => ( ( groups2906978787729119204at_rat
% 0.30/0.62              @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = ( C @ zero_zero_nat ) ) )
% 0.30/0.62        & ( ~ ( ( finite_finite_nat @ A2 )
% 0.30/0.62              & ( member_nat @ zero_zero_nat @ A2 ) )
% 0.30/0.62         => ( ( groups2906978787729119204at_rat
% 0.30/0.62              @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = zero_zero_rat ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_zero_power
% 0.30/0.62  thf(fact_7957_drop__bit__Suc__minus__bit1,axiom,
% 0.30/0.62      ! [N: nat,K: num] :
% 0.30/0.62        ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 0.30/0.62        = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % drop_bit_Suc_minus_bit1
% 0.30/0.62  thf(fact_7958_int__prod,axiom,
% 0.30/0.62      ! [F2: int > nat,A2: set_int] :
% 0.30/0.62        ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F2 @ A2 ) )
% 0.30/0.62        = ( groups1705073143266064639nt_int
% 0.30/0.62          @ ^ [X3: int] : ( semiri1314217659103216013at_int @ ( F2 @ X3 ) )
% 0.30/0.62          @ A2 ) ) ).
% 0.30/0.62  
% 0.30/0.62  % int_prod
% 0.30/0.62  thf(fact_7959_int__prod,axiom,
% 0.30/0.62      ! [F2: nat > nat,A2: set_nat] :
% 0.30/0.62        ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F2 @ A2 ) )
% 0.30/0.62        = ( groups705719431365010083at_int
% 0.30/0.62          @ ^ [X3: nat] : ( semiri1314217659103216013at_int @ ( F2 @ X3 ) )
% 0.30/0.62          @ A2 ) ) ).
% 0.30/0.62  
% 0.30/0.62  % int_prod
% 0.30/0.62  thf(fact_7960_finite__if__eq__beyond__finite,axiom,
% 0.30/0.62      ! [S: set_Pr958786334691620121nt_int,S5: set_Pr958786334691620121nt_int] :
% 0.30/0.62        ( ( finite2998713641127702882nt_int @ S )
% 0.30/0.62       => ( finite8744585540193469122nt_int
% 0.30/0.62          @ ( collec5210948495886036740nt_int
% 0.30/0.62            @ ^ [S2: set_Pr958786334691620121nt_int] :
% 0.30/0.62                ( ( minus_1052850069191792384nt_int @ S2 @ S )
% 0.30/0.62                = ( minus_1052850069191792384nt_int @ S5 @ S ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % finite_if_eq_beyond_finite
% 0.30/0.62  thf(fact_7961_finite__if__eq__beyond__finite,axiom,
% 0.30/0.62      ! [S: set_int,S5: set_int] :
% 0.30/0.62        ( ( finite_finite_int @ S )
% 0.30/0.62       => ( finite6197958912794628473et_int
% 0.30/0.62          @ ( collect_set_int
% 0.30/0.62            @ ^ [S2: set_int] :
% 0.30/0.62                ( ( minus_minus_set_int @ S2 @ S )
% 0.30/0.62                = ( minus_minus_set_int @ S5 @ S ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % finite_if_eq_beyond_finite
% 0.30/0.62  thf(fact_7962_finite__if__eq__beyond__finite,axiom,
% 0.30/0.62      ! [S: set_Pr1261947904930325089at_nat,S5: set_Pr1261947904930325089at_nat] :
% 0.30/0.62        ( ( finite6177210948735845034at_nat @ S )
% 0.30/0.62       => ( finite9047747110432174090at_nat
% 0.30/0.62          @ ( collec5514110066124741708at_nat
% 0.30/0.62            @ ^ [S2: set_Pr1261947904930325089at_nat] :
% 0.30/0.62                ( ( minus_1356011639430497352at_nat @ S2 @ S )
% 0.30/0.62                = ( minus_1356011639430497352at_nat @ S5 @ S ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % finite_if_eq_beyond_finite
% 0.30/0.62  thf(fact_7963_finite__if__eq__beyond__finite,axiom,
% 0.30/0.62      ! [S: set_nat,S5: set_nat] :
% 0.30/0.62        ( ( finite_finite_nat @ S )
% 0.30/0.62       => ( finite1152437895449049373et_nat
% 0.30/0.62          @ ( collect_set_nat
% 0.30/0.62            @ ^ [S2: set_nat] :
% 0.30/0.62                ( ( minus_minus_set_nat @ S2 @ S )
% 0.30/0.62                = ( minus_minus_set_nat @ S5 @ S ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % finite_if_eq_beyond_finite
% 0.30/0.62  thf(fact_7964_sgn__mult,axiom,
% 0.30/0.62      ! [A: code_integer,B: code_integer] :
% 0.30/0.62        ( ( sgn_sgn_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.30/0.62        = ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ B ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_mult
% 0.30/0.62  thf(fact_7965_sgn__mult,axiom,
% 0.30/0.62      ! [A: rat,B: rat] :
% 0.30/0.62        ( ( sgn_sgn_rat @ ( times_times_rat @ A @ B ) )
% 0.30/0.62        = ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_mult
% 0.30/0.62  thf(fact_7966_sgn__mult,axiom,
% 0.30/0.62      ! [A: int,B: int] :
% 0.30/0.62        ( ( sgn_sgn_int @ ( times_times_int @ A @ B ) )
% 0.30/0.62        = ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_mult
% 0.30/0.62  thf(fact_7967_lessThan__non__empty,axiom,
% 0.30/0.62      ! [X: int] :
% 0.30/0.62        ( ( set_ord_lessThan_int @ X )
% 0.30/0.62       != bot_bot_set_int ) ).
% 0.30/0.62  
% 0.30/0.62  % lessThan_non_empty
% 0.30/0.62  thf(fact_7968_finite__M__bounded__by__nat,axiom,
% 0.30/0.62      ! [P: nat > $o,I: nat] :
% 0.30/0.62        ( finite_finite_nat
% 0.30/0.62        @ ( collect_nat
% 0.30/0.62          @ ^ [K4: nat] :
% 0.30/0.62              ( ( P @ K4 )
% 0.30/0.62              & ( ord_less_nat @ K4 @ I ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % finite_M_bounded_by_nat
% 0.30/0.62  thf(fact_7969_finite__less__ub,axiom,
% 0.30/0.62      ! [F2: nat > nat,U: nat] :
% 0.30/0.62        ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F2 @ N3 ) )
% 0.30/0.62       => ( finite_finite_nat
% 0.30/0.62          @ ( collect_nat
% 0.30/0.62            @ ^ [N2: nat] : ( ord_less_eq_nat @ ( F2 @ N2 ) @ U ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % finite_less_ub
% 0.30/0.62  thf(fact_7970_sum_Oswap__restrict,axiom,
% 0.30/0.62      ! [A2: set_int,B2: set_nat,G2: int > nat > nat,R: int > nat > $o] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( finite_finite_nat @ B2 )
% 0.30/0.62         => ( ( groups4541462559716669496nt_nat
% 0.30/0.62              @ ^ [X3: int] :
% 0.30/0.62                  ( groups3542108847815614940at_nat @ ( G2 @ X3 )
% 0.30/0.62                  @ ( collect_nat
% 0.30/0.62                    @ ^ [Y3: nat] :
% 0.30/0.62                        ( ( member_nat @ Y3 @ B2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = ( groups3542108847815614940at_nat
% 0.30/0.62              @ ^ [Y3: nat] :
% 0.30/0.62                  ( groups4541462559716669496nt_nat
% 0.30/0.62                  @ ^ [X3: int] : ( G2 @ X3 @ Y3 )
% 0.30/0.62                  @ ( collect_int
% 0.30/0.62                    @ ^ [X3: int] :
% 0.30/0.62                        ( ( member_int @ X3 @ A2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ B2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.swap_restrict
% 0.30/0.62  thf(fact_7971_sum_Oswap__restrict,axiom,
% 0.30/0.62      ! [A2: set_nat,B2: set_int,G2: nat > int > int,R: nat > int > $o] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( finite_finite_int @ B2 )
% 0.30/0.62         => ( ( groups3539618377306564664at_int
% 0.30/0.62              @ ^ [X3: nat] :
% 0.30/0.62                  ( groups4538972089207619220nt_int @ ( G2 @ X3 )
% 0.30/0.62                  @ ( collect_int
% 0.30/0.62                    @ ^ [Y3: int] :
% 0.30/0.62                        ( ( member_int @ Y3 @ B2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = ( groups4538972089207619220nt_int
% 0.30/0.62              @ ^ [Y3: int] :
% 0.30/0.62                  ( groups3539618377306564664at_int
% 0.30/0.62                  @ ^ [X3: nat] : ( G2 @ X3 @ Y3 )
% 0.30/0.62                  @ ( collect_nat
% 0.30/0.62                    @ ^ [X3: nat] :
% 0.30/0.62                        ( ( member_nat @ X3 @ A2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ B2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.swap_restrict
% 0.30/0.62  thf(fact_7972_sum_Oswap__restrict,axiom,
% 0.30/0.62      ! [A2: set_nat,B2: set_int,G2: nat > int > nat,R: nat > int > $o] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( finite_finite_int @ B2 )
% 0.30/0.62         => ( ( groups3542108847815614940at_nat
% 0.30/0.62              @ ^ [X3: nat] :
% 0.30/0.62                  ( groups4541462559716669496nt_nat @ ( G2 @ X3 )
% 0.30/0.62                  @ ( collect_int
% 0.30/0.62                    @ ^ [Y3: int] :
% 0.30/0.62                        ( ( member_int @ Y3 @ B2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = ( groups4541462559716669496nt_nat
% 0.30/0.62              @ ^ [Y3: int] :
% 0.30/0.62                  ( groups3542108847815614940at_nat
% 0.30/0.62                  @ ^ [X3: nat] : ( G2 @ X3 @ Y3 )
% 0.30/0.62                  @ ( collect_nat
% 0.30/0.62                    @ ^ [X3: nat] :
% 0.30/0.62                        ( ( member_nat @ X3 @ A2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ B2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.swap_restrict
% 0.30/0.62  thf(fact_7973_sum_Oswap__restrict,axiom,
% 0.30/0.62      ! [A2: set_nat,B2: set_nat,G2: nat > nat > nat,R: nat > nat > $o] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( finite_finite_nat @ B2 )
% 0.30/0.62         => ( ( groups3542108847815614940at_nat
% 0.30/0.62              @ ^ [X3: nat] :
% 0.30/0.62                  ( groups3542108847815614940at_nat @ ( G2 @ X3 )
% 0.30/0.62                  @ ( collect_nat
% 0.30/0.62                    @ ^ [Y3: nat] :
% 0.30/0.62                        ( ( member_nat @ Y3 @ B2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = ( groups3542108847815614940at_nat
% 0.30/0.62              @ ^ [Y3: nat] :
% 0.30/0.62                  ( groups3542108847815614940at_nat
% 0.30/0.62                  @ ^ [X3: nat] : ( G2 @ X3 @ Y3 )
% 0.30/0.62                  @ ( collect_nat
% 0.30/0.62                    @ ^ [X3: nat] :
% 0.30/0.62                        ( ( member_nat @ X3 @ A2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ B2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.swap_restrict
% 0.30/0.62  thf(fact_7974_sum_Oswap__restrict,axiom,
% 0.30/0.62      ! [A2: set_int,B2: set_nat,G2: int > nat > int,R: int > nat > $o] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( finite_finite_nat @ B2 )
% 0.30/0.62         => ( ( groups4538972089207619220nt_int
% 0.30/0.62              @ ^ [X3: int] :
% 0.30/0.62                  ( groups3539618377306564664at_int @ ( G2 @ X3 )
% 0.30/0.62                  @ ( collect_nat
% 0.30/0.62                    @ ^ [Y3: nat] :
% 0.30/0.62                        ( ( member_nat @ Y3 @ B2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = ( groups3539618377306564664at_int
% 0.30/0.62              @ ^ [Y3: nat] :
% 0.30/0.62                  ( groups4538972089207619220nt_int
% 0.30/0.62                  @ ^ [X3: int] : ( G2 @ X3 @ Y3 )
% 0.30/0.62                  @ ( collect_int
% 0.30/0.62                    @ ^ [X3: int] :
% 0.30/0.62                        ( ( member_int @ X3 @ A2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ B2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.swap_restrict
% 0.30/0.62  thf(fact_7975_sum_Oswap__restrict,axiom,
% 0.30/0.62      ! [A2: set_int,B2: set_int,G2: int > int > int,R: int > int > $o] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( finite_finite_int @ B2 )
% 0.30/0.62         => ( ( groups4538972089207619220nt_int
% 0.30/0.62              @ ^ [X3: int] :
% 0.30/0.62                  ( groups4538972089207619220nt_int @ ( G2 @ X3 )
% 0.30/0.62                  @ ( collect_int
% 0.30/0.62                    @ ^ [Y3: int] :
% 0.30/0.62                        ( ( member_int @ Y3 @ B2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = ( groups4538972089207619220nt_int
% 0.30/0.62              @ ^ [Y3: int] :
% 0.30/0.62                  ( groups4538972089207619220nt_int
% 0.30/0.62                  @ ^ [X3: int] : ( G2 @ X3 @ Y3 )
% 0.30/0.62                  @ ( collect_int
% 0.30/0.62                    @ ^ [X3: int] :
% 0.30/0.62                        ( ( member_int @ X3 @ A2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ B2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.swap_restrict
% 0.30/0.62  thf(fact_7976_sum_Oswap__restrict,axiom,
% 0.30/0.62      ! [A2: set_set_nat,B2: set_nat,G2: set_nat > nat > nat,R: set_nat > nat > $o] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.62       => ( ( finite_finite_nat @ B2 )
% 0.30/0.62         => ( ( groups8294997508430121362at_nat
% 0.30/0.62              @ ^ [X3: set_nat] :
% 0.30/0.62                  ( groups3542108847815614940at_nat @ ( G2 @ X3 )
% 0.30/0.62                  @ ( collect_nat
% 0.30/0.62                    @ ^ [Y3: nat] :
% 0.30/0.62                        ( ( member_nat @ Y3 @ B2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = ( groups3542108847815614940at_nat
% 0.30/0.62              @ ^ [Y3: nat] :
% 0.30/0.62                  ( groups8294997508430121362at_nat
% 0.30/0.62                  @ ^ [X3: set_nat] : ( G2 @ X3 @ Y3 )
% 0.30/0.62                  @ ( collect_set_nat
% 0.30/0.62                    @ ^ [X3: set_nat] :
% 0.30/0.62                        ( ( member_set_nat @ X3 @ A2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ B2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.swap_restrict
% 0.30/0.62  thf(fact_7977_sum_Oswap__restrict,axiom,
% 0.30/0.62      ! [A2: set_set_nat,B2: set_int,G2: set_nat > int > int,R: set_nat > int > $o] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.62       => ( ( finite_finite_int @ B2 )
% 0.30/0.62         => ( ( groups8292507037921071086at_int
% 0.30/0.62              @ ^ [X3: set_nat] :
% 0.30/0.62                  ( groups4538972089207619220nt_int @ ( G2 @ X3 )
% 0.30/0.62                  @ ( collect_int
% 0.30/0.62                    @ ^ [Y3: int] :
% 0.30/0.62                        ( ( member_int @ Y3 @ B2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = ( groups4538972089207619220nt_int
% 0.30/0.62              @ ^ [Y3: int] :
% 0.30/0.62                  ( groups8292507037921071086at_int
% 0.30/0.62                  @ ^ [X3: set_nat] : ( G2 @ X3 @ Y3 )
% 0.30/0.62                  @ ( collect_set_nat
% 0.30/0.62                    @ ^ [X3: set_nat] :
% 0.30/0.62                        ( ( member_set_nat @ X3 @ A2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ B2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.swap_restrict
% 0.30/0.62  thf(fact_7978_sum_Oswap__restrict,axiom,
% 0.30/0.62      ! [A2: set_nat,B2: set_set_nat,G2: nat > set_nat > nat,R: nat > set_nat > $o] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( finite1152437895449049373et_nat @ B2 )
% 0.30/0.62         => ( ( groups3542108847815614940at_nat
% 0.30/0.62              @ ^ [X3: nat] :
% 0.30/0.62                  ( groups8294997508430121362at_nat @ ( G2 @ X3 )
% 0.30/0.62                  @ ( collect_set_nat
% 0.30/0.62                    @ ^ [Y3: set_nat] :
% 0.30/0.62                        ( ( member_set_nat @ Y3 @ B2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = ( groups8294997508430121362at_nat
% 0.30/0.62              @ ^ [Y3: set_nat] :
% 0.30/0.62                  ( groups3542108847815614940at_nat
% 0.30/0.62                  @ ^ [X3: nat] : ( G2 @ X3 @ Y3 )
% 0.30/0.62                  @ ( collect_nat
% 0.30/0.62                    @ ^ [X3: nat] :
% 0.30/0.62                        ( ( member_nat @ X3 @ A2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ B2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.swap_restrict
% 0.30/0.62  thf(fact_7979_sum_Oswap__restrict,axiom,
% 0.30/0.62      ! [A2: set_int,B2: set_set_nat,G2: int > set_nat > int,R: int > set_nat > $o] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( finite1152437895449049373et_nat @ B2 )
% 0.30/0.62         => ( ( groups4538972089207619220nt_int
% 0.30/0.62              @ ^ [X3: int] :
% 0.30/0.62                  ( groups8292507037921071086at_int @ ( G2 @ X3 )
% 0.30/0.62                  @ ( collect_set_nat
% 0.30/0.62                    @ ^ [Y3: set_nat] :
% 0.30/0.62                        ( ( member_set_nat @ Y3 @ B2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = ( groups8292507037921071086at_int
% 0.30/0.62              @ ^ [Y3: set_nat] :
% 0.30/0.62                  ( groups4538972089207619220nt_int
% 0.30/0.62                  @ ^ [X3: int] : ( G2 @ X3 @ Y3 )
% 0.30/0.62                  @ ( collect_int
% 0.30/0.62                    @ ^ [X3: int] :
% 0.30/0.62                        ( ( member_int @ X3 @ A2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ B2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.swap_restrict
% 0.30/0.62  thf(fact_7980_prod_Oswap__restrict,axiom,
% 0.30/0.62      ! [A2: set_int,B2: set_nat,G2: int > nat > nat,R: int > nat > $o] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( finite_finite_nat @ B2 )
% 0.30/0.62         => ( ( groups1707563613775114915nt_nat
% 0.30/0.62              @ ^ [X3: int] :
% 0.30/0.62                  ( groups708209901874060359at_nat @ ( G2 @ X3 )
% 0.30/0.62                  @ ( collect_nat
% 0.30/0.62                    @ ^ [Y3: nat] :
% 0.30/0.62                        ( ( member_nat @ Y3 @ B2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = ( groups708209901874060359at_nat
% 0.30/0.62              @ ^ [Y3: nat] :
% 0.30/0.62                  ( groups1707563613775114915nt_nat
% 0.30/0.62                  @ ^ [X3: int] : ( G2 @ X3 @ Y3 )
% 0.30/0.62                  @ ( collect_int
% 0.30/0.62                    @ ^ [X3: int] :
% 0.30/0.62                        ( ( member_int @ X3 @ A2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ B2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.swap_restrict
% 0.30/0.62  thf(fact_7981_prod_Oswap__restrict,axiom,
% 0.30/0.62      ! [A2: set_nat,B2: set_int,G2: nat > int > nat,R: nat > int > $o] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( finite_finite_int @ B2 )
% 0.30/0.62         => ( ( groups708209901874060359at_nat
% 0.30/0.62              @ ^ [X3: nat] :
% 0.30/0.62                  ( groups1707563613775114915nt_nat @ ( G2 @ X3 )
% 0.30/0.62                  @ ( collect_int
% 0.30/0.62                    @ ^ [Y3: int] :
% 0.30/0.62                        ( ( member_int @ Y3 @ B2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = ( groups1707563613775114915nt_nat
% 0.30/0.62              @ ^ [Y3: int] :
% 0.30/0.62                  ( groups708209901874060359at_nat
% 0.30/0.62                  @ ^ [X3: nat] : ( G2 @ X3 @ Y3 )
% 0.30/0.62                  @ ( collect_nat
% 0.30/0.62                    @ ^ [X3: nat] :
% 0.30/0.62                        ( ( member_nat @ X3 @ A2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ B2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.swap_restrict
% 0.30/0.62  thf(fact_7982_prod_Oswap__restrict,axiom,
% 0.30/0.62      ! [A2: set_nat,B2: set_nat,G2: nat > nat > nat,R: nat > nat > $o] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( finite_finite_nat @ B2 )
% 0.30/0.62         => ( ( groups708209901874060359at_nat
% 0.30/0.62              @ ^ [X3: nat] :
% 0.30/0.62                  ( groups708209901874060359at_nat @ ( G2 @ X3 )
% 0.30/0.62                  @ ( collect_nat
% 0.30/0.62                    @ ^ [Y3: nat] :
% 0.30/0.62                        ( ( member_nat @ Y3 @ B2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = ( groups708209901874060359at_nat
% 0.30/0.62              @ ^ [Y3: nat] :
% 0.30/0.62                  ( groups708209901874060359at_nat
% 0.30/0.62                  @ ^ [X3: nat] : ( G2 @ X3 @ Y3 )
% 0.30/0.62                  @ ( collect_nat
% 0.30/0.62                    @ ^ [X3: nat] :
% 0.30/0.62                        ( ( member_nat @ X3 @ A2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ B2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.swap_restrict
% 0.30/0.62  thf(fact_7983_prod_Oswap__restrict,axiom,
% 0.30/0.62      ! [A2: set_nat,B2: set_nat,G2: nat > nat > int,R: nat > nat > $o] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( finite_finite_nat @ B2 )
% 0.30/0.62         => ( ( groups705719431365010083at_int
% 0.30/0.62              @ ^ [X3: nat] :
% 0.30/0.62                  ( groups705719431365010083at_int @ ( G2 @ X3 )
% 0.30/0.62                  @ ( collect_nat
% 0.30/0.62                    @ ^ [Y3: nat] :
% 0.30/0.62                        ( ( member_nat @ Y3 @ B2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = ( groups705719431365010083at_int
% 0.30/0.62              @ ^ [Y3: nat] :
% 0.30/0.62                  ( groups705719431365010083at_int
% 0.30/0.62                  @ ^ [X3: nat] : ( G2 @ X3 @ Y3 )
% 0.30/0.62                  @ ( collect_nat
% 0.30/0.62                    @ ^ [X3: nat] :
% 0.30/0.62                        ( ( member_nat @ X3 @ A2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ B2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.swap_restrict
% 0.30/0.62  thf(fact_7984_prod_Oswap__restrict,axiom,
% 0.30/0.62      ! [A2: set_nat,B2: set_int,G2: nat > int > int,R: nat > int > $o] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( finite_finite_int @ B2 )
% 0.30/0.62         => ( ( groups705719431365010083at_int
% 0.30/0.62              @ ^ [X3: nat] :
% 0.30/0.62                  ( groups1705073143266064639nt_int @ ( G2 @ X3 )
% 0.30/0.62                  @ ( collect_int
% 0.30/0.62                    @ ^ [Y3: int] :
% 0.30/0.62                        ( ( member_int @ Y3 @ B2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = ( groups1705073143266064639nt_int
% 0.30/0.62              @ ^ [Y3: int] :
% 0.30/0.62                  ( groups705719431365010083at_int
% 0.30/0.62                  @ ^ [X3: nat] : ( G2 @ X3 @ Y3 )
% 0.30/0.62                  @ ( collect_nat
% 0.30/0.62                    @ ^ [X3: nat] :
% 0.30/0.62                        ( ( member_nat @ X3 @ A2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ B2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.swap_restrict
% 0.30/0.62  thf(fact_7985_prod_Oswap__restrict,axiom,
% 0.30/0.62      ! [A2: set_int,B2: set_nat,G2: int > nat > int,R: int > nat > $o] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( finite_finite_nat @ B2 )
% 0.30/0.62         => ( ( groups1705073143266064639nt_int
% 0.30/0.62              @ ^ [X3: int] :
% 0.30/0.62                  ( groups705719431365010083at_int @ ( G2 @ X3 )
% 0.30/0.62                  @ ( collect_nat
% 0.30/0.62                    @ ^ [Y3: nat] :
% 0.30/0.62                        ( ( member_nat @ Y3 @ B2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = ( groups705719431365010083at_int
% 0.30/0.62              @ ^ [Y3: nat] :
% 0.30/0.62                  ( groups1705073143266064639nt_int
% 0.30/0.62                  @ ^ [X3: int] : ( G2 @ X3 @ Y3 )
% 0.30/0.62                  @ ( collect_int
% 0.30/0.62                    @ ^ [X3: int] :
% 0.30/0.62                        ( ( member_int @ X3 @ A2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ B2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.swap_restrict
% 0.30/0.62  thf(fact_7986_prod_Oswap__restrict,axiom,
% 0.30/0.62      ! [A2: set_int,B2: set_int,G2: int > int > int,R: int > int > $o] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( finite_finite_int @ B2 )
% 0.30/0.62         => ( ( groups1705073143266064639nt_int
% 0.30/0.62              @ ^ [X3: int] :
% 0.30/0.62                  ( groups1705073143266064639nt_int @ ( G2 @ X3 )
% 0.30/0.62                  @ ( collect_int
% 0.30/0.62                    @ ^ [Y3: int] :
% 0.30/0.62                        ( ( member_int @ Y3 @ B2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = ( groups1705073143266064639nt_int
% 0.30/0.62              @ ^ [Y3: int] :
% 0.30/0.62                  ( groups1705073143266064639nt_int
% 0.30/0.62                  @ ^ [X3: int] : ( G2 @ X3 @ Y3 )
% 0.30/0.62                  @ ( collect_int
% 0.30/0.62                    @ ^ [X3: int] :
% 0.30/0.62                        ( ( member_int @ X3 @ A2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ B2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.swap_restrict
% 0.30/0.62  thf(fact_7987_prod_Oswap__restrict,axiom,
% 0.30/0.62      ! [A2: set_set_nat,B2: set_nat,G2: set_nat > nat > nat,R: set_nat > nat > $o] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.62       => ( ( finite_finite_nat @ B2 )
% 0.30/0.62         => ( ( groups4248547760180025341at_nat
% 0.30/0.62              @ ^ [X3: set_nat] :
% 0.30/0.62                  ( groups708209901874060359at_nat @ ( G2 @ X3 )
% 0.30/0.62                  @ ( collect_nat
% 0.30/0.62                    @ ^ [Y3: nat] :
% 0.30/0.62                        ( ( member_nat @ Y3 @ B2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = ( groups708209901874060359at_nat
% 0.30/0.62              @ ^ [Y3: nat] :
% 0.30/0.62                  ( groups4248547760180025341at_nat
% 0.30/0.62                  @ ^ [X3: set_nat] : ( G2 @ X3 @ Y3 )
% 0.30/0.62                  @ ( collect_set_nat
% 0.30/0.62                    @ ^ [X3: set_nat] :
% 0.30/0.62                        ( ( member_set_nat @ X3 @ A2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ B2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.swap_restrict
% 0.30/0.62  thf(fact_7988_prod_Oswap__restrict,axiom,
% 0.30/0.62      ! [A2: set_set_nat,B2: set_nat,G2: set_nat > nat > int,R: set_nat > nat > $o] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.62       => ( ( finite_finite_nat @ B2 )
% 0.30/0.62         => ( ( groups4246057289670975065at_int
% 0.30/0.62              @ ^ [X3: set_nat] :
% 0.30/0.62                  ( groups705719431365010083at_int @ ( G2 @ X3 )
% 0.30/0.62                  @ ( collect_nat
% 0.30/0.62                    @ ^ [Y3: nat] :
% 0.30/0.62                        ( ( member_nat @ Y3 @ B2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = ( groups705719431365010083at_int
% 0.30/0.62              @ ^ [Y3: nat] :
% 0.30/0.62                  ( groups4246057289670975065at_int
% 0.30/0.62                  @ ^ [X3: set_nat] : ( G2 @ X3 @ Y3 )
% 0.30/0.62                  @ ( collect_set_nat
% 0.30/0.62                    @ ^ [X3: set_nat] :
% 0.30/0.62                        ( ( member_set_nat @ X3 @ A2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ B2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.swap_restrict
% 0.30/0.62  thf(fact_7989_prod_Oswap__restrict,axiom,
% 0.30/0.62      ! [A2: set_set_nat,B2: set_int,G2: set_nat > int > int,R: set_nat > int > $o] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.62       => ( ( finite_finite_int @ B2 )
% 0.30/0.62         => ( ( groups4246057289670975065at_int
% 0.30/0.62              @ ^ [X3: set_nat] :
% 0.30/0.62                  ( groups1705073143266064639nt_int @ ( G2 @ X3 )
% 0.30/0.62                  @ ( collect_int
% 0.30/0.62                    @ ^ [Y3: int] :
% 0.30/0.62                        ( ( member_int @ Y3 @ B2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ A2 )
% 0.30/0.62            = ( groups1705073143266064639nt_int
% 0.30/0.62              @ ^ [Y3: int] :
% 0.30/0.62                  ( groups4246057289670975065at_int
% 0.30/0.62                  @ ^ [X3: set_nat] : ( G2 @ X3 @ Y3 )
% 0.30/0.62                  @ ( collect_set_nat
% 0.30/0.62                    @ ^ [X3: set_nat] :
% 0.30/0.62                        ( ( member_set_nat @ X3 @ A2 )
% 0.30/0.62                        & ( R @ X3 @ Y3 ) ) ) )
% 0.30/0.62              @ B2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.swap_restrict
% 0.30/0.62  thf(fact_7990_lessThan__def,axiom,
% 0.30/0.62      ( set_or4940836740269066044nt_int
% 0.30/0.62      = ( ^ [U2: set_Pr958786334691620121nt_int] :
% 0.30/0.62            ( collec5210948495886036740nt_int
% 0.30/0.62            @ ^ [X3: set_Pr958786334691620121nt_int] : ( ord_le7563427860532173253nt_int @ X3 @ U2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % lessThan_def
% 0.30/0.62  thf(fact_7991_lessThan__def,axiom,
% 0.30/0.62      ( set_or890127255671739683et_nat
% 0.30/0.62      = ( ^ [U2: set_nat] :
% 0.30/0.62            ( collect_set_nat
% 0.30/0.62            @ ^ [X3: set_nat] : ( ord_less_set_nat @ X3 @ U2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % lessThan_def
% 0.30/0.62  thf(fact_7992_lessThan__def,axiom,
% 0.30/0.62      ( set_or7240481858991947888_nat_o
% 0.30/0.62      = ( ^ [U2: produc3658429121746597890et_nat > $o] :
% 0.30/0.62            ( collec939566748876313656_nat_o
% 0.30/0.62            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( ord_le8176553561544679545_nat_o @ X3 @ U2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % lessThan_def
% 0.30/0.62  thf(fact_7993_lessThan__def,axiom,
% 0.30/0.62      ( set_or2436086697161274615iteral
% 0.30/0.62      = ( ^ [U2: literal] :
% 0.30/0.62            ( collect_literal
% 0.30/0.62            @ ^ [X3: literal] : ( ord_less_literal @ X3 @ U2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % lessThan_def
% 0.30/0.62  thf(fact_7994_lessThan__def,axiom,
% 0.30/0.62      ( set_ord_lessThan_rat
% 0.30/0.62      = ( ^ [U2: rat] :
% 0.30/0.62            ( collect_rat
% 0.30/0.62            @ ^ [X3: rat] : ( ord_less_rat @ X3 @ U2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % lessThan_def
% 0.30/0.62  thf(fact_7995_lessThan__def,axiom,
% 0.30/0.62      ( set_ord_lessThan_int
% 0.30/0.62      = ( ^ [U2: int] :
% 0.30/0.62            ( collect_int
% 0.30/0.62            @ ^ [X3: int] : ( ord_less_int @ X3 @ U2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % lessThan_def
% 0.30/0.62  thf(fact_7996_lessThan__def,axiom,
% 0.30/0.62      ( set_ord_lessThan_nat
% 0.30/0.62      = ( ^ [U2: nat] :
% 0.30/0.62            ( collect_nat
% 0.30/0.62            @ ^ [X3: nat] : ( ord_less_nat @ X3 @ U2 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % lessThan_def
% 0.30/0.62  thf(fact_7997_lessThan__empty__iff,axiom,
% 0.30/0.62      ! [N: nat] :
% 0.30/0.62        ( ( ( set_ord_lessThan_nat @ N )
% 0.30/0.62          = bot_bot_set_nat )
% 0.30/0.62        = ( N = zero_zero_nat ) ) ).
% 0.30/0.62  
% 0.30/0.62  % lessThan_empty_iff
% 0.30/0.62  thf(fact_7998_sgn__not__eq__imp,axiom,
% 0.30/0.62      ! [B: int,A: int] :
% 0.30/0.62        ( ( ( sgn_sgn_int @ B )
% 0.30/0.62         != ( sgn_sgn_int @ A ) )
% 0.30/0.62       => ( ( ( sgn_sgn_int @ A )
% 0.30/0.62           != zero_zero_int )
% 0.30/0.62         => ( ( ( sgn_sgn_int @ B )
% 0.30/0.62             != zero_zero_int )
% 0.30/0.62           => ( ( sgn_sgn_int @ A )
% 0.30/0.62              = ( uminus_uminus_int @ ( sgn_sgn_int @ B ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_not_eq_imp
% 0.30/0.62  thf(fact_7999_sgn__not__eq__imp,axiom,
% 0.30/0.62      ! [B: code_integer,A: code_integer] :
% 0.30/0.62        ( ( ( sgn_sgn_Code_integer @ B )
% 0.30/0.62         != ( sgn_sgn_Code_integer @ A ) )
% 0.30/0.62       => ( ( ( sgn_sgn_Code_integer @ A )
% 0.30/0.62           != zero_z3403309356797280102nteger )
% 0.30/0.62         => ( ( ( sgn_sgn_Code_integer @ B )
% 0.30/0.62             != zero_z3403309356797280102nteger )
% 0.30/0.62           => ( ( sgn_sgn_Code_integer @ A )
% 0.30/0.62              = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ B ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_not_eq_imp
% 0.30/0.62  thf(fact_8000_sgn__not__eq__imp,axiom,
% 0.30/0.62      ! [B: rat,A: rat] :
% 0.30/0.62        ( ( ( sgn_sgn_rat @ B )
% 0.30/0.62         != ( sgn_sgn_rat @ A ) )
% 0.30/0.62       => ( ( ( sgn_sgn_rat @ A )
% 0.30/0.62           != zero_zero_rat )
% 0.30/0.62         => ( ( ( sgn_sgn_rat @ B )
% 0.30/0.62             != zero_zero_rat )
% 0.30/0.62           => ( ( sgn_sgn_rat @ A )
% 0.30/0.62              = ( uminus_uminus_rat @ ( sgn_sgn_rat @ B ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_not_eq_imp
% 0.30/0.62  thf(fact_8001_sgn__minus__1,axiom,
% 0.30/0.62      ( ( sgn_sgn_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.62      = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_minus_1
% 0.30/0.62  thf(fact_8002_sgn__minus__1,axiom,
% 0.30/0.62      ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.62      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_minus_1
% 0.30/0.62  thf(fact_8003_sgn__minus__1,axiom,
% 0.30/0.62      ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.30/0.62      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_minus_1
% 0.30/0.62  thf(fact_8004_mult__sgn__abs,axiom,
% 0.30/0.62      ! [X: code_integer] :
% 0.30/0.62        ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ X ) @ ( abs_abs_Code_integer @ X ) )
% 0.30/0.62        = X ) ).
% 0.30/0.62  
% 0.30/0.62  % mult_sgn_abs
% 0.30/0.62  thf(fact_8005_mult__sgn__abs,axiom,
% 0.30/0.62      ! [X: rat] :
% 0.30/0.62        ( ( times_times_rat @ ( sgn_sgn_rat @ X ) @ ( abs_abs_rat @ X ) )
% 0.30/0.62        = X ) ).
% 0.30/0.62  
% 0.30/0.62  % mult_sgn_abs
% 0.30/0.62  thf(fact_8006_mult__sgn__abs,axiom,
% 0.30/0.62      ! [X: int] :
% 0.30/0.62        ( ( times_times_int @ ( sgn_sgn_int @ X ) @ ( abs_abs_int @ X ) )
% 0.30/0.62        = X ) ).
% 0.30/0.62  
% 0.30/0.62  % mult_sgn_abs
% 0.30/0.62  thf(fact_8007_sgn__mult__abs,axiom,
% 0.30/0.62      ! [A: code_integer] :
% 0.30/0.62        ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 0.30/0.62        = A ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_mult_abs
% 0.30/0.62  thf(fact_8008_sgn__mult__abs,axiom,
% 0.30/0.62      ! [A: rat] :
% 0.30/0.62        ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( abs_abs_rat @ A ) )
% 0.30/0.62        = A ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_mult_abs
% 0.30/0.62  thf(fact_8009_sgn__mult__abs,axiom,
% 0.30/0.62      ! [A: int] :
% 0.30/0.62        ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( abs_abs_int @ A ) )
% 0.30/0.62        = A ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_mult_abs
% 0.30/0.62  thf(fact_8010_abs__mult__sgn,axiom,
% 0.30/0.62      ! [A: code_integer] :
% 0.30/0.62        ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 0.30/0.62        = A ) ).
% 0.30/0.62  
% 0.30/0.62  % abs_mult_sgn
% 0.30/0.62  thf(fact_8011_abs__mult__sgn,axiom,
% 0.30/0.62      ! [A: rat] :
% 0.30/0.62        ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 0.30/0.62        = A ) ).
% 0.30/0.62  
% 0.30/0.62  % abs_mult_sgn
% 0.30/0.62  thf(fact_8012_abs__mult__sgn,axiom,
% 0.30/0.62      ! [A: int] :
% 0.30/0.62        ( ( times_times_int @ ( abs_abs_int @ A ) @ ( sgn_sgn_int @ A ) )
% 0.30/0.62        = A ) ).
% 0.30/0.62  
% 0.30/0.62  % abs_mult_sgn
% 0.30/0.62  thf(fact_8013_linordered__idom__class_Oabs__sgn,axiom,
% 0.30/0.62      ( abs_abs_Code_integer
% 0.30/0.62      = ( ^ [K4: code_integer] : ( times_3573771949741848930nteger @ K4 @ ( sgn_sgn_Code_integer @ K4 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % linordered_idom_class.abs_sgn
% 0.30/0.62  thf(fact_8014_linordered__idom__class_Oabs__sgn,axiom,
% 0.30/0.62      ( abs_abs_rat
% 0.30/0.62      = ( ^ [K4: rat] : ( times_times_rat @ K4 @ ( sgn_sgn_rat @ K4 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % linordered_idom_class.abs_sgn
% 0.30/0.62  thf(fact_8015_linordered__idom__class_Oabs__sgn,axiom,
% 0.30/0.62      ( abs_abs_int
% 0.30/0.62      = ( ^ [K4: int] : ( times_times_int @ K4 @ ( sgn_sgn_int @ K4 ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % linordered_idom_class.abs_sgn
% 0.30/0.62  thf(fact_8016_Iio__eq__empty__iff,axiom,
% 0.30/0.62      ! [N: $o] :
% 0.30/0.62        ( ( ( set_ord_lessThan_o @ N )
% 0.30/0.62          = bot_bot_set_o )
% 0.30/0.62        = ( N = bot_bot_o ) ) ).
% 0.30/0.62  
% 0.30/0.62  % Iio_eq_empty_iff
% 0.30/0.62  thf(fact_8017_Iio__eq__empty__iff,axiom,
% 0.30/0.62      ! [N: nat] :
% 0.30/0.62        ( ( ( set_ord_lessThan_nat @ N )
% 0.30/0.62          = bot_bot_set_nat )
% 0.30/0.62        = ( N = bot_bot_nat ) ) ).
% 0.30/0.62  
% 0.30/0.62  % Iio_eq_empty_iff
% 0.30/0.62  thf(fact_8018_sum_Ofinite__Collect__op,axiom,
% 0.30/0.62      ! [I4: set_nat,X: nat > code_integer,Y: nat > code_integer] :
% 0.30/0.62        ( ( finite_finite_nat
% 0.30/0.62          @ ( collect_nat
% 0.30/0.62            @ ^ [I3: nat] :
% 0.30/0.62                ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                & ( ( X @ I3 )
% 0.30/0.62                 != zero_z3403309356797280102nteger ) ) ) )
% 0.30/0.62       => ( ( finite_finite_nat
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [I3: nat] :
% 0.30/0.62                  ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( Y @ I3 )
% 0.30/0.62                   != zero_z3403309356797280102nteger ) ) ) )
% 0.30/0.62         => ( finite_finite_nat
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [I3: nat] :
% 0.30/0.62                  ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( plus_p5714425477246183910nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.30/0.62                   != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.finite_Collect_op
% 0.30/0.62  thf(fact_8019_sum_Ofinite__Collect__op,axiom,
% 0.30/0.62      ! [I4: set_int,X: int > code_integer,Y: int > code_integer] :
% 0.30/0.62        ( ( finite_finite_int
% 0.30/0.62          @ ( collect_int
% 0.30/0.62            @ ^ [I3: int] :
% 0.30/0.62                ( ( member_int @ I3 @ I4 )
% 0.30/0.62                & ( ( X @ I3 )
% 0.30/0.62                 != zero_z3403309356797280102nteger ) ) ) )
% 0.30/0.62       => ( ( finite_finite_int
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [I3: int] :
% 0.30/0.62                  ( ( member_int @ I3 @ I4 )
% 0.30/0.62                  & ( ( Y @ I3 )
% 0.30/0.62                   != zero_z3403309356797280102nteger ) ) ) )
% 0.30/0.62         => ( finite_finite_int
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [I3: int] :
% 0.30/0.62                  ( ( member_int @ I3 @ I4 )
% 0.30/0.62                  & ( ( plus_p5714425477246183910nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.30/0.62                   != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.finite_Collect_op
% 0.30/0.62  thf(fact_8020_sum_Ofinite__Collect__op,axiom,
% 0.30/0.62      ! [I4: set_nat,X: nat > rat,Y: nat > rat] :
% 0.30/0.62        ( ( finite_finite_nat
% 0.30/0.62          @ ( collect_nat
% 0.30/0.62            @ ^ [I3: nat] :
% 0.30/0.62                ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                & ( ( X @ I3 )
% 0.30/0.62                 != zero_zero_rat ) ) ) )
% 0.30/0.62       => ( ( finite_finite_nat
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [I3: nat] :
% 0.30/0.62                  ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( Y @ I3 )
% 0.30/0.62                   != zero_zero_rat ) ) ) )
% 0.30/0.62         => ( finite_finite_nat
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [I3: nat] :
% 0.30/0.62                  ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.30/0.62                   != zero_zero_rat ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.finite_Collect_op
% 0.30/0.62  thf(fact_8021_sum_Ofinite__Collect__op,axiom,
% 0.30/0.62      ! [I4: set_int,X: int > rat,Y: int > rat] :
% 0.30/0.62        ( ( finite_finite_int
% 0.30/0.62          @ ( collect_int
% 0.30/0.62            @ ^ [I3: int] :
% 0.30/0.62                ( ( member_int @ I3 @ I4 )
% 0.30/0.62                & ( ( X @ I3 )
% 0.30/0.62                 != zero_zero_rat ) ) ) )
% 0.30/0.62       => ( ( finite_finite_int
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [I3: int] :
% 0.30/0.62                  ( ( member_int @ I3 @ I4 )
% 0.30/0.62                  & ( ( Y @ I3 )
% 0.30/0.62                   != zero_zero_rat ) ) ) )
% 0.30/0.62         => ( finite_finite_int
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [I3: int] :
% 0.30/0.62                  ( ( member_int @ I3 @ I4 )
% 0.30/0.62                  & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.30/0.62                   != zero_zero_rat ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.finite_Collect_op
% 0.30/0.62  thf(fact_8022_sum_Ofinite__Collect__op,axiom,
% 0.30/0.62      ! [I4: set_nat,X: nat > nat,Y: nat > nat] :
% 0.30/0.62        ( ( finite_finite_nat
% 0.30/0.62          @ ( collect_nat
% 0.30/0.62            @ ^ [I3: nat] :
% 0.30/0.62                ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                & ( ( X @ I3 )
% 0.30/0.62                 != zero_zero_nat ) ) ) )
% 0.30/0.62       => ( ( finite_finite_nat
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [I3: nat] :
% 0.30/0.62                  ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( Y @ I3 )
% 0.30/0.62                   != zero_zero_nat ) ) ) )
% 0.30/0.62         => ( finite_finite_nat
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [I3: nat] :
% 0.30/0.62                  ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( plus_plus_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.30/0.62                   != zero_zero_nat ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.finite_Collect_op
% 0.30/0.62  thf(fact_8023_sum_Ofinite__Collect__op,axiom,
% 0.30/0.62      ! [I4: set_int,X: int > nat,Y: int > nat] :
% 0.30/0.62        ( ( finite_finite_int
% 0.30/0.62          @ ( collect_int
% 0.30/0.62            @ ^ [I3: int] :
% 0.30/0.62                ( ( member_int @ I3 @ I4 )
% 0.30/0.62                & ( ( X @ I3 )
% 0.30/0.62                 != zero_zero_nat ) ) ) )
% 0.30/0.62       => ( ( finite_finite_int
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [I3: int] :
% 0.30/0.62                  ( ( member_int @ I3 @ I4 )
% 0.30/0.62                  & ( ( Y @ I3 )
% 0.30/0.62                   != zero_zero_nat ) ) ) )
% 0.30/0.62         => ( finite_finite_int
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [I3: int] :
% 0.30/0.62                  ( ( member_int @ I3 @ I4 )
% 0.30/0.62                  & ( ( plus_plus_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.30/0.62                   != zero_zero_nat ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.finite_Collect_op
% 0.30/0.62  thf(fact_8024_sum_Ofinite__Collect__op,axiom,
% 0.30/0.62      ! [I4: set_nat,X: nat > int,Y: nat > int] :
% 0.30/0.62        ( ( finite_finite_nat
% 0.30/0.62          @ ( collect_nat
% 0.30/0.62            @ ^ [I3: nat] :
% 0.30/0.62                ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                & ( ( X @ I3 )
% 0.30/0.62                 != zero_zero_int ) ) ) )
% 0.30/0.62       => ( ( finite_finite_nat
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [I3: nat] :
% 0.30/0.62                  ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( Y @ I3 )
% 0.30/0.62                   != zero_zero_int ) ) ) )
% 0.30/0.62         => ( finite_finite_nat
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [I3: nat] :
% 0.30/0.62                  ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( plus_plus_int @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.30/0.62                   != zero_zero_int ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.finite_Collect_op
% 0.30/0.62  thf(fact_8025_sum_Ofinite__Collect__op,axiom,
% 0.30/0.62      ! [I4: set_int,X: int > int,Y: int > int] :
% 0.30/0.62        ( ( finite_finite_int
% 0.30/0.62          @ ( collect_int
% 0.30/0.62            @ ^ [I3: int] :
% 0.30/0.62                ( ( member_int @ I3 @ I4 )
% 0.30/0.62                & ( ( X @ I3 )
% 0.30/0.62                 != zero_zero_int ) ) ) )
% 0.30/0.62       => ( ( finite_finite_int
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [I3: int] :
% 0.30/0.62                  ( ( member_int @ I3 @ I4 )
% 0.30/0.62                  & ( ( Y @ I3 )
% 0.30/0.62                   != zero_zero_int ) ) ) )
% 0.30/0.62         => ( finite_finite_int
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [I3: int] :
% 0.30/0.62                  ( ( member_int @ I3 @ I4 )
% 0.30/0.62                  & ( ( plus_plus_int @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.30/0.62                   != zero_zero_int ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.finite_Collect_op
% 0.30/0.62  thf(fact_8026_sum_Ofinite__Collect__op,axiom,
% 0.30/0.62      ! [I4: set_set_nat,X: set_nat > code_integer,Y: set_nat > code_integer] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat
% 0.30/0.62          @ ( collect_set_nat
% 0.30/0.62            @ ^ [I3: set_nat] :
% 0.30/0.62                ( ( member_set_nat @ I3 @ I4 )
% 0.30/0.62                & ( ( X @ I3 )
% 0.30/0.62                 != zero_z3403309356797280102nteger ) ) ) )
% 0.30/0.62       => ( ( finite1152437895449049373et_nat
% 0.30/0.62            @ ( collect_set_nat
% 0.30/0.62              @ ^ [I3: set_nat] :
% 0.30/0.62                  ( ( member_set_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( Y @ I3 )
% 0.30/0.62                   != zero_z3403309356797280102nteger ) ) ) )
% 0.30/0.62         => ( finite1152437895449049373et_nat
% 0.30/0.62            @ ( collect_set_nat
% 0.30/0.62              @ ^ [I3: set_nat] :
% 0.30/0.62                  ( ( member_set_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( plus_p5714425477246183910nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.30/0.62                   != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.finite_Collect_op
% 0.30/0.62  thf(fact_8027_sum_Ofinite__Collect__op,axiom,
% 0.30/0.62      ! [I4: set_set_nat,X: set_nat > rat,Y: set_nat > rat] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat
% 0.30/0.62          @ ( collect_set_nat
% 0.30/0.62            @ ^ [I3: set_nat] :
% 0.30/0.62                ( ( member_set_nat @ I3 @ I4 )
% 0.30/0.62                & ( ( X @ I3 )
% 0.30/0.62                 != zero_zero_rat ) ) ) )
% 0.30/0.62       => ( ( finite1152437895449049373et_nat
% 0.30/0.62            @ ( collect_set_nat
% 0.30/0.62              @ ^ [I3: set_nat] :
% 0.30/0.62                  ( ( member_set_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( Y @ I3 )
% 0.30/0.62                   != zero_zero_rat ) ) ) )
% 0.30/0.62         => ( finite1152437895449049373et_nat
% 0.30/0.62            @ ( collect_set_nat
% 0.30/0.62              @ ^ [I3: set_nat] :
% 0.30/0.62                  ( ( member_set_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.30/0.62                   != zero_zero_rat ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.finite_Collect_op
% 0.30/0.62  thf(fact_8028_prod_Ofinite__Collect__op,axiom,
% 0.30/0.62      ! [I4: set_nat,X: nat > code_integer,Y: nat > code_integer] :
% 0.30/0.62        ( ( finite_finite_nat
% 0.30/0.62          @ ( collect_nat
% 0.30/0.62            @ ^ [I3: nat] :
% 0.30/0.62                ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                & ( ( X @ I3 )
% 0.30/0.62                 != one_one_Code_integer ) ) ) )
% 0.30/0.62       => ( ( finite_finite_nat
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [I3: nat] :
% 0.30/0.62                  ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( Y @ I3 )
% 0.30/0.62                   != one_one_Code_integer ) ) ) )
% 0.30/0.62         => ( finite_finite_nat
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [I3: nat] :
% 0.30/0.62                  ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( times_3573771949741848930nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.30/0.62                   != one_one_Code_integer ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.finite_Collect_op
% 0.30/0.62  thf(fact_8029_prod_Ofinite__Collect__op,axiom,
% 0.30/0.62      ! [I4: set_int,X: int > code_integer,Y: int > code_integer] :
% 0.30/0.62        ( ( finite_finite_int
% 0.30/0.62          @ ( collect_int
% 0.30/0.62            @ ^ [I3: int] :
% 0.30/0.62                ( ( member_int @ I3 @ I4 )
% 0.30/0.62                & ( ( X @ I3 )
% 0.30/0.62                 != one_one_Code_integer ) ) ) )
% 0.30/0.62       => ( ( finite_finite_int
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [I3: int] :
% 0.30/0.62                  ( ( member_int @ I3 @ I4 )
% 0.30/0.62                  & ( ( Y @ I3 )
% 0.30/0.62                   != one_one_Code_integer ) ) ) )
% 0.30/0.62         => ( finite_finite_int
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [I3: int] :
% 0.30/0.62                  ( ( member_int @ I3 @ I4 )
% 0.30/0.62                  & ( ( times_3573771949741848930nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.30/0.62                   != one_one_Code_integer ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.finite_Collect_op
% 0.30/0.62  thf(fact_8030_prod_Ofinite__Collect__op,axiom,
% 0.30/0.62      ! [I4: set_nat,X: nat > assn,Y: nat > assn] :
% 0.30/0.62        ( ( finite_finite_nat
% 0.30/0.62          @ ( collect_nat
% 0.30/0.62            @ ^ [I3: nat] :
% 0.30/0.62                ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                & ( ( X @ I3 )
% 0.30/0.62                 != one_one_assn ) ) ) )
% 0.30/0.62       => ( ( finite_finite_nat
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [I3: nat] :
% 0.30/0.62                  ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( Y @ I3 )
% 0.30/0.62                   != one_one_assn ) ) ) )
% 0.30/0.62         => ( finite_finite_nat
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [I3: nat] :
% 0.30/0.62                  ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( times_times_assn @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.30/0.62                   != one_one_assn ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.finite_Collect_op
% 0.30/0.62  thf(fact_8031_prod_Ofinite__Collect__op,axiom,
% 0.30/0.62      ! [I4: set_int,X: int > assn,Y: int > assn] :
% 0.30/0.62        ( ( finite_finite_int
% 0.30/0.62          @ ( collect_int
% 0.30/0.62            @ ^ [I3: int] :
% 0.30/0.62                ( ( member_int @ I3 @ I4 )
% 0.30/0.62                & ( ( X @ I3 )
% 0.30/0.62                 != one_one_assn ) ) ) )
% 0.30/0.62       => ( ( finite_finite_int
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [I3: int] :
% 0.30/0.62                  ( ( member_int @ I3 @ I4 )
% 0.30/0.62                  & ( ( Y @ I3 )
% 0.30/0.62                   != one_one_assn ) ) ) )
% 0.30/0.62         => ( finite_finite_int
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [I3: int] :
% 0.30/0.62                  ( ( member_int @ I3 @ I4 )
% 0.30/0.62                  & ( ( times_times_assn @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.30/0.62                   != one_one_assn ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.finite_Collect_op
% 0.30/0.62  thf(fact_8032_prod_Ofinite__Collect__op,axiom,
% 0.30/0.62      ! [I4: set_nat,X: nat > rat,Y: nat > rat] :
% 0.30/0.62        ( ( finite_finite_nat
% 0.30/0.62          @ ( collect_nat
% 0.30/0.62            @ ^ [I3: nat] :
% 0.30/0.62                ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                & ( ( X @ I3 )
% 0.30/0.62                 != one_one_rat ) ) ) )
% 0.30/0.62       => ( ( finite_finite_nat
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [I3: nat] :
% 0.30/0.62                  ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( Y @ I3 )
% 0.30/0.62                   != one_one_rat ) ) ) )
% 0.30/0.62         => ( finite_finite_nat
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [I3: nat] :
% 0.30/0.62                  ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.30/0.62                   != one_one_rat ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.finite_Collect_op
% 0.30/0.62  thf(fact_8033_prod_Ofinite__Collect__op,axiom,
% 0.30/0.62      ! [I4: set_int,X: int > rat,Y: int > rat] :
% 0.30/0.62        ( ( finite_finite_int
% 0.30/0.62          @ ( collect_int
% 0.30/0.62            @ ^ [I3: int] :
% 0.30/0.62                ( ( member_int @ I3 @ I4 )
% 0.30/0.62                & ( ( X @ I3 )
% 0.30/0.62                 != one_one_rat ) ) ) )
% 0.30/0.62       => ( ( finite_finite_int
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [I3: int] :
% 0.30/0.62                  ( ( member_int @ I3 @ I4 )
% 0.30/0.62                  & ( ( Y @ I3 )
% 0.30/0.62                   != one_one_rat ) ) ) )
% 0.30/0.62         => ( finite_finite_int
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [I3: int] :
% 0.30/0.62                  ( ( member_int @ I3 @ I4 )
% 0.30/0.62                  & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.30/0.62                   != one_one_rat ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.finite_Collect_op
% 0.30/0.62  thf(fact_8034_prod_Ofinite__Collect__op,axiom,
% 0.30/0.62      ! [I4: set_nat,X: nat > nat,Y: nat > nat] :
% 0.30/0.62        ( ( finite_finite_nat
% 0.30/0.62          @ ( collect_nat
% 0.30/0.62            @ ^ [I3: nat] :
% 0.30/0.62                ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                & ( ( X @ I3 )
% 0.30/0.62                 != one_one_nat ) ) ) )
% 0.30/0.62       => ( ( finite_finite_nat
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [I3: nat] :
% 0.30/0.62                  ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( Y @ I3 )
% 0.30/0.62                   != one_one_nat ) ) ) )
% 0.30/0.62         => ( finite_finite_nat
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [I3: nat] :
% 0.30/0.62                  ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( times_times_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.30/0.62                   != one_one_nat ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.finite_Collect_op
% 0.30/0.62  thf(fact_8035_prod_Ofinite__Collect__op,axiom,
% 0.30/0.62      ! [I4: set_int,X: int > nat,Y: int > nat] :
% 0.30/0.62        ( ( finite_finite_int
% 0.30/0.62          @ ( collect_int
% 0.30/0.62            @ ^ [I3: int] :
% 0.30/0.62                ( ( member_int @ I3 @ I4 )
% 0.30/0.62                & ( ( X @ I3 )
% 0.30/0.62                 != one_one_nat ) ) ) )
% 0.30/0.62       => ( ( finite_finite_int
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [I3: int] :
% 0.30/0.62                  ( ( member_int @ I3 @ I4 )
% 0.30/0.62                  & ( ( Y @ I3 )
% 0.30/0.62                   != one_one_nat ) ) ) )
% 0.30/0.62         => ( finite_finite_int
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [I3: int] :
% 0.30/0.62                  ( ( member_int @ I3 @ I4 )
% 0.30/0.62                  & ( ( times_times_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.30/0.62                   != one_one_nat ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.finite_Collect_op
% 0.30/0.62  thf(fact_8036_prod_Ofinite__Collect__op,axiom,
% 0.30/0.62      ! [I4: set_nat,X: nat > int,Y: nat > int] :
% 0.30/0.62        ( ( finite_finite_nat
% 0.30/0.62          @ ( collect_nat
% 0.30/0.62            @ ^ [I3: nat] :
% 0.30/0.62                ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                & ( ( X @ I3 )
% 0.30/0.62                 != one_one_int ) ) ) )
% 0.30/0.62       => ( ( finite_finite_nat
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [I3: nat] :
% 0.30/0.62                  ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( Y @ I3 )
% 0.30/0.62                   != one_one_int ) ) ) )
% 0.30/0.62         => ( finite_finite_nat
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [I3: nat] :
% 0.30/0.62                  ( ( member_nat @ I3 @ I4 )
% 0.30/0.62                  & ( ( times_times_int @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.30/0.62                   != one_one_int ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.finite_Collect_op
% 0.30/0.62  thf(fact_8037_prod_Ofinite__Collect__op,axiom,
% 0.30/0.62      ! [I4: set_int,X: int > int,Y: int > int] :
% 0.30/0.62        ( ( finite_finite_int
% 0.30/0.62          @ ( collect_int
% 0.30/0.62            @ ^ [I3: int] :
% 0.30/0.62                ( ( member_int @ I3 @ I4 )
% 0.30/0.62                & ( ( X @ I3 )
% 0.30/0.62                 != one_one_int ) ) ) )
% 0.30/0.62       => ( ( finite_finite_int
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [I3: int] :
% 0.30/0.62                  ( ( member_int @ I3 @ I4 )
% 0.30/0.62                  & ( ( Y @ I3 )
% 0.30/0.62                   != one_one_int ) ) ) )
% 0.30/0.62         => ( finite_finite_int
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [I3: int] :
% 0.30/0.62                  ( ( member_int @ I3 @ I4 )
% 0.30/0.62                  & ( ( times_times_int @ ( X @ I3 ) @ ( Y @ I3 ) )
% 0.30/0.62                   != one_one_int ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.finite_Collect_op
% 0.30/0.62  thf(fact_8038_sum_Ointer__filter,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > code_integer,P: nat > $o] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups7501900531339628137nteger @ G2
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [X3: nat] :
% 0.30/0.62                  ( ( member_nat @ X3 @ A2 )
% 0.30/0.62                  & ( P @ X3 ) ) ) )
% 0.30/0.62          = ( groups7501900531339628137nteger
% 0.30/0.62            @ ^ [X3: nat] : ( if_Code_integer @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_z3403309356797280102nteger )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.inter_filter
% 0.30/0.62  thf(fact_8039_sum_Ointer__filter,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > code_integer,P: int > $o] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups7873554091576472773nteger @ G2
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [X3: int] :
% 0.30/0.62                  ( ( member_int @ X3 @ A2 )
% 0.30/0.62                  & ( P @ X3 ) ) ) )
% 0.30/0.62          = ( groups7873554091576472773nteger
% 0.30/0.62            @ ^ [X3: int] : ( if_Code_integer @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_z3403309356797280102nteger )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.inter_filter
% 0.30/0.62  thf(fact_8040_sum_Ointer__filter,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > rat,P: nat > $o] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups2906978787729119204at_rat @ G2
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [X3: nat] :
% 0.30/0.62                  ( ( member_nat @ X3 @ A2 )
% 0.30/0.62                  & ( P @ X3 ) ) ) )
% 0.30/0.62          = ( groups2906978787729119204at_rat
% 0.30/0.62            @ ^ [X3: nat] : ( if_rat @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_rat )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.inter_filter
% 0.30/0.62  thf(fact_8041_sum_Ointer__filter,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > rat,P: int > $o] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups3906332499630173760nt_rat @ G2
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [X3: int] :
% 0.30/0.62                  ( ( member_int @ X3 @ A2 )
% 0.30/0.62                  & ( P @ X3 ) ) ) )
% 0.30/0.62          = ( groups3906332499630173760nt_rat
% 0.30/0.62            @ ^ [X3: int] : ( if_rat @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_rat )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.inter_filter
% 0.30/0.62  thf(fact_8042_sum_Ointer__filter,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > nat,P: int > $o] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups4541462559716669496nt_nat @ G2
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [X3: int] :
% 0.30/0.62                  ( ( member_int @ X3 @ A2 )
% 0.30/0.62                  & ( P @ X3 ) ) ) )
% 0.30/0.62          = ( groups4541462559716669496nt_nat
% 0.30/0.62            @ ^ [X3: int] : ( if_nat @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_nat )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.inter_filter
% 0.30/0.62  thf(fact_8043_sum_Ointer__filter,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > int,P: nat > $o] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups3539618377306564664at_int @ G2
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [X3: nat] :
% 0.30/0.62                  ( ( member_nat @ X3 @ A2 )
% 0.30/0.62                  & ( P @ X3 ) ) ) )
% 0.30/0.62          = ( groups3539618377306564664at_int
% 0.30/0.62            @ ^ [X3: nat] : ( if_int @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_int )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.inter_filter
% 0.30/0.62  thf(fact_8044_sum_Ointer__filter,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > nat,P: nat > $o] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups3542108847815614940at_nat @ G2
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [X3: nat] :
% 0.30/0.62                  ( ( member_nat @ X3 @ A2 )
% 0.30/0.62                  & ( P @ X3 ) ) ) )
% 0.30/0.62          = ( groups3542108847815614940at_nat
% 0.30/0.62            @ ^ [X3: nat] : ( if_nat @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_nat )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.inter_filter
% 0.30/0.62  thf(fact_8045_sum_Ointer__filter,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > int,P: int > $o] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups4538972089207619220nt_int @ G2
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [X3: int] :
% 0.30/0.62                  ( ( member_int @ X3 @ A2 )
% 0.30/0.62                  & ( P @ X3 ) ) ) )
% 0.30/0.62          = ( groups4538972089207619220nt_int
% 0.30/0.62            @ ^ [X3: int] : ( if_int @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_int )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.inter_filter
% 0.30/0.62  thf(fact_8046_sum_Ointer__filter,axiom,
% 0.30/0.62      ! [A2: set_set_nat,G2: set_nat > code_integer,P: set_nat > $o] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.62       => ( ( groups9190459664516455967nteger @ G2
% 0.30/0.62            @ ( collect_set_nat
% 0.30/0.62              @ ^ [X3: set_nat] :
% 0.30/0.62                  ( ( member_set_nat @ X3 @ A2 )
% 0.30/0.62                  & ( P @ X3 ) ) ) )
% 0.30/0.62          = ( groups9190459664516455967nteger
% 0.30/0.62            @ ^ [X3: set_nat] : ( if_Code_integer @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_z3403309356797280102nteger )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.inter_filter
% 0.30/0.62  thf(fact_8047_sum_Ointer__filter,axiom,
% 0.30/0.62      ! [A2: set_set_nat,G2: set_nat > rat,P: set_nat > $o] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.62       => ( ( groups7659867448343625626at_rat @ G2
% 0.30/0.62            @ ( collect_set_nat
% 0.30/0.62              @ ^ [X3: set_nat] :
% 0.30/0.62                  ( ( member_set_nat @ X3 @ A2 )
% 0.30/0.62                  & ( P @ X3 ) ) ) )
% 0.30/0.62          = ( groups7659867448343625626at_rat
% 0.30/0.62            @ ^ [X3: set_nat] : ( if_rat @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_rat )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.inter_filter
% 0.30/0.62  thf(fact_8048_prod_Ointer__filter,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > code_integer,P: nat > $o] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups3455450783089532116nteger @ G2
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [X3: nat] :
% 0.30/0.62                  ( ( member_nat @ X3 @ A2 )
% 0.30/0.62                  & ( P @ X3 ) ) ) )
% 0.30/0.62          = ( groups3455450783089532116nteger
% 0.30/0.62            @ ^ [X3: nat] : ( if_Code_integer @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_Code_integer )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.inter_filter
% 0.30/0.62  thf(fact_8049_prod_Ointer__filter,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > code_integer,P: int > $o] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups3827104343326376752nteger @ G2
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [X3: int] :
% 0.30/0.62                  ( ( member_int @ X3 @ A2 )
% 0.30/0.62                  & ( P @ X3 ) ) ) )
% 0.30/0.62          = ( groups3827104343326376752nteger
% 0.30/0.62            @ ^ [X3: int] : ( if_Code_integer @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_Code_integer )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.inter_filter
% 0.30/0.62  thf(fact_8050_prod_Ointer__filter,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > assn,P: nat > $o] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups6906906614972039071t_assn @ G2
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [X3: nat] :
% 0.30/0.62                  ( ( member_nat @ X3 @ A2 )
% 0.30/0.62                  & ( P @ X3 ) ) ) )
% 0.30/0.62          = ( groups6906906614972039071t_assn
% 0.30/0.62            @ ^ [X3: nat] : ( if_assn @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_assn )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.inter_filter
% 0.30/0.62  thf(fact_8051_prod_Ointer__filter,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > assn,P: int > $o] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups7882442080178216443t_assn @ G2
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [X3: int] :
% 0.30/0.62                  ( ( member_int @ X3 @ A2 )
% 0.30/0.62                  & ( P @ X3 ) ) ) )
% 0.30/0.62          = ( groups7882442080178216443t_assn
% 0.30/0.62            @ ^ [X3: int] : ( if_assn @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_assn )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.inter_filter
% 0.30/0.62  thf(fact_8052_prod_Ointer__filter,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > rat,P: nat > $o] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups73079841787564623at_rat @ G2
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [X3: nat] :
% 0.30/0.62                  ( ( member_nat @ X3 @ A2 )
% 0.30/0.62                  & ( P @ X3 ) ) ) )
% 0.30/0.62          = ( groups73079841787564623at_rat
% 0.30/0.62            @ ^ [X3: nat] : ( if_rat @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_rat )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.inter_filter
% 0.30/0.62  thf(fact_8053_prod_Ointer__filter,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > rat,P: int > $o] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups1072433553688619179nt_rat @ G2
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [X3: int] :
% 0.30/0.62                  ( ( member_int @ X3 @ A2 )
% 0.30/0.62                  & ( P @ X3 ) ) ) )
% 0.30/0.62          = ( groups1072433553688619179nt_rat
% 0.30/0.62            @ ^ [X3: int] : ( if_rat @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_rat )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.inter_filter
% 0.30/0.62  thf(fact_8054_prod_Ointer__filter,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > nat,P: int > $o] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups1707563613775114915nt_nat @ G2
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [X3: int] :
% 0.30/0.62                  ( ( member_int @ X3 @ A2 )
% 0.30/0.62                  & ( P @ X3 ) ) ) )
% 0.30/0.62          = ( groups1707563613775114915nt_nat
% 0.30/0.62            @ ^ [X3: int] : ( if_nat @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_nat )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.inter_filter
% 0.30/0.62  thf(fact_8055_prod_Ointer__filter,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > nat,P: nat > $o] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups708209901874060359at_nat @ G2
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [X3: nat] :
% 0.30/0.62                  ( ( member_nat @ X3 @ A2 )
% 0.30/0.62                  & ( P @ X3 ) ) ) )
% 0.30/0.62          = ( groups708209901874060359at_nat
% 0.30/0.62            @ ^ [X3: nat] : ( if_nat @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_nat )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.inter_filter
% 0.30/0.62  thf(fact_8056_prod_Ointer__filter,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > int,P: nat > $o] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups705719431365010083at_int @ G2
% 0.30/0.62            @ ( collect_nat
% 0.30/0.62              @ ^ [X3: nat] :
% 0.30/0.62                  ( ( member_nat @ X3 @ A2 )
% 0.30/0.62                  & ( P @ X3 ) ) ) )
% 0.30/0.62          = ( groups705719431365010083at_int
% 0.30/0.62            @ ^ [X3: nat] : ( if_int @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_int )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.inter_filter
% 0.30/0.62  thf(fact_8057_prod_Ointer__filter,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > int,P: int > $o] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups1705073143266064639nt_int @ G2
% 0.30/0.62            @ ( collect_int
% 0.30/0.62              @ ^ [X3: int] :
% 0.30/0.62                  ( ( member_int @ X3 @ A2 )
% 0.30/0.62                  & ( P @ X3 ) ) ) )
% 0.30/0.62          = ( groups1705073143266064639nt_int
% 0.30/0.62            @ ^ [X3: int] : ( if_int @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_int )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.inter_filter
% 0.30/0.62  thf(fact_8058_sum__strict__mono,axiom,
% 0.30/0.62      ! [A2: set_o,F2: $o > rat,G2: $o > rat] :
% 0.30/0.62        ( ( finite_finite_o @ A2 )
% 0.30/0.62       => ( ( A2 != bot_bot_set_o )
% 0.30/0.62         => ( ! [X2: $o] :
% 0.30/0.62                ( ( member_o @ X2 @ A2 )
% 0.30/0.62               => ( ord_less_rat @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) )
% 0.30/0.62           => ( ord_less_rat @ ( groups7872700643590313910_o_rat @ F2 @ A2 ) @ ( groups7872700643590313910_o_rat @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_strict_mono
% 0.30/0.62  thf(fact_8059_sum__strict__mono,axiom,
% 0.30/0.62      ! [A2: set_nat,F2: nat > rat,G2: nat > rat] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( A2 != bot_bot_set_nat )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ A2 )
% 0.30/0.62               => ( ord_less_rat @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) )
% 0.30/0.62           => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F2 @ A2 ) @ ( groups2906978787729119204at_rat @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_strict_mono
% 0.30/0.62  thf(fact_8060_sum__strict__mono,axiom,
% 0.30/0.62      ! [A2: set_int,F2: int > rat,G2: int > rat] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( A2 != bot_bot_set_int )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ A2 )
% 0.30/0.62               => ( ord_less_rat @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) )
% 0.30/0.62           => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F2 @ A2 ) @ ( groups3906332499630173760nt_rat @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_strict_mono
% 0.30/0.62  thf(fact_8061_sum__strict__mono,axiom,
% 0.30/0.62      ! [A2: set_o,F2: $o > nat,G2: $o > nat] :
% 0.30/0.62        ( ( finite_finite_o @ A2 )
% 0.30/0.62       => ( ( A2 != bot_bot_set_o )
% 0.30/0.62         => ( ! [X2: $o] :
% 0.30/0.62                ( ( member_o @ X2 @ A2 )
% 0.30/0.62               => ( ord_less_nat @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) )
% 0.30/0.62           => ( ord_less_nat @ ( groups8507830703676809646_o_nat @ F2 @ A2 ) @ ( groups8507830703676809646_o_nat @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_strict_mono
% 0.30/0.62  thf(fact_8062_sum__strict__mono,axiom,
% 0.30/0.62      ! [A2: set_int,F2: int > nat,G2: int > nat] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( A2 != bot_bot_set_int )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ A2 )
% 0.30/0.62               => ( ord_less_nat @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) )
% 0.30/0.62           => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F2 @ A2 ) @ ( groups4541462559716669496nt_nat @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_strict_mono
% 0.30/0.62  thf(fact_8063_sum__strict__mono,axiom,
% 0.30/0.62      ! [A2: set_o,F2: $o > int,G2: $o > int] :
% 0.30/0.62        ( ( finite_finite_o @ A2 )
% 0.30/0.62       => ( ( A2 != bot_bot_set_o )
% 0.30/0.62         => ( ! [X2: $o] :
% 0.30/0.62                ( ( member_o @ X2 @ A2 )
% 0.30/0.62               => ( ord_less_int @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) )
% 0.30/0.62           => ( ord_less_int @ ( groups8505340233167759370_o_int @ F2 @ A2 ) @ ( groups8505340233167759370_o_int @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_strict_mono
% 0.30/0.62  thf(fact_8064_sum__strict__mono,axiom,
% 0.30/0.62      ! [A2: set_nat,F2: nat > int,G2: nat > int] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( A2 != bot_bot_set_nat )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ A2 )
% 0.30/0.62               => ( ord_less_int @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) )
% 0.30/0.62           => ( ord_less_int @ ( groups3539618377306564664at_int @ F2 @ A2 ) @ ( groups3539618377306564664at_int @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_strict_mono
% 0.30/0.62  thf(fact_8065_sum__strict__mono,axiom,
% 0.30/0.62      ! [A2: set_nat,F2: nat > nat,G2: nat > nat] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( A2 != bot_bot_set_nat )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ A2 )
% 0.30/0.62               => ( ord_less_nat @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) )
% 0.30/0.62           => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F2 @ A2 ) @ ( groups3542108847815614940at_nat @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_strict_mono
% 0.30/0.62  thf(fact_8066_sum__strict__mono,axiom,
% 0.30/0.62      ! [A2: set_int,F2: int > int,G2: int > int] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( A2 != bot_bot_set_int )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ A2 )
% 0.30/0.62               => ( ord_less_int @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) )
% 0.30/0.62           => ( ord_less_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) @ ( groups4538972089207619220nt_int @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_strict_mono
% 0.30/0.62  thf(fact_8067_sum__strict__mono,axiom,
% 0.30/0.62      ! [A2: set_set_nat,F2: set_nat > rat,G2: set_nat > rat] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.62       => ( ( A2 != bot_bot_set_set_nat )
% 0.30/0.62         => ( ! [X2: set_nat] :
% 0.30/0.62                ( ( member_set_nat @ X2 @ A2 )
% 0.30/0.62               => ( ord_less_rat @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) )
% 0.30/0.62           => ( ord_less_rat @ ( groups7659867448343625626at_rat @ F2 @ A2 ) @ ( groups7659867448343625626at_rat @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_strict_mono
% 0.30/0.62  thf(fact_8068_sgn__1__pos,axiom,
% 0.30/0.62      ! [A: code_integer] :
% 0.30/0.62        ( ( ( sgn_sgn_Code_integer @ A )
% 0.30/0.62          = one_one_Code_integer )
% 0.30/0.62        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_1_pos
% 0.30/0.62  thf(fact_8069_sgn__1__pos,axiom,
% 0.30/0.62      ! [A: rat] :
% 0.30/0.62        ( ( ( sgn_sgn_rat @ A )
% 0.30/0.62          = one_one_rat )
% 0.30/0.62        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_1_pos
% 0.30/0.62  thf(fact_8070_sgn__1__pos,axiom,
% 0.30/0.62      ! [A: int] :
% 0.30/0.62        ( ( ( sgn_sgn_int @ A )
% 0.30/0.62          = one_one_int )
% 0.30/0.62        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_1_pos
% 0.30/0.62  thf(fact_8071_prod_Orelated,axiom,
% 0.30/0.62      ! [R: code_integer > code_integer > $o,S: set_nat,H3: nat > code_integer,G2: nat > code_integer] :
% 0.30/0.62        ( ( R @ one_one_Code_integer @ one_one_Code_integer )
% 0.30/0.62       => ( ! [X13: code_integer,Y12: code_integer,X24: code_integer,Y23: code_integer] :
% 0.30/0.62              ( ( ( R @ X13 @ X24 )
% 0.30/0.62                & ( R @ Y12 @ Y23 ) )
% 0.30/0.62             => ( R @ ( times_3573771949741848930nteger @ X13 @ Y12 ) @ ( times_3573771949741848930nteger @ X24 @ Y23 ) ) )
% 0.30/0.62         => ( ( finite_finite_nat @ S )
% 0.30/0.62           => ( ! [X2: nat] :
% 0.30/0.62                  ( ( member_nat @ X2 @ S )
% 0.30/0.62                 => ( R @ ( H3 @ X2 ) @ ( G2 @ X2 ) ) )
% 0.30/0.62             => ( R @ ( groups3455450783089532116nteger @ H3 @ S ) @ ( groups3455450783089532116nteger @ G2 @ S ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.related
% 0.30/0.62  thf(fact_8072_prod_Orelated,axiom,
% 0.30/0.62      ! [R: code_integer > code_integer > $o,S: set_int,H3: int > code_integer,G2: int > code_integer] :
% 0.30/0.62        ( ( R @ one_one_Code_integer @ one_one_Code_integer )
% 0.30/0.62       => ( ! [X13: code_integer,Y12: code_integer,X24: code_integer,Y23: code_integer] :
% 0.30/0.62              ( ( ( R @ X13 @ X24 )
% 0.30/0.62                & ( R @ Y12 @ Y23 ) )
% 0.30/0.62             => ( R @ ( times_3573771949741848930nteger @ X13 @ Y12 ) @ ( times_3573771949741848930nteger @ X24 @ Y23 ) ) )
% 0.30/0.62         => ( ( finite_finite_int @ S )
% 0.30/0.62           => ( ! [X2: int] :
% 0.30/0.62                  ( ( member_int @ X2 @ S )
% 0.30/0.62                 => ( R @ ( H3 @ X2 ) @ ( G2 @ X2 ) ) )
% 0.30/0.62             => ( R @ ( groups3827104343326376752nteger @ H3 @ S ) @ ( groups3827104343326376752nteger @ G2 @ S ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.related
% 0.30/0.62  thf(fact_8073_prod_Orelated,axiom,
% 0.30/0.62      ! [R: assn > assn > $o,S: set_nat,H3: nat > assn,G2: nat > assn] :
% 0.30/0.62        ( ( R @ one_one_assn @ one_one_assn )
% 0.30/0.62       => ( ! [X13: assn,Y12: assn,X24: assn,Y23: assn] :
% 0.30/0.62              ( ( ( R @ X13 @ X24 )
% 0.30/0.62                & ( R @ Y12 @ Y23 ) )
% 0.30/0.62             => ( R @ ( times_times_assn @ X13 @ Y12 ) @ ( times_times_assn @ X24 @ Y23 ) ) )
% 0.30/0.62         => ( ( finite_finite_nat @ S )
% 0.30/0.62           => ( ! [X2: nat] :
% 0.30/0.62                  ( ( member_nat @ X2 @ S )
% 0.30/0.62                 => ( R @ ( H3 @ X2 ) @ ( G2 @ X2 ) ) )
% 0.30/0.62             => ( R @ ( groups6906906614972039071t_assn @ H3 @ S ) @ ( groups6906906614972039071t_assn @ G2 @ S ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.related
% 0.30/0.62  thf(fact_8074_prod_Orelated,axiom,
% 0.30/0.62      ! [R: assn > assn > $o,S: set_int,H3: int > assn,G2: int > assn] :
% 0.30/0.62        ( ( R @ one_one_assn @ one_one_assn )
% 0.30/0.62       => ( ! [X13: assn,Y12: assn,X24: assn,Y23: assn] :
% 0.30/0.62              ( ( ( R @ X13 @ X24 )
% 0.30/0.62                & ( R @ Y12 @ Y23 ) )
% 0.30/0.62             => ( R @ ( times_times_assn @ X13 @ Y12 ) @ ( times_times_assn @ X24 @ Y23 ) ) )
% 0.30/0.62         => ( ( finite_finite_int @ S )
% 0.30/0.62           => ( ! [X2: int] :
% 0.30/0.62                  ( ( member_int @ X2 @ S )
% 0.30/0.62                 => ( R @ ( H3 @ X2 ) @ ( G2 @ X2 ) ) )
% 0.30/0.62             => ( R @ ( groups7882442080178216443t_assn @ H3 @ S ) @ ( groups7882442080178216443t_assn @ G2 @ S ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.related
% 0.30/0.62  thf(fact_8075_prod_Orelated,axiom,
% 0.30/0.62      ! [R: rat > rat > $o,S: set_nat,H3: nat > rat,G2: nat > rat] :
% 0.30/0.62        ( ( R @ one_one_rat @ one_one_rat )
% 0.30/0.62       => ( ! [X13: rat,Y12: rat,X24: rat,Y23: rat] :
% 0.30/0.62              ( ( ( R @ X13 @ X24 )
% 0.30/0.62                & ( R @ Y12 @ Y23 ) )
% 0.30/0.62             => ( R @ ( times_times_rat @ X13 @ Y12 ) @ ( times_times_rat @ X24 @ Y23 ) ) )
% 0.30/0.62         => ( ( finite_finite_nat @ S )
% 0.30/0.62           => ( ! [X2: nat] :
% 0.30/0.62                  ( ( member_nat @ X2 @ S )
% 0.30/0.62                 => ( R @ ( H3 @ X2 ) @ ( G2 @ X2 ) ) )
% 0.30/0.62             => ( R @ ( groups73079841787564623at_rat @ H3 @ S ) @ ( groups73079841787564623at_rat @ G2 @ S ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.related
% 0.30/0.62  thf(fact_8076_prod_Orelated,axiom,
% 0.30/0.62      ! [R: rat > rat > $o,S: set_int,H3: int > rat,G2: int > rat] :
% 0.30/0.62        ( ( R @ one_one_rat @ one_one_rat )
% 0.30/0.62       => ( ! [X13: rat,Y12: rat,X24: rat,Y23: rat] :
% 0.30/0.62              ( ( ( R @ X13 @ X24 )
% 0.30/0.62                & ( R @ Y12 @ Y23 ) )
% 0.30/0.62             => ( R @ ( times_times_rat @ X13 @ Y12 ) @ ( times_times_rat @ X24 @ Y23 ) ) )
% 0.30/0.62         => ( ( finite_finite_int @ S )
% 0.30/0.62           => ( ! [X2: int] :
% 0.30/0.62                  ( ( member_int @ X2 @ S )
% 0.30/0.62                 => ( R @ ( H3 @ X2 ) @ ( G2 @ X2 ) ) )
% 0.30/0.62             => ( R @ ( groups1072433553688619179nt_rat @ H3 @ S ) @ ( groups1072433553688619179nt_rat @ G2 @ S ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.related
% 0.30/0.62  thf(fact_8077_prod_Orelated,axiom,
% 0.30/0.62      ! [R: nat > nat > $o,S: set_int,H3: int > nat,G2: int > nat] :
% 0.30/0.62        ( ( R @ one_one_nat @ one_one_nat )
% 0.30/0.62       => ( ! [X13: nat,Y12: nat,X24: nat,Y23: nat] :
% 0.30/0.62              ( ( ( R @ X13 @ X24 )
% 0.30/0.62                & ( R @ Y12 @ Y23 ) )
% 0.30/0.62             => ( R @ ( times_times_nat @ X13 @ Y12 ) @ ( times_times_nat @ X24 @ Y23 ) ) )
% 0.30/0.62         => ( ( finite_finite_int @ S )
% 0.30/0.62           => ( ! [X2: int] :
% 0.30/0.62                  ( ( member_int @ X2 @ S )
% 0.30/0.62                 => ( R @ ( H3 @ X2 ) @ ( G2 @ X2 ) ) )
% 0.30/0.62             => ( R @ ( groups1707563613775114915nt_nat @ H3 @ S ) @ ( groups1707563613775114915nt_nat @ G2 @ S ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.related
% 0.30/0.62  thf(fact_8078_prod_Orelated,axiom,
% 0.30/0.62      ! [R: nat > nat > $o,S: set_nat,H3: nat > nat,G2: nat > nat] :
% 0.30/0.62        ( ( R @ one_one_nat @ one_one_nat )
% 0.30/0.62       => ( ! [X13: nat,Y12: nat,X24: nat,Y23: nat] :
% 0.30/0.62              ( ( ( R @ X13 @ X24 )
% 0.30/0.62                & ( R @ Y12 @ Y23 ) )
% 0.30/0.62             => ( R @ ( times_times_nat @ X13 @ Y12 ) @ ( times_times_nat @ X24 @ Y23 ) ) )
% 0.30/0.62         => ( ( finite_finite_nat @ S )
% 0.30/0.62           => ( ! [X2: nat] :
% 0.30/0.62                  ( ( member_nat @ X2 @ S )
% 0.30/0.62                 => ( R @ ( H3 @ X2 ) @ ( G2 @ X2 ) ) )
% 0.30/0.62             => ( R @ ( groups708209901874060359at_nat @ H3 @ S ) @ ( groups708209901874060359at_nat @ G2 @ S ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.related
% 0.30/0.62  thf(fact_8079_prod_Orelated,axiom,
% 0.30/0.62      ! [R: int > int > $o,S: set_nat,H3: nat > int,G2: nat > int] :
% 0.30/0.62        ( ( R @ one_one_int @ one_one_int )
% 0.30/0.62       => ( ! [X13: int,Y12: int,X24: int,Y23: int] :
% 0.30/0.62              ( ( ( R @ X13 @ X24 )
% 0.30/0.62                & ( R @ Y12 @ Y23 ) )
% 0.30/0.62             => ( R @ ( times_times_int @ X13 @ Y12 ) @ ( times_times_int @ X24 @ Y23 ) ) )
% 0.30/0.62         => ( ( finite_finite_nat @ S )
% 0.30/0.62           => ( ! [X2: nat] :
% 0.30/0.62                  ( ( member_nat @ X2 @ S )
% 0.30/0.62                 => ( R @ ( H3 @ X2 ) @ ( G2 @ X2 ) ) )
% 0.30/0.62             => ( R @ ( groups705719431365010083at_int @ H3 @ S ) @ ( groups705719431365010083at_int @ G2 @ S ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.related
% 0.30/0.62  thf(fact_8080_prod_Orelated,axiom,
% 0.30/0.62      ! [R: int > int > $o,S: set_int,H3: int > int,G2: int > int] :
% 0.30/0.62        ( ( R @ one_one_int @ one_one_int )
% 0.30/0.62       => ( ! [X13: int,Y12: int,X24: int,Y23: int] :
% 0.30/0.62              ( ( ( R @ X13 @ X24 )
% 0.30/0.62                & ( R @ Y12 @ Y23 ) )
% 0.30/0.62             => ( R @ ( times_times_int @ X13 @ Y12 ) @ ( times_times_int @ X24 @ Y23 ) ) )
% 0.30/0.62         => ( ( finite_finite_int @ S )
% 0.30/0.62           => ( ! [X2: int] :
% 0.30/0.62                  ( ( member_int @ X2 @ S )
% 0.30/0.62                 => ( R @ ( H3 @ X2 ) @ ( G2 @ X2 ) ) )
% 0.30/0.62             => ( R @ ( groups1705073143266064639nt_int @ H3 @ S ) @ ( groups1705073143266064639nt_int @ G2 @ S ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.related
% 0.30/0.62  thf(fact_8081_prod_Oinsert__if,axiom,
% 0.30/0.62      ! [A2: set_o,X: $o,G2: $o > code_integer] :
% 0.30/0.62        ( ( finite_finite_o @ A2 )
% 0.30/0.62       => ( ( ( member_o @ X @ A2 )
% 0.30/0.62           => ( ( groups7694694392188491536nteger @ G2 @ ( insert_o @ X @ A2 ) )
% 0.30/0.62              = ( groups7694694392188491536nteger @ G2 @ A2 ) ) )
% 0.30/0.62          & ( ~ ( member_o @ X @ A2 )
% 0.30/0.62           => ( ( groups7694694392188491536nteger @ G2 @ ( insert_o @ X @ A2 ) )
% 0.30/0.62              = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups7694694392188491536nteger @ G2 @ A2 ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.insert_if
% 0.30/0.62  thf(fact_8082_prod_Oinsert__if,axiom,
% 0.30/0.62      ! [A2: set_nat,X: nat,G2: nat > code_integer] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( ( member_nat @ X @ A2 )
% 0.30/0.62           => ( ( groups3455450783089532116nteger @ G2 @ ( insert_nat @ X @ A2 ) )
% 0.30/0.62              = ( groups3455450783089532116nteger @ G2 @ A2 ) ) )
% 0.30/0.62          & ( ~ ( member_nat @ X @ A2 )
% 0.30/0.62           => ( ( groups3455450783089532116nteger @ G2 @ ( insert_nat @ X @ A2 ) )
% 0.30/0.62              = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups3455450783089532116nteger @ G2 @ A2 ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.insert_if
% 0.30/0.62  thf(fact_8083_prod_Oinsert__if,axiom,
% 0.30/0.62      ! [A2: set_int,X: int,G2: int > code_integer] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( ( member_int @ X @ A2 )
% 0.30/0.62           => ( ( groups3827104343326376752nteger @ G2 @ ( insert_int @ X @ A2 ) )
% 0.30/0.62              = ( groups3827104343326376752nteger @ G2 @ A2 ) ) )
% 0.30/0.62          & ( ~ ( member_int @ X @ A2 )
% 0.30/0.62           => ( ( groups3827104343326376752nteger @ G2 @ ( insert_int @ X @ A2 ) )
% 0.30/0.62              = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups3827104343326376752nteger @ G2 @ A2 ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.insert_if
% 0.30/0.62  thf(fact_8084_prod_Oinsert__if,axiom,
% 0.30/0.62      ! [A2: set_o,X: $o,G2: $o > assn] :
% 0.30/0.62        ( ( finite_finite_o @ A2 )
% 0.30/0.62       => ( ( ( member_o @ X @ A2 )
% 0.30/0.62           => ( ( groups5301882518646026715o_assn @ G2 @ ( insert_o @ X @ A2 ) )
% 0.30/0.62              = ( groups5301882518646026715o_assn @ G2 @ A2 ) ) )
% 0.30/0.62          & ( ~ ( member_o @ X @ A2 )
% 0.30/0.62           => ( ( groups5301882518646026715o_assn @ G2 @ ( insert_o @ X @ A2 ) )
% 0.30/0.62              = ( times_times_assn @ ( G2 @ X ) @ ( groups5301882518646026715o_assn @ G2 @ A2 ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.insert_if
% 0.30/0.62  thf(fact_8085_prod_Oinsert__if,axiom,
% 0.30/0.62      ! [A2: set_nat,X: nat,G2: nat > assn] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( ( member_nat @ X @ A2 )
% 0.30/0.62           => ( ( groups6906906614972039071t_assn @ G2 @ ( insert_nat @ X @ A2 ) )
% 0.30/0.62              = ( groups6906906614972039071t_assn @ G2 @ A2 ) ) )
% 0.30/0.62          & ( ~ ( member_nat @ X @ A2 )
% 0.30/0.62           => ( ( groups6906906614972039071t_assn @ G2 @ ( insert_nat @ X @ A2 ) )
% 0.30/0.62              = ( times_times_assn @ ( G2 @ X ) @ ( groups6906906614972039071t_assn @ G2 @ A2 ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.insert_if
% 0.30/0.62  thf(fact_8086_prod_Oinsert__if,axiom,
% 0.30/0.62      ! [A2: set_int,X: int,G2: int > assn] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( ( member_int @ X @ A2 )
% 0.30/0.62           => ( ( groups7882442080178216443t_assn @ G2 @ ( insert_int @ X @ A2 ) )
% 0.30/0.62              = ( groups7882442080178216443t_assn @ G2 @ A2 ) ) )
% 0.30/0.62          & ( ~ ( member_int @ X @ A2 )
% 0.30/0.62           => ( ( groups7882442080178216443t_assn @ G2 @ ( insert_int @ X @ A2 ) )
% 0.30/0.62              = ( times_times_assn @ ( G2 @ X ) @ ( groups7882442080178216443t_assn @ G2 @ A2 ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.insert_if
% 0.30/0.62  thf(fact_8087_prod_Oinsert__if,axiom,
% 0.30/0.62      ! [A2: set_o,X: $o,G2: $o > rat] :
% 0.30/0.62        ( ( finite_finite_o @ A2 )
% 0.30/0.62       => ( ( ( member_o @ X @ A2 )
% 0.30/0.62           => ( ( groups2869687844427037835_o_rat @ G2 @ ( insert_o @ X @ A2 ) )
% 0.30/0.62              = ( groups2869687844427037835_o_rat @ G2 @ A2 ) ) )
% 0.30/0.62          & ( ~ ( member_o @ X @ A2 )
% 0.30/0.62           => ( ( groups2869687844427037835_o_rat @ G2 @ ( insert_o @ X @ A2 ) )
% 0.30/0.62              = ( times_times_rat @ ( G2 @ X ) @ ( groups2869687844427037835_o_rat @ G2 @ A2 ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.insert_if
% 0.30/0.62  thf(fact_8088_prod_Oinsert__if,axiom,
% 0.30/0.62      ! [A2: set_nat,X: nat,G2: nat > rat] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( ( member_nat @ X @ A2 )
% 0.30/0.62           => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A2 ) )
% 0.30/0.62              = ( groups73079841787564623at_rat @ G2 @ A2 ) ) )
% 0.30/0.62          & ( ~ ( member_nat @ X @ A2 )
% 0.30/0.62           => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A2 ) )
% 0.30/0.62              = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ A2 ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.insert_if
% 0.30/0.62  thf(fact_8089_prod_Oinsert__if,axiom,
% 0.30/0.62      ! [A2: set_int,X: int,G2: int > rat] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( ( member_int @ X @ A2 )
% 0.30/0.62           => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A2 ) )
% 0.30/0.62              = ( groups1072433553688619179nt_rat @ G2 @ A2 ) ) )
% 0.30/0.62          & ( ~ ( member_int @ X @ A2 )
% 0.30/0.62           => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A2 ) )
% 0.30/0.62              = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ A2 ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.insert_if
% 0.30/0.62  thf(fact_8090_prod_Oinsert__if,axiom,
% 0.30/0.62      ! [A2: set_o,X: $o,G2: $o > nat] :
% 0.30/0.62        ( ( finite_finite_o @ A2 )
% 0.30/0.62       => ( ( ( member_o @ X @ A2 )
% 0.30/0.62           => ( ( groups3504817904513533571_o_nat @ G2 @ ( insert_o @ X @ A2 ) )
% 0.30/0.62              = ( groups3504817904513533571_o_nat @ G2 @ A2 ) ) )
% 0.30/0.62          & ( ~ ( member_o @ X @ A2 )
% 0.30/0.62           => ( ( groups3504817904513533571_o_nat @ G2 @ ( insert_o @ X @ A2 ) )
% 0.30/0.62              = ( times_times_nat @ ( G2 @ X ) @ ( groups3504817904513533571_o_nat @ G2 @ A2 ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.insert_if
% 0.30/0.62  thf(fact_8091_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.30/0.62      ! [S4: set_int,T4: set_int,S: set_int,I: int > int,J: int > int,T: set_int,G2: int > code_integer,H3: int > code_integer] :
% 0.30/0.62        ( ( finite_finite_int @ S4 )
% 0.30/0.62       => ( ( finite_finite_int @ T4 )
% 0.30/0.62         => ( ! [A6: int] :
% 0.30/0.62                ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 0.30/0.62               => ( ( I @ ( J @ A6 ) )
% 0.30/0.62                  = A6 ) )
% 0.30/0.62           => ( ! [A6: int] :
% 0.30/0.62                  ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 0.30/0.62                 => ( member_int @ ( J @ A6 ) @ ( minus_minus_set_int @ T @ T4 ) ) )
% 0.30/0.62             => ( ! [B6: int] :
% 0.30/0.62                    ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 0.30/0.62                   => ( ( J @ ( I @ B6 ) )
% 0.30/0.62                      = B6 ) )
% 0.30/0.62               => ( ! [B6: int] :
% 0.30/0.62                      ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 0.30/0.62                     => ( member_int @ ( I @ B6 ) @ ( minus_minus_set_int @ S @ S4 ) ) )
% 0.30/0.62                 => ( ! [A6: int] :
% 0.30/0.62                        ( ( member_int @ A6 @ S4 )
% 0.30/0.62                       => ( ( G2 @ A6 )
% 0.30/0.62                          = one_one_Code_integer ) )
% 0.30/0.62                   => ( ! [B6: int] :
% 0.30/0.62                          ( ( member_int @ B6 @ T4 )
% 0.30/0.62                         => ( ( H3 @ B6 )
% 0.30/0.62                            = one_one_Code_integer ) )
% 0.30/0.62                     => ( ! [A6: int] :
% 0.30/0.62                            ( ( member_int @ A6 @ S )
% 0.30/0.62                           => ( ( H3 @ ( J @ A6 ) )
% 0.30/0.62                              = ( G2 @ A6 ) ) )
% 0.30/0.62                       => ( ( groups3827104343326376752nteger @ G2 @ S )
% 0.30/0.62                          = ( groups3827104343326376752nteger @ H3 @ T ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.reindex_bij_witness_not_neutral
% 0.30/0.62  thf(fact_8092_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.30/0.62      ! [S4: set_int,T4: set_int,S: set_int,I: int > int,J: int > int,T: set_int,G2: int > assn,H3: int > assn] :
% 0.30/0.62        ( ( finite_finite_int @ S4 )
% 0.30/0.62       => ( ( finite_finite_int @ T4 )
% 0.30/0.62         => ( ! [A6: int] :
% 0.30/0.62                ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 0.30/0.62               => ( ( I @ ( J @ A6 ) )
% 0.30/0.62                  = A6 ) )
% 0.30/0.62           => ( ! [A6: int] :
% 0.30/0.62                  ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 0.30/0.62                 => ( member_int @ ( J @ A6 ) @ ( minus_minus_set_int @ T @ T4 ) ) )
% 0.30/0.62             => ( ! [B6: int] :
% 0.30/0.62                    ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 0.30/0.62                   => ( ( J @ ( I @ B6 ) )
% 0.30/0.62                      = B6 ) )
% 0.30/0.62               => ( ! [B6: int] :
% 0.30/0.62                      ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 0.30/0.62                     => ( member_int @ ( I @ B6 ) @ ( minus_minus_set_int @ S @ S4 ) ) )
% 0.30/0.62                 => ( ! [A6: int] :
% 0.30/0.62                        ( ( member_int @ A6 @ S4 )
% 0.30/0.62                       => ( ( G2 @ A6 )
% 0.30/0.62                          = one_one_assn ) )
% 0.30/0.62                   => ( ! [B6: int] :
% 0.30/0.62                          ( ( member_int @ B6 @ T4 )
% 0.30/0.62                         => ( ( H3 @ B6 )
% 0.30/0.62                            = one_one_assn ) )
% 0.30/0.62                     => ( ! [A6: int] :
% 0.30/0.62                            ( ( member_int @ A6 @ S )
% 0.30/0.62                           => ( ( H3 @ ( J @ A6 ) )
% 0.30/0.62                              = ( G2 @ A6 ) ) )
% 0.30/0.62                       => ( ( groups7882442080178216443t_assn @ G2 @ S )
% 0.30/0.62                          = ( groups7882442080178216443t_assn @ H3 @ T ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.reindex_bij_witness_not_neutral
% 0.30/0.62  thf(fact_8093_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.30/0.62      ! [S4: set_int,T4: set_int,S: set_int,I: int > int,J: int > int,T: set_int,G2: int > rat,H3: int > rat] :
% 0.30/0.62        ( ( finite_finite_int @ S4 )
% 0.30/0.62       => ( ( finite_finite_int @ T4 )
% 0.30/0.62         => ( ! [A6: int] :
% 0.30/0.62                ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 0.30/0.62               => ( ( I @ ( J @ A6 ) )
% 0.30/0.62                  = A6 ) )
% 0.30/0.62           => ( ! [A6: int] :
% 0.30/0.62                  ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 0.30/0.62                 => ( member_int @ ( J @ A6 ) @ ( minus_minus_set_int @ T @ T4 ) ) )
% 0.30/0.62             => ( ! [B6: int] :
% 0.30/0.62                    ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 0.30/0.62                   => ( ( J @ ( I @ B6 ) )
% 0.30/0.62                      = B6 ) )
% 0.30/0.62               => ( ! [B6: int] :
% 0.30/0.62                      ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 0.30/0.62                     => ( member_int @ ( I @ B6 ) @ ( minus_minus_set_int @ S @ S4 ) ) )
% 0.30/0.62                 => ( ! [A6: int] :
% 0.30/0.62                        ( ( member_int @ A6 @ S4 )
% 0.30/0.62                       => ( ( G2 @ A6 )
% 0.30/0.62                          = one_one_rat ) )
% 0.30/0.62                   => ( ! [B6: int] :
% 0.30/0.62                          ( ( member_int @ B6 @ T4 )
% 0.30/0.62                         => ( ( H3 @ B6 )
% 0.30/0.62                            = one_one_rat ) )
% 0.30/0.62                     => ( ! [A6: int] :
% 0.30/0.62                            ( ( member_int @ A6 @ S )
% 0.30/0.62                           => ( ( H3 @ ( J @ A6 ) )
% 0.30/0.62                              = ( G2 @ A6 ) ) )
% 0.30/0.62                       => ( ( groups1072433553688619179nt_rat @ G2 @ S )
% 0.30/0.62                          = ( groups1072433553688619179nt_rat @ H3 @ T ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.reindex_bij_witness_not_neutral
% 0.30/0.62  thf(fact_8094_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.30/0.62      ! [S4: set_int,T4: set_int,S: set_int,I: int > int,J: int > int,T: set_int,G2: int > nat,H3: int > nat] :
% 0.30/0.62        ( ( finite_finite_int @ S4 )
% 0.30/0.62       => ( ( finite_finite_int @ T4 )
% 0.30/0.62         => ( ! [A6: int] :
% 0.30/0.62                ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 0.30/0.62               => ( ( I @ ( J @ A6 ) )
% 0.30/0.62                  = A6 ) )
% 0.30/0.62           => ( ! [A6: int] :
% 0.30/0.62                  ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 0.30/0.62                 => ( member_int @ ( J @ A6 ) @ ( minus_minus_set_int @ T @ T4 ) ) )
% 0.30/0.62             => ( ! [B6: int] :
% 0.30/0.62                    ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 0.30/0.62                   => ( ( J @ ( I @ B6 ) )
% 0.30/0.62                      = B6 ) )
% 0.30/0.62               => ( ! [B6: int] :
% 0.30/0.62                      ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 0.30/0.62                     => ( member_int @ ( I @ B6 ) @ ( minus_minus_set_int @ S @ S4 ) ) )
% 0.30/0.62                 => ( ! [A6: int] :
% 0.30/0.62                        ( ( member_int @ A6 @ S4 )
% 0.30/0.62                       => ( ( G2 @ A6 )
% 0.30/0.62                          = one_one_nat ) )
% 0.30/0.62                   => ( ! [B6: int] :
% 0.30/0.62                          ( ( member_int @ B6 @ T4 )
% 0.30/0.62                         => ( ( H3 @ B6 )
% 0.30/0.62                            = one_one_nat ) )
% 0.30/0.62                     => ( ! [A6: int] :
% 0.30/0.62                            ( ( member_int @ A6 @ S )
% 0.30/0.62                           => ( ( H3 @ ( J @ A6 ) )
% 0.30/0.62                              = ( G2 @ A6 ) ) )
% 0.30/0.62                       => ( ( groups1707563613775114915nt_nat @ G2 @ S )
% 0.30/0.62                          = ( groups1707563613775114915nt_nat @ H3 @ T ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.reindex_bij_witness_not_neutral
% 0.30/0.62  thf(fact_8095_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.30/0.62      ! [S4: set_int,T4: set_nat,S: set_int,I: nat > int,J: int > nat,T: set_nat,G2: int > code_integer,H3: nat > code_integer] :
% 0.30/0.62        ( ( finite_finite_int @ S4 )
% 0.30/0.62       => ( ( finite_finite_nat @ T4 )
% 0.30/0.62         => ( ! [A6: int] :
% 0.30/0.62                ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 0.30/0.62               => ( ( I @ ( J @ A6 ) )
% 0.30/0.62                  = A6 ) )
% 0.30/0.62           => ( ! [A6: int] :
% 0.30/0.62                  ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 0.30/0.62                 => ( member_nat @ ( J @ A6 ) @ ( minus_minus_set_nat @ T @ T4 ) ) )
% 0.30/0.62             => ( ! [B6: nat] :
% 0.30/0.62                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ T @ T4 ) )
% 0.30/0.62                   => ( ( J @ ( I @ B6 ) )
% 0.30/0.62                      = B6 ) )
% 0.30/0.62               => ( ! [B6: nat] :
% 0.30/0.62                      ( ( member_nat @ B6 @ ( minus_minus_set_nat @ T @ T4 ) )
% 0.30/0.62                     => ( member_int @ ( I @ B6 ) @ ( minus_minus_set_int @ S @ S4 ) ) )
% 0.30/0.62                 => ( ! [A6: int] :
% 0.30/0.62                        ( ( member_int @ A6 @ S4 )
% 0.30/0.62                       => ( ( G2 @ A6 )
% 0.30/0.62                          = one_one_Code_integer ) )
% 0.30/0.62                   => ( ! [B6: nat] :
% 0.30/0.62                          ( ( member_nat @ B6 @ T4 )
% 0.30/0.62                         => ( ( H3 @ B6 )
% 0.30/0.62                            = one_one_Code_integer ) )
% 0.30/0.62                     => ( ! [A6: int] :
% 0.30/0.62                            ( ( member_int @ A6 @ S )
% 0.30/0.62                           => ( ( H3 @ ( J @ A6 ) )
% 0.30/0.62                              = ( G2 @ A6 ) ) )
% 0.30/0.62                       => ( ( groups3827104343326376752nteger @ G2 @ S )
% 0.30/0.62                          = ( groups3455450783089532116nteger @ H3 @ T ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.reindex_bij_witness_not_neutral
% 0.30/0.62  thf(fact_8096_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.30/0.62      ! [S4: set_int,T4: set_nat,S: set_int,I: nat > int,J: int > nat,T: set_nat,G2: int > assn,H3: nat > assn] :
% 0.30/0.62        ( ( finite_finite_int @ S4 )
% 0.30/0.62       => ( ( finite_finite_nat @ T4 )
% 0.30/0.62         => ( ! [A6: int] :
% 0.30/0.62                ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 0.30/0.62               => ( ( I @ ( J @ A6 ) )
% 0.30/0.62                  = A6 ) )
% 0.30/0.62           => ( ! [A6: int] :
% 0.30/0.62                  ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 0.30/0.62                 => ( member_nat @ ( J @ A6 ) @ ( minus_minus_set_nat @ T @ T4 ) ) )
% 0.30/0.62             => ( ! [B6: nat] :
% 0.30/0.62                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ T @ T4 ) )
% 0.30/0.62                   => ( ( J @ ( I @ B6 ) )
% 0.30/0.62                      = B6 ) )
% 0.30/0.62               => ( ! [B6: nat] :
% 0.30/0.62                      ( ( member_nat @ B6 @ ( minus_minus_set_nat @ T @ T4 ) )
% 0.30/0.62                     => ( member_int @ ( I @ B6 ) @ ( minus_minus_set_int @ S @ S4 ) ) )
% 0.30/0.62                 => ( ! [A6: int] :
% 0.30/0.62                        ( ( member_int @ A6 @ S4 )
% 0.30/0.62                       => ( ( G2 @ A6 )
% 0.30/0.62                          = one_one_assn ) )
% 0.30/0.62                   => ( ! [B6: nat] :
% 0.30/0.62                          ( ( member_nat @ B6 @ T4 )
% 0.30/0.62                         => ( ( H3 @ B6 )
% 0.30/0.62                            = one_one_assn ) )
% 0.30/0.62                     => ( ! [A6: int] :
% 0.30/0.62                            ( ( member_int @ A6 @ S )
% 0.30/0.62                           => ( ( H3 @ ( J @ A6 ) )
% 0.30/0.62                              = ( G2 @ A6 ) ) )
% 0.30/0.62                       => ( ( groups7882442080178216443t_assn @ G2 @ S )
% 0.30/0.62                          = ( groups6906906614972039071t_assn @ H3 @ T ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.reindex_bij_witness_not_neutral
% 0.30/0.62  thf(fact_8097_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.30/0.62      ! [S4: set_int,T4: set_nat,S: set_int,I: nat > int,J: int > nat,T: set_nat,G2: int > rat,H3: nat > rat] :
% 0.30/0.62        ( ( finite_finite_int @ S4 )
% 0.30/0.62       => ( ( finite_finite_nat @ T4 )
% 0.30/0.62         => ( ! [A6: int] :
% 0.30/0.62                ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 0.30/0.62               => ( ( I @ ( J @ A6 ) )
% 0.30/0.62                  = A6 ) )
% 0.30/0.62           => ( ! [A6: int] :
% 0.30/0.62                  ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 0.30/0.62                 => ( member_nat @ ( J @ A6 ) @ ( minus_minus_set_nat @ T @ T4 ) ) )
% 0.30/0.62             => ( ! [B6: nat] :
% 0.30/0.62                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ T @ T4 ) )
% 0.30/0.62                   => ( ( J @ ( I @ B6 ) )
% 0.30/0.62                      = B6 ) )
% 0.30/0.62               => ( ! [B6: nat] :
% 0.30/0.62                      ( ( member_nat @ B6 @ ( minus_minus_set_nat @ T @ T4 ) )
% 0.30/0.62                     => ( member_int @ ( I @ B6 ) @ ( minus_minus_set_int @ S @ S4 ) ) )
% 0.30/0.62                 => ( ! [A6: int] :
% 0.30/0.62                        ( ( member_int @ A6 @ S4 )
% 0.30/0.62                       => ( ( G2 @ A6 )
% 0.30/0.62                          = one_one_rat ) )
% 0.30/0.62                   => ( ! [B6: nat] :
% 0.30/0.62                          ( ( member_nat @ B6 @ T4 )
% 0.30/0.62                         => ( ( H3 @ B6 )
% 0.30/0.62                            = one_one_rat ) )
% 0.30/0.62                     => ( ! [A6: int] :
% 0.30/0.62                            ( ( member_int @ A6 @ S )
% 0.30/0.62                           => ( ( H3 @ ( J @ A6 ) )
% 0.30/0.62                              = ( G2 @ A6 ) ) )
% 0.30/0.62                       => ( ( groups1072433553688619179nt_rat @ G2 @ S )
% 0.30/0.62                          = ( groups73079841787564623at_rat @ H3 @ T ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.reindex_bij_witness_not_neutral
% 0.30/0.62  thf(fact_8098_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.30/0.62      ! [S4: set_nat,T4: set_int,S: set_nat,I: int > nat,J: nat > int,T: set_int,G2: nat > code_integer,H3: int > code_integer] :
% 0.30/0.62        ( ( finite_finite_nat @ S4 )
% 0.30/0.62       => ( ( finite_finite_int @ T4 )
% 0.30/0.62         => ( ! [A6: nat] :
% 0.30/0.62                ( ( member_nat @ A6 @ ( minus_minus_set_nat @ S @ S4 ) )
% 0.30/0.62               => ( ( I @ ( J @ A6 ) )
% 0.30/0.62                  = A6 ) )
% 0.30/0.62           => ( ! [A6: nat] :
% 0.30/0.62                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ S @ S4 ) )
% 0.30/0.62                 => ( member_int @ ( J @ A6 ) @ ( minus_minus_set_int @ T @ T4 ) ) )
% 0.30/0.62             => ( ! [B6: int] :
% 0.30/0.62                    ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 0.30/0.62                   => ( ( J @ ( I @ B6 ) )
% 0.30/0.62                      = B6 ) )
% 0.30/0.62               => ( ! [B6: int] :
% 0.30/0.62                      ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 0.30/0.62                     => ( member_nat @ ( I @ B6 ) @ ( minus_minus_set_nat @ S @ S4 ) ) )
% 0.30/0.62                 => ( ! [A6: nat] :
% 0.30/0.62                        ( ( member_nat @ A6 @ S4 )
% 0.30/0.62                       => ( ( G2 @ A6 )
% 0.30/0.62                          = one_one_Code_integer ) )
% 0.30/0.62                   => ( ! [B6: int] :
% 0.30/0.62                          ( ( member_int @ B6 @ T4 )
% 0.30/0.62                         => ( ( H3 @ B6 )
% 0.30/0.62                            = one_one_Code_integer ) )
% 0.30/0.62                     => ( ! [A6: nat] :
% 0.30/0.62                            ( ( member_nat @ A6 @ S )
% 0.30/0.62                           => ( ( H3 @ ( J @ A6 ) )
% 0.30/0.62                              = ( G2 @ A6 ) ) )
% 0.30/0.62                       => ( ( groups3455450783089532116nteger @ G2 @ S )
% 0.30/0.62                          = ( groups3827104343326376752nteger @ H3 @ T ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.reindex_bij_witness_not_neutral
% 0.30/0.62  thf(fact_8099_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.30/0.62      ! [S4: set_nat,T4: set_int,S: set_nat,I: int > nat,J: nat > int,T: set_int,G2: nat > assn,H3: int > assn] :
% 0.30/0.62        ( ( finite_finite_nat @ S4 )
% 0.30/0.62       => ( ( finite_finite_int @ T4 )
% 0.30/0.62         => ( ! [A6: nat] :
% 0.30/0.62                ( ( member_nat @ A6 @ ( minus_minus_set_nat @ S @ S4 ) )
% 0.30/0.62               => ( ( I @ ( J @ A6 ) )
% 0.30/0.62                  = A6 ) )
% 0.30/0.62           => ( ! [A6: nat] :
% 0.30/0.62                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ S @ S4 ) )
% 0.30/0.62                 => ( member_int @ ( J @ A6 ) @ ( minus_minus_set_int @ T @ T4 ) ) )
% 0.30/0.62             => ( ! [B6: int] :
% 0.30/0.62                    ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 0.30/0.62                   => ( ( J @ ( I @ B6 ) )
% 0.30/0.62                      = B6 ) )
% 0.30/0.62               => ( ! [B6: int] :
% 0.30/0.62                      ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 0.30/0.62                     => ( member_nat @ ( I @ B6 ) @ ( minus_minus_set_nat @ S @ S4 ) ) )
% 0.30/0.62                 => ( ! [A6: nat] :
% 0.30/0.62                        ( ( member_nat @ A6 @ S4 )
% 0.30/0.62                       => ( ( G2 @ A6 )
% 0.30/0.62                          = one_one_assn ) )
% 0.30/0.62                   => ( ! [B6: int] :
% 0.30/0.62                          ( ( member_int @ B6 @ T4 )
% 0.30/0.62                         => ( ( H3 @ B6 )
% 0.30/0.62                            = one_one_assn ) )
% 0.30/0.62                     => ( ! [A6: nat] :
% 0.30/0.62                            ( ( member_nat @ A6 @ S )
% 0.30/0.62                           => ( ( H3 @ ( J @ A6 ) )
% 0.30/0.62                              = ( G2 @ A6 ) ) )
% 0.30/0.62                       => ( ( groups6906906614972039071t_assn @ G2 @ S )
% 0.30/0.62                          = ( groups7882442080178216443t_assn @ H3 @ T ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.reindex_bij_witness_not_neutral
% 0.30/0.62  thf(fact_8100_prod_Oreindex__bij__witness__not__neutral,axiom,
% 0.30/0.62      ! [S4: set_nat,T4: set_int,S: set_nat,I: int > nat,J: nat > int,T: set_int,G2: nat > rat,H3: int > rat] :
% 0.30/0.62        ( ( finite_finite_nat @ S4 )
% 0.30/0.62       => ( ( finite_finite_int @ T4 )
% 0.30/0.62         => ( ! [A6: nat] :
% 0.30/0.62                ( ( member_nat @ A6 @ ( minus_minus_set_nat @ S @ S4 ) )
% 0.30/0.62               => ( ( I @ ( J @ A6 ) )
% 0.30/0.62                  = A6 ) )
% 0.30/0.62           => ( ! [A6: nat] :
% 0.30/0.62                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ S @ S4 ) )
% 0.30/0.62                 => ( member_int @ ( J @ A6 ) @ ( minus_minus_set_int @ T @ T4 ) ) )
% 0.30/0.62             => ( ! [B6: int] :
% 0.30/0.62                    ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 0.30/0.62                   => ( ( J @ ( I @ B6 ) )
% 0.30/0.62                      = B6 ) )
% 0.30/0.62               => ( ! [B6: int] :
% 0.30/0.62                      ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 0.30/0.62                     => ( member_nat @ ( I @ B6 ) @ ( minus_minus_set_nat @ S @ S4 ) ) )
% 0.30/0.62                 => ( ! [A6: nat] :
% 0.30/0.62                        ( ( member_nat @ A6 @ S4 )
% 0.30/0.62                       => ( ( G2 @ A6 )
% 0.30/0.62                          = one_one_rat ) )
% 0.30/0.62                   => ( ! [B6: int] :
% 0.30/0.62                          ( ( member_int @ B6 @ T4 )
% 0.30/0.62                         => ( ( H3 @ B6 )
% 0.30/0.62                            = one_one_rat ) )
% 0.30/0.62                     => ( ! [A6: nat] :
% 0.30/0.62                            ( ( member_nat @ A6 @ S )
% 0.30/0.62                           => ( ( H3 @ ( J @ A6 ) )
% 0.30/0.62                              = ( G2 @ A6 ) ) )
% 0.30/0.62                       => ( ( groups73079841787564623at_rat @ G2 @ S )
% 0.30/0.62                          = ( groups1072433553688619179nt_rat @ H3 @ T ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.reindex_bij_witness_not_neutral
% 0.30/0.62  thf(fact_8101_abs__sgn__eq,axiom,
% 0.30/0.62      ! [A: code_integer] :
% 0.30/0.62        ( ( ( A = zero_z3403309356797280102nteger )
% 0.30/0.62         => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 0.30/0.62            = zero_z3403309356797280102nteger ) )
% 0.30/0.62        & ( ( A != zero_z3403309356797280102nteger )
% 0.30/0.62         => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 0.30/0.62            = one_one_Code_integer ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % abs_sgn_eq
% 0.30/0.62  thf(fact_8102_abs__sgn__eq,axiom,
% 0.30/0.62      ! [A: rat] :
% 0.30/0.62        ( ( ( A = zero_zero_rat )
% 0.30/0.62         => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 0.30/0.62            = zero_zero_rat ) )
% 0.30/0.62        & ( ( A != zero_zero_rat )
% 0.30/0.62         => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 0.30/0.62            = one_one_rat ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % abs_sgn_eq
% 0.30/0.62  thf(fact_8103_abs__sgn__eq,axiom,
% 0.30/0.62      ! [A: int] :
% 0.30/0.62        ( ( ( A = zero_zero_int )
% 0.30/0.62         => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 0.30/0.62            = zero_zero_int ) )
% 0.30/0.62        & ( ( A != zero_zero_int )
% 0.30/0.62         => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 0.30/0.62            = one_one_int ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % abs_sgn_eq
% 0.30/0.62  thf(fact_8104_sum_Onat__diff__reindex,axiom,
% 0.30/0.62      ! [G2: nat > nat,N: nat] :
% 0.30/0.62        ( ( groups3542108847815614940at_nat
% 0.30/0.62          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 0.30/0.62          @ ( set_ord_lessThan_nat @ N ) )
% 0.30/0.62        = ( groups3542108847815614940at_nat @ G2 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.nat_diff_reindex
% 0.30/0.62  thf(fact_8105_prod_Onat__diff__reindex,axiom,
% 0.30/0.62      ! [G2: nat > nat,N: nat] :
% 0.30/0.62        ( ( groups708209901874060359at_nat
% 0.30/0.62          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 0.30/0.62          @ ( set_ord_lessThan_nat @ N ) )
% 0.30/0.62        = ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.nat_diff_reindex
% 0.30/0.62  thf(fact_8106_prod_Onat__diff__reindex,axiom,
% 0.30/0.62      ! [G2: nat > int,N: nat] :
% 0.30/0.62        ( ( groups705719431365010083at_int
% 0.30/0.62          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 0.30/0.62          @ ( set_ord_lessThan_nat @ N ) )
% 0.30/0.62        = ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.nat_diff_reindex
% 0.30/0.62  thf(fact_8107_sum__eq__1__iff,axiom,
% 0.30/0.62      ! [A2: set_int,F2: int > nat] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( ( groups4541462559716669496nt_nat @ F2 @ A2 )
% 0.30/0.62            = one_one_nat )
% 0.30/0.62          = ( ? [X3: int] :
% 0.30/0.62                ( ( member_int @ X3 @ A2 )
% 0.30/0.62                & ( ( F2 @ X3 )
% 0.30/0.62                  = one_one_nat )
% 0.30/0.62                & ! [Y3: int] :
% 0.30/0.62                    ( ( member_int @ Y3 @ A2 )
% 0.30/0.62                   => ( ( X3 != Y3 )
% 0.30/0.62                     => ( ( F2 @ Y3 )
% 0.30/0.62                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_eq_1_iff
% 0.30/0.62  thf(fact_8108_sum__eq__1__iff,axiom,
% 0.30/0.62      ! [A2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > nat] :
% 0.30/0.62        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.62       => ( ( ( groups977919841031483927at_nat @ F2 @ A2 )
% 0.30/0.62            = one_one_nat )
% 0.30/0.62          = ( ? [X3: product_prod_nat_nat] :
% 0.30/0.62                ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 0.30/0.62                & ( ( F2 @ X3 )
% 0.30/0.62                  = one_one_nat )
% 0.30/0.62                & ! [Y3: product_prod_nat_nat] :
% 0.30/0.62                    ( ( member8440522571783428010at_nat @ Y3 @ A2 )
% 0.30/0.62                   => ( ( X3 != Y3 )
% 0.30/0.62                     => ( ( F2 @ Y3 )
% 0.30/0.62                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_eq_1_iff
% 0.30/0.62  thf(fact_8109_sum__eq__1__iff,axiom,
% 0.30/0.62      ! [A2: set_nat,F2: nat > nat] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( ( groups3542108847815614940at_nat @ F2 @ A2 )
% 0.30/0.62            = one_one_nat )
% 0.30/0.62          = ( ? [X3: nat] :
% 0.30/0.62                ( ( member_nat @ X3 @ A2 )
% 0.30/0.62                & ( ( F2 @ X3 )
% 0.30/0.62                  = one_one_nat )
% 0.30/0.62                & ! [Y3: nat] :
% 0.30/0.62                    ( ( member_nat @ Y3 @ A2 )
% 0.30/0.62                   => ( ( X3 != Y3 )
% 0.30/0.62                     => ( ( F2 @ Y3 )
% 0.30/0.62                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_eq_1_iff
% 0.30/0.62  thf(fact_8110_prod__int__eq,axiom,
% 0.30/0.62      ! [I: nat,J: nat] :
% 0.30/0.62        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 0.30/0.62        = ( groups1705073143266064639nt_int
% 0.30/0.62          @ ^ [X3: int] : X3
% 0.30/0.62          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod_int_eq
% 0.30/0.62  thf(fact_8111_div__push__bit__of__1__eq__drop__bit,axiom,
% 0.30/0.62      ! [A: code_integer,N: nat] :
% 0.30/0.62        ( ( divide6298287555418463151nteger @ A @ ( bit_se7788150548672797655nteger @ N @ one_one_Code_integer ) )
% 0.30/0.62        = ( bit_se3928097537394005634nteger @ N @ A ) ) ).
% 0.30/0.62  
% 0.30/0.62  % div_push_bit_of_1_eq_drop_bit
% 0.30/0.62  thf(fact_8112_div__push__bit__of__1__eq__drop__bit,axiom,
% 0.30/0.62      ! [A: code_natural,N: nat] :
% 0.30/0.62        ( ( divide5121882707175180666atural @ A @ ( bit_se6611745700429515170atural @ N @ one_one_Code_natural ) )
% 0.30/0.62        = ( bit_se2751692689150723149atural @ N @ A ) ) ).
% 0.30/0.62  
% 0.30/0.62  % div_push_bit_of_1_eq_drop_bit
% 0.30/0.62  thf(fact_8113_div__push__bit__of__1__eq__drop__bit,axiom,
% 0.30/0.62      ! [A: int,N: nat] :
% 0.30/0.62        ( ( divide_divide_int @ A @ ( bit_se545348938243370406it_int @ N @ one_one_int ) )
% 0.30/0.62        = ( bit_se8568078237143864401it_int @ N @ A ) ) ).
% 0.30/0.62  
% 0.30/0.62  % div_push_bit_of_1_eq_drop_bit
% 0.30/0.62  thf(fact_8114_div__push__bit__of__1__eq__drop__bit,axiom,
% 0.30/0.62      ! [A: nat,N: nat] :
% 0.30/0.62        ( ( divide_divide_nat @ A @ ( bit_se547839408752420682it_nat @ N @ one_one_nat ) )
% 0.30/0.62        = ( bit_se8570568707652914677it_nat @ N @ A ) ) ).
% 0.30/0.62  
% 0.30/0.62  % div_push_bit_of_1_eq_drop_bit
% 0.30/0.62  thf(fact_8115_sum__nonneg__leq__bound,axiom,
% 0.30/0.62      ! [S3: set_nat,F2: nat > code_integer,B2: code_integer,I: nat] :
% 0.30/0.62        ( ( finite_finite_nat @ S3 )
% 0.30/0.62       => ( ! [I2: nat] :
% 0.30/0.62              ( ( member_nat @ I2 @ S3 )
% 0.30/0.62             => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) ) )
% 0.30/0.62         => ( ( ( groups7501900531339628137nteger @ F2 @ S3 )
% 0.30/0.62              = B2 )
% 0.30/0.62           => ( ( member_nat @ I @ S3 )
% 0.30/0.62             => ( ord_le3102999989581377725nteger @ ( F2 @ I ) @ B2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_nonneg_leq_bound
% 0.30/0.62  thf(fact_8116_sum__nonneg__leq__bound,axiom,
% 0.30/0.62      ! [S3: set_int,F2: int > code_integer,B2: code_integer,I: int] :
% 0.30/0.62        ( ( finite_finite_int @ S3 )
% 0.30/0.62       => ( ! [I2: int] :
% 0.30/0.62              ( ( member_int @ I2 @ S3 )
% 0.30/0.62             => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) ) )
% 0.30/0.62         => ( ( ( groups7873554091576472773nteger @ F2 @ S3 )
% 0.30/0.62              = B2 )
% 0.30/0.62           => ( ( member_int @ I @ S3 )
% 0.30/0.62             => ( ord_le3102999989581377725nteger @ ( F2 @ I ) @ B2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_nonneg_leq_bound
% 0.30/0.62  thf(fact_8117_sum__nonneg__leq__bound,axiom,
% 0.30/0.62      ! [S3: set_nat,F2: nat > rat,B2: rat,I: nat] :
% 0.30/0.62        ( ( finite_finite_nat @ S3 )
% 0.30/0.62       => ( ! [I2: nat] :
% 0.30/0.62              ( ( member_nat @ I2 @ S3 )
% 0.30/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I2 ) ) )
% 0.30/0.62         => ( ( ( groups2906978787729119204at_rat @ F2 @ S3 )
% 0.30/0.62              = B2 )
% 0.30/0.62           => ( ( member_nat @ I @ S3 )
% 0.30/0.62             => ( ord_less_eq_rat @ ( F2 @ I ) @ B2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_nonneg_leq_bound
% 0.30/0.62  thf(fact_8118_sum__nonneg__leq__bound,axiom,
% 0.30/0.62      ! [S3: set_int,F2: int > rat,B2: rat,I: int] :
% 0.30/0.62        ( ( finite_finite_int @ S3 )
% 0.30/0.62       => ( ! [I2: int] :
% 0.30/0.62              ( ( member_int @ I2 @ S3 )
% 0.30/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I2 ) ) )
% 0.30/0.62         => ( ( ( groups3906332499630173760nt_rat @ F2 @ S3 )
% 0.30/0.62              = B2 )
% 0.30/0.62           => ( ( member_int @ I @ S3 )
% 0.30/0.62             => ( ord_less_eq_rat @ ( F2 @ I ) @ B2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_nonneg_leq_bound
% 0.30/0.62  thf(fact_8119_sum__nonneg__leq__bound,axiom,
% 0.30/0.62      ! [S3: set_int,F2: int > nat,B2: nat,I: int] :
% 0.30/0.62        ( ( finite_finite_int @ S3 )
% 0.30/0.62       => ( ! [I2: int] :
% 0.30/0.62              ( ( member_int @ I2 @ S3 )
% 0.30/0.62             => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I2 ) ) )
% 0.30/0.62         => ( ( ( groups4541462559716669496nt_nat @ F2 @ S3 )
% 0.30/0.62              = B2 )
% 0.30/0.62           => ( ( member_int @ I @ S3 )
% 0.30/0.62             => ( ord_less_eq_nat @ ( F2 @ I ) @ B2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_nonneg_leq_bound
% 0.30/0.62  thf(fact_8120_sum__nonneg__leq__bound,axiom,
% 0.30/0.62      ! [S3: set_nat,F2: nat > int,B2: int,I: nat] :
% 0.30/0.62        ( ( finite_finite_nat @ S3 )
% 0.30/0.62       => ( ! [I2: nat] :
% 0.30/0.62              ( ( member_nat @ I2 @ S3 )
% 0.30/0.62             => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ I2 ) ) )
% 0.30/0.62         => ( ( ( groups3539618377306564664at_int @ F2 @ S3 )
% 0.30/0.62              = B2 )
% 0.30/0.62           => ( ( member_nat @ I @ S3 )
% 0.30/0.62             => ( ord_less_eq_int @ ( F2 @ I ) @ B2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_nonneg_leq_bound
% 0.30/0.62  thf(fact_8121_sum__nonneg__leq__bound,axiom,
% 0.30/0.62      ! [S3: set_nat,F2: nat > nat,B2: nat,I: nat] :
% 0.30/0.62        ( ( finite_finite_nat @ S3 )
% 0.30/0.62       => ( ! [I2: nat] :
% 0.30/0.62              ( ( member_nat @ I2 @ S3 )
% 0.30/0.62             => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I2 ) ) )
% 0.30/0.62         => ( ( ( groups3542108847815614940at_nat @ F2 @ S3 )
% 0.30/0.62              = B2 )
% 0.30/0.62           => ( ( member_nat @ I @ S3 )
% 0.30/0.62             => ( ord_less_eq_nat @ ( F2 @ I ) @ B2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_nonneg_leq_bound
% 0.30/0.62  thf(fact_8122_sum__nonneg__leq__bound,axiom,
% 0.30/0.62      ! [S3: set_int,F2: int > int,B2: int,I: int] :
% 0.30/0.62        ( ( finite_finite_int @ S3 )
% 0.30/0.62       => ( ! [I2: int] :
% 0.30/0.62              ( ( member_int @ I2 @ S3 )
% 0.30/0.62             => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ I2 ) ) )
% 0.30/0.62         => ( ( ( groups4538972089207619220nt_int @ F2 @ S3 )
% 0.30/0.62              = B2 )
% 0.30/0.62           => ( ( member_int @ I @ S3 )
% 0.30/0.62             => ( ord_less_eq_int @ ( F2 @ I ) @ B2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_nonneg_leq_bound
% 0.30/0.62  thf(fact_8123_sum__nonneg__leq__bound,axiom,
% 0.30/0.62      ! [S3: set_set_nat,F2: set_nat > code_integer,B2: code_integer,I: set_nat] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ S3 )
% 0.30/0.62       => ( ! [I2: set_nat] :
% 0.30/0.62              ( ( member_set_nat @ I2 @ S3 )
% 0.30/0.62             => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) ) )
% 0.30/0.62         => ( ( ( groups9190459664516455967nteger @ F2 @ S3 )
% 0.30/0.62              = B2 )
% 0.30/0.62           => ( ( member_set_nat @ I @ S3 )
% 0.30/0.62             => ( ord_le3102999989581377725nteger @ ( F2 @ I ) @ B2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_nonneg_leq_bound
% 0.30/0.62  thf(fact_8124_sum__nonneg__leq__bound,axiom,
% 0.30/0.62      ! [S3: set_set_nat,F2: set_nat > rat,B2: rat,I: set_nat] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ S3 )
% 0.30/0.62       => ( ! [I2: set_nat] :
% 0.30/0.62              ( ( member_set_nat @ I2 @ S3 )
% 0.30/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I2 ) ) )
% 0.30/0.62         => ( ( ( groups7659867448343625626at_rat @ F2 @ S3 )
% 0.30/0.62              = B2 )
% 0.30/0.62           => ( ( member_set_nat @ I @ S3 )
% 0.30/0.62             => ( ord_less_eq_rat @ ( F2 @ I ) @ B2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_nonneg_leq_bound
% 0.30/0.62  thf(fact_8125_sum__nonneg__0,axiom,
% 0.30/0.62      ! [S3: set_nat,F2: nat > code_integer,I: nat] :
% 0.30/0.62        ( ( finite_finite_nat @ S3 )
% 0.30/0.62       => ( ! [I2: nat] :
% 0.30/0.62              ( ( member_nat @ I2 @ S3 )
% 0.30/0.62             => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) ) )
% 0.30/0.62         => ( ( ( groups7501900531339628137nteger @ F2 @ S3 )
% 0.30/0.62              = zero_z3403309356797280102nteger )
% 0.30/0.62           => ( ( member_nat @ I @ S3 )
% 0.30/0.62             => ( ( F2 @ I )
% 0.30/0.62                = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_nonneg_0
% 0.30/0.62  thf(fact_8126_sum__nonneg__0,axiom,
% 0.30/0.62      ! [S3: set_int,F2: int > code_integer,I: int] :
% 0.30/0.62        ( ( finite_finite_int @ S3 )
% 0.30/0.62       => ( ! [I2: int] :
% 0.30/0.62              ( ( member_int @ I2 @ S3 )
% 0.30/0.62             => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) ) )
% 0.30/0.62         => ( ( ( groups7873554091576472773nteger @ F2 @ S3 )
% 0.30/0.62              = zero_z3403309356797280102nteger )
% 0.30/0.62           => ( ( member_int @ I @ S3 )
% 0.30/0.62             => ( ( F2 @ I )
% 0.30/0.62                = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_nonneg_0
% 0.30/0.62  thf(fact_8127_sum__nonneg__0,axiom,
% 0.30/0.62      ! [S3: set_nat,F2: nat > rat,I: nat] :
% 0.30/0.62        ( ( finite_finite_nat @ S3 )
% 0.30/0.62       => ( ! [I2: nat] :
% 0.30/0.62              ( ( member_nat @ I2 @ S3 )
% 0.30/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I2 ) ) )
% 0.30/0.62         => ( ( ( groups2906978787729119204at_rat @ F2 @ S3 )
% 0.30/0.62              = zero_zero_rat )
% 0.30/0.62           => ( ( member_nat @ I @ S3 )
% 0.30/0.62             => ( ( F2 @ I )
% 0.30/0.62                = zero_zero_rat ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_nonneg_0
% 0.30/0.62  thf(fact_8128_sum__nonneg__0,axiom,
% 0.30/0.62      ! [S3: set_int,F2: int > rat,I: int] :
% 0.30/0.62        ( ( finite_finite_int @ S3 )
% 0.30/0.62       => ( ! [I2: int] :
% 0.30/0.62              ( ( member_int @ I2 @ S3 )
% 0.30/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I2 ) ) )
% 0.30/0.62         => ( ( ( groups3906332499630173760nt_rat @ F2 @ S3 )
% 0.30/0.62              = zero_zero_rat )
% 0.30/0.62           => ( ( member_int @ I @ S3 )
% 0.30/0.62             => ( ( F2 @ I )
% 0.30/0.62                = zero_zero_rat ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_nonneg_0
% 0.30/0.62  thf(fact_8129_sum__nonneg__0,axiom,
% 0.30/0.62      ! [S3: set_int,F2: int > nat,I: int] :
% 0.30/0.62        ( ( finite_finite_int @ S3 )
% 0.30/0.62       => ( ! [I2: int] :
% 0.30/0.62              ( ( member_int @ I2 @ S3 )
% 0.30/0.62             => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I2 ) ) )
% 0.30/0.62         => ( ( ( groups4541462559716669496nt_nat @ F2 @ S3 )
% 0.30/0.62              = zero_zero_nat )
% 0.30/0.62           => ( ( member_int @ I @ S3 )
% 0.30/0.62             => ( ( F2 @ I )
% 0.30/0.62                = zero_zero_nat ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_nonneg_0
% 0.30/0.62  thf(fact_8130_sum__nonneg__0,axiom,
% 0.30/0.62      ! [S3: set_nat,F2: nat > int,I: nat] :
% 0.30/0.62        ( ( finite_finite_nat @ S3 )
% 0.30/0.62       => ( ! [I2: nat] :
% 0.30/0.62              ( ( member_nat @ I2 @ S3 )
% 0.30/0.62             => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ I2 ) ) )
% 0.30/0.62         => ( ( ( groups3539618377306564664at_int @ F2 @ S3 )
% 0.30/0.62              = zero_zero_int )
% 0.30/0.62           => ( ( member_nat @ I @ S3 )
% 0.30/0.62             => ( ( F2 @ I )
% 0.30/0.62                = zero_zero_int ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_nonneg_0
% 0.30/0.62  thf(fact_8131_sum__nonneg__0,axiom,
% 0.30/0.62      ! [S3: set_nat,F2: nat > nat,I: nat] :
% 0.30/0.62        ( ( finite_finite_nat @ S3 )
% 0.30/0.62       => ( ! [I2: nat] :
% 0.30/0.62              ( ( member_nat @ I2 @ S3 )
% 0.30/0.62             => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I2 ) ) )
% 0.30/0.62         => ( ( ( groups3542108847815614940at_nat @ F2 @ S3 )
% 0.30/0.62              = zero_zero_nat )
% 0.30/0.62           => ( ( member_nat @ I @ S3 )
% 0.30/0.62             => ( ( F2 @ I )
% 0.30/0.62                = zero_zero_nat ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_nonneg_0
% 0.30/0.62  thf(fact_8132_sum__nonneg__0,axiom,
% 0.30/0.62      ! [S3: set_int,F2: int > int,I: int] :
% 0.30/0.62        ( ( finite_finite_int @ S3 )
% 0.30/0.62       => ( ! [I2: int] :
% 0.30/0.62              ( ( member_int @ I2 @ S3 )
% 0.30/0.62             => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ I2 ) ) )
% 0.30/0.62         => ( ( ( groups4538972089207619220nt_int @ F2 @ S3 )
% 0.30/0.62              = zero_zero_int )
% 0.30/0.62           => ( ( member_int @ I @ S3 )
% 0.30/0.62             => ( ( F2 @ I )
% 0.30/0.62                = zero_zero_int ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_nonneg_0
% 0.30/0.62  thf(fact_8133_sum__nonneg__0,axiom,
% 0.30/0.62      ! [S3: set_set_nat,F2: set_nat > code_integer,I: set_nat] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ S3 )
% 0.30/0.62       => ( ! [I2: set_nat] :
% 0.30/0.62              ( ( member_set_nat @ I2 @ S3 )
% 0.30/0.62             => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) ) )
% 0.30/0.62         => ( ( ( groups9190459664516455967nteger @ F2 @ S3 )
% 0.30/0.62              = zero_z3403309356797280102nteger )
% 0.30/0.62           => ( ( member_set_nat @ I @ S3 )
% 0.30/0.62             => ( ( F2 @ I )
% 0.30/0.62                = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_nonneg_0
% 0.30/0.62  thf(fact_8134_sum__nonneg__0,axiom,
% 0.30/0.62      ! [S3: set_set_nat,F2: set_nat > rat,I: set_nat] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ S3 )
% 0.30/0.62       => ( ! [I2: set_nat] :
% 0.30/0.62              ( ( member_set_nat @ I2 @ S3 )
% 0.30/0.62             => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I2 ) ) )
% 0.30/0.62         => ( ( ( groups7659867448343625626at_rat @ F2 @ S3 )
% 0.30/0.62              = zero_zero_rat )
% 0.30/0.62           => ( ( member_set_nat @ I @ S3 )
% 0.30/0.62             => ( ( F2 @ I )
% 0.30/0.62                = zero_zero_rat ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_nonneg_0
% 0.30/0.62  thf(fact_8135_ivl__disj__un__one_I2_J,axiom,
% 0.30/0.62      ! [L: rat,U: rat] :
% 0.30/0.62        ( ( ord_less_eq_rat @ L @ U )
% 0.30/0.62       => ( ( sup_sup_set_rat @ ( set_ord_lessThan_rat @ L ) @ ( set_or4029947393144176647an_rat @ L @ U ) )
% 0.30/0.62          = ( set_ord_lessThan_rat @ U ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % ivl_disj_un_one(2)
% 0.30/0.62  thf(fact_8136_ivl__disj__un__one_I2_J,axiom,
% 0.30/0.62      ! [L: nat,U: nat] :
% 0.30/0.62        ( ( ord_less_eq_nat @ L @ U )
% 0.30/0.62       => ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 0.30/0.62          = ( set_ord_lessThan_nat @ U ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % ivl_disj_un_one(2)
% 0.30/0.62  thf(fact_8137_ivl__disj__un__one_I2_J,axiom,
% 0.30/0.62      ! [L: code_integer,U: code_integer] :
% 0.30/0.62        ( ( ord_le3102999989581377725nteger @ L @ U )
% 0.30/0.62       => ( ( sup_su848401254843788991nteger @ ( set_or5754767410780653050nteger @ L ) @ ( set_or8404916559141939852nteger @ L @ U ) )
% 0.30/0.62          = ( set_or5754767410780653050nteger @ U ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % ivl_disj_un_one(2)
% 0.30/0.62  thf(fact_8138_ivl__disj__un__one_I2_J,axiom,
% 0.30/0.62      ! [L: int,U: int] :
% 0.30/0.62        ( ( ord_less_eq_int @ L @ U )
% 0.30/0.62       => ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or4662586982721622107an_int @ L @ U ) )
% 0.30/0.62          = ( set_ord_lessThan_int @ U ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % ivl_disj_un_one(2)
% 0.30/0.62  thf(fact_8139_ivl__disj__int__one_I4_J,axiom,
% 0.30/0.62      ! [L: $o,U: $o] :
% 0.30/0.62        ( ( inf_inf_set_o @ ( set_ord_lessThan_o @ L ) @ ( set_or8904488021354931149Most_o @ L @ U ) )
% 0.30/0.62        = bot_bot_set_o ) ).
% 0.30/0.62  
% 0.30/0.62  % ivl_disj_int_one(4)
% 0.30/0.62  thf(fact_8140_ivl__disj__int__one_I4_J,axiom,
% 0.30/0.62      ! [L: nat,U: nat] :
% 0.30/0.62        ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 0.30/0.62        = bot_bot_set_nat ) ).
% 0.30/0.62  
% 0.30/0.62  % ivl_disj_int_one(4)
% 0.30/0.62  thf(fact_8141_ivl__disj__int__one_I4_J,axiom,
% 0.30/0.62      ! [L: int,U: int] :
% 0.30/0.62        ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or1266510415728281911st_int @ L @ U ) )
% 0.30/0.62        = bot_bot_set_int ) ).
% 0.30/0.62  
% 0.30/0.62  % ivl_disj_int_one(4)
% 0.30/0.62  thf(fact_8142_ivl__disj__int__one_I4_J,axiom,
% 0.30/0.62      ! [L: code_integer,U: code_integer] :
% 0.30/0.62        ( ( inf_in1364745209274528805nteger @ ( set_or5754767410780653050nteger @ L ) @ ( set_or189985376899183464nteger @ L @ U ) )
% 0.30/0.62        = bot_bo3990330152332043303nteger ) ).
% 0.30/0.62  
% 0.30/0.62  % ivl_disj_int_one(4)
% 0.30/0.62  thf(fact_8143_prod_Otriangle__reindex,axiom,
% 0.30/0.62      ! [G2: nat > nat > nat,N: nat] :
% 0.30/0.62        ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G2 )
% 0.30/0.62          @ ( collec3392354462482085612at_nat
% 0.30/0.62            @ ( produc6081775807080527818_nat_o
% 0.30/0.62              @ ^ [I3: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 0.30/0.62        = ( groups708209901874060359at_nat
% 0.30/0.62          @ ^ [K4: nat] :
% 0.30/0.62              ( groups708209901874060359at_nat
% 0.30/0.62              @ ^ [I3: nat] : ( G2 @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 0.30/0.62              @ ( set_ord_atMost_nat @ K4 ) )
% 0.30/0.62          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.triangle_reindex
% 0.30/0.62  thf(fact_8144_prod_Otriangle__reindex,axiom,
% 0.30/0.62      ! [G2: nat > nat > int,N: nat] :
% 0.30/0.62        ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G2 )
% 0.30/0.62          @ ( collec3392354462482085612at_nat
% 0.30/0.62            @ ( produc6081775807080527818_nat_o
% 0.30/0.62              @ ^ [I3: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 0.30/0.62        = ( groups705719431365010083at_int
% 0.30/0.62          @ ^ [K4: nat] :
% 0.30/0.62              ( groups705719431365010083at_int
% 0.30/0.62              @ ^ [I3: nat] : ( G2 @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 0.30/0.62              @ ( set_ord_atMost_nat @ K4 ) )
% 0.30/0.62          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.triangle_reindex
% 0.30/0.62  thf(fact_8145_ivl__disj__int__one_I2_J,axiom,
% 0.30/0.62      ! [L: $o,U: $o] :
% 0.30/0.62        ( ( inf_inf_set_o @ ( set_ord_lessThan_o @ L ) @ ( set_or7139685690850216873Than_o @ L @ U ) )
% 0.30/0.62        = bot_bot_set_o ) ).
% 0.30/0.62  
% 0.30/0.62  % ivl_disj_int_one(2)
% 0.30/0.62  thf(fact_8146_ivl__disj__int__one_I2_J,axiom,
% 0.30/0.62      ! [L: nat,U: nat] :
% 0.30/0.62        ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 0.30/0.62        = bot_bot_set_nat ) ).
% 0.30/0.62  
% 0.30/0.62  % ivl_disj_int_one(2)
% 0.30/0.62  thf(fact_8147_ivl__disj__int__one_I2_J,axiom,
% 0.30/0.62      ! [L: code_integer,U: code_integer] :
% 0.30/0.62        ( ( inf_in1364745209274528805nteger @ ( set_or5754767410780653050nteger @ L ) @ ( set_or8404916559141939852nteger @ L @ U ) )
% 0.30/0.62        = bot_bo3990330152332043303nteger ) ).
% 0.30/0.62  
% 0.30/0.62  % ivl_disj_int_one(2)
% 0.30/0.62  thf(fact_8148_ivl__disj__int__one_I2_J,axiom,
% 0.30/0.62      ! [L: int,U: int] :
% 0.30/0.62        ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or4662586982721622107an_int @ L @ U ) )
% 0.30/0.62        = bot_bot_set_int ) ).
% 0.30/0.62  
% 0.30/0.62  % ivl_disj_int_one(2)
% 0.30/0.62  thf(fact_8149_sum_Ointer__restrict,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > code_integer,B2: set_int] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups7873554091576472773nteger @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.30/0.62          = ( groups7873554091576472773nteger
% 0.30/0.62            @ ^ [X3: int] : ( if_Code_integer @ ( member_int @ X3 @ B2 ) @ ( G2 @ X3 ) @ zero_z3403309356797280102nteger )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.inter_restrict
% 0.30/0.62  thf(fact_8150_sum_Ointer__restrict,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > rat,B2: set_int] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups3906332499630173760nt_rat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.30/0.62          = ( groups3906332499630173760nt_rat
% 0.30/0.62            @ ^ [X3: int] : ( if_rat @ ( member_int @ X3 @ B2 ) @ ( G2 @ X3 ) @ zero_zero_rat )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.inter_restrict
% 0.30/0.62  thf(fact_8151_sum_Ointer__restrict,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > nat,B2: set_int] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups4541462559716669496nt_nat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.30/0.62          = ( groups4541462559716669496nt_nat
% 0.30/0.62            @ ^ [X3: int] : ( if_nat @ ( member_int @ X3 @ B2 ) @ ( G2 @ X3 ) @ zero_zero_nat )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.inter_restrict
% 0.30/0.62  thf(fact_8152_sum_Ointer__restrict,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > code_integer,B2: set_nat] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups7501900531339628137nteger @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.30/0.62          = ( groups7501900531339628137nteger
% 0.30/0.62            @ ^ [X3: nat] : ( if_Code_integer @ ( member_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ zero_z3403309356797280102nteger )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.inter_restrict
% 0.30/0.62  thf(fact_8153_sum_Ointer__restrict,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > rat,B2: set_nat] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups2906978787729119204at_rat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.30/0.62          = ( groups2906978787729119204at_rat
% 0.30/0.62            @ ^ [X3: nat] : ( if_rat @ ( member_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ zero_zero_rat )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.inter_restrict
% 0.30/0.62  thf(fact_8154_sum_Ointer__restrict,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > int,B2: set_nat] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups3539618377306564664at_int @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.30/0.62          = ( groups3539618377306564664at_int
% 0.30/0.62            @ ^ [X3: nat] : ( if_int @ ( member_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ zero_zero_int )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.inter_restrict
% 0.30/0.62  thf(fact_8155_sum_Ointer__restrict,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > nat,B2: set_nat] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups3542108847815614940at_nat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.30/0.62          = ( groups3542108847815614940at_nat
% 0.30/0.62            @ ^ [X3: nat] : ( if_nat @ ( member_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ zero_zero_nat )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.inter_restrict
% 0.30/0.62  thf(fact_8156_sum_Ointer__restrict,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > int,B2: set_int] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups4538972089207619220nt_int @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.30/0.62          = ( groups4538972089207619220nt_int
% 0.30/0.62            @ ^ [X3: int] : ( if_int @ ( member_int @ X3 @ B2 ) @ ( G2 @ X3 ) @ zero_zero_int )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.inter_restrict
% 0.30/0.62  thf(fact_8157_sum_Ointer__restrict,axiom,
% 0.30/0.62      ! [A2: set_set_nat,G2: set_nat > code_integer,B2: set_set_nat] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.62       => ( ( groups9190459664516455967nteger @ G2 @ ( inf_inf_set_set_nat @ A2 @ B2 ) )
% 0.30/0.62          = ( groups9190459664516455967nteger
% 0.30/0.62            @ ^ [X3: set_nat] : ( if_Code_integer @ ( member_set_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ zero_z3403309356797280102nteger )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.inter_restrict
% 0.30/0.62  thf(fact_8158_sum_Ointer__restrict,axiom,
% 0.30/0.62      ! [A2: set_set_nat,G2: set_nat > rat,B2: set_set_nat] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.62       => ( ( groups7659867448343625626at_rat @ G2 @ ( inf_inf_set_set_nat @ A2 @ B2 ) )
% 0.30/0.62          = ( groups7659867448343625626at_rat
% 0.30/0.62            @ ^ [X3: set_nat] : ( if_rat @ ( member_set_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ zero_zero_rat )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.inter_restrict
% 0.30/0.62  thf(fact_8159_sum_Osetdiff__irrelevant,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > code_integer] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups7873554091576472773nteger @ G2
% 0.30/0.62            @ ( minus_minus_set_int @ A2
% 0.30/0.62              @ ( collect_int
% 0.30/0.62                @ ^ [X3: int] :
% 0.30/0.62                    ( ( G2 @ X3 )
% 0.30/0.62                    = zero_z3403309356797280102nteger ) ) ) )
% 0.30/0.62          = ( groups7873554091576472773nteger @ G2 @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.setdiff_irrelevant
% 0.30/0.62  thf(fact_8160_sum_Osetdiff__irrelevant,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > rat] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups3906332499630173760nt_rat @ G2
% 0.30/0.62            @ ( minus_minus_set_int @ A2
% 0.30/0.62              @ ( collect_int
% 0.30/0.62                @ ^ [X3: int] :
% 0.30/0.62                    ( ( G2 @ X3 )
% 0.30/0.62                    = zero_zero_rat ) ) ) )
% 0.30/0.62          = ( groups3906332499630173760nt_rat @ G2 @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.setdiff_irrelevant
% 0.30/0.62  thf(fact_8161_sum_Osetdiff__irrelevant,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > nat] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups4541462559716669496nt_nat @ G2
% 0.30/0.62            @ ( minus_minus_set_int @ A2
% 0.30/0.62              @ ( collect_int
% 0.30/0.62                @ ^ [X3: int] :
% 0.30/0.62                    ( ( G2 @ X3 )
% 0.30/0.62                    = zero_zero_nat ) ) ) )
% 0.30/0.62          = ( groups4541462559716669496nt_nat @ G2 @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.setdiff_irrelevant
% 0.30/0.62  thf(fact_8162_sum_Osetdiff__irrelevant,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > code_integer] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups7501900531339628137nteger @ G2
% 0.30/0.62            @ ( minus_minus_set_nat @ A2
% 0.30/0.62              @ ( collect_nat
% 0.30/0.62                @ ^ [X3: nat] :
% 0.30/0.62                    ( ( G2 @ X3 )
% 0.30/0.62                    = zero_z3403309356797280102nteger ) ) ) )
% 0.30/0.62          = ( groups7501900531339628137nteger @ G2 @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.setdiff_irrelevant
% 0.30/0.62  thf(fact_8163_sum_Osetdiff__irrelevant,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > rat] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups2906978787729119204at_rat @ G2
% 0.30/0.62            @ ( minus_minus_set_nat @ A2
% 0.30/0.62              @ ( collect_nat
% 0.30/0.62                @ ^ [X3: nat] :
% 0.30/0.62                    ( ( G2 @ X3 )
% 0.30/0.62                    = zero_zero_rat ) ) ) )
% 0.30/0.62          = ( groups2906978787729119204at_rat @ G2 @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.setdiff_irrelevant
% 0.30/0.62  thf(fact_8164_sum_Osetdiff__irrelevant,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > int] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups3539618377306564664at_int @ G2
% 0.30/0.62            @ ( minus_minus_set_nat @ A2
% 0.30/0.62              @ ( collect_nat
% 0.30/0.62                @ ^ [X3: nat] :
% 0.30/0.62                    ( ( G2 @ X3 )
% 0.30/0.62                    = zero_zero_int ) ) ) )
% 0.30/0.62          = ( groups3539618377306564664at_int @ G2 @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.setdiff_irrelevant
% 0.30/0.62  thf(fact_8165_sum_Osetdiff__irrelevant,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > nat] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups3542108847815614940at_nat @ G2
% 0.30/0.62            @ ( minus_minus_set_nat @ A2
% 0.30/0.62              @ ( collect_nat
% 0.30/0.62                @ ^ [X3: nat] :
% 0.30/0.62                    ( ( G2 @ X3 )
% 0.30/0.62                    = zero_zero_nat ) ) ) )
% 0.30/0.62          = ( groups3542108847815614940at_nat @ G2 @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.setdiff_irrelevant
% 0.30/0.62  thf(fact_8166_sum_Osetdiff__irrelevant,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > int] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups4538972089207619220nt_int @ G2
% 0.30/0.62            @ ( minus_minus_set_int @ A2
% 0.30/0.62              @ ( collect_int
% 0.30/0.62                @ ^ [X3: int] :
% 0.30/0.62                    ( ( G2 @ X3 )
% 0.30/0.62                    = zero_zero_int ) ) ) )
% 0.30/0.62          = ( groups4538972089207619220nt_int @ G2 @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.setdiff_irrelevant
% 0.30/0.62  thf(fact_8167_sum_Osetdiff__irrelevant,axiom,
% 0.30/0.62      ! [A2: set_set_nat,G2: set_nat > code_integer] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.62       => ( ( groups9190459664516455967nteger @ G2
% 0.30/0.62            @ ( minus_2163939370556025621et_nat @ A2
% 0.30/0.62              @ ( collect_set_nat
% 0.30/0.62                @ ^ [X3: set_nat] :
% 0.30/0.62                    ( ( G2 @ X3 )
% 0.30/0.62                    = zero_z3403309356797280102nteger ) ) ) )
% 0.30/0.62          = ( groups9190459664516455967nteger @ G2 @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.setdiff_irrelevant
% 0.30/0.62  thf(fact_8168_sum_Osetdiff__irrelevant,axiom,
% 0.30/0.62      ! [A2: set_set_nat,G2: set_nat > rat] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.62       => ( ( groups7659867448343625626at_rat @ G2
% 0.30/0.62            @ ( minus_2163939370556025621et_nat @ A2
% 0.30/0.62              @ ( collect_set_nat
% 0.30/0.62                @ ^ [X3: set_nat] :
% 0.30/0.62                    ( ( G2 @ X3 )
% 0.30/0.62                    = zero_zero_rat ) ) ) )
% 0.30/0.62          = ( groups7659867448343625626at_rat @ G2 @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.setdiff_irrelevant
% 0.30/0.62  thf(fact_8169_prod_Ointer__restrict,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > code_integer,B2: set_int] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups3827104343326376752nteger @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.30/0.62          = ( groups3827104343326376752nteger
% 0.30/0.62            @ ^ [X3: int] : ( if_Code_integer @ ( member_int @ X3 @ B2 ) @ ( G2 @ X3 ) @ one_one_Code_integer )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.inter_restrict
% 0.30/0.62  thf(fact_8170_prod_Ointer__restrict,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > assn,B2: set_int] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups7882442080178216443t_assn @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.30/0.62          = ( groups7882442080178216443t_assn
% 0.30/0.62            @ ^ [X3: int] : ( if_assn @ ( member_int @ X3 @ B2 ) @ ( G2 @ X3 ) @ one_one_assn )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.inter_restrict
% 0.30/0.62  thf(fact_8171_prod_Ointer__restrict,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > rat,B2: set_int] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.30/0.62          = ( groups1072433553688619179nt_rat
% 0.30/0.62            @ ^ [X3: int] : ( if_rat @ ( member_int @ X3 @ B2 ) @ ( G2 @ X3 ) @ one_one_rat )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.inter_restrict
% 0.30/0.62  thf(fact_8172_prod_Ointer__restrict,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > nat,B2: set_int] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.30/0.62          = ( groups1707563613775114915nt_nat
% 0.30/0.62            @ ^ [X3: int] : ( if_nat @ ( member_int @ X3 @ B2 ) @ ( G2 @ X3 ) @ one_one_nat )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.inter_restrict
% 0.30/0.62  thf(fact_8173_prod_Ointer__restrict,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > code_integer,B2: set_nat] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups3455450783089532116nteger @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.30/0.62          = ( groups3455450783089532116nteger
% 0.30/0.62            @ ^ [X3: nat] : ( if_Code_integer @ ( member_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ one_one_Code_integer )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.inter_restrict
% 0.30/0.62  thf(fact_8174_prod_Ointer__restrict,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > assn,B2: set_nat] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups6906906614972039071t_assn @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.30/0.62          = ( groups6906906614972039071t_assn
% 0.30/0.62            @ ^ [X3: nat] : ( if_assn @ ( member_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ one_one_assn )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.inter_restrict
% 0.30/0.62  thf(fact_8175_prod_Ointer__restrict,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > rat,B2: set_nat] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.30/0.62          = ( groups73079841787564623at_rat
% 0.30/0.62            @ ^ [X3: nat] : ( if_rat @ ( member_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ one_one_rat )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.inter_restrict
% 0.30/0.62  thf(fact_8176_prod_Ointer__restrict,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > nat,B2: set_nat] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups708209901874060359at_nat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.30/0.62          = ( groups708209901874060359at_nat
% 0.30/0.62            @ ^ [X3: nat] : ( if_nat @ ( member_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ one_one_nat )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.inter_restrict
% 0.30/0.62  thf(fact_8177_prod_Ointer__restrict,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > int,B2: set_nat] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups705719431365010083at_int @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.30/0.62          = ( groups705719431365010083at_int
% 0.30/0.62            @ ^ [X3: nat] : ( if_int @ ( member_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ one_one_int )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.inter_restrict
% 0.30/0.62  thf(fact_8178_prod_Ointer__restrict,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > int,B2: set_int] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups1705073143266064639nt_int @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.30/0.62          = ( groups1705073143266064639nt_int
% 0.30/0.62            @ ^ [X3: int] : ( if_int @ ( member_int @ X3 @ B2 ) @ ( G2 @ X3 ) @ one_one_int )
% 0.30/0.62            @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.inter_restrict
% 0.30/0.62  thf(fact_8179_prod_Osetdiff__irrelevant,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > code_integer] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups3827104343326376752nteger @ G2
% 0.30/0.62            @ ( minus_minus_set_int @ A2
% 0.30/0.62              @ ( collect_int
% 0.30/0.62                @ ^ [X3: int] :
% 0.30/0.62                    ( ( G2 @ X3 )
% 0.30/0.62                    = one_one_Code_integer ) ) ) )
% 0.30/0.62          = ( groups3827104343326376752nteger @ G2 @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.setdiff_irrelevant
% 0.30/0.62  thf(fact_8180_prod_Osetdiff__irrelevant,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > assn] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups7882442080178216443t_assn @ G2
% 0.30/0.62            @ ( minus_minus_set_int @ A2
% 0.30/0.62              @ ( collect_int
% 0.30/0.62                @ ^ [X3: int] :
% 0.30/0.62                    ( ( G2 @ X3 )
% 0.30/0.62                    = one_one_assn ) ) ) )
% 0.30/0.62          = ( groups7882442080178216443t_assn @ G2 @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.setdiff_irrelevant
% 0.30/0.62  thf(fact_8181_prod_Osetdiff__irrelevant,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > rat] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups1072433553688619179nt_rat @ G2
% 0.30/0.62            @ ( minus_minus_set_int @ A2
% 0.30/0.62              @ ( collect_int
% 0.30/0.62                @ ^ [X3: int] :
% 0.30/0.62                    ( ( G2 @ X3 )
% 0.30/0.62                    = one_one_rat ) ) ) )
% 0.30/0.62          = ( groups1072433553688619179nt_rat @ G2 @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.setdiff_irrelevant
% 0.30/0.62  thf(fact_8182_prod_Osetdiff__irrelevant,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > nat] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups1707563613775114915nt_nat @ G2
% 0.30/0.62            @ ( minus_minus_set_int @ A2
% 0.30/0.62              @ ( collect_int
% 0.30/0.62                @ ^ [X3: int] :
% 0.30/0.62                    ( ( G2 @ X3 )
% 0.30/0.62                    = one_one_nat ) ) ) )
% 0.30/0.62          = ( groups1707563613775114915nt_nat @ G2 @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.setdiff_irrelevant
% 0.30/0.62  thf(fact_8183_prod_Osetdiff__irrelevant,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > code_integer] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups3455450783089532116nteger @ G2
% 0.30/0.62            @ ( minus_minus_set_nat @ A2
% 0.30/0.62              @ ( collect_nat
% 0.30/0.62                @ ^ [X3: nat] :
% 0.30/0.62                    ( ( G2 @ X3 )
% 0.30/0.62                    = one_one_Code_integer ) ) ) )
% 0.30/0.62          = ( groups3455450783089532116nteger @ G2 @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.setdiff_irrelevant
% 0.30/0.62  thf(fact_8184_prod_Osetdiff__irrelevant,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > assn] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups6906906614972039071t_assn @ G2
% 0.30/0.62            @ ( minus_minus_set_nat @ A2
% 0.30/0.62              @ ( collect_nat
% 0.30/0.62                @ ^ [X3: nat] :
% 0.30/0.62                    ( ( G2 @ X3 )
% 0.30/0.62                    = one_one_assn ) ) ) )
% 0.30/0.62          = ( groups6906906614972039071t_assn @ G2 @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.setdiff_irrelevant
% 0.30/0.62  thf(fact_8185_prod_Osetdiff__irrelevant,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > rat] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups73079841787564623at_rat @ G2
% 0.30/0.62            @ ( minus_minus_set_nat @ A2
% 0.30/0.62              @ ( collect_nat
% 0.30/0.62                @ ^ [X3: nat] :
% 0.30/0.62                    ( ( G2 @ X3 )
% 0.30/0.62                    = one_one_rat ) ) ) )
% 0.30/0.62          = ( groups73079841787564623at_rat @ G2 @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.setdiff_irrelevant
% 0.30/0.62  thf(fact_8186_prod_Osetdiff__irrelevant,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > nat] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups708209901874060359at_nat @ G2
% 0.30/0.62            @ ( minus_minus_set_nat @ A2
% 0.30/0.62              @ ( collect_nat
% 0.30/0.62                @ ^ [X3: nat] :
% 0.30/0.62                    ( ( G2 @ X3 )
% 0.30/0.62                    = one_one_nat ) ) ) )
% 0.30/0.62          = ( groups708209901874060359at_nat @ G2 @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.setdiff_irrelevant
% 0.30/0.62  thf(fact_8187_prod_Osetdiff__irrelevant,axiom,
% 0.30/0.62      ! [A2: set_nat,G2: nat > int] :
% 0.30/0.62        ( ( finite_finite_nat @ A2 )
% 0.30/0.62       => ( ( groups705719431365010083at_int @ G2
% 0.30/0.62            @ ( minus_minus_set_nat @ A2
% 0.30/0.62              @ ( collect_nat
% 0.30/0.62                @ ^ [X3: nat] :
% 0.30/0.62                    ( ( G2 @ X3 )
% 0.30/0.62                    = one_one_int ) ) ) )
% 0.30/0.62          = ( groups705719431365010083at_int @ G2 @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.setdiff_irrelevant
% 0.30/0.62  thf(fact_8188_prod_Osetdiff__irrelevant,axiom,
% 0.30/0.62      ! [A2: set_int,G2: int > int] :
% 0.30/0.62        ( ( finite_finite_int @ A2 )
% 0.30/0.62       => ( ( groups1705073143266064639nt_int @ G2
% 0.30/0.62            @ ( minus_minus_set_int @ A2
% 0.30/0.62              @ ( collect_int
% 0.30/0.62                @ ^ [X3: int] :
% 0.30/0.62                    ( ( G2 @ X3 )
% 0.30/0.62                    = one_one_int ) ) ) )
% 0.30/0.62          = ( groups1705073143266064639nt_int @ G2 @ A2 ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.setdiff_irrelevant
% 0.30/0.62  thf(fact_8189_finite__divisors__nat,axiom,
% 0.30/0.62      ! [M: nat] :
% 0.30/0.62        ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.30/0.62       => ( finite_finite_nat
% 0.30/0.62          @ ( collect_nat
% 0.30/0.62            @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % finite_divisors_nat
% 0.30/0.62  thf(fact_8190_zsgn__def,axiom,
% 0.30/0.62      ( sgn_sgn_int
% 0.30/0.62      = ( ^ [I3: int] : ( if_int @ ( I3 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I3 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % zsgn_def
% 0.30/0.62  thf(fact_8191_sum__diff__distrib,axiom,
% 0.30/0.62      ! [Q2: nat > nat,P: nat > nat,N: nat] :
% 0.30/0.62        ( ! [X2: nat] : ( ord_less_eq_nat @ ( Q2 @ X2 ) @ ( P @ X2 ) )
% 0.30/0.62       => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q2 @ ( set_ord_lessThan_nat @ N ) ) )
% 0.30/0.62          = ( groups3542108847815614940at_nat
% 0.30/0.62            @ ^ [X3: nat] : ( minus_minus_nat @ ( P @ X3 ) @ ( Q2 @ X3 ) )
% 0.30/0.62            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_diff_distrib
% 0.30/0.62  thf(fact_8192_sum__pos,axiom,
% 0.30/0.62      ! [I4: set_o,F2: $o > code_integer] :
% 0.30/0.62        ( ( finite_finite_o @ I4 )
% 0.30/0.62       => ( ( I4 != bot_bot_set_o )
% 0.30/0.62         => ( ! [I2: $o] :
% 0.30/0.62                ( ( member_o @ I2 @ I4 )
% 0.30/0.62               => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) ) )
% 0.30/0.62           => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups4406642042086082107nteger @ F2 @ I4 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_pos
% 0.30/0.62  thf(fact_8193_sum__pos,axiom,
% 0.30/0.62      ! [I4: set_nat,F2: nat > code_integer] :
% 0.30/0.62        ( ( finite_finite_nat @ I4 )
% 0.30/0.62       => ( ( I4 != bot_bot_set_nat )
% 0.30/0.62         => ( ! [I2: nat] :
% 0.30/0.62                ( ( member_nat @ I2 @ I4 )
% 0.30/0.62               => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) ) )
% 0.30/0.62           => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups7501900531339628137nteger @ F2 @ I4 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_pos
% 0.30/0.62  thf(fact_8194_sum__pos,axiom,
% 0.30/0.62      ! [I4: set_int,F2: int > code_integer] :
% 0.30/0.62        ( ( finite_finite_int @ I4 )
% 0.30/0.62       => ( ( I4 != bot_bot_set_int )
% 0.30/0.62         => ( ! [I2: int] :
% 0.30/0.62                ( ( member_int @ I2 @ I4 )
% 0.30/0.62               => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) ) )
% 0.30/0.62           => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups7873554091576472773nteger @ F2 @ I4 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_pos
% 0.30/0.62  thf(fact_8195_sum__pos,axiom,
% 0.30/0.62      ! [I4: set_o,F2: $o > rat] :
% 0.30/0.62        ( ( finite_finite_o @ I4 )
% 0.30/0.62       => ( ( I4 != bot_bot_set_o )
% 0.30/0.62         => ( ! [I2: $o] :
% 0.30/0.62                ( ( member_o @ I2 @ I4 )
% 0.30/0.62               => ( ord_less_rat @ zero_zero_rat @ ( F2 @ I2 ) ) )
% 0.30/0.62           => ( ord_less_rat @ zero_zero_rat @ ( groups7872700643590313910_o_rat @ F2 @ I4 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_pos
% 0.30/0.62  thf(fact_8196_sum__pos,axiom,
% 0.30/0.62      ! [I4: set_nat,F2: nat > rat] :
% 0.30/0.62        ( ( finite_finite_nat @ I4 )
% 0.30/0.62       => ( ( I4 != bot_bot_set_nat )
% 0.30/0.62         => ( ! [I2: nat] :
% 0.30/0.62                ( ( member_nat @ I2 @ I4 )
% 0.30/0.62               => ( ord_less_rat @ zero_zero_rat @ ( F2 @ I2 ) ) )
% 0.30/0.62           => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F2 @ I4 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_pos
% 0.30/0.62  thf(fact_8197_sum__pos,axiom,
% 0.30/0.62      ! [I4: set_int,F2: int > rat] :
% 0.30/0.62        ( ( finite_finite_int @ I4 )
% 0.30/0.62       => ( ( I4 != bot_bot_set_int )
% 0.30/0.62         => ( ! [I2: int] :
% 0.30/0.62                ( ( member_int @ I2 @ I4 )
% 0.30/0.62               => ( ord_less_rat @ zero_zero_rat @ ( F2 @ I2 ) ) )
% 0.30/0.62           => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F2 @ I4 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_pos
% 0.30/0.62  thf(fact_8198_sum__pos,axiom,
% 0.30/0.62      ! [I4: set_o,F2: $o > nat] :
% 0.30/0.62        ( ( finite_finite_o @ I4 )
% 0.30/0.62       => ( ( I4 != bot_bot_set_o )
% 0.30/0.62         => ( ! [I2: $o] :
% 0.30/0.62                ( ( member_o @ I2 @ I4 )
% 0.30/0.62               => ( ord_less_nat @ zero_zero_nat @ ( F2 @ I2 ) ) )
% 0.30/0.62           => ( ord_less_nat @ zero_zero_nat @ ( groups8507830703676809646_o_nat @ F2 @ I4 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_pos
% 0.30/0.62  thf(fact_8199_sum__pos,axiom,
% 0.30/0.62      ! [I4: set_int,F2: int > nat] :
% 0.30/0.62        ( ( finite_finite_int @ I4 )
% 0.30/0.62       => ( ( I4 != bot_bot_set_int )
% 0.30/0.62         => ( ! [I2: int] :
% 0.30/0.62                ( ( member_int @ I2 @ I4 )
% 0.30/0.62               => ( ord_less_nat @ zero_zero_nat @ ( F2 @ I2 ) ) )
% 0.30/0.62           => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F2 @ I4 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_pos
% 0.30/0.62  thf(fact_8200_sum__pos,axiom,
% 0.30/0.62      ! [I4: set_o,F2: $o > int] :
% 0.30/0.62        ( ( finite_finite_o @ I4 )
% 0.30/0.62       => ( ( I4 != bot_bot_set_o )
% 0.30/0.62         => ( ! [I2: $o] :
% 0.30/0.62                ( ( member_o @ I2 @ I4 )
% 0.30/0.62               => ( ord_less_int @ zero_zero_int @ ( F2 @ I2 ) ) )
% 0.30/0.62           => ( ord_less_int @ zero_zero_int @ ( groups8505340233167759370_o_int @ F2 @ I4 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_pos
% 0.30/0.62  thf(fact_8201_sum__pos,axiom,
% 0.30/0.62      ! [I4: set_nat,F2: nat > int] :
% 0.30/0.62        ( ( finite_finite_nat @ I4 )
% 0.30/0.62       => ( ( I4 != bot_bot_set_nat )
% 0.30/0.62         => ( ! [I2: nat] :
% 0.30/0.62                ( ( member_nat @ I2 @ I4 )
% 0.30/0.62               => ( ord_less_int @ zero_zero_int @ ( F2 @ I2 ) ) )
% 0.30/0.62           => ( ord_less_int @ zero_zero_int @ ( groups3539618377306564664at_int @ F2 @ I4 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_pos
% 0.30/0.62  thf(fact_8202_less__1__prod2,axiom,
% 0.30/0.62      ! [I4: set_nat,I: nat,F2: nat > code_integer] :
% 0.30/0.62        ( ( finite_finite_nat @ I4 )
% 0.30/0.62       => ( ( member_nat @ I @ I4 )
% 0.30/0.62         => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I ) )
% 0.30/0.62           => ( ! [I2: nat] :
% 0.30/0.62                  ( ( member_nat @ I2 @ I4 )
% 0.30/0.62                 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ I2 ) ) )
% 0.30/0.62             => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F2 @ I4 ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % less_1_prod2
% 0.30/0.62  thf(fact_8203_less__1__prod2,axiom,
% 0.30/0.62      ! [I4: set_int,I: int,F2: int > code_integer] :
% 0.30/0.62        ( ( finite_finite_int @ I4 )
% 0.30/0.62       => ( ( member_int @ I @ I4 )
% 0.30/0.62         => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I ) )
% 0.30/0.62           => ( ! [I2: int] :
% 0.30/0.62                  ( ( member_int @ I2 @ I4 )
% 0.30/0.62                 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ I2 ) ) )
% 0.30/0.62             => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F2 @ I4 ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % less_1_prod2
% 0.30/0.62  thf(fact_8204_less__1__prod2,axiom,
% 0.30/0.62      ! [I4: set_nat,I: nat,F2: nat > rat] :
% 0.30/0.62        ( ( finite_finite_nat @ I4 )
% 0.30/0.62       => ( ( member_nat @ I @ I4 )
% 0.30/0.62         => ( ( ord_less_rat @ one_one_rat @ ( F2 @ I ) )
% 0.30/0.62           => ( ! [I2: nat] :
% 0.30/0.62                  ( ( member_nat @ I2 @ I4 )
% 0.30/0.62                 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ I2 ) ) )
% 0.30/0.62             => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F2 @ I4 ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % less_1_prod2
% 0.30/0.62  thf(fact_8205_less__1__prod2,axiom,
% 0.30/0.62      ! [I4: set_int,I: int,F2: int > rat] :
% 0.30/0.62        ( ( finite_finite_int @ I4 )
% 0.30/0.62       => ( ( member_int @ I @ I4 )
% 0.30/0.62         => ( ( ord_less_rat @ one_one_rat @ ( F2 @ I ) )
% 0.30/0.62           => ( ! [I2: int] :
% 0.30/0.62                  ( ( member_int @ I2 @ I4 )
% 0.30/0.62                 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ I2 ) ) )
% 0.30/0.62             => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F2 @ I4 ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % less_1_prod2
% 0.30/0.62  thf(fact_8206_less__1__prod2,axiom,
% 0.30/0.62      ! [I4: set_nat,I: nat,F2: nat > int] :
% 0.30/0.62        ( ( finite_finite_nat @ I4 )
% 0.30/0.62       => ( ( member_nat @ I @ I4 )
% 0.30/0.62         => ( ( ord_less_int @ one_one_int @ ( F2 @ I ) )
% 0.30/0.62           => ( ! [I2: nat] :
% 0.30/0.62                  ( ( member_nat @ I2 @ I4 )
% 0.30/0.62                 => ( ord_less_eq_int @ one_one_int @ ( F2 @ I2 ) ) )
% 0.30/0.62             => ( ord_less_int @ one_one_int @ ( groups705719431365010083at_int @ F2 @ I4 ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % less_1_prod2
% 0.30/0.62  thf(fact_8207_less__1__prod2,axiom,
% 0.30/0.62      ! [I4: set_int,I: int,F2: int > int] :
% 0.30/0.62        ( ( finite_finite_int @ I4 )
% 0.30/0.62       => ( ( member_int @ I @ I4 )
% 0.30/0.62         => ( ( ord_less_int @ one_one_int @ ( F2 @ I ) )
% 0.30/0.62           => ( ! [I2: int] :
% 0.30/0.62                  ( ( member_int @ I2 @ I4 )
% 0.30/0.62                 => ( ord_less_eq_int @ one_one_int @ ( F2 @ I2 ) ) )
% 0.30/0.62             => ( ord_less_int @ one_one_int @ ( groups1705073143266064639nt_int @ F2 @ I4 ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % less_1_prod2
% 0.30/0.62  thf(fact_8208_less__1__prod2,axiom,
% 0.30/0.62      ! [I4: set_set_nat,I: set_nat,F2: set_nat > code_integer] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ I4 )
% 0.30/0.62       => ( ( member_set_nat @ I @ I4 )
% 0.30/0.62         => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I ) )
% 0.30/0.62           => ( ! [I2: set_nat] :
% 0.30/0.62                  ( ( member_set_nat @ I2 @ I4 )
% 0.30/0.62                 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ I2 ) ) )
% 0.30/0.62             => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups2761809935038513290nteger @ F2 @ I4 ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % less_1_prod2
% 0.30/0.62  thf(fact_8209_less__1__prod2,axiom,
% 0.30/0.62      ! [I4: set_set_nat,I: set_nat,F2: set_nat > rat] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ I4 )
% 0.30/0.62       => ( ( member_set_nat @ I @ I4 )
% 0.30/0.62         => ( ( ord_less_rat @ one_one_rat @ ( F2 @ I ) )
% 0.30/0.62           => ( ! [I2: set_nat] :
% 0.30/0.62                  ( ( member_set_nat @ I2 @ I4 )
% 0.30/0.62                 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ I2 ) ) )
% 0.30/0.62             => ( ord_less_rat @ one_one_rat @ ( groups3613417700093529605at_rat @ F2 @ I4 ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % less_1_prod2
% 0.30/0.62  thf(fact_8210_less__1__prod2,axiom,
% 0.30/0.62      ! [I4: set_set_nat,I: set_nat,F2: set_nat > int] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ I4 )
% 0.30/0.62       => ( ( member_set_nat @ I @ I4 )
% 0.30/0.62         => ( ( ord_less_int @ one_one_int @ ( F2 @ I ) )
% 0.30/0.62           => ( ! [I2: set_nat] :
% 0.30/0.62                  ( ( member_set_nat @ I2 @ I4 )
% 0.30/0.62                 => ( ord_less_eq_int @ one_one_int @ ( F2 @ I2 ) ) )
% 0.30/0.62             => ( ord_less_int @ one_one_int @ ( groups4246057289670975065at_int @ F2 @ I4 ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % less_1_prod2
% 0.30/0.62  thf(fact_8211_less__1__prod2,axiom,
% 0.30/0.62      ! [I4: set_Pr1261947904930325089at_nat,I: product_prod_nat_nat,F2: product_prod_nat_nat > code_integer] :
% 0.30/0.62        ( ( finite6177210948735845034at_nat @ I4 )
% 0.30/0.62       => ( ( member8440522571783428010at_nat @ I @ I4 )
% 0.30/0.62         => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I ) )
% 0.30/0.62           => ( ! [I2: product_prod_nat_nat] :
% 0.30/0.62                  ( ( member8440522571783428010at_nat @ I2 @ I4 )
% 0.30/0.62                 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ I2 ) ) )
% 0.30/0.62             => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups1230400874837758585nteger @ F2 @ I4 ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % less_1_prod2
% 0.30/0.62  thf(fact_8212_less__1__prod,axiom,
% 0.30/0.62      ! [I4: set_o,F2: $o > code_integer] :
% 0.30/0.62        ( ( finite_finite_o @ I4 )
% 0.30/0.62       => ( ( I4 != bot_bot_set_o )
% 0.30/0.62         => ( ! [I2: $o] :
% 0.30/0.62                ( ( member_o @ I2 @ I4 )
% 0.30/0.62               => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I2 ) ) )
% 0.30/0.62           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups7694694392188491536nteger @ F2 @ I4 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % less_1_prod
% 0.30/0.62  thf(fact_8213_less__1__prod,axiom,
% 0.30/0.62      ! [I4: set_nat,F2: nat > code_integer] :
% 0.30/0.62        ( ( finite_finite_nat @ I4 )
% 0.30/0.62       => ( ( I4 != bot_bot_set_nat )
% 0.30/0.62         => ( ! [I2: nat] :
% 0.30/0.62                ( ( member_nat @ I2 @ I4 )
% 0.30/0.62               => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I2 ) ) )
% 0.30/0.62           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F2 @ I4 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % less_1_prod
% 0.30/0.62  thf(fact_8214_less__1__prod,axiom,
% 0.30/0.62      ! [I4: set_int,F2: int > code_integer] :
% 0.30/0.62        ( ( finite_finite_int @ I4 )
% 0.30/0.62       => ( ( I4 != bot_bot_set_int )
% 0.30/0.62         => ( ! [I2: int] :
% 0.30/0.62                ( ( member_int @ I2 @ I4 )
% 0.30/0.62               => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I2 ) ) )
% 0.30/0.62           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F2 @ I4 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % less_1_prod
% 0.30/0.62  thf(fact_8215_less__1__prod,axiom,
% 0.30/0.62      ! [I4: set_o,F2: $o > rat] :
% 0.30/0.62        ( ( finite_finite_o @ I4 )
% 0.30/0.62       => ( ( I4 != bot_bot_set_o )
% 0.30/0.62         => ( ! [I2: $o] :
% 0.30/0.62                ( ( member_o @ I2 @ I4 )
% 0.30/0.62               => ( ord_less_rat @ one_one_rat @ ( F2 @ I2 ) ) )
% 0.30/0.62           => ( ord_less_rat @ one_one_rat @ ( groups2869687844427037835_o_rat @ F2 @ I4 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % less_1_prod
% 0.30/0.62  thf(fact_8216_less__1__prod,axiom,
% 0.30/0.62      ! [I4: set_nat,F2: nat > rat] :
% 0.30/0.62        ( ( finite_finite_nat @ I4 )
% 0.30/0.62       => ( ( I4 != bot_bot_set_nat )
% 0.30/0.62         => ( ! [I2: nat] :
% 0.30/0.62                ( ( member_nat @ I2 @ I4 )
% 0.30/0.62               => ( ord_less_rat @ one_one_rat @ ( F2 @ I2 ) ) )
% 0.30/0.62           => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F2 @ I4 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % less_1_prod
% 0.30/0.62  thf(fact_8217_less__1__prod,axiom,
% 0.30/0.62      ! [I4: set_int,F2: int > rat] :
% 0.30/0.62        ( ( finite_finite_int @ I4 )
% 0.30/0.62       => ( ( I4 != bot_bot_set_int )
% 0.30/0.62         => ( ! [I2: int] :
% 0.30/0.62                ( ( member_int @ I2 @ I4 )
% 0.30/0.62               => ( ord_less_rat @ one_one_rat @ ( F2 @ I2 ) ) )
% 0.30/0.62           => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F2 @ I4 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % less_1_prod
% 0.30/0.62  thf(fact_8218_less__1__prod,axiom,
% 0.30/0.62      ! [I4: set_o,F2: $o > int] :
% 0.30/0.62        ( ( finite_finite_o @ I4 )
% 0.30/0.62       => ( ( I4 != bot_bot_set_o )
% 0.30/0.62         => ( ! [I2: $o] :
% 0.30/0.62                ( ( member_o @ I2 @ I4 )
% 0.30/0.62               => ( ord_less_int @ one_one_int @ ( F2 @ I2 ) ) )
% 0.30/0.62           => ( ord_less_int @ one_one_int @ ( groups3502327434004483295_o_int @ F2 @ I4 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % less_1_prod
% 0.30/0.62  thf(fact_8219_less__1__prod,axiom,
% 0.30/0.62      ! [I4: set_nat,F2: nat > int] :
% 0.30/0.62        ( ( finite_finite_nat @ I4 )
% 0.30/0.62       => ( ( I4 != bot_bot_set_nat )
% 0.30/0.62         => ( ! [I2: nat] :
% 0.30/0.62                ( ( member_nat @ I2 @ I4 )
% 0.30/0.62               => ( ord_less_int @ one_one_int @ ( F2 @ I2 ) ) )
% 0.30/0.62           => ( ord_less_int @ one_one_int @ ( groups705719431365010083at_int @ F2 @ I4 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % less_1_prod
% 0.30/0.62  thf(fact_8220_less__1__prod,axiom,
% 0.30/0.62      ! [I4: set_int,F2: int > int] :
% 0.30/0.62        ( ( finite_finite_int @ I4 )
% 0.30/0.62       => ( ( I4 != bot_bot_set_int )
% 0.30/0.62         => ( ! [I2: int] :
% 0.30/0.62                ( ( member_int @ I2 @ I4 )
% 0.30/0.62               => ( ord_less_int @ one_one_int @ ( F2 @ I2 ) ) )
% 0.30/0.62           => ( ord_less_int @ one_one_int @ ( groups1705073143266064639nt_int @ F2 @ I4 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % less_1_prod
% 0.30/0.62  thf(fact_8221_less__1__prod,axiom,
% 0.30/0.62      ! [I4: set_set_nat,F2: set_nat > code_integer] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ I4 )
% 0.30/0.62       => ( ( I4 != bot_bot_set_set_nat )
% 0.30/0.62         => ( ! [I2: set_nat] :
% 0.30/0.62                ( ( member_set_nat @ I2 @ I4 )
% 0.30/0.62               => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I2 ) ) )
% 0.30/0.62           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups2761809935038513290nteger @ F2 @ I4 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % less_1_prod
% 0.30/0.62  thf(fact_8222_sum_OlessThan__Suc__shift,axiom,
% 0.30/0.62      ! [G2: nat > rat,N: nat] :
% 0.30/0.62        ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.30/0.62        = ( plus_plus_rat @ ( G2 @ zero_zero_nat )
% 0.30/0.62          @ ( groups2906978787729119204at_rat
% 0.30/0.62            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.62            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.lessThan_Suc_shift
% 0.30/0.62  thf(fact_8223_sum_OlessThan__Suc__shift,axiom,
% 0.30/0.62      ! [G2: nat > int,N: nat] :
% 0.30/0.62        ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.30/0.62        = ( plus_plus_int @ ( G2 @ zero_zero_nat )
% 0.30/0.62          @ ( groups3539618377306564664at_int
% 0.30/0.62            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.62            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.lessThan_Suc_shift
% 0.30/0.62  thf(fact_8224_sum_OlessThan__Suc__shift,axiom,
% 0.30/0.62      ! [G2: nat > nat,N: nat] :
% 0.30/0.62        ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.30/0.62        = ( plus_plus_nat @ ( G2 @ zero_zero_nat )
% 0.30/0.62          @ ( groups3542108847815614940at_nat
% 0.30/0.62            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.62            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.lessThan_Suc_shift
% 0.30/0.62  thf(fact_8225_sum__lessThan__telescope_H,axiom,
% 0.30/0.62      ! [F2: nat > rat,M: nat] :
% 0.30/0.62        ( ( groups2906978787729119204at_rat
% 0.30/0.62          @ ^ [N2: nat] : ( minus_minus_rat @ ( F2 @ N2 ) @ ( F2 @ ( suc @ N2 ) ) )
% 0.30/0.62          @ ( set_ord_lessThan_nat @ M ) )
% 0.30/0.62        = ( minus_minus_rat @ ( F2 @ zero_zero_nat ) @ ( F2 @ M ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_lessThan_telescope'
% 0.30/0.62  thf(fact_8226_sum__lessThan__telescope_H,axiom,
% 0.30/0.62      ! [F2: nat > int,M: nat] :
% 0.30/0.62        ( ( groups3539618377306564664at_int
% 0.30/0.62          @ ^ [N2: nat] : ( minus_minus_int @ ( F2 @ N2 ) @ ( F2 @ ( suc @ N2 ) ) )
% 0.30/0.62          @ ( set_ord_lessThan_nat @ M ) )
% 0.30/0.62        = ( minus_minus_int @ ( F2 @ zero_zero_nat ) @ ( F2 @ M ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_lessThan_telescope'
% 0.30/0.62  thf(fact_8227_sum__lessThan__telescope,axiom,
% 0.30/0.62      ! [F2: nat > rat,M: nat] :
% 0.30/0.62        ( ( groups2906978787729119204at_rat
% 0.30/0.62          @ ^ [N2: nat] : ( minus_minus_rat @ ( F2 @ ( suc @ N2 ) ) @ ( F2 @ N2 ) )
% 0.30/0.62          @ ( set_ord_lessThan_nat @ M ) )
% 0.30/0.62        = ( minus_minus_rat @ ( F2 @ M ) @ ( F2 @ zero_zero_nat ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_lessThan_telescope
% 0.30/0.62  thf(fact_8228_sum__lessThan__telescope,axiom,
% 0.30/0.62      ! [F2: nat > int,M: nat] :
% 0.30/0.62        ( ( groups3539618377306564664at_int
% 0.30/0.62          @ ^ [N2: nat] : ( minus_minus_int @ ( F2 @ ( suc @ N2 ) ) @ ( F2 @ N2 ) )
% 0.30/0.62          @ ( set_ord_lessThan_nat @ M ) )
% 0.30/0.62        = ( minus_minus_int @ ( F2 @ M ) @ ( F2 @ zero_zero_nat ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum_lessThan_telescope
% 0.30/0.62  thf(fact_8229_sgn__1__neg,axiom,
% 0.30/0.62      ! [A: int] :
% 0.30/0.62        ( ( ( sgn_sgn_int @ A )
% 0.30/0.62          = ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.62        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_1_neg
% 0.30/0.62  thf(fact_8230_sgn__1__neg,axiom,
% 0.30/0.62      ! [A: code_integer] :
% 0.30/0.62        ( ( ( sgn_sgn_Code_integer @ A )
% 0.30/0.62          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.30/0.62        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_1_neg
% 0.30/0.62  thf(fact_8231_sgn__1__neg,axiom,
% 0.30/0.62      ! [A: rat] :
% 0.30/0.62        ( ( ( sgn_sgn_rat @ A )
% 0.30/0.62          = ( uminus_uminus_rat @ one_one_rat ) )
% 0.30/0.62        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_1_neg
% 0.30/0.62  thf(fact_8232_sgn__if,axiom,
% 0.30/0.62      ( sgn_sgn_int
% 0.30/0.62      = ( ^ [X3: int] : ( if_int @ ( X3 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ X3 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_if
% 0.30/0.62  thf(fact_8233_sgn__if,axiom,
% 0.30/0.62      ( sgn_sgn_Code_integer
% 0.30/0.62      = ( ^ [X3: code_integer] : ( if_Code_integer @ ( X3 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X3 ) @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_if
% 0.30/0.62  thf(fact_8234_sgn__if,axiom,
% 0.30/0.62      ( sgn_sgn_rat
% 0.30/0.62      = ( ^ [X3: rat] : ( if_rat @ ( X3 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ X3 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sgn_if
% 0.30/0.62  thf(fact_8235_prod_OlessThan__Suc__shift,axiom,
% 0.30/0.62      ! [G2: nat > code_integer,N: nat] :
% 0.30/0.62        ( ( groups3455450783089532116nteger @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.30/0.62        = ( times_3573771949741848930nteger @ ( G2 @ zero_zero_nat )
% 0.30/0.62          @ ( groups3455450783089532116nteger
% 0.30/0.62            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.62            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.lessThan_Suc_shift
% 0.30/0.62  thf(fact_8236_prod_OlessThan__Suc__shift,axiom,
% 0.30/0.62      ! [G2: nat > assn,N: nat] :
% 0.30/0.62        ( ( groups6906906614972039071t_assn @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.30/0.62        = ( times_times_assn @ ( G2 @ zero_zero_nat )
% 0.30/0.62          @ ( groups6906906614972039071t_assn
% 0.30/0.62            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.62            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.lessThan_Suc_shift
% 0.30/0.62  thf(fact_8237_prod_OlessThan__Suc__shift,axiom,
% 0.30/0.62      ! [G2: nat > rat,N: nat] :
% 0.30/0.62        ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.30/0.62        = ( times_times_rat @ ( G2 @ zero_zero_nat )
% 0.30/0.62          @ ( groups73079841787564623at_rat
% 0.30/0.62            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.62            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.lessThan_Suc_shift
% 0.30/0.62  thf(fact_8238_prod_OlessThan__Suc__shift,axiom,
% 0.30/0.62      ! [G2: nat > nat,N: nat] :
% 0.30/0.62        ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.30/0.62        = ( times_times_nat @ ( G2 @ zero_zero_nat )
% 0.30/0.62          @ ( groups708209901874060359at_nat
% 0.30/0.62            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.62            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.lessThan_Suc_shift
% 0.30/0.62  thf(fact_8239_prod_OlessThan__Suc__shift,axiom,
% 0.30/0.62      ! [G2: nat > int,N: nat] :
% 0.30/0.62        ( ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.30/0.62        = ( times_times_int @ ( G2 @ zero_zero_nat )
% 0.30/0.62          @ ( groups705719431365010083at_int
% 0.30/0.62            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.62            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.lessThan_Suc_shift
% 0.30/0.62  thf(fact_8240_sum_Omono__neutral__cong,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,H3: int > code_integer,G2: int > code_integer] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( finite_finite_int @ S )
% 0.30/0.62         => ( ! [I2: int] :
% 0.30/0.62                ( ( member_int @ I2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( H3 @ I2 )
% 0.30/0.62                  = zero_z3403309356797280102nteger ) )
% 0.30/0.62           => ( ! [I2: int] :
% 0.30/0.62                  ( ( member_int @ I2 @ ( minus_minus_set_int @ S @ T ) )
% 0.30/0.62                 => ( ( G2 @ I2 )
% 0.30/0.62                    = zero_z3403309356797280102nteger ) )
% 0.30/0.62             => ( ! [X2: int] :
% 0.30/0.62                    ( ( member_int @ X2 @ ( inf_inf_set_int @ S @ T ) )
% 0.30/0.62                   => ( ( G2 @ X2 )
% 0.30/0.62                      = ( H3 @ X2 ) ) )
% 0.30/0.62               => ( ( groups7873554091576472773nteger @ G2 @ S )
% 0.30/0.62                  = ( groups7873554091576472773nteger @ H3 @ T ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.mono_neutral_cong
% 0.30/0.62  thf(fact_8241_sum_Omono__neutral__cong,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,H3: int > rat,G2: int > rat] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( finite_finite_int @ S )
% 0.30/0.62         => ( ! [I2: int] :
% 0.30/0.62                ( ( member_int @ I2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( H3 @ I2 )
% 0.30/0.62                  = zero_zero_rat ) )
% 0.30/0.62           => ( ! [I2: int] :
% 0.30/0.62                  ( ( member_int @ I2 @ ( minus_minus_set_int @ S @ T ) )
% 0.30/0.62                 => ( ( G2 @ I2 )
% 0.30/0.62                    = zero_zero_rat ) )
% 0.30/0.62             => ( ! [X2: int] :
% 0.30/0.62                    ( ( member_int @ X2 @ ( inf_inf_set_int @ S @ T ) )
% 0.30/0.62                   => ( ( G2 @ X2 )
% 0.30/0.62                      = ( H3 @ X2 ) ) )
% 0.30/0.62               => ( ( groups3906332499630173760nt_rat @ G2 @ S )
% 0.30/0.62                  = ( groups3906332499630173760nt_rat @ H3 @ T ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.mono_neutral_cong
% 0.30/0.62  thf(fact_8242_sum_Omono__neutral__cong,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,H3: int > nat,G2: int > nat] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( finite_finite_int @ S )
% 0.30/0.62         => ( ! [I2: int] :
% 0.30/0.62                ( ( member_int @ I2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( H3 @ I2 )
% 0.30/0.62                  = zero_zero_nat ) )
% 0.30/0.62           => ( ! [I2: int] :
% 0.30/0.62                  ( ( member_int @ I2 @ ( minus_minus_set_int @ S @ T ) )
% 0.30/0.62                 => ( ( G2 @ I2 )
% 0.30/0.62                    = zero_zero_nat ) )
% 0.30/0.62             => ( ! [X2: int] :
% 0.30/0.62                    ( ( member_int @ X2 @ ( inf_inf_set_int @ S @ T ) )
% 0.30/0.62                   => ( ( G2 @ X2 )
% 0.30/0.62                      = ( H3 @ X2 ) ) )
% 0.30/0.62               => ( ( groups4541462559716669496nt_nat @ G2 @ S )
% 0.30/0.62                  = ( groups4541462559716669496nt_nat @ H3 @ T ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.mono_neutral_cong
% 0.30/0.62  thf(fact_8243_sum_Omono__neutral__cong,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,H3: nat > code_integer,G2: nat > code_integer] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( finite_finite_nat @ S )
% 0.30/0.62         => ( ! [I2: nat] :
% 0.30/0.62                ( ( member_nat @ I2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( H3 @ I2 )
% 0.30/0.62                  = zero_z3403309356797280102nteger ) )
% 0.30/0.62           => ( ! [I2: nat] :
% 0.30/0.62                  ( ( member_nat @ I2 @ ( minus_minus_set_nat @ S @ T ) )
% 0.30/0.62                 => ( ( G2 @ I2 )
% 0.30/0.62                    = zero_z3403309356797280102nteger ) )
% 0.30/0.62             => ( ! [X2: nat] :
% 0.30/0.62                    ( ( member_nat @ X2 @ ( inf_inf_set_nat @ S @ T ) )
% 0.30/0.62                   => ( ( G2 @ X2 )
% 0.30/0.62                      = ( H3 @ X2 ) ) )
% 0.30/0.62               => ( ( groups7501900531339628137nteger @ G2 @ S )
% 0.30/0.62                  = ( groups7501900531339628137nteger @ H3 @ T ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.mono_neutral_cong
% 0.30/0.62  thf(fact_8244_sum_Omono__neutral__cong,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,H3: nat > rat,G2: nat > rat] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( finite_finite_nat @ S )
% 0.30/0.62         => ( ! [I2: nat] :
% 0.30/0.62                ( ( member_nat @ I2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( H3 @ I2 )
% 0.30/0.62                  = zero_zero_rat ) )
% 0.30/0.62           => ( ! [I2: nat] :
% 0.30/0.62                  ( ( member_nat @ I2 @ ( minus_minus_set_nat @ S @ T ) )
% 0.30/0.62                 => ( ( G2 @ I2 )
% 0.30/0.62                    = zero_zero_rat ) )
% 0.30/0.62             => ( ! [X2: nat] :
% 0.30/0.62                    ( ( member_nat @ X2 @ ( inf_inf_set_nat @ S @ T ) )
% 0.30/0.62                   => ( ( G2 @ X2 )
% 0.30/0.62                      = ( H3 @ X2 ) ) )
% 0.30/0.62               => ( ( groups2906978787729119204at_rat @ G2 @ S )
% 0.30/0.62                  = ( groups2906978787729119204at_rat @ H3 @ T ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.mono_neutral_cong
% 0.30/0.62  thf(fact_8245_sum_Omono__neutral__cong,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,H3: nat > int,G2: nat > int] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( finite_finite_nat @ S )
% 0.30/0.62         => ( ! [I2: nat] :
% 0.30/0.62                ( ( member_nat @ I2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( H3 @ I2 )
% 0.30/0.62                  = zero_zero_int ) )
% 0.30/0.62           => ( ! [I2: nat] :
% 0.30/0.62                  ( ( member_nat @ I2 @ ( minus_minus_set_nat @ S @ T ) )
% 0.30/0.62                 => ( ( G2 @ I2 )
% 0.30/0.62                    = zero_zero_int ) )
% 0.30/0.62             => ( ! [X2: nat] :
% 0.30/0.62                    ( ( member_nat @ X2 @ ( inf_inf_set_nat @ S @ T ) )
% 0.30/0.62                   => ( ( G2 @ X2 )
% 0.30/0.62                      = ( H3 @ X2 ) ) )
% 0.30/0.62               => ( ( groups3539618377306564664at_int @ G2 @ S )
% 0.30/0.62                  = ( groups3539618377306564664at_int @ H3 @ T ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.mono_neutral_cong
% 0.30/0.62  thf(fact_8246_sum_Omono__neutral__cong,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,H3: nat > nat,G2: nat > nat] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( finite_finite_nat @ S )
% 0.30/0.62         => ( ! [I2: nat] :
% 0.30/0.62                ( ( member_nat @ I2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( H3 @ I2 )
% 0.30/0.62                  = zero_zero_nat ) )
% 0.30/0.62           => ( ! [I2: nat] :
% 0.30/0.62                  ( ( member_nat @ I2 @ ( minus_minus_set_nat @ S @ T ) )
% 0.30/0.62                 => ( ( G2 @ I2 )
% 0.30/0.62                    = zero_zero_nat ) )
% 0.30/0.62             => ( ! [X2: nat] :
% 0.30/0.62                    ( ( member_nat @ X2 @ ( inf_inf_set_nat @ S @ T ) )
% 0.30/0.62                   => ( ( G2 @ X2 )
% 0.30/0.62                      = ( H3 @ X2 ) ) )
% 0.30/0.62               => ( ( groups3542108847815614940at_nat @ G2 @ S )
% 0.30/0.62                  = ( groups3542108847815614940at_nat @ H3 @ T ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.mono_neutral_cong
% 0.30/0.62  thf(fact_8247_sum_Omono__neutral__cong,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,H3: int > int,G2: int > int] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( finite_finite_int @ S )
% 0.30/0.62         => ( ! [I2: int] :
% 0.30/0.62                ( ( member_int @ I2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( H3 @ I2 )
% 0.30/0.62                  = zero_zero_int ) )
% 0.30/0.62           => ( ! [I2: int] :
% 0.30/0.62                  ( ( member_int @ I2 @ ( minus_minus_set_int @ S @ T ) )
% 0.30/0.62                 => ( ( G2 @ I2 )
% 0.30/0.62                    = zero_zero_int ) )
% 0.30/0.62             => ( ! [X2: int] :
% 0.30/0.62                    ( ( member_int @ X2 @ ( inf_inf_set_int @ S @ T ) )
% 0.30/0.62                   => ( ( G2 @ X2 )
% 0.30/0.62                      = ( H3 @ X2 ) ) )
% 0.30/0.62               => ( ( groups4538972089207619220nt_int @ G2 @ S )
% 0.30/0.62                  = ( groups4538972089207619220nt_int @ H3 @ T ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.mono_neutral_cong
% 0.30/0.62  thf(fact_8248_sum_Omono__neutral__cong,axiom,
% 0.30/0.62      ! [T: set_set_nat,S: set_set_nat,H3: set_nat > code_integer,G2: set_nat > code_integer] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ T )
% 0.30/0.62       => ( ( finite1152437895449049373et_nat @ S )
% 0.30/0.62         => ( ! [I2: set_nat] :
% 0.30/0.62                ( ( member_set_nat @ I2 @ ( minus_2163939370556025621et_nat @ T @ S ) )
% 0.30/0.62               => ( ( H3 @ I2 )
% 0.30/0.62                  = zero_z3403309356797280102nteger ) )
% 0.30/0.62           => ( ! [I2: set_nat] :
% 0.30/0.62                  ( ( member_set_nat @ I2 @ ( minus_2163939370556025621et_nat @ S @ T ) )
% 0.30/0.62                 => ( ( G2 @ I2 )
% 0.30/0.62                    = zero_z3403309356797280102nteger ) )
% 0.30/0.62             => ( ! [X2: set_nat] :
% 0.30/0.62                    ( ( member_set_nat @ X2 @ ( inf_inf_set_set_nat @ S @ T ) )
% 0.30/0.62                   => ( ( G2 @ X2 )
% 0.30/0.62                      = ( H3 @ X2 ) ) )
% 0.30/0.62               => ( ( groups9190459664516455967nteger @ G2 @ S )
% 0.30/0.62                  = ( groups9190459664516455967nteger @ H3 @ T ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.mono_neutral_cong
% 0.30/0.62  thf(fact_8249_sum_Omono__neutral__cong,axiom,
% 0.30/0.62      ! [T: set_set_nat,S: set_set_nat,H3: set_nat > rat,G2: set_nat > rat] :
% 0.30/0.62        ( ( finite1152437895449049373et_nat @ T )
% 0.30/0.62       => ( ( finite1152437895449049373et_nat @ S )
% 0.30/0.62         => ( ! [I2: set_nat] :
% 0.30/0.62                ( ( member_set_nat @ I2 @ ( minus_2163939370556025621et_nat @ T @ S ) )
% 0.30/0.62               => ( ( H3 @ I2 )
% 0.30/0.62                  = zero_zero_rat ) )
% 0.30/0.62           => ( ! [I2: set_nat] :
% 0.30/0.62                  ( ( member_set_nat @ I2 @ ( minus_2163939370556025621et_nat @ S @ T ) )
% 0.30/0.62                 => ( ( G2 @ I2 )
% 0.30/0.62                    = zero_zero_rat ) )
% 0.30/0.62             => ( ! [X2: set_nat] :
% 0.30/0.62                    ( ( member_set_nat @ X2 @ ( inf_inf_set_set_nat @ S @ T ) )
% 0.30/0.62                   => ( ( G2 @ X2 )
% 0.30/0.62                      = ( H3 @ X2 ) ) )
% 0.30/0.62               => ( ( groups7659867448343625626at_rat @ G2 @ S )
% 0.30/0.62                  = ( groups7659867448343625626at_rat @ H3 @ T ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % sum.mono_neutral_cong
% 0.30/0.62  thf(fact_8250_prod_Osubset__diff,axiom,
% 0.30/0.62      ! [B2: set_int,A2: set_int,G2: int > code_integer] :
% 0.30/0.62        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 0.30/0.62       => ( ( finite_finite_int @ A2 )
% 0.30/0.62         => ( ( groups3827104343326376752nteger @ G2 @ A2 )
% 0.30/0.62            = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups3827104343326376752nteger @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.subset_diff
% 0.30/0.62  thf(fact_8251_prod_Osubset__diff,axiom,
% 0.30/0.62      ! [B2: set_int,A2: set_int,G2: int > assn] :
% 0.30/0.62        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 0.30/0.62       => ( ( finite_finite_int @ A2 )
% 0.30/0.62         => ( ( groups7882442080178216443t_assn @ G2 @ A2 )
% 0.30/0.62            = ( times_times_assn @ ( groups7882442080178216443t_assn @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups7882442080178216443t_assn @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.subset_diff
% 0.30/0.62  thf(fact_8252_prod_Osubset__diff,axiom,
% 0.30/0.62      ! [B2: set_int,A2: set_int,G2: int > rat] :
% 0.30/0.62        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 0.30/0.62       => ( ( finite_finite_int @ A2 )
% 0.30/0.62         => ( ( groups1072433553688619179nt_rat @ G2 @ A2 )
% 0.30/0.62            = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups1072433553688619179nt_rat @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.subset_diff
% 0.30/0.62  thf(fact_8253_prod_Osubset__diff,axiom,
% 0.30/0.62      ! [B2: set_int,A2: set_int,G2: int > nat] :
% 0.30/0.62        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 0.30/0.62       => ( ( finite_finite_int @ A2 )
% 0.30/0.62         => ( ( groups1707563613775114915nt_nat @ G2 @ A2 )
% 0.30/0.62            = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups1707563613775114915nt_nat @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.subset_diff
% 0.30/0.62  thf(fact_8254_prod_Osubset__diff,axiom,
% 0.30/0.62      ! [B2: set_nat,A2: set_nat,G2: nat > code_integer] :
% 0.30/0.62        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.30/0.62       => ( ( finite_finite_nat @ A2 )
% 0.30/0.62         => ( ( groups3455450783089532116nteger @ G2 @ A2 )
% 0.30/0.62            = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups3455450783089532116nteger @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.subset_diff
% 0.30/0.62  thf(fact_8255_prod_Osubset__diff,axiom,
% 0.30/0.62      ! [B2: set_nat,A2: set_nat,G2: nat > assn] :
% 0.30/0.62        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.30/0.62       => ( ( finite_finite_nat @ A2 )
% 0.30/0.62         => ( ( groups6906906614972039071t_assn @ G2 @ A2 )
% 0.30/0.62            = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups6906906614972039071t_assn @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.subset_diff
% 0.30/0.62  thf(fact_8256_prod_Osubset__diff,axiom,
% 0.30/0.62      ! [B2: set_nat,A2: set_nat,G2: nat > rat] :
% 0.30/0.62        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.30/0.62       => ( ( finite_finite_nat @ A2 )
% 0.30/0.62         => ( ( groups73079841787564623at_rat @ G2 @ A2 )
% 0.30/0.62            = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups73079841787564623at_rat @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.subset_diff
% 0.30/0.62  thf(fact_8257_prod_Osubset__diff,axiom,
% 0.30/0.62      ! [B2: set_nat,A2: set_nat,G2: nat > nat] :
% 0.30/0.62        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.30/0.62       => ( ( finite_finite_nat @ A2 )
% 0.30/0.62         => ( ( groups708209901874060359at_nat @ G2 @ A2 )
% 0.30/0.62            = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups708209901874060359at_nat @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.subset_diff
% 0.30/0.62  thf(fact_8258_prod_Osubset__diff,axiom,
% 0.30/0.62      ! [B2: set_nat,A2: set_nat,G2: nat > int] :
% 0.30/0.62        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 0.30/0.62       => ( ( finite_finite_nat @ A2 )
% 0.30/0.62         => ( ( groups705719431365010083at_int @ G2 @ A2 )
% 0.30/0.62            = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups705719431365010083at_int @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.subset_diff
% 0.30/0.62  thf(fact_8259_prod_Osubset__diff,axiom,
% 0.30/0.62      ! [B2: set_int,A2: set_int,G2: int > int] :
% 0.30/0.62        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 0.30/0.62       => ( ( finite_finite_int @ A2 )
% 0.30/0.62         => ( ( groups1705073143266064639nt_int @ G2 @ A2 )
% 0.30/0.62            = ( times_times_int @ ( groups1705073143266064639nt_int @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups1705073143266064639nt_int @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.subset_diff
% 0.30/0.62  thf(fact_8260_prod_Omono__neutral__cong__right,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,G2: int > code_integer,H3: int > code_integer] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ S @ T )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_Code_integer ) )
% 0.30/0.62           => ( ! [X2: int] :
% 0.30/0.62                  ( ( member_int @ X2 @ S )
% 0.30/0.62                 => ( ( G2 @ X2 )
% 0.30/0.62                    = ( H3 @ X2 ) ) )
% 0.30/0.62             => ( ( groups3827104343326376752nteger @ G2 @ T )
% 0.30/0.62                = ( groups3827104343326376752nteger @ H3 @ S ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_cong_right
% 0.30/0.62  thf(fact_8261_prod_Omono__neutral__cong__right,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,G2: int > assn,H3: int > assn] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ S @ T )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_assn ) )
% 0.30/0.62           => ( ! [X2: int] :
% 0.30/0.62                  ( ( member_int @ X2 @ S )
% 0.30/0.62                 => ( ( G2 @ X2 )
% 0.30/0.62                    = ( H3 @ X2 ) ) )
% 0.30/0.62             => ( ( groups7882442080178216443t_assn @ G2 @ T )
% 0.30/0.62                = ( groups7882442080178216443t_assn @ H3 @ S ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_cong_right
% 0.30/0.62  thf(fact_8262_prod_Omono__neutral__cong__right,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,G2: int > rat,H3: int > rat] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ S @ T )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_rat ) )
% 0.30/0.62           => ( ! [X2: int] :
% 0.30/0.62                  ( ( member_int @ X2 @ S )
% 0.30/0.62                 => ( ( G2 @ X2 )
% 0.30/0.62                    = ( H3 @ X2 ) ) )
% 0.30/0.62             => ( ( groups1072433553688619179nt_rat @ G2 @ T )
% 0.30/0.62                = ( groups1072433553688619179nt_rat @ H3 @ S ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_cong_right
% 0.30/0.62  thf(fact_8263_prod_Omono__neutral__cong__right,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,G2: int > nat,H3: int > nat] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ S @ T )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_nat ) )
% 0.30/0.62           => ( ! [X2: int] :
% 0.30/0.62                  ( ( member_int @ X2 @ S )
% 0.30/0.62                 => ( ( G2 @ X2 )
% 0.30/0.62                    = ( H3 @ X2 ) ) )
% 0.30/0.62             => ( ( groups1707563613775114915nt_nat @ G2 @ T )
% 0.30/0.62                = ( groups1707563613775114915nt_nat @ H3 @ S ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_cong_right
% 0.30/0.62  thf(fact_8264_prod_Omono__neutral__cong__right,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,G2: nat > code_integer,H3: nat > code_integer] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ S @ T )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_Code_integer ) )
% 0.30/0.62           => ( ! [X2: nat] :
% 0.30/0.62                  ( ( member_nat @ X2 @ S )
% 0.30/0.62                 => ( ( G2 @ X2 )
% 0.30/0.62                    = ( H3 @ X2 ) ) )
% 0.30/0.62             => ( ( groups3455450783089532116nteger @ G2 @ T )
% 0.30/0.62                = ( groups3455450783089532116nteger @ H3 @ S ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_cong_right
% 0.30/0.62  thf(fact_8265_prod_Omono__neutral__cong__right,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,G2: nat > assn,H3: nat > assn] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ S @ T )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_assn ) )
% 0.30/0.62           => ( ! [X2: nat] :
% 0.30/0.62                  ( ( member_nat @ X2 @ S )
% 0.30/0.62                 => ( ( G2 @ X2 )
% 0.30/0.62                    = ( H3 @ X2 ) ) )
% 0.30/0.62             => ( ( groups6906906614972039071t_assn @ G2 @ T )
% 0.30/0.62                = ( groups6906906614972039071t_assn @ H3 @ S ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_cong_right
% 0.30/0.62  thf(fact_8266_prod_Omono__neutral__cong__right,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,G2: nat > rat,H3: nat > rat] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ S @ T )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_rat ) )
% 0.30/0.62           => ( ! [X2: nat] :
% 0.30/0.62                  ( ( member_nat @ X2 @ S )
% 0.30/0.62                 => ( ( G2 @ X2 )
% 0.30/0.62                    = ( H3 @ X2 ) ) )
% 0.30/0.62             => ( ( groups73079841787564623at_rat @ G2 @ T )
% 0.30/0.62                = ( groups73079841787564623at_rat @ H3 @ S ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_cong_right
% 0.30/0.62  thf(fact_8267_prod_Omono__neutral__cong__right,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,G2: nat > nat,H3: nat > nat] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ S @ T )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_nat ) )
% 0.30/0.62           => ( ! [X2: nat] :
% 0.30/0.62                  ( ( member_nat @ X2 @ S )
% 0.30/0.62                 => ( ( G2 @ X2 )
% 0.30/0.62                    = ( H3 @ X2 ) ) )
% 0.30/0.62             => ( ( groups708209901874060359at_nat @ G2 @ T )
% 0.30/0.62                = ( groups708209901874060359at_nat @ H3 @ S ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_cong_right
% 0.30/0.62  thf(fact_8268_prod_Omono__neutral__cong__right,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,G2: nat > int,H3: nat > int] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ S @ T )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_int ) )
% 0.30/0.62           => ( ! [X2: nat] :
% 0.30/0.62                  ( ( member_nat @ X2 @ S )
% 0.30/0.62                 => ( ( G2 @ X2 )
% 0.30/0.62                    = ( H3 @ X2 ) ) )
% 0.30/0.62             => ( ( groups705719431365010083at_int @ G2 @ T )
% 0.30/0.62                = ( groups705719431365010083at_int @ H3 @ S ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_cong_right
% 0.30/0.62  thf(fact_8269_prod_Omono__neutral__cong__right,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,G2: int > int,H3: int > int] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ S @ T )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_int ) )
% 0.30/0.62           => ( ! [X2: int] :
% 0.30/0.62                  ( ( member_int @ X2 @ S )
% 0.30/0.62                 => ( ( G2 @ X2 )
% 0.30/0.62                    = ( H3 @ X2 ) ) )
% 0.30/0.62             => ( ( groups1705073143266064639nt_int @ G2 @ T )
% 0.30/0.62                = ( groups1705073143266064639nt_int @ H3 @ S ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_cong_right
% 0.30/0.62  thf(fact_8270_prod_Omono__neutral__cong__left,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,H3: int > code_integer,G2: int > code_integer] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ S @ T )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( H3 @ X2 )
% 0.30/0.62                  = one_one_Code_integer ) )
% 0.30/0.62           => ( ! [X2: int] :
% 0.30/0.62                  ( ( member_int @ X2 @ S )
% 0.30/0.62                 => ( ( G2 @ X2 )
% 0.30/0.62                    = ( H3 @ X2 ) ) )
% 0.30/0.62             => ( ( groups3827104343326376752nteger @ G2 @ S )
% 0.30/0.62                = ( groups3827104343326376752nteger @ H3 @ T ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_cong_left
% 0.30/0.62  thf(fact_8271_prod_Omono__neutral__cong__left,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,H3: int > assn,G2: int > assn] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ S @ T )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( H3 @ X2 )
% 0.30/0.62                  = one_one_assn ) )
% 0.30/0.62           => ( ! [X2: int] :
% 0.30/0.62                  ( ( member_int @ X2 @ S )
% 0.30/0.62                 => ( ( G2 @ X2 )
% 0.30/0.62                    = ( H3 @ X2 ) ) )
% 0.30/0.62             => ( ( groups7882442080178216443t_assn @ G2 @ S )
% 0.30/0.62                = ( groups7882442080178216443t_assn @ H3 @ T ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_cong_left
% 0.30/0.62  thf(fact_8272_prod_Omono__neutral__cong__left,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,H3: int > rat,G2: int > rat] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ S @ T )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( H3 @ X2 )
% 0.30/0.62                  = one_one_rat ) )
% 0.30/0.62           => ( ! [X2: int] :
% 0.30/0.62                  ( ( member_int @ X2 @ S )
% 0.30/0.62                 => ( ( G2 @ X2 )
% 0.30/0.62                    = ( H3 @ X2 ) ) )
% 0.30/0.62             => ( ( groups1072433553688619179nt_rat @ G2 @ S )
% 0.30/0.62                = ( groups1072433553688619179nt_rat @ H3 @ T ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_cong_left
% 0.30/0.62  thf(fact_8273_prod_Omono__neutral__cong__left,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,H3: int > nat,G2: int > nat] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ S @ T )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( H3 @ X2 )
% 0.30/0.62                  = one_one_nat ) )
% 0.30/0.62           => ( ! [X2: int] :
% 0.30/0.62                  ( ( member_int @ X2 @ S )
% 0.30/0.62                 => ( ( G2 @ X2 )
% 0.30/0.62                    = ( H3 @ X2 ) ) )
% 0.30/0.62             => ( ( groups1707563613775114915nt_nat @ G2 @ S )
% 0.30/0.62                = ( groups1707563613775114915nt_nat @ H3 @ T ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_cong_left
% 0.30/0.62  thf(fact_8274_prod_Omono__neutral__cong__left,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,H3: nat > code_integer,G2: nat > code_integer] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ S @ T )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( H3 @ X2 )
% 0.30/0.62                  = one_one_Code_integer ) )
% 0.30/0.62           => ( ! [X2: nat] :
% 0.30/0.62                  ( ( member_nat @ X2 @ S )
% 0.30/0.62                 => ( ( G2 @ X2 )
% 0.30/0.62                    = ( H3 @ X2 ) ) )
% 0.30/0.62             => ( ( groups3455450783089532116nteger @ G2 @ S )
% 0.30/0.62                = ( groups3455450783089532116nteger @ H3 @ T ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_cong_left
% 0.30/0.62  thf(fact_8275_prod_Omono__neutral__cong__left,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,H3: nat > assn,G2: nat > assn] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ S @ T )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( H3 @ X2 )
% 0.30/0.62                  = one_one_assn ) )
% 0.30/0.62           => ( ! [X2: nat] :
% 0.30/0.62                  ( ( member_nat @ X2 @ S )
% 0.30/0.62                 => ( ( G2 @ X2 )
% 0.30/0.62                    = ( H3 @ X2 ) ) )
% 0.30/0.62             => ( ( groups6906906614972039071t_assn @ G2 @ S )
% 0.30/0.62                = ( groups6906906614972039071t_assn @ H3 @ T ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_cong_left
% 0.30/0.62  thf(fact_8276_prod_Omono__neutral__cong__left,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,H3: nat > rat,G2: nat > rat] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ S @ T )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( H3 @ X2 )
% 0.30/0.62                  = one_one_rat ) )
% 0.30/0.62           => ( ! [X2: nat] :
% 0.30/0.62                  ( ( member_nat @ X2 @ S )
% 0.30/0.62                 => ( ( G2 @ X2 )
% 0.30/0.62                    = ( H3 @ X2 ) ) )
% 0.30/0.62             => ( ( groups73079841787564623at_rat @ G2 @ S )
% 0.30/0.62                = ( groups73079841787564623at_rat @ H3 @ T ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_cong_left
% 0.30/0.62  thf(fact_8277_prod_Omono__neutral__cong__left,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,H3: nat > nat,G2: nat > nat] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ S @ T )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( H3 @ X2 )
% 0.30/0.62                  = one_one_nat ) )
% 0.30/0.62           => ( ! [X2: nat] :
% 0.30/0.62                  ( ( member_nat @ X2 @ S )
% 0.30/0.62                 => ( ( G2 @ X2 )
% 0.30/0.62                    = ( H3 @ X2 ) ) )
% 0.30/0.62             => ( ( groups708209901874060359at_nat @ G2 @ S )
% 0.30/0.62                = ( groups708209901874060359at_nat @ H3 @ T ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_cong_left
% 0.30/0.62  thf(fact_8278_prod_Omono__neutral__cong__left,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,H3: nat > int,G2: nat > int] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ S @ T )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( H3 @ X2 )
% 0.30/0.62                  = one_one_int ) )
% 0.30/0.62           => ( ! [X2: nat] :
% 0.30/0.62                  ( ( member_nat @ X2 @ S )
% 0.30/0.62                 => ( ( G2 @ X2 )
% 0.30/0.62                    = ( H3 @ X2 ) ) )
% 0.30/0.62             => ( ( groups705719431365010083at_int @ G2 @ S )
% 0.30/0.62                = ( groups705719431365010083at_int @ H3 @ T ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_cong_left
% 0.30/0.62  thf(fact_8279_prod_Omono__neutral__cong__left,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,H3: int > int,G2: int > int] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ S @ T )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( H3 @ X2 )
% 0.30/0.62                  = one_one_int ) )
% 0.30/0.62           => ( ! [X2: int] :
% 0.30/0.62                  ( ( member_int @ X2 @ S )
% 0.30/0.62                 => ( ( G2 @ X2 )
% 0.30/0.62                    = ( H3 @ X2 ) ) )
% 0.30/0.62             => ( ( groups1705073143266064639nt_int @ G2 @ S )
% 0.30/0.62                = ( groups1705073143266064639nt_int @ H3 @ T ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_cong_left
% 0.30/0.62  thf(fact_8280_prod_Omono__neutral__right,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,G2: int > code_integer] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ S @ T )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_Code_integer ) )
% 0.30/0.62           => ( ( groups3827104343326376752nteger @ G2 @ T )
% 0.30/0.62              = ( groups3827104343326376752nteger @ G2 @ S ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_right
% 0.30/0.62  thf(fact_8281_prod_Omono__neutral__right,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,G2: int > assn] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ S @ T )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_assn ) )
% 0.30/0.62           => ( ( groups7882442080178216443t_assn @ G2 @ T )
% 0.30/0.62              = ( groups7882442080178216443t_assn @ G2 @ S ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_right
% 0.30/0.62  thf(fact_8282_prod_Omono__neutral__right,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,G2: int > rat] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ S @ T )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_rat ) )
% 0.30/0.62           => ( ( groups1072433553688619179nt_rat @ G2 @ T )
% 0.30/0.62              = ( groups1072433553688619179nt_rat @ G2 @ S ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_right
% 0.30/0.62  thf(fact_8283_prod_Omono__neutral__right,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,G2: int > nat] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ S @ T )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_nat ) )
% 0.30/0.62           => ( ( groups1707563613775114915nt_nat @ G2 @ T )
% 0.30/0.62              = ( groups1707563613775114915nt_nat @ G2 @ S ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_right
% 0.30/0.62  thf(fact_8284_prod_Omono__neutral__right,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,G2: nat > code_integer] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ S @ T )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_Code_integer ) )
% 0.30/0.62           => ( ( groups3455450783089532116nteger @ G2 @ T )
% 0.30/0.62              = ( groups3455450783089532116nteger @ G2 @ S ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_right
% 0.30/0.62  thf(fact_8285_prod_Omono__neutral__right,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,G2: nat > assn] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ S @ T )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_assn ) )
% 0.30/0.62           => ( ( groups6906906614972039071t_assn @ G2 @ T )
% 0.30/0.62              = ( groups6906906614972039071t_assn @ G2 @ S ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_right
% 0.30/0.62  thf(fact_8286_prod_Omono__neutral__right,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,G2: nat > rat] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ S @ T )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_rat ) )
% 0.30/0.62           => ( ( groups73079841787564623at_rat @ G2 @ T )
% 0.30/0.62              = ( groups73079841787564623at_rat @ G2 @ S ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_right
% 0.30/0.62  thf(fact_8287_prod_Omono__neutral__right,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,G2: nat > nat] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ S @ T )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_nat ) )
% 0.30/0.62           => ( ( groups708209901874060359at_nat @ G2 @ T )
% 0.30/0.62              = ( groups708209901874060359at_nat @ G2 @ S ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_right
% 0.30/0.62  thf(fact_8288_prod_Omono__neutral__right,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,G2: nat > int] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ S @ T )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_int ) )
% 0.30/0.62           => ( ( groups705719431365010083at_int @ G2 @ T )
% 0.30/0.62              = ( groups705719431365010083at_int @ G2 @ S ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_right
% 0.30/0.62  thf(fact_8289_prod_Omono__neutral__right,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,G2: int > int] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ S @ T )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_int ) )
% 0.30/0.62           => ( ( groups1705073143266064639nt_int @ G2 @ T )
% 0.30/0.62              = ( groups1705073143266064639nt_int @ G2 @ S ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_right
% 0.30/0.62  thf(fact_8290_prod_Omono__neutral__left,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,G2: int > code_integer] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ S @ T )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_Code_integer ) )
% 0.30/0.62           => ( ( groups3827104343326376752nteger @ G2 @ S )
% 0.30/0.62              = ( groups3827104343326376752nteger @ G2 @ T ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_left
% 0.30/0.62  thf(fact_8291_prod_Omono__neutral__left,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,G2: int > assn] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ S @ T )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_assn ) )
% 0.30/0.62           => ( ( groups7882442080178216443t_assn @ G2 @ S )
% 0.30/0.62              = ( groups7882442080178216443t_assn @ G2 @ T ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_left
% 0.30/0.62  thf(fact_8292_prod_Omono__neutral__left,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,G2: int > rat] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ S @ T )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_rat ) )
% 0.30/0.62           => ( ( groups1072433553688619179nt_rat @ G2 @ S )
% 0.30/0.62              = ( groups1072433553688619179nt_rat @ G2 @ T ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_left
% 0.30/0.62  thf(fact_8293_prod_Omono__neutral__left,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,G2: int > nat] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ S @ T )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_nat ) )
% 0.30/0.62           => ( ( groups1707563613775114915nt_nat @ G2 @ S )
% 0.30/0.62              = ( groups1707563613775114915nt_nat @ G2 @ T ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_left
% 0.30/0.62  thf(fact_8294_prod_Omono__neutral__left,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,G2: nat > code_integer] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ S @ T )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_Code_integer ) )
% 0.30/0.62           => ( ( groups3455450783089532116nteger @ G2 @ S )
% 0.30/0.62              = ( groups3455450783089532116nteger @ G2 @ T ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_left
% 0.30/0.62  thf(fact_8295_prod_Omono__neutral__left,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,G2: nat > assn] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ S @ T )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_assn ) )
% 0.30/0.62           => ( ( groups6906906614972039071t_assn @ G2 @ S )
% 0.30/0.62              = ( groups6906906614972039071t_assn @ G2 @ T ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_left
% 0.30/0.62  thf(fact_8296_prod_Omono__neutral__left,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,G2: nat > rat] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ S @ T )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_rat ) )
% 0.30/0.62           => ( ( groups73079841787564623at_rat @ G2 @ S )
% 0.30/0.62              = ( groups73079841787564623at_rat @ G2 @ T ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_left
% 0.30/0.62  thf(fact_8297_prod_Omono__neutral__left,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,G2: nat > nat] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ S @ T )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_nat ) )
% 0.30/0.62           => ( ( groups708209901874060359at_nat @ G2 @ S )
% 0.30/0.62              = ( groups708209901874060359at_nat @ G2 @ T ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_left
% 0.30/0.62  thf(fact_8298_prod_Omono__neutral__left,axiom,
% 0.30/0.62      ! [T: set_nat,S: set_nat,G2: nat > int] :
% 0.30/0.62        ( ( finite_finite_nat @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ S @ T )
% 0.30/0.62         => ( ! [X2: nat] :
% 0.30/0.62                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_int ) )
% 0.30/0.62           => ( ( groups705719431365010083at_int @ G2 @ S )
% 0.30/0.62              = ( groups705719431365010083at_int @ G2 @ T ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_left
% 0.30/0.62  thf(fact_8299_prod_Omono__neutral__left,axiom,
% 0.30/0.62      ! [T: set_int,S: set_int,G2: int > int] :
% 0.30/0.62        ( ( finite_finite_int @ T )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ S @ T )
% 0.30/0.62         => ( ! [X2: int] :
% 0.30/0.62                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.62               => ( ( G2 @ X2 )
% 0.30/0.62                  = one_one_int ) )
% 0.30/0.62           => ( ( groups1705073143266064639nt_int @ G2 @ S )
% 0.30/0.62              = ( groups1705073143266064639nt_int @ G2 @ T ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.mono_neutral_left
% 0.30/0.62  thf(fact_8300_prod_Osame__carrierI,axiom,
% 0.30/0.62      ! [C2: set_int,A2: set_int,B2: set_int,G2: int > code_integer,H3: int > code_integer] :
% 0.30/0.62        ( ( finite_finite_int @ C2 )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ A2 @ C2 )
% 0.30/0.62         => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 0.30/0.62           => ( ! [A6: int] :
% 0.30/0.62                  ( ( member_int @ A6 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 0.30/0.62                 => ( ( G2 @ A6 )
% 0.30/0.62                    = one_one_Code_integer ) )
% 0.30/0.62             => ( ! [B6: int] :
% 0.30/0.62                    ( ( member_int @ B6 @ ( minus_minus_set_int @ C2 @ B2 ) )
% 0.30/0.62                   => ( ( H3 @ B6 )
% 0.30/0.62                      = one_one_Code_integer ) )
% 0.30/0.62               => ( ( ( groups3827104343326376752nteger @ G2 @ C2 )
% 0.30/0.62                    = ( groups3827104343326376752nteger @ H3 @ C2 ) )
% 0.30/0.62                 => ( ( groups3827104343326376752nteger @ G2 @ A2 )
% 0.30/0.62                    = ( groups3827104343326376752nteger @ H3 @ B2 ) ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.same_carrierI
% 0.30/0.62  thf(fact_8301_prod_Osame__carrierI,axiom,
% 0.30/0.62      ! [C2: set_int,A2: set_int,B2: set_int,G2: int > assn,H3: int > assn] :
% 0.30/0.62        ( ( finite_finite_int @ C2 )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ A2 @ C2 )
% 0.30/0.62         => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 0.30/0.62           => ( ! [A6: int] :
% 0.30/0.62                  ( ( member_int @ A6 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 0.30/0.62                 => ( ( G2 @ A6 )
% 0.30/0.62                    = one_one_assn ) )
% 0.30/0.62             => ( ! [B6: int] :
% 0.30/0.62                    ( ( member_int @ B6 @ ( minus_minus_set_int @ C2 @ B2 ) )
% 0.30/0.62                   => ( ( H3 @ B6 )
% 0.30/0.62                      = one_one_assn ) )
% 0.30/0.62               => ( ( ( groups7882442080178216443t_assn @ G2 @ C2 )
% 0.30/0.62                    = ( groups7882442080178216443t_assn @ H3 @ C2 ) )
% 0.30/0.62                 => ( ( groups7882442080178216443t_assn @ G2 @ A2 )
% 0.30/0.62                    = ( groups7882442080178216443t_assn @ H3 @ B2 ) ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.same_carrierI
% 0.30/0.62  thf(fact_8302_prod_Osame__carrierI,axiom,
% 0.30/0.62      ! [C2: set_int,A2: set_int,B2: set_int,G2: int > rat,H3: int > rat] :
% 0.30/0.62        ( ( finite_finite_int @ C2 )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ A2 @ C2 )
% 0.30/0.62         => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 0.30/0.62           => ( ! [A6: int] :
% 0.30/0.62                  ( ( member_int @ A6 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 0.30/0.62                 => ( ( G2 @ A6 )
% 0.30/0.62                    = one_one_rat ) )
% 0.30/0.62             => ( ! [B6: int] :
% 0.30/0.62                    ( ( member_int @ B6 @ ( minus_minus_set_int @ C2 @ B2 ) )
% 0.30/0.62                   => ( ( H3 @ B6 )
% 0.30/0.62                      = one_one_rat ) )
% 0.30/0.62               => ( ( ( groups1072433553688619179nt_rat @ G2 @ C2 )
% 0.30/0.62                    = ( groups1072433553688619179nt_rat @ H3 @ C2 ) )
% 0.30/0.62                 => ( ( groups1072433553688619179nt_rat @ G2 @ A2 )
% 0.30/0.62                    = ( groups1072433553688619179nt_rat @ H3 @ B2 ) ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.same_carrierI
% 0.30/0.62  thf(fact_8303_prod_Osame__carrierI,axiom,
% 0.30/0.62      ! [C2: set_int,A2: set_int,B2: set_int,G2: int > nat,H3: int > nat] :
% 0.30/0.62        ( ( finite_finite_int @ C2 )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ A2 @ C2 )
% 0.30/0.62         => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 0.30/0.62           => ( ! [A6: int] :
% 0.30/0.62                  ( ( member_int @ A6 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 0.30/0.62                 => ( ( G2 @ A6 )
% 0.30/0.62                    = one_one_nat ) )
% 0.30/0.62             => ( ! [B6: int] :
% 0.30/0.62                    ( ( member_int @ B6 @ ( minus_minus_set_int @ C2 @ B2 ) )
% 0.30/0.62                   => ( ( H3 @ B6 )
% 0.30/0.62                      = one_one_nat ) )
% 0.30/0.62               => ( ( ( groups1707563613775114915nt_nat @ G2 @ C2 )
% 0.30/0.62                    = ( groups1707563613775114915nt_nat @ H3 @ C2 ) )
% 0.30/0.62                 => ( ( groups1707563613775114915nt_nat @ G2 @ A2 )
% 0.30/0.62                    = ( groups1707563613775114915nt_nat @ H3 @ B2 ) ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.same_carrierI
% 0.30/0.62  thf(fact_8304_prod_Osame__carrierI,axiom,
% 0.30/0.62      ! [C2: set_nat,A2: set_nat,B2: set_nat,G2: nat > code_integer,H3: nat > code_integer] :
% 0.30/0.62        ( ( finite_finite_nat @ C2 )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 0.30/0.62         => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 0.30/0.62           => ( ! [A6: nat] :
% 0.30/0.62                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 0.30/0.62                 => ( ( G2 @ A6 )
% 0.30/0.62                    = one_one_Code_integer ) )
% 0.30/0.62             => ( ! [B6: nat] :
% 0.30/0.62                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ C2 @ B2 ) )
% 0.30/0.62                   => ( ( H3 @ B6 )
% 0.30/0.62                      = one_one_Code_integer ) )
% 0.30/0.62               => ( ( ( groups3455450783089532116nteger @ G2 @ C2 )
% 0.30/0.62                    = ( groups3455450783089532116nteger @ H3 @ C2 ) )
% 0.30/0.62                 => ( ( groups3455450783089532116nteger @ G2 @ A2 )
% 0.30/0.62                    = ( groups3455450783089532116nteger @ H3 @ B2 ) ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.same_carrierI
% 0.30/0.62  thf(fact_8305_prod_Osame__carrierI,axiom,
% 0.30/0.62      ! [C2: set_nat,A2: set_nat,B2: set_nat,G2: nat > assn,H3: nat > assn] :
% 0.30/0.62        ( ( finite_finite_nat @ C2 )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 0.30/0.62         => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 0.30/0.62           => ( ! [A6: nat] :
% 0.30/0.62                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 0.30/0.62                 => ( ( G2 @ A6 )
% 0.30/0.62                    = one_one_assn ) )
% 0.30/0.62             => ( ! [B6: nat] :
% 0.30/0.62                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ C2 @ B2 ) )
% 0.30/0.62                   => ( ( H3 @ B6 )
% 0.30/0.62                      = one_one_assn ) )
% 0.30/0.62               => ( ( ( groups6906906614972039071t_assn @ G2 @ C2 )
% 0.30/0.62                    = ( groups6906906614972039071t_assn @ H3 @ C2 ) )
% 0.30/0.62                 => ( ( groups6906906614972039071t_assn @ G2 @ A2 )
% 0.30/0.62                    = ( groups6906906614972039071t_assn @ H3 @ B2 ) ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.same_carrierI
% 0.30/0.62  thf(fact_8306_prod_Osame__carrierI,axiom,
% 0.30/0.62      ! [C2: set_nat,A2: set_nat,B2: set_nat,G2: nat > rat,H3: nat > rat] :
% 0.30/0.62        ( ( finite_finite_nat @ C2 )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 0.30/0.62         => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 0.30/0.62           => ( ! [A6: nat] :
% 0.30/0.62                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 0.30/0.62                 => ( ( G2 @ A6 )
% 0.30/0.62                    = one_one_rat ) )
% 0.30/0.62             => ( ! [B6: nat] :
% 0.30/0.62                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ C2 @ B2 ) )
% 0.30/0.62                   => ( ( H3 @ B6 )
% 0.30/0.62                      = one_one_rat ) )
% 0.30/0.62               => ( ( ( groups73079841787564623at_rat @ G2 @ C2 )
% 0.30/0.62                    = ( groups73079841787564623at_rat @ H3 @ C2 ) )
% 0.30/0.62                 => ( ( groups73079841787564623at_rat @ G2 @ A2 )
% 0.30/0.62                    = ( groups73079841787564623at_rat @ H3 @ B2 ) ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.same_carrierI
% 0.30/0.62  thf(fact_8307_prod_Osame__carrierI,axiom,
% 0.30/0.62      ! [C2: set_nat,A2: set_nat,B2: set_nat,G2: nat > nat,H3: nat > nat] :
% 0.30/0.62        ( ( finite_finite_nat @ C2 )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 0.30/0.62         => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 0.30/0.62           => ( ! [A6: nat] :
% 0.30/0.62                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 0.30/0.62                 => ( ( G2 @ A6 )
% 0.30/0.62                    = one_one_nat ) )
% 0.30/0.62             => ( ! [B6: nat] :
% 0.30/0.62                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ C2 @ B2 ) )
% 0.30/0.62                   => ( ( H3 @ B6 )
% 0.30/0.62                      = one_one_nat ) )
% 0.30/0.62               => ( ( ( groups708209901874060359at_nat @ G2 @ C2 )
% 0.30/0.62                    = ( groups708209901874060359at_nat @ H3 @ C2 ) )
% 0.30/0.62                 => ( ( groups708209901874060359at_nat @ G2 @ A2 )
% 0.30/0.62                    = ( groups708209901874060359at_nat @ H3 @ B2 ) ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.same_carrierI
% 0.30/0.62  thf(fact_8308_prod_Osame__carrierI,axiom,
% 0.30/0.62      ! [C2: set_nat,A2: set_nat,B2: set_nat,G2: nat > int,H3: nat > int] :
% 0.30/0.62        ( ( finite_finite_nat @ C2 )
% 0.30/0.62       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 0.30/0.62         => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 0.30/0.62           => ( ! [A6: nat] :
% 0.30/0.62                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 0.30/0.62                 => ( ( G2 @ A6 )
% 0.30/0.62                    = one_one_int ) )
% 0.30/0.62             => ( ! [B6: nat] :
% 0.30/0.62                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ C2 @ B2 ) )
% 0.30/0.62                   => ( ( H3 @ B6 )
% 0.30/0.62                      = one_one_int ) )
% 0.30/0.62               => ( ( ( groups705719431365010083at_int @ G2 @ C2 )
% 0.30/0.62                    = ( groups705719431365010083at_int @ H3 @ C2 ) )
% 0.30/0.62                 => ( ( groups705719431365010083at_int @ G2 @ A2 )
% 0.30/0.62                    = ( groups705719431365010083at_int @ H3 @ B2 ) ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.same_carrierI
% 0.30/0.62  thf(fact_8309_prod_Osame__carrierI,axiom,
% 0.30/0.62      ! [C2: set_int,A2: set_int,B2: set_int,G2: int > int,H3: int > int] :
% 0.30/0.62        ( ( finite_finite_int @ C2 )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ A2 @ C2 )
% 0.30/0.62         => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 0.30/0.62           => ( ! [A6: int] :
% 0.30/0.62                  ( ( member_int @ A6 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 0.30/0.62                 => ( ( G2 @ A6 )
% 0.30/0.62                    = one_one_int ) )
% 0.30/0.62             => ( ! [B6: int] :
% 0.30/0.62                    ( ( member_int @ B6 @ ( minus_minus_set_int @ C2 @ B2 ) )
% 0.30/0.62                   => ( ( H3 @ B6 )
% 0.30/0.62                      = one_one_int ) )
% 0.30/0.62               => ( ( ( groups1705073143266064639nt_int @ G2 @ C2 )
% 0.30/0.62                    = ( groups1705073143266064639nt_int @ H3 @ C2 ) )
% 0.30/0.62                 => ( ( groups1705073143266064639nt_int @ G2 @ A2 )
% 0.30/0.62                    = ( groups1705073143266064639nt_int @ H3 @ B2 ) ) ) ) ) ) ) ) ).
% 0.30/0.62  
% 0.30/0.62  % prod.same_carrierI
% 0.30/0.62  thf(fact_8310_prod_Osame__carrier,axiom,
% 0.30/0.62      ! [C2: set_int,A2: set_int,B2: set_int,G2: int > code_integer,H3: int > code_integer] :
% 0.30/0.62        ( ( finite_finite_int @ C2 )
% 0.30/0.62       => ( ( ord_less_eq_set_int @ A2 @ C2 )
% 0.30/0.62         => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 0.30/0.63           => ( ! [A6: int] :
% 0.30/0.63                  ( ( member_int @ A6 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 0.30/0.63                 => ( ( G2 @ A6 )
% 0.30/0.63                    = one_one_Code_integer ) )
% 0.30/0.63             => ( ! [B6: int] :
% 0.30/0.63                    ( ( member_int @ B6 @ ( minus_minus_set_int @ C2 @ B2 ) )
% 0.30/0.63                   => ( ( H3 @ B6 )
% 0.30/0.63                      = one_one_Code_integer ) )
% 0.30/0.63               => ( ( ( groups3827104343326376752nteger @ G2 @ A2 )
% 0.30/0.63                    = ( groups3827104343326376752nteger @ H3 @ B2 ) )
% 0.30/0.63                  = ( ( groups3827104343326376752nteger @ G2 @ C2 )
% 0.30/0.63                    = ( groups3827104343326376752nteger @ H3 @ C2 ) ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.same_carrier
% 0.30/0.63  thf(fact_8311_prod_Osame__carrier,axiom,
% 0.30/0.63      ! [C2: set_int,A2: set_int,B2: set_int,G2: int > assn,H3: int > assn] :
% 0.30/0.63        ( ( finite_finite_int @ C2 )
% 0.30/0.63       => ( ( ord_less_eq_set_int @ A2 @ C2 )
% 0.30/0.63         => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 0.30/0.63           => ( ! [A6: int] :
% 0.30/0.63                  ( ( member_int @ A6 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 0.30/0.63                 => ( ( G2 @ A6 )
% 0.30/0.63                    = one_one_assn ) )
% 0.30/0.63             => ( ! [B6: int] :
% 0.30/0.63                    ( ( member_int @ B6 @ ( minus_minus_set_int @ C2 @ B2 ) )
% 0.30/0.63                   => ( ( H3 @ B6 )
% 0.30/0.63                      = one_one_assn ) )
% 0.30/0.63               => ( ( ( groups7882442080178216443t_assn @ G2 @ A2 )
% 0.30/0.63                    = ( groups7882442080178216443t_assn @ H3 @ B2 ) )
% 0.30/0.63                  = ( ( groups7882442080178216443t_assn @ G2 @ C2 )
% 0.30/0.63                    = ( groups7882442080178216443t_assn @ H3 @ C2 ) ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.same_carrier
% 0.30/0.63  thf(fact_8312_prod_Osame__carrier,axiom,
% 0.30/0.63      ! [C2: set_int,A2: set_int,B2: set_int,G2: int > rat,H3: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ C2 )
% 0.30/0.63       => ( ( ord_less_eq_set_int @ A2 @ C2 )
% 0.30/0.63         => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 0.30/0.63           => ( ! [A6: int] :
% 0.30/0.63                  ( ( member_int @ A6 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 0.30/0.63                 => ( ( G2 @ A6 )
% 0.30/0.63                    = one_one_rat ) )
% 0.30/0.63             => ( ! [B6: int] :
% 0.30/0.63                    ( ( member_int @ B6 @ ( minus_minus_set_int @ C2 @ B2 ) )
% 0.30/0.63                   => ( ( H3 @ B6 )
% 0.30/0.63                      = one_one_rat ) )
% 0.30/0.63               => ( ( ( groups1072433553688619179nt_rat @ G2 @ A2 )
% 0.30/0.63                    = ( groups1072433553688619179nt_rat @ H3 @ B2 ) )
% 0.30/0.63                  = ( ( groups1072433553688619179nt_rat @ G2 @ C2 )
% 0.30/0.63                    = ( groups1072433553688619179nt_rat @ H3 @ C2 ) ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.same_carrier
% 0.30/0.63  thf(fact_8313_prod_Osame__carrier,axiom,
% 0.30/0.63      ! [C2: set_int,A2: set_int,B2: set_int,G2: int > nat,H3: int > nat] :
% 0.30/0.63        ( ( finite_finite_int @ C2 )
% 0.30/0.63       => ( ( ord_less_eq_set_int @ A2 @ C2 )
% 0.30/0.63         => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 0.30/0.63           => ( ! [A6: int] :
% 0.30/0.63                  ( ( member_int @ A6 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 0.30/0.63                 => ( ( G2 @ A6 )
% 0.30/0.63                    = one_one_nat ) )
% 0.30/0.63             => ( ! [B6: int] :
% 0.30/0.63                    ( ( member_int @ B6 @ ( minus_minus_set_int @ C2 @ B2 ) )
% 0.30/0.63                   => ( ( H3 @ B6 )
% 0.30/0.63                      = one_one_nat ) )
% 0.30/0.63               => ( ( ( groups1707563613775114915nt_nat @ G2 @ A2 )
% 0.30/0.63                    = ( groups1707563613775114915nt_nat @ H3 @ B2 ) )
% 0.30/0.63                  = ( ( groups1707563613775114915nt_nat @ G2 @ C2 )
% 0.30/0.63                    = ( groups1707563613775114915nt_nat @ H3 @ C2 ) ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.same_carrier
% 0.30/0.63  thf(fact_8314_prod_Osame__carrier,axiom,
% 0.30/0.63      ! [C2: set_nat,A2: set_nat,B2: set_nat,G2: nat > code_integer,H3: nat > code_integer] :
% 0.30/0.63        ( ( finite_finite_nat @ C2 )
% 0.30/0.63       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 0.30/0.63         => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 0.30/0.63           => ( ! [A6: nat] :
% 0.30/0.63                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 0.30/0.63                 => ( ( G2 @ A6 )
% 0.30/0.63                    = one_one_Code_integer ) )
% 0.30/0.63             => ( ! [B6: nat] :
% 0.30/0.63                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ C2 @ B2 ) )
% 0.30/0.63                   => ( ( H3 @ B6 )
% 0.30/0.63                      = one_one_Code_integer ) )
% 0.30/0.63               => ( ( ( groups3455450783089532116nteger @ G2 @ A2 )
% 0.30/0.63                    = ( groups3455450783089532116nteger @ H3 @ B2 ) )
% 0.30/0.63                  = ( ( groups3455450783089532116nteger @ G2 @ C2 )
% 0.30/0.63                    = ( groups3455450783089532116nteger @ H3 @ C2 ) ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.same_carrier
% 0.30/0.63  thf(fact_8315_prod_Osame__carrier,axiom,
% 0.30/0.63      ! [C2: set_nat,A2: set_nat,B2: set_nat,G2: nat > assn,H3: nat > assn] :
% 0.30/0.63        ( ( finite_finite_nat @ C2 )
% 0.30/0.63       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 0.30/0.63         => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 0.30/0.63           => ( ! [A6: nat] :
% 0.30/0.63                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 0.30/0.63                 => ( ( G2 @ A6 )
% 0.30/0.63                    = one_one_assn ) )
% 0.30/0.63             => ( ! [B6: nat] :
% 0.30/0.63                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ C2 @ B2 ) )
% 0.30/0.63                   => ( ( H3 @ B6 )
% 0.30/0.63                      = one_one_assn ) )
% 0.30/0.63               => ( ( ( groups6906906614972039071t_assn @ G2 @ A2 )
% 0.30/0.63                    = ( groups6906906614972039071t_assn @ H3 @ B2 ) )
% 0.30/0.63                  = ( ( groups6906906614972039071t_assn @ G2 @ C2 )
% 0.30/0.63                    = ( groups6906906614972039071t_assn @ H3 @ C2 ) ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.same_carrier
% 0.30/0.63  thf(fact_8316_prod_Osame__carrier,axiom,
% 0.30/0.63      ! [C2: set_nat,A2: set_nat,B2: set_nat,G2: nat > rat,H3: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ C2 )
% 0.30/0.63       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 0.30/0.63         => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 0.30/0.63           => ( ! [A6: nat] :
% 0.30/0.63                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 0.30/0.63                 => ( ( G2 @ A6 )
% 0.30/0.63                    = one_one_rat ) )
% 0.30/0.63             => ( ! [B6: nat] :
% 0.30/0.63                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ C2 @ B2 ) )
% 0.30/0.63                   => ( ( H3 @ B6 )
% 0.30/0.63                      = one_one_rat ) )
% 0.30/0.63               => ( ( ( groups73079841787564623at_rat @ G2 @ A2 )
% 0.30/0.63                    = ( groups73079841787564623at_rat @ H3 @ B2 ) )
% 0.30/0.63                  = ( ( groups73079841787564623at_rat @ G2 @ C2 )
% 0.30/0.63                    = ( groups73079841787564623at_rat @ H3 @ C2 ) ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.same_carrier
% 0.30/0.63  thf(fact_8317_prod_Osame__carrier,axiom,
% 0.30/0.63      ! [C2: set_nat,A2: set_nat,B2: set_nat,G2: nat > nat,H3: nat > nat] :
% 0.30/0.63        ( ( finite_finite_nat @ C2 )
% 0.30/0.63       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 0.30/0.63         => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 0.30/0.63           => ( ! [A6: nat] :
% 0.30/0.63                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 0.30/0.63                 => ( ( G2 @ A6 )
% 0.30/0.63                    = one_one_nat ) )
% 0.30/0.63             => ( ! [B6: nat] :
% 0.30/0.63                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ C2 @ B2 ) )
% 0.30/0.63                   => ( ( H3 @ B6 )
% 0.30/0.63                      = one_one_nat ) )
% 0.30/0.63               => ( ( ( groups708209901874060359at_nat @ G2 @ A2 )
% 0.30/0.63                    = ( groups708209901874060359at_nat @ H3 @ B2 ) )
% 0.30/0.63                  = ( ( groups708209901874060359at_nat @ G2 @ C2 )
% 0.30/0.63                    = ( groups708209901874060359at_nat @ H3 @ C2 ) ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.same_carrier
% 0.30/0.63  thf(fact_8318_prod_Osame__carrier,axiom,
% 0.30/0.63      ! [C2: set_nat,A2: set_nat,B2: set_nat,G2: nat > int,H3: nat > int] :
% 0.30/0.63        ( ( finite_finite_nat @ C2 )
% 0.30/0.63       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 0.30/0.63         => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 0.30/0.63           => ( ! [A6: nat] :
% 0.30/0.63                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 0.30/0.63                 => ( ( G2 @ A6 )
% 0.30/0.63                    = one_one_int ) )
% 0.30/0.63             => ( ! [B6: nat] :
% 0.30/0.63                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ C2 @ B2 ) )
% 0.30/0.63                   => ( ( H3 @ B6 )
% 0.30/0.63                      = one_one_int ) )
% 0.30/0.63               => ( ( ( groups705719431365010083at_int @ G2 @ A2 )
% 0.30/0.63                    = ( groups705719431365010083at_int @ H3 @ B2 ) )
% 0.30/0.63                  = ( ( groups705719431365010083at_int @ G2 @ C2 )
% 0.30/0.63                    = ( groups705719431365010083at_int @ H3 @ C2 ) ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.same_carrier
% 0.30/0.63  thf(fact_8319_prod_Osame__carrier,axiom,
% 0.30/0.63      ! [C2: set_int,A2: set_int,B2: set_int,G2: int > int,H3: int > int] :
% 0.30/0.63        ( ( finite_finite_int @ C2 )
% 0.30/0.63       => ( ( ord_less_eq_set_int @ A2 @ C2 )
% 0.30/0.63         => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 0.30/0.63           => ( ! [A6: int] :
% 0.30/0.63                  ( ( member_int @ A6 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 0.30/0.63                 => ( ( G2 @ A6 )
% 0.30/0.63                    = one_one_int ) )
% 0.30/0.63             => ( ! [B6: int] :
% 0.30/0.63                    ( ( member_int @ B6 @ ( minus_minus_set_int @ C2 @ B2 ) )
% 0.30/0.63                   => ( ( H3 @ B6 )
% 0.30/0.63                      = one_one_int ) )
% 0.30/0.63               => ( ( ( groups1705073143266064639nt_int @ G2 @ A2 )
% 0.30/0.63                    = ( groups1705073143266064639nt_int @ H3 @ B2 ) )
% 0.30/0.63                  = ( ( groups1705073143266064639nt_int @ G2 @ C2 )
% 0.30/0.63                    = ( groups1705073143266064639nt_int @ H3 @ C2 ) ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.same_carrier
% 0.30/0.63  thf(fact_8320_sum_Ounion__inter,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) ) @ ( groups3906332499630173760nt_rat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) )
% 0.30/0.63            = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G2 @ A2 ) @ ( groups3906332499630173760nt_rat @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_inter
% 0.30/0.63  thf(fact_8321_sum_Ounion__inter,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > nat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) ) @ ( groups4541462559716669496nt_nat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) )
% 0.30/0.63            = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G2 @ A2 ) @ ( groups4541462559716669496nt_nat @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_inter
% 0.30/0.63  thf(fact_8322_sum_Ounion__inter,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ ( groups2906978787729119204at_rat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) )
% 0.30/0.63            = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ A2 ) @ ( groups2906978787729119204at_rat @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_inter
% 0.30/0.63  thf(fact_8323_sum_Ounion__inter,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > int] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ ( groups3539618377306564664at_int @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) )
% 0.30/0.63            = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ A2 ) @ ( groups3539618377306564664at_int @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_inter
% 0.30/0.63  thf(fact_8324_sum_Ounion__inter,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ ( groups3542108847815614940at_nat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) )
% 0.30/0.63            = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ A2 ) @ ( groups3542108847815614940at_nat @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_inter
% 0.30/0.63  thf(fact_8325_sum_Ounion__inter,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( plus_plus_int @ ( groups4538972089207619220nt_int @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) ) @ ( groups4538972089207619220nt_int @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) )
% 0.30/0.63            = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G2 @ A2 ) @ ( groups4538972089207619220nt_int @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_inter
% 0.30/0.63  thf(fact_8326_sum_Ounion__inter,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > rat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( finite6177210948735845034at_nat @ B2 )
% 0.30/0.63         => ( ( plus_plus_rat @ ( groups342789780944988191at_rat @ G2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) ) @ ( groups342789780944988191at_rat @ G2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) )
% 0.30/0.63            = ( plus_plus_rat @ ( groups342789780944988191at_rat @ G2 @ A2 ) @ ( groups342789780944988191at_rat @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_inter
% 0.30/0.63  thf(fact_8327_sum_Ounion__inter,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > nat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( finite6177210948735845034at_nat @ B2 )
% 0.30/0.63         => ( ( plus_plus_nat @ ( groups977919841031483927at_nat @ G2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) ) @ ( groups977919841031483927at_nat @ G2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) )
% 0.30/0.63            = ( plus_plus_nat @ ( groups977919841031483927at_nat @ G2 @ A2 ) @ ( groups977919841031483927at_nat @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_inter
% 0.30/0.63  thf(fact_8328_sum_Ounion__inter,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > int] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( finite6177210948735845034at_nat @ B2 )
% 0.30/0.63         => ( ( plus_plus_int @ ( groups975429370522433651at_int @ G2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) ) @ ( groups975429370522433651at_int @ G2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) )
% 0.30/0.63            = ( plus_plus_int @ ( groups975429370522433651at_int @ G2 @ A2 ) @ ( groups975429370522433651at_int @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_inter
% 0.30/0.63  thf(fact_8329_sum_Ounion__inter,axiom,
% 0.30/0.63      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,G2: produc4166570645942440679at_nat > rat] :
% 0.30/0.63        ( ( finite1918287321285529104at_nat @ A2 )
% 0.30/0.63       => ( ( finite1918287321285529104at_nat @ B2 )
% 0.30/0.63         => ( ( plus_plus_rat @ ( groups6424767709179651461at_rat @ G2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) ) @ ( groups6424767709179651461at_rat @ G2 @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) ) )
% 0.30/0.63            = ( plus_plus_rat @ ( groups6424767709179651461at_rat @ G2 @ A2 ) @ ( groups6424767709179651461at_rat @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_inter
% 0.30/0.63  thf(fact_8330_sum_OInt__Diff,axiom,
% 0.30/0.63      ! [A2: set_int,G2: int > rat,B2: set_int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups3906332499630173760nt_rat @ G2 @ A2 )
% 0.30/0.63          = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) @ ( groups3906332499630173760nt_rat @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.Int_Diff
% 0.30/0.63  thf(fact_8331_sum_OInt__Diff,axiom,
% 0.30/0.63      ! [A2: set_int,G2: int > nat,B2: set_int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups4541462559716669496nt_nat @ G2 @ A2 )
% 0.30/0.63          = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) @ ( groups4541462559716669496nt_nat @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.Int_Diff
% 0.30/0.63  thf(fact_8332_sum_OInt__Diff,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > rat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( groups342789780944988191at_rat @ G2 @ A2 )
% 0.30/0.63          = ( plus_plus_rat @ ( groups342789780944988191at_rat @ G2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) @ ( groups342789780944988191at_rat @ G2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.Int_Diff
% 0.30/0.63  thf(fact_8333_sum_OInt__Diff,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( groups977919841031483927at_nat @ G2 @ A2 )
% 0.30/0.63          = ( plus_plus_nat @ ( groups977919841031483927at_nat @ G2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) @ ( groups977919841031483927at_nat @ G2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.Int_Diff
% 0.30/0.63  thf(fact_8334_sum_OInt__Diff,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > int,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( groups975429370522433651at_int @ G2 @ A2 )
% 0.30/0.63          = ( plus_plus_int @ ( groups975429370522433651at_int @ G2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) @ ( groups975429370522433651at_int @ G2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.Int_Diff
% 0.30/0.63  thf(fact_8335_sum_OInt__Diff,axiom,
% 0.30/0.63      ! [A2: set_nat,G2: nat > rat,B2: set_nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups2906978787729119204at_rat @ G2 @ A2 )
% 0.30/0.63          = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) @ ( groups2906978787729119204at_rat @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.Int_Diff
% 0.30/0.63  thf(fact_8336_sum_OInt__Diff,axiom,
% 0.30/0.63      ! [A2: set_nat,G2: nat > int,B2: set_nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups3539618377306564664at_int @ G2 @ A2 )
% 0.30/0.63          = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) @ ( groups3539618377306564664at_int @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.Int_Diff
% 0.30/0.63  thf(fact_8337_sum_OInt__Diff,axiom,
% 0.30/0.63      ! [A2: set_nat,G2: nat > nat,B2: set_nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups3542108847815614940at_nat @ G2 @ A2 )
% 0.30/0.63          = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) @ ( groups3542108847815614940at_nat @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.Int_Diff
% 0.30/0.63  thf(fact_8338_sum_OInt__Diff,axiom,
% 0.30/0.63      ! [A2: set_int,G2: int > int,B2: set_int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups4538972089207619220nt_int @ G2 @ A2 )
% 0.30/0.63          = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) @ ( groups4538972089207619220nt_int @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.Int_Diff
% 0.30/0.63  thf(fact_8339_sum_OatLeast1__atMost__eq,axiom,
% 0.30/0.63      ! [G2: nat > nat,N: nat] :
% 0.30/0.63        ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.30/0.63        = ( groups3542108847815614940at_nat
% 0.30/0.63          @ ^ [K4: nat] : ( G2 @ ( suc @ K4 ) )
% 0.30/0.63          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.atLeast1_atMost_eq
% 0.30/0.63  thf(fact_8340_prod_Ounion__inter,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > code_integer] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) ) @ ( groups3827104343326376752nteger @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) )
% 0.30/0.63            = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G2 @ A2 ) @ ( groups3827104343326376752nteger @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_inter
% 0.30/0.63  thf(fact_8341_prod_Ounion__inter,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > code_integer] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ ( groups3455450783089532116nteger @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) )
% 0.30/0.63            = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ A2 ) @ ( groups3455450783089532116nteger @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_inter
% 0.30/0.63  thf(fact_8342_prod_Ounion__inter,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > assn] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( times_times_assn @ ( groups7882442080178216443t_assn @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) ) @ ( groups7882442080178216443t_assn @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) )
% 0.30/0.63            = ( times_times_assn @ ( groups7882442080178216443t_assn @ G2 @ A2 ) @ ( groups7882442080178216443t_assn @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_inter
% 0.30/0.63  thf(fact_8343_prod_Ounion__inter,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > assn] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ ( groups6906906614972039071t_assn @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) )
% 0.30/0.63            = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ A2 ) @ ( groups6906906614972039071t_assn @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_inter
% 0.30/0.63  thf(fact_8344_prod_Ounion__inter,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) )
% 0.30/0.63            = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ A2 ) @ ( groups1072433553688619179nt_rat @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_inter
% 0.30/0.63  thf(fact_8345_prod_Ounion__inter,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) )
% 0.30/0.63            = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ A2 ) @ ( groups73079841787564623at_rat @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_inter
% 0.30/0.63  thf(fact_8346_prod_Ounion__inter,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > nat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) )
% 0.30/0.63            = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ A2 ) @ ( groups1707563613775114915nt_nat @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_inter
% 0.30/0.63  thf(fact_8347_prod_Ounion__inter,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ ( groups708209901874060359at_nat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) )
% 0.30/0.63            = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ A2 ) @ ( groups708209901874060359at_nat @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_inter
% 0.30/0.63  thf(fact_8348_prod_Ounion__inter,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > int] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ ( groups705719431365010083at_int @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) )
% 0.30/0.63            = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ A2 ) @ ( groups705719431365010083at_int @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_inter
% 0.30/0.63  thf(fact_8349_prod_Ounion__inter,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( times_times_int @ ( groups1705073143266064639nt_int @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) ) @ ( groups1705073143266064639nt_int @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) )
% 0.30/0.63            = ( times_times_int @ ( groups1705073143266064639nt_int @ G2 @ A2 ) @ ( groups1705073143266064639nt_int @ G2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_inter
% 0.30/0.63  thf(fact_8350_prod_OInt__Diff,axiom,
% 0.30/0.63      ! [A2: set_int,G2: int > code_integer,B2: set_int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups3827104343326376752nteger @ G2 @ A2 )
% 0.30/0.63          = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) @ ( groups3827104343326376752nteger @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.Int_Diff
% 0.30/0.63  thf(fact_8351_prod_OInt__Diff,axiom,
% 0.30/0.63      ! [A2: set_nat,G2: nat > code_integer,B2: set_nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups3455450783089532116nteger @ G2 @ A2 )
% 0.30/0.63          = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) @ ( groups3455450783089532116nteger @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.Int_Diff
% 0.30/0.63  thf(fact_8352_prod_OInt__Diff,axiom,
% 0.30/0.63      ! [A2: set_int,G2: int > assn,B2: set_int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups7882442080178216443t_assn @ G2 @ A2 )
% 0.30/0.63          = ( times_times_assn @ ( groups7882442080178216443t_assn @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) @ ( groups7882442080178216443t_assn @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.Int_Diff
% 0.30/0.63  thf(fact_8353_prod_OInt__Diff,axiom,
% 0.30/0.63      ! [A2: set_nat,G2: nat > assn,B2: set_nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups6906906614972039071t_assn @ G2 @ A2 )
% 0.30/0.63          = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) @ ( groups6906906614972039071t_assn @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.Int_Diff
% 0.30/0.63  thf(fact_8354_prod_OInt__Diff,axiom,
% 0.30/0.63      ! [A2: set_int,G2: int > rat,B2: set_int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups1072433553688619179nt_rat @ G2 @ A2 )
% 0.30/0.63          = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.Int_Diff
% 0.30/0.63  thf(fact_8355_prod_OInt__Diff,axiom,
% 0.30/0.63      ! [A2: set_nat,G2: nat > rat,B2: set_nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups73079841787564623at_rat @ G2 @ A2 )
% 0.30/0.63          = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.Int_Diff
% 0.30/0.63  thf(fact_8356_prod_OInt__Diff,axiom,
% 0.30/0.63      ! [A2: set_int,G2: int > nat,B2: set_int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups1707563613775114915nt_nat @ G2 @ A2 )
% 0.30/0.63          = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.Int_Diff
% 0.30/0.63  thf(fact_8357_prod_OInt__Diff,axiom,
% 0.30/0.63      ! [A2: set_nat,G2: nat > nat,B2: set_nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups708209901874060359at_nat @ G2 @ A2 )
% 0.30/0.63          = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) @ ( groups708209901874060359at_nat @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.Int_Diff
% 0.30/0.63  thf(fact_8358_prod_OInt__Diff,axiom,
% 0.30/0.63      ! [A2: set_nat,G2: nat > int,B2: set_nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups705719431365010083at_int @ G2 @ A2 )
% 0.30/0.63          = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) @ ( groups705719431365010083at_int @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.Int_Diff
% 0.30/0.63  thf(fact_8359_prod_OInt__Diff,axiom,
% 0.30/0.63      ! [A2: set_int,G2: int > int,B2: set_int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups1705073143266064639nt_int @ G2 @ A2 )
% 0.30/0.63          = ( times_times_int @ ( groups1705073143266064639nt_int @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) @ ( groups1705073143266064639nt_int @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.Int_Diff
% 0.30/0.63  thf(fact_8360_prod_Omono__neutral__cong,axiom,
% 0.30/0.63      ! [T: set_int,S: set_int,H3: int > code_integer,G2: int > code_integer] :
% 0.30/0.63        ( ( finite_finite_int @ T )
% 0.30/0.63       => ( ( finite_finite_int @ S )
% 0.30/0.63         => ( ! [I2: int] :
% 0.30/0.63                ( ( member_int @ I2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.63               => ( ( H3 @ I2 )
% 0.30/0.63                  = one_one_Code_integer ) )
% 0.30/0.63           => ( ! [I2: int] :
% 0.30/0.63                  ( ( member_int @ I2 @ ( minus_minus_set_int @ S @ T ) )
% 0.30/0.63                 => ( ( G2 @ I2 )
% 0.30/0.63                    = one_one_Code_integer ) )
% 0.30/0.63             => ( ! [X2: int] :
% 0.30/0.63                    ( ( member_int @ X2 @ ( inf_inf_set_int @ S @ T ) )
% 0.30/0.63                   => ( ( G2 @ X2 )
% 0.30/0.63                      = ( H3 @ X2 ) ) )
% 0.30/0.63               => ( ( groups3827104343326376752nteger @ G2 @ S )
% 0.30/0.63                  = ( groups3827104343326376752nteger @ H3 @ T ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.mono_neutral_cong
% 0.30/0.63  thf(fact_8361_prod_Omono__neutral__cong,axiom,
% 0.30/0.63      ! [T: set_int,S: set_int,H3: int > assn,G2: int > assn] :
% 0.30/0.63        ( ( finite_finite_int @ T )
% 0.30/0.63       => ( ( finite_finite_int @ S )
% 0.30/0.63         => ( ! [I2: int] :
% 0.30/0.63                ( ( member_int @ I2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.63               => ( ( H3 @ I2 )
% 0.30/0.63                  = one_one_assn ) )
% 0.30/0.63           => ( ! [I2: int] :
% 0.30/0.63                  ( ( member_int @ I2 @ ( minus_minus_set_int @ S @ T ) )
% 0.30/0.63                 => ( ( G2 @ I2 )
% 0.30/0.63                    = one_one_assn ) )
% 0.30/0.63             => ( ! [X2: int] :
% 0.30/0.63                    ( ( member_int @ X2 @ ( inf_inf_set_int @ S @ T ) )
% 0.30/0.63                   => ( ( G2 @ X2 )
% 0.30/0.63                      = ( H3 @ X2 ) ) )
% 0.30/0.63               => ( ( groups7882442080178216443t_assn @ G2 @ S )
% 0.30/0.63                  = ( groups7882442080178216443t_assn @ H3 @ T ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.mono_neutral_cong
% 0.30/0.63  thf(fact_8362_prod_Omono__neutral__cong,axiom,
% 0.30/0.63      ! [T: set_int,S: set_int,H3: int > rat,G2: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ T )
% 0.30/0.63       => ( ( finite_finite_int @ S )
% 0.30/0.63         => ( ! [I2: int] :
% 0.30/0.63                ( ( member_int @ I2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.63               => ( ( H3 @ I2 )
% 0.30/0.63                  = one_one_rat ) )
% 0.30/0.63           => ( ! [I2: int] :
% 0.30/0.63                  ( ( member_int @ I2 @ ( minus_minus_set_int @ S @ T ) )
% 0.30/0.63                 => ( ( G2 @ I2 )
% 0.30/0.63                    = one_one_rat ) )
% 0.30/0.63             => ( ! [X2: int] :
% 0.30/0.63                    ( ( member_int @ X2 @ ( inf_inf_set_int @ S @ T ) )
% 0.30/0.63                   => ( ( G2 @ X2 )
% 0.30/0.63                      = ( H3 @ X2 ) ) )
% 0.30/0.63               => ( ( groups1072433553688619179nt_rat @ G2 @ S )
% 0.30/0.63                  = ( groups1072433553688619179nt_rat @ H3 @ T ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.mono_neutral_cong
% 0.30/0.63  thf(fact_8363_prod_Omono__neutral__cong,axiom,
% 0.30/0.63      ! [T: set_int,S: set_int,H3: int > nat,G2: int > nat] :
% 0.30/0.63        ( ( finite_finite_int @ T )
% 0.30/0.63       => ( ( finite_finite_int @ S )
% 0.30/0.63         => ( ! [I2: int] :
% 0.30/0.63                ( ( member_int @ I2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.63               => ( ( H3 @ I2 )
% 0.30/0.63                  = one_one_nat ) )
% 0.30/0.63           => ( ! [I2: int] :
% 0.30/0.63                  ( ( member_int @ I2 @ ( minus_minus_set_int @ S @ T ) )
% 0.30/0.63                 => ( ( G2 @ I2 )
% 0.30/0.63                    = one_one_nat ) )
% 0.30/0.63             => ( ! [X2: int] :
% 0.30/0.63                    ( ( member_int @ X2 @ ( inf_inf_set_int @ S @ T ) )
% 0.30/0.63                   => ( ( G2 @ X2 )
% 0.30/0.63                      = ( H3 @ X2 ) ) )
% 0.30/0.63               => ( ( groups1707563613775114915nt_nat @ G2 @ S )
% 0.30/0.63                  = ( groups1707563613775114915nt_nat @ H3 @ T ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.mono_neutral_cong
% 0.30/0.63  thf(fact_8364_prod_Omono__neutral__cong,axiom,
% 0.30/0.63      ! [T: set_nat,S: set_nat,H3: nat > code_integer,G2: nat > code_integer] :
% 0.30/0.63        ( ( finite_finite_nat @ T )
% 0.30/0.63       => ( ( finite_finite_nat @ S )
% 0.30/0.63         => ( ! [I2: nat] :
% 0.30/0.63                ( ( member_nat @ I2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.63               => ( ( H3 @ I2 )
% 0.30/0.63                  = one_one_Code_integer ) )
% 0.30/0.63           => ( ! [I2: nat] :
% 0.30/0.63                  ( ( member_nat @ I2 @ ( minus_minus_set_nat @ S @ T ) )
% 0.30/0.63                 => ( ( G2 @ I2 )
% 0.30/0.63                    = one_one_Code_integer ) )
% 0.30/0.63             => ( ! [X2: nat] :
% 0.30/0.63                    ( ( member_nat @ X2 @ ( inf_inf_set_nat @ S @ T ) )
% 0.30/0.63                   => ( ( G2 @ X2 )
% 0.30/0.63                      = ( H3 @ X2 ) ) )
% 0.30/0.63               => ( ( groups3455450783089532116nteger @ G2 @ S )
% 0.30/0.63                  = ( groups3455450783089532116nteger @ H3 @ T ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.mono_neutral_cong
% 0.30/0.63  thf(fact_8365_prod_Omono__neutral__cong,axiom,
% 0.30/0.63      ! [T: set_nat,S: set_nat,H3: nat > assn,G2: nat > assn] :
% 0.30/0.63        ( ( finite_finite_nat @ T )
% 0.30/0.63       => ( ( finite_finite_nat @ S )
% 0.30/0.63         => ( ! [I2: nat] :
% 0.30/0.63                ( ( member_nat @ I2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.63               => ( ( H3 @ I2 )
% 0.30/0.63                  = one_one_assn ) )
% 0.30/0.63           => ( ! [I2: nat] :
% 0.30/0.63                  ( ( member_nat @ I2 @ ( minus_minus_set_nat @ S @ T ) )
% 0.30/0.63                 => ( ( G2 @ I2 )
% 0.30/0.63                    = one_one_assn ) )
% 0.30/0.63             => ( ! [X2: nat] :
% 0.30/0.63                    ( ( member_nat @ X2 @ ( inf_inf_set_nat @ S @ T ) )
% 0.30/0.63                   => ( ( G2 @ X2 )
% 0.30/0.63                      = ( H3 @ X2 ) ) )
% 0.30/0.63               => ( ( groups6906906614972039071t_assn @ G2 @ S )
% 0.30/0.63                  = ( groups6906906614972039071t_assn @ H3 @ T ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.mono_neutral_cong
% 0.30/0.63  thf(fact_8366_prod_Omono__neutral__cong,axiom,
% 0.30/0.63      ! [T: set_nat,S: set_nat,H3: nat > rat,G2: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ T )
% 0.30/0.63       => ( ( finite_finite_nat @ S )
% 0.30/0.63         => ( ! [I2: nat] :
% 0.30/0.63                ( ( member_nat @ I2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.63               => ( ( H3 @ I2 )
% 0.30/0.63                  = one_one_rat ) )
% 0.30/0.63           => ( ! [I2: nat] :
% 0.30/0.63                  ( ( member_nat @ I2 @ ( minus_minus_set_nat @ S @ T ) )
% 0.30/0.63                 => ( ( G2 @ I2 )
% 0.30/0.63                    = one_one_rat ) )
% 0.30/0.63             => ( ! [X2: nat] :
% 0.30/0.63                    ( ( member_nat @ X2 @ ( inf_inf_set_nat @ S @ T ) )
% 0.30/0.63                   => ( ( G2 @ X2 )
% 0.30/0.63                      = ( H3 @ X2 ) ) )
% 0.30/0.63               => ( ( groups73079841787564623at_rat @ G2 @ S )
% 0.30/0.63                  = ( groups73079841787564623at_rat @ H3 @ T ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.mono_neutral_cong
% 0.30/0.63  thf(fact_8367_prod_Omono__neutral__cong,axiom,
% 0.30/0.63      ! [T: set_nat,S: set_nat,H3: nat > nat,G2: nat > nat] :
% 0.30/0.63        ( ( finite_finite_nat @ T )
% 0.30/0.63       => ( ( finite_finite_nat @ S )
% 0.30/0.63         => ( ! [I2: nat] :
% 0.30/0.63                ( ( member_nat @ I2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.63               => ( ( H3 @ I2 )
% 0.30/0.63                  = one_one_nat ) )
% 0.30/0.63           => ( ! [I2: nat] :
% 0.30/0.63                  ( ( member_nat @ I2 @ ( minus_minus_set_nat @ S @ T ) )
% 0.30/0.63                 => ( ( G2 @ I2 )
% 0.30/0.63                    = one_one_nat ) )
% 0.30/0.63             => ( ! [X2: nat] :
% 0.30/0.63                    ( ( member_nat @ X2 @ ( inf_inf_set_nat @ S @ T ) )
% 0.30/0.63                   => ( ( G2 @ X2 )
% 0.30/0.63                      = ( H3 @ X2 ) ) )
% 0.30/0.63               => ( ( groups708209901874060359at_nat @ G2 @ S )
% 0.30/0.63                  = ( groups708209901874060359at_nat @ H3 @ T ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.mono_neutral_cong
% 0.30/0.63  thf(fact_8368_prod_Omono__neutral__cong,axiom,
% 0.30/0.63      ! [T: set_nat,S: set_nat,H3: nat > int,G2: nat > int] :
% 0.30/0.63        ( ( finite_finite_nat @ T )
% 0.30/0.63       => ( ( finite_finite_nat @ S )
% 0.30/0.63         => ( ! [I2: nat] :
% 0.30/0.63                ( ( member_nat @ I2 @ ( minus_minus_set_nat @ T @ S ) )
% 0.30/0.63               => ( ( H3 @ I2 )
% 0.30/0.63                  = one_one_int ) )
% 0.30/0.63           => ( ! [I2: nat] :
% 0.30/0.63                  ( ( member_nat @ I2 @ ( minus_minus_set_nat @ S @ T ) )
% 0.30/0.63                 => ( ( G2 @ I2 )
% 0.30/0.63                    = one_one_int ) )
% 0.30/0.63             => ( ! [X2: nat] :
% 0.30/0.63                    ( ( member_nat @ X2 @ ( inf_inf_set_nat @ S @ T ) )
% 0.30/0.63                   => ( ( G2 @ X2 )
% 0.30/0.63                      = ( H3 @ X2 ) ) )
% 0.30/0.63               => ( ( groups705719431365010083at_int @ G2 @ S )
% 0.30/0.63                  = ( groups705719431365010083at_int @ H3 @ T ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.mono_neutral_cong
% 0.30/0.63  thf(fact_8369_prod_Omono__neutral__cong,axiom,
% 0.30/0.63      ! [T: set_int,S: set_int,H3: int > int,G2: int > int] :
% 0.30/0.63        ( ( finite_finite_int @ T )
% 0.30/0.63       => ( ( finite_finite_int @ S )
% 0.30/0.63         => ( ! [I2: int] :
% 0.30/0.63                ( ( member_int @ I2 @ ( minus_minus_set_int @ T @ S ) )
% 0.30/0.63               => ( ( H3 @ I2 )
% 0.30/0.63                  = one_one_int ) )
% 0.30/0.63           => ( ! [I2: int] :
% 0.30/0.63                  ( ( member_int @ I2 @ ( minus_minus_set_int @ S @ T ) )
% 0.30/0.63                 => ( ( G2 @ I2 )
% 0.30/0.63                    = one_one_int ) )
% 0.30/0.63             => ( ! [X2: int] :
% 0.30/0.63                    ( ( member_int @ X2 @ ( inf_inf_set_int @ S @ T ) )
% 0.30/0.63                   => ( ( G2 @ X2 )
% 0.30/0.63                      = ( H3 @ X2 ) ) )
% 0.30/0.63               => ( ( groups1705073143266064639nt_int @ G2 @ S )
% 0.30/0.63                  = ( groups1705073143266064639nt_int @ H3 @ T ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.mono_neutral_cong
% 0.30/0.63  thf(fact_8370_prod_OatLeast1__atMost__eq,axiom,
% 0.30/0.63      ! [G2: nat > nat,N: nat] :
% 0.30/0.63        ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.30/0.63        = ( groups708209901874060359at_nat
% 0.30/0.63          @ ^ [K4: nat] : ( G2 @ ( suc @ K4 ) )
% 0.30/0.63          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.atLeast1_atMost_eq
% 0.30/0.63  thf(fact_8371_prod_OatLeast1__atMost__eq,axiom,
% 0.30/0.63      ! [G2: nat > int,N: nat] :
% 0.30/0.63        ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.30/0.63        = ( groups705719431365010083at_int
% 0.30/0.63          @ ^ [K4: nat] : ( G2 @ ( suc @ K4 ) )
% 0.30/0.63          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.atLeast1_atMost_eq
% 0.30/0.63  thf(fact_8372_sum__bounds__lt__plus1,axiom,
% 0.30/0.63      ! [F2: nat > nat,Mm: nat] :
% 0.30/0.63        ( ( groups3542108847815614940at_nat
% 0.30/0.63          @ ^ [K4: nat] : ( F2 @ ( suc @ K4 ) )
% 0.30/0.63          @ ( set_ord_lessThan_nat @ Mm ) )
% 0.30/0.63        = ( groups3542108847815614940at_nat @ F2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_bounds_lt_plus1
% 0.30/0.63  thf(fact_8373_prod__int__plus__eq,axiom,
% 0.30/0.63      ! [I: nat,J: nat] :
% 0.30/0.63        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 0.30/0.63        = ( groups1705073143266064639nt_int
% 0.30/0.63          @ ^ [X3: int] : X3
% 0.30/0.63          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_int_plus_eq
% 0.30/0.63  thf(fact_8374_sum_Onat__group,axiom,
% 0.30/0.63      ! [G2: nat > nat,K: nat,N: nat] :
% 0.30/0.63        ( ( groups3542108847815614940at_nat
% 0.30/0.63          @ ^ [M2: nat] : ( groups3542108847815614940at_nat @ G2 @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M2 @ K ) @ ( plus_plus_nat @ ( times_times_nat @ M2 @ K ) @ K ) ) )
% 0.30/0.63          @ ( set_ord_lessThan_nat @ N ) )
% 0.30/0.63        = ( groups3542108847815614940at_nat @ G2 @ ( set_ord_lessThan_nat @ ( times_times_nat @ N @ K ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.nat_group
% 0.30/0.63  thf(fact_8375_prod_Onat__group,axiom,
% 0.30/0.63      ! [G2: nat > nat,K: nat,N: nat] :
% 0.30/0.63        ( ( groups708209901874060359at_nat
% 0.30/0.63          @ ^ [M2: nat] : ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M2 @ K ) @ ( plus_plus_nat @ ( times_times_nat @ M2 @ K ) @ K ) ) )
% 0.30/0.63          @ ( set_ord_lessThan_nat @ N ) )
% 0.30/0.63        = ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ ( times_times_nat @ N @ K ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.nat_group
% 0.30/0.63  thf(fact_8376_prod_Onat__group,axiom,
% 0.30/0.63      ! [G2: nat > int,K: nat,N: nat] :
% 0.30/0.63        ( ( groups705719431365010083at_int
% 0.30/0.63          @ ^ [M2: nat] : ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M2 @ K ) @ ( plus_plus_nat @ ( times_times_nat @ M2 @ K ) @ K ) ) )
% 0.30/0.63          @ ( set_ord_lessThan_nat @ N ) )
% 0.30/0.63        = ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ ( times_times_nat @ N @ K ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.nat_group
% 0.30/0.63  thf(fact_8377_sum_Onested__swap_H,axiom,
% 0.30/0.63      ! [A: nat > nat > nat,N: nat] :
% 0.30/0.63        ( ( groups3542108847815614940at_nat
% 0.30/0.63          @ ^ [I3: nat] : ( groups3542108847815614940at_nat @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 0.30/0.63          @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.63        = ( groups3542108847815614940at_nat
% 0.30/0.63          @ ^ [J3: nat] :
% 0.30/0.63              ( groups3542108847815614940at_nat
% 0.30/0.63              @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 0.30/0.63              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 0.30/0.63          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.nested_swap'
% 0.30/0.63  thf(fact_8378_prod_Onested__swap_H,axiom,
% 0.30/0.63      ! [A: nat > nat > nat,N: nat] :
% 0.30/0.63        ( ( groups708209901874060359at_nat
% 0.30/0.63          @ ^ [I3: nat] : ( groups708209901874060359at_nat @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 0.30/0.63          @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.63        = ( groups708209901874060359at_nat
% 0.30/0.63          @ ^ [J3: nat] :
% 0.30/0.63              ( groups708209901874060359at_nat
% 0.30/0.63              @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 0.30/0.63              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 0.30/0.63          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.nested_swap'
% 0.30/0.63  thf(fact_8379_prod_Onested__swap_H,axiom,
% 0.30/0.63      ! [A: nat > nat > int,N: nat] :
% 0.30/0.63        ( ( groups705719431365010083at_int
% 0.30/0.63          @ ^ [I3: nat] : ( groups705719431365010083at_int @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 0.30/0.63          @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.63        = ( groups705719431365010083at_int
% 0.30/0.63          @ ^ [J3: nat] :
% 0.30/0.63              ( groups705719431365010083at_int
% 0.30/0.63              @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 0.30/0.63              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 0.30/0.63          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.nested_swap'
% 0.30/0.63  thf(fact_8380_Iio__Int__singleton,axiom,
% 0.30/0.63      ! [X: $o,K: $o] :
% 0.30/0.63        ( ( ( ord_less_o @ X @ K )
% 0.30/0.63         => ( ( inf_inf_set_o @ ( set_ord_lessThan_o @ K ) @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.30/0.63            = ( insert_o @ X @ bot_bot_set_o ) ) )
% 0.30/0.63        & ( ~ ( ord_less_o @ X @ K )
% 0.30/0.63         => ( ( inf_inf_set_o @ ( set_ord_lessThan_o @ K ) @ ( insert_o @ X @ bot_bot_set_o ) )
% 0.30/0.63            = bot_bot_set_o ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % Iio_Int_singleton
% 0.30/0.63  thf(fact_8381_Iio__Int__singleton,axiom,
% 0.30/0.63      ! [X: literal,K: literal] :
% 0.30/0.63        ( ( ( ord_less_literal @ X @ K )
% 0.30/0.63         => ( ( inf_inf_set_literal @ ( set_or2436086697161274615iteral @ K ) @ ( insert_literal @ X @ bot_bot_set_literal ) )
% 0.30/0.63            = ( insert_literal @ X @ bot_bot_set_literal ) ) )
% 0.30/0.63        & ( ~ ( ord_less_literal @ X @ K )
% 0.30/0.63         => ( ( inf_inf_set_literal @ ( set_or2436086697161274615iteral @ K ) @ ( insert_literal @ X @ bot_bot_set_literal ) )
% 0.30/0.63            = bot_bot_set_literal ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % Iio_Int_singleton
% 0.30/0.63  thf(fact_8382_Iio__Int__singleton,axiom,
% 0.30/0.63      ! [X: rat,K: rat] :
% 0.30/0.63        ( ( ( ord_less_rat @ X @ K )
% 0.30/0.63         => ( ( inf_inf_set_rat @ ( set_ord_lessThan_rat @ K ) @ ( insert_rat @ X @ bot_bot_set_rat ) )
% 0.30/0.63            = ( insert_rat @ X @ bot_bot_set_rat ) ) )
% 0.30/0.63        & ( ~ ( ord_less_rat @ X @ K )
% 0.30/0.63         => ( ( inf_inf_set_rat @ ( set_ord_lessThan_rat @ K ) @ ( insert_rat @ X @ bot_bot_set_rat ) )
% 0.30/0.63            = bot_bot_set_rat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % Iio_Int_singleton
% 0.30/0.63  thf(fact_8383_Iio__Int__singleton,axiom,
% 0.30/0.63      ! [X: int,K: int] :
% 0.30/0.63        ( ( ( ord_less_int @ X @ K )
% 0.30/0.63         => ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ K ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.30/0.63            = ( insert_int @ X @ bot_bot_set_int ) ) )
% 0.30/0.63        & ( ~ ( ord_less_int @ X @ K )
% 0.30/0.63         => ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ K ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.30/0.63            = bot_bot_set_int ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % Iio_Int_singleton
% 0.30/0.63  thf(fact_8384_Iio__Int__singleton,axiom,
% 0.30/0.63      ! [X: nat,K: nat] :
% 0.30/0.63        ( ( ( ord_less_nat @ X @ K )
% 0.30/0.63         => ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ K ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.30/0.63            = ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 0.30/0.63        & ( ~ ( ord_less_nat @ X @ K )
% 0.30/0.63         => ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ K ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.30/0.63            = bot_bot_set_nat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % Iio_Int_singleton
% 0.30/0.63  thf(fact_8385_ivl__disj__un__singleton_I2_J,axiom,
% 0.30/0.63      ! [U: $o] :
% 0.30/0.63        ( ( sup_sup_set_o @ ( set_ord_lessThan_o @ U ) @ ( insert_o @ U @ bot_bot_set_o ) )
% 0.30/0.63        = ( set_ord_atMost_o @ U ) ) ).
% 0.30/0.63  
% 0.30/0.63  % ivl_disj_un_singleton(2)
% 0.30/0.63  thf(fact_8386_ivl__disj__un__singleton_I2_J,axiom,
% 0.30/0.63      ! [U: int] :
% 0.30/0.63        ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ U ) @ ( insert_int @ U @ bot_bot_set_int ) )
% 0.30/0.63        = ( set_ord_atMost_int @ U ) ) ).
% 0.30/0.63  
% 0.30/0.63  % ivl_disj_un_singleton(2)
% 0.30/0.63  thf(fact_8387_ivl__disj__un__singleton_I2_J,axiom,
% 0.30/0.63      ! [U: nat] :
% 0.30/0.63        ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ U ) @ ( insert_nat @ U @ bot_bot_set_nat ) )
% 0.30/0.63        = ( set_ord_atMost_nat @ U ) ) ).
% 0.30/0.63  
% 0.30/0.63  % ivl_disj_un_singleton(2)
% 0.30/0.63  thf(fact_8388_ivl__disj__un__one_I4_J,axiom,
% 0.30/0.63      ! [L: rat,U: rat] :
% 0.30/0.63        ( ( ord_less_eq_rat @ L @ U )
% 0.30/0.63       => ( ( sup_sup_set_rat @ ( set_ord_lessThan_rat @ L ) @ ( set_or633870826150836451st_rat @ L @ U ) )
% 0.30/0.63          = ( set_ord_atMost_rat @ U ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % ivl_disj_un_one(4)
% 0.30/0.63  thf(fact_8389_ivl__disj__un__one_I4_J,axiom,
% 0.30/0.63      ! [L: nat,U: nat] :
% 0.30/0.63        ( ( ord_less_eq_nat @ L @ U )
% 0.30/0.63       => ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 0.30/0.63          = ( set_ord_atMost_nat @ U ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % ivl_disj_un_one(4)
% 0.30/0.63  thf(fact_8390_ivl__disj__un__one_I4_J,axiom,
% 0.30/0.63      ! [L: int,U: int] :
% 0.30/0.63        ( ( ord_less_eq_int @ L @ U )
% 0.30/0.63       => ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or1266510415728281911st_int @ L @ U ) )
% 0.30/0.63          = ( set_ord_atMost_int @ U ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % ivl_disj_un_one(4)
% 0.30/0.63  thf(fact_8391_ivl__disj__un__one_I4_J,axiom,
% 0.30/0.63      ! [L: code_integer,U: code_integer] :
% 0.30/0.63        ( ( ord_le3102999989581377725nteger @ L @ U )
% 0.30/0.63       => ( ( sup_su848401254843788991nteger @ ( set_or5754767410780653050nteger @ L ) @ ( set_or189985376899183464nteger @ L @ U ) )
% 0.30/0.63          = ( set_or9101266186257409494nteger @ U ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % ivl_disj_un_one(4)
% 0.30/0.63  thf(fact_8392_sum_OIf__cases,axiom,
% 0.30/0.63      ! [A2: set_int,P: int > $o,H3: int > rat,G2: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups3906332499630173760nt_rat
% 0.30/0.63            @ ^ [X3: int] : ( if_rat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.63            @ A2 )
% 0.30/0.63          = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ H3 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) @ ( groups3906332499630173760nt_rat @ G2 @ ( inf_inf_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.If_cases
% 0.30/0.63  thf(fact_8393_sum_OIf__cases,axiom,
% 0.30/0.63      ! [A2: set_int,P: int > $o,H3: int > nat,G2: int > nat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups4541462559716669496nt_nat
% 0.30/0.63            @ ^ [X3: int] : ( if_nat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.63            @ A2 )
% 0.30/0.63          = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ H3 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) @ ( groups4541462559716669496nt_nat @ G2 @ ( inf_inf_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.If_cases
% 0.30/0.63  thf(fact_8394_sum_OIf__cases,axiom,
% 0.30/0.63      ! [A2: set_nat,P: nat > $o,H3: nat > rat,G2: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups2906978787729119204at_rat
% 0.30/0.63            @ ^ [X3: nat] : ( if_rat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.63            @ A2 )
% 0.30/0.63          = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ H3 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) @ ( groups2906978787729119204at_rat @ G2 @ ( inf_inf_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.If_cases
% 0.30/0.63  thf(fact_8395_sum_OIf__cases,axiom,
% 0.30/0.63      ! [A2: set_nat,P: nat > $o,H3: nat > int,G2: nat > int] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups3539618377306564664at_int
% 0.30/0.63            @ ^ [X3: nat] : ( if_int @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.63            @ A2 )
% 0.30/0.63          = ( plus_plus_int @ ( groups3539618377306564664at_int @ H3 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) @ ( groups3539618377306564664at_int @ G2 @ ( inf_inf_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.If_cases
% 0.30/0.63  thf(fact_8396_sum_OIf__cases,axiom,
% 0.30/0.63      ! [A2: set_nat,P: nat > $o,H3: nat > nat,G2: nat > nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups3542108847815614940at_nat
% 0.30/0.63            @ ^ [X3: nat] : ( if_nat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.63            @ A2 )
% 0.30/0.63          = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ H3 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) @ ( groups3542108847815614940at_nat @ G2 @ ( inf_inf_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.If_cases
% 0.30/0.63  thf(fact_8397_sum_OIf__cases,axiom,
% 0.30/0.63      ! [A2: set_int,P: int > $o,H3: int > int,G2: int > int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups4538972089207619220nt_int
% 0.30/0.63            @ ^ [X3: int] : ( if_int @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.63            @ A2 )
% 0.30/0.63          = ( plus_plus_int @ ( groups4538972089207619220nt_int @ H3 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) @ ( groups4538972089207619220nt_int @ G2 @ ( inf_inf_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.If_cases
% 0.30/0.63  thf(fact_8398_sum_OIf__cases,axiom,
% 0.30/0.63      ! [A2: set_set_nat,P: set_nat > $o,H3: set_nat > rat,G2: set_nat > rat] :
% 0.30/0.63        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.63       => ( ( groups7659867448343625626at_rat
% 0.30/0.63            @ ^ [X3: set_nat] : ( if_rat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.63            @ A2 )
% 0.30/0.63          = ( plus_plus_rat @ ( groups7659867448343625626at_rat @ H3 @ ( inf_inf_set_set_nat @ A2 @ ( collect_set_nat @ P ) ) ) @ ( groups7659867448343625626at_rat @ G2 @ ( inf_inf_set_set_nat @ A2 @ ( uminus613421341184616069et_nat @ ( collect_set_nat @ P ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.If_cases
% 0.30/0.63  thf(fact_8399_sum_OIf__cases,axiom,
% 0.30/0.63      ! [A2: set_set_nat,P: set_nat > $o,H3: set_nat > nat,G2: set_nat > nat] :
% 0.30/0.63        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.63       => ( ( groups8294997508430121362at_nat
% 0.30/0.63            @ ^ [X3: set_nat] : ( if_nat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.63            @ A2 )
% 0.30/0.63          = ( plus_plus_nat @ ( groups8294997508430121362at_nat @ H3 @ ( inf_inf_set_set_nat @ A2 @ ( collect_set_nat @ P ) ) ) @ ( groups8294997508430121362at_nat @ G2 @ ( inf_inf_set_set_nat @ A2 @ ( uminus613421341184616069et_nat @ ( collect_set_nat @ P ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.If_cases
% 0.30/0.63  thf(fact_8400_sum_OIf__cases,axiom,
% 0.30/0.63      ! [A2: set_set_nat,P: set_nat > $o,H3: set_nat > int,G2: set_nat > int] :
% 0.30/0.63        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.63       => ( ( groups8292507037921071086at_int
% 0.30/0.63            @ ^ [X3: set_nat] : ( if_int @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.63            @ A2 )
% 0.30/0.63          = ( plus_plus_int @ ( groups8292507037921071086at_int @ H3 @ ( inf_inf_set_set_nat @ A2 @ ( collect_set_nat @ P ) ) ) @ ( groups8292507037921071086at_int @ G2 @ ( inf_inf_set_set_nat @ A2 @ ( uminus613421341184616069et_nat @ ( collect_set_nat @ P ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.If_cases
% 0.30/0.63  thf(fact_8401_sum_OIf__cases,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o,H3: product_prod_nat_nat > rat,G2: product_prod_nat_nat > rat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( groups342789780944988191at_rat
% 0.30/0.63            @ ^ [X3: product_prod_nat_nat] : ( if_rat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.63            @ A2 )
% 0.30/0.63          = ( plus_plus_rat @ ( groups342789780944988191at_rat @ H3 @ ( inf_in2572325071724192079at_nat @ A2 @ ( collec3392354462482085612at_nat @ P ) ) ) @ ( groups342789780944988191at_rat @ G2 @ ( inf_in2572325071724192079at_nat @ A2 @ ( uminus6524753893492686040at_nat @ ( collec3392354462482085612at_nat @ P ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.If_cases
% 0.30/0.63  thf(fact_8402_prod_OIf__cases,axiom,
% 0.30/0.63      ! [A2: set_int,P: int > $o,H3: int > code_integer,G2: int > code_integer] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups3827104343326376752nteger
% 0.30/0.63            @ ^ [X3: int] : ( if_Code_integer @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.63            @ A2 )
% 0.30/0.63          = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ H3 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) @ ( groups3827104343326376752nteger @ G2 @ ( inf_inf_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.If_cases
% 0.30/0.63  thf(fact_8403_prod_OIf__cases,axiom,
% 0.30/0.63      ! [A2: set_nat,P: nat > $o,H3: nat > code_integer,G2: nat > code_integer] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups3455450783089532116nteger
% 0.30/0.63            @ ^ [X3: nat] : ( if_Code_integer @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.63            @ A2 )
% 0.30/0.63          = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ H3 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) @ ( groups3455450783089532116nteger @ G2 @ ( inf_inf_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.If_cases
% 0.30/0.63  thf(fact_8404_prod_OIf__cases,axiom,
% 0.30/0.63      ! [A2: set_int,P: int > $o,H3: int > assn,G2: int > assn] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups7882442080178216443t_assn
% 0.30/0.63            @ ^ [X3: int] : ( if_assn @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.63            @ A2 )
% 0.30/0.63          = ( times_times_assn @ ( groups7882442080178216443t_assn @ H3 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) @ ( groups7882442080178216443t_assn @ G2 @ ( inf_inf_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.If_cases
% 0.30/0.63  thf(fact_8405_prod_OIf__cases,axiom,
% 0.30/0.63      ! [A2: set_nat,P: nat > $o,H3: nat > assn,G2: nat > assn] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups6906906614972039071t_assn
% 0.30/0.63            @ ^ [X3: nat] : ( if_assn @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.63            @ A2 )
% 0.30/0.63          = ( times_times_assn @ ( groups6906906614972039071t_assn @ H3 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) @ ( groups6906906614972039071t_assn @ G2 @ ( inf_inf_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.If_cases
% 0.30/0.63  thf(fact_8406_prod_OIf__cases,axiom,
% 0.30/0.63      ! [A2: set_int,P: int > $o,H3: int > rat,G2: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups1072433553688619179nt_rat
% 0.30/0.63            @ ^ [X3: int] : ( if_rat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.63            @ A2 )
% 0.30/0.63          = ( times_times_rat @ ( groups1072433553688619179nt_rat @ H3 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.If_cases
% 0.30/0.63  thf(fact_8407_prod_OIf__cases,axiom,
% 0.30/0.63      ! [A2: set_nat,P: nat > $o,H3: nat > rat,G2: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups73079841787564623at_rat
% 0.30/0.63            @ ^ [X3: nat] : ( if_rat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.63            @ A2 )
% 0.30/0.63          = ( times_times_rat @ ( groups73079841787564623at_rat @ H3 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) @ ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.If_cases
% 0.30/0.63  thf(fact_8408_prod_OIf__cases,axiom,
% 0.30/0.63      ! [A2: set_int,P: int > $o,H3: int > nat,G2: int > nat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups1707563613775114915nt_nat
% 0.30/0.63            @ ^ [X3: int] : ( if_nat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.63            @ A2 )
% 0.30/0.63          = ( times_times_nat @ ( groups1707563613775114915nt_nat @ H3 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.If_cases
% 0.30/0.63  thf(fact_8409_prod_OIf__cases,axiom,
% 0.30/0.63      ! [A2: set_nat,P: nat > $o,H3: nat > nat,G2: nat > nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups708209901874060359at_nat
% 0.30/0.63            @ ^ [X3: nat] : ( if_nat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.63            @ A2 )
% 0.30/0.63          = ( times_times_nat @ ( groups708209901874060359at_nat @ H3 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) @ ( groups708209901874060359at_nat @ G2 @ ( inf_inf_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.If_cases
% 0.30/0.63  thf(fact_8410_prod_OIf__cases,axiom,
% 0.30/0.63      ! [A2: set_nat,P: nat > $o,H3: nat > int,G2: nat > int] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups705719431365010083at_int
% 0.30/0.63            @ ^ [X3: nat] : ( if_int @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.63            @ A2 )
% 0.30/0.63          = ( times_times_int @ ( groups705719431365010083at_int @ H3 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) @ ( groups705719431365010083at_int @ G2 @ ( inf_inf_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.If_cases
% 0.30/0.63  thf(fact_8411_prod_OIf__cases,axiom,
% 0.30/0.63      ! [A2: set_int,P: int > $o,H3: int > int,G2: int > int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups1705073143266064639nt_int
% 0.30/0.63            @ ^ [X3: int] : ( if_int @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 0.30/0.63            @ A2 )
% 0.30/0.63          = ( times_times_int @ ( groups1705073143266064639nt_int @ H3 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) @ ( groups1705073143266064639nt_int @ G2 @ ( inf_inf_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.If_cases
% 0.30/0.63  thf(fact_8412_one__diff__power__eq,axiom,
% 0.30/0.63      ! [X: code_integer,N: nat] :
% 0.30/0.63        ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) )
% 0.30/0.63        = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % one_diff_power_eq
% 0.30/0.63  thf(fact_8413_one__diff__power__eq,axiom,
% 0.30/0.63      ! [X: rat,N: nat] :
% 0.30/0.63        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 0.30/0.63        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % one_diff_power_eq
% 0.30/0.63  thf(fact_8414_one__diff__power__eq,axiom,
% 0.30/0.63      ! [X: int,N: nat] :
% 0.30/0.63        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 0.30/0.63        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % one_diff_power_eq
% 0.30/0.63  thf(fact_8415_power__diff__1__eq,axiom,
% 0.30/0.63      ! [X: code_integer,N: nat] :
% 0.30/0.63        ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ N ) @ one_one_Code_integer )
% 0.30/0.63        = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % power_diff_1_eq
% 0.30/0.63  thf(fact_8416_power__diff__1__eq,axiom,
% 0.30/0.63      ! [X: rat,N: nat] :
% 0.30/0.63        ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat )
% 0.30/0.63        = ( times_times_rat @ ( minus_minus_rat @ X @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % power_diff_1_eq
% 0.30/0.63  thf(fact_8417_power__diff__1__eq,axiom,
% 0.30/0.63      ! [X: int,N: nat] :
% 0.30/0.63        ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ one_one_int )
% 0.30/0.63        = ( times_times_int @ ( minus_minus_int @ X @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % power_diff_1_eq
% 0.30/0.63  thf(fact_8418_geometric__sum,axiom,
% 0.30/0.63      ! [X: rat,N: nat] :
% 0.30/0.63        ( ( X != one_one_rat )
% 0.30/0.63       => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.30/0.63          = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % geometric_sum
% 0.30/0.63  thf(fact_8419_prod__mono__strict,axiom,
% 0.30/0.63      ! [A2: set_o,F2: $o > code_integer,G2: $o > code_integer] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ! [I2: $o] :
% 0.30/0.63              ( ( member_o @ I2 @ A2 )
% 0.30/0.63             => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) )
% 0.30/0.63                & ( ord_le6747313008572928689nteger @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) ) )
% 0.30/0.63         => ( ( A2 != bot_bot_set_o )
% 0.30/0.63           => ( ord_le6747313008572928689nteger @ ( groups7694694392188491536nteger @ F2 @ A2 ) @ ( groups7694694392188491536nteger @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_mono_strict
% 0.30/0.63  thf(fact_8420_prod__mono__strict,axiom,
% 0.30/0.63      ! [A2: set_nat,F2: nat > code_integer,G2: nat > code_integer] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ! [I2: nat] :
% 0.30/0.63              ( ( member_nat @ I2 @ A2 )
% 0.30/0.63             => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) )
% 0.30/0.63                & ( ord_le6747313008572928689nteger @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) ) )
% 0.30/0.63         => ( ( A2 != bot_bot_set_nat )
% 0.30/0.63           => ( ord_le6747313008572928689nteger @ ( groups3455450783089532116nteger @ F2 @ A2 ) @ ( groups3455450783089532116nteger @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_mono_strict
% 0.30/0.63  thf(fact_8421_prod__mono__strict,axiom,
% 0.30/0.63      ! [A2: set_int,F2: int > code_integer,G2: int > code_integer] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ! [I2: int] :
% 0.30/0.63              ( ( member_int @ I2 @ A2 )
% 0.30/0.63             => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) )
% 0.30/0.63                & ( ord_le6747313008572928689nteger @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) ) )
% 0.30/0.63         => ( ( A2 != bot_bot_set_int )
% 0.30/0.63           => ( ord_le6747313008572928689nteger @ ( groups3827104343326376752nteger @ F2 @ A2 ) @ ( groups3827104343326376752nteger @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_mono_strict
% 0.30/0.63  thf(fact_8422_prod__mono__strict,axiom,
% 0.30/0.63      ! [A2: set_o,F2: $o > rat,G2: $o > rat] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ! [I2: $o] :
% 0.30/0.63              ( ( member_o @ I2 @ A2 )
% 0.30/0.63             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I2 ) )
% 0.30/0.63                & ( ord_less_rat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) ) )
% 0.30/0.63         => ( ( A2 != bot_bot_set_o )
% 0.30/0.63           => ( ord_less_rat @ ( groups2869687844427037835_o_rat @ F2 @ A2 ) @ ( groups2869687844427037835_o_rat @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_mono_strict
% 0.30/0.63  thf(fact_8423_prod__mono__strict,axiom,
% 0.30/0.63      ! [A2: set_nat,F2: nat > rat,G2: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ! [I2: nat] :
% 0.30/0.63              ( ( member_nat @ I2 @ A2 )
% 0.30/0.63             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I2 ) )
% 0.30/0.63                & ( ord_less_rat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) ) )
% 0.30/0.63         => ( ( A2 != bot_bot_set_nat )
% 0.30/0.63           => ( ord_less_rat @ ( groups73079841787564623at_rat @ F2 @ A2 ) @ ( groups73079841787564623at_rat @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_mono_strict
% 0.30/0.63  thf(fact_8424_prod__mono__strict,axiom,
% 0.30/0.63      ! [A2: set_int,F2: int > rat,G2: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ! [I2: int] :
% 0.30/0.63              ( ( member_int @ I2 @ A2 )
% 0.30/0.63             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I2 ) )
% 0.30/0.63                & ( ord_less_rat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) ) )
% 0.30/0.63         => ( ( A2 != bot_bot_set_int )
% 0.30/0.63           => ( ord_less_rat @ ( groups1072433553688619179nt_rat @ F2 @ A2 ) @ ( groups1072433553688619179nt_rat @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_mono_strict
% 0.30/0.63  thf(fact_8425_prod__mono__strict,axiom,
% 0.30/0.63      ! [A2: set_o,F2: $o > nat,G2: $o > nat] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ! [I2: $o] :
% 0.30/0.63              ( ( member_o @ I2 @ A2 )
% 0.30/0.63             => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I2 ) )
% 0.30/0.63                & ( ord_less_nat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) ) )
% 0.30/0.63         => ( ( A2 != bot_bot_set_o )
% 0.30/0.63           => ( ord_less_nat @ ( groups3504817904513533571_o_nat @ F2 @ A2 ) @ ( groups3504817904513533571_o_nat @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_mono_strict
% 0.30/0.63  thf(fact_8426_prod__mono__strict,axiom,
% 0.30/0.63      ! [A2: set_int,F2: int > nat,G2: int > nat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ! [I2: int] :
% 0.30/0.63              ( ( member_int @ I2 @ A2 )
% 0.30/0.63             => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I2 ) )
% 0.30/0.63                & ( ord_less_nat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) ) )
% 0.30/0.63         => ( ( A2 != bot_bot_set_int )
% 0.30/0.63           => ( ord_less_nat @ ( groups1707563613775114915nt_nat @ F2 @ A2 ) @ ( groups1707563613775114915nt_nat @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_mono_strict
% 0.30/0.63  thf(fact_8427_prod__mono__strict,axiom,
% 0.30/0.63      ! [A2: set_o,F2: $o > int,G2: $o > int] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ! [I2: $o] :
% 0.30/0.63              ( ( member_o @ I2 @ A2 )
% 0.30/0.63             => ( ( ord_less_eq_int @ zero_zero_int @ ( F2 @ I2 ) )
% 0.30/0.63                & ( ord_less_int @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) ) )
% 0.30/0.63         => ( ( A2 != bot_bot_set_o )
% 0.30/0.63           => ( ord_less_int @ ( groups3502327434004483295_o_int @ F2 @ A2 ) @ ( groups3502327434004483295_o_int @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_mono_strict
% 0.30/0.63  thf(fact_8428_prod__mono__strict,axiom,
% 0.30/0.63      ! [A2: set_nat,F2: nat > nat,G2: nat > nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ! [I2: nat] :
% 0.30/0.63              ( ( member_nat @ I2 @ A2 )
% 0.30/0.63             => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I2 ) )
% 0.30/0.63                & ( ord_less_nat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) ) )
% 0.30/0.63         => ( ( A2 != bot_bot_set_nat )
% 0.30/0.63           => ( ord_less_nat @ ( groups708209901874060359at_nat @ F2 @ A2 ) @ ( groups708209901874060359at_nat @ G2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_mono_strict
% 0.30/0.63  thf(fact_8429_sum_OatMost__shift,axiom,
% 0.30/0.63      ! [G2: nat > rat,N: nat] :
% 0.30/0.63        ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.63        = ( plus_plus_rat @ ( G2 @ zero_zero_nat )
% 0.30/0.63          @ ( groups2906978787729119204at_rat
% 0.30/0.63            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.atMost_shift
% 0.30/0.63  thf(fact_8430_sum_OatMost__shift,axiom,
% 0.30/0.63      ! [G2: nat > int,N: nat] :
% 0.30/0.63        ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.63        = ( plus_plus_int @ ( G2 @ zero_zero_nat )
% 0.30/0.63          @ ( groups3539618377306564664at_int
% 0.30/0.63            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.atMost_shift
% 0.30/0.63  thf(fact_8431_sum_OatMost__shift,axiom,
% 0.30/0.63      ! [G2: nat > nat,N: nat] :
% 0.30/0.63        ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.63        = ( plus_plus_nat @ ( G2 @ zero_zero_nat )
% 0.30/0.63          @ ( groups3542108847815614940at_nat
% 0.30/0.63            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.atMost_shift
% 0.30/0.63  thf(fact_8432_sum_Ounion__inter__neutral,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > code_integer] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ! [X2: int] :
% 0.30/0.63                ( ( member_int @ X2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.30/0.63               => ( ( G2 @ X2 )
% 0.30/0.63                  = zero_z3403309356797280102nteger ) )
% 0.30/0.63           => ( ( groups7873554091576472773nteger @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63              = ( plus_p5714425477246183910nteger @ ( groups7873554091576472773nteger @ G2 @ A2 ) @ ( groups7873554091576472773nteger @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_inter_neutral
% 0.30/0.63  thf(fact_8433_sum_Ounion__inter__neutral,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ! [X2: int] :
% 0.30/0.63                ( ( member_int @ X2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.30/0.63               => ( ( G2 @ X2 )
% 0.30/0.63                  = zero_zero_rat ) )
% 0.30/0.63           => ( ( groups3906332499630173760nt_rat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63              = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G2 @ A2 ) @ ( groups3906332499630173760nt_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_inter_neutral
% 0.30/0.63  thf(fact_8434_sum_Ounion__inter__neutral,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > nat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ! [X2: int] :
% 0.30/0.63                ( ( member_int @ X2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.30/0.63               => ( ( G2 @ X2 )
% 0.30/0.63                  = zero_zero_nat ) )
% 0.30/0.63           => ( ( groups4541462559716669496nt_nat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63              = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G2 @ A2 ) @ ( groups4541462559716669496nt_nat @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_inter_neutral
% 0.30/0.63  thf(fact_8435_sum_Ounion__inter__neutral,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > code_integer] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ! [X2: nat] :
% 0.30/0.63                ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.30/0.63               => ( ( G2 @ X2 )
% 0.30/0.63                  = zero_z3403309356797280102nteger ) )
% 0.30/0.63           => ( ( groups7501900531339628137nteger @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( plus_p5714425477246183910nteger @ ( groups7501900531339628137nteger @ G2 @ A2 ) @ ( groups7501900531339628137nteger @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_inter_neutral
% 0.30/0.63  thf(fact_8436_sum_Ounion__inter__neutral,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ! [X2: nat] :
% 0.30/0.63                ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.30/0.63               => ( ( G2 @ X2 )
% 0.30/0.63                  = zero_zero_rat ) )
% 0.30/0.63           => ( ( groups2906978787729119204at_rat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ A2 ) @ ( groups2906978787729119204at_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_inter_neutral
% 0.30/0.63  thf(fact_8437_sum_Ounion__inter__neutral,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > int] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ! [X2: nat] :
% 0.30/0.63                ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.30/0.63               => ( ( G2 @ X2 )
% 0.30/0.63                  = zero_zero_int ) )
% 0.30/0.63           => ( ( groups3539618377306564664at_int @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ A2 ) @ ( groups3539618377306564664at_int @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_inter_neutral
% 0.30/0.63  thf(fact_8438_sum_Ounion__inter__neutral,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ! [X2: nat] :
% 0.30/0.63                ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.30/0.63               => ( ( G2 @ X2 )
% 0.30/0.63                  = zero_zero_nat ) )
% 0.30/0.63           => ( ( groups3542108847815614940at_nat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ A2 ) @ ( groups3542108847815614940at_nat @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_inter_neutral
% 0.30/0.63  thf(fact_8439_sum_Ounion__inter__neutral,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ! [X2: int] :
% 0.30/0.63                ( ( member_int @ X2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.30/0.63               => ( ( G2 @ X2 )
% 0.30/0.63                  = zero_zero_int ) )
% 0.30/0.63           => ( ( groups4538972089207619220nt_int @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63              = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G2 @ A2 ) @ ( groups4538972089207619220nt_int @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_inter_neutral
% 0.30/0.63  thf(fact_8440_sum_Ounion__inter__neutral,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > code_integer] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( finite6177210948735845034at_nat @ B2 )
% 0.30/0.63         => ( ! [X2: product_prod_nat_nat] :
% 0.30/0.63                ( ( member8440522571783428010at_nat @ X2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 0.30/0.63               => ( ( G2 @ X2 )
% 0.30/0.63                  = zero_z3403309356797280102nteger ) )
% 0.30/0.63           => ( ( groups196832835297161892nteger @ G2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( plus_p5714425477246183910nteger @ ( groups196832835297161892nteger @ G2 @ A2 ) @ ( groups196832835297161892nteger @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_inter_neutral
% 0.30/0.63  thf(fact_8441_sum_Ounion__inter__neutral,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > rat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( finite6177210948735845034at_nat @ B2 )
% 0.30/0.63         => ( ! [X2: product_prod_nat_nat] :
% 0.30/0.63                ( ( member8440522571783428010at_nat @ X2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 0.30/0.63               => ( ( G2 @ X2 )
% 0.30/0.63                  = zero_zero_rat ) )
% 0.30/0.63           => ( ( groups342789780944988191at_rat @ G2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( plus_plus_rat @ ( groups342789780944988191at_rat @ G2 @ A2 ) @ ( groups342789780944988191at_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_inter_neutral
% 0.30/0.63  thf(fact_8442_sum_Oremove,axiom,
% 0.30/0.63      ! [A2: set_o,X: $o,G2: $o > rat] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( member_o @ X @ A2 )
% 0.30/0.63         => ( ( groups7872700643590313910_o_rat @ G2 @ A2 )
% 0.30/0.63            = ( plus_plus_rat @ ( G2 @ X ) @ ( groups7872700643590313910_o_rat @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.remove
% 0.30/0.63  thf(fact_8443_sum_Oremove,axiom,
% 0.30/0.63      ! [A2: set_o,X: $o,G2: $o > nat] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( member_o @ X @ A2 )
% 0.30/0.63         => ( ( groups8507830703676809646_o_nat @ G2 @ A2 )
% 0.30/0.63            = ( plus_plus_nat @ ( G2 @ X ) @ ( groups8507830703676809646_o_nat @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.remove
% 0.30/0.63  thf(fact_8444_sum_Oremove,axiom,
% 0.30/0.63      ! [A2: set_o,X: $o,G2: $o > int] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( member_o @ X @ A2 )
% 0.30/0.63         => ( ( groups8505340233167759370_o_int @ G2 @ A2 )
% 0.30/0.63            = ( plus_plus_int @ ( G2 @ X ) @ ( groups8505340233167759370_o_int @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.remove
% 0.30/0.63  thf(fact_8445_sum_Oremove,axiom,
% 0.30/0.63      ! [A2: set_int,X: int,G2: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( member_int @ X @ A2 )
% 0.30/0.63         => ( ( groups3906332499630173760nt_rat @ G2 @ A2 )
% 0.30/0.63            = ( plus_plus_rat @ ( G2 @ X ) @ ( groups3906332499630173760nt_rat @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.remove
% 0.30/0.63  thf(fact_8446_sum_Oremove,axiom,
% 0.30/0.63      ! [A2: set_int,X: int,G2: int > nat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( member_int @ X @ A2 )
% 0.30/0.63         => ( ( groups4541462559716669496nt_nat @ G2 @ A2 )
% 0.30/0.63            = ( plus_plus_nat @ ( G2 @ X ) @ ( groups4541462559716669496nt_nat @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.remove
% 0.30/0.63  thf(fact_8447_sum_Oremove,axiom,
% 0.30/0.63      ! [A2: set_nat,X: nat,G2: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( member_nat @ X @ A2 )
% 0.30/0.63         => ( ( groups2906978787729119204at_rat @ G2 @ A2 )
% 0.30/0.63            = ( plus_plus_rat @ ( G2 @ X ) @ ( groups2906978787729119204at_rat @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.remove
% 0.30/0.63  thf(fact_8448_sum_Oremove,axiom,
% 0.30/0.63      ! [A2: set_nat,X: nat,G2: nat > int] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( member_nat @ X @ A2 )
% 0.30/0.63         => ( ( groups3539618377306564664at_int @ G2 @ A2 )
% 0.30/0.63            = ( plus_plus_int @ ( G2 @ X ) @ ( groups3539618377306564664at_int @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.remove
% 0.30/0.63  thf(fact_8449_sum_Oremove,axiom,
% 0.30/0.63      ! [A2: set_nat,X: nat,G2: nat > nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( member_nat @ X @ A2 )
% 0.30/0.63         => ( ( groups3542108847815614940at_nat @ G2 @ A2 )
% 0.30/0.63            = ( plus_plus_nat @ ( G2 @ X ) @ ( groups3542108847815614940at_nat @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.remove
% 0.30/0.63  thf(fact_8450_sum_Oremove,axiom,
% 0.30/0.63      ! [A2: set_int,X: int,G2: int > int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( member_int @ X @ A2 )
% 0.30/0.63         => ( ( groups4538972089207619220nt_int @ G2 @ A2 )
% 0.30/0.63            = ( plus_plus_int @ ( G2 @ X ) @ ( groups4538972089207619220nt_int @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.remove
% 0.30/0.63  thf(fact_8451_sum_Oremove,axiom,
% 0.30/0.63      ! [A2: set_set_nat,X: set_nat,G2: set_nat > rat] :
% 0.30/0.63        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.63       => ( ( member_set_nat @ X @ A2 )
% 0.30/0.63         => ( ( groups7659867448343625626at_rat @ G2 @ A2 )
% 0.30/0.63            = ( plus_plus_rat @ ( G2 @ X ) @ ( groups7659867448343625626at_rat @ G2 @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.remove
% 0.30/0.63  thf(fact_8452_sum_Oinsert__remove,axiom,
% 0.30/0.63      ! [A2: set_o,G2: $o > rat,X: $o] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( groups7872700643590313910_o_rat @ G2 @ ( insert_o @ X @ A2 ) )
% 0.30/0.63          = ( plus_plus_rat @ ( G2 @ X ) @ ( groups7872700643590313910_o_rat @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.insert_remove
% 0.30/0.63  thf(fact_8453_sum_Oinsert__remove,axiom,
% 0.30/0.63      ! [A2: set_o,G2: $o > nat,X: $o] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( groups8507830703676809646_o_nat @ G2 @ ( insert_o @ X @ A2 ) )
% 0.30/0.63          = ( plus_plus_nat @ ( G2 @ X ) @ ( groups8507830703676809646_o_nat @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.insert_remove
% 0.30/0.63  thf(fact_8454_sum_Oinsert__remove,axiom,
% 0.30/0.63      ! [A2: set_o,G2: $o > int,X: $o] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( groups8505340233167759370_o_int @ G2 @ ( insert_o @ X @ A2 ) )
% 0.30/0.63          = ( plus_plus_int @ ( G2 @ X ) @ ( groups8505340233167759370_o_int @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.insert_remove
% 0.30/0.63  thf(fact_8455_sum_Oinsert__remove,axiom,
% 0.30/0.63      ! [A2: set_int,G2: int > rat,X: int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups3906332499630173760nt_rat @ G2 @ ( insert_int @ X @ A2 ) )
% 0.30/0.63          = ( plus_plus_rat @ ( G2 @ X ) @ ( groups3906332499630173760nt_rat @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.insert_remove
% 0.30/0.63  thf(fact_8456_sum_Oinsert__remove,axiom,
% 0.30/0.63      ! [A2: set_int,G2: int > nat,X: int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups4541462559716669496nt_nat @ G2 @ ( insert_int @ X @ A2 ) )
% 0.30/0.63          = ( plus_plus_nat @ ( G2 @ X ) @ ( groups4541462559716669496nt_nat @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.insert_remove
% 0.30/0.63  thf(fact_8457_sum_Oinsert__remove,axiom,
% 0.30/0.63      ! [A2: set_nat,G2: nat > rat,X: nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups2906978787729119204at_rat @ G2 @ ( insert_nat @ X @ A2 ) )
% 0.30/0.63          = ( plus_plus_rat @ ( G2 @ X ) @ ( groups2906978787729119204at_rat @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.insert_remove
% 0.30/0.63  thf(fact_8458_sum_Oinsert__remove,axiom,
% 0.30/0.63      ! [A2: set_nat,G2: nat > int,X: nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups3539618377306564664at_int @ G2 @ ( insert_nat @ X @ A2 ) )
% 0.30/0.63          = ( plus_plus_int @ ( G2 @ X ) @ ( groups3539618377306564664at_int @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.insert_remove
% 0.30/0.63  thf(fact_8459_sum_Oinsert__remove,axiom,
% 0.30/0.63      ! [A2: set_nat,G2: nat > nat,X: nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups3542108847815614940at_nat @ G2 @ ( insert_nat @ X @ A2 ) )
% 0.30/0.63          = ( plus_plus_nat @ ( G2 @ X ) @ ( groups3542108847815614940at_nat @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.insert_remove
% 0.30/0.63  thf(fact_8460_sum_Oinsert__remove,axiom,
% 0.30/0.63      ! [A2: set_int,G2: int > int,X: int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups4538972089207619220nt_int @ G2 @ ( insert_int @ X @ A2 ) )
% 0.30/0.63          = ( plus_plus_int @ ( G2 @ X ) @ ( groups4538972089207619220nt_int @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.insert_remove
% 0.30/0.63  thf(fact_8461_sum_Oinsert__remove,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > rat,X: product_prod_nat_nat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( groups342789780944988191at_rat @ G2 @ ( insert8211810215607154385at_nat @ X @ A2 ) )
% 0.30/0.63          = ( plus_plus_rat @ ( G2 @ X ) @ ( groups342789780944988191at_rat @ G2 @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.insert_remove
% 0.30/0.63  thf(fact_8462_prod_OatMost__shift,axiom,
% 0.30/0.63      ! [G2: nat > code_integer,N: nat] :
% 0.30/0.63        ( ( groups3455450783089532116nteger @ G2 @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.63        = ( times_3573771949741848930nteger @ ( G2 @ zero_zero_nat )
% 0.30/0.63          @ ( groups3455450783089532116nteger
% 0.30/0.63            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.atMost_shift
% 0.30/0.63  thf(fact_8463_prod_OatMost__shift,axiom,
% 0.30/0.63      ! [G2: nat > assn,N: nat] :
% 0.30/0.63        ( ( groups6906906614972039071t_assn @ G2 @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.63        = ( times_times_assn @ ( G2 @ zero_zero_nat )
% 0.30/0.63          @ ( groups6906906614972039071t_assn
% 0.30/0.63            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.atMost_shift
% 0.30/0.63  thf(fact_8464_prod_OatMost__shift,axiom,
% 0.30/0.63      ! [G2: nat > rat,N: nat] :
% 0.30/0.63        ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.63        = ( times_times_rat @ ( G2 @ zero_zero_nat )
% 0.30/0.63          @ ( groups73079841787564623at_rat
% 0.30/0.63            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.atMost_shift
% 0.30/0.63  thf(fact_8465_prod_OatMost__shift,axiom,
% 0.30/0.63      ! [G2: nat > nat,N: nat] :
% 0.30/0.63        ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.63        = ( times_times_nat @ ( G2 @ zero_zero_nat )
% 0.30/0.63          @ ( groups708209901874060359at_nat
% 0.30/0.63            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.atMost_shift
% 0.30/0.63  thf(fact_8466_prod_OatMost__shift,axiom,
% 0.30/0.63      ! [G2: nat > int,N: nat] :
% 0.30/0.63        ( ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.63        = ( times_times_int @ ( G2 @ zero_zero_nat )
% 0.30/0.63          @ ( groups705719431365010083at_int
% 0.30/0.63            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 0.30/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.atMost_shift
% 0.30/0.63  thf(fact_8467_sum__diff1,axiom,
% 0.30/0.63      ! [A2: set_o,A: $o,F2: $o > rat] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( ( member_o @ A @ A2 )
% 0.30/0.63           => ( ( groups7872700643590313910_o_rat @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.30/0.63              = ( minus_minus_rat @ ( groups7872700643590313910_o_rat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.63          & ( ~ ( member_o @ A @ A2 )
% 0.30/0.63           => ( ( groups7872700643590313910_o_rat @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.30/0.63              = ( groups7872700643590313910_o_rat @ F2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_diff1
% 0.30/0.63  thf(fact_8468_sum__diff1,axiom,
% 0.30/0.63      ! [A2: set_int,A: int,F2: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( ( member_int @ A @ A2 )
% 0.30/0.63           => ( ( groups3906332499630173760nt_rat @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.30/0.63              = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.63          & ( ~ ( member_int @ A @ A2 )
% 0.30/0.63           => ( ( groups3906332499630173760nt_rat @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.30/0.63              = ( groups3906332499630173760nt_rat @ F2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_diff1
% 0.30/0.63  thf(fact_8469_sum__diff1,axiom,
% 0.30/0.63      ! [A2: set_o,A: $o,F2: $o > int] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( ( member_o @ A @ A2 )
% 0.30/0.63           => ( ( groups8505340233167759370_o_int @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.30/0.63              = ( minus_minus_int @ ( groups8505340233167759370_o_int @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.63          & ( ~ ( member_o @ A @ A2 )
% 0.30/0.63           => ( ( groups8505340233167759370_o_int @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.30/0.63              = ( groups8505340233167759370_o_int @ F2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_diff1
% 0.30/0.63  thf(fact_8470_sum__diff1,axiom,
% 0.30/0.63      ! [A2: set_nat,A: nat,F2: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( ( member_nat @ A @ A2 )
% 0.30/0.63           => ( ( groups2906978787729119204at_rat @ F2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.30/0.63              = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.63          & ( ~ ( member_nat @ A @ A2 )
% 0.30/0.63           => ( ( groups2906978787729119204at_rat @ F2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.30/0.63              = ( groups2906978787729119204at_rat @ F2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_diff1
% 0.30/0.63  thf(fact_8471_sum__diff1,axiom,
% 0.30/0.63      ! [A2: set_nat,A: nat,F2: nat > int] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( ( member_nat @ A @ A2 )
% 0.30/0.63           => ( ( groups3539618377306564664at_int @ F2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.30/0.63              = ( minus_minus_int @ ( groups3539618377306564664at_int @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.63          & ( ~ ( member_nat @ A @ A2 )
% 0.30/0.63           => ( ( groups3539618377306564664at_int @ F2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.30/0.63              = ( groups3539618377306564664at_int @ F2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_diff1
% 0.30/0.63  thf(fact_8472_sum__diff1,axiom,
% 0.30/0.63      ! [A2: set_int,A: int,F2: int > int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( ( member_int @ A @ A2 )
% 0.30/0.63           => ( ( groups4538972089207619220nt_int @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.30/0.63              = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.63          & ( ~ ( member_int @ A @ A2 )
% 0.30/0.63           => ( ( groups4538972089207619220nt_int @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.30/0.63              = ( groups4538972089207619220nt_int @ F2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_diff1
% 0.30/0.63  thf(fact_8473_sum__diff1,axiom,
% 0.30/0.63      ! [A2: set_set_nat,A: set_nat,F2: set_nat > rat] :
% 0.30/0.63        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.63       => ( ( ( member_set_nat @ A @ A2 )
% 0.30/0.63           => ( ( groups7659867448343625626at_rat @ F2 @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.30/0.63              = ( minus_minus_rat @ ( groups7659867448343625626at_rat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.63          & ( ~ ( member_set_nat @ A @ A2 )
% 0.30/0.63           => ( ( groups7659867448343625626at_rat @ F2 @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.30/0.63              = ( groups7659867448343625626at_rat @ F2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_diff1
% 0.30/0.63  thf(fact_8474_sum__diff1,axiom,
% 0.30/0.63      ! [A2: set_set_nat,A: set_nat,F2: set_nat > int] :
% 0.30/0.63        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.63       => ( ( ( member_set_nat @ A @ A2 )
% 0.30/0.63           => ( ( groups8292507037921071086at_int @ F2 @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.30/0.63              = ( minus_minus_int @ ( groups8292507037921071086at_int @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.63          & ( ~ ( member_set_nat @ A @ A2 )
% 0.30/0.63           => ( ( groups8292507037921071086at_int @ F2 @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 0.30/0.63              = ( groups8292507037921071086at_int @ F2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_diff1
% 0.30/0.63  thf(fact_8475_sum__diff1,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,F2: product_prod_nat_nat > rat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( ( member8440522571783428010at_nat @ A @ A2 )
% 0.30/0.63           => ( ( groups342789780944988191at_rat @ F2 @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 0.30/0.63              = ( minus_minus_rat @ ( groups342789780944988191at_rat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.63          & ( ~ ( member8440522571783428010at_nat @ A @ A2 )
% 0.30/0.63           => ( ( groups342789780944988191at_rat @ F2 @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 0.30/0.63              = ( groups342789780944988191at_rat @ F2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_diff1
% 0.30/0.63  thf(fact_8476_sum__diff1,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,F2: product_prod_nat_nat > int] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( ( member8440522571783428010at_nat @ A @ A2 )
% 0.30/0.63           => ( ( groups975429370522433651at_int @ F2 @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 0.30/0.63              = ( minus_minus_int @ ( groups975429370522433651at_int @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.63          & ( ~ ( member8440522571783428010at_nat @ A @ A2 )
% 0.30/0.63           => ( ( groups975429370522433651at_int @ F2 @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 0.30/0.63              = ( groups975429370522433651at_int @ F2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_diff1
% 0.30/0.63  thf(fact_8477_sum__Un,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,F2: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( groups3906332499630173760nt_rat @ F2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63            = ( minus_minus_rat @ ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ F2 @ A2 ) @ ( groups3906332499630173760nt_rat @ F2 @ B2 ) ) @ ( groups3906332499630173760nt_rat @ F2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un
% 0.30/0.63  thf(fact_8478_sum__Un,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > rat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( finite6177210948735845034at_nat @ B2 )
% 0.30/0.63         => ( ( groups342789780944988191at_rat @ F2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( minus_minus_rat @ ( plus_plus_rat @ ( groups342789780944988191at_rat @ F2 @ A2 ) @ ( groups342789780944988191at_rat @ F2 @ B2 ) ) @ ( groups342789780944988191at_rat @ F2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un
% 0.30/0.63  thf(fact_8479_sum__Un,axiom,
% 0.30/0.63      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,F2: produc4166570645942440679at_nat > rat] :
% 0.30/0.63        ( ( finite1918287321285529104at_nat @ A2 )
% 0.30/0.63       => ( ( finite1918287321285529104at_nat @ B2 )
% 0.30/0.63         => ( ( groups6424767709179651461at_rat @ F2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( minus_minus_rat @ ( plus_plus_rat @ ( groups6424767709179651461at_rat @ F2 @ A2 ) @ ( groups6424767709179651461at_rat @ F2 @ B2 ) ) @ ( groups6424767709179651461at_rat @ F2 @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un
% 0.30/0.63  thf(fact_8480_sum__Un,axiom,
% 0.30/0.63      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,F2: produc3843707927480180839at_nat > rat] :
% 0.30/0.63        ( ( finite4343798906461161616at_nat @ A2 )
% 0.30/0.63       => ( ( finite4343798906461161616at_nat @ B2 )
% 0.30/0.63         => ( ( groups3225780264831618053at_rat @ F2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( minus_minus_rat @ ( plus_plus_rat @ ( groups3225780264831618053at_rat @ F2 @ A2 ) @ ( groups3225780264831618053at_rat @ F2 @ B2 ) ) @ ( groups3225780264831618053at_rat @ F2 @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un
% 0.30/0.63  thf(fact_8481_sum__Un,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,F2: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( groups2906978787729119204at_rat @ F2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( minus_minus_rat @ ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F2 @ A2 ) @ ( groups2906978787729119204at_rat @ F2 @ B2 ) ) @ ( groups2906978787729119204at_rat @ F2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un
% 0.30/0.63  thf(fact_8482_sum__Un,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > int] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( finite6177210948735845034at_nat @ B2 )
% 0.30/0.63         => ( ( groups975429370522433651at_int @ F2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( minus_minus_int @ ( plus_plus_int @ ( groups975429370522433651at_int @ F2 @ A2 ) @ ( groups975429370522433651at_int @ F2 @ B2 ) ) @ ( groups975429370522433651at_int @ F2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un
% 0.30/0.63  thf(fact_8483_sum__Un,axiom,
% 0.30/0.63      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,F2: produc4166570645942440679at_nat > int] :
% 0.30/0.63        ( ( finite1918287321285529104at_nat @ A2 )
% 0.30/0.63       => ( ( finite1918287321285529104at_nat @ B2 )
% 0.30/0.63         => ( ( groups7057407298757096921at_int @ F2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( minus_minus_int @ ( plus_plus_int @ ( groups7057407298757096921at_int @ F2 @ A2 ) @ ( groups7057407298757096921at_int @ F2 @ B2 ) ) @ ( groups7057407298757096921at_int @ F2 @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un
% 0.30/0.63  thf(fact_8484_sum__Un,axiom,
% 0.30/0.63      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,F2: produc3843707927480180839at_nat > int] :
% 0.30/0.63        ( ( finite4343798906461161616at_nat @ A2 )
% 0.30/0.63       => ( ( finite4343798906461161616at_nat @ B2 )
% 0.30/0.63         => ( ( groups3858419854409063513at_int @ F2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( minus_minus_int @ ( plus_plus_int @ ( groups3858419854409063513at_int @ F2 @ A2 ) @ ( groups3858419854409063513at_int @ F2 @ B2 ) ) @ ( groups3858419854409063513at_int @ F2 @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un
% 0.30/0.63  thf(fact_8485_sum__Un,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,F2: nat > int] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( groups3539618377306564664at_int @ F2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( minus_minus_int @ ( plus_plus_int @ ( groups3539618377306564664at_int @ F2 @ A2 ) @ ( groups3539618377306564664at_int @ F2 @ B2 ) ) @ ( groups3539618377306564664at_int @ F2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un
% 0.30/0.63  thf(fact_8486_sum__Un,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,F2: int > int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( groups4538972089207619220nt_int @ F2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63            = ( minus_minus_int @ ( plus_plus_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) @ ( groups4538972089207619220nt_int @ F2 @ B2 ) ) @ ( groups4538972089207619220nt_int @ F2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un
% 0.30/0.63  thf(fact_8487_sum_Ounion__disjoint,axiom,
% 0.30/0.63      ! [A2: set_o,B2: set_o,G2: $o > rat] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( finite_finite_o @ B2 )
% 0.30/0.63         => ( ( ( inf_inf_set_o @ A2 @ B2 )
% 0.30/0.63              = bot_bot_set_o )
% 0.30/0.63           => ( ( groups7872700643590313910_o_rat @ G2 @ ( sup_sup_set_o @ A2 @ B2 ) )
% 0.30/0.63              = ( plus_plus_rat @ ( groups7872700643590313910_o_rat @ G2 @ A2 ) @ ( groups7872700643590313910_o_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_disjoint
% 0.30/0.63  thf(fact_8488_sum_Ounion__disjoint,axiom,
% 0.30/0.63      ! [A2: set_o,B2: set_o,G2: $o > nat] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( finite_finite_o @ B2 )
% 0.30/0.63         => ( ( ( inf_inf_set_o @ A2 @ B2 )
% 0.30/0.63              = bot_bot_set_o )
% 0.30/0.63           => ( ( groups8507830703676809646_o_nat @ G2 @ ( sup_sup_set_o @ A2 @ B2 ) )
% 0.30/0.63              = ( plus_plus_nat @ ( groups8507830703676809646_o_nat @ G2 @ A2 ) @ ( groups8507830703676809646_o_nat @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_disjoint
% 0.30/0.63  thf(fact_8489_sum_Ounion__disjoint,axiom,
% 0.30/0.63      ! [A2: set_o,B2: set_o,G2: $o > int] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( finite_finite_o @ B2 )
% 0.30/0.63         => ( ( ( inf_inf_set_o @ A2 @ B2 )
% 0.30/0.63              = bot_bot_set_o )
% 0.30/0.63           => ( ( groups8505340233167759370_o_int @ G2 @ ( sup_sup_set_o @ A2 @ B2 ) )
% 0.30/0.63              = ( plus_plus_int @ ( groups8505340233167759370_o_int @ G2 @ A2 ) @ ( groups8505340233167759370_o_int @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_disjoint
% 0.30/0.63  thf(fact_8490_sum_Ounion__disjoint,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 0.30/0.63              = bot_bot_set_nat )
% 0.30/0.63           => ( ( groups2906978787729119204at_rat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ A2 ) @ ( groups2906978787729119204at_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_disjoint
% 0.30/0.63  thf(fact_8491_sum_Ounion__disjoint,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > int] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 0.30/0.63              = bot_bot_set_nat )
% 0.30/0.63           => ( ( groups3539618377306564664at_int @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ A2 ) @ ( groups3539618377306564664at_int @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_disjoint
% 0.30/0.63  thf(fact_8492_sum_Ounion__disjoint,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( ( inf_inf_set_int @ A2 @ B2 )
% 0.30/0.63              = bot_bot_set_int )
% 0.30/0.63           => ( ( groups3906332499630173760nt_rat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63              = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G2 @ A2 ) @ ( groups3906332499630173760nt_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_disjoint
% 0.30/0.63  thf(fact_8493_sum_Ounion__disjoint,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > nat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( ( inf_inf_set_int @ A2 @ B2 )
% 0.30/0.63              = bot_bot_set_int )
% 0.30/0.63           => ( ( groups4541462559716669496nt_nat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63              = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G2 @ A2 ) @ ( groups4541462559716669496nt_nat @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_disjoint
% 0.30/0.63  thf(fact_8494_sum_Ounion__disjoint,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 0.30/0.63              = bot_bot_set_nat )
% 0.30/0.63           => ( ( groups3542108847815614940at_nat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ A2 ) @ ( groups3542108847815614940at_nat @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_disjoint
% 0.30/0.63  thf(fact_8495_sum_Ounion__disjoint,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( ( inf_inf_set_int @ A2 @ B2 )
% 0.30/0.63              = bot_bot_set_int )
% 0.30/0.63           => ( ( groups4538972089207619220nt_int @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63              = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G2 @ A2 ) @ ( groups4538972089207619220nt_int @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_disjoint
% 0.30/0.63  thf(fact_8496_sum_Ounion__disjoint,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > rat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( finite6177210948735845034at_nat @ B2 )
% 0.30/0.63         => ( ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 0.30/0.63              = bot_bo2099793752762293965at_nat )
% 0.30/0.63           => ( ( groups342789780944988191at_rat @ G2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( plus_plus_rat @ ( groups342789780944988191at_rat @ G2 @ A2 ) @ ( groups342789780944988191at_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_disjoint
% 0.30/0.63  thf(fact_8497_prod_Oremove,axiom,
% 0.30/0.63      ! [A2: set_o,X: $o,G2: $o > code_integer] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( member_o @ X @ A2 )
% 0.30/0.63         => ( ( groups7694694392188491536nteger @ G2 @ A2 )
% 0.30/0.63            = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups7694694392188491536nteger @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.remove
% 0.30/0.63  thf(fact_8498_prod_Oremove,axiom,
% 0.30/0.63      ! [A2: set_int,X: int,G2: int > code_integer] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( member_int @ X @ A2 )
% 0.30/0.63         => ( ( groups3827104343326376752nteger @ G2 @ A2 )
% 0.30/0.63            = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups3827104343326376752nteger @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.remove
% 0.30/0.63  thf(fact_8499_prod_Oremove,axiom,
% 0.30/0.63      ! [A2: set_nat,X: nat,G2: nat > code_integer] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( member_nat @ X @ A2 )
% 0.30/0.63         => ( ( groups3455450783089532116nteger @ G2 @ A2 )
% 0.30/0.63            = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups3455450783089532116nteger @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.remove
% 0.30/0.63  thf(fact_8500_prod_Oremove,axiom,
% 0.30/0.63      ! [A2: set_o,X: $o,G2: $o > assn] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( member_o @ X @ A2 )
% 0.30/0.63         => ( ( groups5301882518646026715o_assn @ G2 @ A2 )
% 0.30/0.63            = ( times_times_assn @ ( G2 @ X ) @ ( groups5301882518646026715o_assn @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.remove
% 0.30/0.63  thf(fact_8501_prod_Oremove,axiom,
% 0.30/0.63      ! [A2: set_int,X: int,G2: int > assn] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( member_int @ X @ A2 )
% 0.30/0.63         => ( ( groups7882442080178216443t_assn @ G2 @ A2 )
% 0.30/0.63            = ( times_times_assn @ ( G2 @ X ) @ ( groups7882442080178216443t_assn @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.remove
% 0.30/0.63  thf(fact_8502_prod_Oremove,axiom,
% 0.30/0.63      ! [A2: set_nat,X: nat,G2: nat > assn] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( member_nat @ X @ A2 )
% 0.30/0.63         => ( ( groups6906906614972039071t_assn @ G2 @ A2 )
% 0.30/0.63            = ( times_times_assn @ ( G2 @ X ) @ ( groups6906906614972039071t_assn @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.remove
% 0.30/0.63  thf(fact_8503_prod_Oremove,axiom,
% 0.30/0.63      ! [A2: set_o,X: $o,G2: $o > rat] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( member_o @ X @ A2 )
% 0.30/0.63         => ( ( groups2869687844427037835_o_rat @ G2 @ A2 )
% 0.30/0.63            = ( times_times_rat @ ( G2 @ X ) @ ( groups2869687844427037835_o_rat @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.remove
% 0.30/0.63  thf(fact_8504_prod_Oremove,axiom,
% 0.30/0.63      ! [A2: set_int,X: int,G2: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( member_int @ X @ A2 )
% 0.30/0.63         => ( ( groups1072433553688619179nt_rat @ G2 @ A2 )
% 0.30/0.63            = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.remove
% 0.30/0.63  thf(fact_8505_prod_Oremove,axiom,
% 0.30/0.63      ! [A2: set_nat,X: nat,G2: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( member_nat @ X @ A2 )
% 0.30/0.63         => ( ( groups73079841787564623at_rat @ G2 @ A2 )
% 0.30/0.63            = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.remove
% 0.30/0.63  thf(fact_8506_prod_Oremove,axiom,
% 0.30/0.63      ! [A2: set_o,X: $o,G2: $o > nat] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( member_o @ X @ A2 )
% 0.30/0.63         => ( ( groups3504817904513533571_o_nat @ G2 @ A2 )
% 0.30/0.63            = ( times_times_nat @ ( G2 @ X ) @ ( groups3504817904513533571_o_nat @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.remove
% 0.30/0.63  thf(fact_8507_prod_Oinsert__remove,axiom,
% 0.30/0.63      ! [A2: set_o,G2: $o > code_integer,X: $o] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( groups7694694392188491536nteger @ G2 @ ( insert_o @ X @ A2 ) )
% 0.30/0.63          = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups7694694392188491536nteger @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.insert_remove
% 0.30/0.63  thf(fact_8508_prod_Oinsert__remove,axiom,
% 0.30/0.63      ! [A2: set_int,G2: int > code_integer,X: int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups3827104343326376752nteger @ G2 @ ( insert_int @ X @ A2 ) )
% 0.30/0.63          = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups3827104343326376752nteger @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.insert_remove
% 0.30/0.63  thf(fact_8509_prod_Oinsert__remove,axiom,
% 0.30/0.63      ! [A2: set_nat,G2: nat > code_integer,X: nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups3455450783089532116nteger @ G2 @ ( insert_nat @ X @ A2 ) )
% 0.30/0.63          = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups3455450783089532116nteger @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.insert_remove
% 0.30/0.63  thf(fact_8510_prod_Oinsert__remove,axiom,
% 0.30/0.63      ! [A2: set_o,G2: $o > assn,X: $o] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( groups5301882518646026715o_assn @ G2 @ ( insert_o @ X @ A2 ) )
% 0.30/0.63          = ( times_times_assn @ ( G2 @ X ) @ ( groups5301882518646026715o_assn @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.insert_remove
% 0.30/0.63  thf(fact_8511_prod_Oinsert__remove,axiom,
% 0.30/0.63      ! [A2: set_int,G2: int > assn,X: int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups7882442080178216443t_assn @ G2 @ ( insert_int @ X @ A2 ) )
% 0.30/0.63          = ( times_times_assn @ ( G2 @ X ) @ ( groups7882442080178216443t_assn @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.insert_remove
% 0.30/0.63  thf(fact_8512_prod_Oinsert__remove,axiom,
% 0.30/0.63      ! [A2: set_nat,G2: nat > assn,X: nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups6906906614972039071t_assn @ G2 @ ( insert_nat @ X @ A2 ) )
% 0.30/0.63          = ( times_times_assn @ ( G2 @ X ) @ ( groups6906906614972039071t_assn @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.insert_remove
% 0.30/0.63  thf(fact_8513_prod_Oinsert__remove,axiom,
% 0.30/0.63      ! [A2: set_o,G2: $o > rat,X: $o] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( groups2869687844427037835_o_rat @ G2 @ ( insert_o @ X @ A2 ) )
% 0.30/0.63          = ( times_times_rat @ ( G2 @ X ) @ ( groups2869687844427037835_o_rat @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.insert_remove
% 0.30/0.63  thf(fact_8514_prod_Oinsert__remove,axiom,
% 0.30/0.63      ! [A2: set_int,G2: int > rat,X: int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A2 ) )
% 0.30/0.63          = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.insert_remove
% 0.30/0.63  thf(fact_8515_prod_Oinsert__remove,axiom,
% 0.30/0.63      ! [A2: set_nat,G2: nat > rat,X: nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A2 ) )
% 0.30/0.63          = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.insert_remove
% 0.30/0.63  thf(fact_8516_prod_Oinsert__remove,axiom,
% 0.30/0.63      ! [A2: set_o,G2: $o > nat,X: $o] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( groups3504817904513533571_o_nat @ G2 @ ( insert_o @ X @ A2 ) )
% 0.30/0.63          = ( times_times_nat @ ( G2 @ X ) @ ( groups3504817904513533571_o_nat @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.insert_remove
% 0.30/0.63  thf(fact_8517_prod_Ounion__inter__neutral,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > code_integer] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ! [X2: int] :
% 0.30/0.63                ( ( member_int @ X2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.30/0.63               => ( ( G2 @ X2 )
% 0.30/0.63                  = one_one_Code_integer ) )
% 0.30/0.63           => ( ( groups3827104343326376752nteger @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63              = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G2 @ A2 ) @ ( groups3827104343326376752nteger @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_inter_neutral
% 0.30/0.63  thf(fact_8518_prod_Ounion__inter__neutral,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > code_integer] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ! [X2: nat] :
% 0.30/0.63                ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.30/0.63               => ( ( G2 @ X2 )
% 0.30/0.63                  = one_one_Code_integer ) )
% 0.30/0.63           => ( ( groups3455450783089532116nteger @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ A2 ) @ ( groups3455450783089532116nteger @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_inter_neutral
% 0.30/0.63  thf(fact_8519_prod_Ounion__inter__neutral,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > assn] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ! [X2: int] :
% 0.30/0.63                ( ( member_int @ X2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.30/0.63               => ( ( G2 @ X2 )
% 0.30/0.63                  = one_one_assn ) )
% 0.30/0.63           => ( ( groups7882442080178216443t_assn @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63              = ( times_times_assn @ ( groups7882442080178216443t_assn @ G2 @ A2 ) @ ( groups7882442080178216443t_assn @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_inter_neutral
% 0.30/0.63  thf(fact_8520_prod_Ounion__inter__neutral,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > assn] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ! [X2: nat] :
% 0.30/0.63                ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.30/0.63               => ( ( G2 @ X2 )
% 0.30/0.63                  = one_one_assn ) )
% 0.30/0.63           => ( ( groups6906906614972039071t_assn @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ A2 ) @ ( groups6906906614972039071t_assn @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_inter_neutral
% 0.30/0.63  thf(fact_8521_prod_Ounion__inter__neutral,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ! [X2: int] :
% 0.30/0.63                ( ( member_int @ X2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.30/0.63               => ( ( G2 @ X2 )
% 0.30/0.63                  = one_one_rat ) )
% 0.30/0.63           => ( ( groups1072433553688619179nt_rat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63              = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ A2 ) @ ( groups1072433553688619179nt_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_inter_neutral
% 0.30/0.63  thf(fact_8522_prod_Ounion__inter__neutral,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ! [X2: nat] :
% 0.30/0.63                ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.30/0.63               => ( ( G2 @ X2 )
% 0.30/0.63                  = one_one_rat ) )
% 0.30/0.63           => ( ( groups73079841787564623at_rat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ A2 ) @ ( groups73079841787564623at_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_inter_neutral
% 0.30/0.63  thf(fact_8523_prod_Ounion__inter__neutral,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > nat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ! [X2: int] :
% 0.30/0.63                ( ( member_int @ X2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.30/0.63               => ( ( G2 @ X2 )
% 0.30/0.63                  = one_one_nat ) )
% 0.30/0.63           => ( ( groups1707563613775114915nt_nat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63              = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ A2 ) @ ( groups1707563613775114915nt_nat @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_inter_neutral
% 0.30/0.63  thf(fact_8524_prod_Ounion__inter__neutral,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ! [X2: nat] :
% 0.30/0.63                ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.30/0.63               => ( ( G2 @ X2 )
% 0.30/0.63                  = one_one_nat ) )
% 0.30/0.63           => ( ( groups708209901874060359at_nat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ A2 ) @ ( groups708209901874060359at_nat @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_inter_neutral
% 0.30/0.63  thf(fact_8525_prod_Ounion__inter__neutral,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > int] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ! [X2: nat] :
% 0.30/0.63                ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.30/0.63               => ( ( G2 @ X2 )
% 0.30/0.63                  = one_one_int ) )
% 0.30/0.63           => ( ( groups705719431365010083at_int @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ A2 ) @ ( groups705719431365010083at_int @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_inter_neutral
% 0.30/0.63  thf(fact_8526_prod_Ounion__inter__neutral,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ! [X2: int] :
% 0.30/0.63                ( ( member_int @ X2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.30/0.63               => ( ( G2 @ X2 )
% 0.30/0.63                  = one_one_int ) )
% 0.30/0.63           => ( ( groups1705073143266064639nt_int @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63              = ( times_times_int @ ( groups1705073143266064639nt_int @ G2 @ A2 ) @ ( groups1705073143266064639nt_int @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_inter_neutral
% 0.30/0.63  thf(fact_8527_prod_Ounion__disjoint,axiom,
% 0.30/0.63      ! [A2: set_o,B2: set_o,G2: $o > code_integer] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( finite_finite_o @ B2 )
% 0.30/0.63         => ( ( ( inf_inf_set_o @ A2 @ B2 )
% 0.30/0.63              = bot_bot_set_o )
% 0.30/0.63           => ( ( groups7694694392188491536nteger @ G2 @ ( sup_sup_set_o @ A2 @ B2 ) )
% 0.30/0.63              = ( times_3573771949741848930nteger @ ( groups7694694392188491536nteger @ G2 @ A2 ) @ ( groups7694694392188491536nteger @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_disjoint
% 0.30/0.63  thf(fact_8528_prod_Ounion__disjoint,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > code_integer] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 0.30/0.63              = bot_bot_set_nat )
% 0.30/0.63           => ( ( groups3455450783089532116nteger @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ A2 ) @ ( groups3455450783089532116nteger @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_disjoint
% 0.30/0.63  thf(fact_8529_prod_Ounion__disjoint,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > code_integer] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( ( inf_inf_set_int @ A2 @ B2 )
% 0.30/0.63              = bot_bot_set_int )
% 0.30/0.63           => ( ( groups3827104343326376752nteger @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63              = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G2 @ A2 ) @ ( groups3827104343326376752nteger @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_disjoint
% 0.30/0.63  thf(fact_8530_prod_Ounion__disjoint,axiom,
% 0.30/0.63      ! [A2: set_o,B2: set_o,G2: $o > assn] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( finite_finite_o @ B2 )
% 0.30/0.63         => ( ( ( inf_inf_set_o @ A2 @ B2 )
% 0.30/0.63              = bot_bot_set_o )
% 0.30/0.63           => ( ( groups5301882518646026715o_assn @ G2 @ ( sup_sup_set_o @ A2 @ B2 ) )
% 0.30/0.63              = ( times_times_assn @ ( groups5301882518646026715o_assn @ G2 @ A2 ) @ ( groups5301882518646026715o_assn @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_disjoint
% 0.30/0.63  thf(fact_8531_prod_Ounion__disjoint,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > assn] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 0.30/0.63              = bot_bot_set_nat )
% 0.30/0.63           => ( ( groups6906906614972039071t_assn @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ A2 ) @ ( groups6906906614972039071t_assn @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_disjoint
% 0.30/0.63  thf(fact_8532_prod_Ounion__disjoint,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > assn] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( ( inf_inf_set_int @ A2 @ B2 )
% 0.30/0.63              = bot_bot_set_int )
% 0.30/0.63           => ( ( groups7882442080178216443t_assn @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63              = ( times_times_assn @ ( groups7882442080178216443t_assn @ G2 @ A2 ) @ ( groups7882442080178216443t_assn @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_disjoint
% 0.30/0.63  thf(fact_8533_prod_Ounion__disjoint,axiom,
% 0.30/0.63      ! [A2: set_o,B2: set_o,G2: $o > rat] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( finite_finite_o @ B2 )
% 0.30/0.63         => ( ( ( inf_inf_set_o @ A2 @ B2 )
% 0.30/0.63              = bot_bot_set_o )
% 0.30/0.63           => ( ( groups2869687844427037835_o_rat @ G2 @ ( sup_sup_set_o @ A2 @ B2 ) )
% 0.30/0.63              = ( times_times_rat @ ( groups2869687844427037835_o_rat @ G2 @ A2 ) @ ( groups2869687844427037835_o_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_disjoint
% 0.30/0.63  thf(fact_8534_prod_Ounion__disjoint,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 0.30/0.63              = bot_bot_set_nat )
% 0.30/0.63           => ( ( groups73079841787564623at_rat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ A2 ) @ ( groups73079841787564623at_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_disjoint
% 0.30/0.63  thf(fact_8535_prod_Ounion__disjoint,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( ( inf_inf_set_int @ A2 @ B2 )
% 0.30/0.63              = bot_bot_set_int )
% 0.30/0.63           => ( ( groups1072433553688619179nt_rat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63              = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ A2 ) @ ( groups1072433553688619179nt_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_disjoint
% 0.30/0.63  thf(fact_8536_prod_Ounion__disjoint,axiom,
% 0.30/0.63      ! [A2: set_o,B2: set_o,G2: $o > nat] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( finite_finite_o @ B2 )
% 0.30/0.63         => ( ( ( inf_inf_set_o @ A2 @ B2 )
% 0.30/0.63              = bot_bot_set_o )
% 0.30/0.63           => ( ( groups3504817904513533571_o_nat @ G2 @ ( sup_sup_set_o @ A2 @ B2 ) )
% 0.30/0.63              = ( times_times_nat @ ( groups3504817904513533571_o_nat @ G2 @ A2 ) @ ( groups3504817904513533571_o_nat @ G2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_disjoint
% 0.30/0.63  thf(fact_8537_sum_Ounion__diff2,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( groups3906332499630173760nt_rat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63            = ( plus_plus_rat @ ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups3906332499630173760nt_rat @ G2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups3906332499630173760nt_rat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_diff2
% 0.30/0.63  thf(fact_8538_sum_Ounion__diff2,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > nat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( groups4541462559716669496nt_nat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63            = ( plus_plus_nat @ ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups4541462559716669496nt_nat @ G2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups4541462559716669496nt_nat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_diff2
% 0.30/0.63  thf(fact_8539_sum_Ounion__diff2,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( groups2906978787729119204at_rat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( plus_plus_rat @ ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups2906978787729119204at_rat @ G2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups2906978787729119204at_rat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_diff2
% 0.30/0.63  thf(fact_8540_sum_Ounion__diff2,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > int] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( groups3539618377306564664at_int @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( plus_plus_int @ ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups3539618377306564664at_int @ G2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups3539618377306564664at_int @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_diff2
% 0.30/0.63  thf(fact_8541_sum_Ounion__diff2,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( groups3542108847815614940at_nat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( plus_plus_nat @ ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups3542108847815614940at_nat @ G2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups3542108847815614940at_nat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_diff2
% 0.30/0.63  thf(fact_8542_sum_Ounion__diff2,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( groups4538972089207619220nt_int @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63            = ( plus_plus_int @ ( plus_plus_int @ ( groups4538972089207619220nt_int @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups4538972089207619220nt_int @ G2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups4538972089207619220nt_int @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_diff2
% 0.30/0.63  thf(fact_8543_sum_Ounion__diff2,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > rat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( finite6177210948735845034at_nat @ B2 )
% 0.30/0.63         => ( ( groups342789780944988191at_rat @ G2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( plus_plus_rat @ ( plus_plus_rat @ ( groups342789780944988191at_rat @ G2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) @ ( groups342789780944988191at_rat @ G2 @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) ) ) @ ( groups342789780944988191at_rat @ G2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_diff2
% 0.30/0.63  thf(fact_8544_sum_Ounion__diff2,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > nat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( finite6177210948735845034at_nat @ B2 )
% 0.30/0.63         => ( ( groups977919841031483927at_nat @ G2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( plus_plus_nat @ ( plus_plus_nat @ ( groups977919841031483927at_nat @ G2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) @ ( groups977919841031483927at_nat @ G2 @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) ) ) @ ( groups977919841031483927at_nat @ G2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_diff2
% 0.30/0.63  thf(fact_8545_sum_Ounion__diff2,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > int] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( finite6177210948735845034at_nat @ B2 )
% 0.30/0.63         => ( ( groups975429370522433651at_int @ G2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( plus_plus_int @ ( plus_plus_int @ ( groups975429370522433651at_int @ G2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) @ ( groups975429370522433651at_int @ G2 @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) ) ) @ ( groups975429370522433651at_int @ G2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_diff2
% 0.30/0.63  thf(fact_8546_sum_Ounion__diff2,axiom,
% 0.30/0.63      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,G2: produc4166570645942440679at_nat > rat] :
% 0.30/0.63        ( ( finite1918287321285529104at_nat @ A2 )
% 0.30/0.63       => ( ( finite1918287321285529104at_nat @ B2 )
% 0.30/0.63         => ( ( groups6424767709179651461at_rat @ G2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( plus_plus_rat @ ( plus_plus_rat @ ( groups6424767709179651461at_rat @ G2 @ ( minus_5060654252129873198at_nat @ A2 @ B2 ) ) @ ( groups6424767709179651461at_rat @ G2 @ ( minus_5060654252129873198at_nat @ B2 @ A2 ) ) ) @ ( groups6424767709179651461at_rat @ G2 @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.union_diff2
% 0.30/0.63  thf(fact_8547_sum__Un2,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,F2: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63       => ( ( groups3906332499630173760nt_rat @ F2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63          = ( plus_plus_rat @ ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ F2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups3906332499630173760nt_rat @ F2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups3906332499630173760nt_rat @ F2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un2
% 0.30/0.63  thf(fact_8548_sum__Un2,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,F2: int > nat] :
% 0.30/0.63        ( ( finite_finite_int @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63       => ( ( groups4541462559716669496nt_nat @ F2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63          = ( plus_plus_nat @ ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ F2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups4541462559716669496nt_nat @ F2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups4541462559716669496nt_nat @ F2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un2
% 0.30/0.63  thf(fact_8549_sum__Un2,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,F2: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63       => ( ( groups2906978787729119204at_rat @ F2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63          = ( plus_plus_rat @ ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups2906978787729119204at_rat @ F2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups2906978787729119204at_rat @ F2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un2
% 0.30/0.63  thf(fact_8550_sum__Un2,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,F2: nat > int] :
% 0.30/0.63        ( ( finite_finite_nat @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63       => ( ( groups3539618377306564664at_int @ F2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63          = ( plus_plus_int @ ( plus_plus_int @ ( groups3539618377306564664at_int @ F2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups3539618377306564664at_int @ F2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups3539618377306564664at_int @ F2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un2
% 0.30/0.63  thf(fact_8551_sum__Un2,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,F2: nat > nat] :
% 0.30/0.63        ( ( finite_finite_nat @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63       => ( ( groups3542108847815614940at_nat @ F2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63          = ( plus_plus_nat @ ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups3542108847815614940at_nat @ F2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups3542108847815614940at_nat @ F2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un2
% 0.30/0.63  thf(fact_8552_sum__Un2,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,F2: int > int] :
% 0.30/0.63        ( ( finite_finite_int @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63       => ( ( groups4538972089207619220nt_int @ F2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63          = ( plus_plus_int @ ( plus_plus_int @ ( groups4538972089207619220nt_int @ F2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups4538972089207619220nt_int @ F2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups4538972089207619220nt_int @ F2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un2
% 0.30/0.63  thf(fact_8553_sum__Un2,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > rat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 0.30/0.63       => ( ( groups342789780944988191at_rat @ F2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 0.30/0.63          = ( plus_plus_rat @ ( plus_plus_rat @ ( groups342789780944988191at_rat @ F2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) @ ( groups342789780944988191at_rat @ F2 @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) ) ) @ ( groups342789780944988191at_rat @ F2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un2
% 0.30/0.63  thf(fact_8554_sum__Un2,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > nat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 0.30/0.63       => ( ( groups977919841031483927at_nat @ F2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 0.30/0.63          = ( plus_plus_nat @ ( plus_plus_nat @ ( groups977919841031483927at_nat @ F2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) @ ( groups977919841031483927at_nat @ F2 @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) ) ) @ ( groups977919841031483927at_nat @ F2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un2
% 0.30/0.63  thf(fact_8555_sum__Un2,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > int] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 0.30/0.63       => ( ( groups975429370522433651at_int @ F2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 0.30/0.63          = ( plus_plus_int @ ( plus_plus_int @ ( groups975429370522433651at_int @ F2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) @ ( groups975429370522433651at_int @ F2 @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) ) ) @ ( groups975429370522433651at_int @ F2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un2
% 0.30/0.63  thf(fact_8556_sum__Un2,axiom,
% 0.30/0.63      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,F2: produc4166570645942440679at_nat > rat] :
% 0.30/0.63        ( ( finite1918287321285529104at_nat @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 0.30/0.63       => ( ( groups6424767709179651461at_rat @ F2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 0.30/0.63          = ( plus_plus_rat @ ( plus_plus_rat @ ( groups6424767709179651461at_rat @ F2 @ ( minus_5060654252129873198at_nat @ A2 @ B2 ) ) @ ( groups6424767709179651461at_rat @ F2 @ ( minus_5060654252129873198at_nat @ B2 @ A2 ) ) ) @ ( groups6424767709179651461at_rat @ F2 @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un2
% 0.30/0.63  thf(fact_8557_prod_Ounion__diff2,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > code_integer] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( groups3827104343326376752nteger @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63            = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups3827104343326376752nteger @ G2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups3827104343326376752nteger @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_diff2
% 0.30/0.63  thf(fact_8558_prod_Ounion__diff2,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > code_integer] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( groups3455450783089532116nteger @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups3455450783089532116nteger @ G2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups3455450783089532116nteger @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_diff2
% 0.30/0.63  thf(fact_8559_prod_Ounion__diff2,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > assn] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( groups7882442080178216443t_assn @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63            = ( times_times_assn @ ( times_times_assn @ ( groups7882442080178216443t_assn @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups7882442080178216443t_assn @ G2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups7882442080178216443t_assn @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_diff2
% 0.30/0.63  thf(fact_8560_prod_Ounion__diff2,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > assn] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( groups6906906614972039071t_assn @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( times_times_assn @ ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups6906906614972039071t_assn @ G2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups6906906614972039071t_assn @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_diff2
% 0.30/0.63  thf(fact_8561_prod_Ounion__diff2,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( groups1072433553688619179nt_rat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63            = ( times_times_rat @ ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_diff2
% 0.30/0.63  thf(fact_8562_prod_Ounion__diff2,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( groups73079841787564623at_rat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( times_times_rat @ ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_diff2
% 0.30/0.63  thf(fact_8563_prod_Ounion__diff2,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > nat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( groups1707563613775114915nt_nat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63            = ( times_times_nat @ ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_diff2
% 0.30/0.63  thf(fact_8564_prod_Ounion__diff2,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( groups708209901874060359at_nat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( times_times_nat @ ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups708209901874060359at_nat @ G2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups708209901874060359at_nat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_diff2
% 0.30/0.63  thf(fact_8565_prod_Ounion__diff2,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,G2: nat > int] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( groups705719431365010083at_int @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( times_times_int @ ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups705719431365010083at_int @ G2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups705719431365010083at_int @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_diff2
% 0.30/0.63  thf(fact_8566_prod_Ounion__diff2,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,G2: int > int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( groups1705073143266064639nt_int @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63            = ( times_times_int @ ( times_times_int @ ( groups1705073143266064639nt_int @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups1705073143266064639nt_int @ G2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups1705073143266064639nt_int @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.union_diff2
% 0.30/0.63  thf(fact_8567_sum__Un__nat,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,F2: int > nat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ( groups4541462559716669496nt_nat @ F2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63            = ( minus_minus_nat @ ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ F2 @ A2 ) @ ( groups4541462559716669496nt_nat @ F2 @ B2 ) ) @ ( groups4541462559716669496nt_nat @ F2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un_nat
% 0.30/0.63  thf(fact_8568_sum__Un__nat,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > nat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( finite6177210948735845034at_nat @ B2 )
% 0.30/0.63         => ( ( groups977919841031483927at_nat @ F2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( minus_minus_nat @ ( plus_plus_nat @ ( groups977919841031483927at_nat @ F2 @ A2 ) @ ( groups977919841031483927at_nat @ F2 @ B2 ) ) @ ( groups977919841031483927at_nat @ F2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un_nat
% 0.30/0.63  thf(fact_8569_sum__Un__nat,axiom,
% 0.30/0.63      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,F2: produc4166570645942440679at_nat > nat] :
% 0.30/0.63        ( ( finite1918287321285529104at_nat @ A2 )
% 0.30/0.63       => ( ( finite1918287321285529104at_nat @ B2 )
% 0.30/0.63         => ( ( groups7059897769266147197at_nat @ F2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( minus_minus_nat @ ( plus_plus_nat @ ( groups7059897769266147197at_nat @ F2 @ A2 ) @ ( groups7059897769266147197at_nat @ F2 @ B2 ) ) @ ( groups7059897769266147197at_nat @ F2 @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un_nat
% 0.30/0.63  thf(fact_8570_sum__Un__nat,axiom,
% 0.30/0.63      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,F2: produc3843707927480180839at_nat > nat] :
% 0.30/0.63        ( ( finite4343798906461161616at_nat @ A2 )
% 0.30/0.63       => ( ( finite4343798906461161616at_nat @ B2 )
% 0.30/0.63         => ( ( groups3860910324918113789at_nat @ F2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( minus_minus_nat @ ( plus_plus_nat @ ( groups3860910324918113789at_nat @ F2 @ A2 ) @ ( groups3860910324918113789at_nat @ F2 @ B2 ) ) @ ( groups3860910324918113789at_nat @ F2 @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un_nat
% 0.30/0.63  thf(fact_8571_sum__Un__nat,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,F2: nat > nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ( groups3542108847815614940at_nat @ F2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63            = ( minus_minus_nat @ ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F2 @ A2 ) @ ( groups3542108847815614940at_nat @ F2 @ B2 ) ) @ ( groups3542108847815614940at_nat @ F2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_Un_nat
% 0.30/0.63  thf(fact_8572_sum_Odelta__remove,axiom,
% 0.30/0.63      ! [S: set_o,A: $o,B: $o > rat,C: $o > rat] :
% 0.30/0.63        ( ( finite_finite_o @ S )
% 0.30/0.63       => ( ( ( member_o @ A @ S )
% 0.30/0.63           => ( ( groups7872700643590313910_o_rat
% 0.30/0.63                @ ^ [K4: $o] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( plus_plus_rat @ ( B @ A ) @ ( groups7872700643590313910_o_rat @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 0.30/0.63          & ( ~ ( member_o @ A @ S )
% 0.30/0.63           => ( ( groups7872700643590313910_o_rat
% 0.30/0.63                @ ^ [K4: $o] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( groups7872700643590313910_o_rat @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.delta_remove
% 0.30/0.63  thf(fact_8573_sum_Odelta__remove,axiom,
% 0.30/0.63      ! [S: set_o,A: $o,B: $o > nat,C: $o > nat] :
% 0.30/0.63        ( ( finite_finite_o @ S )
% 0.30/0.63       => ( ( ( member_o @ A @ S )
% 0.30/0.63           => ( ( groups8507830703676809646_o_nat
% 0.30/0.63                @ ^ [K4: $o] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( plus_plus_nat @ ( B @ A ) @ ( groups8507830703676809646_o_nat @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 0.30/0.63          & ( ~ ( member_o @ A @ S )
% 0.30/0.63           => ( ( groups8507830703676809646_o_nat
% 0.30/0.63                @ ^ [K4: $o] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( groups8507830703676809646_o_nat @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.delta_remove
% 0.30/0.63  thf(fact_8574_sum_Odelta__remove,axiom,
% 0.30/0.63      ! [S: set_o,A: $o,B: $o > int,C: $o > int] :
% 0.30/0.63        ( ( finite_finite_o @ S )
% 0.30/0.63       => ( ( ( member_o @ A @ S )
% 0.30/0.63           => ( ( groups8505340233167759370_o_int
% 0.30/0.63                @ ^ [K4: $o] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( plus_plus_int @ ( B @ A ) @ ( groups8505340233167759370_o_int @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 0.30/0.63          & ( ~ ( member_o @ A @ S )
% 0.30/0.63           => ( ( groups8505340233167759370_o_int
% 0.30/0.63                @ ^ [K4: $o] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( groups8505340233167759370_o_int @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.delta_remove
% 0.30/0.63  thf(fact_8575_sum_Odelta__remove,axiom,
% 0.30/0.63      ! [S: set_int,A: int,B: int > rat,C: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ S )
% 0.30/0.63       => ( ( ( member_int @ A @ S )
% 0.30/0.63           => ( ( groups3906332499630173760nt_rat
% 0.30/0.63                @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( plus_plus_rat @ ( B @ A ) @ ( groups3906332499630173760nt_rat @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 0.30/0.63          & ( ~ ( member_int @ A @ S )
% 0.30/0.63           => ( ( groups3906332499630173760nt_rat
% 0.30/0.63                @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( groups3906332499630173760nt_rat @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.delta_remove
% 0.30/0.63  thf(fact_8576_sum_Odelta__remove,axiom,
% 0.30/0.63      ! [S: set_int,A: int,B: int > nat,C: int > nat] :
% 0.30/0.63        ( ( finite_finite_int @ S )
% 0.30/0.63       => ( ( ( member_int @ A @ S )
% 0.30/0.63           => ( ( groups4541462559716669496nt_nat
% 0.30/0.63                @ ^ [K4: int] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( plus_plus_nat @ ( B @ A ) @ ( groups4541462559716669496nt_nat @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 0.30/0.63          & ( ~ ( member_int @ A @ S )
% 0.30/0.63           => ( ( groups4541462559716669496nt_nat
% 0.30/0.63                @ ^ [K4: int] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( groups4541462559716669496nt_nat @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.delta_remove
% 0.30/0.63  thf(fact_8577_sum_Odelta__remove,axiom,
% 0.30/0.63      ! [S: set_nat,A: nat,B: nat > rat,C: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ S )
% 0.30/0.63       => ( ( ( member_nat @ A @ S )
% 0.30/0.63           => ( ( groups2906978787729119204at_rat
% 0.30/0.63                @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( plus_plus_rat @ ( B @ A ) @ ( groups2906978787729119204at_rat @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 0.30/0.63          & ( ~ ( member_nat @ A @ S )
% 0.30/0.63           => ( ( groups2906978787729119204at_rat
% 0.30/0.63                @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( groups2906978787729119204at_rat @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.delta_remove
% 0.30/0.63  thf(fact_8578_sum_Odelta__remove,axiom,
% 0.30/0.63      ! [S: set_nat,A: nat,B: nat > int,C: nat > int] :
% 0.30/0.63        ( ( finite_finite_nat @ S )
% 0.30/0.63       => ( ( ( member_nat @ A @ S )
% 0.30/0.63           => ( ( groups3539618377306564664at_int
% 0.30/0.63                @ ^ [K4: nat] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( plus_plus_int @ ( B @ A ) @ ( groups3539618377306564664at_int @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 0.30/0.63          & ( ~ ( member_nat @ A @ S )
% 0.30/0.63           => ( ( groups3539618377306564664at_int
% 0.30/0.63                @ ^ [K4: nat] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( groups3539618377306564664at_int @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.delta_remove
% 0.30/0.63  thf(fact_8579_sum_Odelta__remove,axiom,
% 0.30/0.63      ! [S: set_nat,A: nat,B: nat > nat,C: nat > nat] :
% 0.30/0.63        ( ( finite_finite_nat @ S )
% 0.30/0.63       => ( ( ( member_nat @ A @ S )
% 0.30/0.63           => ( ( groups3542108847815614940at_nat
% 0.30/0.63                @ ^ [K4: nat] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( plus_plus_nat @ ( B @ A ) @ ( groups3542108847815614940at_nat @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 0.30/0.63          & ( ~ ( member_nat @ A @ S )
% 0.30/0.63           => ( ( groups3542108847815614940at_nat
% 0.30/0.63                @ ^ [K4: nat] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( groups3542108847815614940at_nat @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.delta_remove
% 0.30/0.63  thf(fact_8580_sum_Odelta__remove,axiom,
% 0.30/0.63      ! [S: set_int,A: int,B: int > int,C: int > int] :
% 0.30/0.63        ( ( finite_finite_int @ S )
% 0.30/0.63       => ( ( ( member_int @ A @ S )
% 0.30/0.63           => ( ( groups4538972089207619220nt_int
% 0.30/0.63                @ ^ [K4: int] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( plus_plus_int @ ( B @ A ) @ ( groups4538972089207619220nt_int @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 0.30/0.63          & ( ~ ( member_int @ A @ S )
% 0.30/0.63           => ( ( groups4538972089207619220nt_int
% 0.30/0.63                @ ^ [K4: int] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( groups4538972089207619220nt_int @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.delta_remove
% 0.30/0.63  thf(fact_8581_sum_Odelta__remove,axiom,
% 0.30/0.63      ! [S: set_set_nat,A: set_nat,B: set_nat > rat,C: set_nat > rat] :
% 0.30/0.63        ( ( finite1152437895449049373et_nat @ S )
% 0.30/0.63       => ( ( ( member_set_nat @ A @ S )
% 0.30/0.63           => ( ( groups7659867448343625626at_rat
% 0.30/0.63                @ ^ [K4: set_nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( plus_plus_rat @ ( B @ A ) @ ( groups7659867448343625626at_rat @ C @ ( minus_2163939370556025621et_nat @ S @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ) ) ) )
% 0.30/0.63          & ( ~ ( member_set_nat @ A @ S )
% 0.30/0.63           => ( ( groups7659867448343625626at_rat
% 0.30/0.63                @ ^ [K4: set_nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( groups7659867448343625626at_rat @ C @ ( minus_2163939370556025621et_nat @ S @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum.delta_remove
% 0.30/0.63  thf(fact_8582_sum__div__partition,axiom,
% 0.30/0.63      ! [A2: set_int,F2: int > nat,B: nat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( divide_divide_nat @ ( groups4541462559716669496nt_nat @ F2 @ A2 ) @ B )
% 0.30/0.63          = ( plus_plus_nat
% 0.30/0.63            @ ( groups4541462559716669496nt_nat
% 0.30/0.63              @ ^ [A3: int] : ( divide_divide_nat @ ( F2 @ A3 ) @ B )
% 0.30/0.63              @ ( inf_inf_set_int @ A2
% 0.30/0.63                @ ( collect_int
% 0.30/0.63                  @ ^ [A3: int] : ( dvd_dvd_nat @ B @ ( F2 @ A3 ) ) ) ) )
% 0.30/0.63            @ ( divide_divide_nat
% 0.30/0.63              @ ( groups4541462559716669496nt_nat @ F2
% 0.30/0.63                @ ( inf_inf_set_int @ A2
% 0.30/0.63                  @ ( collect_int
% 0.30/0.63                    @ ^ [A3: int] :
% 0.30/0.63                        ~ ( dvd_dvd_nat @ B @ ( F2 @ A3 ) ) ) ) )
% 0.30/0.63              @ B ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_div_partition
% 0.30/0.63  thf(fact_8583_sum__div__partition,axiom,
% 0.30/0.63      ! [A2: set_nat,F2: nat > int,B: int] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( divide_divide_int @ ( groups3539618377306564664at_int @ F2 @ A2 ) @ B )
% 0.30/0.63          = ( plus_plus_int
% 0.30/0.63            @ ( groups3539618377306564664at_int
% 0.30/0.63              @ ^ [A3: nat] : ( divide_divide_int @ ( F2 @ A3 ) @ B )
% 0.30/0.63              @ ( inf_inf_set_nat @ A2
% 0.30/0.63                @ ( collect_nat
% 0.30/0.63                  @ ^ [A3: nat] : ( dvd_dvd_int @ B @ ( F2 @ A3 ) ) ) ) )
% 0.30/0.63            @ ( divide_divide_int
% 0.30/0.63              @ ( groups3539618377306564664at_int @ F2
% 0.30/0.63                @ ( inf_inf_set_nat @ A2
% 0.30/0.63                  @ ( collect_nat
% 0.30/0.63                    @ ^ [A3: nat] :
% 0.30/0.63                        ~ ( dvd_dvd_int @ B @ ( F2 @ A3 ) ) ) ) )
% 0.30/0.63              @ B ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_div_partition
% 0.30/0.63  thf(fact_8584_sum__div__partition,axiom,
% 0.30/0.63      ! [A2: set_int,F2: int > code_integer,B: code_integer] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( divide6298287555418463151nteger @ ( groups7873554091576472773nteger @ F2 @ A2 ) @ B )
% 0.30/0.63          = ( plus_p5714425477246183910nteger
% 0.30/0.63            @ ( groups7873554091576472773nteger
% 0.30/0.63              @ ^ [A3: int] : ( divide6298287555418463151nteger @ ( F2 @ A3 ) @ B )
% 0.30/0.63              @ ( inf_inf_set_int @ A2
% 0.30/0.63                @ ( collect_int
% 0.30/0.63                  @ ^ [A3: int] : ( dvd_dvd_Code_integer @ B @ ( F2 @ A3 ) ) ) ) )
% 0.30/0.63            @ ( divide6298287555418463151nteger
% 0.30/0.63              @ ( groups7873554091576472773nteger @ F2
% 0.30/0.63                @ ( inf_inf_set_int @ A2
% 0.30/0.63                  @ ( collect_int
% 0.30/0.63                    @ ^ [A3: int] :
% 0.30/0.63                        ~ ( dvd_dvd_Code_integer @ B @ ( F2 @ A3 ) ) ) ) )
% 0.30/0.63              @ B ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_div_partition
% 0.30/0.63  thf(fact_8585_sum__div__partition,axiom,
% 0.30/0.63      ! [A2: set_nat,F2: nat > code_integer,B: code_integer] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( divide6298287555418463151nteger @ ( groups7501900531339628137nteger @ F2 @ A2 ) @ B )
% 0.30/0.63          = ( plus_p5714425477246183910nteger
% 0.30/0.63            @ ( groups7501900531339628137nteger
% 0.30/0.63              @ ^ [A3: nat] : ( divide6298287555418463151nteger @ ( F2 @ A3 ) @ B )
% 0.30/0.63              @ ( inf_inf_set_nat @ A2
% 0.30/0.63                @ ( collect_nat
% 0.30/0.63                  @ ^ [A3: nat] : ( dvd_dvd_Code_integer @ B @ ( F2 @ A3 ) ) ) ) )
% 0.30/0.63            @ ( divide6298287555418463151nteger
% 0.30/0.63              @ ( groups7501900531339628137nteger @ F2
% 0.30/0.63                @ ( inf_inf_set_nat @ A2
% 0.30/0.63                  @ ( collect_nat
% 0.30/0.63                    @ ^ [A3: nat] :
% 0.30/0.63                        ~ ( dvd_dvd_Code_integer @ B @ ( F2 @ A3 ) ) ) ) )
% 0.30/0.63              @ B ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_div_partition
% 0.30/0.63  thf(fact_8586_sum__div__partition,axiom,
% 0.30/0.63      ! [A2: set_int,F2: int > code_natural,B: code_natural] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( divide5121882707175180666atural @ ( groups6697149243333190288atural @ F2 @ A2 ) @ B )
% 0.30/0.63          = ( plus_p4538020629002901425atural
% 0.30/0.63            @ ( groups6697149243333190288atural
% 0.30/0.63              @ ^ [A3: int] : ( divide5121882707175180666atural @ ( F2 @ A3 ) @ B )
% 0.30/0.63              @ ( inf_inf_set_int @ A2
% 0.30/0.63                @ ( collect_int
% 0.30/0.63                  @ ^ [A3: int] : ( dvd_dvd_Code_natural @ B @ ( F2 @ A3 ) ) ) ) )
% 0.30/0.63            @ ( divide5121882707175180666atural
% 0.30/0.63              @ ( groups6697149243333190288atural @ F2
% 0.30/0.63                @ ( inf_inf_set_int @ A2
% 0.30/0.63                  @ ( collect_int
% 0.30/0.63                    @ ^ [A3: int] :
% 0.30/0.63                        ~ ( dvd_dvd_Code_natural @ B @ ( F2 @ A3 ) ) ) ) )
% 0.30/0.63              @ B ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_div_partition
% 0.30/0.63  thf(fact_8587_sum__div__partition,axiom,
% 0.30/0.63      ! [A2: set_nat,F2: nat > code_natural,B: code_natural] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( divide5121882707175180666atural @ ( groups6325495683096345652atural @ F2 @ A2 ) @ B )
% 0.30/0.63          = ( plus_p4538020629002901425atural
% 0.30/0.63            @ ( groups6325495683096345652atural
% 0.30/0.63              @ ^ [A3: nat] : ( divide5121882707175180666atural @ ( F2 @ A3 ) @ B )
% 0.30/0.63              @ ( inf_inf_set_nat @ A2
% 0.30/0.63                @ ( collect_nat
% 0.30/0.63                  @ ^ [A3: nat] : ( dvd_dvd_Code_natural @ B @ ( F2 @ A3 ) ) ) ) )
% 0.30/0.63            @ ( divide5121882707175180666atural
% 0.30/0.63              @ ( groups6325495683096345652atural @ F2
% 0.30/0.63                @ ( inf_inf_set_nat @ A2
% 0.30/0.63                  @ ( collect_nat
% 0.30/0.63                    @ ^ [A3: nat] :
% 0.30/0.63                        ~ ( dvd_dvd_Code_natural @ B @ ( F2 @ A3 ) ) ) ) )
% 0.30/0.63              @ B ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_div_partition
% 0.30/0.63  thf(fact_8588_sum__div__partition,axiom,
% 0.30/0.63      ! [A2: set_nat,F2: nat > nat,B: nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( divide_divide_nat @ ( groups3542108847815614940at_nat @ F2 @ A2 ) @ B )
% 0.30/0.63          = ( plus_plus_nat
% 0.30/0.63            @ ( groups3542108847815614940at_nat
% 0.30/0.63              @ ^ [A3: nat] : ( divide_divide_nat @ ( F2 @ A3 ) @ B )
% 0.30/0.63              @ ( inf_inf_set_nat @ A2
% 0.30/0.63                @ ( collect_nat
% 0.30/0.63                  @ ^ [A3: nat] : ( dvd_dvd_nat @ B @ ( F2 @ A3 ) ) ) ) )
% 0.30/0.63            @ ( divide_divide_nat
% 0.30/0.63              @ ( groups3542108847815614940at_nat @ F2
% 0.30/0.63                @ ( inf_inf_set_nat @ A2
% 0.30/0.63                  @ ( collect_nat
% 0.30/0.63                    @ ^ [A3: nat] :
% 0.30/0.63                        ~ ( dvd_dvd_nat @ B @ ( F2 @ A3 ) ) ) ) )
% 0.30/0.63              @ B ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_div_partition
% 0.30/0.63  thf(fact_8589_sum__div__partition,axiom,
% 0.30/0.63      ! [A2: set_int,F2: int > int,B: int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( divide_divide_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) @ B )
% 0.30/0.63          = ( plus_plus_int
% 0.30/0.63            @ ( groups4538972089207619220nt_int
% 0.30/0.63              @ ^ [A3: int] : ( divide_divide_int @ ( F2 @ A3 ) @ B )
% 0.30/0.63              @ ( inf_inf_set_int @ A2
% 0.30/0.63                @ ( collect_int
% 0.30/0.63                  @ ^ [A3: int] : ( dvd_dvd_int @ B @ ( F2 @ A3 ) ) ) ) )
% 0.30/0.63            @ ( divide_divide_int
% 0.30/0.63              @ ( groups4538972089207619220nt_int @ F2
% 0.30/0.63                @ ( inf_inf_set_int @ A2
% 0.30/0.63                  @ ( collect_int
% 0.30/0.63                    @ ^ [A3: int] :
% 0.30/0.63                        ~ ( dvd_dvd_int @ B @ ( F2 @ A3 ) ) ) ) )
% 0.30/0.63              @ B ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_div_partition
% 0.30/0.63  thf(fact_8590_sum__div__partition,axiom,
% 0.30/0.63      ! [A2: set_set_nat,F2: set_nat > nat,B: nat] :
% 0.30/0.63        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.63       => ( ( divide_divide_nat @ ( groups8294997508430121362at_nat @ F2 @ A2 ) @ B )
% 0.30/0.63          = ( plus_plus_nat
% 0.30/0.63            @ ( groups8294997508430121362at_nat
% 0.30/0.63              @ ^ [A3: set_nat] : ( divide_divide_nat @ ( F2 @ A3 ) @ B )
% 0.30/0.63              @ ( inf_inf_set_set_nat @ A2
% 0.30/0.63                @ ( collect_set_nat
% 0.30/0.63                  @ ^ [A3: set_nat] : ( dvd_dvd_nat @ B @ ( F2 @ A3 ) ) ) ) )
% 0.30/0.63            @ ( divide_divide_nat
% 0.30/0.63              @ ( groups8294997508430121362at_nat @ F2
% 0.30/0.63                @ ( inf_inf_set_set_nat @ A2
% 0.30/0.63                  @ ( collect_set_nat
% 0.30/0.63                    @ ^ [A3: set_nat] :
% 0.30/0.63                        ~ ( dvd_dvd_nat @ B @ ( F2 @ A3 ) ) ) ) )
% 0.30/0.63              @ B ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_div_partition
% 0.30/0.63  thf(fact_8591_sum__div__partition,axiom,
% 0.30/0.63      ! [A2: set_set_nat,F2: set_nat > int,B: int] :
% 0.30/0.63        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.63       => ( ( divide_divide_int @ ( groups8292507037921071086at_int @ F2 @ A2 ) @ B )
% 0.30/0.63          = ( plus_plus_int
% 0.30/0.63            @ ( groups8292507037921071086at_int
% 0.30/0.63              @ ^ [A3: set_nat] : ( divide_divide_int @ ( F2 @ A3 ) @ B )
% 0.30/0.63              @ ( inf_inf_set_set_nat @ A2
% 0.30/0.63                @ ( collect_set_nat
% 0.30/0.63                  @ ^ [A3: set_nat] : ( dvd_dvd_int @ B @ ( F2 @ A3 ) ) ) ) )
% 0.30/0.63            @ ( divide_divide_int
% 0.30/0.63              @ ( groups8292507037921071086at_int @ F2
% 0.30/0.63                @ ( inf_inf_set_set_nat @ A2
% 0.30/0.63                  @ ( collect_set_nat
% 0.30/0.63                    @ ^ [A3: set_nat] :
% 0.30/0.63                        ~ ( dvd_dvd_int @ B @ ( F2 @ A3 ) ) ) ) )
% 0.30/0.63              @ B ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_div_partition
% 0.30/0.63  thf(fact_8592_prod_Odelta__remove,axiom,
% 0.30/0.63      ! [S: set_o,A: $o,B: $o > code_integer,C: $o > code_integer] :
% 0.30/0.63        ( ( finite_finite_o @ S )
% 0.30/0.63       => ( ( ( member_o @ A @ S )
% 0.30/0.63           => ( ( groups7694694392188491536nteger
% 0.30/0.63                @ ^ [K4: $o] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( times_3573771949741848930nteger @ ( B @ A ) @ ( groups7694694392188491536nteger @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 0.30/0.63          & ( ~ ( member_o @ A @ S )
% 0.30/0.63           => ( ( groups7694694392188491536nteger
% 0.30/0.63                @ ^ [K4: $o] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( groups7694694392188491536nteger @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.delta_remove
% 0.30/0.63  thf(fact_8593_prod_Odelta__remove,axiom,
% 0.30/0.63      ! [S: set_int,A: int,B: int > code_integer,C: int > code_integer] :
% 0.30/0.63        ( ( finite_finite_int @ S )
% 0.30/0.63       => ( ( ( member_int @ A @ S )
% 0.30/0.63           => ( ( groups3827104343326376752nteger
% 0.30/0.63                @ ^ [K4: int] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( times_3573771949741848930nteger @ ( B @ A ) @ ( groups3827104343326376752nteger @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 0.30/0.63          & ( ~ ( member_int @ A @ S )
% 0.30/0.63           => ( ( groups3827104343326376752nteger
% 0.30/0.63                @ ^ [K4: int] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( groups3827104343326376752nteger @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.delta_remove
% 0.30/0.63  thf(fact_8594_prod_Odelta__remove,axiom,
% 0.30/0.63      ! [S: set_nat,A: nat,B: nat > code_integer,C: nat > code_integer] :
% 0.30/0.63        ( ( finite_finite_nat @ S )
% 0.30/0.63       => ( ( ( member_nat @ A @ S )
% 0.30/0.63           => ( ( groups3455450783089532116nteger
% 0.30/0.63                @ ^ [K4: nat] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( times_3573771949741848930nteger @ ( B @ A ) @ ( groups3455450783089532116nteger @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 0.30/0.63          & ( ~ ( member_nat @ A @ S )
% 0.30/0.63           => ( ( groups3455450783089532116nteger
% 0.30/0.63                @ ^ [K4: nat] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( groups3455450783089532116nteger @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.delta_remove
% 0.30/0.63  thf(fact_8595_prod_Odelta__remove,axiom,
% 0.30/0.63      ! [S: set_o,A: $o,B: $o > assn,C: $o > assn] :
% 0.30/0.63        ( ( finite_finite_o @ S )
% 0.30/0.63       => ( ( ( member_o @ A @ S )
% 0.30/0.63           => ( ( groups5301882518646026715o_assn
% 0.30/0.63                @ ^ [K4: $o] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( times_times_assn @ ( B @ A ) @ ( groups5301882518646026715o_assn @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 0.30/0.63          & ( ~ ( member_o @ A @ S )
% 0.30/0.63           => ( ( groups5301882518646026715o_assn
% 0.30/0.63                @ ^ [K4: $o] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( groups5301882518646026715o_assn @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.delta_remove
% 0.30/0.63  thf(fact_8596_prod_Odelta__remove,axiom,
% 0.30/0.63      ! [S: set_int,A: int,B: int > assn,C: int > assn] :
% 0.30/0.63        ( ( finite_finite_int @ S )
% 0.30/0.63       => ( ( ( member_int @ A @ S )
% 0.30/0.63           => ( ( groups7882442080178216443t_assn
% 0.30/0.63                @ ^ [K4: int] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( times_times_assn @ ( B @ A ) @ ( groups7882442080178216443t_assn @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 0.30/0.63          & ( ~ ( member_int @ A @ S )
% 0.30/0.63           => ( ( groups7882442080178216443t_assn
% 0.30/0.63                @ ^ [K4: int] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( groups7882442080178216443t_assn @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.delta_remove
% 0.30/0.63  thf(fact_8597_prod_Odelta__remove,axiom,
% 0.30/0.63      ! [S: set_nat,A: nat,B: nat > assn,C: nat > assn] :
% 0.30/0.63        ( ( finite_finite_nat @ S )
% 0.30/0.63       => ( ( ( member_nat @ A @ S )
% 0.30/0.63           => ( ( groups6906906614972039071t_assn
% 0.30/0.63                @ ^ [K4: nat] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( times_times_assn @ ( B @ A ) @ ( groups6906906614972039071t_assn @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 0.30/0.63          & ( ~ ( member_nat @ A @ S )
% 0.30/0.63           => ( ( groups6906906614972039071t_assn
% 0.30/0.63                @ ^ [K4: nat] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( groups6906906614972039071t_assn @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.delta_remove
% 0.30/0.63  thf(fact_8598_prod_Odelta__remove,axiom,
% 0.30/0.63      ! [S: set_o,A: $o,B: $o > rat,C: $o > rat] :
% 0.30/0.63        ( ( finite_finite_o @ S )
% 0.30/0.63       => ( ( ( member_o @ A @ S )
% 0.30/0.63           => ( ( groups2869687844427037835_o_rat
% 0.30/0.63                @ ^ [K4: $o] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( times_times_rat @ ( B @ A ) @ ( groups2869687844427037835_o_rat @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 0.30/0.63          & ( ~ ( member_o @ A @ S )
% 0.30/0.63           => ( ( groups2869687844427037835_o_rat
% 0.30/0.63                @ ^ [K4: $o] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( groups2869687844427037835_o_rat @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.delta_remove
% 0.30/0.63  thf(fact_8599_prod_Odelta__remove,axiom,
% 0.30/0.63      ! [S: set_int,A: int,B: int > rat,C: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ S )
% 0.30/0.63       => ( ( ( member_int @ A @ S )
% 0.30/0.63           => ( ( groups1072433553688619179nt_rat
% 0.30/0.63                @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( times_times_rat @ ( B @ A ) @ ( groups1072433553688619179nt_rat @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 0.30/0.63          & ( ~ ( member_int @ A @ S )
% 0.30/0.63           => ( ( groups1072433553688619179nt_rat
% 0.30/0.63                @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( groups1072433553688619179nt_rat @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.delta_remove
% 0.30/0.63  thf(fact_8600_prod_Odelta__remove,axiom,
% 0.30/0.63      ! [S: set_nat,A: nat,B: nat > rat,C: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ S )
% 0.30/0.63       => ( ( ( member_nat @ A @ S )
% 0.30/0.63           => ( ( groups73079841787564623at_rat
% 0.30/0.63                @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( times_times_rat @ ( B @ A ) @ ( groups73079841787564623at_rat @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 0.30/0.63          & ( ~ ( member_nat @ A @ S )
% 0.30/0.63           => ( ( groups73079841787564623at_rat
% 0.30/0.63                @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( groups73079841787564623at_rat @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.delta_remove
% 0.30/0.63  thf(fact_8601_prod_Odelta__remove,axiom,
% 0.30/0.63      ! [S: set_o,A: $o,B: $o > nat,C: $o > nat] :
% 0.30/0.63        ( ( finite_finite_o @ S )
% 0.30/0.63       => ( ( ( member_o @ A @ S )
% 0.30/0.63           => ( ( groups3504817904513533571_o_nat
% 0.30/0.63                @ ^ [K4: $o] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( times_times_nat @ ( B @ A ) @ ( groups3504817904513533571_o_nat @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 0.30/0.63          & ( ~ ( member_o @ A @ S )
% 0.30/0.63           => ( ( groups3504817904513533571_o_nat
% 0.30/0.63                @ ^ [K4: $o] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 0.30/0.63                @ S )
% 0.30/0.63              = ( groups3504817904513533571_o_nat @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.delta_remove
% 0.30/0.63  thf(fact_8602_sum__gp__strict,axiom,
% 0.30/0.63      ! [X: rat,N: nat] :
% 0.30/0.63        ( ( ( X = one_one_rat )
% 0.30/0.63         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.30/0.63            = ( semiri681578069525770553at_rat @ N ) ) )
% 0.30/0.63        & ( ( X != one_one_rat )
% 0.30/0.63         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.30/0.63            = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sum_gp_strict
% 0.30/0.63  thf(fact_8603_power__diff__sumr2,axiom,
% 0.30/0.63      ! [X: code_integer,N: nat,Y: code_integer] :
% 0.30/0.63        ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y @ N ) )
% 0.30/0.63        = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X @ Y )
% 0.30/0.63          @ ( groups7501900531339628137nteger
% 0.30/0.63            @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ Y @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_8256067586552552935nteger @ X @ I3 ) )
% 0.30/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % power_diff_sumr2
% 0.30/0.63  thf(fact_8604_power__diff__sumr2,axiom,
% 0.30/0.63      ! [X: rat,N: nat,Y: rat] :
% 0.30/0.63        ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y @ N ) )
% 0.30/0.63        = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 0.30/0.63          @ ( groups2906978787729119204at_rat
% 0.30/0.63            @ ^ [I3: nat] : ( times_times_rat @ ( power_power_rat @ Y @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_rat @ X @ I3 ) )
% 0.30/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % power_diff_sumr2
% 0.30/0.63  thf(fact_8605_power__diff__sumr2,axiom,
% 0.30/0.63      ! [X: int,N: nat,Y: int] :
% 0.30/0.63        ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 0.30/0.63        = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 0.30/0.63          @ ( groups3539618377306564664at_int
% 0.30/0.63            @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_int @ X @ I3 ) )
% 0.30/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % power_diff_sumr2
% 0.30/0.63  thf(fact_8606_diff__power__eq__sum,axiom,
% 0.30/0.63      ! [X: code_integer,N: nat,Y: code_integer] :
% 0.30/0.63        ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ ( suc @ N ) ) @ ( power_8256067586552552935nteger @ Y @ ( suc @ N ) ) )
% 0.30/0.63        = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X @ Y )
% 0.30/0.63          @ ( groups7501900531339628137nteger
% 0.30/0.63            @ ^ [P6: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ P6 ) @ ( power_8256067586552552935nteger @ Y @ ( minus_minus_nat @ N @ P6 ) ) )
% 0.30/0.63            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % diff_power_eq_sum
% 0.30/0.63  thf(fact_8607_diff__power__eq__sum,axiom,
% 0.30/0.63      ! [X: rat,N: nat,Y: rat] :
% 0.30/0.63        ( ( minus_minus_rat @ ( power_power_rat @ X @ ( suc @ N ) ) @ ( power_power_rat @ Y @ ( suc @ N ) ) )
% 0.30/0.63        = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 0.30/0.63          @ ( groups2906978787729119204at_rat
% 0.30/0.63            @ ^ [P6: nat] : ( times_times_rat @ ( power_power_rat @ X @ P6 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ N @ P6 ) ) )
% 0.30/0.63            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % diff_power_eq_sum
% 0.30/0.63  thf(fact_8608_diff__power__eq__sum,axiom,
% 0.30/0.63      ! [X: int,N: nat,Y: int] :
% 0.30/0.63        ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N ) ) @ ( power_power_int @ Y @ ( suc @ N ) ) )
% 0.30/0.63        = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 0.30/0.63          @ ( groups3539618377306564664at_int
% 0.30/0.63            @ ^ [P6: nat] : ( times_times_int @ ( power_power_int @ X @ P6 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ P6 ) ) )
% 0.30/0.63            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % diff_power_eq_sum
% 0.30/0.63  thf(fact_8609_eucl__rel__int__remainderI,axiom,
% 0.30/0.63      ! [R3: int,L: int,K: int,Q4: int] :
% 0.30/0.63        ( ( ( sgn_sgn_int @ R3 )
% 0.30/0.63          = ( sgn_sgn_int @ L ) )
% 0.30/0.63       => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ L ) )
% 0.30/0.63         => ( ( K
% 0.30/0.63              = ( plus_plus_int @ ( times_times_int @ Q4 @ L ) @ R3 ) )
% 0.30/0.63           => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q4 @ R3 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % eucl_rel_int_remainderI
% 0.30/0.63  thf(fact_8610_member__le__sum,axiom,
% 0.30/0.63      ! [I: $o,A2: set_o,F2: $o > code_integer] :
% 0.30/0.63        ( ( member_o @ I @ A2 )
% 0.30/0.63       => ( ! [X2: $o] :
% 0.30/0.63              ( ( member_o @ X2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 0.30/0.63             => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X2 ) ) )
% 0.30/0.63         => ( ( finite_finite_o @ A2 )
% 0.30/0.63           => ( ord_le3102999989581377725nteger @ ( F2 @ I ) @ ( groups4406642042086082107nteger @ F2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % member_le_sum
% 0.30/0.63  thf(fact_8611_member__le__sum,axiom,
% 0.30/0.63      ! [I: int,A2: set_int,F2: int > code_integer] :
% 0.30/0.63        ( ( member_int @ I @ A2 )
% 0.30/0.63       => ( ! [X2: int] :
% 0.30/0.63              ( ( member_int @ X2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 0.30/0.63             => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X2 ) ) )
% 0.30/0.63         => ( ( finite_finite_int @ A2 )
% 0.30/0.63           => ( ord_le3102999989581377725nteger @ ( F2 @ I ) @ ( groups7873554091576472773nteger @ F2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % member_le_sum
% 0.30/0.63  thf(fact_8612_member__le__sum,axiom,
% 0.30/0.63      ! [I: nat,A2: set_nat,F2: nat > code_integer] :
% 0.30/0.63        ( ( member_nat @ I @ A2 )
% 0.30/0.63       => ( ! [X2: nat] :
% 0.30/0.63              ( ( member_nat @ X2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 0.30/0.63             => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X2 ) ) )
% 0.30/0.63         => ( ( finite_finite_nat @ A2 )
% 0.30/0.63           => ( ord_le3102999989581377725nteger @ ( F2 @ I ) @ ( groups7501900531339628137nteger @ F2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % member_le_sum
% 0.30/0.63  thf(fact_8613_member__le__sum,axiom,
% 0.30/0.63      ! [I: $o,A2: set_o,F2: $o > rat] :
% 0.30/0.63        ( ( member_o @ I @ A2 )
% 0.30/0.63       => ( ! [X2: $o] :
% 0.30/0.63              ( ( member_o @ X2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 0.30/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X2 ) ) )
% 0.30/0.63         => ( ( finite_finite_o @ A2 )
% 0.30/0.63           => ( ord_less_eq_rat @ ( F2 @ I ) @ ( groups7872700643590313910_o_rat @ F2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % member_le_sum
% 0.30/0.63  thf(fact_8614_member__le__sum,axiom,
% 0.30/0.63      ! [I: int,A2: set_int,F2: int > rat] :
% 0.30/0.63        ( ( member_int @ I @ A2 )
% 0.30/0.63       => ( ! [X2: int] :
% 0.30/0.63              ( ( member_int @ X2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 0.30/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X2 ) ) )
% 0.30/0.63         => ( ( finite_finite_int @ A2 )
% 0.30/0.63           => ( ord_less_eq_rat @ ( F2 @ I ) @ ( groups3906332499630173760nt_rat @ F2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % member_le_sum
% 0.30/0.63  thf(fact_8615_member__le__sum,axiom,
% 0.30/0.63      ! [I: nat,A2: set_nat,F2: nat > rat] :
% 0.30/0.63        ( ( member_nat @ I @ A2 )
% 0.30/0.63       => ( ! [X2: nat] :
% 0.30/0.63              ( ( member_nat @ X2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 0.30/0.63             => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X2 ) ) )
% 0.30/0.63         => ( ( finite_finite_nat @ A2 )
% 0.30/0.63           => ( ord_less_eq_rat @ ( F2 @ I ) @ ( groups2906978787729119204at_rat @ F2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % member_le_sum
% 0.30/0.63  thf(fact_8616_member__le__sum,axiom,
% 0.30/0.63      ! [I: $o,A2: set_o,F2: $o > nat] :
% 0.30/0.63        ( ( member_o @ I @ A2 )
% 0.30/0.63       => ( ! [X2: $o] :
% 0.30/0.63              ( ( member_o @ X2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 0.30/0.63             => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X2 ) ) )
% 0.30/0.63         => ( ( finite_finite_o @ A2 )
% 0.30/0.63           => ( ord_less_eq_nat @ ( F2 @ I ) @ ( groups8507830703676809646_o_nat @ F2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % member_le_sum
% 0.30/0.63  thf(fact_8617_member__le__sum,axiom,
% 0.30/0.63      ! [I: int,A2: set_int,F2: int > nat] :
% 0.30/0.63        ( ( member_int @ I @ A2 )
% 0.30/0.63       => ( ! [X2: int] :
% 0.30/0.63              ( ( member_int @ X2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 0.30/0.63             => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X2 ) ) )
% 0.30/0.63         => ( ( finite_finite_int @ A2 )
% 0.30/0.63           => ( ord_less_eq_nat @ ( F2 @ I ) @ ( groups4541462559716669496nt_nat @ F2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % member_le_sum
% 0.30/0.63  thf(fact_8618_member__le__sum,axiom,
% 0.30/0.63      ! [I: $o,A2: set_o,F2: $o > int] :
% 0.30/0.63        ( ( member_o @ I @ A2 )
% 0.30/0.63       => ( ! [X2: $o] :
% 0.30/0.63              ( ( member_o @ X2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 0.30/0.63             => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ X2 ) ) )
% 0.30/0.63         => ( ( finite_finite_o @ A2 )
% 0.30/0.63           => ( ord_less_eq_int @ ( F2 @ I ) @ ( groups8505340233167759370_o_int @ F2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % member_le_sum
% 0.30/0.63  thf(fact_8619_member__le__sum,axiom,
% 0.30/0.63      ! [I: nat,A2: set_nat,F2: nat > int] :
% 0.30/0.63        ( ( member_nat @ I @ A2 )
% 0.30/0.63       => ( ! [X2: nat] :
% 0.30/0.63              ( ( member_nat @ X2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 0.30/0.63             => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ X2 ) ) )
% 0.30/0.63         => ( ( finite_finite_nat @ A2 )
% 0.30/0.63           => ( ord_less_eq_int @ ( F2 @ I ) @ ( groups3539618377306564664at_int @ F2 @ A2 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % member_le_sum
% 0.30/0.63  thf(fact_8620_prod__mono2,axiom,
% 0.30/0.63      ! [B2: set_int,A2: set_int,F2: int > code_integer] :
% 0.30/0.63        ( ( finite_finite_int @ B2 )
% 0.30/0.63       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.30/0.63         => ( ! [B6: int] :
% 0.30/0.63                ( ( member_int @ B6 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 0.30/0.63               => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ B6 ) ) )
% 0.30/0.63           => ( ! [A6: int] :
% 0.30/0.63                  ( ( member_int @ A6 @ A2 )
% 0.30/0.63                 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ A6 ) ) )
% 0.30/0.63             => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F2 @ A2 ) @ ( groups3827104343326376752nteger @ F2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_mono2
% 0.30/0.63  thf(fact_8621_prod__mono2,axiom,
% 0.30/0.63      ! [B2: set_int,A2: set_int,F2: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ B2 )
% 0.30/0.63       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.30/0.63         => ( ! [B6: int] :
% 0.30/0.63                ( ( member_int @ B6 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 0.30/0.63               => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ B6 ) ) )
% 0.30/0.63           => ( ! [A6: int] :
% 0.30/0.63                  ( ( member_int @ A6 @ A2 )
% 0.30/0.63                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ A6 ) ) )
% 0.30/0.63             => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F2 @ A2 ) @ ( groups1072433553688619179nt_rat @ F2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_mono2
% 0.30/0.63  thf(fact_8622_prod__mono2,axiom,
% 0.30/0.63      ! [B2: set_nat,A2: set_nat,F2: nat > code_integer] :
% 0.30/0.63        ( ( finite_finite_nat @ B2 )
% 0.30/0.63       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.30/0.63         => ( ! [B6: nat] :
% 0.30/0.63                ( ( member_nat @ B6 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 0.30/0.63               => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ B6 ) ) )
% 0.30/0.63           => ( ! [A6: nat] :
% 0.30/0.63                  ( ( member_nat @ A6 @ A2 )
% 0.30/0.63                 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ A6 ) ) )
% 0.30/0.63             => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F2 @ A2 ) @ ( groups3455450783089532116nteger @ F2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_mono2
% 0.30/0.63  thf(fact_8623_prod__mono2,axiom,
% 0.30/0.63      ! [B2: set_nat,A2: set_nat,F2: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ B2 )
% 0.30/0.63       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.30/0.63         => ( ! [B6: nat] :
% 0.30/0.63                ( ( member_nat @ B6 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 0.30/0.63               => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ B6 ) ) )
% 0.30/0.63           => ( ! [A6: nat] :
% 0.30/0.63                  ( ( member_nat @ A6 @ A2 )
% 0.30/0.63                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ A6 ) ) )
% 0.30/0.63             => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F2 @ A2 ) @ ( groups73079841787564623at_rat @ F2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_mono2
% 0.30/0.63  thf(fact_8624_prod__mono2,axiom,
% 0.30/0.63      ! [B2: set_nat,A2: set_nat,F2: nat > int] :
% 0.30/0.63        ( ( finite_finite_nat @ B2 )
% 0.30/0.63       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 0.30/0.63         => ( ! [B6: nat] :
% 0.30/0.63                ( ( member_nat @ B6 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 0.30/0.63               => ( ord_less_eq_int @ one_one_int @ ( F2 @ B6 ) ) )
% 0.30/0.63           => ( ! [A6: nat] :
% 0.30/0.63                  ( ( member_nat @ A6 @ A2 )
% 0.30/0.63                 => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ A6 ) ) )
% 0.30/0.63             => ( ord_less_eq_int @ ( groups705719431365010083at_int @ F2 @ A2 ) @ ( groups705719431365010083at_int @ F2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_mono2
% 0.30/0.63  thf(fact_8625_prod__mono2,axiom,
% 0.30/0.63      ! [B2: set_int,A2: set_int,F2: int > int] :
% 0.30/0.63        ( ( finite_finite_int @ B2 )
% 0.30/0.63       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 0.30/0.63         => ( ! [B6: int] :
% 0.30/0.63                ( ( member_int @ B6 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 0.30/0.63               => ( ord_less_eq_int @ one_one_int @ ( F2 @ B6 ) ) )
% 0.30/0.63           => ( ! [A6: int] :
% 0.30/0.63                  ( ( member_int @ A6 @ A2 )
% 0.30/0.63                 => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ A6 ) ) )
% 0.30/0.63             => ( ord_less_eq_int @ ( groups1705073143266064639nt_int @ F2 @ A2 ) @ ( groups1705073143266064639nt_int @ F2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_mono2
% 0.30/0.63  thf(fact_8626_prod__mono2,axiom,
% 0.30/0.63      ! [B2: set_set_nat,A2: set_set_nat,F2: set_nat > code_integer] :
% 0.30/0.63        ( ( finite1152437895449049373et_nat @ B2 )
% 0.30/0.63       => ( ( ord_le6893508408891458716et_nat @ A2 @ B2 )
% 0.30/0.63         => ( ! [B6: set_nat] :
% 0.30/0.63                ( ( member_set_nat @ B6 @ ( minus_2163939370556025621et_nat @ B2 @ A2 ) )
% 0.30/0.63               => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ B6 ) ) )
% 0.30/0.63           => ( ! [A6: set_nat] :
% 0.30/0.63                  ( ( member_set_nat @ A6 @ A2 )
% 0.30/0.63                 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ A6 ) ) )
% 0.30/0.63             => ( ord_le3102999989581377725nteger @ ( groups2761809935038513290nteger @ F2 @ A2 ) @ ( groups2761809935038513290nteger @ F2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_mono2
% 0.30/0.63  thf(fact_8627_prod__mono2,axiom,
% 0.30/0.63      ! [B2: set_set_nat,A2: set_set_nat,F2: set_nat > rat] :
% 0.30/0.63        ( ( finite1152437895449049373et_nat @ B2 )
% 0.30/0.63       => ( ( ord_le6893508408891458716et_nat @ A2 @ B2 )
% 0.30/0.63         => ( ! [B6: set_nat] :
% 0.30/0.63                ( ( member_set_nat @ B6 @ ( minus_2163939370556025621et_nat @ B2 @ A2 ) )
% 0.30/0.63               => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ B6 ) ) )
% 0.30/0.63           => ( ! [A6: set_nat] :
% 0.30/0.63                  ( ( member_set_nat @ A6 @ A2 )
% 0.30/0.63                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ A6 ) ) )
% 0.30/0.63             => ( ord_less_eq_rat @ ( groups3613417700093529605at_rat @ F2 @ A2 ) @ ( groups3613417700093529605at_rat @ F2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_mono2
% 0.30/0.63  thf(fact_8628_prod__mono2,axiom,
% 0.30/0.63      ! [B2: set_set_nat,A2: set_set_nat,F2: set_nat > int] :
% 0.30/0.63        ( ( finite1152437895449049373et_nat @ B2 )
% 0.30/0.63       => ( ( ord_le6893508408891458716et_nat @ A2 @ B2 )
% 0.30/0.63         => ( ! [B6: set_nat] :
% 0.30/0.63                ( ( member_set_nat @ B6 @ ( minus_2163939370556025621et_nat @ B2 @ A2 ) )
% 0.30/0.63               => ( ord_less_eq_int @ one_one_int @ ( F2 @ B6 ) ) )
% 0.30/0.63           => ( ! [A6: set_nat] :
% 0.30/0.63                  ( ( member_set_nat @ A6 @ A2 )
% 0.30/0.63                 => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ A6 ) ) )
% 0.30/0.63             => ( ord_less_eq_int @ ( groups4246057289670975065at_int @ F2 @ A2 ) @ ( groups4246057289670975065at_int @ F2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_mono2
% 0.30/0.63  thf(fact_8629_prod__mono2,axiom,
% 0.30/0.63      ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > code_integer] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ B2 )
% 0.30/0.63       => ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 0.30/0.63         => ( ! [B6: product_prod_nat_nat] :
% 0.30/0.63                ( ( member8440522571783428010at_nat @ B6 @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) )
% 0.30/0.63               => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ B6 ) ) )
% 0.30/0.63           => ( ! [A6: product_prod_nat_nat] :
% 0.30/0.63                  ( ( member8440522571783428010at_nat @ A6 @ A2 )
% 0.30/0.63                 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ A6 ) ) )
% 0.30/0.63             => ( ord_le3102999989581377725nteger @ ( groups1230400874837758585nteger @ F2 @ A2 ) @ ( groups1230400874837758585nteger @ F2 @ B2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_mono2
% 0.30/0.63  thf(fact_8630_prod__diff1,axiom,
% 0.30/0.63      ! [A2: set_o,F2: $o > nat,A: $o] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( ( F2 @ A )
% 0.30/0.63           != zero_zero_nat )
% 0.30/0.63         => ( ( ( member_o @ A @ A2 )
% 0.30/0.63             => ( ( groups3504817904513533571_o_nat @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.30/0.63                = ( divide_divide_nat @ ( groups3504817904513533571_o_nat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.63            & ( ~ ( member_o @ A @ A2 )
% 0.30/0.63             => ( ( groups3504817904513533571_o_nat @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.30/0.63                = ( groups3504817904513533571_o_nat @ F2 @ A2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_diff1
% 0.30/0.63  thf(fact_8631_prod__diff1,axiom,
% 0.30/0.63      ! [A2: set_int,F2: int > nat,A: int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( ( F2 @ A )
% 0.30/0.63           != zero_zero_nat )
% 0.30/0.63         => ( ( ( member_int @ A @ A2 )
% 0.30/0.63             => ( ( groups1707563613775114915nt_nat @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.30/0.63                = ( divide_divide_nat @ ( groups1707563613775114915nt_nat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.63            & ( ~ ( member_int @ A @ A2 )
% 0.30/0.63             => ( ( groups1707563613775114915nt_nat @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.30/0.63                = ( groups1707563613775114915nt_nat @ F2 @ A2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_diff1
% 0.30/0.63  thf(fact_8632_prod__diff1,axiom,
% 0.30/0.63      ! [A2: set_o,F2: $o > int,A: $o] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( ( F2 @ A )
% 0.30/0.63           != zero_zero_int )
% 0.30/0.63         => ( ( ( member_o @ A @ A2 )
% 0.30/0.63             => ( ( groups3502327434004483295_o_int @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.30/0.63                = ( divide_divide_int @ ( groups3502327434004483295_o_int @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.63            & ( ~ ( member_o @ A @ A2 )
% 0.30/0.63             => ( ( groups3502327434004483295_o_int @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.30/0.63                = ( groups3502327434004483295_o_int @ F2 @ A2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_diff1
% 0.30/0.63  thf(fact_8633_prod__diff1,axiom,
% 0.30/0.63      ! [A2: set_o,F2: $o > code_integer,A: $o] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( ( F2 @ A )
% 0.30/0.63           != zero_z3403309356797280102nteger )
% 0.30/0.63         => ( ( ( member_o @ A @ A2 )
% 0.30/0.63             => ( ( groups7694694392188491536nteger @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.30/0.63                = ( divide6298287555418463151nteger @ ( groups7694694392188491536nteger @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.63            & ( ~ ( member_o @ A @ A2 )
% 0.30/0.63             => ( ( groups7694694392188491536nteger @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.30/0.63                = ( groups7694694392188491536nteger @ F2 @ A2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_diff1
% 0.30/0.63  thf(fact_8634_prod__diff1,axiom,
% 0.30/0.63      ! [A2: set_int,F2: int > code_integer,A: int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( ( F2 @ A )
% 0.30/0.63           != zero_z3403309356797280102nteger )
% 0.30/0.63         => ( ( ( member_int @ A @ A2 )
% 0.30/0.63             => ( ( groups3827104343326376752nteger @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.30/0.63                = ( divide6298287555418463151nteger @ ( groups3827104343326376752nteger @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.63            & ( ~ ( member_int @ A @ A2 )
% 0.30/0.63             => ( ( groups3827104343326376752nteger @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.30/0.63                = ( groups3827104343326376752nteger @ F2 @ A2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_diff1
% 0.30/0.63  thf(fact_8635_prod__diff1,axiom,
% 0.30/0.63      ! [A2: set_nat,F2: nat > code_integer,A: nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( ( F2 @ A )
% 0.30/0.63           != zero_z3403309356797280102nteger )
% 0.30/0.63         => ( ( ( member_nat @ A @ A2 )
% 0.30/0.63             => ( ( groups3455450783089532116nteger @ F2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.30/0.63                = ( divide6298287555418463151nteger @ ( groups3455450783089532116nteger @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.63            & ( ~ ( member_nat @ A @ A2 )
% 0.30/0.63             => ( ( groups3455450783089532116nteger @ F2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.30/0.63                = ( groups3455450783089532116nteger @ F2 @ A2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_diff1
% 0.30/0.63  thf(fact_8636_prod__diff1,axiom,
% 0.30/0.63      ! [A2: set_o,F2: $o > rat,A: $o] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( ( F2 @ A )
% 0.30/0.63           != zero_zero_rat )
% 0.30/0.63         => ( ( ( member_o @ A @ A2 )
% 0.30/0.63             => ( ( groups2869687844427037835_o_rat @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.30/0.63                = ( divide_divide_rat @ ( groups2869687844427037835_o_rat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.63            & ( ~ ( member_o @ A @ A2 )
% 0.30/0.63             => ( ( groups2869687844427037835_o_rat @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.30/0.63                = ( groups2869687844427037835_o_rat @ F2 @ A2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_diff1
% 0.30/0.63  thf(fact_8637_prod__diff1,axiom,
% 0.30/0.63      ! [A2: set_int,F2: int > rat,A: int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( ( F2 @ A )
% 0.30/0.63           != zero_zero_rat )
% 0.30/0.63         => ( ( ( member_int @ A @ A2 )
% 0.30/0.63             => ( ( groups1072433553688619179nt_rat @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.30/0.63                = ( divide_divide_rat @ ( groups1072433553688619179nt_rat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.63            & ( ~ ( member_int @ A @ A2 )
% 0.30/0.63             => ( ( groups1072433553688619179nt_rat @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.30/0.63                = ( groups1072433553688619179nt_rat @ F2 @ A2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_diff1
% 0.30/0.63  thf(fact_8638_prod__diff1,axiom,
% 0.30/0.63      ! [A2: set_nat,F2: nat > rat,A: nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( ( F2 @ A )
% 0.30/0.63           != zero_zero_rat )
% 0.30/0.63         => ( ( ( member_nat @ A @ A2 )
% 0.30/0.63             => ( ( groups73079841787564623at_rat @ F2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.30/0.63                = ( divide_divide_rat @ ( groups73079841787564623at_rat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.63            & ( ~ ( member_nat @ A @ A2 )
% 0.30/0.63             => ( ( groups73079841787564623at_rat @ F2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.30/0.63                = ( groups73079841787564623at_rat @ F2 @ A2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_diff1
% 0.30/0.63  thf(fact_8639_prod__diff1,axiom,
% 0.30/0.63      ! [A2: set_o,F2: $o > code_natural,A: $o] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( ( F2 @ A )
% 0.30/0.63           != zero_z2226904508553997617atural )
% 0.30/0.63         => ( ( ( member_o @ A @ A2 )
% 0.30/0.63             => ( ( groups6518289543945209051atural @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.30/0.63                = ( divide5121882707175180666atural @ ( groups6518289543945209051atural @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 0.30/0.63            & ( ~ ( member_o @ A @ A2 )
% 0.30/0.63             => ( ( groups6518289543945209051atural @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 0.30/0.63                = ( groups6518289543945209051atural @ F2 @ A2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_diff1
% 0.30/0.63  thf(fact_8640_prod__Un,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,F2: int > rat] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ! [X2: int] :
% 0.30/0.63                ( ( member_int @ X2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 0.30/0.63               => ( ( F2 @ X2 )
% 0.30/0.63                 != zero_zero_rat ) )
% 0.30/0.63           => ( ( groups1072433553688619179nt_rat @ F2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 0.30/0.63              = ( divide_divide_rat @ ( times_times_rat @ ( groups1072433553688619179nt_rat @ F2 @ A2 ) @ ( groups1072433553688619179nt_rat @ F2 @ B2 ) ) @ ( groups1072433553688619179nt_rat @ F2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_Un
% 0.30/0.63  thf(fact_8641_prod__Un,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > rat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( finite6177210948735845034at_nat @ B2 )
% 0.30/0.63         => ( ! [X2: product_prod_nat_nat] :
% 0.30/0.63                ( ( member8440522571783428010at_nat @ X2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 0.30/0.63               => ( ( F2 @ X2 )
% 0.30/0.63                 != zero_zero_rat ) )
% 0.30/0.63           => ( ( groups3442636767675653108at_rat @ F2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( divide_divide_rat @ ( times_times_rat @ ( groups3442636767675653108at_rat @ F2 @ A2 ) @ ( groups3442636767675653108at_rat @ F2 @ B2 ) ) @ ( groups3442636767675653108at_rat @ F2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_Un
% 0.30/0.63  thf(fact_8642_prod__Un,axiom,
% 0.30/0.63      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,F2: produc4166570645942440679at_nat > rat] :
% 0.30/0.63        ( ( finite1918287321285529104at_nat @ A2 )
% 0.30/0.63       => ( ( finite1918287321285529104at_nat @ B2 )
% 0.30/0.63         => ( ! [X2: produc4166570645942440679at_nat] :
% 0.30/0.63                ( ( member6689249552917799696at_nat @ X2 @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) )
% 0.30/0.63               => ( ( F2 @ X2 )
% 0.30/0.63                 != zero_zero_rat ) )
% 0.30/0.63           => ( ( groups5938585286922990810at_rat @ F2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( divide_divide_rat @ ( times_times_rat @ ( groups5938585286922990810at_rat @ F2 @ A2 ) @ ( groups5938585286922990810at_rat @ F2 @ B2 ) ) @ ( groups5938585286922990810at_rat @ F2 @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_Un
% 0.30/0.63  thf(fact_8643_prod__Un,axiom,
% 0.30/0.63      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,F2: produc3843707927480180839at_nat > rat] :
% 0.30/0.63        ( ( finite4343798906461161616at_nat @ A2 )
% 0.30/0.63       => ( ( finite4343798906461161616at_nat @ B2 )
% 0.30/0.63         => ( ! [X2: produc3843707927480180839at_nat] :
% 0.30/0.63                ( ( member8757157785044589968at_nat @ X2 @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) )
% 0.30/0.63               => ( ( F2 @ X2 )
% 0.30/0.63                 != zero_zero_rat ) )
% 0.30/0.63           => ( ( groups8874911130973611098at_rat @ F2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( divide_divide_rat @ ( times_times_rat @ ( groups8874911130973611098at_rat @ F2 @ A2 ) @ ( groups8874911130973611098at_rat @ F2 @ B2 ) ) @ ( groups8874911130973611098at_rat @ F2 @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_Un
% 0.30/0.63  thf(fact_8644_prod__Un,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,F2: nat > rat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ! [X2: nat] :
% 0.30/0.63                ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 0.30/0.63               => ( ( F2 @ X2 )
% 0.30/0.63                 != zero_zero_rat ) )
% 0.30/0.63           => ( ( groups73079841787564623at_rat @ F2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 0.30/0.63              = ( divide_divide_rat @ ( times_times_rat @ ( groups73079841787564623at_rat @ F2 @ A2 ) @ ( groups73079841787564623at_rat @ F2 @ B2 ) ) @ ( groups73079841787564623at_rat @ F2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod_Un
% 0.30/0.63  thf(fact_8645_atLeast1__lessThan__eq__remove0,axiom,
% 0.30/0.63      ! [N: nat] :
% 0.30/0.63        ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.30/0.63        = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % atLeast1_lessThan_eq_remove0
% 0.30/0.63  thf(fact_8646_one__diff__power__eq_H,axiom,
% 0.30/0.63      ! [X: code_integer,N: nat] :
% 0.30/0.63        ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) )
% 0.30/0.63        = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X )
% 0.30/0.63          @ ( groups7501900531339628137nteger
% 0.30/0.63            @ ^ [I3: nat] : ( power_8256067586552552935nteger @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 0.30/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % one_diff_power_eq'
% 0.30/0.63  thf(fact_8647_one__diff__power__eq_H,axiom,
% 0.30/0.63      ! [X: rat,N: nat] :
% 0.30/0.63        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 0.30/0.63        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X )
% 0.30/0.63          @ ( groups2906978787729119204at_rat
% 0.30/0.63            @ ^ [I3: nat] : ( power_power_rat @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 0.30/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % one_diff_power_eq'
% 0.30/0.63  thf(fact_8648_one__diff__power__eq_H,axiom,
% 0.30/0.63      ! [X: int,N: nat] :
% 0.30/0.63        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 0.30/0.63        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 0.30/0.63          @ ( groups3539618377306564664at_int
% 0.30/0.63            @ ^ [I3: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 0.30/0.63            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % one_diff_power_eq'
% 0.30/0.63  thf(fact_8649_eucl__rel__int_Ocases,axiom,
% 0.30/0.63      ! [A1: int,A22: int,A32: product_prod_int_int] :
% 0.30/0.63        ( ( eucl_rel_int @ A1 @ A22 @ A32 )
% 0.30/0.63       => ( ( ( A22 = zero_zero_int )
% 0.30/0.63           => ( A32
% 0.30/0.63             != ( product_Pair_int_int @ zero_zero_int @ A1 ) ) )
% 0.30/0.63         => ( ! [Q7: int] :
% 0.30/0.63                ( ( A32
% 0.30/0.63                  = ( product_Pair_int_int @ Q7 @ zero_zero_int ) )
% 0.30/0.63               => ( ( A22 != zero_zero_int )
% 0.30/0.63                 => ( A1
% 0.30/0.63                   != ( times_times_int @ Q7 @ A22 ) ) ) )
% 0.30/0.63           => ~ ! [R6: int,Q7: int] :
% 0.30/0.63                  ( ( A32
% 0.30/0.63                    = ( product_Pair_int_int @ Q7 @ R6 ) )
% 0.30/0.63                 => ( ( ( sgn_sgn_int @ R6 )
% 0.30/0.63                      = ( sgn_sgn_int @ A22 ) )
% 0.30/0.63                   => ( ( ord_less_int @ ( abs_abs_int @ R6 ) @ ( abs_abs_int @ A22 ) )
% 0.30/0.63                     => ( A1
% 0.30/0.63                       != ( plus_plus_int @ ( times_times_int @ Q7 @ A22 ) @ R6 ) ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % eucl_rel_int.cases
% 0.30/0.63  thf(fact_8650_eucl__rel__int_Osimps,axiom,
% 0.30/0.63      ( eucl_rel_int
% 0.30/0.63      = ( ^ [A12: int,A23: int,A33: product_prod_int_int] :
% 0.30/0.63            ( ? [K4: int] :
% 0.30/0.63                ( ( A12 = K4 )
% 0.30/0.63                & ( A23 = zero_zero_int )
% 0.30/0.63                & ( A33
% 0.30/0.63                  = ( product_Pair_int_int @ zero_zero_int @ K4 ) ) )
% 0.30/0.63            | ? [L2: int,K4: int,Q5: int] :
% 0.30/0.63                ( ( A12 = K4 )
% 0.30/0.63                & ( A23 = L2 )
% 0.30/0.63                & ( A33
% 0.30/0.63                  = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 0.30/0.63                & ( L2 != zero_zero_int )
% 0.30/0.63                & ( K4
% 0.30/0.63                  = ( times_times_int @ Q5 @ L2 ) ) )
% 0.30/0.63            | ? [R4: int,L2: int,K4: int,Q5: int] :
% 0.30/0.63                ( ( A12 = K4 )
% 0.30/0.63                & ( A23 = L2 )
% 0.30/0.63                & ( A33
% 0.30/0.63                  = ( product_Pair_int_int @ Q5 @ R4 ) )
% 0.30/0.63                & ( ( sgn_sgn_int @ R4 )
% 0.30/0.63                  = ( sgn_sgn_int @ L2 ) )
% 0.30/0.63                & ( ord_less_int @ ( abs_abs_int @ R4 ) @ ( abs_abs_int @ L2 ) )
% 0.30/0.63                & ( K4
% 0.30/0.63                  = ( plus_plus_int @ ( times_times_int @ Q5 @ L2 ) @ R4 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % eucl_rel_int.simps
% 0.30/0.63  thf(fact_8651_div__noneq__sgn__abs,axiom,
% 0.30/0.63      ! [L: int,K: int] :
% 0.30/0.63        ( ( L != zero_zero_int )
% 0.30/0.63       => ( ( ( sgn_sgn_int @ K )
% 0.30/0.63           != ( sgn_sgn_int @ L ) )
% 0.30/0.63         => ( ( divide_divide_int @ K @ L )
% 0.30/0.63            = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) )
% 0.30/0.63              @ ( zero_n2684676970156552555ol_int
% 0.30/0.63                @ ~ ( dvd_dvd_int @ L @ K ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % div_noneq_sgn_abs
% 0.30/0.63  thf(fact_8652_prod_Otriangle__reindex__eq,axiom,
% 0.30/0.63      ! [G2: nat > nat > nat,N: nat] :
% 0.30/0.63        ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G2 )
% 0.30/0.63          @ ( collec3392354462482085612at_nat
% 0.30/0.63            @ ( produc6081775807080527818_nat_o
% 0.30/0.63              @ ^ [I3: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 0.30/0.63        = ( groups708209901874060359at_nat
% 0.30/0.63          @ ^ [K4: nat] :
% 0.30/0.63              ( groups708209901874060359at_nat
% 0.30/0.63              @ ^ [I3: nat] : ( G2 @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 0.30/0.63              @ ( set_ord_atMost_nat @ K4 ) )
% 0.30/0.63          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.triangle_reindex_eq
% 0.30/0.63  thf(fact_8653_prod_Otriangle__reindex__eq,axiom,
% 0.30/0.63      ! [G2: nat > nat > int,N: nat] :
% 0.30/0.63        ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G2 )
% 0.30/0.63          @ ( collec3392354462482085612at_nat
% 0.30/0.63            @ ( produc6081775807080527818_nat_o
% 0.30/0.63              @ ^ [I3: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 0.30/0.63        = ( groups705719431365010083at_int
% 0.30/0.63          @ ^ [K4: nat] :
% 0.30/0.63              ( groups705719431365010083at_int
% 0.30/0.63              @ ^ [I3: nat] : ( G2 @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 0.30/0.63              @ ( set_ord_atMost_nat @ K4 ) )
% 0.30/0.63          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % prod.triangle_reindex_eq
% 0.30/0.63  thf(fact_8654_drop__bit__rec,axiom,
% 0.30/0.63      ( bit_se8570568707652914677it_nat
% 0.30/0.63      = ( ^ [N2: nat,A3: nat] : ( if_nat @ ( N2 = zero_zero_nat ) @ A3 @ ( bit_se8570568707652914677it_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % drop_bit_rec
% 0.30/0.63  thf(fact_8655_drop__bit__rec,axiom,
% 0.30/0.63      ( bit_se3928097537394005634nteger
% 0.30/0.63      = ( ^ [N2: nat,A3: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ A3 @ ( bit_se3928097537394005634nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % drop_bit_rec
% 0.30/0.63  thf(fact_8656_drop__bit__rec,axiom,
% 0.30/0.63      ( bit_se2751692689150723149atural
% 0.30/0.63      = ( ^ [N2: nat,A3: code_natural] : ( if_Code_natural @ ( N2 = zero_zero_nat ) @ A3 @ ( bit_se2751692689150723149atural @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide5121882707175180666atural @ A3 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % drop_bit_rec
% 0.30/0.63  thf(fact_8657_drop__bit__rec,axiom,
% 0.30/0.63      ( bit_se8568078237143864401it_int
% 0.30/0.63      = ( ^ [N2: nat,A3: int] : ( if_int @ ( N2 = zero_zero_nat ) @ A3 @ ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % drop_bit_rec
% 0.30/0.63  thf(fact_8658_finite__compl,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( finite6177210948735845034at_nat @ ( uminus6524753893492686040at_nat @ A2 ) )
% 0.30/0.63          = ( finite6177210948735845034at_nat @ top_to4669805908274784177at_nat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_compl
% 0.30/0.63  thf(fact_8659_finite__compl,axiom,
% 0.30/0.63      ! [A2: set_list_nat] :
% 0.30/0.63        ( ( finite8100373058378681591st_nat @ A2 )
% 0.30/0.63       => ( ( finite8100373058378681591st_nat @ ( uminus3195874150345416415st_nat @ A2 ) )
% 0.30/0.63          = ( finite8100373058378681591st_nat @ top_top_set_list_nat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_compl
% 0.30/0.63  thf(fact_8660_finite__compl,axiom,
% 0.30/0.63      ! [A2: set_o] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( finite_finite_o @ ( uminus_uminus_set_o @ A2 ) )
% 0.30/0.63          = ( finite_finite_o @ top_top_set_o ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_compl
% 0.30/0.63  thf(fact_8661_finite__compl,axiom,
% 0.30/0.63      ! [A2: set_rat] :
% 0.30/0.63        ( ( finite_finite_rat @ A2 )
% 0.30/0.63       => ( ( finite_finite_rat @ ( uminus2201863774496077783et_rat @ A2 ) )
% 0.30/0.63          = ( finite_finite_rat @ top_top_set_rat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_compl
% 0.30/0.63  thf(fact_8662_finite__compl,axiom,
% 0.30/0.63      ! [A2: set_nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ ( uminus5710092332889474511et_nat @ A2 ) )
% 0.30/0.63          = ( finite_finite_nat @ top_top_set_nat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_compl
% 0.30/0.63  thf(fact_8663_finite__compl,axiom,
% 0.30/0.63      ! [A2: set_int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ ( uminus1532241313380277803et_int @ A2 ) )
% 0.30/0.63          = ( finite_finite_int @ top_top_set_int ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_compl
% 0.30/0.63  thf(fact_8664_finite__Collect__le__nat,axiom,
% 0.30/0.63      ! [K: nat] :
% 0.30/0.63        ( finite_finite_nat
% 0.30/0.63        @ ( collect_nat
% 0.30/0.63          @ ^ [N2: nat] : ( ord_less_eq_nat @ N2 @ K ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_le_nat
% 0.30/0.63  thf(fact_8665_finite__Collect__less__nat,axiom,
% 0.30/0.63      ! [K: nat] :
% 0.30/0.63        ( finite_finite_nat
% 0.30/0.63        @ ( collect_nat
% 0.30/0.63          @ ^ [N2: nat] : ( ord_less_nat @ N2 @ K ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_less_nat
% 0.30/0.63  thf(fact_8666_finite__Collect__not,axiom,
% 0.30/0.63      ! [P: set_Pr958786334691620121nt_int > $o] :
% 0.30/0.63        ( ( finite8744585540193469122nt_int @ ( collec5210948495886036740nt_int @ P ) )
% 0.30/0.63       => ( ( finite8744585540193469122nt_int
% 0.30/0.63            @ ( collec5210948495886036740nt_int
% 0.30/0.63              @ ^ [X3: set_Pr958786334691620121nt_int] :
% 0.30/0.63                  ~ ( P @ X3 ) ) )
% 0.30/0.63          = ( finite8744585540193469122nt_int @ top_to6034159466715884489nt_int ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_not
% 0.30/0.63  thf(fact_8667_finite__Collect__not,axiom,
% 0.30/0.63      ! [P: set_nat > $o] :
% 0.30/0.63        ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 0.30/0.63       => ( ( finite1152437895449049373et_nat
% 0.30/0.63            @ ( collect_set_nat
% 0.30/0.63              @ ^ [X3: set_nat] :
% 0.30/0.63                  ~ ( P @ X3 ) ) )
% 0.30/0.63          = ( finite1152437895449049373et_nat @ top_top_set_set_nat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_not
% 0.30/0.63  thf(fact_8668_finite__Collect__not,axiom,
% 0.30/0.63      ! [P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.30/0.63        ( ( finite3252695134891459830_nat_o @ ( collec939566748876313656_nat_o @ P ) )
% 0.30/0.63       => ( ( finite3252695134891459830_nat_o
% 0.30/0.63            @ ( collec939566748876313656_nat_o
% 0.30/0.63              @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.30/0.63                  ~ ( P @ X3 ) ) )
% 0.30/0.63          = ( finite3252695134891459830_nat_o @ top_to4869887016220417533_nat_o ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_not
% 0.30/0.63  thf(fact_8669_finite__Collect__not,axiom,
% 0.30/0.63      ! [P: product_prod_nat_nat > $o] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ P ) )
% 0.30/0.63       => ( ( finite6177210948735845034at_nat
% 0.30/0.63            @ ( collec3392354462482085612at_nat
% 0.30/0.63              @ ^ [X3: product_prod_nat_nat] :
% 0.30/0.63                  ~ ( P @ X3 ) ) )
% 0.30/0.63          = ( finite6177210948735845034at_nat @ top_to4669805908274784177at_nat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_not
% 0.30/0.63  thf(fact_8670_finite__Collect__not,axiom,
% 0.30/0.63      ! [P: list_nat > $o] :
% 0.30/0.63        ( ( finite8100373058378681591st_nat @ ( collect_list_nat @ P ) )
% 0.30/0.63       => ( ( finite8100373058378681591st_nat
% 0.30/0.63            @ ( collect_list_nat
% 0.30/0.63              @ ^ [X3: list_nat] :
% 0.30/0.63                  ~ ( P @ X3 ) ) )
% 0.30/0.63          = ( finite8100373058378681591st_nat @ top_top_set_list_nat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_not
% 0.30/0.63  thf(fact_8671_finite__Collect__not,axiom,
% 0.30/0.63      ! [P: $o > $o] :
% 0.30/0.63        ( ( finite_finite_o @ ( collect_o @ P ) )
% 0.30/0.63       => ( ( finite_finite_o
% 0.30/0.63            @ ( collect_o
% 0.30/0.63              @ ^ [X3: $o] :
% 0.30/0.63                  ~ ( P @ X3 ) ) )
% 0.30/0.63          = ( finite_finite_o @ top_top_set_o ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_not
% 0.30/0.63  thf(fact_8672_finite__Collect__not,axiom,
% 0.30/0.63      ! [P: rat > $o] :
% 0.30/0.63        ( ( finite_finite_rat @ ( collect_rat @ P ) )
% 0.30/0.63       => ( ( finite_finite_rat
% 0.30/0.63            @ ( collect_rat
% 0.30/0.63              @ ^ [X3: rat] :
% 0.30/0.63                  ~ ( P @ X3 ) ) )
% 0.30/0.63          = ( finite_finite_rat @ top_top_set_rat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_not
% 0.30/0.63  thf(fact_8673_finite__Collect__not,axiom,
% 0.30/0.63      ! [P: nat > $o] :
% 0.30/0.63        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 0.30/0.63       => ( ( finite_finite_nat
% 0.30/0.63            @ ( collect_nat
% 0.30/0.63              @ ^ [X3: nat] :
% 0.30/0.63                  ~ ( P @ X3 ) ) )
% 0.30/0.63          = ( finite_finite_nat @ top_top_set_nat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_not
% 0.30/0.63  thf(fact_8674_finite__Collect__not,axiom,
% 0.30/0.63      ! [P: int > $o] :
% 0.30/0.63        ( ( finite_finite_int @ ( collect_int @ P ) )
% 0.30/0.63       => ( ( finite_finite_int
% 0.30/0.63            @ ( collect_int
% 0.30/0.63              @ ^ [X3: int] :
% 0.30/0.63                  ~ ( P @ X3 ) ) )
% 0.30/0.63          = ( finite_finite_int @ top_top_set_int ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_not
% 0.30/0.63  thf(fact_8675_finite__Collect__subsets,axiom,
% 0.30/0.63      ! [A2: set_Pr958786334691620121nt_int] :
% 0.30/0.63        ( ( finite2998713641127702882nt_int @ A2 )
% 0.30/0.63       => ( finite8744585540193469122nt_int
% 0.30/0.63          @ ( collec5210948495886036740nt_int
% 0.30/0.63            @ ^ [B4: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ B4 @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_subsets
% 0.30/0.63  thf(fact_8676_finite__Collect__subsets,axiom,
% 0.30/0.63      ! [A2: set_int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( finite6197958912794628473et_int
% 0.30/0.63          @ ( collect_set_int
% 0.30/0.63            @ ^ [B4: set_int] : ( ord_less_eq_set_int @ B4 @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_subsets
% 0.30/0.63  thf(fact_8677_finite__Collect__subsets,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( finite9047747110432174090at_nat
% 0.30/0.63          @ ( collec5514110066124741708at_nat
% 0.30/0.63            @ ^ [B4: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ B4 @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_subsets
% 0.30/0.63  thf(fact_8678_finite__Collect__subsets,axiom,
% 0.30/0.63      ! [A2: set_nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( finite1152437895449049373et_nat
% 0.30/0.63          @ ( collect_set_nat
% 0.30/0.63            @ ^ [B4: set_nat] : ( ord_less_eq_set_nat @ B4 @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_subsets
% 0.30/0.63  thf(fact_8679_finite__finite__vimage__IntI,axiom,
% 0.30/0.63      ! [F4: set_o,H3: int > $o,A2: set_int] :
% 0.30/0.63        ( ( finite_finite_o @ F4 )
% 0.30/0.63       => ( ! [Y2: $o] :
% 0.30/0.63              ( ( member_o @ Y2 @ F4 )
% 0.30/0.63             => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_o @ H3 @ ( insert_o @ Y2 @ bot_bot_set_o ) ) @ A2 ) ) )
% 0.30/0.63         => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_o @ H3 @ F4 ) @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_finite_vimage_IntI
% 0.30/0.63  thf(fact_8680_finite__finite__vimage__IntI,axiom,
% 0.30/0.63      ! [F4: set_o,H3: nat > $o,A2: set_nat] :
% 0.30/0.63        ( ( finite_finite_o @ F4 )
% 0.30/0.63       => ( ! [Y2: $o] :
% 0.30/0.63              ( ( member_o @ Y2 @ F4 )
% 0.30/0.63             => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_o @ H3 @ ( insert_o @ Y2 @ bot_bot_set_o ) ) @ A2 ) ) )
% 0.30/0.63         => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_o @ H3 @ F4 ) @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_finite_vimage_IntI
% 0.30/0.63  thf(fact_8681_finite__finite__vimage__IntI,axiom,
% 0.30/0.63      ! [F4: set_nat,H3: int > nat,A2: set_int] :
% 0.30/0.63        ( ( finite_finite_nat @ F4 )
% 0.30/0.63       => ( ! [Y2: nat] :
% 0.30/0.63              ( ( member_nat @ Y2 @ F4 )
% 0.30/0.63             => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_nat @ H3 @ ( insert_nat @ Y2 @ bot_bot_set_nat ) ) @ A2 ) ) )
% 0.30/0.63         => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_nat @ H3 @ F4 ) @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_finite_vimage_IntI
% 0.30/0.63  thf(fact_8682_finite__finite__vimage__IntI,axiom,
% 0.30/0.63      ! [F4: set_nat,H3: nat > nat,A2: set_nat] :
% 0.30/0.63        ( ( finite_finite_nat @ F4 )
% 0.30/0.63       => ( ! [Y2: nat] :
% 0.30/0.63              ( ( member_nat @ Y2 @ F4 )
% 0.30/0.63             => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_nat @ H3 @ ( insert_nat @ Y2 @ bot_bot_set_nat ) ) @ A2 ) ) )
% 0.30/0.63         => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_nat @ H3 @ F4 ) @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_finite_vimage_IntI
% 0.30/0.63  thf(fact_8683_finite__finite__vimage__IntI,axiom,
% 0.30/0.63      ! [F4: set_int,H3: int > int,A2: set_int] :
% 0.30/0.63        ( ( finite_finite_int @ F4 )
% 0.30/0.63       => ( ! [Y2: int] :
% 0.30/0.63              ( ( member_int @ Y2 @ F4 )
% 0.30/0.63             => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_int @ H3 @ ( insert_int @ Y2 @ bot_bot_set_int ) ) @ A2 ) ) )
% 0.30/0.63         => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_int @ H3 @ F4 ) @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_finite_vimage_IntI
% 0.30/0.63  thf(fact_8684_finite__finite__vimage__IntI,axiom,
% 0.30/0.63      ! [F4: set_int,H3: nat > int,A2: set_nat] :
% 0.30/0.63        ( ( finite_finite_int @ F4 )
% 0.30/0.63       => ( ! [Y2: int] :
% 0.30/0.63              ( ( member_int @ Y2 @ F4 )
% 0.30/0.63             => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_int @ H3 @ ( insert_int @ Y2 @ bot_bot_set_int ) ) @ A2 ) ) )
% 0.30/0.63         => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_int @ H3 @ F4 ) @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_finite_vimage_IntI
% 0.30/0.63  thf(fact_8685_finite__finite__vimage__IntI,axiom,
% 0.30/0.63      ! [F4: set_set_nat,H3: int > set_nat,A2: set_int] :
% 0.30/0.63        ( ( finite1152437895449049373et_nat @ F4 )
% 0.30/0.63       => ( ! [Y2: set_nat] :
% 0.30/0.63              ( ( member_set_nat @ Y2 @ F4 )
% 0.30/0.63             => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_set_nat @ H3 @ ( insert_set_nat @ Y2 @ bot_bot_set_set_nat ) ) @ A2 ) ) )
% 0.30/0.63         => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_set_nat @ H3 @ F4 ) @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_finite_vimage_IntI
% 0.30/0.63  thf(fact_8686_finite__finite__vimage__IntI,axiom,
% 0.30/0.63      ! [F4: set_set_nat,H3: nat > set_nat,A2: set_nat] :
% 0.30/0.63        ( ( finite1152437895449049373et_nat @ F4 )
% 0.30/0.63       => ( ! [Y2: set_nat] :
% 0.30/0.63              ( ( member_set_nat @ Y2 @ F4 )
% 0.30/0.63             => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_set_nat @ H3 @ ( insert_set_nat @ Y2 @ bot_bot_set_set_nat ) ) @ A2 ) ) )
% 0.30/0.63         => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_set_nat @ H3 @ F4 ) @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_finite_vimage_IntI
% 0.30/0.63  thf(fact_8687_finite__finite__vimage__IntI,axiom,
% 0.30/0.63      ! [F4: set_Pr1261947904930325089at_nat,H3: int > product_prod_nat_nat,A2: set_int] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ F4 )
% 0.30/0.63       => ( ! [Y2: product_prod_nat_nat] :
% 0.30/0.63              ( ( member8440522571783428010at_nat @ Y2 @ F4 )
% 0.30/0.63             => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage1827798767263827160at_nat @ H3 @ ( insert8211810215607154385at_nat @ Y2 @ bot_bo2099793752762293965at_nat ) ) @ A2 ) ) )
% 0.30/0.63         => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage1827798767263827160at_nat @ H3 @ F4 ) @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_finite_vimage_IntI
% 0.30/0.63  thf(fact_8688_finite__finite__vimage__IntI,axiom,
% 0.30/0.63      ! [F4: set_Pr1261947904930325089at_nat,H3: nat > product_prod_nat_nat,A2: set_nat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ F4 )
% 0.30/0.63       => ( ! [Y2: product_prod_nat_nat] :
% 0.30/0.63              ( ( member8440522571783428010at_nat @ Y2 @ F4 )
% 0.30/0.63             => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage8013328719654469172at_nat @ H3 @ ( insert8211810215607154385at_nat @ Y2 @ bot_bo2099793752762293965at_nat ) ) @ A2 ) ) )
% 0.30/0.63         => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage8013328719654469172at_nat @ H3 @ F4 ) @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_finite_vimage_IntI
% 0.30/0.63  thf(fact_8689_finite__Collect__conjI,axiom,
% 0.30/0.63      ! [P: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 0.30/0.63        ( ( ( finite8744585540193469122nt_int @ ( collec5210948495886036740nt_int @ P ) )
% 0.30/0.63          | ( finite8744585540193469122nt_int @ ( collec5210948495886036740nt_int @ Q2 ) ) )
% 0.30/0.63       => ( finite8744585540193469122nt_int
% 0.30/0.63          @ ( collec5210948495886036740nt_int
% 0.30/0.63            @ ^ [X3: set_Pr958786334691620121nt_int] :
% 0.30/0.63                ( ( P @ X3 )
% 0.30/0.63                & ( Q2 @ X3 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_conjI
% 0.30/0.63  thf(fact_8690_finite__Collect__conjI,axiom,
% 0.30/0.63      ! [P: set_nat > $o,Q2: set_nat > $o] :
% 0.30/0.63        ( ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 0.30/0.63          | ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q2 ) ) )
% 0.30/0.63       => ( finite1152437895449049373et_nat
% 0.30/0.63          @ ( collect_set_nat
% 0.30/0.63            @ ^ [X3: set_nat] :
% 0.30/0.63                ( ( P @ X3 )
% 0.30/0.63                & ( Q2 @ X3 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_conjI
% 0.30/0.63  thf(fact_8691_finite__Collect__conjI,axiom,
% 0.30/0.63      ! [P: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.30/0.63        ( ( ( finite3252695134891459830_nat_o @ ( collec939566748876313656_nat_o @ P ) )
% 0.30/0.63          | ( finite3252695134891459830_nat_o @ ( collec939566748876313656_nat_o @ Q2 ) ) )
% 0.30/0.63       => ( finite3252695134891459830_nat_o
% 0.30/0.63          @ ( collec939566748876313656_nat_o
% 0.30/0.63            @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.30/0.63                ( ( P @ X3 )
% 0.30/0.63                & ( Q2 @ X3 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_conjI
% 0.30/0.63  thf(fact_8692_finite__Collect__conjI,axiom,
% 0.30/0.63      ! [P: nat > $o,Q2: nat > $o] :
% 0.30/0.63        ( ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 0.30/0.63          | ( finite_finite_nat @ ( collect_nat @ Q2 ) ) )
% 0.30/0.63       => ( finite_finite_nat
% 0.30/0.63          @ ( collect_nat
% 0.30/0.63            @ ^ [X3: nat] :
% 0.30/0.63                ( ( P @ X3 )
% 0.30/0.63                & ( Q2 @ X3 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_conjI
% 0.30/0.63  thf(fact_8693_finite__Collect__conjI,axiom,
% 0.30/0.63      ! [P: int > $o,Q2: int > $o] :
% 0.30/0.63        ( ( ( finite_finite_int @ ( collect_int @ P ) )
% 0.30/0.63          | ( finite_finite_int @ ( collect_int @ Q2 ) ) )
% 0.30/0.63       => ( finite_finite_int
% 0.30/0.63          @ ( collect_int
% 0.30/0.63            @ ^ [X3: int] :
% 0.30/0.63                ( ( P @ X3 )
% 0.30/0.63                & ( Q2 @ X3 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_conjI
% 0.30/0.63  thf(fact_8694_finite__Collect__conjI,axiom,
% 0.30/0.63      ! [P: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > $o] :
% 0.30/0.63        ( ( ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ P ) )
% 0.30/0.63          | ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ Q2 ) ) )
% 0.30/0.63       => ( finite6177210948735845034at_nat
% 0.30/0.63          @ ( collec3392354462482085612at_nat
% 0.30/0.63            @ ^ [X3: product_prod_nat_nat] :
% 0.30/0.63                ( ( P @ X3 )
% 0.30/0.63                & ( Q2 @ X3 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_conjI
% 0.30/0.63  thf(fact_8695_finite__Collect__disjI,axiom,
% 0.30/0.63      ! [P: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 0.30/0.63        ( ( finite8744585540193469122nt_int
% 0.30/0.63          @ ( collec5210948495886036740nt_int
% 0.30/0.63            @ ^ [X3: set_Pr958786334691620121nt_int] :
% 0.30/0.63                ( ( P @ X3 )
% 0.30/0.63                | ( Q2 @ X3 ) ) ) )
% 0.30/0.63        = ( ( finite8744585540193469122nt_int @ ( collec5210948495886036740nt_int @ P ) )
% 0.30/0.63          & ( finite8744585540193469122nt_int @ ( collec5210948495886036740nt_int @ Q2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_disjI
% 0.30/0.63  thf(fact_8696_finite__Collect__disjI,axiom,
% 0.30/0.63      ! [P: set_nat > $o,Q2: set_nat > $o] :
% 0.30/0.63        ( ( finite1152437895449049373et_nat
% 0.30/0.63          @ ( collect_set_nat
% 0.30/0.63            @ ^ [X3: set_nat] :
% 0.30/0.63                ( ( P @ X3 )
% 0.30/0.63                | ( Q2 @ X3 ) ) ) )
% 0.30/0.63        = ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 0.30/0.63          & ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_disjI
% 0.30/0.63  thf(fact_8697_finite__Collect__disjI,axiom,
% 0.30/0.63      ! [P: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.30/0.63        ( ( finite3252695134891459830_nat_o
% 0.30/0.63          @ ( collec939566748876313656_nat_o
% 0.30/0.63            @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 0.30/0.63                ( ( P @ X3 )
% 0.30/0.63                | ( Q2 @ X3 ) ) ) )
% 0.30/0.63        = ( ( finite3252695134891459830_nat_o @ ( collec939566748876313656_nat_o @ P ) )
% 0.30/0.63          & ( finite3252695134891459830_nat_o @ ( collec939566748876313656_nat_o @ Q2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_disjI
% 0.30/0.63  thf(fact_8698_finite__Collect__disjI,axiom,
% 0.30/0.63      ! [P: nat > $o,Q2: nat > $o] :
% 0.30/0.63        ( ( finite_finite_nat
% 0.30/0.63          @ ( collect_nat
% 0.30/0.63            @ ^ [X3: nat] :
% 0.30/0.63                ( ( P @ X3 )
% 0.30/0.63                | ( Q2 @ X3 ) ) ) )
% 0.30/0.63        = ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 0.30/0.63          & ( finite_finite_nat @ ( collect_nat @ Q2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_disjI
% 0.30/0.63  thf(fact_8699_finite__Collect__disjI,axiom,
% 0.30/0.63      ! [P: int > $o,Q2: int > $o] :
% 0.30/0.63        ( ( finite_finite_int
% 0.30/0.63          @ ( collect_int
% 0.30/0.63            @ ^ [X3: int] :
% 0.30/0.63                ( ( P @ X3 )
% 0.30/0.63                | ( Q2 @ X3 ) ) ) )
% 0.30/0.63        = ( ( finite_finite_int @ ( collect_int @ P ) )
% 0.30/0.63          & ( finite_finite_int @ ( collect_int @ Q2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_disjI
% 0.30/0.63  thf(fact_8700_finite__Collect__disjI,axiom,
% 0.30/0.63      ! [P: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > $o] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat
% 0.30/0.63          @ ( collec3392354462482085612at_nat
% 0.30/0.63            @ ^ [X3: product_prod_nat_nat] :
% 0.30/0.63                ( ( P @ X3 )
% 0.30/0.63                | ( Q2 @ X3 ) ) ) )
% 0.30/0.63        = ( ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ P ) )
% 0.30/0.63          & ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ Q2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Collect_disjI
% 0.30/0.63  thf(fact_8701_finite__interval__int1,axiom,
% 0.30/0.63      ! [A: int,B: int] :
% 0.30/0.63        ( finite_finite_int
% 0.30/0.63        @ ( collect_int
% 0.30/0.63          @ ^ [I3: int] :
% 0.30/0.63              ( ( ord_less_eq_int @ A @ I3 )
% 0.30/0.63              & ( ord_less_eq_int @ I3 @ B ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_interval_int1
% 0.30/0.63  thf(fact_8702_finite__interval__int4,axiom,
% 0.30/0.63      ! [A: int,B: int] :
% 0.30/0.63        ( finite_finite_int
% 0.30/0.63        @ ( collect_int
% 0.30/0.63          @ ^ [I3: int] :
% 0.30/0.63              ( ( ord_less_int @ A @ I3 )
% 0.30/0.63              & ( ord_less_int @ I3 @ B ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_interval_int4
% 0.30/0.63  thf(fact_8703_finite__Plus__UNIV__iff,axiom,
% 0.30/0.63      ( ( finite6699802884135759036um_o_o @ top_to1686961084667892491um_o_o )
% 0.30/0.63      = ( ( finite_finite_o @ top_top_set_o )
% 0.30/0.63        & ( finite_finite_o @ top_top_set_o ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Plus_UNIV_iff
% 0.30/0.63  thf(fact_8704_finite__Plus__UNIV__iff,axiom,
% 0.30/0.63      ( ( finite2301497163391418442_o_rat @ top_to8915897456388626257_o_rat )
% 0.30/0.63      = ( ( finite_finite_o @ top_top_set_o )
% 0.30/0.63        & ( finite_finite_rat @ top_top_set_rat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Plus_UNIV_iff
% 0.30/0.63  thf(fact_8705_finite__Plus__UNIV__iff,axiom,
% 0.30/0.63      ( ( finite5809725721784815170_o_nat @ top_to6072511757011528009_o_nat )
% 0.30/0.63      = ( ( finite_finite_o @ top_top_set_o )
% 0.30/0.63        & ( finite_finite_nat @ top_top_set_nat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Plus_UNIV_iff
% 0.30/0.63  thf(fact_8706_finite__Plus__UNIV__iff,axiom,
% 0.30/0.63      ( ( finite1631874702275618462_o_int @ top_to3582428612079801253_o_int )
% 0.30/0.63      = ( ( finite_finite_o @ top_top_set_o )
% 0.30/0.63        & ( finite_finite_int @ top_top_set_int ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Plus_UNIV_iff
% 0.30/0.63  thf(fact_8707_finite__Plus__UNIV__iff,axiom,
% 0.30/0.63      ( ( finite5580927318523740128_rat_o @ top_to6370680384054995943_rat_o )
% 0.30/0.63      = ( ( finite_finite_rat @ top_top_set_rat )
% 0.30/0.63        & ( finite_finite_o @ top_top_set_o ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Plus_UNIV_iff
% 0.30/0.63  thf(fact_8708_finite__Plus__UNIV__iff,axiom,
% 0.30/0.63      ( ( finite2362923481445498406at_rat @ top_to5104522503381003637at_rat )
% 0.30/0.63      = ( ( finite_finite_rat @ top_top_set_rat )
% 0.30/0.63        & ( finite_finite_rat @ top_top_set_rat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Plus_UNIV_iff
% 0.30/0.63  thf(fact_8709_finite__Plus__UNIV__iff,axiom,
% 0.30/0.63      ( ( finite5871152039838895134at_nat @ top_to2261136804003905389at_nat )
% 0.30/0.63      = ( ( finite_finite_rat @ top_top_set_rat )
% 0.30/0.63        & ( finite_finite_nat @ top_top_set_nat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Plus_UNIV_iff
% 0.30/0.63  thf(fact_8710_finite__Plus__UNIV__iff,axiom,
% 0.30/0.63      ( ( finite1693301020329698426at_int @ top_to8994425695926954441at_int )
% 0.30/0.63      = ( ( finite_finite_rat @ top_top_set_rat )
% 0.30/0.63        & ( finite_finite_int @ top_top_set_int ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Plus_UNIV_iff
% 0.30/0.63  thf(fact_8711_finite__Plus__UNIV__iff,axiom,
% 0.30/0.63      ( ( finite94888208985532392_nat_o @ top_to7120114879189831663_nat_o )
% 0.30/0.63      = ( ( finite_finite_nat @ top_top_set_nat )
% 0.30/0.63        & ( finite_finite_o @ top_top_set_o ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Plus_UNIV_iff
% 0.30/0.63  thf(fact_8712_finite__Plus__UNIV__iff,axiom,
% 0.30/0.63      ( ( finite2679478125380364318at_rat @ top_to281834657035230061at_rat )
% 0.30/0.63      = ( ( finite_finite_nat @ top_top_set_nat )
% 0.30/0.63        & ( finite_finite_rat @ top_top_set_rat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Plus_UNIV_iff
% 0.30/0.63  thf(fact_8713_finite__Int,axiom,
% 0.30/0.63      ! [F4: set_int,G3: set_int] :
% 0.30/0.63        ( ( ( finite_finite_int @ F4 )
% 0.30/0.63          | ( finite_finite_int @ G3 ) )
% 0.30/0.63       => ( finite_finite_int @ ( inf_inf_set_int @ F4 @ G3 ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Int
% 0.30/0.63  thf(fact_8714_finite__Int,axiom,
% 0.30/0.63      ! [F4: set_Pr1261947904930325089at_nat,G3: set_Pr1261947904930325089at_nat] :
% 0.30/0.63        ( ( ( finite6177210948735845034at_nat @ F4 )
% 0.30/0.63          | ( finite6177210948735845034at_nat @ G3 ) )
% 0.30/0.63       => ( finite6177210948735845034at_nat @ ( inf_in2572325071724192079at_nat @ F4 @ G3 ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Int
% 0.30/0.63  thf(fact_8715_finite__Int,axiom,
% 0.30/0.63      ! [F4: set_nat,G3: set_nat] :
% 0.30/0.63        ( ( ( finite_finite_nat @ F4 )
% 0.30/0.63          | ( finite_finite_nat @ G3 ) )
% 0.30/0.63       => ( finite_finite_nat @ ( inf_inf_set_nat @ F4 @ G3 ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Int
% 0.30/0.63  thf(fact_8716_finite__Un,axiom,
% 0.30/0.63      ! [F4: set_int,G3: set_int] :
% 0.30/0.63        ( ( finite_finite_int @ ( sup_sup_set_int @ F4 @ G3 ) )
% 0.30/0.63        = ( ( finite_finite_int @ F4 )
% 0.30/0.63          & ( finite_finite_int @ G3 ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Un
% 0.30/0.63  thf(fact_8717_finite__Un,axiom,
% 0.30/0.63      ! [F4: set_Pr1261947904930325089at_nat,G3: set_Pr1261947904930325089at_nat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ F4 @ G3 ) )
% 0.30/0.63        = ( ( finite6177210948735845034at_nat @ F4 )
% 0.30/0.63          & ( finite6177210948735845034at_nat @ G3 ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Un
% 0.30/0.63  thf(fact_8718_finite__Un,axiom,
% 0.30/0.63      ! [F4: set_Pr8551490117392284871at_nat,G3: set_Pr8551490117392284871at_nat] :
% 0.30/0.63        ( ( finite1918287321285529104at_nat @ ( sup_su3035147773818789531at_nat @ F4 @ G3 ) )
% 0.30/0.63        = ( ( finite1918287321285529104at_nat @ F4 )
% 0.30/0.63          & ( finite1918287321285529104at_nat @ G3 ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Un
% 0.30/0.63  thf(fact_8719_finite__Un,axiom,
% 0.30/0.63      ! [F4: set_Pr4329608150637261639at_nat,G3: set_Pr4329608150637261639at_nat] :
% 0.30/0.63        ( ( finite4343798906461161616at_nat @ ( sup_su5525570899277871387at_nat @ F4 @ G3 ) )
% 0.30/0.63        = ( ( finite4343798906461161616at_nat @ F4 )
% 0.30/0.63          & ( finite4343798906461161616at_nat @ G3 ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Un
% 0.30/0.63  thf(fact_8720_finite__Un,axiom,
% 0.30/0.63      ! [F4: set_nat,G3: set_nat] :
% 0.30/0.63        ( ( finite_finite_nat @ ( sup_sup_set_nat @ F4 @ G3 ) )
% 0.30/0.63        = ( ( finite_finite_nat @ F4 )
% 0.30/0.63          & ( finite_finite_nat @ G3 ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Un
% 0.30/0.63  thf(fact_8721_finite__interval__int2,axiom,
% 0.30/0.63      ! [A: int,B: int] :
% 0.30/0.63        ( finite_finite_int
% 0.30/0.63        @ ( collect_int
% 0.30/0.63          @ ^ [I3: int] :
% 0.30/0.63              ( ( ord_less_eq_int @ A @ I3 )
% 0.30/0.63              & ( ord_less_int @ I3 @ B ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_interval_int2
% 0.30/0.63  thf(fact_8722_finite__interval__int3,axiom,
% 0.30/0.63      ! [A: int,B: int] :
% 0.30/0.63        ( finite_finite_int
% 0.30/0.63        @ ( collect_int
% 0.30/0.63          @ ^ [I3: int] :
% 0.30/0.63              ( ( ord_less_int @ A @ I3 )
% 0.30/0.63              & ( ord_less_eq_int @ I3 @ B ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_interval_int3
% 0.30/0.63  thf(fact_8723_infinite__UNIV__int,axiom,
% 0.30/0.63      ~ ( finite_finite_int @ top_top_set_int ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_UNIV_int
% 0.30/0.63  thf(fact_8724_finite__divisors__int,axiom,
% 0.30/0.63      ! [I: int] :
% 0.30/0.63        ( ( I != zero_zero_int )
% 0.30/0.63       => ( finite_finite_int
% 0.30/0.63          @ ( collect_int
% 0.30/0.63            @ ^ [D4: int] : ( dvd_dvd_int @ D4 @ I ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_divisors_int
% 0.30/0.63  thf(fact_8725_infinite__UNIV__nat,axiom,
% 0.30/0.63      ~ ( finite_finite_nat @ top_top_set_nat ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_UNIV_nat
% 0.30/0.63  thf(fact_8726_not__finite__existsD,axiom,
% 0.30/0.63      ! [P: set_Pr958786334691620121nt_int > $o] :
% 0.30/0.63        ( ~ ( finite8744585540193469122nt_int @ ( collec5210948495886036740nt_int @ P ) )
% 0.30/0.63       => ? [X_1: set_Pr958786334691620121nt_int] : ( P @ X_1 ) ) ).
% 0.30/0.63  
% 0.30/0.63  % not_finite_existsD
% 0.30/0.63  thf(fact_8727_not__finite__existsD,axiom,
% 0.30/0.63      ! [P: set_nat > $o] :
% 0.30/0.63        ( ~ ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 0.30/0.63       => ? [X_1: set_nat] : ( P @ X_1 ) ) ).
% 0.30/0.63  
% 0.30/0.63  % not_finite_existsD
% 0.30/0.63  thf(fact_8728_not__finite__existsD,axiom,
% 0.30/0.63      ! [P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.30/0.63        ( ~ ( finite3252695134891459830_nat_o @ ( collec939566748876313656_nat_o @ P ) )
% 0.30/0.63       => ? [X_1: produc3658429121746597890et_nat > $o] : ( P @ X_1 ) ) ).
% 0.30/0.63  
% 0.30/0.63  % not_finite_existsD
% 0.30/0.63  thf(fact_8729_not__finite__existsD,axiom,
% 0.30/0.63      ! [P: nat > $o] :
% 0.30/0.63        ( ~ ( finite_finite_nat @ ( collect_nat @ P ) )
% 0.30/0.63       => ? [X_1: nat] : ( P @ X_1 ) ) ).
% 0.30/0.63  
% 0.30/0.63  % not_finite_existsD
% 0.30/0.63  thf(fact_8730_not__finite__existsD,axiom,
% 0.30/0.63      ! [P: int > $o] :
% 0.30/0.63        ( ~ ( finite_finite_int @ ( collect_int @ P ) )
% 0.30/0.63       => ? [X_1: int] : ( P @ X_1 ) ) ).
% 0.30/0.63  
% 0.30/0.63  % not_finite_existsD
% 0.30/0.63  thf(fact_8731_not__finite__existsD,axiom,
% 0.30/0.63      ! [P: product_prod_nat_nat > $o] :
% 0.30/0.63        ( ~ ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ P ) )
% 0.30/0.63       => ? [X_1: product_prod_nat_nat] : ( P @ X_1 ) ) ).
% 0.30/0.63  
% 0.30/0.63  % not_finite_existsD
% 0.30/0.63  thf(fact_8732_pigeonhole__infinite__rel,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_nat,R: nat > nat > $o] :
% 0.30/0.63        ( ~ ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ! [X2: nat] :
% 0.30/0.63                ( ( member_nat @ X2 @ A2 )
% 0.30/0.63               => ? [Xa2: nat] :
% 0.30/0.63                    ( ( member_nat @ Xa2 @ B2 )
% 0.30/0.63                    & ( R @ X2 @ Xa2 ) ) )
% 0.30/0.63           => ? [X2: nat] :
% 0.30/0.63                ( ( member_nat @ X2 @ B2 )
% 0.30/0.63                & ~ ( finite_finite_nat
% 0.30/0.63                    @ ( collect_nat
% 0.30/0.63                      @ ^ [A3: nat] :
% 0.30/0.63                          ( ( member_nat @ A3 @ A2 )
% 0.30/0.63                          & ( R @ A3 @ X2 ) ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % pigeonhole_infinite_rel
% 0.30/0.63  thf(fact_8733_pigeonhole__infinite__rel,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_int,R: nat > int > $o] :
% 0.30/0.63        ( ~ ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ! [X2: nat] :
% 0.30/0.63                ( ( member_nat @ X2 @ A2 )
% 0.30/0.63               => ? [Xa2: int] :
% 0.30/0.63                    ( ( member_int @ Xa2 @ B2 )
% 0.30/0.63                    & ( R @ X2 @ Xa2 ) ) )
% 0.30/0.63           => ? [X2: int] :
% 0.30/0.63                ( ( member_int @ X2 @ B2 )
% 0.30/0.63                & ~ ( finite_finite_nat
% 0.30/0.63                    @ ( collect_nat
% 0.30/0.63                      @ ^ [A3: nat] :
% 0.30/0.63                          ( ( member_nat @ A3 @ A2 )
% 0.30/0.63                          & ( R @ A3 @ X2 ) ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % pigeonhole_infinite_rel
% 0.30/0.63  thf(fact_8734_pigeonhole__infinite__rel,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_nat,R: int > nat > $o] :
% 0.30/0.63        ( ~ ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ! [X2: int] :
% 0.30/0.63                ( ( member_int @ X2 @ A2 )
% 0.30/0.63               => ? [Xa2: nat] :
% 0.30/0.63                    ( ( member_nat @ Xa2 @ B2 )
% 0.30/0.63                    & ( R @ X2 @ Xa2 ) ) )
% 0.30/0.63           => ? [X2: nat] :
% 0.30/0.63                ( ( member_nat @ X2 @ B2 )
% 0.30/0.63                & ~ ( finite_finite_int
% 0.30/0.63                    @ ( collect_int
% 0.30/0.63                      @ ^ [A3: int] :
% 0.30/0.63                          ( ( member_int @ A3 @ A2 )
% 0.30/0.63                          & ( R @ A3 @ X2 ) ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % pigeonhole_infinite_rel
% 0.30/0.63  thf(fact_8735_pigeonhole__infinite__rel,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_int,R: int > int > $o] :
% 0.30/0.63        ( ~ ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ! [X2: int] :
% 0.30/0.63                ( ( member_int @ X2 @ A2 )
% 0.30/0.63               => ? [Xa2: int] :
% 0.30/0.63                    ( ( member_int @ Xa2 @ B2 )
% 0.30/0.63                    & ( R @ X2 @ Xa2 ) ) )
% 0.30/0.63           => ? [X2: int] :
% 0.30/0.63                ( ( member_int @ X2 @ B2 )
% 0.30/0.63                & ~ ( finite_finite_int
% 0.30/0.63                    @ ( collect_int
% 0.30/0.63                      @ ^ [A3: int] :
% 0.30/0.63                          ( ( member_int @ A3 @ A2 )
% 0.30/0.63                          & ( R @ A3 @ X2 ) ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % pigeonhole_infinite_rel
% 0.30/0.63  thf(fact_8736_pigeonhole__infinite__rel,axiom,
% 0.30/0.63      ! [A2: set_set_nat,B2: set_nat,R: set_nat > nat > $o] :
% 0.30/0.63        ( ~ ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ! [X2: set_nat] :
% 0.30/0.63                ( ( member_set_nat @ X2 @ A2 )
% 0.30/0.63               => ? [Xa2: nat] :
% 0.30/0.63                    ( ( member_nat @ Xa2 @ B2 )
% 0.30/0.63                    & ( R @ X2 @ Xa2 ) ) )
% 0.30/0.63           => ? [X2: nat] :
% 0.30/0.63                ( ( member_nat @ X2 @ B2 )
% 0.30/0.63                & ~ ( finite1152437895449049373et_nat
% 0.30/0.63                    @ ( collect_set_nat
% 0.30/0.63                      @ ^ [A3: set_nat] :
% 0.30/0.63                          ( ( member_set_nat @ A3 @ A2 )
% 0.30/0.63                          & ( R @ A3 @ X2 ) ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % pigeonhole_infinite_rel
% 0.30/0.63  thf(fact_8737_pigeonhole__infinite__rel,axiom,
% 0.30/0.63      ! [A2: set_set_nat,B2: set_int,R: set_nat > int > $o] :
% 0.30/0.63        ( ~ ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ! [X2: set_nat] :
% 0.30/0.63                ( ( member_set_nat @ X2 @ A2 )
% 0.30/0.63               => ? [Xa2: int] :
% 0.30/0.63                    ( ( member_int @ Xa2 @ B2 )
% 0.30/0.63                    & ( R @ X2 @ Xa2 ) ) )
% 0.30/0.63           => ? [X2: int] :
% 0.30/0.63                ( ( member_int @ X2 @ B2 )
% 0.30/0.63                & ~ ( finite1152437895449049373et_nat
% 0.30/0.63                    @ ( collect_set_nat
% 0.30/0.63                      @ ^ [A3: set_nat] :
% 0.30/0.63                          ( ( member_set_nat @ A3 @ A2 )
% 0.30/0.63                          & ( R @ A3 @ X2 ) ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % pigeonhole_infinite_rel
% 0.30/0.63  thf(fact_8738_pigeonhole__infinite__rel,axiom,
% 0.30/0.63      ! [A2: set_nat,B2: set_Pr1261947904930325089at_nat,R: nat > product_prod_nat_nat > $o] :
% 0.30/0.63        ( ~ ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( finite6177210948735845034at_nat @ B2 )
% 0.30/0.63         => ( ! [X2: nat] :
% 0.30/0.63                ( ( member_nat @ X2 @ A2 )
% 0.30/0.63               => ? [Xa2: product_prod_nat_nat] :
% 0.30/0.63                    ( ( member8440522571783428010at_nat @ Xa2 @ B2 )
% 0.30/0.63                    & ( R @ X2 @ Xa2 ) ) )
% 0.30/0.63           => ? [X2: product_prod_nat_nat] :
% 0.30/0.63                ( ( member8440522571783428010at_nat @ X2 @ B2 )
% 0.30/0.63                & ~ ( finite_finite_nat
% 0.30/0.63                    @ ( collect_nat
% 0.30/0.63                      @ ^ [A3: nat] :
% 0.30/0.63                          ( ( member_nat @ A3 @ A2 )
% 0.30/0.63                          & ( R @ A3 @ X2 ) ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % pigeonhole_infinite_rel
% 0.30/0.63  thf(fact_8739_pigeonhole__infinite__rel,axiom,
% 0.30/0.63      ! [A2: set_int,B2: set_Pr1261947904930325089at_nat,R: int > product_prod_nat_nat > $o] :
% 0.30/0.63        ( ~ ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( finite6177210948735845034at_nat @ B2 )
% 0.30/0.63         => ( ! [X2: int] :
% 0.30/0.63                ( ( member_int @ X2 @ A2 )
% 0.30/0.63               => ? [Xa2: product_prod_nat_nat] :
% 0.30/0.63                    ( ( member8440522571783428010at_nat @ Xa2 @ B2 )
% 0.30/0.63                    & ( R @ X2 @ Xa2 ) ) )
% 0.30/0.63           => ? [X2: product_prod_nat_nat] :
% 0.30/0.63                ( ( member8440522571783428010at_nat @ X2 @ B2 )
% 0.30/0.63                & ~ ( finite_finite_int
% 0.30/0.63                    @ ( collect_int
% 0.30/0.63                      @ ^ [A3: int] :
% 0.30/0.63                          ( ( member_int @ A3 @ A2 )
% 0.30/0.63                          & ( R @ A3 @ X2 ) ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % pigeonhole_infinite_rel
% 0.30/0.63  thf(fact_8740_pigeonhole__infinite__rel,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,B2: set_nat,R: product_prod_nat_nat > nat > $o] :
% 0.30/0.63        ( ~ ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_nat @ B2 )
% 0.30/0.63         => ( ! [X2: product_prod_nat_nat] :
% 0.30/0.63                ( ( member8440522571783428010at_nat @ X2 @ A2 )
% 0.30/0.63               => ? [Xa2: nat] :
% 0.30/0.63                    ( ( member_nat @ Xa2 @ B2 )
% 0.30/0.63                    & ( R @ X2 @ Xa2 ) ) )
% 0.30/0.63           => ? [X2: nat] :
% 0.30/0.63                ( ( member_nat @ X2 @ B2 )
% 0.30/0.63                & ~ ( finite6177210948735845034at_nat
% 0.30/0.63                    @ ( collec3392354462482085612at_nat
% 0.30/0.63                      @ ^ [A3: product_prod_nat_nat] :
% 0.30/0.63                          ( ( member8440522571783428010at_nat @ A3 @ A2 )
% 0.30/0.63                          & ( R @ A3 @ X2 ) ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % pigeonhole_infinite_rel
% 0.30/0.63  thf(fact_8741_pigeonhole__infinite__rel,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat,B2: set_int,R: product_prod_nat_nat > int > $o] :
% 0.30/0.63        ( ~ ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63       => ( ( finite_finite_int @ B2 )
% 0.30/0.63         => ( ! [X2: product_prod_nat_nat] :
% 0.30/0.63                ( ( member8440522571783428010at_nat @ X2 @ A2 )
% 0.30/0.63               => ? [Xa2: int] :
% 0.30/0.63                    ( ( member_int @ Xa2 @ B2 )
% 0.30/0.63                    & ( R @ X2 @ Xa2 ) ) )
% 0.30/0.63           => ? [X2: int] :
% 0.30/0.63                ( ( member_int @ X2 @ B2 )
% 0.30/0.63                & ~ ( finite6177210948735845034at_nat
% 0.30/0.63                    @ ( collec3392354462482085612at_nat
% 0.30/0.63                      @ ^ [A3: product_prod_nat_nat] :
% 0.30/0.63                          ( ( member8440522571783428010at_nat @ A3 @ A2 )
% 0.30/0.63                          & ( R @ A3 @ X2 ) ) ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % pigeonhole_infinite_rel
% 0.30/0.63  thf(fact_8742_sgn__integer__code,axiom,
% 0.30/0.63      ( sgn_sgn_Code_integer
% 0.30/0.63      = ( ^ [K4: code_integer] : ( if_Code_integer @ ( K4 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % sgn_integer_code
% 0.30/0.63  thf(fact_8743_finite_OemptyI,axiom,
% 0.30/0.63      finite6177210948735845034at_nat @ bot_bo2099793752762293965at_nat ).
% 0.30/0.63  
% 0.30/0.63  % finite.emptyI
% 0.30/0.63  thf(fact_8744_finite_OemptyI,axiom,
% 0.30/0.63      finite_finite_o @ bot_bot_set_o ).
% 0.30/0.63  
% 0.30/0.63  % finite.emptyI
% 0.30/0.63  thf(fact_8745_finite_OemptyI,axiom,
% 0.30/0.63      finite_finite_nat @ bot_bot_set_nat ).
% 0.30/0.63  
% 0.30/0.63  % finite.emptyI
% 0.30/0.63  thf(fact_8746_finite_OemptyI,axiom,
% 0.30/0.63      finite_finite_int @ bot_bot_set_int ).
% 0.30/0.63  
% 0.30/0.63  % finite.emptyI
% 0.30/0.63  thf(fact_8747_infinite__imp__nonempty,axiom,
% 0.30/0.63      ! [S: set_Pr1261947904930325089at_nat] :
% 0.30/0.63        ( ~ ( finite6177210948735845034at_nat @ S )
% 0.30/0.63       => ( S != bot_bo2099793752762293965at_nat ) ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_imp_nonempty
% 0.30/0.63  thf(fact_8748_infinite__imp__nonempty,axiom,
% 0.30/0.63      ! [S: set_o] :
% 0.30/0.63        ( ~ ( finite_finite_o @ S )
% 0.30/0.63       => ( S != bot_bot_set_o ) ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_imp_nonempty
% 0.30/0.63  thf(fact_8749_infinite__imp__nonempty,axiom,
% 0.30/0.63      ! [S: set_nat] :
% 0.30/0.63        ( ~ ( finite_finite_nat @ S )
% 0.30/0.63       => ( S != bot_bot_set_nat ) ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_imp_nonempty
% 0.30/0.63  thf(fact_8750_infinite__imp__nonempty,axiom,
% 0.30/0.63      ! [S: set_int] :
% 0.30/0.63        ( ~ ( finite_finite_int @ S )
% 0.30/0.63       => ( S != bot_bot_set_int ) ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_imp_nonempty
% 0.30/0.63  thf(fact_8751_finite__UNIV,axiom,
% 0.30/0.63      finite_finite_o @ top_top_set_o ).
% 0.30/0.63  
% 0.30/0.63  % finite_UNIV
% 0.30/0.63  thf(fact_8752_ex__new__if__finite,axiom,
% 0.30/0.63      ! [A2: set_se6260736226359567993nt_int] :
% 0.30/0.63        ( ~ ( finite8744585540193469122nt_int @ top_to6034159466715884489nt_int )
% 0.30/0.63       => ( ( finite8744585540193469122nt_int @ A2 )
% 0.30/0.63         => ? [A6: set_Pr958786334691620121nt_int] :
% 0.30/0.63              ~ ( member2340774599025711042nt_int @ A6 @ A2 ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % ex_new_if_finite
% 0.30/0.63  thf(fact_8753_ex__new__if__finite,axiom,
% 0.30/0.63      ! [A2: set_set_nat] :
% 0.30/0.63        ( ~ ( finite1152437895449049373et_nat @ top_top_set_set_nat )
% 0.30/0.63       => ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.63         => ? [A6: set_nat] :
% 0.30/0.63              ~ ( member_set_nat @ A6 @ A2 ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % ex_new_if_finite
% 0.30/0.63  thf(fact_8754_ex__new__if__finite,axiom,
% 0.30/0.63      ! [A2: set_Pr4532377907799695533_nat_o] :
% 0.30/0.63        ( ~ ( finite3252695134891459830_nat_o @ top_to4869887016220417533_nat_o )
% 0.30/0.63       => ( ( finite3252695134891459830_nat_o @ A2 )
% 0.30/0.63         => ? [A6: produc3658429121746597890et_nat > $o] :
% 0.30/0.63              ~ ( member6576561426505652726_nat_o @ A6 @ A2 ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % ex_new_if_finite
% 0.30/0.63  thf(fact_8755_ex__new__if__finite,axiom,
% 0.30/0.63      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.30/0.63        ( ~ ( finite6177210948735845034at_nat @ top_to4669805908274784177at_nat )
% 0.30/0.63       => ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.63         => ? [A6: product_prod_nat_nat] :
% 0.30/0.63              ~ ( member8440522571783428010at_nat @ A6 @ A2 ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % ex_new_if_finite
% 0.30/0.63  thf(fact_8756_ex__new__if__finite,axiom,
% 0.30/0.63      ! [A2: set_list_nat] :
% 0.30/0.63        ( ~ ( finite8100373058378681591st_nat @ top_top_set_list_nat )
% 0.30/0.63       => ( ( finite8100373058378681591st_nat @ A2 )
% 0.30/0.63         => ? [A6: list_nat] :
% 0.30/0.63              ~ ( member_list_nat @ A6 @ A2 ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % ex_new_if_finite
% 0.30/0.63  thf(fact_8757_ex__new__if__finite,axiom,
% 0.30/0.63      ! [A2: set_o] :
% 0.30/0.63        ( ~ ( finite_finite_o @ top_top_set_o )
% 0.30/0.63       => ( ( finite_finite_o @ A2 )
% 0.30/0.63         => ? [A6: $o] :
% 0.30/0.63              ~ ( member_o @ A6 @ A2 ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % ex_new_if_finite
% 0.30/0.63  thf(fact_8758_ex__new__if__finite,axiom,
% 0.30/0.63      ! [A2: set_rat] :
% 0.30/0.63        ( ~ ( finite_finite_rat @ top_top_set_rat )
% 0.30/0.63       => ( ( finite_finite_rat @ A2 )
% 0.30/0.63         => ? [A6: rat] :
% 0.30/0.63              ~ ( member_rat @ A6 @ A2 ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % ex_new_if_finite
% 0.30/0.63  thf(fact_8759_ex__new__if__finite,axiom,
% 0.30/0.63      ! [A2: set_nat] :
% 0.30/0.63        ( ~ ( finite_finite_nat @ top_top_set_nat )
% 0.30/0.63       => ( ( finite_finite_nat @ A2 )
% 0.30/0.63         => ? [A6: nat] :
% 0.30/0.63              ~ ( member_nat @ A6 @ A2 ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % ex_new_if_finite
% 0.30/0.63  thf(fact_8760_ex__new__if__finite,axiom,
% 0.30/0.63      ! [A2: set_int] :
% 0.30/0.63        ( ~ ( finite_finite_int @ top_top_set_int )
% 0.30/0.63       => ( ( finite_finite_int @ A2 )
% 0.30/0.63         => ? [A6: int] :
% 0.30/0.63              ~ ( member_int @ A6 @ A2 ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % ex_new_if_finite
% 0.30/0.63  thf(fact_8761_infinite__UNIV__char__0,axiom,
% 0.30/0.63      ~ ( finite_finite_rat @ top_top_set_rat ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_UNIV_char_0
% 0.30/0.63  thf(fact_8762_infinite__UNIV__char__0,axiom,
% 0.30/0.63      ~ ( finite_finite_nat @ top_top_set_nat ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_UNIV_char_0
% 0.30/0.63  thf(fact_8763_infinite__UNIV__char__0,axiom,
% 0.30/0.63      ~ ( finite_finite_int @ top_top_set_int ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_UNIV_char_0
% 0.30/0.63  thf(fact_8764_finite__UnI,axiom,
% 0.30/0.63      ! [F4: set_int,G3: set_int] :
% 0.30/0.63        ( ( finite_finite_int @ F4 )
% 0.30/0.63       => ( ( finite_finite_int @ G3 )
% 0.30/0.63         => ( finite_finite_int @ ( sup_sup_set_int @ F4 @ G3 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_UnI
% 0.30/0.63  thf(fact_8765_finite__UnI,axiom,
% 0.30/0.63      ! [F4: set_Pr1261947904930325089at_nat,G3: set_Pr1261947904930325089at_nat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ F4 )
% 0.30/0.63       => ( ( finite6177210948735845034at_nat @ G3 )
% 0.30/0.63         => ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ F4 @ G3 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_UnI
% 0.30/0.63  thf(fact_8766_finite__UnI,axiom,
% 0.30/0.63      ! [F4: set_Pr8551490117392284871at_nat,G3: set_Pr8551490117392284871at_nat] :
% 0.30/0.63        ( ( finite1918287321285529104at_nat @ F4 )
% 0.30/0.63       => ( ( finite1918287321285529104at_nat @ G3 )
% 0.30/0.63         => ( finite1918287321285529104at_nat @ ( sup_su3035147773818789531at_nat @ F4 @ G3 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_UnI
% 0.30/0.63  thf(fact_8767_finite__UnI,axiom,
% 0.30/0.63      ! [F4: set_Pr4329608150637261639at_nat,G3: set_Pr4329608150637261639at_nat] :
% 0.30/0.63        ( ( finite4343798906461161616at_nat @ F4 )
% 0.30/0.63       => ( ( finite4343798906461161616at_nat @ G3 )
% 0.30/0.63         => ( finite4343798906461161616at_nat @ ( sup_su5525570899277871387at_nat @ F4 @ G3 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_UnI
% 0.30/0.63  thf(fact_8768_finite__UnI,axiom,
% 0.30/0.63      ! [F4: set_nat,G3: set_nat] :
% 0.30/0.63        ( ( finite_finite_nat @ F4 )
% 0.30/0.63       => ( ( finite_finite_nat @ G3 )
% 0.30/0.63         => ( finite_finite_nat @ ( sup_sup_set_nat @ F4 @ G3 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_UnI
% 0.30/0.63  thf(fact_8769_Un__infinite,axiom,
% 0.30/0.63      ! [S: set_int,T: set_int] :
% 0.30/0.63        ( ~ ( finite_finite_int @ S )
% 0.30/0.63       => ~ ( finite_finite_int @ ( sup_sup_set_int @ S @ T ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % Un_infinite
% 0.30/0.63  thf(fact_8770_Un__infinite,axiom,
% 0.30/0.63      ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 0.30/0.63        ( ~ ( finite6177210948735845034at_nat @ S )
% 0.30/0.63       => ~ ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ S @ T ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % Un_infinite
% 0.30/0.63  thf(fact_8771_Un__infinite,axiom,
% 0.30/0.63      ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 0.30/0.63        ( ~ ( finite1918287321285529104at_nat @ S )
% 0.30/0.63       => ~ ( finite1918287321285529104at_nat @ ( sup_su3035147773818789531at_nat @ S @ T ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % Un_infinite
% 0.30/0.63  thf(fact_8772_Un__infinite,axiom,
% 0.30/0.63      ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 0.30/0.63        ( ~ ( finite4343798906461161616at_nat @ S )
% 0.30/0.63       => ~ ( finite4343798906461161616at_nat @ ( sup_su5525570899277871387at_nat @ S @ T ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % Un_infinite
% 0.30/0.63  thf(fact_8773_Un__infinite,axiom,
% 0.30/0.63      ! [S: set_nat,T: set_nat] :
% 0.30/0.63        ( ~ ( finite_finite_nat @ S )
% 0.30/0.63       => ~ ( finite_finite_nat @ ( sup_sup_set_nat @ S @ T ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % Un_infinite
% 0.30/0.63  thf(fact_8774_infinite__Un,axiom,
% 0.30/0.63      ! [S: set_int,T: set_int] :
% 0.30/0.63        ( ( ~ ( finite_finite_int @ ( sup_sup_set_int @ S @ T ) ) )
% 0.30/0.63        = ( ~ ( finite_finite_int @ S )
% 0.30/0.63          | ~ ( finite_finite_int @ T ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_Un
% 0.30/0.63  thf(fact_8775_infinite__Un,axiom,
% 0.30/0.63      ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 0.30/0.63        ( ( ~ ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ S @ T ) ) )
% 0.30/0.63        = ( ~ ( finite6177210948735845034at_nat @ S )
% 0.30/0.63          | ~ ( finite6177210948735845034at_nat @ T ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_Un
% 0.30/0.63  thf(fact_8776_infinite__Un,axiom,
% 0.30/0.63      ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 0.30/0.63        ( ( ~ ( finite1918287321285529104at_nat @ ( sup_su3035147773818789531at_nat @ S @ T ) ) )
% 0.30/0.63        = ( ~ ( finite1918287321285529104at_nat @ S )
% 0.30/0.63          | ~ ( finite1918287321285529104at_nat @ T ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_Un
% 0.30/0.63  thf(fact_8777_infinite__Un,axiom,
% 0.30/0.63      ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 0.30/0.63        ( ( ~ ( finite4343798906461161616at_nat @ ( sup_su5525570899277871387at_nat @ S @ T ) ) )
% 0.30/0.63        = ( ~ ( finite4343798906461161616at_nat @ S )
% 0.30/0.63          | ~ ( finite4343798906461161616at_nat @ T ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_Un
% 0.30/0.63  thf(fact_8778_infinite__Un,axiom,
% 0.30/0.63      ! [S: set_nat,T: set_nat] :
% 0.30/0.63        ( ( ~ ( finite_finite_nat @ ( sup_sup_set_nat @ S @ T ) ) )
% 0.30/0.63        = ( ~ ( finite_finite_nat @ S )
% 0.30/0.63          | ~ ( finite_finite_nat @ T ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_Un
% 0.30/0.63  thf(fact_8779_finite__has__minimal,axiom,
% 0.30/0.63      ! [A2: set_o] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( A2 != bot_bot_set_o )
% 0.30/0.63         => ? [X2: $o] :
% 0.30/0.63              ( ( member_o @ X2 @ A2 )
% 0.30/0.63              & ! [Xa2: $o] :
% 0.30/0.63                  ( ( member_o @ Xa2 @ A2 )
% 0.30/0.63                 => ( ( ord_less_eq_o @ Xa2 @ X2 )
% 0.30/0.63                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_has_minimal
% 0.30/0.63  thf(fact_8780_finite__has__minimal,axiom,
% 0.30/0.63      ! [A2: set_filter_nat] :
% 0.30/0.63        ( ( finite2119507909894593271er_nat @ A2 )
% 0.30/0.63       => ( ( A2 != bot_bo498966703094740906er_nat )
% 0.30/0.63         => ? [X2: filter_nat] :
% 0.30/0.63              ( ( member_filter_nat @ X2 @ A2 )
% 0.30/0.63              & ! [Xa2: filter_nat] :
% 0.30/0.63                  ( ( member_filter_nat @ Xa2 @ A2 )
% 0.30/0.63                 => ( ( ord_le2510731241096832064er_nat @ Xa2 @ X2 )
% 0.30/0.63                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_has_minimal
% 0.30/0.63  thf(fact_8781_finite__has__minimal,axiom,
% 0.30/0.63      ! [A2: set_set_nat] :
% 0.30/0.63        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.63       => ( ( A2 != bot_bot_set_set_nat )
% 0.30/0.63         => ? [X2: set_nat] :
% 0.30/0.63              ( ( member_set_nat @ X2 @ A2 )
% 0.30/0.63              & ! [Xa2: set_nat] :
% 0.30/0.63                  ( ( member_set_nat @ Xa2 @ A2 )
% 0.30/0.63                 => ( ( ord_less_eq_set_nat @ Xa2 @ X2 )
% 0.30/0.63                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_has_minimal
% 0.30/0.63  thf(fact_8782_finite__has__minimal,axiom,
% 0.30/0.63      ! [A2: set_rat] :
% 0.30/0.63        ( ( finite_finite_rat @ A2 )
% 0.30/0.63       => ( ( A2 != bot_bot_set_rat )
% 0.30/0.63         => ? [X2: rat] :
% 0.30/0.63              ( ( member_rat @ X2 @ A2 )
% 0.30/0.63              & ! [Xa2: rat] :
% 0.30/0.63                  ( ( member_rat @ Xa2 @ A2 )
% 0.30/0.63                 => ( ( ord_less_eq_rat @ Xa2 @ X2 )
% 0.30/0.63                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_has_minimal
% 0.30/0.63  thf(fact_8783_finite__has__minimal,axiom,
% 0.30/0.63      ! [A2: set_nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( A2 != bot_bot_set_nat )
% 0.30/0.63         => ? [X2: nat] :
% 0.30/0.63              ( ( member_nat @ X2 @ A2 )
% 0.30/0.63              & ! [Xa2: nat] :
% 0.30/0.63                  ( ( member_nat @ Xa2 @ A2 )
% 0.30/0.63                 => ( ( ord_less_eq_nat @ Xa2 @ X2 )
% 0.30/0.63                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_has_minimal
% 0.30/0.63  thf(fact_8784_finite__has__minimal,axiom,
% 0.30/0.63      ! [A2: set_int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( A2 != bot_bot_set_int )
% 0.30/0.63         => ? [X2: int] :
% 0.30/0.63              ( ( member_int @ X2 @ A2 )
% 0.30/0.63              & ! [Xa2: int] :
% 0.30/0.63                  ( ( member_int @ Xa2 @ A2 )
% 0.30/0.63                 => ( ( ord_less_eq_int @ Xa2 @ X2 )
% 0.30/0.63                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_has_minimal
% 0.30/0.63  thf(fact_8785_finite__has__maximal,axiom,
% 0.30/0.63      ! [A2: set_o] :
% 0.30/0.63        ( ( finite_finite_o @ A2 )
% 0.30/0.63       => ( ( A2 != bot_bot_set_o )
% 0.30/0.63         => ? [X2: $o] :
% 0.30/0.63              ( ( member_o @ X2 @ A2 )
% 0.30/0.63              & ! [Xa2: $o] :
% 0.30/0.63                  ( ( member_o @ Xa2 @ A2 )
% 0.30/0.63                 => ( ( ord_less_eq_o @ X2 @ Xa2 )
% 0.30/0.63                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_has_maximal
% 0.30/0.63  thf(fact_8786_finite__has__maximal,axiom,
% 0.30/0.63      ! [A2: set_filter_nat] :
% 0.30/0.63        ( ( finite2119507909894593271er_nat @ A2 )
% 0.30/0.63       => ( ( A2 != bot_bo498966703094740906er_nat )
% 0.30/0.63         => ? [X2: filter_nat] :
% 0.30/0.63              ( ( member_filter_nat @ X2 @ A2 )
% 0.30/0.63              & ! [Xa2: filter_nat] :
% 0.30/0.63                  ( ( member_filter_nat @ Xa2 @ A2 )
% 0.30/0.63                 => ( ( ord_le2510731241096832064er_nat @ X2 @ Xa2 )
% 0.30/0.63                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_has_maximal
% 0.30/0.63  thf(fact_8787_finite__has__maximal,axiom,
% 0.30/0.63      ! [A2: set_set_nat] :
% 0.30/0.63        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.63       => ( ( A2 != bot_bot_set_set_nat )
% 0.30/0.63         => ? [X2: set_nat] :
% 0.30/0.63              ( ( member_set_nat @ X2 @ A2 )
% 0.30/0.63              & ! [Xa2: set_nat] :
% 0.30/0.63                  ( ( member_set_nat @ Xa2 @ A2 )
% 0.30/0.63                 => ( ( ord_less_eq_set_nat @ X2 @ Xa2 )
% 0.30/0.63                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_has_maximal
% 0.30/0.63  thf(fact_8788_finite__has__maximal,axiom,
% 0.30/0.63      ! [A2: set_rat] :
% 0.30/0.63        ( ( finite_finite_rat @ A2 )
% 0.30/0.63       => ( ( A2 != bot_bot_set_rat )
% 0.30/0.63         => ? [X2: rat] :
% 0.30/0.63              ( ( member_rat @ X2 @ A2 )
% 0.30/0.63              & ! [Xa2: rat] :
% 0.30/0.63                  ( ( member_rat @ Xa2 @ A2 )
% 0.30/0.63                 => ( ( ord_less_eq_rat @ X2 @ Xa2 )
% 0.30/0.63                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_has_maximal
% 0.30/0.63  thf(fact_8789_finite__has__maximal,axiom,
% 0.30/0.63      ! [A2: set_nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A2 )
% 0.30/0.63       => ( ( A2 != bot_bot_set_nat )
% 0.30/0.63         => ? [X2: nat] :
% 0.30/0.63              ( ( member_nat @ X2 @ A2 )
% 0.30/0.63              & ! [Xa2: nat] :
% 0.30/0.63                  ( ( member_nat @ Xa2 @ A2 )
% 0.30/0.63                 => ( ( ord_less_eq_nat @ X2 @ Xa2 )
% 0.30/0.63                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_has_maximal
% 0.30/0.63  thf(fact_8790_finite__has__maximal,axiom,
% 0.30/0.63      ! [A2: set_int] :
% 0.30/0.63        ( ( finite_finite_int @ A2 )
% 0.30/0.63       => ( ( A2 != bot_bot_set_int )
% 0.30/0.63         => ? [X2: int] :
% 0.30/0.63              ( ( member_int @ X2 @ A2 )
% 0.30/0.63              & ! [Xa2: int] :
% 0.30/0.63                  ( ( member_int @ Xa2 @ A2 )
% 0.30/0.63                 => ( ( ord_less_eq_int @ X2 @ Xa2 )
% 0.30/0.63                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_has_maximal
% 0.30/0.63  thf(fact_8791_finite_Ocases,axiom,
% 0.30/0.63      ! [A: set_Pr4329608150637261639at_nat] :
% 0.30/0.63        ( ( finite4343798906461161616at_nat @ A )
% 0.30/0.63       => ( ( A != bot_bo228742789529271731at_nat )
% 0.30/0.63         => ~ ! [A8: set_Pr4329608150637261639at_nat] :
% 0.30/0.63                ( ? [A6: produc3843707927480180839at_nat] :
% 0.30/0.63                    ( A
% 0.30/0.63                    = ( insert9069300056098147895at_nat @ A6 @ A8 ) )
% 0.30/0.63               => ~ ( finite4343798906461161616at_nat @ A8 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite.cases
% 0.30/0.63  thf(fact_8792_finite_Ocases,axiom,
% 0.30/0.63      ! [A: set_Pr1261947904930325089at_nat] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ A )
% 0.30/0.63       => ( ( A != bot_bo2099793752762293965at_nat )
% 0.30/0.63         => ~ ! [A8: set_Pr1261947904930325089at_nat] :
% 0.30/0.63                ( ? [A6: product_prod_nat_nat] :
% 0.30/0.63                    ( A
% 0.30/0.63                    = ( insert8211810215607154385at_nat @ A6 @ A8 ) )
% 0.30/0.63               => ~ ( finite6177210948735845034at_nat @ A8 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite.cases
% 0.30/0.63  thf(fact_8793_finite_Ocases,axiom,
% 0.30/0.63      ! [A: set_o] :
% 0.30/0.63        ( ( finite_finite_o @ A )
% 0.30/0.63       => ( ( A != bot_bot_set_o )
% 0.30/0.63         => ~ ! [A8: set_o] :
% 0.30/0.63                ( ? [A6: $o] :
% 0.30/0.63                    ( A
% 0.30/0.63                    = ( insert_o @ A6 @ A8 ) )
% 0.30/0.63               => ~ ( finite_finite_o @ A8 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite.cases
% 0.30/0.63  thf(fact_8794_finite_Ocases,axiom,
% 0.30/0.63      ! [A: set_nat] :
% 0.30/0.63        ( ( finite_finite_nat @ A )
% 0.30/0.63       => ( ( A != bot_bot_set_nat )
% 0.30/0.63         => ~ ! [A8: set_nat] :
% 0.30/0.63                ( ? [A6: nat] :
% 0.30/0.63                    ( A
% 0.30/0.63                    = ( insert_nat @ A6 @ A8 ) )
% 0.30/0.63               => ~ ( finite_finite_nat @ A8 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite.cases
% 0.30/0.63  thf(fact_8795_finite_Ocases,axiom,
% 0.30/0.63      ! [A: set_int] :
% 0.30/0.63        ( ( finite_finite_int @ A )
% 0.30/0.63       => ( ( A != bot_bot_set_int )
% 0.30/0.63         => ~ ! [A8: set_int] :
% 0.30/0.63                ( ? [A6: int] :
% 0.30/0.63                    ( A
% 0.30/0.63                    = ( insert_int @ A6 @ A8 ) )
% 0.30/0.63               => ~ ( finite_finite_int @ A8 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite.cases
% 0.30/0.63  thf(fact_8796_finite_Osimps,axiom,
% 0.30/0.63      ( finite4343798906461161616at_nat
% 0.30/0.63      = ( ^ [A3: set_Pr4329608150637261639at_nat] :
% 0.30/0.63            ( ( A3 = bot_bo228742789529271731at_nat )
% 0.30/0.63            | ? [A4: set_Pr4329608150637261639at_nat,B3: produc3843707927480180839at_nat] :
% 0.30/0.63                ( ( A3
% 0.30/0.63                  = ( insert9069300056098147895at_nat @ B3 @ A4 ) )
% 0.30/0.63                & ( finite4343798906461161616at_nat @ A4 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite.simps
% 0.30/0.63  thf(fact_8797_finite_Osimps,axiom,
% 0.30/0.63      ( finite6177210948735845034at_nat
% 0.30/0.63      = ( ^ [A3: set_Pr1261947904930325089at_nat] :
% 0.30/0.63            ( ( A3 = bot_bo2099793752762293965at_nat )
% 0.30/0.63            | ? [A4: set_Pr1261947904930325089at_nat,B3: product_prod_nat_nat] :
% 0.30/0.63                ( ( A3
% 0.30/0.63                  = ( insert8211810215607154385at_nat @ B3 @ A4 ) )
% 0.30/0.63                & ( finite6177210948735845034at_nat @ A4 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite.simps
% 0.30/0.63  thf(fact_8798_finite_Osimps,axiom,
% 0.30/0.63      ( finite_finite_o
% 0.30/0.63      = ( ^ [A3: set_o] :
% 0.30/0.63            ( ( A3 = bot_bot_set_o )
% 0.30/0.63            | ? [A4: set_o,B3: $o] :
% 0.30/0.63                ( ( A3
% 0.30/0.63                  = ( insert_o @ B3 @ A4 ) )
% 0.30/0.63                & ( finite_finite_o @ A4 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite.simps
% 0.30/0.63  thf(fact_8799_finite_Osimps,axiom,
% 0.30/0.63      ( finite_finite_nat
% 0.30/0.63      = ( ^ [A3: set_nat] :
% 0.30/0.63            ( ( A3 = bot_bot_set_nat )
% 0.30/0.63            | ? [A4: set_nat,B3: nat] :
% 0.30/0.63                ( ( A3
% 0.30/0.63                  = ( insert_nat @ B3 @ A4 ) )
% 0.30/0.63                & ( finite_finite_nat @ A4 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite.simps
% 0.30/0.63  thf(fact_8800_finite_Osimps,axiom,
% 0.30/0.63      ( finite_finite_int
% 0.30/0.63      = ( ^ [A3: set_int] :
% 0.30/0.63            ( ( A3 = bot_bot_set_int )
% 0.30/0.63            | ? [A4: set_int,B3: int] :
% 0.30/0.63                ( ( A3
% 0.30/0.63                  = ( insert_int @ B3 @ A4 ) )
% 0.30/0.63                & ( finite_finite_int @ A4 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite.simps
% 0.30/0.63  thf(fact_8801_finite__induct,axiom,
% 0.30/0.63      ! [F4: set_Pr4329608150637261639at_nat,P: set_Pr4329608150637261639at_nat > $o] :
% 0.30/0.63        ( ( finite4343798906461161616at_nat @ F4 )
% 0.30/0.63       => ( ( P @ bot_bo228742789529271731at_nat )
% 0.30/0.63         => ( ! [X2: produc3843707927480180839at_nat,F5: set_Pr4329608150637261639at_nat] :
% 0.30/0.63                ( ( finite4343798906461161616at_nat @ F5 )
% 0.30/0.63               => ( ~ ( member8757157785044589968at_nat @ X2 @ F5 )
% 0.30/0.63                 => ( ( P @ F5 )
% 0.30/0.63                   => ( P @ ( insert9069300056098147895at_nat @ X2 @ F5 ) ) ) ) )
% 0.30/0.63           => ( P @ F4 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_induct
% 0.30/0.63  thf(fact_8802_finite__induct,axiom,
% 0.30/0.63      ! [F4: set_se6260736226359567993nt_int,P: set_se6260736226359567993nt_int > $o] :
% 0.30/0.63        ( ( finite8744585540193469122nt_int @ F4 )
% 0.30/0.63       => ( ( P @ bot_bo1488462491386950373nt_int )
% 0.30/0.63         => ( ! [X2: set_Pr958786334691620121nt_int,F5: set_se6260736226359567993nt_int] :
% 0.30/0.63                ( ( finite8744585540193469122nt_int @ F5 )
% 0.30/0.63               => ( ~ ( member2340774599025711042nt_int @ X2 @ F5 )
% 0.30/0.63                 => ( ( P @ F5 )
% 0.30/0.63                   => ( P @ ( insert8897473484851387113nt_int @ X2 @ F5 ) ) ) ) )
% 0.30/0.63           => ( P @ F4 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_induct
% 0.30/0.63  thf(fact_8803_finite__induct,axiom,
% 0.30/0.63      ! [F4: set_set_nat,P: set_set_nat > $o] :
% 0.30/0.63        ( ( finite1152437895449049373et_nat @ F4 )
% 0.30/0.63       => ( ( P @ bot_bot_set_set_nat )
% 0.30/0.63         => ( ! [X2: set_nat,F5: set_set_nat] :
% 0.30/0.63                ( ( finite1152437895449049373et_nat @ F5 )
% 0.30/0.63               => ( ~ ( member_set_nat @ X2 @ F5 )
% 0.30/0.63                 => ( ( P @ F5 )
% 0.30/0.63                   => ( P @ ( insert_set_nat @ X2 @ F5 ) ) ) ) )
% 0.30/0.63           => ( P @ F4 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_induct
% 0.30/0.63  thf(fact_8804_finite__induct,axiom,
% 0.30/0.63      ! [F4: set_Pr4532377907799695533_nat_o,P: set_Pr4532377907799695533_nat_o > $o] :
% 0.30/0.63        ( ( finite3252695134891459830_nat_o @ F4 )
% 0.30/0.63       => ( ( P @ bot_bo7824918357723582233_nat_o )
% 0.30/0.63         => ( ! [X2: produc3658429121746597890et_nat > $o,F5: set_Pr4532377907799695533_nat_o] :
% 0.30/0.63                ( ( finite3252695134891459830_nat_o @ F5 )
% 0.30/0.63               => ( ~ ( member6576561426505652726_nat_o @ X2 @ F5 )
% 0.30/0.63                 => ( ( P @ F5 )
% 0.30/0.63                   => ( P @ ( insert5175938949040314269_nat_o @ X2 @ F5 ) ) ) ) )
% 0.30/0.63           => ( P @ F4 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_induct
% 0.30/0.63  thf(fact_8805_finite__induct,axiom,
% 0.30/0.63      ! [F4: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ F4 )
% 0.30/0.63       => ( ( P @ bot_bo2099793752762293965at_nat )
% 0.30/0.63         => ( ! [X2: product_prod_nat_nat,F5: set_Pr1261947904930325089at_nat] :
% 0.30/0.63                ( ( finite6177210948735845034at_nat @ F5 )
% 0.30/0.63               => ( ~ ( member8440522571783428010at_nat @ X2 @ F5 )
% 0.30/0.63                 => ( ( P @ F5 )
% 0.30/0.63                   => ( P @ ( insert8211810215607154385at_nat @ X2 @ F5 ) ) ) ) )
% 0.30/0.63           => ( P @ F4 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_induct
% 0.30/0.63  thf(fact_8806_finite__induct,axiom,
% 0.30/0.63      ! [F4: set_o,P: set_o > $o] :
% 0.30/0.63        ( ( finite_finite_o @ F4 )
% 0.30/0.63       => ( ( P @ bot_bot_set_o )
% 0.30/0.63         => ( ! [X2: $o,F5: set_o] :
% 0.30/0.63                ( ( finite_finite_o @ F5 )
% 0.30/0.63               => ( ~ ( member_o @ X2 @ F5 )
% 0.30/0.63                 => ( ( P @ F5 )
% 0.30/0.63                   => ( P @ ( insert_o @ X2 @ F5 ) ) ) ) )
% 0.30/0.63           => ( P @ F4 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_induct
% 0.30/0.63  thf(fact_8807_finite__induct,axiom,
% 0.30/0.63      ! [F4: set_nat,P: set_nat > $o] :
% 0.30/0.63        ( ( finite_finite_nat @ F4 )
% 0.30/0.63       => ( ( P @ bot_bot_set_nat )
% 0.30/0.63         => ( ! [X2: nat,F5: set_nat] :
% 0.30/0.63                ( ( finite_finite_nat @ F5 )
% 0.30/0.63               => ( ~ ( member_nat @ X2 @ F5 )
% 0.30/0.63                 => ( ( P @ F5 )
% 0.30/0.63                   => ( P @ ( insert_nat @ X2 @ F5 ) ) ) ) )
% 0.30/0.63           => ( P @ F4 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_induct
% 0.30/0.63  thf(fact_8808_finite__induct,axiom,
% 0.30/0.63      ! [F4: set_int,P: set_int > $o] :
% 0.30/0.63        ( ( finite_finite_int @ F4 )
% 0.30/0.63       => ( ( P @ bot_bot_set_int )
% 0.30/0.63         => ( ! [X2: int,F5: set_int] :
% 0.30/0.63                ( ( finite_finite_int @ F5 )
% 0.30/0.63               => ( ~ ( member_int @ X2 @ F5 )
% 0.30/0.63                 => ( ( P @ F5 )
% 0.30/0.63                   => ( P @ ( insert_int @ X2 @ F5 ) ) ) ) )
% 0.30/0.63           => ( P @ F4 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_induct
% 0.30/0.63  thf(fact_8809_finite__ne__induct,axiom,
% 0.30/0.63      ! [F4: set_Pr4329608150637261639at_nat,P: set_Pr4329608150637261639at_nat > $o] :
% 0.30/0.63        ( ( finite4343798906461161616at_nat @ F4 )
% 0.30/0.63       => ( ( F4 != bot_bo228742789529271731at_nat )
% 0.30/0.63         => ( ! [X2: produc3843707927480180839at_nat] : ( P @ ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) )
% 0.30/0.63           => ( ! [X2: produc3843707927480180839at_nat,F5: set_Pr4329608150637261639at_nat] :
% 0.30/0.63                  ( ( finite4343798906461161616at_nat @ F5 )
% 0.30/0.63                 => ( ( F5 != bot_bo228742789529271731at_nat )
% 0.30/0.63                   => ( ~ ( member8757157785044589968at_nat @ X2 @ F5 )
% 0.30/0.63                     => ( ( P @ F5 )
% 0.30/0.63                       => ( P @ ( insert9069300056098147895at_nat @ X2 @ F5 ) ) ) ) ) )
% 0.30/0.63             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_ne_induct
% 0.30/0.63  thf(fact_8810_finite__ne__induct,axiom,
% 0.30/0.63      ! [F4: set_se6260736226359567993nt_int,P: set_se6260736226359567993nt_int > $o] :
% 0.30/0.63        ( ( finite8744585540193469122nt_int @ F4 )
% 0.30/0.63       => ( ( F4 != bot_bo1488462491386950373nt_int )
% 0.30/0.63         => ( ! [X2: set_Pr958786334691620121nt_int] : ( P @ ( insert8897473484851387113nt_int @ X2 @ bot_bo1488462491386950373nt_int ) )
% 0.30/0.63           => ( ! [X2: set_Pr958786334691620121nt_int,F5: set_se6260736226359567993nt_int] :
% 0.30/0.63                  ( ( finite8744585540193469122nt_int @ F5 )
% 0.30/0.63                 => ( ( F5 != bot_bo1488462491386950373nt_int )
% 0.30/0.63                   => ( ~ ( member2340774599025711042nt_int @ X2 @ F5 )
% 0.30/0.63                     => ( ( P @ F5 )
% 0.30/0.63                       => ( P @ ( insert8897473484851387113nt_int @ X2 @ F5 ) ) ) ) ) )
% 0.30/0.63             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_ne_induct
% 0.30/0.63  thf(fact_8811_finite__ne__induct,axiom,
% 0.30/0.63      ! [F4: set_set_nat,P: set_set_nat > $o] :
% 0.30/0.63        ( ( finite1152437895449049373et_nat @ F4 )
% 0.30/0.63       => ( ( F4 != bot_bot_set_set_nat )
% 0.30/0.63         => ( ! [X2: set_nat] : ( P @ ( insert_set_nat @ X2 @ bot_bot_set_set_nat ) )
% 0.30/0.63           => ( ! [X2: set_nat,F5: set_set_nat] :
% 0.30/0.63                  ( ( finite1152437895449049373et_nat @ F5 )
% 0.30/0.63                 => ( ( F5 != bot_bot_set_set_nat )
% 0.30/0.63                   => ( ~ ( member_set_nat @ X2 @ F5 )
% 0.30/0.63                     => ( ( P @ F5 )
% 0.30/0.63                       => ( P @ ( insert_set_nat @ X2 @ F5 ) ) ) ) ) )
% 0.30/0.63             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_ne_induct
% 0.30/0.63  thf(fact_8812_finite__ne__induct,axiom,
% 0.30/0.63      ! [F4: set_Pr4532377907799695533_nat_o,P: set_Pr4532377907799695533_nat_o > $o] :
% 0.30/0.63        ( ( finite3252695134891459830_nat_o @ F4 )
% 0.30/0.63       => ( ( F4 != bot_bo7824918357723582233_nat_o )
% 0.30/0.63         => ( ! [X2: produc3658429121746597890et_nat > $o] : ( P @ ( insert5175938949040314269_nat_o @ X2 @ bot_bo7824918357723582233_nat_o ) )
% 0.30/0.63           => ( ! [X2: produc3658429121746597890et_nat > $o,F5: set_Pr4532377907799695533_nat_o] :
% 0.30/0.63                  ( ( finite3252695134891459830_nat_o @ F5 )
% 0.30/0.63                 => ( ( F5 != bot_bo7824918357723582233_nat_o )
% 0.30/0.63                   => ( ~ ( member6576561426505652726_nat_o @ X2 @ F5 )
% 0.30/0.63                     => ( ( P @ F5 )
% 0.30/0.63                       => ( P @ ( insert5175938949040314269_nat_o @ X2 @ F5 ) ) ) ) ) )
% 0.30/0.63             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_ne_induct
% 0.30/0.63  thf(fact_8813_finite__ne__induct,axiom,
% 0.30/0.63      ! [F4: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 0.30/0.63        ( ( finite6177210948735845034at_nat @ F4 )
% 0.30/0.63       => ( ( F4 != bot_bo2099793752762293965at_nat )
% 0.30/0.63         => ( ! [X2: product_prod_nat_nat] : ( P @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) )
% 0.30/0.63           => ( ! [X2: product_prod_nat_nat,F5: set_Pr1261947904930325089at_nat] :
% 0.30/0.63                  ( ( finite6177210948735845034at_nat @ F5 )
% 0.30/0.63                 => ( ( F5 != bot_bo2099793752762293965at_nat )
% 0.30/0.63                   => ( ~ ( member8440522571783428010at_nat @ X2 @ F5 )
% 0.30/0.63                     => ( ( P @ F5 )
% 0.30/0.63                       => ( P @ ( insert8211810215607154385at_nat @ X2 @ F5 ) ) ) ) ) )
% 0.30/0.63             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_ne_induct
% 0.30/0.63  thf(fact_8814_finite__ne__induct,axiom,
% 0.30/0.63      ! [F4: set_o,P: set_o > $o] :
% 0.30/0.63        ( ( finite_finite_o @ F4 )
% 0.30/0.63       => ( ( F4 != bot_bot_set_o )
% 0.30/0.63         => ( ! [X2: $o] : ( P @ ( insert_o @ X2 @ bot_bot_set_o ) )
% 0.30/0.63           => ( ! [X2: $o,F5: set_o] :
% 0.30/0.63                  ( ( finite_finite_o @ F5 )
% 0.30/0.63                 => ( ( F5 != bot_bot_set_o )
% 0.30/0.63                   => ( ~ ( member_o @ X2 @ F5 )
% 0.30/0.63                     => ( ( P @ F5 )
% 0.30/0.63                       => ( P @ ( insert_o @ X2 @ F5 ) ) ) ) ) )
% 0.30/0.63             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_ne_induct
% 0.30/0.63  thf(fact_8815_finite__ne__induct,axiom,
% 0.30/0.63      ! [F4: set_nat,P: set_nat > $o] :
% 0.30/0.63        ( ( finite_finite_nat @ F4 )
% 0.30/0.63       => ( ( F4 != bot_bot_set_nat )
% 0.30/0.63         => ( ! [X2: nat] : ( P @ ( insert_nat @ X2 @ bot_bot_set_nat ) )
% 0.30/0.63           => ( ! [X2: nat,F5: set_nat] :
% 0.30/0.63                  ( ( finite_finite_nat @ F5 )
% 0.30/0.63                 => ( ( F5 != bot_bot_set_nat )
% 0.30/0.63                   => ( ~ ( member_nat @ X2 @ F5 )
% 0.30/0.63                     => ( ( P @ F5 )
% 0.30/0.63                       => ( P @ ( insert_nat @ X2 @ F5 ) ) ) ) ) )
% 0.30/0.63             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_ne_induct
% 0.30/0.63  thf(fact_8816_finite__ne__induct,axiom,
% 0.30/0.63      ! [F4: set_int,P: set_int > $o] :
% 0.30/0.63        ( ( finite_finite_int @ F4 )
% 0.30/0.63       => ( ( F4 != bot_bot_set_int )
% 0.30/0.63         => ( ! [X2: int] : ( P @ ( insert_int @ X2 @ bot_bot_set_int ) )
% 0.30/0.63           => ( ! [X2: int,F5: set_int] :
% 0.30/0.63                  ( ( finite_finite_int @ F5 )
% 0.30/0.63                 => ( ( F5 != bot_bot_set_int )
% 0.30/0.63                   => ( ~ ( member_int @ X2 @ F5 )
% 0.30/0.63                     => ( ( P @ F5 )
% 0.30/0.63                       => ( P @ ( insert_int @ X2 @ F5 ) ) ) ) ) )
% 0.30/0.63             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_ne_induct
% 0.30/0.63  thf(fact_8817_infinite__finite__induct,axiom,
% 0.30/0.63      ! [P: set_Pr4329608150637261639at_nat > $o,A2: set_Pr4329608150637261639at_nat] :
% 0.30/0.63        ( ! [A8: set_Pr4329608150637261639at_nat] :
% 0.30/0.63            ( ~ ( finite4343798906461161616at_nat @ A8 )
% 0.30/0.63           => ( P @ A8 ) )
% 0.30/0.63       => ( ( P @ bot_bo228742789529271731at_nat )
% 0.30/0.63         => ( ! [X2: produc3843707927480180839at_nat,F5: set_Pr4329608150637261639at_nat] :
% 0.30/0.63                ( ( finite4343798906461161616at_nat @ F5 )
% 0.30/0.63               => ( ~ ( member8757157785044589968at_nat @ X2 @ F5 )
% 0.30/0.63                 => ( ( P @ F5 )
% 0.30/0.63                   => ( P @ ( insert9069300056098147895at_nat @ X2 @ F5 ) ) ) ) )
% 0.30/0.63           => ( P @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_finite_induct
% 0.30/0.63  thf(fact_8818_infinite__finite__induct,axiom,
% 0.30/0.63      ! [P: set_se6260736226359567993nt_int > $o,A2: set_se6260736226359567993nt_int] :
% 0.30/0.63        ( ! [A8: set_se6260736226359567993nt_int] :
% 0.30/0.63            ( ~ ( finite8744585540193469122nt_int @ A8 )
% 0.30/0.63           => ( P @ A8 ) )
% 0.30/0.63       => ( ( P @ bot_bo1488462491386950373nt_int )
% 0.30/0.63         => ( ! [X2: set_Pr958786334691620121nt_int,F5: set_se6260736226359567993nt_int] :
% 0.30/0.63                ( ( finite8744585540193469122nt_int @ F5 )
% 0.30/0.63               => ( ~ ( member2340774599025711042nt_int @ X2 @ F5 )
% 0.30/0.63                 => ( ( P @ F5 )
% 0.30/0.63                   => ( P @ ( insert8897473484851387113nt_int @ X2 @ F5 ) ) ) ) )
% 0.30/0.63           => ( P @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_finite_induct
% 0.30/0.63  thf(fact_8819_infinite__finite__induct,axiom,
% 0.30/0.63      ! [P: set_set_nat > $o,A2: set_set_nat] :
% 0.30/0.63        ( ! [A8: set_set_nat] :
% 0.30/0.63            ( ~ ( finite1152437895449049373et_nat @ A8 )
% 0.30/0.63           => ( P @ A8 ) )
% 0.30/0.63       => ( ( P @ bot_bot_set_set_nat )
% 0.30/0.63         => ( ! [X2: set_nat,F5: set_set_nat] :
% 0.30/0.63                ( ( finite1152437895449049373et_nat @ F5 )
% 0.30/0.63               => ( ~ ( member_set_nat @ X2 @ F5 )
% 0.30/0.63                 => ( ( P @ F5 )
% 0.30/0.63                   => ( P @ ( insert_set_nat @ X2 @ F5 ) ) ) ) )
% 0.30/0.63           => ( P @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_finite_induct
% 0.30/0.63  thf(fact_8820_infinite__finite__induct,axiom,
% 0.30/0.63      ! [P: set_Pr4532377907799695533_nat_o > $o,A2: set_Pr4532377907799695533_nat_o] :
% 0.30/0.63        ( ! [A8: set_Pr4532377907799695533_nat_o] :
% 0.30/0.63            ( ~ ( finite3252695134891459830_nat_o @ A8 )
% 0.30/0.63           => ( P @ A8 ) )
% 0.30/0.63       => ( ( P @ bot_bo7824918357723582233_nat_o )
% 0.30/0.63         => ( ! [X2: produc3658429121746597890et_nat > $o,F5: set_Pr4532377907799695533_nat_o] :
% 0.30/0.63                ( ( finite3252695134891459830_nat_o @ F5 )
% 0.30/0.63               => ( ~ ( member6576561426505652726_nat_o @ X2 @ F5 )
% 0.30/0.63                 => ( ( P @ F5 )
% 0.30/0.63                   => ( P @ ( insert5175938949040314269_nat_o @ X2 @ F5 ) ) ) ) )
% 0.30/0.63           => ( P @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_finite_induct
% 0.30/0.63  thf(fact_8821_infinite__finite__induct,axiom,
% 0.30/0.63      ! [P: set_Pr1261947904930325089at_nat > $o,A2: set_Pr1261947904930325089at_nat] :
% 0.30/0.63        ( ! [A8: set_Pr1261947904930325089at_nat] :
% 0.30/0.63            ( ~ ( finite6177210948735845034at_nat @ A8 )
% 0.30/0.63           => ( P @ A8 ) )
% 0.30/0.63       => ( ( P @ bot_bo2099793752762293965at_nat )
% 0.30/0.63         => ( ! [X2: product_prod_nat_nat,F5: set_Pr1261947904930325089at_nat] :
% 0.30/0.63                ( ( finite6177210948735845034at_nat @ F5 )
% 0.30/0.63               => ( ~ ( member8440522571783428010at_nat @ X2 @ F5 )
% 0.30/0.63                 => ( ( P @ F5 )
% 0.30/0.63                   => ( P @ ( insert8211810215607154385at_nat @ X2 @ F5 ) ) ) ) )
% 0.30/0.63           => ( P @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_finite_induct
% 0.30/0.63  thf(fact_8822_infinite__finite__induct,axiom,
% 0.30/0.63      ! [P: set_o > $o,A2: set_o] :
% 0.30/0.63        ( ! [A8: set_o] :
% 0.30/0.63            ( ~ ( finite_finite_o @ A8 )
% 0.30/0.63           => ( P @ A8 ) )
% 0.30/0.63       => ( ( P @ bot_bot_set_o )
% 0.30/0.63         => ( ! [X2: $o,F5: set_o] :
% 0.30/0.63                ( ( finite_finite_o @ F5 )
% 0.30/0.63               => ( ~ ( member_o @ X2 @ F5 )
% 0.30/0.63                 => ( ( P @ F5 )
% 0.30/0.63                   => ( P @ ( insert_o @ X2 @ F5 ) ) ) ) )
% 0.30/0.63           => ( P @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_finite_induct
% 0.30/0.63  thf(fact_8823_infinite__finite__induct,axiom,
% 0.30/0.63      ! [P: set_nat > $o,A2: set_nat] :
% 0.30/0.63        ( ! [A8: set_nat] :
% 0.30/0.63            ( ~ ( finite_finite_nat @ A8 )
% 0.30/0.63           => ( P @ A8 ) )
% 0.30/0.63       => ( ( P @ bot_bot_set_nat )
% 0.30/0.63         => ( ! [X2: nat,F5: set_nat] :
% 0.30/0.63                ( ( finite_finite_nat @ F5 )
% 0.30/0.63               => ( ~ ( member_nat @ X2 @ F5 )
% 0.30/0.63                 => ( ( P @ F5 )
% 0.30/0.63                   => ( P @ ( insert_nat @ X2 @ F5 ) ) ) ) )
% 0.30/0.63           => ( P @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_finite_induct
% 0.30/0.63  thf(fact_8824_infinite__finite__induct,axiom,
% 0.30/0.63      ! [P: set_int > $o,A2: set_int] :
% 0.30/0.63        ( ! [A8: set_int] :
% 0.30/0.63            ( ~ ( finite_finite_int @ A8 )
% 0.30/0.63           => ( P @ A8 ) )
% 0.30/0.63       => ( ( P @ bot_bot_set_int )
% 0.30/0.63         => ( ! [X2: int,F5: set_int] :
% 0.30/0.63                ( ( finite_finite_int @ F5 )
% 0.30/0.63               => ( ~ ( member_int @ X2 @ F5 )
% 0.30/0.63                 => ( ( P @ F5 )
% 0.30/0.63                   => ( P @ ( insert_int @ X2 @ F5 ) ) ) ) )
% 0.30/0.63           => ( P @ A2 ) ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % infinite_finite_induct
% 0.30/0.63  thf(fact_8825_finite__prod,axiom,
% 0.30/0.63      ( ( finite6120865539452801872od_o_o @ top_to7721136755696657239od_o_o )
% 0.30/0.63      = ( ( finite_finite_o @ top_top_set_o )
% 0.30/0.63        & ( finite_finite_o @ top_top_set_o ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_prod
% 0.30/0.63  thf(fact_8826_finite__prod,axiom,
% 0.30/0.63      ( ( finite7561617386449315510_o_rat @ top_to642698169864860165_o_rat )
% 0.30/0.63      = ( ( finite_finite_o @ top_top_set_o )
% 0.30/0.63        & ( finite_finite_rat @ top_top_set_rat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_prod
% 0.30/0.63  thf(fact_8827_finite__prod,axiom,
% 0.30/0.63      ( ( finite1846473907987936430_o_nat @ top_to7022684507342537725_o_nat )
% 0.30/0.63      = ( ( finite_finite_o @ top_top_set_o )
% 0.30/0.63        & ( finite_finite_nat @ top_top_set_nat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_prod
% 0.30/0.63  thf(fact_8828_finite__prod,axiom,
% 0.30/0.63      ( ( finite6891994925333515530_o_int @ top_to4532601362410810969_o_int )
% 0.30/0.63      = ( ( finite_finite_o @ top_top_set_o )
% 0.30/0.63        & ( finite_finite_int @ top_top_set_int ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_prod
% 0.30/0.63  thf(fact_8829_finite__prod,axiom,
% 0.30/0.63      ( ( finite1617675504726861388_rat_o @ top_to7320853134386005659_rat_o )
% 0.30/0.63      = ( ( finite_finite_rat @ top_top_set_rat )
% 0.30/0.63        & ( finite_finite_o @ top_top_set_o ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_prod
% 0.30/0.63  thf(fact_8830_finite__prod,axiom,
% 0.30/0.63      ( ( finite2352427746407582394at_rat @ top_to3112507417142880193at_rat )
% 0.30/0.63      = ( ( finite_finite_rat @ top_top_set_rat )
% 0.30/0.63        & ( finite_finite_rat @ top_top_set_rat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_prod
% 0.30/0.63  thf(fact_8831_finite__prod,axiom,
% 0.30/0.63      ( ( finite5860656304800979122at_nat @ top_to269121717765781945at_nat )
% 0.30/0.63      = ( ( finite_finite_rat @ top_top_set_rat )
% 0.30/0.63        & ( finite_finite_nat @ top_top_set_nat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_prod
% 0.30/0.63  thf(fact_8832_finite__prod,axiom,
% 0.30/0.63      ( ( finite1682805285291782414at_int @ top_to7002410609688830997at_int )
% 0.30/0.63      = ( ( finite_finite_rat @ top_top_set_rat )
% 0.30/0.63        & ( finite_finite_int @ top_top_set_int ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_prod
% 0.30/0.63  thf(fact_8833_finite__prod,axiom,
% 0.30/0.63      ( ( finite5355008432043429460_nat_o @ top_to8070287629520841379_nat_o )
% 0.30/0.63      = ( ( finite_finite_nat @ top_top_set_nat )
% 0.30/0.63        & ( finite_finite_o @ top_top_set_o ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_prod
% 0.30/0.63  thf(fact_8834_finite__prod,axiom,
% 0.30/0.63      ( ( finite2668982390342448306at_rat @ top_to7513191607651882425at_rat )
% 0.30/0.63      = ( ( finite_finite_nat @ top_top_set_nat )
% 0.30/0.63        & ( finite_finite_rat @ top_top_set_rat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_prod
% 0.30/0.63  thf(fact_8835_finite__Prod__UNIV,axiom,
% 0.30/0.63      ( ( finite_finite_o @ top_top_set_o )
% 0.30/0.63     => ( ( finite_finite_o @ top_top_set_o )
% 0.30/0.63       => ( finite6120865539452801872od_o_o @ top_to7721136755696657239od_o_o ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Prod_UNIV
% 0.30/0.63  thf(fact_8836_finite__Prod__UNIV,axiom,
% 0.30/0.63      ( ( finite_finite_o @ top_top_set_o )
% 0.30/0.63     => ( ( finite_finite_rat @ top_top_set_rat )
% 0.30/0.63       => ( finite7561617386449315510_o_rat @ top_to642698169864860165_o_rat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Prod_UNIV
% 0.30/0.63  thf(fact_8837_finite__Prod__UNIV,axiom,
% 0.30/0.63      ( ( finite_finite_o @ top_top_set_o )
% 0.30/0.63     => ( ( finite_finite_nat @ top_top_set_nat )
% 0.30/0.63       => ( finite1846473907987936430_o_nat @ top_to7022684507342537725_o_nat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Prod_UNIV
% 0.30/0.63  thf(fact_8838_finite__Prod__UNIV,axiom,
% 0.30/0.63      ( ( finite_finite_o @ top_top_set_o )
% 0.30/0.63     => ( ( finite_finite_int @ top_top_set_int )
% 0.30/0.63       => ( finite6891994925333515530_o_int @ top_to4532601362410810969_o_int ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Prod_UNIV
% 0.30/0.63  thf(fact_8839_finite__Prod__UNIV,axiom,
% 0.30/0.63      ( ( finite_finite_rat @ top_top_set_rat )
% 0.30/0.63     => ( ( finite_finite_o @ top_top_set_o )
% 0.30/0.63       => ( finite1617675504726861388_rat_o @ top_to7320853134386005659_rat_o ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Prod_UNIV
% 0.30/0.63  thf(fact_8840_finite__Prod__UNIV,axiom,
% 0.30/0.63      ( ( finite_finite_rat @ top_top_set_rat )
% 0.30/0.63     => ( ( finite_finite_rat @ top_top_set_rat )
% 0.30/0.63       => ( finite2352427746407582394at_rat @ top_to3112507417142880193at_rat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Prod_UNIV
% 0.30/0.63  thf(fact_8841_finite__Prod__UNIV,axiom,
% 0.30/0.63      ( ( finite_finite_rat @ top_top_set_rat )
% 0.30/0.63     => ( ( finite_finite_nat @ top_top_set_nat )
% 0.30/0.63       => ( finite5860656304800979122at_nat @ top_to269121717765781945at_nat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Prod_UNIV
% 0.30/0.63  thf(fact_8842_finite__Prod__UNIV,axiom,
% 0.30/0.63      ( ( finite_finite_rat @ top_top_set_rat )
% 0.30/0.63     => ( ( finite_finite_int @ top_top_set_int )
% 0.30/0.63       => ( finite1682805285291782414at_int @ top_to7002410609688830997at_int ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Prod_UNIV
% 0.30/0.63  thf(fact_8843_finite__Prod__UNIV,axiom,
% 0.30/0.63      ( ( finite_finite_nat @ top_top_set_nat )
% 0.30/0.63     => ( ( finite_finite_o @ top_top_set_o )
% 0.30/0.63       => ( finite5355008432043429460_nat_o @ top_to8070287629520841379_nat_o ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Prod_UNIV
% 0.30/0.63  thf(fact_8844_finite__Prod__UNIV,axiom,
% 0.30/0.63      ( ( finite_finite_nat @ top_top_set_nat )
% 0.30/0.63     => ( ( finite_finite_rat @ top_top_set_rat )
% 0.30/0.63       => ( finite2668982390342448306at_rat @ top_to7513191607651882425at_rat ) ) ) ).
% 0.30/0.63  
% 0.30/0.63  % finite_Prod_UNIV
% 0.30/0.63  thf(fact_8845_Finite__Set_Ofinite__set,axiom,
% 0.30/0.63      ( ( finite9047747110432174090at_nat @ top_to7629004291339433233at_nat )
% 0.30/0.63      = ( finite6177210948735845034at_nat @ top_to4669805908274784177at_nat ) ) ).
% 0.30/0.63  
% 0.30/0.63  % Finite_Set.finite_set
% 0.30/0.63  thf(fact_8846_Finite__Set_Ofinite__set,axiom,
% 0.30/0.63      ( ( finite7047420756378620717st_nat @ top_to1619013496918823676st_nat )
% 0.30/0.63      = ( finite8100373058378681591st_nat @ top_top_set_list_nat ) ) ).
% 0.30/0.63  
% 0.30/0.63  % Finite_Set.finite_set
% 0.30/0.63  thf(fact_8847_Finite__Set_Ofinite__set,axiom,
% 0.30/0.64      ( ( finite_finite_set_o @ top_top_set_set_o )
% 0.30/0.64      = ( finite_finite_o @ top_top_set_o ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Finite_Set.finite_set
% 0.30/0.64  thf(fact_8848_Finite__Set_Ofinite__set,axiom,
% 0.30/0.64      ( ( finite6867581373910428453et_rat @ top_top_set_set_rat )
% 0.30/0.64      = ( finite_finite_rat @ top_top_set_rat ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Finite_Set.finite_set
% 0.30/0.64  thf(fact_8849_Finite__Set_Ofinite__set,axiom,
% 0.30/0.64      ( ( finite1152437895449049373et_nat @ top_top_set_set_nat )
% 0.30/0.64      = ( finite_finite_nat @ top_top_set_nat ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Finite_Set.finite_set
% 0.30/0.64  thf(fact_8850_Finite__Set_Ofinite__set,axiom,
% 0.30/0.64      ( ( finite6197958912794628473et_int @ top_top_set_set_int )
% 0.30/0.64      = ( finite_finite_int @ top_top_set_int ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Finite_Set.finite_set
% 0.30/0.64  thf(fact_8851_finite__subset__induct_H,axiom,
% 0.30/0.64      ! [F4: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,P: set_Pr4329608150637261639at_nat > $o] :
% 0.30/0.64        ( ( finite4343798906461161616at_nat @ F4 )
% 0.30/0.64       => ( ( ord_le1268244103169919719at_nat @ F4 @ A2 )
% 0.30/0.64         => ( ( P @ bot_bo228742789529271731at_nat )
% 0.30/0.64           => ( ! [A6: produc3843707927480180839at_nat,F5: set_Pr4329608150637261639at_nat] :
% 0.30/0.64                  ( ( finite4343798906461161616at_nat @ F5 )
% 0.30/0.64                 => ( ( member8757157785044589968at_nat @ A6 @ A2 )
% 0.30/0.64                   => ( ( ord_le1268244103169919719at_nat @ F5 @ A2 )
% 0.30/0.64                     => ( ~ ( member8757157785044589968at_nat @ A6 @ F5 )
% 0.30/0.64                       => ( ( P @ F5 )
% 0.30/0.64                         => ( P @ ( insert9069300056098147895at_nat @ A6 @ F5 ) ) ) ) ) ) )
% 0.30/0.64             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_subset_induct'
% 0.30/0.64  thf(fact_8852_finite__subset__induct_H,axiom,
% 0.30/0.64      ! [F4: set_se6260736226359567993nt_int,A2: set_se6260736226359567993nt_int,P: set_se6260736226359567993nt_int > $o] :
% 0.30/0.64        ( ( finite8744585540193469122nt_int @ F4 )
% 0.30/0.64       => ( ( ord_le483042692224249369nt_int @ F4 @ A2 )
% 0.30/0.64         => ( ( P @ bot_bo1488462491386950373nt_int )
% 0.30/0.64           => ( ! [A6: set_Pr958786334691620121nt_int,F5: set_se6260736226359567993nt_int] :
% 0.30/0.64                  ( ( finite8744585540193469122nt_int @ F5 )
% 0.30/0.64                 => ( ( member2340774599025711042nt_int @ A6 @ A2 )
% 0.30/0.64                   => ( ( ord_le483042692224249369nt_int @ F5 @ A2 )
% 0.30/0.64                     => ( ~ ( member2340774599025711042nt_int @ A6 @ F5 )
% 0.30/0.64                       => ( ( P @ F5 )
% 0.30/0.64                         => ( P @ ( insert8897473484851387113nt_int @ A6 @ F5 ) ) ) ) ) ) )
% 0.30/0.64             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_subset_induct'
% 0.30/0.64  thf(fact_8853_finite__subset__induct_H,axiom,
% 0.30/0.64      ! [F4: set_set_nat,A2: set_set_nat,P: set_set_nat > $o] :
% 0.30/0.64        ( ( finite1152437895449049373et_nat @ F4 )
% 0.30/0.64       => ( ( ord_le6893508408891458716et_nat @ F4 @ A2 )
% 0.30/0.64         => ( ( P @ bot_bot_set_set_nat )
% 0.30/0.64           => ( ! [A6: set_nat,F5: set_set_nat] :
% 0.30/0.64                  ( ( finite1152437895449049373et_nat @ F5 )
% 0.30/0.64                 => ( ( member_set_nat @ A6 @ A2 )
% 0.30/0.64                   => ( ( ord_le6893508408891458716et_nat @ F5 @ A2 )
% 0.30/0.64                     => ( ~ ( member_set_nat @ A6 @ F5 )
% 0.30/0.64                       => ( ( P @ F5 )
% 0.30/0.64                         => ( P @ ( insert_set_nat @ A6 @ F5 ) ) ) ) ) ) )
% 0.30/0.64             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_subset_induct'
% 0.30/0.64  thf(fact_8854_finite__subset__induct_H,axiom,
% 0.30/0.64      ! [F4: set_Pr4532377907799695533_nat_o,A2: set_Pr4532377907799695533_nat_o,P: set_Pr4532377907799695533_nat_o > $o] :
% 0.30/0.64        ( ( finite3252695134891459830_nat_o @ F4 )
% 0.30/0.64       => ( ( ord_le2965882846123202637_nat_o @ F4 @ A2 )
% 0.30/0.64         => ( ( P @ bot_bo7824918357723582233_nat_o )
% 0.30/0.64           => ( ! [A6: produc3658429121746597890et_nat > $o,F5: set_Pr4532377907799695533_nat_o] :
% 0.30/0.64                  ( ( finite3252695134891459830_nat_o @ F5 )
% 0.30/0.64                 => ( ( member6576561426505652726_nat_o @ A6 @ A2 )
% 0.30/0.64                   => ( ( ord_le2965882846123202637_nat_o @ F5 @ A2 )
% 0.30/0.64                     => ( ~ ( member6576561426505652726_nat_o @ A6 @ F5 )
% 0.30/0.64                       => ( ( P @ F5 )
% 0.30/0.64                         => ( P @ ( insert5175938949040314269_nat_o @ A6 @ F5 ) ) ) ) ) ) )
% 0.30/0.64             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_subset_induct'
% 0.30/0.64  thf(fact_8855_finite__subset__induct_H,axiom,
% 0.30/0.64      ! [F4: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 0.30/0.64        ( ( finite6177210948735845034at_nat @ F4 )
% 0.30/0.64       => ( ( ord_le3146513528884898305at_nat @ F4 @ A2 )
% 0.30/0.64         => ( ( P @ bot_bo2099793752762293965at_nat )
% 0.30/0.64           => ( ! [A6: product_prod_nat_nat,F5: set_Pr1261947904930325089at_nat] :
% 0.30/0.64                  ( ( finite6177210948735845034at_nat @ F5 )
% 0.30/0.64                 => ( ( member8440522571783428010at_nat @ A6 @ A2 )
% 0.30/0.64                   => ( ( ord_le3146513528884898305at_nat @ F5 @ A2 )
% 0.30/0.64                     => ( ~ ( member8440522571783428010at_nat @ A6 @ F5 )
% 0.30/0.64                       => ( ( P @ F5 )
% 0.30/0.64                         => ( P @ ( insert8211810215607154385at_nat @ A6 @ F5 ) ) ) ) ) ) )
% 0.30/0.64             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_subset_induct'
% 0.30/0.64  thf(fact_8856_finite__subset__induct_H,axiom,
% 0.30/0.64      ! [F4: set_o,A2: set_o,P: set_o > $o] :
% 0.30/0.64        ( ( finite_finite_o @ F4 )
% 0.30/0.64       => ( ( ord_less_eq_set_o @ F4 @ A2 )
% 0.30/0.64         => ( ( P @ bot_bot_set_o )
% 0.30/0.64           => ( ! [A6: $o,F5: set_o] :
% 0.30/0.64                  ( ( finite_finite_o @ F5 )
% 0.30/0.64                 => ( ( member_o @ A6 @ A2 )
% 0.30/0.64                   => ( ( ord_less_eq_set_o @ F5 @ A2 )
% 0.30/0.64                     => ( ~ ( member_o @ A6 @ F5 )
% 0.30/0.64                       => ( ( P @ F5 )
% 0.30/0.64                         => ( P @ ( insert_o @ A6 @ F5 ) ) ) ) ) ) )
% 0.30/0.64             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_subset_induct'
% 0.30/0.64  thf(fact_8857_finite__subset__induct_H,axiom,
% 0.30/0.64      ! [F4: set_int,A2: set_int,P: set_int > $o] :
% 0.30/0.64        ( ( finite_finite_int @ F4 )
% 0.30/0.64       => ( ( ord_less_eq_set_int @ F4 @ A2 )
% 0.30/0.64         => ( ( P @ bot_bot_set_int )
% 0.30/0.64           => ( ! [A6: int,F5: set_int] :
% 0.30/0.64                  ( ( finite_finite_int @ F5 )
% 0.30/0.64                 => ( ( member_int @ A6 @ A2 )
% 0.30/0.64                   => ( ( ord_less_eq_set_int @ F5 @ A2 )
% 0.30/0.64                     => ( ~ ( member_int @ A6 @ F5 )
% 0.30/0.64                       => ( ( P @ F5 )
% 0.30/0.64                         => ( P @ ( insert_int @ A6 @ F5 ) ) ) ) ) ) )
% 0.30/0.64             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_subset_induct'
% 0.30/0.64  thf(fact_8858_finite__subset__induct_H,axiom,
% 0.30/0.64      ! [F4: set_nat,A2: set_nat,P: set_nat > $o] :
% 0.30/0.64        ( ( finite_finite_nat @ F4 )
% 0.30/0.64       => ( ( ord_less_eq_set_nat @ F4 @ A2 )
% 0.30/0.64         => ( ( P @ bot_bot_set_nat )
% 0.30/0.64           => ( ! [A6: nat,F5: set_nat] :
% 0.30/0.64                  ( ( finite_finite_nat @ F5 )
% 0.30/0.64                 => ( ( member_nat @ A6 @ A2 )
% 0.30/0.64                   => ( ( ord_less_eq_set_nat @ F5 @ A2 )
% 0.30/0.64                     => ( ~ ( member_nat @ A6 @ F5 )
% 0.30/0.64                       => ( ( P @ F5 )
% 0.30/0.64                         => ( P @ ( insert_nat @ A6 @ F5 ) ) ) ) ) ) )
% 0.30/0.64             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_subset_induct'
% 0.30/0.64  thf(fact_8859_finite__subset__induct,axiom,
% 0.30/0.64      ! [F4: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,P: set_Pr4329608150637261639at_nat > $o] :
% 0.30/0.64        ( ( finite4343798906461161616at_nat @ F4 )
% 0.30/0.64       => ( ( ord_le1268244103169919719at_nat @ F4 @ A2 )
% 0.30/0.64         => ( ( P @ bot_bo228742789529271731at_nat )
% 0.30/0.64           => ( ! [A6: produc3843707927480180839at_nat,F5: set_Pr4329608150637261639at_nat] :
% 0.30/0.64                  ( ( finite4343798906461161616at_nat @ F5 )
% 0.30/0.64                 => ( ( member8757157785044589968at_nat @ A6 @ A2 )
% 0.30/0.64                   => ( ~ ( member8757157785044589968at_nat @ A6 @ F5 )
% 0.30/0.64                     => ( ( P @ F5 )
% 0.30/0.64                       => ( P @ ( insert9069300056098147895at_nat @ A6 @ F5 ) ) ) ) ) )
% 0.30/0.64             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_subset_induct
% 0.30/0.64  thf(fact_8860_finite__subset__induct,axiom,
% 0.30/0.64      ! [F4: set_se6260736226359567993nt_int,A2: set_se6260736226359567993nt_int,P: set_se6260736226359567993nt_int > $o] :
% 0.30/0.64        ( ( finite8744585540193469122nt_int @ F4 )
% 0.30/0.64       => ( ( ord_le483042692224249369nt_int @ F4 @ A2 )
% 0.30/0.64         => ( ( P @ bot_bo1488462491386950373nt_int )
% 0.30/0.64           => ( ! [A6: set_Pr958786334691620121nt_int,F5: set_se6260736226359567993nt_int] :
% 0.30/0.64                  ( ( finite8744585540193469122nt_int @ F5 )
% 0.30/0.64                 => ( ( member2340774599025711042nt_int @ A6 @ A2 )
% 0.30/0.64                   => ( ~ ( member2340774599025711042nt_int @ A6 @ F5 )
% 0.30/0.64                     => ( ( P @ F5 )
% 0.30/0.64                       => ( P @ ( insert8897473484851387113nt_int @ A6 @ F5 ) ) ) ) ) )
% 0.30/0.64             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_subset_induct
% 0.30/0.64  thf(fact_8861_finite__subset__induct,axiom,
% 0.30/0.64      ! [F4: set_set_nat,A2: set_set_nat,P: set_set_nat > $o] :
% 0.30/0.64        ( ( finite1152437895449049373et_nat @ F4 )
% 0.30/0.64       => ( ( ord_le6893508408891458716et_nat @ F4 @ A2 )
% 0.30/0.64         => ( ( P @ bot_bot_set_set_nat )
% 0.30/0.64           => ( ! [A6: set_nat,F5: set_set_nat] :
% 0.30/0.64                  ( ( finite1152437895449049373et_nat @ F5 )
% 0.30/0.64                 => ( ( member_set_nat @ A6 @ A2 )
% 0.30/0.64                   => ( ~ ( member_set_nat @ A6 @ F5 )
% 0.30/0.64                     => ( ( P @ F5 )
% 0.30/0.64                       => ( P @ ( insert_set_nat @ A6 @ F5 ) ) ) ) ) )
% 0.30/0.64             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_subset_induct
% 0.30/0.64  thf(fact_8862_finite__subset__induct,axiom,
% 0.30/0.64      ! [F4: set_Pr4532377907799695533_nat_o,A2: set_Pr4532377907799695533_nat_o,P: set_Pr4532377907799695533_nat_o > $o] :
% 0.30/0.64        ( ( finite3252695134891459830_nat_o @ F4 )
% 0.30/0.64       => ( ( ord_le2965882846123202637_nat_o @ F4 @ A2 )
% 0.30/0.64         => ( ( P @ bot_bo7824918357723582233_nat_o )
% 0.30/0.64           => ( ! [A6: produc3658429121746597890et_nat > $o,F5: set_Pr4532377907799695533_nat_o] :
% 0.30/0.64                  ( ( finite3252695134891459830_nat_o @ F5 )
% 0.30/0.64                 => ( ( member6576561426505652726_nat_o @ A6 @ A2 )
% 0.30/0.64                   => ( ~ ( member6576561426505652726_nat_o @ A6 @ F5 )
% 0.30/0.64                     => ( ( P @ F5 )
% 0.30/0.64                       => ( P @ ( insert5175938949040314269_nat_o @ A6 @ F5 ) ) ) ) ) )
% 0.30/0.64             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_subset_induct
% 0.30/0.64  thf(fact_8863_finite__subset__induct,axiom,
% 0.30/0.64      ! [F4: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 0.30/0.64        ( ( finite6177210948735845034at_nat @ F4 )
% 0.30/0.64       => ( ( ord_le3146513528884898305at_nat @ F4 @ A2 )
% 0.30/0.64         => ( ( P @ bot_bo2099793752762293965at_nat )
% 0.30/0.64           => ( ! [A6: product_prod_nat_nat,F5: set_Pr1261947904930325089at_nat] :
% 0.30/0.64                  ( ( finite6177210948735845034at_nat @ F5 )
% 0.30/0.64                 => ( ( member8440522571783428010at_nat @ A6 @ A2 )
% 0.30/0.64                   => ( ~ ( member8440522571783428010at_nat @ A6 @ F5 )
% 0.30/0.64                     => ( ( P @ F5 )
% 0.30/0.64                       => ( P @ ( insert8211810215607154385at_nat @ A6 @ F5 ) ) ) ) ) )
% 0.30/0.64             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_subset_induct
% 0.30/0.64  thf(fact_8864_finite__subset__induct,axiom,
% 0.30/0.64      ! [F4: set_o,A2: set_o,P: set_o > $o] :
% 0.30/0.64        ( ( finite_finite_o @ F4 )
% 0.30/0.64       => ( ( ord_less_eq_set_o @ F4 @ A2 )
% 0.30/0.64         => ( ( P @ bot_bot_set_o )
% 0.30/0.64           => ( ! [A6: $o,F5: set_o] :
% 0.30/0.64                  ( ( finite_finite_o @ F5 )
% 0.30/0.64                 => ( ( member_o @ A6 @ A2 )
% 0.30/0.64                   => ( ~ ( member_o @ A6 @ F5 )
% 0.30/0.64                     => ( ( P @ F5 )
% 0.30/0.64                       => ( P @ ( insert_o @ A6 @ F5 ) ) ) ) ) )
% 0.30/0.64             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_subset_induct
% 0.30/0.64  thf(fact_8865_finite__subset__induct,axiom,
% 0.30/0.64      ! [F4: set_int,A2: set_int,P: set_int > $o] :
% 0.30/0.64        ( ( finite_finite_int @ F4 )
% 0.30/0.64       => ( ( ord_less_eq_set_int @ F4 @ A2 )
% 0.30/0.64         => ( ( P @ bot_bot_set_int )
% 0.30/0.64           => ( ! [A6: int,F5: set_int] :
% 0.30/0.64                  ( ( finite_finite_int @ F5 )
% 0.30/0.64                 => ( ( member_int @ A6 @ A2 )
% 0.30/0.64                   => ( ~ ( member_int @ A6 @ F5 )
% 0.30/0.64                     => ( ( P @ F5 )
% 0.30/0.64                       => ( P @ ( insert_int @ A6 @ F5 ) ) ) ) ) )
% 0.30/0.64             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_subset_induct
% 0.30/0.64  thf(fact_8866_finite__subset__induct,axiom,
% 0.30/0.64      ! [F4: set_nat,A2: set_nat,P: set_nat > $o] :
% 0.30/0.64        ( ( finite_finite_nat @ F4 )
% 0.30/0.64       => ( ( ord_less_eq_set_nat @ F4 @ A2 )
% 0.30/0.64         => ( ( P @ bot_bot_set_nat )
% 0.30/0.64           => ( ! [A6: nat,F5: set_nat] :
% 0.30/0.64                  ( ( finite_finite_nat @ F5 )
% 0.30/0.64                 => ( ( member_nat @ A6 @ A2 )
% 0.30/0.64                   => ( ~ ( member_nat @ A6 @ F5 )
% 0.30/0.64                     => ( ( P @ F5 )
% 0.30/0.64                       => ( P @ ( insert_nat @ A6 @ F5 ) ) ) ) ) )
% 0.30/0.64             => ( P @ F4 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_subset_induct
% 0.30/0.64  thf(fact_8867_infinite__remove,axiom,
% 0.30/0.64      ! [S: set_Pr4329608150637261639at_nat,A: produc3843707927480180839at_nat] :
% 0.30/0.64        ( ~ ( finite4343798906461161616at_nat @ S )
% 0.30/0.64       => ~ ( finite4343798906461161616at_nat @ ( minus_3314409938677909166at_nat @ S @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % infinite_remove
% 0.30/0.64  thf(fact_8868_infinite__remove,axiom,
% 0.30/0.64      ! [S: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
% 0.30/0.64        ( ~ ( finite6177210948735845034at_nat @ S )
% 0.30/0.64       => ~ ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ S @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % infinite_remove
% 0.30/0.64  thf(fact_8869_infinite__remove,axiom,
% 0.30/0.64      ! [S: set_o,A: $o] :
% 0.30/0.64        ( ~ ( finite_finite_o @ S )
% 0.30/0.64       => ~ ( finite_finite_o @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % infinite_remove
% 0.30/0.64  thf(fact_8870_infinite__remove,axiom,
% 0.30/0.64      ! [S: set_int,A: int] :
% 0.30/0.64        ( ~ ( finite_finite_int @ S )
% 0.30/0.64       => ~ ( finite_finite_int @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % infinite_remove
% 0.30/0.64  thf(fact_8871_infinite__remove,axiom,
% 0.30/0.64      ! [S: set_nat,A: nat] :
% 0.30/0.64        ( ~ ( finite_finite_nat @ S )
% 0.30/0.64       => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % infinite_remove
% 0.30/0.64  thf(fact_8872_infinite__coinduct,axiom,
% 0.30/0.64      ! [X7: set_Pr4329608150637261639at_nat > $o,A2: set_Pr4329608150637261639at_nat] :
% 0.30/0.64        ( ( X7 @ A2 )
% 0.30/0.64       => ( ! [A8: set_Pr4329608150637261639at_nat] :
% 0.30/0.64              ( ( X7 @ A8 )
% 0.30/0.64             => ? [X5: produc3843707927480180839at_nat] :
% 0.30/0.64                  ( ( member8757157785044589968at_nat @ X5 @ A8 )
% 0.30/0.64                  & ( ( X7 @ ( minus_3314409938677909166at_nat @ A8 @ ( insert9069300056098147895at_nat @ X5 @ bot_bo228742789529271731at_nat ) ) )
% 0.30/0.64                    | ~ ( finite4343798906461161616at_nat @ ( minus_3314409938677909166at_nat @ A8 @ ( insert9069300056098147895at_nat @ X5 @ bot_bo228742789529271731at_nat ) ) ) ) ) )
% 0.30/0.64         => ~ ( finite4343798906461161616at_nat @ A2 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % infinite_coinduct
% 0.30/0.64  thf(fact_8873_infinite__coinduct,axiom,
% 0.30/0.64      ! [X7: set_Pr1261947904930325089at_nat > $o,A2: set_Pr1261947904930325089at_nat] :
% 0.30/0.64        ( ( X7 @ A2 )
% 0.30/0.64       => ( ! [A8: set_Pr1261947904930325089at_nat] :
% 0.30/0.64              ( ( X7 @ A8 )
% 0.30/0.64             => ? [X5: product_prod_nat_nat] :
% 0.30/0.64                  ( ( member8440522571783428010at_nat @ X5 @ A8 )
% 0.30/0.64                  & ( ( X7 @ ( minus_1356011639430497352at_nat @ A8 @ ( insert8211810215607154385at_nat @ X5 @ bot_bo2099793752762293965at_nat ) ) )
% 0.30/0.64                    | ~ ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A8 @ ( insert8211810215607154385at_nat @ X5 @ bot_bo2099793752762293965at_nat ) ) ) ) ) )
% 0.30/0.64         => ~ ( finite6177210948735845034at_nat @ A2 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % infinite_coinduct
% 0.30/0.64  thf(fact_8874_infinite__coinduct,axiom,
% 0.30/0.64      ! [X7: set_o > $o,A2: set_o] :
% 0.30/0.64        ( ( X7 @ A2 )
% 0.30/0.64       => ( ! [A8: set_o] :
% 0.30/0.64              ( ( X7 @ A8 )
% 0.30/0.64             => ? [X5: $o] :
% 0.30/0.64                  ( ( member_o @ X5 @ A8 )
% 0.30/0.64                  & ( ( X7 @ ( minus_minus_set_o @ A8 @ ( insert_o @ X5 @ bot_bot_set_o ) ) )
% 0.30/0.64                    | ~ ( finite_finite_o @ ( minus_minus_set_o @ A8 @ ( insert_o @ X5 @ bot_bot_set_o ) ) ) ) ) )
% 0.30/0.64         => ~ ( finite_finite_o @ A2 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % infinite_coinduct
% 0.30/0.64  thf(fact_8875_infinite__coinduct,axiom,
% 0.30/0.64      ! [X7: set_int > $o,A2: set_int] :
% 0.30/0.64        ( ( X7 @ A2 )
% 0.30/0.64       => ( ! [A8: set_int] :
% 0.30/0.64              ( ( X7 @ A8 )
% 0.30/0.64             => ? [X5: int] :
% 0.30/0.64                  ( ( member_int @ X5 @ A8 )
% 0.30/0.64                  & ( ( X7 @ ( minus_minus_set_int @ A8 @ ( insert_int @ X5 @ bot_bot_set_int ) ) )
% 0.30/0.64                    | ~ ( finite_finite_int @ ( minus_minus_set_int @ A8 @ ( insert_int @ X5 @ bot_bot_set_int ) ) ) ) ) )
% 0.30/0.64         => ~ ( finite_finite_int @ A2 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % infinite_coinduct
% 0.30/0.64  thf(fact_8876_infinite__coinduct,axiom,
% 0.30/0.64      ! [X7: set_nat > $o,A2: set_nat] :
% 0.30/0.64        ( ( X7 @ A2 )
% 0.30/0.64       => ( ! [A8: set_nat] :
% 0.30/0.64              ( ( X7 @ A8 )
% 0.30/0.64             => ? [X5: nat] :
% 0.30/0.64                  ( ( member_nat @ X5 @ A8 )
% 0.30/0.64                  & ( ( X7 @ ( minus_minus_set_nat @ A8 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) )
% 0.30/0.64                    | ~ ( finite_finite_nat @ ( minus_minus_set_nat @ A8 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) ) ) )
% 0.30/0.64         => ~ ( finite_finite_nat @ A2 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % infinite_coinduct
% 0.30/0.64  thf(fact_8877_finite__empty__induct,axiom,
% 0.30/0.64      ! [A2: set_Pr4329608150637261639at_nat,P: set_Pr4329608150637261639at_nat > $o] :
% 0.30/0.64        ( ( finite4343798906461161616at_nat @ A2 )
% 0.30/0.64       => ( ( P @ A2 )
% 0.30/0.64         => ( ! [A6: produc3843707927480180839at_nat,A8: set_Pr4329608150637261639at_nat] :
% 0.30/0.64                ( ( finite4343798906461161616at_nat @ A8 )
% 0.30/0.64               => ( ( member8757157785044589968at_nat @ A6 @ A8 )
% 0.30/0.64                 => ( ( P @ A8 )
% 0.30/0.64                   => ( P @ ( minus_3314409938677909166at_nat @ A8 @ ( insert9069300056098147895at_nat @ A6 @ bot_bo228742789529271731at_nat ) ) ) ) ) )
% 0.30/0.64           => ( P @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_empty_induct
% 0.30/0.64  thf(fact_8878_finite__empty__induct,axiom,
% 0.30/0.64      ! [A2: set_se6260736226359567993nt_int,P: set_se6260736226359567993nt_int > $o] :
% 0.30/0.64        ( ( finite8744585540193469122nt_int @ A2 )
% 0.30/0.64       => ( ( P @ A2 )
% 0.30/0.64         => ( ! [A6: set_Pr958786334691620121nt_int,A8: set_se6260736226359567993nt_int] :
% 0.30/0.64                ( ( finite8744585540193469122nt_int @ A8 )
% 0.30/0.64               => ( ( member2340774599025711042nt_int @ A6 @ A8 )
% 0.30/0.64                 => ( ( P @ A8 )
% 0.30/0.64                   => ( P @ ( minus_2612819937483484256nt_int @ A8 @ ( insert8897473484851387113nt_int @ A6 @ bot_bo1488462491386950373nt_int ) ) ) ) ) )
% 0.30/0.64           => ( P @ bot_bo1488462491386950373nt_int ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_empty_induct
% 0.30/0.64  thf(fact_8879_finite__empty__induct,axiom,
% 0.30/0.64      ! [A2: set_set_nat,P: set_set_nat > $o] :
% 0.30/0.64        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.64       => ( ( P @ A2 )
% 0.30/0.64         => ( ! [A6: set_nat,A8: set_set_nat] :
% 0.30/0.64                ( ( finite1152437895449049373et_nat @ A8 )
% 0.30/0.64               => ( ( member_set_nat @ A6 @ A8 )
% 0.30/0.64                 => ( ( P @ A8 )
% 0.30/0.64                   => ( P @ ( minus_2163939370556025621et_nat @ A8 @ ( insert_set_nat @ A6 @ bot_bot_set_set_nat ) ) ) ) ) )
% 0.30/0.64           => ( P @ bot_bot_set_set_nat ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_empty_induct
% 0.30/0.64  thf(fact_8880_finite__empty__induct,axiom,
% 0.30/0.64      ! [A2: set_Pr4532377907799695533_nat_o,P: set_Pr4532377907799695533_nat_o > $o] :
% 0.30/0.64        ( ( finite3252695134891459830_nat_o @ A2 )
% 0.30/0.64       => ( ( P @ A2 )
% 0.30/0.64         => ( ! [A6: produc3658429121746597890et_nat > $o,A8: set_Pr4532377907799695533_nat_o] :
% 0.30/0.64                ( ( finite3252695134891459830_nat_o @ A8 )
% 0.30/0.64               => ( ( member6576561426505652726_nat_o @ A6 @ A8 )
% 0.30/0.64                 => ( ( P @ A8 )
% 0.30/0.64                   => ( P @ ( minus_1801376950450012436_nat_o @ A8 @ ( insert5175938949040314269_nat_o @ A6 @ bot_bo7824918357723582233_nat_o ) ) ) ) ) )
% 0.30/0.64           => ( P @ bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_empty_induct
% 0.30/0.64  thf(fact_8881_finite__empty__induct,axiom,
% 0.30/0.64      ! [A2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 0.30/0.64        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.64       => ( ( P @ A2 )
% 0.30/0.64         => ( ! [A6: product_prod_nat_nat,A8: set_Pr1261947904930325089at_nat] :
% 0.30/0.64                ( ( finite6177210948735845034at_nat @ A8 )
% 0.30/0.64               => ( ( member8440522571783428010at_nat @ A6 @ A8 )
% 0.30/0.64                 => ( ( P @ A8 )
% 0.30/0.64                   => ( P @ ( minus_1356011639430497352at_nat @ A8 @ ( insert8211810215607154385at_nat @ A6 @ bot_bo2099793752762293965at_nat ) ) ) ) ) )
% 0.30/0.64           => ( P @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_empty_induct
% 0.30/0.64  thf(fact_8882_finite__empty__induct,axiom,
% 0.30/0.64      ! [A2: set_o,P: set_o > $o] :
% 0.30/0.64        ( ( finite_finite_o @ A2 )
% 0.30/0.64       => ( ( P @ A2 )
% 0.30/0.64         => ( ! [A6: $o,A8: set_o] :
% 0.30/0.64                ( ( finite_finite_o @ A8 )
% 0.30/0.64               => ( ( member_o @ A6 @ A8 )
% 0.30/0.64                 => ( ( P @ A8 )
% 0.30/0.64                   => ( P @ ( minus_minus_set_o @ A8 @ ( insert_o @ A6 @ bot_bot_set_o ) ) ) ) ) )
% 0.30/0.64           => ( P @ bot_bot_set_o ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_empty_induct
% 0.30/0.64  thf(fact_8883_finite__empty__induct,axiom,
% 0.30/0.64      ! [A2: set_int,P: set_int > $o] :
% 0.30/0.64        ( ( finite_finite_int @ A2 )
% 0.30/0.64       => ( ( P @ A2 )
% 0.30/0.64         => ( ! [A6: int,A8: set_int] :
% 0.30/0.64                ( ( finite_finite_int @ A8 )
% 0.30/0.64               => ( ( member_int @ A6 @ A8 )
% 0.30/0.64                 => ( ( P @ A8 )
% 0.30/0.64                   => ( P @ ( minus_minus_set_int @ A8 @ ( insert_int @ A6 @ bot_bot_set_int ) ) ) ) ) )
% 0.30/0.64           => ( P @ bot_bot_set_int ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_empty_induct
% 0.30/0.64  thf(fact_8884_finite__empty__induct,axiom,
% 0.30/0.64      ! [A2: set_nat,P: set_nat > $o] :
% 0.30/0.64        ( ( finite_finite_nat @ A2 )
% 0.30/0.64       => ( ( P @ A2 )
% 0.30/0.64         => ( ! [A6: nat,A8: set_nat] :
% 0.30/0.64                ( ( finite_finite_nat @ A8 )
% 0.30/0.64               => ( ( member_nat @ A6 @ A8 )
% 0.30/0.64                 => ( ( P @ A8 )
% 0.30/0.64                   => ( P @ ( minus_minus_set_nat @ A8 @ ( insert_nat @ A6 @ bot_bot_set_nat ) ) ) ) ) )
% 0.30/0.64           => ( P @ bot_bot_set_nat ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_empty_induct
% 0.30/0.64  thf(fact_8885_finite__remove__induct,axiom,
% 0.30/0.64      ! [B2: set_Pr4329608150637261639at_nat,P: set_Pr4329608150637261639at_nat > $o] :
% 0.30/0.64        ( ( finite4343798906461161616at_nat @ B2 )
% 0.30/0.64       => ( ( P @ bot_bo228742789529271731at_nat )
% 0.30/0.64         => ( ! [A8: set_Pr4329608150637261639at_nat] :
% 0.30/0.64                ( ( finite4343798906461161616at_nat @ A8 )
% 0.30/0.64               => ( ( A8 != bot_bo228742789529271731at_nat )
% 0.30/0.64                 => ( ( ord_le1268244103169919719at_nat @ A8 @ B2 )
% 0.30/0.64                   => ( ! [X5: produc3843707927480180839at_nat] :
% 0.30/0.64                          ( ( member8757157785044589968at_nat @ X5 @ A8 )
% 0.30/0.64                         => ( P @ ( minus_3314409938677909166at_nat @ A8 @ ( insert9069300056098147895at_nat @ X5 @ bot_bo228742789529271731at_nat ) ) ) )
% 0.30/0.64                     => ( P @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ B2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_remove_induct
% 0.30/0.64  thf(fact_8886_finite__remove__induct,axiom,
% 0.30/0.64      ! [B2: set_se6260736226359567993nt_int,P: set_se6260736226359567993nt_int > $o] :
% 0.30/0.64        ( ( finite8744585540193469122nt_int @ B2 )
% 0.30/0.64       => ( ( P @ bot_bo1488462491386950373nt_int )
% 0.30/0.64         => ( ! [A8: set_se6260736226359567993nt_int] :
% 0.30/0.64                ( ( finite8744585540193469122nt_int @ A8 )
% 0.30/0.64               => ( ( A8 != bot_bo1488462491386950373nt_int )
% 0.30/0.64                 => ( ( ord_le483042692224249369nt_int @ A8 @ B2 )
% 0.30/0.64                   => ( ! [X5: set_Pr958786334691620121nt_int] :
% 0.30/0.64                          ( ( member2340774599025711042nt_int @ X5 @ A8 )
% 0.30/0.64                         => ( P @ ( minus_2612819937483484256nt_int @ A8 @ ( insert8897473484851387113nt_int @ X5 @ bot_bo1488462491386950373nt_int ) ) ) )
% 0.30/0.64                     => ( P @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ B2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_remove_induct
% 0.30/0.64  thf(fact_8887_finite__remove__induct,axiom,
% 0.30/0.64      ! [B2: set_set_nat,P: set_set_nat > $o] :
% 0.30/0.64        ( ( finite1152437895449049373et_nat @ B2 )
% 0.30/0.64       => ( ( P @ bot_bot_set_set_nat )
% 0.30/0.64         => ( ! [A8: set_set_nat] :
% 0.30/0.64                ( ( finite1152437895449049373et_nat @ A8 )
% 0.30/0.64               => ( ( A8 != bot_bot_set_set_nat )
% 0.30/0.64                 => ( ( ord_le6893508408891458716et_nat @ A8 @ B2 )
% 0.30/0.64                   => ( ! [X5: set_nat] :
% 0.30/0.64                          ( ( member_set_nat @ X5 @ A8 )
% 0.30/0.64                         => ( P @ ( minus_2163939370556025621et_nat @ A8 @ ( insert_set_nat @ X5 @ bot_bot_set_set_nat ) ) ) )
% 0.30/0.64                     => ( P @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ B2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_remove_induct
% 0.30/0.64  thf(fact_8888_finite__remove__induct,axiom,
% 0.30/0.64      ! [B2: set_Pr4532377907799695533_nat_o,P: set_Pr4532377907799695533_nat_o > $o] :
% 0.30/0.64        ( ( finite3252695134891459830_nat_o @ B2 )
% 0.30/0.64       => ( ( P @ bot_bo7824918357723582233_nat_o )
% 0.30/0.64         => ( ! [A8: set_Pr4532377907799695533_nat_o] :
% 0.30/0.64                ( ( finite3252695134891459830_nat_o @ A8 )
% 0.30/0.64               => ( ( A8 != bot_bo7824918357723582233_nat_o )
% 0.30/0.64                 => ( ( ord_le2965882846123202637_nat_o @ A8 @ B2 )
% 0.30/0.64                   => ( ! [X5: produc3658429121746597890et_nat > $o] :
% 0.30/0.64                          ( ( member6576561426505652726_nat_o @ X5 @ A8 )
% 0.30/0.64                         => ( P @ ( minus_1801376950450012436_nat_o @ A8 @ ( insert5175938949040314269_nat_o @ X5 @ bot_bo7824918357723582233_nat_o ) ) ) )
% 0.30/0.64                     => ( P @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ B2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_remove_induct
% 0.30/0.64  thf(fact_8889_finite__remove__induct,axiom,
% 0.30/0.64      ! [B2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 0.30/0.64        ( ( finite6177210948735845034at_nat @ B2 )
% 0.30/0.64       => ( ( P @ bot_bo2099793752762293965at_nat )
% 0.30/0.64         => ( ! [A8: set_Pr1261947904930325089at_nat] :
% 0.30/0.64                ( ( finite6177210948735845034at_nat @ A8 )
% 0.30/0.64               => ( ( A8 != bot_bo2099793752762293965at_nat )
% 0.30/0.64                 => ( ( ord_le3146513528884898305at_nat @ A8 @ B2 )
% 0.30/0.64                   => ( ! [X5: product_prod_nat_nat] :
% 0.30/0.64                          ( ( member8440522571783428010at_nat @ X5 @ A8 )
% 0.30/0.64                         => ( P @ ( minus_1356011639430497352at_nat @ A8 @ ( insert8211810215607154385at_nat @ X5 @ bot_bo2099793752762293965at_nat ) ) ) )
% 0.30/0.64                     => ( P @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ B2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_remove_induct
% 0.30/0.64  thf(fact_8890_finite__remove__induct,axiom,
% 0.30/0.64      ! [B2: set_o,P: set_o > $o] :
% 0.30/0.64        ( ( finite_finite_o @ B2 )
% 0.30/0.64       => ( ( P @ bot_bot_set_o )
% 0.30/0.64         => ( ! [A8: set_o] :
% 0.30/0.64                ( ( finite_finite_o @ A8 )
% 0.30/0.64               => ( ( A8 != bot_bot_set_o )
% 0.30/0.64                 => ( ( ord_less_eq_set_o @ A8 @ B2 )
% 0.30/0.64                   => ( ! [X5: $o] :
% 0.30/0.64                          ( ( member_o @ X5 @ A8 )
% 0.30/0.64                         => ( P @ ( minus_minus_set_o @ A8 @ ( insert_o @ X5 @ bot_bot_set_o ) ) ) )
% 0.30/0.64                     => ( P @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ B2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_remove_induct
% 0.30/0.64  thf(fact_8891_finite__remove__induct,axiom,
% 0.30/0.64      ! [B2: set_int,P: set_int > $o] :
% 0.30/0.64        ( ( finite_finite_int @ B2 )
% 0.30/0.64       => ( ( P @ bot_bot_set_int )
% 0.30/0.64         => ( ! [A8: set_int] :
% 0.30/0.64                ( ( finite_finite_int @ A8 )
% 0.30/0.64               => ( ( A8 != bot_bot_set_int )
% 0.30/0.64                 => ( ( ord_less_eq_set_int @ A8 @ B2 )
% 0.30/0.64                   => ( ! [X5: int] :
% 0.30/0.64                          ( ( member_int @ X5 @ A8 )
% 0.30/0.64                         => ( P @ ( minus_minus_set_int @ A8 @ ( insert_int @ X5 @ bot_bot_set_int ) ) ) )
% 0.30/0.64                     => ( P @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ B2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_remove_induct
% 0.30/0.64  thf(fact_8892_finite__remove__induct,axiom,
% 0.30/0.64      ! [B2: set_nat,P: set_nat > $o] :
% 0.30/0.64        ( ( finite_finite_nat @ B2 )
% 0.30/0.64       => ( ( P @ bot_bot_set_nat )
% 0.30/0.64         => ( ! [A8: set_nat] :
% 0.30/0.64                ( ( finite_finite_nat @ A8 )
% 0.30/0.64               => ( ( A8 != bot_bot_set_nat )
% 0.30/0.64                 => ( ( ord_less_eq_set_nat @ A8 @ B2 )
% 0.30/0.64                   => ( ! [X5: nat] :
% 0.30/0.64                          ( ( member_nat @ X5 @ A8 )
% 0.30/0.64                         => ( P @ ( minus_minus_set_nat @ A8 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) )
% 0.30/0.64                     => ( P @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ B2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_remove_induct
% 0.30/0.64  thf(fact_8893_remove__induct,axiom,
% 0.30/0.64      ! [P: set_Pr4329608150637261639at_nat > $o,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.64        ( ( P @ bot_bo228742789529271731at_nat )
% 0.30/0.64       => ( ( ~ ( finite4343798906461161616at_nat @ B2 )
% 0.30/0.64           => ( P @ B2 ) )
% 0.30/0.64         => ( ! [A8: set_Pr4329608150637261639at_nat] :
% 0.30/0.64                ( ( finite4343798906461161616at_nat @ A8 )
% 0.30/0.64               => ( ( A8 != bot_bo228742789529271731at_nat )
% 0.30/0.64                 => ( ( ord_le1268244103169919719at_nat @ A8 @ B2 )
% 0.30/0.64                   => ( ! [X5: produc3843707927480180839at_nat] :
% 0.30/0.64                          ( ( member8757157785044589968at_nat @ X5 @ A8 )
% 0.30/0.64                         => ( P @ ( minus_3314409938677909166at_nat @ A8 @ ( insert9069300056098147895at_nat @ X5 @ bot_bo228742789529271731at_nat ) ) ) )
% 0.30/0.64                     => ( P @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ B2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % remove_induct
% 0.30/0.64  thf(fact_8894_remove__induct,axiom,
% 0.30/0.64      ! [P: set_se6260736226359567993nt_int > $o,B2: set_se6260736226359567993nt_int] :
% 0.30/0.64        ( ( P @ bot_bo1488462491386950373nt_int )
% 0.30/0.64       => ( ( ~ ( finite8744585540193469122nt_int @ B2 )
% 0.30/0.64           => ( P @ B2 ) )
% 0.30/0.64         => ( ! [A8: set_se6260736226359567993nt_int] :
% 0.30/0.64                ( ( finite8744585540193469122nt_int @ A8 )
% 0.30/0.64               => ( ( A8 != bot_bo1488462491386950373nt_int )
% 0.30/0.64                 => ( ( ord_le483042692224249369nt_int @ A8 @ B2 )
% 0.30/0.64                   => ( ! [X5: set_Pr958786334691620121nt_int] :
% 0.30/0.64                          ( ( member2340774599025711042nt_int @ X5 @ A8 )
% 0.30/0.64                         => ( P @ ( minus_2612819937483484256nt_int @ A8 @ ( insert8897473484851387113nt_int @ X5 @ bot_bo1488462491386950373nt_int ) ) ) )
% 0.30/0.64                     => ( P @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ B2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % remove_induct
% 0.30/0.64  thf(fact_8895_remove__induct,axiom,
% 0.30/0.64      ! [P: set_set_nat > $o,B2: set_set_nat] :
% 0.30/0.64        ( ( P @ bot_bot_set_set_nat )
% 0.30/0.64       => ( ( ~ ( finite1152437895449049373et_nat @ B2 )
% 0.30/0.64           => ( P @ B2 ) )
% 0.30/0.64         => ( ! [A8: set_set_nat] :
% 0.30/0.64                ( ( finite1152437895449049373et_nat @ A8 )
% 0.30/0.64               => ( ( A8 != bot_bot_set_set_nat )
% 0.30/0.64                 => ( ( ord_le6893508408891458716et_nat @ A8 @ B2 )
% 0.30/0.64                   => ( ! [X5: set_nat] :
% 0.30/0.64                          ( ( member_set_nat @ X5 @ A8 )
% 0.30/0.64                         => ( P @ ( minus_2163939370556025621et_nat @ A8 @ ( insert_set_nat @ X5 @ bot_bot_set_set_nat ) ) ) )
% 0.30/0.64                     => ( P @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ B2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % remove_induct
% 0.30/0.64  thf(fact_8896_remove__induct,axiom,
% 0.30/0.64      ! [P: set_Pr4532377907799695533_nat_o > $o,B2: set_Pr4532377907799695533_nat_o] :
% 0.30/0.64        ( ( P @ bot_bo7824918357723582233_nat_o )
% 0.30/0.64       => ( ( ~ ( finite3252695134891459830_nat_o @ B2 )
% 0.30/0.64           => ( P @ B2 ) )
% 0.30/0.64         => ( ! [A8: set_Pr4532377907799695533_nat_o] :
% 0.30/0.64                ( ( finite3252695134891459830_nat_o @ A8 )
% 0.30/0.64               => ( ( A8 != bot_bo7824918357723582233_nat_o )
% 0.30/0.64                 => ( ( ord_le2965882846123202637_nat_o @ A8 @ B2 )
% 0.30/0.64                   => ( ! [X5: produc3658429121746597890et_nat > $o] :
% 0.30/0.64                          ( ( member6576561426505652726_nat_o @ X5 @ A8 )
% 0.30/0.64                         => ( P @ ( minus_1801376950450012436_nat_o @ A8 @ ( insert5175938949040314269_nat_o @ X5 @ bot_bo7824918357723582233_nat_o ) ) ) )
% 0.30/0.64                     => ( P @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ B2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % remove_induct
% 0.30/0.64  thf(fact_8897_remove__induct,axiom,
% 0.30/0.64      ! [P: set_Pr1261947904930325089at_nat > $o,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.64        ( ( P @ bot_bo2099793752762293965at_nat )
% 0.30/0.64       => ( ( ~ ( finite6177210948735845034at_nat @ B2 )
% 0.30/0.64           => ( P @ B2 ) )
% 0.30/0.64         => ( ! [A8: set_Pr1261947904930325089at_nat] :
% 0.30/0.64                ( ( finite6177210948735845034at_nat @ A8 )
% 0.30/0.64               => ( ( A8 != bot_bo2099793752762293965at_nat )
% 0.30/0.64                 => ( ( ord_le3146513528884898305at_nat @ A8 @ B2 )
% 0.30/0.64                   => ( ! [X5: product_prod_nat_nat] :
% 0.30/0.64                          ( ( member8440522571783428010at_nat @ X5 @ A8 )
% 0.30/0.64                         => ( P @ ( minus_1356011639430497352at_nat @ A8 @ ( insert8211810215607154385at_nat @ X5 @ bot_bo2099793752762293965at_nat ) ) ) )
% 0.30/0.64                     => ( P @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ B2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % remove_induct
% 0.30/0.64  thf(fact_8898_remove__induct,axiom,
% 0.30/0.64      ! [P: set_o > $o,B2: set_o] :
% 0.30/0.64        ( ( P @ bot_bot_set_o )
% 0.30/0.64       => ( ( ~ ( finite_finite_o @ B2 )
% 0.30/0.64           => ( P @ B2 ) )
% 0.30/0.64         => ( ! [A8: set_o] :
% 0.30/0.64                ( ( finite_finite_o @ A8 )
% 0.30/0.64               => ( ( A8 != bot_bot_set_o )
% 0.30/0.64                 => ( ( ord_less_eq_set_o @ A8 @ B2 )
% 0.30/0.64                   => ( ! [X5: $o] :
% 0.30/0.64                          ( ( member_o @ X5 @ A8 )
% 0.30/0.64                         => ( P @ ( minus_minus_set_o @ A8 @ ( insert_o @ X5 @ bot_bot_set_o ) ) ) )
% 0.30/0.64                     => ( P @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ B2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % remove_induct
% 0.30/0.64  thf(fact_8899_remove__induct,axiom,
% 0.30/0.64      ! [P: set_int > $o,B2: set_int] :
% 0.30/0.64        ( ( P @ bot_bot_set_int )
% 0.30/0.64       => ( ( ~ ( finite_finite_int @ B2 )
% 0.30/0.64           => ( P @ B2 ) )
% 0.30/0.64         => ( ! [A8: set_int] :
% 0.30/0.64                ( ( finite_finite_int @ A8 )
% 0.30/0.64               => ( ( A8 != bot_bot_set_int )
% 0.30/0.64                 => ( ( ord_less_eq_set_int @ A8 @ B2 )
% 0.30/0.64                   => ( ! [X5: int] :
% 0.30/0.64                          ( ( member_int @ X5 @ A8 )
% 0.30/0.64                         => ( P @ ( minus_minus_set_int @ A8 @ ( insert_int @ X5 @ bot_bot_set_int ) ) ) )
% 0.30/0.64                     => ( P @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ B2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % remove_induct
% 0.30/0.64  thf(fact_8900_remove__induct,axiom,
% 0.30/0.64      ! [P: set_nat > $o,B2: set_nat] :
% 0.30/0.64        ( ( P @ bot_bot_set_nat )
% 0.30/0.64       => ( ( ~ ( finite_finite_nat @ B2 )
% 0.30/0.64           => ( P @ B2 ) )
% 0.30/0.64         => ( ! [A8: set_nat] :
% 0.30/0.64                ( ( finite_finite_nat @ A8 )
% 0.30/0.64               => ( ( A8 != bot_bot_set_nat )
% 0.30/0.64                 => ( ( ord_less_eq_set_nat @ A8 @ B2 )
% 0.30/0.64                   => ( ! [X5: nat] :
% 0.30/0.64                          ( ( member_nat @ X5 @ A8 )
% 0.30/0.64                         => ( P @ ( minus_minus_set_nat @ A8 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) )
% 0.30/0.64                     => ( P @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ B2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % remove_induct
% 0.30/0.64  thf(fact_8901_finite__induct__select,axiom,
% 0.30/0.64      ! [S: set_Pr4329608150637261639at_nat,P: set_Pr4329608150637261639at_nat > $o] :
% 0.30/0.64        ( ( finite4343798906461161616at_nat @ S )
% 0.30/0.64       => ( ( P @ bot_bo228742789529271731at_nat )
% 0.30/0.64         => ( ! [T5: set_Pr4329608150637261639at_nat] :
% 0.30/0.64                ( ( ord_le2604355607129572851at_nat @ T5 @ S )
% 0.30/0.64               => ( ( P @ T5 )
% 0.30/0.64                 => ? [X5: produc3843707927480180839at_nat] :
% 0.30/0.64                      ( ( member8757157785044589968at_nat @ X5 @ ( minus_3314409938677909166at_nat @ S @ T5 ) )
% 0.30/0.64                      & ( P @ ( insert9069300056098147895at_nat @ X5 @ T5 ) ) ) ) )
% 0.30/0.64           => ( P @ S ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_induct_select
% 0.30/0.64  thf(fact_8902_finite__induct__select,axiom,
% 0.30/0.64      ! [S: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 0.30/0.64        ( ( finite6177210948735845034at_nat @ S )
% 0.30/0.64       => ( ( P @ bot_bo2099793752762293965at_nat )
% 0.30/0.64         => ( ! [T5: set_Pr1261947904930325089at_nat] :
% 0.30/0.64                ( ( ord_le7866589430770878221at_nat @ T5 @ S )
% 0.30/0.64               => ( ( P @ T5 )
% 0.30/0.64                 => ? [X5: product_prod_nat_nat] :
% 0.30/0.64                      ( ( member8440522571783428010at_nat @ X5 @ ( minus_1356011639430497352at_nat @ S @ T5 ) )
% 0.30/0.64                      & ( P @ ( insert8211810215607154385at_nat @ X5 @ T5 ) ) ) ) )
% 0.30/0.64           => ( P @ S ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_induct_select
% 0.30/0.64  thf(fact_8903_finite__induct__select,axiom,
% 0.30/0.64      ! [S: set_o,P: set_o > $o] :
% 0.30/0.64        ( ( finite_finite_o @ S )
% 0.30/0.64       => ( ( P @ bot_bot_set_o )
% 0.30/0.64         => ( ! [T5: set_o] :
% 0.30/0.64                ( ( ord_less_set_o @ T5 @ S )
% 0.30/0.64               => ( ( P @ T5 )
% 0.30/0.64                 => ? [X5: $o] :
% 0.30/0.64                      ( ( member_o @ X5 @ ( minus_minus_set_o @ S @ T5 ) )
% 0.30/0.64                      & ( P @ ( insert_o @ X5 @ T5 ) ) ) ) )
% 0.30/0.64           => ( P @ S ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_induct_select
% 0.30/0.64  thf(fact_8904_finite__induct__select,axiom,
% 0.30/0.64      ! [S: set_int,P: set_int > $o] :
% 0.30/0.64        ( ( finite_finite_int @ S )
% 0.30/0.64       => ( ( P @ bot_bot_set_int )
% 0.30/0.64         => ( ! [T5: set_int] :
% 0.30/0.64                ( ( ord_less_set_int @ T5 @ S )
% 0.30/0.64               => ( ( P @ T5 )
% 0.30/0.64                 => ? [X5: int] :
% 0.30/0.64                      ( ( member_int @ X5 @ ( minus_minus_set_int @ S @ T5 ) )
% 0.30/0.64                      & ( P @ ( insert_int @ X5 @ T5 ) ) ) ) )
% 0.30/0.64           => ( P @ S ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_induct_select
% 0.30/0.64  thf(fact_8905_finite__induct__select,axiom,
% 0.30/0.64      ! [S: set_nat,P: set_nat > $o] :
% 0.30/0.64        ( ( finite_finite_nat @ S )
% 0.30/0.64       => ( ( P @ bot_bot_set_nat )
% 0.30/0.64         => ( ! [T5: set_nat] :
% 0.30/0.64                ( ( ord_less_set_nat @ T5 @ S )
% 0.30/0.64               => ( ( P @ T5 )
% 0.30/0.64                 => ? [X5: nat] :
% 0.30/0.64                      ( ( member_nat @ X5 @ ( minus_minus_set_nat @ S @ T5 ) )
% 0.30/0.64                      & ( P @ ( insert_nat @ X5 @ T5 ) ) ) ) )
% 0.30/0.64           => ( P @ S ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_induct_select
% 0.30/0.64  thf(fact_8906_finite__option__UNIV,axiom,
% 0.30/0.64      ( ( finite6732403688824079472at_nat @ top_to3251141154256563319at_nat )
% 0.30/0.64      = ( finite6177210948735845034at_nat @ top_to4669805908274784177at_nat ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_option_UNIV
% 0.30/0.64  thf(fact_8907_finite__option__UNIV,axiom,
% 0.30/0.64      ( ( finite7857960318081769799st_nat @ top_to1113147461230312982st_nat )
% 0.30/0.64      = ( finite8100373058378681591st_nat @ top_top_set_list_nat ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_option_UNIV
% 0.30/0.64  thf(fact_8908_finite__option__UNIV,axiom,
% 0.30/0.64      ( ( finite4093902646404507527tion_o @ top_top_set_option_o )
% 0.30/0.64      = ( finite_finite_o @ top_top_set_o ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_option_UNIV
% 0.30/0.64  thf(fact_8909_finite__option__UNIV,axiom,
% 0.30/0.64      ( ( finite2014924581280026175on_rat @ top_to2540212048668676366on_rat )
% 0.30/0.64      = ( finite_finite_rat @ top_top_set_rat ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_option_UNIV
% 0.30/0.64  thf(fact_8910_finite__option__UNIV,axiom,
% 0.30/0.64      ( ( finite5523153139673422903on_nat @ top_to8920198386146353926on_nat )
% 0.30/0.64      = ( finite_finite_nat @ top_top_set_nat ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_option_UNIV
% 0.30/0.64  thf(fact_8911_finite__option__UNIV,axiom,
% 0.30/0.64      ( ( finite1345302120164226195on_int @ top_to6430115241214627170on_int )
% 0.30/0.64      = ( finite_finite_int @ top_top_set_int ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_option_UNIV
% 0.30/0.64  thf(fact_8912_diff__preserves__multiset,axiom,
% 0.30/0.64      ! [M4: set_Pr958786334691620121nt_int > nat,N4: set_Pr958786334691620121nt_int > nat] :
% 0.30/0.64        ( ( finite8744585540193469122nt_int
% 0.30/0.64          @ ( collec5210948495886036740nt_int
% 0.30/0.64            @ ^ [X3: set_Pr958786334691620121nt_int] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 0.30/0.64       => ( finite8744585540193469122nt_int
% 0.30/0.64          @ ( collec5210948495886036740nt_int
% 0.30/0.64            @ ^ [X3: set_Pr958786334691620121nt_int] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M4 @ X3 ) @ ( N4 @ X3 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % diff_preserves_multiset
% 0.30/0.64  thf(fact_8913_diff__preserves__multiset,axiom,
% 0.30/0.64      ! [M4: set_nat > nat,N4: set_nat > nat] :
% 0.30/0.64        ( ( finite1152437895449049373et_nat
% 0.30/0.64          @ ( collect_set_nat
% 0.30/0.64            @ ^ [X3: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 0.30/0.64       => ( finite1152437895449049373et_nat
% 0.30/0.64          @ ( collect_set_nat
% 0.30/0.64            @ ^ [X3: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M4 @ X3 ) @ ( N4 @ X3 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % diff_preserves_multiset
% 0.30/0.64  thf(fact_8914_diff__preserves__multiset,axiom,
% 0.30/0.64      ! [M4: ( produc3658429121746597890et_nat > $o ) > nat,N4: ( produc3658429121746597890et_nat > $o ) > nat] :
% 0.30/0.64        ( ( finite3252695134891459830_nat_o
% 0.30/0.64          @ ( collec939566748876313656_nat_o
% 0.30/0.64            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 0.30/0.64       => ( finite3252695134891459830_nat_o
% 0.30/0.64          @ ( collec939566748876313656_nat_o
% 0.30/0.64            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M4 @ X3 ) @ ( N4 @ X3 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % diff_preserves_multiset
% 0.30/0.64  thf(fact_8915_diff__preserves__multiset,axiom,
% 0.30/0.64      ! [M4: nat > nat,N4: nat > nat] :
% 0.30/0.64        ( ( finite_finite_nat
% 0.30/0.64          @ ( collect_nat
% 0.30/0.64            @ ^ [X3: nat] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 0.30/0.64       => ( finite_finite_nat
% 0.30/0.64          @ ( collect_nat
% 0.30/0.64            @ ^ [X3: nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M4 @ X3 ) @ ( N4 @ X3 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % diff_preserves_multiset
% 0.30/0.64  thf(fact_8916_diff__preserves__multiset,axiom,
% 0.30/0.64      ! [M4: int > nat,N4: int > nat] :
% 0.30/0.64        ( ( finite_finite_int
% 0.30/0.64          @ ( collect_int
% 0.30/0.64            @ ^ [X3: int] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 0.30/0.64       => ( finite_finite_int
% 0.30/0.64          @ ( collect_int
% 0.30/0.64            @ ^ [X3: int] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M4 @ X3 ) @ ( N4 @ X3 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % diff_preserves_multiset
% 0.30/0.64  thf(fact_8917_diff__preserves__multiset,axiom,
% 0.30/0.64      ! [M4: product_prod_nat_nat > nat,N4: product_prod_nat_nat > nat] :
% 0.30/0.64        ( ( finite6177210948735845034at_nat
% 0.30/0.64          @ ( collec3392354462482085612at_nat
% 0.30/0.64            @ ^ [X3: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 0.30/0.64       => ( finite6177210948735845034at_nat
% 0.30/0.64          @ ( collec3392354462482085612at_nat
% 0.30/0.64            @ ^ [X3: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M4 @ X3 ) @ ( N4 @ X3 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % diff_preserves_multiset
% 0.30/0.64  thf(fact_8918_add__mset__in__multiset,axiom,
% 0.30/0.64      ! [M4: set_Pr958786334691620121nt_int > nat,A: set_Pr958786334691620121nt_int] :
% 0.30/0.64        ( ( finite8744585540193469122nt_int
% 0.30/0.64          @ ( collec5210948495886036740nt_int
% 0.30/0.64            @ ^ [X3: set_Pr958786334691620121nt_int] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 0.30/0.64       => ( finite8744585540193469122nt_int
% 0.30/0.64          @ ( collec5210948495886036740nt_int
% 0.30/0.64            @ ^ [X3: set_Pr958786334691620121nt_int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X3 = A ) @ ( suc @ ( M4 @ X3 ) ) @ ( M4 @ X3 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % add_mset_in_multiset
% 0.30/0.64  thf(fact_8919_add__mset__in__multiset,axiom,
% 0.30/0.64      ! [M4: set_nat > nat,A: set_nat] :
% 0.30/0.64        ( ( finite1152437895449049373et_nat
% 0.30/0.64          @ ( collect_set_nat
% 0.30/0.64            @ ^ [X3: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 0.30/0.64       => ( finite1152437895449049373et_nat
% 0.30/0.64          @ ( collect_set_nat
% 0.30/0.64            @ ^ [X3: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X3 = A ) @ ( suc @ ( M4 @ X3 ) ) @ ( M4 @ X3 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % add_mset_in_multiset
% 0.30/0.64  thf(fact_8920_add__mset__in__multiset,axiom,
% 0.30/0.64      ! [M4: ( produc3658429121746597890et_nat > $o ) > nat,A: produc3658429121746597890et_nat > $o] :
% 0.30/0.64        ( ( finite3252695134891459830_nat_o
% 0.30/0.64          @ ( collec939566748876313656_nat_o
% 0.30/0.64            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 0.30/0.64       => ( finite3252695134891459830_nat_o
% 0.30/0.64          @ ( collec939566748876313656_nat_o
% 0.30/0.64            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X3 = A ) @ ( suc @ ( M4 @ X3 ) ) @ ( M4 @ X3 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % add_mset_in_multiset
% 0.30/0.64  thf(fact_8921_add__mset__in__multiset,axiom,
% 0.30/0.64      ! [M4: nat > nat,A: nat] :
% 0.30/0.64        ( ( finite_finite_nat
% 0.30/0.64          @ ( collect_nat
% 0.30/0.64            @ ^ [X3: nat] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 0.30/0.64       => ( finite_finite_nat
% 0.30/0.64          @ ( collect_nat
% 0.30/0.64            @ ^ [X3: nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X3 = A ) @ ( suc @ ( M4 @ X3 ) ) @ ( M4 @ X3 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % add_mset_in_multiset
% 0.30/0.64  thf(fact_8922_add__mset__in__multiset,axiom,
% 0.30/0.64      ! [M4: int > nat,A: int] :
% 0.30/0.64        ( ( finite_finite_int
% 0.30/0.64          @ ( collect_int
% 0.30/0.64            @ ^ [X3: int] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 0.30/0.64       => ( finite_finite_int
% 0.30/0.64          @ ( collect_int
% 0.30/0.64            @ ^ [X3: int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X3 = A ) @ ( suc @ ( M4 @ X3 ) ) @ ( M4 @ X3 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % add_mset_in_multiset
% 0.30/0.64  thf(fact_8923_add__mset__in__multiset,axiom,
% 0.30/0.64      ! [M4: product_prod_nat_nat > nat,A: product_prod_nat_nat] :
% 0.30/0.64        ( ( finite6177210948735845034at_nat
% 0.30/0.64          @ ( collec3392354462482085612at_nat
% 0.30/0.64            @ ^ [X3: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 0.30/0.64       => ( finite6177210948735845034at_nat
% 0.30/0.64          @ ( collec3392354462482085612at_nat
% 0.30/0.64            @ ^ [X3: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X3 = A ) @ ( suc @ ( M4 @ X3 ) ) @ ( M4 @ X3 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % add_mset_in_multiset
% 0.30/0.64  thf(fact_8924_finite__linorder__min__induct,axiom,
% 0.30/0.64      ! [A2: set_o,P: set_o > $o] :
% 0.30/0.64        ( ( finite_finite_o @ A2 )
% 0.30/0.64       => ( ( P @ bot_bot_set_o )
% 0.30/0.64         => ( ! [B6: $o,A8: set_o] :
% 0.30/0.64                ( ( finite_finite_o @ A8 )
% 0.30/0.64               => ( ! [X5: $o] :
% 0.30/0.64                      ( ( member_o @ X5 @ A8 )
% 0.30/0.64                     => ( ord_less_o @ B6 @ X5 ) )
% 0.30/0.64                 => ( ( P @ A8 )
% 0.30/0.64                   => ( P @ ( insert_o @ B6 @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ A2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_linorder_min_induct
% 0.30/0.64  thf(fact_8925_finite__linorder__min__induct,axiom,
% 0.30/0.64      ! [A2: set_literal,P: set_literal > $o] :
% 0.30/0.64        ( ( finite5847741373460823677iteral @ A2 )
% 0.30/0.64       => ( ( P @ bot_bot_set_literal )
% 0.30/0.64         => ( ! [B6: literal,A8: set_literal] :
% 0.30/0.64                ( ( finite5847741373460823677iteral @ A8 )
% 0.30/0.64               => ( ! [X5: literal] :
% 0.30/0.64                      ( ( member_literal @ X5 @ A8 )
% 0.30/0.64                     => ( ord_less_literal @ B6 @ X5 ) )
% 0.30/0.64                 => ( ( P @ A8 )
% 0.30/0.64                   => ( P @ ( insert_literal @ B6 @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ A2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_linorder_min_induct
% 0.30/0.64  thf(fact_8926_finite__linorder__min__induct,axiom,
% 0.30/0.64      ! [A2: set_rat,P: set_rat > $o] :
% 0.30/0.64        ( ( finite_finite_rat @ A2 )
% 0.30/0.64       => ( ( P @ bot_bot_set_rat )
% 0.30/0.64         => ( ! [B6: rat,A8: set_rat] :
% 0.30/0.64                ( ( finite_finite_rat @ A8 )
% 0.30/0.64               => ( ! [X5: rat] :
% 0.30/0.64                      ( ( member_rat @ X5 @ A8 )
% 0.30/0.64                     => ( ord_less_rat @ B6 @ X5 ) )
% 0.30/0.64                 => ( ( P @ A8 )
% 0.30/0.64                   => ( P @ ( insert_rat @ B6 @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ A2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_linorder_min_induct
% 0.30/0.64  thf(fact_8927_finite__linorder__min__induct,axiom,
% 0.30/0.64      ! [A2: set_nat,P: set_nat > $o] :
% 0.30/0.64        ( ( finite_finite_nat @ A2 )
% 0.30/0.64       => ( ( P @ bot_bot_set_nat )
% 0.30/0.64         => ( ! [B6: nat,A8: set_nat] :
% 0.30/0.64                ( ( finite_finite_nat @ A8 )
% 0.30/0.64               => ( ! [X5: nat] :
% 0.30/0.64                      ( ( member_nat @ X5 @ A8 )
% 0.30/0.64                     => ( ord_less_nat @ B6 @ X5 ) )
% 0.30/0.64                 => ( ( P @ A8 )
% 0.30/0.64                   => ( P @ ( insert_nat @ B6 @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ A2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_linorder_min_induct
% 0.30/0.64  thf(fact_8928_finite__linorder__min__induct,axiom,
% 0.30/0.64      ! [A2: set_int,P: set_int > $o] :
% 0.30/0.64        ( ( finite_finite_int @ A2 )
% 0.30/0.64       => ( ( P @ bot_bot_set_int )
% 0.30/0.64         => ( ! [B6: int,A8: set_int] :
% 0.30/0.64                ( ( finite_finite_int @ A8 )
% 0.30/0.64               => ( ! [X5: int] :
% 0.30/0.64                      ( ( member_int @ X5 @ A8 )
% 0.30/0.64                     => ( ord_less_int @ B6 @ X5 ) )
% 0.30/0.64                 => ( ( P @ A8 )
% 0.30/0.64                   => ( P @ ( insert_int @ B6 @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ A2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_linorder_min_induct
% 0.30/0.64  thf(fact_8929_finite__linorder__max__induct,axiom,
% 0.30/0.64      ! [A2: set_o,P: set_o > $o] :
% 0.30/0.64        ( ( finite_finite_o @ A2 )
% 0.30/0.64       => ( ( P @ bot_bot_set_o )
% 0.30/0.64         => ( ! [B6: $o,A8: set_o] :
% 0.30/0.64                ( ( finite_finite_o @ A8 )
% 0.30/0.64               => ( ! [X5: $o] :
% 0.30/0.64                      ( ( member_o @ X5 @ A8 )
% 0.30/0.64                     => ( ord_less_o @ X5 @ B6 ) )
% 0.30/0.64                 => ( ( P @ A8 )
% 0.30/0.64                   => ( P @ ( insert_o @ B6 @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ A2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_linorder_max_induct
% 0.30/0.64  thf(fact_8930_finite__linorder__max__induct,axiom,
% 0.30/0.64      ! [A2: set_literal,P: set_literal > $o] :
% 0.30/0.64        ( ( finite5847741373460823677iteral @ A2 )
% 0.30/0.64       => ( ( P @ bot_bot_set_literal )
% 0.30/0.64         => ( ! [B6: literal,A8: set_literal] :
% 0.30/0.64                ( ( finite5847741373460823677iteral @ A8 )
% 0.30/0.64               => ( ! [X5: literal] :
% 0.30/0.64                      ( ( member_literal @ X5 @ A8 )
% 0.30/0.64                     => ( ord_less_literal @ X5 @ B6 ) )
% 0.30/0.64                 => ( ( P @ A8 )
% 0.30/0.64                   => ( P @ ( insert_literal @ B6 @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ A2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_linorder_max_induct
% 0.30/0.64  thf(fact_8931_finite__linorder__max__induct,axiom,
% 0.30/0.64      ! [A2: set_rat,P: set_rat > $o] :
% 0.30/0.64        ( ( finite_finite_rat @ A2 )
% 0.30/0.64       => ( ( P @ bot_bot_set_rat )
% 0.30/0.64         => ( ! [B6: rat,A8: set_rat] :
% 0.30/0.64                ( ( finite_finite_rat @ A8 )
% 0.30/0.64               => ( ! [X5: rat] :
% 0.30/0.64                      ( ( member_rat @ X5 @ A8 )
% 0.30/0.64                     => ( ord_less_rat @ X5 @ B6 ) )
% 0.30/0.64                 => ( ( P @ A8 )
% 0.30/0.64                   => ( P @ ( insert_rat @ B6 @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ A2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_linorder_max_induct
% 0.30/0.64  thf(fact_8932_finite__linorder__max__induct,axiom,
% 0.30/0.64      ! [A2: set_nat,P: set_nat > $o] :
% 0.30/0.64        ( ( finite_finite_nat @ A2 )
% 0.30/0.64       => ( ( P @ bot_bot_set_nat )
% 0.30/0.64         => ( ! [B6: nat,A8: set_nat] :
% 0.30/0.64                ( ( finite_finite_nat @ A8 )
% 0.30/0.64               => ( ! [X5: nat] :
% 0.30/0.64                      ( ( member_nat @ X5 @ A8 )
% 0.30/0.64                     => ( ord_less_nat @ X5 @ B6 ) )
% 0.30/0.64                 => ( ( P @ A8 )
% 0.30/0.64                   => ( P @ ( insert_nat @ B6 @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ A2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_linorder_max_induct
% 0.30/0.64  thf(fact_8933_finite__linorder__max__induct,axiom,
% 0.30/0.64      ! [A2: set_int,P: set_int > $o] :
% 0.30/0.64        ( ( finite_finite_int @ A2 )
% 0.30/0.64       => ( ( P @ bot_bot_set_int )
% 0.30/0.64         => ( ! [B6: int,A8: set_int] :
% 0.30/0.64                ( ( finite_finite_int @ A8 )
% 0.30/0.64               => ( ! [X5: int] :
% 0.30/0.64                      ( ( member_int @ X5 @ A8 )
% 0.30/0.64                     => ( ord_less_int @ X5 @ B6 ) )
% 0.30/0.64                 => ( ( P @ A8 )
% 0.30/0.64                   => ( P @ ( insert_int @ B6 @ A8 ) ) ) ) )
% 0.30/0.64           => ( P @ A2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_linorder_max_induct
% 0.30/0.64  thf(fact_8934_finite__ranking__induct,axiom,
% 0.30/0.64      ! [S: set_o,P: set_o > $o,F2: $o > rat] :
% 0.30/0.64        ( ( finite_finite_o @ S )
% 0.30/0.64       => ( ( P @ bot_bot_set_o )
% 0.30/0.64         => ( ! [X2: $o,S6: set_o] :
% 0.30/0.64                ( ( finite_finite_o @ S6 )
% 0.30/0.64               => ( ! [Y5: $o] :
% 0.30/0.64                      ( ( member_o @ Y5 @ S6 )
% 0.30/0.64                     => ( ord_less_eq_rat @ ( F2 @ Y5 ) @ ( F2 @ X2 ) ) )
% 0.30/0.64                 => ( ( P @ S6 )
% 0.30/0.64                   => ( P @ ( insert_o @ X2 @ S6 ) ) ) ) )
% 0.30/0.64           => ( P @ S ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_ranking_induct
% 0.30/0.64  thf(fact_8935_finite__ranking__induct,axiom,
% 0.30/0.64      ! [S: set_nat,P: set_nat > $o,F2: nat > rat] :
% 0.30/0.64        ( ( finite_finite_nat @ S )
% 0.30/0.64       => ( ( P @ bot_bot_set_nat )
% 0.30/0.64         => ( ! [X2: nat,S6: set_nat] :
% 0.30/0.64                ( ( finite_finite_nat @ S6 )
% 0.30/0.64               => ( ! [Y5: nat] :
% 0.30/0.64                      ( ( member_nat @ Y5 @ S6 )
% 0.30/0.64                     => ( ord_less_eq_rat @ ( F2 @ Y5 ) @ ( F2 @ X2 ) ) )
% 0.30/0.64                 => ( ( P @ S6 )
% 0.30/0.64                   => ( P @ ( insert_nat @ X2 @ S6 ) ) ) ) )
% 0.30/0.64           => ( P @ S ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_ranking_induct
% 0.30/0.64  thf(fact_8936_finite__ranking__induct,axiom,
% 0.30/0.64      ! [S: set_int,P: set_int > $o,F2: int > rat] :
% 0.30/0.64        ( ( finite_finite_int @ S )
% 0.30/0.64       => ( ( P @ bot_bot_set_int )
% 0.30/0.64         => ( ! [X2: int,S6: set_int] :
% 0.30/0.64                ( ( finite_finite_int @ S6 )
% 0.30/0.64               => ( ! [Y5: int] :
% 0.30/0.64                      ( ( member_int @ Y5 @ S6 )
% 0.30/0.64                     => ( ord_less_eq_rat @ ( F2 @ Y5 ) @ ( F2 @ X2 ) ) )
% 0.30/0.64                 => ( ( P @ S6 )
% 0.30/0.64                   => ( P @ ( insert_int @ X2 @ S6 ) ) ) ) )
% 0.30/0.64           => ( P @ S ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_ranking_induct
% 0.30/0.64  thf(fact_8937_finite__ranking__induct,axiom,
% 0.30/0.64      ! [S: set_o,P: set_o > $o,F2: $o > nat] :
% 0.30/0.64        ( ( finite_finite_o @ S )
% 0.30/0.64       => ( ( P @ bot_bot_set_o )
% 0.30/0.64         => ( ! [X2: $o,S6: set_o] :
% 0.30/0.64                ( ( finite_finite_o @ S6 )
% 0.30/0.64               => ( ! [Y5: $o] :
% 0.30/0.64                      ( ( member_o @ Y5 @ S6 )
% 0.30/0.64                     => ( ord_less_eq_nat @ ( F2 @ Y5 ) @ ( F2 @ X2 ) ) )
% 0.30/0.64                 => ( ( P @ S6 )
% 0.30/0.64                   => ( P @ ( insert_o @ X2 @ S6 ) ) ) ) )
% 0.30/0.64           => ( P @ S ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_ranking_induct
% 0.30/0.64  thf(fact_8938_finite__ranking__induct,axiom,
% 0.30/0.64      ! [S: set_nat,P: set_nat > $o,F2: nat > nat] :
% 0.30/0.64        ( ( finite_finite_nat @ S )
% 0.30/0.64       => ( ( P @ bot_bot_set_nat )
% 0.30/0.64         => ( ! [X2: nat,S6: set_nat] :
% 0.30/0.64                ( ( finite_finite_nat @ S6 )
% 0.30/0.64               => ( ! [Y5: nat] :
% 0.30/0.64                      ( ( member_nat @ Y5 @ S6 )
% 0.30/0.64                     => ( ord_less_eq_nat @ ( F2 @ Y5 ) @ ( F2 @ X2 ) ) )
% 0.30/0.64                 => ( ( P @ S6 )
% 0.30/0.64                   => ( P @ ( insert_nat @ X2 @ S6 ) ) ) ) )
% 0.30/0.64           => ( P @ S ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_ranking_induct
% 0.30/0.64  thf(fact_8939_finite__ranking__induct,axiom,
% 0.30/0.64      ! [S: set_int,P: set_int > $o,F2: int > nat] :
% 0.30/0.64        ( ( finite_finite_int @ S )
% 0.30/0.64       => ( ( P @ bot_bot_set_int )
% 0.30/0.64         => ( ! [X2: int,S6: set_int] :
% 0.30/0.64                ( ( finite_finite_int @ S6 )
% 0.30/0.64               => ( ! [Y5: int] :
% 0.30/0.64                      ( ( member_int @ Y5 @ S6 )
% 0.30/0.64                     => ( ord_less_eq_nat @ ( F2 @ Y5 ) @ ( F2 @ X2 ) ) )
% 0.30/0.64                 => ( ( P @ S6 )
% 0.30/0.64                   => ( P @ ( insert_int @ X2 @ S6 ) ) ) ) )
% 0.30/0.64           => ( P @ S ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_ranking_induct
% 0.30/0.64  thf(fact_8940_finite__ranking__induct,axiom,
% 0.30/0.64      ! [S: set_o,P: set_o > $o,F2: $o > int] :
% 0.30/0.64        ( ( finite_finite_o @ S )
% 0.30/0.64       => ( ( P @ bot_bot_set_o )
% 0.30/0.64         => ( ! [X2: $o,S6: set_o] :
% 0.30/0.64                ( ( finite_finite_o @ S6 )
% 0.30/0.64               => ( ! [Y5: $o] :
% 0.30/0.64                      ( ( member_o @ Y5 @ S6 )
% 0.30/0.64                     => ( ord_less_eq_int @ ( F2 @ Y5 ) @ ( F2 @ X2 ) ) )
% 0.30/0.64                 => ( ( P @ S6 )
% 0.30/0.64                   => ( P @ ( insert_o @ X2 @ S6 ) ) ) ) )
% 0.30/0.64           => ( P @ S ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_ranking_induct
% 0.30/0.64  thf(fact_8941_finite__ranking__induct,axiom,
% 0.30/0.64      ! [S: set_nat,P: set_nat > $o,F2: nat > int] :
% 0.30/0.64        ( ( finite_finite_nat @ S )
% 0.30/0.64       => ( ( P @ bot_bot_set_nat )
% 0.30/0.64         => ( ! [X2: nat,S6: set_nat] :
% 0.30/0.64                ( ( finite_finite_nat @ S6 )
% 0.30/0.64               => ( ! [Y5: nat] :
% 0.30/0.64                      ( ( member_nat @ Y5 @ S6 )
% 0.30/0.64                     => ( ord_less_eq_int @ ( F2 @ Y5 ) @ ( F2 @ X2 ) ) )
% 0.30/0.64                 => ( ( P @ S6 )
% 0.30/0.64                   => ( P @ ( insert_nat @ X2 @ S6 ) ) ) ) )
% 0.30/0.64           => ( P @ S ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_ranking_induct
% 0.30/0.64  thf(fact_8942_finite__ranking__induct,axiom,
% 0.30/0.64      ! [S: set_int,P: set_int > $o,F2: int > int] :
% 0.30/0.64        ( ( finite_finite_int @ S )
% 0.30/0.64       => ( ( P @ bot_bot_set_int )
% 0.30/0.64         => ( ! [X2: int,S6: set_int] :
% 0.30/0.64                ( ( finite_finite_int @ S6 )
% 0.30/0.64               => ( ! [Y5: int] :
% 0.30/0.64                      ( ( member_int @ Y5 @ S6 )
% 0.30/0.64                     => ( ord_less_eq_int @ ( F2 @ Y5 ) @ ( F2 @ X2 ) ) )
% 0.30/0.64                 => ( ( P @ S6 )
% 0.30/0.64                   => ( P @ ( insert_int @ X2 @ S6 ) ) ) ) )
% 0.30/0.64           => ( P @ S ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_ranking_induct
% 0.30/0.64  thf(fact_8943_finite__ranking__induct,axiom,
% 0.30/0.64      ! [S: set_set_nat,P: set_set_nat > $o,F2: set_nat > rat] :
% 0.30/0.64        ( ( finite1152437895449049373et_nat @ S )
% 0.30/0.64       => ( ( P @ bot_bot_set_set_nat )
% 0.30/0.64         => ( ! [X2: set_nat,S6: set_set_nat] :
% 0.30/0.64                ( ( finite1152437895449049373et_nat @ S6 )
% 0.30/0.64               => ( ! [Y5: set_nat] :
% 0.30/0.64                      ( ( member_set_nat @ Y5 @ S6 )
% 0.30/0.64                     => ( ord_less_eq_rat @ ( F2 @ Y5 ) @ ( F2 @ X2 ) ) )
% 0.30/0.64                 => ( ( P @ S6 )
% 0.30/0.64                   => ( P @ ( insert_set_nat @ X2 @ S6 ) ) ) ) )
% 0.30/0.64           => ( P @ S ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % finite_ranking_induct
% 0.30/0.64  thf(fact_8944_infinite__growing,axiom,
% 0.30/0.64      ! [X7: set_o] :
% 0.30/0.64        ( ( X7 != bot_bot_set_o )
% 0.30/0.64       => ( ! [X2: $o] :
% 0.30/0.64              ( ( member_o @ X2 @ X7 )
% 0.30/0.64             => ? [Xa2: $o] :
% 0.30/0.64                  ( ( member_o @ Xa2 @ X7 )
% 0.30/0.64                  & ( ord_less_o @ X2 @ Xa2 ) ) )
% 0.30/0.64         => ~ ( finite_finite_o @ X7 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % infinite_growing
% 0.30/0.64  thf(fact_8945_infinite__growing,axiom,
% 0.30/0.64      ! [X7: set_literal] :
% 0.30/0.64        ( ( X7 != bot_bot_set_literal )
% 0.30/0.64       => ( ! [X2: literal] :
% 0.30/0.64              ( ( member_literal @ X2 @ X7 )
% 0.30/0.64             => ? [Xa2: literal] :
% 0.30/0.64                  ( ( member_literal @ Xa2 @ X7 )
% 0.30/0.64                  & ( ord_less_literal @ X2 @ Xa2 ) ) )
% 0.30/0.64         => ~ ( finite5847741373460823677iteral @ X7 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % infinite_growing
% 0.30/0.64  thf(fact_8946_infinite__growing,axiom,
% 0.30/0.64      ! [X7: set_rat] :
% 0.30/0.64        ( ( X7 != bot_bot_set_rat )
% 0.30/0.64       => ( ! [X2: rat] :
% 0.30/0.64              ( ( member_rat @ X2 @ X7 )
% 0.30/0.64             => ? [Xa2: rat] :
% 0.30/0.64                  ( ( member_rat @ Xa2 @ X7 )
% 0.30/0.64                  & ( ord_less_rat @ X2 @ Xa2 ) ) )
% 0.30/0.64         => ~ ( finite_finite_rat @ X7 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % infinite_growing
% 0.30/0.64  thf(fact_8947_infinite__growing,axiom,
% 0.30/0.64      ! [X7: set_nat] :
% 0.30/0.64        ( ( X7 != bot_bot_set_nat )
% 0.30/0.64       => ( ! [X2: nat] :
% 0.30/0.64              ( ( member_nat @ X2 @ X7 )
% 0.30/0.64             => ? [Xa2: nat] :
% 0.30/0.64                  ( ( member_nat @ Xa2 @ X7 )
% 0.30/0.64                  & ( ord_less_nat @ X2 @ Xa2 ) ) )
% 0.30/0.64         => ~ ( finite_finite_nat @ X7 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % infinite_growing
% 0.30/0.64  thf(fact_8948_infinite__growing,axiom,
% 0.30/0.64      ! [X7: set_int] :
% 0.30/0.64        ( ( X7 != bot_bot_set_int )
% 0.30/0.64       => ( ! [X2: int] :
% 0.30/0.64              ( ( member_int @ X2 @ X7 )
% 0.30/0.64             => ? [Xa2: int] :
% 0.30/0.64                  ( ( member_int @ Xa2 @ X7 )
% 0.30/0.64                  & ( ord_less_int @ X2 @ Xa2 ) ) )
% 0.30/0.64         => ~ ( finite_finite_int @ X7 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % infinite_growing
% 0.30/0.64  thf(fact_8949_ex__min__if__finite,axiom,
% 0.30/0.64      ! [S: set_o] :
% 0.30/0.64        ( ( finite_finite_o @ S )
% 0.30/0.64       => ( ( S != bot_bot_set_o )
% 0.30/0.64         => ? [X2: $o] :
% 0.30/0.64              ( ( member_o @ X2 @ S )
% 0.30/0.64              & ~ ? [Xa2: $o] :
% 0.30/0.64                    ( ( member_o @ Xa2 @ S )
% 0.30/0.64                    & ( ord_less_o @ Xa2 @ X2 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % ex_min_if_finite
% 0.30/0.64  thf(fact_8950_ex__min__if__finite,axiom,
% 0.30/0.64      ! [S: set_literal] :
% 0.30/0.64        ( ( finite5847741373460823677iteral @ S )
% 0.30/0.64       => ( ( S != bot_bot_set_literal )
% 0.30/0.64         => ? [X2: literal] :
% 0.30/0.64              ( ( member_literal @ X2 @ S )
% 0.30/0.64              & ~ ? [Xa2: literal] :
% 0.30/0.64                    ( ( member_literal @ Xa2 @ S )
% 0.30/0.64                    & ( ord_less_literal @ Xa2 @ X2 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % ex_min_if_finite
% 0.30/0.64  thf(fact_8951_ex__min__if__finite,axiom,
% 0.30/0.64      ! [S: set_rat] :
% 0.30/0.64        ( ( finite_finite_rat @ S )
% 0.30/0.64       => ( ( S != bot_bot_set_rat )
% 0.30/0.64         => ? [X2: rat] :
% 0.30/0.64              ( ( member_rat @ X2 @ S )
% 0.30/0.64              & ~ ? [Xa2: rat] :
% 0.30/0.64                    ( ( member_rat @ Xa2 @ S )
% 0.30/0.64                    & ( ord_less_rat @ Xa2 @ X2 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % ex_min_if_finite
% 0.30/0.64  thf(fact_8952_ex__min__if__finite,axiom,
% 0.30/0.64      ! [S: set_nat] :
% 0.30/0.64        ( ( finite_finite_nat @ S )
% 0.30/0.64       => ( ( S != bot_bot_set_nat )
% 0.30/0.64         => ? [X2: nat] :
% 0.30/0.64              ( ( member_nat @ X2 @ S )
% 0.30/0.64              & ~ ? [Xa2: nat] :
% 0.30/0.64                    ( ( member_nat @ Xa2 @ S )
% 0.30/0.64                    & ( ord_less_nat @ Xa2 @ X2 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % ex_min_if_finite
% 0.30/0.64  thf(fact_8953_ex__min__if__finite,axiom,
% 0.30/0.64      ! [S: set_int] :
% 0.30/0.64        ( ( finite_finite_int @ S )
% 0.30/0.64       => ( ( S != bot_bot_set_int )
% 0.30/0.64         => ? [X2: int] :
% 0.30/0.64              ( ( member_int @ X2 @ S )
% 0.30/0.64              & ~ ? [Xa2: int] :
% 0.30/0.64                    ( ( member_int @ Xa2 @ S )
% 0.30/0.64                    & ( ord_less_int @ Xa2 @ X2 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % ex_min_if_finite
% 0.30/0.64  thf(fact_8954_filter__preserves__multiset,axiom,
% 0.30/0.64      ! [M4: set_Pr958786334691620121nt_int > nat,P: set_Pr958786334691620121nt_int > $o] :
% 0.30/0.64        ( ( finite8744585540193469122nt_int
% 0.30/0.64          @ ( collec5210948495886036740nt_int
% 0.30/0.64            @ ^ [X3: set_Pr958786334691620121nt_int] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 0.30/0.64       => ( finite8744585540193469122nt_int
% 0.30/0.64          @ ( collec5210948495886036740nt_int
% 0.30/0.64            @ ^ [X3: set_Pr958786334691620121nt_int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X3 ) @ ( M4 @ X3 ) @ zero_zero_nat ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % filter_preserves_multiset
% 0.30/0.64  thf(fact_8955_filter__preserves__multiset,axiom,
% 0.30/0.64      ! [M4: set_nat > nat,P: set_nat > $o] :
% 0.30/0.64        ( ( finite1152437895449049373et_nat
% 0.30/0.64          @ ( collect_set_nat
% 0.30/0.64            @ ^ [X3: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 0.30/0.64       => ( finite1152437895449049373et_nat
% 0.30/0.64          @ ( collect_set_nat
% 0.30/0.64            @ ^ [X3: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X3 ) @ ( M4 @ X3 ) @ zero_zero_nat ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % filter_preserves_multiset
% 0.30/0.64  thf(fact_8956_filter__preserves__multiset,axiom,
% 0.30/0.64      ! [M4: ( produc3658429121746597890et_nat > $o ) > nat,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 0.30/0.64        ( ( finite3252695134891459830_nat_o
% 0.30/0.64          @ ( collec939566748876313656_nat_o
% 0.30/0.64            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 0.30/0.64       => ( finite3252695134891459830_nat_o
% 0.30/0.64          @ ( collec939566748876313656_nat_o
% 0.30/0.64            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X3 ) @ ( M4 @ X3 ) @ zero_zero_nat ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % filter_preserves_multiset
% 0.30/0.64  thf(fact_8957_filter__preserves__multiset,axiom,
% 0.30/0.64      ! [M4: nat > nat,P: nat > $o] :
% 0.30/0.64        ( ( finite_finite_nat
% 0.30/0.64          @ ( collect_nat
% 0.30/0.64            @ ^ [X3: nat] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 0.30/0.64       => ( finite_finite_nat
% 0.30/0.64          @ ( collect_nat
% 0.30/0.64            @ ^ [X3: nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X3 ) @ ( M4 @ X3 ) @ zero_zero_nat ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % filter_preserves_multiset
% 0.30/0.64  thf(fact_8958_filter__preserves__multiset,axiom,
% 0.30/0.64      ! [M4: int > nat,P: int > $o] :
% 0.30/0.64        ( ( finite_finite_int
% 0.30/0.64          @ ( collect_int
% 0.30/0.64            @ ^ [X3: int] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 0.30/0.64       => ( finite_finite_int
% 0.30/0.64          @ ( collect_int
% 0.30/0.64            @ ^ [X3: int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X3 ) @ ( M4 @ X3 ) @ zero_zero_nat ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % filter_preserves_multiset
% 0.30/0.64  thf(fact_8959_filter__preserves__multiset,axiom,
% 0.30/0.64      ! [M4: product_prod_nat_nat > nat,P: product_prod_nat_nat > $o] :
% 0.30/0.64        ( ( finite6177210948735845034at_nat
% 0.30/0.64          @ ( collec3392354462482085612at_nat
% 0.30/0.64            @ ^ [X3: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 0.30/0.64       => ( finite6177210948735845034at_nat
% 0.30/0.64          @ ( collec3392354462482085612at_nat
% 0.30/0.64            @ ^ [X3: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X3 ) @ ( M4 @ X3 ) @ zero_zero_nat ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % filter_preserves_multiset
% 0.30/0.64  thf(fact_8960_divide__int__def,axiom,
% 0.30/0.64      ( divide_divide_int
% 0.30/0.64      = ( ^ [K4: int,L2: int] :
% 0.30/0.64            ( if_int @ ( L2 = zero_zero_int ) @ zero_zero_int
% 0.30/0.64            @ ( if_int
% 0.30/0.64              @ ( ( sgn_sgn_int @ K4 )
% 0.30/0.64                = ( sgn_sgn_int @ L2 ) )
% 0.30/0.64              @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K4 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) )
% 0.30/0.64              @ ( uminus_uminus_int
% 0.30/0.64                @ ( semiri1314217659103216013at_int
% 0.30/0.64                  @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K4 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) )
% 0.30/0.64                    @ ( zero_n2687167440665602831ol_nat
% 0.30/0.64                      @ ~ ( dvd_dvd_int @ L2 @ K4 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % divide_int_def
% 0.30/0.64  thf(fact_8961_sum__diff1_H__aux,axiom,
% 0.30/0.64      ! [F4: set_o,I4: set_o,F2: $o > code_integer,I: $o] :
% 0.30/0.64        ( ( finite_finite_o @ F4 )
% 0.30/0.64       => ( ( ord_less_eq_set_o
% 0.30/0.64            @ ( collect_o
% 0.30/0.64              @ ^ [I3: $o] :
% 0.30/0.64                  ( ( member_o @ I3 @ I4 )
% 0.30/0.64                  & ( ( F2 @ I3 )
% 0.30/0.64                   != zero_z3403309356797280102nteger ) ) )
% 0.30/0.64            @ F4 )
% 0.30/0.64         => ( ( ( member_o @ I @ I4 )
% 0.30/0.64             => ( ( groups1402912129352969042nteger @ F2 @ ( minus_minus_set_o @ I4 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 0.30/0.64                = ( minus_8373710615458151222nteger @ ( groups1402912129352969042nteger @ F2 @ I4 ) @ ( F2 @ I ) ) ) )
% 0.30/0.64            & ( ~ ( member_o @ I @ I4 )
% 0.30/0.64             => ( ( groups1402912129352969042nteger @ F2 @ ( minus_minus_set_o @ I4 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 0.30/0.64                = ( groups1402912129352969042nteger @ F2 @ I4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_diff1'_aux
% 0.30/0.64  thf(fact_8962_sum__diff1_H__aux,axiom,
% 0.30/0.64      ! [F4: set_int,I4: set_int,F2: int > code_integer,I: int] :
% 0.30/0.64        ( ( finite_finite_int @ F4 )
% 0.30/0.64       => ( ( ord_less_eq_set_int
% 0.30/0.64            @ ( collect_int
% 0.30/0.64              @ ^ [I3: int] :
% 0.30/0.64                  ( ( member_int @ I3 @ I4 )
% 0.30/0.64                  & ( ( F2 @ I3 )
% 0.30/0.64                   != zero_z3403309356797280102nteger ) ) )
% 0.30/0.64            @ F4 )
% 0.30/0.64         => ( ( ( member_int @ I @ I4 )
% 0.30/0.64             => ( ( groups926780983652909934nteger @ F2 @ ( minus_minus_set_int @ I4 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 0.30/0.64                = ( minus_8373710615458151222nteger @ ( groups926780983652909934nteger @ F2 @ I4 ) @ ( F2 @ I ) ) ) )
% 0.30/0.64            & ( ~ ( member_int @ I @ I4 )
% 0.30/0.64             => ( ( groups926780983652909934nteger @ F2 @ ( minus_minus_set_int @ I4 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 0.30/0.64                = ( groups926780983652909934nteger @ F2 @ I4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_diff1'_aux
% 0.30/0.64  thf(fact_8963_sum__diff1_H__aux,axiom,
% 0.30/0.64      ! [F4: set_o,I4: set_o,F2: $o > rat,I: $o] :
% 0.30/0.64        ( ( finite_finite_o @ F4 )
% 0.30/0.64       => ( ( ord_less_eq_set_o
% 0.30/0.64            @ ( collect_o
% 0.30/0.64              @ ^ [I3: $o] :
% 0.30/0.64                  ( ( member_o @ I3 @ I4 )
% 0.30/0.64                  & ( ( F2 @ I3 )
% 0.30/0.64                   != zero_zero_rat ) ) )
% 0.30/0.64            @ F4 )
% 0.30/0.64         => ( ( ( member_o @ I @ I4 )
% 0.30/0.64             => ( ( groups3921277224699582669_o_rat @ F2 @ ( minus_minus_set_o @ I4 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 0.30/0.64                = ( minus_minus_rat @ ( groups3921277224699582669_o_rat @ F2 @ I4 ) @ ( F2 @ I ) ) ) )
% 0.30/0.64            & ( ~ ( member_o @ I @ I4 )
% 0.30/0.64             => ( ( groups3921277224699582669_o_rat @ F2 @ ( minus_minus_set_o @ I4 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 0.30/0.64                = ( groups3921277224699582669_o_rat @ F2 @ I4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_diff1'_aux
% 0.30/0.64  thf(fact_8964_sum__diff1_H__aux,axiom,
% 0.30/0.64      ! [F4: set_int,I4: set_int,F2: int > rat,I: int] :
% 0.30/0.64        ( ( finite_finite_int @ F4 )
% 0.30/0.64       => ( ( ord_less_eq_set_int
% 0.30/0.64            @ ( collect_int
% 0.30/0.64              @ ^ [I3: int] :
% 0.30/0.64                  ( ( member_int @ I3 @ I4 )
% 0.30/0.64                  & ( ( F2 @ I3 )
% 0.30/0.64                   != zero_zero_rat ) ) )
% 0.30/0.64            @ F4 )
% 0.30/0.64         => ( ( ( member_int @ I @ I4 )
% 0.30/0.64             => ( ( groups2350640619554545897nt_rat @ F2 @ ( minus_minus_set_int @ I4 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 0.30/0.64                = ( minus_minus_rat @ ( groups2350640619554545897nt_rat @ F2 @ I4 ) @ ( F2 @ I ) ) ) )
% 0.30/0.64            & ( ~ ( member_int @ I @ I4 )
% 0.30/0.64             => ( ( groups2350640619554545897nt_rat @ F2 @ ( minus_minus_set_int @ I4 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 0.30/0.64                = ( groups2350640619554545897nt_rat @ F2 @ I4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_diff1'_aux
% 0.30/0.64  thf(fact_8965_sum__diff1_H__aux,axiom,
% 0.30/0.64      ! [F4: set_o,I4: set_o,F2: $o > int,I: $o] :
% 0.30/0.64        ( ( finite_finite_o @ F4 )
% 0.30/0.64       => ( ( ord_less_eq_set_o
% 0.30/0.64            @ ( collect_o
% 0.30/0.64              @ ^ [I3: $o] :
% 0.30/0.64                  ( ( member_o @ I3 @ I4 )
% 0.30/0.64                  & ( ( F2 @ I3 )
% 0.30/0.64                   != zero_zero_int ) ) )
% 0.30/0.64            @ F4 )
% 0.30/0.64         => ( ( ( member_o @ I @ I4 )
% 0.30/0.64             => ( ( groups4553916814277028129_o_int @ F2 @ ( minus_minus_set_o @ I4 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 0.30/0.64                = ( minus_minus_int @ ( groups4553916814277028129_o_int @ F2 @ I4 ) @ ( F2 @ I ) ) ) )
% 0.30/0.64            & ( ~ ( member_o @ I @ I4 )
% 0.30/0.64             => ( ( groups4553916814277028129_o_int @ F2 @ ( minus_minus_set_o @ I4 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 0.30/0.64                = ( groups4553916814277028129_o_int @ F2 @ I4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_diff1'_aux
% 0.30/0.64  thf(fact_8966_sum__diff1_H__aux,axiom,
% 0.30/0.64      ! [F4: set_int,I4: set_int,F2: int > int,I: int] :
% 0.30/0.64        ( ( finite_finite_int @ F4 )
% 0.30/0.64       => ( ( ord_less_eq_set_int
% 0.30/0.64            @ ( collect_int
% 0.30/0.64              @ ^ [I3: int] :
% 0.30/0.64                  ( ( member_int @ I3 @ I4 )
% 0.30/0.64                  & ( ( F2 @ I3 )
% 0.30/0.64                   != zero_zero_int ) ) )
% 0.30/0.64            @ F4 )
% 0.30/0.64         => ( ( ( member_int @ I @ I4 )
% 0.30/0.64             => ( ( groups2983280209131991357nt_int @ F2 @ ( minus_minus_set_int @ I4 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 0.30/0.64                = ( minus_minus_int @ ( groups2983280209131991357nt_int @ F2 @ I4 ) @ ( F2 @ I ) ) ) )
% 0.30/0.64            & ( ~ ( member_int @ I @ I4 )
% 0.30/0.64             => ( ( groups2983280209131991357nt_int @ F2 @ ( minus_minus_set_int @ I4 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 0.30/0.64                = ( groups2983280209131991357nt_int @ F2 @ I4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_diff1'_aux
% 0.30/0.64  thf(fact_8967_sum__diff1_H__aux,axiom,
% 0.30/0.64      ! [F4: set_nat,I4: set_nat,F2: nat > code_integer,I: nat] :
% 0.30/0.64        ( ( finite_finite_nat @ F4 )
% 0.30/0.64       => ( ( ord_less_eq_set_nat
% 0.30/0.64            @ ( collect_nat
% 0.30/0.64              @ ^ [I3: nat] :
% 0.30/0.64                  ( ( member_nat @ I3 @ I4 )
% 0.30/0.64                  & ( ( F2 @ I3 )
% 0.30/0.64                   != zero_z3403309356797280102nteger ) ) )
% 0.30/0.64            @ F4 )
% 0.30/0.64         => ( ( ( member_nat @ I @ I4 )
% 0.30/0.64             => ( ( groups555127423416065298nteger @ F2 @ ( minus_minus_set_nat @ I4 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 0.30/0.64                = ( minus_8373710615458151222nteger @ ( groups555127423416065298nteger @ F2 @ I4 ) @ ( F2 @ I ) ) ) )
% 0.30/0.64            & ( ~ ( member_nat @ I @ I4 )
% 0.30/0.64             => ( ( groups555127423416065298nteger @ F2 @ ( minus_minus_set_nat @ I4 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 0.30/0.64                = ( groups555127423416065298nteger @ F2 @ I4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_diff1'_aux
% 0.30/0.64  thf(fact_8968_sum__diff1_H__aux,axiom,
% 0.30/0.64      ! [F4: set_nat,I4: set_nat,F2: nat > rat,I: nat] :
% 0.30/0.64        ( ( finite_finite_nat @ F4 )
% 0.30/0.64       => ( ( ord_less_eq_set_nat
% 0.30/0.64            @ ( collect_nat
% 0.30/0.64              @ ^ [I3: nat] :
% 0.30/0.64                  ( ( member_nat @ I3 @ I4 )
% 0.30/0.64                  & ( ( F2 @ I3 )
% 0.30/0.64                   != zero_zero_rat ) ) )
% 0.30/0.64            @ F4 )
% 0.30/0.64         => ( ( ( member_nat @ I @ I4 )
% 0.30/0.64             => ( ( groups1351286907653491341at_rat @ F2 @ ( minus_minus_set_nat @ I4 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 0.30/0.64                = ( minus_minus_rat @ ( groups1351286907653491341at_rat @ F2 @ I4 ) @ ( F2 @ I ) ) ) )
% 0.30/0.64            & ( ~ ( member_nat @ I @ I4 )
% 0.30/0.64             => ( ( groups1351286907653491341at_rat @ F2 @ ( minus_minus_set_nat @ I4 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 0.30/0.64                = ( groups1351286907653491341at_rat @ F2 @ I4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_diff1'_aux
% 0.30/0.64  thf(fact_8969_sum__diff1_H__aux,axiom,
% 0.30/0.64      ! [F4: set_nat,I4: set_nat,F2: nat > int,I: nat] :
% 0.30/0.64        ( ( finite_finite_nat @ F4 )
% 0.30/0.64       => ( ( ord_less_eq_set_nat
% 0.30/0.64            @ ( collect_nat
% 0.30/0.64              @ ^ [I3: nat] :
% 0.30/0.64                  ( ( member_nat @ I3 @ I4 )
% 0.30/0.64                  & ( ( F2 @ I3 )
% 0.30/0.64                   != zero_zero_int ) ) )
% 0.30/0.64            @ F4 )
% 0.30/0.64         => ( ( ( member_nat @ I @ I4 )
% 0.30/0.64             => ( ( groups1983926497230936801at_int @ F2 @ ( minus_minus_set_nat @ I4 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 0.30/0.64                = ( minus_minus_int @ ( groups1983926497230936801at_int @ F2 @ I4 ) @ ( F2 @ I ) ) ) )
% 0.30/0.64            & ( ~ ( member_nat @ I @ I4 )
% 0.30/0.64             => ( ( groups1983926497230936801at_int @ F2 @ ( minus_minus_set_nat @ I4 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 0.30/0.64                = ( groups1983926497230936801at_int @ F2 @ I4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_diff1'_aux
% 0.30/0.64  thf(fact_8970_sum__diff1_H__aux,axiom,
% 0.30/0.64      ! [F4: set_set_nat,I4: set_set_nat,F2: set_nat > code_integer,I: set_nat] :
% 0.30/0.64        ( ( finite1152437895449049373et_nat @ F4 )
% 0.30/0.64       => ( ( ord_le6893508408891458716et_nat
% 0.30/0.64            @ ( collect_set_nat
% 0.30/0.64              @ ^ [I3: set_nat] :
% 0.30/0.64                  ( ( member_set_nat @ I3 @ I4 )
% 0.30/0.64                  & ( ( F2 @ I3 )
% 0.30/0.64                   != zero_z3403309356797280102nteger ) ) )
% 0.30/0.64            @ F4 )
% 0.30/0.64         => ( ( ( member_set_nat @ I @ I4 )
% 0.30/0.64             => ( ( groups9221925307898054856nteger @ F2 @ ( minus_2163939370556025621et_nat @ I4 @ ( insert_set_nat @ I @ bot_bot_set_set_nat ) ) )
% 0.30/0.64                = ( minus_8373710615458151222nteger @ ( groups9221925307898054856nteger @ F2 @ I4 ) @ ( F2 @ I ) ) ) )
% 0.30/0.64            & ( ~ ( member_set_nat @ I @ I4 )
% 0.30/0.64             => ( ( groups9221925307898054856nteger @ F2 @ ( minus_2163939370556025621et_nat @ I4 @ ( insert_set_nat @ I @ bot_bot_set_set_nat ) ) )
% 0.30/0.64                = ( groups9221925307898054856nteger @ F2 @ I4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_diff1'_aux
% 0.30/0.64  thf(fact_8971_even__sum__iff,axiom,
% 0.30/0.64      ! [A2: set_o,F2: $o > nat] :
% 0.30/0.64        ( ( finite_finite_o @ A2 )
% 0.30/0.64       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups8507830703676809646_o_nat @ F2 @ A2 ) )
% 0.30/0.64          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.30/0.64            @ ( finite_card_o
% 0.30/0.64              @ ( collect_o
% 0.30/0.64                @ ^ [A3: $o] :
% 0.30/0.64                    ( ( member_o @ A3 @ A2 )
% 0.30/0.64                    & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F2 @ A3 ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % even_sum_iff
% 0.30/0.64  thf(fact_8972_even__sum__iff,axiom,
% 0.30/0.64      ! [A2: set_int,F2: int > nat] :
% 0.30/0.64        ( ( finite_finite_int @ A2 )
% 0.30/0.64       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups4541462559716669496nt_nat @ F2 @ A2 ) )
% 0.30/0.64          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.30/0.64            @ ( finite_card_int
% 0.30/0.64              @ ( collect_int
% 0.30/0.64                @ ^ [A3: int] :
% 0.30/0.64                    ( ( member_int @ A3 @ A2 )
% 0.30/0.64                    & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F2 @ A3 ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % even_sum_iff
% 0.30/0.64  thf(fact_8973_even__sum__iff,axiom,
% 0.30/0.64      ! [A2: set_o,F2: $o > int] :
% 0.30/0.64        ( ( finite_finite_o @ A2 )
% 0.30/0.64       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups8505340233167759370_o_int @ F2 @ A2 ) )
% 0.30/0.64          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.30/0.64            @ ( finite_card_o
% 0.30/0.64              @ ( collect_o
% 0.30/0.64                @ ^ [A3: $o] :
% 0.30/0.64                    ( ( member_o @ A3 @ A2 )
% 0.30/0.64                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F2 @ A3 ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % even_sum_iff
% 0.30/0.64  thf(fact_8974_even__sum__iff,axiom,
% 0.30/0.64      ! [A2: set_nat,F2: nat > int] :
% 0.30/0.64        ( ( finite_finite_nat @ A2 )
% 0.30/0.64       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ F2 @ A2 ) )
% 0.30/0.64          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.30/0.64            @ ( finite_card_nat
% 0.30/0.64              @ ( collect_nat
% 0.30/0.64                @ ^ [A3: nat] :
% 0.30/0.64                    ( ( member_nat @ A3 @ A2 )
% 0.30/0.64                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F2 @ A3 ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % even_sum_iff
% 0.30/0.64  thf(fact_8975_even__sum__iff,axiom,
% 0.30/0.64      ! [A2: set_o,F2: $o > code_integer] :
% 0.30/0.64        ( ( finite_finite_o @ A2 )
% 0.30/0.64       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups4406642042086082107nteger @ F2 @ A2 ) )
% 0.30/0.64          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.30/0.64            @ ( finite_card_o
% 0.30/0.64              @ ( collect_o
% 0.30/0.64                @ ^ [A3: $o] :
% 0.30/0.64                    ( ( member_o @ A3 @ A2 )
% 0.30/0.64                    & ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F2 @ A3 ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % even_sum_iff
% 0.30/0.64  thf(fact_8976_even__sum__iff,axiom,
% 0.30/0.64      ! [A2: set_nat,F2: nat > code_integer] :
% 0.30/0.64        ( ( finite_finite_nat @ A2 )
% 0.30/0.64       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ F2 @ A2 ) )
% 0.30/0.64          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.30/0.64            @ ( finite_card_nat
% 0.30/0.64              @ ( collect_nat
% 0.30/0.64                @ ^ [A3: nat] :
% 0.30/0.64                    ( ( member_nat @ A3 @ A2 )
% 0.30/0.64                    & ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F2 @ A3 ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % even_sum_iff
% 0.30/0.64  thf(fact_8977_even__sum__iff,axiom,
% 0.30/0.64      ! [A2: set_int,F2: int > code_integer] :
% 0.30/0.64        ( ( finite_finite_int @ A2 )
% 0.30/0.64       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7873554091576472773nteger @ F2 @ A2 ) )
% 0.30/0.64          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.30/0.64            @ ( finite_card_int
% 0.30/0.64              @ ( collect_int
% 0.30/0.64                @ ^ [A3: int] :
% 0.30/0.64                    ( ( member_int @ A3 @ A2 )
% 0.30/0.64                    & ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F2 @ A3 ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % even_sum_iff
% 0.30/0.64  thf(fact_8978_even__sum__iff,axiom,
% 0.30/0.64      ! [A2: set_o,F2: $o > code_natural] :
% 0.30/0.64        ( ( finite_finite_o @ A2 )
% 0.30/0.64       => ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups3230237193842799622atural @ F2 @ A2 ) )
% 0.30/0.64          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.30/0.64            @ ( finite_card_o
% 0.30/0.64              @ ( collect_o
% 0.30/0.64                @ ^ [A3: $o] :
% 0.30/0.64                    ( ( member_o @ A3 @ A2 )
% 0.30/0.64                    & ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( F2 @ A3 ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % even_sum_iff
% 0.30/0.64  thf(fact_8979_even__sum__iff,axiom,
% 0.30/0.64      ! [A2: set_nat,F2: nat > code_natural] :
% 0.30/0.64        ( ( finite_finite_nat @ A2 )
% 0.30/0.64       => ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups6325495683096345652atural @ F2 @ A2 ) )
% 0.30/0.64          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.30/0.64            @ ( finite_card_nat
% 0.30/0.64              @ ( collect_nat
% 0.30/0.64                @ ^ [A3: nat] :
% 0.30/0.64                    ( ( member_nat @ A3 @ A2 )
% 0.30/0.64                    & ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( F2 @ A3 ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % even_sum_iff
% 0.30/0.64  thf(fact_8980_even__sum__iff,axiom,
% 0.30/0.64      ! [A2: set_int,F2: int > code_natural] :
% 0.30/0.64        ( ( finite_finite_int @ A2 )
% 0.30/0.64       => ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups6697149243333190288atural @ F2 @ A2 ) )
% 0.30/0.64          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.30/0.64            @ ( finite_card_int
% 0.30/0.64              @ ( collect_int
% 0.30/0.64                @ ^ [A3: int] :
% 0.30/0.64                    ( ( member_int @ A3 @ A2 )
% 0.30/0.64                    & ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( F2 @ A3 ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % even_sum_iff
% 0.30/0.64  thf(fact_8981_nat__not__finite,axiom,
% 0.30/0.64      ~ ( finite_finite_nat @ top_top_set_nat ) ).
% 0.30/0.64  
% 0.30/0.64  % nat_not_finite
% 0.30/0.64  thf(fact_8982_card__UNIV__unit,axiom,
% 0.30/0.64      ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 0.30/0.64      = one_one_nat ) ).
% 0.30/0.64  
% 0.30/0.64  % card_UNIV_unit
% 0.30/0.64  thf(fact_8983_card__Collect__less__nat,axiom,
% 0.30/0.64      ! [N: nat] :
% 0.30/0.64        ( ( finite_card_nat
% 0.30/0.64          @ ( collect_nat
% 0.30/0.64            @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N ) ) )
% 0.30/0.64        = N ) ).
% 0.30/0.64  
% 0.30/0.64  % card_Collect_less_nat
% 0.30/0.64  thf(fact_8984_card__eq__UNIV,axiom,
% 0.30/0.64      ! [S: set_o] :
% 0.30/0.64        ( ( ( finite_card_o @ S )
% 0.30/0.64          = ( finite_card_o @ top_top_set_o ) )
% 0.30/0.64        = ( S = top_top_set_o ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_eq_UNIV
% 0.30/0.64  thf(fact_8985_card__eq__UNIV2,axiom,
% 0.30/0.64      ! [S: set_o] :
% 0.30/0.64        ( ( ( finite_card_o @ top_top_set_o )
% 0.30/0.64          = ( finite_card_o @ S ) )
% 0.30/0.64        = ( S = top_top_set_o ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_eq_UNIV2
% 0.30/0.64  thf(fact_8986_card__Collect__le__nat,axiom,
% 0.30/0.64      ! [N: nat] :
% 0.30/0.64        ( ( finite_card_nat
% 0.30/0.64          @ ( collect_nat
% 0.30/0.64            @ ^ [I3: nat] : ( ord_less_eq_nat @ I3 @ N ) ) )
% 0.30/0.64        = ( suc @ N ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_Collect_le_nat
% 0.30/0.64  thf(fact_8987_card__UNIV__bool,axiom,
% 0.30/0.64      ( ( finite_card_o @ top_top_set_o )
% 0.30/0.64      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_UNIV_bool
% 0.30/0.64  thf(fact_8988_card_Oempty,axiom,
% 0.30/0.64      ( ( finite_card_list_nat @ bot_bot_set_list_nat )
% 0.30/0.64      = zero_zero_nat ) ).
% 0.30/0.64  
% 0.30/0.64  % card.empty
% 0.30/0.64  thf(fact_8989_card_Oempty,axiom,
% 0.30/0.64      ( ( finite_card_set_nat @ bot_bot_set_set_nat )
% 0.30/0.64      = zero_zero_nat ) ).
% 0.30/0.64  
% 0.30/0.64  % card.empty
% 0.30/0.64  thf(fact_8990_card_Oempty,axiom,
% 0.30/0.64      ( ( finite711546835091564841at_nat @ bot_bo2099793752762293965at_nat )
% 0.30/0.64      = zero_zero_nat ) ).
% 0.30/0.64  
% 0.30/0.64  % card.empty
% 0.30/0.64  thf(fact_8991_card_Oempty,axiom,
% 0.30/0.64      ( ( finite_card_o @ bot_bot_set_o )
% 0.30/0.64      = zero_zero_nat ) ).
% 0.30/0.64  
% 0.30/0.64  % card.empty
% 0.30/0.64  thf(fact_8992_card_Oempty,axiom,
% 0.30/0.64      ( ( finite_card_nat @ bot_bot_set_nat )
% 0.30/0.64      = zero_zero_nat ) ).
% 0.30/0.64  
% 0.30/0.64  % card.empty
% 0.30/0.64  thf(fact_8993_card_Oempty,axiom,
% 0.30/0.64      ( ( finite_card_int @ bot_bot_set_int )
% 0.30/0.64      = zero_zero_nat ) ).
% 0.30/0.64  
% 0.30/0.64  % card.empty
% 0.30/0.64  thf(fact_8994_card__ge__UNIV,axiom,
% 0.30/0.64      ! [S: set_o] :
% 0.30/0.64        ( ( ord_less_eq_nat @ ( finite_card_o @ top_top_set_o ) @ ( finite_card_o @ S ) )
% 0.30/0.64        = ( S = top_top_set_o ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_ge_UNIV
% 0.30/0.64  thf(fact_8995_sum_Oempty_H,axiom,
% 0.30/0.64      ! [P4: $o > code_integer] :
% 0.30/0.64        ( ( groups1402912129352969042nteger @ P4 @ bot_bot_set_o )
% 0.30/0.64        = zero_z3403309356797280102nteger ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.empty'
% 0.30/0.64  thf(fact_8996_sum_Oempty_H,axiom,
% 0.30/0.64      ! [P4: $o > rat] :
% 0.30/0.64        ( ( groups3921277224699582669_o_rat @ P4 @ bot_bot_set_o )
% 0.30/0.64        = zero_zero_rat ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.empty'
% 0.30/0.64  thf(fact_8997_sum_Oempty_H,axiom,
% 0.30/0.64      ! [P4: $o > nat] :
% 0.30/0.64        ( ( groups4556407284786078405_o_nat @ P4 @ bot_bot_set_o )
% 0.30/0.64        = zero_zero_nat ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.empty'
% 0.30/0.64  thf(fact_8998_sum_Oempty_H,axiom,
% 0.30/0.64      ! [P4: $o > int] :
% 0.30/0.64        ( ( groups4553916814277028129_o_int @ P4 @ bot_bot_set_o )
% 0.30/0.64        = zero_zero_int ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.empty'
% 0.30/0.64  thf(fact_8999_sum_Oempty_H,axiom,
% 0.30/0.64      ! [P4: nat > code_integer] :
% 0.30/0.64        ( ( groups555127423416065298nteger @ P4 @ bot_bot_set_nat )
% 0.30/0.64        = zero_z3403309356797280102nteger ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.empty'
% 0.30/0.64  thf(fact_9000_sum_Oempty_H,axiom,
% 0.30/0.64      ! [P4: nat > rat] :
% 0.30/0.64        ( ( groups1351286907653491341at_rat @ P4 @ bot_bot_set_nat )
% 0.30/0.64        = zero_zero_rat ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.empty'
% 0.30/0.64  thf(fact_9001_sum_Oempty_H,axiom,
% 0.30/0.64      ! [P4: nat > nat] :
% 0.30/0.64        ( ( groups1986416967739987077at_nat @ P4 @ bot_bot_set_nat )
% 0.30/0.64        = zero_zero_nat ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.empty'
% 0.30/0.64  thf(fact_9002_sum_Oempty_H,axiom,
% 0.30/0.64      ! [P4: nat > int] :
% 0.30/0.64        ( ( groups1983926497230936801at_int @ P4 @ bot_bot_set_nat )
% 0.30/0.64        = zero_zero_int ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.empty'
% 0.30/0.64  thf(fact_9003_sum_Oempty_H,axiom,
% 0.30/0.64      ! [P4: int > code_integer] :
% 0.30/0.64        ( ( groups926780983652909934nteger @ P4 @ bot_bot_set_int )
% 0.30/0.64        = zero_z3403309356797280102nteger ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.empty'
% 0.30/0.64  thf(fact_9004_sum_Oempty_H,axiom,
% 0.30/0.64      ! [P4: int > rat] :
% 0.30/0.64        ( ( groups2350640619554545897nt_rat @ P4 @ bot_bot_set_int )
% 0.30/0.64        = zero_zero_rat ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.empty'
% 0.30/0.64  thf(fact_9005_prod__constant,axiom,
% 0.30/0.64      ! [Y: int,A2: set_list_nat] :
% 0.30/0.64        ( ( groups2905156660866384563at_int
% 0.30/0.64          @ ^ [X3: list_nat] : Y
% 0.30/0.64          @ A2 )
% 0.30/0.64        = ( power_power_int @ Y @ ( finite_card_list_nat @ A2 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % prod_constant
% 0.30/0.64  thf(fact_9006_prod__constant,axiom,
% 0.30/0.64      ! [Y: int,A2: set_o] :
% 0.30/0.64        ( ( groups3502327434004483295_o_int
% 0.30/0.64          @ ^ [X3: $o] : Y
% 0.30/0.64          @ A2 )
% 0.30/0.64        = ( power_power_int @ Y @ ( finite_card_o @ A2 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % prod_constant
% 0.30/0.64  thf(fact_9007_prod__constant,axiom,
% 0.30/0.64      ! [Y: int,A2: set_set_nat] :
% 0.30/0.64        ( ( groups4246057289670975065at_int
% 0.30/0.64          @ ^ [X3: set_nat] : Y
% 0.30/0.64          @ A2 )
% 0.30/0.64        = ( power_power_int @ Y @ ( finite_card_set_nat @ A2 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % prod_constant
% 0.30/0.64  thf(fact_9008_prod__constant,axiom,
% 0.30/0.64      ! [Y: nat,A2: set_list_nat] :
% 0.30/0.64        ( ( groups2907647131375434839at_nat
% 0.30/0.64          @ ^ [X3: list_nat] : Y
% 0.30/0.64          @ A2 )
% 0.30/0.64        = ( power_power_nat @ Y @ ( finite_card_list_nat @ A2 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % prod_constant
% 0.30/0.64  thf(fact_9009_prod__constant,axiom,
% 0.30/0.64      ! [Y: nat,A2: set_o] :
% 0.30/0.64        ( ( groups3504817904513533571_o_nat
% 0.30/0.64          @ ^ [X3: $o] : Y
% 0.30/0.64          @ A2 )
% 0.30/0.64        = ( power_power_nat @ Y @ ( finite_card_o @ A2 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % prod_constant
% 0.30/0.64  thf(fact_9010_prod__constant,axiom,
% 0.30/0.64      ! [Y: nat,A2: set_set_nat] :
% 0.30/0.64        ( ( groups4248547760180025341at_nat
% 0.30/0.64          @ ^ [X3: set_nat] : Y
% 0.30/0.64          @ A2 )
% 0.30/0.64        = ( power_power_nat @ Y @ ( finite_card_set_nat @ A2 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % prod_constant
% 0.30/0.64  thf(fact_9011_prod__constant,axiom,
% 0.30/0.64      ! [Y: nat,A2: set_int] :
% 0.30/0.64        ( ( groups1707563613775114915nt_nat
% 0.30/0.64          @ ^ [X3: int] : Y
% 0.30/0.64          @ A2 )
% 0.30/0.64        = ( power_power_nat @ Y @ ( finite_card_int @ A2 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % prod_constant
% 0.30/0.64  thf(fact_9012_prod__constant,axiom,
% 0.30/0.64      ! [Y: nat,A2: set_nat] :
% 0.30/0.64        ( ( groups708209901874060359at_nat
% 0.30/0.64          @ ^ [X3: nat] : Y
% 0.30/0.64          @ A2 )
% 0.30/0.64        = ( power_power_nat @ Y @ ( finite_card_nat @ A2 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % prod_constant
% 0.30/0.64  thf(fact_9013_prod__constant,axiom,
% 0.30/0.64      ! [Y: int,A2: set_nat] :
% 0.30/0.64        ( ( groups705719431365010083at_int
% 0.30/0.64          @ ^ [X3: nat] : Y
% 0.30/0.64          @ A2 )
% 0.30/0.64        = ( power_power_int @ Y @ ( finite_card_nat @ A2 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % prod_constant
% 0.30/0.64  thf(fact_9014_prod__constant,axiom,
% 0.30/0.64      ! [Y: int,A2: set_int] :
% 0.30/0.64        ( ( groups1705073143266064639nt_int
% 0.30/0.64          @ ^ [X3: int] : Y
% 0.30/0.64          @ A2 )
% 0.30/0.64        = ( power_power_int @ Y @ ( finite_card_int @ A2 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % prod_constant
% 0.30/0.64  thf(fact_9015_card__0__eq,axiom,
% 0.30/0.64      ! [A2: set_list_nat] :
% 0.30/0.64        ( ( finite8100373058378681591st_nat @ A2 )
% 0.30/0.64       => ( ( ( finite_card_list_nat @ A2 )
% 0.30/0.64            = zero_zero_nat )
% 0.30/0.64          = ( A2 = bot_bot_set_list_nat ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_0_eq
% 0.30/0.64  thf(fact_9016_card__0__eq,axiom,
% 0.30/0.64      ! [A2: set_set_nat] :
% 0.30/0.64        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.64       => ( ( ( finite_card_set_nat @ A2 )
% 0.30/0.64            = zero_zero_nat )
% 0.30/0.64          = ( A2 = bot_bot_set_set_nat ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_0_eq
% 0.30/0.64  thf(fact_9017_card__0__eq,axiom,
% 0.30/0.64      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.30/0.64        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.64       => ( ( ( finite711546835091564841at_nat @ A2 )
% 0.30/0.64            = zero_zero_nat )
% 0.30/0.64          = ( A2 = bot_bo2099793752762293965at_nat ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_0_eq
% 0.30/0.64  thf(fact_9018_card__0__eq,axiom,
% 0.30/0.64      ! [A2: set_o] :
% 0.30/0.64        ( ( finite_finite_o @ A2 )
% 0.30/0.64       => ( ( ( finite_card_o @ A2 )
% 0.30/0.64            = zero_zero_nat )
% 0.30/0.64          = ( A2 = bot_bot_set_o ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_0_eq
% 0.30/0.64  thf(fact_9019_card__0__eq,axiom,
% 0.30/0.64      ! [A2: set_nat] :
% 0.30/0.64        ( ( finite_finite_nat @ A2 )
% 0.30/0.64       => ( ( ( finite_card_nat @ A2 )
% 0.30/0.64            = zero_zero_nat )
% 0.30/0.64          = ( A2 = bot_bot_set_nat ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_0_eq
% 0.30/0.64  thf(fact_9020_card__0__eq,axiom,
% 0.30/0.64      ! [A2: set_int] :
% 0.30/0.64        ( ( finite_finite_int @ A2 )
% 0.30/0.64       => ( ( ( finite_card_int @ A2 )
% 0.30/0.64            = zero_zero_nat )
% 0.30/0.64          = ( A2 = bot_bot_set_int ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_0_eq
% 0.30/0.64  thf(fact_9021_nat__1,axiom,
% 0.30/0.64      ( ( nat2 @ one_one_int )
% 0.30/0.64      = ( suc @ zero_zero_nat ) ) ).
% 0.30/0.64  
% 0.30/0.64  % nat_1
% 0.30/0.64  thf(fact_9022_nat__neg__numeral,axiom,
% 0.30/0.64      ! [K: num] :
% 0.30/0.64        ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 0.30/0.64        = zero_zero_nat ) ).
% 0.30/0.64  
% 0.30/0.64  % nat_neg_numeral
% 0.30/0.64  thf(fact_9023_nat__zminus__int,axiom,
% 0.30/0.64      ! [N: nat] :
% 0.30/0.64        ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.30/0.64        = zero_zero_nat ) ).
% 0.30/0.64  
% 0.30/0.64  % nat_zminus_int
% 0.30/0.64  thf(fact_9024_sum__constant,axiom,
% 0.30/0.64      ! [Y: code_integer,A2: set_o] :
% 0.30/0.64        ( ( groups4406642042086082107nteger
% 0.30/0.64          @ ^ [X3: $o] : Y
% 0.30/0.64          @ A2 )
% 0.30/0.64        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_o @ A2 ) ) @ Y ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_constant
% 0.30/0.64  thf(fact_9025_sum__constant,axiom,
% 0.30/0.64      ! [Y: code_integer,A2: set_nat] :
% 0.30/0.64        ( ( groups7501900531339628137nteger
% 0.30/0.64          @ ^ [X3: nat] : Y
% 0.30/0.64          @ A2 )
% 0.30/0.64        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_nat @ A2 ) ) @ Y ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_constant
% 0.30/0.64  thf(fact_9026_sum__constant,axiom,
% 0.30/0.64      ! [Y: code_integer,A2: set_int] :
% 0.30/0.64        ( ( groups7873554091576472773nteger
% 0.30/0.64          @ ^ [X3: int] : Y
% 0.30/0.64          @ A2 )
% 0.30/0.64        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_int @ A2 ) ) @ Y ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_constant
% 0.30/0.64  thf(fact_9027_sum__constant,axiom,
% 0.30/0.64      ! [Y: int,A2: set_o] :
% 0.30/0.64        ( ( groups8505340233167759370_o_int
% 0.30/0.64          @ ^ [X3: $o] : Y
% 0.30/0.64          @ A2 )
% 0.30/0.64        = ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_o @ A2 ) ) @ Y ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_constant
% 0.30/0.64  thf(fact_9028_sum__constant,axiom,
% 0.30/0.64      ! [Y: int,A2: set_nat] :
% 0.30/0.64        ( ( groups3539618377306564664at_int
% 0.30/0.64          @ ^ [X3: nat] : Y
% 0.30/0.64          @ A2 )
% 0.30/0.64        = ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_nat @ A2 ) ) @ Y ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_constant
% 0.30/0.64  thf(fact_9029_sum__constant,axiom,
% 0.30/0.64      ! [Y: nat,A2: set_o] :
% 0.30/0.64        ( ( groups8507830703676809646_o_nat
% 0.30/0.64          @ ^ [X3: $o] : Y
% 0.30/0.64          @ A2 )
% 0.30/0.64        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_o @ A2 ) ) @ Y ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_constant
% 0.30/0.64  thf(fact_9030_sum__constant,axiom,
% 0.30/0.64      ! [Y: nat,A2: set_int] :
% 0.30/0.64        ( ( groups4541462559716669496nt_nat
% 0.30/0.64          @ ^ [X3: int] : Y
% 0.30/0.64          @ A2 )
% 0.30/0.64        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_int @ A2 ) ) @ Y ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_constant
% 0.30/0.64  thf(fact_9031_sum__constant,axiom,
% 0.30/0.64      ! [Y: rat,A2: set_o] :
% 0.30/0.64        ( ( groups7872700643590313910_o_rat
% 0.30/0.64          @ ^ [X3: $o] : Y
% 0.30/0.64          @ A2 )
% 0.30/0.64        = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_o @ A2 ) ) @ Y ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_constant
% 0.30/0.64  thf(fact_9032_sum__constant,axiom,
% 0.30/0.64      ! [Y: rat,A2: set_nat] :
% 0.30/0.64        ( ( groups2906978787729119204at_rat
% 0.30/0.64          @ ^ [X3: nat] : Y
% 0.30/0.64          @ A2 )
% 0.30/0.64        = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A2 ) ) @ Y ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_constant
% 0.30/0.64  thf(fact_9033_sum__constant,axiom,
% 0.30/0.64      ! [Y: rat,A2: set_int] :
% 0.30/0.64        ( ( groups3906332499630173760nt_rat
% 0.30/0.64          @ ^ [X3: int] : Y
% 0.30/0.64          @ A2 )
% 0.30/0.64        = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A2 ) ) @ Y ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_constant
% 0.30/0.64  thf(fact_9034_card__Diff__insert,axiom,
% 0.30/0.64      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 0.30/0.64        ( ( member8757157785044589968at_nat @ A @ A2 )
% 0.30/0.64       => ( ~ ( member8757157785044589968at_nat @ A @ B2 )
% 0.30/0.64         => ( ( finite3771342082235030671at_nat @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ B2 ) ) )
% 0.30/0.64            = ( minus_minus_nat @ ( finite3771342082235030671at_nat @ ( minus_3314409938677909166at_nat @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_Diff_insert
% 0.30/0.64  thf(fact_9035_card__Diff__insert,axiom,
% 0.30/0.64      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.64        ( ( member8440522571783428010at_nat @ A @ A2 )
% 0.30/0.64       => ( ~ ( member8440522571783428010at_nat @ A @ B2 )
% 0.30/0.64         => ( ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) ) )
% 0.30/0.64            = ( minus_minus_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_Diff_insert
% 0.30/0.64  thf(fact_9036_card__Diff__insert,axiom,
% 0.30/0.64      ! [A: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 0.30/0.64        ( ( member2340774599025711042nt_int @ A @ A2 )
% 0.30/0.64       => ( ~ ( member2340774599025711042nt_int @ A @ B2 )
% 0.30/0.64         => ( ( finite4053189226111446337nt_int @ ( minus_2612819937483484256nt_int @ A2 @ ( insert8897473484851387113nt_int @ A @ B2 ) ) )
% 0.30/0.64            = ( minus_minus_nat @ ( finite4053189226111446337nt_int @ ( minus_2612819937483484256nt_int @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_Diff_insert
% 0.30/0.64  thf(fact_9037_card__Diff__insert,axiom,
% 0.30/0.64      ! [A: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 0.30/0.64        ( ( member6576561426505652726_nat_o @ A @ A2 )
% 0.30/0.64       => ( ~ ( member6576561426505652726_nat_o @ A @ B2 )
% 0.30/0.64         => ( ( finite1363419556375932405_nat_o @ ( minus_1801376950450012436_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ A @ B2 ) ) )
% 0.30/0.64            = ( minus_minus_nat @ ( finite1363419556375932405_nat_o @ ( minus_1801376950450012436_nat_o @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_Diff_insert
% 0.30/0.64  thf(fact_9038_card__Diff__insert,axiom,
% 0.30/0.64      ! [A: list_nat,A2: set_list_nat,B2: set_list_nat] :
% 0.30/0.64        ( ( member_list_nat @ A @ A2 )
% 0.30/0.64       => ( ~ ( member_list_nat @ A @ B2 )
% 0.30/0.64         => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ ( insert_list_nat @ A @ B2 ) ) )
% 0.30/0.64            = ( minus_minus_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_Diff_insert
% 0.30/0.64  thf(fact_9039_card__Diff__insert,axiom,
% 0.30/0.64      ! [A: $o,A2: set_o,B2: set_o] :
% 0.30/0.64        ( ( member_o @ A @ A2 )
% 0.30/0.64       => ( ~ ( member_o @ A @ B2 )
% 0.30/0.64         => ( ( finite_card_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ B2 ) ) )
% 0.30/0.64            = ( minus_minus_nat @ ( finite_card_o @ ( minus_minus_set_o @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_Diff_insert
% 0.30/0.64  thf(fact_9040_card__Diff__insert,axiom,
% 0.30/0.64      ! [A: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 0.30/0.64        ( ( member_set_nat @ A @ A2 )
% 0.30/0.64       => ( ~ ( member_set_nat @ A @ B2 )
% 0.30/0.64         => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ B2 ) ) )
% 0.30/0.64            = ( minus_minus_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_Diff_insert
% 0.30/0.64  thf(fact_9041_card__Diff__insert,axiom,
% 0.30/0.64      ! [A: int,A2: set_int,B2: set_int] :
% 0.30/0.64        ( ( member_int @ A @ A2 )
% 0.30/0.64       => ( ~ ( member_int @ A @ B2 )
% 0.30/0.64         => ( ( finite_card_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) ) )
% 0.30/0.64            = ( minus_minus_nat @ ( finite_card_int @ ( minus_minus_set_int @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_Diff_insert
% 0.30/0.64  thf(fact_9042_card__Diff__insert,axiom,
% 0.30/0.64      ! [A: nat,A2: set_nat,B2: set_nat] :
% 0.30/0.64        ( ( member_nat @ A @ A2 )
% 0.30/0.64       => ( ~ ( member_nat @ A @ B2 )
% 0.30/0.64         => ( ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) ) )
% 0.30/0.64            = ( minus_minus_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_Diff_insert
% 0.30/0.64  thf(fact_9043_card__atLeastAtMost__int,axiom,
% 0.30/0.64      ! [L: int,U: int] :
% 0.30/0.64        ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 0.30/0.64        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_atLeastAtMost_int
% 0.30/0.64  thf(fact_9044_sum_Oinsert_H,axiom,
% 0.30/0.64      ! [I4: set_o,P4: $o > code_integer,I: $o] :
% 0.30/0.64        ( ( finite_finite_o
% 0.30/0.64          @ ( collect_o
% 0.30/0.64            @ ^ [X3: $o] :
% 0.30/0.64                ( ( member_o @ X3 @ I4 )
% 0.30/0.64                & ( ( P4 @ X3 )
% 0.30/0.64                 != zero_z3403309356797280102nteger ) ) ) )
% 0.30/0.64       => ( ( ( member_o @ I @ I4 )
% 0.30/0.64           => ( ( groups1402912129352969042nteger @ P4 @ ( insert_o @ I @ I4 ) )
% 0.30/0.64              = ( groups1402912129352969042nteger @ P4 @ I4 ) ) )
% 0.30/0.64          & ( ~ ( member_o @ I @ I4 )
% 0.30/0.64           => ( ( groups1402912129352969042nteger @ P4 @ ( insert_o @ I @ I4 ) )
% 0.30/0.64              = ( plus_p5714425477246183910nteger @ ( P4 @ I ) @ ( groups1402912129352969042nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.insert'
% 0.30/0.64  thf(fact_9045_sum_Oinsert_H,axiom,
% 0.30/0.64      ! [I4: set_nat,P4: nat > code_integer,I: nat] :
% 0.30/0.64        ( ( finite_finite_nat
% 0.30/0.64          @ ( collect_nat
% 0.30/0.64            @ ^ [X3: nat] :
% 0.30/0.64                ( ( member_nat @ X3 @ I4 )
% 0.30/0.64                & ( ( P4 @ X3 )
% 0.30/0.64                 != zero_z3403309356797280102nteger ) ) ) )
% 0.30/0.64       => ( ( ( member_nat @ I @ I4 )
% 0.30/0.64           => ( ( groups555127423416065298nteger @ P4 @ ( insert_nat @ I @ I4 ) )
% 0.30/0.64              = ( groups555127423416065298nteger @ P4 @ I4 ) ) )
% 0.30/0.64          & ( ~ ( member_nat @ I @ I4 )
% 0.30/0.64           => ( ( groups555127423416065298nteger @ P4 @ ( insert_nat @ I @ I4 ) )
% 0.30/0.64              = ( plus_p5714425477246183910nteger @ ( P4 @ I ) @ ( groups555127423416065298nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.insert'
% 0.30/0.64  thf(fact_9046_sum_Oinsert_H,axiom,
% 0.30/0.64      ! [I4: set_int,P4: int > code_integer,I: int] :
% 0.30/0.64        ( ( finite_finite_int
% 0.30/0.64          @ ( collect_int
% 0.30/0.64            @ ^ [X3: int] :
% 0.30/0.64                ( ( member_int @ X3 @ I4 )
% 0.30/0.64                & ( ( P4 @ X3 )
% 0.30/0.64                 != zero_z3403309356797280102nteger ) ) ) )
% 0.30/0.64       => ( ( ( member_int @ I @ I4 )
% 0.30/0.64           => ( ( groups926780983652909934nteger @ P4 @ ( insert_int @ I @ I4 ) )
% 0.30/0.64              = ( groups926780983652909934nteger @ P4 @ I4 ) ) )
% 0.30/0.64          & ( ~ ( member_int @ I @ I4 )
% 0.30/0.64           => ( ( groups926780983652909934nteger @ P4 @ ( insert_int @ I @ I4 ) )
% 0.30/0.64              = ( plus_p5714425477246183910nteger @ ( P4 @ I ) @ ( groups926780983652909934nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.insert'
% 0.30/0.64  thf(fact_9047_sum_Oinsert_H,axiom,
% 0.30/0.64      ! [I4: set_o,P4: $o > rat,I: $o] :
% 0.30/0.64        ( ( finite_finite_o
% 0.30/0.64          @ ( collect_o
% 0.30/0.64            @ ^ [X3: $o] :
% 0.30/0.64                ( ( member_o @ X3 @ I4 )
% 0.30/0.64                & ( ( P4 @ X3 )
% 0.30/0.64                 != zero_zero_rat ) ) ) )
% 0.30/0.64       => ( ( ( member_o @ I @ I4 )
% 0.30/0.64           => ( ( groups3921277224699582669_o_rat @ P4 @ ( insert_o @ I @ I4 ) )
% 0.30/0.64              = ( groups3921277224699582669_o_rat @ P4 @ I4 ) ) )
% 0.30/0.64          & ( ~ ( member_o @ I @ I4 )
% 0.30/0.64           => ( ( groups3921277224699582669_o_rat @ P4 @ ( insert_o @ I @ I4 ) )
% 0.30/0.64              = ( plus_plus_rat @ ( P4 @ I ) @ ( groups3921277224699582669_o_rat @ P4 @ I4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.insert'
% 0.30/0.64  thf(fact_9048_sum_Oinsert_H,axiom,
% 0.30/0.64      ! [I4: set_nat,P4: nat > rat,I: nat] :
% 0.30/0.64        ( ( finite_finite_nat
% 0.30/0.64          @ ( collect_nat
% 0.30/0.64            @ ^ [X3: nat] :
% 0.30/0.64                ( ( member_nat @ X3 @ I4 )
% 0.30/0.64                & ( ( P4 @ X3 )
% 0.30/0.64                 != zero_zero_rat ) ) ) )
% 0.30/0.64       => ( ( ( member_nat @ I @ I4 )
% 0.30/0.64           => ( ( groups1351286907653491341at_rat @ P4 @ ( insert_nat @ I @ I4 ) )
% 0.30/0.64              = ( groups1351286907653491341at_rat @ P4 @ I4 ) ) )
% 0.30/0.64          & ( ~ ( member_nat @ I @ I4 )
% 0.30/0.64           => ( ( groups1351286907653491341at_rat @ P4 @ ( insert_nat @ I @ I4 ) )
% 0.30/0.64              = ( plus_plus_rat @ ( P4 @ I ) @ ( groups1351286907653491341at_rat @ P4 @ I4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.insert'
% 0.30/0.64  thf(fact_9049_sum_Oinsert_H,axiom,
% 0.30/0.64      ! [I4: set_int,P4: int > rat,I: int] :
% 0.30/0.64        ( ( finite_finite_int
% 0.30/0.64          @ ( collect_int
% 0.30/0.64            @ ^ [X3: int] :
% 0.30/0.64                ( ( member_int @ X3 @ I4 )
% 0.30/0.64                & ( ( P4 @ X3 )
% 0.30/0.64                 != zero_zero_rat ) ) ) )
% 0.30/0.64       => ( ( ( member_int @ I @ I4 )
% 0.30/0.64           => ( ( groups2350640619554545897nt_rat @ P4 @ ( insert_int @ I @ I4 ) )
% 0.30/0.64              = ( groups2350640619554545897nt_rat @ P4 @ I4 ) ) )
% 0.30/0.64          & ( ~ ( member_int @ I @ I4 )
% 0.30/0.64           => ( ( groups2350640619554545897nt_rat @ P4 @ ( insert_int @ I @ I4 ) )
% 0.30/0.64              = ( plus_plus_rat @ ( P4 @ I ) @ ( groups2350640619554545897nt_rat @ P4 @ I4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.insert'
% 0.30/0.64  thf(fact_9050_sum_Oinsert_H,axiom,
% 0.30/0.64      ! [I4: set_o,P4: $o > nat,I: $o] :
% 0.30/0.64        ( ( finite_finite_o
% 0.30/0.64          @ ( collect_o
% 0.30/0.64            @ ^ [X3: $o] :
% 0.30/0.64                ( ( member_o @ X3 @ I4 )
% 0.30/0.64                & ( ( P4 @ X3 )
% 0.30/0.64                 != zero_zero_nat ) ) ) )
% 0.30/0.64       => ( ( ( member_o @ I @ I4 )
% 0.30/0.64           => ( ( groups4556407284786078405_o_nat @ P4 @ ( insert_o @ I @ I4 ) )
% 0.30/0.64              = ( groups4556407284786078405_o_nat @ P4 @ I4 ) ) )
% 0.30/0.64          & ( ~ ( member_o @ I @ I4 )
% 0.30/0.64           => ( ( groups4556407284786078405_o_nat @ P4 @ ( insert_o @ I @ I4 ) )
% 0.30/0.64              = ( plus_plus_nat @ ( P4 @ I ) @ ( groups4556407284786078405_o_nat @ P4 @ I4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.insert'
% 0.30/0.64  thf(fact_9051_sum_Oinsert_H,axiom,
% 0.30/0.64      ! [I4: set_nat,P4: nat > nat,I: nat] :
% 0.30/0.64        ( ( finite_finite_nat
% 0.30/0.64          @ ( collect_nat
% 0.30/0.64            @ ^ [X3: nat] :
% 0.30/0.64                ( ( member_nat @ X3 @ I4 )
% 0.30/0.64                & ( ( P4 @ X3 )
% 0.30/0.64                 != zero_zero_nat ) ) ) )
% 0.30/0.64       => ( ( ( member_nat @ I @ I4 )
% 0.30/0.64           => ( ( groups1986416967739987077at_nat @ P4 @ ( insert_nat @ I @ I4 ) )
% 0.30/0.64              = ( groups1986416967739987077at_nat @ P4 @ I4 ) ) )
% 0.30/0.64          & ( ~ ( member_nat @ I @ I4 )
% 0.30/0.64           => ( ( groups1986416967739987077at_nat @ P4 @ ( insert_nat @ I @ I4 ) )
% 0.30/0.64              = ( plus_plus_nat @ ( P4 @ I ) @ ( groups1986416967739987077at_nat @ P4 @ I4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.insert'
% 0.30/0.64  thf(fact_9052_sum_Oinsert_H,axiom,
% 0.30/0.64      ! [I4: set_int,P4: int > nat,I: int] :
% 0.30/0.64        ( ( finite_finite_int
% 0.30/0.64          @ ( collect_int
% 0.30/0.64            @ ^ [X3: int] :
% 0.30/0.64                ( ( member_int @ X3 @ I4 )
% 0.30/0.64                & ( ( P4 @ X3 )
% 0.30/0.64                 != zero_zero_nat ) ) ) )
% 0.30/0.64       => ( ( ( member_int @ I @ I4 )
% 0.30/0.64           => ( ( groups2985770679641041633nt_nat @ P4 @ ( insert_int @ I @ I4 ) )
% 0.30/0.64              = ( groups2985770679641041633nt_nat @ P4 @ I4 ) ) )
% 0.30/0.64          & ( ~ ( member_int @ I @ I4 )
% 0.30/0.64           => ( ( groups2985770679641041633nt_nat @ P4 @ ( insert_int @ I @ I4 ) )
% 0.30/0.64              = ( plus_plus_nat @ ( P4 @ I ) @ ( groups2985770679641041633nt_nat @ P4 @ I4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.insert'
% 0.30/0.64  thf(fact_9053_sum_Oinsert_H,axiom,
% 0.30/0.64      ! [I4: set_o,P4: $o > int,I: $o] :
% 0.30/0.64        ( ( finite_finite_o
% 0.30/0.64          @ ( collect_o
% 0.30/0.64            @ ^ [X3: $o] :
% 0.30/0.64                ( ( member_o @ X3 @ I4 )
% 0.30/0.64                & ( ( P4 @ X3 )
% 0.30/0.64                 != zero_zero_int ) ) ) )
% 0.30/0.64       => ( ( ( member_o @ I @ I4 )
% 0.30/0.64           => ( ( groups4553916814277028129_o_int @ P4 @ ( insert_o @ I @ I4 ) )
% 0.30/0.64              = ( groups4553916814277028129_o_int @ P4 @ I4 ) ) )
% 0.30/0.64          & ( ~ ( member_o @ I @ I4 )
% 0.30/0.64           => ( ( groups4553916814277028129_o_int @ P4 @ ( insert_o @ I @ I4 ) )
% 0.30/0.64              = ( plus_plus_int @ ( P4 @ I ) @ ( groups4553916814277028129_o_int @ P4 @ I4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.insert'
% 0.30/0.64  thf(fact_9054_card__doubleton__eq__2__iff,axiom,
% 0.30/0.64      ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
% 0.30/0.64        ( ( ( finite3771342082235030671at_nat @ ( insert9069300056098147895at_nat @ A @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) )
% 0.30/0.64          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.64        = ( A != B ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_doubleton_eq_2_iff
% 0.30/0.64  thf(fact_9055_card__doubleton__eq__2__iff,axiom,
% 0.30/0.64      ! [A: list_nat,B: list_nat] :
% 0.30/0.64        ( ( ( finite_card_list_nat @ ( insert_list_nat @ A @ ( insert_list_nat @ B @ bot_bot_set_list_nat ) ) )
% 0.30/0.64          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.64        = ( A != B ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_doubleton_eq_2_iff
% 0.30/0.64  thf(fact_9056_card__doubleton__eq__2__iff,axiom,
% 0.30/0.64      ! [A: set_nat,B: set_nat] :
% 0.30/0.64        ( ( ( finite_card_set_nat @ ( insert_set_nat @ A @ ( insert_set_nat @ B @ bot_bot_set_set_nat ) ) )
% 0.30/0.64          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.64        = ( A != B ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_doubleton_eq_2_iff
% 0.30/0.64  thf(fact_9057_card__doubleton__eq__2__iff,axiom,
% 0.30/0.64      ! [A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 0.30/0.64        ( ( ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ A @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) )
% 0.30/0.64          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.64        = ( A != B ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_doubleton_eq_2_iff
% 0.30/0.64  thf(fact_9058_card__doubleton__eq__2__iff,axiom,
% 0.30/0.64      ! [A: $o,B: $o] :
% 0.30/0.64        ( ( ( finite_card_o @ ( insert_o @ A @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 0.30/0.64          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.64        = ( A != B ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_doubleton_eq_2_iff
% 0.30/0.64  thf(fact_9059_card__doubleton__eq__2__iff,axiom,
% 0.30/0.64      ! [A: nat,B: nat] :
% 0.30/0.64        ( ( ( finite_card_nat @ ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 0.30/0.64          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.64        = ( A != B ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_doubleton_eq_2_iff
% 0.30/0.64  thf(fact_9060_card__doubleton__eq__2__iff,axiom,
% 0.30/0.64      ! [A: int,B: int] :
% 0.30/0.64        ( ( ( finite_card_int @ ( insert_int @ A @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 0.30/0.64          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.64        = ( A != B ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_doubleton_eq_2_iff
% 0.30/0.64  thf(fact_9061_one__less__nat__eq,axiom,
% 0.30/0.64      ! [Z: int] :
% 0.30/0.64        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 0.30/0.64        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 0.30/0.64  
% 0.30/0.64  % one_less_nat_eq
% 0.30/0.64  thf(fact_9062_sum__of__bool__eq,axiom,
% 0.30/0.64      ! [A2: set_o,P: $o > $o] :
% 0.30/0.64        ( ( finite_finite_o @ A2 )
% 0.30/0.64       => ( ( finite_finite_o @ A2 )
% 0.30/0.64         => ( ( groups7872700643590313910_o_rat
% 0.30/0.64              @ ^ [X3: $o] : ( zero_n2052037380579107095ol_rat @ ( P @ X3 ) )
% 0.30/0.64              @ A2 )
% 0.30/0.64            = ( semiri681578069525770553at_rat @ ( finite_card_o @ ( inf_inf_set_o @ A2 @ ( collect_o @ P ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_of_bool_eq
% 0.30/0.64  thf(fact_9063_sum__of__bool__eq,axiom,
% 0.30/0.64      ! [A2: set_int,P: int > $o] :
% 0.30/0.64        ( ( finite_finite_int @ A2 )
% 0.30/0.64       => ( ( finite_finite_int @ A2 )
% 0.30/0.64         => ( ( groups3906332499630173760nt_rat
% 0.30/0.64              @ ^ [X3: int] : ( zero_n2052037380579107095ol_rat @ ( P @ X3 ) )
% 0.30/0.64              @ A2 )
% 0.30/0.64            = ( semiri681578069525770553at_rat @ ( finite_card_int @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_of_bool_eq
% 0.30/0.64  thf(fact_9064_sum__of__bool__eq,axiom,
% 0.30/0.64      ! [A2: set_nat,P: nat > $o] :
% 0.30/0.64        ( ( finite_finite_nat @ A2 )
% 0.30/0.64       => ( ( finite_finite_nat @ A2 )
% 0.30/0.64         => ( ( groups2906978787729119204at_rat
% 0.30/0.64              @ ^ [X3: nat] : ( zero_n2052037380579107095ol_rat @ ( P @ X3 ) )
% 0.30/0.64              @ A2 )
% 0.30/0.64            = ( semiri681578069525770553at_rat @ ( finite_card_nat @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_of_bool_eq
% 0.30/0.64  thf(fact_9065_sum__of__bool__eq,axiom,
% 0.30/0.64      ! [A2: set_o,P: $o > $o] :
% 0.30/0.64        ( ( finite_finite_o @ A2 )
% 0.30/0.64       => ( ( finite_finite_o @ A2 )
% 0.30/0.64         => ( ( groups8505340233167759370_o_int
% 0.30/0.64              @ ^ [X3: $o] : ( zero_n2684676970156552555ol_int @ ( P @ X3 ) )
% 0.30/0.64              @ A2 )
% 0.30/0.64            = ( semiri1314217659103216013at_int @ ( finite_card_o @ ( inf_inf_set_o @ A2 @ ( collect_o @ P ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_of_bool_eq
% 0.30/0.64  thf(fact_9066_sum__of__bool__eq,axiom,
% 0.30/0.64      ! [A2: set_nat,P: nat > $o] :
% 0.30/0.64        ( ( finite_finite_nat @ A2 )
% 0.30/0.64       => ( ( finite_finite_nat @ A2 )
% 0.30/0.64         => ( ( groups3539618377306564664at_int
% 0.30/0.64              @ ^ [X3: nat] : ( zero_n2684676970156552555ol_int @ ( P @ X3 ) )
% 0.30/0.64              @ A2 )
% 0.30/0.64            = ( semiri1314217659103216013at_int @ ( finite_card_nat @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_of_bool_eq
% 0.30/0.64  thf(fact_9067_sum__of__bool__eq,axiom,
% 0.30/0.64      ! [A2: set_o,P: $o > $o] :
% 0.30/0.64        ( ( finite_finite_o @ A2 )
% 0.30/0.64       => ( ( finite_finite_o @ A2 )
% 0.30/0.64         => ( ( groups8507830703676809646_o_nat
% 0.30/0.64              @ ^ [X3: $o] : ( zero_n2687167440665602831ol_nat @ ( P @ X3 ) )
% 0.30/0.64              @ A2 )
% 0.30/0.64            = ( semiri1316708129612266289at_nat @ ( finite_card_o @ ( inf_inf_set_o @ A2 @ ( collect_o @ P ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_of_bool_eq
% 0.30/0.64  thf(fact_9068_sum__of__bool__eq,axiom,
% 0.30/0.64      ! [A2: set_int,P: int > $o] :
% 0.30/0.64        ( ( finite_finite_int @ A2 )
% 0.30/0.64       => ( ( finite_finite_int @ A2 )
% 0.30/0.64         => ( ( groups4541462559716669496nt_nat
% 0.30/0.64              @ ^ [X3: int] : ( zero_n2687167440665602831ol_nat @ ( P @ X3 ) )
% 0.30/0.64              @ A2 )
% 0.30/0.64            = ( semiri1316708129612266289at_nat @ ( finite_card_int @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_of_bool_eq
% 0.30/0.64  thf(fact_9069_sum__of__bool__eq,axiom,
% 0.30/0.64      ! [A2: set_nat,P: nat > $o] :
% 0.30/0.64        ( ( finite_finite_nat @ A2 )
% 0.30/0.64       => ( ( finite_finite_nat @ A2 )
% 0.30/0.64         => ( ( groups3542108847815614940at_nat
% 0.30/0.64              @ ^ [X3: nat] : ( zero_n2687167440665602831ol_nat @ ( P @ X3 ) )
% 0.30/0.64              @ A2 )
% 0.30/0.64            = ( semiri1316708129612266289at_nat @ ( finite_card_nat @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_of_bool_eq
% 0.30/0.64  thf(fact_9070_sum__of__bool__eq,axiom,
% 0.30/0.64      ! [A2: set_int,P: int > $o] :
% 0.30/0.64        ( ( finite_finite_int @ A2 )
% 0.30/0.64       => ( ( finite_finite_int @ A2 )
% 0.30/0.64         => ( ( groups4538972089207619220nt_int
% 0.30/0.64              @ ^ [X3: int] : ( zero_n2684676970156552555ol_int @ ( P @ X3 ) )
% 0.30/0.64              @ A2 )
% 0.30/0.64            = ( semiri1314217659103216013at_int @ ( finite_card_int @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_of_bool_eq
% 0.30/0.64  thf(fact_9071_sum__of__bool__eq,axiom,
% 0.30/0.64      ! [A2: set_list_nat,P: list_nat > $o] :
% 0.30/0.64        ( ( finite8100373058378681591st_nat @ A2 )
% 0.30/0.64       => ( ( finite8100373058378681591st_nat @ A2 )
% 0.30/0.64         => ( ( groups3760926236672600436at_rat
% 0.30/0.64              @ ^ [X3: list_nat] : ( zero_n2052037380579107095ol_rat @ ( P @ X3 ) )
% 0.30/0.64              @ A2 )
% 0.30/0.64            = ( semiri681578069525770553at_rat @ ( finite_card_list_nat @ ( inf_inf_set_list_nat @ A2 @ ( collect_list_nat @ P ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_of_bool_eq
% 0.30/0.64  thf(fact_9072_nat__numeral__diff__1,axiom,
% 0.30/0.64      ! [V: num] :
% 0.30/0.64        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 0.30/0.64        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % nat_numeral_diff_1
% 0.30/0.64  thf(fact_9073_n__subsets,axiom,
% 0.30/0.64      ! [A2: set_Pr958786334691620121nt_int,K: nat] :
% 0.30/0.64        ( ( finite2998713641127702882nt_int @ A2 )
% 0.30/0.64       => ( ( finite4053189226111446337nt_int
% 0.30/0.64            @ ( collec5210948495886036740nt_int
% 0.30/0.64              @ ^ [B4: set_Pr958786334691620121nt_int] :
% 0.30/0.64                  ( ( ord_le2843351958646193337nt_int @ B4 @ A2 )
% 0.30/0.64                  & ( ( finite6756421564338198497nt_int @ B4 )
% 0.30/0.64                    = K ) ) ) )
% 0.30/0.64          = ( binomial @ ( finite6756421564338198497nt_int @ A2 ) @ K ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % n_subsets
% 0.30/0.64  thf(fact_9074_n__subsets,axiom,
% 0.30/0.64      ! [A2: set_list_nat,K: nat] :
% 0.30/0.64        ( ( finite8100373058378681591st_nat @ A2 )
% 0.30/0.64       => ( ( finite2364142230527598318st_nat
% 0.30/0.64            @ ( collect_set_list_nat
% 0.30/0.64              @ ^ [B4: set_list_nat] :
% 0.30/0.64                  ( ( ord_le6045566169113846134st_nat @ B4 @ A2 )
% 0.30/0.64                  & ( ( finite_card_list_nat @ B4 )
% 0.30/0.64                    = K ) ) ) )
% 0.30/0.64          = ( binomial @ ( finite_card_list_nat @ A2 ) @ K ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % n_subsets
% 0.30/0.64  thf(fact_9075_n__subsets,axiom,
% 0.30/0.64      ! [A2: set_o,K: nat] :
% 0.30/0.64        ( ( finite_finite_o @ A2 )
% 0.30/0.64       => ( ( finite_card_set_o
% 0.30/0.64            @ ( collect_set_o
% 0.30/0.64              @ ^ [B4: set_o] :
% 0.30/0.64                  ( ( ord_less_eq_set_o @ B4 @ A2 )
% 0.30/0.64                  & ( ( finite_card_o @ B4 )
% 0.30/0.64                    = K ) ) ) )
% 0.30/0.64          = ( binomial @ ( finite_card_o @ A2 ) @ K ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % n_subsets
% 0.30/0.64  thf(fact_9076_n__subsets,axiom,
% 0.30/0.64      ! [A2: set_set_nat,K: nat] :
% 0.30/0.64        ( ( finite1152437895449049373et_nat @ A2 )
% 0.30/0.64       => ( ( finite1149291290879098388et_nat
% 0.30/0.64            @ ( collect_set_set_nat
% 0.30/0.64              @ ^ [B4: set_set_nat] :
% 0.30/0.64                  ( ( ord_le6893508408891458716et_nat @ B4 @ A2 )
% 0.30/0.64                  & ( ( finite_card_set_nat @ B4 )
% 0.30/0.64                    = K ) ) ) )
% 0.30/0.64          = ( binomial @ ( finite_card_set_nat @ A2 ) @ K ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % n_subsets
% 0.30/0.64  thf(fact_9077_n__subsets,axiom,
% 0.30/0.64      ! [A2: set_int,K: nat] :
% 0.30/0.64        ( ( finite_finite_int @ A2 )
% 0.30/0.64       => ( ( finite_card_set_int
% 0.30/0.64            @ ( collect_set_int
% 0.30/0.64              @ ^ [B4: set_int] :
% 0.30/0.64                  ( ( ord_less_eq_set_int @ B4 @ A2 )
% 0.30/0.64                  & ( ( finite_card_int @ B4 )
% 0.30/0.64                    = K ) ) ) )
% 0.30/0.64          = ( binomial @ ( finite_card_int @ A2 ) @ K ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % n_subsets
% 0.30/0.64  thf(fact_9078_n__subsets,axiom,
% 0.30/0.64      ! [A2: set_Pr1261947904930325089at_nat,K: nat] :
% 0.30/0.64        ( ( finite6177210948735845034at_nat @ A2 )
% 0.30/0.64       => ( ( finite4356350796350151305at_nat
% 0.30/0.64            @ ( collec5514110066124741708at_nat
% 0.30/0.64              @ ^ [B4: set_Pr1261947904930325089at_nat] :
% 0.30/0.64                  ( ( ord_le3146513528884898305at_nat @ B4 @ A2 )
% 0.30/0.64                  & ( ( finite711546835091564841at_nat @ B4 )
% 0.30/0.64                    = K ) ) ) )
% 0.30/0.64          = ( binomial @ ( finite711546835091564841at_nat @ A2 ) @ K ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % n_subsets
% 0.30/0.64  thf(fact_9079_n__subsets,axiom,
% 0.30/0.64      ! [A2: set_nat,K: nat] :
% 0.30/0.64        ( ( finite_finite_nat @ A2 )
% 0.30/0.64       => ( ( finite_card_set_nat
% 0.30/0.64            @ ( collect_set_nat
% 0.30/0.64              @ ^ [B4: set_nat] :
% 0.30/0.64                  ( ( ord_less_eq_set_nat @ B4 @ A2 )
% 0.30/0.64                  & ( ( finite_card_nat @ B4 )
% 0.30/0.64                    = K ) ) ) )
% 0.30/0.64          = ( binomial @ ( finite_card_nat @ A2 ) @ K ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % n_subsets
% 0.30/0.64  thf(fact_9080_sum_Onon__neutral_H,axiom,
% 0.30/0.64      ! [G2: nat > code_integer,I4: set_nat] :
% 0.30/0.64        ( ( groups555127423416065298nteger @ G2
% 0.30/0.64          @ ( collect_nat
% 0.30/0.64            @ ^ [X3: nat] :
% 0.30/0.64                ( ( member_nat @ X3 @ I4 )
% 0.30/0.64                & ( ( G2 @ X3 )
% 0.30/0.64                 != zero_z3403309356797280102nteger ) ) ) )
% 0.30/0.64        = ( groups555127423416065298nteger @ G2 @ I4 ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.non_neutral'
% 0.30/0.64  thf(fact_9081_sum_Onon__neutral_H,axiom,
% 0.30/0.64      ! [G2: int > code_integer,I4: set_int] :
% 0.30/0.64        ( ( groups926780983652909934nteger @ G2
% 0.30/0.64          @ ( collect_int
% 0.30/0.64            @ ^ [X3: int] :
% 0.30/0.64                ( ( member_int @ X3 @ I4 )
% 0.30/0.64                & ( ( G2 @ X3 )
% 0.30/0.64                 != zero_z3403309356797280102nteger ) ) ) )
% 0.30/0.64        = ( groups926780983652909934nteger @ G2 @ I4 ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.non_neutral'
% 0.30/0.64  thf(fact_9082_sum_Onon__neutral_H,axiom,
% 0.30/0.64      ! [G2: nat > rat,I4: set_nat] :
% 0.30/0.64        ( ( groups1351286907653491341at_rat @ G2
% 0.30/0.64          @ ( collect_nat
% 0.30/0.64            @ ^ [X3: nat] :
% 0.30/0.64                ( ( member_nat @ X3 @ I4 )
% 0.30/0.64                & ( ( G2 @ X3 )
% 0.30/0.64                 != zero_zero_rat ) ) ) )
% 0.30/0.64        = ( groups1351286907653491341at_rat @ G2 @ I4 ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.non_neutral'
% 0.30/0.64  thf(fact_9083_sum_Onon__neutral_H,axiom,
% 0.30/0.64      ! [G2: int > rat,I4: set_int] :
% 0.30/0.64        ( ( groups2350640619554545897nt_rat @ G2
% 0.30/0.64          @ ( collect_int
% 0.30/0.64            @ ^ [X3: int] :
% 0.30/0.64                ( ( member_int @ X3 @ I4 )
% 0.30/0.64                & ( ( G2 @ X3 )
% 0.30/0.64                 != zero_zero_rat ) ) ) )
% 0.30/0.64        = ( groups2350640619554545897nt_rat @ G2 @ I4 ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.non_neutral'
% 0.30/0.64  thf(fact_9084_sum_Onon__neutral_H,axiom,
% 0.30/0.64      ! [G2: nat > nat,I4: set_nat] :
% 0.30/0.64        ( ( groups1986416967739987077at_nat @ G2
% 0.30/0.64          @ ( collect_nat
% 0.30/0.64            @ ^ [X3: nat] :
% 0.30/0.64                ( ( member_nat @ X3 @ I4 )
% 0.30/0.64                & ( ( G2 @ X3 )
% 0.30/0.64                 != zero_zero_nat ) ) ) )
% 0.30/0.64        = ( groups1986416967739987077at_nat @ G2 @ I4 ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.non_neutral'
% 0.30/0.64  thf(fact_9085_sum_Onon__neutral_H,axiom,
% 0.30/0.64      ! [G2: int > nat,I4: set_int] :
% 0.30/0.64        ( ( groups2985770679641041633nt_nat @ G2
% 0.30/0.64          @ ( collect_int
% 0.30/0.64            @ ^ [X3: int] :
% 0.30/0.64                ( ( member_int @ X3 @ I4 )
% 0.30/0.64                & ( ( G2 @ X3 )
% 0.30/0.64                 != zero_zero_nat ) ) ) )
% 0.30/0.64        = ( groups2985770679641041633nt_nat @ G2 @ I4 ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.non_neutral'
% 0.30/0.64  thf(fact_9086_sum_Onon__neutral_H,axiom,
% 0.30/0.64      ! [G2: nat > int,I4: set_nat] :
% 0.30/0.64        ( ( groups1983926497230936801at_int @ G2
% 0.30/0.64          @ ( collect_nat
% 0.30/0.64            @ ^ [X3: nat] :
% 0.30/0.64                ( ( member_nat @ X3 @ I4 )
% 0.30/0.64                & ( ( G2 @ X3 )
% 0.30/0.64                 != zero_zero_int ) ) ) )
% 0.30/0.64        = ( groups1983926497230936801at_int @ G2 @ I4 ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.non_neutral'
% 0.30/0.64  thf(fact_9087_sum_Onon__neutral_H,axiom,
% 0.30/0.64      ! [G2: int > int,I4: set_int] :
% 0.30/0.64        ( ( groups2983280209131991357nt_int @ G2
% 0.30/0.64          @ ( collect_int
% 0.30/0.64            @ ^ [X3: int] :
% 0.30/0.64                ( ( member_int @ X3 @ I4 )
% 0.30/0.64                & ( ( G2 @ X3 )
% 0.30/0.64                 != zero_zero_int ) ) ) )
% 0.30/0.64        = ( groups2983280209131991357nt_int @ G2 @ I4 ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.non_neutral'
% 0.30/0.64  thf(fact_9088_sum_Onon__neutral_H,axiom,
% 0.30/0.64      ! [G2: set_nat > code_integer,I4: set_set_nat] :
% 0.30/0.64        ( ( groups9221925307898054856nteger @ G2
% 0.30/0.64          @ ( collect_set_nat
% 0.30/0.64            @ ^ [X3: set_nat] :
% 0.30/0.64                ( ( member_set_nat @ X3 @ I4 )
% 0.30/0.64                & ( ( G2 @ X3 )
% 0.30/0.64                 != zero_z3403309356797280102nteger ) ) ) )
% 0.30/0.64        = ( groups9221925307898054856nteger @ G2 @ I4 ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.non_neutral'
% 0.30/0.64  thf(fact_9089_sum_Onon__neutral_H,axiom,
% 0.30/0.64      ! [G2: set_nat > rat,I4: set_set_nat] :
% 0.30/0.64        ( ( groups713094340420062787at_rat @ G2
% 0.30/0.64          @ ( collect_set_nat
% 0.30/0.64            @ ^ [X3: set_nat] :
% 0.30/0.64                ( ( member_set_nat @ X3 @ I4 )
% 0.30/0.64                & ( ( G2 @ X3 )
% 0.30/0.64                 != zero_zero_rat ) ) ) )
% 0.30/0.64        = ( groups713094340420062787at_rat @ G2 @ I4 ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum.non_neutral'
% 0.30/0.64  thf(fact_9090_card__eq__UNIV__imp__eq__UNIV,axiom,
% 0.30/0.64      ! [A2: set_set_nat] :
% 0.30/0.64        ( ( finite1152437895449049373et_nat @ top_top_set_set_nat )
% 0.30/0.64       => ( ( ( finite_card_set_nat @ A2 )
% 0.30/0.64            = ( finite_card_set_nat @ top_top_set_set_nat ) )
% 0.30/0.64         => ( A2 = top_top_set_set_nat ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_eq_UNIV_imp_eq_UNIV
% 0.30/0.64  thf(fact_9091_card__eq__UNIV__imp__eq__UNIV,axiom,
% 0.30/0.64      ! [A2: set_Pr1261947904930325089at_nat] :
% 0.30/0.64        ( ( finite6177210948735845034at_nat @ top_to4669805908274784177at_nat )
% 0.30/0.64       => ( ( ( finite711546835091564841at_nat @ A2 )
% 0.30/0.64            = ( finite711546835091564841at_nat @ top_to4669805908274784177at_nat ) )
% 0.30/0.64         => ( A2 = top_to4669805908274784177at_nat ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_eq_UNIV_imp_eq_UNIV
% 0.30/0.64  thf(fact_9092_card__eq__UNIV__imp__eq__UNIV,axiom,
% 0.30/0.64      ! [A2: set_list_nat] :
% 0.30/0.64        ( ( finite8100373058378681591st_nat @ top_top_set_list_nat )
% 0.30/0.64       => ( ( ( finite_card_list_nat @ A2 )
% 0.30/0.64            = ( finite_card_list_nat @ top_top_set_list_nat ) )
% 0.30/0.64         => ( A2 = top_top_set_list_nat ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_eq_UNIV_imp_eq_UNIV
% 0.30/0.64  thf(fact_9093_card__eq__UNIV__imp__eq__UNIV,axiom,
% 0.30/0.64      ! [A2: set_o] :
% 0.30/0.64        ( ( finite_finite_o @ top_top_set_o )
% 0.30/0.64       => ( ( ( finite_card_o @ A2 )
% 0.30/0.64            = ( finite_card_o @ top_top_set_o ) )
% 0.30/0.64         => ( A2 = top_top_set_o ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_eq_UNIV_imp_eq_UNIV
% 0.30/0.64  thf(fact_9094_card__eq__UNIV__imp__eq__UNIV,axiom,
% 0.30/0.64      ! [A2: set_rat] :
% 0.30/0.64        ( ( finite_finite_rat @ top_top_set_rat )
% 0.30/0.64       => ( ( ( finite_card_rat @ A2 )
% 0.30/0.64            = ( finite_card_rat @ top_top_set_rat ) )
% 0.30/0.64         => ( A2 = top_top_set_rat ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_eq_UNIV_imp_eq_UNIV
% 0.30/0.64  thf(fact_9095_card__eq__UNIV__imp__eq__UNIV,axiom,
% 0.30/0.64      ! [A2: set_nat] :
% 0.30/0.64        ( ( finite_finite_nat @ top_top_set_nat )
% 0.30/0.64       => ( ( ( finite_card_nat @ A2 )
% 0.30/0.64            = ( finite_card_nat @ top_top_set_nat ) )
% 0.30/0.64         => ( A2 = top_top_set_nat ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_eq_UNIV_imp_eq_UNIV
% 0.30/0.64  thf(fact_9096_card__eq__UNIV__imp__eq__UNIV,axiom,
% 0.30/0.64      ! [A2: set_int] :
% 0.30/0.64        ( ( finite_finite_int @ top_top_set_int )
% 0.30/0.64       => ( ( ( finite_card_int @ A2 )
% 0.30/0.64            = ( finite_card_int @ top_top_set_int ) )
% 0.30/0.64         => ( A2 = top_top_set_int ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_eq_UNIV_imp_eq_UNIV
% 0.30/0.64  thf(fact_9097_nat__one__as__int,axiom,
% 0.30/0.64      ( one_one_nat
% 0.30/0.64      = ( nat2 @ one_one_int ) ) ).
% 0.30/0.64  
% 0.30/0.64  % nat_one_as_int
% 0.30/0.64  thf(fact_9098_sum__multicount__gen,axiom,
% 0.30/0.64      ! [S3: set_o,T3: set_nat,R: $o > nat > $o,K: nat > nat] :
% 0.30/0.64        ( ( finite_finite_o @ S3 )
% 0.30/0.64       => ( ( finite_finite_nat @ T3 )
% 0.30/0.64         => ( ! [X2: nat] :
% 0.30/0.64                ( ( member_nat @ X2 @ T3 )
% 0.30/0.64               => ( ( finite_card_o
% 0.30/0.64                    @ ( collect_o
% 0.30/0.64                      @ ^ [I3: $o] :
% 0.30/0.64                          ( ( member_o @ I3 @ S3 )
% 0.30/0.64                          & ( R @ I3 @ X2 ) ) ) )
% 0.30/0.64                  = ( K @ X2 ) ) )
% 0.30/0.64           => ( ( groups8507830703676809646_o_nat
% 0.30/0.64                @ ^ [I3: $o] :
% 0.30/0.64                    ( finite_card_nat
% 0.30/0.64                    @ ( collect_nat
% 0.30/0.64                      @ ^ [J3: nat] :
% 0.30/0.64                          ( ( member_nat @ J3 @ T3 )
% 0.30/0.64                          & ( R @ I3 @ J3 ) ) ) )
% 0.30/0.64                @ S3 )
% 0.30/0.64              = ( groups3542108847815614940at_nat @ K @ T3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_multicount_gen
% 0.30/0.64  thf(fact_9099_sum__multicount__gen,axiom,
% 0.30/0.64      ! [S3: set_int,T3: set_nat,R: int > nat > $o,K: nat > nat] :
% 0.30/0.64        ( ( finite_finite_int @ S3 )
% 0.30/0.64       => ( ( finite_finite_nat @ T3 )
% 0.30/0.64         => ( ! [X2: nat] :
% 0.30/0.64                ( ( member_nat @ X2 @ T3 )
% 0.30/0.64               => ( ( finite_card_int
% 0.30/0.64                    @ ( collect_int
% 0.30/0.64                      @ ^ [I3: int] :
% 0.30/0.64                          ( ( member_int @ I3 @ S3 )
% 0.30/0.64                          & ( R @ I3 @ X2 ) ) ) )
% 0.30/0.64                  = ( K @ X2 ) ) )
% 0.30/0.64           => ( ( groups4541462559716669496nt_nat
% 0.30/0.64                @ ^ [I3: int] :
% 0.30/0.64                    ( finite_card_nat
% 0.30/0.64                    @ ( collect_nat
% 0.30/0.64                      @ ^ [J3: nat] :
% 0.30/0.64                          ( ( member_nat @ J3 @ T3 )
% 0.30/0.64                          & ( R @ I3 @ J3 ) ) ) )
% 0.30/0.64                @ S3 )
% 0.30/0.64              = ( groups3542108847815614940at_nat @ K @ T3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_multicount_gen
% 0.30/0.64  thf(fact_9100_sum__multicount__gen,axiom,
% 0.30/0.64      ! [S3: set_nat,T3: set_o,R: nat > $o > $o,K: $o > nat] :
% 0.30/0.64        ( ( finite_finite_nat @ S3 )
% 0.30/0.64       => ( ( finite_finite_o @ T3 )
% 0.30/0.64         => ( ! [X2: $o] :
% 0.30/0.64                ( ( member_o @ X2 @ T3 )
% 0.30/0.64               => ( ( finite_card_nat
% 0.30/0.64                    @ ( collect_nat
% 0.30/0.64                      @ ^ [I3: nat] :
% 0.30/0.64                          ( ( member_nat @ I3 @ S3 )
% 0.30/0.64                          & ( R @ I3 @ X2 ) ) ) )
% 0.30/0.64                  = ( K @ X2 ) ) )
% 0.30/0.64           => ( ( groups3542108847815614940at_nat
% 0.30/0.64                @ ^ [I3: nat] :
% 0.30/0.64                    ( finite_card_o
% 0.30/0.64                    @ ( collect_o
% 0.30/0.64                      @ ^ [J3: $o] :
% 0.30/0.64                          ( ( member_o @ J3 @ T3 )
% 0.30/0.64                          & ( R @ I3 @ J3 ) ) ) )
% 0.30/0.64                @ S3 )
% 0.30/0.64              = ( groups8507830703676809646_o_nat @ K @ T3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_multicount_gen
% 0.30/0.64  thf(fact_9101_sum__multicount__gen,axiom,
% 0.30/0.64      ! [S3: set_nat,T3: set_int,R: nat > int > $o,K: int > nat] :
% 0.30/0.64        ( ( finite_finite_nat @ S3 )
% 0.30/0.64       => ( ( finite_finite_int @ T3 )
% 0.30/0.64         => ( ! [X2: int] :
% 0.30/0.64                ( ( member_int @ X2 @ T3 )
% 0.30/0.64               => ( ( finite_card_nat
% 0.30/0.64                    @ ( collect_nat
% 0.30/0.64                      @ ^ [I3: nat] :
% 0.30/0.64                          ( ( member_nat @ I3 @ S3 )
% 0.30/0.64                          & ( R @ I3 @ X2 ) ) ) )
% 0.30/0.64                  = ( K @ X2 ) ) )
% 0.30/0.64           => ( ( groups3542108847815614940at_nat
% 0.30/0.64                @ ^ [I3: nat] :
% 0.30/0.64                    ( finite_card_int
% 0.30/0.64                    @ ( collect_int
% 0.30/0.64                      @ ^ [J3: int] :
% 0.30/0.64                          ( ( member_int @ J3 @ T3 )
% 0.30/0.64                          & ( R @ I3 @ J3 ) ) ) )
% 0.30/0.64                @ S3 )
% 0.30/0.64              = ( groups4541462559716669496nt_nat @ K @ T3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_multicount_gen
% 0.30/0.64  thf(fact_9102_sum__multicount__gen,axiom,
% 0.30/0.64      ! [S3: set_nat,T3: set_nat,R: nat > nat > $o,K: nat > nat] :
% 0.30/0.64        ( ( finite_finite_nat @ S3 )
% 0.30/0.64       => ( ( finite_finite_nat @ T3 )
% 0.30/0.64         => ( ! [X2: nat] :
% 0.30/0.64                ( ( member_nat @ X2 @ T3 )
% 0.30/0.64               => ( ( finite_card_nat
% 0.30/0.64                    @ ( collect_nat
% 0.30/0.64                      @ ^ [I3: nat] :
% 0.30/0.64                          ( ( member_nat @ I3 @ S3 )
% 0.30/0.64                          & ( R @ I3 @ X2 ) ) ) )
% 0.30/0.64                  = ( K @ X2 ) ) )
% 0.30/0.64           => ( ( groups3542108847815614940at_nat
% 0.30/0.64                @ ^ [I3: nat] :
% 0.30/0.64                    ( finite_card_nat
% 0.30/0.64                    @ ( collect_nat
% 0.30/0.64                      @ ^ [J3: nat] :
% 0.30/0.64                          ( ( member_nat @ J3 @ T3 )
% 0.30/0.64                          & ( R @ I3 @ J3 ) ) ) )
% 0.30/0.64                @ S3 )
% 0.30/0.64              = ( groups3542108847815614940at_nat @ K @ T3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_multicount_gen
% 0.30/0.64  thf(fact_9103_sum__multicount__gen,axiom,
% 0.30/0.64      ! [S3: set_list_nat,T3: set_nat,R: list_nat > nat > $o,K: nat > nat] :
% 0.30/0.64        ( ( finite8100373058378681591st_nat @ S3 )
% 0.30/0.64       => ( ( finite_finite_nat @ T3 )
% 0.30/0.64         => ( ! [X2: nat] :
% 0.30/0.64                ( ( member_nat @ X2 @ T3 )
% 0.30/0.64               => ( ( finite_card_list_nat
% 0.30/0.64                    @ ( collect_list_nat
% 0.30/0.64                      @ ^ [I3: list_nat] :
% 0.30/0.64                          ( ( member_list_nat @ I3 @ S3 )
% 0.30/0.64                          & ( R @ I3 @ X2 ) ) ) )
% 0.30/0.64                  = ( K @ X2 ) ) )
% 0.30/0.64           => ( ( groups4396056296759096172at_nat
% 0.30/0.64                @ ^ [I3: list_nat] :
% 0.30/0.64                    ( finite_card_nat
% 0.30/0.64                    @ ( collect_nat
% 0.30/0.64                      @ ^ [J3: nat] :
% 0.30/0.64                          ( ( member_nat @ J3 @ T3 )
% 0.30/0.64                          & ( R @ I3 @ J3 ) ) ) )
% 0.30/0.64                @ S3 )
% 0.30/0.64              = ( groups3542108847815614940at_nat @ K @ T3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_multicount_gen
% 0.30/0.64  thf(fact_9104_sum__multicount__gen,axiom,
% 0.30/0.64      ! [S3: set_set_nat,T3: set_nat,R: set_nat > nat > $o,K: nat > nat] :
% 0.30/0.64        ( ( finite1152437895449049373et_nat @ S3 )
% 0.30/0.64       => ( ( finite_finite_nat @ T3 )
% 0.30/0.64         => ( ! [X2: nat] :
% 0.30/0.64                ( ( member_nat @ X2 @ T3 )
% 0.30/0.64               => ( ( finite_card_set_nat
% 0.30/0.64                    @ ( collect_set_nat
% 0.30/0.64                      @ ^ [I3: set_nat] :
% 0.30/0.64                          ( ( member_set_nat @ I3 @ S3 )
% 0.30/0.64                          & ( R @ I3 @ X2 ) ) ) )
% 0.30/0.64                  = ( K @ X2 ) ) )
% 0.30/0.64           => ( ( groups8294997508430121362at_nat
% 0.30/0.64                @ ^ [I3: set_nat] :
% 0.30/0.64                    ( finite_card_nat
% 0.30/0.64                    @ ( collect_nat
% 0.30/0.64                      @ ^ [J3: nat] :
% 0.30/0.64                          ( ( member_nat @ J3 @ T3 )
% 0.30/0.64                          & ( R @ I3 @ J3 ) ) ) )
% 0.30/0.64                @ S3 )
% 0.30/0.64              = ( groups3542108847815614940at_nat @ K @ T3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_multicount_gen
% 0.30/0.64  thf(fact_9105_sum__multicount__gen,axiom,
% 0.30/0.64      ! [S3: set_nat,T3: set_list_nat,R: nat > list_nat > $o,K: list_nat > nat] :
% 0.30/0.64        ( ( finite_finite_nat @ S3 )
% 0.30/0.64       => ( ( finite8100373058378681591st_nat @ T3 )
% 0.30/0.64         => ( ! [X2: list_nat] :
% 0.30/0.64                ( ( member_list_nat @ X2 @ T3 )
% 0.30/0.64               => ( ( finite_card_nat
% 0.30/0.64                    @ ( collect_nat
% 0.30/0.64                      @ ^ [I3: nat] :
% 0.30/0.64                          ( ( member_nat @ I3 @ S3 )
% 0.30/0.64                          & ( R @ I3 @ X2 ) ) ) )
% 0.30/0.64                  = ( K @ X2 ) ) )
% 0.30/0.64           => ( ( groups3542108847815614940at_nat
% 0.30/0.64                @ ^ [I3: nat] :
% 0.30/0.64                    ( finite_card_list_nat
% 0.30/0.64                    @ ( collect_list_nat
% 0.30/0.64                      @ ^ [J3: list_nat] :
% 0.30/0.64                          ( ( member_list_nat @ J3 @ T3 )
% 0.30/0.64                          & ( R @ I3 @ J3 ) ) ) )
% 0.30/0.64                @ S3 )
% 0.30/0.64              = ( groups4396056296759096172at_nat @ K @ T3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_multicount_gen
% 0.30/0.64  thf(fact_9106_sum__multicount__gen,axiom,
% 0.30/0.64      ! [S3: set_nat,T3: set_set_nat,R: nat > set_nat > $o,K: set_nat > nat] :
% 0.30/0.64        ( ( finite_finite_nat @ S3 )
% 0.30/0.64       => ( ( finite1152437895449049373et_nat @ T3 )
% 0.30/0.64         => ( ! [X2: set_nat] :
% 0.30/0.64                ( ( member_set_nat @ X2 @ T3 )
% 0.30/0.64               => ( ( finite_card_nat
% 0.30/0.64                    @ ( collect_nat
% 0.30/0.64                      @ ^ [I3: nat] :
% 0.30/0.64                          ( ( member_nat @ I3 @ S3 )
% 0.30/0.64                          & ( R @ I3 @ X2 ) ) ) )
% 0.30/0.64                  = ( K @ X2 ) ) )
% 0.30/0.64           => ( ( groups3542108847815614940at_nat
% 0.30/0.64                @ ^ [I3: nat] :
% 0.30/0.64                    ( finite_card_set_nat
% 0.30/0.64                    @ ( collect_set_nat
% 0.30/0.64                      @ ^ [J3: set_nat] :
% 0.30/0.64                          ( ( member_set_nat @ J3 @ T3 )
% 0.30/0.64                          & ( R @ I3 @ J3 ) ) ) )
% 0.30/0.64                @ S3 )
% 0.30/0.64              = ( groups8294997508430121362at_nat @ K @ T3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_multicount_gen
% 0.30/0.64  thf(fact_9107_sum__multicount__gen,axiom,
% 0.30/0.64      ! [S3: set_Pr1261947904930325089at_nat,T3: set_nat,R: product_prod_nat_nat > nat > $o,K: nat > nat] :
% 0.30/0.64        ( ( finite6177210948735845034at_nat @ S3 )
% 0.30/0.64       => ( ( finite_finite_nat @ T3 )
% 0.30/0.64         => ( ! [X2: nat] :
% 0.30/0.64                ( ( member_nat @ X2 @ T3 )
% 0.30/0.64               => ( ( finite711546835091564841at_nat
% 0.30/0.64                    @ ( collec3392354462482085612at_nat
% 0.30/0.64                      @ ^ [I3: product_prod_nat_nat] :
% 0.30/0.64                          ( ( member8440522571783428010at_nat @ I3 @ S3 )
% 0.30/0.64                          & ( R @ I3 @ X2 ) ) ) )
% 0.30/0.64                  = ( K @ X2 ) ) )
% 0.30/0.64           => ( ( groups977919841031483927at_nat
% 0.30/0.64                @ ^ [I3: product_prod_nat_nat] :
% 0.30/0.64                    ( finite_card_nat
% 0.30/0.64                    @ ( collect_nat
% 0.30/0.64                      @ ^ [J3: nat] :
% 0.30/0.64                          ( ( member_nat @ J3 @ T3 )
% 0.30/0.64                          & ( R @ I3 @ J3 ) ) ) )
% 0.30/0.64                @ S3 )
% 0.30/0.64              = ( groups3542108847815614940at_nat @ K @ T3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sum_multicount_gen
% 0.30/0.64  thf(fact_9108_card__less,axiom,
% 0.30/0.64      ! [M4: set_nat,I: nat] :
% 0.30/0.64        ( ( member_nat @ zero_zero_nat @ M4 )
% 0.30/0.64       => ( ( finite_card_nat
% 0.30/0.64            @ ( collect_nat
% 0.30/0.64              @ ^ [K4: nat] :
% 0.30/0.64                  ( ( member_nat @ K4 @ M4 )
% 0.30/0.64                  & ( ord_less_nat @ K4 @ ( suc @ I ) ) ) ) )
% 0.30/0.64         != zero_zero_nat ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_less
% 0.30/0.64  thf(fact_9109_card__less__Suc,axiom,
% 0.30/0.64      ! [M4: set_nat,I: nat] :
% 0.30/0.64        ( ( member_nat @ zero_zero_nat @ M4 )
% 0.30/0.64       => ( ( suc
% 0.30/0.64            @ ( finite_card_nat
% 0.30/0.64              @ ( collect_nat
% 0.30/0.64                @ ^ [K4: nat] :
% 0.30/0.64                    ( ( member_nat @ ( suc @ K4 ) @ M4 )
% 0.30/0.64                    & ( ord_less_nat @ K4 @ I ) ) ) ) )
% 0.30/0.64          = ( finite_card_nat
% 0.30/0.64            @ ( collect_nat
% 0.30/0.64              @ ^ [K4: nat] :
% 0.30/0.64                  ( ( member_nat @ K4 @ M4 )
% 0.30/0.64                  & ( ord_less_nat @ K4 @ ( suc @ I ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_less_Suc
% 0.30/0.64  thf(fact_9110_card__less__Suc2,axiom,
% 0.30/0.64      ! [M4: set_nat,I: nat] :
% 0.30/0.64        ( ~ ( member_nat @ zero_zero_nat @ M4 )
% 0.30/0.64       => ( ( finite_card_nat
% 0.30/0.64            @ ( collect_nat
% 0.30/0.64              @ ^ [K4: nat] :
% 0.30/0.64                  ( ( member_nat @ ( suc @ K4 ) @ M4 )
% 0.30/0.64                  & ( ord_less_nat @ K4 @ I ) ) ) )
% 0.30/0.64          = ( finite_card_nat
% 0.30/0.64            @ ( collect_nat
% 0.30/0.64              @ ^ [K4: nat] :
% 0.30/0.64                  ( ( member_nat @ K4 @ M4 )
% 0.30/0.64                  & ( ord_less_nat @ K4 @ ( suc @ I ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_less_Suc2
% 0.30/0.64  thf(fact_9111_nat__plus__as__int,axiom,
% 0.30/0.64      ( plus_plus_nat
% 0.30/0.64      = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % nat_plus_as_int
% 0.30/0.64  thf(fact_9112_nat__times__as__int,axiom,
% 0.30/0.64      ( times_times_nat
% 0.30/0.64      = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % nat_times_as_int
% 0.30/0.64  thf(fact_9113_nat__minus__as__int,axiom,
% 0.30/0.64      ( minus_minus_nat
% 0.30/0.64      = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % nat_minus_as_int
% 0.30/0.64  thf(fact_9114_nat__div__as__int,axiom,
% 0.30/0.64      ( divide_divide_nat
% 0.30/0.64      = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % nat_div_as_int
% 0.30/0.64  thf(fact_9115_nat__mod__as__int,axiom,
% 0.30/0.64      ( modulo_modulo_nat
% 0.30/0.64      = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % nat_mod_as_int
% 0.30/0.64  thf(fact_9116_Suc__as__int,axiom,
% 0.30/0.64      ( suc
% 0.30/0.64      = ( ^ [A3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ one_one_int ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Suc_as_int
% 0.30/0.64  thf(fact_9117_card__sum__le__nat__sum,axiom,
% 0.30/0.64      ! [S: set_nat] :
% 0.30/0.64        ( ord_less_eq_nat
% 0.30/0.64        @ ( groups3542108847815614940at_nat
% 0.30/0.64          @ ^ [X3: nat] : X3
% 0.30/0.64          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S ) ) )
% 0.30/0.64        @ ( groups3542108847815614940at_nat
% 0.30/0.64          @ ^ [X3: nat] : X3
% 0.30/0.64          @ S ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_sum_le_nat_sum
% 0.30/0.64  thf(fact_9118_Suc__nat__eq__nat__zadd1,axiom,
% 0.30/0.64      ! [Z: int] :
% 0.30/0.64        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.30/0.64       => ( ( suc @ ( nat2 @ Z ) )
% 0.30/0.64          = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Suc_nat_eq_nat_zadd1
% 0.30/0.64  thf(fact_9119_nat__mult__distrib__neg,axiom,
% 0.30/0.64      ! [Z: int,Z8: int] :
% 0.30/0.64        ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 0.30/0.64       => ( ( nat2 @ ( times_times_int @ Z @ Z8 ) )
% 0.30/0.64          = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z8 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % nat_mult_distrib_neg
% 0.30/0.64  thf(fact_9120_diff__nat__eq__if,axiom,
% 0.30/0.64      ! [Z8: int,Z: int] :
% 0.30/0.64        ( ( ( ord_less_int @ Z8 @ zero_zero_int )
% 0.30/0.64         => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z8 ) )
% 0.30/0.64            = ( nat2 @ Z ) ) )
% 0.30/0.64        & ( ~ ( ord_less_int @ Z8 @ zero_zero_int )
% 0.30/0.64         => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z8 ) )
% 0.30/0.64            = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z8 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z8 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % diff_nat_eq_if
% 0.30/0.64  thf(fact_9121_card__UNIV__char,axiom,
% 0.30/0.64      ( ( finite_card_char @ top_top_set_char )
% 0.30/0.64      = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_UNIV_char
% 0.30/0.64  thf(fact_9122_divmod__integer__eq__cases,axiom,
% 0.30/0.64      ( code_divmod_integer
% 0.30/0.64      = ( ^ [K4: code_integer,L2: code_integer] :
% 0.30/0.64            ( if_Pro6119634080678213985nteger @ ( K4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.30/0.64            @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K4 )
% 0.30/0.64              @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L2
% 0.30/0.64                @ ( if_Pro6119634080678213985nteger
% 0.30/0.64                  @ ( ( sgn_sgn_Code_integer @ K4 )
% 0.30/0.64                    = ( sgn_sgn_Code_integer @ L2 ) )
% 0.30/0.64                  @ ( code_divmod_abs @ K4 @ L2 )
% 0.30/0.64                  @ ( produc6916734918728496179nteger
% 0.30/0.64                    @ ^ [R4: code_integer,S2: code_integer] : ( if_Pro6119634080678213985nteger @ ( S2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R4 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L2 ) @ S2 ) ) )
% 0.30/0.64                    @ ( code_divmod_abs @ K4 @ L2 ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % divmod_integer_eq_cases
% 0.30/0.64  thf(fact_9123_or__minus__numerals_I2_J,axiom,
% 0.30/0.64      ! [N: num] :
% 0.30/0.64        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.30/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % or_minus_numerals(2)
% 0.30/0.64  thf(fact_9124_or__minus__numerals_I6_J,axiom,
% 0.30/0.64      ! [N: num] :
% 0.30/0.64        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 0.30/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % or_minus_numerals(6)
% 0.30/0.64  thf(fact_9125_or__minus__minus__numerals,axiom,
% 0.30/0.64      ! [M: num,N: num] :
% 0.30/0.64        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.64        = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % or_minus_minus_numerals
% 0.30/0.64  thf(fact_9126_and__minus__minus__numerals,axiom,
% 0.30/0.64      ! [M: num,N: num] :
% 0.30/0.64        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.64        = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % and_minus_minus_numerals
% 0.30/0.64  thf(fact_9127_UNIV__bool,axiom,
% 0.30/0.64      ( top_top_set_o
% 0.30/0.64      = ( insert_o @ $false @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % UNIV_bool
% 0.30/0.64  thf(fact_9128_set__bit__int__def,axiom,
% 0.30/0.64      ( bit_se7879613467334960850it_int
% 0.30/0.64      = ( ^ [N2: nat,K4: int] : ( bit_se1409905431419307370or_int @ K4 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % set_bit_int_def
% 0.30/0.64  thf(fact_9129_set__bit__nat__def,axiom,
% 0.30/0.64      ( bit_se7882103937844011126it_nat
% 0.30/0.64      = ( ^ [M2: nat,N2: nat] : ( bit_se1412395901928357646or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M2 @ one_one_nat ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % set_bit_nat_def
% 0.30/0.64  thf(fact_9130_or__not__numerals_I1_J,axiom,
% 0.30/0.64      ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.30/0.64      = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 0.30/0.64  
% 0.30/0.64  % or_not_numerals(1)
% 0.30/0.64  thf(fact_9131_or__not__numerals_I2_J,axiom,
% 0.30/0.64      ! [N: num] :
% 0.30/0.64        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.30/0.64        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % or_not_numerals(2)
% 0.30/0.64  thf(fact_9132_or__not__numerals_I4_J,axiom,
% 0.30/0.64      ! [M: num] :
% 0.30/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.30/0.64        = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 0.30/0.64  
% 0.30/0.64  % or_not_numerals(4)
% 0.30/0.64  thf(fact_9133_or__not__numerals_I3_J,axiom,
% 0.30/0.64      ! [N: num] :
% 0.30/0.64        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.30/0.64        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % or_not_numerals(3)
% 0.30/0.64  thf(fact_9134_or__not__numerals_I7_J,axiom,
% 0.30/0.64      ! [M: num] :
% 0.30/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 0.30/0.64        = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 0.30/0.64  
% 0.30/0.64  % or_not_numerals(7)
% 0.30/0.64  thf(fact_9135_or__not__numerals_I5_J,axiom,
% 0.30/0.64      ! [M: num,N: num] :
% 0.30/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.30/0.64        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % or_not_numerals(5)
% 0.30/0.64  thf(fact_9136_or__not__numerals_I9_J,axiom,
% 0.30/0.64      ! [M: num,N: num] :
% 0.30/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.30/0.64        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % or_not_numerals(9)
% 0.30/0.64  thf(fact_9137_or__not__numerals_I8_J,axiom,
% 0.30/0.64      ! [M: num,N: num] :
% 0.30/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.30/0.64        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % or_not_numerals(8)
% 0.30/0.64  thf(fact_9138_or__int__unfold,axiom,
% 0.30/0.64      ( bit_se1409905431419307370or_int
% 0.30/0.64      = ( ^ [K4: int,L2: int] :
% 0.30/0.64            ( if_int
% 0.30/0.64            @ ( ( K4
% 0.30/0.64                = ( uminus_uminus_int @ one_one_int ) )
% 0.30/0.64              | ( L2
% 0.30/0.64                = ( uminus_uminus_int @ one_one_int ) ) )
% 0.30/0.64            @ ( uminus_uminus_int @ one_one_int )
% 0.30/0.64            @ ( if_int @ ( K4 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K4 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K4 @ ( 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 @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % or_int_unfold
% 0.30/0.64  thf(fact_9139_or__minus__numerals_I5_J,axiom,
% 0.30/0.64      ! [N: num] :
% 0.30/0.64        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 0.30/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % or_minus_numerals(5)
% 0.30/0.64  thf(fact_9140_or__minus__numerals_I1_J,axiom,
% 0.30/0.64      ! [N: num] :
% 0.30/0.64        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.30/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % or_minus_numerals(1)
% 0.30/0.64  thf(fact_9141_card__greaterThanLessThan__int,axiom,
% 0.30/0.64      ! [L: int,U: int] :
% 0.30/0.64        ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 0.30/0.64        = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % card_greaterThanLessThan_int
% 0.30/0.64  thf(fact_9142_or__minus__numerals_I8_J,axiom,
% 0.30/0.64      ! [N: num,M: num] :
% 0.30/0.64        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.30/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % or_minus_numerals(8)
% 0.30/0.64  thf(fact_9143_or__minus__numerals_I4_J,axiom,
% 0.30/0.64      ! [M: num,N: num] :
% 0.30/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.30/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % or_minus_numerals(4)
% 0.30/0.64  thf(fact_9144_or__minus__numerals_I3_J,axiom,
% 0.30/0.64      ! [M: num,N: num] :
% 0.30/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.30/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % or_minus_numerals(3)
% 0.30/0.64  thf(fact_9145_or__minus__numerals_I7_J,axiom,
% 0.30/0.64      ! [N: num,M: num] :
% 0.30/0.64        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.30/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % or_minus_numerals(7)
% 0.30/0.64  thf(fact_9146_sup__int__def,axiom,
% 0.30/0.64      sup_sup_int = ord_max_int ).
% 0.30/0.64  
% 0.30/0.64  % sup_int_def
% 0.30/0.64  thf(fact_9147_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 0.30/0.64      ! [L: int,U: int] :
% 0.30/0.64        ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 0.30/0.64        = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 0.30/0.64  
% 0.30/0.64  % atLeastPlusOneLessThan_greaterThanLessThan_int
% 0.30/0.64  thf(fact_9148_int__numeral__or__not__num__neg,axiom,
% 0.30/0.64      ! [M: num,N: num] :
% 0.30/0.64        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % int_numeral_or_not_num_neg
% 0.30/0.64  thf(fact_9149_int__numeral__not__or__num__neg,axiom,
% 0.30/0.64      ! [M: num,N: num] :
% 0.30/0.64        ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.30/0.64        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N @ M ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % int_numeral_not_or_num_neg
% 0.30/0.64  thf(fact_9150_numeral__or__not__num__eq,axiom,
% 0.30/0.64      ! [M: num,N: num] :
% 0.30/0.64        ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) )
% 0.30/0.64        = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % numeral_or_not_num_eq
% 0.30/0.64  thf(fact_9151_Sup__nat__empty,axiom,
% 0.30/0.64      ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 0.30/0.64      = zero_zero_nat ) ).
% 0.30/0.64  
% 0.30/0.64  % Sup_nat_empty
% 0.30/0.64  thf(fact_9152_max__nat_Osemilattice__neutr__axioms,axiom,
% 0.30/0.64      semila9081495762789891438tr_nat @ ord_max_nat @ zero_zero_nat ).
% 0.30/0.64  
% 0.30/0.64  % max_nat.semilattice_neutr_axioms
% 0.30/0.64  thf(fact_9153_max__nat_Ocomm__monoid__axioms,axiom,
% 0.30/0.64      comm_monoid_nat @ ord_max_nat @ zero_zero_nat ).
% 0.30/0.64  
% 0.30/0.64  % max_nat.comm_monoid_axioms
% 0.30/0.64  thf(fact_9154_max__nat_Omonoid__axioms,axiom,
% 0.30/0.64      monoid_nat @ ord_max_nat @ zero_zero_nat ).
% 0.30/0.64  
% 0.30/0.64  % max_nat.monoid_axioms
% 0.30/0.64  thf(fact_9155_max__Suc2,axiom,
% 0.30/0.64      ! [M: nat,N: nat] :
% 0.30/0.64        ( ( ord_max_nat @ M @ ( suc @ N ) )
% 0.30/0.64        = ( case_nat_nat @ ( suc @ N )
% 0.30/0.64          @ ^ [M5: nat] : ( suc @ ( ord_max_nat @ M5 @ N ) )
% 0.30/0.64          @ M ) ) ).
% 0.30/0.64  
% 0.30/0.64  % max_Suc2
% 0.30/0.64  thf(fact_9156_max__Suc1,axiom,
% 0.30/0.64      ! [N: nat,M: nat] :
% 0.30/0.64        ( ( ord_max_nat @ ( suc @ N ) @ M )
% 0.30/0.64        = ( case_nat_nat @ ( suc @ N )
% 0.30/0.64          @ ^ [M5: nat] : ( suc @ ( ord_max_nat @ N @ M5 ) )
% 0.30/0.64          @ M ) ) ).
% 0.30/0.64  
% 0.30/0.64  % max_Suc1
% 0.30/0.64  thf(fact_9157_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 0.30/0.64      ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 0.30/0.64      @ ^ [X3: nat,Y3: nat] : ( ord_less_eq_nat @ Y3 @ X3 )
% 0.30/0.64      @ ^ [X3: nat,Y3: nat] : ( ord_less_nat @ Y3 @ X3 ) ) ).
% 0.30/0.64  
% 0.30/0.64  % max_nat.semilattice_neutr_order_axioms
% 0.30/0.64  thf(fact_9158_atLeastPlusOneLessThan__greaterThanLessThan__integer,axiom,
% 0.30/0.64      ! [L: code_integer,U: code_integer] :
% 0.30/0.64        ( ( set_or8404916559141939852nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 0.30/0.64        = ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 0.30/0.64  
% 0.30/0.64  % atLeastPlusOneLessThan_greaterThanLessThan_integer
% 0.30/0.64  thf(fact_9159_Code__Numeral_Onegative__def,axiom,
% 0.30/0.64      ( code_negative
% 0.30/0.64      = ( comp_C3531382070062128313er_num @ uminus1351360451143612070nteger @ numera6620942414471956472nteger ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Code_Numeral.negative_def
% 0.30/0.64  thf(fact_9160_sup__nat__def,axiom,
% 0.30/0.64      sup_sup_nat = ord_max_nat ).
% 0.30/0.64  
% 0.30/0.64  % sup_nat_def
% 0.30/0.64  thf(fact_9161_UN__atMost__UNIV,axiom,
% 0.30/0.64      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 0.30/0.64      = top_top_set_nat ) ).
% 0.30/0.64  
% 0.30/0.64  % UN_atMost_UNIV
% 0.30/0.64  thf(fact_9162_UN__lessThan__UNIV,axiom,
% 0.30/0.64      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 0.30/0.64      = top_top_set_nat ) ).
% 0.30/0.64  
% 0.30/0.64  % UN_lessThan_UNIV
% 0.30/0.64  thf(fact_9163_Inf__int__def,axiom,
% 0.30/0.64      ( complete_Inf_Inf_int
% 0.30/0.64      = ( ^ [X4: set_int] : ( uminus_uminus_int @ ( complete_Sup_Sup_int @ ( image_int_int @ uminus_uminus_int @ X4 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Inf_int_def
% 0.30/0.64  thf(fact_9164_Inf__nat__def1,axiom,
% 0.30/0.64      ! [K5: set_nat] :
% 0.30/0.64        ( ( K5 != bot_bot_set_nat )
% 0.30/0.64       => ( member_nat @ ( complete_Inf_Inf_nat @ K5 ) @ K5 ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Inf_nat_def1
% 0.30/0.64  thf(fact_9165_int__in__range__abs,axiom,
% 0.30/0.64      ! [N: nat] : ( member_int @ ( semiri1314217659103216013at_int @ N ) @ ( image_int_int @ abs_abs_int @ top_top_set_int ) ) ).
% 0.30/0.64  
% 0.30/0.64  % int_in_range_abs
% 0.30/0.64  thf(fact_9166_image__Suc__atMost,axiom,
% 0.30/0.64      ! [N: nat] :
% 0.30/0.64        ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 0.30/0.64        = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % image_Suc_atMost
% 0.30/0.64  thf(fact_9167_image__Suc__lessThan,axiom,
% 0.30/0.64      ! [N: nat] :
% 0.30/0.64        ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 0.30/0.64        = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 0.30/0.64  
% 0.30/0.64  % image_Suc_lessThan
% 0.30/0.64  thf(fact_9168_image__add__int__atLeastLessThan,axiom,
% 0.30/0.64      ! [L: int,U: int] :
% 0.30/0.64        ( ( image_int_int
% 0.30/0.64          @ ^ [X3: int] : ( plus_plus_int @ X3 @ L )
% 0.30/0.64          @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 0.30/0.64        = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 0.30/0.64  
% 0.30/0.64  % image_add_int_atLeastLessThan
% 0.30/0.64  thf(fact_9169_image__add__integer__atLeastLessThan,axiom,
% 0.30/0.64      ! [L: code_integer,U: code_integer] :
% 0.30/0.64        ( ( image_4470545334726330049nteger
% 0.30/0.64          @ ^ [X3: code_integer] : ( plus_p5714425477246183910nteger @ X3 @ L )
% 0.30/0.64          @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ U @ L ) ) )
% 0.30/0.64        = ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 0.30/0.64  
% 0.30/0.64  % image_add_integer_atLeastLessThan
% 0.30/0.64  thf(fact_9170_range__mod,axiom,
% 0.30/0.64      ! [N: nat] :
% 0.30/0.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.64       => ( ( image_nat_nat
% 0.30/0.64            @ ^ [M2: nat] : ( modulo_modulo_nat @ M2 @ N )
% 0.30/0.64            @ top_top_set_nat )
% 0.30/0.64          = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % range_mod
% 0.30/0.64  thf(fact_9171_image__minus__const__atLeastLessThan__nat,axiom,
% 0.30/0.64      ! [C: nat,Y: nat,X: nat] :
% 0.30/0.64        ( ( ( ord_less_nat @ C @ Y )
% 0.30/0.64         => ( ( image_nat_nat
% 0.30/0.64              @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 0.30/0.64              @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 0.30/0.64            = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 0.30/0.64        & ( ~ ( ord_less_nat @ C @ Y )
% 0.30/0.64         => ( ( ( ord_less_nat @ X @ Y )
% 0.30/0.64             => ( ( image_nat_nat
% 0.30/0.64                  @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 0.30/0.64                  @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 0.30/0.64                = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 0.30/0.64            & ( ~ ( ord_less_nat @ X @ Y )
% 0.30/0.64             => ( ( image_nat_nat
% 0.30/0.64                  @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 0.30/0.64                  @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 0.30/0.64                = bot_bot_set_nat ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % image_minus_const_atLeastLessThan_nat
% 0.30/0.64  thf(fact_9172_UNIV__char__of__nat,axiom,
% 0.30/0.64      ( top_top_set_char
% 0.30/0.64      = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % UNIV_char_of_nat
% 0.30/0.64  thf(fact_9173_range__nat__of__char,axiom,
% 0.30/0.64      ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 0.30/0.64      = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % range_nat_of_char
% 0.30/0.64  thf(fact_9174_pred__def,axiom,
% 0.30/0.64      ( pred
% 0.30/0.64      = ( case_nat_nat @ zero_zero_nat
% 0.30/0.64        @ ^ [X23: nat] : X23 ) ) ).
% 0.30/0.64  
% 0.30/0.64  % pred_def
% 0.30/0.64  thf(fact_9175_range__abs__Nats,axiom,
% 0.30/0.64      ( ( image_int_int @ abs_abs_int @ top_top_set_int )
% 0.30/0.64      = semiring_1_Nats_int ) ).
% 0.30/0.64  
% 0.30/0.64  % range_abs_Nats
% 0.30/0.64  thf(fact_9176_binomial__def,axiom,
% 0.30/0.64      ( binomial
% 0.30/0.64      = ( ^ [N2: nat,K4: nat] :
% 0.30/0.64            ( finite_card_set_nat
% 0.30/0.64            @ ( collect_set_nat
% 0.30/0.64              @ ^ [K6: set_nat] :
% 0.30/0.64                  ( ( member_set_nat @ K6 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) )
% 0.30/0.64                  & ( ( finite_card_nat @ K6 )
% 0.30/0.64                    = K4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % binomial_def
% 0.30/0.64  thf(fact_9177_times__int_Oabs__eq,axiom,
% 0.30/0.64      ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.30/0.64        ( ( times_times_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 0.30/0.64        = ( abs_Integ
% 0.30/0.64          @ ( produc27273713700761075at_nat
% 0.30/0.64            @ ^ [X3: nat,Y3: nat] :
% 0.30/0.64                ( produc2626176000494625587at_nat
% 0.30/0.64                @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V2 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) )
% 0.30/0.64            @ Xa
% 0.30/0.64            @ X ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % times_int.abs_eq
% 0.30/0.64  thf(fact_9178_rat__minus__code,axiom,
% 0.30/0.64      ! [P4: rat,Q4: rat] :
% 0.30/0.64        ( ( quotient_of @ ( minus_minus_rat @ P4 @ Q4 ) )
% 0.30/0.64        = ( produc4245557441103728435nt_int
% 0.30/0.64          @ ^ [A3: int,C4: int] :
% 0.30/0.64              ( produc4245557441103728435nt_int
% 0.30/0.64              @ ^ [B3: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A3 @ D4 ) @ ( times_times_int @ B3 @ C4 ) ) @ ( times_times_int @ C4 @ D4 ) ) )
% 0.30/0.64              @ ( quotient_of @ Q4 ) )
% 0.30/0.64          @ ( quotient_of @ P4 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % rat_minus_code
% 0.30/0.64  thf(fact_9179_rat__one__code,axiom,
% 0.30/0.64      ( ( quotient_of @ one_one_rat )
% 0.30/0.64      = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 0.30/0.64  
% 0.30/0.64  % rat_one_code
% 0.30/0.64  thf(fact_9180_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 0.30/0.64      ! [W: num,N: nat] :
% 0.30/0.64        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N ) )
% 0.30/0.64        = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N ) ) ).
% 0.30/0.64  
% 0.30/0.64  % bit_minus_numeral_Bit0_Suc_iff
% 0.30/0.64  thf(fact_9181_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 0.30/0.64      ! [W: num,N: nat] :
% 0.30/0.64        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N ) )
% 0.30/0.64        = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % bit_minus_numeral_Bit1_Suc_iff
% 0.30/0.64  thf(fact_9182_rat__zero__code,axiom,
% 0.30/0.64      ( ( quotient_of @ zero_zero_rat )
% 0.30/0.64      = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 0.30/0.64  
% 0.30/0.64  % rat_zero_code
% 0.30/0.64  thf(fact_9183_quotient__of__number_I3_J,axiom,
% 0.30/0.64      ! [K: num] :
% 0.30/0.64        ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 0.30/0.64        = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 0.30/0.64  
% 0.30/0.64  % quotient_of_number(3)
% 0.30/0.64  thf(fact_9184_quotient__of__number_I4_J,axiom,
% 0.30/0.64      ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.30/0.64      = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 0.30/0.64  
% 0.30/0.64  % quotient_of_number(4)
% 0.30/0.64  thf(fact_9185_bit__minus__numeral__int_I1_J,axiom,
% 0.30/0.64      ! [W: num,N: num] :
% 0.30/0.64        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 0.30/0.64        = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % bit_minus_numeral_int(1)
% 0.30/0.64  thf(fact_9186_bit__minus__numeral__int_I2_J,axiom,
% 0.30/0.64      ! [W: num,N: num] :
% 0.30/0.64        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 0.30/0.64        = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % bit_minus_numeral_int(2)
% 0.30/0.64  thf(fact_9187_quotient__of__number_I5_J,axiom,
% 0.30/0.64      ! [K: num] :
% 0.30/0.64        ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 0.30/0.64        = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 0.30/0.64  
% 0.30/0.64  % quotient_of_number(5)
% 0.30/0.64  thf(fact_9188_diff__rat__def,axiom,
% 0.30/0.64      ( minus_minus_rat
% 0.30/0.64      = ( ^ [Q5: rat,R4: rat] : ( plus_plus_rat @ Q5 @ ( uminus_uminus_rat @ R4 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % diff_rat_def
% 0.30/0.64  thf(fact_9189_quotient__of__div,axiom,
% 0.30/0.64      ! [R3: rat,N: int,D2: int] :
% 0.30/0.64        ( ( ( quotient_of @ R3 )
% 0.30/0.64          = ( product_Pair_int_int @ N @ D2 ) )
% 0.30/0.64       => ( R3
% 0.30/0.64          = ( divide_divide_rat @ ( ring_1_of_int_rat @ N ) @ ( ring_1_of_int_rat @ D2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % quotient_of_div
% 0.30/0.64  thf(fact_9190_eq__Abs__Integ,axiom,
% 0.30/0.64      ! [Z: int] :
% 0.30/0.64        ~ ! [X2: nat,Y2: nat] :
% 0.30/0.64            ( Z
% 0.30/0.64           != ( abs_Integ @ ( product_Pair_nat_nat @ X2 @ Y2 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % eq_Abs_Integ
% 0.30/0.64  thf(fact_9191_bit__not__int__iff_H,axiom,
% 0.30/0.64      ! [K: int,N: nat] :
% 0.30/0.64        ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 0.30/0.64        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % bit_not_int_iff'
% 0.30/0.64  thf(fact_9192_quotient__of__denom__pos,axiom,
% 0.30/0.64      ! [R3: rat,P4: int,Q4: int] :
% 0.30/0.64        ( ( ( quotient_of @ R3 )
% 0.30/0.64          = ( product_Pair_int_int @ P4 @ Q4 ) )
% 0.30/0.64       => ( ord_less_int @ zero_zero_int @ Q4 ) ) ).
% 0.30/0.64  
% 0.30/0.64  % quotient_of_denom_pos
% 0.30/0.64  thf(fact_9193_zero__int__def,axiom,
% 0.30/0.64      ( zero_zero_int
% 0.30/0.64      = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % zero_int_def
% 0.30/0.64  thf(fact_9194_int__def,axiom,
% 0.30/0.64      ( semiri1314217659103216013at_int
% 0.30/0.64      = ( ^ [N2: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N2 @ zero_zero_nat ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % int_def
% 0.30/0.64  thf(fact_9195_bit__minus__int__iff,axiom,
% 0.30/0.64      ! [K: int,N: nat] :
% 0.30/0.64        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 0.30/0.64        = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 0.30/0.64  
% 0.30/0.64  % bit_minus_int_iff
% 0.30/0.64  thf(fact_9196_rat__floor__code,axiom,
% 0.30/0.64      ( archim3151403230148437115or_rat
% 0.30/0.64      = ( ^ [P6: rat] : ( produc8211389475949308722nt_int @ divide_divide_int @ ( quotient_of @ P6 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % rat_floor_code
% 0.30/0.64  thf(fact_9197_rat__uminus__code,axiom,
% 0.30/0.64      ! [P4: rat] :
% 0.30/0.64        ( ( quotient_of @ ( uminus_uminus_rat @ P4 ) )
% 0.30/0.64        = ( produc4245557441103728435nt_int
% 0.30/0.64          @ ^ [A3: int] : ( product_Pair_int_int @ ( uminus_uminus_int @ A3 ) )
% 0.30/0.64          @ ( quotient_of @ P4 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % rat_uminus_code
% 0.30/0.64  thf(fact_9198_rat__abs__code,axiom,
% 0.30/0.64      ! [P4: rat] :
% 0.30/0.64        ( ( quotient_of @ ( abs_abs_rat @ P4 ) )
% 0.30/0.64        = ( produc4245557441103728435nt_int
% 0.30/0.64          @ ^ [A3: int] : ( product_Pair_int_int @ ( abs_abs_int @ A3 ) )
% 0.30/0.64          @ ( quotient_of @ P4 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % rat_abs_code
% 0.30/0.64  thf(fact_9199_rat__less__eq__code,axiom,
% 0.30/0.64      ( ord_less_eq_rat
% 0.30/0.64      = ( ^ [P6: rat,Q5: rat] :
% 0.30/0.64            ( produc4947309494688390418_int_o
% 0.30/0.64            @ ^ [A3: int,C4: int] :
% 0.30/0.64                ( produc4947309494688390418_int_o
% 0.30/0.64                @ ^ [B3: int,D4: int] : ( ord_less_eq_int @ ( times_times_int @ A3 @ D4 ) @ ( times_times_int @ C4 @ B3 ) )
% 0.30/0.64                @ ( quotient_of @ Q5 ) )
% 0.30/0.64            @ ( quotient_of @ P6 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % rat_less_eq_code
% 0.30/0.64  thf(fact_9200_rat__less__code,axiom,
% 0.30/0.64      ( ord_less_rat
% 0.30/0.64      = ( ^ [P6: rat,Q5: rat] :
% 0.30/0.64            ( produc4947309494688390418_int_o
% 0.30/0.64            @ ^ [A3: int,C4: int] :
% 0.30/0.64                ( produc4947309494688390418_int_o
% 0.30/0.64                @ ^ [B3: int,D4: int] : ( ord_less_int @ ( times_times_int @ A3 @ D4 ) @ ( times_times_int @ C4 @ B3 ) )
% 0.30/0.64                @ ( quotient_of @ Q5 ) )
% 0.30/0.64            @ ( quotient_of @ P6 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % rat_less_code
% 0.30/0.64  thf(fact_9201_uminus__int_Oabs__eq,axiom,
% 0.30/0.64      ! [X: product_prod_nat_nat] :
% 0.30/0.64        ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 0.30/0.64        = ( abs_Integ
% 0.30/0.64          @ ( produc2626176000494625587at_nat
% 0.30/0.64            @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 )
% 0.30/0.64            @ X ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % uminus_int.abs_eq
% 0.30/0.64  thf(fact_9202_int__bit__bound,axiom,
% 0.30/0.64      ! [K: int] :
% 0.30/0.64        ~ ! [N3: nat] :
% 0.30/0.64            ( ! [M6: nat] :
% 0.30/0.64                ( ( ord_less_eq_nat @ N3 @ M6 )
% 0.30/0.64               => ( ( bit_se1146084159140164899it_int @ K @ M6 )
% 0.30/0.64                  = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 0.30/0.64           => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.30/0.64               => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 0.30/0.64                  = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % int_bit_bound
% 0.30/0.64  thf(fact_9203_one__int__def,axiom,
% 0.30/0.64      ( one_one_int
% 0.30/0.64      = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % one_int_def
% 0.30/0.64  thf(fact_9204_less__int_Oabs__eq,axiom,
% 0.30/0.64      ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.30/0.64        ( ( ord_less_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 0.30/0.64        = ( produc8739625826339149834_nat_o
% 0.30/0.64          @ ^ [X3: nat,Y3: nat] :
% 0.30/0.64              ( produc6081775807080527818_nat_o
% 0.30/0.64              @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) )
% 0.30/0.64          @ Xa
% 0.30/0.64          @ X ) ) ).
% 0.30/0.64  
% 0.30/0.64  % less_int.abs_eq
% 0.30/0.64  thf(fact_9205_less__eq__int_Oabs__eq,axiom,
% 0.30/0.64      ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.30/0.64        ( ( ord_less_eq_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 0.30/0.64        = ( produc8739625826339149834_nat_o
% 0.30/0.64          @ ^ [X3: nat,Y3: nat] :
% 0.30/0.64              ( produc6081775807080527818_nat_o
% 0.30/0.64              @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) )
% 0.30/0.64          @ Xa
% 0.30/0.64          @ X ) ) ).
% 0.30/0.64  
% 0.30/0.64  % less_eq_int.abs_eq
% 0.30/0.64  thf(fact_9206_plus__int_Oabs__eq,axiom,
% 0.30/0.64      ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.30/0.64        ( ( plus_plus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 0.30/0.64        = ( abs_Integ
% 0.30/0.64          @ ( produc27273713700761075at_nat
% 0.30/0.64            @ ^ [X3: nat,Y3: nat] :
% 0.30/0.64                ( produc2626176000494625587at_nat
% 0.30/0.64                @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V2 ) ) )
% 0.30/0.64            @ Xa
% 0.30/0.64            @ X ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % plus_int.abs_eq
% 0.30/0.64  thf(fact_9207_minus__int_Oabs__eq,axiom,
% 0.30/0.64      ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.30/0.64        ( ( minus_minus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 0.30/0.64        = ( abs_Integ
% 0.30/0.64          @ ( produc27273713700761075at_nat
% 0.30/0.64            @ ^ [X3: nat,Y3: nat] :
% 0.30/0.64                ( produc2626176000494625587at_nat
% 0.30/0.64                @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) )
% 0.30/0.64            @ Xa
% 0.30/0.64            @ X ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % minus_int.abs_eq
% 0.30/0.64  thf(fact_9208_rat__divide__code,axiom,
% 0.30/0.64      ! [P4: rat,Q4: rat] :
% 0.30/0.64        ( ( quotient_of @ ( divide_divide_rat @ P4 @ Q4 ) )
% 0.30/0.64        = ( produc4245557441103728435nt_int
% 0.30/0.64          @ ^ [A3: int,C4: int] :
% 0.30/0.64              ( produc4245557441103728435nt_int
% 0.30/0.64              @ ^ [B3: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ D4 ) @ ( times_times_int @ C4 @ B3 ) ) )
% 0.30/0.64              @ ( quotient_of @ Q4 ) )
% 0.30/0.64          @ ( quotient_of @ P4 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % rat_divide_code
% 0.30/0.64  thf(fact_9209_rat__times__code,axiom,
% 0.30/0.64      ! [P4: rat,Q4: rat] :
% 0.30/0.64        ( ( quotient_of @ ( times_times_rat @ P4 @ Q4 ) )
% 0.30/0.64        = ( produc4245557441103728435nt_int
% 0.30/0.64          @ ^ [A3: int,C4: int] :
% 0.30/0.64              ( produc4245557441103728435nt_int
% 0.30/0.64              @ ^ [B3: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ B3 ) @ ( times_times_int @ C4 @ D4 ) ) )
% 0.30/0.64              @ ( quotient_of @ Q4 ) )
% 0.30/0.64          @ ( quotient_of @ P4 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % rat_times_code
% 0.30/0.64  thf(fact_9210_rat__plus__code,axiom,
% 0.30/0.64      ! [P4: rat,Q4: rat] :
% 0.30/0.64        ( ( quotient_of @ ( plus_plus_rat @ P4 @ Q4 ) )
% 0.30/0.64        = ( produc4245557441103728435nt_int
% 0.30/0.64          @ ^ [A3: int,C4: int] :
% 0.30/0.64              ( produc4245557441103728435nt_int
% 0.30/0.64              @ ^ [B3: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A3 @ D4 ) @ ( times_times_int @ B3 @ C4 ) ) @ ( times_times_int @ C4 @ D4 ) ) )
% 0.30/0.64              @ ( quotient_of @ Q4 ) )
% 0.30/0.64          @ ( quotient_of @ P4 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % rat_plus_code
% 0.30/0.64  thf(fact_9211_quotient__of__int,axiom,
% 0.30/0.64      ! [A: int] :
% 0.30/0.64        ( ( quotient_of @ ( of_int @ A ) )
% 0.30/0.64        = ( product_Pair_int_int @ A @ one_one_int ) ) ).
% 0.30/0.64  
% 0.30/0.64  % quotient_of_int
% 0.30/0.64  thf(fact_9212_rat__inverse__code,axiom,
% 0.30/0.64      ! [P4: rat] :
% 0.30/0.64        ( ( quotient_of @ ( inverse_inverse_rat @ P4 ) )
% 0.30/0.64        = ( produc4245557441103728435nt_int
% 0.30/0.64          @ ^ [A3: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( A3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A3 ) @ B3 ) @ ( abs_abs_int @ A3 ) ) )
% 0.30/0.64          @ ( quotient_of @ P4 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % rat_inverse_code
% 0.30/0.64  thf(fact_9213_abs__rat__def,axiom,
% 0.30/0.64      ( abs_abs_rat
% 0.30/0.64      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % abs_rat_def
% 0.30/0.64  thf(fact_9214_sgn__rat__def,axiom,
% 0.30/0.64      ( sgn_sgn_rat
% 0.30/0.64      = ( ^ [A3: rat] : ( if_rat @ ( A3 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A3 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sgn_rat_def
% 0.30/0.64  thf(fact_9215_char__of__integer__code,axiom,
% 0.30/0.64      ( char_of_integer
% 0.30/0.64      = ( ^ [K4: code_integer] :
% 0.30/0.64            ( produc4188289175737317920o_char
% 0.30/0.64            @ ^ [Q0: code_integer,B0: $o] :
% 0.30/0.64                ( produc4188289175737317920o_char
% 0.30/0.64                @ ^ [Q1: code_integer,B1: $o] :
% 0.30/0.64                    ( produc4188289175737317920o_char
% 0.30/0.64                    @ ^ [Q22: code_integer,B22: $o] :
% 0.30/0.64                        ( produc4188289175737317920o_char
% 0.30/0.64                        @ ^ [Q32: code_integer,B32: $o] :
% 0.30/0.64                            ( produc4188289175737317920o_char
% 0.30/0.64                            @ ^ [Q42: code_integer,B42: $o] :
% 0.30/0.64                                ( produc4188289175737317920o_char
% 0.30/0.64                                @ ^ [Q52: code_integer,B52: $o] :
% 0.30/0.64                                    ( produc4188289175737317920o_char
% 0.30/0.64                                    @ ^ [Q62: code_integer,B62: $o] :
% 0.30/0.64                                        ( produc4188289175737317920o_char
% 0.30/0.64                                        @ ^ [Uu: code_integer] : ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 )
% 0.30/0.64                                        @ ( code_bit_cut_integer @ Q62 ) )
% 0.30/0.64                                    @ ( code_bit_cut_integer @ Q52 ) )
% 0.30/0.64                                @ ( code_bit_cut_integer @ Q42 ) )
% 0.30/0.64                            @ ( code_bit_cut_integer @ Q32 ) )
% 0.30/0.64                        @ ( code_bit_cut_integer @ Q22 ) )
% 0.30/0.64                    @ ( code_bit_cut_integer @ Q1 ) )
% 0.30/0.64                @ ( code_bit_cut_integer @ Q0 ) )
% 0.30/0.64            @ ( code_bit_cut_integer @ K4 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % char_of_integer_code
% 0.30/0.64  thf(fact_9216_Frct__code__post_I5_J,axiom,
% 0.30/0.64      ! [K: num] :
% 0.30/0.64        ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 0.30/0.64        = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Frct_code_post(5)
% 0.30/0.64  thf(fact_9217_floor__rat__def,axiom,
% 0.30/0.64      ( archim3151403230148437115or_rat
% 0.30/0.64      = ( ^ [X3: rat] :
% 0.30/0.64            ( the_int
% 0.30/0.64            @ ^ [Z3: int] :
% 0.30/0.64                ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X3 )
% 0.30/0.64                & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % floor_rat_def
% 0.30/0.64  thf(fact_9218_Frct__code__post_I9_J,axiom,
% 0.30/0.64      ! [Q4: product_prod_int_int] :
% 0.30/0.64        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ ( frct @ Q4 ) ) )
% 0.30/0.64        = ( frct @ Q4 ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Frct_code_post(9)
% 0.30/0.64  thf(fact_9219_Frct__code__post_I1_J,axiom,
% 0.30/0.64      ! [A: int] :
% 0.30/0.64        ( ( frct @ ( product_Pair_int_int @ zero_zero_int @ A ) )
% 0.30/0.64        = zero_zero_rat ) ).
% 0.30/0.64  
% 0.30/0.64  % Frct_code_post(1)
% 0.30/0.64  thf(fact_9220_Frct__code__post_I2_J,axiom,
% 0.30/0.64      ! [A: int] :
% 0.30/0.64        ( ( frct @ ( product_Pair_int_int @ A @ zero_zero_int ) )
% 0.30/0.64        = zero_zero_rat ) ).
% 0.30/0.64  
% 0.30/0.64  % Frct_code_post(2)
% 0.30/0.64  thf(fact_9221_Frct__code__post_I3_J,axiom,
% 0.30/0.64      ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 0.30/0.64      = one_one_rat ) ).
% 0.30/0.64  
% 0.30/0.64  % Frct_code_post(3)
% 0.30/0.64  thf(fact_9222_Frct__code__post_I7_J,axiom,
% 0.30/0.64      ! [A: int,B: int] :
% 0.30/0.64        ( ( frct @ ( product_Pair_int_int @ ( uminus_uminus_int @ A ) @ B ) )
% 0.30/0.64        = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Frct_code_post(7)
% 0.30/0.64  thf(fact_9223_Frct__code__post_I8_J,axiom,
% 0.30/0.64      ! [A: int,B: int] :
% 0.30/0.64        ( ( frct @ ( product_Pair_int_int @ A @ ( uminus_uminus_int @ B ) ) )
% 0.30/0.64        = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Frct_code_post(8)
% 0.30/0.64  thf(fact_9224_Frct__code__post_I4_J,axiom,
% 0.30/0.64      ! [K: num] :
% 0.30/0.64        ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 0.30/0.64        = ( numeral_numeral_rat @ K ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Frct_code_post(4)
% 0.30/0.64  thf(fact_9225_Frct__code__post_I6_J,axiom,
% 0.30/0.64      ! [K: num,L: num] :
% 0.30/0.64        ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L ) ) )
% 0.30/0.64        = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Frct_code_post(6)
% 0.30/0.64  thf(fact_9226_less__eq__int_Orep__eq,axiom,
% 0.30/0.64      ( ord_less_eq_int
% 0.30/0.64      = ( ^ [X3: int,Xa4: int] :
% 0.30/0.64            ( produc8739625826339149834_nat_o
% 0.30/0.64            @ ^ [Y3: nat,Z3: nat] :
% 0.30/0.64                ( produc6081775807080527818_nat_o
% 0.30/0.64                @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y3 @ V2 ) @ ( plus_plus_nat @ U2 @ Z3 ) ) )
% 0.30/0.64            @ ( rep_Integ @ X3 )
% 0.30/0.64            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % less_eq_int.rep_eq
% 0.30/0.64  thf(fact_9227_less__int_Orep__eq,axiom,
% 0.30/0.64      ( ord_less_int
% 0.30/0.64      = ( ^ [X3: int,Xa4: int] :
% 0.30/0.64            ( produc8739625826339149834_nat_o
% 0.30/0.64            @ ^ [Y3: nat,Z3: nat] :
% 0.30/0.64                ( produc6081775807080527818_nat_o
% 0.30/0.64                @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y3 @ V2 ) @ ( plus_plus_nat @ U2 @ Z3 ) ) )
% 0.30/0.64            @ ( rep_Integ @ X3 )
% 0.30/0.64            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % less_int.rep_eq
% 0.30/0.64  thf(fact_9228_uminus__int__def,axiom,
% 0.30/0.64      ( uminus_uminus_int
% 0.30/0.64      = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 0.30/0.64        @ ( produc2626176000494625587at_nat
% 0.30/0.64          @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % uminus_int_def
% 0.30/0.64  thf(fact_9229_pred__nat__def,axiom,
% 0.30/0.64      ( pred_nat
% 0.30/0.64      = ( collec3392354462482085612at_nat
% 0.30/0.64        @ ( produc6081775807080527818_nat_o
% 0.30/0.64          @ ^ [M2: nat,N2: nat] :
% 0.30/0.64              ( N2
% 0.30/0.64              = ( suc @ M2 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % pred_nat_def
% 0.30/0.64  thf(fact_9230_less__eq,axiom,
% 0.30/0.64      ! [M: nat,N: nat] :
% 0.30/0.64        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 0.30/0.64        = ( ord_less_nat @ M @ N ) ) ).
% 0.30/0.64  
% 0.30/0.64  % less_eq
% 0.30/0.64  thf(fact_9231_pred__nat__trancl__eq__le,axiom,
% 0.30/0.64      ! [M: nat,N: nat] :
% 0.30/0.64        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 0.30/0.64        = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.30/0.64  
% 0.30/0.64  % pred_nat_trancl_eq_le
% 0.30/0.64  thf(fact_9232_times__int__def,axiom,
% 0.30/0.64      ( times_times_int
% 0.30/0.64      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.30/0.64        @ ( produc27273713700761075at_nat
% 0.30/0.64          @ ^ [X3: nat,Y3: nat] :
% 0.30/0.64              ( produc2626176000494625587at_nat
% 0.30/0.64              @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V2 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % times_int_def
% 0.30/0.64  thf(fact_9233_natLess__def,axiom,
% 0.30/0.64      ( bNF_Ca8459412986667044542atLess
% 0.30/0.64      = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % natLess_def
% 0.30/0.64  thf(fact_9234_minus__int__def,axiom,
% 0.30/0.64      ( minus_minus_int
% 0.30/0.64      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.30/0.64        @ ( produc27273713700761075at_nat
% 0.30/0.64          @ ^ [X3: nat,Y3: nat] :
% 0.30/0.64              ( produc2626176000494625587at_nat
% 0.30/0.64              @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % minus_int_def
% 0.30/0.64  thf(fact_9235_plus__int__def,axiom,
% 0.30/0.64      ( plus_plus_int
% 0.30/0.64      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.30/0.64        @ ( produc27273713700761075at_nat
% 0.30/0.64          @ ^ [X3: nat,Y3: nat] :
% 0.30/0.64              ( produc2626176000494625587at_nat
% 0.30/0.64              @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V2 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % plus_int_def
% 0.30/0.64  thf(fact_9236_Gcd__remove0__nat,axiom,
% 0.30/0.64      ! [M4: set_nat] :
% 0.30/0.64        ( ( finite_finite_nat @ M4 )
% 0.30/0.64       => ( ( gcd_Gcd_nat @ M4 )
% 0.30/0.64          = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M4 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Gcd_remove0_nat
% 0.30/0.64  thf(fact_9237_take__bit__numeral__minus__numeral__int,axiom,
% 0.30/0.64      ! [M: num,N: num] :
% 0.30/0.64        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.64        = ( case_option_int_num @ zero_zero_int
% 0.30/0.64          @ ^ [Q5: num] : ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_int @ Q5 ) ) )
% 0.30/0.64          @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % take_bit_numeral_minus_numeral_int
% 0.30/0.64  thf(fact_9238_rat__floor__lemma,axiom,
% 0.30/0.64      ! [A: int,B: int] :
% 0.30/0.64        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 0.30/0.64        & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % rat_floor_lemma
% 0.30/0.64  thf(fact_9239_minus__rat__cancel,axiom,
% 0.30/0.64      ! [A: int,B: int] :
% 0.30/0.64        ( ( fract @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 0.30/0.64        = ( fract @ A @ B ) ) ).
% 0.30/0.64  
% 0.30/0.64  % minus_rat_cancel
% 0.30/0.64  thf(fact_9240_minus__rat,axiom,
% 0.30/0.64      ! [A: int,B: int] :
% 0.30/0.64        ( ( uminus_uminus_rat @ ( fract @ A @ B ) )
% 0.30/0.64        = ( fract @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.30/0.64  
% 0.30/0.64  % minus_rat
% 0.30/0.64  thf(fact_9241_Gcd__nat__eq__one,axiom,
% 0.30/0.64      ! [N4: set_nat] :
% 0.30/0.64        ( ( member_nat @ one_one_nat @ N4 )
% 0.30/0.64       => ( ( gcd_Gcd_nat @ N4 )
% 0.30/0.64          = one_one_nat ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Gcd_nat_eq_one
% 0.30/0.64  thf(fact_9242_eq__rat_I2_J,axiom,
% 0.30/0.64      ! [A: int] :
% 0.30/0.64        ( ( fract @ A @ zero_zero_int )
% 0.30/0.64        = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 0.30/0.64  
% 0.30/0.64  % eq_rat(2)
% 0.30/0.64  thf(fact_9243_Fract__of__nat__eq,axiom,
% 0.30/0.64      ! [K: nat] :
% 0.30/0.64        ( ( fract @ ( semiri1314217659103216013at_int @ K ) @ one_one_int )
% 0.30/0.64        = ( semiri681578069525770553at_rat @ K ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Fract_of_nat_eq
% 0.30/0.64  thf(fact_9244_quotient__of__eq,axiom,
% 0.30/0.64      ! [A: int,B: int,P4: int,Q4: int] :
% 0.30/0.64        ( ( ( quotient_of @ ( fract @ A @ B ) )
% 0.30/0.64          = ( product_Pair_int_int @ P4 @ Q4 ) )
% 0.30/0.64       => ( ( fract @ P4 @ Q4 )
% 0.30/0.64          = ( fract @ A @ B ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % quotient_of_eq
% 0.30/0.64  thf(fact_9245_One__rat__def,axiom,
% 0.30/0.64      ( one_one_rat
% 0.30/0.64      = ( fract @ one_one_int @ one_one_int ) ) ).
% 0.30/0.64  
% 0.30/0.64  % One_rat_def
% 0.30/0.64  thf(fact_9246_Fract__of__int__eq,axiom,
% 0.30/0.64      ! [K: int] :
% 0.30/0.64        ( ( fract @ K @ one_one_int )
% 0.30/0.64        = ( ring_1_of_int_rat @ K ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Fract_of_int_eq
% 0.30/0.64  thf(fact_9247_normalize__eq,axiom,
% 0.30/0.64      ! [A: int,B: int,P4: int,Q4: int] :
% 0.30/0.64        ( ( ( normalize @ ( product_Pair_int_int @ A @ B ) )
% 0.30/0.64          = ( product_Pair_int_int @ P4 @ Q4 ) )
% 0.30/0.64       => ( ( fract @ P4 @ Q4 )
% 0.30/0.64          = ( fract @ A @ B ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % normalize_eq
% 0.30/0.64  thf(fact_9248_Zero__rat__def,axiom,
% 0.30/0.64      ( zero_zero_rat
% 0.30/0.64      = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Zero_rat_def
% 0.30/0.64  thf(fact_9249_rat__number__expand_I3_J,axiom,
% 0.30/0.64      ( numeral_numeral_rat
% 0.30/0.64      = ( ^ [K4: num] : ( fract @ ( numeral_numeral_int @ K4 ) @ one_one_int ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % rat_number_expand(3)
% 0.30/0.64  thf(fact_9250_rat__number__collapse_I3_J,axiom,
% 0.30/0.64      ! [W: num] :
% 0.30/0.64        ( ( fract @ ( numeral_numeral_int @ W ) @ one_one_int )
% 0.30/0.64        = ( numeral_numeral_rat @ W ) ) ).
% 0.30/0.64  
% 0.30/0.64  % rat_number_collapse(3)
% 0.30/0.64  thf(fact_9251_quotient__of__Fract,axiom,
% 0.30/0.64      ! [A: int,B: int] :
% 0.30/0.64        ( ( quotient_of @ ( fract @ A @ B ) )
% 0.30/0.64        = ( normalize @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % quotient_of_Fract
% 0.30/0.64  thf(fact_9252_one__less__Fract__iff,axiom,
% 0.30/0.64      ! [B: int,A: int] :
% 0.30/0.64        ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.64       => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 0.30/0.64          = ( ord_less_int @ B @ A ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % one_less_Fract_iff
% 0.30/0.64  thf(fact_9253_Fract__less__one__iff,axiom,
% 0.30/0.64      ! [B: int,A: int] :
% 0.30/0.64        ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.64       => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 0.30/0.64          = ( ord_less_int @ A @ B ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Fract_less_one_iff
% 0.30/0.64  thf(fact_9254_rat__number__collapse_I5_J,axiom,
% 0.30/0.64      ( ( fract @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 0.30/0.64      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.30/0.64  
% 0.30/0.64  % rat_number_collapse(5)
% 0.30/0.64  thf(fact_9255_Fract__add__one,axiom,
% 0.30/0.64      ! [N: int,M: int] :
% 0.30/0.64        ( ( N != zero_zero_int )
% 0.30/0.64       => ( ( fract @ ( plus_plus_int @ M @ N ) @ N )
% 0.30/0.64          = ( plus_plus_rat @ ( fract @ M @ N ) @ one_one_rat ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Fract_add_one
% 0.30/0.64  thf(fact_9256_one__le__Fract__iff,axiom,
% 0.30/0.64      ! [B: int,A: int] :
% 0.30/0.64        ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.64       => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 0.30/0.64          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % one_le_Fract_iff
% 0.30/0.64  thf(fact_9257_Fract__le__one__iff,axiom,
% 0.30/0.64      ! [B: int,A: int] :
% 0.30/0.64        ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.64       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 0.30/0.64          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Fract_le_one_iff
% 0.30/0.64  thf(fact_9258_rat__number__collapse_I4_J,axiom,
% 0.30/0.64      ! [W: num] :
% 0.30/0.64        ( ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ one_one_int )
% 0.30/0.64        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % rat_number_collapse(4)
% 0.30/0.64  thf(fact_9259_rat__number__expand_I5_J,axiom,
% 0.30/0.64      ! [K: num] :
% 0.30/0.64        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) )
% 0.30/0.64        = ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 0.30/0.64  
% 0.30/0.64  % rat_number_expand(5)
% 0.30/0.64  thf(fact_9260_and__minus__numerals_I3_J,axiom,
% 0.30/0.64      ! [M: num,N: num] :
% 0.30/0.64        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.30/0.64        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % and_minus_numerals(3)
% 0.30/0.64  thf(fact_9261_and__minus__numerals_I7_J,axiom,
% 0.30/0.64      ! [N: num,M: num] :
% 0.30/0.64        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.30/0.64        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % and_minus_numerals(7)
% 0.30/0.64  thf(fact_9262_and__minus__numerals_I8_J,axiom,
% 0.30/0.64      ! [N: num,M: num] :
% 0.30/0.64        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 0.30/0.64        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % and_minus_numerals(8)
% 0.30/0.64  thf(fact_9263_and__minus__numerals_I4_J,axiom,
% 0.30/0.64      ! [M: num,N: num] :
% 0.30/0.64        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.30/0.64        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % and_minus_numerals(4)
% 0.30/0.64  thf(fact_9264_Gcd__int__eq,axiom,
% 0.30/0.64      ! [N4: set_nat] :
% 0.30/0.64        ( ( gcd_Gcd_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N4 ) )
% 0.30/0.64        = ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ N4 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Gcd_int_eq
% 0.30/0.64  thf(fact_9265_Gcd__abs__eq,axiom,
% 0.30/0.64      ! [K5: set_int] :
% 0.30/0.64        ( ( gcd_Gcd_int @ ( image_int_int @ abs_abs_int @ K5 ) )
% 0.30/0.64        = ( gcd_Gcd_int @ K5 ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Gcd_abs_eq
% 0.30/0.64  thf(fact_9266_Gcd__nat__abs__eq,axiom,
% 0.30/0.64      ! [K5: set_int] :
% 0.30/0.64        ( ( gcd_Gcd_nat
% 0.30/0.64          @ ( image_int_nat
% 0.30/0.64            @ ^ [K4: int] : ( nat2 @ ( abs_abs_int @ K4 ) )
% 0.30/0.64            @ K5 ) )
% 0.30/0.64        = ( nat2 @ ( gcd_Gcd_int @ K5 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Gcd_nat_abs_eq
% 0.30/0.64  thf(fact_9267_Gcd__int__def,axiom,
% 0.30/0.64      ( gcd_Gcd_int
% 0.30/0.64      = ( ^ [K6: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K6 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Gcd_int_def
% 0.30/0.64  thf(fact_9268_int__numeral__and__not__num,axiom,
% 0.30/0.64      ! [M: num,N: num] :
% 0.30/0.64        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.64        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % int_numeral_and_not_num
% 0.30/0.64  thf(fact_9269_int__numeral__not__and__num,axiom,
% 0.30/0.64      ! [M: num,N: num] :
% 0.30/0.64        ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.30/0.64        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N @ M ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % int_numeral_not_and_num
% 0.30/0.64  thf(fact_9270_Gcd__eq__Max,axiom,
% 0.30/0.64      ! [M4: set_nat] :
% 0.30/0.64        ( ( finite_finite_nat @ M4 )
% 0.30/0.64       => ( ( M4 != bot_bot_set_nat )
% 0.30/0.64         => ( ~ ( member_nat @ zero_zero_nat @ M4 )
% 0.30/0.64           => ( ( gcd_Gcd_nat @ M4 )
% 0.30/0.64              = ( lattic8265883725875713057ax_nat
% 0.30/0.64                @ ( comple7806235888213564991et_nat
% 0.30/0.64                  @ ( image_nat_set_nat
% 0.30/0.64                    @ ^ [M2: nat] :
% 0.30/0.64                        ( collect_nat
% 0.30/0.64                        @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M2 ) )
% 0.30/0.64                    @ M4 ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Gcd_eq_Max
% 0.30/0.64  thf(fact_9271_take__bit__num__simps_I7_J,axiom,
% 0.30/0.64      ! [R3: num,M: num] :
% 0.30/0.64        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R3 ) @ ( bit1 @ M ) )
% 0.30/0.64        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R3 ) @ M ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % take_bit_num_simps(7)
% 0.30/0.64  thf(fact_9272_set__decode__def,axiom,
% 0.30/0.64      ( nat_set_decode
% 0.30/0.64      = ( ^ [X3: nat] :
% 0.30/0.64            ( collect_nat
% 0.30/0.64            @ ^ [N2: nat] :
% 0.30/0.64                ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % set_decode_def
% 0.30/0.64  thf(fact_9273_set__decode__zero,axiom,
% 0.30/0.64      ( ( nat_set_decode @ zero_zero_nat )
% 0.30/0.64      = bot_bot_set_nat ) ).
% 0.30/0.64  
% 0.30/0.64  % set_decode_zero
% 0.30/0.64  thf(fact_9274_Max__divisors__self__nat,axiom,
% 0.30/0.64      ! [N: nat] :
% 0.30/0.64        ( ( N != zero_zero_nat )
% 0.30/0.64       => ( ( lattic8265883725875713057ax_nat
% 0.30/0.64            @ ( collect_nat
% 0.30/0.64              @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ N ) ) )
% 0.30/0.64          = N ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Max_divisors_self_nat
% 0.30/0.64  thf(fact_9275_take__bit__num__simps_I4_J,axiom,
% 0.30/0.64      ! [N: nat,M: num] :
% 0.30/0.64        ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 0.30/0.64        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % take_bit_num_simps(4)
% 0.30/0.64  thf(fact_9276_prod__decode__aux_Ocases,axiom,
% 0.30/0.64      ! [X: product_prod_nat_nat] :
% 0.30/0.64        ~ ! [K2: nat,M3: nat] :
% 0.30/0.64            ( X
% 0.30/0.64           != ( product_Pair_nat_nat @ K2 @ M3 ) ) ).
% 0.30/0.64  
% 0.30/0.64  % prod_decode_aux.cases
% 0.30/0.64  thf(fact_9277_Sup__nat__def,axiom,
% 0.30/0.64      ( complete_Sup_Sup_nat
% 0.30/0.64      = ( ^ [X4: set_nat] : ( if_nat @ ( X4 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X4 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Sup_nat_def
% 0.30/0.64  thf(fact_9278_and__not__num_Osimps_I8_J,axiom,
% 0.30/0.64      ! [M: num,N: num] :
% 0.30/0.64        ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.30/0.64        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.30/0.64          @ ^ [N5: num] : ( some_num @ ( bit1 @ N5 ) )
% 0.30/0.64          @ ( bit_and_not_num @ M @ N ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % and_not_num.simps(8)
% 0.30/0.64  thf(fact_9279_divide__nat__def,axiom,
% 0.30/0.64      ( divide_divide_nat
% 0.30/0.64      = ( ^ [M2: nat,N2: nat] :
% 0.30/0.64            ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 0.30/0.64            @ ( lattic8265883725875713057ax_nat
% 0.30/0.64              @ ( collect_nat
% 0.30/0.64                @ ^ [K4: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K4 @ N2 ) @ M2 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % divide_nat_def
% 0.30/0.64  thf(fact_9280_Max__divisors__self__int,axiom,
% 0.30/0.64      ! [N: int] :
% 0.30/0.64        ( ( N != zero_zero_int )
% 0.30/0.64       => ( ( lattic8263393255366662781ax_int
% 0.30/0.64            @ ( collect_int
% 0.30/0.64              @ ^ [D4: int] : ( dvd_dvd_int @ D4 @ N ) ) )
% 0.30/0.64          = ( abs_abs_int @ N ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Max_divisors_self_int
% 0.30/0.64  thf(fact_9281_take__bit__num__simps_I6_J,axiom,
% 0.30/0.64      ! [R3: num,M: num] :
% 0.30/0.64        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R3 ) @ ( bit0 @ M ) )
% 0.30/0.64        = ( case_o6005452278849405969um_num @ none_num
% 0.30/0.64          @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 0.30/0.64          @ ( bit_take_bit_num @ ( pred_numeral @ R3 ) @ M ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % take_bit_num_simps(6)
% 0.30/0.64  thf(fact_9282_surj__int__encode,axiom,
% 0.30/0.64      ( ( image_int_nat @ nat_int_encode @ top_top_set_int )
% 0.30/0.64      = top_top_set_nat ) ).
% 0.30/0.64  
% 0.30/0.64  % surj_int_encode
% 0.30/0.64  thf(fact_9283_prod__decode__aux_Oelims,axiom,
% 0.30/0.64      ! [X: nat,Xa: nat,Y: product_prod_nat_nat] :
% 0.30/0.64        ( ( ( nat_prod_decode_aux @ X @ Xa )
% 0.30/0.64          = Y )
% 0.30/0.64       => ( ( ( ord_less_eq_nat @ Xa @ X )
% 0.30/0.64           => ( Y
% 0.30/0.64              = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X @ Xa ) ) ) )
% 0.30/0.64          & ( ~ ( ord_less_eq_nat @ Xa @ X )
% 0.30/0.64           => ( Y
% 0.30/0.64              = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa @ ( suc @ X ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % prod_decode_aux.elims
% 0.30/0.64  thf(fact_9284_take__bit__num__simps_I3_J,axiom,
% 0.30/0.64      ! [N: nat,M: num] :
% 0.30/0.64        ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 0.30/0.64        = ( case_o6005452278849405969um_num @ none_num
% 0.30/0.64          @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 0.30/0.64          @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % take_bit_num_simps(3)
% 0.30/0.64  thf(fact_9285_prod__decode__aux_Osimps,axiom,
% 0.30/0.64      ( nat_prod_decode_aux
% 0.30/0.64      = ( ^ [K4: nat,M2: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M2 @ K4 ) @ ( product_Pair_nat_nat @ M2 @ ( minus_minus_nat @ K4 @ M2 ) ) @ ( nat_prod_decode_aux @ ( suc @ K4 ) @ ( minus_minus_nat @ M2 @ ( suc @ K4 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % prod_decode_aux.simps
% 0.30/0.64  thf(fact_9286_take__bit__num__code,axiom,
% 0.30/0.64      ( bit_take_bit_num
% 0.30/0.64      = ( ^ [N2: nat,M2: num] :
% 0.30/0.64            ( produc478579273971653890on_num
% 0.30/0.64            @ ^ [A3: nat,X3: num] :
% 0.30/0.64                ( case_nat_option_num @ none_num
% 0.30/0.64                @ ^ [O: nat] :
% 0.30/0.64                    ( case_num_option_num @ ( some_num @ one )
% 0.30/0.64                    @ ^ [P6: num] :
% 0.30/0.64                        ( case_o6005452278849405969um_num @ none_num
% 0.30/0.64                        @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 0.30/0.64                        @ ( bit_take_bit_num @ O @ P6 ) )
% 0.30/0.64                    @ ^ [P6: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P6 ) ) )
% 0.30/0.64                    @ X3 )
% 0.30/0.64                @ A3 )
% 0.30/0.64            @ ( product_Pair_nat_num @ N2 @ M2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % take_bit_num_code
% 0.30/0.64  thf(fact_9287_INT__greaterThan__UNIV,axiom,
% 0.30/0.64      ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 0.30/0.64      = bot_bot_set_nat ) ).
% 0.30/0.64  
% 0.30/0.64  % INT_greaterThan_UNIV
% 0.30/0.64  thf(fact_9288_greaterThan__0,axiom,
% 0.30/0.64      ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 0.30/0.64      = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 0.30/0.64  
% 0.30/0.64  % greaterThan_0
% 0.30/0.64  thf(fact_9289_greaterThan__Suc,axiom,
% 0.30/0.64      ! [K: nat] :
% 0.30/0.64        ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 0.30/0.64        = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % greaterThan_Suc
% 0.30/0.64  thf(fact_9290_and__not__num_Oelims,axiom,
% 0.30/0.64      ! [X: num,Xa: num,Y: option_num] :
% 0.30/0.64        ( ( ( bit_and_not_num @ X @ Xa )
% 0.30/0.64          = Y )
% 0.30/0.64       => ( ( ( X = one )
% 0.30/0.64           => ( ( Xa = one )
% 0.30/0.64             => ( Y != none_num ) ) )
% 0.30/0.64         => ( ( ( X = one )
% 0.30/0.64             => ( ? [N3: num] :
% 0.30/0.64                    ( Xa
% 0.30/0.64                    = ( bit0 @ N3 ) )
% 0.30/0.64               => ( Y
% 0.30/0.64                 != ( some_num @ one ) ) ) )
% 0.30/0.64           => ( ( ( X = one )
% 0.30/0.64               => ( ? [N3: num] :
% 0.30/0.64                      ( Xa
% 0.30/0.64                      = ( bit1 @ N3 ) )
% 0.30/0.64                 => ( Y != none_num ) ) )
% 0.30/0.64             => ( ! [M3: num] :
% 0.30/0.64                    ( ( X
% 0.30/0.64                      = ( bit0 @ M3 ) )
% 0.30/0.64                   => ( ( Xa = one )
% 0.30/0.64                     => ( Y
% 0.30/0.64                       != ( some_num @ ( bit0 @ M3 ) ) ) ) )
% 0.30/0.64               => ( ! [M3: num] :
% 0.30/0.64                      ( ( X
% 0.30/0.64                        = ( bit0 @ M3 ) )
% 0.30/0.64                     => ! [N3: num] :
% 0.30/0.64                          ( ( Xa
% 0.30/0.64                            = ( bit0 @ N3 ) )
% 0.30/0.64                         => ( Y
% 0.30/0.64                           != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N3 ) ) ) ) )
% 0.30/0.64                 => ( ! [M3: num] :
% 0.30/0.64                        ( ( X
% 0.30/0.64                          = ( bit0 @ M3 ) )
% 0.30/0.64                       => ! [N3: num] :
% 0.30/0.64                            ( ( Xa
% 0.30/0.64                              = ( bit1 @ N3 ) )
% 0.30/0.64                           => ( Y
% 0.30/0.64                             != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N3 ) ) ) ) )
% 0.30/0.64                   => ( ! [M3: num] :
% 0.30/0.64                          ( ( X
% 0.30/0.64                            = ( bit1 @ M3 ) )
% 0.30/0.64                         => ( ( Xa = one )
% 0.30/0.64                           => ( Y
% 0.30/0.64                             != ( some_num @ ( bit0 @ M3 ) ) ) ) )
% 0.30/0.64                     => ( ! [M3: num] :
% 0.30/0.64                            ( ( X
% 0.30/0.64                              = ( bit1 @ M3 ) )
% 0.30/0.64                           => ! [N3: num] :
% 0.30/0.64                                ( ( Xa
% 0.30/0.64                                  = ( bit0 @ N3 ) )
% 0.30/0.64                               => ( Y
% 0.30/0.64                                 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.30/0.64                                    @ ^ [N5: num] : ( some_num @ ( bit1 @ N5 ) )
% 0.30/0.64                                    @ ( bit_and_not_num @ M3 @ N3 ) ) ) ) )
% 0.30/0.64                       => ~ ! [M3: num] :
% 0.30/0.64                              ( ( X
% 0.30/0.64                                = ( bit1 @ M3 ) )
% 0.30/0.64                             => ! [N3: num] :
% 0.30/0.64                                  ( ( Xa
% 0.30/0.64                                    = ( bit1 @ N3 ) )
% 0.30/0.64                                 => ( Y
% 0.30/0.64                                   != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % and_not_num.elims
% 0.30/0.64  thf(fact_9291_surj__int__decode,axiom,
% 0.30/0.64      ( ( image_nat_int @ nat_int_decode @ top_top_set_nat )
% 0.30/0.64      = top_top_set_int ) ).
% 0.30/0.64  
% 0.30/0.64  % surj_int_decode
% 0.30/0.64  thf(fact_9292_mono__ge2__power__minus__self,axiom,
% 0.30/0.64      ! [K: nat] :
% 0.30/0.64        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 0.30/0.64       => ( order_mono_nat_nat
% 0.30/0.64          @ ^ [M2: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M2 ) @ M2 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % mono_ge2_power_minus_self
% 0.30/0.64  thf(fact_9293_and__num_Oelims,axiom,
% 0.30/0.64      ! [X: num,Xa: num,Y: option_num] :
% 0.30/0.64        ( ( ( bit_un7362597486090784418nd_num @ X @ Xa )
% 0.30/0.64          = Y )
% 0.30/0.64       => ( ( ( X = one )
% 0.30/0.64           => ( ( Xa = one )
% 0.30/0.64             => ( Y
% 0.30/0.64               != ( some_num @ one ) ) ) )
% 0.30/0.64         => ( ( ( X = one )
% 0.30/0.64             => ( ? [N3: num] :
% 0.30/0.64                    ( Xa
% 0.30/0.64                    = ( bit0 @ N3 ) )
% 0.30/0.64               => ( Y != none_num ) ) )
% 0.30/0.64           => ( ( ( X = one )
% 0.30/0.64               => ( ? [N3: num] :
% 0.30/0.64                      ( Xa
% 0.30/0.64                      = ( bit1 @ N3 ) )
% 0.30/0.64                 => ( Y
% 0.30/0.64                   != ( some_num @ one ) ) ) )
% 0.30/0.64             => ( ( ? [M3: num] :
% 0.30/0.64                      ( X
% 0.30/0.64                      = ( bit0 @ M3 ) )
% 0.30/0.64                 => ( ( Xa = one )
% 0.30/0.64                   => ( Y != none_num ) ) )
% 0.30/0.64               => ( ! [M3: num] :
% 0.30/0.64                      ( ( X
% 0.30/0.64                        = ( bit0 @ M3 ) )
% 0.30/0.64                     => ! [N3: num] :
% 0.30/0.64                          ( ( Xa
% 0.30/0.64                            = ( bit0 @ N3 ) )
% 0.30/0.64                         => ( Y
% 0.30/0.64                           != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N3 ) ) ) ) )
% 0.30/0.64                 => ( ! [M3: num] :
% 0.30/0.64                        ( ( X
% 0.30/0.64                          = ( bit0 @ M3 ) )
% 0.30/0.64                       => ! [N3: num] :
% 0.30/0.64                            ( ( Xa
% 0.30/0.64                              = ( bit1 @ N3 ) )
% 0.30/0.64                           => ( Y
% 0.30/0.64                             != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N3 ) ) ) ) )
% 0.30/0.64                   => ( ( ? [M3: num] :
% 0.30/0.64                            ( X
% 0.30/0.64                            = ( bit1 @ M3 ) )
% 0.30/0.64                       => ( ( Xa = one )
% 0.30/0.64                         => ( Y
% 0.30/0.64                           != ( some_num @ one ) ) ) )
% 0.30/0.64                     => ( ! [M3: num] :
% 0.30/0.64                            ( ( X
% 0.30/0.64                              = ( bit1 @ M3 ) )
% 0.30/0.64                           => ! [N3: num] :
% 0.30/0.64                                ( ( Xa
% 0.30/0.64                                  = ( bit0 @ N3 ) )
% 0.30/0.64                               => ( Y
% 0.30/0.64                                 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N3 ) ) ) ) )
% 0.30/0.64                       => ~ ! [M3: num] :
% 0.30/0.64                              ( ( X
% 0.30/0.64                                = ( bit1 @ M3 ) )
% 0.30/0.64                             => ! [N3: num] :
% 0.30/0.64                                  ( ( Xa
% 0.30/0.64                                    = ( bit1 @ N3 ) )
% 0.30/0.64                                 => ( Y
% 0.30/0.64                                   != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.30/0.64                                      @ ^ [N5: num] : ( some_num @ ( bit1 @ N5 ) )
% 0.30/0.64                                      @ ( bit_un7362597486090784418nd_num @ M3 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % and_num.elims
% 0.30/0.64  thf(fact_9294_nat__def,axiom,
% 0.30/0.64      ( nat2
% 0.30/0.64      = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % nat_def
% 0.30/0.64  thf(fact_9295_less__int__def,axiom,
% 0.30/0.64      ( ord_less_int
% 0.30/0.64      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 0.30/0.64        @ ( produc8739625826339149834_nat_o
% 0.30/0.64          @ ^ [X3: nat,Y3: nat] :
% 0.30/0.64              ( produc6081775807080527818_nat_o
% 0.30/0.64              @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % less_int_def
% 0.30/0.64  thf(fact_9296_less__eq__int__def,axiom,
% 0.30/0.64      ( ord_less_eq_int
% 0.30/0.64      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 0.30/0.64        @ ( produc8739625826339149834_nat_o
% 0.30/0.64          @ ^ [X3: nat,Y3: nat] :
% 0.30/0.64              ( produc6081775807080527818_nat_o
% 0.30/0.64              @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % less_eq_int_def
% 0.30/0.64  thf(fact_9297_and__num_Osimps_I9_J,axiom,
% 0.30/0.64      ! [M: num,N: num] :
% 0.30/0.64        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.30/0.64        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.30/0.64          @ ^ [N5: num] : ( some_num @ ( bit1 @ N5 ) )
% 0.30/0.64          @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % and_num.simps(9)
% 0.30/0.64  thf(fact_9298_uminus__integer__def,axiom,
% 0.30/0.64      ( uminus1351360451143612070nteger
% 0.30/0.64      = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ uminus_uminus_int ) ) ).
% 0.30/0.64  
% 0.30/0.64  % uminus_integer_def
% 0.30/0.64  thf(fact_9299_inf__nat__def,axiom,
% 0.30/0.64      inf_inf_nat = ord_min_nat ).
% 0.30/0.64  
% 0.30/0.64  % inf_nat_def
% 0.30/0.64  thf(fact_9300_min__Suc2,axiom,
% 0.30/0.64      ! [M: nat,N: nat] :
% 0.30/0.64        ( ( ord_min_nat @ M @ ( suc @ N ) )
% 0.30/0.64        = ( case_nat_nat @ zero_zero_nat
% 0.30/0.64          @ ^ [M5: nat] : ( suc @ ( ord_min_nat @ M5 @ N ) )
% 0.30/0.64          @ M ) ) ).
% 0.30/0.64  
% 0.30/0.64  % min_Suc2
% 0.30/0.64  thf(fact_9301_min__Suc1,axiom,
% 0.30/0.64      ! [N: nat,M: nat] :
% 0.30/0.64        ( ( ord_min_nat @ ( suc @ N ) @ M )
% 0.30/0.64        = ( case_nat_nat @ zero_zero_nat
% 0.30/0.64          @ ^ [M5: nat] : ( suc @ ( ord_min_nat @ N @ M5 ) )
% 0.30/0.64          @ M ) ) ).
% 0.30/0.64  
% 0.30/0.64  % min_Suc1
% 0.30/0.64  thf(fact_9302_Code__Numeral_Odup__def,axiom,
% 0.30/0.64      ( code_dup
% 0.30/0.64      = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int
% 0.30/0.64        @ ^ [K4: int] : ( plus_plus_int @ K4 @ K4 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Code_Numeral.dup_def
% 0.30/0.64  thf(fact_9303_Code__Numeral_Osub__code_I9_J,axiom,
% 0.30/0.64      ! [M: num,N: num] :
% 0.30/0.64        ( ( code_sub @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.30/0.64        = ( minus_8373710615458151222nteger @ ( code_dup @ ( code_sub @ M @ N ) ) @ one_one_Code_integer ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Code_Numeral.sub_code(9)
% 0.30/0.64  thf(fact_9304_Code__Numeral_Osub__code_I8_J,axiom,
% 0.30/0.64      ! [M: num,N: num] :
% 0.30/0.64        ( ( code_sub @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.30/0.64        = ( plus_p5714425477246183910nteger @ ( code_dup @ ( code_sub @ M @ N ) ) @ one_one_Code_integer ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Code_Numeral.sub_code(8)
% 0.30/0.64  thf(fact_9305_Code__Numeral_Osub__def,axiom,
% 0.30/0.64      ( code_sub
% 0.30/0.64      = ( map_fu6891787308814931657nteger @ id_num @ ( map_fu8638147718074629079nteger @ id_num @ code_integer_of_int )
% 0.30/0.64        @ ^ [M2: num,N2: num] : ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Code_Numeral.sub_def
% 0.30/0.64  thf(fact_9306_and__not__num_Opelims,axiom,
% 0.30/0.64      ! [X: num,Xa: num,Y: option_num] :
% 0.30/0.64        ( ( ( bit_and_not_num @ X @ Xa )
% 0.30/0.64          = Y )
% 0.30/0.64       => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 0.30/0.64         => ( ( ( X = one )
% 0.30/0.64             => ( ( Xa = one )
% 0.30/0.64               => ( ( Y = none_num )
% 0.30/0.64                 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.30/0.64           => ( ( ( X = one )
% 0.30/0.64               => ! [N3: num] :
% 0.30/0.64                    ( ( Xa
% 0.30/0.64                      = ( bit0 @ N3 ) )
% 0.30/0.64                   => ( ( Y
% 0.30/0.64                        = ( some_num @ one ) )
% 0.30/0.64                     => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 0.30/0.64             => ( ( ( X = one )
% 0.30/0.64                 => ! [N3: num] :
% 0.30/0.64                      ( ( Xa
% 0.30/0.64                        = ( bit1 @ N3 ) )
% 0.30/0.64                     => ( ( Y = none_num )
% 0.30/0.64                       => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 0.30/0.64               => ( ! [M3: num] :
% 0.30/0.64                      ( ( X
% 0.30/0.64                        = ( bit0 @ M3 ) )
% 0.30/0.64                     => ( ( Xa = one )
% 0.30/0.64                       => ( ( Y
% 0.30/0.64                            = ( some_num @ ( bit0 @ M3 ) ) )
% 0.30/0.64                         => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ one ) ) ) ) )
% 0.30/0.64                 => ( ! [M3: num] :
% 0.30/0.64                        ( ( X
% 0.30/0.64                          = ( bit0 @ M3 ) )
% 0.30/0.64                       => ! [N3: num] :
% 0.30/0.64                            ( ( Xa
% 0.30/0.64                              = ( bit0 @ N3 ) )
% 0.30/0.64                           => ( ( Y
% 0.30/0.64                                = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N3 ) ) )
% 0.30/0.64                             => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 0.30/0.64                   => ( ! [M3: num] :
% 0.30/0.64                          ( ( X
% 0.30/0.64                            = ( bit0 @ M3 ) )
% 0.30/0.64                         => ! [N3: num] :
% 0.30/0.64                              ( ( Xa
% 0.30/0.64                                = ( bit1 @ N3 ) )
% 0.30/0.64                             => ( ( Y
% 0.30/0.64                                  = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N3 ) ) )
% 0.30/0.64                               => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 0.30/0.64                     => ( ! [M3: num] :
% 0.30/0.64                            ( ( X
% 0.30/0.64                              = ( bit1 @ M3 ) )
% 0.30/0.64                           => ( ( Xa = one )
% 0.30/0.64                             => ( ( Y
% 0.30/0.64                                  = ( some_num @ ( bit0 @ M3 ) ) )
% 0.30/0.64                               => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ one ) ) ) ) )
% 0.30/0.64                       => ( ! [M3: num] :
% 0.30/0.64                              ( ( X
% 0.30/0.64                                = ( bit1 @ M3 ) )
% 0.30/0.64                             => ! [N3: num] :
% 0.30/0.64                                  ( ( Xa
% 0.30/0.64                                    = ( bit0 @ N3 ) )
% 0.30/0.64                                 => ( ( Y
% 0.30/0.64                                      = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.30/0.64                                        @ ^ [N5: num] : ( some_num @ ( bit1 @ N5 ) )
% 0.30/0.64                                        @ ( bit_and_not_num @ M3 @ N3 ) ) )
% 0.30/0.64                                   => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 0.30/0.64                         => ~ ! [M3: num] :
% 0.30/0.64                                ( ( X
% 0.30/0.64                                  = ( bit1 @ M3 ) )
% 0.30/0.64                               => ! [N3: num] :
% 0.30/0.64                                    ( ( Xa
% 0.30/0.64                                      = ( bit1 @ N3 ) )
% 0.30/0.64                                   => ( ( Y
% 0.30/0.64                                        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N3 ) ) )
% 0.30/0.64                                     => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % and_not_num.pelims
% 0.30/0.64  thf(fact_9307_and__num_Opelims,axiom,
% 0.30/0.64      ! [X: num,Xa: num,Y: option_num] :
% 0.30/0.64        ( ( ( bit_un7362597486090784418nd_num @ X @ Xa )
% 0.30/0.64          = Y )
% 0.30/0.64       => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 0.30/0.64         => ( ( ( X = one )
% 0.30/0.64             => ( ( Xa = one )
% 0.30/0.64               => ( ( Y
% 0.30/0.64                    = ( some_num @ one ) )
% 0.30/0.64                 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.30/0.64           => ( ( ( X = one )
% 0.30/0.64               => ! [N3: num] :
% 0.30/0.64                    ( ( Xa
% 0.30/0.64                      = ( bit0 @ N3 ) )
% 0.30/0.64                   => ( ( Y = none_num )
% 0.30/0.64                     => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 0.30/0.64             => ( ( ( X = one )
% 0.30/0.64                 => ! [N3: num] :
% 0.30/0.64                      ( ( Xa
% 0.30/0.64                        = ( bit1 @ N3 ) )
% 0.30/0.64                     => ( ( Y
% 0.30/0.64                          = ( some_num @ one ) )
% 0.30/0.64                       => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 0.30/0.64               => ( ! [M3: num] :
% 0.30/0.64                      ( ( X
% 0.30/0.64                        = ( bit0 @ M3 ) )
% 0.30/0.64                     => ( ( Xa = one )
% 0.30/0.64                       => ( ( Y = none_num )
% 0.30/0.64                         => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ one ) ) ) ) )
% 0.30/0.64                 => ( ! [M3: num] :
% 0.30/0.64                        ( ( X
% 0.30/0.64                          = ( bit0 @ M3 ) )
% 0.30/0.64                       => ! [N3: num] :
% 0.30/0.64                            ( ( Xa
% 0.30/0.64                              = ( bit0 @ N3 ) )
% 0.30/0.64                           => ( ( Y
% 0.30/0.64                                = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N3 ) ) )
% 0.30/0.64                             => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 0.30/0.64                   => ( ! [M3: num] :
% 0.30/0.64                          ( ( X
% 0.30/0.64                            = ( bit0 @ M3 ) )
% 0.30/0.64                         => ! [N3: num] :
% 0.30/0.64                              ( ( Xa
% 0.30/0.64                                = ( bit1 @ N3 ) )
% 0.30/0.64                             => ( ( Y
% 0.30/0.64                                  = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N3 ) ) )
% 0.30/0.64                               => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 0.30/0.64                     => ( ! [M3: num] :
% 0.30/0.64                            ( ( X
% 0.30/0.64                              = ( bit1 @ M3 ) )
% 0.30/0.64                           => ( ( Xa = one )
% 0.30/0.64                             => ( ( Y
% 0.30/0.64                                  = ( some_num @ one ) )
% 0.30/0.64                               => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ one ) ) ) ) )
% 0.30/0.64                       => ( ! [M3: num] :
% 0.30/0.64                              ( ( X
% 0.30/0.64                                = ( bit1 @ M3 ) )
% 0.30/0.64                             => ! [N3: num] :
% 0.30/0.64                                  ( ( Xa
% 0.30/0.64                                    = ( bit0 @ N3 ) )
% 0.30/0.64                                 => ( ( Y
% 0.30/0.64                                      = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N3 ) ) )
% 0.30/0.64                                   => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 0.30/0.64                         => ~ ! [M3: num] :
% 0.30/0.64                                ( ( X
% 0.30/0.64                                  = ( bit1 @ M3 ) )
% 0.30/0.64                               => ! [N3: num] :
% 0.30/0.64                                    ( ( Xa
% 0.30/0.64                                      = ( bit1 @ N3 ) )
% 0.30/0.64                                   => ( ( Y
% 0.30/0.64                                        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 0.30/0.64                                          @ ^ [N5: num] : ( some_num @ ( bit1 @ N5 ) )
% 0.30/0.64                                          @ ( bit_un7362597486090784418nd_num @ M3 @ N3 ) ) )
% 0.30/0.64                                     => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % and_num.pelims
% 0.30/0.64  thf(fact_9308_or__not__num__neg_Opelims,axiom,
% 0.30/0.64      ! [X: num,Xa: num,Y: num] :
% 0.30/0.64        ( ( ( bit_or_not_num_neg @ X @ Xa )
% 0.30/0.64          = Y )
% 0.30/0.64       => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 0.30/0.64         => ( ( ( X = one )
% 0.30/0.64             => ( ( Xa = one )
% 0.30/0.64               => ( ( Y = one )
% 0.30/0.64                 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.30/0.64           => ( ( ( X = one )
% 0.30/0.64               => ! [M3: num] :
% 0.30/0.64                    ( ( Xa
% 0.30/0.64                      = ( bit0 @ M3 ) )
% 0.30/0.64                   => ( ( Y
% 0.30/0.64                        = ( bit1 @ M3 ) )
% 0.30/0.64                     => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M3 ) ) ) ) ) )
% 0.30/0.64             => ( ( ( X = one )
% 0.30/0.64                 => ! [M3: num] :
% 0.30/0.64                      ( ( Xa
% 0.30/0.64                        = ( bit1 @ M3 ) )
% 0.30/0.64                     => ( ( Y
% 0.30/0.64                          = ( bit1 @ M3 ) )
% 0.30/0.64                       => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M3 ) ) ) ) ) )
% 0.30/0.64               => ( ! [N3: num] :
% 0.30/0.64                      ( ( X
% 0.30/0.64                        = ( bit0 @ N3 ) )
% 0.30/0.64                     => ( ( Xa = one )
% 0.30/0.64                       => ( ( Y
% 0.30/0.64                            = ( bit0 @ one ) )
% 0.30/0.64                         => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ one ) ) ) ) )
% 0.30/0.64                 => ( ! [N3: num] :
% 0.30/0.64                        ( ( X
% 0.30/0.64                          = ( bit0 @ N3 ) )
% 0.30/0.64                       => ! [M3: num] :
% 0.30/0.64                            ( ( Xa
% 0.30/0.64                              = ( bit0 @ M3 ) )
% 0.30/0.64                           => ( ( Y
% 0.30/0.64                                = ( bitM @ ( bit_or_not_num_neg @ N3 @ M3 ) ) )
% 0.30/0.64                             => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit0 @ M3 ) ) ) ) ) )
% 0.30/0.64                   => ( ! [N3: num] :
% 0.30/0.64                          ( ( X
% 0.30/0.64                            = ( bit0 @ N3 ) )
% 0.30/0.64                         => ! [M3: num] :
% 0.30/0.64                              ( ( Xa
% 0.30/0.64                                = ( bit1 @ M3 ) )
% 0.30/0.64                             => ( ( Y
% 0.30/0.64                                  = ( bit0 @ ( bit_or_not_num_neg @ N3 @ M3 ) ) )
% 0.30/0.64                               => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit1 @ M3 ) ) ) ) ) )
% 0.30/0.64                     => ( ! [N3: num] :
% 0.30/0.64                            ( ( X
% 0.30/0.64                              = ( bit1 @ N3 ) )
% 0.30/0.64                           => ( ( Xa = one )
% 0.30/0.64                             => ( ( Y = one )
% 0.30/0.64                               => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ one ) ) ) ) )
% 0.30/0.64                       => ( ! [N3: num] :
% 0.30/0.64                              ( ( X
% 0.30/0.64                                = ( bit1 @ N3 ) )
% 0.30/0.64                             => ! [M3: num] :
% 0.30/0.64                                  ( ( Xa
% 0.30/0.64                                    = ( bit0 @ M3 ) )
% 0.30/0.64                                 => ( ( Y
% 0.30/0.64                                      = ( bitM @ ( bit_or_not_num_neg @ N3 @ M3 ) ) )
% 0.30/0.64                                   => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit0 @ M3 ) ) ) ) ) )
% 0.30/0.64                         => ~ ! [N3: num] :
% 0.30/0.64                                ( ( X
% 0.30/0.64                                  = ( bit1 @ N3 ) )
% 0.30/0.64                               => ! [M3: num] :
% 0.30/0.64                                    ( ( Xa
% 0.30/0.64                                      = ( bit1 @ M3 ) )
% 0.30/0.64                                   => ( ( Y
% 0.30/0.64                                        = ( bitM @ ( bit_or_not_num_neg @ N3 @ M3 ) ) )
% 0.30/0.64                                     => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit1 @ M3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % or_not_num_neg.pelims
% 0.30/0.64  thf(fact_9309_xor__num_Opelims,axiom,
% 0.30/0.64      ! [X: num,Xa: num,Y: option_num] :
% 0.30/0.64        ( ( ( bit_un2480387367778600638or_num @ X @ Xa )
% 0.30/0.64          = Y )
% 0.30/0.64       => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 0.30/0.64         => ( ( ( X = one )
% 0.30/0.64             => ( ( Xa = one )
% 0.30/0.64               => ( ( Y = none_num )
% 0.30/0.64                 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.30/0.64           => ( ( ( X = one )
% 0.30/0.64               => ! [N3: num] :
% 0.30/0.64                    ( ( Xa
% 0.30/0.64                      = ( bit0 @ N3 ) )
% 0.30/0.64                   => ( ( Y
% 0.30/0.64                        = ( some_num @ ( bit1 @ N3 ) ) )
% 0.30/0.64                     => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 0.30/0.64             => ( ( ( X = one )
% 0.30/0.64                 => ! [N3: num] :
% 0.30/0.64                      ( ( Xa
% 0.30/0.64                        = ( bit1 @ N3 ) )
% 0.30/0.64                     => ( ( Y
% 0.30/0.64                          = ( some_num @ ( bit0 @ N3 ) ) )
% 0.30/0.64                       => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 0.30/0.64               => ( ! [M3: num] :
% 0.30/0.64                      ( ( X
% 0.30/0.64                        = ( bit0 @ M3 ) )
% 0.30/0.64                     => ( ( Xa = one )
% 0.30/0.64                       => ( ( Y
% 0.30/0.64                            = ( some_num @ ( bit1 @ M3 ) ) )
% 0.30/0.64                         => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ one ) ) ) ) )
% 0.30/0.64                 => ( ! [M3: num] :
% 0.30/0.64                        ( ( X
% 0.30/0.64                          = ( bit0 @ M3 ) )
% 0.30/0.64                       => ! [N3: num] :
% 0.30/0.64                            ( ( Xa
% 0.30/0.64                              = ( bit0 @ N3 ) )
% 0.30/0.64                           => ( ( Y
% 0.30/0.64                                = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M3 @ N3 ) ) )
% 0.30/0.64                             => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 0.30/0.64                   => ( ! [M3: num] :
% 0.30/0.64                          ( ( X
% 0.30/0.64                            = ( bit0 @ M3 ) )
% 0.30/0.64                         => ! [N3: num] :
% 0.30/0.64                              ( ( Xa
% 0.30/0.64                                = ( bit1 @ N3 ) )
% 0.30/0.64                             => ( ( Y
% 0.30/0.64                                  = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M3 @ N3 ) ) ) )
% 0.30/0.64                               => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 0.30/0.64                     => ( ! [M3: num] :
% 0.30/0.64                            ( ( X
% 0.30/0.64                              = ( bit1 @ M3 ) )
% 0.30/0.64                           => ( ( Xa = one )
% 0.30/0.64                             => ( ( Y
% 0.30/0.64                                  = ( some_num @ ( bit0 @ M3 ) ) )
% 0.30/0.64                               => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ one ) ) ) ) )
% 0.30/0.64                       => ( ! [M3: num] :
% 0.30/0.64                              ( ( X
% 0.30/0.64                                = ( bit1 @ M3 ) )
% 0.30/0.64                             => ! [N3: num] :
% 0.30/0.64                                  ( ( Xa
% 0.30/0.64                                    = ( bit0 @ N3 ) )
% 0.30/0.64                                 => ( ( Y
% 0.30/0.64                                      = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M3 @ N3 ) ) ) )
% 0.30/0.64                                   => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 0.30/0.64                         => ~ ! [M3: num] :
% 0.30/0.64                                ( ( X
% 0.30/0.64                                  = ( bit1 @ M3 ) )
% 0.30/0.64                               => ! [N3: num] :
% 0.30/0.64                                    ( ( Xa
% 0.30/0.64                                      = ( bit1 @ N3 ) )
% 0.30/0.64                                   => ( ( Y
% 0.30/0.64                                        = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M3 @ N3 ) ) )
% 0.30/0.64                                     => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % xor_num.pelims
% 0.30/0.64  thf(fact_9310_Field__natLeq__on,axiom,
% 0.30/0.64      ! [N: nat] :
% 0.30/0.64        ( ( field_nat
% 0.30/0.64          @ ( collec3392354462482085612at_nat
% 0.30/0.64            @ ( produc6081775807080527818_nat_o
% 0.30/0.64              @ ^ [X3: nat,Y3: nat] :
% 0.30/0.64                  ( ( ord_less_nat @ X3 @ N )
% 0.30/0.64                  & ( ord_less_nat @ Y3 @ N )
% 0.30/0.64                  & ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) )
% 0.30/0.64        = ( collect_nat
% 0.30/0.64          @ ^ [X3: nat] : ( ord_less_nat @ X3 @ N ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Field_natLeq_on
% 0.30/0.64  thf(fact_9311_range__enumerate,axiom,
% 0.30/0.64      ! [S: set_nat] :
% 0.30/0.64        ( ~ ( finite_finite_nat @ S )
% 0.30/0.64       => ( ( image_nat_nat @ ( infini8530281810654367211te_nat @ S ) @ top_top_set_nat )
% 0.30/0.64          = S ) ) ).
% 0.30/0.64  
% 0.30/0.64  % range_enumerate
% 0.30/0.64  thf(fact_9312_Inf__nat__def,axiom,
% 0.30/0.64      ( complete_Inf_Inf_nat
% 0.30/0.64      = ( ^ [X4: set_nat] :
% 0.30/0.64            ( ord_Least_nat
% 0.30/0.64            @ ^ [N2: nat] : ( member_nat @ N2 @ X4 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Inf_nat_def
% 0.30/0.64  thf(fact_9313_wf__less,axiom,
% 0.30/0.64      wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 0.30/0.64  
% 0.30/0.64  % wf_less
% 0.30/0.64  thf(fact_9314_Least__Suc,axiom,
% 0.30/0.64      ! [P: nat > $o,N: nat] :
% 0.30/0.64        ( ( P @ N )
% 0.30/0.64       => ( ~ ( P @ zero_zero_nat )
% 0.30/0.64         => ( ( ord_Least_nat @ P )
% 0.30/0.64            = ( suc
% 0.30/0.64              @ ( ord_Least_nat
% 0.30/0.64                @ ^ [M2: nat] : ( P @ ( suc @ M2 ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Least_Suc
% 0.30/0.64  thf(fact_9315_rat__sgn__code,axiom,
% 0.30/0.64      ! [P4: rat] :
% 0.30/0.64        ( ( quotient_of @ ( sgn_sgn_rat @ P4 ) )
% 0.30/0.64        = ( product_Pair_int_int @ ( sgn_sgn_int @ ( product_fst_int_int @ ( quotient_of @ P4 ) ) ) @ one_one_int ) ) ).
% 0.30/0.64  
% 0.30/0.64  % rat_sgn_code
% 0.30/0.64  thf(fact_9316_bezw_Oelims,axiom,
% 0.30/0.64      ! [X: nat,Xa: nat,Y: product_prod_int_int] :
% 0.30/0.64        ( ( ( bezw @ X @ Xa )
% 0.30/0.64          = Y )
% 0.30/0.64       => ( ( ( Xa = zero_zero_nat )
% 0.30/0.64           => ( Y
% 0.30/0.64              = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 0.30/0.64          & ( ( Xa != zero_zero_nat )
% 0.30/0.64           => ( Y
% 0.30/0.64              = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa ) ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % bezw.elims
% 0.30/0.64  thf(fact_9317_bezw_Osimps,axiom,
% 0.30/0.64      ( bezw
% 0.30/0.64      = ( ^ [X3: nat,Y3: nat] : ( if_Pro3027730157355071871nt_int @ ( Y3 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X3 @ Y3 ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % bezw.simps
% 0.30/0.64  thf(fact_9318_bezw__non__0,axiom,
% 0.30/0.64      ! [Y: nat,X: nat] :
% 0.30/0.64        ( ( ord_less_nat @ zero_zero_nat @ Y )
% 0.30/0.64       => ( ( bezw @ X @ Y )
% 0.30/0.64          = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % bezw_non_0
% 0.30/0.64  thf(fact_9319_one__mod__minus__numeral,axiom,
% 0.30/0.64      ! [N: num] :
% 0.30/0.64        ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.64        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % one_mod_minus_numeral
% 0.30/0.64  thf(fact_9320_minus__one__mod__numeral,axiom,
% 0.30/0.64      ! [N: num] :
% 0.30/0.64        ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 0.30/0.64        = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % minus_one_mod_numeral
% 0.30/0.64  thf(fact_9321_minus__numeral__mod__numeral,axiom,
% 0.30/0.64      ! [M: num,N: num] :
% 0.30/0.64        ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.30/0.64        = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % minus_numeral_mod_numeral
% 0.30/0.64  thf(fact_9322_numeral__mod__minus__numeral,axiom,
% 0.30/0.64      ! [M: num,N: num] :
% 0.30/0.64        ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.64        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % numeral_mod_minus_numeral
% 0.30/0.64  thf(fact_9323_bezw_Opelims,axiom,
% 0.30/0.64      ! [X: nat,Xa: nat,Y: product_prod_int_int] :
% 0.30/0.64        ( ( ( bezw @ X @ Xa )
% 0.30/0.64          = Y )
% 0.30/0.64       => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 0.30/0.64         => ~ ( ( ( ( Xa = zero_zero_nat )
% 0.30/0.64                 => ( Y
% 0.30/0.64                    = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 0.30/0.64                & ( ( Xa != zero_zero_nat )
% 0.30/0.64                 => ( Y
% 0.30/0.64                    = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa ) ) ) ) ) ) ) )
% 0.30/0.64             => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % bezw.pelims
% 0.30/0.64  thf(fact_9324_normalize__def,axiom,
% 0.30/0.64      ( normalize
% 0.30/0.64      = ( ^ [P6: product_prod_int_int] :
% 0.30/0.64            ( 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 ) ) ) )
% 0.30/0.64            @ ( if_Pro3027730157355071871nt_int
% 0.30/0.64              @ ( ( product_snd_int_int @ P6 )
% 0.30/0.64                = zero_zero_int )
% 0.30/0.64              @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.30/0.64              @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % normalize_def
% 0.30/0.64  thf(fact_9325_gcd__1__int,axiom,
% 0.30/0.64      ! [M: int] :
% 0.30/0.64        ( ( gcd_gcd_int @ M @ one_one_int )
% 0.30/0.64        = one_one_int ) ).
% 0.30/0.64  
% 0.30/0.64  % gcd_1_int
% 0.30/0.64  thf(fact_9326_gcd__neg1__int,axiom,
% 0.30/0.64      ! [X: int,Y: int] :
% 0.30/0.64        ( ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ Y )
% 0.30/0.64        = ( gcd_gcd_int @ X @ Y ) ) ).
% 0.30/0.64  
% 0.30/0.64  % gcd_neg1_int
% 0.30/0.64  thf(fact_9327_gcd__neg2__int,axiom,
% 0.30/0.64      ! [X: int,Y: int] :
% 0.30/0.64        ( ( gcd_gcd_int @ X @ ( uminus_uminus_int @ Y ) )
% 0.30/0.64        = ( gcd_gcd_int @ X @ Y ) ) ).
% 0.30/0.64  
% 0.30/0.64  % gcd_neg2_int
% 0.30/0.64  thf(fact_9328_gcd__neg__numeral__2__int,axiom,
% 0.30/0.64      ! [X: int,N: num] :
% 0.30/0.64        ( ( gcd_gcd_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.64        = ( gcd_gcd_int @ X @ ( numeral_numeral_int @ N ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % gcd_neg_numeral_2_int
% 0.30/0.64  thf(fact_9329_gcd__neg__numeral__1__int,axiom,
% 0.30/0.64      ! [N: num,X: int] :
% 0.30/0.64        ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ X )
% 0.30/0.64        = ( gcd_gcd_int @ ( numeral_numeral_int @ N ) @ X ) ) ).
% 0.30/0.64  
% 0.30/0.64  % gcd_neg_numeral_1_int
% 0.30/0.64  thf(fact_9330_dup_Orsp,axiom,
% 0.30/0.64      ( bNF_re4712519889275205905nt_int
% 0.30/0.64      @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 0.30/0.64      @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 0.30/0.64      @ ^ [K4: int] : ( plus_plus_int @ K4 @ K4 )
% 0.30/0.64      @ ^ [K4: int] : ( plus_plus_int @ K4 @ K4 ) ) ).
% 0.30/0.64  
% 0.30/0.64  % dup.rsp
% 0.30/0.64  thf(fact_9331_sub_Orsp,axiom,
% 0.30/0.64      ( bNF_re8402795839162346335um_int
% 0.30/0.64      @ ^ [Y4: num,Z4: num] : ( Y4 = Z4 )
% 0.30/0.64      @ ( bNF_re1822329894187522285nt_int
% 0.30/0.64        @ ^ [Y4: num,Z4: num] : ( Y4 = Z4 )
% 0.30/0.64        @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 0.30/0.64      @ ^ [M2: num,N2: num] : ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 0.30/0.64      @ ^ [M2: num,N2: num] : ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % sub.rsp
% 0.30/0.64  thf(fact_9332_uminus__integer_Orsp,axiom,
% 0.30/0.64      ( bNF_re4712519889275205905nt_int
% 0.30/0.64      @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 0.30/0.64      @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 0.30/0.64      @ uminus_uminus_int
% 0.30/0.64      @ uminus_uminus_int ) ).
% 0.30/0.64  
% 0.30/0.64  % uminus_integer.rsp
% 0.30/0.64  thf(fact_9333_gcd__cases__int,axiom,
% 0.30/0.64      ! [X: int,Y: int,P: int > $o] :
% 0.30/0.64        ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.30/0.64         => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.30/0.64           => ( P @ ( gcd_gcd_int @ X @ Y ) ) ) )
% 0.30/0.64       => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.30/0.64           => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 0.30/0.64             => ( P @ ( gcd_gcd_int @ X @ ( uminus_uminus_int @ Y ) ) ) ) )
% 0.30/0.64         => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 0.30/0.64             => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.30/0.64               => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ Y ) ) ) )
% 0.30/0.64           => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 0.30/0.64               => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 0.30/0.64                 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 0.30/0.64             => ( P @ ( gcd_gcd_int @ X @ Y ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % gcd_cases_int
% 0.30/0.64  thf(fact_9334_gcd__is__Max__divisors__int,axiom,
% 0.30/0.64      ! [N: int,M: int] :
% 0.30/0.64        ( ( N != zero_zero_int )
% 0.30/0.64       => ( ( gcd_gcd_int @ M @ N )
% 0.30/0.64          = ( lattic8263393255366662781ax_int
% 0.30/0.64            @ ( collect_int
% 0.30/0.64              @ ^ [D4: int] :
% 0.30/0.64                  ( ( dvd_dvd_int @ D4 @ M )
% 0.30/0.64                  & ( dvd_dvd_int @ D4 @ N ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % gcd_is_Max_divisors_int
% 0.30/0.64  thf(fact_9335_prod__decode__aux_Opelims,axiom,
% 0.30/0.64      ! [X: nat,Xa: nat,Y: product_prod_nat_nat] :
% 0.30/0.64        ( ( ( nat_prod_decode_aux @ X @ Xa )
% 0.30/0.64          = Y )
% 0.30/0.64       => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 0.30/0.64         => ~ ( ( ( ( ord_less_eq_nat @ Xa @ X )
% 0.30/0.64                 => ( Y
% 0.30/0.64                    = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X @ Xa ) ) ) )
% 0.30/0.64                & ( ~ ( ord_less_eq_nat @ Xa @ X )
% 0.30/0.64                 => ( Y
% 0.30/0.64                    = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa @ ( suc @ X ) ) ) ) ) )
% 0.30/0.64             => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % prod_decode_aux.pelims
% 0.30/0.64  thf(fact_9336_plus__rat_Otransfer,axiom,
% 0.30/0.64      ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 0.30/0.64      @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) )
% 0.30/0.64      @ plus_plus_rat ) ).
% 0.30/0.64  
% 0.30/0.64  % plus_rat.transfer
% 0.30/0.64  thf(fact_9337_gcd__1__nat,axiom,
% 0.30/0.64      ! [M: nat] :
% 0.30/0.64        ( ( gcd_gcd_nat @ M @ one_one_nat )
% 0.30/0.64        = one_one_nat ) ).
% 0.30/0.64  
% 0.30/0.64  % gcd_1_nat
% 0.30/0.64  thf(fact_9338_Gcd__in,axiom,
% 0.30/0.64      ! [A2: set_nat] :
% 0.30/0.64        ( ! [A6: nat,B6: nat] :
% 0.30/0.64            ( ( member_nat @ A6 @ A2 )
% 0.30/0.64           => ( ( member_nat @ B6 @ A2 )
% 0.30/0.64             => ( member_nat @ ( gcd_gcd_nat @ A6 @ B6 ) @ A2 ) ) )
% 0.30/0.64       => ( ( A2 != bot_bot_set_nat )
% 0.30/0.64         => ( member_nat @ ( gcd_Gcd_nat @ A2 ) @ A2 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Gcd_in
% 0.30/0.64  thf(fact_9339_gcd__nat_Osemilattice__neutr__axioms,axiom,
% 0.30/0.64      semila9081495762789891438tr_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 0.30/0.64  
% 0.30/0.64  % gcd_nat.semilattice_neutr_axioms
% 0.30/0.64  thf(fact_9340_gcd__nat_Ocomm__monoid__axioms,axiom,
% 0.30/0.64      comm_monoid_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 0.30/0.64  
% 0.30/0.64  % gcd_nat.comm_monoid_axioms
% 0.30/0.64  thf(fact_9341_gcd__nat_Omonoid__axioms,axiom,
% 0.30/0.64      monoid_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 0.30/0.64  
% 0.30/0.64  % gcd_nat.monoid_axioms
% 0.30/0.64  thf(fact_9342_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 0.30/0.64      ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 0.30/0.64      @ ^ [M2: nat,N2: nat] :
% 0.30/0.64          ( ( dvd_dvd_nat @ M2 @ N2 )
% 0.30/0.64          & ( M2 != N2 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % gcd_nat.semilattice_neutr_order_axioms
% 0.30/0.64  thf(fact_9343_one__rat_Otransfer,axiom,
% 0.30/0.64      pcr_rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ one_one_rat ).
% 0.30/0.64  
% 0.30/0.64  % one_rat.transfer
% 0.30/0.64  thf(fact_9344_gcd__is__Max__divisors__nat,axiom,
% 0.30/0.64      ! [N: nat,M: nat] :
% 0.30/0.64        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.64       => ( ( gcd_gcd_nat @ M @ N )
% 0.30/0.64          = ( lattic8265883725875713057ax_nat
% 0.30/0.64            @ ( collect_nat
% 0.30/0.64              @ ^ [D4: nat] :
% 0.30/0.64                  ( ( dvd_dvd_nat @ D4 @ M )
% 0.30/0.64                  & ( dvd_dvd_nat @ D4 @ N ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % gcd_is_Max_divisors_nat
% 0.30/0.64  thf(fact_9345_zero__rat_Otransfer,axiom,
% 0.30/0.64      pcr_rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ zero_zero_rat ).
% 0.30/0.64  
% 0.30/0.64  % zero_rat.transfer
% 0.30/0.64  thf(fact_9346_Fract_Otransfer,axiom,
% 0.30/0.64      ( bNF_re3461391660133120880nt_rat
% 0.30/0.64      @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 0.30/0.64      @ ( bNF_re2214769303045360666nt_rat
% 0.30/0.64        @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 0.30/0.64        @ pcr_rat )
% 0.30/0.64      @ ^ [A3: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( B3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A3 @ B3 ) )
% 0.30/0.64      @ fract ) ).
% 0.30/0.64  
% 0.30/0.64  % Fract.transfer
% 0.30/0.64  thf(fact_9347_uminus__rat_Otransfer,axiom,
% 0.30/0.64      ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 0.30/0.64      @ ^ [X3: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X3 ) ) @ ( product_snd_int_int @ X3 ) )
% 0.30/0.64      @ uminus_uminus_rat ) ).
% 0.30/0.64  
% 0.30/0.64  % uminus_rat.transfer
% 0.30/0.64  thf(fact_9348_times__rat_Otransfer,axiom,
% 0.30/0.64      ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 0.30/0.64      @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_fst_int_int @ Y3 ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) )
% 0.30/0.64      @ times_times_rat ) ).
% 0.30/0.64  
% 0.30/0.64  % times_rat.transfer
% 0.30/0.64  thf(fact_9349_inverse__rat_Otransfer,axiom,
% 0.30/0.64      ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 0.30/0.64      @ ^ [X3: product_prod_int_int] :
% 0.30/0.64          ( if_Pro3027730157355071871nt_int
% 0.30/0.64          @ ( ( product_fst_int_int @ X3 )
% 0.30/0.64            = zero_zero_int )
% 0.30/0.64          @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.30/0.64          @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) )
% 0.30/0.64      @ inverse_inverse_rat ) ).
% 0.30/0.64  
% 0.30/0.64  % inverse_rat.transfer
% 0.30/0.64  thf(fact_9350_gcd__nat_Opelims,axiom,
% 0.30/0.64      ! [X: nat,Xa: nat,Y: nat] :
% 0.30/0.64        ( ( ( gcd_gcd_nat @ X @ Xa )
% 0.30/0.64          = Y )
% 0.30/0.64       => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 0.30/0.64         => ~ ( ( ( ( Xa = zero_zero_nat )
% 0.30/0.64                 => ( Y = X ) )
% 0.30/0.64                & ( ( Xa != zero_zero_nat )
% 0.30/0.64                 => ( Y
% 0.30/0.64                    = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) ) )
% 0.30/0.64             => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % gcd_nat.pelims
% 0.30/0.64  thf(fact_9351_positive_Otransfer,axiom,
% 0.30/0.64      ( bNF_re1494630372529172596at_o_o @ pcr_rat
% 0.30/0.64      @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 0.30/0.64      @ ^ [X3: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) )
% 0.30/0.64      @ positive ) ).
% 0.30/0.64  
% 0.30/0.64  % positive.transfer
% 0.30/0.64  thf(fact_9352_times__int_Otransfer,axiom,
% 0.30/0.64      ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 0.30/0.64      @ ( produc27273713700761075at_nat
% 0.30/0.64        @ ^ [X3: nat,Y3: nat] :
% 0.30/0.64            ( produc2626176000494625587at_nat
% 0.30/0.64            @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V2 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) ) )
% 0.30/0.64      @ times_times_int ) ).
% 0.30/0.64  
% 0.30/0.64  % times_int.transfer
% 0.30/0.64  thf(fact_9353_zero__int_Otransfer,axiom,
% 0.30/0.64      pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 0.30/0.64  
% 0.30/0.64  % zero_int.transfer
% 0.30/0.64  thf(fact_9354_positive__minus,axiom,
% 0.30/0.64      ! [X: rat] :
% 0.30/0.64        ( ~ ( positive @ X )
% 0.30/0.64       => ( ( X != zero_zero_rat )
% 0.30/0.64         => ( positive @ ( uminus_uminus_rat @ X ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % positive_minus
% 0.30/0.64  thf(fact_9355_int__transfer,axiom,
% 0.30/0.64      ( bNF_re6830278522597306478at_int
% 0.30/0.64      @ ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 )
% 0.30/0.64      @ pcr_int
% 0.30/0.64      @ ^ [N2: nat] : ( product_Pair_nat_nat @ N2 @ zero_zero_nat )
% 0.30/0.64      @ semiri1314217659103216013at_int ) ).
% 0.30/0.64  
% 0.30/0.64  % int_transfer
% 0.30/0.64  thf(fact_9356_uminus__int_Otransfer,axiom,
% 0.30/0.64      ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 0.30/0.64      @ ( produc2626176000494625587at_nat
% 0.30/0.64        @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 ) )
% 0.30/0.64      @ uminus_uminus_int ) ).
% 0.30/0.64  
% 0.30/0.64  % uminus_int.transfer
% 0.30/0.64  thf(fact_9357_nat_Otransfer,axiom,
% 0.30/0.64      ( bNF_re4555766996558763186at_nat @ pcr_int
% 0.30/0.64      @ ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 )
% 0.30/0.64      @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 0.30/0.64      @ nat2 ) ).
% 0.30/0.64  
% 0.30/0.64  % nat.transfer
% 0.30/0.64  thf(fact_9358_one__int_Otransfer,axiom,
% 0.30/0.64      pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 0.30/0.64  
% 0.30/0.64  % one_int.transfer
% 0.30/0.64  thf(fact_9359_less__int_Otransfer,axiom,
% 0.30/0.64      ( bNF_re717283939379294677_int_o @ pcr_int
% 0.30/0.64      @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 0.30/0.64        @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 ) )
% 0.30/0.64      @ ( produc8739625826339149834_nat_o
% 0.30/0.64        @ ^ [X3: nat,Y3: nat] :
% 0.30/0.64            ( produc6081775807080527818_nat_o
% 0.30/0.64            @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) )
% 0.30/0.64      @ ord_less_int ) ).
% 0.30/0.64  
% 0.30/0.64  % less_int.transfer
% 0.30/0.64  thf(fact_9360_less__eq__int_Otransfer,axiom,
% 0.30/0.64      ( bNF_re717283939379294677_int_o @ pcr_int
% 0.30/0.64      @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 0.30/0.64        @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 ) )
% 0.30/0.64      @ ( produc8739625826339149834_nat_o
% 0.30/0.64        @ ^ [X3: nat,Y3: nat] :
% 0.30/0.64            ( produc6081775807080527818_nat_o
% 0.30/0.64            @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) )
% 0.30/0.64      @ ord_less_eq_int ) ).
% 0.30/0.64  
% 0.30/0.64  % less_eq_int.transfer
% 0.30/0.64  thf(fact_9361_plus__int_Otransfer,axiom,
% 0.30/0.64      ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 0.30/0.64      @ ( produc27273713700761075at_nat
% 0.30/0.64        @ ^ [X3: nat,Y3: nat] :
% 0.30/0.64            ( produc2626176000494625587at_nat
% 0.30/0.64            @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V2 ) ) ) )
% 0.30/0.64      @ plus_plus_int ) ).
% 0.30/0.64  
% 0.30/0.64  % plus_int.transfer
% 0.30/0.64  thf(fact_9362_minus__int_Otransfer,axiom,
% 0.30/0.64      ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 0.30/0.64      @ ( produc27273713700761075at_nat
% 0.30/0.64        @ ^ [X3: nat,Y3: nat] :
% 0.30/0.64            ( produc2626176000494625587at_nat
% 0.30/0.64            @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) ) )
% 0.30/0.64      @ minus_minus_int ) ).
% 0.30/0.64  
% 0.30/0.64  % minus_int.transfer
% 0.30/0.64  thf(fact_9363_positive__def,axiom,
% 0.30/0.64      ( positive
% 0.30/0.64      = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 0.30/0.64        @ ^ [X3: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % positive_def
% 0.30/0.64  thf(fact_9364_plus__rat__def,axiom,
% 0.30/0.64      ( plus_plus_rat
% 0.30/0.64      = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 0.30/0.64        @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % plus_rat_def
% 0.30/0.64  thf(fact_9365_inverse__rat__def,axiom,
% 0.30/0.64      ( inverse_inverse_rat
% 0.30/0.64      = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 0.30/0.64        @ ^ [X3: product_prod_int_int] :
% 0.30/0.64            ( if_Pro3027730157355071871nt_int
% 0.30/0.64            @ ( ( product_fst_int_int @ X3 )
% 0.30/0.64              = zero_zero_int )
% 0.30/0.64            @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.30/0.64            @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % inverse_rat_def
% 0.30/0.64  thf(fact_9366_times__rat__def,axiom,
% 0.30/0.64      ( times_times_rat
% 0.30/0.64      = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 0.30/0.64        @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_fst_int_int @ Y3 ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % times_rat_def
% 0.30/0.64  thf(fact_9367_uminus__rat__def,axiom,
% 0.30/0.64      ( uminus_uminus_rat
% 0.30/0.64      = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 0.30/0.64        @ ^ [X3: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X3 ) ) @ ( product_snd_int_int @ X3 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % uminus_rat_def
% 0.30/0.64  thf(fact_9368_one__rat__def,axiom,
% 0.30/0.64      ( one_one_rat
% 0.30/0.64      = ( abs_Rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % one_rat_def
% 0.30/0.64  thf(fact_9369_Fract_Oabs__eq,axiom,
% 0.30/0.64      ( fract
% 0.30/0.64      = ( ^ [Xa4: int,X3: int] : ( abs_Rat @ ( if_Pro3027730157355071871nt_int @ ( X3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ Xa4 @ X3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Fract.abs_eq
% 0.30/0.64  thf(fact_9370_zero__rat__def,axiom,
% 0.30/0.64      ( zero_zero_rat
% 0.30/0.64      = ( abs_Rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % zero_rat_def
% 0.30/0.64  thf(fact_9371_Fract__def,axiom,
% 0.30/0.64      ( fract
% 0.30/0.64      = ( map_fu7831380289885515383nt_rat @ id_int @ ( map_fu3424225382358772769nt_rat @ id_int @ abs_Rat )
% 0.30/0.64        @ ^ [A3: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( B3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A3 @ B3 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Fract_def
% 0.30/0.64  thf(fact_9372_plus__rat_Oabs__eq,axiom,
% 0.30/0.64      ! [Xa: product_prod_int_int,X: product_prod_int_int] :
% 0.30/0.64        ( ( ratrel @ Xa @ Xa )
% 0.30/0.64       => ( ( ratrel @ X @ X )
% 0.30/0.64         => ( ( plus_plus_rat @ ( abs_Rat @ Xa ) @ ( abs_Rat @ X ) )
% 0.30/0.64            = ( abs_Rat @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % plus_rat.abs_eq
% 0.30/0.64  thf(fact_9373_inverse__rat_Oabs__eq,axiom,
% 0.30/0.64      ! [X: product_prod_int_int] :
% 0.30/0.64        ( ( ratrel @ X @ X )
% 0.30/0.64       => ( ( inverse_inverse_rat @ ( abs_Rat @ X ) )
% 0.30/0.64          = ( abs_Rat
% 0.30/0.64            @ ( if_Pro3027730157355071871nt_int
% 0.30/0.64              @ ( ( product_fst_int_int @ X )
% 0.30/0.64                = zero_zero_int )
% 0.30/0.64              @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.30/0.64              @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % inverse_rat.abs_eq
% 0.30/0.64  thf(fact_9374_times__rat_Oabs__eq,axiom,
% 0.30/0.64      ! [Xa: product_prod_int_int,X: product_prod_int_int] :
% 0.30/0.64        ( ( ratrel @ Xa @ Xa )
% 0.30/0.64       => ( ( ratrel @ X @ X )
% 0.30/0.64         => ( ( times_times_rat @ ( abs_Rat @ Xa ) @ ( abs_Rat @ X ) )
% 0.30/0.64            = ( abs_Rat @ ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ Xa ) @ ( product_fst_int_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % times_rat.abs_eq
% 0.30/0.64  thf(fact_9375_one__rat_Orsp,axiom,
% 0.30/0.64      ratrel @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ).
% 0.30/0.64  
% 0.30/0.64  % one_rat.rsp
% 0.30/0.64  thf(fact_9376_zero__rat_Orsp,axiom,
% 0.30/0.64      ratrel @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ).
% 0.30/0.64  
% 0.30/0.64  % zero_rat.rsp
% 0.30/0.64  thf(fact_9377_Fract_Orsp,axiom,
% 0.30/0.64      ( bNF_re157797125943740599nt_int
% 0.30/0.64      @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 0.30/0.64      @ ( bNF_re6250860962936578807nt_int
% 0.30/0.64        @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 0.30/0.64        @ ratrel )
% 0.30/0.64      @ ^ [A3: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( B3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A3 @ B3 ) )
% 0.30/0.64      @ ^ [A3: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( B3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A3 @ B3 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % Fract.rsp
% 0.30/0.64  thf(fact_9378_ratrel__def,axiom,
% 0.30/0.64      ( ratrel
% 0.30/0.64      = ( ^ [X3: product_prod_int_int,Y3: product_prod_int_int] :
% 0.30/0.64            ( ( ( product_snd_int_int @ X3 )
% 0.30/0.64             != zero_zero_int )
% 0.30/0.64            & ( ( product_snd_int_int @ Y3 )
% 0.30/0.64             != zero_zero_int )
% 0.30/0.64            & ( ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) )
% 0.30/0.64              = ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X3 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % ratrel_def
% 0.30/0.64  thf(fact_9379_times__rat_Orsp,axiom,
% 0.30/0.64      ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 0.30/0.64      @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_fst_int_int @ Y3 ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) )
% 0.30/0.64      @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_fst_int_int @ Y3 ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % times_rat.rsp
% 0.30/0.64  thf(fact_9380_uminus__rat_Orsp,axiom,
% 0.30/0.64      ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 0.30/0.64      @ ^ [X3: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X3 ) ) @ ( product_snd_int_int @ X3 ) )
% 0.30/0.64      @ ^ [X3: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X3 ) ) @ ( product_snd_int_int @ X3 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % uminus_rat.rsp
% 0.30/0.64  thf(fact_9381_positive_Orsp,axiom,
% 0.30/0.64      ( bNF_re8699439704749558557nt_o_o @ ratrel
% 0.30/0.64      @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 0.30/0.64      @ ^ [X3: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) )
% 0.30/0.64      @ ^ [X3: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % positive.rsp
% 0.30/0.64  thf(fact_9382_inverse__rat_Orsp,axiom,
% 0.30/0.64      ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 0.30/0.64      @ ^ [X3: product_prod_int_int] :
% 0.30/0.64          ( if_Pro3027730157355071871nt_int
% 0.30/0.64          @ ( ( product_fst_int_int @ X3 )
% 0.30/0.64            = zero_zero_int )
% 0.30/0.64          @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.30/0.64          @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) )
% 0.30/0.64      @ ^ [X3: product_prod_int_int] :
% 0.30/0.64          ( if_Pro3027730157355071871nt_int
% 0.30/0.64          @ ( ( product_fst_int_int @ X3 )
% 0.30/0.64            = zero_zero_int )
% 0.30/0.64          @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 0.30/0.64          @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % inverse_rat.rsp
% 0.30/0.64  thf(fact_9383_plus__rat_Orsp,axiom,
% 0.30/0.64      ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 0.30/0.64      @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) )
% 0.30/0.64      @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % plus_rat.rsp
% 0.30/0.64  thf(fact_9384_uminus__rat_Oabs__eq,axiom,
% 0.30/0.64      ! [X: product_prod_int_int] :
% 0.30/0.64        ( ( ratrel @ X @ X )
% 0.30/0.64       => ( ( uminus_uminus_rat @ ( abs_Rat @ X ) )
% 0.30/0.64          = ( abs_Rat @ ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X ) ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % uminus_rat.abs_eq
% 0.30/0.64  thf(fact_9385_cr__rat__def,axiom,
% 0.30/0.64      ( cr_rat
% 0.30/0.64      = ( ^ [X3: product_prod_int_int,Y3: rat] :
% 0.30/0.64            ( ( ratrel @ X3 @ X3 )
% 0.30/0.64            & ( ( abs_Rat @ X3 )
% 0.30/0.64              = Y3 ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % cr_rat_def
% 0.30/0.64  thf(fact_9386_times__int_Orsp,axiom,
% 0.30/0.64      ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 0.30/0.64      @ ( produc27273713700761075at_nat
% 0.30/0.64        @ ^ [X3: nat,Y3: nat] :
% 0.30/0.64            ( produc2626176000494625587at_nat
% 0.30/0.64            @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V2 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) ) )
% 0.30/0.64      @ ( produc27273713700761075at_nat
% 0.30/0.64        @ ^ [X3: nat,Y3: nat] :
% 0.30/0.64            ( produc2626176000494625587at_nat
% 0.30/0.64            @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V2 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % times_int.rsp
% 0.30/0.64  thf(fact_9387_intrel__iff,axiom,
% 0.30/0.64      ! [X: nat,Y: nat,U: nat,V: nat] :
% 0.30/0.64        ( ( intrel @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ U @ V ) )
% 0.30/0.64        = ( ( plus_plus_nat @ X @ V )
% 0.30/0.64          = ( plus_plus_nat @ U @ Y ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % intrel_iff
% 0.30/0.64  thf(fact_9388_zero__int_Orsp,axiom,
% 0.30/0.64      intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.30/0.64  
% 0.30/0.64  % zero_int.rsp
% 0.30/0.64  thf(fact_9389_uminus__int_Orsp,axiom,
% 0.30/0.64      ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 0.30/0.64      @ ( produc2626176000494625587at_nat
% 0.30/0.64        @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 ) )
% 0.30/0.64      @ ( produc2626176000494625587at_nat
% 0.30/0.64        @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % uminus_int.rsp
% 0.30/0.64  thf(fact_9390_nat_Orsp,axiom,
% 0.30/0.64      ( bNF_re8246922863344978751at_nat @ intrel
% 0.30/0.64      @ ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 )
% 0.30/0.64      @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 0.30/0.64      @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ).
% 0.30/0.64  
% 0.30/0.64  % nat.rsp
% 0.30/0.64  thf(fact_9391_one__int_Orsp,axiom,
% 0.30/0.64      intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.30/0.64  
% 0.30/0.64  % one_int.rsp
% 0.30/0.64  thf(fact_9392_intrel__def,axiom,
% 0.30/0.64      ( intrel
% 0.30/0.64      = ( produc8739625826339149834_nat_o
% 0.30/0.64        @ ^ [X3: nat,Y3: nat] :
% 0.30/0.64            ( produc6081775807080527818_nat_o
% 0.30/0.64            @ ^ [U2: nat,V2: nat] :
% 0.30/0.64                ( ( plus_plus_nat @ X3 @ V2 )
% 0.30/0.64                = ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ).
% 0.30/0.64  
% 0.30/0.64  % intrel_def
% 0.30/0.64  thf(fact_9393_less__int_Orsp,axiom,
% 0.30/0.64      ( bNF_re4202695980764964119_nat_o @ intrel
% 0.30/0.64      @ ( bNF_re3666534408544137501at_o_o @ intrel
% 0.30/0.64        @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 ) )
% 0.30/0.65      @ ( produc8739625826339149834_nat_o
% 0.30/0.65        @ ^ [X3: nat,Y3: nat] :
% 0.30/0.65            ( produc6081775807080527818_nat_o
% 0.30/0.65            @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) )
% 0.30/0.65      @ ( produc8739625826339149834_nat_o
% 0.30/0.65        @ ^ [X3: nat,Y3: nat] :
% 0.30/0.65            ( produc6081775807080527818_nat_o
% 0.30/0.65            @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % less_int.rsp
% 0.30/0.65  thf(fact_9394_less__eq__int_Orsp,axiom,
% 0.30/0.65      ( bNF_re4202695980764964119_nat_o @ intrel
% 0.30/0.65      @ ( bNF_re3666534408544137501at_o_o @ intrel
% 0.30/0.65        @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 ) )
% 0.30/0.65      @ ( produc8739625826339149834_nat_o
% 0.30/0.65        @ ^ [X3: nat,Y3: nat] :
% 0.30/0.65            ( produc6081775807080527818_nat_o
% 0.30/0.65            @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) )
% 0.30/0.65      @ ( produc8739625826339149834_nat_o
% 0.30/0.65        @ ^ [X3: nat,Y3: nat] :
% 0.30/0.65            ( produc6081775807080527818_nat_o
% 0.30/0.65            @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % less_eq_int.rsp
% 0.30/0.65  thf(fact_9395_plus__int_Orsp,axiom,
% 0.30/0.65      ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 0.30/0.65      @ ( produc27273713700761075at_nat
% 0.30/0.65        @ ^ [X3: nat,Y3: nat] :
% 0.30/0.65            ( produc2626176000494625587at_nat
% 0.30/0.65            @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V2 ) ) ) )
% 0.30/0.65      @ ( produc27273713700761075at_nat
% 0.30/0.65        @ ^ [X3: nat,Y3: nat] :
% 0.30/0.65            ( produc2626176000494625587at_nat
% 0.30/0.65            @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V2 ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % plus_int.rsp
% 0.30/0.65  thf(fact_9396_minus__int_Orsp,axiom,
% 0.30/0.65      ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 0.30/0.65      @ ( produc27273713700761075at_nat
% 0.30/0.65        @ ^ [X3: nat,Y3: nat] :
% 0.30/0.65            ( produc2626176000494625587at_nat
% 0.30/0.65            @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) ) )
% 0.30/0.65      @ ( produc27273713700761075at_nat
% 0.30/0.65        @ ^ [X3: nat,Y3: nat] :
% 0.30/0.65            ( produc2626176000494625587at_nat
% 0.30/0.65            @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % minus_int.rsp
% 0.30/0.65  thf(fact_9397_quotient__of__def,axiom,
% 0.30/0.65      ( quotient_of
% 0.30/0.65      = ( ^ [X3: rat] :
% 0.30/0.65            ( the_Pr4378521158711661632nt_int
% 0.30/0.65            @ ^ [Pair: product_prod_int_int] :
% 0.30/0.65                ( ( X3
% 0.30/0.65                  = ( fract @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) )
% 0.30/0.65                & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Pair ) )
% 0.30/0.65                & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % quotient_of_def
% 0.30/0.65  thf(fact_9398_signed__take__bit__eq__concat__bit,axiom,
% 0.30/0.65      ( bit_ri631733984087533419it_int
% 0.30/0.65      = ( ^ [N2: nat,K4: int] : ( bit_concat_bit @ N2 @ K4 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K4 @ N2 ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % signed_take_bit_eq_concat_bit
% 0.30/0.65  thf(fact_9399_normalize__stable,axiom,
% 0.30/0.65      ! [Q4: int,P4: int] :
% 0.30/0.65        ( ( ord_less_int @ zero_zero_int @ Q4 )
% 0.30/0.65       => ( ( algebr932160517623751201me_int @ P4 @ Q4 )
% 0.30/0.65         => ( ( normalize @ ( product_Pair_int_int @ P4 @ Q4 ) )
% 0.30/0.65            = ( product_Pair_int_int @ P4 @ Q4 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % normalize_stable
% 0.30/0.65  thf(fact_9400_quotient__of__coprime,axiom,
% 0.30/0.65      ! [R3: rat,P4: int,Q4: int] :
% 0.30/0.65        ( ( ( quotient_of @ R3 )
% 0.30/0.65          = ( product_Pair_int_int @ P4 @ Q4 ) )
% 0.30/0.65       => ( algebr932160517623751201me_int @ P4 @ Q4 ) ) ).
% 0.30/0.65  
% 0.30/0.65  % quotient_of_coprime
% 0.30/0.65  thf(fact_9401_normalize__coprime,axiom,
% 0.30/0.65      ! [R3: product_prod_int_int,P4: int,Q4: int] :
% 0.30/0.65        ( ( ( normalize @ R3 )
% 0.30/0.65          = ( product_Pair_int_int @ P4 @ Q4 ) )
% 0.30/0.65       => ( algebr932160517623751201me_int @ P4 @ Q4 ) ) ).
% 0.30/0.65  
% 0.30/0.65  % normalize_coprime
% 0.30/0.65  thf(fact_9402_coprime__common__divisor__int,axiom,
% 0.30/0.65      ! [A: int,B: int,X: int] :
% 0.30/0.65        ( ( algebr932160517623751201me_int @ A @ B )
% 0.30/0.65       => ( ( dvd_dvd_int @ X @ A )
% 0.30/0.65         => ( ( dvd_dvd_int @ X @ B )
% 0.30/0.65           => ( ( abs_abs_int @ X )
% 0.30/0.65              = one_one_int ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % coprime_common_divisor_int
% 0.30/0.65  thf(fact_9403_coprime__common__divisor__nat,axiom,
% 0.30/0.65      ! [A: nat,B: nat,X: nat] :
% 0.30/0.65        ( ( algebr934650988132801477me_nat @ A @ B )
% 0.30/0.65       => ( ( dvd_dvd_nat @ X @ A )
% 0.30/0.65         => ( ( dvd_dvd_nat @ X @ B )
% 0.30/0.65           => ( X = one_one_nat ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % coprime_common_divisor_nat
% 0.30/0.65  thf(fact_9404_coprime__diff__one__left__nat,axiom,
% 0.30/0.65      ! [N: nat] :
% 0.30/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.65       => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ N ) ) ).
% 0.30/0.65  
% 0.30/0.65  % coprime_diff_one_left_nat
% 0.30/0.65  thf(fact_9405_coprime__diff__one__right__nat,axiom,
% 0.30/0.65      ! [N: nat] :
% 0.30/0.65        ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.65       => ( algebr934650988132801477me_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % coprime_diff_one_right_nat
% 0.30/0.65  thf(fact_9406_upto__aux__rec,axiom,
% 0.30/0.65      ( upto_aux
% 0.30/0.65      = ( ^ [I3: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I3 ) @ Js @ ( upto_aux @ I3 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % upto_aux_rec
% 0.30/0.65  thf(fact_9407_upto_Opsimps,axiom,
% 0.30/0.65      ! [I: int,J: int] :
% 0.30/0.65        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 0.30/0.65       => ( ( ( ord_less_eq_int @ I @ J )
% 0.30/0.65           => ( ( upto @ I @ J )
% 0.30/0.65              = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 0.30/0.65          & ( ~ ( ord_less_eq_int @ I @ J )
% 0.30/0.65           => ( ( upto @ I @ J )
% 0.30/0.65              = nil_int ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % upto.psimps
% 0.30/0.65  thf(fact_9408_upto_Opelims,axiom,
% 0.30/0.65      ! [X: int,Xa: int,Y: list_int] :
% 0.30/0.65        ( ( ( upto @ X @ Xa )
% 0.30/0.65          = Y )
% 0.30/0.65       => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa ) )
% 0.30/0.65         => ~ ( ( ( ( ord_less_eq_int @ X @ Xa )
% 0.30/0.65                 => ( Y
% 0.30/0.65                    = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa ) ) ) )
% 0.30/0.65                & ( ~ ( ord_less_eq_int @ X @ Xa )
% 0.30/0.65                 => ( Y = nil_int ) ) )
% 0.30/0.65             => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % upto.pelims
% 0.30/0.65  thf(fact_9409_upto__rec__numeral_I4_J,axiom,
% 0.30/0.65      ! [M: num,N: num] :
% 0.30/0.65        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.65         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.65            = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 0.30/0.65        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.65         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.65            = nil_int ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % upto_rec_numeral(4)
% 0.30/0.65  thf(fact_9410_upto__rec__numeral_I3_J,axiom,
% 0.30/0.65      ! [M: num,N: num] :
% 0.30/0.65        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.30/0.65         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.30/0.65            = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 0.30/0.65        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.30/0.65         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 0.30/0.65            = nil_int ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % upto_rec_numeral(3)
% 0.30/0.65  thf(fact_9411_length__upto,axiom,
% 0.30/0.65      ! [I: int,J: int] :
% 0.30/0.65        ( ( size_size_list_int @ ( upto @ I @ J ) )
% 0.30/0.65        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % length_upto
% 0.30/0.65  thf(fact_9412_upto__rec__numeral_I1_J,axiom,
% 0.30/0.65      ! [M: num,N: num] :
% 0.30/0.65        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.30/0.65         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.30/0.65            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 0.30/0.65        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.30/0.65         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 0.30/0.65            = nil_int ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % upto_rec_numeral(1)
% 0.30/0.65  thf(fact_9413_upto__rec__numeral_I2_J,axiom,
% 0.30/0.65      ! [M: num,N: num] :
% 0.30/0.65        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.65         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.65            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 0.30/0.65        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.65         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.30/0.65            = nil_int ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % upto_rec_numeral(2)
% 0.30/0.65  thf(fact_9414_atLeastLessThan__upto,axiom,
% 0.30/0.65      ( set_or4662586982721622107an_int
% 0.30/0.65      = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ I3 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % atLeastLessThan_upto
% 0.30/0.65  thf(fact_9415_upto_Oelims,axiom,
% 0.30/0.65      ! [X: int,Xa: int,Y: list_int] :
% 0.30/0.65        ( ( ( upto @ X @ Xa )
% 0.30/0.65          = Y )
% 0.30/0.65       => ( ( ( ord_less_eq_int @ X @ Xa )
% 0.30/0.65           => ( Y
% 0.30/0.65              = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa ) ) ) )
% 0.30/0.65          & ( ~ ( ord_less_eq_int @ X @ Xa )
% 0.30/0.65           => ( Y = nil_int ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % upto.elims
% 0.30/0.65  thf(fact_9416_upto_Osimps,axiom,
% 0.30/0.65      ( upto
% 0.30/0.65      = ( ^ [I3: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I3 @ J3 ) @ ( cons_int @ I3 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % upto.simps
% 0.30/0.65  thf(fact_9417_upto__rec1,axiom,
% 0.30/0.65      ! [I: int,J: int] :
% 0.30/0.65        ( ( ord_less_eq_int @ I @ J )
% 0.30/0.65       => ( ( upto @ I @ J )
% 0.30/0.65          = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % upto_rec1
% 0.30/0.65  thf(fact_9418_greaterThanLessThan__upto,axiom,
% 0.30/0.65      ( set_or5832277885323065728an_int
% 0.30/0.65      = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % greaterThanLessThan_upto
% 0.30/0.65  thf(fact_9419_upto__split2,axiom,
% 0.30/0.65      ! [I: int,J: int,K: int] :
% 0.30/0.65        ( ( ord_less_eq_int @ I @ J )
% 0.30/0.65       => ( ( ord_less_eq_int @ J @ K )
% 0.30/0.65         => ( ( upto @ I @ K )
% 0.30/0.65            = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % upto_split2
% 0.30/0.65  thf(fact_9420_upto__split1,axiom,
% 0.30/0.65      ! [I: int,J: int,K: int] :
% 0.30/0.65        ( ( ord_less_eq_int @ I @ J )
% 0.30/0.65       => ( ( ord_less_eq_int @ J @ K )
% 0.30/0.65         => ( ( upto @ I @ K )
% 0.30/0.65            = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % upto_split1
% 0.30/0.65  thf(fact_9421_upto__split3,axiom,
% 0.30/0.65      ! [I: int,J: int,K: int] :
% 0.30/0.65        ( ( ord_less_eq_int @ I @ J )
% 0.30/0.65       => ( ( ord_less_eq_int @ J @ K )
% 0.30/0.65         => ( ( upto @ I @ K )
% 0.30/0.65            = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % upto_split3
% 0.30/0.65  thf(fact_9422_upto__rec2,axiom,
% 0.30/0.65      ! [I: int,J: int] :
% 0.30/0.65        ( ( ord_less_eq_int @ I @ J )
% 0.30/0.65       => ( ( upto @ I @ J )
% 0.30/0.65          = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % upto_rec2
% 0.30/0.65  thf(fact_9423_sort__upto,axiom,
% 0.30/0.65      ! [I: int,J: int] :
% 0.30/0.65        ( ( linord1735203802627413978nt_int
% 0.30/0.65          @ ^ [X3: int] : X3
% 0.30/0.65          @ ( upto @ I @ J ) )
% 0.30/0.65        = ( upto @ I @ J ) ) ).
% 0.30/0.65  
% 0.30/0.65  % sort_upto
% 0.30/0.65  thf(fact_9424_sort__upt,axiom,
% 0.30/0.65      ! [M: nat,N: nat] :
% 0.30/0.65        ( ( linord738340561235409698at_nat
% 0.30/0.65          @ ^ [X3: nat] : X3
% 0.30/0.65          @ ( upt @ M @ N ) )
% 0.30/0.65        = ( upt @ M @ N ) ) ).
% 0.30/0.65  
% 0.30/0.65  % sort_upt
% 0.30/0.65  thf(fact_9425_map__add__upt_H,axiom,
% 0.30/0.65      ! [Ofs: nat,A: nat,B: nat] :
% 0.30/0.65        ( ( map_nat_nat
% 0.30/0.65          @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ Ofs )
% 0.30/0.65          @ ( upt @ A @ B ) )
% 0.30/0.65        = ( upt @ ( plus_plus_nat @ A @ Ofs ) @ ( plus_plus_nat @ B @ Ofs ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % map_add_upt'
% 0.30/0.65  thf(fact_9426_map__add__upt,axiom,
% 0.30/0.65      ! [N: nat,M: nat] :
% 0.30/0.65        ( ( map_nat_nat
% 0.30/0.65          @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ N )
% 0.30/0.65          @ ( upt @ zero_zero_nat @ M ) )
% 0.30/0.65        = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % map_add_upt
% 0.30/0.65  thf(fact_9427_upt__eq__Cons__conv,axiom,
% 0.30/0.65      ! [I: nat,J: nat,X: nat,Xs: list_nat] :
% 0.30/0.65        ( ( ( upt @ I @ J )
% 0.30/0.65          = ( cons_nat @ X @ Xs ) )
% 0.30/0.65        = ( ( ord_less_nat @ I @ J )
% 0.30/0.65          & ( I = X )
% 0.30/0.65          & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 0.30/0.65            = Xs ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % upt_eq_Cons_conv
% 0.30/0.65  thf(fact_9428_upt__filter__extend,axiom,
% 0.30/0.65      ! [U: nat,U3: nat,P: nat > $o] :
% 0.30/0.65        ( ( ord_less_eq_nat @ U @ U3 )
% 0.30/0.65       => ( ! [I2: nat] :
% 0.30/0.65              ( ( ( ord_less_eq_nat @ U @ I2 )
% 0.30/0.65                & ( ord_less_nat @ I2 @ U3 ) )
% 0.30/0.65             => ~ ( P @ I2 ) )
% 0.30/0.65         => ( ( filter_nat2 @ P @ ( upt @ zero_zero_nat @ U ) )
% 0.30/0.65            = ( filter_nat2 @ P @ ( upt @ zero_zero_nat @ U3 ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % upt_filter_extend
% 0.30/0.65  thf(fact_9429_map__decr__upt,axiom,
% 0.30/0.65      ! [M: nat,N: nat] :
% 0.30/0.65        ( ( map_nat_nat
% 0.30/0.65          @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 0.30/0.65          @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 0.30/0.65        = ( upt @ M @ N ) ) ).
% 0.30/0.65  
% 0.30/0.65  % map_decr_upt
% 0.30/0.65  thf(fact_9430_sum__list__upt,axiom,
% 0.30/0.65      ! [M: nat,N: nat] :
% 0.30/0.65        ( ( ord_less_eq_nat @ M @ N )
% 0.30/0.65       => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 0.30/0.65          = ( groups3542108847815614940at_nat
% 0.30/0.65            @ ^ [X3: nat] : X3
% 0.30/0.65            @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % sum_list_upt
% 0.30/0.65  thf(fact_9431_card__length__sum__list__rec,axiom,
% 0.30/0.65      ! [M: nat,N4: nat] :
% 0.30/0.65        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 0.30/0.65       => ( ( finite_card_list_nat
% 0.30/0.65            @ ( collect_list_nat
% 0.30/0.65              @ ^ [L2: list_nat] :
% 0.30/0.65                  ( ( ( size_size_list_nat @ L2 )
% 0.30/0.65                    = M )
% 0.30/0.65                  & ( ( groups4561878855575611511st_nat @ L2 )
% 0.30/0.65                    = N4 ) ) ) )
% 0.30/0.65          = ( plus_plus_nat
% 0.30/0.65            @ ( finite_card_list_nat
% 0.30/0.65              @ ( collect_list_nat
% 0.30/0.65                @ ^ [L2: list_nat] :
% 0.30/0.65                    ( ( ( size_size_list_nat @ L2 )
% 0.30/0.65                      = ( minus_minus_nat @ M @ one_one_nat ) )
% 0.30/0.65                    & ( ( groups4561878855575611511st_nat @ L2 )
% 0.30/0.65                      = N4 ) ) ) )
% 0.30/0.65            @ ( finite_card_list_nat
% 0.30/0.65              @ ( collect_list_nat
% 0.30/0.65                @ ^ [L2: list_nat] :
% 0.30/0.65                    ( ( ( size_size_list_nat @ L2 )
% 0.30/0.65                      = M )
% 0.30/0.65                    & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 0.30/0.65                      = N4 ) ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % card_length_sum_list_rec
% 0.30/0.65  thf(fact_9432_card__length__sum__list,axiom,
% 0.30/0.65      ! [M: nat,N4: nat] :
% 0.30/0.65        ( ( finite_card_list_nat
% 0.30/0.65          @ ( collect_list_nat
% 0.30/0.65            @ ^ [L2: list_nat] :
% 0.30/0.65                ( ( ( size_size_list_nat @ L2 )
% 0.30/0.65                  = M )
% 0.30/0.65                & ( ( groups4561878855575611511st_nat @ L2 )
% 0.30/0.65                  = N4 ) ) ) )
% 0.30/0.65        = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N4 @ M ) @ one_one_nat ) @ N4 ) ) ).
% 0.30/0.65  
% 0.30/0.65  % card_length_sum_list
% 0.30/0.65  thf(fact_9433_inj__on__diff__nat,axiom,
% 0.30/0.65      ! [N4: set_nat,K: nat] :
% 0.30/0.65        ( ! [N3: nat] :
% 0.30/0.65            ( ( member_nat @ N3 @ N4 )
% 0.30/0.65           => ( ord_less_eq_nat @ K @ N3 ) )
% 0.30/0.65       => ( inj_on_nat_nat
% 0.30/0.65          @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ K )
% 0.30/0.65          @ N4 ) ) ).
% 0.30/0.65  
% 0.30/0.65  % inj_on_diff_nat
% 0.30/0.65  thf(fact_9434_rat__denum,axiom,
% 0.30/0.65      ? [F3: nat > rat] :
% 0.30/0.65        ( ( image_nat_rat @ F3 @ top_top_set_nat )
% 0.30/0.65        = top_top_set_rat ) ).
% 0.30/0.65  
% 0.30/0.65  % rat_denum
% 0.30/0.65  thf(fact_9435_surj__nat__to__rat__surj,axiom,
% 0.30/0.65      ( ( image_nat_rat @ nat_to_rat_surj @ top_top_set_nat )
% 0.30/0.65      = top_top_set_rat ) ).
% 0.30/0.65  
% 0.30/0.65  % surj_nat_to_rat_surj
% 0.30/0.65  thf(fact_9436_last__upt,axiom,
% 0.30/0.65      ! [I: nat,J: nat] :
% 0.30/0.65        ( ( ord_less_nat @ I @ J )
% 0.30/0.65       => ( ( last_nat @ ( upt @ I @ J ) )
% 0.30/0.65          = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % last_upt
% 0.30/0.65  thf(fact_9437_Sup__int__def,axiom,
% 0.30/0.65      ( complete_Sup_Sup_int
% 0.30/0.65      = ( ^ [X4: set_int] :
% 0.30/0.65            ( the_int
% 0.30/0.65            @ ^ [X3: int] :
% 0.30/0.65                ( ( member_int @ X3 @ X4 )
% 0.30/0.65                & ! [Y3: int] :
% 0.30/0.65                    ( ( member_int @ Y3 @ X4 )
% 0.30/0.65                   => ( ord_less_eq_int @ Y3 @ X3 ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Sup_int_def
% 0.30/0.65  thf(fact_9438_Rats__eq__range__nat__to__rat__surj,axiom,
% 0.30/0.65      ( field_6020823756834552118ts_rat
% 0.30/0.65      = ( image_nat_rat @ nat_to_rat_surj @ top_top_set_nat ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Rats_eq_range_nat_to_rat_surj
% 0.30/0.65  thf(fact_9439_nat__to__rat__surj__def,axiom,
% 0.30/0.65      ( nat_to_rat_surj
% 0.30/0.65      = ( ^ [N2: nat] :
% 0.30/0.65            ( produc6207742614233964070at_rat
% 0.30/0.65            @ ^ [A3: nat,B3: nat] : ( fract @ ( nat_int_decode @ A3 ) @ ( nat_int_decode @ B3 ) )
% 0.30/0.65            @ ( nat_prod_decode @ N2 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % nat_to_rat_surj_def
% 0.30/0.65  thf(fact_9440_surj__prod__decode,axiom,
% 0.30/0.65      ( ( image_5846123807819985514at_nat @ nat_prod_decode @ top_top_set_nat )
% 0.30/0.65      = top_to4669805908274784177at_nat ) ).
% 0.30/0.65  
% 0.30/0.65  % surj_prod_decode
% 0.30/0.65  thf(fact_9441_list__decode_Oelims,axiom,
% 0.30/0.65      ! [X: nat,Y: list_nat] :
% 0.30/0.65        ( ( ( nat_list_decode @ X )
% 0.30/0.65          = Y )
% 0.30/0.65       => ( ( ( X = zero_zero_nat )
% 0.30/0.65           => ( Y != nil_nat ) )
% 0.30/0.65         => ~ ! [N3: nat] :
% 0.30/0.65                ( ( X
% 0.30/0.65                  = ( suc @ N3 ) )
% 0.30/0.65               => ( Y
% 0.30/0.65                 != ( produc2761476792215241774st_nat
% 0.30/0.65                    @ ^ [X3: nat,Y3: nat] : ( cons_nat @ X3 @ ( nat_list_decode @ Y3 ) )
% 0.30/0.65                    @ ( nat_prod_decode @ N3 ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % list_decode.elims
% 0.30/0.65  thf(fact_9442_surj__list__decode,axiom,
% 0.30/0.65      ( ( image_nat_list_nat @ nat_list_decode @ top_top_set_nat )
% 0.30/0.65      = top_top_set_list_nat ) ).
% 0.30/0.65  
% 0.30/0.65  % surj_list_decode
% 0.30/0.65  thf(fact_9443_list__decode_Osimps_I2_J,axiom,
% 0.30/0.65      ! [N: nat] :
% 0.30/0.65        ( ( nat_list_decode @ ( suc @ N ) )
% 0.30/0.65        = ( produc2761476792215241774st_nat
% 0.30/0.65          @ ^ [X3: nat,Y3: nat] : ( cons_nat @ X3 @ ( nat_list_decode @ Y3 ) )
% 0.30/0.65          @ ( nat_prod_decode @ N ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % list_decode.simps(2)
% 0.30/0.65  thf(fact_9444_list__decode_Opelims,axiom,
% 0.30/0.65      ! [X: nat,Y: list_nat] :
% 0.30/0.65        ( ( ( nat_list_decode @ X )
% 0.30/0.65          = Y )
% 0.30/0.65       => ( ( accp_nat @ nat_list_decode_rel @ X )
% 0.30/0.65         => ( ( ( X = zero_zero_nat )
% 0.30/0.65             => ( ( Y = nil_nat )
% 0.30/0.65               => ~ ( accp_nat @ nat_list_decode_rel @ zero_zero_nat ) ) )
% 0.30/0.65           => ~ ! [N3: nat] :
% 0.30/0.65                  ( ( X
% 0.30/0.65                    = ( suc @ N3 ) )
% 0.30/0.65                 => ( ( Y
% 0.30/0.65                      = ( produc2761476792215241774st_nat
% 0.30/0.65                        @ ^ [X3: nat,Y3: nat] : ( cons_nat @ X3 @ ( nat_list_decode @ Y3 ) )
% 0.30/0.65                        @ ( nat_prod_decode @ N3 ) ) )
% 0.30/0.65                   => ~ ( accp_nat @ nat_list_decode_rel @ ( suc @ N3 ) ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % list_decode.pelims
% 0.30/0.65  thf(fact_9445_list__decode_Opinduct,axiom,
% 0.30/0.65      ! [A0: nat,P: nat > $o] :
% 0.30/0.65        ( ( accp_nat @ nat_list_decode_rel @ A0 )
% 0.30/0.65       => ( ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 0.30/0.65           => ( P @ zero_zero_nat ) )
% 0.30/0.65         => ( ! [N3: nat] :
% 0.30/0.65                ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N3 ) )
% 0.30/0.65               => ( ! [X5: nat,Y5: nat] :
% 0.30/0.65                      ( ( ( product_Pair_nat_nat @ X5 @ Y5 )
% 0.30/0.65                        = ( nat_prod_decode @ N3 ) )
% 0.30/0.65                     => ( P @ Y5 ) )
% 0.30/0.65                 => ( P @ ( suc @ N3 ) ) ) )
% 0.30/0.65           => ( P @ A0 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % list_decode.pinduct
% 0.30/0.65  thf(fact_9446_list__decode_Opsimps_I2_J,axiom,
% 0.30/0.65      ! [N: nat] :
% 0.30/0.65        ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N ) )
% 0.30/0.65       => ( ( nat_list_decode @ ( suc @ N ) )
% 0.30/0.65          = ( produc2761476792215241774st_nat
% 0.30/0.65            @ ^ [X3: nat,Y3: nat] : ( cons_nat @ X3 @ ( nat_list_decode @ Y3 ) )
% 0.30/0.65            @ ( nat_prod_decode @ N ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % list_decode.psimps(2)
% 0.30/0.65  thf(fact_9447_bij__int__decode,axiom,
% 0.30/0.65      bij_betw_nat_int @ nat_int_decode @ top_top_set_nat @ top_top_set_int ).
% 0.30/0.65  
% 0.30/0.65  % bij_int_decode
% 0.30/0.65  thf(fact_9448_bij__enumerate,axiom,
% 0.30/0.65      ! [S: set_nat] :
% 0.30/0.65        ( ~ ( finite_finite_nat @ S )
% 0.30/0.65       => ( bij_betw_nat_nat @ ( infini8530281810654367211te_nat @ S ) @ top_top_set_nat @ S ) ) ).
% 0.30/0.65  
% 0.30/0.65  % bij_enumerate
% 0.30/0.65  thf(fact_9449_bij__int__encode,axiom,
% 0.30/0.65      bij_betw_int_nat @ nat_int_encode @ top_top_set_int @ top_top_set_nat ).
% 0.30/0.65  
% 0.30/0.65  % bij_int_encode
% 0.30/0.65  thf(fact_9450_bij__prod__decode,axiom,
% 0.30/0.65      bij_be8693218025023041337at_nat @ nat_prod_decode @ top_top_set_nat @ top_to4669805908274784177at_nat ).
% 0.30/0.65  
% 0.30/0.65  % bij_prod_decode
% 0.30/0.65  thf(fact_9451_bij__list__decode,axiom,
% 0.30/0.65      bij_be6293887246118711976st_nat @ nat_list_decode @ top_top_set_nat @ top_top_set_list_nat ).
% 0.30/0.65  
% 0.30/0.65  % bij_list_decode
% 0.30/0.65  thf(fact_9452_Rep__unit,axiom,
% 0.30/0.65      ! [X: product_unit] : ( member_o @ ( product_Rep_unit @ X ) @ ( insert_o @ $true @ bot_bot_set_o ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Rep_unit
% 0.30/0.65  thf(fact_9453_Rep__unit__induct,axiom,
% 0.30/0.65      ! [Y: $o,P: $o > $o] :
% 0.30/0.65        ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 0.30/0.65       => ( ! [X2: product_unit] : ( P @ ( product_Rep_unit @ X2 ) )
% 0.30/0.65         => ( P @ Y ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Rep_unit_induct
% 0.30/0.65  thf(fact_9454_Rep__unit__cases,axiom,
% 0.30/0.65      ! [Y: $o] :
% 0.30/0.65        ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 0.30/0.65       => ~ ! [X2: product_unit] :
% 0.30/0.65              ( Y
% 0.30/0.65              = ( ~ ( product_Rep_unit @ X2 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Rep_unit_cases
% 0.30/0.65  thf(fact_9455_type__definition__unit,axiom,
% 0.30/0.65      type_d6188575255521822967unit_o @ product_Rep_unit @ product_Abs_unit @ ( insert_o @ $true @ bot_bot_set_o ) ).
% 0.30/0.65  
% 0.30/0.65  % type_definition_unit
% 0.30/0.65  thf(fact_9456_Abs__unit__inverse,axiom,
% 0.30/0.65      ! [Y: $o] :
% 0.30/0.65        ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 0.30/0.65       => ( ( product_Rep_unit @ ( product_Abs_unit @ Y ) )
% 0.30/0.65          = Y ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Abs_unit_inverse
% 0.30/0.65  thf(fact_9457_Abs__unit__inject,axiom,
% 0.30/0.65      ! [X: $o,Y: $o] :
% 0.30/0.65        ( ( member_o @ X @ ( insert_o @ $true @ bot_bot_set_o ) )
% 0.30/0.65       => ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 0.30/0.65         => ( ( ( product_Abs_unit @ X )
% 0.30/0.65              = ( product_Abs_unit @ Y ) )
% 0.30/0.65            = ( X = Y ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Abs_unit_inject
% 0.30/0.65  thf(fact_9458_Abs__unit__cases,axiom,
% 0.30/0.65      ! [X: product_unit] :
% 0.30/0.65        ~ ! [Y2: $o] :
% 0.30/0.65            ( ( X
% 0.30/0.65              = ( product_Abs_unit @ Y2 ) )
% 0.30/0.65           => ~ ( member_o @ Y2 @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Abs_unit_cases
% 0.30/0.65  thf(fact_9459_Abs__unit__induct,axiom,
% 0.30/0.65      ! [P: product_unit > $o,X: product_unit] :
% 0.30/0.65        ( ! [Y2: $o] :
% 0.30/0.65            ( ( member_o @ Y2 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 0.30/0.65           => ( P @ ( product_Abs_unit @ Y2 ) ) )
% 0.30/0.65       => ( P @ X ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Abs_unit_induct
% 0.30/0.65  thf(fact_9460_natLeq__on__wo__rel,axiom,
% 0.30/0.65      ! [N: nat] :
% 0.30/0.65        ( bNF_We3818239936649020644el_nat
% 0.30/0.65        @ ( collec3392354462482085612at_nat
% 0.30/0.65          @ ( produc6081775807080527818_nat_o
% 0.30/0.65            @ ^ [X3: nat,Y3: nat] :
% 0.30/0.65                ( ( ord_less_nat @ X3 @ N )
% 0.30/0.65                & ( ord_less_nat @ Y3 @ N )
% 0.30/0.65                & ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % natLeq_on_wo_rel
% 0.30/0.65  thf(fact_9461_pair__lessI2,axiom,
% 0.30/0.65      ! [A: nat,B: nat,S3: nat,T3: nat] :
% 0.30/0.65        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.65       => ( ( ord_less_nat @ S3 @ T3 )
% 0.30/0.65         => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S3 ) @ ( product_Pair_nat_nat @ B @ T3 ) ) @ fun_pair_less ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % pair_lessI2
% 0.30/0.65  thf(fact_9462_pair__less__iff1,axiom,
% 0.30/0.65      ! [X: nat,Y: nat,Z: nat] :
% 0.30/0.65        ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ X @ Z ) ) @ fun_pair_less )
% 0.30/0.65        = ( ord_less_nat @ Y @ Z ) ) ).
% 0.30/0.65  
% 0.30/0.65  % pair_less_iff1
% 0.30/0.65  thf(fact_9463_butlast__upt,axiom,
% 0.30/0.65      ! [M: nat,N: nat] :
% 0.30/0.65        ( ( butlast_nat @ ( upt @ M @ N ) )
% 0.30/0.65        = ( upt @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % butlast_upt
% 0.30/0.65  thf(fact_9464_pair__lessI1,axiom,
% 0.30/0.65      ! [A: nat,B: nat,S3: nat,T3: nat] :
% 0.30/0.65        ( ( ord_less_nat @ A @ B )
% 0.30/0.65       => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S3 ) @ ( product_Pair_nat_nat @ B @ T3 ) ) @ fun_pair_less ) ) ).
% 0.30/0.65  
% 0.30/0.65  % pair_lessI1
% 0.30/0.65  thf(fact_9465_smin__insertI,axiom,
% 0.30/0.65      ! [X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 0.30/0.65        ( ( member8440522571783428010at_nat @ X @ XS )
% 0.30/0.65       => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_less )
% 0.30/0.65         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_strict )
% 0.30/0.65           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y @ YS ) ) @ fun_min_strict ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % smin_insertI
% 0.30/0.65  thf(fact_9466_smin__emptyI,axiom,
% 0.30/0.65      ! [X7: set_Pr1261947904930325089at_nat] :
% 0.30/0.65        ( ( X7 != bot_bo2099793752762293965at_nat )
% 0.30/0.65       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X7 @ bot_bo2099793752762293965at_nat ) @ fun_min_strict ) ) ).
% 0.30/0.65  
% 0.30/0.65  % smin_emptyI
% 0.30/0.65  thf(fact_9467_smax__insertI,axiom,
% 0.30/0.65      ! [Y: product_prod_nat_nat,Y6: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,X7: set_Pr1261947904930325089at_nat] :
% 0.30/0.65        ( ( member8440522571783428010at_nat @ Y @ Y6 )
% 0.30/0.65       => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_less )
% 0.30/0.65         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X7 @ Y6 ) @ fun_max_strict )
% 0.30/0.65           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X @ X7 ) @ Y6 ) @ fun_max_strict ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % smax_insertI
% 0.30/0.65  thf(fact_9468_pair__leqI2,axiom,
% 0.30/0.65      ! [A: nat,B: nat,S3: nat,T3: nat] :
% 0.30/0.65        ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.65       => ( ( ord_less_eq_nat @ S3 @ T3 )
% 0.30/0.65         => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S3 ) @ ( product_Pair_nat_nat @ B @ T3 ) ) @ fun_pair_leq ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % pair_leqI2
% 0.30/0.65  thf(fact_9469_eventually__sequentially__Suc,axiom,
% 0.30/0.65      ! [P: nat > $o] :
% 0.30/0.65        ( ( eventually_nat
% 0.30/0.65          @ ^ [I3: nat] : ( P @ ( suc @ I3 ) )
% 0.30/0.65          @ at_top_nat )
% 0.30/0.65        = ( eventually_nat @ P @ at_top_nat ) ) ).
% 0.30/0.65  
% 0.30/0.65  % eventually_sequentially_Suc
% 0.30/0.65  thf(fact_9470_eventually__sequentially__seg,axiom,
% 0.30/0.65      ! [P: nat > $o,K: nat] :
% 0.30/0.65        ( ( eventually_nat
% 0.30/0.65          @ ^ [N2: nat] : ( P @ ( plus_plus_nat @ N2 @ K ) )
% 0.30/0.65          @ at_top_nat )
% 0.30/0.65        = ( eventually_nat @ P @ at_top_nat ) ) ).
% 0.30/0.65  
% 0.30/0.65  % eventually_sequentially_seg
% 0.30/0.65  thf(fact_9471_le__sequentially,axiom,
% 0.30/0.65      ! [F4: filter_nat] :
% 0.30/0.65        ( ( ord_le2510731241096832064er_nat @ F4 @ at_top_nat )
% 0.30/0.65        = ( ! [N6: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N6 ) @ F4 ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % le_sequentially
% 0.30/0.65  thf(fact_9472_pair__leq__def,axiom,
% 0.30/0.65      ( fun_pair_leq
% 0.30/0.65      = ( sup_su718114333110466843at_nat @ fun_pair_less @ id_Pro2258643101195443293at_nat ) ) ).
% 0.30/0.65  
% 0.30/0.65  % pair_leq_def
% 0.30/0.65  thf(fact_9473_smax__emptyI,axiom,
% 0.30/0.65      ! [Y6: set_Pr1261947904930325089at_nat] :
% 0.30/0.65        ( ( finite6177210948735845034at_nat @ Y6 )
% 0.30/0.65       => ( ( Y6 != bot_bo2099793752762293965at_nat )
% 0.30/0.65         => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ Y6 ) @ fun_max_strict ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % smax_emptyI
% 0.30/0.65  thf(fact_9474_filterlim__atMost__at__top,axiom,
% 0.30/0.65      filter3212408913953519116et_nat @ set_ord_atMost_nat @ ( finite3254316476582989077op_nat @ top_top_set_nat ) @ at_top_nat ).
% 0.30/0.65  
% 0.30/0.65  % filterlim_atMost_at_top
% 0.30/0.65  thf(fact_9475_filterlim__lessThan__at__top,axiom,
% 0.30/0.65      filter3212408913953519116et_nat @ set_ord_lessThan_nat @ ( finite3254316476582989077op_nat @ top_top_set_nat ) @ at_top_nat ).
% 0.30/0.65  
% 0.30/0.65  % filterlim_lessThan_at_top
% 0.30/0.65  thf(fact_9476_pair__leqI1,axiom,
% 0.30/0.65      ! [A: nat,B: nat,S3: nat,T3: nat] :
% 0.30/0.65        ( ( ord_less_nat @ A @ B )
% 0.30/0.65       => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S3 ) @ ( product_Pair_nat_nat @ B @ T3 ) ) @ fun_pair_leq ) ) ).
% 0.30/0.65  
% 0.30/0.65  % pair_leqI1
% 0.30/0.65  thf(fact_9477_wmin__insertI,axiom,
% 0.30/0.65      ! [X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 0.30/0.65        ( ( member8440522571783428010at_nat @ X @ XS )
% 0.30/0.65       => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 0.30/0.65         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_weak )
% 0.30/0.65           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y @ YS ) ) @ fun_min_weak ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % wmin_insertI
% 0.30/0.65  thf(fact_9478_wmax__insertI,axiom,
% 0.30/0.65      ! [Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat] :
% 0.30/0.65        ( ( member8440522571783428010at_nat @ Y @ YS )
% 0.30/0.65       => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 0.30/0.65         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_max_weak )
% 0.30/0.65           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X @ XS ) @ YS ) @ fun_max_weak ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % wmax_insertI
% 0.30/0.65  thf(fact_9479_max__weak__def,axiom,
% 0.30/0.65      ( fun_max_weak
% 0.30/0.65      = ( sup_su5525570899277871387at_nat @ ( max_ex8135407076693332796at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % max_weak_def
% 0.30/0.65  thf(fact_9480_trivial__limit__sequentially,axiom,
% 0.30/0.65      at_top_nat != bot_bot_filter_nat ).
% 0.30/0.65  
% 0.30/0.65  % trivial_limit_sequentially
% 0.30/0.65  thf(fact_9481_eventually__False__sequentially,axiom,
% 0.30/0.65      ~ ( eventually_nat
% 0.30/0.65        @ ^ [N2: nat] : $false
% 0.30/0.65        @ at_top_nat ) ).
% 0.30/0.65  
% 0.30/0.65  % eventually_False_sequentially
% 0.30/0.65  thf(fact_9482_max__rpair__set,axiom,
% 0.30/0.65      fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_max_strict @ fun_max_weak ) ).
% 0.30/0.65  
% 0.30/0.65  % max_rpair_set
% 0.30/0.65  thf(fact_9483_min__rpair__set,axiom,
% 0.30/0.65      fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_min_strict @ fun_min_weak ) ).
% 0.30/0.65  
% 0.30/0.65  % min_rpair_set
% 0.30/0.65  thf(fact_9484_wmax__emptyI,axiom,
% 0.30/0.65      ! [X7: set_Pr1261947904930325089at_nat] :
% 0.30/0.65        ( ( finite6177210948735845034at_nat @ X7 )
% 0.30/0.65       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ X7 ) @ fun_max_weak ) ) ).
% 0.30/0.65  
% 0.30/0.65  % wmax_emptyI
% 0.30/0.65  thf(fact_9485_wmin__emptyI,axiom,
% 0.30/0.65      ! [X7: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X7 @ bot_bo2099793752762293965at_nat ) @ fun_min_weak ) ).
% 0.30/0.65  
% 0.30/0.65  % wmin_emptyI
% 0.30/0.65  thf(fact_9486_min__weak__def,axiom,
% 0.30/0.65      ( fun_min_weak
% 0.30/0.65      = ( sup_su5525570899277871387at_nat @ ( min_ex6901939911449802026at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % min_weak_def
% 0.30/0.65  thf(fact_9487_atLeast__0,axiom,
% 0.30/0.65      ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 0.30/0.65      = top_top_set_nat ) ).
% 0.30/0.65  
% 0.30/0.65  % atLeast_0
% 0.30/0.65  thf(fact_9488_atLeast__Suc,axiom,
% 0.30/0.65      ! [K: nat] :
% 0.30/0.65        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 0.30/0.65        = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % atLeast_Suc
% 0.30/0.65  thf(fact_9489_UN__atLeast__UNIV,axiom,
% 0.30/0.65      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 0.30/0.65      = top_top_set_nat ) ).
% 0.30/0.65  
% 0.30/0.65  % UN_atLeast_UNIV
% 0.30/0.65  thf(fact_9490_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 0.30/0.65      ! [L: int,U: int] :
% 0.30/0.65        ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 0.30/0.65        = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 0.30/0.65  
% 0.30/0.65  % atLeastPlusOneAtMost_greaterThanAtMost_int
% 0.30/0.65  thf(fact_9491_atLeastPlusOneAtMost__greaterThanAtMost__integer,axiom,
% 0.30/0.65      ! [L: code_integer,U: code_integer] :
% 0.30/0.65        ( ( set_or189985376899183464nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 0.30/0.65        = ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 0.30/0.65  
% 0.30/0.65  % atLeastPlusOneAtMost_greaterThanAtMost_integer
% 0.30/0.65  thf(fact_9492_greaterThanAtMost__upto,axiom,
% 0.30/0.65      ( set_or6656581121297822940st_int
% 0.30/0.65      = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % greaterThanAtMost_upto
% 0.30/0.65  thf(fact_9493_abs__division__segment,axiom,
% 0.30/0.65      ! [K: int] :
% 0.30/0.65        ( ( abs_abs_int @ ( euclid3395696857347342551nt_int @ K ) )
% 0.30/0.65        = one_one_int ) ).
% 0.30/0.65  
% 0.30/0.65  % abs_division_segment
% 0.30/0.65  thf(fact_9494_division__segment__nat__def,axiom,
% 0.30/0.65      ( euclid3398187327856392827nt_nat
% 0.30/0.65      = ( ^ [N2: nat] : one_one_nat ) ) ).
% 0.30/0.65  
% 0.30/0.65  % division_segment_nat_def
% 0.30/0.65  thf(fact_9495_division__segment__int__def,axiom,
% 0.30/0.65      ( euclid3395696857347342551nt_int
% 0.30/0.65      = ( ^ [K4: int] : ( if_int @ ( ord_less_eq_int @ zero_zero_int @ K4 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % division_segment_int_def
% 0.30/0.65  thf(fact_9496_less__than__iff,axiom,
% 0.30/0.65      ! [X: nat,Y: nat] :
% 0.30/0.65        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ less_than )
% 0.30/0.65        = ( ord_less_nat @ X @ Y ) ) ).
% 0.30/0.65  
% 0.30/0.65  % less_than_iff
% 0.30/0.65  thf(fact_9497_total__less__than,axiom,
% 0.30/0.65      total_on_nat @ top_top_set_nat @ less_than ).
% 0.30/0.65  
% 0.30/0.65  % total_less_than
% 0.30/0.65  thf(fact_9498_natLeq__on__well__order__on,axiom,
% 0.30/0.65      ! [N: nat] :
% 0.30/0.65        ( order_2888998067076097458on_nat
% 0.30/0.65        @ ( collect_nat
% 0.30/0.65          @ ^ [X3: nat] : ( ord_less_nat @ X3 @ N ) )
% 0.30/0.65        @ ( collec3392354462482085612at_nat
% 0.30/0.65          @ ( produc6081775807080527818_nat_o
% 0.30/0.65            @ ^ [X3: nat,Y3: nat] :
% 0.30/0.65                ( ( ord_less_nat @ X3 @ N )
% 0.30/0.65                & ( ord_less_nat @ Y3 @ N )
% 0.30/0.65                & ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % natLeq_on_well_order_on
% 0.30/0.65  thf(fact_9499_natLeq__on__Well__order,axiom,
% 0.30/0.65      ! [N: nat] :
% 0.30/0.65        ( order_2888998067076097458on_nat
% 0.30/0.65        @ ( field_nat
% 0.30/0.65          @ ( collec3392354462482085612at_nat
% 0.30/0.65            @ ( produc6081775807080527818_nat_o
% 0.30/0.65              @ ^ [X3: nat,Y3: nat] :
% 0.30/0.65                  ( ( ord_less_nat @ X3 @ N )
% 0.30/0.65                  & ( ord_less_nat @ Y3 @ N )
% 0.30/0.65                  & ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) )
% 0.30/0.65        @ ( collec3392354462482085612at_nat
% 0.30/0.65          @ ( produc6081775807080527818_nat_o
% 0.30/0.65            @ ^ [X3: nat,Y3: nat] :
% 0.30/0.65                ( ( ord_less_nat @ X3 @ N )
% 0.30/0.65                & ( ord_less_nat @ Y3 @ N )
% 0.30/0.65                & ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % natLeq_on_Well_order
% 0.30/0.65  thf(fact_9500_ctwo__Cnotzero,axiom,
% 0.30/0.65      ( ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ bNF_Cardinal_ctwo @ bNF_Cardinal_czero_o ) @ bNF_We2654380646378065620so_o_o )
% 0.30/0.65      & ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ bNF_Cardinal_ctwo ) @ bNF_Cardinal_ctwo ) ) ).
% 0.30/0.65  
% 0.30/0.65  % ctwo_Cnotzero
% 0.30/0.65  thf(fact_9501_ctwo__def,axiom,
% 0.30/0.65      ( bNF_Cardinal_ctwo
% 0.30/0.65      = ( bNF_Ca3172636760949973492d_of_o @ top_top_set_o ) ) ).
% 0.30/0.65  
% 0.30/0.65  % ctwo_def
% 0.30/0.65  thf(fact_9502_ctwo__ordLess__natLeq,axiom,
% 0.30/0.65      member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ bNF_Cardinal_ctwo @ bNF_Ca8665028551170535155natLeq ) @ bNF_We8182288985678559134_o_nat ).
% 0.30/0.65  
% 0.30/0.65  % ctwo_ordLess_natLeq
% 0.30/0.65  thf(fact_9503_natLeq__card__order,axiom,
% 0.30/0.65      bNF_Ca1281551314933786834on_nat @ top_top_set_nat @ bNF_Ca8665028551170535155natLeq ).
% 0.30/0.65  
% 0.30/0.65  % natLeq_card_order
% 0.30/0.65  thf(fact_9504_natLeq__underS__less,axiom,
% 0.30/0.65      ! [N: nat] :
% 0.30/0.65        ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 0.30/0.65        = ( collect_nat
% 0.30/0.65          @ ^ [X3: nat] : ( ord_less_nat @ X3 @ N ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % natLeq_underS_less
% 0.30/0.65  thf(fact_9505_Field__natLeq,axiom,
% 0.30/0.65      ( ( field_nat @ bNF_Ca8665028551170535155natLeq )
% 0.30/0.65      = top_top_set_nat ) ).
% 0.30/0.65  
% 0.30/0.65  % Field_natLeq
% 0.30/0.65  thf(fact_9506_natLeq__def,axiom,
% 0.30/0.65      ( bNF_Ca8665028551170535155natLeq
% 0.30/0.65      = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % natLeq_def
% 0.30/0.65  thf(fact_9507_Restr__natLeq2,axiom,
% 0.30/0.65      ! [N: nat] :
% 0.30/0.65        ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 0.30/0.65          @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 0.30/0.65            @ ^ [Uu: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N ) ) )
% 0.30/0.65        = ( collec3392354462482085612at_nat
% 0.30/0.65          @ ( produc6081775807080527818_nat_o
% 0.30/0.65            @ ^ [X3: nat,Y3: nat] :
% 0.30/0.65                ( ( ord_less_nat @ X3 @ N )
% 0.30/0.65                & ( ord_less_nat @ Y3 @ N )
% 0.30/0.65                & ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Restr_natLeq2
% 0.30/0.65  thf(fact_9508_Restr__natLeq,axiom,
% 0.30/0.65      ! [N: nat] :
% 0.30/0.65        ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 0.30/0.65          @ ( produc457027306803732586at_nat
% 0.30/0.65            @ ( collect_nat
% 0.30/0.65              @ ^ [X3: nat] : ( ord_less_nat @ X3 @ N ) )
% 0.30/0.65            @ ^ [Uu: nat] :
% 0.30/0.65                ( collect_nat
% 0.30/0.65                @ ^ [X3: nat] : ( ord_less_nat @ X3 @ N ) ) ) )
% 0.30/0.65        = ( collec3392354462482085612at_nat
% 0.30/0.65          @ ( produc6081775807080527818_nat_o
% 0.30/0.65            @ ^ [X3: nat,Y3: nat] :
% 0.30/0.65                ( ( ord_less_nat @ X3 @ N )
% 0.30/0.65                & ( ord_less_nat @ Y3 @ N )
% 0.30/0.65                & ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Restr_natLeq
% 0.30/0.65  thf(fact_9509_card__of__nat,axiom,
% 0.30/0.65      member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ top_top_set_nat ) @ bNF_Ca8665028551170535155natLeq ) @ bNF_We5258908940166488438at_nat ).
% 0.30/0.65  
% 0.30/0.65  % card_of_nat
% 0.30/0.65  thf(fact_9510_card__of__Field__natLeq,axiom,
% 0.30/0.65      member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) ) @ bNF_Ca8665028551170535155natLeq ) @ bNF_We5258908940166488438at_nat ).
% 0.30/0.65  
% 0.30/0.65  % card_of_Field_natLeq
% 0.30/0.65  thf(fact_9511_num__of__nat__One,axiom,
% 0.30/0.65      ! [N: nat] :
% 0.30/0.65        ( ( ord_less_eq_nat @ N @ one_one_nat )
% 0.30/0.65       => ( ( num_of_nat @ N )
% 0.30/0.65          = one ) ) ).
% 0.30/0.65  
% 0.30/0.65  % num_of_nat_One
% 0.30/0.65  thf(fact_9512_eventually__prod__sequentially,axiom,
% 0.30/0.65      ! [P: product_prod_nat_nat > $o] :
% 0.30/0.65        ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 0.30/0.65        = ( ? [N6: nat] :
% 0.30/0.65            ! [M2: nat] :
% 0.30/0.65              ( ( ord_less_eq_nat @ N6 @ M2 )
% 0.30/0.65             => ! [N2: nat] :
% 0.30/0.65                  ( ( ord_less_eq_nat @ N6 @ N2 )
% 0.30/0.65                 => ( P @ ( product_Pair_nat_nat @ N2 @ M2 ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % eventually_prod_sequentially
% 0.30/0.65  thf(fact_9513_set__encode__empty,axiom,
% 0.30/0.65      ( ( nat_set_encode @ bot_bot_set_nat )
% 0.30/0.65      = zero_zero_nat ) ).
% 0.30/0.65  
% 0.30/0.65  % set_encode_empty
% 0.30/0.65  thf(fact_9514_int_Oid__abs__transfer,axiom,
% 0.30/0.65      ( bNF_re7934895593101944656at_int
% 0.30/0.65      @ ( basic_5328504652464829177at_nat
% 0.30/0.65        @ ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 )
% 0.30/0.65        @ ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 ) )
% 0.30/0.65      @ pcr_int
% 0.30/0.65      @ ^ [X3: product_prod_nat_nat] : X3
% 0.30/0.65      @ abs_Integ ) ).
% 0.30/0.65  
% 0.30/0.65  % int.id_abs_transfer
% 0.30/0.65  thf(fact_9515_smsI,axiom,
% 0.30/0.65      ! [A2: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat,Z5: multis2468970476368604999at_nat] :
% 0.30/0.65        ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A2 ) @ ( set_ms8126754132646256062at_nat @ B2 ) ) @ fun_max_strict )
% 0.30/0.65       => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z5 @ A2 ) @ ( plus_p7104986032573967614at_nat @ Z5 @ B2 ) ) @ ms_strict ) ) ).
% 0.30/0.65  
% 0.30/0.65  % smsI
% 0.30/0.65  thf(fact_9516_wmsI,axiom,
% 0.30/0.65      ! [A2: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat,Z5: multis2468970476368604999at_nat] :
% 0.30/0.65        ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A2 ) @ ( set_ms8126754132646256062at_nat @ B2 ) ) @ fun_max_strict )
% 0.30/0.65          | ( ( A2 = zero_z1048942125864253310at_nat )
% 0.30/0.65            & ( B2 = zero_z1048942125864253310at_nat ) ) )
% 0.30/0.65       => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z5 @ A2 ) @ ( plus_p7104986032573967614at_nat @ Z5 @ B2 ) ) @ ms_weak ) ) ).
% 0.30/0.65  
% 0.30/0.65  % wmsI
% 0.30/0.65  thf(fact_9517_ms__weak__def,axiom,
% 0.30/0.65      ( ms_weak
% 0.30/0.65      = ( sup_su3035147773818789531at_nat @ ms_strict @ id_mul2649389997224486051at_nat ) ) ).
% 0.30/0.65  
% 0.30/0.65  % ms_weak_def
% 0.30/0.65  thf(fact_9518_ms__reduction__pair,axiom,
% 0.30/0.65      fun_re7357418987779152907at_nat @ ( produc5245064249948416855at_nat @ ms_strict @ ms_weak ) ).
% 0.30/0.65  
% 0.30/0.65  % ms_reduction_pair
% 0.30/0.65  thf(fact_9519_ms__strictI,axiom,
% 0.30/0.65      ! [Z5: multis2468970476368604999at_nat,Z9: multis2468970476368604999at_nat,A2: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat] :
% 0.30/0.65        ( ( pw_leq @ Z5 @ Z9 )
% 0.30/0.65       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A2 ) @ ( set_ms8126754132646256062at_nat @ B2 ) ) @ fun_max_strict )
% 0.30/0.65         => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z5 @ A2 ) @ ( plus_p7104986032573967614at_nat @ Z9 @ B2 ) ) @ ms_strict ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % ms_strictI
% 0.30/0.65  thf(fact_9520_ms__weakI1,axiom,
% 0.30/0.65      ! [Z5: multis2468970476368604999at_nat,Z9: multis2468970476368604999at_nat,A2: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat] :
% 0.30/0.65        ( ( pw_leq @ Z5 @ Z9 )
% 0.30/0.65       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A2 ) @ ( set_ms8126754132646256062at_nat @ B2 ) ) @ fun_max_strict )
% 0.30/0.65         => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z5 @ A2 ) @ ( plus_p7104986032573967614at_nat @ Z9 @ B2 ) ) @ ms_weak ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % ms_weakI1
% 0.30/0.65  thf(fact_9521_pw__leq__lstep,axiom,
% 0.30/0.65      ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.30/0.65        ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 0.30/0.65       => ( pw_leq @ ( add_ms2612439473150266591at_nat @ X @ zero_z1048942125864253310at_nat ) @ ( add_ms2612439473150266591at_nat @ Y @ zero_z1048942125864253310at_nat ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % pw_leq_lstep
% 0.30/0.65  thf(fact_9522_pw__leq_Ocases,axiom,
% 0.30/0.65      ! [A1: multis2468970476368604999at_nat,A22: multis2468970476368604999at_nat] :
% 0.30/0.65        ( ( pw_leq @ A1 @ A22 )
% 0.30/0.65       => ( ( ( A1 = zero_z1048942125864253310at_nat )
% 0.30/0.65           => ( A22 != zero_z1048942125864253310at_nat ) )
% 0.30/0.65         => ~ ! [X2: product_prod_nat_nat,Y2: product_prod_nat_nat,X8: multis2468970476368604999at_nat] :
% 0.30/0.65                ( ( A1
% 0.30/0.65                  = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ X2 @ zero_z1048942125864253310at_nat ) @ X8 ) )
% 0.30/0.65               => ! [Y7: multis2468970476368604999at_nat] :
% 0.30/0.65                    ( ( A22
% 0.30/0.65                      = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ Y2 @ zero_z1048942125864253310at_nat ) @ Y7 ) )
% 0.30/0.65                   => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y2 ) @ fun_pair_leq )
% 0.30/0.65                     => ~ ( pw_leq @ X8 @ Y7 ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % pw_leq.cases
% 0.30/0.65  thf(fact_9523_pw__leq_Osimps,axiom,
% 0.30/0.65      ( pw_leq
% 0.30/0.65      = ( ^ [A12: multis2468970476368604999at_nat,A23: multis2468970476368604999at_nat] :
% 0.30/0.65            ( ( ( A12 = zero_z1048942125864253310at_nat )
% 0.30/0.65              & ( A23 = zero_z1048942125864253310at_nat ) )
% 0.30/0.65            | ? [X3: product_prod_nat_nat,Y3: product_prod_nat_nat,X4: multis2468970476368604999at_nat,Y8: multis2468970476368604999at_nat] :
% 0.30/0.65                ( ( A12
% 0.30/0.65                  = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ X3 @ zero_z1048942125864253310at_nat ) @ X4 ) )
% 0.30/0.65                & ( A23
% 0.30/0.65                  = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ Y3 @ zero_z1048942125864253310at_nat ) @ Y8 ) )
% 0.30/0.65                & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y3 ) @ fun_pair_leq )
% 0.30/0.65                & ( pw_leq @ X4 @ Y8 ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % pw_leq.simps
% 0.30/0.65  thf(fact_9524_pw__leq__step,axiom,
% 0.30/0.65      ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,X7: multis2468970476368604999at_nat,Y6: multis2468970476368604999at_nat] :
% 0.30/0.65        ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 0.30/0.65       => ( ( pw_leq @ X7 @ Y6 )
% 0.30/0.65         => ( pw_leq @ ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ X @ zero_z1048942125864253310at_nat ) @ X7 ) @ ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ Y @ zero_z1048942125864253310at_nat ) @ Y6 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % pw_leq_step
% 0.30/0.65  thf(fact_9525_ms__weakI2,axiom,
% 0.30/0.65      ! [Z5: multis2468970476368604999at_nat,Z9: multis2468970476368604999at_nat] :
% 0.30/0.65        ( ( pw_leq @ Z5 @ Z9 )
% 0.30/0.65       => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z5 @ zero_z1048942125864253310at_nat ) @ ( plus_p7104986032573967614at_nat @ Z9 @ zero_z1048942125864253310at_nat ) ) @ ms_weak ) ) ).
% 0.30/0.65  
% 0.30/0.65  % ms_weakI2
% 0.30/0.65  thf(fact_9526_pw__leq__split,axiom,
% 0.30/0.65      ! [X7: multis2468970476368604999at_nat,Y6: multis2468970476368604999at_nat] :
% 0.30/0.65        ( ( pw_leq @ X7 @ Y6 )
% 0.30/0.65       => ? [A8: multis2468970476368604999at_nat,B9: multis2468970476368604999at_nat,Z10: multis2468970476368604999at_nat] :
% 0.30/0.65            ( ( X7
% 0.30/0.65              = ( plus_p7104986032573967614at_nat @ A8 @ Z10 ) )
% 0.30/0.65            & ( Y6
% 0.30/0.65              = ( plus_p7104986032573967614at_nat @ B9 @ Z10 ) )
% 0.30/0.65            & ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A8 ) @ ( set_ms8126754132646256062at_nat @ B9 ) ) @ fun_max_strict )
% 0.30/0.65              | ( ( B9 = zero_z1048942125864253310at_nat )
% 0.30/0.65                & ( A8 = zero_z1048942125864253310at_nat ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % pw_leq_split
% 0.30/0.65  thf(fact_9527_rat_Odomain,axiom,
% 0.30/0.65      ( ( domain9213661015745956397nt_rat @ pcr_rat )
% 0.30/0.65      = ( ^ [X3: product_prod_int_int] :
% 0.30/0.65          ? [Y3: product_prod_int_int] :
% 0.30/0.65            ( ( basic_4387203522000727145nt_int
% 0.30/0.65              @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 0.30/0.65              @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 0.30/0.65              @ X3
% 0.30/0.65              @ Y3 )
% 0.30/0.65            & ( ratrel @ Y3 @ Y3 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % rat.domain
% 0.30/0.65  thf(fact_9528_rat_Odomain__par,axiom,
% 0.30/0.65      ! [DR1: int > $o,DR2: int > $o,P22: product_prod_int_int > $o] :
% 0.30/0.65        ( ( ( domainp_int_int
% 0.30/0.65            @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 0.30/0.65          = DR1 )
% 0.30/0.65       => ( ( ( domainp_int_int
% 0.30/0.65              @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 0.30/0.65            = DR2 )
% 0.30/0.65         => ( ( bNF_re8699439704749558557nt_o_o
% 0.30/0.65              @ ( basic_4387203522000727145nt_int
% 0.30/0.65                @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 0.30/0.65                @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 0.30/0.65              @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 0.30/0.65              @ P22
% 0.30/0.65              @ ^ [X3: product_prod_int_int] : ( ratrel @ X3 @ X3 ) )
% 0.30/0.65           => ( ( domain9213661015745956397nt_rat @ pcr_rat )
% 0.30/0.65              = ( inf_in3604695632404883862_int_o @ ( basic_1567116559311922317nt_int @ DR1 @ DR2 ) @ P22 ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % rat.domain_par
% 0.30/0.65  thf(fact_9529_rat_Odomain__par__left__total,axiom,
% 0.30/0.65      ! [P7: product_prod_int_int > $o] :
% 0.30/0.65        ( ( left_t3131394472396969446nt_int
% 0.30/0.65          @ ( basic_4387203522000727145nt_int
% 0.30/0.65            @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 0.30/0.65            @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) ) )
% 0.30/0.65       => ( ( bNF_re8699439704749558557nt_o_o
% 0.30/0.65            @ ( basic_4387203522000727145nt_int
% 0.30/0.65              @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 0.30/0.65              @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 0.30/0.65            @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 0.30/0.65            @ P7
% 0.30/0.65            @ ^ [X3: product_prod_int_int] : ( ratrel @ X3 @ X3 ) )
% 0.30/0.65         => ( ( domain9213661015745956397nt_rat @ pcr_rat )
% 0.30/0.65            = P7 ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % rat.domain_par_left_total
% 0.30/0.65  thf(fact_9530_Abs__rat__inject,axiom,
% 0.30/0.65      ! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
% 0.30/0.65        ( ( member2340774599025711042nt_int @ X
% 0.30/0.65          @ ( collec5210948495886036740nt_int
% 0.30/0.65            @ ^ [C4: set_Pr958786334691620121nt_int] :
% 0.30/0.65              ? [X3: product_prod_int_int] :
% 0.30/0.65                ( ( ratrel @ X3 @ X3 )
% 0.30/0.65                & ( C4
% 0.30/0.65                  = ( collec213857154873943460nt_int @ ( ratrel @ X3 ) ) ) ) ) )
% 0.30/0.65       => ( ( member2340774599025711042nt_int @ Y
% 0.30/0.65            @ ( collec5210948495886036740nt_int
% 0.30/0.65              @ ^ [C4: set_Pr958786334691620121nt_int] :
% 0.30/0.65                ? [X3: product_prod_int_int] :
% 0.30/0.65                  ( ( ratrel @ X3 @ X3 )
% 0.30/0.65                  & ( C4
% 0.30/0.65                    = ( collec213857154873943460nt_int @ ( ratrel @ X3 ) ) ) ) ) )
% 0.30/0.65         => ( ( ( abs_rat @ X )
% 0.30/0.65              = ( abs_rat @ Y ) )
% 0.30/0.65            = ( X = Y ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Abs_rat_inject
% 0.30/0.65  thf(fact_9531_Abs__rat__induct,axiom,
% 0.30/0.65      ! [P: rat > $o,X: rat] :
% 0.30/0.65        ( ! [Y2: set_Pr958786334691620121nt_int] :
% 0.30/0.65            ( ( member2340774599025711042nt_int @ Y2
% 0.30/0.65              @ ( collec5210948495886036740nt_int
% 0.30/0.65                @ ^ [C4: set_Pr958786334691620121nt_int] :
% 0.30/0.65                  ? [X3: product_prod_int_int] :
% 0.30/0.65                    ( ( ratrel @ X3 @ X3 )
% 0.30/0.65                    & ( C4
% 0.30/0.65                      = ( collec213857154873943460nt_int @ ( ratrel @ X3 ) ) ) ) ) )
% 0.30/0.65           => ( P @ ( abs_rat @ Y2 ) ) )
% 0.30/0.65       => ( P @ X ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Abs_rat_induct
% 0.30/0.65  thf(fact_9532_Abs__rat__cases,axiom,
% 0.30/0.65      ! [X: rat] :
% 0.30/0.65        ~ ! [Y2: set_Pr958786334691620121nt_int] :
% 0.30/0.65            ( ( X
% 0.30/0.65              = ( abs_rat @ Y2 ) )
% 0.30/0.65           => ~ ( member2340774599025711042nt_int @ Y2
% 0.30/0.65                @ ( collec5210948495886036740nt_int
% 0.30/0.65                  @ ^ [C4: set_Pr958786334691620121nt_int] :
% 0.30/0.65                    ? [X3: product_prod_int_int] :
% 0.30/0.65                      ( ( ratrel @ X3 @ X3 )
% 0.30/0.65                      & ( C4
% 0.30/0.65                        = ( collec213857154873943460nt_int @ ( ratrel @ X3 ) ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Abs_rat_cases
% 0.30/0.65  thf(fact_9533_type__definition__rat,axiom,
% 0.30/0.65      ( type_d8554052265237484179nt_int @ rep_rat @ abs_rat
% 0.30/0.65      @ ( collec5210948495886036740nt_int
% 0.30/0.65        @ ^ [C4: set_Pr958786334691620121nt_int] :
% 0.30/0.65          ? [X3: product_prod_int_int] :
% 0.30/0.65            ( ( ratrel @ X3 @ X3 )
% 0.30/0.65            & ( C4
% 0.30/0.65              = ( collec213857154873943460nt_int @ ( ratrel @ X3 ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % type_definition_rat
% 0.30/0.65  thf(fact_9534_Abs__rat__inverse,axiom,
% 0.30/0.65      ! [Y: set_Pr958786334691620121nt_int] :
% 0.30/0.65        ( ( member2340774599025711042nt_int @ Y
% 0.30/0.65          @ ( collec5210948495886036740nt_int
% 0.30/0.65            @ ^ [C4: set_Pr958786334691620121nt_int] :
% 0.30/0.65              ? [X3: product_prod_int_int] :
% 0.30/0.65                ( ( ratrel @ X3 @ X3 )
% 0.30/0.65                & ( C4
% 0.30/0.65                  = ( collec213857154873943460nt_int @ ( ratrel @ X3 ) ) ) ) ) )
% 0.30/0.65       => ( ( rep_rat @ ( abs_rat @ Y ) )
% 0.30/0.65          = Y ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Abs_rat_inverse
% 0.30/0.65  thf(fact_9535_Rep__rat__induct,axiom,
% 0.30/0.65      ! [Y: set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 0.30/0.65        ( ( member2340774599025711042nt_int @ Y
% 0.30/0.65          @ ( collec5210948495886036740nt_int
% 0.30/0.65            @ ^ [C4: set_Pr958786334691620121nt_int] :
% 0.30/0.65              ? [X3: product_prod_int_int] :
% 0.30/0.65                ( ( ratrel @ X3 @ X3 )
% 0.30/0.65                & ( C4
% 0.30/0.65                  = ( collec213857154873943460nt_int @ ( ratrel @ X3 ) ) ) ) ) )
% 0.30/0.65       => ( ! [X2: rat] : ( P @ ( rep_rat @ X2 ) )
% 0.30/0.65         => ( P @ Y ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Rep_rat_induct
% 0.30/0.65  thf(fact_9536_Rep__rat__cases,axiom,
% 0.30/0.65      ! [Y: set_Pr958786334691620121nt_int] :
% 0.30/0.65        ( ( member2340774599025711042nt_int @ Y
% 0.30/0.65          @ ( collec5210948495886036740nt_int
% 0.30/0.65            @ ^ [C4: set_Pr958786334691620121nt_int] :
% 0.30/0.65              ? [X3: product_prod_int_int] :
% 0.30/0.65                ( ( ratrel @ X3 @ X3 )
% 0.30/0.65                & ( C4
% 0.30/0.65                  = ( collec213857154873943460nt_int @ ( ratrel @ X3 ) ) ) ) ) )
% 0.30/0.65       => ~ ! [X2: rat] :
% 0.30/0.65              ( Y
% 0.30/0.65             != ( rep_rat @ X2 ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Rep_rat_cases
% 0.30/0.65  thf(fact_9537_Rep__rat,axiom,
% 0.30/0.65      ! [X: rat] :
% 0.30/0.65        ( member2340774599025711042nt_int @ ( rep_rat @ X )
% 0.30/0.65        @ ( collec5210948495886036740nt_int
% 0.30/0.65          @ ^ [C4: set_Pr958786334691620121nt_int] :
% 0.30/0.65            ? [X3: product_prod_int_int] :
% 0.30/0.65              ( ( ratrel @ X3 @ X3 )
% 0.30/0.65              & ( C4
% 0.30/0.65                = ( collec213857154873943460nt_int @ ( ratrel @ X3 ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Rep_rat
% 0.30/0.65  thf(fact_9538_cr__int__def,axiom,
% 0.30/0.65      ( cr_int
% 0.30/0.65      = ( ^ [X3: product_prod_nat_nat] :
% 0.30/0.65            ( ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 0.30/0.65            @ ( abs_Integ @ X3 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % cr_int_def
% 0.30/0.65  thf(fact_9539_in__range_Osimps,axiom,
% 0.30/0.65      ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 0.30/0.65        ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 0.30/0.65        = ( ! [X3: nat] :
% 0.30/0.65              ( ( member_nat @ X3 @ As )
% 0.30/0.65             => ( ord_less_nat @ X3 @ ( lim_Product_unit @ H3 ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % in_range.simps
% 0.30/0.65  thf(fact_9540_in__range_Oelims_I3_J,axiom,
% 0.30/0.65      ! [X: produc3658429121746597890et_nat] :
% 0.30/0.65        ( ~ ( in_range @ X )
% 0.30/0.65       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 0.30/0.65              ( ( X
% 0.30/0.65                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.30/0.65             => ! [X2: nat] :
% 0.30/0.65                  ( ( member_nat @ X2 @ As4 )
% 0.30/0.65                 => ( ord_less_nat @ X2 @ ( lim_Product_unit @ H ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % in_range.elims(3)
% 0.30/0.65  thf(fact_9541_in__range_Oelims_I2_J,axiom,
% 0.30/0.65      ! [X: produc3658429121746597890et_nat] :
% 0.30/0.65        ( ( in_range @ X )
% 0.30/0.65       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 0.30/0.65              ( ( X
% 0.30/0.65                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.30/0.65             => ~ ! [X5: nat] :
% 0.30/0.65                    ( ( member_nat @ X5 @ As4 )
% 0.30/0.65                   => ( ord_less_nat @ X5 @ ( lim_Product_unit @ H ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % in_range.elims(2)
% 0.30/0.65  thf(fact_9542_in__range_Oelims_I1_J,axiom,
% 0.30/0.65      ! [X: produc3658429121746597890et_nat,Y: $o] :
% 0.30/0.65        ( ( ( in_range @ X )
% 0.30/0.65          = Y )
% 0.30/0.65       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 0.30/0.65              ( ( X
% 0.30/0.65                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 0.30/0.65             => ( Y
% 0.30/0.65                = ( ~ ! [X3: nat] :
% 0.30/0.65                        ( ( member_nat @ X3 @ As4 )
% 0.30/0.65                       => ( ord_less_nat @ X3 @ ( lim_Product_unit @ H ) ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % in_range.elims(1)
% 0.30/0.65  thf(fact_9543_surj__prod__encode,axiom,
% 0.30/0.65      ( ( image_2486076414777270412at_nat @ nat_prod_encode @ top_to4669805908274784177at_nat )
% 0.30/0.65      = top_top_set_nat ) ).
% 0.30/0.65  
% 0.30/0.65  % surj_prod_encode
% 0.30/0.65  thf(fact_9544_le__prod__encode__1,axiom,
% 0.30/0.65      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % le_prod_encode_1
% 0.30/0.65  thf(fact_9545_le__prod__encode__2,axiom,
% 0.30/0.65      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % le_prod_encode_2
% 0.30/0.65  thf(fact_9546_bij__prod__encode,axiom,
% 0.30/0.65      bij_be5333170631980326235at_nat @ nat_prod_encode @ top_to4669805908274784177at_nat @ top_top_set_nat ).
% 0.30/0.65  
% 0.30/0.65  % bij_prod_encode
% 0.30/0.65  thf(fact_9547_list__encode_Oelims,axiom,
% 0.30/0.65      ! [X: list_nat,Y: nat] :
% 0.30/0.65        ( ( ( nat_list_encode @ X )
% 0.30/0.65          = Y )
% 0.30/0.65       => ( ( ( X = nil_nat )
% 0.30/0.65           => ( Y != zero_zero_nat ) )
% 0.30/0.65         => ~ ! [X2: nat,Xs2: list_nat] :
% 0.30/0.65                ( ( X
% 0.30/0.65                  = ( cons_nat @ X2 @ Xs2 ) )
% 0.30/0.65               => ( Y
% 0.30/0.65                 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X2 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % list_encode.elims
% 0.30/0.65  thf(fact_9548_prod__encode__def,axiom,
% 0.30/0.65      ( nat_prod_encode
% 0.30/0.65      = ( produc6842872674320459806at_nat
% 0.30/0.65        @ ^ [M2: nat,N2: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M2 @ N2 ) ) @ M2 ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % prod_encode_def
% 0.30/0.65  thf(fact_9549_surj__list__encode,axiom,
% 0.30/0.65      ( ( image_list_nat_nat @ nat_list_encode @ top_top_set_list_nat )
% 0.30/0.65      = top_top_set_nat ) ).
% 0.30/0.65  
% 0.30/0.65  % surj_list_encode
% 0.30/0.65  thf(fact_9550_bij__list__encode,axiom,
% 0.30/0.65      bij_be8532844293280997160at_nat @ nat_list_encode @ top_top_set_list_nat @ top_top_set_nat ).
% 0.30/0.65  
% 0.30/0.65  % bij_list_encode
% 0.30/0.65  thf(fact_9551_list__encode_Osimps_I2_J,axiom,
% 0.30/0.65      ! [X: nat,Xs: list_nat] :
% 0.30/0.65        ( ( nat_list_encode @ ( cons_nat @ X @ Xs ) )
% 0.30/0.65        = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % list_encode.simps(2)
% 0.30/0.65  thf(fact_9552_list__encode_Opelims,axiom,
% 0.30/0.65      ! [X: list_nat,Y: nat] :
% 0.30/0.65        ( ( ( nat_list_encode @ X )
% 0.30/0.65          = Y )
% 0.30/0.65       => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 0.30/0.65         => ( ( ( X = nil_nat )
% 0.30/0.65             => ( ( Y = zero_zero_nat )
% 0.30/0.65               => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 0.30/0.65           => ~ ! [X2: nat,Xs2: list_nat] :
% 0.30/0.65                  ( ( X
% 0.30/0.65                    = ( cons_nat @ X2 @ Xs2 ) )
% 0.30/0.65                 => ( ( Y
% 0.30/0.65                      = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X2 @ ( nat_list_encode @ Xs2 ) ) ) ) )
% 0.30/0.65                   => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X2 @ Xs2 ) ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % list_encode.pelims
% 0.30/0.65  thf(fact_9553_String_Oless__literal__def,axiom,
% 0.30/0.65      ( ord_less_literal
% 0.30/0.65      = ( map_fu2661873803724901240eral_o @ explode @ ( map_fu6698795530259886495ar_o_o @ explode @ id_o )
% 0.30/0.65        @ ( lexordp_char
% 0.30/0.65          @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % String.less_literal_def
% 0.30/0.65  thf(fact_9554_less__literal_Orep__eq,axiom,
% 0.30/0.65      ( ord_less_literal
% 0.30/0.65      = ( ^ [X3: literal,Xa4: literal] :
% 0.30/0.65            ( lexordp_char
% 0.30/0.65            @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) )
% 0.30/0.65            @ ( explode @ X3 )
% 0.30/0.65            @ ( explode @ Xa4 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % less_literal.rep_eq
% 0.30/0.65  thf(fact_9555_String_Oless__eq__literal__def,axiom,
% 0.30/0.65      ( ord_less_eq_literal
% 0.30/0.65      = ( map_fu2661873803724901240eral_o @ explode @ ( map_fu6698795530259886495ar_o_o @ explode @ id_o )
% 0.30/0.65        @ ( lexordp_eq_char
% 0.30/0.65          @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % String.less_eq_literal_def
% 0.30/0.65  thf(fact_9556_less__literal_Otransfer,axiom,
% 0.30/0.65      ( bNF_re7831395832754058691eral_o @ pcr_literal
% 0.30/0.65      @ ( bNF_re8730477052009823892al_o_o @ pcr_literal
% 0.30/0.65        @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 ) )
% 0.30/0.65      @ ( lexordp_char
% 0.30/0.65        @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) ) )
% 0.30/0.65      @ ord_less_literal ) ).
% 0.30/0.65  
% 0.30/0.65  % less_literal.transfer
% 0.30/0.65  thf(fact_9557_literal_Orep__transfer,axiom,
% 0.30/0.65      ( bNF_re4991257583289732696t_char @ pcr_literal
% 0.30/0.65      @ ( list_all2_char_char
% 0.30/0.65        @ ^ [Y4: char,Z4: char] : ( Y4 = Z4 ) )
% 0.30/0.65      @ ^ [X3: list_char] : X3
% 0.30/0.65      @ explode ) ).
% 0.30/0.65  
% 0.30/0.65  % literal.rep_transfer
% 0.30/0.65  thf(fact_9558_less__eq__literal_Otransfer,axiom,
% 0.30/0.65      ( bNF_re7831395832754058691eral_o @ pcr_literal
% 0.30/0.65      @ ( bNF_re8730477052009823892al_o_o @ pcr_literal
% 0.30/0.65        @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 ) )
% 0.30/0.65      @ ( lexordp_eq_char
% 0.30/0.65        @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) ) )
% 0.30/0.65      @ ord_less_eq_literal ) ).
% 0.30/0.65  
% 0.30/0.65  % less_eq_literal.transfer
% 0.30/0.65  thf(fact_9559_less__eq__literal_Orep__eq,axiom,
% 0.30/0.65      ( ord_less_eq_literal
% 0.30/0.65      = ( ^ [X3: literal,Xa4: literal] :
% 0.30/0.65            ( lexordp_eq_char
% 0.30/0.65            @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) )
% 0.30/0.65            @ ( explode @ X3 )
% 0.30/0.65            @ ( explode @ Xa4 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % less_eq_literal.rep_eq
% 0.30/0.65  thf(fact_9560_String_Ocr__literal__def,axiom,
% 0.30/0.65      ( cr_literal
% 0.30/0.65      = ( ^ [X3: list_char,Y3: literal] :
% 0.30/0.65            ( X3
% 0.30/0.65            = ( explode @ Y3 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % String.cr_literal_def
% 0.30/0.65  thf(fact_9561_MOST__SucD,axiom,
% 0.30/0.65      ! [P: nat > $o] :
% 0.30/0.65        ( ( eventually_nat
% 0.30/0.65          @ ^ [N2: nat] : ( P @ ( suc @ N2 ) )
% 0.30/0.65          @ cofinite_nat )
% 0.30/0.65       => ( eventually_nat @ P @ cofinite_nat ) ) ).
% 0.30/0.65  
% 0.30/0.65  % MOST_SucD
% 0.30/0.65  thf(fact_9562_MOST__SucI,axiom,
% 0.30/0.65      ! [P: nat > $o] :
% 0.30/0.65        ( ( eventually_nat @ P @ cofinite_nat )
% 0.30/0.65       => ( eventually_nat
% 0.30/0.65          @ ^ [N2: nat] : ( P @ ( suc @ N2 ) )
% 0.30/0.65          @ cofinite_nat ) ) ).
% 0.30/0.65  
% 0.30/0.65  % MOST_SucI
% 0.30/0.65  thf(fact_9563_MOST__Suc__iff,axiom,
% 0.30/0.65      ! [P: nat > $o] :
% 0.30/0.65        ( ( eventually_nat
% 0.30/0.65          @ ^ [N2: nat] : ( P @ ( suc @ N2 ) )
% 0.30/0.65          @ cofinite_nat )
% 0.30/0.65        = ( eventually_nat @ P @ cofinite_nat ) ) ).
% 0.30/0.65  
% 0.30/0.65  % MOST_Suc_iff
% 0.30/0.65  thf(fact_9564_MOST__nat,axiom,
% 0.30/0.65      ! [P: nat > $o] :
% 0.30/0.65        ( ( eventually_nat @ P @ cofinite_nat )
% 0.30/0.65        = ( ? [M2: nat] :
% 0.30/0.65            ! [N2: nat] :
% 0.30/0.65              ( ( ord_less_nat @ M2 @ N2 )
% 0.30/0.65             => ( P @ N2 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % MOST_nat
% 0.30/0.65  thf(fact_9565_MOST__ge__nat,axiom,
% 0.30/0.65      ! [M: nat] : ( eventually_nat @ ( ord_less_eq_nat @ M ) @ cofinite_nat ) ).
% 0.30/0.65  
% 0.30/0.65  % MOST_ge_nat
% 0.30/0.65  thf(fact_9566_MOST__nat__le,axiom,
% 0.30/0.65      ! [P: nat > $o] :
% 0.30/0.65        ( ( eventually_nat @ P @ cofinite_nat )
% 0.30/0.65        = ( ? [M2: nat] :
% 0.30/0.65            ! [N2: nat] :
% 0.30/0.65              ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.30/0.65             => ( P @ N2 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % MOST_nat_le
% 0.30/0.65  thf(fact_9567_less__literal_Orsp,axiom,
% 0.30/0.65      ( bNF_re7775871201573978401char_o
% 0.30/0.65      @ ( bNF_eq_onp_list_char
% 0.30/0.65        @ ^ [Cs: list_char] :
% 0.30/0.65          ! [X3: char] :
% 0.30/0.65            ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65           => ~ ( digit7 @ X3 ) ) )
% 0.30/0.65      @ ( bNF_re6668474094832959905ar_o_o
% 0.30/0.65        @ ( bNF_eq_onp_list_char
% 0.30/0.65          @ ^ [Cs: list_char] :
% 0.30/0.65            ! [X3: char] :
% 0.30/0.65              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65             => ~ ( digit7 @ X3 ) ) )
% 0.30/0.65        @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 ) )
% 0.30/0.65      @ ( lexordp_char
% 0.30/0.65        @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) ) )
% 0.30/0.65      @ ( lexordp_char
% 0.30/0.65        @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % less_literal.rsp
% 0.30/0.65  thf(fact_9568_plus__literal_Orsp,axiom,
% 0.30/0.65      ( bNF_re7399511318543894245t_char
% 0.30/0.65      @ ( bNF_eq_onp_list_char
% 0.30/0.65        @ ^ [Cs: list_char] :
% 0.30/0.65          ! [X3: char] :
% 0.30/0.65            ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65           => ~ ( digit7 @ X3 ) ) )
% 0.30/0.65      @ ( bNF_re1407854171455731685t_char
% 0.30/0.65        @ ( bNF_eq_onp_list_char
% 0.30/0.65          @ ^ [Cs: list_char] :
% 0.30/0.65            ! [X3: char] :
% 0.30/0.65              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65             => ~ ( digit7 @ X3 ) ) )
% 0.30/0.65        @ ( bNF_eq_onp_list_char
% 0.30/0.65          @ ^ [Cs: list_char] :
% 0.30/0.65            ! [X3: char] :
% 0.30/0.65              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65             => ~ ( digit7 @ X3 ) ) ) )
% 0.30/0.65      @ append_char
% 0.30/0.65      @ append_char ) ).
% 0.30/0.65  
% 0.30/0.65  % plus_literal.rsp
% 0.30/0.65  thf(fact_9569_asciis__of__literal_Orsp,axiom,
% 0.30/0.65      ( bNF_re901197953848981245nteger
% 0.30/0.65      @ ( bNF_eq_onp_list_char
% 0.30/0.65        @ ^ [Cs: list_char] :
% 0.30/0.65          ! [X3: char] :
% 0.30/0.65            ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65           => ~ ( digit7 @ X3 ) ) )
% 0.30/0.65      @ ^ [Y4: list_Code_integer,Z4: list_Code_integer] : ( Y4 = Z4 )
% 0.30/0.65      @ ( map_ch5843194146513361140nteger @ comm_s4049598766089966537nteger )
% 0.30/0.65      @ ( map_ch5843194146513361140nteger @ comm_s4049598766089966537nteger ) ) ).
% 0.30/0.65  
% 0.30/0.65  % asciis_of_literal.rsp
% 0.30/0.65  thf(fact_9570_size__literal_Orsp,axiom,
% 0.30/0.65      ( bNF_re76688982720252355at_nat
% 0.30/0.65      @ ( bNF_eq_onp_list_char
% 0.30/0.65        @ ^ [Cs: list_char] :
% 0.30/0.65          ! [X3: char] :
% 0.30/0.65            ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65           => ~ ( digit7 @ X3 ) ) )
% 0.30/0.65      @ ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 )
% 0.30/0.65      @ size_size_list_char
% 0.30/0.65      @ size_size_list_char ) ).
% 0.30/0.65  
% 0.30/0.65  % size_literal.rsp
% 0.30/0.65  thf(fact_9571_Literal_Orsp,axiom,
% 0.30/0.65      ( bNF_re5598663031114558885t_char
% 0.30/0.65      @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 0.30/0.65      @ ( bNF_re7347849368244578525t_char
% 0.30/0.65        @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 0.30/0.65        @ ( bNF_re7972843584066424825t_char
% 0.30/0.65          @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 0.30/0.65          @ ( bNF_re796896441190010845t_char
% 0.30/0.65            @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 0.30/0.65            @ ( bNF_re4583855572895197261t_char
% 0.30/0.65              @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 0.30/0.65              @ ( bNF_re441219624009962717t_char
% 0.30/0.65                @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 0.30/0.65                @ ( bNF_re6157522605288126113t_char
% 0.30/0.65                  @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 0.30/0.65                  @ ( bNF_re1407854171455731685t_char
% 0.30/0.65                    @ ( bNF_eq_onp_list_char
% 0.30/0.65                      @ ^ [Cs: list_char] :
% 0.30/0.65                        ! [X3: char] :
% 0.30/0.65                          ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65                         => ~ ( digit7 @ X3 ) ) )
% 0.30/0.65                    @ ( bNF_eq_onp_list_char
% 0.30/0.65                      @ ^ [Cs: list_char] :
% 0.30/0.65                        ! [X3: char] :
% 0.30/0.65                          ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65                         => ~ ( digit7 @ X3 ) ) ) ) ) ) ) ) ) )
% 0.30/0.65      @ ^ [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o] : ( cons_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ $false ) )
% 0.30/0.65      @ ^ [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o] : ( cons_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ $false ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Literal.rsp
% 0.30/0.65  thf(fact_9572_literal_Oexplode,axiom,
% 0.30/0.65      ! [X: literal] :
% 0.30/0.65        ( member_list_char @ ( explode @ X )
% 0.30/0.65        @ ( collect_list_char
% 0.30/0.65          @ ^ [Cs: list_char] :
% 0.30/0.65            ! [X3: char] :
% 0.30/0.65              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65             => ~ ( digit7 @ X3 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % literal.explode
% 0.30/0.65  thf(fact_9573_literal_Oexplode__cases,axiom,
% 0.30/0.65      ! [Y: list_char] :
% 0.30/0.65        ( ( member_list_char @ Y
% 0.30/0.65          @ ( collect_list_char
% 0.30/0.65            @ ^ [Cs: list_char] :
% 0.30/0.65              ! [X3: char] :
% 0.30/0.65                ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65               => ~ ( digit7 @ X3 ) ) ) )
% 0.30/0.65       => ~ ! [X2: literal] :
% 0.30/0.65              ( Y
% 0.30/0.65             != ( explode @ X2 ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % literal.explode_cases
% 0.30/0.65  thf(fact_9574_literal_Oexplode__induct,axiom,
% 0.30/0.65      ! [Y: list_char,P: list_char > $o] :
% 0.30/0.65        ( ( member_list_char @ Y
% 0.30/0.65          @ ( collect_list_char
% 0.30/0.65            @ ^ [Cs: list_char] :
% 0.30/0.65              ! [X3: char] :
% 0.30/0.65                ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65               => ~ ( digit7 @ X3 ) ) ) )
% 0.30/0.65       => ( ! [X2: literal] : ( P @ ( explode @ X2 ) )
% 0.30/0.65         => ( P @ Y ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % literal.explode_induct
% 0.30/0.65  thf(fact_9575_zero__literal_Orsp,axiom,
% 0.30/0.65      ( bNF_eq_onp_list_char
% 0.30/0.65      @ ^ [Cs: list_char] :
% 0.30/0.65        ! [X3: char] :
% 0.30/0.65          ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65         => ~ ( digit7 @ X3 ) )
% 0.30/0.65      @ nil_char
% 0.30/0.65      @ nil_char ) ).
% 0.30/0.65  
% 0.30/0.65  % zero_literal.rsp
% 0.30/0.65  thf(fact_9576_literal_Odomain__eq,axiom,
% 0.30/0.65      ( ( domain7888411570377768909iteral @ pcr_literal )
% 0.30/0.65      = ( ^ [Cs: list_char] :
% 0.30/0.65          ! [X3: char] :
% 0.30/0.65            ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65           => ~ ( digit7 @ X3 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % literal.domain_eq
% 0.30/0.65  thf(fact_9577_literal_Odomain,axiom,
% 0.30/0.65      ( ( domain7888411570377768909iteral @ pcr_literal )
% 0.30/0.65      = ( ^ [X3: list_char] :
% 0.30/0.65          ? [Y3: list_char] :
% 0.30/0.65            ( ( list_all2_char_char
% 0.30/0.65              @ ^ [Y4: char,Z4: char] : ( Y4 = Z4 )
% 0.30/0.65              @ X3
% 0.30/0.65              @ Y3 )
% 0.30/0.65            & ! [Z3: char] :
% 0.30/0.65                ( ( member_char @ Z3 @ ( set_char2 @ Y3 ) )
% 0.30/0.65               => ~ ( digit7 @ Z3 ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % literal.domain
% 0.30/0.65  thf(fact_9578_less__eq__literal_Orsp,axiom,
% 0.30/0.65      ( bNF_re7775871201573978401char_o
% 0.30/0.65      @ ( bNF_eq_onp_list_char
% 0.30/0.65        @ ^ [Cs: list_char] :
% 0.30/0.65          ! [X3: char] :
% 0.30/0.65            ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65           => ~ ( digit7 @ X3 ) ) )
% 0.30/0.65      @ ( bNF_re6668474094832959905ar_o_o
% 0.30/0.65        @ ( bNF_eq_onp_list_char
% 0.30/0.65          @ ^ [Cs: list_char] :
% 0.30/0.65            ! [X3: char] :
% 0.30/0.65              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65             => ~ ( digit7 @ X3 ) ) )
% 0.30/0.65        @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 ) )
% 0.30/0.65      @ ( lexordp_eq_char
% 0.30/0.65        @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) ) )
% 0.30/0.65      @ ( lexordp_eq_char
% 0.30/0.65        @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % less_eq_literal.rsp
% 0.30/0.65  thf(fact_9579_less__eq__literal_Oabs__eq,axiom,
% 0.30/0.65      ! [Xa: list_char,X: list_char] :
% 0.30/0.65        ( ( bNF_eq_onp_list_char
% 0.30/0.65          @ ^ [Cs: list_char] :
% 0.30/0.65            ! [X3: char] :
% 0.30/0.65              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65             => ~ ( digit7 @ X3 ) )
% 0.30/0.65          @ Xa
% 0.30/0.65          @ Xa )
% 0.30/0.65       => ( ( bNF_eq_onp_list_char
% 0.30/0.65            @ ^ [Cs: list_char] :
% 0.30/0.65              ! [X3: char] :
% 0.30/0.65                ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65               => ~ ( digit7 @ X3 ) )
% 0.30/0.65            @ X
% 0.30/0.65            @ X )
% 0.30/0.65         => ( ( ord_less_eq_literal @ ( abs_literal @ Xa ) @ ( abs_literal @ X ) )
% 0.30/0.65            = ( lexordp_eq_char
% 0.30/0.65              @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) )
% 0.30/0.65              @ Xa
% 0.30/0.65              @ X ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % less_eq_literal.abs_eq
% 0.30/0.65  thf(fact_9580_less__literal_Oabs__eq,axiom,
% 0.30/0.65      ! [Xa: list_char,X: list_char] :
% 0.30/0.65        ( ( bNF_eq_onp_list_char
% 0.30/0.65          @ ^ [Cs: list_char] :
% 0.30/0.65            ! [X3: char] :
% 0.30/0.65              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65             => ~ ( digit7 @ X3 ) )
% 0.30/0.65          @ Xa
% 0.30/0.65          @ Xa )
% 0.30/0.65       => ( ( bNF_eq_onp_list_char
% 0.30/0.65            @ ^ [Cs: list_char] :
% 0.30/0.65              ! [X3: char] :
% 0.30/0.65                ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65               => ~ ( digit7 @ X3 ) )
% 0.30/0.65            @ X
% 0.30/0.65            @ X )
% 0.30/0.65         => ( ( ord_less_literal @ ( abs_literal @ Xa ) @ ( abs_literal @ X ) )
% 0.30/0.65            = ( lexordp_char
% 0.30/0.65              @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) )
% 0.30/0.65              @ Xa
% 0.30/0.65              @ X ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % less_literal.abs_eq
% 0.30/0.65  thf(fact_9581_literal_OAbs__literal__cases,axiom,
% 0.30/0.65      ! [X: literal] :
% 0.30/0.65        ~ ! [Y2: list_char] :
% 0.30/0.65            ( ( X
% 0.30/0.65              = ( abs_literal @ Y2 ) )
% 0.30/0.65           => ~ ( member_list_char @ Y2
% 0.30/0.65                @ ( collect_list_char
% 0.30/0.65                  @ ^ [Cs: list_char] :
% 0.30/0.65                    ! [X3: char] :
% 0.30/0.65                      ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65                     => ~ ( digit7 @ X3 ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % literal.Abs_literal_cases
% 0.30/0.65  thf(fact_9582_literal_OAbs__literal__induct,axiom,
% 0.30/0.65      ! [P: literal > $o,X: literal] :
% 0.30/0.65        ( ! [Y2: list_char] :
% 0.30/0.65            ( ( member_list_char @ Y2
% 0.30/0.65              @ ( collect_list_char
% 0.30/0.65                @ ^ [Cs: list_char] :
% 0.30/0.65                  ! [X3: char] :
% 0.30/0.65                    ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65                   => ~ ( digit7 @ X3 ) ) ) )
% 0.30/0.65           => ( P @ ( abs_literal @ Y2 ) ) )
% 0.30/0.65       => ( P @ X ) ) ).
% 0.30/0.65  
% 0.30/0.65  % literal.Abs_literal_induct
% 0.30/0.65  thf(fact_9583_literal_OAbs__literal__inject,axiom,
% 0.30/0.65      ! [X: list_char,Y: list_char] :
% 0.30/0.65        ( ( member_list_char @ X
% 0.30/0.65          @ ( collect_list_char
% 0.30/0.65            @ ^ [Cs: list_char] :
% 0.30/0.65              ! [X3: char] :
% 0.30/0.65                ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65               => ~ ( digit7 @ X3 ) ) ) )
% 0.30/0.65       => ( ( member_list_char @ Y
% 0.30/0.65            @ ( collect_list_char
% 0.30/0.65              @ ^ [Cs: list_char] :
% 0.30/0.65                ! [X3: char] :
% 0.30/0.65                  ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65                 => ~ ( digit7 @ X3 ) ) ) )
% 0.30/0.65         => ( ( ( abs_literal @ X )
% 0.30/0.65              = ( abs_literal @ Y ) )
% 0.30/0.65            = ( X = Y ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % literal.Abs_literal_inject
% 0.30/0.65  thf(fact_9584_literal_Otype__definition__literal,axiom,
% 0.30/0.65      ( type_d4752411451802217481t_char @ explode @ abs_literal
% 0.30/0.65      @ ( collect_list_char
% 0.30/0.65        @ ^ [Cs: list_char] :
% 0.30/0.65          ! [X3: char] :
% 0.30/0.65            ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65           => ~ ( digit7 @ X3 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % literal.type_definition_literal
% 0.30/0.65  thf(fact_9585_literal_OAbs__literal__inverse,axiom,
% 0.30/0.65      ! [Y: list_char] :
% 0.30/0.65        ( ( member_list_char @ Y
% 0.30/0.65          @ ( collect_list_char
% 0.30/0.65            @ ^ [Cs: list_char] :
% 0.30/0.65              ! [X3: char] :
% 0.30/0.65                ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65               => ~ ( digit7 @ X3 ) ) ) )
% 0.30/0.65       => ( ( explode @ ( abs_literal @ Y ) )
% 0.30/0.65          = Y ) ) ).
% 0.30/0.65  
% 0.30/0.65  % literal.Abs_literal_inverse
% 0.30/0.65  thf(fact_9586_plus__literal_Oabs__eq,axiom,
% 0.30/0.65      ! [Xa: list_char,X: list_char] :
% 0.30/0.65        ( ( bNF_eq_onp_list_char
% 0.30/0.65          @ ^ [Cs: list_char] :
% 0.30/0.65            ! [X3: char] :
% 0.30/0.65              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65             => ~ ( digit7 @ X3 ) )
% 0.30/0.65          @ Xa
% 0.30/0.65          @ Xa )
% 0.30/0.65       => ( ( bNF_eq_onp_list_char
% 0.30/0.65            @ ^ [Cs: list_char] :
% 0.30/0.65              ! [X3: char] :
% 0.30/0.65                ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65               => ~ ( digit7 @ X3 ) )
% 0.30/0.65            @ X
% 0.30/0.65            @ X )
% 0.30/0.65         => ( ( plus_plus_literal @ ( abs_literal @ Xa ) @ ( abs_literal @ X ) )
% 0.30/0.65            = ( abs_literal @ ( append_char @ Xa @ X ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % plus_literal.abs_eq
% 0.30/0.65  thf(fact_9587_String_OQuotient__literal,axiom,
% 0.30/0.65      ( quotie6109894551476798619iteral
% 0.30/0.65      @ ( bNF_eq_onp_list_char
% 0.30/0.65        @ ^ [Cs: list_char] :
% 0.30/0.65          ! [X3: char] :
% 0.30/0.65            ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65           => ~ ( digit7 @ X3 ) ) )
% 0.30/0.65      @ abs_literal
% 0.30/0.65      @ explode
% 0.30/0.65      @ cr_literal ) ).
% 0.30/0.65  
% 0.30/0.65  % String.Quotient_literal
% 0.30/0.65  thf(fact_9588_asciis__of__literal_Oabs__eq,axiom,
% 0.30/0.65      ! [X: list_char] :
% 0.30/0.65        ( ( bNF_eq_onp_list_char
% 0.30/0.65          @ ^ [Cs: list_char] :
% 0.30/0.65            ! [X3: char] :
% 0.30/0.65              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65             => ~ ( digit7 @ X3 ) )
% 0.30/0.65          @ X
% 0.30/0.65          @ X )
% 0.30/0.65       => ( ( asciis_of_literal @ ( abs_literal @ X ) )
% 0.30/0.65          = ( map_ch5843194146513361140nteger @ comm_s4049598766089966537nteger @ X ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % asciis_of_literal.abs_eq
% 0.30/0.65  thf(fact_9589_size__literal_Oabs__eq,axiom,
% 0.30/0.65      ! [X: list_char] :
% 0.30/0.65        ( ( bNF_eq_onp_list_char
% 0.30/0.65          @ ^ [Cs: list_char] :
% 0.30/0.65            ! [X3: char] :
% 0.30/0.65              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65             => ~ ( digit7 @ X3 ) )
% 0.30/0.65          @ X
% 0.30/0.65          @ X )
% 0.30/0.65       => ( ( size_size_literal @ ( abs_literal @ X ) )
% 0.30/0.65          = ( size_size_list_char @ X ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % size_literal.abs_eq
% 0.30/0.65  thf(fact_9590_literal_Odomain__par__left__total,axiom,
% 0.30/0.65      ! [P7: list_char > $o] :
% 0.30/0.65        ( ( left_t8440299596084406506t_char
% 0.30/0.65          @ ( list_all2_char_char
% 0.30/0.65            @ ^ [Y4: char,Z4: char] : ( Y4 = Z4 ) ) )
% 0.30/0.65       => ( ( bNF_re6668474094832959905ar_o_o
% 0.30/0.65            @ ( list_all2_char_char
% 0.30/0.65              @ ^ [Y4: char,Z4: char] : ( Y4 = Z4 ) )
% 0.30/0.65            @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 0.30/0.65            @ P7
% 0.30/0.65            @ ^ [Cs: list_char] :
% 0.30/0.65              ! [X3: char] :
% 0.30/0.65                ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65               => ~ ( digit7 @ X3 ) ) )
% 0.30/0.65         => ( ( domain7888411570377768909iteral @ pcr_literal )
% 0.30/0.65            = P7 ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % literal.domain_par_left_total
% 0.30/0.65  thf(fact_9591_literal_Odomain__par,axiom,
% 0.30/0.65      ! [DR: char > $o,P22: list_char > $o] :
% 0.30/0.65        ( ( ( domainp_char_char
% 0.30/0.65            @ ^ [Y4: char,Z4: char] : ( Y4 = Z4 ) )
% 0.30/0.65          = DR )
% 0.30/0.65       => ( ( bNF_re6668474094832959905ar_o_o
% 0.30/0.65            @ ( list_all2_char_char
% 0.30/0.65              @ ^ [Y4: char,Z4: char] : ( Y4 = Z4 ) )
% 0.30/0.65            @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 0.30/0.65            @ P22
% 0.30/0.65            @ ^ [Cs: list_char] :
% 0.30/0.65              ! [X3: char] :
% 0.30/0.65                ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65               => ~ ( digit7 @ X3 ) ) )
% 0.30/0.65         => ( ( domain7888411570377768909iteral @ pcr_literal )
% 0.30/0.65            = ( inf_inf_list_char_o @ ( list_all_char @ DR ) @ P22 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % literal.domain_par
% 0.30/0.65  thf(fact_9592_implode_Orsp,axiom,
% 0.30/0.65      ( bNF_re1407854171455731685t_char
% 0.30/0.65      @ ^ [Y4: list_char,Z4: list_char] : ( Y4 = Z4 )
% 0.30/0.65      @ ( bNF_eq_onp_list_char
% 0.30/0.65        @ ^ [Cs: list_char] :
% 0.30/0.65          ! [X3: char] :
% 0.30/0.65            ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65           => ~ ( digit7 @ X3 ) ) )
% 0.30/0.65      @ ( map_char_char @ ascii_of )
% 0.30/0.65      @ ( map_char_char @ ascii_of ) ) ).
% 0.30/0.65  
% 0.30/0.65  % implode.rsp
% 0.30/0.65  thf(fact_9593_literal__of__asciis_Orsp,axiom,
% 0.30/0.65      ( bNF_re5828396963709814525t_char
% 0.30/0.65      @ ^ [Y4: list_Code_integer,Z4: list_Code_integer] : ( Y4 = Z4 )
% 0.30/0.65      @ ( bNF_eq_onp_list_char
% 0.30/0.65        @ ^ [Cs: list_char] :
% 0.30/0.65          ! [X3: char] :
% 0.30/0.65            ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65           => ~ ( digit7 @ X3 ) ) )
% 0.30/0.65      @ ( map_Co843364623960961780r_char @ ( comp_c4562247934908617188nteger @ ascii_of @ unique1708501630192214702nteger ) )
% 0.30/0.65      @ ( map_Co843364623960961780r_char @ ( comp_c4562247934908617188nteger @ ascii_of @ unique1708501630192214702nteger ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % literal_of_asciis.rsp
% 0.30/0.65  thf(fact_9594_Literal_Oabs__eq,axiom,
% 0.30/0.65      ! [X: list_char,Xg: $o,Xf: $o,Xe: $o,Xd: $o,Xc: $o,Xb: $o,Xa: $o] :
% 0.30/0.65        ( ( bNF_eq_onp_list_char
% 0.30/0.65          @ ^ [Cs: list_char] :
% 0.30/0.65            ! [X3: char] :
% 0.30/0.65              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 0.30/0.65             => ~ ( digit7 @ X3 ) )
% 0.30/0.65          @ X
% 0.30/0.65          @ X )
% 0.30/0.65       => ( ( literal2 @ Xg @ Xf @ Xe @ Xd @ Xc @ Xb @ Xa @ ( abs_literal @ X ) )
% 0.30/0.65          = ( abs_literal @ ( cons_char @ ( char2 @ Xg @ Xf @ Xe @ Xd @ Xc @ Xb @ Xa @ $false ) @ X ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Literal.abs_eq
% 0.30/0.65  thf(fact_9595_String_OLiteral__def,axiom,
% 0.30/0.65      ( literal2
% 0.30/0.65      = ( map_fu1104370778922912482iteral @ id_o @ ( map_fu7309004089335677210iteral @ id_o @ ( map_fu1929762555066093878iteral @ id_o @ ( map_fu5333924603067766298iteral @ id_o @ ( map_fu1888220742600445322iteral @ id_o @ ( map_fu5700776415251466522iteral @ id_o @ ( map_fu4627020735845646302iteral @ id_o @ ( map_fu7398138089906338514iteral @ explode @ abs_literal ) ) ) ) ) ) )
% 0.30/0.65        @ ^ [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o] : ( cons_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ $false ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % String.Literal_def
% 0.30/0.65  thf(fact_9596_Literal_Otransfer,axiom,
% 0.30/0.65      ( bNF_re8691941649098027561iteral
% 0.30/0.65      @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 0.30/0.65      @ ( bNF_re5719858693005739489iteral
% 0.30/0.65        @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 0.30/0.65        @ ( bNF_re136309367175754621iteral
% 0.30/0.65          @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 0.30/0.65          @ ( bNF_re2365650225897248225iteral
% 0.30/0.65            @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 0.30/0.65            @ ( bNF_re5778109699181701841iteral
% 0.30/0.65              @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 0.30/0.65              @ ( bNF_re1595102025518187489iteral
% 0.30/0.65                @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 0.30/0.65                @ ( bNF_re6148748351543924773iteral
% 0.30/0.65                  @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 0.30/0.65                  @ ( bNF_re5453467372598631581iteral @ pcr_literal @ pcr_literal ) ) ) ) ) ) )
% 0.30/0.65      @ ^ [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o] : ( cons_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ $false ) )
% 0.30/0.65      @ literal2 ) ).
% 0.30/0.65  
% 0.30/0.65  % Literal.transfer
% 0.30/0.65  thf(fact_9597_cr__integer__def,axiom,
% 0.30/0.65      ( code_cr_integer
% 0.30/0.65      = ( ^ [X3: int,Y3: code_integer] :
% 0.30/0.65            ( X3
% 0.30/0.65            = ( code_int_of_integer @ Y3 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % cr_integer_def
% 0.30/0.65  thf(fact_9598_int__encode__def,axiom,
% 0.30/0.65      ( nat_int_encode
% 0.30/0.65      = ( ^ [I3: int] : ( nat_sum_encode @ ( if_Sum_sum_nat_nat @ ( ord_less_eq_int @ zero_zero_int @ I3 ) @ ( sum_Inl_nat_nat @ ( nat2 @ I3 ) ) @ ( sum_Inr_nat_nat @ ( nat2 @ ( minus_minus_int @ ( uminus_uminus_int @ I3 ) @ one_one_int ) ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % int_encode_def
% 0.30/0.65  thf(fact_9599_surj__sum__encode,axiom,
% 0.30/0.65      ( ( image_1320371278474632150at_nat @ nat_sum_encode @ top_to6661820994512907621at_nat )
% 0.30/0.65      = top_top_set_nat ) ).
% 0.30/0.65  
% 0.30/0.65  % surj_sum_encode
% 0.30/0.65  thf(fact_9600_bij__sum__encode,axiom,
% 0.30/0.65      bij_be5432664580149595207at_nat @ nat_sum_encode @ top_to6661820994512907621at_nat @ top_top_set_nat ).
% 0.30/0.65  
% 0.30/0.65  % bij_sum_encode
% 0.30/0.65  thf(fact_9601_sum__encode__def,axiom,
% 0.30/0.65      ( nat_sum_encode
% 0.30/0.65      = ( sum_ca6763686470577984908at_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.30/0.65        @ ^ [B3: nat] : ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % sum_encode_def
% 0.30/0.65  thf(fact_9602_surj__sum__decode,axiom,
% 0.30/0.65      ( ( image_678696785212003926at_nat @ nat_sum_decode @ top_top_set_nat )
% 0.30/0.65      = top_to6661820994512907621at_nat ) ).
% 0.30/0.65  
% 0.30/0.65  % surj_sum_decode
% 0.30/0.65  thf(fact_9603_bij__sum__decode,axiom,
% 0.30/0.65      bij_be4790990086886966983at_nat @ nat_sum_decode @ top_top_set_nat @ top_to6661820994512907621at_nat ).
% 0.30/0.65  
% 0.30/0.65  % bij_sum_decode
% 0.30/0.65  thf(fact_9604_nth__item_Opinduct,axiom,
% 0.30/0.65      ! [A0: nat,P: nat > $o] :
% 0.30/0.65        ( ( accp_nat @ nth_item_rel @ A0 )
% 0.30/0.65       => ( ( ( accp_nat @ nth_item_rel @ zero_zero_nat )
% 0.30/0.65           => ( P @ zero_zero_nat ) )
% 0.30/0.65         => ( ! [N3: nat] :
% 0.30/0.65                ( ( accp_nat @ nth_item_rel @ ( suc @ N3 ) )
% 0.30/0.65               => ( ! [A9: nat,Aa: nat] :
% 0.30/0.65                      ( ( ( nat_sum_decode @ N3 )
% 0.30/0.65                        = ( sum_Inl_nat_nat @ A9 ) )
% 0.30/0.65                     => ( ( ( nat_sum_decode @ A9 )
% 0.30/0.65                          = ( sum_Inl_nat_nat @ Aa ) )
% 0.30/0.65                       => ( P @ Aa ) ) )
% 0.30/0.65                 => ( ! [A9: nat,B10: nat] :
% 0.30/0.65                        ( ( ( nat_sum_decode @ N3 )
% 0.30/0.65                          = ( sum_Inl_nat_nat @ A9 ) )
% 0.30/0.65                       => ( ( ( nat_sum_decode @ A9 )
% 0.30/0.65                            = ( sum_Inr_nat_nat @ B10 ) )
% 0.30/0.65                         => ( P @ B10 ) ) )
% 0.30/0.65                   => ( ! [B10: nat,Ba: nat,X5: nat,Y5: nat] :
% 0.30/0.65                          ( ( ( nat_sum_decode @ N3 )
% 0.30/0.65                            = ( sum_Inr_nat_nat @ B10 ) )
% 0.30/0.65                         => ( ( ( nat_sum_decode @ B10 )
% 0.30/0.65                              = ( sum_Inr_nat_nat @ Ba ) )
% 0.30/0.65                           => ( ( ( product_Pair_nat_nat @ X5 @ Y5 )
% 0.30/0.65                                = ( nat_prod_decode @ Ba ) )
% 0.30/0.65                             => ( P @ X5 ) ) ) )
% 0.30/0.65                     => ( ! [B10: nat,Ba: nat,X5: nat,Y5: nat] :
% 0.30/0.65                            ( ( ( nat_sum_decode @ N3 )
% 0.30/0.65                              = ( sum_Inr_nat_nat @ B10 ) )
% 0.30/0.65                           => ( ( ( nat_sum_decode @ B10 )
% 0.30/0.65                                = ( sum_Inr_nat_nat @ Ba ) )
% 0.30/0.65                             => ( ( ( product_Pair_nat_nat @ X5 @ Y5 )
% 0.30/0.65                                  = ( nat_prod_decode @ Ba ) )
% 0.30/0.65                               => ( P @ Y5 ) ) ) )
% 0.30/0.65                       => ( P @ ( suc @ N3 ) ) ) ) ) ) )
% 0.30/0.65           => ( P @ A0 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % nth_item.pinduct
% 0.30/0.65  thf(fact_9605_int__decode__def,axiom,
% 0.30/0.65      ( nat_int_decode
% 0.30/0.65      = ( ^ [N2: nat] :
% 0.30/0.65            ( sum_ca7763040182479039464nt_nat @ semiri1314217659103216013at_int
% 0.30/0.65            @ ^ [B3: nat] : ( minus_minus_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ B3 ) ) @ one_one_int )
% 0.30/0.65            @ ( nat_sum_decode @ N2 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % int_decode_def
% 0.30/0.65  thf(fact_9606_sup__unit__def,axiom,
% 0.30/0.65      ( sup_sup_Product_unit
% 0.30/0.65      = ( ^ [Uu2: product_unit,Uv2: product_unit] : product_Unity ) ) ).
% 0.30/0.65  
% 0.30/0.65  % sup_unit_def
% 0.30/0.65  thf(fact_9607_cone__def,axiom,
% 0.30/0.65      ( bNF_Cardinal_cone
% 0.30/0.65      = ( bNF_Ca7083678892733797993t_unit @ ( insert_Product_unit @ product_Unity @ bot_bo3957492148770167129t_unit ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % cone_def
% 0.30/0.65  thf(fact_9608_bot__unit__def,axiom,
% 0.30/0.65      bot_bot_Product_unit = product_Unity ).
% 0.30/0.65  
% 0.30/0.65  % bot_unit_def
% 0.30/0.65  thf(fact_9609_uminus__unit__def,axiom,
% 0.30/0.65      ( uminus2952777764628376836t_unit
% 0.30/0.65      = ( ^ [Uu2: product_unit] : product_Unity ) ) ).
% 0.30/0.65  
% 0.30/0.65  % uminus_unit_def
% 0.30/0.65  thf(fact_9610_inf__unit__def,axiom,
% 0.30/0.65      ( inf_inf_Product_unit
% 0.30/0.65      = ( ^ [Uu2: product_unit,Uv2: product_unit] : product_Unity ) ) ).
% 0.30/0.65  
% 0.30/0.65  % inf_unit_def
% 0.30/0.65  thf(fact_9611_top__unit__def,axiom,
% 0.30/0.65      top_top_Product_unit = product_Unity ).
% 0.30/0.65  
% 0.30/0.65  % top_unit_def
% 0.30/0.65  thf(fact_9612_UNIV__unit,axiom,
% 0.30/0.65      ( top_to1996260823553986621t_unit
% 0.30/0.65      = ( insert_Product_unit @ product_Unity @ bot_bo3957492148770167129t_unit ) ) ).
% 0.30/0.65  
% 0.30/0.65  % UNIV_unit
% 0.30/0.65  thf(fact_9613_natural__zero__minus__one,axiom,
% 0.30/0.65      ( ( minus_7197305767214868737atural @ zero_z2226904508553997617atural @ one_one_Code_natural )
% 0.30/0.65      = zero_z2226904508553997617atural ) ).
% 0.30/0.65  
% 0.30/0.65  % natural_zero_minus_one
% 0.30/0.65  thf(fact_9614_log_Oelims,axiom,
% 0.30/0.65      ! [X: code_natural,Xa: code_natural,Y: code_natural] :
% 0.30/0.65        ( ( ( log @ X @ Xa )
% 0.30/0.65          = Y )
% 0.30/0.65       => ( ( ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 0.30/0.65              | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 0.30/0.65           => ( Y = one_one_Code_natural ) )
% 0.30/0.65          & ( ~ ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 0.30/0.65                | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 0.30/0.65           => ( Y
% 0.30/0.65              = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ X @ ( divide5121882707175180666atural @ Xa @ X ) ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % log.elims
% 0.30/0.65  thf(fact_9615_log_Osimps,axiom,
% 0.30/0.65      ( log
% 0.30/0.65      = ( ^ [B3: code_natural,I3: code_natural] :
% 0.30/0.65            ( if_Code_natural
% 0.30/0.65            @ ( ( ord_le1926595141338095240atural @ B3 @ one_one_Code_natural )
% 0.30/0.65              | ( ord_le5570908160329646204atural @ I3 @ B3 ) )
% 0.30/0.65            @ one_one_Code_natural
% 0.30/0.65            @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ B3 @ ( divide5121882707175180666atural @ I3 @ B3 ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % log.simps
% 0.30/0.65  thf(fact_9616_Random_Orange__def,axiom,
% 0.30/0.65      ( range
% 0.30/0.65      = ( ^ [K4: code_natural] :
% 0.30/0.65            ( produc5538323210962509403atural
% 0.30/0.65            @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ K4 )
% 0.30/0.65              @ ^ [L2: code_natural] :
% 0.30/0.65                  ( produc5538323210962509403atural @ next
% 0.30/0.65                  @ ^ [V2: code_natural] : ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ V2 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.30/0.65              @ one_one_Code_natural )
% 0.30/0.65            @ ^ [V2: code_natural] : ( produc6639722614265839536atural @ ( modulo8411746178871703098atural @ V2 @ K4 ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Random.range_def
% 0.30/0.65  thf(fact_9617_next_Osimps,axiom,
% 0.30/0.65      ! [V: code_natural,W: code_natural] :
% 0.30/0.65        ( ( next @ ( produc3574140220909816553atural @ V @ W ) )
% 0.30/0.65        = ( 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 @ W @ ( 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 @ W @ ( 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 @ W @ ( 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 @ W @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % next.simps
% 0.30/0.65  thf(fact_9618_log_Ocases,axiom,
% 0.30/0.65      ! [X: produc7822875418678951345atural] :
% 0.30/0.65        ~ ! [B6: code_natural,I2: code_natural] :
% 0.30/0.65            ( X
% 0.30/0.65           != ( produc3574140220909816553atural @ B6 @ I2 ) ) ).
% 0.30/0.65  
% 0.30/0.65  % log.cases
% 0.30/0.65  thf(fact_9619_full__exhaustive__natural_H_Ocases,axiom,
% 0.30/0.65      ! [X: produc989692990947075319atural] :
% 0.30/0.65        ~ ! [F3: produc4972180933644002618e_term > option6357759511663192854e_term,D: code_natural,I2: code_natural] :
% 0.30/0.65            ( X
% 0.30/0.65           != ( produc3831813291587773865atural @ F3 @ ( produc3574140220909816553atural @ D @ I2 ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % full_exhaustive_natural'.cases
% 0.30/0.65  thf(fact_9620_exhaustive__natural_H_Ocases,axiom,
% 0.30/0.65      ! [X: produc8731074985263844745atural] :
% 0.30/0.65        ~ ! [F3: code_natural > option6357759511663192854e_term,D: code_natural,I2: code_natural] :
% 0.30/0.65            ( X
% 0.30/0.65           != ( produc2252593628808123835atural @ F3 @ ( produc3574140220909816553atural @ D @ I2 ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % exhaustive_natural'.cases
% 0.30/0.65  thf(fact_9621_split__seed__def,axiom,
% 0.30/0.65      ( split_seed
% 0.30/0.65      = ( ^ [S2: produc7822875418678951345atural] :
% 0.30/0.65            ( produc8282080750456430313atural
% 0.30/0.65            @ ^ [V2: code_natural,W3: code_natural] :
% 0.30/0.65                ( produc8282080750456430313atural
% 0.30/0.65                @ ^ [V3: 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ V2 ) @ W4 ) @ ( produc3574140220909816553atural @ V3 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ W3 ) ) )
% 0.30/0.65                @ ( produc6591912806276919810atural @ ( next @ S2 ) ) )
% 0.30/0.65            @ S2 ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % split_seed_def
% 0.30/0.65  thf(fact_9622_inc__shift__def,axiom,
% 0.30/0.65      ( inc_shift
% 0.30/0.65      = ( ^ [V2: code_natural,K4: code_natural] : ( if_Code_natural @ ( V2 = K4 ) @ one_one_Code_natural @ ( plus_p4538020629002901425atural @ K4 @ one_one_Code_natural ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % inc_shift_def
% 0.30/0.65  thf(fact_9623_log_Opelims,axiom,
% 0.30/0.65      ! [X: code_natural,Xa: code_natural,Y: code_natural] :
% 0.30/0.65        ( ( ( log @ X @ Xa )
% 0.30/0.65          = Y )
% 0.30/0.65       => ( ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X @ Xa ) )
% 0.30/0.65         => ~ ( ( ( ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 0.30/0.65                    | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 0.30/0.65                 => ( Y = one_one_Code_natural ) )
% 0.30/0.65                & ( ~ ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 0.30/0.65                      | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 0.30/0.65                 => ( Y
% 0.30/0.65                    = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ X @ ( divide5121882707175180666atural @ Xa @ X ) ) ) ) ) )
% 0.30/0.65             => ~ ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X @ Xa ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % log.pelims
% 0.30/0.65  thf(fact_9624_one__natural__def,axiom,
% 0.30/0.65      ( one_one_Code_natural
% 0.30/0.65      = ( code_natural_of_nat @ one_one_nat ) ) ).
% 0.30/0.65  
% 0.30/0.65  % one_natural_def
% 0.30/0.65  thf(fact_9625_natural__of__nat__cases,axiom,
% 0.30/0.65      ! [X: code_natural] :
% 0.30/0.65        ~ ! [Y2: nat] :
% 0.30/0.65            ( ( X
% 0.30/0.65              = ( code_natural_of_nat @ Y2 ) )
% 0.30/0.65           => ~ ( member_nat @ Y2 @ top_top_set_nat ) ) ).
% 0.30/0.65  
% 0.30/0.65  % natural_of_nat_cases
% 0.30/0.65  thf(fact_9626_natural__of__nat__induct,axiom,
% 0.30/0.65      ! [P: code_natural > $o,X: code_natural] :
% 0.30/0.65        ( ! [Y2: nat] :
% 0.30/0.65            ( ( member_nat @ Y2 @ top_top_set_nat )
% 0.30/0.65           => ( P @ ( code_natural_of_nat @ Y2 ) ) )
% 0.30/0.65       => ( P @ X ) ) ).
% 0.30/0.65  
% 0.30/0.65  % natural_of_nat_induct
% 0.30/0.65  thf(fact_9627_natural__of__nat__inject,axiom,
% 0.30/0.65      ! [X: nat,Y: nat] :
% 0.30/0.65        ( ( member_nat @ X @ top_top_set_nat )
% 0.30/0.65       => ( ( member_nat @ Y @ top_top_set_nat )
% 0.30/0.65         => ( ( ( code_natural_of_nat @ X )
% 0.30/0.65              = ( code_natural_of_nat @ Y ) )
% 0.30/0.65            = ( X = Y ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % natural_of_nat_inject
% 0.30/0.65  thf(fact_9628_one__natural_Orep__eq,axiom,
% 0.30/0.65      ( ( code_nat_of_natural @ one_one_Code_natural )
% 0.30/0.65      = one_one_nat ) ).
% 0.30/0.65  
% 0.30/0.65  % one_natural.rep_eq
% 0.30/0.65  thf(fact_9629_type__definition__natural,axiom,
% 0.30/0.65      type_d4410041424927559462al_nat @ code_nat_of_natural @ code_natural_of_nat @ top_top_set_nat ).
% 0.30/0.65  
% 0.30/0.65  % type_definition_natural
% 0.30/0.65  thf(fact_9630_natural__of__nat__inverse,axiom,
% 0.30/0.65      ! [Y: nat] :
% 0.30/0.65        ( ( member_nat @ Y @ top_top_set_nat )
% 0.30/0.65       => ( ( code_nat_of_natural @ ( code_natural_of_nat @ Y ) )
% 0.30/0.65          = Y ) ) ).
% 0.30/0.65  
% 0.30/0.65  % natural_of_nat_inverse
% 0.30/0.65  thf(fact_9631_nat__of__natural__induct,axiom,
% 0.30/0.65      ! [Y: nat,P: nat > $o] :
% 0.30/0.65        ( ( member_nat @ Y @ top_top_set_nat )
% 0.30/0.65       => ( ! [X2: code_natural] : ( P @ ( code_nat_of_natural @ X2 ) )
% 0.30/0.65         => ( P @ Y ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % nat_of_natural_induct
% 0.30/0.65  thf(fact_9632_nat__of__natural__cases,axiom,
% 0.30/0.65      ! [Y: nat] :
% 0.30/0.65        ( ( member_nat @ Y @ top_top_set_nat )
% 0.30/0.65       => ~ ! [X2: code_natural] :
% 0.30/0.65              ( Y
% 0.30/0.65             != ( code_nat_of_natural @ X2 ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % nat_of_natural_cases
% 0.30/0.65  thf(fact_9633_nat__of__natural,axiom,
% 0.30/0.65      ! [X: code_natural] : ( member_nat @ ( code_nat_of_natural @ X ) @ top_top_set_nat ) ).
% 0.30/0.65  
% 0.30/0.65  % nat_of_natural
% 0.30/0.65  thf(fact_9634_cr__natural__def,axiom,
% 0.30/0.65      ( code_cr_natural
% 0.30/0.65      = ( ^ [X3: nat,Y3: code_natural] :
% 0.30/0.65            ( X3
% 0.30/0.65            = ( code_nat_of_natural @ Y3 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % cr_natural_def
% 0.30/0.65  thf(fact_9635_INFM__nat,axiom,
% 0.30/0.65      ! [P: nat > $o] :
% 0.30/0.65        ( ( frequently_nat @ P @ cofinite_nat )
% 0.30/0.65        = ( ! [M2: nat] :
% 0.30/0.65            ? [N2: nat] :
% 0.30/0.65              ( ( ord_less_nat @ M2 @ N2 )
% 0.30/0.65              & ( P @ N2 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % INFM_nat
% 0.30/0.65  thf(fact_9636_INFM__nat__le,axiom,
% 0.30/0.65      ! [P: nat > $o] :
% 0.30/0.65        ( ( frequently_nat @ P @ cofinite_nat )
% 0.30/0.65        = ( ! [M2: nat] :
% 0.30/0.65            ? [N2: nat] :
% 0.30/0.65              ( ( ord_less_eq_nat @ M2 @ N2 )
% 0.30/0.65              & ( P @ N2 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % INFM_nat_le
% 0.30/0.65  thf(fact_9637_INFM__nat__inductI,axiom,
% 0.30/0.65      ! [P: nat > $o,Q2: nat > $o] :
% 0.30/0.65        ( ( P @ zero_zero_nat )
% 0.30/0.65       => ( ! [I2: nat] :
% 0.30/0.65              ( ( P @ I2 )
% 0.30/0.65             => ? [J4: nat] :
% 0.30/0.65                  ( ( ord_less_nat @ I2 @ J4 )
% 0.30/0.65                  & ( P @ J4 )
% 0.30/0.65                  & ( Q2 @ J4 ) ) )
% 0.30/0.65         => ( frequently_nat @ Q2 @ cofinite_nat ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % INFM_nat_inductI
% 0.30/0.65  thf(fact_9638_integer__of__nat__1,axiom,
% 0.30/0.65      ( ( code_integer_of_nat @ one_one_nat )
% 0.30/0.65      = one_one_Code_integer ) ).
% 0.30/0.65  
% 0.30/0.65  % integer_of_nat_1
% 0.30/0.65  thf(fact_9639_Lcm__abs__eq,axiom,
% 0.30/0.65      ! [K5: set_int] :
% 0.30/0.65        ( ( gcd_Lcm_int @ ( image_int_int @ abs_abs_int @ K5 ) )
% 0.30/0.65        = ( gcd_Lcm_int @ K5 ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Lcm_abs_eq
% 0.30/0.65  thf(fact_9640_Lcm__int__eq,axiom,
% 0.30/0.65      ! [N4: set_nat] :
% 0.30/0.65        ( ( gcd_Lcm_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N4 ) )
% 0.30/0.65        = ( semiri1314217659103216013at_int @ ( gcd_Lcm_nat @ N4 ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Lcm_int_eq
% 0.30/0.65  thf(fact_9641_Lcm__nat__abs__eq,axiom,
% 0.30/0.65      ! [K5: set_int] :
% 0.30/0.65        ( ( gcd_Lcm_nat
% 0.30/0.65          @ ( image_int_nat
% 0.30/0.65            @ ^ [K4: int] : ( nat2 @ ( abs_abs_int @ K4 ) )
% 0.30/0.65            @ K5 ) )
% 0.30/0.65        = ( nat2 @ ( gcd_Lcm_int @ K5 ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Lcm_nat_abs_eq
% 0.30/0.65  thf(fact_9642_Lcm__nat__empty,axiom,
% 0.30/0.65      ( ( gcd_Lcm_nat @ bot_bot_set_nat )
% 0.30/0.65      = one_one_nat ) ).
% 0.30/0.65  
% 0.30/0.65  % Lcm_nat_empty
% 0.30/0.65  thf(fact_9643_Gcd__nat__def,axiom,
% 0.30/0.65      ( gcd_Gcd_nat
% 0.30/0.65      = ( ^ [M7: set_nat] :
% 0.30/0.65            ( gcd_Lcm_nat
% 0.30/0.65            @ ( collect_nat
% 0.30/0.65              @ ^ [D4: nat] :
% 0.30/0.65                ! [X3: nat] :
% 0.30/0.65                  ( ( member_nat @ X3 @ M7 )
% 0.30/0.65                 => ( dvd_dvd_nat @ D4 @ X3 ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Gcd_nat_def
% 0.30/0.65  thf(fact_9644_Lcm__int__def,axiom,
% 0.30/0.65      ( gcd_Lcm_int
% 0.30/0.65      = ( ^ [K6: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Lcm_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K6 ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Lcm_int_def
% 0.30/0.65  thf(fact_9645_Lcm__eq__Max__nat,axiom,
% 0.30/0.65      ! [M4: set_nat] :
% 0.30/0.65        ( ( finite_finite_nat @ M4 )
% 0.30/0.65       => ( ( M4 != bot_bot_set_nat )
% 0.30/0.65         => ( ~ ( member_nat @ zero_zero_nat @ M4 )
% 0.30/0.65           => ( ! [M3: nat,N3: nat] :
% 0.30/0.65                  ( ( member_nat @ M3 @ M4 )
% 0.30/0.65                 => ( ( member_nat @ N3 @ M4 )
% 0.30/0.65                   => ( member_nat @ ( gcd_lcm_nat @ M3 @ N3 ) @ M4 ) ) )
% 0.30/0.65             => ( ( gcd_Lcm_nat @ M4 )
% 0.30/0.65                = ( lattic8265883725875713057ax_nat @ M4 ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Lcm_eq_Max_nat
% 0.30/0.65  thf(fact_9646_Lcm__nat__set__eq__fold,axiom,
% 0.30/0.65      ! [Xs: list_nat] :
% 0.30/0.65        ( ( gcd_Lcm_nat @ ( set_nat2 @ Xs ) )
% 0.30/0.65        = ( fold_nat_nat @ gcd_lcm_nat @ Xs @ one_one_nat ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Lcm_nat_set_eq_fold
% 0.30/0.65  thf(fact_9647_Lcm__in__lcm__closed__set__nat,axiom,
% 0.30/0.65      ! [M4: set_nat] :
% 0.30/0.65        ( ( finite_finite_nat @ M4 )
% 0.30/0.65       => ( ( M4 != bot_bot_set_nat )
% 0.30/0.65         => ( ! [M3: nat,N3: nat] :
% 0.30/0.65                ( ( member_nat @ M3 @ M4 )
% 0.30/0.65               => ( ( member_nat @ N3 @ M4 )
% 0.30/0.65                 => ( member_nat @ ( gcd_lcm_nat @ M3 @ N3 ) @ M4 ) ) )
% 0.30/0.65           => ( member_nat @ ( gcd_Lcm_nat @ M4 ) @ M4 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Lcm_in_lcm_closed_set_nat
% 0.30/0.65  thf(fact_9648_Lcm__nat__def,axiom,
% 0.30/0.65      ( gcd_Lcm_nat
% 0.30/0.65      = ( ^ [M7: set_nat] : ( if_nat @ ( finite_finite_nat @ M7 ) @ ( lattic7826324295020591184_F_nat @ gcd_lcm_nat @ one_one_nat @ M7 ) @ zero_zero_nat ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Lcm_nat_def
% 0.30/0.65  thf(fact_9649_lcm__1__iff__int,axiom,
% 0.30/0.65      ! [M: int,N: int] :
% 0.30/0.65        ( ( ( gcd_lcm_int @ M @ N )
% 0.30/0.65          = one_one_int )
% 0.30/0.65        = ( ( ( M = one_one_int )
% 0.30/0.65            | ( M
% 0.30/0.65              = ( uminus_uminus_int @ one_one_int ) ) )
% 0.30/0.65          & ( ( N = one_one_int )
% 0.30/0.65            | ( N
% 0.30/0.65              = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % lcm_1_iff_int
% 0.30/0.65  thf(fact_9650_lcm__neg1__int,axiom,
% 0.30/0.65      ! [X: int,Y: int] :
% 0.30/0.65        ( ( gcd_lcm_int @ ( uminus_uminus_int @ X ) @ Y )
% 0.30/0.65        = ( gcd_lcm_int @ X @ Y ) ) ).
% 0.30/0.65  
% 0.30/0.65  % lcm_neg1_int
% 0.30/0.65  thf(fact_9651_lcm__neg2__int,axiom,
% 0.30/0.65      ! [X: int,Y: int] :
% 0.30/0.65        ( ( gcd_lcm_int @ X @ ( uminus_uminus_int @ Y ) )
% 0.30/0.65        = ( gcd_lcm_int @ X @ Y ) ) ).
% 0.30/0.65  
% 0.30/0.65  % lcm_neg2_int
% 0.30/0.65  thf(fact_9652_lcm__cases__int,axiom,
% 0.30/0.65      ! [X: int,Y: int,P: int > $o] :
% 0.30/0.65        ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.30/0.65         => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.30/0.65           => ( P @ ( gcd_lcm_int @ X @ Y ) ) ) )
% 0.30/0.65       => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.30/0.65           => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 0.30/0.65             => ( P @ ( gcd_lcm_int @ X @ ( uminus_uminus_int @ Y ) ) ) ) )
% 0.30/0.65         => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 0.30/0.65             => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.30/0.65               => ( P @ ( gcd_lcm_int @ ( uminus_uminus_int @ X ) @ Y ) ) ) )
% 0.30/0.65           => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 0.30/0.65               => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 0.30/0.65                 => ( P @ ( gcd_lcm_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 0.30/0.65             => ( P @ ( gcd_lcm_int @ X @ Y ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % lcm_cases_int
% 0.30/0.65  thf(fact_9653_Lcm__int__set__eq__fold,axiom,
% 0.30/0.65      ! [Xs: list_int] :
% 0.30/0.65        ( ( gcd_Lcm_int @ ( set_int2 @ Xs ) )
% 0.30/0.65        = ( fold_int_int @ gcd_lcm_int @ Xs @ one_one_int ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Lcm_int_set_eq_fold
% 0.30/0.65  thf(fact_9654_unit__factor__simps_I2_J,axiom,
% 0.30/0.65      ! [N: nat] :
% 0.30/0.65        ( ( unit_f2748546683901255202or_nat @ ( suc @ N ) )
% 0.30/0.65        = one_one_nat ) ).
% 0.30/0.65  
% 0.30/0.65  % unit_factor_simps(2)
% 0.30/0.65  thf(fact_9655_unit__factor__nat__def,axiom,
% 0.30/0.65      ( unit_f2748546683901255202or_nat
% 0.30/0.65      = ( ^ [N2: nat] : ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat @ one_one_nat ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % unit_factor_nat_def
% 0.30/0.65  thf(fact_9656_unit__pred__cases,axiom,
% 0.30/0.65      ! [P: pred_Product_unit > $o,Q2: pred_Product_unit] :
% 0.30/0.65        ( ( P @ bot_bo2717538794563056311t_unit )
% 0.30/0.65       => ( ( P @ ( single_Product_unit @ product_Unity ) )
% 0.30/0.65         => ( P @ Q2 ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % unit_pred_cases
% 0.30/0.65  thf(fact_9657_Random__Pred_Onot__randompred__def,axiom,
% 0.30/0.65      ( random6974930770145893639ompred
% 0.30/0.65      = ( ^ [P2: produc7822875418678951345atural > produc4675096598859438275atural,S2: produc7822875418678951345atural] :
% 0.30/0.65            ( produc6665183775751917029atural
% 0.30/0.65            @ ^ [P8: pred_Product_unit,S7: produc7822875418678951345atural] : ( if_Pro3444522238938527101atural @ ( eval_Product_unit @ P8 @ product_Unity ) @ ( produc5069803637994805237atural @ bot_bo2717538794563056311t_unit @ S7 ) @ ( produc5069803637994805237atural @ ( single_Product_unit @ product_Unity ) @ S7 ) )
% 0.30/0.65            @ ( P2 @ S2 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Random_Pred.not_randompred_def
% 0.30/0.65  thf(fact_9658_not__pred__eq,axiom,
% 0.30/0.65      ( not_pred
% 0.30/0.65      = ( ^ [P2: pred_Product_unit] : ( if_pred_Product_unit @ ( eval_Product_unit @ P2 @ product_Unity ) @ bot_bo2717538794563056311t_unit @ ( single_Product_unit @ product_Unity ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % not_pred_eq
% 0.30/0.65  thf(fact_9659_if__pred__eq,axiom,
% 0.30/0.65      ( if_pred
% 0.30/0.65      = ( ^ [B3: $o] : ( if_pred_Product_unit @ B3 @ ( single_Product_unit @ product_Unity ) @ bot_bo2717538794563056311t_unit ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % if_pred_eq
% 0.30/0.65  thf(fact_9660_not__predE,axiom,
% 0.30/0.65      ! [P: $o,X: product_unit] :
% 0.30/0.65        ( ( eval_Product_unit
% 0.30/0.65          @ ( not_pred
% 0.30/0.65            @ ( pred_Product_unit2
% 0.30/0.65              @ ^ [U2: product_unit] : P ) )
% 0.30/0.65          @ X )
% 0.30/0.65       => ~ P ) ).
% 0.30/0.65  
% 0.30/0.65  % not_predE
% 0.30/0.65  thf(fact_9661_not__predI,axiom,
% 0.30/0.65      ! [P: $o] :
% 0.30/0.65        ( ~ P
% 0.30/0.65       => ( eval_Product_unit
% 0.30/0.65          @ ( not_pred
% 0.30/0.65            @ ( pred_Product_unit2
% 0.30/0.65              @ ^ [U2: product_unit] : P ) )
% 0.30/0.65          @ product_Unity ) ) ).
% 0.30/0.65  
% 0.30/0.65  % not_predI
% 0.30/0.65  thf(fact_9662_nat__of__num__code_I3_J,axiom,
% 0.30/0.65      ! [N: num] :
% 0.30/0.65        ( ( nat_of_num @ ( bit1 @ N ) )
% 0.30/0.65        = ( suc @ ( plus_plus_nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % nat_of_num_code(3)
% 0.30/0.65  thf(fact_9663_nat__of__num__code_I1_J,axiom,
% 0.30/0.65      ( ( nat_of_num @ one )
% 0.30/0.65      = one_one_nat ) ).
% 0.30/0.65  
% 0.30/0.65  % nat_of_num_code(1)
% 0.30/0.65  thf(fact_9664_nat__of__num__code_I2_J,axiom,
% 0.30/0.65      ! [N: num] :
% 0.30/0.65        ( ( nat_of_num @ ( bit0 @ N ) )
% 0.30/0.65        = ( plus_plus_nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % nat_of_num_code(2)
% 0.30/0.65  thf(fact_9665_Suc__natural__minus__one,axiom,
% 0.30/0.65      ! [N: code_natural] :
% 0.30/0.65        ( ( minus_7197305767214868737atural @ ( code_Suc @ N ) @ one_one_Code_natural )
% 0.30/0.65        = N ) ).
% 0.30/0.65  
% 0.30/0.65  % Suc_natural_minus_one
% 0.30/0.65  thf(fact_9666_gcd__nat_Osemilattice__order__axioms,axiom,
% 0.30/0.65      ( semila1248733672344298208er_nat @ gcd_gcd_nat @ dvd_dvd_nat
% 0.30/0.65      @ ^ [M2: nat,N2: nat] :
% 0.30/0.65          ( ( dvd_dvd_nat @ M2 @ N2 )
% 0.30/0.65          & ( M2 != N2 ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % gcd_nat.semilattice_order_axioms
% 0.30/0.65  thf(fact_9667_random__aux__set_Ocases,axiom,
% 0.30/0.65      ! [X: produc7822875418678951345atural] :
% 0.30/0.65        ( ! [J2: code_natural] :
% 0.30/0.65            ( X
% 0.30/0.65           != ( produc3574140220909816553atural @ zero_z2226904508553997617atural @ J2 ) )
% 0.30/0.65       => ~ ! [I2: code_natural,J2: code_natural] :
% 0.30/0.65              ( X
% 0.30/0.65             != ( produc3574140220909816553atural @ ( code_Suc @ I2 ) @ J2 ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % random_aux_set.cases
% 0.30/0.65  thf(fact_9668_or__num_Opelims,axiom,
% 0.30/0.65      ! [X: num,Xa: num,Y: num] :
% 0.30/0.65        ( ( ( bit_un6697907153464112080or_num @ X @ Xa )
% 0.30/0.65          = Y )
% 0.30/0.65       => ( ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 0.30/0.65         => ( ( ( X = one )
% 0.30/0.65             => ( ( Xa = one )
% 0.30/0.65               => ( ( Y = one )
% 0.30/0.65                 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 0.30/0.65           => ( ( ( X = one )
% 0.30/0.65               => ! [N3: num] :
% 0.30/0.65                    ( ( Xa
% 0.30/0.65                      = ( bit0 @ N3 ) )
% 0.30/0.65                   => ( ( Y
% 0.30/0.65                        = ( bit1 @ N3 ) )
% 0.30/0.65                     => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 0.30/0.65             => ( ( ( X = one )
% 0.30/0.65                 => ! [N3: num] :
% 0.30/0.65                      ( ( Xa
% 0.30/0.65                        = ( bit1 @ N3 ) )
% 0.30/0.65                     => ( ( Y
% 0.30/0.65                          = ( bit1 @ N3 ) )
% 0.30/0.65                       => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 0.30/0.65               => ( ! [M3: num] :
% 0.30/0.65                      ( ( X
% 0.30/0.65                        = ( bit0 @ M3 ) )
% 0.30/0.65                     => ( ( Xa = one )
% 0.30/0.65                       => ( ( Y
% 0.30/0.65                            = ( bit1 @ M3 ) )
% 0.30/0.65                         => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ one ) ) ) ) )
% 0.30/0.65                 => ( ! [M3: num] :
% 0.30/0.65                        ( ( X
% 0.30/0.65                          = ( bit0 @ M3 ) )
% 0.30/0.65                       => ! [N3: num] :
% 0.30/0.65                            ( ( Xa
% 0.30/0.65                              = ( bit0 @ N3 ) )
% 0.30/0.65                           => ( ( Y
% 0.30/0.65                                = ( bit0 @ ( bit_un6697907153464112080or_num @ M3 @ N3 ) ) )
% 0.30/0.65                             => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 0.30/0.65                   => ( ! [M3: num] :
% 0.30/0.65                          ( ( X
% 0.30/0.65                            = ( bit0 @ M3 ) )
% 0.30/0.65                         => ! [N3: num] :
% 0.30/0.65                              ( ( Xa
% 0.30/0.65                                = ( bit1 @ N3 ) )
% 0.30/0.65                             => ( ( Y
% 0.30/0.65                                  = ( bit1 @ ( bit_un6697907153464112080or_num @ M3 @ N3 ) ) )
% 0.30/0.65                               => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 0.30/0.65                     => ( ! [M3: num] :
% 0.30/0.65                            ( ( X
% 0.30/0.65                              = ( bit1 @ M3 ) )
% 0.30/0.65                           => ( ( Xa = one )
% 0.30/0.65                             => ( ( Y
% 0.30/0.65                                  = ( bit1 @ M3 ) )
% 0.30/0.65                               => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ one ) ) ) ) )
% 0.30/0.65                       => ( ! [M3: num] :
% 0.30/0.65                              ( ( X
% 0.30/0.65                                = ( bit1 @ M3 ) )
% 0.30/0.65                             => ! [N3: num] :
% 0.30/0.65                                  ( ( Xa
% 0.30/0.65                                    = ( bit0 @ N3 ) )
% 0.30/0.65                                 => ( ( Y
% 0.30/0.65                                      = ( bit1 @ ( bit_un6697907153464112080or_num @ M3 @ N3 ) ) )
% 0.30/0.65                                   => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 0.30/0.65                         => ~ ! [M3: num] :
% 0.30/0.65                                ( ( X
% 0.30/0.65                                  = ( bit1 @ M3 ) )
% 0.30/0.65                               => ! [N3: num] :
% 0.30/0.65                                    ( ( Xa
% 0.30/0.65                                      = ( bit1 @ N3 ) )
% 0.30/0.65                                   => ( ( Y
% 0.30/0.65                                        = ( bit1 @ ( bit_un6697907153464112080or_num @ M3 @ N3 ) ) )
% 0.30/0.65                                     => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % or_num.pelims
% 0.30/0.65  thf(fact_9669_less__nat__rel,axiom,
% 0.30/0.65      ( ord_less_nat
% 0.30/0.65      = ( transi2163837189807498211lp_nat
% 0.30/0.65        @ ^ [M2: nat,N2: nat] :
% 0.30/0.65            ( N2
% 0.30/0.65            = ( suc @ M2 ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % less_nat_rel
% 0.30/0.65  thf(fact_9670_sub_Otransfer,axiom,
% 0.30/0.65      ( bNF_re7876454716742015248nteger
% 0.30/0.65      @ ^ [Y4: num,Z4: num] : ( Y4 = Z4 )
% 0.30/0.65      @ ( bNF_re6501075790457514782nteger
% 0.30/0.65        @ ^ [Y4: num,Z4: num] : ( Y4 = Z4 )
% 0.30/0.65        @ code_pcr_integer )
% 0.30/0.65      @ ^ [M2: num,N2: num] : ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 0.30/0.65      @ code_sub ) ).
% 0.30/0.65  
% 0.30/0.65  % sub.transfer
% 0.30/0.65  thf(fact_9671_uminus__integer_Otransfer,axiom,
% 0.30/0.65      bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ uminus_uminus_int @ uminus1351360451143612070nteger ).
% 0.30/0.65  
% 0.30/0.65  % uminus_integer.transfer
% 0.30/0.65  thf(fact_9672_integer_Oid__abs__transfer,axiom,
% 0.30/0.65      ( bNF_re982302072995117890nteger
% 0.30/0.65      @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 0.30/0.65      @ code_pcr_integer
% 0.30/0.65      @ ^ [X3: int] : X3
% 0.30/0.65      @ code_integer_of_int ) ).
% 0.30/0.65  
% 0.30/0.65  % integer.id_abs_transfer
% 0.30/0.65  thf(fact_9673_integer_Orep__transfer,axiom,
% 0.30/0.65      ( bNF_re3804157879324367682nt_int @ code_pcr_integer
% 0.30/0.65      @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 0.30/0.65      @ ^ [X3: int] : X3
% 0.30/0.65      @ code_int_of_integer ) ).
% 0.30/0.65  
% 0.30/0.65  % integer.rep_transfer
% 0.30/0.65  thf(fact_9674_dup_Otransfer,axiom,
% 0.30/0.65      ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer
% 0.30/0.65      @ ^ [K4: int] : ( plus_plus_int @ K4 @ K4 )
% 0.30/0.65      @ code_dup ) ).
% 0.30/0.65  
% 0.30/0.65  % dup.transfer
% 0.30/0.65  thf(fact_9675_one__integer_Otransfer,axiom,
% 0.30/0.65      code_pcr_integer @ one_one_int @ one_one_Code_integer ).
% 0.30/0.65  
% 0.30/0.65  % one_integer.transfer
% 0.30/0.65  thf(fact_9676_gcd__nat_Oordering__axioms,axiom,
% 0.30/0.65      ( ordering_nat @ dvd_dvd_nat
% 0.30/0.65      @ ^ [M2: nat,N2: nat] :
% 0.30/0.65          ( ( dvd_dvd_nat @ M2 @ N2 )
% 0.30/0.65          & ( M2 != N2 ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % gcd_nat.ordering_axioms
% 0.30/0.65  thf(fact_9677_Abs__int__cases,axiom,
% 0.30/0.65      ! [X: int] :
% 0.30/0.65        ~ ! [Y2: set_Pr1261947904930325089at_nat] :
% 0.30/0.65            ( ( X
% 0.30/0.65              = ( abs_int @ Y2 ) )
% 0.30/0.65           => ~ ( member2643936169264416010at_nat @ Y2
% 0.30/0.65                @ ( collec5514110066124741708at_nat
% 0.30/0.65                  @ ^ [C4: set_Pr1261947904930325089at_nat] :
% 0.30/0.65                    ? [X3: product_prod_nat_nat] :
% 0.30/0.65                      ( ( intrel @ X3 @ X3 )
% 0.30/0.65                      & ( C4
% 0.30/0.65                        = ( collec3392354462482085612at_nat @ ( intrel @ X3 ) ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Abs_int_cases
% 0.30/0.65  thf(fact_9678_Abs__int__induct,axiom,
% 0.30/0.65      ! [P: int > $o,X: int] :
% 0.30/0.65        ( ! [Y2: set_Pr1261947904930325089at_nat] :
% 0.30/0.65            ( ( member2643936169264416010at_nat @ Y2
% 0.30/0.65              @ ( collec5514110066124741708at_nat
% 0.30/0.65                @ ^ [C4: set_Pr1261947904930325089at_nat] :
% 0.30/0.65                  ? [X3: product_prod_nat_nat] :
% 0.30/0.65                    ( ( intrel @ X3 @ X3 )
% 0.30/0.65                    & ( C4
% 0.30/0.65                      = ( collec3392354462482085612at_nat @ ( intrel @ X3 ) ) ) ) ) )
% 0.30/0.65           => ( P @ ( abs_int @ Y2 ) ) )
% 0.30/0.65       => ( P @ X ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Abs_int_induct
% 0.30/0.65  thf(fact_9679_Abs__int__inject,axiom,
% 0.30/0.65      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.30/0.65        ( ( member2643936169264416010at_nat @ X
% 0.30/0.65          @ ( collec5514110066124741708at_nat
% 0.30/0.65            @ ^ [C4: set_Pr1261947904930325089at_nat] :
% 0.30/0.65              ? [X3: product_prod_nat_nat] :
% 0.30/0.65                ( ( intrel @ X3 @ X3 )
% 0.30/0.65                & ( C4
% 0.30/0.65                  = ( collec3392354462482085612at_nat @ ( intrel @ X3 ) ) ) ) ) )
% 0.30/0.65       => ( ( member2643936169264416010at_nat @ Y
% 0.30/0.65            @ ( collec5514110066124741708at_nat
% 0.30/0.65              @ ^ [C4: set_Pr1261947904930325089at_nat] :
% 0.30/0.65                ? [X3: product_prod_nat_nat] :
% 0.30/0.65                  ( ( intrel @ X3 @ X3 )
% 0.30/0.65                  & ( C4
% 0.30/0.65                    = ( collec3392354462482085612at_nat @ ( intrel @ X3 ) ) ) ) ) )
% 0.30/0.65         => ( ( ( abs_int @ X )
% 0.30/0.65              = ( abs_int @ Y ) )
% 0.30/0.65            = ( X = Y ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Abs_int_inject
% 0.30/0.65  thf(fact_9680_Abs__int__inverse,axiom,
% 0.30/0.65      ! [Y: set_Pr1261947904930325089at_nat] :
% 0.30/0.65        ( ( member2643936169264416010at_nat @ Y
% 0.30/0.65          @ ( collec5514110066124741708at_nat
% 0.30/0.65            @ ^ [C4: set_Pr1261947904930325089at_nat] :
% 0.30/0.65              ? [X3: product_prod_nat_nat] :
% 0.30/0.65                ( ( intrel @ X3 @ X3 )
% 0.30/0.65                & ( C4
% 0.30/0.65                  = ( collec3392354462482085612at_nat @ ( intrel @ X3 ) ) ) ) ) )
% 0.30/0.65       => ( ( rep_int @ ( abs_int @ Y ) )
% 0.30/0.65          = Y ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Abs_int_inverse
% 0.30/0.65  thf(fact_9681_type__definition__int,axiom,
% 0.30/0.65      ( type_d8752208705193531015at_nat @ rep_int @ abs_int
% 0.30/0.65      @ ( collec5514110066124741708at_nat
% 0.30/0.65        @ ^ [C4: set_Pr1261947904930325089at_nat] :
% 0.30/0.65          ? [X3: product_prod_nat_nat] :
% 0.30/0.65            ( ( intrel @ X3 @ X3 )
% 0.30/0.65            & ( C4
% 0.30/0.65              = ( collec3392354462482085612at_nat @ ( intrel @ X3 ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % type_definition_int
% 0.30/0.65  thf(fact_9682_Rep__int__induct,axiom,
% 0.30/0.65      ! [Y: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 0.30/0.65        ( ( member2643936169264416010at_nat @ Y
% 0.30/0.65          @ ( collec5514110066124741708at_nat
% 0.30/0.65            @ ^ [C4: set_Pr1261947904930325089at_nat] :
% 0.30/0.65              ? [X3: product_prod_nat_nat] :
% 0.30/0.65                ( ( intrel @ X3 @ X3 )
% 0.30/0.65                & ( C4
% 0.30/0.65                  = ( collec3392354462482085612at_nat @ ( intrel @ X3 ) ) ) ) ) )
% 0.30/0.65       => ( ! [X2: int] : ( P @ ( rep_int @ X2 ) )
% 0.30/0.65         => ( P @ Y ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Rep_int_induct
% 0.30/0.65  thf(fact_9683_Rep__int__cases,axiom,
% 0.30/0.65      ! [Y: set_Pr1261947904930325089at_nat] :
% 0.30/0.65        ( ( member2643936169264416010at_nat @ Y
% 0.30/0.65          @ ( collec5514110066124741708at_nat
% 0.30/0.65            @ ^ [C4: set_Pr1261947904930325089at_nat] :
% 0.30/0.65              ? [X3: product_prod_nat_nat] :
% 0.30/0.65                ( ( intrel @ X3 @ X3 )
% 0.30/0.65                & ( C4
% 0.30/0.65                  = ( collec3392354462482085612at_nat @ ( intrel @ X3 ) ) ) ) ) )
% 0.30/0.65       => ~ ! [X2: int] :
% 0.30/0.65              ( Y
% 0.30/0.65             != ( rep_int @ X2 ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Rep_int_cases
% 0.30/0.65  thf(fact_9684_Rep__int,axiom,
% 0.30/0.65      ! [X: int] :
% 0.30/0.65        ( member2643936169264416010at_nat @ ( rep_int @ X )
% 0.30/0.65        @ ( collec5514110066124741708at_nat
% 0.30/0.65          @ ^ [C4: set_Pr1261947904930325089at_nat] :
% 0.30/0.65            ? [X3: product_prod_nat_nat] :
% 0.30/0.65              ( ( intrel @ X3 @ X3 )
% 0.30/0.65              & ( C4
% 0.30/0.65                = ( collec3392354462482085612at_nat @ ( intrel @ X3 ) ) ) ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Rep_int
% 0.30/0.65  thf(fact_9685_Int_Osub__code_I9_J,axiom,
% 0.30/0.65      ! [M: num,N: num] :
% 0.30/0.65        ( ( sub @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.30/0.65        = ( minus_minus_int @ ( dup @ ( sub @ M @ N ) ) @ one_one_int ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Int.sub_code(9)
% 0.30/0.65  thf(fact_9686_Int_Osub__code_I8_J,axiom,
% 0.30/0.65      ! [M: num,N: num] :
% 0.30/0.65        ( ( sub @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.30/0.65        = ( plus_plus_int @ ( dup @ ( sub @ M @ N ) ) @ one_one_int ) ) ).
% 0.30/0.65  
% 0.30/0.65  % Int.sub_code(8)
% 0.30/0.65  thf(fact_9687_gcd__nat_Opreordering__axioms,axiom,
% 0.30/0.65      ( preordering_nat @ dvd_dvd_nat
% 0.30/0.65      @ ^ [M2: nat,N2: nat] :
% 0.30/0.65          ( ( dvd_dvd_nat @ M2 @ N2 )
% 0.30/0.65          & ( M2 != N2 ) ) ) ).
% 0.30/0.65  
% 0.30/0.65  % gcd_nat.preordering_axioms
% 0.30/0.65  
% 0.30/0.65  % Helper facts (37)
% 0.30/0.65  thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 0.30/0.65      ! [X: int,Y: int] :
% 0.30/0.65        ( ( if_int @ $false @ X @ Y )
% 0.30/0.65        = Y ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 0.30/0.65      ! [X: int,Y: int] :
% 0.30/0.65        ( ( if_int @ $true @ X @ Y )
% 0.30/0.65        = X ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 0.30/0.65      ! [X: nat,Y: nat] :
% 0.30/0.65        ( ( if_nat @ $false @ X @ Y )
% 0.30/0.65        = Y ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 0.30/0.65      ! [X: nat,Y: nat] :
% 0.30/0.65        ( ( if_nat @ $true @ X @ Y )
% 0.30/0.65        = X ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 0.30/0.65      ! [X: num,Y: num] :
% 0.30/0.65        ( ( if_num @ $false @ X @ Y )
% 0.30/0.65        = Y ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 0.30/0.65      ! [X: num,Y: num] :
% 0.30/0.65        ( ( if_num @ $true @ X @ Y )
% 0.30/0.65        = X ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 0.30/0.65      ! [X: rat,Y: rat] :
% 0.30/0.65        ( ( if_rat @ $false @ X @ Y )
% 0.30/0.65        = Y ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 0.30/0.65      ! [X: rat,Y: rat] :
% 0.30/0.65        ( ( if_rat @ $true @ X @ Y )
% 0.30/0.65        = X ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_2_1_If_001t__Assertions__Oassn_T,axiom,
% 0.30/0.65      ! [X: assn,Y: assn] :
% 0.30/0.65        ( ( if_assn @ $false @ X @ Y )
% 0.30/0.65        = Y ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_1_1_If_001t__Assertions__Oassn_T,axiom,
% 0.30/0.65      ! [X: assn,Y: assn] :
% 0.30/0.65        ( ( if_assn @ $true @ X @ Y )
% 0.30/0.65        = X ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.30/0.65      ! [X: code_integer,Y: code_integer] :
% 0.30/0.65        ( ( if_Code_integer @ $false @ X @ Y )
% 0.30/0.65        = Y ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.30/0.65      ! [X: code_integer,Y: code_integer] :
% 0.30/0.65        ( ( if_Code_integer @ $true @ X @ Y )
% 0.30/0.65        = X ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_2_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 0.30/0.65      ! [X: code_natural,Y: code_natural] :
% 0.30/0.65        ( ( if_Code_natural @ $false @ X @ Y )
% 0.30/0.65        = Y ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_1_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 0.30/0.65      ! [X: code_natural,Y: code_natural] :
% 0.30/0.65        ( ( if_Code_natural @ $true @ X @ Y )
% 0.30/0.65        = X ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 0.30/0.65      ! [X: set_int,Y: set_int] :
% 0.30/0.65        ( ( if_set_int @ $false @ X @ Y )
% 0.30/0.65        = Y ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 0.30/0.65      ! [X: set_int,Y: set_int] :
% 0.30/0.65        ( ( if_set_int @ $true @ X @ Y )
% 0.30/0.65        = X ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 0.30/0.65      ! [X: list_int,Y: list_int] :
% 0.30/0.65        ( ( if_list_int @ $false @ X @ Y )
% 0.30/0.65        = Y ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 0.30/0.65      ! [X: list_int,Y: list_int] :
% 0.30/0.65        ( ( if_list_int @ $true @ X @ Y )
% 0.30/0.65        = X ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 0.30/0.65      ! [X: option_num,Y: option_num] :
% 0.30/0.65        ( ( if_option_num @ $false @ X @ Y )
% 0.30/0.65        = Y ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 0.30/0.65      ! [X: option_num,Y: option_num] :
% 0.30/0.65        ( ( if_option_num @ $true @ X @ Y )
% 0.30/0.65        = X ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_2_1_If_001t__Predicate__Opred_It__Product____Type__Ounit_J_T,axiom,
% 0.30/0.65      ! [X: pred_Product_unit,Y: pred_Product_unit] :
% 0.30/0.65        ( ( if_pred_Product_unit @ $false @ X @ Y )
% 0.30/0.65        = Y ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_1_1_If_001t__Predicate__Opred_It__Product____Type__Ounit_J_T,axiom,
% 0.30/0.65      ! [X: pred_Product_unit,Y: pred_Product_unit] :
% 0.30/0.65        ( ( if_pred_Product_unit @ $true @ X @ Y )
% 0.30/0.65        = X ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_2_1_If_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.30/0.65      ! [X: sum_sum_nat_nat,Y: sum_sum_nat_nat] :
% 0.30/0.65        ( ( if_Sum_sum_nat_nat @ $false @ X @ Y )
% 0.30/0.65        = Y ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_1_1_If_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.30/0.65      ! [X: sum_sum_nat_nat,Y: sum_sum_nat_nat] :
% 0.30/0.65        ( ( if_Sum_sum_nat_nat @ $true @ X @ Y )
% 0.30/0.65        = X ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.30/0.65      ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 0.30/0.65        ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 0.30/0.65        = Y ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.30/0.65      ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 0.30/0.65        ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 0.30/0.65        = X ) ).
% 0.30/0.65  
% 0.30/0.65  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
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% 0.30/0.65        ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
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% 0.30/0.65  
% 0.30/0.65  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
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% 0.30/0.65        ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
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% 0.30/0.65        ( ( if_Pro5737122678794959658eger_o @ $false @ X @ Y )
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% 0.30/0.65  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
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% 0.30/0.65  
% 0.30/0.65  % Conjectures (1)
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% 0.30/0.65      ( ( ( x
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% 0.30/0.65  %------------------------------------------------------------------------------
% 0.30/0.65  ------------------------
% 6.56/2.54  ---- Embedded in THF ---
% 6.56/2.55  %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 6.56/2.55  %%% Generated on Thu Feb 26 02:30:40 EST 2026
% 6.56/2.55  %%% using '$$dhol' embedding, version 1.3.0.
% 6.56/2.55  %%% Logic specification used:
% 6.56/2.55  %%% thf(spec, logic, $$dhol).
% 6.56/2.55  
% 6.56/2.55  % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.q4ZIkRLcku/DTF2DTF32141.p
% See solution above
% 6.56/2.60  ------------------------
% 9.16/5.09  ---- Cleaned THF ---
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% 9.16/5.09      archim3151403230148437115or_rat: rat > int ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_Archimedean__Field_Ofrac_001t__Rat__Orat,type,
% 9.16/5.09      archimedean_frac_rat: rat > rat ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_Archimedean__Field_Oround_001t__Rat__Orat,type,
% 9.16/5.09      archim7778729529865785530nd_rat: rat > int ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_Assertions_Oassn_OAbs__assn,type,
% 9.16/5.09      abs_assn: ( produc3658429121746597890et_nat > $o ) > assn ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_Assertions_Oassn_ORep__assn,type,
% 9.16/5.09      rep_assn: assn > produc3658429121746597890et_nat > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_Assertions_Oin__range,type,
% 9.16/5.09      in_range: produc3658429121746597890et_nat > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_Assertions_Oone__assn__raw,type,
% 9.16/5.09      one_assn_raw: produc3658429121746597890et_nat > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_Assertions_Oproper,type,
% 9.16/5.09      proper: ( produc3658429121746597890et_nat > $o ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_Assertions_OrelH,type,
% 9.16/5.09      relH: set_nat > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_Assertions_Otimes__assn__raw,type,
% 9.16/5.09      times_assn_raw: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_Assertions_Otimes__assn__raw__rel,type,
% 9.16/5.09      times_assn_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_Assertions_Owand__assn,type,
% 9.16/5.09      wand_assn: assn > assn > assn ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_Assertions_Owand__raw,type,
% 9.16/5.09      wand_raw: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_Assertions_Owand__raw__rel,type,
% 9.16/5.09      wand_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Cardinal__Arithmetic_Ocone,type,
% 9.16/5.09      bNF_Cardinal_cone: set_Pr5094982260447487303t_unit ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Cardinal__Arithmetic_Octwo,type,
% 9.16/5.09      bNF_Cardinal_ctwo: set_Product_prod_o_o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Cardinal__Arithmetic_Oczero_001_Eo,type,
% 9.16/5.09      bNF_Cardinal_czero_o: set_Product_prod_o_o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001_Eo,type,
% 9.16/5.09      bNF_Ca3172636760949973492d_of_o: set_o > set_Product_prod_o_o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001t__Nat__Onat,type,
% 9.16/5.09      bNF_Ca3793111618940312692of_nat: set_nat > set_Pr1261947904930325089at_nat ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001t__Product____Type__Ounit,type,
% 9.16/5.09      bNF_Ca7083678892733797993t_unit: set_Product_unit > set_Pr5094982260447487303t_unit ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__order__on_001_Eo,type,
% 9.16/5.09      bNF_Ca8331644756375544342r_on_o: set_o > set_Product_prod_o_o > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__order__on_001t__Nat__Onat,type,
% 9.16/5.09      bNF_Ca1281551314933786834on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Cardinal__Order__Relation_OnatLeq,type,
% 9.16/5.09      bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Cardinal__Order__Relation_OnatLess,type,
% 9.16/5.09      bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_Eo_J_J,type,
% 9.16/5.09      bNF_id2059982186938784458at_o_o: ( ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ) > ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_Eo_J,type,
% 9.16/5.09      bNF_id4470576313039291732at_o_o: ( ( produc3658429121746597890et_nat > $o ) > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_I_Eo_M_062_I_Eo_M_Eo_J_J,type,
% 9.16/5.09      bNF_id_bnf_o_o_o: ( $o > $o > $o ) > $o > $o > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_I_Eo_M_062_It__Int__Oint_M_Eo_J_J,type,
% 9.16/5.09      bNF_id_bnf_o_int_o: ( $o > int > $o ) > $o > int > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_I_Eo_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 9.16/5.09      bNF_id_bnf_o_nat_o: ( $o > nat > $o ) > $o > nat > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_I_Eo_M_Eo_J,type,
% 9.16/5.09      bNF_id_bnf_o_o: ( $o > $o ) > $o > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Int__Oint_M_062_I_Eo_M_Eo_J_J,type,
% 9.16/5.09      bNF_id_bnf_int_o_o: ( int > $o > $o ) > int > $o > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
% 9.16/5.09      bNF_id_bnf_int_int_o: ( int > int > $o ) > int > int > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Int__Oint_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 9.16/5.09      bNF_id_bnf_int_nat_o: ( int > nat > $o ) > int > nat > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Int__Oint_M_Eo_J,type,
% 9.16/5.09      bNF_id_bnf_int_o: ( int > $o ) > int > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Nat__Onat_M_062_I_Eo_M_Eo_J_J,type,
% 9.16/5.09      bNF_id_bnf_nat_o_o: ( nat > $o > $o ) > nat > $o > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Nat__Onat_M_062_It__Int__Oint_M_Eo_J_J,type,
% 9.16/5.09      bNF_id_bnf_nat_int_o: ( nat > int > $o ) > nat > int > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 9.16/5.09      bNF_id_bnf_nat_nat_o: ( nat > nat > $o ) > nat > nat > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Nat__Onat_M_Eo_J,type,
% 9.16/5.09      bNF_id_bnf_nat_o: ( nat > $o ) > nat > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
% 9.16/5.09      bNF_id146787821168362314_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 9.16/5.09      bNF_id5045731369644952736_nat_o: ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_062_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J_J,type,
% 9.16/5.09      bNF_id5557877041440844106_nat_o: ( produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o ) > produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
% 9.16/5.09      bNF_id1044457264471098170_nat_o: ( produc3843707927480180839at_nat > $o ) > produc3843707927480180839at_nat > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Set__Oset_It__Nat__Onat_J_M_062_I_Eo_M_Eo_J_J,type,
% 9.16/5.09      bNF_id1382368747416007662at_o_o: ( set_nat > $o > $o ) > set_nat > $o > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Set__Oset_It__Nat__Onat_J_M_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J_J,type,
% 9.16/5.09      bNF_id293821497076346774_nat_o: ( set_nat > set_nat > $o ) > set_nat > set_nat > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
% 9.16/5.09      bNF_id_bnf_set_nat_o: ( set_nat > $o ) > set_nat > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_062_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J_J,type,
% 9.16/5.09      bNF_id745042670895148362_int_o: ( set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o ) > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
% 9.16/5.09      bNF_id9176111459293603464_int_o: ( set_Pr958786334691620121nt_int > $o ) > set_Pr958786334691620121nt_int > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001_Eo,type,
% 9.16/5.09      bNF_id_bnf_o: $o > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001t__Int__Oint,type,
% 9.16/5.09      bNF_id_bnf_int: int > int ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001t__List__Olist_It__Nat__Onat_J,type,
% 9.16/5.09      bNF_id_bnf_list_nat: list_nat > list_nat ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001t__Nat__Onat,type,
% 9.16/5.09      bNF_id_bnf_nat: nat > nat ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Composition_Oid__bnf_001t__Rat__Orat,type,
% 9.16/5.09      bNF_id_bnf_rat: rat > rat ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Oeq__onp_001t__List__Olist_It__String__Ochar_J,type,
% 9.16/5.09      bNF_eq_onp_list_char: ( list_char > $o ) > list_char > list_char > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J_J_J,type,
% 9.16/5.09      bNF_re5598663031114558885t_char: ( $o > $o > $o ) > ( ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > $o ) > ( $o > $o > $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > $o > $o > list_char > list_char ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J_J_J_J_J_J,type,
% 9.16/5.09      bNF_re8691941649098027561iteral: ( $o > $o > $o ) > ( ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > $o > literal > literal ) > $o ) > ( $o > $o > $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > $o > $o > literal > literal ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J_J,type,
% 9.16/5.09      bNF_re7347849368244578525t_char: ( $o > $o > $o ) > ( ( $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > list_char > list_char ) > $o ) > ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J_J_J_J_J,type,
% 9.16/5.09      bNF_re5719858693005739489iteral: ( $o > $o > $o ) > ( ( $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > literal > literal ) > $o ) > ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > $o > literal > literal ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J,type,
% 9.16/5.09      bNF_re7972843584066424825t_char: ( $o > $o > $o ) > ( ( $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > list_char > list_char ) > $o ) > ( $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > list_char > list_char ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J_J_J_J,type,
% 9.16/5.09      bNF_re136309367175754621iteral: ( $o > $o > $o ) > ( ( $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > literal > literal ) > $o ) > ( $o > $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > $o > literal > literal ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J,type,
% 9.16/5.09      bNF_re796896441190010845t_char: ( $o > $o > $o ) > ( ( $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > list_char > list_char ) > $o ) > ( $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > list_char > list_char ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J_J_J,type,
% 9.16/5.09      bNF_re2365650225897248225iteral: ( $o > $o > $o ) > ( ( $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > literal > literal ) > $o ) > ( $o > $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > $o > literal > literal ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J,type,
% 9.16/5.09      bNF_re4583855572895197261t_char: ( $o > $o > $o ) > ( ( $o > $o > list_char > list_char ) > ( $o > $o > list_char > list_char ) > $o ) > ( $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > list_char > list_char ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J_J,type,
% 9.16/5.09      bNF_re5778109699181701841iteral: ( $o > $o > $o ) > ( ( $o > $o > list_char > list_char ) > ( $o > $o > literal > literal ) > $o ) > ( $o > $o > $o > list_char > list_char ) > ( $o > $o > $o > literal > literal ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_001_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J,type,
% 9.16/5.09      bNF_re441219624009962717t_char: ( $o > $o > $o ) > ( ( $o > list_char > list_char ) > ( $o > list_char > list_char ) > $o ) > ( $o > $o > list_char > list_char ) > ( $o > $o > list_char > list_char ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_001_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J,type,
% 9.16/5.09      bNF_re1595102025518187489iteral: ( $o > $o > $o ) > ( ( $o > list_char > list_char ) > ( $o > literal > literal ) > $o ) > ( $o > $o > list_char > list_char ) > ( $o > $o > literal > literal ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J,type,
% 9.16/5.09      bNF_re6157522605288126113t_char: ( $o > $o > $o ) > ( ( list_char > list_char ) > ( list_char > list_char ) > $o ) > ( $o > list_char > list_char ) > ( $o > list_char > list_char ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001_Eo_001_Eo_001_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_001_062_It__String__Oliteral_Mt__String__Oliteral_J,type,
% 9.16/5.09      bNF_re6148748351543924773iteral: ( $o > $o > $o ) > ( ( list_char > list_char ) > ( literal > literal ) > $o ) > ( $o > list_char > list_char ) > ( $o > literal > literal ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 9.16/5.09      bNF_re3379532845092657523nteger: ( int > code_integer > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( code_integer > code_integer ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Int__Oint,type,
% 9.16/5.09      bNF_re3804157879324367682nt_int: ( int > code_integer > $o ) > ( int > int > $o ) > ( int > int ) > ( code_integer > int ) > $o ).
% 9.16/5.09  
% 9.16/5.09  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,
% 9.16/5.09      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 ).
% 9.16/5.09  
% 9.16/5.09  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,
% 9.16/5.09      bNF_re3461391660133120880nt_rat: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > rat ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 9.16/5.09      bNF_re982302072995117890nteger: ( int > int > $o ) > ( int > code_integer > $o ) > ( int > int ) > ( int > code_integer ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 9.16/5.09      bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
% 9.16/5.09  
% 9.16/5.09  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,
% 9.16/5.09      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 ).
% 9.16/5.09  
% 9.16/5.09  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,
% 9.16/5.09      bNF_re2214769303045360666nt_rat: ( int > int > $o ) > ( product_prod_int_int > rat > $o ) > ( int > product_prod_int_int ) > ( int > rat ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__Code____Numeral__Ointeger_J_001t__List__Olist_It__Code____Numeral__Ointeger_J_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J,type,
% 9.16/5.09      bNF_re5828396963709814525t_char: ( list_Code_integer > list_Code_integer > $o ) > ( list_char > list_char > $o ) > ( list_Code_integer > list_char ) > ( list_Code_integer > list_char ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J,type,
% 9.16/5.09      bNF_re7775871201573978401char_o: ( list_char > list_char > $o ) > ( ( list_char > $o ) > ( list_char > $o ) > $o ) > ( list_char > list_char > $o ) > ( list_char > list_char > $o ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_001_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J,type,
% 9.16/5.09      bNF_re7399511318543894245t_char: ( list_char > list_char > $o ) > ( ( list_char > list_char ) > ( list_char > list_char ) > $o ) > ( list_char > list_char > list_char ) > ( list_char > list_char > list_char ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J_001_Eo_001_Eo,type,
% 9.16/5.09      bNF_re6668474094832959905ar_o_o: ( list_char > list_char > $o ) > ( $o > $o > $o ) > ( list_char > $o ) > ( list_char > $o ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__Code____Numeral__Ointeger_J_001t__List__Olist_It__Code____Numeral__Ointeger_J,type,
% 9.16/5.09      bNF_re901197953848981245nteger: ( list_char > list_char > $o ) > ( list_Code_integer > list_Code_integer > $o ) > ( list_char > list_Code_integer ) > ( list_char > list_Code_integer ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J,type,
% 9.16/5.09      bNF_re1407854171455731685t_char: ( list_char > list_char > $o ) > ( list_char > list_char > $o ) > ( list_char > list_char ) > ( list_char > list_char ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.16/5.09      bNF_re76688982720252355at_nat: ( list_char > list_char > $o ) > ( nat > nat > $o ) > ( list_char > nat ) > ( list_char > nat ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__String__Ochar_J_001t__String__Oliteral_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J_001_062_It__String__Oliteral_M_Eo_J,type,
% 9.16/5.09      bNF_re7831395832754058691eral_o: ( list_char > literal > $o ) > ( ( list_char > $o ) > ( literal > $o ) > $o ) > ( list_char > list_char > $o ) > ( literal > literal > $o ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__String__Ochar_J_001t__String__Oliteral_001_Eo_001_Eo,type,
% 9.16/5.09      bNF_re8730477052009823892al_o_o: ( list_char > literal > $o ) > ( $o > $o > $o ) > ( list_char > $o ) > ( literal > $o ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__String__Ochar_J_001t__String__Oliteral_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J,type,
% 9.16/5.09      bNF_re4991257583289732696t_char: ( list_char > literal > $o ) > ( list_char > list_char > $o ) > ( list_char > list_char ) > ( literal > list_char ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001t__List__Olist_It__String__Ochar_J_001t__String__Oliteral_001t__List__Olist_It__String__Ochar_J_001t__String__Oliteral,type,
% 9.16/5.09      bNF_re5453467372598631581iteral: ( list_char > literal > $o ) > ( list_char > literal > $o ) > ( list_char > list_char ) > ( literal > literal ) > $o ).
% 9.16/5.09  
% 9.16/5.09  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,
% 9.16/5.09      bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
% 9.16/5.09  
% 9.16/5.09  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,
% 9.16/5.09      bNF_re7876454716742015248nteger: ( num > num > $o ) > ( ( num > int ) > ( num > code_integer ) > $o ) > ( num > num > int ) > ( num > num > code_integer ) > $o ).
% 9.16/5.09  
% 9.16/5.09  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,
% 9.16/5.09      bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 9.16/5.09      bNF_re6501075790457514782nteger: ( num > num > $o ) > ( int > code_integer > $o ) > ( num > int ) > ( num > code_integer ) > $o ).
% 9.16/5.09  
% 9.16/5.09  thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Int__Oint,type,
% 9.16/5.09      bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).
% 9.16/5.09  
% 9.16/5.09  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,
% 9.16/5.09      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 ).
% 9.16/5.09  
% 9.16/5.09  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,
% 9.16/5.09      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 ).
% 9.16/5.09  
% 9.16/5.09  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,
% 9.16/5.09      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 ).
% 9.16/5.09  
% 9.16/5.09  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,
% 9.16/5.09      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 ).
% 9.16/5.09  
% 9.16/5.09  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,
% 9.16/5.09      bNF_re1494630372529172596at_o_o: ( product_prod_int_int > rat > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( rat > $o ) > $o ).
% 9.16/5.09  
% 9.16/5.09  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,
% 9.16/5.09      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 ).
% 9.16/5.09  
% 9.16/5.09  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,
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% 9.16/5.10  thf(sy_c_Bit__Operations_Osemiring__bits__class_Obit_001t__Int__Oint,type,
% 9.16/5.10      bit_se1146084159140164899it_int: int > nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Bit__Operations_Otake__bit__num,type,
% 9.16/5.10      bit_take_bit_num: nat > num > option_num ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations__class_Oand__num,type,
% 9.16/5.10      bit_un7362597486090784418nd_num: num > num > option_num ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations__class_Oand__num__rel,type,
% 9.16/5.10      bit_un4731106466462545111um_rel: product_prod_num_num > product_prod_num_num > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations__class_Oor__num,type,
% 9.16/5.10      bit_un6697907153464112080or_num: num > num > num ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations__class_Oor__num__rel,type,
% 9.16/5.10      bit_un4773296044027857193um_rel: product_prod_num_num > product_prod_num_num > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations__class_Oxor__num,type,
% 9.16/5.10      bit_un2480387367778600638or_num: num > num > option_num ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Bit__Operations_Ounique__euclidean__semiring__with__bit__operations__class_Oxor__num__rel,type,
% 9.16/5.10      bit_un2901131394128224187um_rel: product_prod_num_num > product_prod_num_num > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Boolean__Algebras_Oabstract__boolean__algebra_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J,type,
% 9.16/5.10      boolea934052484356091300char_o: ( ( list_char > $o ) > ( list_char > $o ) > list_char > $o ) > ( ( list_char > $o ) > ( list_char > $o ) > list_char > $o ) > ( ( list_char > $o ) > list_char > $o ) > ( list_char > $o ) > ( list_char > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Boolean__Algebras_Oabstract__boolean__algebra_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 9.16/5.10      boolea1849928419393854478_int_o: ( ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ) > ( ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ) > ( ( product_prod_int_int > $o ) > product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Boolean__Algebras_Oabstract__boolean__algebra_001t__Product____Type__Ounit,type,
% 9.16/5.10      boolea7165431671056489859t_unit: ( product_unit > product_unit > product_unit ) > ( product_unit > product_unit > product_unit ) > ( product_unit > product_unit ) > product_unit > product_unit > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Boolean__Algebras_Oabstract__boolean__algebra_001t__Set__Oset_I_Eo_J,type,
% 9.16/5.10      boolea379910186789422830_set_o: ( set_o > set_o > set_o ) > ( set_o > set_o > set_o ) > ( set_o > set_o ) > set_o > set_o > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Boolean__Algebras_Oabstract__boolean__algebra_001t__Set__Oset_It__Int__Oint_J,type,
% 9.16/5.10      boolea5824373010784320748et_int: ( set_int > set_int > set_int ) > ( set_int > set_int > set_int ) > ( set_int > set_int ) > set_int > set_int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Boolean__Algebras_Oabstract__boolean__algebra_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 9.16/5.10      boolea9074081411689916704st_nat: ( set_list_nat > set_list_nat > set_list_nat ) > ( set_list_nat > set_list_nat > set_list_nat ) > ( set_list_nat > set_list_nat ) > set_list_nat > set_list_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Boolean__Algebras_Oabstract__boolean__algebra_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.16/5.10      boolea778851993438741648et_nat: ( set_nat > set_nat > set_nat ) > ( set_nat > set_nat > set_nat ) > ( set_nat > set_nat ) > set_nat > set_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Boolean__Algebras_Oabstract__boolean__algebra_001t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 9.16/5.10      boolea51845251928480829at_nat: ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ) > ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ) > ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ) > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Boolean__Algebras_Oabstract__boolean__algebra_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.16/5.10      boolea949959532490082519at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Boolean__Algebras_Oabstract__boolean__algebra_001t__Set__Oset_It__Rat__Orat_J,type,
% 9.16/5.10      boolea6493995471900120728et_rat: ( set_rat > set_rat > set_rat ) > ( set_rat > set_rat > set_rat ) > ( set_rat > set_rat ) > set_rat > set_rat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Code__Numeral_OSuc,type,
% 9.16/5.10      code_Suc: code_natural > code_natural ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Code__Numeral_Obit__cut__integer,type,
% 9.16/5.10      code_bit_cut_integer: code_integer > produc6271795597528267376eger_o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Code__Numeral_Ocr__integer,type,
% 9.16/5.10      code_cr_integer: int > code_integer > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Code__Numeral_Ocr__natural,type,
% 9.16/5.10      code_cr_natural: nat > code_natural > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Code__Numeral_Odivmod__abs,type,
% 9.16/5.10      code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Code__Numeral_Odivmod__integer,type,
% 9.16/5.10      code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Code__Numeral_Odup,type,
% 9.16/5.10      code_dup: code_integer > code_integer ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Code__Numeral_Ointeger_Oint__of__integer,type,
% 9.16/5.10      code_int_of_integer: code_integer > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Code__Numeral_Ointeger_Ointeger__of__int,type,
% 9.16/5.10      code_integer_of_int: int > code_integer ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Code__Numeral_Ointeger__of__nat,type,
% 9.16/5.10      code_integer_of_nat: nat > code_integer ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Code__Numeral_Ointeger__of__num,type,
% 9.16/5.10      code_integer_of_num: num > code_integer ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Code__Numeral_Onat__of__integer,type,
% 9.16/5.10      code_nat_of_integer: code_integer > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Code__Numeral_Onatural_Onat__of__natural,type,
% 9.16/5.10      code_nat_of_natural: code_natural > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Code__Numeral_Onatural_Onatural__of__nat,type,
% 9.16/5.10      code_natural_of_nat: nat > code_natural ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Code__Numeral_Onegative,type,
% 9.16/5.10      code_negative: num > code_integer ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Code__Numeral_Onum__of__integer,type,
% 9.16/5.10      code_num_of_integer: code_integer > num ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Code__Numeral_Opcr__integer,type,
% 9.16/5.10      code_pcr_integer: int > code_integer > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Code__Numeral_Osub,type,
% 9.16/5.10      code_sub: num > num > code_integer ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Int__Oint,type,
% 9.16/5.10      complete_Inf_Inf_int: set_int > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Nat__Onat,type,
% 9.16/5.10      complete_Inf_Inf_nat: set_nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Complete__Lattices_OInf__class_OInf_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.16/5.10      comple7806235888213564991et_nat: set_set_nat > set_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Int__Oint,type,
% 9.16/5.10      complete_Sup_Sup_int: set_int > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Nat__Onat,type,
% 9.16/5.10      complete_Sup_Sup_nat: set_nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Complete__Lattices_OSup__class_OSup_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.16/5.10      comple7399068483239264473et_nat: set_set_nat > set_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Countable_Onat__to__rat__surj,type,
% 9.16/5.10      nat_to_rat_surj: nat > rat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Countable_Onth__item__rel,type,
% 9.16/5.10      nth_item_rel: nat > nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Divides_Oadjust__div,type,
% 9.16/5.10      adjust_div: product_prod_int_int > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Divides_Oadjust__mod,type,
% 9.16/5.10      adjust_mod: int > int > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Divides_Odivmod__nat,type,
% 9.16/5.10      divmod_nat: nat > nat > product_prod_nat_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Divides_Oeucl__rel__int,type,
% 9.16/5.10      eucl_rel_int: int > int > product_prod_int_int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Code____Numeral__Ointeger,type,
% 9.16/5.10      unique5706413561485394159nteger: produc8923325533196201883nteger > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Int__Oint,type,
% 9.16/5.10      unique6319869463603278526ux_int: product_prod_int_int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivides__aux_001t__Nat__Onat,type,
% 9.16/5.10      unique6322359934112328802ux_nat: product_prod_nat_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Code____Numeral__Ointeger,type,
% 9.16/5.10      unique3479559517661332726nteger: num > num > produc8923325533196201883nteger ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Int__Oint,type,
% 9.16/5.10      unique5052692396658037445od_int: num > num > product_prod_int_int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod_001t__Nat__Onat,type,
% 9.16/5.10      unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Code____Numeral__Ointeger,type,
% 9.16/5.10      unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Int__Oint,type,
% 9.16/5.10      unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Nat__Onat,type,
% 9.16/5.10      unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Euclidean__Division_Ounique__euclidean__semiring__class_Odivision__segment_001t__Int__Oint,type,
% 9.16/5.10      euclid3395696857347342551nt_int: int > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Euclidean__Division_Ounique__euclidean__semiring__class_Odivision__segment_001t__Nat__Onat,type,
% 9.16/5.10      euclid3398187327856392827nt_nat: nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Code____Numeral__Ointeger,type,
% 9.16/5.10      comm_s8582702949713902594nteger: code_integer > nat > code_integer ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Int__Oint,type,
% 9.16/5.10      comm_s4660882817536571857er_int: int > nat > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Nat__Onat,type,
% 9.16/5.10      comm_s4663373288045622133er_nat: nat > nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Factorial_Ocomm__semiring__1__class_Opochhammer_001t__Rat__Orat,type,
% 9.16/5.10      comm_s4028243227959126397er_rat: rat > nat > rat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Code____Numeral__Ointeger,type,
% 9.16/5.10      semiri3624122377584611663nteger: nat > code_integer ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Code____Numeral__Onatural,type,
% 9.16/5.10      semiri2447717529341329178atural: nat > code_natural ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Int__Oint,type,
% 9.16/5.10      semiri1406184849735516958ct_int: nat > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Nat__Onat,type,
% 9.16/5.10      semiri1408675320244567234ct_nat: nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Rat__Orat,type,
% 9.16/5.10      semiri773545260158071498ct_rat: nat > rat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Rat__Orat,type,
% 9.16/5.10      inverse_inverse_rat: rat > rat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Filter_Oat__top_001t__Nat__Onat,type,
% 9.16/5.10      at_top_nat: filter_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Filter_Ocofinite_001t__Nat__Onat,type,
% 9.16/5.10      cofinite_nat: filter_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Filter_Oeventually_001t__Nat__Onat,type,
% 9.16/5.10      eventually_nat: ( nat > $o ) > filter_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Filter_Oeventually_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.16/5.10      eventu1038000079068216329at_nat: ( product_prod_nat_nat > $o ) > filter1242075044329608583at_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.16/5.10      filter3212408913953519116et_nat: ( nat > set_nat ) > filter_set_nat > filter_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Filter_Ofinite__subsets__at__top_001t__Nat__Onat,type,
% 9.16/5.10      finite3254316476582989077op_nat: set_nat > filter_set_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Filter_Ofrequently_001t__Nat__Onat,type,
% 9.16/5.10      frequently_nat: ( nat > $o ) > filter_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Filter_Oprod__filter_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.16/5.10      prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Finite__Set_Ocard_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
% 9.16/5.10      finite1363419556375932405_nat_o: set_Pr4532377907799695533_nat_o > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Finite__Set_Ocard_001_Eo,type,
% 9.16/5.10      finite_card_o: set_o > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Finite__Set_Ocard_001t__Int__Oint,type,
% 9.16/5.10      finite_card_int: set_int > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__Nat__Onat_J,type,
% 9.16/5.10      finite_card_list_nat: set_list_nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
% 9.16/5.10      finite_card_nat: set_nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Finite__Set_Ocard_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.16/5.10      finite6756421564338198497nt_int: set_Pr958786334691620121nt_int > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Finite__Set_Ocard_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Fun_Omap__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J_J_J_J_J,type,
% 9.16/5.10      map_fu7309004089335677210iteral: ( $o > $o ) > ( ( $o > $o > $o > $o > $o > list_char > list_char ) > $o > $o > $o > $o > $o > literal > literal ) > ( $o > $o > $o > $o > $o > $o > list_char > list_char ) > $o > $o > $o > $o > $o > $o > literal > literal ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Fun_Omap__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J_J_J_J,type,
% 9.16/5.10      map_fu1929762555066093878iteral: ( $o > $o ) > ( ( $o > $o > $o > $o > list_char > list_char ) > $o > $o > $o > $o > literal > literal ) > ( $o > $o > $o > $o > $o > list_char > list_char ) > $o > $o > $o > $o > $o > literal > literal ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Fun_Omap__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J_J_J,type,
% 9.16/5.10      map_fu5333924603067766298iteral: ( $o > $o ) > ( ( $o > $o > $o > list_char > list_char ) > $o > $o > $o > literal > literal ) > ( $o > $o > $o > $o > list_char > list_char ) > $o > $o > $o > $o > literal > literal ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Fun_Omap__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_J_001_062_I_Eo_M_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J_J,type,
% 9.16/5.10      map_fu1888220742600445322iteral: ( $o > $o ) > ( ( $o > $o > list_char > list_char ) > $o > $o > literal > literal ) > ( $o > $o > $o > list_char > list_char ) > $o > $o > $o > literal > literal ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Fun_Omap__fun_001_Eo_001_Eo_001_062_I_Eo_M_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_J_001_062_I_Eo_M_062_It__String__Oliteral_Mt__String__Oliteral_J_J,type,
% 9.16/5.10      map_fu5700776415251466522iteral: ( $o > $o ) > ( ( $o > list_char > list_char ) > $o > literal > literal ) > ( $o > $o > list_char > list_char ) > $o > $o > literal > literal ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Fun_Omap__fun_001_Eo_001_Eo_001_062_It__List__Olist_It__String__Ochar_J_Mt__List__Olist_It__String__Ochar_J_J_001_062_It__String__Oliteral_Mt__String__Oliteral_J,type,
% 9.16/5.10      map_fu4627020735845646302iteral: ( $o > $o ) > ( ( list_char > list_char ) > literal > literal ) > ( $o > list_char > list_char ) > $o > literal > literal ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 9.16/5.10      map_fu2599414010547811884nteger: ( code_integer > int ) > ( int > code_integer ) > ( int > int ) > code_integer > code_integer ).
% 9.16/5.10  
% 9.16/5.10  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,
% 9.16/5.10      map_fu7831380289885515383nt_rat: ( int > int ) > ( ( int > product_prod_int_int ) > int > rat ) > ( int > int > product_prod_int_int ) > int > int > rat ).
% 9.16/5.10  
% 9.16/5.10  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,
% 9.16/5.10      map_fu3424225382358772769nt_rat: ( int > int ) > ( product_prod_int_int > rat ) > ( int > product_prod_int_int ) > int > rat ).
% 9.16/5.10  
% 9.16/5.10  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,
% 9.16/5.10      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 ).
% 9.16/5.10  
% 9.16/5.10  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,
% 9.16/5.10      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 ).
% 9.16/5.10  
% 9.16/5.10  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,
% 9.16/5.10      map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
% 9.16/5.10  
% 9.16/5.10  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,
% 9.16/5.10      map_fu2345160673673942751at_nat: ( int > product_prod_nat_nat ) > ( nat > nat ) > ( product_prod_nat_nat > nat ) > int > nat ).
% 9.16/5.10  
% 9.16/5.10  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,
% 9.16/5.10      map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
% 9.16/5.10  
% 9.16/5.10  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,
% 9.16/5.10      map_fu6891787308814931657nteger: ( num > num ) > ( ( num > int ) > num > code_integer ) > ( num > num > int ) > num > num > code_integer ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Fun_Omap__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
% 9.16/5.10      map_fu8638147718074629079nteger: ( num > num ) > ( int > code_integer ) > ( num > int ) > num > code_integer ).
% 9.16/5.10  
% 9.16/5.10  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,
% 9.16/5.10      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 ).
% 9.16/5.10  
% 9.16/5.10  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,
% 9.16/5.10      map_fu898904425404107465nt_o_o: ( rat > product_prod_int_int ) > ( $o > $o ) > ( product_prod_int_int > $o ) > rat > $o ).
% 9.16/5.10  
% 9.16/5.10  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,
% 9.16/5.10      map_fu5673905371560938248nt_rat: ( rat > product_prod_int_int ) > ( product_prod_int_int > rat ) > ( product_prod_int_int > product_prod_int_int ) > rat > rat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Fun_Omap__fun_001t__String__Oliteral_001t__List__Olist_It__String__Ochar_J_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J_001_062_It__String__Oliteral_M_Eo_J,type,
% 9.16/5.10      map_fu2661873803724901240eral_o: ( literal > list_char ) > ( ( list_char > $o ) > literal > $o ) > ( list_char > list_char > $o ) > literal > literal > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Fun_Omap__fun_001t__String__Oliteral_001t__List__Olist_It__String__Ochar_J_001_Eo_001_Eo,type,
% 9.16/5.10      map_fu6698795530259886495ar_o_o: ( literal > list_char ) > ( $o > $o ) > ( list_char > $o ) > literal > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Fun_Omap__fun_001t__String__Oliteral_001t__List__Olist_It__String__Ochar_J_001t__List__Olist_It__String__Ochar_J_001t__String__Oliteral,type,
% 9.16/5.10      map_fu7398138089906338514iteral: ( literal > list_char ) > ( list_char > literal ) > ( list_char > list_char ) > literal > literal ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Fun__Def_Omax__strict,type,
% 9.16/5.10      fun_max_strict: set_Pr4329608150637261639at_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Fun__Def_Omax__weak,type,
% 9.16/5.10      fun_max_weak: set_Pr4329608150637261639at_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Fun__Def_Omin__strict,type,
% 9.16/5.10      fun_min_strict: set_Pr4329608150637261639at_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Fun__Def_Omin__weak,type,
% 9.16/5.10      fun_min_weak: set_Pr4329608150637261639at_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Fun__Def_Opair__leq,type,
% 9.16/5.10      fun_pair_leq: set_Pr8693737435421807431at_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Fun__Def_Opair__less,type,
% 9.16/5.10      fun_pair_less: set_Pr8693737435421807431at_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Fun__Def_Oreduction__pair_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.16/5.10      fun_re7357418987779152907at_nat: produc4193628355235574503at_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Fun__Def_Oreduction__pair_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.16/5.10      fun_re2478310338295953701at_nat: produc1319942482725812455at_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_GCD_OGcd__class_OGcd_001t__Int__Oint,type,
% 9.16/5.10      gcd_Gcd_int: set_int > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_GCD_OGcd__class_OGcd_001t__Nat__Onat,type,
% 9.16/5.10      gcd_Gcd_nat: set_nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_GCD_OGcd__class_OLcm_001t__Int__Oint,type,
% 9.16/5.10      gcd_Lcm_int: set_int > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_GCD_OGcd__class_OLcm_001t__Nat__Onat,type,
% 9.16/5.10      gcd_Lcm_nat: set_nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_GCD_Obezw,type,
% 9.16/5.10      bezw: nat > nat > product_prod_int_int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_GCD_Obezw__rel,type,
% 9.16/5.10      bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Int__Oint,type,
% 9.16/5.10      gcd_gcd_int: int > int > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
% 9.16/5.10      gcd_gcd_nat: nat > nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_GCD_Ogcd__class_Olcm_001t__Int__Oint,type,
% 9.16/5.10      gcd_lcm_int: int > int > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_GCD_Ogcd__class_Olcm_001t__Nat__Onat,type,
% 9.16/5.10      gcd_lcm_nat: nat > nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_GCD_Ogcd__nat__rel,type,
% 9.16/5.10      gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Groups_Oabs__class_Oabs_001t__Code____Numeral__Ointeger,type,
% 9.16/5.10      abs_abs_Code_integer: code_integer > code_integer ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
% 9.16/5.10      abs_abs_int: int > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Groups_Oabs__class_Oabs_001t__Rat__Orat,type,
% 9.16/5.10      abs_abs_rat: rat > rat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Groups_Ocomm__monoid_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J,type,
% 9.16/5.10      comm_m8764728085499324515char_o: ( ( list_char > $o ) > ( list_char > $o ) > list_char > $o ) > ( list_char > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Groups_Ocomm__monoid_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 9.16/5.10      comm_m5839176995973721103_int_o: ( ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Groups_Ocomm__monoid_001t__Assertions__Oassn,type,
% 9.16/5.10      comm_monoid_assn: ( assn > assn > assn ) > assn > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Groups_Ocomm__monoid_001t__Code____Numeral__Ointeger,type,
% 9.16/5.10      comm_m1654649897431166824nteger: ( code_integer > code_integer > code_integer ) > code_integer > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Groups_Ocomm__monoid_001t__Int__Oint,type,
% 9.16/5.10      comm_monoid_int: ( int > int > int ) > int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Groups_Ocomm__monoid_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.16/5.10      comm_m1862543879040115196at_nat: ( multis2468970476368604999at_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat ) > multis2468970476368604999at_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Groups_Ocomm__monoid_001t__Nat__Onat,type,
% 9.16/5.10      comm_monoid_nat: ( nat > nat > nat ) > nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Groups_Ocomm__monoid_001t__Rat__Orat,type,
% 9.16/5.10      comm_monoid_rat: ( rat > rat > rat ) > rat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Groups_Ocomm__monoid_001t__Set__Oset_I_Eo_J,type,
% 9.16/5.10      comm_monoid_set_o: ( set_o > set_o > set_o ) > set_o > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Groups_Ocomm__monoid_001t__Set__Oset_It__Int__Oint_J,type,
% 9.16/5.10      comm_monoid_set_int: ( set_int > set_int > set_int ) > set_int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Groups_Ocomm__monoid_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 9.16/5.10      comm_m4511514676032769697st_nat: ( set_list_nat > set_list_nat > set_list_nat ) > set_list_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Groups_Ocomm__monoid_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.16/5.10      comm_monoid_set_nat: ( set_nat > set_nat > set_nat ) > set_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Groups_Ocomm__monoid_001t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 9.16/5.10      comm_m4707310049023135612at_nat: ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ) > set_Pr8551490117392284871at_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Groups_Ocomm__monoid_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.16/5.10      comm_m5709050211238513046at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Groups_Ocomm__monoid_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
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% 9.16/5.10  thf(sy_c_Int_Onat,type,
% 9.16/5.10      nat2: int > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Int_Opcr__int,type,
% 9.16/5.10      pcr_int: product_prod_nat_nat > int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Code____Numeral__Ointeger,type,
% 9.16/5.10      ring_18347121197199848620nteger: int > code_integer ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 9.16/5.10      ring_1_of_int_int: int > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 9.16/5.10      ring_1_of_int_rat: int > rat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Int_Osub,type,
% 9.16/5.10      sub: num > num > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
% 9.16/5.10      inf_in8201999774870019094_int_o: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
% 9.16/5.10      inf_in3563340378267265229eger_o: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_062_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J,type,
% 9.16/5.10      inf_in2641120393918057659_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
% 9.16/5.10      inf_in3295504058751909687_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_Eo_J,type,
% 9.16/5.10      inf_in9018898317438245890at_o_o: ( ( produc3658429121746597890et_nat > $o ) > $o ) > ( ( produc3658429121746597890et_nat > $o ) > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
% 9.16/5.10      inf_in8045883074377559328_int_o: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Int__Oint_M_Eo_J,type,
% 9.16/5.10      inf_inf_int_o: ( int > $o ) > ( int > $o ) > int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J,type,
% 9.16/5.10      inf_inf_list_char_o: ( list_char > $o ) > ( list_char > $o ) > list_char > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 9.16/5.10      inf_inf_nat_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Nat__Onat_M_Eo_J,type,
% 9.16/5.10      inf_inf_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 9.16/5.10      inf_in3604695632404883862_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 9.16/5.10      inf_in5163264567034779214_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
% 9.16/5.10      inf_inf_set_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > set_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
% 9.16/5.10      inf_in5102985939729578038_int_o: ( set_Pr958786334691620121nt_int > $o ) > ( set_Pr958786334691620121nt_int > $o ) > set_Pr958786334691620121nt_int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001_Eo,type,
% 9.16/5.10      inf_inf_o: $o > $o > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Assertions__Oassn,type,
% 9.16/5.10      inf_inf_assn: assn > assn > assn ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 9.16/5.10      inf_inf_filter_nat: filter_nat > filter_nat > filter_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Int__Oint,type,
% 9.16/5.10      inf_inf_int: int > int > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
% 9.16/5.10      inf_inf_nat: nat > nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Product____Type__Ounit,type,
% 9.16/5.10      inf_inf_Product_unit: product_unit > product_unit > product_unit ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Rat__Orat,type,
% 9.16/5.10      inf_inf_rat: rat > rat > rat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
% 9.16/5.10      inf_in1906310914598751387_nat_o: set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_Eo_J,type,
% 9.16/5.10      inf_inf_set_o: set_o > set_o > set_o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 9.16/5.10      inf_in1364745209274528805nteger: set_Code_integer > set_Code_integer > set_Code_integer ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Int__Oint_J,type,
% 9.16/5.10      inf_inf_set_int: set_int > set_int > set_int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 9.16/5.10      inf_inf_set_list_nat: set_list_nat > set_list_nat > set_list_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__List__Olist_It__String__Ochar_J_J,type,
% 9.16/5.10      inf_in6177012701088388009t_char: set_list_char > set_list_char > set_list_char ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.16/5.10      inf_inf_set_nat: set_nat > set_nat > set_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 9.16/5.10      inf_in8806012763027673301nt_int: set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
% 9.16/5.10      inf_in3408396081536963678nteger: set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
% 9.16/5.10      inf_in3088352823822785602et_nat: set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
% 9.16/5.10      inf_in1768905781608824518et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 9.16/5.10      inf_in2576786181675586251nt_int: set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 9.16/5.10      inf_in2269163501485487111nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 9.16/5.10      inf_in1697001100524423349at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.16/5.10      inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 9.16/5.10      inf_in7913087082777306421at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Rat__Orat_J,type,
% 9.16/5.10      inf_inf_set_rat: set_rat > set_rat > set_rat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 9.16/5.10      inf_inf_set_set_nat: set_set_nat > set_set_nat > set_set_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 9.16/5.10      inf_in8396524679539076455nt_int: set_se6260736226359567993nt_int > set_se6260736226359567993nt_int > set_se6260736226359567993nt_int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__String__Oliteral_J,type,
% 9.16/5.10      inf_inf_set_literal: set_literal > set_literal > set_literal ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J,type,
% 9.16/5.10      semila3963277552210239504char_o: ( ( list_char > $o ) > ( list_char > $o ) > list_char > $o ) > ( list_char > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 9.16/5.10      semila6538661356715008162_int_o: ( ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr_001t__Code____Numeral__Ointeger,type,
% 9.16/5.10      semila6106414119144251899nteger: ( code_integer > code_integer > code_integer ) > code_integer > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr_001t__Int__Oint,type,
% 9.16/5.10      semila9079005292280841162tr_int: ( int > int > int ) > int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr_001t__Nat__Onat,type,
% 9.16/5.10      semila9081495762789891438tr_nat: ( nat > nat > nat ) > nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr_001t__Set__Oset_I_Eo_J,type,
% 9.16/5.10      semila1065760912024005978_set_o: ( set_o > set_o > set_o ) > set_o > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr_001t__Set__Oset_It__Int__Oint_J,type,
% 9.16/5.10      semila6287294981380917632et_int: ( set_int > set_int > set_int ) > set_int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 9.16/5.10      semila7136768128396663732st_nat: ( set_list_nat > set_list_nat > set_list_nat ) > set_list_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.16/5.10      semila1241773964035338532et_nat: ( set_nat > set_nat > set_nat ) > set_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr_001t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 9.16/5.10      semila6683195626996185257at_nat: ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ) > set_Pr8551490117392284871at_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.16/5.10      semila858173770281612099at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 9.16/5.10      semila3675781407871293737at_nat: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ) > set_Pr4329608150637261639at_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr_001t__Set__Oset_It__Rat__Orat_J,type,
% 9.16/5.10      semila6956917442496717612et_rat: ( set_rat > set_rat > set_rat ) > set_rat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr__order_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J,type,
% 9.16/5.10      semila3134969884451571676char_o: ( ( list_char > $o ) > ( list_char > $o ) > list_char > $o ) > ( list_char > $o ) > ( ( list_char > $o ) > ( list_char > $o ) > $o ) > ( ( list_char > $o ) > ( list_char > $o ) > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr__order_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 9.16/5.10      semila8052717425514686422_int_o: ( ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > ( ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ) > ( ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 9.16/5.10      semila5926144314033625522er_nat: ( filter_nat > filter_nat > filter_nat ) > filter_nat > ( filter_nat > filter_nat > $o ) > ( filter_nat > filter_nat > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 9.16/5.10      semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_I_Eo_J,type,
% 9.16/5.10      semila2554085542299052326_set_o: ( set_o > set_o > set_o ) > set_o > ( set_o > set_o > $o ) > ( set_o > set_o > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__Int__Oint_J,type,
% 9.16/5.10      semila6712789903965657268et_int: ( set_int > set_int > set_int ) > set_int > ( set_int > set_int > $o ) > ( set_int > set_int > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 9.16/5.10      semila2613578647866687720st_nat: ( set_list_nat > set_list_nat > set_list_nat ) > set_list_nat > ( set_list_nat > set_list_nat > $o ) > ( set_list_nat > set_list_nat > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.16/5.10      semila1667268886620078168et_nat: ( set_nat > set_nat > set_nat ) > set_nat > ( set_nat > set_nat > $o ) > ( set_nat > set_nat > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 9.16/5.10      semila5207306265035627125at_nat: ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ) > set_Pr8551490117392284871at_nat > ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > $o ) > ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.16/5.10      semila4918476307565957903at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 9.16/5.10      semila6534579987270727413at_nat: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ) > set_Pr4329608150637261639at_nat > ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__Rat__Orat_J,type,
% 9.16/5.10      semila7382412365081457248et_rat: ( set_rat > set_rat > set_rat ) > set_rat > ( set_rat > set_rat > $o ) > ( set_rat > set_rat > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osemilattice__order_001t__Nat__Onat,type,
% 9.16/5.10      semila1248733672344298208er_nat: ( nat > nat > nat ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
% 9.16/5.10      sup_su600977994968626096_int_o: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
% 9.16/5.10      sup_su234547053653886311eger_o: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_062_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J,type,
% 9.16/5.10      sup_su6535292691877529429_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
% 9.16/5.10      sup_su1630790145277462993_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_Eo_J,type,
% 9.16/5.10      sup_su8003631835303541148at_o_o: ( ( produc3658429121746597890et_nat > $o ) > $o ) > ( ( produc3658429121746597890et_nat > $o ) > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
% 9.16/5.10      sup_su4182031696650224058_int_o: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Int__Oint_M_Eo_J,type,
% 9.16/5.10      sup_sup_int_o: ( int > $o ) > ( int > $o ) > int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J,type,
% 9.16/5.10      sup_sup_list_char_o: ( list_char > $o ) > ( list_char > $o ) > list_char > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_062_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J,type,
% 9.16/5.10      sup_su2200014604384089602_nat_o: ( multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o ) > ( multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o ) > multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Nat__Onat_M_Eo_J,type,
% 9.16/5.10      sup_sup_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 9.16/5.10      sup_su8463660629351352368_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
% 9.16/5.10      sup_su6256023009775730178_nat_o: ( produc4166570645942440679at_nat > $o ) > ( produc4166570645942440679at_nat > $o ) > produc4166570645942440679at_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
% 9.16/5.10      sup_su2080679670758317954_nat_o: ( produc3843707927480180839at_nat > $o ) > ( produc3843707927480180839at_nat > $o ) > produc3843707927480180839at_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
% 9.16/5.10      sup_sup_set_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > set_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_M_Eo_J,type,
% 9.16/5.10      sup_su1852724690005176016_int_o: ( set_Pr958786334691620121nt_int > $o ) > ( set_Pr958786334691620121nt_int > $o ) > set_Pr958786334691620121nt_int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_062_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J,type,
% 9.16/5.10      sup_su7519161239522478338_nat_o: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001t__Assertions__Oassn,type,
% 9.16/5.10      sup_sup_assn: assn > assn > assn ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 9.16/5.10      sup_sup_filter_nat: filter_nat > filter_nat > filter_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001t__Int__Oint,type,
% 9.16/5.10      sup_sup_int: int > int > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 9.16/5.10      sup_sup_nat: nat > nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001t__Product____Type__Ounit,type,
% 9.16/5.10      sup_sup_Product_unit: product_unit > product_unit > product_unit ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001t__Rat__Orat,type,
% 9.16/5.10      sup_sup_rat: rat > rat > rat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
% 9.16/5.10      sup_su5209123915105501825_nat_o: set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_Eo_J,type,
% 9.16/5.10      sup_sup_set_o: set_o > set_o > set_o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 9.16/5.10      sup_su848401254843788991nteger: set_Code_integer > set_Code_integer > set_Code_integer ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Int__Oint_J,type,
% 9.16/5.10      sup_sup_set_int: set_int > set_int > set_int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 9.16/5.10      sup_sup_set_list_nat: set_list_nat > set_list_nat > set_list_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.16/5.10      sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 9.16/5.10      sup_su3298353300217089135nt_int: set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_J,type,
% 9.16/5.10      sup_su4591284015454442744nteger: set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger ).
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% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
% 9.16/5.10      sup_su7128418612487073120et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
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% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
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% 9.16/5.10  
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% 9.16/5.10      sup_su718114333110466843at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat ).
% 9.16/5.10  
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% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Rat__Orat_J,type,
% 9.16/5.10      sup_sup_set_rat: set_rat > set_rat > set_rat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 9.16/5.10      sup_sup_set_set_nat: set_set_nat > set_set_nat > set_set_nat ).
% 9.16/5.10  
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% 9.16/5.10  
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% 9.16/5.10  
% 9.16/5.10  thf(sy_c_List_Ofold_001t__Int__Oint_001t__Int__Oint,type,
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% 9.16/5.10  thf(sy_c_List_Ofold_001t__Nat__Onat_001t__Nat__Onat,type,
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% 9.16/5.10  
% 9.16/5.10  thf(sy_c_List_Olast_001t__Nat__Onat,type,
% 9.16/5.10      last_nat: list_nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_List_Olinorder__class_Osort__key_001t__Int__Oint_001t__Int__Oint,type,
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% 9.16/5.10  
% 9.16/5.10  thf(sy_c_List_Olinorder__class_Osort__key_001t__Nat__Onat_001t__Nat__Onat,type,
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% 9.16/5.10  
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% 9.16/5.10      cons_int: int > list_int > list_int ).
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% 9.16/5.10  thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 9.16/5.10      cons_nat: nat > list_nat > list_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_List_Olist_OCons_001t__String__Ochar,type,
% 9.16/5.10      cons_char: char > list_char > list_char ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 9.16/5.10      nil_int: list_int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 9.16/5.10      nil_nat: list_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_List_Olist_ONil_001t__String__Ochar,type,
% 9.16/5.10      nil_char: list_char ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_List_Olist_Olist__all2_001t__String__Ochar_001t__String__Ochar,type,
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% 9.16/5.10  thf(sy_c_List_Olist_Olist__all_001t__String__Ochar,type,
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% 9.16/5.10  thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
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% 9.16/5.10  
% 9.16/5.10  thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
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% 9.16/5.10  
% 9.16/5.10  thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
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% 9.16/5.10  
% 9.16/5.10  thf(sy_c_List_Olist_Oset_001t__String__Ochar,type,
% 9.16/5.10      set_char2: list_char > set_char ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_List_Oord_Olexordp_001t__String__Ochar,type,
% 9.16/5.10      lexordp_char: ( char > char > $o ) > list_char > list_char > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_List_Oord_Olexordp__eq_001t__String__Ochar,type,
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% 9.16/5.10  
% 9.16/5.10  thf(sy_c_List_Oupt,type,
% 9.16/5.10      upt: nat > nat > list_nat ).
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% 9.16/5.10  
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% 9.16/5.10  
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% 9.16/5.10  
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% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Misc_Ouncurry_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 9.16/5.10      uncurr7511940902602773877_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Misc_Ouncurry_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.16/5.10      uncurr8011562610307062878at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Multiset_Oadd__mset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.16/5.10      add_ms2612439473150266591at_nat: product_prod_nat_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Multiset_Oms__strict,type,
% 9.16/5.10      ms_strict: set_Pr8551490117392284871at_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Multiset_Oms__weak,type,
% 9.16/5.10      ms_weak: set_Pr8551490117392284871at_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Multiset_Opw__leq,type,
% 9.16/5.10      pw_leq: multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Multiset_Oset__mset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.16/5.10      set_ms8126754132646256062at_nat: multis2468970476368604999at_nat > set_Pr1261947904930325089at_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat_OSuc,type,
% 9.16/5.10      suc: nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 9.16/5.10      case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 9.16/5.10      case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 9.16/5.10      case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat_Onat_Opred,type,
% 9.16/5.10      pred: nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat_Osemiring__1__class_ONats_001t__Int__Oint,type,
% 9.16/5.10      semiring_1_Nats_int: set_int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 9.16/5.10      semiri4939895301339042750nteger: nat > code_integer ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Onatural,type,
% 9.16/5.10      semiri3763490453095760265atural: nat > code_natural ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 9.16/5.10      semiri1314217659103216013at_int: nat > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 9.16/5.10      semiri1316708129612266289at_nat: nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 9.16/5.10      semiri681578069525770553at_rat: nat > rat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Code____Numeral__Ointeger,type,
% 9.16/5.10      semiri4055485073559036834nteger: ( code_integer > code_integer ) > nat > code_integer > code_integer ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
% 9.16/5.10      semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Nat__Onat,type,
% 9.16/5.10      semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Rat__Orat,type,
% 9.16/5.10      semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 9.16/5.10      size_size_list_int: list_int > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 9.16/5.10      size_size_list_nat: list_nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__String__Ochar_J,type,
% 9.16/5.10      size_size_list_char: list_char > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat_Osize__class_Osize_001t__String__Oliteral,type,
% 9.16/5.10      size_size_literal: literal > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat__Bijection_Oint__decode,type,
% 9.16/5.10      nat_int_decode: nat > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat__Bijection_Oint__encode,type,
% 9.16/5.10      nat_int_encode: int > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat__Bijection_Olist__decode,type,
% 9.16/5.10      nat_list_decode: nat > list_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat__Bijection_Olist__decode__rel,type,
% 9.16/5.10      nat_list_decode_rel: nat > nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat__Bijection_Olist__encode,type,
% 9.16/5.10      nat_list_encode: list_nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 9.16/5.10      nat_list_encode_rel: list_nat > list_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat__Bijection_Oprod__decode,type,
% 9.16/5.10      nat_prod_decode: nat > product_prod_nat_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 9.16/5.10      nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 9.16/5.10      nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 9.16/5.10      nat_prod_encode: product_prod_nat_nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat__Bijection_Oset__decode,type,
% 9.16/5.10      nat_set_decode: nat > set_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat__Bijection_Oset__encode,type,
% 9.16/5.10      nat_set_encode: set_nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat__Bijection_Osum__decode,type,
% 9.16/5.10      nat_sum_decode: nat > sum_sum_nat_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat__Bijection_Osum__encode,type,
% 9.16/5.10      nat_sum_encode: sum_sum_nat_nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Nat__Bijection_Otriangle,type,
% 9.16/5.10      nat_triangle: nat > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_OBitM,type,
% 9.16/5.10      bitM: num > num ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Oinc,type,
% 9.16/5.10      inc: num > num ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Onat__of__num,type,
% 9.16/5.10      nat_of_num: num > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 9.16/5.10      neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 9.16/5.10      neg_numeral_dbl_int: int > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 9.16/5.10      neg_numeral_dbl_rat: rat > rat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 9.16/5.10      neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 9.16/5.10      neg_nu3811975205180677377ec_int: int > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 9.16/5.10      neg_nu3179335615603231917ec_rat: rat > rat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
% 9.16/5.10      neg_nu5831290666863070958nteger: code_integer > code_integer ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 9.16/5.10      neg_nu5851722552734809277nc_int: int > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 9.16/5.10      neg_nu5219082963157363817nc_rat: rat > rat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Code____Numeral__Ointeger,type,
% 9.16/5.10      neg_nu5755505904847501662nteger: num > num > code_integer ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 9.16/5.10      neg_numeral_sub_int: num > num > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Rat__Orat,type,
% 9.16/5.10      neg_numeral_sub_rat: num > num > rat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Onum_OBit0,type,
% 9.16/5.10      bit0: num > num ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Onum_OBit1,type,
% 9.16/5.10      bit1: num > num ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Onum_OOne,type,
% 9.16/5.10      one: num ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
% 9.16/5.10      case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Onum__of__nat,type,
% 9.16/5.10      num_of_nat: nat > num ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 9.16/5.10      numera6620942414471956472nteger: num > code_integer ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Onatural,type,
% 9.16/5.10      numera5444537566228673987atural: num > code_natural ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
% 9.16/5.10      numeral_numeral_int: num > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 9.16/5.10      numeral_numeral_nat: num > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
% 9.16/5.10      numeral_numeral_rat: num > rat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Opred__numeral,type,
% 9.16/5.10      pred_numeral: num > nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Oring__1__class_Oiszero_001t__Code____Numeral__Ointeger,type,
% 9.16/5.10      ring_16219924574208605041nteger: code_integer > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Oring__1__class_Oiszero_001t__Int__Oint,type,
% 9.16/5.10      ring_1_iszero_int: int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Num_Oring__1__class_Oiszero_001t__Rat__Orat,type,
% 9.16/5.10      ring_1_iszero_rat: rat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Option_Ooption_ONone_001t__Num__Onum,type,
% 9.16/5.10      none_num: option_num ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
% 9.16/5.10      some_num: num > option_num ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Option_Ooption_Ocase__option_001t__Int__Oint_001t__Num__Onum,type,
% 9.16/5.10      case_option_int_num: int > ( num > int ) > option_num > int ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Num__Onum,type,
% 9.16/5.10      case_option_num_num: num > ( num > num ) > option_num > num ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
% 9.16/5.10      case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Num__Onum,type,
% 9.16/5.10      map_option_num_num: ( num > num ) > option_num > option_num ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Order__Relation_OunderS_001t__Nat__Onat,type,
% 9.16/5.10      order_underS_nat: set_Pr1261947904930325089at_nat > nat > set_nat ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Order__Relation_Owell__order__on_001t__Nat__Onat,type,
% 9.16/5.10      order_2888998067076097458on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
% 9.16/5.10      bot_bo1403522918969695512_int_o: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_M_Eo_J_J,type,
% 9.16/5.10      bot_bo3000040243691356879eger_o: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_062_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J,type,
% 9.16/5.10      bot_bo3790638025767943357_nat_o: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
% 9.16/5.10      bot_bo5580076615179976505_nat_o: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_Eo_J,type,
% 9.16/5.10      bot_bo7963750851167320836at_o_o: ( produc3658429121746597890et_nat > $o ) > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Orderings_Obot__class_Obot_001_062_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
% 9.16/5.10      bot_bo8662317086119403298_int_o: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Orderings_Obot__class_Obot_001_062_I_Eo_M_Eo_J,type,
% 9.16/5.10      bot_bot_o_o: $o > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Int__Oint_M_Eo_J,type,
% 9.16/5.10      bot_bot_int_o: int > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Orderings_Obot__class_Obot_001_062_It__List__Olist_It__String__Ochar_J_M_Eo_J,type,
% 9.16/5.10      bot_bot_list_char_o: list_char > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 9.16/5.10      bot_bot_nat_nat_o: nat > nat > $o ).
% 9.16/5.10  
% 9.16/5.10  thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Nat__Onat_M_Eo_J,type,
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% 9.16/5.11      produc1515462096303866701_nat_o: ( produc3925858234332021118et_nat > produc3658429121746597890et_nat ) > produc2732055786443039994et_nat > produc3925858234332021118et_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Oapsnd_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
% 9.16/5.11      produc717174245515237944e_term: ( produc8923325533196201883nteger > produc8923325533196201883nteger ) > produc1908205239877642774nteger > produc1908205239877642774nteger ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Oapsnd_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
% 9.16/5.11      produc7714581247149323085_nat_o: ( produc3658429121746597890et_nat > produc3925858234332021118et_nat ) > produc3925858234332021118et_nat > produc2732055786443039994et_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Oapsnd_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J,type,
% 9.16/5.11      produc8750854537940449737_nat_o: ( produc3658429121746597890et_nat > produc3658429121746597890et_nat ) > produc3925858234332021118et_nat > produc3925858234332021118et_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Oapsnd_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__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
% 9.16/5.11      produc7011684061226097695e_term: ( product_prod_int_int > product_prod_int_int ) > produc7773217078559923341nt_int > produc7773217078559923341nt_int ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Oapsnd_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_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J,type,
% 9.16/5.11      produc4973430039190721449e_term: ( product_prod_int_int > product_prod_int_int ) > produc2285326912895808259nt_int > produc2285326912895808259nt_int ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo,type,
% 9.16/5.11      produc2558449545302689196_int_o: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc7773217078559923341nt_int > $o ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 9.16/5.11      produc5122537100556696953nt_int: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > produc7773217078559923341nt_int ) > produc7773217078559923341nt_int > produc7773217078559923341nt_int ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J,type,
% 9.16/5.11      produc4111701587417901774et_int: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_int ) > produc7773217078559923341nt_int > set_int ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.16/5.11      produc8289552606927098482et_nat: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat ) > produc7773217078559923341nt_int > set_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 9.16/5.11      produc3577156405726439208et_nat: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_set_nat ) > produc7773217078559923341nt_int > set_set_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 9.16/5.11      produc575502675617541261nt_int: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_se6260736226359567993nt_int ) > produc7773217078559923341nt_int > set_se6260736226359567993nt_int ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_Eo,type,
% 9.16/5.11      produc6253627499356882019eger_o: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc1908205239877642774nteger > $o ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J,type,
% 9.16/5.11      produc6512950862096126219nteger: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > produc1908205239877642774nteger ) > produc1908205239877642774nteger > produc1908205239877642774nteger ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Int__Oint_J,type,
% 9.16/5.11      produc5700143819190870999et_int: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int ) > produc1908205239877642774nteger > set_int ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.16/5.11      produc654622801845291899et_nat: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat ) > produc1908205239877642774nteger > set_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001_Eo,type,
% 9.16/5.11      produc5150382289251079596at_o_o: ( ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o ) > produc4928098042776334183_nat_o > $o ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001_Eo,type,
% 9.16/5.11      produc838355143741117751_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > produc2732055786443039994et_nat > $o ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
% 9.16/5.11      produc2377985495875741467et_nat: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > produc2732055786443039994et_nat ) > produc2732055786443039994et_nat > produc2732055786443039994et_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001_Eo,type,
% 9.16/5.11      produc1437786849005270451_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
% 9.16/5.11  
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% 9.16/5.11      produc4058941399401191971et_nat: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > produc3925858234332021118et_nat ) > produc3925858234332021118et_nat > produc3925858234332021118et_nat ).
% 9.16/5.11  
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% 9.16/5.11      produc4627640435386541703et_int: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_int ) > produc3925858234332021118et_nat > set_int ).
% 9.16/5.11  
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% 9.16/5.11      produc8805491454895738411et_nat: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_nat ) > produc3925858234332021118et_nat > set_nat ).
% 9.16/5.11  
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% 9.16/5.11      produc2333231157791014625et_nat: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_set_nat ) > produc3925858234332021118et_nat > set_set_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo,type,
% 9.16/5.11      produc1573362020775583542_int_o: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc2285326912895808259nt_int > $o ).
% 9.16/5.11  
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% 9.16/5.11      produc8492565224438309093nt_int: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > produc2285326912895808259nt_int ) > produc2285326912895808259nt_int > produc2285326912895808259nt_int ).
% 9.16/5.11  
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% 9.16/5.11      produc3619988815162578792et_nat: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > set_nat ) > produc2285326912895808259nt_int > set_nat ).
% 9.16/5.11  
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% 9.16/5.11  
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% 9.16/5.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
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% 9.16/5.11  
% 9.16/5.11  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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% 9.16/5.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
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% 9.16/5.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
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% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat,type,
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% 9.16/5.11  thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J_001_Eo,type,
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% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Product__Type_Ounit_OAbs__unit,type,
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% 9.16/5.11  thf(sy_c_Random_Olog,type,
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% 9.16/5.11  thf(sy_c_Random_Olog__rel,type,
% 9.16/5.11      log_rel: produc7822875418678951345atural > produc7822875418678951345atural > $o ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Random_Ominus__shift,type,
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% 9.16/5.11  thf(sy_c_Random_Osplit__seed,type,
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% 9.16/5.11  thf(sy_c_Random__Pred_Onot__randompred,type,
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% 9.16/5.11  
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% 9.16/5.11  thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Rat__Orat,type,
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% 9.16/5.11  thf(sy_c_Set_Othe__elem_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 9.16/5.11      the_el221668144340439132at_nat: set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001_Eo_001_Eo,type,
% 9.16/5.11      vimage_o_o: ( $o > $o ) > set_o > set_o ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001_Eo_001t__Int__Oint,type,
% 9.16/5.11      vimage_o_int: ( $o > int ) > set_int > set_o ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001_Eo_001t__Nat__Onat,type,
% 9.16/5.11      vimage_o_nat: ( $o > nat ) > set_nat > set_o ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001_Eo_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.16/5.11      vimage2606541041029201316at_nat: ( $o > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > set_o ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001_Eo_001t__Rat__Orat,type,
% 9.16/5.11      vimage_o_rat: ( $o > rat ) > set_rat > set_o ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Int__Oint_001_Eo,type,
% 9.16/5.11      vimage_int_o: ( int > $o ) > set_o > set_int ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Int__Oint_001t__Int__Oint,type,
% 9.16/5.11      vimage_int_int: ( int > int ) > set_int > set_int ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Int__Oint_001t__Nat__Onat,type,
% 9.16/5.11      vimage_int_nat: ( int > nat ) > set_nat > set_int ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.16/5.11      vimage1827798767263827160at_nat: ( int > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > set_int ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Int__Oint_001t__Rat__Orat,type,
% 9.16/5.11      vimage_int_rat: ( int > rat ) > set_rat > set_int ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Int__Oint_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.16/5.11      vimage_int_set_nat: ( int > set_nat ) > set_set_nat > set_int ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__List__Olist_It__Nat__Onat_J_001t__Int__Oint,type,
% 9.16/5.11      vimage_list_nat_int: ( list_nat > int ) > set_int > set_list_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat,type,
% 9.16/5.11      vimage_list_nat_nat: ( list_nat > nat ) > set_nat > set_list_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Nat__Onat_001_Eo,type,
% 9.16/5.11      vimage_nat_o: ( nat > $o ) > set_o > set_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Nat__Onat_001t__Int__Oint,type,
% 9.16/5.11      vimage_nat_int: ( nat > int ) > set_int > set_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 9.16/5.11      vimage_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Nat__Onat_001t__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 9.16/5.11      vimage7262694317370708122at_nat: ( nat > produc4166570645942440679at_nat ) > set_Pr8551490117392284871at_nat > set_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.16/5.11      vimage8013328719654469172at_nat: ( nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > set_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Nat__Onat_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 9.16/5.11      vimage6435164912253009178at_nat: ( nat > produc3843707927480180839at_nat ) > set_Pr4329608150637261639at_nat > set_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Nat__Onat_001t__Rat__Orat,type,
% 9.16/5.11      vimage_nat_rat: ( nat > rat ) > set_rat > set_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.16/5.11      vimage_nat_set_nat: ( nat > set_nat ) > set_set_nat > set_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Nat__Onat_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 9.16/5.11      vimage2935056327143036492nt_int: ( nat > set_Pr958786334691620121nt_int ) > set_se6260736226359567993nt_int > set_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001_Eo,type,
% 9.16/5.11      vimage2280073292226551852_nat_o: ( produc4166570645942440679at_nat > $o ) > set_o > set_Pr8551490117392284871at_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Int__Oint,type,
% 9.16/5.11      vimage7949981338974167704at_int: ( produc4166570645942440679at_nat > int ) > set_int > set_Pr8551490117392284871at_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Nat__Onat,type,
% 9.16/5.11      vimage7952471809483217980at_nat: ( produc4166570645942440679at_nat > nat ) > set_nat > set_Pr8551490117392284871at_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 9.16/5.11      vimage3529983231074640251at_nat: ( produc4166570645942440679at_nat > produc4166570645942440679at_nat ) > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 9.16/5.11      vimage5412736291816116987at_nat: ( produc4166570645942440679at_nat > produc3843707927480180839at_nat ) > set_Pr4329608150637261639at_nat > set_Pr8551490117392284871at_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 9.16/5.11      vimage4653281326611754070at_nat: ( product_prod_nat_nat > nat ) > set_nat > set_Pr1261947904930325089at_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 9.16/5.11      vimage2449269961533847803at_nat: ( product_prod_nat_nat > product_prod_nat_nat ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001_Eo,type,
% 9.16/5.11      vimage3307185822755684012_nat_o: ( produc3843707927480180839at_nat > $o ) > set_o > set_Pr4329608150637261639at_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Nat__Onat,type,
% 9.16/5.11      vimage7134676753939176892at_nat: ( produc3843707927480180839at_nat > nat ) > set_nat > set_Pr4329608150637261639at_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 9.16/5.11      vimage2716263466903273467at_nat: ( produc3843707927480180839at_nat > produc4166570645942440679at_nat ) > set_Pr8551490117392284871at_nat > set_Pr4329608150637261639at_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 9.16/5.11      vimage6896080417876799867at_nat: ( produc3843707927480180839at_nat > produc3843707927480180839at_nat ) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Rat__Orat_001_Eo,type,
% 9.16/5.11      vimage_rat_o: ( rat > $o ) > set_o > set_rat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Rat__Orat_001t__Int__Oint,type,
% 9.16/5.11      vimage_rat_int: ( rat > int ) > set_int > set_rat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Rat__Orat_001t__Nat__Onat,type,
% 9.16/5.11      vimage_rat_nat: ( rat > nat ) > set_nat > set_rat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Rat__Orat_001t__Rat__Orat,type,
% 9.16/5.11      vimage_rat_rat: ( rat > rat ) > set_rat > set_rat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Set__Oset_It__Nat__Onat_J_001_Eo,type,
% 9.16/5.11      vimage_set_nat_o: ( set_nat > $o ) > set_o > set_set_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Set__Oset_It__Nat__Onat_J_001t__Int__Oint,type,
% 9.16/5.11      vimage_set_nat_int: ( set_nat > int ) > set_int > set_set_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Set__Oset_It__Nat__Onat_J_001t__Nat__Onat,type,
% 9.16/5.11      vimage_set_nat_nat: ( set_nat > nat ) > set_nat > set_set_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.16/5.11      vimage4765135879290611145et_nat: ( set_nat > set_nat ) > set_set_nat > set_set_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set_Ovimage_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001t__Nat__Onat,type,
% 9.16/5.11      vimage928727498438615150nt_nat: ( set_Pr958786334691620121nt_int > nat ) > set_nat > set_se6260736226359567993nt_int ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Assertions__Oassn,type,
% 9.16/5.11      set_fo1959793692361082170t_assn: ( nat > assn > assn ) > nat > nat > assn > assn ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Code____Numeral__Ointeger,type,
% 9.16/5.11      set_fo1084959871951514735nteger: ( nat > code_integer > code_integer ) > nat > nat > code_integer > code_integer ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Int__Oint,type,
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% 9.16/5.11      set_fo4497565046347964853at_nat: ( nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat ) > nat > nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Nat__Onat,type,
% 9.16/5.11      set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Rat__Orat,type,
% 9.16/5.11      set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat__rel_001t__Nat__Onat,type,
% 9.16/5.11      set_fo3699595496184130361el_nat: produc4471711990508489141at_nat > produc4471711990508489141at_nat > $o ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001_Eo,type,
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% 9.16/5.11  
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% 9.16/5.11      set_or1955772592623580779er_nat: filter_nat > filter_nat > set_filter_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Int__Oint,type,
% 9.16/5.11      set_or1266510415728281911st_int: int > int > set_int ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
% 9.16/5.11      set_or1269000886237332187st_nat: nat > nat > set_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Rat__Orat,type,
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% 9.16/5.11  
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% 9.16/5.11      set_or266616469461849773_set_o: set_o > set_o > set_set_o ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Int__Oint_J,type,
% 9.16/5.11      set_or370866239135849197et_int: set_int > set_int > set_set_int ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 9.16/5.11      set_or1270514513317581473st_nat: set_list_nat > set_list_nat > set_set_list_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.16/5.11      set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Rat__Orat_J,type,
% 9.16/5.11      set_or1040488700251649177et_rat: set_rat > set_rat > set_set_rat ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__String__Oliteral,type,
% 9.16/5.11      set_or8436436507035938825iteral: literal > literal > set_literal ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001_Eo,type,
% 9.16/5.11      set_or7139685690850216873Than_o: $o > $o > set_o ).
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% 9.16/5.11  thf(sy_c_Wellfounded_Opred__nat,type,
% 9.16/5.11      pred_nat: set_Pr1261947904930325089at_nat ).
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% 9.16/5.11      wf_nat: set_Pr1261947904930325089at_nat > $o ).
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% 9.16/5.11  thf(sy_c_member_001_Eo,type,
% 9.16/5.11      member_o: $o > set_o > $o ).
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% 9.16/5.11  thf(sy_c_member_001t__Filter__Ofilter_It__Nat__Onat_J,type,
% 9.16/5.11      member_filter_nat: filter_nat > set_filter_nat > $o ).
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% 9.16/5.11  thf(sy_c_member_001t__Int__Oint,type,
% 9.16/5.11      member_int: int > set_int > $o ).
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% 9.16/5.11  thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 9.16/5.11      member_list_nat: list_nat > set_list_nat > $o ).
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% 9.16/5.11      member_list_char: list_char > set_list_char > $o ).
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% 9.16/5.11      member_nat: nat > set_nat > $o ).
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% 9.16/5.11      member4164122664394876845nteger: produc1908205239877642774nteger > set_Pr1281608226676607948nteger > $o ).
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% 9.16/5.11      member1996754912294343701et_nat: produc3925858234332021118et_nat > set_Pr3286484037609594932et_nat > $o ).
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% 9.16/5.11      member7618704894036264090nt_int: produc2285326912895808259nt_int > set_Pr9222295170931077689nt_int > $o ).
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% 9.16/5.11  thf(sy_c_member_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 9.16/5.11      member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
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% 9.16/5.11      member6689249552917799696at_nat: produc4166570645942440679at_nat > set_Pr8551490117392284871at_nat > $o ).
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% 9.16/5.11      member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
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% 9.16/5.11      member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
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% 9.16/5.11      member8277197624267554838et_nat: produc7819656566062154093et_nat > set_Pr5488025237498180813et_nat > $o ).
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% 9.16/5.11      member4095101504841534314at_nat: produc732395585841259969at_nat > set_Pr457366540195662369at_nat > $o ).
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% 9.16/5.11      member5325734588016868240nt_int: produc412284730452459111nt_int > set_Pr8057934254988874055nt_int > $o ).
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% 9.16/5.11      member8757157785044589968at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > $o ).
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% 9.16/5.11      member_rat: rat > set_rat > $o ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 9.16/5.11      member_set_nat: set_nat > set_set_nat > $o ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 9.16/5.11      member2340774599025711042nt_int: set_Pr958786334691620121nt_int > set_se6260736226359567993nt_int > $o ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 9.16/5.11      member2643936169264416010at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat > $o ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_member_001t__String__Ochar,type,
% 9.16/5.11      member_char: char > set_char > $o ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_c_member_001t__String__Oliteral,type,
% 9.16/5.11      member_literal: literal > set_literal > $o ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_v_x,type,
% 9.16/5.11      x: assn ).
% 9.16/5.11  
% 9.16/5.11  thf(sy_v_y,type,
% 9.16/5.11      y: assn ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_0_Rep__assn__inject,axiom,
% 9.16/5.11      ! [X: assn,Y: assn] :
% 9.16/5.11        ( ( ( rep_assn @ X )
% 9.16/5.11          = ( rep_assn @ Y ) )
% 9.16/5.11        = ( X = Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_1_Rep__assn__inverse,axiom,
% 9.16/5.11      ! [X: assn] :
% 9.16/5.11        ( ( abs_assn @ ( rep_assn @ X ) )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_2_Abs__assn__eqI_I2_J,axiom,
% 9.16/5.11      ! [P: produc3658429121746597890et_nat > $o,Pr: assn] :
% 9.16/5.11        ( ! [H: produc3658429121746597890et_nat] :
% 9.16/5.11            ( ( P @ H )
% 9.16/5.11            = ( rep_assn @ Pr @ H ) )
% 9.16/5.11       => ( Pr
% 9.16/5.11          = ( abs_assn @ P ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_3_Abs__assn__eqI_I1_J,axiom,
% 9.16/5.11      ! [P: produc3658429121746597890et_nat > $o,Pr: assn] :
% 9.16/5.11        ( ! [H: produc3658429121746597890et_nat] :
% 9.16/5.11            ( ( P @ H )
% 9.16/5.11            = ( rep_assn @ Pr @ H ) )
% 9.16/5.11       => ( ( abs_assn @ P )
% 9.16/5.11          = Pr ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_4_wand__assn__def,axiom,
% 9.16/5.11      ( wand_assn
% 9.16/5.11      = ( ^ [P2: assn,Q: assn] : ( abs_assn @ ( wand_raw @ ( rep_assn @ P2 ) @ ( rep_assn @ Q ) ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_5_Abs__assn__inverse,axiom,
% 9.16/5.11      ! [Y: produc3658429121746597890et_nat > $o] :
% 9.16/5.11        ( ( member6576561426505652726_nat_o @ Y @ ( collec939566748876313656_nat_o @ proper ) )
% 9.16/5.11       => ( ( rep_assn @ ( abs_assn @ Y ) )
% 9.16/5.11          = Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_6_inf__assn__def,axiom,
% 9.16/5.11      ( inf_inf_assn
% 9.16/5.11      = ( ^ [P2: assn,Q: assn] :
% 9.16/5.11            ( abs_assn
% 9.16/5.11            @ ^ [H2: produc3658429121746597890et_nat] :
% 9.16/5.11                ( ( rep_assn @ P2 @ H2 )
% 9.16/5.11                & ( rep_assn @ Q @ H2 ) ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_7_sup__assn__def,axiom,
% 9.16/5.11      ( sup_sup_assn
% 9.16/5.11      = ( ^ [P2: assn,Q: assn] :
% 9.16/5.11            ( abs_assn
% 9.16/5.11            @ ^ [H2: produc3658429121746597890et_nat] :
% 9.16/5.11                ( ( rep_assn @ P2 @ H2 )
% 9.16/5.11                | ( rep_assn @ Q @ H2 ) ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_8_bot__assn__def,axiom,
% 9.16/5.11      ( bot_bot_assn
% 9.16/5.11      = ( abs_assn
% 9.16/5.11        @ ^ [Uu: produc3658429121746597890et_nat] : $false ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_9_Abs__assn__cases,axiom,
% 9.16/5.11      ! [X: assn] :
% 9.16/5.11        ~ ! [Y2: produc3658429121746597890et_nat > $o] :
% 9.16/5.11            ( ( X
% 9.16/5.11              = ( abs_assn @ Y2 ) )
% 9.16/5.11           => ~ ( member6576561426505652726_nat_o @ Y2 @ ( collec939566748876313656_nat_o @ proper ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_10_Abs__assn__induct,axiom,
% 9.16/5.11      ! [P: assn > $o,X: assn] :
% 9.16/5.11        ( ! [Y2: produc3658429121746597890et_nat > $o] :
% 9.16/5.11            ( ( member6576561426505652726_nat_o @ Y2 @ ( collec939566748876313656_nat_o @ proper ) )
% 9.16/5.11           => ( P @ ( abs_assn @ Y2 ) ) )
% 9.16/5.11       => ( P @ X ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_11_Abs__assn__inject,axiom,
% 9.16/5.11      ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 9.16/5.11        ( ( member6576561426505652726_nat_o @ X @ ( collec939566748876313656_nat_o @ proper ) )
% 9.16/5.11       => ( ( member6576561426505652726_nat_o @ Y @ ( collec939566748876313656_nat_o @ proper ) )
% 9.16/5.11         => ( ( ( abs_assn @ X )
% 9.16/5.11              = ( abs_assn @ Y ) )
% 9.16/5.11            = ( X = Y ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_12_Rep__assn,axiom,
% 9.16/5.11      ! [X: assn] : ( member6576561426505652726_nat_o @ ( rep_assn @ X ) @ ( collec939566748876313656_nat_o @ proper ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_13_Rep__assn__cases,axiom,
% 9.16/5.11      ! [Y: produc3658429121746597890et_nat > $o] :
% 9.16/5.11        ( ( member6576561426505652726_nat_o @ Y @ ( collec939566748876313656_nat_o @ proper ) )
% 9.16/5.11       => ~ ! [X2: assn] :
% 9.16/5.11              ( Y
% 9.16/5.11             != ( rep_assn @ X2 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_14_Rep__assn__induct,axiom,
% 9.16/5.11      ! [Y: produc3658429121746597890et_nat > $o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.16/5.11        ( ( member6576561426505652726_nat_o @ Y @ ( collec939566748876313656_nat_o @ proper ) )
% 9.16/5.11       => ( ! [X2: assn] : ( P @ ( rep_assn @ X2 ) )
% 9.16/5.11         => ( P @ Y ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_15_times__assn__def,axiom,
% 9.16/5.11      ( times_times_assn
% 9.16/5.11      = ( ^ [P2: assn,Q: assn] : ( abs_assn @ ( times_assn_raw @ ( rep_assn @ P2 ) @ ( rep_assn @ Q ) ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_16_bool__assn__proper_I2_J,axiom,
% 9.16/5.11      ( proper
% 9.16/5.11      @ ^ [Uu: produc3658429121746597890et_nat] : $false ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_17_bool__assn__proper_I3_J,axiom,
% 9.16/5.11      ! [P: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o] :
% 9.16/5.11        ( ( proper @ P )
% 9.16/5.11       => ( ( proper @ Q2 )
% 9.16/5.11         => ( proper
% 9.16/5.11            @ ^ [H2: produc3658429121746597890et_nat] :
% 9.16/5.11                ( ( P @ H2 )
% 9.16/5.11                | ( Q2 @ H2 ) ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_18_bool__assn__proper_I4_J,axiom,
% 9.16/5.11      ! [P: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o] :
% 9.16/5.11        ( ( proper @ P )
% 9.16/5.11       => ( ( proper @ Q2 )
% 9.16/5.11         => ( proper
% 9.16/5.11            @ ^ [H2: produc3658429121746597890et_nat] :
% 9.16/5.11                ( ( P @ H2 )
% 9.16/5.11                & ( Q2 @ H2 ) ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_19_wand__proper,axiom,
% 9.16/5.11      ! [P: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o] : ( proper @ ( wand_raw @ P @ Q2 ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_20_times__assn__proper,axiom,
% 9.16/5.11      ! [P: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o] :
% 9.16/5.11        ( ( proper @ P )
% 9.16/5.11       => ( ( proper @ Q2 )
% 9.16/5.11         => ( proper @ ( times_assn_raw @ P @ Q2 ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_21_assn__times__comm,axiom,
% 9.16/5.11      ( times_times_assn
% 9.16/5.11      = ( ^ [P2: assn,Q: assn] : ( times_times_assn @ Q @ P2 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_22_assn__times__assoc,axiom,
% 9.16/5.11      ! [P: assn,Q2: assn,R: assn] :
% 9.16/5.11        ( ( times_times_assn @ ( times_times_assn @ P @ Q2 ) @ R )
% 9.16/5.11        = ( times_times_assn @ P @ ( times_times_assn @ Q2 @ R ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_23_mod__starE,axiom,
% 9.16/5.11      ! [A: assn,B: assn,H3: produc3658429121746597890et_nat] :
% 9.16/5.11        ( ( rep_assn @ ( times_times_assn @ A @ B ) @ H3 )
% 9.16/5.11       => ~ ( ? [X_1: produc3658429121746597890et_nat] : ( rep_assn @ A @ X_1 )
% 9.16/5.11           => ! [H_2: produc3658429121746597890et_nat] :
% 9.16/5.11                ~ ( rep_assn @ B @ H_2 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_24_mod__starD,axiom,
% 9.16/5.11      ! [A2: assn,B2: assn,H3: produc3658429121746597890et_nat] :
% 9.16/5.11        ( ( rep_assn @ ( times_times_assn @ A2 @ B2 ) @ H3 )
% 9.16/5.11       => ? [H1: produc3658429121746597890et_nat,H22: produc3658429121746597890et_nat] :
% 9.16/5.11            ( ( rep_assn @ A2 @ H1 )
% 9.16/5.11            & ( rep_assn @ B2 @ H22 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_25_inf__sup__absorb,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ X @ Y ) )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_26_inf__sup__absorb,axiom,
% 9.16/5.11      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 9.16/5.11        ( ( inf_in3604695632404883862_int_o @ X @ ( sup_su8463660629351352368_int_o @ X @ Y ) )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_27_inf__sup__absorb,axiom,
% 9.16/5.11      ! [X: list_char > $o,Y: list_char > $o] :
% 9.16/5.11        ( ( inf_inf_list_char_o @ X @ ( sup_sup_list_char_o @ X @ Y ) )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_28_inf__sup__absorb,axiom,
% 9.16/5.11      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( inf_in1697001100524423349at_nat @ X @ ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_29_inf__sup__absorb,axiom,
% 9.16/5.11      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_30_inf__sup__absorb,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat] :
% 9.16/5.11        ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_31_inf__sup__absorb,axiom,
% 9.16/5.11      ! [X: nat,Y: nat] :
% 9.16/5.11        ( ( inf_inf_nat @ X @ ( sup_sup_nat @ X @ Y ) )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_32_inf__sup__absorb,axiom,
% 9.16/5.11      ! [X: int,Y: int] :
% 9.16/5.11        ( ( inf_inf_int @ X @ ( sup_sup_int @ X @ Y ) )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_33_sup__inf__absorb,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_34_sup__inf__absorb,axiom,
% 9.16/5.11      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 9.16/5.11        ( ( sup_su8463660629351352368_int_o @ X @ ( inf_in3604695632404883862_int_o @ X @ Y ) )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_35_sup__inf__absorb,axiom,
% 9.16/5.11      ! [X: list_char > $o,Y: list_char > $o] :
% 9.16/5.11        ( ( sup_sup_list_char_o @ X @ ( inf_inf_list_char_o @ X @ Y ) )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_36_sup__inf__absorb,axiom,
% 9.16/5.11      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( sup_su3035147773818789531at_nat @ X @ ( inf_in1697001100524423349at_nat @ X @ Y ) )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_37_sup__inf__absorb,axiom,
% 9.16/5.11      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ X @ Y ) )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_38_sup__inf__absorb,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat] :
% 9.16/5.11        ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ X @ Y ) )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_39_sup__inf__absorb,axiom,
% 9.16/5.11      ! [X: nat,Y: nat] :
% 9.16/5.11        ( ( sup_sup_nat @ X @ ( inf_inf_nat @ X @ Y ) )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_40_sup__inf__absorb,axiom,
% 9.16/5.11      ! [X: int,Y: int] :
% 9.16/5.11        ( ( sup_sup_int @ X @ ( inf_inf_int @ X @ Y ) )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_41_sup__bot__left,axiom,
% 9.16/5.11      ! [X: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat @ X )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_42_sup__bot__left,axiom,
% 9.16/5.11      ! [X: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat @ X )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_43_sup__bot__left,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat @ X )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_44_sup__bot__left,axiom,
% 9.16/5.11      ! [X: set_o] :
% 9.16/5.11        ( ( sup_sup_set_o @ bot_bot_set_o @ X )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_45_sup__bot__left,axiom,
% 9.16/5.11      ! [X: set_nat] :
% 9.16/5.11        ( ( sup_sup_set_nat @ bot_bot_set_nat @ X )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_46_sup__bot__left,axiom,
% 9.16/5.11      ! [X: set_int] :
% 9.16/5.11        ( ( sup_sup_set_int @ bot_bot_set_int @ X )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_47_sup__bot__right,axiom,
% 9.16/5.11      ! [X: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( sup_su3035147773818789531at_nat @ X @ bot_bo8422036546324065075at_nat )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_48_sup__bot__right,axiom,
% 9.16/5.11      ! [X: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( sup_su5525570899277871387at_nat @ X @ bot_bo228742789529271731at_nat )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_49_sup__bot__right,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( sup_su6327502436637775413at_nat @ X @ bot_bo2099793752762293965at_nat )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_50_sup__bot__right,axiom,
% 9.16/5.11      ! [X: set_o] :
% 9.16/5.11        ( ( sup_sup_set_o @ X @ bot_bot_set_o )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_51_sup__bot__right,axiom,
% 9.16/5.11      ! [X: set_nat] :
% 9.16/5.11        ( ( sup_sup_set_nat @ X @ bot_bot_set_nat )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_52_sup__bot__right,axiom,
% 9.16/5.11      ! [X: set_int] :
% 9.16/5.11        ( ( sup_sup_set_int @ X @ bot_bot_set_int )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_53_bot__eq__sup__iff,axiom,
% 9.16/5.11      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( bot_bo8422036546324065075at_nat
% 9.16/5.11          = ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 9.16/5.11        = ( ( X = bot_bo8422036546324065075at_nat )
% 9.16/5.11          & ( Y = bot_bo8422036546324065075at_nat ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_54_bot__eq__sup__iff,axiom,
% 9.16/5.11      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( bot_bo228742789529271731at_nat
% 9.16/5.11          = ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 9.16/5.11        = ( ( X = bot_bo228742789529271731at_nat )
% 9.16/5.11          & ( Y = bot_bo228742789529271731at_nat ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_55_bot__eq__sup__iff,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( bot_bo2099793752762293965at_nat
% 9.16/5.11          = ( sup_su6327502436637775413at_nat @ X @ Y ) )
% 9.16/5.11        = ( ( X = bot_bo2099793752762293965at_nat )
% 9.16/5.11          & ( Y = bot_bo2099793752762293965at_nat ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_56_bot__eq__sup__iff,axiom,
% 9.16/5.11      ! [X: set_o,Y: set_o] :
% 9.16/5.11        ( ( bot_bot_set_o
% 9.16/5.11          = ( sup_sup_set_o @ X @ Y ) )
% 9.16/5.11        = ( ( X = bot_bot_set_o )
% 9.16/5.11          & ( Y = bot_bot_set_o ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_57_bot__eq__sup__iff,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat] :
% 9.16/5.11        ( ( bot_bot_set_nat
% 9.16/5.11          = ( sup_sup_set_nat @ X @ Y ) )
% 9.16/5.11        = ( ( X = bot_bot_set_nat )
% 9.16/5.11          & ( Y = bot_bot_set_nat ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_58_bot__eq__sup__iff,axiom,
% 9.16/5.11      ! [X: set_int,Y: set_int] :
% 9.16/5.11        ( ( bot_bot_set_int
% 9.16/5.11          = ( sup_sup_set_int @ X @ Y ) )
% 9.16/5.11        = ( ( X = bot_bot_set_int )
% 9.16/5.11          & ( Y = bot_bot_set_int ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_59_sup__eq__bot__iff,axiom,
% 9.16/5.11      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( ( sup_su3035147773818789531at_nat @ X @ Y )
% 9.16/5.11          = bot_bo8422036546324065075at_nat )
% 9.16/5.11        = ( ( X = bot_bo8422036546324065075at_nat )
% 9.16/5.11          & ( Y = bot_bo8422036546324065075at_nat ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_60_sup__eq__bot__iff,axiom,
% 9.16/5.11      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 9.16/5.11          = bot_bo228742789529271731at_nat )
% 9.16/5.11        = ( ( X = bot_bo228742789529271731at_nat )
% 9.16/5.11          & ( Y = bot_bo228742789529271731at_nat ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_61_sup__eq__bot__iff,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( ( sup_su6327502436637775413at_nat @ X @ Y )
% 9.16/5.11          = bot_bo2099793752762293965at_nat )
% 9.16/5.11        = ( ( X = bot_bo2099793752762293965at_nat )
% 9.16/5.11          & ( Y = bot_bo2099793752762293965at_nat ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_62_sup__eq__bot__iff,axiom,
% 9.16/5.11      ! [X: set_o,Y: set_o] :
% 9.16/5.11        ( ( ( sup_sup_set_o @ X @ Y )
% 9.16/5.11          = bot_bot_set_o )
% 9.16/5.11        = ( ( X = bot_bot_set_o )
% 9.16/5.11          & ( Y = bot_bot_set_o ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_63_sup__eq__bot__iff,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat] :
% 9.16/5.11        ( ( ( sup_sup_set_nat @ X @ Y )
% 9.16/5.11          = bot_bot_set_nat )
% 9.16/5.11        = ( ( X = bot_bot_set_nat )
% 9.16/5.11          & ( Y = bot_bot_set_nat ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_64_sup__eq__bot__iff,axiom,
% 9.16/5.11      ! [X: set_int,Y: set_int] :
% 9.16/5.11        ( ( ( sup_sup_set_int @ X @ Y )
% 9.16/5.11          = bot_bot_set_int )
% 9.16/5.11        = ( ( X = bot_bot_set_int )
% 9.16/5.11          & ( Y = bot_bot_set_int ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_65_sup__bot_Oeq__neutr__iff,axiom,
% 9.16/5.11      ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( ( sup_su3035147773818789531at_nat @ A @ B )
% 9.16/5.11          = bot_bo8422036546324065075at_nat )
% 9.16/5.11        = ( ( A = bot_bo8422036546324065075at_nat )
% 9.16/5.11          & ( B = bot_bo8422036546324065075at_nat ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_66_sup__bot_Oeq__neutr__iff,axiom,
% 9.16/5.11      ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( ( sup_su5525570899277871387at_nat @ A @ B )
% 9.16/5.11          = bot_bo228742789529271731at_nat )
% 9.16/5.11        = ( ( A = bot_bo228742789529271731at_nat )
% 9.16/5.11          & ( B = bot_bo228742789529271731at_nat ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_67_sup__bot_Oeq__neutr__iff,axiom,
% 9.16/5.11      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( ( sup_su6327502436637775413at_nat @ A @ B )
% 9.16/5.11          = bot_bo2099793752762293965at_nat )
% 9.16/5.11        = ( ( A = bot_bo2099793752762293965at_nat )
% 9.16/5.11          & ( B = bot_bo2099793752762293965at_nat ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_68_sup__bot_Oeq__neutr__iff,axiom,
% 9.16/5.11      ! [A: set_o,B: set_o] :
% 9.16/5.11        ( ( ( sup_sup_set_o @ A @ B )
% 9.16/5.11          = bot_bot_set_o )
% 9.16/5.11        = ( ( A = bot_bot_set_o )
% 9.16/5.11          & ( B = bot_bot_set_o ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_69_sup__bot_Oeq__neutr__iff,axiom,
% 9.16/5.11      ! [A: set_nat,B: set_nat] :
% 9.16/5.11        ( ( ( sup_sup_set_nat @ A @ B )
% 9.16/5.11          = bot_bot_set_nat )
% 9.16/5.11        = ( ( A = bot_bot_set_nat )
% 9.16/5.11          & ( B = bot_bot_set_nat ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_70_sup__bot_Oeq__neutr__iff,axiom,
% 9.16/5.11      ! [A: set_int,B: set_int] :
% 9.16/5.11        ( ( ( sup_sup_set_int @ A @ B )
% 9.16/5.11          = bot_bot_set_int )
% 9.16/5.11        = ( ( A = bot_bot_set_int )
% 9.16/5.11          & ( B = bot_bot_set_int ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_71_sup__bot_Oleft__neutral,axiom,
% 9.16/5.11      ! [A: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat @ A )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_72_sup__bot_Oleft__neutral,axiom,
% 9.16/5.11      ! [A: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat @ A )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_73_sup__bot_Oleft__neutral,axiom,
% 9.16/5.11      ! [A: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat @ A )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_74_sup__bot_Oleft__neutral,axiom,
% 9.16/5.11      ! [A: set_o] :
% 9.16/5.11        ( ( sup_sup_set_o @ bot_bot_set_o @ A )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_75_sup__bot_Oleft__neutral,axiom,
% 9.16/5.11      ! [A: set_nat] :
% 9.16/5.11        ( ( sup_sup_set_nat @ bot_bot_set_nat @ A )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_76_sup__bot_Oleft__neutral,axiom,
% 9.16/5.11      ! [A: set_int] :
% 9.16/5.11        ( ( sup_sup_set_int @ bot_bot_set_int @ A )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_77_sup__bot_Oneutr__eq__iff,axiom,
% 9.16/5.11      ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( bot_bo8422036546324065075at_nat
% 9.16/5.11          = ( sup_su3035147773818789531at_nat @ A @ B ) )
% 9.16/5.11        = ( ( A = bot_bo8422036546324065075at_nat )
% 9.16/5.11          & ( B = bot_bo8422036546324065075at_nat ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_78_sup__bot_Oneutr__eq__iff,axiom,
% 9.16/5.11      ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( bot_bo228742789529271731at_nat
% 9.16/5.11          = ( sup_su5525570899277871387at_nat @ A @ B ) )
% 9.16/5.11        = ( ( A = bot_bo228742789529271731at_nat )
% 9.16/5.11          & ( B = bot_bo228742789529271731at_nat ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_79_sup__bot_Oneutr__eq__iff,axiom,
% 9.16/5.11      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( bot_bo2099793752762293965at_nat
% 9.16/5.11          = ( sup_su6327502436637775413at_nat @ A @ B ) )
% 9.16/5.11        = ( ( A = bot_bo2099793752762293965at_nat )
% 9.16/5.11          & ( B = bot_bo2099793752762293965at_nat ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_80_sup__bot_Oneutr__eq__iff,axiom,
% 9.16/5.11      ! [A: set_o,B: set_o] :
% 9.16/5.11        ( ( bot_bot_set_o
% 9.16/5.11          = ( sup_sup_set_o @ A @ B ) )
% 9.16/5.11        = ( ( A = bot_bot_set_o )
% 9.16/5.11          & ( B = bot_bot_set_o ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_81_sup__bot_Oneutr__eq__iff,axiom,
% 9.16/5.11      ! [A: set_nat,B: set_nat] :
% 9.16/5.11        ( ( bot_bot_set_nat
% 9.16/5.11          = ( sup_sup_set_nat @ A @ B ) )
% 9.16/5.11        = ( ( A = bot_bot_set_nat )
% 9.16/5.11          & ( B = bot_bot_set_nat ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_82_sup__bot_Oneutr__eq__iff,axiom,
% 9.16/5.11      ! [A: set_int,B: set_int] :
% 9.16/5.11        ( ( bot_bot_set_int
% 9.16/5.11          = ( sup_sup_set_int @ A @ B ) )
% 9.16/5.11        = ( ( A = bot_bot_set_int )
% 9.16/5.11          & ( B = bot_bot_set_int ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_83_sup__bot_Oright__neutral,axiom,
% 9.16/5.11      ! [A: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( sup_su3035147773818789531at_nat @ A @ bot_bo8422036546324065075at_nat )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_84_sup__bot_Oright__neutral,axiom,
% 9.16/5.11      ! [A: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( sup_su5525570899277871387at_nat @ A @ bot_bo228742789529271731at_nat )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_85_sup__bot_Oright__neutral,axiom,
% 9.16/5.11      ! [A: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( sup_su6327502436637775413at_nat @ A @ bot_bo2099793752762293965at_nat )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_86_sup__bot_Oright__neutral,axiom,
% 9.16/5.11      ! [A: set_o] :
% 9.16/5.11        ( ( sup_sup_set_o @ A @ bot_bot_set_o )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_87_sup__bot_Oright__neutral,axiom,
% 9.16/5.11      ! [A: set_nat] :
% 9.16/5.11        ( ( sup_sup_set_nat @ A @ bot_bot_set_nat )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_88_sup__bot_Oright__neutral,axiom,
% 9.16/5.11      ! [A: set_int] :
% 9.16/5.11        ( ( sup_sup_set_int @ A @ bot_bot_set_int )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_89_inf__bot__left,axiom,
% 9.16/5.11      ! [X: product_prod_int_int > $o] :
% 9.16/5.11        ( ( inf_in3604695632404883862_int_o @ bot_bo8147686125503663512_int_o @ X )
% 9.16/5.11        = bot_bo8147686125503663512_int_o ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_90_inf__bot__left,axiom,
% 9.16/5.11      ! [X: list_char > $o] :
% 9.16/5.11        ( ( inf_inf_list_char_o @ bot_bot_list_char_o @ X )
% 9.16/5.11        = bot_bot_list_char_o ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_91_inf__bot__left,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ bot_bo2099793752762293965at_nat @ X )
% 9.16/5.11        = bot_bo2099793752762293965at_nat ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_92_inf__bot__left,axiom,
% 9.16/5.11      ! [X: set_o] :
% 9.16/5.11        ( ( inf_inf_set_o @ bot_bot_set_o @ X )
% 9.16/5.11        = bot_bot_set_o ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_93_inf__bot__left,axiom,
% 9.16/5.11      ! [X: set_nat] :
% 9.16/5.11        ( ( inf_inf_set_nat @ bot_bot_set_nat @ X )
% 9.16/5.11        = bot_bot_set_nat ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_94_inf__bot__left,axiom,
% 9.16/5.11      ! [X: set_int] :
% 9.16/5.11        ( ( inf_inf_set_int @ bot_bot_set_int @ X )
% 9.16/5.11        = bot_bot_set_int ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_95_inf__bot__right,axiom,
% 9.16/5.11      ! [X: product_prod_int_int > $o] :
% 9.16/5.11        ( ( inf_in3604695632404883862_int_o @ X @ bot_bo8147686125503663512_int_o )
% 9.16/5.11        = bot_bo8147686125503663512_int_o ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_96_inf__bot__right,axiom,
% 9.16/5.11      ! [X: list_char > $o] :
% 9.16/5.11        ( ( inf_inf_list_char_o @ X @ bot_bot_list_char_o )
% 9.16/5.11        = bot_bot_list_char_o ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_97_inf__bot__right,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ X @ bot_bo2099793752762293965at_nat )
% 9.16/5.11        = bot_bo2099793752762293965at_nat ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_98_inf__bot__right,axiom,
% 9.16/5.11      ! [X: set_o] :
% 9.16/5.11        ( ( inf_inf_set_o @ X @ bot_bot_set_o )
% 9.16/5.11        = bot_bot_set_o ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_99_inf__bot__right,axiom,
% 9.16/5.11      ! [X: set_nat] :
% 9.16/5.11        ( ( inf_inf_set_nat @ X @ bot_bot_set_nat )
% 9.16/5.11        = bot_bot_set_nat ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_100_inf__bot__right,axiom,
% 9.16/5.11      ! [X: set_int] :
% 9.16/5.11        ( ( inf_inf_set_int @ X @ bot_bot_set_int )
% 9.16/5.11        = bot_bot_set_int ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_101_inf__apply,axiom,
% 9.16/5.11      ( inf_in3604695632404883862_int_o
% 9.16/5.11      = ( ^ [F: product_prod_int_int > $o,G: product_prod_int_int > $o,X3: product_prod_int_int] : ( inf_inf_o @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_102_inf__apply,axiom,
% 9.16/5.11      ( inf_inf_list_char_o
% 9.16/5.11      = ( ^ [F: list_char > $o,G: list_char > $o,X3: list_char] : ( inf_inf_o @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_103_inf__right__idem,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y )
% 9.16/5.11        = ( inf_in2572325071724192079at_nat @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_104_inf__right__idem,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat] :
% 9.16/5.11        ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y )
% 9.16/5.11        = ( inf_inf_set_nat @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_105_inf__right__idem,axiom,
% 9.16/5.11      ! [X: nat,Y: nat] :
% 9.16/5.11        ( ( inf_inf_nat @ ( inf_inf_nat @ X @ Y ) @ Y )
% 9.16/5.11        = ( inf_inf_nat @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_106_inf__right__idem,axiom,
% 9.16/5.11      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 9.16/5.11        ( ( inf_in3604695632404883862_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ Y )
% 9.16/5.11        = ( inf_in3604695632404883862_int_o @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_107_inf__right__idem,axiom,
% 9.16/5.11      ! [X: list_char > $o,Y: list_char > $o] :
% 9.16/5.11        ( ( inf_inf_list_char_o @ ( inf_inf_list_char_o @ X @ Y ) @ Y )
% 9.16/5.11        = ( inf_inf_list_char_o @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_108_inf_Oright__idem,axiom,
% 9.16/5.11      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ B )
% 9.16/5.11        = ( inf_in2572325071724192079at_nat @ A @ B ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_109_inf_Oright__idem,axiom,
% 9.16/5.11      ! [A: set_nat,B: set_nat] :
% 9.16/5.11        ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A @ B ) @ B )
% 9.16/5.11        = ( inf_inf_set_nat @ A @ B ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_110_inf_Oright__idem,axiom,
% 9.16/5.11      ! [A: nat,B: nat] :
% 9.16/5.11        ( ( inf_inf_nat @ ( inf_inf_nat @ A @ B ) @ B )
% 9.16/5.11        = ( inf_inf_nat @ A @ B ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_111_inf_Oright__idem,axiom,
% 9.16/5.11      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 9.16/5.11        ( ( inf_in3604695632404883862_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ B )
% 9.16/5.11        = ( inf_in3604695632404883862_int_o @ A @ B ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_112_inf_Oright__idem,axiom,
% 9.16/5.11      ! [A: list_char > $o,B: list_char > $o] :
% 9.16/5.11        ( ( inf_inf_list_char_o @ ( inf_inf_list_char_o @ A @ B ) @ B )
% 9.16/5.11        = ( inf_inf_list_char_o @ A @ B ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_113_inf__left__idem,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 9.16/5.11        = ( inf_in2572325071724192079at_nat @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_114_inf__left__idem,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat] :
% 9.16/5.11        ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ X @ Y ) )
% 9.16/5.11        = ( inf_inf_set_nat @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_115_inf__left__idem,axiom,
% 9.16/5.11      ! [X: nat,Y: nat] :
% 9.16/5.11        ( ( inf_inf_nat @ X @ ( inf_inf_nat @ X @ Y ) )
% 9.16/5.11        = ( inf_inf_nat @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_116_inf__left__idem,axiom,
% 9.16/5.11      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 9.16/5.11        ( ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ X @ Y ) )
% 9.16/5.11        = ( inf_in3604695632404883862_int_o @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_117_inf__left__idem,axiom,
% 9.16/5.11      ! [X: list_char > $o,Y: list_char > $o] :
% 9.16/5.11        ( ( inf_inf_list_char_o @ X @ ( inf_inf_list_char_o @ X @ Y ) )
% 9.16/5.11        = ( inf_inf_list_char_o @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_118_inf_Oleft__idem,axiom,
% 9.16/5.11      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ A @ ( inf_in2572325071724192079at_nat @ A @ B ) )
% 9.16/5.11        = ( inf_in2572325071724192079at_nat @ A @ B ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_119_inf_Oleft__idem,axiom,
% 9.16/5.11      ! [A: set_nat,B: set_nat] :
% 9.16/5.11        ( ( inf_inf_set_nat @ A @ ( inf_inf_set_nat @ A @ B ) )
% 9.16/5.11        = ( inf_inf_set_nat @ A @ B ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_120_inf_Oleft__idem,axiom,
% 9.16/5.11      ! [A: nat,B: nat] :
% 9.16/5.11        ( ( inf_inf_nat @ A @ ( inf_inf_nat @ A @ B ) )
% 9.16/5.11        = ( inf_inf_nat @ A @ B ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_121_inf_Oleft__idem,axiom,
% 9.16/5.11      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 9.16/5.11        ( ( inf_in3604695632404883862_int_o @ A @ ( inf_in3604695632404883862_int_o @ A @ B ) )
% 9.16/5.11        = ( inf_in3604695632404883862_int_o @ A @ B ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_122_inf_Oleft__idem,axiom,
% 9.16/5.11      ! [A: list_char > $o,B: list_char > $o] :
% 9.16/5.11        ( ( inf_inf_list_char_o @ A @ ( inf_inf_list_char_o @ A @ B ) )
% 9.16/5.11        = ( inf_inf_list_char_o @ A @ B ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_123_inf__idem,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ X @ X )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_124_inf__idem,axiom,
% 9.16/5.11      ! [X: set_nat] :
% 9.16/5.11        ( ( inf_inf_set_nat @ X @ X )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_125_inf__idem,axiom,
% 9.16/5.11      ! [X: nat] :
% 9.16/5.11        ( ( inf_inf_nat @ X @ X )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_126_inf__idem,axiom,
% 9.16/5.11      ! [X: product_prod_int_int > $o] :
% 9.16/5.11        ( ( inf_in3604695632404883862_int_o @ X @ X )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_127_inf__idem,axiom,
% 9.16/5.11      ! [X: list_char > $o] :
% 9.16/5.11        ( ( inf_inf_list_char_o @ X @ X )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_128_inf_Oidem,axiom,
% 9.16/5.11      ! [A: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ A @ A )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_129_inf_Oidem,axiom,
% 9.16/5.11      ! [A: set_nat] :
% 9.16/5.11        ( ( inf_inf_set_nat @ A @ A )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_130_inf_Oidem,axiom,
% 9.16/5.11      ! [A: nat] :
% 9.16/5.11        ( ( inf_inf_nat @ A @ A )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_131_inf_Oidem,axiom,
% 9.16/5.11      ! [A: product_prod_int_int > $o] :
% 9.16/5.11        ( ( inf_in3604695632404883862_int_o @ A @ A )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_132_inf_Oidem,axiom,
% 9.16/5.11      ! [A: list_char > $o] :
% 9.16/5.11        ( ( inf_inf_list_char_o @ A @ A )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_133_mem__Collect__eq,axiom,
% 9.16/5.11      ! [A: set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 9.16/5.11        ( ( member2340774599025711042nt_int @ A @ ( collec5210948495886036740nt_int @ P ) )
% 9.16/5.11        = ( P @ A ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_134_mem__Collect__eq,axiom,
% 9.16/5.11      ! [A: set_nat,P: set_nat > $o] :
% 9.16/5.11        ( ( member_set_nat @ A @ ( collect_set_nat @ P ) )
% 9.16/5.11        = ( P @ A ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_135_mem__Collect__eq,axiom,
% 9.16/5.11      ! [A: nat,P: nat > $o] :
% 9.16/5.11        ( ( member_nat @ A @ ( collect_nat @ P ) )
% 9.16/5.11        = ( P @ A ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_136_mem__Collect__eq,axiom,
% 9.16/5.11      ! [A: int,P: int > $o] :
% 9.16/5.11        ( ( member_int @ A @ ( collect_int @ P ) )
% 9.16/5.11        = ( P @ A ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_137_mem__Collect__eq,axiom,
% 9.16/5.11      ! [A: produc3658429121746597890et_nat > $o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.16/5.11        ( ( member6576561426505652726_nat_o @ A @ ( collec939566748876313656_nat_o @ P ) )
% 9.16/5.11        = ( P @ A ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_138_Collect__mem__eq,axiom,
% 9.16/5.11      ! [A2: set_se6260736226359567993nt_int] :
% 9.16/5.11        ( ( collec5210948495886036740nt_int
% 9.16/5.11          @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ A2 ) )
% 9.16/5.11        = A2 ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_139_Collect__mem__eq,axiom,
% 9.16/5.11      ! [A2: set_set_nat] :
% 9.16/5.11        ( ( collect_set_nat
% 9.16/5.11          @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A2 ) )
% 9.16/5.11        = A2 ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_140_Collect__mem__eq,axiom,
% 9.16/5.11      ! [A2: set_nat] :
% 9.16/5.11        ( ( collect_nat
% 9.16/5.11          @ ^ [X3: nat] : ( member_nat @ X3 @ A2 ) )
% 9.16/5.11        = A2 ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_141_Collect__mem__eq,axiom,
% 9.16/5.11      ! [A2: set_int] :
% 9.16/5.11        ( ( collect_int
% 9.16/5.11          @ ^ [X3: int] : ( member_int @ X3 @ A2 ) )
% 9.16/5.11        = A2 ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_142_Collect__mem__eq,axiom,
% 9.16/5.11      ! [A2: set_Pr4532377907799695533_nat_o] :
% 9.16/5.11        ( ( collec939566748876313656_nat_o
% 9.16/5.11          @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ A2 ) )
% 9.16/5.11        = A2 ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_143_Collect__cong,axiom,
% 9.16/5.11      ! [P: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 9.16/5.11        ( ! [X2: set_Pr958786334691620121nt_int] :
% 9.16/5.11            ( ( P @ X2 )
% 9.16/5.11            = ( Q2 @ X2 ) )
% 9.16/5.11       => ( ( collec5210948495886036740nt_int @ P )
% 9.16/5.11          = ( collec5210948495886036740nt_int @ Q2 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_144_Collect__cong,axiom,
% 9.16/5.11      ! [P: set_nat > $o,Q2: set_nat > $o] :
% 9.16/5.11        ( ! [X2: set_nat] :
% 9.16/5.11            ( ( P @ X2 )
% 9.16/5.11            = ( Q2 @ X2 ) )
% 9.16/5.11       => ( ( collect_set_nat @ P )
% 9.16/5.11          = ( collect_set_nat @ Q2 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_145_Collect__cong,axiom,
% 9.16/5.11      ! [P: nat > $o,Q2: nat > $o] :
% 9.16/5.11        ( ! [X2: nat] :
% 9.16/5.11            ( ( P @ X2 )
% 9.16/5.11            = ( Q2 @ X2 ) )
% 9.16/5.11       => ( ( collect_nat @ P )
% 9.16/5.11          = ( collect_nat @ Q2 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_146_Collect__cong,axiom,
% 9.16/5.11      ! [P: int > $o,Q2: int > $o] :
% 9.16/5.11        ( ! [X2: int] :
% 9.16/5.11            ( ( P @ X2 )
% 9.16/5.11            = ( Q2 @ X2 ) )
% 9.16/5.11       => ( ( collect_int @ P )
% 9.16/5.11          = ( collect_int @ Q2 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_147_Collect__cong,axiom,
% 9.16/5.11      ! [P: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.16/5.11        ( ! [X2: produc3658429121746597890et_nat > $o] :
% 9.16/5.11            ( ( P @ X2 )
% 9.16/5.11            = ( Q2 @ X2 ) )
% 9.16/5.11       => ( ( collec939566748876313656_nat_o @ P )
% 9.16/5.11          = ( collec939566748876313656_nat_o @ Q2 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_148_sup_Oright__idem,axiom,
% 9.16/5.11      ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ A @ B ) @ B )
% 9.16/5.11        = ( sup_su3035147773818789531at_nat @ A @ B ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_149_sup_Oright__idem,axiom,
% 9.16/5.11      ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ B )
% 9.16/5.11        = ( sup_su5525570899277871387at_nat @ A @ B ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_150_sup_Oright__idem,axiom,
% 9.16/5.11      ! [A: set_nat,B: set_nat] :
% 9.16/5.11        ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A @ B ) @ B )
% 9.16/5.11        = ( sup_sup_set_nat @ A @ B ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_151_sup_Oright__idem,axiom,
% 9.16/5.11      ! [A: nat,B: nat] :
% 9.16/5.11        ( ( sup_sup_nat @ ( sup_sup_nat @ A @ B ) @ B )
% 9.16/5.11        = ( sup_sup_nat @ A @ B ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_152_sup_Oright__idem,axiom,
% 9.16/5.11      ! [A: int,B: int] :
% 9.16/5.11        ( ( sup_sup_int @ ( sup_sup_int @ A @ B ) @ B )
% 9.16/5.11        = ( sup_sup_int @ A @ B ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_153_sup__left__idem,axiom,
% 9.16/5.11      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 9.16/5.11        = ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_154_sup__left__idem,axiom,
% 9.16/5.11      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 9.16/5.11        = ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_155_sup__left__idem,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat] :
% 9.16/5.11        ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) )
% 9.16/5.11        = ( sup_sup_set_nat @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_156_sup__left__idem,axiom,
% 9.16/5.11      ! [X: nat,Y: nat] :
% 9.16/5.11        ( ( sup_sup_nat @ X @ ( sup_sup_nat @ X @ Y ) )
% 9.16/5.11        = ( sup_sup_nat @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_157_sup__left__idem,axiom,
% 9.16/5.11      ! [X: int,Y: int] :
% 9.16/5.11        ( ( sup_sup_int @ X @ ( sup_sup_int @ X @ Y ) )
% 9.16/5.11        = ( sup_sup_int @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_158_sup_Oleft__idem,axiom,
% 9.16/5.11      ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( sup_su3035147773818789531at_nat @ A @ ( sup_su3035147773818789531at_nat @ A @ B ) )
% 9.16/5.11        = ( sup_su3035147773818789531at_nat @ A @ B ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_159_sup_Oleft__idem,axiom,
% 9.16/5.11      ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( sup_su5525570899277871387at_nat @ A @ ( sup_su5525570899277871387at_nat @ A @ B ) )
% 9.16/5.11        = ( sup_su5525570899277871387at_nat @ A @ B ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_160_sup_Oleft__idem,axiom,
% 9.16/5.11      ! [A: set_nat,B: set_nat] :
% 9.16/5.11        ( ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ A @ B ) )
% 9.16/5.11        = ( sup_sup_set_nat @ A @ B ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_161_sup_Oleft__idem,axiom,
% 9.16/5.11      ! [A: nat,B: nat] :
% 9.16/5.11        ( ( sup_sup_nat @ A @ ( sup_sup_nat @ A @ B ) )
% 9.16/5.11        = ( sup_sup_nat @ A @ B ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_162_sup_Oleft__idem,axiom,
% 9.16/5.11      ! [A: int,B: int] :
% 9.16/5.11        ( ( sup_sup_int @ A @ ( sup_sup_int @ A @ B ) )
% 9.16/5.11        = ( sup_sup_int @ A @ B ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_163_sup__idem,axiom,
% 9.16/5.11      ! [X: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( sup_su3035147773818789531at_nat @ X @ X )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_164_sup__idem,axiom,
% 9.16/5.11      ! [X: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( sup_su5525570899277871387at_nat @ X @ X )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_165_sup__idem,axiom,
% 9.16/5.11      ! [X: set_nat] :
% 9.16/5.11        ( ( sup_sup_set_nat @ X @ X )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_166_sup__idem,axiom,
% 9.16/5.11      ! [X: nat] :
% 9.16/5.11        ( ( sup_sup_nat @ X @ X )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_167_sup__idem,axiom,
% 9.16/5.11      ! [X: int] :
% 9.16/5.11        ( ( sup_sup_int @ X @ X )
% 9.16/5.11        = X ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_168_sup_Oidem,axiom,
% 9.16/5.11      ! [A: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( sup_su3035147773818789531at_nat @ A @ A )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_169_sup_Oidem,axiom,
% 9.16/5.11      ! [A: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( sup_su5525570899277871387at_nat @ A @ A )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_170_sup_Oidem,axiom,
% 9.16/5.11      ! [A: set_nat] :
% 9.16/5.11        ( ( sup_sup_set_nat @ A @ A )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_171_sup_Oidem,axiom,
% 9.16/5.11      ! [A: nat] :
% 9.16/5.11        ( ( sup_sup_nat @ A @ A )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_172_sup_Oidem,axiom,
% 9.16/5.11      ! [A: int] :
% 9.16/5.11        ( ( sup_sup_int @ A @ A )
% 9.16/5.11        = A ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_173_inf__fun__def,axiom,
% 9.16/5.11      ( inf_in3604695632404883862_int_o
% 9.16/5.11      = ( ^ [F: product_prod_int_int > $o,G: product_prod_int_int > $o,X3: product_prod_int_int] : ( inf_inf_o @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_174_inf__fun__def,axiom,
% 9.16/5.11      ( inf_inf_list_char_o
% 9.16/5.11      = ( ^ [F: list_char > $o,G: list_char > $o,X3: list_char] : ( inf_inf_o @ ( F @ X3 ) @ ( G @ X3 ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_175_inf__left__commute,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 9.16/5.11        = ( inf_in2572325071724192079at_nat @ Y @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_176_inf__left__commute,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.16/5.11        ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 9.16/5.11        = ( inf_inf_set_nat @ Y @ ( inf_inf_set_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_177_inf__left__commute,axiom,
% 9.16/5.11      ! [X: nat,Y: nat,Z: nat] :
% 9.16/5.11        ( ( inf_inf_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 9.16/5.11        = ( inf_inf_nat @ Y @ ( inf_inf_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_178_inf__left__commute,axiom,
% 9.16/5.11      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 9.16/5.11        ( ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) )
% 9.16/5.11        = ( inf_in3604695632404883862_int_o @ Y @ ( inf_in3604695632404883862_int_o @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_179_inf__left__commute,axiom,
% 9.16/5.11      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 9.16/5.11        ( ( inf_inf_list_char_o @ X @ ( inf_inf_list_char_o @ Y @ Z ) )
% 9.16/5.11        = ( inf_inf_list_char_o @ Y @ ( inf_inf_list_char_o @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_180_inf_Oleft__commute,axiom,
% 9.16/5.11      ! [B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ B @ ( inf_in2572325071724192079at_nat @ A @ C ) )
% 9.16/5.11        = ( inf_in2572325071724192079at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_181_inf_Oleft__commute,axiom,
% 9.16/5.11      ! [B: set_nat,A: set_nat,C: set_nat] :
% 9.16/5.11        ( ( inf_inf_set_nat @ B @ ( inf_inf_set_nat @ A @ C ) )
% 9.16/5.11        = ( inf_inf_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_182_inf_Oleft__commute,axiom,
% 9.16/5.11      ! [B: nat,A: nat,C: nat] :
% 9.16/5.11        ( ( inf_inf_nat @ B @ ( inf_inf_nat @ A @ C ) )
% 9.16/5.11        = ( inf_inf_nat @ A @ ( inf_inf_nat @ B @ C ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_183_inf_Oleft__commute,axiom,
% 9.16/5.11      ! [B: product_prod_int_int > $o,A: product_prod_int_int > $o,C: product_prod_int_int > $o] :
% 9.16/5.11        ( ( inf_in3604695632404883862_int_o @ B @ ( inf_in3604695632404883862_int_o @ A @ C ) )
% 9.16/5.11        = ( inf_in3604695632404883862_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_184_inf_Oleft__commute,axiom,
% 9.16/5.11      ! [B: list_char > $o,A: list_char > $o,C: list_char > $o] :
% 9.16/5.11        ( ( inf_inf_list_char_o @ B @ ( inf_inf_list_char_o @ A @ C ) )
% 9.16/5.11        = ( inf_inf_list_char_o @ A @ ( inf_inf_list_char_o @ B @ C ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_185_inf__commute,axiom,
% 9.16/5.11      ( inf_in2572325071724192079at_nat
% 9.16/5.11      = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ Y3 @ X3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_186_inf__commute,axiom,
% 9.16/5.11      ( inf_inf_set_nat
% 9.16/5.11      = ( ^ [X3: set_nat,Y3: set_nat] : ( inf_inf_set_nat @ Y3 @ X3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_187_inf__commute,axiom,
% 9.16/5.11      ( inf_inf_nat
% 9.16/5.11      = ( ^ [X3: nat,Y3: nat] : ( inf_inf_nat @ Y3 @ X3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_188_inf__commute,axiom,
% 9.16/5.11      ( inf_in3604695632404883862_int_o
% 9.16/5.11      = ( ^ [X3: product_prod_int_int > $o,Y3: product_prod_int_int > $o] : ( inf_in3604695632404883862_int_o @ Y3 @ X3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_189_inf__commute,axiom,
% 9.16/5.11      ( inf_inf_list_char_o
% 9.16/5.11      = ( ^ [X3: list_char > $o,Y3: list_char > $o] : ( inf_inf_list_char_o @ Y3 @ X3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_190_inf_Ocommute,axiom,
% 9.16/5.11      ( inf_in2572325071724192079at_nat
% 9.16/5.11      = ( ^ [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ B3 @ A3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_191_inf_Ocommute,axiom,
% 9.16/5.11      ( inf_inf_set_nat
% 9.16/5.11      = ( ^ [A3: set_nat,B3: set_nat] : ( inf_inf_set_nat @ B3 @ A3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_192_inf_Ocommute,axiom,
% 9.16/5.11      ( inf_inf_nat
% 9.16/5.11      = ( ^ [A3: nat,B3: nat] : ( inf_inf_nat @ B3 @ A3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_193_inf_Ocommute,axiom,
% 9.16/5.11      ( inf_in3604695632404883862_int_o
% 9.16/5.11      = ( ^ [A3: product_prod_int_int > $o,B3: product_prod_int_int > $o] : ( inf_in3604695632404883862_int_o @ B3 @ A3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_194_inf_Ocommute,axiom,
% 9.16/5.11      ( inf_inf_list_char_o
% 9.16/5.11      = ( ^ [A3: list_char > $o,B3: list_char > $o] : ( inf_inf_list_char_o @ B3 @ A3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_195_inf__assoc,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Z )
% 9.16/5.11        = ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_196_inf__assoc,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.16/5.11        ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Z )
% 9.16/5.11        = ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_197_inf__assoc,axiom,
% 9.16/5.11      ! [X: nat,Y: nat,Z: nat] :
% 9.16/5.11        ( ( inf_inf_nat @ ( inf_inf_nat @ X @ Y ) @ Z )
% 9.16/5.11        = ( inf_inf_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_198_inf__assoc,axiom,
% 9.16/5.11      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 9.16/5.11        ( ( inf_in3604695632404883862_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ Z )
% 9.16/5.11        = ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_199_inf__assoc,axiom,
% 9.16/5.11      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 9.16/5.11        ( ( inf_inf_list_char_o @ ( inf_inf_list_char_o @ X @ Y ) @ Z )
% 9.16/5.11        = ( inf_inf_list_char_o @ X @ ( inf_inf_list_char_o @ Y @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_200_inf_Oassoc,axiom,
% 9.16/5.11      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C )
% 9.16/5.11        = ( inf_in2572325071724192079at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_201_inf_Oassoc,axiom,
% 9.16/5.11      ! [A: set_nat,B: set_nat,C: set_nat] :
% 9.16/5.11        ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C )
% 9.16/5.11        = ( inf_inf_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_202_inf_Oassoc,axiom,
% 9.16/5.11      ! [A: nat,B: nat,C: nat] :
% 9.16/5.11        ( ( inf_inf_nat @ ( inf_inf_nat @ A @ B ) @ C )
% 9.16/5.11        = ( inf_inf_nat @ A @ ( inf_inf_nat @ B @ C ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_203_inf_Oassoc,axiom,
% 9.16/5.11      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o,C: product_prod_int_int > $o] :
% 9.16/5.11        ( ( inf_in3604695632404883862_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ C )
% 9.16/5.11        = ( inf_in3604695632404883862_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_204_inf_Oassoc,axiom,
% 9.16/5.11      ! [A: list_char > $o,B: list_char > $o,C: list_char > $o] :
% 9.16/5.11        ( ( inf_inf_list_char_o @ ( inf_inf_list_char_o @ A @ B ) @ C )
% 9.16/5.11        = ( inf_inf_list_char_o @ A @ ( inf_inf_list_char_o @ B @ C ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_205_inf__sup__aci_I1_J,axiom,
% 9.16/5.11      ( inf_in2572325071724192079at_nat
% 9.16/5.11      = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ Y3 @ X3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_206_inf__sup__aci_I1_J,axiom,
% 9.16/5.11      ( inf_inf_set_nat
% 9.16/5.11      = ( ^ [X3: set_nat,Y3: set_nat] : ( inf_inf_set_nat @ Y3 @ X3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_207_inf__sup__aci_I1_J,axiom,
% 9.16/5.11      ( inf_inf_nat
% 9.16/5.11      = ( ^ [X3: nat,Y3: nat] : ( inf_inf_nat @ Y3 @ X3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_208_inf__sup__aci_I1_J,axiom,
% 9.16/5.11      ( inf_in3604695632404883862_int_o
% 9.16/5.11      = ( ^ [X3: product_prod_int_int > $o,Y3: product_prod_int_int > $o] : ( inf_in3604695632404883862_int_o @ Y3 @ X3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_209_inf__sup__aci_I1_J,axiom,
% 9.16/5.11      ( inf_inf_list_char_o
% 9.16/5.11      = ( ^ [X3: list_char > $o,Y3: list_char > $o] : ( inf_inf_list_char_o @ Y3 @ X3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_210_inf__sup__aci_I2_J,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Z )
% 9.16/5.11        = ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_211_inf__sup__aci_I2_J,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.16/5.11        ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Z )
% 9.16/5.11        = ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_212_inf__sup__aci_I2_J,axiom,
% 9.16/5.11      ! [X: nat,Y: nat,Z: nat] :
% 9.16/5.11        ( ( inf_inf_nat @ ( inf_inf_nat @ X @ Y ) @ Z )
% 9.16/5.11        = ( inf_inf_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_213_inf__sup__aci_I2_J,axiom,
% 9.16/5.11      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 9.16/5.11        ( ( inf_in3604695632404883862_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ Z )
% 9.16/5.11        = ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_214_inf__sup__aci_I2_J,axiom,
% 9.16/5.11      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 9.16/5.11        ( ( inf_inf_list_char_o @ ( inf_inf_list_char_o @ X @ Y ) @ Z )
% 9.16/5.11        = ( inf_inf_list_char_o @ X @ ( inf_inf_list_char_o @ Y @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_215_inf__sup__aci_I3_J,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 9.16/5.11        = ( inf_in2572325071724192079at_nat @ Y @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_216_inf__sup__aci_I3_J,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.16/5.11        ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 9.16/5.11        = ( inf_inf_set_nat @ Y @ ( inf_inf_set_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_217_inf__sup__aci_I3_J,axiom,
% 9.16/5.11      ! [X: nat,Y: nat,Z: nat] :
% 9.16/5.11        ( ( inf_inf_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 9.16/5.11        = ( inf_inf_nat @ Y @ ( inf_inf_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_218_inf__sup__aci_I3_J,axiom,
% 9.16/5.11      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 9.16/5.11        ( ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) )
% 9.16/5.11        = ( inf_in3604695632404883862_int_o @ Y @ ( inf_in3604695632404883862_int_o @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_219_inf__sup__aci_I3_J,axiom,
% 9.16/5.11      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 9.16/5.11        ( ( inf_inf_list_char_o @ X @ ( inf_inf_list_char_o @ Y @ Z ) )
% 9.16/5.11        = ( inf_inf_list_char_o @ Y @ ( inf_inf_list_char_o @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_220_inf__sup__aci_I4_J,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 9.16/5.11        = ( inf_in2572325071724192079at_nat @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_221_inf__sup__aci_I4_J,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat] :
% 9.16/5.11        ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ X @ Y ) )
% 9.16/5.11        = ( inf_inf_set_nat @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_222_inf__sup__aci_I4_J,axiom,
% 9.16/5.11      ! [X: nat,Y: nat] :
% 9.16/5.11        ( ( inf_inf_nat @ X @ ( inf_inf_nat @ X @ Y ) )
% 9.16/5.11        = ( inf_inf_nat @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_223_inf__sup__aci_I4_J,axiom,
% 9.16/5.11      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 9.16/5.11        ( ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ X @ Y ) )
% 9.16/5.11        = ( inf_in3604695632404883862_int_o @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_224_inf__sup__aci_I4_J,axiom,
% 9.16/5.11      ! [X: list_char > $o,Y: list_char > $o] :
% 9.16/5.11        ( ( inf_inf_list_char_o @ X @ ( inf_inf_list_char_o @ X @ Y ) )
% 9.16/5.11        = ( inf_inf_list_char_o @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_225_sup__left__commute,axiom,
% 9.16/5.11      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) )
% 9.16/5.11        = ( sup_su3035147773818789531at_nat @ Y @ ( sup_su3035147773818789531at_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_226_sup__left__commute,axiom,
% 9.16/5.11      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) )
% 9.16/5.11        = ( sup_su5525570899277871387at_nat @ Y @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_227_sup__left__commute,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.16/5.11        ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 9.16/5.11        = ( sup_sup_set_nat @ Y @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_228_sup__left__commute,axiom,
% 9.16/5.11      ! [X: nat,Y: nat,Z: nat] :
% 9.16/5.11        ( ( sup_sup_nat @ X @ ( sup_sup_nat @ Y @ Z ) )
% 9.16/5.11        = ( sup_sup_nat @ Y @ ( sup_sup_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_229_sup__left__commute,axiom,
% 9.16/5.11      ! [X: int,Y: int,Z: int] :
% 9.16/5.11        ( ( sup_sup_int @ X @ ( sup_sup_int @ Y @ Z ) )
% 9.16/5.11        = ( sup_sup_int @ Y @ ( sup_sup_int @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_230_sup_Oleft__commute,axiom,
% 9.16/5.11      ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,C: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( sup_su3035147773818789531at_nat @ B @ ( sup_su3035147773818789531at_nat @ A @ C ) )
% 9.16/5.11        = ( sup_su3035147773818789531at_nat @ A @ ( sup_su3035147773818789531at_nat @ B @ C ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_231_sup_Oleft__commute,axiom,
% 9.16/5.11      ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( sup_su5525570899277871387at_nat @ B @ ( sup_su5525570899277871387at_nat @ A @ C ) )
% 9.16/5.11        = ( sup_su5525570899277871387at_nat @ A @ ( sup_su5525570899277871387at_nat @ B @ C ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_232_sup_Oleft__commute,axiom,
% 9.16/5.11      ! [B: set_nat,A: set_nat,C: set_nat] :
% 9.16/5.11        ( ( sup_sup_set_nat @ B @ ( sup_sup_set_nat @ A @ C ) )
% 9.16/5.11        = ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ B @ C ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_233_sup_Oleft__commute,axiom,
% 9.16/5.11      ! [B: nat,A: nat,C: nat] :
% 9.16/5.11        ( ( sup_sup_nat @ B @ ( sup_sup_nat @ A @ C ) )
% 9.16/5.11        = ( sup_sup_nat @ A @ ( sup_sup_nat @ B @ C ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_234_sup_Oleft__commute,axiom,
% 9.16/5.11      ! [B: int,A: int,C: int] :
% 9.16/5.11        ( ( sup_sup_int @ B @ ( sup_sup_int @ A @ C ) )
% 9.16/5.11        = ( sup_sup_int @ A @ ( sup_sup_int @ B @ C ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_235_sup__commute,axiom,
% 9.16/5.11      ( sup_su3035147773818789531at_nat
% 9.16/5.11      = ( ^ [X3: set_Pr8551490117392284871at_nat,Y3: set_Pr8551490117392284871at_nat] : ( sup_su3035147773818789531at_nat @ Y3 @ X3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_236_sup__commute,axiom,
% 9.16/5.11      ( sup_su5525570899277871387at_nat
% 9.16/5.11      = ( ^ [X3: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ Y3 @ X3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_237_sup__commute,axiom,
% 9.16/5.11      ( sup_sup_set_nat
% 9.16/5.11      = ( ^ [X3: set_nat,Y3: set_nat] : ( sup_sup_set_nat @ Y3 @ X3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_238_sup__commute,axiom,
% 9.16/5.11      ( sup_sup_nat
% 9.16/5.11      = ( ^ [X3: nat,Y3: nat] : ( sup_sup_nat @ Y3 @ X3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_239_sup__commute,axiom,
% 9.16/5.11      ( sup_sup_int
% 9.16/5.11      = ( ^ [X3: int,Y3: int] : ( sup_sup_int @ Y3 @ X3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_240_sup_Ocommute,axiom,
% 9.16/5.11      ( sup_su3035147773818789531at_nat
% 9.16/5.11      = ( ^ [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] : ( sup_su3035147773818789531at_nat @ B3 @ A3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_241_sup_Ocommute,axiom,
% 9.16/5.11      ( sup_su5525570899277871387at_nat
% 9.16/5.11      = ( ^ [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ B3 @ A3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_242_sup_Ocommute,axiom,
% 9.16/5.11      ( sup_sup_set_nat
% 9.16/5.11      = ( ^ [A3: set_nat,B3: set_nat] : ( sup_sup_set_nat @ B3 @ A3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_243_sup_Ocommute,axiom,
% 9.16/5.11      ( sup_sup_nat
% 9.16/5.11      = ( ^ [A3: nat,B3: nat] : ( sup_sup_nat @ B3 @ A3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_244_sup_Ocommute,axiom,
% 9.16/5.11      ( sup_sup_int
% 9.16/5.11      = ( ^ [A3: int,B3: int] : ( sup_sup_int @ B3 @ A3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_245_sup__assoc,axiom,
% 9.16/5.11      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ Z )
% 9.16/5.11        = ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_246_sup__assoc,axiom,
% 9.16/5.11      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ Z )
% 9.16/5.11        = ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_247_sup__assoc,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.16/5.11        ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z )
% 9.16/5.11        = ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_248_sup__assoc,axiom,
% 9.16/5.11      ! [X: nat,Y: nat,Z: nat] :
% 9.16/5.11        ( ( sup_sup_nat @ ( sup_sup_nat @ X @ Y ) @ Z )
% 9.16/5.11        = ( sup_sup_nat @ X @ ( sup_sup_nat @ Y @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_249_sup__assoc,axiom,
% 9.16/5.11      ! [X: int,Y: int,Z: int] :
% 9.16/5.11        ( ( sup_sup_int @ ( sup_sup_int @ X @ Y ) @ Z )
% 9.16/5.11        = ( sup_sup_int @ X @ ( sup_sup_int @ Y @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_250_sup_Oassoc,axiom,
% 9.16/5.11      ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,C: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ A @ B ) @ C )
% 9.16/5.11        = ( sup_su3035147773818789531at_nat @ A @ ( sup_su3035147773818789531at_nat @ B @ C ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_251_sup_Oassoc,axiom,
% 9.16/5.11      ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ C )
% 9.16/5.11        = ( sup_su5525570899277871387at_nat @ A @ ( sup_su5525570899277871387at_nat @ B @ C ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_252_sup_Oassoc,axiom,
% 9.16/5.11      ! [A: set_nat,B: set_nat,C: set_nat] :
% 9.16/5.11        ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A @ B ) @ C )
% 9.16/5.11        = ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ B @ C ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_253_sup_Oassoc,axiom,
% 9.16/5.11      ! [A: nat,B: nat,C: nat] :
% 9.16/5.11        ( ( sup_sup_nat @ ( sup_sup_nat @ A @ B ) @ C )
% 9.16/5.11        = ( sup_sup_nat @ A @ ( sup_sup_nat @ B @ C ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_254_sup_Oassoc,axiom,
% 9.16/5.11      ! [A: int,B: int,C: int] :
% 9.16/5.11        ( ( sup_sup_int @ ( sup_sup_int @ A @ B ) @ C )
% 9.16/5.11        = ( sup_sup_int @ A @ ( sup_sup_int @ B @ C ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_255_inf__sup__aci_I5_J,axiom,
% 9.16/5.11      ( sup_su3035147773818789531at_nat
% 9.16/5.11      = ( ^ [X3: set_Pr8551490117392284871at_nat,Y3: set_Pr8551490117392284871at_nat] : ( sup_su3035147773818789531at_nat @ Y3 @ X3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_256_inf__sup__aci_I5_J,axiom,
% 9.16/5.11      ( sup_su5525570899277871387at_nat
% 9.16/5.11      = ( ^ [X3: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ Y3 @ X3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_257_inf__sup__aci_I5_J,axiom,
% 9.16/5.11      ( sup_sup_set_nat
% 9.16/5.11      = ( ^ [X3: set_nat,Y3: set_nat] : ( sup_sup_set_nat @ Y3 @ X3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_258_inf__sup__aci_I5_J,axiom,
% 9.16/5.11      ( sup_sup_nat
% 9.16/5.11      = ( ^ [X3: nat,Y3: nat] : ( sup_sup_nat @ Y3 @ X3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_259_inf__sup__aci_I5_J,axiom,
% 9.16/5.11      ( sup_sup_int
% 9.16/5.11      = ( ^ [X3: int,Y3: int] : ( sup_sup_int @ Y3 @ X3 ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_260_inf__sup__aci_I6_J,axiom,
% 9.16/5.11      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ Z )
% 9.16/5.11        = ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_261_inf__sup__aci_I6_J,axiom,
% 9.16/5.11      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ Z )
% 9.16/5.11        = ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_262_inf__sup__aci_I6_J,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.16/5.11        ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z )
% 9.16/5.11        = ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_263_inf__sup__aci_I6_J,axiom,
% 9.16/5.11      ! [X: nat,Y: nat,Z: nat] :
% 9.16/5.11        ( ( sup_sup_nat @ ( sup_sup_nat @ X @ Y ) @ Z )
% 9.16/5.11        = ( sup_sup_nat @ X @ ( sup_sup_nat @ Y @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_264_inf__sup__aci_I6_J,axiom,
% 9.16/5.11      ! [X: int,Y: int,Z: int] :
% 9.16/5.11        ( ( sup_sup_int @ ( sup_sup_int @ X @ Y ) @ Z )
% 9.16/5.11        = ( sup_sup_int @ X @ ( sup_sup_int @ Y @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_265_inf__sup__aci_I7_J,axiom,
% 9.16/5.11      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) )
% 9.16/5.11        = ( sup_su3035147773818789531at_nat @ Y @ ( sup_su3035147773818789531at_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_266_inf__sup__aci_I7_J,axiom,
% 9.16/5.11      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) )
% 9.16/5.11        = ( sup_su5525570899277871387at_nat @ Y @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_267_inf__sup__aci_I7_J,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.16/5.11        ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 9.16/5.11        = ( sup_sup_set_nat @ Y @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_268_inf__sup__aci_I7_J,axiom,
% 9.16/5.11      ! [X: nat,Y: nat,Z: nat] :
% 9.16/5.11        ( ( sup_sup_nat @ X @ ( sup_sup_nat @ Y @ Z ) )
% 9.16/5.11        = ( sup_sup_nat @ Y @ ( sup_sup_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_269_inf__sup__aci_I7_J,axiom,
% 9.16/5.11      ! [X: int,Y: int,Z: int] :
% 9.16/5.11        ( ( sup_sup_int @ X @ ( sup_sup_int @ Y @ Z ) )
% 9.16/5.11        = ( sup_sup_int @ Y @ ( sup_sup_int @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_270_inf__sup__aci_I8_J,axiom,
% 9.16/5.11      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 9.16/5.11        = ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_271_inf__sup__aci_I8_J,axiom,
% 9.16/5.11      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 9.16/5.11        = ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_272_inf__sup__aci_I8_J,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat] :
% 9.16/5.11        ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) )
% 9.16/5.11        = ( sup_sup_set_nat @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_273_inf__sup__aci_I8_J,axiom,
% 9.16/5.11      ! [X: nat,Y: nat] :
% 9.16/5.11        ( ( sup_sup_nat @ X @ ( sup_sup_nat @ X @ Y ) )
% 9.16/5.11        = ( sup_sup_nat @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_274_inf__sup__aci_I8_J,axiom,
% 9.16/5.11      ! [X: int,Y: int] :
% 9.16/5.11        ( ( sup_sup_int @ X @ ( sup_sup_int @ X @ Y ) )
% 9.16/5.11        = ( sup_sup_int @ X @ Y ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_275_sup__inf__distrib2,axiom,
% 9.16/5.11      ! [Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ Z ) @ X )
% 9.16/5.11        = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ X ) @ ( sup_su6327502436637775413at_nat @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_276_sup__inf__distrib2,axiom,
% 9.16/5.11      ! [Y: product_prod_int_int > $o,Z: product_prod_int_int > $o,X: product_prod_int_int > $o] :
% 9.16/5.11        ( ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ Y @ Z ) @ X )
% 9.16/5.11        = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ Y @ X ) @ ( sup_su8463660629351352368_int_o @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_277_sup__inf__distrib2,axiom,
% 9.16/5.11      ! [Y: list_char > $o,Z: list_char > $o,X: list_char > $o] :
% 9.16/5.11        ( ( sup_sup_list_char_o @ ( inf_inf_list_char_o @ Y @ Z ) @ X )
% 9.16/5.11        = ( inf_inf_list_char_o @ ( sup_sup_list_char_o @ Y @ X ) @ ( sup_sup_list_char_o @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_278_sup__inf__distrib2,axiom,
% 9.16/5.11      ! [Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ Y @ Z ) @ X )
% 9.16/5.11        = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ Y @ X ) @ ( sup_su3035147773818789531at_nat @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_279_sup__inf__distrib2,axiom,
% 9.16/5.11      ! [Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ Y @ Z ) @ X )
% 9.16/5.11        = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ Y @ X ) @ ( sup_su5525570899277871387at_nat @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_280_sup__inf__distrib2,axiom,
% 9.16/5.11      ! [Y: set_nat,Z: set_nat,X: set_nat] :
% 9.16/5.11        ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ Z ) @ X )
% 9.16/5.11        = ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ X ) @ ( sup_sup_set_nat @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_281_sup__inf__distrib2,axiom,
% 9.16/5.11      ! [Y: nat,Z: nat,X: nat] :
% 9.16/5.11        ( ( sup_sup_nat @ ( inf_inf_nat @ Y @ Z ) @ X )
% 9.16/5.11        = ( inf_inf_nat @ ( sup_sup_nat @ Y @ X ) @ ( sup_sup_nat @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_282_sup__inf__distrib2,axiom,
% 9.16/5.11      ! [Y: int,Z: int,X: int] :
% 9.16/5.11        ( ( sup_sup_int @ ( inf_inf_int @ Y @ Z ) @ X )
% 9.16/5.11        = ( inf_inf_int @ ( sup_sup_int @ Y @ X ) @ ( sup_sup_int @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_283_sup__inf__distrib1,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 9.16/5.11        = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_284_sup__inf__distrib1,axiom,
% 9.16/5.11      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 9.16/5.11        ( ( sup_su8463660629351352368_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) )
% 9.16/5.11        = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ X @ Y ) @ ( sup_su8463660629351352368_int_o @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_285_sup__inf__distrib1,axiom,
% 9.16/5.11      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 9.16/5.11        ( ( sup_sup_list_char_o @ X @ ( inf_inf_list_char_o @ Y @ Z ) )
% 9.16/5.11        = ( inf_inf_list_char_o @ ( sup_sup_list_char_o @ X @ Y ) @ ( sup_sup_list_char_o @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_286_sup__inf__distrib1,axiom,
% 9.16/5.11      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( sup_su3035147773818789531at_nat @ X @ ( inf_in1697001100524423349at_nat @ Y @ Z ) )
% 9.16/5.11        = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ ( sup_su3035147773818789531at_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_287_sup__inf__distrib1,axiom,
% 9.16/5.11      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ Y @ Z ) )
% 9.16/5.11        = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_288_sup__inf__distrib1,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.16/5.11        ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 9.16/5.11        = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_289_sup__inf__distrib1,axiom,
% 9.16/5.11      ! [X: nat,Y: nat,Z: nat] :
% 9.16/5.11        ( ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 9.16/5.11        = ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_290_sup__inf__distrib1,axiom,
% 9.16/5.11      ! [X: int,Y: int,Z: int] :
% 9.16/5.11        ( ( sup_sup_int @ X @ ( inf_inf_int @ Y @ Z ) )
% 9.16/5.11        = ( inf_inf_int @ ( sup_sup_int @ X @ Y ) @ ( sup_sup_int @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_291_inf__sup__distrib2,axiom,
% 9.16/5.11      ! [Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ Z ) @ X )
% 9.16/5.11        = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ X ) @ ( inf_in2572325071724192079at_nat @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_292_inf__sup__distrib2,axiom,
% 9.16/5.11      ! [Y: product_prod_int_int > $o,Z: product_prod_int_int > $o,X: product_prod_int_int > $o] :
% 9.16/5.11        ( ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ Y @ Z ) @ X )
% 9.16/5.11        = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ Y @ X ) @ ( inf_in3604695632404883862_int_o @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_293_inf__sup__distrib2,axiom,
% 9.16/5.11      ! [Y: list_char > $o,Z: list_char > $o,X: list_char > $o] :
% 9.16/5.11        ( ( inf_inf_list_char_o @ ( sup_sup_list_char_o @ Y @ Z ) @ X )
% 9.16/5.11        = ( sup_sup_list_char_o @ ( inf_inf_list_char_o @ Y @ X ) @ ( inf_inf_list_char_o @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_294_inf__sup__distrib2,axiom,
% 9.16/5.11      ! [Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ Y @ Z ) @ X )
% 9.16/5.11        = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ Y @ X ) @ ( inf_in1697001100524423349at_nat @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_295_inf__sup__distrib2,axiom,
% 9.16/5.11      ! [Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ Y @ Z ) @ X )
% 9.16/5.11        = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ Y @ X ) @ ( inf_in7913087082777306421at_nat @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_296_inf__sup__distrib2,axiom,
% 9.16/5.11      ! [Y: set_nat,Z: set_nat,X: set_nat] :
% 9.16/5.11        ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ Z ) @ X )
% 9.16/5.11        = ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ X ) @ ( inf_inf_set_nat @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_297_inf__sup__distrib2,axiom,
% 9.16/5.11      ! [Y: nat,Z: nat,X: nat] :
% 9.16/5.11        ( ( inf_inf_nat @ ( sup_sup_nat @ Y @ Z ) @ X )
% 9.16/5.11        = ( sup_sup_nat @ ( inf_inf_nat @ Y @ X ) @ ( inf_inf_nat @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_298_inf__sup__distrib2,axiom,
% 9.16/5.11      ! [Y: int,Z: int,X: int] :
% 9.16/5.11        ( ( inf_inf_int @ ( sup_sup_int @ Y @ Z ) @ X )
% 9.16/5.11        = ( sup_sup_int @ ( inf_inf_int @ Y @ X ) @ ( inf_inf_int @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_299_inf__sup__distrib1,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) )
% 9.16/5.11        = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_300_inf__sup__distrib1,axiom,
% 9.16/5.11      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 9.16/5.11        ( ( inf_in3604695632404883862_int_o @ X @ ( sup_su8463660629351352368_int_o @ Y @ Z ) )
% 9.16/5.11        = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ ( inf_in3604695632404883862_int_o @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_301_inf__sup__distrib1,axiom,
% 9.16/5.11      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 9.16/5.11        ( ( inf_inf_list_char_o @ X @ ( sup_sup_list_char_o @ Y @ Z ) )
% 9.16/5.11        = ( sup_sup_list_char_o @ ( inf_inf_list_char_o @ X @ Y ) @ ( inf_inf_list_char_o @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_302_inf__sup__distrib1,axiom,
% 9.16/5.11      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( inf_in1697001100524423349at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) )
% 9.16/5.11        = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) @ ( inf_in1697001100524423349at_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_303_inf__sup__distrib1,axiom,
% 9.16/5.11      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) )
% 9.16/5.11        = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ ( inf_in7913087082777306421at_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_304_inf__sup__distrib1,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.16/5.11        ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 9.16/5.11        = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_305_inf__sup__distrib1,axiom,
% 9.16/5.11      ! [X: nat,Y: nat,Z: nat] :
% 9.16/5.11        ( ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z ) )
% 9.16/5.11        = ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_306_inf__sup__distrib1,axiom,
% 9.16/5.11      ! [X: int,Y: int,Z: int] :
% 9.16/5.11        ( ( inf_inf_int @ X @ ( sup_sup_int @ Y @ Z ) )
% 9.16/5.11        = ( sup_sup_int @ ( inf_inf_int @ X @ Y ) @ ( inf_inf_int @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_307_distrib__imp2,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ! [X2: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
% 9.16/5.11            ( ( sup_su6327502436637775413at_nat @ X2 @ ( inf_in2572325071724192079at_nat @ Y2 @ Z2 ) )
% 9.16/5.11            = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X2 @ Y2 ) @ ( sup_su6327502436637775413at_nat @ X2 @ Z2 ) ) )
% 9.16/5.11       => ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) )
% 9.16/5.11          = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_308_distrib__imp2,axiom,
% 9.16/5.11      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 9.16/5.11        ( ! [X2: product_prod_int_int > $o,Y2: product_prod_int_int > $o,Z2: product_prod_int_int > $o] :
% 9.16/5.11            ( ( sup_su8463660629351352368_int_o @ X2 @ ( inf_in3604695632404883862_int_o @ Y2 @ Z2 ) )
% 9.16/5.11            = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ X2 @ Y2 ) @ ( sup_su8463660629351352368_int_o @ X2 @ Z2 ) ) )
% 9.16/5.11       => ( ( inf_in3604695632404883862_int_o @ X @ ( sup_su8463660629351352368_int_o @ Y @ Z ) )
% 9.16/5.11          = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ ( inf_in3604695632404883862_int_o @ X @ Z ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_309_distrib__imp2,axiom,
% 9.16/5.11      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 9.16/5.11        ( ! [X2: list_char > $o,Y2: list_char > $o,Z2: list_char > $o] :
% 9.16/5.11            ( ( sup_sup_list_char_o @ X2 @ ( inf_inf_list_char_o @ Y2 @ Z2 ) )
% 9.16/5.11            = ( inf_inf_list_char_o @ ( sup_sup_list_char_o @ X2 @ Y2 ) @ ( sup_sup_list_char_o @ X2 @ Z2 ) ) )
% 9.16/5.11       => ( ( inf_inf_list_char_o @ X @ ( sup_sup_list_char_o @ Y @ Z ) )
% 9.16/5.11          = ( sup_sup_list_char_o @ ( inf_inf_list_char_o @ X @ Y ) @ ( inf_inf_list_char_o @ X @ Z ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_310_distrib__imp2,axiom,
% 9.16/5.11      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ! [X2: set_Pr8551490117392284871at_nat,Y2: set_Pr8551490117392284871at_nat,Z2: set_Pr8551490117392284871at_nat] :
% 9.16/5.11            ( ( sup_su3035147773818789531at_nat @ X2 @ ( inf_in1697001100524423349at_nat @ Y2 @ Z2 ) )
% 9.16/5.11            = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ X2 @ Y2 ) @ ( sup_su3035147773818789531at_nat @ X2 @ Z2 ) ) )
% 9.16/5.11       => ( ( inf_in1697001100524423349at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) )
% 9.16/5.11          = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) @ ( inf_in1697001100524423349at_nat @ X @ Z ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_311_distrib__imp2,axiom,
% 9.16/5.11      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ! [X2: set_Pr4329608150637261639at_nat,Y2: set_Pr4329608150637261639at_nat,Z2: set_Pr4329608150637261639at_nat] :
% 9.16/5.11            ( ( sup_su5525570899277871387at_nat @ X2 @ ( inf_in7913087082777306421at_nat @ Y2 @ Z2 ) )
% 9.16/5.11            = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X2 @ Y2 ) @ ( sup_su5525570899277871387at_nat @ X2 @ Z2 ) ) )
% 9.16/5.11       => ( ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) )
% 9.16/5.11          = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ ( inf_in7913087082777306421at_nat @ X @ Z ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_312_distrib__imp2,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.16/5.11        ( ! [X2: set_nat,Y2: set_nat,Z2: set_nat] :
% 9.16/5.11            ( ( sup_sup_set_nat @ X2 @ ( inf_inf_set_nat @ Y2 @ Z2 ) )
% 9.16/5.11            = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X2 @ Y2 ) @ ( sup_sup_set_nat @ X2 @ Z2 ) ) )
% 9.16/5.11       => ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 9.16/5.11          = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_313_distrib__imp2,axiom,
% 9.16/5.11      ! [X: nat,Y: nat,Z: nat] :
% 9.16/5.11        ( ! [X2: nat,Y2: nat,Z2: nat] :
% 9.16/5.11            ( ( sup_sup_nat @ X2 @ ( inf_inf_nat @ Y2 @ Z2 ) )
% 9.16/5.11            = ( inf_inf_nat @ ( sup_sup_nat @ X2 @ Y2 ) @ ( sup_sup_nat @ X2 @ Z2 ) ) )
% 9.16/5.11       => ( ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z ) )
% 9.16/5.11          = ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_314_distrib__imp2,axiom,
% 9.16/5.11      ! [X: int,Y: int,Z: int] :
% 9.16/5.11        ( ! [X2: int,Y2: int,Z2: int] :
% 9.16/5.11            ( ( sup_sup_int @ X2 @ ( inf_inf_int @ Y2 @ Z2 ) )
% 9.16/5.11            = ( inf_inf_int @ ( sup_sup_int @ X2 @ Y2 ) @ ( sup_sup_int @ X2 @ Z2 ) ) )
% 9.16/5.11       => ( ( inf_inf_int @ X @ ( sup_sup_int @ Y @ Z ) )
% 9.16/5.11          = ( sup_sup_int @ ( inf_inf_int @ X @ Y ) @ ( inf_inf_int @ X @ Z ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_315_distrib__imp1,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ! [X2: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
% 9.16/5.11            ( ( inf_in2572325071724192079at_nat @ X2 @ ( sup_su6327502436637775413at_nat @ Y2 @ Z2 ) )
% 9.16/5.11            = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X2 @ Y2 ) @ ( inf_in2572325071724192079at_nat @ X2 @ Z2 ) ) )
% 9.16/5.11       => ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 9.16/5.11          = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_316_distrib__imp1,axiom,
% 9.16/5.11      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 9.16/5.11        ( ! [X2: product_prod_int_int > $o,Y2: product_prod_int_int > $o,Z2: product_prod_int_int > $o] :
% 9.16/5.11            ( ( inf_in3604695632404883862_int_o @ X2 @ ( sup_su8463660629351352368_int_o @ Y2 @ Z2 ) )
% 9.16/5.11            = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ X2 @ Y2 ) @ ( inf_in3604695632404883862_int_o @ X2 @ Z2 ) ) )
% 9.16/5.11       => ( ( sup_su8463660629351352368_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) )
% 9.16/5.11          = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ X @ Y ) @ ( sup_su8463660629351352368_int_o @ X @ Z ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_317_distrib__imp1,axiom,
% 9.16/5.11      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 9.16/5.11        ( ! [X2: list_char > $o,Y2: list_char > $o,Z2: list_char > $o] :
% 9.16/5.11            ( ( inf_inf_list_char_o @ X2 @ ( sup_sup_list_char_o @ Y2 @ Z2 ) )
% 9.16/5.11            = ( sup_sup_list_char_o @ ( inf_inf_list_char_o @ X2 @ Y2 ) @ ( inf_inf_list_char_o @ X2 @ Z2 ) ) )
% 9.16/5.11       => ( ( sup_sup_list_char_o @ X @ ( inf_inf_list_char_o @ Y @ Z ) )
% 9.16/5.11          = ( inf_inf_list_char_o @ ( sup_sup_list_char_o @ X @ Y ) @ ( sup_sup_list_char_o @ X @ Z ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_318_distrib__imp1,axiom,
% 9.16/5.11      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ! [X2: set_Pr8551490117392284871at_nat,Y2: set_Pr8551490117392284871at_nat,Z2: set_Pr8551490117392284871at_nat] :
% 9.16/5.11            ( ( inf_in1697001100524423349at_nat @ X2 @ ( sup_su3035147773818789531at_nat @ Y2 @ Z2 ) )
% 9.16/5.11            = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ X2 @ Y2 ) @ ( inf_in1697001100524423349at_nat @ X2 @ Z2 ) ) )
% 9.16/5.11       => ( ( sup_su3035147773818789531at_nat @ X @ ( inf_in1697001100524423349at_nat @ Y @ Z ) )
% 9.16/5.11          = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ ( sup_su3035147773818789531at_nat @ X @ Z ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_319_distrib__imp1,axiom,
% 9.16/5.11      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ! [X2: set_Pr4329608150637261639at_nat,Y2: set_Pr4329608150637261639at_nat,Z2: set_Pr4329608150637261639at_nat] :
% 9.16/5.11            ( ( inf_in7913087082777306421at_nat @ X2 @ ( sup_su5525570899277871387at_nat @ Y2 @ Z2 ) )
% 9.16/5.11            = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X2 @ Y2 ) @ ( inf_in7913087082777306421at_nat @ X2 @ Z2 ) ) )
% 9.16/5.11       => ( ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ Y @ Z ) )
% 9.16/5.11          = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_320_distrib__imp1,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.16/5.11        ( ! [X2: set_nat,Y2: set_nat,Z2: set_nat] :
% 9.16/5.11            ( ( inf_inf_set_nat @ X2 @ ( sup_sup_set_nat @ Y2 @ Z2 ) )
% 9.16/5.11            = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X2 @ Y2 ) @ ( inf_inf_set_nat @ X2 @ Z2 ) ) )
% 9.16/5.11       => ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 9.16/5.11          = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_321_distrib__imp1,axiom,
% 9.16/5.11      ! [X: nat,Y: nat,Z: nat] :
% 9.16/5.11        ( ! [X2: nat,Y2: nat,Z2: nat] :
% 9.16/5.11            ( ( inf_inf_nat @ X2 @ ( sup_sup_nat @ Y2 @ Z2 ) )
% 9.16/5.11            = ( sup_sup_nat @ ( inf_inf_nat @ X2 @ Y2 ) @ ( inf_inf_nat @ X2 @ Z2 ) ) )
% 9.16/5.11       => ( ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 9.16/5.11          = ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_322_distrib__imp1,axiom,
% 9.16/5.11      ! [X: int,Y: int,Z: int] :
% 9.16/5.11        ( ! [X2: int,Y2: int,Z2: int] :
% 9.16/5.11            ( ( inf_inf_int @ X2 @ ( sup_sup_int @ Y2 @ Z2 ) )
% 9.16/5.11            = ( sup_sup_int @ ( inf_inf_int @ X2 @ Y2 ) @ ( inf_inf_int @ X2 @ Z2 ) ) )
% 9.16/5.11       => ( ( sup_sup_int @ X @ ( inf_inf_int @ Y @ Z ) )
% 9.16/5.11          = ( inf_inf_int @ ( sup_sup_int @ X @ Y ) @ ( sup_sup_int @ X @ Z ) ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_323_boolean__algebra_Oconj__zero__right,axiom,
% 9.16/5.11      ! [X: product_prod_int_int > $o] :
% 9.16/5.11        ( ( inf_in3604695632404883862_int_o @ X @ bot_bo8147686125503663512_int_o )
% 9.16/5.11        = bot_bo8147686125503663512_int_o ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_324_boolean__algebra_Oconj__zero__right,axiom,
% 9.16/5.11      ! [X: list_char > $o] :
% 9.16/5.11        ( ( inf_inf_list_char_o @ X @ bot_bot_list_char_o )
% 9.16/5.11        = bot_bot_list_char_o ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_325_boolean__algebra_Oconj__zero__right,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ X @ bot_bo2099793752762293965at_nat )
% 9.16/5.11        = bot_bo2099793752762293965at_nat ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_326_boolean__algebra_Oconj__zero__right,axiom,
% 9.16/5.11      ! [X: set_o] :
% 9.16/5.11        ( ( inf_inf_set_o @ X @ bot_bot_set_o )
% 9.16/5.11        = bot_bot_set_o ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_327_boolean__algebra_Oconj__zero__right,axiom,
% 9.16/5.11      ! [X: set_nat] :
% 9.16/5.11        ( ( inf_inf_set_nat @ X @ bot_bot_set_nat )
% 9.16/5.11        = bot_bot_set_nat ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_328_boolean__algebra_Oconj__zero__right,axiom,
% 9.16/5.11      ! [X: set_int] :
% 9.16/5.11        ( ( inf_inf_set_int @ X @ bot_bot_set_int )
% 9.16/5.11        = bot_bot_set_int ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_329_boolean__algebra_Oconj__zero__left,axiom,
% 9.16/5.11      ! [X: product_prod_int_int > $o] :
% 9.16/5.11        ( ( inf_in3604695632404883862_int_o @ bot_bo8147686125503663512_int_o @ X )
% 9.16/5.11        = bot_bo8147686125503663512_int_o ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_330_boolean__algebra_Oconj__zero__left,axiom,
% 9.16/5.11      ! [X: list_char > $o] :
% 9.16/5.11        ( ( inf_inf_list_char_o @ bot_bot_list_char_o @ X )
% 9.16/5.11        = bot_bot_list_char_o ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_331_boolean__algebra_Oconj__zero__left,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ bot_bo2099793752762293965at_nat @ X )
% 9.16/5.11        = bot_bo2099793752762293965at_nat ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_332_boolean__algebra_Oconj__zero__left,axiom,
% 9.16/5.11      ! [X: set_o] :
% 9.16/5.11        ( ( inf_inf_set_o @ bot_bot_set_o @ X )
% 9.16/5.11        = bot_bot_set_o ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_333_boolean__algebra_Oconj__zero__left,axiom,
% 9.16/5.11      ! [X: set_nat] :
% 9.16/5.11        ( ( inf_inf_set_nat @ bot_bot_set_nat @ X )
% 9.16/5.11        = bot_bot_set_nat ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_334_boolean__algebra_Oconj__zero__left,axiom,
% 9.16/5.11      ! [X: set_int] :
% 9.16/5.11        ( ( inf_inf_set_int @ bot_bot_set_int @ X )
% 9.16/5.11        = bot_bot_set_int ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_335_boolean__algebra_Odisj__conj__distrib2,axiom,
% 9.16/5.11      ! [Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ Z ) @ X )
% 9.16/5.11        = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ X ) @ ( sup_su6327502436637775413at_nat @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_336_boolean__algebra_Odisj__conj__distrib2,axiom,
% 9.16/5.11      ! [Y: product_prod_int_int > $o,Z: product_prod_int_int > $o,X: product_prod_int_int > $o] :
% 9.16/5.11        ( ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ Y @ Z ) @ X )
% 9.16/5.11        = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ Y @ X ) @ ( sup_su8463660629351352368_int_o @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_337_boolean__algebra_Odisj__conj__distrib2,axiom,
% 9.16/5.11      ! [Y: list_char > $o,Z: list_char > $o,X: list_char > $o] :
% 9.16/5.11        ( ( sup_sup_list_char_o @ ( inf_inf_list_char_o @ Y @ Z ) @ X )
% 9.16/5.11        = ( inf_inf_list_char_o @ ( sup_sup_list_char_o @ Y @ X ) @ ( sup_sup_list_char_o @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_338_boolean__algebra_Odisj__conj__distrib2,axiom,
% 9.16/5.11      ! [Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ Y @ Z ) @ X )
% 9.16/5.11        = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ Y @ X ) @ ( sup_su3035147773818789531at_nat @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_339_boolean__algebra_Odisj__conj__distrib2,axiom,
% 9.16/5.11      ! [Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ Y @ Z ) @ X )
% 9.16/5.11        = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ Y @ X ) @ ( sup_su5525570899277871387at_nat @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_340_boolean__algebra_Odisj__conj__distrib2,axiom,
% 9.16/5.11      ! [Y: set_nat,Z: set_nat,X: set_nat] :
% 9.16/5.11        ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ Z ) @ X )
% 9.16/5.11        = ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ X ) @ ( sup_sup_set_nat @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_341_boolean__algebra_Oconj__disj__distrib2,axiom,
% 9.16/5.11      ! [Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ Z ) @ X )
% 9.16/5.11        = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ X ) @ ( inf_in2572325071724192079at_nat @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_342_boolean__algebra_Oconj__disj__distrib2,axiom,
% 9.16/5.11      ! [Y: product_prod_int_int > $o,Z: product_prod_int_int > $o,X: product_prod_int_int > $o] :
% 9.16/5.11        ( ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ Y @ Z ) @ X )
% 9.16/5.11        = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ Y @ X ) @ ( inf_in3604695632404883862_int_o @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_343_boolean__algebra_Oconj__disj__distrib2,axiom,
% 9.16/5.11      ! [Y: list_char > $o,Z: list_char > $o,X: list_char > $o] :
% 9.16/5.11        ( ( inf_inf_list_char_o @ ( sup_sup_list_char_o @ Y @ Z ) @ X )
% 9.16/5.11        = ( sup_sup_list_char_o @ ( inf_inf_list_char_o @ Y @ X ) @ ( inf_inf_list_char_o @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_344_boolean__algebra_Oconj__disj__distrib2,axiom,
% 9.16/5.11      ! [Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ Y @ Z ) @ X )
% 9.16/5.11        = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ Y @ X ) @ ( inf_in1697001100524423349at_nat @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_345_boolean__algebra_Oconj__disj__distrib2,axiom,
% 9.16/5.11      ! [Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ Y @ Z ) @ X )
% 9.16/5.11        = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ Y @ X ) @ ( inf_in7913087082777306421at_nat @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_346_boolean__algebra_Oconj__disj__distrib2,axiom,
% 9.16/5.11      ! [Y: set_nat,Z: set_nat,X: set_nat] :
% 9.16/5.11        ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ Z ) @ X )
% 9.16/5.11        = ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ X ) @ ( inf_inf_set_nat @ Z @ X ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_347_boolean__algebra_Odisj__conj__distrib,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 9.16/5.11        = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_348_boolean__algebra_Odisj__conj__distrib,axiom,
% 9.16/5.11      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 9.16/5.11        ( ( sup_su8463660629351352368_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) )
% 9.16/5.11        = ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ X @ Y ) @ ( sup_su8463660629351352368_int_o @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_349_boolean__algebra_Odisj__conj__distrib,axiom,
% 9.16/5.11      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 9.16/5.11        ( ( sup_sup_list_char_o @ X @ ( inf_inf_list_char_o @ Y @ Z ) )
% 9.16/5.11        = ( inf_inf_list_char_o @ ( sup_sup_list_char_o @ X @ Y ) @ ( sup_sup_list_char_o @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_350_boolean__algebra_Odisj__conj__distrib,axiom,
% 9.16/5.11      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 9.16/5.11        ( ( sup_su3035147773818789531at_nat @ X @ ( inf_in1697001100524423349at_nat @ Y @ Z ) )
% 9.16/5.11        = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ ( sup_su3035147773818789531at_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_351_boolean__algebra_Odisj__conj__distrib,axiom,
% 9.16/5.11      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 9.16/5.11        ( ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ Y @ Z ) )
% 9.16/5.11        = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_352_boolean__algebra_Odisj__conj__distrib,axiom,
% 9.16/5.11      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.16/5.11        ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 9.16/5.11        = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_353_boolean__algebra_Oconj__disj__distrib,axiom,
% 9.16/5.11      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 9.16/5.11        ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) )
% 9.16/5.11        = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ).
% 9.16/5.11  
% 9.16/5.11  thf(fact_354_boolean__algebra_Oconj__disj__distrib,axiom,
% 9.16/5.12      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 9.16/5.12        ( ( inf_in3604695632404883862_int_o @ X @ ( sup_su8463660629351352368_int_o @ Y @ Z ) )
% 9.16/5.12        = ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ ( inf_in3604695632404883862_int_o @ X @ Z ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_355_boolean__algebra_Oconj__disj__distrib,axiom,
% 9.16/5.12      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 9.16/5.12        ( ( inf_inf_list_char_o @ X @ ( sup_sup_list_char_o @ Y @ Z ) )
% 9.16/5.12        = ( sup_sup_list_char_o @ ( inf_inf_list_char_o @ X @ Y ) @ ( inf_inf_list_char_o @ X @ Z ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_356_boolean__algebra_Oconj__disj__distrib,axiom,
% 9.16/5.12      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 9.16/5.12        ( ( inf_in1697001100524423349at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) )
% 9.16/5.12        = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) @ ( inf_in1697001100524423349at_nat @ X @ Z ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_357_boolean__algebra_Oconj__disj__distrib,axiom,
% 9.16/5.12      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 9.16/5.12        ( ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) )
% 9.16/5.12        = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ ( inf_in7913087082777306421at_nat @ X @ Z ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_358_boolean__algebra_Oconj__disj__distrib,axiom,
% 9.16/5.12      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.16/5.12        ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 9.16/5.12        = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_359_boolean__algebra_Odisj__zero__right,axiom,
% 9.16/5.12      ! [X: set_Pr8551490117392284871at_nat] :
% 9.16/5.12        ( ( sup_su3035147773818789531at_nat @ X @ bot_bo8422036546324065075at_nat )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_360_boolean__algebra_Odisj__zero__right,axiom,
% 9.16/5.12      ! [X: set_Pr4329608150637261639at_nat] :
% 9.16/5.12        ( ( sup_su5525570899277871387at_nat @ X @ bot_bo228742789529271731at_nat )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_361_boolean__algebra_Odisj__zero__right,axiom,
% 9.16/5.12      ! [X: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( sup_su6327502436637775413at_nat @ X @ bot_bo2099793752762293965at_nat )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_362_boolean__algebra_Odisj__zero__right,axiom,
% 9.16/5.12      ! [X: set_o] :
% 9.16/5.12        ( ( sup_sup_set_o @ X @ bot_bot_set_o )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_363_boolean__algebra_Odisj__zero__right,axiom,
% 9.16/5.12      ! [X: set_nat] :
% 9.16/5.12        ( ( sup_sup_set_nat @ X @ bot_bot_set_nat )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_364_boolean__algebra_Odisj__zero__right,axiom,
% 9.16/5.12      ! [X: set_int] :
% 9.16/5.12        ( ( sup_sup_set_int @ X @ bot_bot_set_int )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_365_one__assn__proper,axiom,
% 9.16/5.12      proper @ one_assn_raw ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_366_type__definition__assn,axiom,
% 9.16/5.12      type_d3909072315231072503_nat_o @ rep_assn @ abs_assn @ ( collec939566748876313656_nat_o @ proper ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_367_boolean__algebra__cancel_Osup2,axiom,
% 9.16/5.12      ! [B2: set_Pr8551490117392284871at_nat,K: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 9.16/5.12        ( ( B2
% 9.16/5.12          = ( sup_su3035147773818789531at_nat @ K @ B ) )
% 9.16/5.12       => ( ( sup_su3035147773818789531at_nat @ A @ B2 )
% 9.16/5.12          = ( sup_su3035147773818789531at_nat @ K @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_368_boolean__algebra__cancel_Osup2,axiom,
% 9.16/5.12      ! [B2: set_Pr4329608150637261639at_nat,K: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 9.16/5.12        ( ( B2
% 9.16/5.12          = ( sup_su5525570899277871387at_nat @ K @ B ) )
% 9.16/5.12       => ( ( sup_su5525570899277871387at_nat @ A @ B2 )
% 9.16/5.12          = ( sup_su5525570899277871387at_nat @ K @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_369_boolean__algebra__cancel_Osup2,axiom,
% 9.16/5.12      ! [B2: set_nat,K: set_nat,B: set_nat,A: set_nat] :
% 9.16/5.12        ( ( B2
% 9.16/5.12          = ( sup_sup_set_nat @ K @ B ) )
% 9.16/5.12       => ( ( sup_sup_set_nat @ A @ B2 )
% 9.16/5.12          = ( sup_sup_set_nat @ K @ ( sup_sup_set_nat @ A @ B ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_370_boolean__algebra__cancel_Osup2,axiom,
% 9.16/5.12      ! [B2: nat,K: nat,B: nat,A: nat] :
% 9.16/5.12        ( ( B2
% 9.16/5.12          = ( sup_sup_nat @ K @ B ) )
% 9.16/5.12       => ( ( sup_sup_nat @ A @ B2 )
% 9.16/5.12          = ( sup_sup_nat @ K @ ( sup_sup_nat @ A @ B ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_371_boolean__algebra__cancel_Osup2,axiom,
% 9.16/5.12      ! [B2: int,K: int,B: int,A: int] :
% 9.16/5.12        ( ( B2
% 9.16/5.12          = ( sup_sup_int @ K @ B ) )
% 9.16/5.12       => ( ( sup_sup_int @ A @ B2 )
% 9.16/5.12          = ( sup_sup_int @ K @ ( sup_sup_int @ A @ B ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_372_boolean__algebra__cancel_Osup1,axiom,
% 9.16/5.12      ! [A2: set_Pr8551490117392284871at_nat,K: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 9.16/5.12        ( ( A2
% 9.16/5.12          = ( sup_su3035147773818789531at_nat @ K @ A ) )
% 9.16/5.12       => ( ( sup_su3035147773818789531at_nat @ A2 @ B )
% 9.16/5.12          = ( sup_su3035147773818789531at_nat @ K @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_373_boolean__algebra__cancel_Osup1,axiom,
% 9.16/5.12      ! [A2: set_Pr4329608150637261639at_nat,K: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 9.16/5.12        ( ( A2
% 9.16/5.12          = ( sup_su5525570899277871387at_nat @ K @ A ) )
% 9.16/5.12       => ( ( sup_su5525570899277871387at_nat @ A2 @ B )
% 9.16/5.12          = ( sup_su5525570899277871387at_nat @ K @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_374_boolean__algebra__cancel_Osup1,axiom,
% 9.16/5.12      ! [A2: set_nat,K: set_nat,A: set_nat,B: set_nat] :
% 9.16/5.12        ( ( A2
% 9.16/5.12          = ( sup_sup_set_nat @ K @ A ) )
% 9.16/5.12       => ( ( sup_sup_set_nat @ A2 @ B )
% 9.16/5.12          = ( sup_sup_set_nat @ K @ ( sup_sup_set_nat @ A @ B ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_375_boolean__algebra__cancel_Osup1,axiom,
% 9.16/5.12      ! [A2: nat,K: nat,A: nat,B: nat] :
% 9.16/5.12        ( ( A2
% 9.16/5.12          = ( sup_sup_nat @ K @ A ) )
% 9.16/5.12       => ( ( sup_sup_nat @ A2 @ B )
% 9.16/5.12          = ( sup_sup_nat @ K @ ( sup_sup_nat @ A @ B ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_376_boolean__algebra__cancel_Osup1,axiom,
% 9.16/5.12      ! [A2: int,K: int,A: int,B: int] :
% 9.16/5.12        ( ( A2
% 9.16/5.12          = ( sup_sup_int @ K @ A ) )
% 9.16/5.12       => ( ( sup_sup_int @ A2 @ B )
% 9.16/5.12          = ( sup_sup_int @ K @ ( sup_sup_int @ A @ B ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_377_boolean__algebra__cancel_Oinf1,axiom,
% 9.16/5.12      ! [A2: set_Pr1261947904930325089at_nat,K: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( A2
% 9.16/5.12          = ( inf_in2572325071724192079at_nat @ K @ A ) )
% 9.16/5.12       => ( ( inf_in2572325071724192079at_nat @ A2 @ B )
% 9.16/5.12          = ( inf_in2572325071724192079at_nat @ K @ ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_378_boolean__algebra__cancel_Oinf1,axiom,
% 9.16/5.12      ! [A2: set_nat,K: set_nat,A: set_nat,B: set_nat] :
% 9.16/5.12        ( ( A2
% 9.16/5.12          = ( inf_inf_set_nat @ K @ A ) )
% 9.16/5.12       => ( ( inf_inf_set_nat @ A2 @ B )
% 9.16/5.12          = ( inf_inf_set_nat @ K @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_379_boolean__algebra__cancel_Oinf1,axiom,
% 9.16/5.12      ! [A2: nat,K: nat,A: nat,B: nat] :
% 9.16/5.12        ( ( A2
% 9.16/5.12          = ( inf_inf_nat @ K @ A ) )
% 9.16/5.12       => ( ( inf_inf_nat @ A2 @ B )
% 9.16/5.12          = ( inf_inf_nat @ K @ ( inf_inf_nat @ A @ B ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_380_boolean__algebra__cancel_Oinf1,axiom,
% 9.16/5.12      ! [A2: product_prod_int_int > $o,K: product_prod_int_int > $o,A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 9.16/5.12        ( ( A2
% 9.16/5.12          = ( inf_in3604695632404883862_int_o @ K @ A ) )
% 9.16/5.12       => ( ( inf_in3604695632404883862_int_o @ A2 @ B )
% 9.16/5.12          = ( inf_in3604695632404883862_int_o @ K @ ( inf_in3604695632404883862_int_o @ A @ B ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_381_boolean__algebra__cancel_Oinf1,axiom,
% 9.16/5.12      ! [A2: list_char > $o,K: list_char > $o,A: list_char > $o,B: list_char > $o] :
% 9.16/5.12        ( ( A2
% 9.16/5.12          = ( inf_inf_list_char_o @ K @ A ) )
% 9.16/5.12       => ( ( inf_inf_list_char_o @ A2 @ B )
% 9.16/5.12          = ( inf_inf_list_char_o @ K @ ( inf_inf_list_char_o @ A @ B ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_382_boolean__algebra__cancel_Oinf2,axiom,
% 9.16/5.12      ! [B2: set_Pr1261947904930325089at_nat,K: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( B2
% 9.16/5.12          = ( inf_in2572325071724192079at_nat @ K @ B ) )
% 9.16/5.12       => ( ( inf_in2572325071724192079at_nat @ A @ B2 )
% 9.16/5.12          = ( inf_in2572325071724192079at_nat @ K @ ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_383_boolean__algebra__cancel_Oinf2,axiom,
% 9.16/5.12      ! [B2: set_nat,K: set_nat,B: set_nat,A: set_nat] :
% 9.16/5.12        ( ( B2
% 9.16/5.12          = ( inf_inf_set_nat @ K @ B ) )
% 9.16/5.12       => ( ( inf_inf_set_nat @ A @ B2 )
% 9.16/5.12          = ( inf_inf_set_nat @ K @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_384_boolean__algebra__cancel_Oinf2,axiom,
% 9.16/5.12      ! [B2: nat,K: nat,B: nat,A: nat] :
% 9.16/5.12        ( ( B2
% 9.16/5.12          = ( inf_inf_nat @ K @ B ) )
% 9.16/5.12       => ( ( inf_inf_nat @ A @ B2 )
% 9.16/5.12          = ( inf_inf_nat @ K @ ( inf_inf_nat @ A @ B ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_385_boolean__algebra__cancel_Oinf2,axiom,
% 9.16/5.12      ! [B2: product_prod_int_int > $o,K: product_prod_int_int > $o,B: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 9.16/5.12        ( ( B2
% 9.16/5.12          = ( inf_in3604695632404883862_int_o @ K @ B ) )
% 9.16/5.12       => ( ( inf_in3604695632404883862_int_o @ A @ B2 )
% 9.16/5.12          = ( inf_in3604695632404883862_int_o @ K @ ( inf_in3604695632404883862_int_o @ A @ B ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_386_boolean__algebra__cancel_Oinf2,axiom,
% 9.16/5.12      ! [B2: list_char > $o,K: list_char > $o,B: list_char > $o,A: list_char > $o] :
% 9.16/5.12        ( ( B2
% 9.16/5.12          = ( inf_inf_list_char_o @ K @ B ) )
% 9.16/5.12       => ( ( inf_inf_list_char_o @ A @ B2 )
% 9.16/5.12          = ( inf_inf_list_char_o @ K @ ( inf_inf_list_char_o @ A @ B ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_387_type__definition_ORep,axiom,
% 9.16/5.12      ! [Rep: product_unit > $o,Abs: $o > product_unit,A2: set_o,X: product_unit] :
% 9.16/5.12        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( member_o @ ( Rep @ X ) @ A2 ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_388_type__definition_ORep,axiom,
% 9.16/5.12      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,A2: set_Pr4532377907799695533_nat_o,X: assn] :
% 9.16/5.12        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( member6576561426505652726_nat_o @ ( Rep @ X ) @ A2 ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_389_type__definition_ORep,axiom,
% 9.16/5.12      ! [Rep: literal > list_char,Abs: list_char > literal,A2: set_list_char,X: literal] :
% 9.16/5.12        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( member_list_char @ ( Rep @ X ) @ A2 ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_390_type__definition_ORep,axiom,
% 9.16/5.12      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,A2: set_se6260736226359567993nt_int,X: rat] :
% 9.16/5.12        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( member2340774599025711042nt_int @ ( Rep @ X ) @ A2 ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_391_type__definition_ORep,axiom,
% 9.16/5.12      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,A2: set_se7855581050983116737at_nat,X: int] :
% 9.16/5.12        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( member2643936169264416010at_nat @ ( Rep @ X ) @ A2 ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_392_type__definition_Ointro,axiom,
% 9.16/5.12      ! [Rep: product_unit > $o,A2: set_o,Abs: $o > product_unit] :
% 9.16/5.12        ( ! [X2: product_unit] : ( member_o @ ( Rep @ X2 ) @ A2 )
% 9.16/5.12       => ( ! [X2: product_unit] :
% 9.16/5.12              ( ( Abs @ ( Rep @ X2 ) )
% 9.16/5.12              = X2 )
% 9.16/5.12         => ( ! [Y2: $o] :
% 9.16/5.12                ( ( member_o @ Y2 @ A2 )
% 9.16/5.12               => ( ( Rep @ ( Abs @ Y2 ) )
% 9.16/5.12                  = Y2 ) )
% 9.16/5.12           => ( type_d6188575255521822967unit_o @ Rep @ Abs @ A2 ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_393_type__definition_Ointro,axiom,
% 9.16/5.12      ! [Rep: assn > produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,Abs: ( produc3658429121746597890et_nat > $o ) > assn] :
% 9.16/5.12        ( ! [X2: assn] : ( member6576561426505652726_nat_o @ ( Rep @ X2 ) @ A2 )
% 9.16/5.12       => ( ! [X2: assn] :
% 9.16/5.12              ( ( Abs @ ( Rep @ X2 ) )
% 9.16/5.12              = X2 )
% 9.16/5.12         => ( ! [Y2: produc3658429121746597890et_nat > $o] :
% 9.16/5.12                ( ( member6576561426505652726_nat_o @ Y2 @ A2 )
% 9.16/5.12               => ( ( Rep @ ( Abs @ Y2 ) )
% 9.16/5.12                  = Y2 ) )
% 9.16/5.12           => ( type_d3909072315231072503_nat_o @ Rep @ Abs @ A2 ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_394_type__definition_Ointro,axiom,
% 9.16/5.12      ! [Rep: literal > list_char,A2: set_list_char,Abs: list_char > literal] :
% 9.16/5.12        ( ! [X2: literal] : ( member_list_char @ ( Rep @ X2 ) @ A2 )
% 9.16/5.12       => ( ! [X2: literal] :
% 9.16/5.12              ( ( Abs @ ( Rep @ X2 ) )
% 9.16/5.12              = X2 )
% 9.16/5.12         => ( ! [Y2: list_char] :
% 9.16/5.12                ( ( member_list_char @ Y2 @ A2 )
% 9.16/5.12               => ( ( Rep @ ( Abs @ Y2 ) )
% 9.16/5.12                  = Y2 ) )
% 9.16/5.12           => ( type_d4752411451802217481t_char @ Rep @ Abs @ A2 ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_395_type__definition_Ointro,axiom,
% 9.16/5.12      ! [Rep: rat > set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,Abs: set_Pr958786334691620121nt_int > rat] :
% 9.16/5.12        ( ! [X2: rat] : ( member2340774599025711042nt_int @ ( Rep @ X2 ) @ A2 )
% 9.16/5.12       => ( ! [X2: rat] :
% 9.16/5.12              ( ( Abs @ ( Rep @ X2 ) )
% 9.16/5.12              = X2 )
% 9.16/5.12         => ( ! [Y2: set_Pr958786334691620121nt_int] :
% 9.16/5.12                ( ( member2340774599025711042nt_int @ Y2 @ A2 )
% 9.16/5.12               => ( ( Rep @ ( Abs @ Y2 ) )
% 9.16/5.12                  = Y2 ) )
% 9.16/5.12           => ( type_d8554052265237484179nt_int @ Rep @ Abs @ A2 ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_396_type__definition_Ointro,axiom,
% 9.16/5.12      ! [Rep: int > set_Pr1261947904930325089at_nat,A2: set_se7855581050983116737at_nat,Abs: set_Pr1261947904930325089at_nat > int] :
% 9.16/5.12        ( ! [X2: int] : ( member2643936169264416010at_nat @ ( Rep @ X2 ) @ A2 )
% 9.16/5.12       => ( ! [X2: int] :
% 9.16/5.12              ( ( Abs @ ( Rep @ X2 ) )
% 9.16/5.12              = X2 )
% 9.16/5.12         => ( ! [Y2: set_Pr1261947904930325089at_nat] :
% 9.16/5.12                ( ( member2643936169264416010at_nat @ Y2 @ A2 )
% 9.16/5.12               => ( ( Rep @ ( Abs @ Y2 ) )
% 9.16/5.12                  = Y2 ) )
% 9.16/5.12           => ( type_d8752208705193531015at_nat @ Rep @ Abs @ A2 ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_397_type__definition_OAbs__cases,axiom,
% 9.16/5.12      ! [Rep: product_unit > $o,Abs: $o > product_unit,A2: set_o,X: product_unit] :
% 9.16/5.12        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A2 )
% 9.16/5.12       => ~ ! [Y2: $o] :
% 9.16/5.12              ( ( X
% 9.16/5.12                = ( Abs @ Y2 ) )
% 9.16/5.12             => ~ ( member_o @ Y2 @ A2 ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_398_type__definition_OAbs__cases,axiom,
% 9.16/5.12      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,A2: set_Pr4532377907799695533_nat_o,X: assn] :
% 9.16/5.12        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ A2 )
% 9.16/5.12       => ~ ! [Y2: produc3658429121746597890et_nat > $o] :
% 9.16/5.12              ( ( X
% 9.16/5.12                = ( Abs @ Y2 ) )
% 9.16/5.12             => ~ ( member6576561426505652726_nat_o @ Y2 @ A2 ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_399_type__definition_OAbs__cases,axiom,
% 9.16/5.12      ! [Rep: literal > list_char,Abs: list_char > literal,A2: set_list_char,X: literal] :
% 9.16/5.12        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ A2 )
% 9.16/5.12       => ~ ! [Y2: list_char] :
% 9.16/5.12              ( ( X
% 9.16/5.12                = ( Abs @ Y2 ) )
% 9.16/5.12             => ~ ( member_list_char @ Y2 @ A2 ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_400_type__definition_OAbs__cases,axiom,
% 9.16/5.12      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,A2: set_se6260736226359567993nt_int,X: rat] :
% 9.16/5.12        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ A2 )
% 9.16/5.12       => ~ ! [Y2: set_Pr958786334691620121nt_int] :
% 9.16/5.12              ( ( X
% 9.16/5.12                = ( Abs @ Y2 ) )
% 9.16/5.12             => ~ ( member2340774599025711042nt_int @ Y2 @ A2 ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_401_type__definition_OAbs__cases,axiom,
% 9.16/5.12      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,A2: set_se7855581050983116737at_nat,X: int] :
% 9.16/5.12        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ A2 )
% 9.16/5.12       => ~ ! [Y2: set_Pr1261947904930325089at_nat] :
% 9.16/5.12              ( ( X
% 9.16/5.12                = ( Abs @ Y2 ) )
% 9.16/5.12             => ~ ( member2643936169264416010at_nat @ Y2 @ A2 ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_402_type__definition_ORep__cases,axiom,
% 9.16/5.12      ! [Rep: product_unit > $o,Abs: $o > product_unit,A2: set_o,Y: $o] :
% 9.16/5.12        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( member_o @ Y @ A2 )
% 9.16/5.12         => ~ ! [X2: product_unit] :
% 9.16/5.12                ( Y
% 9.16/5.12                = ( ~ ( Rep @ X2 ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_403_type__definition_ORep__cases,axiom,
% 9.16/5.12      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,A2: set_Pr4532377907799695533_nat_o,Y: produc3658429121746597890et_nat > $o] :
% 9.16/5.12        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( member6576561426505652726_nat_o @ Y @ A2 )
% 9.16/5.12         => ~ ! [X2: assn] :
% 9.16/5.12                ( Y
% 9.16/5.12               != ( Rep @ X2 ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_404_type__definition_ORep__cases,axiom,
% 9.16/5.12      ! [Rep: literal > list_char,Abs: list_char > literal,A2: set_list_char,Y: list_char] :
% 9.16/5.12        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( member_list_char @ Y @ A2 )
% 9.16/5.12         => ~ ! [X2: literal] :
% 9.16/5.12                ( Y
% 9.16/5.12               != ( Rep @ X2 ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_405_type__definition_ORep__cases,axiom,
% 9.16/5.12      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,A2: set_se6260736226359567993nt_int,Y: set_Pr958786334691620121nt_int] :
% 9.16/5.12        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( member2340774599025711042nt_int @ Y @ A2 )
% 9.16/5.12         => ~ ! [X2: rat] :
% 9.16/5.12                ( Y
% 9.16/5.12               != ( Rep @ X2 ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_406_type__definition_ORep__cases,axiom,
% 9.16/5.12      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,A2: set_se7855581050983116737at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( member2643936169264416010at_nat @ Y @ A2 )
% 9.16/5.12         => ~ ! [X2: int] :
% 9.16/5.12                ( Y
% 9.16/5.12               != ( Rep @ X2 ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_407_type__definition_OAbs__induct,axiom,
% 9.16/5.12      ! [Rep: product_unit > $o,Abs: $o > product_unit,A2: set_o,P: product_unit > $o,X: product_unit] :
% 9.16/5.12        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ! [Y2: $o] :
% 9.16/5.12              ( ( member_o @ Y2 @ A2 )
% 9.16/5.12             => ( P @ ( Abs @ Y2 ) ) )
% 9.16/5.12         => ( P @ X ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_408_type__definition_OAbs__induct,axiom,
% 9.16/5.12      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,A2: set_Pr4532377907799695533_nat_o,P: assn > $o,X: assn] :
% 9.16/5.12        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ! [Y2: produc3658429121746597890et_nat > $o] :
% 9.16/5.12              ( ( member6576561426505652726_nat_o @ Y2 @ A2 )
% 9.16/5.12             => ( P @ ( Abs @ Y2 ) ) )
% 9.16/5.12         => ( P @ X ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_409_type__definition_OAbs__induct,axiom,
% 9.16/5.12      ! [Rep: literal > list_char,Abs: list_char > literal,A2: set_list_char,P: literal > $o,X: literal] :
% 9.16/5.12        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ! [Y2: list_char] :
% 9.16/5.12              ( ( member_list_char @ Y2 @ A2 )
% 9.16/5.12             => ( P @ ( Abs @ Y2 ) ) )
% 9.16/5.12         => ( P @ X ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_410_type__definition_OAbs__induct,axiom,
% 9.16/5.12      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,A2: set_se6260736226359567993nt_int,P: rat > $o,X: rat] :
% 9.16/5.12        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ! [Y2: set_Pr958786334691620121nt_int] :
% 9.16/5.12              ( ( member2340774599025711042nt_int @ Y2 @ A2 )
% 9.16/5.12             => ( P @ ( Abs @ Y2 ) ) )
% 9.16/5.12         => ( P @ X ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_411_type__definition_OAbs__induct,axiom,
% 9.16/5.12      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,A2: set_se7855581050983116737at_nat,P: int > $o,X: int] :
% 9.16/5.12        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ! [Y2: set_Pr1261947904930325089at_nat] :
% 9.16/5.12              ( ( member2643936169264416010at_nat @ Y2 @ A2 )
% 9.16/5.12             => ( P @ ( Abs @ Y2 ) ) )
% 9.16/5.12         => ( P @ X ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_412_type__definition_OAbs__inject,axiom,
% 9.16/5.12      ! [Rep: product_unit > $o,Abs: $o > product_unit,A2: set_o,X: $o,Y: $o] :
% 9.16/5.12        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( member_o @ X @ A2 )
% 9.16/5.12         => ( ( member_o @ Y @ A2 )
% 9.16/5.12           => ( ( ( Abs @ X )
% 9.16/5.12                = ( Abs @ Y ) )
% 9.16/5.12              = ( X = Y ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_413_type__definition_OAbs__inject,axiom,
% 9.16/5.12      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,A2: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o] :
% 9.16/5.12        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( member6576561426505652726_nat_o @ X @ A2 )
% 9.16/5.12         => ( ( member6576561426505652726_nat_o @ Y @ A2 )
% 9.16/5.12           => ( ( ( Abs @ X )
% 9.16/5.12                = ( Abs @ Y ) )
% 9.16/5.12              = ( X = Y ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_414_type__definition_OAbs__inject,axiom,
% 9.16/5.12      ! [Rep: literal > list_char,Abs: list_char > literal,A2: set_list_char,X: list_char,Y: list_char] :
% 9.16/5.12        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( member_list_char @ X @ A2 )
% 9.16/5.12         => ( ( member_list_char @ Y @ A2 )
% 9.16/5.12           => ( ( ( Abs @ X )
% 9.16/5.12                = ( Abs @ Y ) )
% 9.16/5.12              = ( X = Y ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_415_type__definition_OAbs__inject,axiom,
% 9.16/5.12      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,A2: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
% 9.16/5.12        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( member2340774599025711042nt_int @ X @ A2 )
% 9.16/5.12         => ( ( member2340774599025711042nt_int @ Y @ A2 )
% 9.16/5.12           => ( ( ( Abs @ X )
% 9.16/5.12                = ( Abs @ Y ) )
% 9.16/5.12              = ( X = Y ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_416_type__definition_OAbs__inject,axiom,
% 9.16/5.12      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,A2: set_se7855581050983116737at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( member2643936169264416010at_nat @ X @ A2 )
% 9.16/5.12         => ( ( member2643936169264416010at_nat @ Y @ A2 )
% 9.16/5.12           => ( ( ( Abs @ X )
% 9.16/5.12                = ( Abs @ Y ) )
% 9.16/5.12              = ( X = Y ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_417_type__definition_ORep__induct,axiom,
% 9.16/5.12      ! [Rep: product_unit > $o,Abs: $o > product_unit,A2: set_o,Y: $o,P: $o > $o] :
% 9.16/5.12        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( member_o @ Y @ A2 )
% 9.16/5.12         => ( ! [X2: product_unit] : ( P @ ( Rep @ X2 ) )
% 9.16/5.12           => ( P @ Y ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_418_type__definition_ORep__induct,axiom,
% 9.16/5.12      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,A2: set_Pr4532377907799695533_nat_o,Y: produc3658429121746597890et_nat > $o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.16/5.12        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( member6576561426505652726_nat_o @ Y @ A2 )
% 9.16/5.12         => ( ! [X2: assn] : ( P @ ( Rep @ X2 ) )
% 9.16/5.12           => ( P @ Y ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_419_type__definition_ORep__induct,axiom,
% 9.16/5.12      ! [Rep: literal > list_char,Abs: list_char > literal,A2: set_list_char,Y: list_char,P: list_char > $o] :
% 9.16/5.12        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( member_list_char @ Y @ A2 )
% 9.16/5.12         => ( ! [X2: literal] : ( P @ ( Rep @ X2 ) )
% 9.16/5.12           => ( P @ Y ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_420_type__definition_ORep__induct,axiom,
% 9.16/5.12      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,A2: set_se6260736226359567993nt_int,Y: set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 9.16/5.12        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( member2340774599025711042nt_int @ Y @ A2 )
% 9.16/5.12         => ( ! [X2: rat] : ( P @ ( Rep @ X2 ) )
% 9.16/5.12           => ( P @ Y ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_421_type__definition_ORep__induct,axiom,
% 9.16/5.12      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,A2: set_se7855581050983116737at_nat,Y: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 9.16/5.12        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( member2643936169264416010at_nat @ Y @ A2 )
% 9.16/5.12         => ( ! [X2: int] : ( P @ ( Rep @ X2 ) )
% 9.16/5.12           => ( P @ Y ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_422_type__definition_ORep__inject,axiom,
% 9.16/5.12      ! [Rep: product_unit > $o,Abs: $o > product_unit,A2: set_o,X: product_unit,Y: product_unit] :
% 9.16/5.12        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( ( Rep @ X )
% 9.16/5.12            = ( Rep @ Y ) )
% 9.16/5.12          = ( X = Y ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_423_type__definition_ORep__inject,axiom,
% 9.16/5.12      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,A2: set_Pr4532377907799695533_nat_o,X: assn,Y: assn] :
% 9.16/5.12        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( ( Rep @ X )
% 9.16/5.12            = ( Rep @ Y ) )
% 9.16/5.12          = ( X = Y ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_424_type__definition_ORep__inject,axiom,
% 9.16/5.12      ! [Rep: literal > list_char,Abs: list_char > literal,A2: set_list_char,X: literal,Y: literal] :
% 9.16/5.12        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( ( Rep @ X )
% 9.16/5.12            = ( Rep @ Y ) )
% 9.16/5.12          = ( X = Y ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_425_type__definition_ORep__inject,axiom,
% 9.16/5.12      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,A2: set_se6260736226359567993nt_int,X: rat,Y: rat] :
% 9.16/5.12        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( ( Rep @ X )
% 9.16/5.12            = ( Rep @ Y ) )
% 9.16/5.12          = ( X = Y ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_426_type__definition_ORep__inject,axiom,
% 9.16/5.12      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,A2: set_se7855581050983116737at_nat,X: int,Y: int] :
% 9.16/5.12        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( ( Rep @ X )
% 9.16/5.12            = ( Rep @ Y ) )
% 9.16/5.12          = ( X = Y ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_427_type__definition_OAbs__inverse,axiom,
% 9.16/5.12      ! [Rep: product_unit > $o,Abs: $o > product_unit,A2: set_o,Y: $o] :
% 9.16/5.12        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( member_o @ Y @ A2 )
% 9.16/5.12         => ( ( Rep @ ( Abs @ Y ) )
% 9.16/5.12            = Y ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_428_type__definition_OAbs__inverse,axiom,
% 9.16/5.12      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,A2: set_Pr4532377907799695533_nat_o,Y: produc3658429121746597890et_nat > $o] :
% 9.16/5.12        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( member6576561426505652726_nat_o @ Y @ A2 )
% 9.16/5.12         => ( ( Rep @ ( Abs @ Y ) )
% 9.16/5.12            = Y ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_429_type__definition_OAbs__inverse,axiom,
% 9.16/5.12      ! [Rep: literal > list_char,Abs: list_char > literal,A2: set_list_char,Y: list_char] :
% 9.16/5.12        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( member_list_char @ Y @ A2 )
% 9.16/5.12         => ( ( Rep @ ( Abs @ Y ) )
% 9.16/5.12            = Y ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_430_type__definition_OAbs__inverse,axiom,
% 9.16/5.12      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,A2: set_se6260736226359567993nt_int,Y: set_Pr958786334691620121nt_int] :
% 9.16/5.12        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( member2340774599025711042nt_int @ Y @ A2 )
% 9.16/5.12         => ( ( Rep @ ( Abs @ Y ) )
% 9.16/5.12            = Y ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_431_type__definition_OAbs__inverse,axiom,
% 9.16/5.12      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,A2: set_se7855581050983116737at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( member2643936169264416010at_nat @ Y @ A2 )
% 9.16/5.12         => ( ( Rep @ ( Abs @ Y ) )
% 9.16/5.12            = Y ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_432_type__definition_ORep__inverse,axiom,
% 9.16/5.12      ! [Rep: product_unit > $o,Abs: $o > product_unit,A2: set_o,X: product_unit] :
% 9.16/5.12        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( Abs @ ( Rep @ X ) )
% 9.16/5.12          = X ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_433_type__definition_ORep__inverse,axiom,
% 9.16/5.12      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,A2: set_Pr4532377907799695533_nat_o,X: assn] :
% 9.16/5.12        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( Abs @ ( Rep @ X ) )
% 9.16/5.12          = X ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_434_type__definition_ORep__inverse,axiom,
% 9.16/5.12      ! [Rep: literal > list_char,Abs: list_char > literal,A2: set_list_char,X: literal] :
% 9.16/5.12        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( Abs @ ( Rep @ X ) )
% 9.16/5.12          = X ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_435_type__definition_ORep__inverse,axiom,
% 9.16/5.12      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,A2: set_se6260736226359567993nt_int,X: rat] :
% 9.16/5.12        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( Abs @ ( Rep @ X ) )
% 9.16/5.12          = X ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_436_type__definition_ORep__inverse,axiom,
% 9.16/5.12      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,A2: set_se7855581050983116737at_nat,X: int] :
% 9.16/5.12        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ A2 )
% 9.16/5.12       => ( ( Abs @ ( Rep @ X ) )
% 9.16/5.12          = X ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_437_type__definition__def,axiom,
% 9.16/5.12      ( type_d6188575255521822967unit_o
% 9.16/5.12      = ( ^ [Rep2: product_unit > $o,Abs2: $o > product_unit,A4: set_o] :
% 9.16/5.12            ( ! [X3: product_unit] : ( member_o @ ( Rep2 @ X3 ) @ A4 )
% 9.16/5.12            & ! [X3: product_unit] :
% 9.16/5.12                ( ( Abs2 @ ( Rep2 @ X3 ) )
% 9.16/5.12                = X3 )
% 9.16/5.12            & ! [Y3: $o] :
% 9.16/5.12                ( ( member_o @ Y3 @ A4 )
% 9.16/5.12               => ( ( Rep2 @ ( Abs2 @ Y3 ) )
% 9.16/5.12                  = Y3 ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_438_type__definition__def,axiom,
% 9.16/5.12      ( type_d3909072315231072503_nat_o
% 9.16/5.12      = ( ^ [Rep2: assn > produc3658429121746597890et_nat > $o,Abs2: ( produc3658429121746597890et_nat > $o ) > assn,A4: set_Pr4532377907799695533_nat_o] :
% 9.16/5.12            ( ! [X3: assn] : ( member6576561426505652726_nat_o @ ( Rep2 @ X3 ) @ A4 )
% 9.16/5.12            & ! [X3: assn] :
% 9.16/5.12                ( ( Abs2 @ ( Rep2 @ X3 ) )
% 9.16/5.12                = X3 )
% 9.16/5.12            & ! [Y3: produc3658429121746597890et_nat > $o] :
% 9.16/5.12                ( ( member6576561426505652726_nat_o @ Y3 @ A4 )
% 9.16/5.12               => ( ( Rep2 @ ( Abs2 @ Y3 ) )
% 9.16/5.12                  = Y3 ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_439_type__definition__def,axiom,
% 9.16/5.12      ( type_d4752411451802217481t_char
% 9.16/5.12      = ( ^ [Rep2: literal > list_char,Abs2: list_char > literal,A4: set_list_char] :
% 9.16/5.12            ( ! [X3: literal] : ( member_list_char @ ( Rep2 @ X3 ) @ A4 )
% 9.16/5.12            & ! [X3: literal] :
% 9.16/5.12                ( ( Abs2 @ ( Rep2 @ X3 ) )
% 9.16/5.12                = X3 )
% 9.16/5.12            & ! [Y3: list_char] :
% 9.16/5.12                ( ( member_list_char @ Y3 @ A4 )
% 9.16/5.12               => ( ( Rep2 @ ( Abs2 @ Y3 ) )
% 9.16/5.12                  = Y3 ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_440_type__definition__def,axiom,
% 9.16/5.12      ( type_d8554052265237484179nt_int
% 9.16/5.12      = ( ^ [Rep2: rat > set_Pr958786334691620121nt_int,Abs2: set_Pr958786334691620121nt_int > rat,A4: set_se6260736226359567993nt_int] :
% 9.16/5.12            ( ! [X3: rat] : ( member2340774599025711042nt_int @ ( Rep2 @ X3 ) @ A4 )
% 9.16/5.12            & ! [X3: rat] :
% 9.16/5.12                ( ( Abs2 @ ( Rep2 @ X3 ) )
% 9.16/5.12                = X3 )
% 9.16/5.12            & ! [Y3: set_Pr958786334691620121nt_int] :
% 9.16/5.12                ( ( member2340774599025711042nt_int @ Y3 @ A4 )
% 9.16/5.12               => ( ( Rep2 @ ( Abs2 @ Y3 ) )
% 9.16/5.12                  = Y3 ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_441_type__definition__def,axiom,
% 9.16/5.12      ( type_d8752208705193531015at_nat
% 9.16/5.12      = ( ^ [Rep2: int > set_Pr1261947904930325089at_nat,Abs2: set_Pr1261947904930325089at_nat > int,A4: set_se7855581050983116737at_nat] :
% 9.16/5.12            ( ! [X3: int] : ( member2643936169264416010at_nat @ ( Rep2 @ X3 ) @ A4 )
% 9.16/5.12            & ! [X3: int] :
% 9.16/5.12                ( ( Abs2 @ ( Rep2 @ X3 ) )
% 9.16/5.12                = X3 )
% 9.16/5.12            & ! [Y3: set_Pr1261947904930325089at_nat] :
% 9.16/5.12                ( ( member2643936169264416010at_nat @ Y3 @ A4 )
% 9.16/5.12               => ( ( Rep2 @ ( Abs2 @ Y3 ) )
% 9.16/5.12                  = Y3 ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_442_mult_Oright__assoc,axiom,
% 9.16/5.12      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.16/5.12        ( ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 9.16/5.12        = ( times_3573771949741848930nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_443_mult_Oright__assoc,axiom,
% 9.16/5.12      ! [A: assn,B: assn,C: assn] :
% 9.16/5.12        ( ( times_times_assn @ ( times_times_assn @ A @ B ) @ C )
% 9.16/5.12        = ( times_times_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_444_mult_Oright__assoc,axiom,
% 9.16/5.12      ! [A: rat,B: rat,C: rat] :
% 9.16/5.12        ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 9.16/5.12        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_445_mult_Oright__assoc,axiom,
% 9.16/5.12      ! [A: nat,B: nat,C: nat] :
% 9.16/5.12        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 9.16/5.12        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_446_mult_Oright__assoc,axiom,
% 9.16/5.12      ! [A: int,B: int,C: int] :
% 9.16/5.12        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 9.16/5.12        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_447_mult_Oright__commute,axiom,
% 9.16/5.12      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.16/5.12        ( ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 9.16/5.12        = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_448_mult_Oright__commute,axiom,
% 9.16/5.12      ! [A: assn,B: assn,C: assn] :
% 9.16/5.12        ( ( times_times_assn @ ( times_times_assn @ A @ B ) @ C )
% 9.16/5.12        = ( times_times_assn @ ( times_times_assn @ A @ C ) @ B ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_449_mult_Oright__commute,axiom,
% 9.16/5.12      ! [A: rat,B: rat,C: rat] :
% 9.16/5.12        ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 9.16/5.12        = ( times_times_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_450_mult_Oright__commute,axiom,
% 9.16/5.12      ! [A: nat,B: nat,C: nat] :
% 9.16/5.12        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 9.16/5.12        = ( times_times_nat @ ( times_times_nat @ A @ C ) @ B ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_451_mult_Oright__commute,axiom,
% 9.16/5.12      ! [A: int,B: int,C: int] :
% 9.16/5.12        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 9.16/5.12        = ( times_times_int @ ( times_times_int @ A @ C ) @ B ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_452_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 9.16/5.12      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.16/5.12        ( ( times_3573771949741848930nteger @ B @ ( times_3573771949741848930nteger @ A @ C ) )
% 9.16/5.12        = ( times_3573771949741848930nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_453_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 9.16/5.12      ! [B: assn,A: assn,C: assn] :
% 9.16/5.12        ( ( times_times_assn @ B @ ( times_times_assn @ A @ C ) )
% 9.16/5.12        = ( times_times_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_454_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 9.16/5.12      ! [B: rat,A: rat,C: rat] :
% 9.16/5.12        ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 9.16/5.12        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_455_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 9.16/5.12      ! [B: nat,A: nat,C: nat] :
% 9.16/5.12        ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 9.16/5.12        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_456_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 9.16/5.12      ! [B: int,A: int,C: int] :
% 9.16/5.12        ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 9.16/5.12        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_457_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 9.16/5.12      ( times_3573771949741848930nteger
% 9.16/5.12      = ( ^ [A3: code_integer,B3: code_integer] : ( times_3573771949741848930nteger @ B3 @ A3 ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_458_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 9.16/5.12      ( times_times_assn
% 9.16/5.12      = ( ^ [A3: assn,B3: assn] : ( times_times_assn @ B3 @ A3 ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_459_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 9.16/5.12      ( times_times_rat
% 9.16/5.12      = ( ^ [A3: rat,B3: rat] : ( times_times_rat @ B3 @ A3 ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_460_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 9.16/5.12      ( times_times_nat
% 9.16/5.12      = ( ^ [A3: nat,B3: nat] : ( times_times_nat @ B3 @ A3 ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_461_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 9.16/5.12      ( times_times_int
% 9.16/5.12      = ( ^ [A3: int,B3: int] : ( times_times_int @ B3 @ A3 ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_462_mult_Oassoc,axiom,
% 9.16/5.12      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.16/5.12        ( ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 9.16/5.12        = ( times_3573771949741848930nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_463_mult_Oassoc,axiom,
% 9.16/5.12      ! [A: assn,B: assn,C: assn] :
% 9.16/5.12        ( ( times_times_assn @ ( times_times_assn @ A @ B ) @ C )
% 9.16/5.12        = ( times_times_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_464_mult_Oassoc,axiom,
% 9.16/5.12      ! [A: rat,B: rat,C: rat] :
% 9.16/5.12        ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 9.16/5.12        = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_465_mult_Oassoc,axiom,
% 9.16/5.12      ! [A: nat,B: nat,C: nat] :
% 9.16/5.12        ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 9.16/5.12        = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_466_mult_Oassoc,axiom,
% 9.16/5.12      ! [A: int,B: int,C: int] :
% 9.16/5.12        ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 9.16/5.12        = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_467_mult_Osafe__commute,axiom,
% 9.16/5.12      ! [X: code_integer,Y: code_integer,A: code_integer,B: code_integer] :
% 9.16/5.12        ( ( syntax380677951125133566nteger @ ( times_3573771949741848930nteger @ X @ Y ) @ A )
% 9.16/5.12       => ( ( times_3573771949741848930nteger @ A @ B )
% 9.16/5.12          = ( times_3573771949741848930nteger @ B @ A ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_468_mult_Osafe__commute,axiom,
% 9.16/5.12      ! [X: assn,Y: assn,A: assn,B: assn] :
% 9.16/5.12        ( ( syntax7398250324933576852n_assn @ ( times_times_assn @ X @ Y ) @ A )
% 9.16/5.12       => ( ( times_times_assn @ A @ B )
% 9.16/5.12          = ( times_times_assn @ B @ A ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_469_mult_Osafe__commute,axiom,
% 9.16/5.12      ! [X: rat,Y: rat,A: rat,B: rat] :
% 9.16/5.12        ( ( syntax3730441303064801268at_rat @ ( times_times_rat @ X @ Y ) @ A )
% 9.16/5.12       => ( ( times_times_rat @ A @ B )
% 9.16/5.12          = ( times_times_rat @ B @ A ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_470_mult_Osafe__commute,axiom,
% 9.16/5.12      ! [X: nat,Y: nat,A: nat,B: nat] :
% 9.16/5.12        ( ( syntax4682126007086162916at_nat @ ( times_times_nat @ X @ Y ) @ A )
% 9.16/5.12       => ( ( times_times_nat @ A @ B )
% 9.16/5.12          = ( times_times_nat @ B @ A ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_471_mult_Osafe__commute,axiom,
% 9.16/5.12      ! [X: int,Y: int,A: int,B: int] :
% 9.16/5.12        ( ( syntax5678989248478167196nt_int @ ( times_times_int @ X @ Y ) @ A )
% 9.16/5.12       => ( ( times_times_int @ A @ B )
% 9.16/5.12          = ( times_times_int @ B @ A ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_472_sup__bot_Osemilattice__neutr__axioms,axiom,
% 9.16/5.12      semila6683195626996185257at_nat @ sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_473_sup__bot_Osemilattice__neutr__axioms,axiom,
% 9.16/5.12      semila3675781407871293737at_nat @ sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_474_sup__bot_Osemilattice__neutr__axioms,axiom,
% 9.16/5.12      semila858173770281612099at_nat @ sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_475_sup__bot_Osemilattice__neutr__axioms,axiom,
% 9.16/5.12      semila1065760912024005978_set_o @ sup_sup_set_o @ bot_bot_set_o ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_476_sup__bot_Osemilattice__neutr__axioms,axiom,
% 9.16/5.12      semila1241773964035338532et_nat @ sup_sup_set_nat @ bot_bot_set_nat ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_477_sup__bot_Osemilattice__neutr__axioms,axiom,
% 9.16/5.12      semila6287294981380917632et_int @ sup_sup_set_int @ bot_bot_set_int ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_478_sup__bot_Omonoid__axioms,axiom,
% 9.16/5.12      monoid3323479476634721864at_nat @ sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_479_sup__bot_Omonoid__axioms,axiom,
% 9.16/5.12      monoid534952638934301128at_nat @ sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_480_sup__bot_Omonoid__axioms,axiom,
% 9.16/5.12      monoid1519094961268053602at_nat @ sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_481_sup__bot_Omonoid__axioms,axiom,
% 9.16/5.12      monoid_set_o @ sup_sup_set_o @ bot_bot_set_o ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_482_sup__bot_Omonoid__axioms,axiom,
% 9.16/5.12      monoid_set_nat @ sup_sup_set_nat @ bot_bot_set_nat ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_483_sup__bot_Omonoid__axioms,axiom,
% 9.16/5.12      monoid_set_int @ sup_sup_set_int @ bot_bot_set_int ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_484_one__assn__def,axiom,
% 9.16/5.12      ( one_one_assn
% 9.16/5.12      = ( abs_assn @ one_assn_raw ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_485_boolean__algebra_Ocomplement__unique,axiom,
% 9.16/5.12      ! [A: product_prod_int_int > $o,X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 9.16/5.12        ( ( ( inf_in3604695632404883862_int_o @ A @ X )
% 9.16/5.12          = bot_bo8147686125503663512_int_o )
% 9.16/5.12       => ( ( ( sup_su8463660629351352368_int_o @ A @ X )
% 9.16/5.12            = top_to1578927101902068148_int_o )
% 9.16/5.12         => ( ( ( inf_in3604695632404883862_int_o @ A @ Y )
% 9.16/5.12              = bot_bo8147686125503663512_int_o )
% 9.16/5.12           => ( ( ( sup_su8463660629351352368_int_o @ A @ Y )
% 9.16/5.12                = top_to1578927101902068148_int_o )
% 9.16/5.12             => ( X = Y ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_486_boolean__algebra_Ocomplement__unique,axiom,
% 9.16/5.12      ! [A: list_char > $o,X: list_char > $o,Y: list_char > $o] :
% 9.16/5.12        ( ( ( inf_inf_list_char_o @ A @ X )
% 9.16/5.12          = bot_bot_list_char_o )
% 9.16/5.12       => ( ( ( sup_sup_list_char_o @ A @ X )
% 9.16/5.12            = top_top_list_char_o )
% 9.16/5.12         => ( ( ( inf_inf_list_char_o @ A @ Y )
% 9.16/5.12              = bot_bot_list_char_o )
% 9.16/5.12           => ( ( ( sup_sup_list_char_o @ A @ Y )
% 9.16/5.12                = top_top_list_char_o )
% 9.16/5.12             => ( X = Y ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_487_boolean__algebra_Ocomplement__unique,axiom,
% 9.16/5.12      ! [A: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 9.16/5.12        ( ( ( inf_in1697001100524423349at_nat @ A @ X )
% 9.16/5.12          = bot_bo8422036546324065075at_nat )
% 9.16/5.12       => ( ( ( sup_su3035147773818789531at_nat @ A @ X )
% 9.16/5.12            = top_to8764741339697478167at_nat )
% 9.16/5.12         => ( ( ( inf_in1697001100524423349at_nat @ A @ Y )
% 9.16/5.12              = bot_bo8422036546324065075at_nat )
% 9.16/5.12           => ( ( ( sup_su3035147773818789531at_nat @ A @ Y )
% 9.16/5.12                = top_to8764741339697478167at_nat )
% 9.16/5.12             => ( X = Y ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_488_boolean__algebra_Ocomplement__unique,axiom,
% 9.16/5.12      ! [A: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 9.16/5.12        ( ( ( inf_in7913087082777306421at_nat @ A @ X )
% 9.16/5.12          = bot_bo228742789529271731at_nat )
% 9.16/5.12       => ( ( ( sup_su5525570899277871387at_nat @ A @ X )
% 9.16/5.12            = top_to6833984726390702231at_nat )
% 9.16/5.12         => ( ( ( inf_in7913087082777306421at_nat @ A @ Y )
% 9.16/5.12              = bot_bo228742789529271731at_nat )
% 9.16/5.12           => ( ( ( sup_su5525570899277871387at_nat @ A @ Y )
% 9.16/5.12                = top_to6833984726390702231at_nat )
% 9.16/5.12             => ( X = Y ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_489_boolean__algebra_Ocomplement__unique,axiom,
% 9.16/5.12      ! [A: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( ( inf_in2572325071724192079at_nat @ A @ X )
% 9.16/5.12          = bot_bo2099793752762293965at_nat )
% 9.16/5.12       => ( ( ( sup_su6327502436637775413at_nat @ A @ X )
% 9.16/5.12            = top_to4669805908274784177at_nat )
% 9.16/5.12         => ( ( ( inf_in2572325071724192079at_nat @ A @ Y )
% 9.16/5.12              = bot_bo2099793752762293965at_nat )
% 9.16/5.12           => ( ( ( sup_su6327502436637775413at_nat @ A @ Y )
% 9.16/5.12                = top_to4669805908274784177at_nat )
% 9.16/5.12             => ( X = Y ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_490_boolean__algebra_Ocomplement__unique,axiom,
% 9.16/5.12      ! [A: set_list_nat,X: set_list_nat,Y: set_list_nat] :
% 9.16/5.12        ( ( ( inf_inf_set_list_nat @ A @ X )
% 9.16/5.12          = bot_bot_set_list_nat )
% 9.16/5.12       => ( ( ( sup_sup_set_list_nat @ A @ X )
% 9.16/5.12            = top_top_set_list_nat )
% 9.16/5.12         => ( ( ( inf_inf_set_list_nat @ A @ Y )
% 9.16/5.12              = bot_bot_set_list_nat )
% 9.16/5.12           => ( ( ( sup_sup_set_list_nat @ A @ Y )
% 9.16/5.12                = top_top_set_list_nat )
% 9.16/5.12             => ( X = Y ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_491_boolean__algebra_Ocomplement__unique,axiom,
% 9.16/5.12      ! [A: set_o,X: set_o,Y: set_o] :
% 9.16/5.12        ( ( ( inf_inf_set_o @ A @ X )
% 9.16/5.12          = bot_bot_set_o )
% 9.16/5.12       => ( ( ( sup_sup_set_o @ A @ X )
% 9.16/5.12            = top_top_set_o )
% 9.16/5.12         => ( ( ( inf_inf_set_o @ A @ Y )
% 9.16/5.12              = bot_bot_set_o )
% 9.16/5.12           => ( ( ( sup_sup_set_o @ A @ Y )
% 9.16/5.12                = top_top_set_o )
% 9.16/5.12             => ( X = Y ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_492_boolean__algebra_Ocomplement__unique,axiom,
% 9.16/5.12      ! [A: set_rat,X: set_rat,Y: set_rat] :
% 9.16/5.12        ( ( ( inf_inf_set_rat @ A @ X )
% 9.16/5.12          = bot_bot_set_rat )
% 9.16/5.12       => ( ( ( sup_sup_set_rat @ A @ X )
% 9.16/5.12            = top_top_set_rat )
% 9.16/5.12         => ( ( ( inf_inf_set_rat @ A @ Y )
% 9.16/5.12              = bot_bot_set_rat )
% 9.16/5.12           => ( ( ( sup_sup_set_rat @ A @ Y )
% 9.16/5.12                = top_top_set_rat )
% 9.16/5.12             => ( X = Y ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_493_boolean__algebra_Ocomplement__unique,axiom,
% 9.16/5.12      ! [A: set_nat,X: set_nat,Y: set_nat] :
% 9.16/5.12        ( ( ( inf_inf_set_nat @ A @ X )
% 9.16/5.12          = bot_bot_set_nat )
% 9.16/5.12       => ( ( ( sup_sup_set_nat @ A @ X )
% 9.16/5.12            = top_top_set_nat )
% 9.16/5.12         => ( ( ( inf_inf_set_nat @ A @ Y )
% 9.16/5.12              = bot_bot_set_nat )
% 9.16/5.12           => ( ( ( sup_sup_set_nat @ A @ Y )
% 9.16/5.12                = top_top_set_nat )
% 9.16/5.12             => ( X = Y ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_494_boolean__algebra_Ocomplement__unique,axiom,
% 9.16/5.12      ! [A: set_int,X: set_int,Y: set_int] :
% 9.16/5.12        ( ( ( inf_inf_set_int @ A @ X )
% 9.16/5.12          = bot_bot_set_int )
% 9.16/5.12       => ( ( ( sup_sup_set_int @ A @ X )
% 9.16/5.12            = top_top_set_int )
% 9.16/5.12         => ( ( ( inf_inf_set_int @ A @ Y )
% 9.16/5.12              = bot_bot_set_int )
% 9.16/5.12           => ( ( ( sup_sup_set_int @ A @ Y )
% 9.16/5.12                = top_top_set_int )
% 9.16/5.12             => ( X = Y ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_495_mod__star__conv,axiom,
% 9.16/5.12      ! [A2: assn,B2: assn,H3: produc3658429121746597890et_nat] :
% 9.16/5.12        ( ( rep_assn @ ( times_times_assn @ A2 @ B2 ) @ H3 )
% 9.16/5.12        = ( ? [Hr: heap_e7401611519738050253t_unit,As1: set_nat,As2: set_nat] :
% 9.16/5.12              ( ( H3
% 9.16/5.12                = ( produc7507926704131184380et_nat @ Hr @ ( sup_sup_set_nat @ As1 @ As2 ) ) )
% 9.16/5.12              & ( ( inf_inf_set_nat @ As1 @ As2 )
% 9.16/5.12                = bot_bot_set_nat )
% 9.16/5.12              & ( rep_assn @ A2 @ ( produc7507926704131184380et_nat @ Hr @ As1 ) )
% 9.16/5.12              & ( rep_assn @ B2 @ ( produc7507926704131184380et_nat @ Hr @ As2 ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_496_star__assnI,axiom,
% 9.16/5.12      ! [P: assn,H3: heap_e7401611519738050253t_unit,As: set_nat,Q2: assn,As3: set_nat] :
% 9.16/5.12        ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 9.16/5.12       => ( ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 9.16/5.12         => ( ( ( inf_inf_set_nat @ As @ As3 )
% 9.16/5.12              = bot_bot_set_nat )
% 9.16/5.12           => ( rep_assn @ ( times_times_assn @ P @ Q2 ) @ ( produc7507926704131184380et_nat @ H3 @ ( sup_sup_set_nat @ As @ As3 ) ) ) ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_497_sup__bot_Ocomm__monoid__axioms,axiom,
% 9.16/5.12      comm_m4707310049023135612at_nat @ sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_498_sup__bot_Ocomm__monoid__axioms,axiom,
% 9.16/5.12      comm_m2457627138559323900at_nat @ sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_499_sup__bot_Ocomm__monoid__axioms,axiom,
% 9.16/5.12      comm_m5709050211238513046at_nat @ sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_500_sup__bot_Ocomm__monoid__axioms,axiom,
% 9.16/5.12      comm_monoid_set_o @ sup_sup_set_o @ bot_bot_set_o ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_501_sup__bot_Ocomm__monoid__axioms,axiom,
% 9.16/5.12      comm_monoid_set_nat @ sup_sup_set_nat @ bot_bot_set_nat ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_502_sup__bot_Ocomm__monoid__axioms,axiom,
% 9.16/5.12      comm_monoid_set_int @ sup_sup_set_int @ bot_bot_set_int ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_503_boolean__algebra_Ode__Morgan__disj,axiom,
% 9.16/5.12      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( uminus6524753893492686040at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) )
% 9.16/5.12        = ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ ( uminus6524753893492686040at_nat @ Y ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_504_boolean__algebra_Ode__Morgan__disj,axiom,
% 9.16/5.12      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 9.16/5.12        ( ( uminus7117520113953359693_int_o @ ( sup_su8463660629351352368_int_o @ X @ Y ) )
% 9.16/5.12        = ( inf_in3604695632404883862_int_o @ ( uminus7117520113953359693_int_o @ X ) @ ( uminus7117520113953359693_int_o @ Y ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_505_boolean__algebra_Ode__Morgan__disj,axiom,
% 9.16/5.12      ! [X: list_char > $o,Y: list_char > $o] :
% 9.16/5.12        ( ( uminus7154032370948614053char_o @ ( sup_sup_list_char_o @ X @ Y ) )
% 9.16/5.12        = ( inf_inf_list_char_o @ ( uminus7154032370948614053char_o @ X ) @ ( uminus7154032370948614053char_o @ Y ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_506_boolean__algebra_Ode__Morgan__disj,axiom,
% 9.16/5.12      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 9.16/5.12        ( ( uminus2330091110623919550at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 9.16/5.12        = ( inf_in1697001100524423349at_nat @ ( uminus2330091110623919550at_nat @ X ) @ ( uminus2330091110623919550at_nat @ Y ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_507_boolean__algebra_Ode__Morgan__disj,axiom,
% 9.16/5.12      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 9.16/5.12        ( ( uminus935396558254630718at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 9.16/5.12        = ( inf_in7913087082777306421at_nat @ ( uminus935396558254630718at_nat @ X ) @ ( uminus935396558254630718at_nat @ Y ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_508_boolean__algebra_Ode__Morgan__disj,axiom,
% 9.16/5.12      ! [X: set_nat,Y: set_nat] :
% 9.16/5.12        ( ( uminus5710092332889474511et_nat @ ( sup_sup_set_nat @ X @ Y ) )
% 9.16/5.12        = ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_509_boolean__algebra_Ode__Morgan__disj,axiom,
% 9.16/5.12      ! [X: product_unit,Y: product_unit] :
% 9.16/5.12        ( ( uminus2952777764628376836t_unit @ ( sup_sup_Product_unit @ X @ Y ) )
% 9.16/5.12        = ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( uminus2952777764628376836t_unit @ Y ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_510_add_Oinverse__inverse,axiom,
% 9.16/5.12      ! [A: int] :
% 9.16/5.12        ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_511_add_Oinverse__inverse,axiom,
% 9.16/5.12      ! [A: code_integer] :
% 9.16/5.12        ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_512_add_Oinverse__inverse,axiom,
% 9.16/5.12      ! [A: rat] :
% 9.16/5.12        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_513_neg__equal__iff__equal,axiom,
% 9.16/5.12      ! [A: int,B: int] :
% 9.16/5.12        ( ( ( uminus_uminus_int @ A )
% 9.16/5.12          = ( uminus_uminus_int @ B ) )
% 9.16/5.12        = ( A = B ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_514_neg__equal__iff__equal,axiom,
% 9.16/5.12      ! [A: code_integer,B: code_integer] :
% 9.16/5.12        ( ( ( uminus1351360451143612070nteger @ A )
% 9.16/5.12          = ( uminus1351360451143612070nteger @ B ) )
% 9.16/5.12        = ( A = B ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_515_neg__equal__iff__equal,axiom,
% 9.16/5.12      ! [A: rat,B: rat] :
% 9.16/5.12        ( ( ( uminus_uminus_rat @ A )
% 9.16/5.12          = ( uminus_uminus_rat @ B ) )
% 9.16/5.12        = ( A = B ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_516_boolean__algebra__class_Oboolean__algebra_Ocompl__eq__compl__iff,axiom,
% 9.16/5.12      ! [X: product_unit,Y: product_unit] :
% 9.16/5.12        ( ( ( uminus2952777764628376836t_unit @ X )
% 9.16/5.12          = ( uminus2952777764628376836t_unit @ Y ) )
% 9.16/5.12        = ( X = Y ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_517_boolean__algebra__class_Oboolean__algebra_Odouble__compl,axiom,
% 9.16/5.12      ! [X: product_unit] :
% 9.16/5.12        ( ( uminus2952777764628376836t_unit @ ( uminus2952777764628376836t_unit @ X ) )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_518_mult_Oright__neutral,axiom,
% 9.16/5.12      ! [A: code_integer] :
% 9.16/5.12        ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_519_mult_Oright__neutral,axiom,
% 9.16/5.12      ! [A: assn] :
% 9.16/5.12        ( ( times_times_assn @ A @ one_one_assn )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_520_mult_Oright__neutral,axiom,
% 9.16/5.12      ! [A: rat] :
% 9.16/5.12        ( ( times_times_rat @ A @ one_one_rat )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_521_mult_Oright__neutral,axiom,
% 9.16/5.12      ! [A: nat] :
% 9.16/5.12        ( ( times_times_nat @ A @ one_one_nat )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_522_mult_Oright__neutral,axiom,
% 9.16/5.12      ! [A: int] :
% 9.16/5.12        ( ( times_times_int @ A @ one_one_int )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_523_mult__1,axiom,
% 9.16/5.12      ! [A: code_integer] :
% 9.16/5.12        ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_524_mult__1,axiom,
% 9.16/5.12      ! [A: assn] :
% 9.16/5.12        ( ( times_times_assn @ one_one_assn @ A )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_525_mult__1,axiom,
% 9.16/5.12      ! [A: rat] :
% 9.16/5.12        ( ( times_times_rat @ one_one_rat @ A )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_526_mult__1,axiom,
% 9.16/5.12      ! [A: nat] :
% 9.16/5.12        ( ( times_times_nat @ one_one_nat @ A )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_527_mult__1,axiom,
% 9.16/5.12      ! [A: int] :
% 9.16/5.12        ( ( times_times_int @ one_one_int @ A )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_528_inf__top__left,axiom,
% 9.16/5.12      ! [X: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( inf_in2572325071724192079at_nat @ top_to4669805908274784177at_nat @ X )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_529_inf__top__left,axiom,
% 9.16/5.12      ! [X: product_prod_int_int > $o] :
% 9.16/5.12        ( ( inf_in3604695632404883862_int_o @ top_to1578927101902068148_int_o @ X )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_530_inf__top__left,axiom,
% 9.16/5.12      ! [X: list_char > $o] :
% 9.16/5.12        ( ( inf_inf_list_char_o @ top_top_list_char_o @ X )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_531_inf__top__left,axiom,
% 9.16/5.12      ! [X: set_list_nat] :
% 9.16/5.12        ( ( inf_inf_set_list_nat @ top_top_set_list_nat @ X )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_532_inf__top__left,axiom,
% 9.16/5.12      ! [X: set_o] :
% 9.16/5.12        ( ( inf_inf_set_o @ top_top_set_o @ X )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_533_inf__top__left,axiom,
% 9.16/5.12      ! [X: set_rat] :
% 9.16/5.12        ( ( inf_inf_set_rat @ top_top_set_rat @ X )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_534_inf__top__left,axiom,
% 9.16/5.12      ! [X: set_nat] :
% 9.16/5.12        ( ( inf_inf_set_nat @ top_top_set_nat @ X )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_535_inf__top__left,axiom,
% 9.16/5.12      ! [X: set_int] :
% 9.16/5.12        ( ( inf_inf_set_int @ top_top_set_int @ X )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_536_inf__top__right,axiom,
% 9.16/5.12      ! [X: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( inf_in2572325071724192079at_nat @ X @ top_to4669805908274784177at_nat )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_537_inf__top__right,axiom,
% 9.16/5.12      ! [X: product_prod_int_int > $o] :
% 9.16/5.12        ( ( inf_in3604695632404883862_int_o @ X @ top_to1578927101902068148_int_o )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_538_inf__top__right,axiom,
% 9.16/5.12      ! [X: list_char > $o] :
% 9.16/5.12        ( ( inf_inf_list_char_o @ X @ top_top_list_char_o )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_539_inf__top__right,axiom,
% 9.16/5.12      ! [X: set_list_nat] :
% 9.16/5.12        ( ( inf_inf_set_list_nat @ X @ top_top_set_list_nat )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_540_inf__top__right,axiom,
% 9.16/5.12      ! [X: set_o] :
% 9.16/5.12        ( ( inf_inf_set_o @ X @ top_top_set_o )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_541_inf__top__right,axiom,
% 9.16/5.12      ! [X: set_rat] :
% 9.16/5.12        ( ( inf_inf_set_rat @ X @ top_top_set_rat )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_542_inf__top__right,axiom,
% 9.16/5.12      ! [X: set_nat] :
% 9.16/5.12        ( ( inf_inf_set_nat @ X @ top_top_set_nat )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_543_inf__top__right,axiom,
% 9.16/5.12      ! [X: set_int] :
% 9.16/5.12        ( ( inf_inf_set_int @ X @ top_top_set_int )
% 9.16/5.12        = X ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_544_inf__eq__top__iff,axiom,
% 9.16/5.12      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 9.16/5.12          = top_to4669805908274784177at_nat )
% 9.16/5.12        = ( ( X = top_to4669805908274784177at_nat )
% 9.16/5.12          & ( Y = top_to4669805908274784177at_nat ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_545_inf__eq__top__iff,axiom,
% 9.16/5.12      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 9.16/5.12        ( ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 9.16/5.12          = top_to1578927101902068148_int_o )
% 9.16/5.12        = ( ( X = top_to1578927101902068148_int_o )
% 9.16/5.12          & ( Y = top_to1578927101902068148_int_o ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_546_inf__eq__top__iff,axiom,
% 9.16/5.12      ! [X: list_char > $o,Y: list_char > $o] :
% 9.16/5.12        ( ( ( inf_inf_list_char_o @ X @ Y )
% 9.16/5.12          = top_top_list_char_o )
% 9.16/5.12        = ( ( X = top_top_list_char_o )
% 9.16/5.12          & ( Y = top_top_list_char_o ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_547_inf__eq__top__iff,axiom,
% 9.16/5.12      ! [X: set_list_nat,Y: set_list_nat] :
% 9.16/5.12        ( ( ( inf_inf_set_list_nat @ X @ Y )
% 9.16/5.12          = top_top_set_list_nat )
% 9.16/5.12        = ( ( X = top_top_set_list_nat )
% 9.16/5.12          & ( Y = top_top_set_list_nat ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_548_inf__eq__top__iff,axiom,
% 9.16/5.12      ! [X: set_o,Y: set_o] :
% 9.16/5.12        ( ( ( inf_inf_set_o @ X @ Y )
% 9.16/5.12          = top_top_set_o )
% 9.16/5.12        = ( ( X = top_top_set_o )
% 9.16/5.12          & ( Y = top_top_set_o ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_549_inf__eq__top__iff,axiom,
% 9.16/5.12      ! [X: set_rat,Y: set_rat] :
% 9.16/5.12        ( ( ( inf_inf_set_rat @ X @ Y )
% 9.16/5.12          = top_top_set_rat )
% 9.16/5.12        = ( ( X = top_top_set_rat )
% 9.16/5.12          & ( Y = top_top_set_rat ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_550_inf__eq__top__iff,axiom,
% 9.16/5.12      ! [X: set_nat,Y: set_nat] :
% 9.16/5.12        ( ( ( inf_inf_set_nat @ X @ Y )
% 9.16/5.12          = top_top_set_nat )
% 9.16/5.12        = ( ( X = top_top_set_nat )
% 9.16/5.12          & ( Y = top_top_set_nat ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_551_inf__eq__top__iff,axiom,
% 9.16/5.12      ! [X: set_int,Y: set_int] :
% 9.16/5.12        ( ( ( inf_inf_set_int @ X @ Y )
% 9.16/5.12          = top_top_set_int )
% 9.16/5.12        = ( ( X = top_top_set_int )
% 9.16/5.12          & ( Y = top_top_set_int ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_552_top__eq__inf__iff,axiom,
% 9.16/5.12      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( top_to4669805908274784177at_nat
% 9.16/5.12          = ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 9.16/5.12        = ( ( X = top_to4669805908274784177at_nat )
% 9.16/5.12          & ( Y = top_to4669805908274784177at_nat ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_553_top__eq__inf__iff,axiom,
% 9.16/5.12      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 9.16/5.12        ( ( top_to1578927101902068148_int_o
% 9.16/5.12          = ( inf_in3604695632404883862_int_o @ X @ Y ) )
% 9.16/5.12        = ( ( X = top_to1578927101902068148_int_o )
% 9.16/5.12          & ( Y = top_to1578927101902068148_int_o ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_554_top__eq__inf__iff,axiom,
% 9.16/5.12      ! [X: list_char > $o,Y: list_char > $o] :
% 9.16/5.12        ( ( top_top_list_char_o
% 9.16/5.12          = ( inf_inf_list_char_o @ X @ Y ) )
% 9.16/5.12        = ( ( X = top_top_list_char_o )
% 9.16/5.12          & ( Y = top_top_list_char_o ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_555_top__eq__inf__iff,axiom,
% 9.16/5.12      ! [X: set_list_nat,Y: set_list_nat] :
% 9.16/5.12        ( ( top_top_set_list_nat
% 9.16/5.12          = ( inf_inf_set_list_nat @ X @ Y ) )
% 9.16/5.12        = ( ( X = top_top_set_list_nat )
% 9.16/5.12          & ( Y = top_top_set_list_nat ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_556_top__eq__inf__iff,axiom,
% 9.16/5.12      ! [X: set_o,Y: set_o] :
% 9.16/5.12        ( ( top_top_set_o
% 9.16/5.12          = ( inf_inf_set_o @ X @ Y ) )
% 9.16/5.12        = ( ( X = top_top_set_o )
% 9.16/5.12          & ( Y = top_top_set_o ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_557_top__eq__inf__iff,axiom,
% 9.16/5.12      ! [X: set_rat,Y: set_rat] :
% 9.16/5.12        ( ( top_top_set_rat
% 9.16/5.12          = ( inf_inf_set_rat @ X @ Y ) )
% 9.16/5.12        = ( ( X = top_top_set_rat )
% 9.16/5.12          & ( Y = top_top_set_rat ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_558_top__eq__inf__iff,axiom,
% 9.16/5.12      ! [X: set_nat,Y: set_nat] :
% 9.16/5.12        ( ( top_top_set_nat
% 9.16/5.12          = ( inf_inf_set_nat @ X @ Y ) )
% 9.16/5.12        = ( ( X = top_top_set_nat )
% 9.16/5.12          & ( Y = top_top_set_nat ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_559_top__eq__inf__iff,axiom,
% 9.16/5.12      ! [X: set_int,Y: set_int] :
% 9.16/5.12        ( ( top_top_set_int
% 9.16/5.12          = ( inf_inf_set_int @ X @ Y ) )
% 9.16/5.12        = ( ( X = top_top_set_int )
% 9.16/5.12          & ( Y = top_top_set_int ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_560_inf__top_Oeq__neutr__iff,axiom,
% 9.16/5.12      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( ( inf_in2572325071724192079at_nat @ A @ B )
% 9.16/5.12          = top_to4669805908274784177at_nat )
% 9.16/5.12        = ( ( A = top_to4669805908274784177at_nat )
% 9.16/5.12          & ( B = top_to4669805908274784177at_nat ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_561_inf__top_Oeq__neutr__iff,axiom,
% 9.16/5.12      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 9.16/5.12        ( ( ( inf_in3604695632404883862_int_o @ A @ B )
% 9.16/5.12          = top_to1578927101902068148_int_o )
% 9.16/5.12        = ( ( A = top_to1578927101902068148_int_o )
% 9.16/5.12          & ( B = top_to1578927101902068148_int_o ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_562_inf__top_Oeq__neutr__iff,axiom,
% 9.16/5.12      ! [A: list_char > $o,B: list_char > $o] :
% 9.16/5.12        ( ( ( inf_inf_list_char_o @ A @ B )
% 9.16/5.12          = top_top_list_char_o )
% 9.16/5.12        = ( ( A = top_top_list_char_o )
% 9.16/5.12          & ( B = top_top_list_char_o ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_563_inf__top_Oeq__neutr__iff,axiom,
% 9.16/5.12      ! [A: set_list_nat,B: set_list_nat] :
% 9.16/5.12        ( ( ( inf_inf_set_list_nat @ A @ B )
% 9.16/5.12          = top_top_set_list_nat )
% 9.16/5.12        = ( ( A = top_top_set_list_nat )
% 9.16/5.12          & ( B = top_top_set_list_nat ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_564_inf__top_Oeq__neutr__iff,axiom,
% 9.16/5.12      ! [A: set_o,B: set_o] :
% 9.16/5.12        ( ( ( inf_inf_set_o @ A @ B )
% 9.16/5.12          = top_top_set_o )
% 9.16/5.12        = ( ( A = top_top_set_o )
% 9.16/5.12          & ( B = top_top_set_o ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_565_inf__top_Oeq__neutr__iff,axiom,
% 9.16/5.12      ! [A: set_rat,B: set_rat] :
% 9.16/5.12        ( ( ( inf_inf_set_rat @ A @ B )
% 9.16/5.12          = top_top_set_rat )
% 9.16/5.12        = ( ( A = top_top_set_rat )
% 9.16/5.12          & ( B = top_top_set_rat ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_566_inf__top_Oeq__neutr__iff,axiom,
% 9.16/5.12      ! [A: set_nat,B: set_nat] :
% 9.16/5.12        ( ( ( inf_inf_set_nat @ A @ B )
% 9.16/5.12          = top_top_set_nat )
% 9.16/5.12        = ( ( A = top_top_set_nat )
% 9.16/5.12          & ( B = top_top_set_nat ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_567_inf__top_Oeq__neutr__iff,axiom,
% 9.16/5.12      ! [A: set_int,B: set_int] :
% 9.16/5.12        ( ( ( inf_inf_set_int @ A @ B )
% 9.16/5.12          = top_top_set_int )
% 9.16/5.12        = ( ( A = top_top_set_int )
% 9.16/5.12          & ( B = top_top_set_int ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_568_inf__top_Oleft__neutral,axiom,
% 9.16/5.12      ! [A: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( inf_in2572325071724192079at_nat @ top_to4669805908274784177at_nat @ A )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_569_inf__top_Oleft__neutral,axiom,
% 9.16/5.12      ! [A: product_prod_int_int > $o] :
% 9.16/5.12        ( ( inf_in3604695632404883862_int_o @ top_to1578927101902068148_int_o @ A )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_570_inf__top_Oleft__neutral,axiom,
% 9.16/5.12      ! [A: list_char > $o] :
% 9.16/5.12        ( ( inf_inf_list_char_o @ top_top_list_char_o @ A )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_571_inf__top_Oleft__neutral,axiom,
% 9.16/5.12      ! [A: set_list_nat] :
% 9.16/5.12        ( ( inf_inf_set_list_nat @ top_top_set_list_nat @ A )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_572_inf__top_Oleft__neutral,axiom,
% 9.16/5.12      ! [A: set_o] :
% 9.16/5.12        ( ( inf_inf_set_o @ top_top_set_o @ A )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_573_inf__top_Oleft__neutral,axiom,
% 9.16/5.12      ! [A: set_rat] :
% 9.16/5.12        ( ( inf_inf_set_rat @ top_top_set_rat @ A )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_574_inf__top_Oleft__neutral,axiom,
% 9.16/5.12      ! [A: set_nat] :
% 9.16/5.12        ( ( inf_inf_set_nat @ top_top_set_nat @ A )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_575_inf__top_Oleft__neutral,axiom,
% 9.16/5.12      ! [A: set_int] :
% 9.16/5.12        ( ( inf_inf_set_int @ top_top_set_int @ A )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_576_inf__top_Oneutr__eq__iff,axiom,
% 9.16/5.12      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( top_to4669805908274784177at_nat
% 9.16/5.12          = ( inf_in2572325071724192079at_nat @ A @ B ) )
% 9.16/5.12        = ( ( A = top_to4669805908274784177at_nat )
% 9.16/5.12          & ( B = top_to4669805908274784177at_nat ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_577_inf__top_Oneutr__eq__iff,axiom,
% 9.16/5.12      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 9.16/5.12        ( ( top_to1578927101902068148_int_o
% 9.16/5.12          = ( inf_in3604695632404883862_int_o @ A @ B ) )
% 9.16/5.12        = ( ( A = top_to1578927101902068148_int_o )
% 9.16/5.12          & ( B = top_to1578927101902068148_int_o ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_578_inf__top_Oneutr__eq__iff,axiom,
% 9.16/5.12      ! [A: list_char > $o,B: list_char > $o] :
% 9.16/5.12        ( ( top_top_list_char_o
% 9.16/5.12          = ( inf_inf_list_char_o @ A @ B ) )
% 9.16/5.12        = ( ( A = top_top_list_char_o )
% 9.16/5.12          & ( B = top_top_list_char_o ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_579_inf__top_Oneutr__eq__iff,axiom,
% 9.16/5.12      ! [A: set_list_nat,B: set_list_nat] :
% 9.16/5.12        ( ( top_top_set_list_nat
% 9.16/5.12          = ( inf_inf_set_list_nat @ A @ B ) )
% 9.16/5.12        = ( ( A = top_top_set_list_nat )
% 9.16/5.12          & ( B = top_top_set_list_nat ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_580_inf__top_Oneutr__eq__iff,axiom,
% 9.16/5.12      ! [A: set_o,B: set_o] :
% 9.16/5.12        ( ( top_top_set_o
% 9.16/5.12          = ( inf_inf_set_o @ A @ B ) )
% 9.16/5.12        = ( ( A = top_top_set_o )
% 9.16/5.12          & ( B = top_top_set_o ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_581_inf__top_Oneutr__eq__iff,axiom,
% 9.16/5.12      ! [A: set_rat,B: set_rat] :
% 9.16/5.12        ( ( top_top_set_rat
% 9.16/5.12          = ( inf_inf_set_rat @ A @ B ) )
% 9.16/5.12        = ( ( A = top_top_set_rat )
% 9.16/5.12          & ( B = top_top_set_rat ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_582_inf__top_Oneutr__eq__iff,axiom,
% 9.16/5.12      ! [A: set_nat,B: set_nat] :
% 9.16/5.12        ( ( top_top_set_nat
% 9.16/5.12          = ( inf_inf_set_nat @ A @ B ) )
% 9.16/5.12        = ( ( A = top_top_set_nat )
% 9.16/5.12          & ( B = top_top_set_nat ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_583_inf__top_Oneutr__eq__iff,axiom,
% 9.16/5.12      ! [A: set_int,B: set_int] :
% 9.16/5.12        ( ( top_top_set_int
% 9.16/5.12          = ( inf_inf_set_int @ A @ B ) )
% 9.16/5.12        = ( ( A = top_top_set_int )
% 9.16/5.12          & ( B = top_top_set_int ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_584_inf__top_Oright__neutral,axiom,
% 9.16/5.12      ! [A: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( inf_in2572325071724192079at_nat @ A @ top_to4669805908274784177at_nat )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_585_inf__top_Oright__neutral,axiom,
% 9.16/5.12      ! [A: product_prod_int_int > $o] :
% 9.16/5.12        ( ( inf_in3604695632404883862_int_o @ A @ top_to1578927101902068148_int_o )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_586_inf__top_Oright__neutral,axiom,
% 9.16/5.12      ! [A: list_char > $o] :
% 9.16/5.12        ( ( inf_inf_list_char_o @ A @ top_top_list_char_o )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_587_inf__top_Oright__neutral,axiom,
% 9.16/5.12      ! [A: set_list_nat] :
% 9.16/5.12        ( ( inf_inf_set_list_nat @ A @ top_top_set_list_nat )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_588_inf__top_Oright__neutral,axiom,
% 9.16/5.12      ! [A: set_o] :
% 9.16/5.12        ( ( inf_inf_set_o @ A @ top_top_set_o )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_589_inf__top_Oright__neutral,axiom,
% 9.16/5.12      ! [A: set_rat] :
% 9.16/5.12        ( ( inf_inf_set_rat @ A @ top_top_set_rat )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_590_inf__top_Oright__neutral,axiom,
% 9.16/5.12      ! [A: set_nat] :
% 9.16/5.12        ( ( inf_inf_set_nat @ A @ top_top_set_nat )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_591_inf__top_Oright__neutral,axiom,
% 9.16/5.12      ! [A: set_int] :
% 9.16/5.12        ( ( inf_inf_set_int @ A @ top_top_set_int )
% 9.16/5.12        = A ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_592_boolean__algebra_Odisj__one__left,axiom,
% 9.16/5.12      ! [X: set_Pr8551490117392284871at_nat] :
% 9.16/5.12        ( ( sup_su3035147773818789531at_nat @ top_to8764741339697478167at_nat @ X )
% 9.16/5.12        = top_to8764741339697478167at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_593_boolean__algebra_Odisj__one__left,axiom,
% 9.16/5.12      ! [X: set_Pr4329608150637261639at_nat] :
% 9.16/5.12        ( ( sup_su5525570899277871387at_nat @ top_to6833984726390702231at_nat @ X )
% 9.16/5.12        = top_to6833984726390702231at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_594_boolean__algebra_Odisj__one__left,axiom,
% 9.16/5.12      ! [X: set_list_nat] :
% 9.16/5.12        ( ( sup_sup_set_list_nat @ top_top_set_list_nat @ X )
% 9.16/5.12        = top_top_set_list_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_595_boolean__algebra_Odisj__one__left,axiom,
% 9.16/5.12      ! [X: set_o] :
% 9.16/5.12        ( ( sup_sup_set_o @ top_top_set_o @ X )
% 9.16/5.12        = top_top_set_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_596_boolean__algebra_Odisj__one__left,axiom,
% 9.16/5.12      ! [X: set_rat] :
% 9.16/5.12        ( ( sup_sup_set_rat @ top_top_set_rat @ X )
% 9.16/5.12        = top_top_set_rat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_597_boolean__algebra_Odisj__one__left,axiom,
% 9.16/5.12      ! [X: set_nat] :
% 9.16/5.12        ( ( sup_sup_set_nat @ top_top_set_nat @ X )
% 9.16/5.12        = top_top_set_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_598_boolean__algebra_Odisj__one__left,axiom,
% 9.16/5.12      ! [X: set_int] :
% 9.16/5.12        ( ( sup_sup_set_int @ top_top_set_int @ X )
% 9.16/5.12        = top_top_set_int ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_599_boolean__algebra_Odisj__one__right,axiom,
% 9.16/5.12      ! [X: set_Pr8551490117392284871at_nat] :
% 9.16/5.12        ( ( sup_su3035147773818789531at_nat @ X @ top_to8764741339697478167at_nat )
% 9.16/5.12        = top_to8764741339697478167at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_600_boolean__algebra_Odisj__one__right,axiom,
% 9.16/5.12      ! [X: set_Pr4329608150637261639at_nat] :
% 9.16/5.12        ( ( sup_su5525570899277871387at_nat @ X @ top_to6833984726390702231at_nat )
% 9.16/5.12        = top_to6833984726390702231at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_601_boolean__algebra_Odisj__one__right,axiom,
% 9.16/5.12      ! [X: set_list_nat] :
% 9.16/5.12        ( ( sup_sup_set_list_nat @ X @ top_top_set_list_nat )
% 9.16/5.12        = top_top_set_list_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_602_boolean__algebra_Odisj__one__right,axiom,
% 9.16/5.12      ! [X: set_o] :
% 9.16/5.12        ( ( sup_sup_set_o @ X @ top_top_set_o )
% 9.16/5.12        = top_top_set_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_603_boolean__algebra_Odisj__one__right,axiom,
% 9.16/5.12      ! [X: set_rat] :
% 9.16/5.12        ( ( sup_sup_set_rat @ X @ top_top_set_rat )
% 9.16/5.12        = top_top_set_rat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_604_boolean__algebra_Odisj__one__right,axiom,
% 9.16/5.12      ! [X: set_nat] :
% 9.16/5.12        ( ( sup_sup_set_nat @ X @ top_top_set_nat )
% 9.16/5.12        = top_top_set_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_605_boolean__algebra_Odisj__one__right,axiom,
% 9.16/5.12      ! [X: set_int] :
% 9.16/5.12        ( ( sup_sup_set_int @ X @ top_top_set_int )
% 9.16/5.12        = top_top_set_int ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_606_sup__top__left,axiom,
% 9.16/5.12      ! [X: set_Pr8551490117392284871at_nat] :
% 9.16/5.12        ( ( sup_su3035147773818789531at_nat @ top_to8764741339697478167at_nat @ X )
% 9.16/5.12        = top_to8764741339697478167at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_607_sup__top__left,axiom,
% 9.16/5.12      ! [X: set_Pr4329608150637261639at_nat] :
% 9.16/5.12        ( ( sup_su5525570899277871387at_nat @ top_to6833984726390702231at_nat @ X )
% 9.16/5.12        = top_to6833984726390702231at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_608_sup__top__left,axiom,
% 9.16/5.12      ! [X: set_list_nat] :
% 9.16/5.12        ( ( sup_sup_set_list_nat @ top_top_set_list_nat @ X )
% 9.16/5.12        = top_top_set_list_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_609_sup__top__left,axiom,
% 9.16/5.12      ! [X: set_o] :
% 9.16/5.12        ( ( sup_sup_set_o @ top_top_set_o @ X )
% 9.16/5.12        = top_top_set_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_610_sup__top__left,axiom,
% 9.16/5.12      ! [X: set_rat] :
% 9.16/5.12        ( ( sup_sup_set_rat @ top_top_set_rat @ X )
% 9.16/5.12        = top_top_set_rat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_611_sup__top__left,axiom,
% 9.16/5.12      ! [X: set_nat] :
% 9.16/5.12        ( ( sup_sup_set_nat @ top_top_set_nat @ X )
% 9.16/5.12        = top_top_set_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_612_sup__top__left,axiom,
% 9.16/5.12      ! [X: set_int] :
% 9.16/5.12        ( ( sup_sup_set_int @ top_top_set_int @ X )
% 9.16/5.12        = top_top_set_int ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_613_sup__top__right,axiom,
% 9.16/5.12      ! [X: set_Pr8551490117392284871at_nat] :
% 9.16/5.12        ( ( sup_su3035147773818789531at_nat @ X @ top_to8764741339697478167at_nat )
% 9.16/5.12        = top_to8764741339697478167at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_614_sup__top__right,axiom,
% 9.16/5.12      ! [X: set_Pr4329608150637261639at_nat] :
% 9.16/5.12        ( ( sup_su5525570899277871387at_nat @ X @ top_to6833984726390702231at_nat )
% 9.16/5.12        = top_to6833984726390702231at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_615_sup__top__right,axiom,
% 9.16/5.12      ! [X: set_list_nat] :
% 9.16/5.12        ( ( sup_sup_set_list_nat @ X @ top_top_set_list_nat )
% 9.16/5.12        = top_top_set_list_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_616_sup__top__right,axiom,
% 9.16/5.12      ! [X: set_o] :
% 9.16/5.12        ( ( sup_sup_set_o @ X @ top_top_set_o )
% 9.16/5.12        = top_top_set_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_617_sup__top__right,axiom,
% 9.16/5.12      ! [X: set_rat] :
% 9.16/5.12        ( ( sup_sup_set_rat @ X @ top_top_set_rat )
% 9.16/5.12        = top_top_set_rat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_618_sup__top__right,axiom,
% 9.16/5.12      ! [X: set_nat] :
% 9.16/5.12        ( ( sup_sup_set_nat @ X @ top_top_set_nat )
% 9.16/5.12        = top_top_set_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_619_sup__top__right,axiom,
% 9.16/5.12      ! [X: set_int] :
% 9.16/5.12        ( ( sup_sup_set_int @ X @ top_top_set_int )
% 9.16/5.12        = top_top_set_int ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_620_boolean__algebra_Ocompl__one,axiom,
% 9.16/5.12      ( ( uminus6524753893492686040at_nat @ top_to4669805908274784177at_nat )
% 9.16/5.12      = bot_bo2099793752762293965at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_621_boolean__algebra_Ocompl__one,axiom,
% 9.16/5.12      ( ( uminus3195874150345416415st_nat @ top_top_set_list_nat )
% 9.16/5.12      = bot_bot_set_list_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_622_boolean__algebra_Ocompl__one,axiom,
% 9.16/5.12      ( ( uminus_uminus_set_o @ top_top_set_o )
% 9.16/5.12      = bot_bot_set_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_623_boolean__algebra_Ocompl__one,axiom,
% 9.16/5.12      ( ( uminus2201863774496077783et_rat @ top_top_set_rat )
% 9.16/5.12      = bot_bot_set_rat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_624_boolean__algebra_Ocompl__one,axiom,
% 9.16/5.12      ( ( uminus5710092332889474511et_nat @ top_top_set_nat )
% 9.16/5.12      = bot_bot_set_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_625_boolean__algebra_Ocompl__one,axiom,
% 9.16/5.12      ( ( uminus1532241313380277803et_int @ top_top_set_int )
% 9.16/5.12      = bot_bot_set_int ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_626_boolean__algebra_Ocompl__one,axiom,
% 9.16/5.12      ( ( uminus2952777764628376836t_unit @ top_top_Product_unit )
% 9.16/5.12      = bot_bot_Product_unit ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_627_boolean__algebra_Ocompl__zero,axiom,
% 9.16/5.12      ( ( uminus6524753893492686040at_nat @ bot_bo2099793752762293965at_nat )
% 9.16/5.12      = top_to4669805908274784177at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_628_boolean__algebra_Ocompl__zero,axiom,
% 9.16/5.12      ( ( uminus3195874150345416415st_nat @ bot_bot_set_list_nat )
% 9.16/5.12      = top_top_set_list_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_629_boolean__algebra_Ocompl__zero,axiom,
% 9.16/5.12      ( ( uminus_uminus_set_o @ bot_bot_set_o )
% 9.16/5.12      = top_top_set_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_630_boolean__algebra_Ocompl__zero,axiom,
% 9.16/5.12      ( ( uminus2201863774496077783et_rat @ bot_bot_set_rat )
% 9.16/5.12      = top_top_set_rat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_631_boolean__algebra_Ocompl__zero,axiom,
% 9.16/5.12      ( ( uminus5710092332889474511et_nat @ bot_bot_set_nat )
% 9.16/5.12      = top_top_set_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_632_boolean__algebra_Ocompl__zero,axiom,
% 9.16/5.12      ( ( uminus1532241313380277803et_int @ bot_bot_set_int )
% 9.16/5.12      = top_top_set_int ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_633_boolean__algebra_Ocompl__zero,axiom,
% 9.16/5.12      ( ( uminus2952777764628376836t_unit @ bot_bot_Product_unit )
% 9.16/5.12      = top_top_Product_unit ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_634_inf__compl__bot__left1,axiom,
% 9.16/5.12      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 9.16/5.12        ( ( inf_in3604695632404883862_int_o @ ( uminus7117520113953359693_int_o @ X ) @ ( inf_in3604695632404883862_int_o @ X @ Y ) )
% 9.16/5.12        = bot_bo8147686125503663512_int_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_635_inf__compl__bot__left1,axiom,
% 9.16/5.12      ! [X: list_char > $o,Y: list_char > $o] :
% 9.16/5.12        ( ( inf_inf_list_char_o @ ( uminus7154032370948614053char_o @ X ) @ ( inf_inf_list_char_o @ X @ Y ) )
% 9.16/5.12        = bot_bot_list_char_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_636_inf__compl__bot__left1,axiom,
% 9.16/5.12      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 9.16/5.12        = bot_bo2099793752762293965at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_637_inf__compl__bot__left1,axiom,
% 9.16/5.12      ! [X: set_o,Y: set_o] :
% 9.16/5.12        ( ( inf_inf_set_o @ ( uminus_uminus_set_o @ X ) @ ( inf_inf_set_o @ X @ Y ) )
% 9.16/5.12        = bot_bot_set_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_638_inf__compl__bot__left1,axiom,
% 9.16/5.12      ! [X: set_nat,Y: set_nat] :
% 9.16/5.12        ( ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( inf_inf_set_nat @ X @ Y ) )
% 9.16/5.12        = bot_bot_set_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_639_inf__compl__bot__left1,axiom,
% 9.16/5.12      ! [X: set_int,Y: set_int] :
% 9.16/5.12        ( ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ ( inf_inf_set_int @ X @ Y ) )
% 9.16/5.12        = bot_bot_set_int ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_640_inf__compl__bot__left1,axiom,
% 9.16/5.12      ! [X: product_unit,Y: product_unit] :
% 9.16/5.12        ( ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( inf_inf_Product_unit @ X @ Y ) )
% 9.16/5.12        = bot_bot_Product_unit ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_641_inf__compl__bot__left2,axiom,
% 9.16/5.12      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 9.16/5.12        ( ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ ( uminus7117520113953359693_int_o @ X ) @ Y ) )
% 9.16/5.12        = bot_bo8147686125503663512_int_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_642_inf__compl__bot__left2,axiom,
% 9.16/5.12      ! [X: list_char > $o,Y: list_char > $o] :
% 9.16/5.12        ( ( inf_inf_list_char_o @ X @ ( inf_inf_list_char_o @ ( uminus7154032370948614053char_o @ X ) @ Y ) )
% 9.16/5.12        = bot_bot_list_char_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_643_inf__compl__bot__left2,axiom,
% 9.16/5.12      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ Y ) )
% 9.16/5.12        = bot_bo2099793752762293965at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_644_inf__compl__bot__left2,axiom,
% 9.16/5.12      ! [X: set_o,Y: set_o] :
% 9.16/5.12        ( ( inf_inf_set_o @ X @ ( inf_inf_set_o @ ( uminus_uminus_set_o @ X ) @ Y ) )
% 9.16/5.12        = bot_bot_set_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_645_inf__compl__bot__left2,axiom,
% 9.16/5.12      ! [X: set_nat,Y: set_nat] :
% 9.16/5.12        ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ Y ) )
% 9.16/5.12        = bot_bot_set_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_646_inf__compl__bot__left2,axiom,
% 9.16/5.12      ! [X: set_int,Y: set_int] :
% 9.16/5.12        ( ( inf_inf_set_int @ X @ ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ Y ) )
% 9.16/5.12        = bot_bot_set_int ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_647_inf__compl__bot__left2,axiom,
% 9.16/5.12      ! [X: product_unit,Y: product_unit] :
% 9.16/5.12        ( ( inf_inf_Product_unit @ X @ ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ Y ) )
% 9.16/5.12        = bot_bot_Product_unit ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_648_inf__compl__bot__right,axiom,
% 9.16/5.12      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 9.16/5.12        ( ( inf_in3604695632404883862_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ ( uminus7117520113953359693_int_o @ X ) ) )
% 9.16/5.12        = bot_bo8147686125503663512_int_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_649_inf__compl__bot__right,axiom,
% 9.16/5.12      ! [X: list_char > $o,Y: list_char > $o] :
% 9.16/5.12        ( ( inf_inf_list_char_o @ X @ ( inf_inf_list_char_o @ Y @ ( uminus7154032370948614053char_o @ X ) ) )
% 9.16/5.12        = bot_bot_list_char_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_650_inf__compl__bot__right,axiom,
% 9.16/5.12      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ ( uminus6524753893492686040at_nat @ X ) ) )
% 9.16/5.12        = bot_bo2099793752762293965at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_651_inf__compl__bot__right,axiom,
% 9.16/5.12      ! [X: set_o,Y: set_o] :
% 9.16/5.12        ( ( inf_inf_set_o @ X @ ( inf_inf_set_o @ Y @ ( uminus_uminus_set_o @ X ) ) )
% 9.16/5.12        = bot_bot_set_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_652_inf__compl__bot__right,axiom,
% 9.16/5.12      ! [X: set_nat,Y: set_nat] :
% 9.16/5.12        ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ ( uminus5710092332889474511et_nat @ X ) ) )
% 9.16/5.12        = bot_bot_set_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_653_inf__compl__bot__right,axiom,
% 9.16/5.12      ! [X: set_int,Y: set_int] :
% 9.16/5.12        ( ( inf_inf_set_int @ X @ ( inf_inf_set_int @ Y @ ( uminus1532241313380277803et_int @ X ) ) )
% 9.16/5.12        = bot_bot_set_int ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_654_inf__compl__bot__right,axiom,
% 9.16/5.12      ! [X: product_unit,Y: product_unit] :
% 9.16/5.12        ( ( inf_inf_Product_unit @ X @ ( inf_inf_Product_unit @ Y @ ( uminus2952777764628376836t_unit @ X ) ) )
% 9.16/5.12        = bot_bot_Product_unit ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_655_boolean__algebra_Oconj__cancel__left,axiom,
% 9.16/5.12      ! [X: product_prod_int_int > $o] :
% 9.16/5.12        ( ( inf_in3604695632404883862_int_o @ ( uminus7117520113953359693_int_o @ X ) @ X )
% 9.16/5.12        = bot_bo8147686125503663512_int_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_656_boolean__algebra_Oconj__cancel__left,axiom,
% 9.16/5.12      ! [X: list_char > $o] :
% 9.16/5.12        ( ( inf_inf_list_char_o @ ( uminus7154032370948614053char_o @ X ) @ X )
% 9.16/5.12        = bot_bot_list_char_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_657_boolean__algebra_Oconj__cancel__left,axiom,
% 9.16/5.12      ! [X: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ X )
% 9.16/5.12        = bot_bo2099793752762293965at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_658_boolean__algebra_Oconj__cancel__left,axiom,
% 9.16/5.12      ! [X: set_o] :
% 9.16/5.12        ( ( inf_inf_set_o @ ( uminus_uminus_set_o @ X ) @ X )
% 9.16/5.12        = bot_bot_set_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_659_boolean__algebra_Oconj__cancel__left,axiom,
% 9.16/5.12      ! [X: set_nat] :
% 9.16/5.12        ( ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ X )
% 9.16/5.12        = bot_bot_set_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_660_boolean__algebra_Oconj__cancel__left,axiom,
% 9.16/5.12      ! [X: set_int] :
% 9.16/5.12        ( ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ X )
% 9.16/5.12        = bot_bot_set_int ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_661_boolean__algebra_Oconj__cancel__left,axiom,
% 9.16/5.12      ! [X: product_unit] :
% 9.16/5.12        ( ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ X )
% 9.16/5.12        = bot_bot_Product_unit ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_662_boolean__algebra_Oconj__cancel__right,axiom,
% 9.16/5.12      ! [X: product_prod_int_int > $o] :
% 9.16/5.12        ( ( inf_in3604695632404883862_int_o @ X @ ( uminus7117520113953359693_int_o @ X ) )
% 9.16/5.12        = bot_bo8147686125503663512_int_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_663_boolean__algebra_Oconj__cancel__right,axiom,
% 9.16/5.12      ! [X: list_char > $o] :
% 9.16/5.12        ( ( inf_inf_list_char_o @ X @ ( uminus7154032370948614053char_o @ X ) )
% 9.16/5.12        = bot_bot_list_char_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_664_boolean__algebra_Oconj__cancel__right,axiom,
% 9.16/5.12      ! [X: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( inf_in2572325071724192079at_nat @ X @ ( uminus6524753893492686040at_nat @ X ) )
% 9.16/5.12        = bot_bo2099793752762293965at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_665_boolean__algebra_Oconj__cancel__right,axiom,
% 9.16/5.12      ! [X: set_o] :
% 9.16/5.12        ( ( inf_inf_set_o @ X @ ( uminus_uminus_set_o @ X ) )
% 9.16/5.12        = bot_bot_set_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_666_boolean__algebra_Oconj__cancel__right,axiom,
% 9.16/5.12      ! [X: set_nat] :
% 9.16/5.12        ( ( inf_inf_set_nat @ X @ ( uminus5710092332889474511et_nat @ X ) )
% 9.16/5.12        = bot_bot_set_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_667_boolean__algebra_Oconj__cancel__right,axiom,
% 9.16/5.12      ! [X: set_int] :
% 9.16/5.12        ( ( inf_inf_set_int @ X @ ( uminus1532241313380277803et_int @ X ) )
% 9.16/5.12        = bot_bot_set_int ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_668_boolean__algebra_Oconj__cancel__right,axiom,
% 9.16/5.12      ! [X: product_unit] :
% 9.16/5.12        ( ( inf_inf_Product_unit @ X @ ( uminus2952777764628376836t_unit @ X ) )
% 9.16/5.12        = bot_bot_Product_unit ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_669_sup__compl__top__left1,axiom,
% 9.16/5.12      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 9.16/5.12        ( ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ X ) @ ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 9.16/5.12        = top_to8764741339697478167at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_670_sup__compl__top__left1,axiom,
% 9.16/5.12      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 9.16/5.12        ( ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ X ) @ ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 9.16/5.12        = top_to6833984726390702231at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_671_sup__compl__top__left1,axiom,
% 9.16/5.12      ! [X: set_list_nat,Y: set_list_nat] :
% 9.16/5.12        ( ( sup_sup_set_list_nat @ ( uminus3195874150345416415st_nat @ X ) @ ( sup_sup_set_list_nat @ X @ Y ) )
% 9.16/5.12        = top_top_set_list_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_672_sup__compl__top__left1,axiom,
% 9.16/5.12      ! [X: set_o,Y: set_o] :
% 9.16/5.12        ( ( sup_sup_set_o @ ( uminus_uminus_set_o @ X ) @ ( sup_sup_set_o @ X @ Y ) )
% 9.16/5.12        = top_top_set_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_673_sup__compl__top__left1,axiom,
% 9.16/5.12      ! [X: set_rat,Y: set_rat] :
% 9.16/5.12        ( ( sup_sup_set_rat @ ( uminus2201863774496077783et_rat @ X ) @ ( sup_sup_set_rat @ X @ Y ) )
% 9.16/5.12        = top_top_set_rat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_674_sup__compl__top__left1,axiom,
% 9.16/5.12      ! [X: set_nat,Y: set_nat] :
% 9.16/5.12        ( ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( sup_sup_set_nat @ X @ Y ) )
% 9.16/5.12        = top_top_set_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_675_sup__compl__top__left1,axiom,
% 9.16/5.12      ! [X: set_int,Y: set_int] :
% 9.16/5.12        ( ( sup_sup_set_int @ ( uminus1532241313380277803et_int @ X ) @ ( sup_sup_set_int @ X @ Y ) )
% 9.16/5.12        = top_top_set_int ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_676_sup__compl__top__left1,axiom,
% 9.16/5.12      ! [X: product_unit,Y: product_unit] :
% 9.16/5.12        ( ( sup_sup_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( sup_sup_Product_unit @ X @ Y ) )
% 9.16/5.12        = top_top_Product_unit ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_677_sup__compl__top__left2,axiom,
% 9.16/5.12      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 9.16/5.12        ( ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ X ) @ Y ) )
% 9.16/5.12        = top_to8764741339697478167at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_678_sup__compl__top__left2,axiom,
% 9.16/5.12      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 9.16/5.12        ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ X ) @ Y ) )
% 9.16/5.12        = top_to6833984726390702231at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_679_sup__compl__top__left2,axiom,
% 9.16/5.12      ! [X: set_list_nat,Y: set_list_nat] :
% 9.16/5.12        ( ( sup_sup_set_list_nat @ X @ ( sup_sup_set_list_nat @ ( uminus3195874150345416415st_nat @ X ) @ Y ) )
% 9.16/5.12        = top_top_set_list_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_680_sup__compl__top__left2,axiom,
% 9.16/5.12      ! [X: set_o,Y: set_o] :
% 9.16/5.12        ( ( sup_sup_set_o @ X @ ( sup_sup_set_o @ ( uminus_uminus_set_o @ X ) @ Y ) )
% 9.16/5.12        = top_top_set_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_681_sup__compl__top__left2,axiom,
% 9.16/5.12      ! [X: set_rat,Y: set_rat] :
% 9.16/5.12        ( ( sup_sup_set_rat @ X @ ( sup_sup_set_rat @ ( uminus2201863774496077783et_rat @ X ) @ Y ) )
% 9.16/5.12        = top_top_set_rat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_682_sup__compl__top__left2,axiom,
% 9.16/5.12      ! [X: set_nat,Y: set_nat] :
% 9.16/5.12        ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ Y ) )
% 9.16/5.12        = top_top_set_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_683_sup__compl__top__left2,axiom,
% 9.16/5.12      ! [X: set_int,Y: set_int] :
% 9.16/5.12        ( ( sup_sup_set_int @ X @ ( sup_sup_set_int @ ( uminus1532241313380277803et_int @ X ) @ Y ) )
% 9.16/5.12        = top_top_set_int ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_684_sup__compl__top__left2,axiom,
% 9.16/5.12      ! [X: product_unit,Y: product_unit] :
% 9.16/5.12        ( ( sup_sup_Product_unit @ X @ ( sup_sup_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ Y ) )
% 9.16/5.12        = top_top_Product_unit ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_685_boolean__algebra_Odisj__cancel__left,axiom,
% 9.16/5.12      ! [X: set_Pr8551490117392284871at_nat] :
% 9.16/5.12        ( ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ X ) @ X )
% 9.16/5.12        = top_to8764741339697478167at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_686_boolean__algebra_Odisj__cancel__left,axiom,
% 9.16/5.12      ! [X: set_Pr4329608150637261639at_nat] :
% 9.16/5.12        ( ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ X ) @ X )
% 9.16/5.12        = top_to6833984726390702231at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_687_boolean__algebra_Odisj__cancel__left,axiom,
% 9.16/5.12      ! [X: set_list_nat] :
% 9.16/5.12        ( ( sup_sup_set_list_nat @ ( uminus3195874150345416415st_nat @ X ) @ X )
% 9.16/5.12        = top_top_set_list_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_688_boolean__algebra_Odisj__cancel__left,axiom,
% 9.16/5.12      ! [X: set_o] :
% 9.16/5.12        ( ( sup_sup_set_o @ ( uminus_uminus_set_o @ X ) @ X )
% 9.16/5.12        = top_top_set_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_689_boolean__algebra_Odisj__cancel__left,axiom,
% 9.16/5.12      ! [X: set_rat] :
% 9.16/5.12        ( ( sup_sup_set_rat @ ( uminus2201863774496077783et_rat @ X ) @ X )
% 9.16/5.12        = top_top_set_rat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_690_boolean__algebra_Odisj__cancel__left,axiom,
% 9.16/5.12      ! [X: set_nat] :
% 9.16/5.12        ( ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ X )
% 9.16/5.12        = top_top_set_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_691_boolean__algebra_Odisj__cancel__left,axiom,
% 9.16/5.12      ! [X: set_int] :
% 9.16/5.12        ( ( sup_sup_set_int @ ( uminus1532241313380277803et_int @ X ) @ X )
% 9.16/5.12        = top_top_set_int ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_692_boolean__algebra_Odisj__cancel__left,axiom,
% 9.16/5.12      ! [X: product_unit] :
% 9.16/5.12        ( ( sup_sup_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ X )
% 9.16/5.12        = top_top_Product_unit ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_693_boolean__algebra_Odisj__cancel__right,axiom,
% 9.16/5.12      ! [X: set_Pr8551490117392284871at_nat] :
% 9.16/5.12        ( ( sup_su3035147773818789531at_nat @ X @ ( uminus2330091110623919550at_nat @ X ) )
% 9.16/5.12        = top_to8764741339697478167at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_694_boolean__algebra_Odisj__cancel__right,axiom,
% 9.16/5.12      ! [X: set_Pr4329608150637261639at_nat] :
% 9.16/5.12        ( ( sup_su5525570899277871387at_nat @ X @ ( uminus935396558254630718at_nat @ X ) )
% 9.16/5.12        = top_to6833984726390702231at_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_695_boolean__algebra_Odisj__cancel__right,axiom,
% 9.16/5.12      ! [X: set_list_nat] :
% 9.16/5.12        ( ( sup_sup_set_list_nat @ X @ ( uminus3195874150345416415st_nat @ X ) )
% 9.16/5.12        = top_top_set_list_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_696_boolean__algebra_Odisj__cancel__right,axiom,
% 9.16/5.12      ! [X: set_o] :
% 9.16/5.12        ( ( sup_sup_set_o @ X @ ( uminus_uminus_set_o @ X ) )
% 9.16/5.12        = top_top_set_o ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_697_boolean__algebra_Odisj__cancel__right,axiom,
% 9.16/5.12      ! [X: set_rat] :
% 9.16/5.12        ( ( sup_sup_set_rat @ X @ ( uminus2201863774496077783et_rat @ X ) )
% 9.16/5.12        = top_top_set_rat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_698_boolean__algebra_Odisj__cancel__right,axiom,
% 9.16/5.12      ! [X: set_nat] :
% 9.16/5.12        ( ( sup_sup_set_nat @ X @ ( uminus5710092332889474511et_nat @ X ) )
% 9.16/5.12        = top_top_set_nat ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_699_boolean__algebra_Odisj__cancel__right,axiom,
% 9.16/5.12      ! [X: set_int] :
% 9.16/5.12        ( ( sup_sup_set_int @ X @ ( uminus1532241313380277803et_int @ X ) )
% 9.16/5.12        = top_top_set_int ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_700_boolean__algebra_Odisj__cancel__right,axiom,
% 9.16/5.12      ! [X: product_unit] :
% 9.16/5.12        ( ( sup_sup_Product_unit @ X @ ( uminus2952777764628376836t_unit @ X ) )
% 9.16/5.12        = top_top_Product_unit ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_701_boolean__algebra_Ode__Morgan__conj,axiom,
% 9.16/5.12      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.16/5.12        ( ( uminus6524753893492686040at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 9.16/5.12        = ( sup_su6327502436637775413at_nat @ ( uminus6524753893492686040at_nat @ X ) @ ( uminus6524753893492686040at_nat @ Y ) ) ) ).
% 9.16/5.12  
% 9.16/5.12  thf(fact_702_boolean__algebra_Ode__Morgan__conj,axiom,
% 9.16/5.12      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 9.25/5.12        ( ( uminus7117520113953359693_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) )
% 9.25/5.12        = ( sup_su8463660629351352368_int_o @ ( uminus7117520113953359693_int_o @ X ) @ ( uminus7117520113953359693_int_o @ Y ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_703_boolean__algebra_Ode__Morgan__conj,axiom,
% 9.25/5.12      ! [X: list_char > $o,Y: list_char > $o] :
% 9.25/5.12        ( ( uminus7154032370948614053char_o @ ( inf_inf_list_char_o @ X @ Y ) )
% 9.25/5.12        = ( sup_sup_list_char_o @ ( uminus7154032370948614053char_o @ X ) @ ( uminus7154032370948614053char_o @ Y ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_704_boolean__algebra_Ode__Morgan__conj,axiom,
% 9.25/5.12      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 9.25/5.12        ( ( uminus2330091110623919550at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) )
% 9.25/5.12        = ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ X ) @ ( uminus2330091110623919550at_nat @ Y ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_705_boolean__algebra_Ode__Morgan__conj,axiom,
% 9.25/5.12      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 9.25/5.12        ( ( uminus935396558254630718at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) )
% 9.25/5.12        = ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ X ) @ ( uminus935396558254630718at_nat @ Y ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_706_boolean__algebra_Ode__Morgan__conj,axiom,
% 9.25/5.12      ! [X: set_nat,Y: set_nat] :
% 9.25/5.12        ( ( uminus5710092332889474511et_nat @ ( inf_inf_set_nat @ X @ Y ) )
% 9.25/5.12        = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_707_boolean__algebra_Ode__Morgan__conj,axiom,
% 9.25/5.12      ! [X: product_unit,Y: product_unit] :
% 9.25/5.12        ( ( uminus2952777764628376836t_unit @ ( inf_inf_Product_unit @ X @ Y ) )
% 9.25/5.12        = ( sup_sup_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( uminus2952777764628376836t_unit @ Y ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_708_mult_Omonoid__axioms,axiom,
% 9.25/5.12      monoid_Code_integer @ times_3573771949741848930nteger @ one_one_Code_integer ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_709_mult_Omonoid__axioms,axiom,
% 9.25/5.12      monoid_assn @ times_times_assn @ one_one_assn ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_710_mult_Omonoid__axioms,axiom,
% 9.25/5.12      monoid_rat @ times_times_rat @ one_one_rat ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_711_mult_Omonoid__axioms,axiom,
% 9.25/5.12      monoid_nat @ times_times_nat @ one_one_nat ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_712_mult_Omonoid__axioms,axiom,
% 9.25/5.12      monoid_int @ times_times_int @ one_one_int ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_713_mult_Ocomm__monoid__axioms,axiom,
% 9.25/5.12      comm_m1654649897431166824nteger @ times_3573771949741848930nteger @ one_one_Code_integer ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_714_mult_Ocomm__monoid__axioms,axiom,
% 9.25/5.12      comm_monoid_assn @ times_times_assn @ one_one_assn ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_715_mult_Ocomm__monoid__axioms,axiom,
% 9.25/5.12      comm_monoid_rat @ times_times_rat @ one_one_rat ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_716_mult_Ocomm__monoid__axioms,axiom,
% 9.25/5.12      comm_monoid_nat @ times_times_nat @ one_one_nat ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_717_mult_Ocomm__monoid__axioms,axiom,
% 9.25/5.12      comm_monoid_int @ times_times_int @ one_one_int ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_718_semilattice__neutr_Oaxioms_I2_J,axiom,
% 9.25/5.12      ! [F2: nat > nat > nat,Z: nat] :
% 9.25/5.12        ( ( semila9081495762789891438tr_nat @ F2 @ Z )
% 9.25/5.12       => ( comm_monoid_nat @ F2 @ Z ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_719_monoid_Oleft__neutral,axiom,
% 9.25/5.12      ! [F2: nat > nat > nat,Z: nat,A: nat] :
% 9.25/5.12        ( ( monoid_nat @ F2 @ Z )
% 9.25/5.12       => ( ( F2 @ Z @ A )
% 9.25/5.12          = A ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_720_monoid_Oright__neutral,axiom,
% 9.25/5.12      ! [F2: nat > nat > nat,Z: nat,A: nat] :
% 9.25/5.12        ( ( monoid_nat @ F2 @ Z )
% 9.25/5.12       => ( ( F2 @ A @ Z )
% 9.25/5.12          = A ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_721_one__assn__raw_Ocases,axiom,
% 9.25/5.12      ! [X: produc3658429121746597890et_nat] :
% 9.25/5.12        ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 9.25/5.12            ( X
% 9.25/5.12           != ( produc7507926704131184380et_nat @ H @ As4 ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_722_comm__monoid_Ocomm__neutral,axiom,
% 9.25/5.12      ! [F2: nat > nat > nat,Z: nat,A: nat] :
% 9.25/5.12        ( ( comm_monoid_nat @ F2 @ Z )
% 9.25/5.12       => ( ( F2 @ A @ Z )
% 9.25/5.12          = A ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_723_equation__minus__iff,axiom,
% 9.25/5.12      ! [A: int,B: int] :
% 9.25/5.12        ( ( A
% 9.25/5.12          = ( uminus_uminus_int @ B ) )
% 9.25/5.12        = ( B
% 9.25/5.12          = ( uminus_uminus_int @ A ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_724_equation__minus__iff,axiom,
% 9.25/5.12      ! [A: code_integer,B: code_integer] :
% 9.25/5.12        ( ( A
% 9.25/5.12          = ( uminus1351360451143612070nteger @ B ) )
% 9.25/5.12        = ( B
% 9.25/5.12          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_725_equation__minus__iff,axiom,
% 9.25/5.12      ! [A: rat,B: rat] :
% 9.25/5.12        ( ( A
% 9.25/5.12          = ( uminus_uminus_rat @ B ) )
% 9.25/5.12        = ( B
% 9.25/5.12          = ( uminus_uminus_rat @ A ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_726_minus__equation__iff,axiom,
% 9.25/5.12      ! [A: int,B: int] :
% 9.25/5.12        ( ( ( uminus_uminus_int @ A )
% 9.25/5.12          = B )
% 9.25/5.12        = ( ( uminus_uminus_int @ B )
% 9.25/5.12          = A ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_727_minus__equation__iff,axiom,
% 9.25/5.12      ! [A: code_integer,B: code_integer] :
% 9.25/5.12        ( ( ( uminus1351360451143612070nteger @ A )
% 9.25/5.12          = B )
% 9.25/5.12        = ( ( uminus1351360451143612070nteger @ B )
% 9.25/5.12          = A ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_728_minus__equation__iff,axiom,
% 9.25/5.12      ! [A: rat,B: rat] :
% 9.25/5.12        ( ( ( uminus_uminus_rat @ A )
% 9.25/5.12          = B )
% 9.25/5.12        = ( ( uminus_uminus_rat @ B )
% 9.25/5.12          = A ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_729_one__reorient,axiom,
% 9.25/5.12      ! [X: code_integer] :
% 9.25/5.12        ( ( one_one_Code_integer = X )
% 9.25/5.12        = ( X = one_one_Code_integer ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_730_one__reorient,axiom,
% 9.25/5.12      ! [X: assn] :
% 9.25/5.12        ( ( one_one_assn = X )
% 9.25/5.12        = ( X = one_one_assn ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_731_one__reorient,axiom,
% 9.25/5.12      ! [X: rat] :
% 9.25/5.12        ( ( one_one_rat = X )
% 9.25/5.12        = ( X = one_one_rat ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_732_one__reorient,axiom,
% 9.25/5.12      ! [X: nat] :
% 9.25/5.12        ( ( one_one_nat = X )
% 9.25/5.12        = ( X = one_one_nat ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_733_one__reorient,axiom,
% 9.25/5.12      ! [X: int] :
% 9.25/5.12        ( ( one_one_int = X )
% 9.25/5.12        = ( X = one_one_int ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_734_sup__cancel__left1,axiom,
% 9.25/5.12      ! [X: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 9.25/5.12        ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ X @ A ) @ ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ X ) @ B ) )
% 9.25/5.12        = top_to8764741339697478167at_nat ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_735_sup__cancel__left1,axiom,
% 9.25/5.12      ! [X: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 9.25/5.12        ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ X @ A ) @ ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ X ) @ B ) )
% 9.25/5.12        = top_to6833984726390702231at_nat ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_736_sup__cancel__left1,axiom,
% 9.25/5.12      ! [X: set_list_nat,A: set_list_nat,B: set_list_nat] :
% 9.25/5.12        ( ( sup_sup_set_list_nat @ ( sup_sup_set_list_nat @ X @ A ) @ ( sup_sup_set_list_nat @ ( uminus3195874150345416415st_nat @ X ) @ B ) )
% 9.25/5.12        = top_top_set_list_nat ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_737_sup__cancel__left1,axiom,
% 9.25/5.12      ! [X: set_o,A: set_o,B: set_o] :
% 9.25/5.12        ( ( sup_sup_set_o @ ( sup_sup_set_o @ X @ A ) @ ( sup_sup_set_o @ ( uminus_uminus_set_o @ X ) @ B ) )
% 9.25/5.12        = top_top_set_o ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_738_sup__cancel__left1,axiom,
% 9.25/5.12      ! [X: set_rat,A: set_rat,B: set_rat] :
% 9.25/5.12        ( ( sup_sup_set_rat @ ( sup_sup_set_rat @ X @ A ) @ ( sup_sup_set_rat @ ( uminus2201863774496077783et_rat @ X ) @ B ) )
% 9.25/5.12        = top_top_set_rat ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_739_sup__cancel__left1,axiom,
% 9.25/5.12      ! [X: set_nat,A: set_nat,B: set_nat] :
% 9.25/5.12        ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ X @ A ) @ ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ B ) )
% 9.25/5.12        = top_top_set_nat ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_740_sup__cancel__left1,axiom,
% 9.25/5.12      ! [X: set_int,A: set_int,B: set_int] :
% 9.25/5.12        ( ( sup_sup_set_int @ ( sup_sup_set_int @ X @ A ) @ ( sup_sup_set_int @ ( uminus1532241313380277803et_int @ X ) @ B ) )
% 9.25/5.12        = top_top_set_int ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_741_sup__cancel__left1,axiom,
% 9.25/5.12      ! [X: product_unit,A: product_unit,B: product_unit] :
% 9.25/5.12        ( ( sup_sup_Product_unit @ ( sup_sup_Product_unit @ X @ A ) @ ( sup_sup_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ B ) )
% 9.25/5.12        = top_top_Product_unit ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_742_sup__cancel__left2,axiom,
% 9.25/5.12      ! [X: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 9.25/5.12        ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ X ) @ A ) @ ( sup_su3035147773818789531at_nat @ X @ B ) )
% 9.25/5.12        = top_to8764741339697478167at_nat ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_743_sup__cancel__left2,axiom,
% 9.25/5.12      ! [X: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 9.25/5.12        ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ X ) @ A ) @ ( sup_su5525570899277871387at_nat @ X @ B ) )
% 9.25/5.12        = top_to6833984726390702231at_nat ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_744_sup__cancel__left2,axiom,
% 9.25/5.12      ! [X: set_list_nat,A: set_list_nat,B: set_list_nat] :
% 9.25/5.12        ( ( sup_sup_set_list_nat @ ( sup_sup_set_list_nat @ ( uminus3195874150345416415st_nat @ X ) @ A ) @ ( sup_sup_set_list_nat @ X @ B ) )
% 9.25/5.12        = top_top_set_list_nat ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_745_sup__cancel__left2,axiom,
% 9.25/5.12      ! [X: set_o,A: set_o,B: set_o] :
% 9.25/5.12        ( ( sup_sup_set_o @ ( sup_sup_set_o @ ( uminus_uminus_set_o @ X ) @ A ) @ ( sup_sup_set_o @ X @ B ) )
% 9.25/5.12        = top_top_set_o ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_746_sup__cancel__left2,axiom,
% 9.25/5.12      ! [X: set_rat,A: set_rat,B: set_rat] :
% 9.25/5.12        ( ( sup_sup_set_rat @ ( sup_sup_set_rat @ ( uminus2201863774496077783et_rat @ X ) @ A ) @ ( sup_sup_set_rat @ X @ B ) )
% 9.25/5.12        = top_top_set_rat ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_747_sup__cancel__left2,axiom,
% 9.25/5.12      ! [X: set_nat,A: set_nat,B: set_nat] :
% 9.25/5.12        ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ A ) @ ( sup_sup_set_nat @ X @ B ) )
% 9.25/5.12        = top_top_set_nat ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_748_sup__cancel__left2,axiom,
% 9.25/5.12      ! [X: set_int,A: set_int,B: set_int] :
% 9.25/5.12        ( ( sup_sup_set_int @ ( sup_sup_set_int @ ( uminus1532241313380277803et_int @ X ) @ A ) @ ( sup_sup_set_int @ X @ B ) )
% 9.25/5.12        = top_top_set_int ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_749_sup__cancel__left2,axiom,
% 9.25/5.12      ! [X: product_unit,A: product_unit,B: product_unit] :
% 9.25/5.12        ( ( sup_sup_Product_unit @ ( sup_sup_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ A ) @ ( sup_sup_Product_unit @ X @ B ) )
% 9.25/5.12        = top_top_Product_unit ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_750_inf__top_Ocomm__monoid__axioms,axiom,
% 9.25/5.12      comm_m5709050211238513046at_nat @ inf_in2572325071724192079at_nat @ top_to4669805908274784177at_nat ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_751_inf__top_Ocomm__monoid__axioms,axiom,
% 9.25/5.12      comm_m5839176995973721103_int_o @ inf_in3604695632404883862_int_o @ top_to1578927101902068148_int_o ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_752_inf__top_Ocomm__monoid__axioms,axiom,
% 9.25/5.12      comm_m8764728085499324515char_o @ inf_inf_list_char_o @ top_top_list_char_o ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_753_inf__top_Ocomm__monoid__axioms,axiom,
% 9.25/5.12      comm_m4511514676032769697st_nat @ inf_inf_set_list_nat @ top_top_set_list_nat ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_754_inf__top_Ocomm__monoid__axioms,axiom,
% 9.25/5.12      comm_monoid_set_o @ inf_inf_set_o @ top_top_set_o ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_755_inf__top_Ocomm__monoid__axioms,axiom,
% 9.25/5.12      comm_monoid_set_rat @ inf_inf_set_rat @ top_top_set_rat ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_756_inf__top_Ocomm__monoid__axioms,axiom,
% 9.25/5.12      comm_monoid_set_nat @ inf_inf_set_nat @ top_top_set_nat ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_757_inf__top_Ocomm__monoid__axioms,axiom,
% 9.25/5.12      comm_monoid_set_int @ inf_inf_set_int @ top_top_set_int ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_758_inf__top_Omonoid__axioms,axiom,
% 9.25/5.12      monoid1519094961268053602at_nat @ inf_in2572325071724192079at_nat @ top_to4669805908274784177at_nat ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_759_inf__top_Omonoid__axioms,axiom,
% 9.25/5.12      monoid6910981727789844035_int_o @ inf_in3604695632404883862_int_o @ top_to1578927101902068148_int_o ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_760_inf__top_Omonoid__axioms,axiom,
% 9.25/5.12      monoid_list_char_o @ inf_inf_list_char_o @ top_top_list_char_o ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_761_inf__top_Omonoid__axioms,axiom,
% 9.25/5.12      monoid_set_list_nat @ inf_inf_set_list_nat @ top_top_set_list_nat ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_762_inf__top_Omonoid__axioms,axiom,
% 9.25/5.12      monoid_set_o @ inf_inf_set_o @ top_top_set_o ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_763_inf__top_Omonoid__axioms,axiom,
% 9.25/5.12      monoid_set_rat @ inf_inf_set_rat @ top_top_set_rat ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_764_inf__top_Omonoid__axioms,axiom,
% 9.25/5.12      monoid_set_nat @ inf_inf_set_nat @ top_top_set_nat ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_765_inf__top_Omonoid__axioms,axiom,
% 9.25/5.12      monoid_set_int @ inf_inf_set_int @ top_top_set_int ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_766_comm__monoid__mult__class_Omult__1,axiom,
% 9.25/5.12      ! [A: code_integer] :
% 9.25/5.12        ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 9.25/5.12        = A ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_767_comm__monoid__mult__class_Omult__1,axiom,
% 9.25/5.12      ! [A: assn] :
% 9.25/5.12        ( ( times_times_assn @ one_one_assn @ A )
% 9.25/5.12        = A ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_768_comm__monoid__mult__class_Omult__1,axiom,
% 9.25/5.12      ! [A: rat] :
% 9.25/5.12        ( ( times_times_rat @ one_one_rat @ A )
% 9.25/5.12        = A ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_769_comm__monoid__mult__class_Omult__1,axiom,
% 9.25/5.12      ! [A: nat] :
% 9.25/5.12        ( ( times_times_nat @ one_one_nat @ A )
% 9.25/5.12        = A ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_770_comm__monoid__mult__class_Omult__1,axiom,
% 9.25/5.12      ! [A: int] :
% 9.25/5.12        ( ( times_times_int @ one_one_int @ A )
% 9.25/5.12        = A ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_771_mult_Ocomm__neutral,axiom,
% 9.25/5.12      ! [A: code_integer] :
% 9.25/5.12        ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 9.25/5.12        = A ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_772_mult_Ocomm__neutral,axiom,
% 9.25/5.12      ! [A: assn] :
% 9.25/5.12        ( ( times_times_assn @ A @ one_one_assn )
% 9.25/5.12        = A ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_773_mult_Ocomm__neutral,axiom,
% 9.25/5.12      ! [A: rat] :
% 9.25/5.12        ( ( times_times_rat @ A @ one_one_rat )
% 9.25/5.12        = A ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_774_mult_Ocomm__neutral,axiom,
% 9.25/5.12      ! [A: nat] :
% 9.25/5.12        ( ( times_times_nat @ A @ one_one_nat )
% 9.25/5.12        = A ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_775_mult_Ocomm__neutral,axiom,
% 9.25/5.12      ! [A: int] :
% 9.25/5.12        ( ( times_times_int @ A @ one_one_int )
% 9.25/5.12        = A ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_776_inf__top_Osemilattice__neutr__axioms,axiom,
% 9.25/5.12      semila858173770281612099at_nat @ inf_in2572325071724192079at_nat @ top_to4669805908274784177at_nat ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_777_inf__top_Osemilattice__neutr__axioms,axiom,
% 9.25/5.12      semila6538661356715008162_int_o @ inf_in3604695632404883862_int_o @ top_to1578927101902068148_int_o ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_778_inf__top_Osemilattice__neutr__axioms,axiom,
% 9.25/5.12      semila3963277552210239504char_o @ inf_inf_list_char_o @ top_top_list_char_o ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_779_inf__top_Osemilattice__neutr__axioms,axiom,
% 9.25/5.12      semila7136768128396663732st_nat @ inf_inf_set_list_nat @ top_top_set_list_nat ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_780_inf__top_Osemilattice__neutr__axioms,axiom,
% 9.25/5.12      semila1065760912024005978_set_o @ inf_inf_set_o @ top_top_set_o ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_781_inf__top_Osemilattice__neutr__axioms,axiom,
% 9.25/5.12      semila6956917442496717612et_rat @ inf_inf_set_rat @ top_top_set_rat ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_782_inf__top_Osemilattice__neutr__axioms,axiom,
% 9.25/5.12      semila1241773964035338532et_nat @ inf_inf_set_nat @ top_top_set_nat ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_783_inf__top_Osemilattice__neutr__axioms,axiom,
% 9.25/5.12      semila6287294981380917632et_int @ inf_inf_set_int @ top_top_set_int ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_784_boolean__algebra_Oconj__one__right,axiom,
% 9.25/5.12      ! [X: set_Pr1261947904930325089at_nat] :
% 9.25/5.12        ( ( inf_in2572325071724192079at_nat @ X @ top_to4669805908274784177at_nat )
% 9.25/5.12        = X ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_785_boolean__algebra_Oconj__one__right,axiom,
% 9.25/5.12      ! [X: product_prod_int_int > $o] :
% 9.25/5.12        ( ( inf_in3604695632404883862_int_o @ X @ top_to1578927101902068148_int_o )
% 9.25/5.12        = X ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_786_boolean__algebra_Oconj__one__right,axiom,
% 9.25/5.12      ! [X: list_char > $o] :
% 9.25/5.12        ( ( inf_inf_list_char_o @ X @ top_top_list_char_o )
% 9.25/5.12        = X ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_787_boolean__algebra_Oconj__one__right,axiom,
% 9.25/5.12      ! [X: set_list_nat] :
% 9.25/5.12        ( ( inf_inf_set_list_nat @ X @ top_top_set_list_nat )
% 9.25/5.12        = X ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_788_boolean__algebra_Oconj__one__right,axiom,
% 9.25/5.12      ! [X: set_o] :
% 9.25/5.12        ( ( inf_inf_set_o @ X @ top_top_set_o )
% 9.25/5.12        = X ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_789_boolean__algebra_Oconj__one__right,axiom,
% 9.25/5.12      ! [X: set_rat] :
% 9.25/5.12        ( ( inf_inf_set_rat @ X @ top_top_set_rat )
% 9.25/5.12        = X ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_790_boolean__algebra_Oconj__one__right,axiom,
% 9.25/5.12      ! [X: set_nat] :
% 9.25/5.12        ( ( inf_inf_set_nat @ X @ top_top_set_nat )
% 9.25/5.12        = X ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_791_boolean__algebra_Oconj__one__right,axiom,
% 9.25/5.12      ! [X: set_int] :
% 9.25/5.12        ( ( inf_inf_set_int @ X @ top_top_set_int )
% 9.25/5.12        = X ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_792_mod__h__bot__indep,axiom,
% 9.25/5.12      ! [P: assn,H3: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 9.25/5.12        ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) )
% 9.25/5.12        = ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H4 @ bot_bot_set_nat ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_793_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 9.25/5.12      ! [X: product_unit,Y: product_unit] :
% 9.25/5.12        ( ( ( inf_inf_Product_unit @ X @ Y )
% 9.25/5.12          = bot_bot_Product_unit )
% 9.25/5.12       => ( ( ( sup_sup_Product_unit @ X @ Y )
% 9.25/5.12            = top_top_Product_unit )
% 9.25/5.12         => ( ( uminus2952777764628376836t_unit @ X )
% 9.25/5.12            = Y ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_794_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 9.25/5.12      ! [X: set_o,Y: set_o] :
% 9.25/5.12        ( ( ( inf_inf_set_o @ X @ Y )
% 9.25/5.12          = bot_bot_set_o )
% 9.25/5.12       => ( ( ( sup_sup_set_o @ X @ Y )
% 9.25/5.12            = top_top_set_o )
% 9.25/5.12         => ( ( uminus_uminus_set_o @ X )
% 9.25/5.12            = Y ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_795_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 9.25/5.12      ! [X: set_rat,Y: set_rat] :
% 9.25/5.12        ( ( ( inf_inf_set_rat @ X @ Y )
% 9.25/5.12          = bot_bot_set_rat )
% 9.25/5.12       => ( ( ( sup_sup_set_rat @ X @ Y )
% 9.25/5.12            = top_top_set_rat )
% 9.25/5.12         => ( ( uminus2201863774496077783et_rat @ X )
% 9.25/5.12            = Y ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_796_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 9.25/5.12      ! [X: set_nat,Y: set_nat] :
% 9.25/5.12        ( ( ( inf_inf_set_nat @ X @ Y )
% 9.25/5.12          = bot_bot_set_nat )
% 9.25/5.12       => ( ( ( sup_sup_set_nat @ X @ Y )
% 9.25/5.12            = top_top_set_nat )
% 9.25/5.12         => ( ( uminus5710092332889474511et_nat @ X )
% 9.25/5.12            = Y ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_797_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 9.25/5.12      ! [X: set_int,Y: set_int] :
% 9.25/5.12        ( ( ( inf_inf_set_int @ X @ Y )
% 9.25/5.12          = bot_bot_set_int )
% 9.25/5.12       => ( ( ( sup_sup_set_int @ X @ Y )
% 9.25/5.12            = top_top_set_int )
% 9.25/5.12         => ( ( uminus1532241313380277803et_int @ X )
% 9.25/5.12            = Y ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_798_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 9.25/5.12      ! [X: set_list_nat,Y: set_list_nat] :
% 9.25/5.12        ( ( ( inf_inf_set_list_nat @ X @ Y )
% 9.25/5.12          = bot_bot_set_list_nat )
% 9.25/5.12       => ( ( ( sup_sup_set_list_nat @ X @ Y )
% 9.25/5.12            = top_top_set_list_nat )
% 9.25/5.12         => ( ( uminus3195874150345416415st_nat @ X )
% 9.25/5.12            = Y ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_799_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 9.25/5.12      ! [X: list_char > $o,Y: list_char > $o] :
% 9.25/5.12        ( ( ( inf_inf_list_char_o @ X @ Y )
% 9.25/5.12          = bot_bot_list_char_o )
% 9.25/5.12       => ( ( ( sup_sup_list_char_o @ X @ Y )
% 9.25/5.12            = top_top_list_char_o )
% 9.25/5.12         => ( ( uminus7154032370948614053char_o @ X )
% 9.25/5.12            = Y ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_800_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 9.25/5.12      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.25/5.12        ( ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 9.25/5.12          = bot_bo2099793752762293965at_nat )
% 9.25/5.12       => ( ( ( sup_su6327502436637775413at_nat @ X @ Y )
% 9.25/5.12            = top_to4669805908274784177at_nat )
% 9.25/5.12         => ( ( uminus6524753893492686040at_nat @ X )
% 9.25/5.12            = Y ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_801_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 9.25/5.12      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 9.25/5.12        ( ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 9.25/5.12          = bot_bo8147686125503663512_int_o )
% 9.25/5.12       => ( ( ( sup_su8463660629351352368_int_o @ X @ Y )
% 9.25/5.12            = top_to1578927101902068148_int_o )
% 9.25/5.12         => ( ( uminus7117520113953359693_int_o @ X )
% 9.25/5.12            = Y ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_802_boolean__algebra__class_Oboolean__algebra_Ocompl__unique,axiom,
% 9.25/5.12      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 9.25/5.12        ( ( ( inf_in1697001100524423349at_nat @ X @ Y )
% 9.25/5.12          = bot_bo8422036546324065075at_nat )
% 9.25/5.12       => ( ( ( sup_su3035147773818789531at_nat @ X @ Y )
% 9.25/5.12            = top_to8764741339697478167at_nat )
% 9.25/5.12         => ( ( uminus2330091110623919550at_nat @ X )
% 9.25/5.12            = Y ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_803_one__assn__raw_Oelims_I3_J,axiom,
% 9.25/5.12      ! [X: produc3658429121746597890et_nat] :
% 9.25/5.12        ( ~ ( one_assn_raw @ X )
% 9.25/5.12       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 9.25/5.12              ( ( X
% 9.25/5.12                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.12             => ( As4 = bot_bot_set_nat ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_804_one__assn__raw_Oelims_I2_J,axiom,
% 9.25/5.12      ! [X: produc3658429121746597890et_nat] :
% 9.25/5.12        ( ( one_assn_raw @ X )
% 9.25/5.12       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 9.25/5.12              ( ( X
% 9.25/5.12                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.12             => ( As4 != bot_bot_set_nat ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_805_one__assn__raw_Oelims_I1_J,axiom,
% 9.25/5.12      ! [X: produc3658429121746597890et_nat,Y: $o] :
% 9.25/5.12        ( ( ( one_assn_raw @ X )
% 9.25/5.12          = Y )
% 9.25/5.12       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 9.25/5.12              ( ( X
% 9.25/5.12                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.12             => ( Y
% 9.25/5.12                = ( As4 != bot_bot_set_nat ) ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_806_one__assn__raw_Osimps,axiom,
% 9.25/5.12      ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.25/5.12        ( ( one_assn_raw @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 9.25/5.12        = ( As = bot_bot_set_nat ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_807_times__assn__raw_Osimps,axiom,
% 9.25/5.12      ! [P: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o,H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.25/5.12        ( ( times_assn_raw @ P @ Q2 @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 9.25/5.12        = ( ? [As1: set_nat,As2: set_nat] :
% 9.25/5.12              ( ( As
% 9.25/5.12                = ( sup_sup_set_nat @ As1 @ As2 ) )
% 9.25/5.12              & ( ( inf_inf_set_nat @ As1 @ As2 )
% 9.25/5.12                = bot_bot_set_nat )
% 9.25/5.12              & ( P @ ( produc7507926704131184380et_nat @ H3 @ As1 ) )
% 9.25/5.12              & ( Q2 @ ( produc7507926704131184380et_nat @ H3 @ As2 ) ) ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_808_times__assn__raw_Oelims_I1_J,axiom,
% 9.25/5.12      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 9.25/5.12        ( ( ( times_assn_raw @ X @ Xa @ Xb )
% 9.25/5.12          = Y )
% 9.25/5.12       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 9.25/5.12              ( ( Xb
% 9.25/5.12                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.12             => ( Y
% 9.25/5.12                = ( ~ ? [As1: set_nat,As2: set_nat] :
% 9.25/5.12                        ( ( As4
% 9.25/5.12                          = ( sup_sup_set_nat @ As1 @ As2 ) )
% 9.25/5.12                        & ( ( inf_inf_set_nat @ As1 @ As2 )
% 9.25/5.12                          = bot_bot_set_nat )
% 9.25/5.12                        & ( X @ ( produc7507926704131184380et_nat @ H @ As1 ) )
% 9.25/5.12                        & ( Xa @ ( produc7507926704131184380et_nat @ H @ As2 ) ) ) ) ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_809_times__assn__raw_Oelims_I2_J,axiom,
% 9.25/5.12      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 9.25/5.12        ( ( times_assn_raw @ X @ Xa @ Xb )
% 9.25/5.12       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 9.25/5.12              ( ( Xb
% 9.25/5.12                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.12             => ~ ? [As12: set_nat,As22: set_nat] :
% 9.25/5.12                    ( ( As4
% 9.25/5.12                      = ( sup_sup_set_nat @ As12 @ As22 ) )
% 9.25/5.12                    & ( ( inf_inf_set_nat @ As12 @ As22 )
% 9.25/5.12                      = bot_bot_set_nat )
% 9.25/5.12                    & ( X @ ( produc7507926704131184380et_nat @ H @ As12 ) )
% 9.25/5.12                    & ( Xa @ ( produc7507926704131184380et_nat @ H @ As22 ) ) ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_810_times__assn__raw_Oelims_I3_J,axiom,
% 9.25/5.12      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 9.25/5.12        ( ~ ( times_assn_raw @ X @ Xa @ Xb )
% 9.25/5.12       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 9.25/5.12              ( ( Xb
% 9.25/5.12                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.12             => ? [As13: set_nat,As23: set_nat] :
% 9.25/5.12                  ( ( As4
% 9.25/5.12                    = ( sup_sup_set_nat @ As13 @ As23 ) )
% 9.25/5.12                  & ( ( inf_inf_set_nat @ As13 @ As23 )
% 9.25/5.12                    = bot_bot_set_nat )
% 9.25/5.12                  & ( X @ ( produc7507926704131184380et_nat @ H @ As13 ) )
% 9.25/5.12                  & ( Xa @ ( produc7507926704131184380et_nat @ H @ As23 ) ) ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_811_assn__one__left,axiom,
% 9.25/5.12      ! [P: assn] :
% 9.25/5.12        ( ( times_times_assn @ one_one_assn @ P )
% 9.25/5.12        = P ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_812_inf__cancel__left1,axiom,
% 9.25/5.12      ! [X: product_prod_int_int > $o,A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 9.25/5.12        ( ( inf_in3604695632404883862_int_o @ ( inf_in3604695632404883862_int_o @ X @ A ) @ ( inf_in3604695632404883862_int_o @ ( uminus7117520113953359693_int_o @ X ) @ B ) )
% 9.25/5.12        = bot_bo8147686125503663512_int_o ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_813_inf__cancel__left1,axiom,
% 9.25/5.12      ! [X: list_char > $o,A: list_char > $o,B: list_char > $o] :
% 9.25/5.12        ( ( inf_inf_list_char_o @ ( inf_inf_list_char_o @ X @ A ) @ ( inf_inf_list_char_o @ ( uminus7154032370948614053char_o @ X ) @ B ) )
% 9.25/5.12        = bot_bot_list_char_o ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_814_inf__cancel__left1,axiom,
% 9.25/5.12      ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 9.25/5.12        ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ X @ A ) @ ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ B ) )
% 9.25/5.12        = bot_bo2099793752762293965at_nat ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_815_inf__cancel__left1,axiom,
% 9.25/5.12      ! [X: set_o,A: set_o,B: set_o] :
% 9.25/5.12        ( ( inf_inf_set_o @ ( inf_inf_set_o @ X @ A ) @ ( inf_inf_set_o @ ( uminus_uminus_set_o @ X ) @ B ) )
% 9.25/5.12        = bot_bot_set_o ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_816_inf__cancel__left1,axiom,
% 9.25/5.12      ! [X: set_nat,A: set_nat,B: set_nat] :
% 9.25/5.12        ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ A ) @ ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ B ) )
% 9.25/5.12        = bot_bot_set_nat ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_817_inf__cancel__left1,axiom,
% 9.25/5.12      ! [X: set_int,A: set_int,B: set_int] :
% 9.25/5.12        ( ( inf_inf_set_int @ ( inf_inf_set_int @ X @ A ) @ ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ B ) )
% 9.25/5.12        = bot_bot_set_int ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_818_inf__cancel__left1,axiom,
% 9.25/5.12      ! [X: product_unit,A: product_unit,B: product_unit] :
% 9.25/5.12        ( ( inf_inf_Product_unit @ ( inf_inf_Product_unit @ X @ A ) @ ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ B ) )
% 9.25/5.12        = bot_bot_Product_unit ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_819_inf__cancel__left2,axiom,
% 9.25/5.12      ! [X: product_prod_int_int > $o,A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 9.25/5.12        ( ( inf_in3604695632404883862_int_o @ ( inf_in3604695632404883862_int_o @ ( uminus7117520113953359693_int_o @ X ) @ A ) @ ( inf_in3604695632404883862_int_o @ X @ B ) )
% 9.25/5.12        = bot_bo8147686125503663512_int_o ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_820_inf__cancel__left2,axiom,
% 9.25/5.12      ! [X: list_char > $o,A: list_char > $o,B: list_char > $o] :
% 9.25/5.12        ( ( inf_inf_list_char_o @ ( inf_inf_list_char_o @ ( uminus7154032370948614053char_o @ X ) @ A ) @ ( inf_inf_list_char_o @ X @ B ) )
% 9.25/5.12        = bot_bot_list_char_o ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_821_inf__cancel__left2,axiom,
% 9.25/5.12      ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 9.25/5.12        ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ A ) @ ( inf_in2572325071724192079at_nat @ X @ B ) )
% 9.25/5.12        = bot_bo2099793752762293965at_nat ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_822_inf__cancel__left2,axiom,
% 9.25/5.12      ! [X: set_o,A: set_o,B: set_o] :
% 9.25/5.12        ( ( inf_inf_set_o @ ( inf_inf_set_o @ ( uminus_uminus_set_o @ X ) @ A ) @ ( inf_inf_set_o @ X @ B ) )
% 9.25/5.12        = bot_bot_set_o ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_823_inf__cancel__left2,axiom,
% 9.25/5.12      ! [X: set_nat,A: set_nat,B: set_nat] :
% 9.25/5.12        ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ A ) @ ( inf_inf_set_nat @ X @ B ) )
% 9.25/5.12        = bot_bot_set_nat ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_824_inf__cancel__left2,axiom,
% 9.25/5.12      ! [X: set_int,A: set_int,B: set_int] :
% 9.25/5.12        ( ( inf_inf_set_int @ ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ A ) @ ( inf_inf_set_int @ X @ B ) )
% 9.25/5.12        = bot_bot_set_int ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_825_inf__cancel__left2,axiom,
% 9.25/5.12      ! [X: product_unit,A: product_unit,B: product_unit] :
% 9.25/5.12        ( ( inf_inf_Product_unit @ ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ A ) @ ( inf_inf_Product_unit @ X @ B ) )
% 9.25/5.12        = bot_bot_Product_unit ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_826_mult__minus1,axiom,
% 9.25/5.12      ! [Z: int] :
% 9.25/5.12        ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 9.25/5.12        = ( uminus_uminus_int @ Z ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_827_mult__minus1,axiom,
% 9.25/5.12      ! [Z: code_integer] :
% 9.25/5.12        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 9.25/5.12        = ( uminus1351360451143612070nteger @ Z ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_828_mult__minus1,axiom,
% 9.25/5.12      ! [Z: rat] :
% 9.25/5.12        ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 9.25/5.12        = ( uminus_uminus_rat @ Z ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_829_mult__minus1__right,axiom,
% 9.25/5.12      ! [Z: int] :
% 9.25/5.12        ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.12        = ( uminus_uminus_int @ Z ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_830_mult__minus1__right,axiom,
% 9.25/5.12      ! [Z: code_integer] :
% 9.25/5.12        ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.12        = ( uminus1351360451143612070nteger @ Z ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_831_mult__minus1__right,axiom,
% 9.25/5.12      ! [Z: rat] :
% 9.25/5.12        ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.25/5.12        = ( uminus_uminus_rat @ Z ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_832_Un__Int__eq_I1_J,axiom,
% 9.25/5.12      ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 9.25/5.12        ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ S @ T ) @ S )
% 9.25/5.12        = S ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_833_Un__Int__eq_I1_J,axiom,
% 9.25/5.12      ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 9.25/5.12        ( ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ S @ T ) @ S )
% 9.25/5.12        = S ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_834_Un__Int__eq_I1_J,axiom,
% 9.25/5.12      ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 9.25/5.12        ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ S @ T ) @ S )
% 9.25/5.12        = S ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_835_Un__Int__eq_I1_J,axiom,
% 9.25/5.12      ! [S: set_nat,T: set_nat] :
% 9.25/5.12        ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ S @ T ) @ S )
% 9.25/5.12        = S ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_836_Un__Int__eq_I2_J,axiom,
% 9.25/5.12      ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 9.25/5.12        ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ S @ T ) @ T )
% 9.25/5.12        = T ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_837_Un__Int__eq_I2_J,axiom,
% 9.25/5.12      ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 9.25/5.12        ( ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ S @ T ) @ T )
% 9.25/5.12        = T ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_838_Un__Int__eq_I2_J,axiom,
% 9.25/5.12      ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 9.25/5.12        ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ S @ T ) @ T )
% 9.25/5.12        = T ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_839_Un__Int__eq_I2_J,axiom,
% 9.25/5.12      ! [S: set_nat,T: set_nat] :
% 9.25/5.12        ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ S @ T ) @ T )
% 9.25/5.12        = T ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_840_Un__Int__eq_I3_J,axiom,
% 9.25/5.12      ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 9.25/5.12        ( ( inf_in2572325071724192079at_nat @ S @ ( sup_su6327502436637775413at_nat @ S @ T ) )
% 9.25/5.12        = S ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_841_Un__Int__eq_I3_J,axiom,
% 9.25/5.12      ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 9.25/5.12        ( ( inf_in1697001100524423349at_nat @ S @ ( sup_su3035147773818789531at_nat @ S @ T ) )
% 9.25/5.12        = S ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_842_Un__Int__eq_I3_J,axiom,
% 9.25/5.12      ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 9.25/5.12        ( ( inf_in7913087082777306421at_nat @ S @ ( sup_su5525570899277871387at_nat @ S @ T ) )
% 9.25/5.12        = S ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_843_Un__Int__eq_I3_J,axiom,
% 9.25/5.12      ! [S: set_nat,T: set_nat] :
% 9.25/5.12        ( ( inf_inf_set_nat @ S @ ( sup_sup_set_nat @ S @ T ) )
% 9.25/5.12        = S ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_844_Un__Int__eq_I4_J,axiom,
% 9.25/5.12      ! [T: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 9.25/5.12        ( ( inf_in2572325071724192079at_nat @ T @ ( sup_su6327502436637775413at_nat @ S @ T ) )
% 9.25/5.12        = T ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_845_Un__Int__eq_I4_J,axiom,
% 9.25/5.12      ! [T: set_Pr8551490117392284871at_nat,S: set_Pr8551490117392284871at_nat] :
% 9.25/5.12        ( ( inf_in1697001100524423349at_nat @ T @ ( sup_su3035147773818789531at_nat @ S @ T ) )
% 9.25/5.12        = T ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_846_Un__Int__eq_I4_J,axiom,
% 9.25/5.12      ! [T: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 9.25/5.12        ( ( inf_in7913087082777306421at_nat @ T @ ( sup_su5525570899277871387at_nat @ S @ T ) )
% 9.25/5.12        = T ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_847_Un__Int__eq_I4_J,axiom,
% 9.25/5.12      ! [T: set_nat,S: set_nat] :
% 9.25/5.12        ( ( inf_inf_set_nat @ T @ ( sup_sup_set_nat @ S @ T ) )
% 9.25/5.12        = T ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_848_Int__Un__eq_I1_J,axiom,
% 9.25/5.12      ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 9.25/5.12        ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ S @ T ) @ S )
% 9.25/5.12        = S ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_849_Int__Un__eq_I1_J,axiom,
% 9.25/5.12      ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 9.25/5.12        ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ S @ T ) @ S )
% 9.25/5.12        = S ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_850_Int__Un__eq_I1_J,axiom,
% 9.25/5.12      ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 9.25/5.12        ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ S @ T ) @ S )
% 9.25/5.12        = S ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_851_Int__Un__eq_I1_J,axiom,
% 9.25/5.12      ! [S: set_nat,T: set_nat] :
% 9.25/5.12        ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ S @ T ) @ S )
% 9.25/5.12        = S ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_852_Int__Un__eq_I2_J,axiom,
% 9.25/5.12      ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 9.25/5.12        ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ S @ T ) @ T )
% 9.25/5.12        = T ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_853_Int__Un__eq_I2_J,axiom,
% 9.25/5.12      ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 9.25/5.12        ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ S @ T ) @ T )
% 9.25/5.12        = T ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_854_Int__Un__eq_I2_J,axiom,
% 9.25/5.12      ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 9.25/5.12        ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ S @ T ) @ T )
% 9.25/5.12        = T ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_855_Int__Un__eq_I2_J,axiom,
% 9.25/5.12      ! [S: set_nat,T: set_nat] :
% 9.25/5.12        ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ S @ T ) @ T )
% 9.25/5.12        = T ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_856_Int__Un__eq_I3_J,axiom,
% 9.25/5.12      ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 9.25/5.12        ( ( sup_su6327502436637775413at_nat @ S @ ( inf_in2572325071724192079at_nat @ S @ T ) )
% 9.25/5.12        = S ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_857_Int__Un__eq_I3_J,axiom,
% 9.25/5.12      ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 9.25/5.12        ( ( sup_su3035147773818789531at_nat @ S @ ( inf_in1697001100524423349at_nat @ S @ T ) )
% 9.25/5.12        = S ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_858_Int__Un__eq_I3_J,axiom,
% 9.25/5.12      ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 9.25/5.12        ( ( sup_su5525570899277871387at_nat @ S @ ( inf_in7913087082777306421at_nat @ S @ T ) )
% 9.25/5.12        = S ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_859_Int__Un__eq_I3_J,axiom,
% 9.25/5.12      ! [S: set_nat,T: set_nat] :
% 9.25/5.12        ( ( sup_sup_set_nat @ S @ ( inf_inf_set_nat @ S @ T ) )
% 9.25/5.12        = S ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_860_Int__Un__eq_I4_J,axiom,
% 9.25/5.12      ! [T: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 9.25/5.12        ( ( sup_su6327502436637775413at_nat @ T @ ( inf_in2572325071724192079at_nat @ S @ T ) )
% 9.25/5.12        = T ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_861_Int__Un__eq_I4_J,axiom,
% 9.25/5.12      ! [T: set_Pr8551490117392284871at_nat,S: set_Pr8551490117392284871at_nat] :
% 9.25/5.12        ( ( sup_su3035147773818789531at_nat @ T @ ( inf_in1697001100524423349at_nat @ S @ T ) )
% 9.25/5.12        = T ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_862_Int__Un__eq_I4_J,axiom,
% 9.25/5.12      ! [T: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 9.25/5.12        ( ( sup_su5525570899277871387at_nat @ T @ ( inf_in7913087082777306421at_nat @ S @ T ) )
% 9.25/5.12        = T ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_863_Int__Un__eq_I4_J,axiom,
% 9.25/5.12      ! [T: set_nat,S: set_nat] :
% 9.25/5.12        ( ( sup_sup_set_nat @ T @ ( inf_inf_set_nat @ S @ T ) )
% 9.25/5.12        = T ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_864_Un__empty,axiom,
% 9.25/5.12      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.12        ( ( ( sup_su3035147773818789531at_nat @ A2 @ B2 )
% 9.25/5.12          = bot_bo8422036546324065075at_nat )
% 9.25/5.12        = ( ( A2 = bot_bo8422036546324065075at_nat )
% 9.25/5.12          & ( B2 = bot_bo8422036546324065075at_nat ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_865_Un__empty,axiom,
% 9.25/5.12      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.12        ( ( ( sup_su5525570899277871387at_nat @ A2 @ B2 )
% 9.25/5.12          = bot_bo228742789529271731at_nat )
% 9.25/5.12        = ( ( A2 = bot_bo228742789529271731at_nat )
% 9.25/5.12          & ( B2 = bot_bo228742789529271731at_nat ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_866_Un__empty,axiom,
% 9.25/5.12      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.12        ( ( ( sup_su6327502436637775413at_nat @ A2 @ B2 )
% 9.25/5.12          = bot_bo2099793752762293965at_nat )
% 9.25/5.12        = ( ( A2 = bot_bo2099793752762293965at_nat )
% 9.25/5.12          & ( B2 = bot_bo2099793752762293965at_nat ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_867_Un__empty,axiom,
% 9.25/5.12      ! [A2: set_o,B2: set_o] :
% 9.25/5.12        ( ( ( sup_sup_set_o @ A2 @ B2 )
% 9.25/5.12          = bot_bot_set_o )
% 9.25/5.12        = ( ( A2 = bot_bot_set_o )
% 9.25/5.12          & ( B2 = bot_bot_set_o ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_868_Un__empty,axiom,
% 9.25/5.12      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.12        ( ( ( sup_sup_set_nat @ A2 @ B2 )
% 9.25/5.12          = bot_bot_set_nat )
% 9.25/5.12        = ( ( A2 = bot_bot_set_nat )
% 9.25/5.12          & ( B2 = bot_bot_set_nat ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_869_Un__empty,axiom,
% 9.25/5.12      ! [A2: set_int,B2: set_int] :
% 9.25/5.12        ( ( ( sup_sup_set_int @ A2 @ B2 )
% 9.25/5.12          = bot_bot_set_int )
% 9.25/5.12        = ( ( A2 = bot_bot_set_int )
% 9.25/5.12          & ( B2 = bot_bot_set_int ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_870_Compl__disjoint2,axiom,
% 9.25/5.12      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.12        ( ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ A2 ) @ A2 )
% 9.25/5.12        = bot_bo2099793752762293965at_nat ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_871_Compl__disjoint2,axiom,
% 9.25/5.12      ! [A2: set_o] :
% 9.25/5.12        ( ( inf_inf_set_o @ ( uminus_uminus_set_o @ A2 ) @ A2 )
% 9.25/5.12        = bot_bot_set_o ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_872_Compl__disjoint2,axiom,
% 9.25/5.12      ! [A2: set_nat] :
% 9.25/5.12        ( ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ A2 )
% 9.25/5.12        = bot_bot_set_nat ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_873_Compl__disjoint2,axiom,
% 9.25/5.12      ! [A2: set_int] :
% 9.25/5.12        ( ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ A2 )
% 9.25/5.12        = bot_bot_set_int ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_874_empty__iff,axiom,
% 9.25/5.12      ! [C: set_Pr958786334691620121nt_int] :
% 9.25/5.12        ~ ( member2340774599025711042nt_int @ C @ bot_bo1488462491386950373nt_int ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_875_empty__iff,axiom,
% 9.25/5.12      ! [C: set_nat] :
% 9.25/5.12        ~ ( member_set_nat @ C @ bot_bot_set_set_nat ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_876_empty__iff,axiom,
% 9.25/5.12      ! [C: produc3658429121746597890et_nat > $o] :
% 9.25/5.12        ~ ( member6576561426505652726_nat_o @ C @ bot_bo7824918357723582233_nat_o ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_877_empty__iff,axiom,
% 9.25/5.12      ! [C: product_prod_nat_nat] :
% 9.25/5.12        ~ ( member8440522571783428010at_nat @ C @ bot_bo2099793752762293965at_nat ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_878_empty__iff,axiom,
% 9.25/5.12      ! [C: $o] :
% 9.25/5.12        ~ ( member_o @ C @ bot_bot_set_o ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_879_empty__iff,axiom,
% 9.25/5.12      ! [C: nat] :
% 9.25/5.12        ~ ( member_nat @ C @ bot_bot_set_nat ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_880_empty__iff,axiom,
% 9.25/5.12      ! [C: int] :
% 9.25/5.12        ~ ( member_int @ C @ bot_bot_set_int ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_881_all__not__in__conv,axiom,
% 9.25/5.12      ! [A2: set_se6260736226359567993nt_int] :
% 9.25/5.12        ( ( ! [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.12              ~ ( member2340774599025711042nt_int @ X3 @ A2 ) )
% 9.25/5.12        = ( A2 = bot_bo1488462491386950373nt_int ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_882_all__not__in__conv,axiom,
% 9.25/5.12      ! [A2: set_set_nat] :
% 9.25/5.12        ( ( ! [X3: set_nat] :
% 9.25/5.12              ~ ( member_set_nat @ X3 @ A2 ) )
% 9.25/5.12        = ( A2 = bot_bot_set_set_nat ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_883_all__not__in__conv,axiom,
% 9.25/5.12      ! [A2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.12        ( ( ! [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.12              ~ ( member6576561426505652726_nat_o @ X3 @ A2 ) )
% 9.25/5.12        = ( A2 = bot_bo7824918357723582233_nat_o ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_884_all__not__in__conv,axiom,
% 9.25/5.12      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.12        ( ( ! [X3: product_prod_nat_nat] :
% 9.25/5.12              ~ ( member8440522571783428010at_nat @ X3 @ A2 ) )
% 9.25/5.12        = ( A2 = bot_bo2099793752762293965at_nat ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_885_all__not__in__conv,axiom,
% 9.25/5.12      ! [A2: set_o] :
% 9.25/5.12        ( ( ! [X3: $o] :
% 9.25/5.12              ~ ( member_o @ X3 @ A2 ) )
% 9.25/5.12        = ( A2 = bot_bot_set_o ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_886_all__not__in__conv,axiom,
% 9.25/5.12      ! [A2: set_nat] :
% 9.25/5.12        ( ( ! [X3: nat] :
% 9.25/5.12              ~ ( member_nat @ X3 @ A2 ) )
% 9.25/5.12        = ( A2 = bot_bot_set_nat ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_887_all__not__in__conv,axiom,
% 9.25/5.12      ! [A2: set_int] :
% 9.25/5.12        ( ( ! [X3: int] :
% 9.25/5.12              ~ ( member_int @ X3 @ A2 ) )
% 9.25/5.12        = ( A2 = bot_bot_set_int ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_888_Collect__empty__eq,axiom,
% 9.25/5.12      ! [P: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.12        ( ( ( collec5210948495886036740nt_int @ P )
% 9.25/5.12          = bot_bo1488462491386950373nt_int )
% 9.25/5.12        = ( ! [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.12              ~ ( P @ X3 ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_889_Collect__empty__eq,axiom,
% 9.25/5.12      ! [P: set_nat > $o] :
% 9.25/5.12        ( ( ( collect_set_nat @ P )
% 9.25/5.12          = bot_bot_set_set_nat )
% 9.25/5.12        = ( ! [X3: set_nat] :
% 9.25/5.12              ~ ( P @ X3 ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_890_Collect__empty__eq,axiom,
% 9.25/5.12      ! [P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.12        ( ( ( collec939566748876313656_nat_o @ P )
% 9.25/5.12          = bot_bo7824918357723582233_nat_o )
% 9.25/5.12        = ( ! [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.12              ~ ( P @ X3 ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_891_Collect__empty__eq,axiom,
% 9.25/5.12      ! [P: product_prod_nat_nat > $o] :
% 9.25/5.12        ( ( ( collec3392354462482085612at_nat @ P )
% 9.25/5.12          = bot_bo2099793752762293965at_nat )
% 9.25/5.12        = ( ! [X3: product_prod_nat_nat] :
% 9.25/5.12              ~ ( P @ X3 ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_892_Collect__empty__eq,axiom,
% 9.25/5.12      ! [P: $o > $o] :
% 9.25/5.12        ( ( ( collect_o @ P )
% 9.25/5.12          = bot_bot_set_o )
% 9.25/5.12        = ( ! [X3: $o] :
% 9.25/5.12              ~ ( P @ X3 ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_893_Collect__empty__eq,axiom,
% 9.25/5.12      ! [P: nat > $o] :
% 9.25/5.12        ( ( ( collect_nat @ P )
% 9.25/5.12          = bot_bot_set_nat )
% 9.25/5.12        = ( ! [X3: nat] :
% 9.25/5.12              ~ ( P @ X3 ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_894_Collect__empty__eq,axiom,
% 9.25/5.12      ! [P: int > $o] :
% 9.25/5.12        ( ( ( collect_int @ P )
% 9.25/5.12          = bot_bot_set_int )
% 9.25/5.12        = ( ! [X3: int] :
% 9.25/5.12              ~ ( P @ X3 ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_895_empty__Collect__eq,axiom,
% 9.25/5.12      ! [P: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.12        ( ( bot_bo1488462491386950373nt_int
% 9.25/5.12          = ( collec5210948495886036740nt_int @ P ) )
% 9.25/5.12        = ( ! [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.12              ~ ( P @ X3 ) ) ) ).
% 9.25/5.12  
% 9.25/5.12  thf(fact_896_empty__Collect__eq,axiom,
% 9.25/5.12      ! [P: set_nat > $o] :
% 9.25/5.12        ( ( bot_bot_set_set_nat
% 9.25/5.13          = ( collect_set_nat @ P ) )
% 9.25/5.13        = ( ! [X3: set_nat] :
% 9.25/5.13              ~ ( P @ X3 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_897_empty__Collect__eq,axiom,
% 9.25/5.13      ! [P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.13        ( ( bot_bo7824918357723582233_nat_o
% 9.25/5.13          = ( collec939566748876313656_nat_o @ P ) )
% 9.25/5.13        = ( ! [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.13              ~ ( P @ X3 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_898_empty__Collect__eq,axiom,
% 9.25/5.13      ! [P: product_prod_nat_nat > $o] :
% 9.25/5.13        ( ( bot_bo2099793752762293965at_nat
% 9.25/5.13          = ( collec3392354462482085612at_nat @ P ) )
% 9.25/5.13        = ( ! [X3: product_prod_nat_nat] :
% 9.25/5.13              ~ ( P @ X3 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_899_empty__Collect__eq,axiom,
% 9.25/5.13      ! [P: $o > $o] :
% 9.25/5.13        ( ( bot_bot_set_o
% 9.25/5.13          = ( collect_o @ P ) )
% 9.25/5.13        = ( ! [X3: $o] :
% 9.25/5.13              ~ ( P @ X3 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_900_empty__Collect__eq,axiom,
% 9.25/5.13      ! [P: nat > $o] :
% 9.25/5.13        ( ( bot_bot_set_nat
% 9.25/5.13          = ( collect_nat @ P ) )
% 9.25/5.13        = ( ! [X3: nat] :
% 9.25/5.13              ~ ( P @ X3 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_901_empty__Collect__eq,axiom,
% 9.25/5.13      ! [P: int > $o] :
% 9.25/5.13        ( ( bot_bot_set_int
% 9.25/5.13          = ( collect_int @ P ) )
% 9.25/5.13        = ( ! [X3: int] :
% 9.25/5.13              ~ ( P @ X3 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_902_IntI,axiom,
% 9.25/5.13      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.13        ( ( member2340774599025711042nt_int @ C @ A2 )
% 9.25/5.13       => ( ( member2340774599025711042nt_int @ C @ B2 )
% 9.25/5.13         => ( member2340774599025711042nt_int @ C @ ( inf_in8396524679539076455nt_int @ A2 @ B2 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_903_IntI,axiom,
% 9.25/5.13      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 9.25/5.13        ( ( member_set_nat @ C @ A2 )
% 9.25/5.13       => ( ( member_set_nat @ C @ B2 )
% 9.25/5.13         => ( member_set_nat @ C @ ( inf_inf_set_set_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_904_IntI,axiom,
% 9.25/5.13      ! [C: int,A2: set_int,B2: set_int] :
% 9.25/5.13        ( ( member_int @ C @ A2 )
% 9.25/5.13       => ( ( member_int @ C @ B2 )
% 9.25/5.13         => ( member_int @ C @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_905_IntI,axiom,
% 9.25/5.13      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13        ( ( member6576561426505652726_nat_o @ C @ A2 )
% 9.25/5.13       => ( ( member6576561426505652726_nat_o @ C @ B2 )
% 9.25/5.13         => ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_906_IntI,axiom,
% 9.25/5.13      ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( member8440522571783428010at_nat @ C @ A2 )
% 9.25/5.13       => ( ( member8440522571783428010at_nat @ C @ B2 )
% 9.25/5.13         => ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_907_IntI,axiom,
% 9.25/5.13      ! [C: nat,A2: set_nat,B2: set_nat] :
% 9.25/5.13        ( ( member_nat @ C @ A2 )
% 9.25/5.13       => ( ( member_nat @ C @ B2 )
% 9.25/5.13         => ( member_nat @ C @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_908_Int__iff,axiom,
% 9.25/5.13      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.13        ( ( member2340774599025711042nt_int @ C @ ( inf_in8396524679539076455nt_int @ A2 @ B2 ) )
% 9.25/5.13        = ( ( member2340774599025711042nt_int @ C @ A2 )
% 9.25/5.13          & ( member2340774599025711042nt_int @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_909_Int__iff,axiom,
% 9.25/5.13      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 9.25/5.13        ( ( member_set_nat @ C @ ( inf_inf_set_set_nat @ A2 @ B2 ) )
% 9.25/5.13        = ( ( member_set_nat @ C @ A2 )
% 9.25/5.13          & ( member_set_nat @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_910_Int__iff,axiom,
% 9.25/5.13      ! [C: int,A2: set_int,B2: set_int] :
% 9.25/5.13        ( ( member_int @ C @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.13        = ( ( member_int @ C @ A2 )
% 9.25/5.13          & ( member_int @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_911_Int__iff,axiom,
% 9.25/5.13      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13        ( ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) )
% 9.25/5.13        = ( ( member6576561426505652726_nat_o @ C @ A2 )
% 9.25/5.13          & ( member6576561426505652726_nat_o @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_912_Int__iff,axiom,
% 9.25/5.13      ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 9.25/5.13        = ( ( member8440522571783428010at_nat @ C @ A2 )
% 9.25/5.13          & ( member8440522571783428010at_nat @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_913_Int__iff,axiom,
% 9.25/5.13      ! [C: nat,A2: set_nat,B2: set_nat] :
% 9.25/5.13        ( ( member_nat @ C @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.13        = ( ( member_nat @ C @ A2 )
% 9.25/5.13          & ( member_nat @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_914_Int__UNIV,axiom,
% 9.25/5.13      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 9.25/5.13          = top_to4669805908274784177at_nat )
% 9.25/5.13        = ( ( A2 = top_to4669805908274784177at_nat )
% 9.25/5.13          & ( B2 = top_to4669805908274784177at_nat ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_915_Int__UNIV,axiom,
% 9.25/5.13      ! [A2: set_list_nat,B2: set_list_nat] :
% 9.25/5.13        ( ( ( inf_inf_set_list_nat @ A2 @ B2 )
% 9.25/5.13          = top_top_set_list_nat )
% 9.25/5.13        = ( ( A2 = top_top_set_list_nat )
% 9.25/5.13          & ( B2 = top_top_set_list_nat ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_916_Int__UNIV,axiom,
% 9.25/5.13      ! [A2: set_o,B2: set_o] :
% 9.25/5.13        ( ( ( inf_inf_set_o @ A2 @ B2 )
% 9.25/5.13          = top_top_set_o )
% 9.25/5.13        = ( ( A2 = top_top_set_o )
% 9.25/5.13          & ( B2 = top_top_set_o ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_917_Int__UNIV,axiom,
% 9.25/5.13      ! [A2: set_rat,B2: set_rat] :
% 9.25/5.13        ( ( ( inf_inf_set_rat @ A2 @ B2 )
% 9.25/5.13          = top_top_set_rat )
% 9.25/5.13        = ( ( A2 = top_top_set_rat )
% 9.25/5.13          & ( B2 = top_top_set_rat ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_918_Int__UNIV,axiom,
% 9.25/5.13      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.13        ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 9.25/5.13          = top_top_set_nat )
% 9.25/5.13        = ( ( A2 = top_top_set_nat )
% 9.25/5.13          & ( B2 = top_top_set_nat ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_919_Int__UNIV,axiom,
% 9.25/5.13      ! [A2: set_int,B2: set_int] :
% 9.25/5.13        ( ( ( inf_inf_set_int @ A2 @ B2 )
% 9.25/5.13          = top_top_set_int )
% 9.25/5.13        = ( ( A2 = top_top_set_int )
% 9.25/5.13          & ( B2 = top_top_set_int ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_920_UnCI,axiom,
% 9.25/5.13      ! [C: set_Pr958786334691620121nt_int,B2: set_se6260736226359567993nt_int,A2: set_se6260736226359567993nt_int] :
% 9.25/5.13        ( ( ~ ( member2340774599025711042nt_int @ C @ B2 )
% 9.25/5.13         => ( member2340774599025711042nt_int @ C @ A2 ) )
% 9.25/5.13       => ( member2340774599025711042nt_int @ C @ ( sup_su2047564715030645325nt_int @ A2 @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_921_UnCI,axiom,
% 9.25/5.13      ! [C: set_nat,B2: set_set_nat,A2: set_set_nat] :
% 9.25/5.13        ( ( ~ ( member_set_nat @ C @ B2 )
% 9.25/5.13         => ( member_set_nat @ C @ A2 ) )
% 9.25/5.13       => ( member_set_nat @ C @ ( sup_sup_set_set_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_922_UnCI,axiom,
% 9.25/5.13      ! [C: int,B2: set_int,A2: set_int] :
% 9.25/5.13        ( ( ~ ( member_int @ C @ B2 )
% 9.25/5.13         => ( member_int @ C @ A2 ) )
% 9.25/5.13       => ( member_int @ C @ ( sup_sup_set_int @ A2 @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_923_UnCI,axiom,
% 9.25/5.13      ! [C: produc3658429121746597890et_nat > $o,B2: set_Pr4532377907799695533_nat_o,A2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13        ( ( ~ ( member6576561426505652726_nat_o @ C @ B2 )
% 9.25/5.13         => ( member6576561426505652726_nat_o @ C @ A2 ) )
% 9.25/5.13       => ( member6576561426505652726_nat_o @ C @ ( sup_su5209123915105501825_nat_o @ A2 @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_924_UnCI,axiom,
% 9.25/5.13      ! [C: produc4166570645942440679at_nat,B2: set_Pr8551490117392284871at_nat,A2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( ~ ( member6689249552917799696at_nat @ C @ B2 )
% 9.25/5.13         => ( member6689249552917799696at_nat @ C @ A2 ) )
% 9.25/5.13       => ( member6689249552917799696at_nat @ C @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_925_UnCI,axiom,
% 9.25/5.13      ! [C: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( ~ ( member8757157785044589968at_nat @ C @ B2 )
% 9.25/5.13         => ( member8757157785044589968at_nat @ C @ A2 ) )
% 9.25/5.13       => ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_926_UnCI,axiom,
% 9.25/5.13      ! [C: nat,B2: set_nat,A2: set_nat] :
% 9.25/5.13        ( ( ~ ( member_nat @ C @ B2 )
% 9.25/5.13         => ( member_nat @ C @ A2 ) )
% 9.25/5.13       => ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_927_Un__iff,axiom,
% 9.25/5.13      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.13        ( ( member2340774599025711042nt_int @ C @ ( sup_su2047564715030645325nt_int @ A2 @ B2 ) )
% 9.25/5.13        = ( ( member2340774599025711042nt_int @ C @ A2 )
% 9.25/5.13          | ( member2340774599025711042nt_int @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_928_Un__iff,axiom,
% 9.25/5.13      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 9.25/5.13        ( ( member_set_nat @ C @ ( sup_sup_set_set_nat @ A2 @ B2 ) )
% 9.25/5.13        = ( ( member_set_nat @ C @ A2 )
% 9.25/5.13          | ( member_set_nat @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_929_Un__iff,axiom,
% 9.25/5.13      ! [C: int,A2: set_int,B2: set_int] :
% 9.25/5.13        ( ( member_int @ C @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.13        = ( ( member_int @ C @ A2 )
% 9.25/5.13          | ( member_int @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_930_Un__iff,axiom,
% 9.25/5.13      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13        ( ( member6576561426505652726_nat_o @ C @ ( sup_su5209123915105501825_nat_o @ A2 @ B2 ) )
% 9.25/5.13        = ( ( member6576561426505652726_nat_o @ C @ A2 )
% 9.25/5.13          | ( member6576561426505652726_nat_o @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_931_Un__iff,axiom,
% 9.25/5.13      ! [C: produc4166570645942440679at_nat,A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( member6689249552917799696at_nat @ C @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 9.25/5.13        = ( ( member6689249552917799696at_nat @ C @ A2 )
% 9.25/5.13          | ( member6689249552917799696at_nat @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_932_Un__iff,axiom,
% 9.25/5.13      ! [C: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 9.25/5.13        = ( ( member8757157785044589968at_nat @ C @ A2 )
% 9.25/5.13          | ( member8757157785044589968at_nat @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_933_Un__iff,axiom,
% 9.25/5.13      ! [C: nat,A2: set_nat,B2: set_nat] :
% 9.25/5.13        ( ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.13        = ( ( member_nat @ C @ A2 )
% 9.25/5.13          | ( member_nat @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_934_ComplI,axiom,
% 9.25/5.13      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int] :
% 9.25/5.13        ( ~ ( member2340774599025711042nt_int @ C @ A2 )
% 9.25/5.13       => ( member2340774599025711042nt_int @ C @ ( uminus6423885277529793776nt_int @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_935_ComplI,axiom,
% 9.25/5.13      ! [C: set_nat,A2: set_set_nat] :
% 9.25/5.13        ( ~ ( member_set_nat @ C @ A2 )
% 9.25/5.13       => ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_936_ComplI,axiom,
% 9.25/5.13      ! [C: nat,A2: set_nat] :
% 9.25/5.13        ( ~ ( member_nat @ C @ A2 )
% 9.25/5.13       => ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_937_ComplI,axiom,
% 9.25/5.13      ! [C: int,A2: set_int] :
% 9.25/5.13        ( ~ ( member_int @ C @ A2 )
% 9.25/5.13       => ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_938_ComplI,axiom,
% 9.25/5.13      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13        ( ~ ( member6576561426505652726_nat_o @ C @ A2 )
% 9.25/5.13       => ( member6576561426505652726_nat_o @ C @ ( uminus5254974436814262692_nat_o @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_939_Compl__iff,axiom,
% 9.25/5.13      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int] :
% 9.25/5.13        ( ( member2340774599025711042nt_int @ C @ ( uminus6423885277529793776nt_int @ A2 ) )
% 9.25/5.13        = ( ~ ( member2340774599025711042nt_int @ C @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_940_Compl__iff,axiom,
% 9.25/5.13      ! [C: set_nat,A2: set_set_nat] :
% 9.25/5.13        ( ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) )
% 9.25/5.13        = ( ~ ( member_set_nat @ C @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_941_Compl__iff,axiom,
% 9.25/5.13      ! [C: nat,A2: set_nat] :
% 9.25/5.13        ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) )
% 9.25/5.13        = ( ~ ( member_nat @ C @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_942_Compl__iff,axiom,
% 9.25/5.13      ! [C: int,A2: set_int] :
% 9.25/5.13        ( ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) )
% 9.25/5.13        = ( ~ ( member_int @ C @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_943_Compl__iff,axiom,
% 9.25/5.13      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13        ( ( member6576561426505652726_nat_o @ C @ ( uminus5254974436814262692_nat_o @ A2 ) )
% 9.25/5.13        = ( ~ ( member6576561426505652726_nat_o @ C @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_944_Collect__const,axiom,
% 9.25/5.13      ! [P: $o] :
% 9.25/5.13        ( ( P
% 9.25/5.13         => ( ( collec5210948495886036740nt_int
% 9.25/5.13              @ ^ [S2: set_Pr958786334691620121nt_int] : P )
% 9.25/5.13            = top_to6034159466715884489nt_int ) )
% 9.25/5.13        & ( ~ P
% 9.25/5.13         => ( ( collec5210948495886036740nt_int
% 9.25/5.13              @ ^ [S2: set_Pr958786334691620121nt_int] : P )
% 9.25/5.13            = bot_bo1488462491386950373nt_int ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_945_Collect__const,axiom,
% 9.25/5.13      ! [P: $o] :
% 9.25/5.13        ( ( P
% 9.25/5.13         => ( ( collect_set_nat
% 9.25/5.13              @ ^ [S2: set_nat] : P )
% 9.25/5.13            = top_top_set_set_nat ) )
% 9.25/5.13        & ( ~ P
% 9.25/5.13         => ( ( collect_set_nat
% 9.25/5.13              @ ^ [S2: set_nat] : P )
% 9.25/5.13            = bot_bot_set_set_nat ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_946_Collect__const,axiom,
% 9.25/5.13      ! [P: $o] :
% 9.25/5.13        ( ( P
% 9.25/5.13         => ( ( collec939566748876313656_nat_o
% 9.25/5.13              @ ^ [S2: produc3658429121746597890et_nat > $o] : P )
% 9.25/5.13            = top_to4869887016220417533_nat_o ) )
% 9.25/5.13        & ( ~ P
% 9.25/5.13         => ( ( collec939566748876313656_nat_o
% 9.25/5.13              @ ^ [S2: produc3658429121746597890et_nat > $o] : P )
% 9.25/5.13            = bot_bo7824918357723582233_nat_o ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_947_Collect__const,axiom,
% 9.25/5.13      ! [P: $o] :
% 9.25/5.13        ( ( P
% 9.25/5.13         => ( ( collec3392354462482085612at_nat
% 9.25/5.13              @ ^ [S2: product_prod_nat_nat] : P )
% 9.25/5.13            = top_to4669805908274784177at_nat ) )
% 9.25/5.13        & ( ~ P
% 9.25/5.13         => ( ( collec3392354462482085612at_nat
% 9.25/5.13              @ ^ [S2: product_prod_nat_nat] : P )
% 9.25/5.13            = bot_bo2099793752762293965at_nat ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_948_Collect__const,axiom,
% 9.25/5.13      ! [P: $o] :
% 9.25/5.13        ( ( P
% 9.25/5.13         => ( ( collect_list_nat
% 9.25/5.13              @ ^ [S2: list_nat] : P )
% 9.25/5.13            = top_top_set_list_nat ) )
% 9.25/5.13        & ( ~ P
% 9.25/5.13         => ( ( collect_list_nat
% 9.25/5.13              @ ^ [S2: list_nat] : P )
% 9.25/5.13            = bot_bot_set_list_nat ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_949_Collect__const,axiom,
% 9.25/5.13      ! [P: $o] :
% 9.25/5.13        ( ( P
% 9.25/5.13         => ( ( collect_o
% 9.25/5.13              @ ^ [S2: $o] : P )
% 9.25/5.13            = top_top_set_o ) )
% 9.25/5.13        & ( ~ P
% 9.25/5.13         => ( ( collect_o
% 9.25/5.13              @ ^ [S2: $o] : P )
% 9.25/5.13            = bot_bot_set_o ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_950_Collect__const,axiom,
% 9.25/5.13      ! [P: $o] :
% 9.25/5.13        ( ( P
% 9.25/5.13         => ( ( collect_rat
% 9.25/5.13              @ ^ [S2: rat] : P )
% 9.25/5.13            = top_top_set_rat ) )
% 9.25/5.13        & ( ~ P
% 9.25/5.13         => ( ( collect_rat
% 9.25/5.13              @ ^ [S2: rat] : P )
% 9.25/5.13            = bot_bot_set_rat ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_951_Collect__const,axiom,
% 9.25/5.13      ! [P: $o] :
% 9.25/5.13        ( ( P
% 9.25/5.13         => ( ( collect_nat
% 9.25/5.13              @ ^ [S2: nat] : P )
% 9.25/5.13            = top_top_set_nat ) )
% 9.25/5.13        & ( ~ P
% 9.25/5.13         => ( ( collect_nat
% 9.25/5.13              @ ^ [S2: nat] : P )
% 9.25/5.13            = bot_bot_set_nat ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_952_Collect__const,axiom,
% 9.25/5.13      ! [P: $o] :
% 9.25/5.13        ( ( P
% 9.25/5.13         => ( ( collect_int
% 9.25/5.13              @ ^ [S2: int] : P )
% 9.25/5.13            = top_top_set_int ) )
% 9.25/5.13        & ( ~ P
% 9.25/5.13         => ( ( collect_int
% 9.25/5.13              @ ^ [S2: int] : P )
% 9.25/5.13            = bot_bot_set_int ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_953_Compl__disjoint,axiom,
% 9.25/5.13      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( inf_in2572325071724192079at_nat @ A2 @ ( uminus6524753893492686040at_nat @ A2 ) )
% 9.25/5.13        = bot_bo2099793752762293965at_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_954_Compl__disjoint,axiom,
% 9.25/5.13      ! [A2: set_o] :
% 9.25/5.13        ( ( inf_inf_set_o @ A2 @ ( uminus_uminus_set_o @ A2 ) )
% 9.25/5.13        = bot_bot_set_o ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_955_Compl__disjoint,axiom,
% 9.25/5.13      ! [A2: set_nat] :
% 9.25/5.13        ( ( inf_inf_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ A2 ) )
% 9.25/5.13        = bot_bot_set_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_956_Compl__disjoint,axiom,
% 9.25/5.13      ! [A2: set_int] :
% 9.25/5.13        ( ( inf_inf_set_int @ A2 @ ( uminus1532241313380277803et_int @ A2 ) )
% 9.25/5.13        = bot_bot_set_int ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_957_ComplD,axiom,
% 9.25/5.13      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int] :
% 9.25/5.13        ( ( member2340774599025711042nt_int @ C @ ( uminus6423885277529793776nt_int @ A2 ) )
% 9.25/5.13       => ~ ( member2340774599025711042nt_int @ C @ A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_958_ComplD,axiom,
% 9.25/5.13      ! [C: set_nat,A2: set_set_nat] :
% 9.25/5.13        ( ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A2 ) )
% 9.25/5.13       => ~ ( member_set_nat @ C @ A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_959_ComplD,axiom,
% 9.25/5.13      ! [C: nat,A2: set_nat] :
% 9.25/5.13        ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A2 ) )
% 9.25/5.13       => ~ ( member_nat @ C @ A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_960_ComplD,axiom,
% 9.25/5.13      ! [C: int,A2: set_int] :
% 9.25/5.13        ( ( member_int @ C @ ( uminus1532241313380277803et_int @ A2 ) )
% 9.25/5.13       => ~ ( member_int @ C @ A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_961_ComplD,axiom,
% 9.25/5.13      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13        ( ( member6576561426505652726_nat_o @ C @ ( uminus5254974436814262692_nat_o @ A2 ) )
% 9.25/5.13       => ~ ( member6576561426505652726_nat_o @ C @ A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_962_Compl__eq,axiom,
% 9.25/5.13      ( uminus6423885277529793776nt_int
% 9.25/5.13      = ( ^ [A4: set_se6260736226359567993nt_int] :
% 9.25/5.13            ( collec5210948495886036740nt_int
% 9.25/5.13            @ ^ [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.13                ~ ( member2340774599025711042nt_int @ X3 @ A4 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_963_Compl__eq,axiom,
% 9.25/5.13      ( uminus613421341184616069et_nat
% 9.25/5.13      = ( ^ [A4: set_set_nat] :
% 9.25/5.13            ( collect_set_nat
% 9.25/5.13            @ ^ [X3: set_nat] :
% 9.25/5.13                ~ ( member_set_nat @ X3 @ A4 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_964_Compl__eq,axiom,
% 9.25/5.13      ( uminus5710092332889474511et_nat
% 9.25/5.13      = ( ^ [A4: set_nat] :
% 9.25/5.13            ( collect_nat
% 9.25/5.13            @ ^ [X3: nat] :
% 9.25/5.13                ~ ( member_nat @ X3 @ A4 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_965_Compl__eq,axiom,
% 9.25/5.13      ( uminus1532241313380277803et_int
% 9.25/5.13      = ( ^ [A4: set_int] :
% 9.25/5.13            ( collect_int
% 9.25/5.13            @ ^ [X3: int] :
% 9.25/5.13                ~ ( member_int @ X3 @ A4 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_966_Compl__eq,axiom,
% 9.25/5.13      ( uminus5254974436814262692_nat_o
% 9.25/5.13      = ( ^ [A4: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13            ( collec939566748876313656_nat_o
% 9.25/5.13            @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.13                ~ ( member6576561426505652726_nat_o @ X3 @ A4 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_967_Collect__neg__eq,axiom,
% 9.25/5.13      ! [P: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.13        ( ( collec5210948495886036740nt_int
% 9.25/5.13          @ ^ [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.13              ~ ( P @ X3 ) )
% 9.25/5.13        = ( uminus6423885277529793776nt_int @ ( collec5210948495886036740nt_int @ P ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_968_Collect__neg__eq,axiom,
% 9.25/5.13      ! [P: set_nat > $o] :
% 9.25/5.13        ( ( collect_set_nat
% 9.25/5.13          @ ^ [X3: set_nat] :
% 9.25/5.13              ~ ( P @ X3 ) )
% 9.25/5.13        = ( uminus613421341184616069et_nat @ ( collect_set_nat @ P ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_969_Collect__neg__eq,axiom,
% 9.25/5.13      ! [P: nat > $o] :
% 9.25/5.13        ( ( collect_nat
% 9.25/5.13          @ ^ [X3: nat] :
% 9.25/5.13              ~ ( P @ X3 ) )
% 9.25/5.13        = ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_970_Collect__neg__eq,axiom,
% 9.25/5.13      ! [P: int > $o] :
% 9.25/5.13        ( ( collect_int
% 9.25/5.13          @ ^ [X3: int] :
% 9.25/5.13              ~ ( P @ X3 ) )
% 9.25/5.13        = ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_971_Collect__neg__eq,axiom,
% 9.25/5.13      ! [P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.13        ( ( collec939566748876313656_nat_o
% 9.25/5.13          @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.13              ~ ( P @ X3 ) )
% 9.25/5.13        = ( uminus5254974436814262692_nat_o @ ( collec939566748876313656_nat_o @ P ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_972_uminus__set__def,axiom,
% 9.25/5.13      ( uminus6423885277529793776nt_int
% 9.25/5.13      = ( ^ [A4: set_se6260736226359567993nt_int] :
% 9.25/5.13            ( collec5210948495886036740nt_int
% 9.25/5.13            @ ( uminus8147837162492574189_int_o
% 9.25/5.13              @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ A4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_973_uminus__set__def,axiom,
% 9.25/5.13      ( uminus613421341184616069et_nat
% 9.25/5.13      = ( ^ [A4: set_set_nat] :
% 9.25/5.13            ( collect_set_nat
% 9.25/5.13            @ ( uminus6401447641752708672_nat_o
% 9.25/5.13              @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_974_uminus__set__def,axiom,
% 9.25/5.13      ( uminus5710092332889474511et_nat
% 9.25/5.13      = ( ^ [A4: set_nat] :
% 9.25/5.13            ( collect_nat
% 9.25/5.13            @ ( uminus_uminus_nat_o
% 9.25/5.13              @ ^ [X3: nat] : ( member_nat @ X3 @ A4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_975_uminus__set__def,axiom,
% 9.25/5.13      ( uminus1532241313380277803et_int
% 9.25/5.13      = ( ^ [A4: set_int] :
% 9.25/5.13            ( collect_int
% 9.25/5.13            @ ( uminus_uminus_int_o
% 9.25/5.13              @ ^ [X3: int] : ( member_int @ X3 @ A4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_976_uminus__set__def,axiom,
% 9.25/5.13      ( uminus5254974436814262692_nat_o
% 9.25/5.13      = ( ^ [A4: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13            ( collec939566748876313656_nat_o
% 9.25/5.13            @ ( uminus8928876914783121465at_o_o
% 9.25/5.13              @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ A4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_977_emptyE,axiom,
% 9.25/5.13      ! [A: set_Pr958786334691620121nt_int] :
% 9.25/5.13        ~ ( member2340774599025711042nt_int @ A @ bot_bo1488462491386950373nt_int ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_978_emptyE,axiom,
% 9.25/5.13      ! [A: set_nat] :
% 9.25/5.13        ~ ( member_set_nat @ A @ bot_bot_set_set_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_979_emptyE,axiom,
% 9.25/5.13      ! [A: produc3658429121746597890et_nat > $o] :
% 9.25/5.13        ~ ( member6576561426505652726_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_980_emptyE,axiom,
% 9.25/5.13      ! [A: product_prod_nat_nat] :
% 9.25/5.13        ~ ( member8440522571783428010at_nat @ A @ bot_bo2099793752762293965at_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_981_emptyE,axiom,
% 9.25/5.13      ! [A: $o] :
% 9.25/5.13        ~ ( member_o @ A @ bot_bot_set_o ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_982_emptyE,axiom,
% 9.25/5.13      ! [A: nat] :
% 9.25/5.13        ~ ( member_nat @ A @ bot_bot_set_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_983_emptyE,axiom,
% 9.25/5.13      ! [A: int] :
% 9.25/5.13        ~ ( member_int @ A @ bot_bot_set_int ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_984_equals0D,axiom,
% 9.25/5.13      ! [A2: set_se6260736226359567993nt_int,A: set_Pr958786334691620121nt_int] :
% 9.25/5.13        ( ( A2 = bot_bo1488462491386950373nt_int )
% 9.25/5.13       => ~ ( member2340774599025711042nt_int @ A @ A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_985_equals0D,axiom,
% 9.25/5.13      ! [A2: set_set_nat,A: set_nat] :
% 9.25/5.13        ( ( A2 = bot_bot_set_set_nat )
% 9.25/5.13       => ~ ( member_set_nat @ A @ A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_986_equals0D,axiom,
% 9.25/5.13      ! [A2: set_Pr4532377907799695533_nat_o,A: produc3658429121746597890et_nat > $o] :
% 9.25/5.13        ( ( A2 = bot_bo7824918357723582233_nat_o )
% 9.25/5.13       => ~ ( member6576561426505652726_nat_o @ A @ A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_987_equals0D,axiom,
% 9.25/5.13      ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
% 9.25/5.13        ( ( A2 = bot_bo2099793752762293965at_nat )
% 9.25/5.13       => ~ ( member8440522571783428010at_nat @ A @ A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_988_equals0D,axiom,
% 9.25/5.13      ! [A2: set_o,A: $o] :
% 9.25/5.13        ( ( A2 = bot_bot_set_o )
% 9.25/5.13       => ~ ( member_o @ A @ A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_989_equals0D,axiom,
% 9.25/5.13      ! [A2: set_nat,A: nat] :
% 9.25/5.13        ( ( A2 = bot_bot_set_nat )
% 9.25/5.13       => ~ ( member_nat @ A @ A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_990_equals0D,axiom,
% 9.25/5.13      ! [A2: set_int,A: int] :
% 9.25/5.13        ( ( A2 = bot_bot_set_int )
% 9.25/5.13       => ~ ( member_int @ A @ A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_991_equals0I,axiom,
% 9.25/5.13      ! [A2: set_se6260736226359567993nt_int] :
% 9.25/5.13        ( ! [Y2: set_Pr958786334691620121nt_int] :
% 9.25/5.13            ~ ( member2340774599025711042nt_int @ Y2 @ A2 )
% 9.25/5.13       => ( A2 = bot_bo1488462491386950373nt_int ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_992_equals0I,axiom,
% 9.25/5.13      ! [A2: set_set_nat] :
% 9.25/5.13        ( ! [Y2: set_nat] :
% 9.25/5.13            ~ ( member_set_nat @ Y2 @ A2 )
% 9.25/5.13       => ( A2 = bot_bot_set_set_nat ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_993_equals0I,axiom,
% 9.25/5.13      ! [A2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13        ( ! [Y2: produc3658429121746597890et_nat > $o] :
% 9.25/5.13            ~ ( member6576561426505652726_nat_o @ Y2 @ A2 )
% 9.25/5.13       => ( A2 = bot_bo7824918357723582233_nat_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_994_equals0I,axiom,
% 9.25/5.13      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ! [Y2: product_prod_nat_nat] :
% 9.25/5.13            ~ ( member8440522571783428010at_nat @ Y2 @ A2 )
% 9.25/5.13       => ( A2 = bot_bo2099793752762293965at_nat ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_995_equals0I,axiom,
% 9.25/5.13      ! [A2: set_o] :
% 9.25/5.13        ( ! [Y2: $o] :
% 9.25/5.13            ~ ( member_o @ Y2 @ A2 )
% 9.25/5.13       => ( A2 = bot_bot_set_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_996_equals0I,axiom,
% 9.25/5.13      ! [A2: set_nat] :
% 9.25/5.13        ( ! [Y2: nat] :
% 9.25/5.13            ~ ( member_nat @ Y2 @ A2 )
% 9.25/5.13       => ( A2 = bot_bot_set_nat ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_997_equals0I,axiom,
% 9.25/5.13      ! [A2: set_int] :
% 9.25/5.13        ( ! [Y2: int] :
% 9.25/5.13            ~ ( member_int @ Y2 @ A2 )
% 9.25/5.13       => ( A2 = bot_bot_set_int ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_998_ex__in__conv,axiom,
% 9.25/5.13      ! [A2: set_se6260736226359567993nt_int] :
% 9.25/5.13        ( ( ? [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ A2 ) )
% 9.25/5.13        = ( A2 != bot_bo1488462491386950373nt_int ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_999_ex__in__conv,axiom,
% 9.25/5.13      ! [A2: set_set_nat] :
% 9.25/5.13        ( ( ? [X3: set_nat] : ( member_set_nat @ X3 @ A2 ) )
% 9.25/5.13        = ( A2 != bot_bot_set_set_nat ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1000_ex__in__conv,axiom,
% 9.25/5.13      ! [A2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13        ( ( ? [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ A2 ) )
% 9.25/5.13        = ( A2 != bot_bo7824918357723582233_nat_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1001_ex__in__conv,axiom,
% 9.25/5.13      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( ? [X3: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X3 @ A2 ) )
% 9.25/5.13        = ( A2 != bot_bo2099793752762293965at_nat ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1002_ex__in__conv,axiom,
% 9.25/5.13      ! [A2: set_o] :
% 9.25/5.13        ( ( ? [X3: $o] : ( member_o @ X3 @ A2 ) )
% 9.25/5.13        = ( A2 != bot_bot_set_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1003_ex__in__conv,axiom,
% 9.25/5.13      ! [A2: set_nat] :
% 9.25/5.13        ( ( ? [X3: nat] : ( member_nat @ X3 @ A2 ) )
% 9.25/5.13        = ( A2 != bot_bot_set_nat ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1004_ex__in__conv,axiom,
% 9.25/5.13      ! [A2: set_int] :
% 9.25/5.13        ( ( ? [X3: int] : ( member_int @ X3 @ A2 ) )
% 9.25/5.13        = ( A2 != bot_bot_set_int ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1005_bot__set__def,axiom,
% 9.25/5.13      ( bot_bo1488462491386950373nt_int
% 9.25/5.13      = ( collec5210948495886036740nt_int @ bot_bo2686080419298087992_int_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1006_bot__set__def,axiom,
% 9.25/5.13      ( bot_bot_set_set_nat
% 9.25/5.13      = ( collect_set_nat @ bot_bot_set_nat_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1007_bot__set__def,axiom,
% 9.25/5.13      ( bot_bo7824918357723582233_nat_o
% 9.25/5.13      = ( collec939566748876313656_nat_o @ bot_bo7963750851167320836at_o_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1008_bot__set__def,axiom,
% 9.25/5.13      ( bot_bo2099793752762293965at_nat
% 9.25/5.13      = ( collec3392354462482085612at_nat @ bot_bo482883023278783056_nat_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1009_bot__set__def,axiom,
% 9.25/5.13      ( bot_bot_set_o
% 9.25/5.13      = ( collect_o @ bot_bot_o_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1010_bot__set__def,axiom,
% 9.25/5.13      ( bot_bot_set_nat
% 9.25/5.13      = ( collect_nat @ bot_bot_nat_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1011_bot__set__def,axiom,
% 9.25/5.13      ( bot_bot_set_int
% 9.25/5.13      = ( collect_int @ bot_bot_int_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1012_Compl__UNIV__eq,axiom,
% 9.25/5.13      ( ( uminus6524753893492686040at_nat @ top_to4669805908274784177at_nat )
% 9.25/5.13      = bot_bo2099793752762293965at_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1013_Compl__UNIV__eq,axiom,
% 9.25/5.13      ( ( uminus3195874150345416415st_nat @ top_top_set_list_nat )
% 9.25/5.13      = bot_bot_set_list_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1014_Compl__UNIV__eq,axiom,
% 9.25/5.13      ( ( uminus_uminus_set_o @ top_top_set_o )
% 9.25/5.13      = bot_bot_set_o ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1015_Compl__UNIV__eq,axiom,
% 9.25/5.13      ( ( uminus2201863774496077783et_rat @ top_top_set_rat )
% 9.25/5.13      = bot_bot_set_rat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1016_Compl__UNIV__eq,axiom,
% 9.25/5.13      ( ( uminus5710092332889474511et_nat @ top_top_set_nat )
% 9.25/5.13      = bot_bot_set_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1017_Compl__UNIV__eq,axiom,
% 9.25/5.13      ( ( uminus1532241313380277803et_int @ top_top_set_int )
% 9.25/5.13      = bot_bot_set_int ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1018_Compl__empty__eq,axiom,
% 9.25/5.13      ( ( uminus6524753893492686040at_nat @ bot_bo2099793752762293965at_nat )
% 9.25/5.13      = top_to4669805908274784177at_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1019_Compl__empty__eq,axiom,
% 9.25/5.13      ( ( uminus3195874150345416415st_nat @ bot_bot_set_list_nat )
% 9.25/5.13      = top_top_set_list_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1020_Compl__empty__eq,axiom,
% 9.25/5.13      ( ( uminus_uminus_set_o @ bot_bot_set_o )
% 9.25/5.13      = top_top_set_o ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1021_Compl__empty__eq,axiom,
% 9.25/5.13      ( ( uminus2201863774496077783et_rat @ bot_bot_set_rat )
% 9.25/5.13      = top_top_set_rat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1022_Compl__empty__eq,axiom,
% 9.25/5.13      ( ( uminus5710092332889474511et_nat @ bot_bot_set_nat )
% 9.25/5.13      = top_top_set_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1023_Compl__empty__eq,axiom,
% 9.25/5.13      ( ( uminus1532241313380277803et_int @ bot_bot_set_int )
% 9.25/5.13      = top_top_set_int ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1024_empty__not__UNIV,axiom,
% 9.25/5.13      bot_bo2099793752762293965at_nat != top_to4669805908274784177at_nat ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1025_empty__not__UNIV,axiom,
% 9.25/5.13      bot_bot_set_list_nat != top_top_set_list_nat ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1026_empty__not__UNIV,axiom,
% 9.25/5.13      bot_bot_set_o != top_top_set_o ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1027_empty__not__UNIV,axiom,
% 9.25/5.13      bot_bot_set_rat != top_top_set_rat ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1028_empty__not__UNIV,axiom,
% 9.25/5.13      bot_bot_set_nat != top_top_set_nat ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1029_empty__not__UNIV,axiom,
% 9.25/5.13      bot_bot_set_int != top_top_set_int ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1030_IntE,axiom,
% 9.25/5.13      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.13        ( ( member2340774599025711042nt_int @ C @ ( inf_in8396524679539076455nt_int @ A2 @ B2 ) )
% 9.25/5.13       => ~ ( ( member2340774599025711042nt_int @ C @ A2 )
% 9.25/5.13           => ~ ( member2340774599025711042nt_int @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1031_IntE,axiom,
% 9.25/5.13      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 9.25/5.13        ( ( member_set_nat @ C @ ( inf_inf_set_set_nat @ A2 @ B2 ) )
% 9.25/5.13       => ~ ( ( member_set_nat @ C @ A2 )
% 9.25/5.13           => ~ ( member_set_nat @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1032_IntE,axiom,
% 9.25/5.13      ! [C: int,A2: set_int,B2: set_int] :
% 9.25/5.13        ( ( member_int @ C @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.13       => ~ ( ( member_int @ C @ A2 )
% 9.25/5.13           => ~ ( member_int @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1033_IntE,axiom,
% 9.25/5.13      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13        ( ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) )
% 9.25/5.13       => ~ ( ( member6576561426505652726_nat_o @ C @ A2 )
% 9.25/5.13           => ~ ( member6576561426505652726_nat_o @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1034_IntE,axiom,
% 9.25/5.13      ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 9.25/5.13       => ~ ( ( member8440522571783428010at_nat @ C @ A2 )
% 9.25/5.13           => ~ ( member8440522571783428010at_nat @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1035_IntE,axiom,
% 9.25/5.13      ! [C: nat,A2: set_nat,B2: set_nat] :
% 9.25/5.13        ( ( member_nat @ C @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.13       => ~ ( ( member_nat @ C @ A2 )
% 9.25/5.13           => ~ ( member_nat @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1036_IntD1,axiom,
% 9.25/5.13      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.13        ( ( member2340774599025711042nt_int @ C @ ( inf_in8396524679539076455nt_int @ A2 @ B2 ) )
% 9.25/5.13       => ( member2340774599025711042nt_int @ C @ A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1037_IntD1,axiom,
% 9.25/5.13      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 9.25/5.13        ( ( member_set_nat @ C @ ( inf_inf_set_set_nat @ A2 @ B2 ) )
% 9.25/5.13       => ( member_set_nat @ C @ A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1038_IntD1,axiom,
% 9.25/5.13      ! [C: int,A2: set_int,B2: set_int] :
% 9.25/5.13        ( ( member_int @ C @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.13       => ( member_int @ C @ A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1039_IntD1,axiom,
% 9.25/5.13      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13        ( ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) )
% 9.25/5.13       => ( member6576561426505652726_nat_o @ C @ A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1040_IntD1,axiom,
% 9.25/5.13      ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 9.25/5.13       => ( member8440522571783428010at_nat @ C @ A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1041_IntD1,axiom,
% 9.25/5.13      ! [C: nat,A2: set_nat,B2: set_nat] :
% 9.25/5.13        ( ( member_nat @ C @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.13       => ( member_nat @ C @ A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1042_IntD2,axiom,
% 9.25/5.13      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.13        ( ( member2340774599025711042nt_int @ C @ ( inf_in8396524679539076455nt_int @ A2 @ B2 ) )
% 9.25/5.13       => ( member2340774599025711042nt_int @ C @ B2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1043_IntD2,axiom,
% 9.25/5.13      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 9.25/5.13        ( ( member_set_nat @ C @ ( inf_inf_set_set_nat @ A2 @ B2 ) )
% 9.25/5.13       => ( member_set_nat @ C @ B2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1044_IntD2,axiom,
% 9.25/5.13      ! [C: int,A2: set_int,B2: set_int] :
% 9.25/5.13        ( ( member_int @ C @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.13       => ( member_int @ C @ B2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1045_IntD2,axiom,
% 9.25/5.13      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13        ( ( member6576561426505652726_nat_o @ C @ ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) )
% 9.25/5.13       => ( member6576561426505652726_nat_o @ C @ B2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1046_IntD2,axiom,
% 9.25/5.13      ! [C: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 9.25/5.13       => ( member8440522571783428010at_nat @ C @ B2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1047_IntD2,axiom,
% 9.25/5.13      ! [C: nat,A2: set_nat,B2: set_nat] :
% 9.25/5.13        ( ( member_nat @ C @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.13       => ( member_nat @ C @ B2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1048_Int__assoc,axiom,
% 9.25/5.13      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.13        = ( inf_in2572325071724192079at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1049_Int__assoc,axiom,
% 9.25/5.13      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 9.25/5.13        ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.13        = ( inf_inf_set_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1050_Int__absorb,axiom,
% 9.25/5.13      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( inf_in2572325071724192079at_nat @ A2 @ A2 )
% 9.25/5.13        = A2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1051_Int__absorb,axiom,
% 9.25/5.13      ! [A2: set_nat] :
% 9.25/5.13        ( ( inf_inf_set_nat @ A2 @ A2 )
% 9.25/5.13        = A2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1052_Int__commute,axiom,
% 9.25/5.13      ( inf_in2572325071724192079at_nat
% 9.25/5.13      = ( ^ [A4: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ B4 @ A4 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1053_Int__commute,axiom,
% 9.25/5.13      ( inf_inf_set_nat
% 9.25/5.13      = ( ^ [A4: set_nat,B4: set_nat] : ( inf_inf_set_nat @ B4 @ A4 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1054_Int__UNIV__left,axiom,
% 9.25/5.13      ! [B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( inf_in2572325071724192079at_nat @ top_to4669805908274784177at_nat @ B2 )
% 9.25/5.13        = B2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1055_Int__UNIV__left,axiom,
% 9.25/5.13      ! [B2: set_list_nat] :
% 9.25/5.13        ( ( inf_inf_set_list_nat @ top_top_set_list_nat @ B2 )
% 9.25/5.13        = B2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1056_Int__UNIV__left,axiom,
% 9.25/5.13      ! [B2: set_o] :
% 9.25/5.13        ( ( inf_inf_set_o @ top_top_set_o @ B2 )
% 9.25/5.13        = B2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1057_Int__UNIV__left,axiom,
% 9.25/5.13      ! [B2: set_rat] :
% 9.25/5.13        ( ( inf_inf_set_rat @ top_top_set_rat @ B2 )
% 9.25/5.13        = B2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1058_Int__UNIV__left,axiom,
% 9.25/5.13      ! [B2: set_nat] :
% 9.25/5.13        ( ( inf_inf_set_nat @ top_top_set_nat @ B2 )
% 9.25/5.13        = B2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1059_Int__UNIV__left,axiom,
% 9.25/5.13      ! [B2: set_int] :
% 9.25/5.13        ( ( inf_inf_set_int @ top_top_set_int @ B2 )
% 9.25/5.13        = B2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1060_Int__UNIV__right,axiom,
% 9.25/5.13      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( inf_in2572325071724192079at_nat @ A2 @ top_to4669805908274784177at_nat )
% 9.25/5.13        = A2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1061_Int__UNIV__right,axiom,
% 9.25/5.13      ! [A2: set_list_nat] :
% 9.25/5.13        ( ( inf_inf_set_list_nat @ A2 @ top_top_set_list_nat )
% 9.25/5.13        = A2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1062_Int__UNIV__right,axiom,
% 9.25/5.13      ! [A2: set_o] :
% 9.25/5.13        ( ( inf_inf_set_o @ A2 @ top_top_set_o )
% 9.25/5.13        = A2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1063_Int__UNIV__right,axiom,
% 9.25/5.13      ! [A2: set_rat] :
% 9.25/5.13        ( ( inf_inf_set_rat @ A2 @ top_top_set_rat )
% 9.25/5.13        = A2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1064_Int__UNIV__right,axiom,
% 9.25/5.13      ! [A2: set_nat] :
% 9.25/5.13        ( ( inf_inf_set_nat @ A2 @ top_top_set_nat )
% 9.25/5.13        = A2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1065_Int__UNIV__right,axiom,
% 9.25/5.13      ! [A2: set_int] :
% 9.25/5.13        ( ( inf_inf_set_int @ A2 @ top_top_set_int )
% 9.25/5.13        = A2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1066_Int__left__absorb,axiom,
% 9.25/5.13      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( inf_in2572325071724192079at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 9.25/5.13        = ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1067_Int__left__absorb,axiom,
% 9.25/5.13      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.13        ( ( inf_inf_set_nat @ A2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.13        = ( inf_inf_set_nat @ A2 @ B2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1068_Int__left__commute,axiom,
% 9.25/5.13      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( inf_in2572325071724192079at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) )
% 9.25/5.13        = ( inf_in2572325071724192079at_nat @ B2 @ ( inf_in2572325071724192079at_nat @ A2 @ C2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1069_Int__left__commute,axiom,
% 9.25/5.13      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 9.25/5.13        ( ( inf_inf_set_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C2 ) )
% 9.25/5.13        = ( inf_inf_set_nat @ B2 @ ( inf_inf_set_nat @ A2 @ C2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1070_UnE,axiom,
% 9.25/5.13      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.13        ( ( member2340774599025711042nt_int @ C @ ( sup_su2047564715030645325nt_int @ A2 @ B2 ) )
% 9.25/5.13       => ( ~ ( member2340774599025711042nt_int @ C @ A2 )
% 9.25/5.13         => ( member2340774599025711042nt_int @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1071_UnE,axiom,
% 9.25/5.13      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 9.25/5.13        ( ( member_set_nat @ C @ ( sup_sup_set_set_nat @ A2 @ B2 ) )
% 9.25/5.13       => ( ~ ( member_set_nat @ C @ A2 )
% 9.25/5.13         => ( member_set_nat @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1072_UnE,axiom,
% 9.25/5.13      ! [C: int,A2: set_int,B2: set_int] :
% 9.25/5.13        ( ( member_int @ C @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.13       => ( ~ ( member_int @ C @ A2 )
% 9.25/5.13         => ( member_int @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1073_UnE,axiom,
% 9.25/5.13      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13        ( ( member6576561426505652726_nat_o @ C @ ( sup_su5209123915105501825_nat_o @ A2 @ B2 ) )
% 9.25/5.13       => ( ~ ( member6576561426505652726_nat_o @ C @ A2 )
% 9.25/5.13         => ( member6576561426505652726_nat_o @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1074_UnE,axiom,
% 9.25/5.13      ! [C: produc4166570645942440679at_nat,A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( member6689249552917799696at_nat @ C @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 9.25/5.13       => ( ~ ( member6689249552917799696at_nat @ C @ A2 )
% 9.25/5.13         => ( member6689249552917799696at_nat @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1075_UnE,axiom,
% 9.25/5.13      ! [C: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 9.25/5.13       => ( ~ ( member8757157785044589968at_nat @ C @ A2 )
% 9.25/5.13         => ( member8757157785044589968at_nat @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1076_UnE,axiom,
% 9.25/5.13      ! [C: nat,A2: set_nat,B2: set_nat] :
% 9.25/5.13        ( ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.13       => ( ~ ( member_nat @ C @ A2 )
% 9.25/5.13         => ( member_nat @ C @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1077_UnI1,axiom,
% 9.25/5.13      ! [C: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.13        ( ( member2340774599025711042nt_int @ C @ A2 )
% 9.25/5.13       => ( member2340774599025711042nt_int @ C @ ( sup_su2047564715030645325nt_int @ A2 @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1078_UnI1,axiom,
% 9.25/5.13      ! [C: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 9.25/5.13        ( ( member_set_nat @ C @ A2 )
% 9.25/5.13       => ( member_set_nat @ C @ ( sup_sup_set_set_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1079_UnI1,axiom,
% 9.25/5.13      ! [C: int,A2: set_int,B2: set_int] :
% 9.25/5.13        ( ( member_int @ C @ A2 )
% 9.25/5.13       => ( member_int @ C @ ( sup_sup_set_int @ A2 @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1080_UnI1,axiom,
% 9.25/5.13      ! [C: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13        ( ( member6576561426505652726_nat_o @ C @ A2 )
% 9.25/5.13       => ( member6576561426505652726_nat_o @ C @ ( sup_su5209123915105501825_nat_o @ A2 @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1081_UnI1,axiom,
% 9.25/5.13      ! [C: produc4166570645942440679at_nat,A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( member6689249552917799696at_nat @ C @ A2 )
% 9.25/5.13       => ( member6689249552917799696at_nat @ C @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1082_UnI1,axiom,
% 9.25/5.13      ! [C: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( member8757157785044589968at_nat @ C @ A2 )
% 9.25/5.13       => ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1083_UnI1,axiom,
% 9.25/5.13      ! [C: nat,A2: set_nat,B2: set_nat] :
% 9.25/5.13        ( ( member_nat @ C @ A2 )
% 9.25/5.13       => ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1084_UnI2,axiom,
% 9.25/5.13      ! [C: set_Pr958786334691620121nt_int,B2: set_se6260736226359567993nt_int,A2: set_se6260736226359567993nt_int] :
% 9.25/5.13        ( ( member2340774599025711042nt_int @ C @ B2 )
% 9.25/5.13       => ( member2340774599025711042nt_int @ C @ ( sup_su2047564715030645325nt_int @ A2 @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1085_UnI2,axiom,
% 9.25/5.13      ! [C: set_nat,B2: set_set_nat,A2: set_set_nat] :
% 9.25/5.13        ( ( member_set_nat @ C @ B2 )
% 9.25/5.13       => ( member_set_nat @ C @ ( sup_sup_set_set_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1086_UnI2,axiom,
% 9.25/5.13      ! [C: int,B2: set_int,A2: set_int] :
% 9.25/5.13        ( ( member_int @ C @ B2 )
% 9.25/5.13       => ( member_int @ C @ ( sup_sup_set_int @ A2 @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1087_UnI2,axiom,
% 9.25/5.13      ! [C: produc3658429121746597890et_nat > $o,B2: set_Pr4532377907799695533_nat_o,A2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13        ( ( member6576561426505652726_nat_o @ C @ B2 )
% 9.25/5.13       => ( member6576561426505652726_nat_o @ C @ ( sup_su5209123915105501825_nat_o @ A2 @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1088_UnI2,axiom,
% 9.25/5.13      ! [C: produc4166570645942440679at_nat,B2: set_Pr8551490117392284871at_nat,A2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( member6689249552917799696at_nat @ C @ B2 )
% 9.25/5.13       => ( member6689249552917799696at_nat @ C @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1089_UnI2,axiom,
% 9.25/5.13      ! [C: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( member8757157785044589968at_nat @ C @ B2 )
% 9.25/5.13       => ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1090_UnI2,axiom,
% 9.25/5.13      ! [C: nat,B2: set_nat,A2: set_nat] :
% 9.25/5.13        ( ( member_nat @ C @ B2 )
% 9.25/5.13       => ( member_nat @ C @ ( sup_sup_set_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1091_bex__Un,axiom,
% 9.25/5.13      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,P: produc4166570645942440679at_nat > $o] :
% 9.25/5.13        ( ( ? [X3: produc4166570645942440679at_nat] :
% 9.25/5.13              ( ( member6689249552917799696at_nat @ X3 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 9.25/5.13              & ( P @ X3 ) ) )
% 9.25/5.13        = ( ? [X3: produc4166570645942440679at_nat] :
% 9.25/5.13              ( ( member6689249552917799696at_nat @ X3 @ A2 )
% 9.25/5.13              & ( P @ X3 ) )
% 9.25/5.13          | ? [X3: produc4166570645942440679at_nat] :
% 9.25/5.13              ( ( member6689249552917799696at_nat @ X3 @ B2 )
% 9.25/5.13              & ( P @ X3 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1092_bex__Un,axiom,
% 9.25/5.13      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,P: produc3843707927480180839at_nat > $o] :
% 9.25/5.13        ( ( ? [X3: produc3843707927480180839at_nat] :
% 9.25/5.13              ( ( member8757157785044589968at_nat @ X3 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 9.25/5.13              & ( P @ X3 ) ) )
% 9.25/5.13        = ( ? [X3: produc3843707927480180839at_nat] :
% 9.25/5.13              ( ( member8757157785044589968at_nat @ X3 @ A2 )
% 9.25/5.13              & ( P @ X3 ) )
% 9.25/5.13          | ? [X3: produc3843707927480180839at_nat] :
% 9.25/5.13              ( ( member8757157785044589968at_nat @ X3 @ B2 )
% 9.25/5.13              & ( P @ X3 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1093_bex__Un,axiom,
% 9.25/5.13      ! [A2: set_nat,B2: set_nat,P: nat > $o] :
% 9.25/5.13        ( ( ? [X3: nat] :
% 9.25/5.13              ( ( member_nat @ X3 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.13              & ( P @ X3 ) ) )
% 9.25/5.13        = ( ? [X3: nat] :
% 9.25/5.13              ( ( member_nat @ X3 @ A2 )
% 9.25/5.13              & ( P @ X3 ) )
% 9.25/5.13          | ? [X3: nat] :
% 9.25/5.13              ( ( member_nat @ X3 @ B2 )
% 9.25/5.13              & ( P @ X3 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1094_ball__Un,axiom,
% 9.25/5.13      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,P: produc4166570645942440679at_nat > $o] :
% 9.25/5.13        ( ( ! [X3: produc4166570645942440679at_nat] :
% 9.25/5.13              ( ( member6689249552917799696at_nat @ X3 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 9.25/5.13             => ( P @ X3 ) ) )
% 9.25/5.13        = ( ! [X3: produc4166570645942440679at_nat] :
% 9.25/5.13              ( ( member6689249552917799696at_nat @ X3 @ A2 )
% 9.25/5.13             => ( P @ X3 ) )
% 9.25/5.13          & ! [X3: produc4166570645942440679at_nat] :
% 9.25/5.13              ( ( member6689249552917799696at_nat @ X3 @ B2 )
% 9.25/5.13             => ( P @ X3 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1095_ball__Un,axiom,
% 9.25/5.13      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,P: produc3843707927480180839at_nat > $o] :
% 9.25/5.13        ( ( ! [X3: produc3843707927480180839at_nat] :
% 9.25/5.13              ( ( member8757157785044589968at_nat @ X3 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 9.25/5.13             => ( P @ X3 ) ) )
% 9.25/5.13        = ( ! [X3: produc3843707927480180839at_nat] :
% 9.25/5.13              ( ( member8757157785044589968at_nat @ X3 @ A2 )
% 9.25/5.13             => ( P @ X3 ) )
% 9.25/5.13          & ! [X3: produc3843707927480180839at_nat] :
% 9.25/5.13              ( ( member8757157785044589968at_nat @ X3 @ B2 )
% 9.25/5.13             => ( P @ X3 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1096_ball__Un,axiom,
% 9.25/5.13      ! [A2: set_nat,B2: set_nat,P: nat > $o] :
% 9.25/5.13        ( ( ! [X3: nat] :
% 9.25/5.13              ( ( member_nat @ X3 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.13             => ( P @ X3 ) ) )
% 9.25/5.13        = ( ! [X3: nat] :
% 9.25/5.13              ( ( member_nat @ X3 @ A2 )
% 9.25/5.13             => ( P @ X3 ) )
% 9.25/5.13          & ! [X3: nat] :
% 9.25/5.13              ( ( member_nat @ X3 @ B2 )
% 9.25/5.13             => ( P @ X3 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1097_Un__assoc,axiom,
% 9.25/5.13      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.13        = ( sup_su3035147773818789531at_nat @ A2 @ ( sup_su3035147773818789531at_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1098_Un__assoc,axiom,
% 9.25/5.13      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.13        = ( sup_su5525570899277871387at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1099_Un__assoc,axiom,
% 9.25/5.13      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 9.25/5.13        ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.13        = ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1100_Un__absorb,axiom,
% 9.25/5.13      ! [A2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( sup_su3035147773818789531at_nat @ A2 @ A2 )
% 9.25/5.13        = A2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1101_Un__absorb,axiom,
% 9.25/5.13      ! [A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( sup_su5525570899277871387at_nat @ A2 @ A2 )
% 9.25/5.13        = A2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1102_Un__absorb,axiom,
% 9.25/5.13      ! [A2: set_nat] :
% 9.25/5.13        ( ( sup_sup_set_nat @ A2 @ A2 )
% 9.25/5.13        = A2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1103_Un__commute,axiom,
% 9.25/5.13      ( sup_su3035147773818789531at_nat
% 9.25/5.13      = ( ^ [A4: set_Pr8551490117392284871at_nat,B4: set_Pr8551490117392284871at_nat] : ( sup_su3035147773818789531at_nat @ B4 @ A4 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1104_Un__commute,axiom,
% 9.25/5.13      ( sup_su5525570899277871387at_nat
% 9.25/5.13      = ( ^ [A4: set_Pr4329608150637261639at_nat,B4: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ B4 @ A4 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1105_Un__commute,axiom,
% 9.25/5.13      ( sup_sup_set_nat
% 9.25/5.13      = ( ^ [A4: set_nat,B4: set_nat] : ( sup_sup_set_nat @ B4 @ A4 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1106_Un__UNIV__left,axiom,
% 9.25/5.13      ! [B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( sup_su3035147773818789531at_nat @ top_to8764741339697478167at_nat @ B2 )
% 9.25/5.13        = top_to8764741339697478167at_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1107_Un__UNIV__left,axiom,
% 9.25/5.13      ! [B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( sup_su5525570899277871387at_nat @ top_to6833984726390702231at_nat @ B2 )
% 9.25/5.13        = top_to6833984726390702231at_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1108_Un__UNIV__left,axiom,
% 9.25/5.13      ! [B2: set_list_nat] :
% 9.25/5.13        ( ( sup_sup_set_list_nat @ top_top_set_list_nat @ B2 )
% 9.25/5.13        = top_top_set_list_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1109_Un__UNIV__left,axiom,
% 9.25/5.13      ! [B2: set_o] :
% 9.25/5.13        ( ( sup_sup_set_o @ top_top_set_o @ B2 )
% 9.25/5.13        = top_top_set_o ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1110_Un__UNIV__left,axiom,
% 9.25/5.13      ! [B2: set_rat] :
% 9.25/5.13        ( ( sup_sup_set_rat @ top_top_set_rat @ B2 )
% 9.25/5.13        = top_top_set_rat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1111_Un__UNIV__left,axiom,
% 9.25/5.13      ! [B2: set_nat] :
% 9.25/5.13        ( ( sup_sup_set_nat @ top_top_set_nat @ B2 )
% 9.25/5.13        = top_top_set_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1112_Un__UNIV__left,axiom,
% 9.25/5.13      ! [B2: set_int] :
% 9.25/5.13        ( ( sup_sup_set_int @ top_top_set_int @ B2 )
% 9.25/5.13        = top_top_set_int ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1113_Un__UNIV__right,axiom,
% 9.25/5.13      ! [A2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( sup_su3035147773818789531at_nat @ A2 @ top_to8764741339697478167at_nat )
% 9.25/5.13        = top_to8764741339697478167at_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1114_Un__UNIV__right,axiom,
% 9.25/5.13      ! [A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( sup_su5525570899277871387at_nat @ A2 @ top_to6833984726390702231at_nat )
% 9.25/5.13        = top_to6833984726390702231at_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1115_Un__UNIV__right,axiom,
% 9.25/5.13      ! [A2: set_list_nat] :
% 9.25/5.13        ( ( sup_sup_set_list_nat @ A2 @ top_top_set_list_nat )
% 9.25/5.13        = top_top_set_list_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1116_Un__UNIV__right,axiom,
% 9.25/5.13      ! [A2: set_o] :
% 9.25/5.13        ( ( sup_sup_set_o @ A2 @ top_top_set_o )
% 9.25/5.13        = top_top_set_o ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1117_Un__UNIV__right,axiom,
% 9.25/5.13      ! [A2: set_rat] :
% 9.25/5.13        ( ( sup_sup_set_rat @ A2 @ top_top_set_rat )
% 9.25/5.13        = top_top_set_rat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1118_Un__UNIV__right,axiom,
% 9.25/5.13      ! [A2: set_nat] :
% 9.25/5.13        ( ( sup_sup_set_nat @ A2 @ top_top_set_nat )
% 9.25/5.13        = top_top_set_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1119_Un__UNIV__right,axiom,
% 9.25/5.13      ! [A2: set_int] :
% 9.25/5.13        ( ( sup_sup_set_int @ A2 @ top_top_set_int )
% 9.25/5.13        = top_top_set_int ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1120_Un__left__absorb,axiom,
% 9.25/5.13      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( sup_su3035147773818789531at_nat @ A2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 9.25/5.13        = ( sup_su3035147773818789531at_nat @ A2 @ B2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1121_Un__left__absorb,axiom,
% 9.25/5.13      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( sup_su5525570899277871387at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 9.25/5.13        = ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1122_Un__left__absorb,axiom,
% 9.25/5.13      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.13        ( ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.13        = ( sup_sup_set_nat @ A2 @ B2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1123_Compl__partition,axiom,
% 9.25/5.13      ! [A2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( sup_su3035147773818789531at_nat @ A2 @ ( uminus2330091110623919550at_nat @ A2 ) )
% 9.25/5.13        = top_to8764741339697478167at_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1124_Compl__partition,axiom,
% 9.25/5.13      ! [A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( sup_su5525570899277871387at_nat @ A2 @ ( uminus935396558254630718at_nat @ A2 ) )
% 9.25/5.13        = top_to6833984726390702231at_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1125_Compl__partition,axiom,
% 9.25/5.13      ! [A2: set_list_nat] :
% 9.25/5.13        ( ( sup_sup_set_list_nat @ A2 @ ( uminus3195874150345416415st_nat @ A2 ) )
% 9.25/5.13        = top_top_set_list_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1126_Compl__partition,axiom,
% 9.25/5.13      ! [A2: set_o] :
% 9.25/5.13        ( ( sup_sup_set_o @ A2 @ ( uminus_uminus_set_o @ A2 ) )
% 9.25/5.13        = top_top_set_o ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1127_Compl__partition,axiom,
% 9.25/5.13      ! [A2: set_rat] :
% 9.25/5.13        ( ( sup_sup_set_rat @ A2 @ ( uminus2201863774496077783et_rat @ A2 ) )
% 9.25/5.13        = top_top_set_rat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1128_Compl__partition,axiom,
% 9.25/5.13      ! [A2: set_nat] :
% 9.25/5.13        ( ( sup_sup_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ A2 ) )
% 9.25/5.13        = top_top_set_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1129_Compl__partition,axiom,
% 9.25/5.13      ! [A2: set_int] :
% 9.25/5.13        ( ( sup_sup_set_int @ A2 @ ( uminus1532241313380277803et_int @ A2 ) )
% 9.25/5.13        = top_top_set_int ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1130_Un__left__commute,axiom,
% 9.25/5.13      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( sup_su3035147773818789531at_nat @ A2 @ ( sup_su3035147773818789531at_nat @ B2 @ C2 ) )
% 9.25/5.13        = ( sup_su3035147773818789531at_nat @ B2 @ ( sup_su3035147773818789531at_nat @ A2 @ C2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1131_Un__left__commute,axiom,
% 9.25/5.13      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( sup_su5525570899277871387at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) )
% 9.25/5.13        = ( sup_su5525570899277871387at_nat @ B2 @ ( sup_su5525570899277871387at_nat @ A2 @ C2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1132_Un__left__commute,axiom,
% 9.25/5.13      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 9.25/5.13        ( ( sup_sup_set_nat @ A2 @ ( sup_sup_set_nat @ B2 @ C2 ) )
% 9.25/5.13        = ( sup_sup_set_nat @ B2 @ ( sup_sup_set_nat @ A2 @ C2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1133_Compl__partition2,axiom,
% 9.25/5.13      ! [A2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ A2 ) @ A2 )
% 9.25/5.13        = top_to8764741339697478167at_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1134_Compl__partition2,axiom,
% 9.25/5.13      ! [A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ A2 ) @ A2 )
% 9.25/5.13        = top_to6833984726390702231at_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1135_Compl__partition2,axiom,
% 9.25/5.13      ! [A2: set_list_nat] :
% 9.25/5.13        ( ( sup_sup_set_list_nat @ ( uminus3195874150345416415st_nat @ A2 ) @ A2 )
% 9.25/5.13        = top_top_set_list_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1136_Compl__partition2,axiom,
% 9.25/5.13      ! [A2: set_o] :
% 9.25/5.13        ( ( sup_sup_set_o @ ( uminus_uminus_set_o @ A2 ) @ A2 )
% 9.25/5.13        = top_top_set_o ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1137_Compl__partition2,axiom,
% 9.25/5.13      ! [A2: set_rat] :
% 9.25/5.13        ( ( sup_sup_set_rat @ ( uminus2201863774496077783et_rat @ A2 ) @ A2 )
% 9.25/5.13        = top_top_set_rat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1138_Compl__partition2,axiom,
% 9.25/5.13      ! [A2: set_nat] :
% 9.25/5.13        ( ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ A2 )
% 9.25/5.13        = top_top_set_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1139_Compl__partition2,axiom,
% 9.25/5.13      ! [A2: set_int] :
% 9.25/5.13        ( ( sup_sup_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ A2 )
% 9.25/5.13        = top_top_set_int ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1140_Set_Oempty__def,axiom,
% 9.25/5.13      ( bot_bo1488462491386950373nt_int
% 9.25/5.13      = ( collec5210948495886036740nt_int
% 9.25/5.13        @ ^ [X3: set_Pr958786334691620121nt_int] : $false ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1141_Set_Oempty__def,axiom,
% 9.25/5.13      ( bot_bot_set_set_nat
% 9.25/5.13      = ( collect_set_nat
% 9.25/5.13        @ ^ [X3: set_nat] : $false ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1142_Set_Oempty__def,axiom,
% 9.25/5.13      ( bot_bo7824918357723582233_nat_o
% 9.25/5.13      = ( collec939566748876313656_nat_o
% 9.25/5.13        @ ^ [X3: produc3658429121746597890et_nat > $o] : $false ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1143_Set_Oempty__def,axiom,
% 9.25/5.13      ( bot_bo2099793752762293965at_nat
% 9.25/5.13      = ( collec3392354462482085612at_nat
% 9.25/5.13        @ ^ [X3: product_prod_nat_nat] : $false ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1144_Set_Oempty__def,axiom,
% 9.25/5.13      ( bot_bot_set_o
% 9.25/5.13      = ( collect_o
% 9.25/5.13        @ ^ [X3: $o] : $false ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1145_Set_Oempty__def,axiom,
% 9.25/5.13      ( bot_bot_set_nat
% 9.25/5.13      = ( collect_nat
% 9.25/5.13        @ ^ [X3: nat] : $false ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1146_Set_Oempty__def,axiom,
% 9.25/5.13      ( bot_bot_set_int
% 9.25/5.13      = ( collect_int
% 9.25/5.13        @ ^ [X3: int] : $false ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1147_Int__def,axiom,
% 9.25/5.13      ( inf_in8396524679539076455nt_int
% 9.25/5.13      = ( ^ [A4: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
% 9.25/5.13            ( collec5210948495886036740nt_int
% 9.25/5.13            @ ^ [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.13                ( ( member2340774599025711042nt_int @ X3 @ A4 )
% 9.25/5.13                & ( member2340774599025711042nt_int @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1148_Int__def,axiom,
% 9.25/5.13      ( inf_inf_set_set_nat
% 9.25/5.13      = ( ^ [A4: set_set_nat,B4: set_set_nat] :
% 9.25/5.13            ( collect_set_nat
% 9.25/5.13            @ ^ [X3: set_nat] :
% 9.25/5.13                ( ( member_set_nat @ X3 @ A4 )
% 9.25/5.13                & ( member_set_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1149_Int__def,axiom,
% 9.25/5.13      ( inf_inf_set_int
% 9.25/5.13      = ( ^ [A4: set_int,B4: set_int] :
% 9.25/5.13            ( collect_int
% 9.25/5.13            @ ^ [X3: int] :
% 9.25/5.13                ( ( member_int @ X3 @ A4 )
% 9.25/5.13                & ( member_int @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1150_Int__def,axiom,
% 9.25/5.13      ( inf_in1906310914598751387_nat_o
% 9.25/5.13      = ( ^ [A4: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13            ( collec939566748876313656_nat_o
% 9.25/5.13            @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.13                ( ( member6576561426505652726_nat_o @ X3 @ A4 )
% 9.25/5.13                & ( member6576561426505652726_nat_o @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1151_Int__def,axiom,
% 9.25/5.13      ( inf_in2572325071724192079at_nat
% 9.25/5.13      = ( ^ [A4: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 9.25/5.13            ( collec3392354462482085612at_nat
% 9.25/5.13            @ ^ [X3: product_prod_nat_nat] :
% 9.25/5.13                ( ( member8440522571783428010at_nat @ X3 @ A4 )
% 9.25/5.13                & ( member8440522571783428010at_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1152_Int__def,axiom,
% 9.25/5.13      ( inf_inf_set_nat
% 9.25/5.13      = ( ^ [A4: set_nat,B4: set_nat] :
% 9.25/5.13            ( collect_nat
% 9.25/5.13            @ ^ [X3: nat] :
% 9.25/5.13                ( ( member_nat @ X3 @ A4 )
% 9.25/5.13                & ( member_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1153_Int__Collect,axiom,
% 9.25/5.13      ! [X: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.13        ( ( member2340774599025711042nt_int @ X @ ( inf_in8396524679539076455nt_int @ A2 @ ( collec5210948495886036740nt_int @ P ) ) )
% 9.25/5.13        = ( ( member2340774599025711042nt_int @ X @ A2 )
% 9.25/5.13          & ( P @ X ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1154_Int__Collect,axiom,
% 9.25/5.13      ! [X: set_nat,A2: set_set_nat,P: set_nat > $o] :
% 9.25/5.13        ( ( member_set_nat @ X @ ( inf_inf_set_set_nat @ A2 @ ( collect_set_nat @ P ) ) )
% 9.25/5.13        = ( ( member_set_nat @ X @ A2 )
% 9.25/5.13          & ( P @ X ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1155_Int__Collect,axiom,
% 9.25/5.13      ! [X: int,A2: set_int,P: int > $o] :
% 9.25/5.13        ( ( member_int @ X @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) )
% 9.25/5.13        = ( ( member_int @ X @ A2 )
% 9.25/5.13          & ( P @ X ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1156_Int__Collect,axiom,
% 9.25/5.13      ! [X: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.13        ( ( member6576561426505652726_nat_o @ X @ ( inf_in1906310914598751387_nat_o @ A2 @ ( collec939566748876313656_nat_o @ P ) ) )
% 9.25/5.13        = ( ( member6576561426505652726_nat_o @ X @ A2 )
% 9.25/5.13          & ( P @ X ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1157_Int__Collect,axiom,
% 9.25/5.13      ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o] :
% 9.25/5.13        ( ( member8440522571783428010at_nat @ X @ ( inf_in2572325071724192079at_nat @ A2 @ ( collec3392354462482085612at_nat @ P ) ) )
% 9.25/5.13        = ( ( member8440522571783428010at_nat @ X @ A2 )
% 9.25/5.13          & ( P @ X ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1158_Int__Collect,axiom,
% 9.25/5.13      ! [X: nat,A2: set_nat,P: nat > $o] :
% 9.25/5.13        ( ( member_nat @ X @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) )
% 9.25/5.13        = ( ( member_nat @ X @ A2 )
% 9.25/5.13          & ( P @ X ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1159_inf__set__def,axiom,
% 9.25/5.13      ( inf_in8396524679539076455nt_int
% 9.25/5.13      = ( ^ [A4: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
% 9.25/5.13            ( collec5210948495886036740nt_int
% 9.25/5.13            @ ( inf_in5102985939729578038_int_o
% 9.25/5.13              @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ A4 )
% 9.25/5.13              @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1160_inf__set__def,axiom,
% 9.25/5.13      ( inf_inf_set_set_nat
% 9.25/5.13      = ( ^ [A4: set_set_nat,B4: set_set_nat] :
% 9.25/5.13            ( collect_set_nat
% 9.25/5.13            @ ( inf_inf_set_nat_o
% 9.25/5.13              @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A4 )
% 9.25/5.13              @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1161_inf__set__def,axiom,
% 9.25/5.13      ( inf_inf_set_int
% 9.25/5.13      = ( ^ [A4: set_int,B4: set_int] :
% 9.25/5.13            ( collect_int
% 9.25/5.13            @ ( inf_inf_int_o
% 9.25/5.13              @ ^ [X3: int] : ( member_int @ X3 @ A4 )
% 9.25/5.13              @ ^ [X3: int] : ( member_int @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1162_inf__set__def,axiom,
% 9.25/5.13      ( inf_in1906310914598751387_nat_o
% 9.25/5.13      = ( ^ [A4: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13            ( collec939566748876313656_nat_o
% 9.25/5.13            @ ( inf_in9018898317438245890at_o_o
% 9.25/5.13              @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ A4 )
% 9.25/5.13              @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1163_inf__set__def,axiom,
% 9.25/5.13      ( inf_in2269163501485487111nt_int
% 9.25/5.13      = ( ^ [A4: set_Pr958786334691620121nt_int,B4: set_Pr958786334691620121nt_int] :
% 9.25/5.13            ( collec213857154873943460nt_int
% 9.25/5.13            @ ( inf_in3604695632404883862_int_o
% 9.25/5.13              @ ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ A4 )
% 9.25/5.13              @ ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1164_inf__set__def,axiom,
% 9.25/5.13      ( inf_in6177012701088388009t_char
% 9.25/5.13      = ( ^ [A4: set_list_char,B4: set_list_char] :
% 9.25/5.13            ( collect_list_char
% 9.25/5.13            @ ( inf_inf_list_char_o
% 9.25/5.13              @ ^ [X3: list_char] : ( member_list_char @ X3 @ A4 )
% 9.25/5.13              @ ^ [X3: list_char] : ( member_list_char @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1165_inf__set__def,axiom,
% 9.25/5.13      ( inf_in2572325071724192079at_nat
% 9.25/5.13      = ( ^ [A4: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 9.25/5.13            ( collec3392354462482085612at_nat
% 9.25/5.13            @ ( inf_in5163264567034779214_nat_o
% 9.25/5.13              @ ^ [X3: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X3 @ A4 )
% 9.25/5.13              @ ^ [X3: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1166_inf__set__def,axiom,
% 9.25/5.13      ( inf_inf_set_nat
% 9.25/5.13      = ( ^ [A4: set_nat,B4: set_nat] :
% 9.25/5.13            ( collect_nat
% 9.25/5.13            @ ( inf_inf_nat_o
% 9.25/5.13              @ ^ [X3: nat] : ( member_nat @ X3 @ A4 )
% 9.25/5.13              @ ^ [X3: nat] : ( member_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1167_Collect__conj__eq,axiom,
% 9.25/5.13      ! [P: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.13        ( ( collec5210948495886036740nt_int
% 9.25/5.13          @ ^ [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.13              ( ( P @ X3 )
% 9.25/5.13              & ( Q2 @ X3 ) ) )
% 9.25/5.13        = ( inf_in8396524679539076455nt_int @ ( collec5210948495886036740nt_int @ P ) @ ( collec5210948495886036740nt_int @ Q2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1168_Collect__conj__eq,axiom,
% 9.25/5.13      ! [P: set_nat > $o,Q2: set_nat > $o] :
% 9.25/5.13        ( ( collect_set_nat
% 9.25/5.13          @ ^ [X3: set_nat] :
% 9.25/5.13              ( ( P @ X3 )
% 9.25/5.13              & ( Q2 @ X3 ) ) )
% 9.25/5.13        = ( inf_inf_set_set_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1169_Collect__conj__eq,axiom,
% 9.25/5.13      ! [P: int > $o,Q2: int > $o] :
% 9.25/5.13        ( ( collect_int
% 9.25/5.13          @ ^ [X3: int] :
% 9.25/5.13              ( ( P @ X3 )
% 9.25/5.13              & ( Q2 @ X3 ) ) )
% 9.25/5.13        = ( inf_inf_set_int @ ( collect_int @ P ) @ ( collect_int @ Q2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1170_Collect__conj__eq,axiom,
% 9.25/5.13      ! [P: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.13        ( ( collec939566748876313656_nat_o
% 9.25/5.13          @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.13              ( ( P @ X3 )
% 9.25/5.13              & ( Q2 @ X3 ) ) )
% 9.25/5.13        = ( inf_in1906310914598751387_nat_o @ ( collec939566748876313656_nat_o @ P ) @ ( collec939566748876313656_nat_o @ Q2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1171_Collect__conj__eq,axiom,
% 9.25/5.13      ! [P: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > $o] :
% 9.25/5.13        ( ( collec3392354462482085612at_nat
% 9.25/5.13          @ ^ [X3: product_prod_nat_nat] :
% 9.25/5.13              ( ( P @ X3 )
% 9.25/5.13              & ( Q2 @ X3 ) ) )
% 9.25/5.13        = ( inf_in2572325071724192079at_nat @ ( collec3392354462482085612at_nat @ P ) @ ( collec3392354462482085612at_nat @ Q2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1172_Collect__conj__eq,axiom,
% 9.25/5.13      ! [P: nat > $o,Q2: nat > $o] :
% 9.25/5.13        ( ( collect_nat
% 9.25/5.13          @ ^ [X3: nat] :
% 9.25/5.13              ( ( P @ X3 )
% 9.25/5.13              & ( Q2 @ X3 ) ) )
% 9.25/5.13        = ( inf_inf_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1173_Un__def,axiom,
% 9.25/5.13      ( sup_su2047564715030645325nt_int
% 9.25/5.13      = ( ^ [A4: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
% 9.25/5.13            ( collec5210948495886036740nt_int
% 9.25/5.13            @ ^ [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.13                ( ( member2340774599025711042nt_int @ X3 @ A4 )
% 9.25/5.13                | ( member2340774599025711042nt_int @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1174_Un__def,axiom,
% 9.25/5.13      ( sup_sup_set_set_nat
% 9.25/5.13      = ( ^ [A4: set_set_nat,B4: set_set_nat] :
% 9.25/5.13            ( collect_set_nat
% 9.25/5.13            @ ^ [X3: set_nat] :
% 9.25/5.13                ( ( member_set_nat @ X3 @ A4 )
% 9.25/5.13                | ( member_set_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1175_Un__def,axiom,
% 9.25/5.13      ( sup_sup_set_int
% 9.25/5.13      = ( ^ [A4: set_int,B4: set_int] :
% 9.25/5.13            ( collect_int
% 9.25/5.13            @ ^ [X3: int] :
% 9.25/5.13                ( ( member_int @ X3 @ A4 )
% 9.25/5.13                | ( member_int @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1176_Un__def,axiom,
% 9.25/5.13      ( sup_su5209123915105501825_nat_o
% 9.25/5.13      = ( ^ [A4: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13            ( collec939566748876313656_nat_o
% 9.25/5.13            @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.13                ( ( member6576561426505652726_nat_o @ X3 @ A4 )
% 9.25/5.13                | ( member6576561426505652726_nat_o @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1177_Un__def,axiom,
% 9.25/5.13      ( sup_su3035147773818789531at_nat
% 9.25/5.13      = ( ^ [A4: set_Pr8551490117392284871at_nat,B4: set_Pr8551490117392284871at_nat] :
% 9.25/5.13            ( collec5204685387357076818at_nat
% 9.25/5.13            @ ^ [X3: produc4166570645942440679at_nat] :
% 9.25/5.13                ( ( member6689249552917799696at_nat @ X3 @ A4 )
% 9.25/5.13                | ( member6689249552917799696at_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1178_Un__def,axiom,
% 9.25/5.13      ( sup_su5525570899277871387at_nat
% 9.25/5.13      = ( ^ [A4: set_Pr4329608150637261639at_nat,B4: set_Pr4329608150637261639at_nat] :
% 9.25/5.13            ( collec6321179662152712658at_nat
% 9.25/5.13            @ ^ [X3: produc3843707927480180839at_nat] :
% 9.25/5.13                ( ( member8757157785044589968at_nat @ X3 @ A4 )
% 9.25/5.13                | ( member8757157785044589968at_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1179_Un__def,axiom,
% 9.25/5.13      ( sup_sup_set_nat
% 9.25/5.13      = ( ^ [A4: set_nat,B4: set_nat] :
% 9.25/5.13            ( collect_nat
% 9.25/5.13            @ ^ [X3: nat] :
% 9.25/5.13                ( ( member_nat @ X3 @ A4 )
% 9.25/5.13                | ( member_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1180_sup__set__def,axiom,
% 9.25/5.13      ( sup_su2047564715030645325nt_int
% 9.25/5.13      = ( ^ [A4: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
% 9.25/5.13            ( collec5210948495886036740nt_int
% 9.25/5.13            @ ( sup_su1852724690005176016_int_o
% 9.25/5.13              @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ A4 )
% 9.25/5.13              @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1181_sup__set__def,axiom,
% 9.25/5.13      ( sup_sup_set_set_nat
% 9.25/5.13      = ( ^ [A4: set_set_nat,B4: set_set_nat] :
% 9.25/5.13            ( collect_set_nat
% 9.25/5.13            @ ( sup_sup_set_nat_o
% 9.25/5.13              @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A4 )
% 9.25/5.13              @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1182_sup__set__def,axiom,
% 9.25/5.13      ( sup_sup_set_int
% 9.25/5.13      = ( ^ [A4: set_int,B4: set_int] :
% 9.25/5.13            ( collect_int
% 9.25/5.13            @ ( sup_sup_int_o
% 9.25/5.13              @ ^ [X3: int] : ( member_int @ X3 @ A4 )
% 9.25/5.13              @ ^ [X3: int] : ( member_int @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1183_sup__set__def,axiom,
% 9.25/5.13      ( sup_su5209123915105501825_nat_o
% 9.25/5.13      = ( ^ [A4: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13            ( collec939566748876313656_nat_o
% 9.25/5.13            @ ( sup_su8003631835303541148at_o_o
% 9.25/5.13              @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ A4 )
% 9.25/5.13              @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1184_sup__set__def,axiom,
% 9.25/5.13      ( sup_su3035147773818789531at_nat
% 9.25/5.13      = ( ^ [A4: set_Pr8551490117392284871at_nat,B4: set_Pr8551490117392284871at_nat] :
% 9.25/5.13            ( collec5204685387357076818at_nat
% 9.25/5.13            @ ( sup_su6256023009775730178_nat_o
% 9.25/5.13              @ ^ [X3: produc4166570645942440679at_nat] : ( member6689249552917799696at_nat @ X3 @ A4 )
% 9.25/5.13              @ ^ [X3: produc4166570645942440679at_nat] : ( member6689249552917799696at_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1185_sup__set__def,axiom,
% 9.25/5.13      ( sup_su5525570899277871387at_nat
% 9.25/5.13      = ( ^ [A4: set_Pr4329608150637261639at_nat,B4: set_Pr4329608150637261639at_nat] :
% 9.25/5.13            ( collec6321179662152712658at_nat
% 9.25/5.13            @ ( sup_su2080679670758317954_nat_o
% 9.25/5.13              @ ^ [X3: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X3 @ A4 )
% 9.25/5.13              @ ^ [X3: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1186_sup__set__def,axiom,
% 9.25/5.13      ( sup_sup_set_nat
% 9.25/5.13      = ( ^ [A4: set_nat,B4: set_nat] :
% 9.25/5.13            ( collect_nat
% 9.25/5.13            @ ( sup_sup_nat_o
% 9.25/5.13              @ ^ [X3: nat] : ( member_nat @ X3 @ A4 )
% 9.25/5.13              @ ^ [X3: nat] : ( member_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1187_Collect__imp__eq,axiom,
% 9.25/5.13      ! [P: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.13        ( ( collec5210948495886036740nt_int
% 9.25/5.13          @ ^ [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.13              ( ( P @ X3 )
% 9.25/5.13             => ( Q2 @ X3 ) ) )
% 9.25/5.13        = ( sup_su2047564715030645325nt_int @ ( uminus6423885277529793776nt_int @ ( collec5210948495886036740nt_int @ P ) ) @ ( collec5210948495886036740nt_int @ Q2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1188_Collect__imp__eq,axiom,
% 9.25/5.13      ! [P: set_nat > $o,Q2: set_nat > $o] :
% 9.25/5.13        ( ( collect_set_nat
% 9.25/5.13          @ ^ [X3: set_nat] :
% 9.25/5.13              ( ( P @ X3 )
% 9.25/5.13             => ( Q2 @ X3 ) ) )
% 9.25/5.13        = ( sup_sup_set_set_nat @ ( uminus613421341184616069et_nat @ ( collect_set_nat @ P ) ) @ ( collect_set_nat @ Q2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1189_Collect__imp__eq,axiom,
% 9.25/5.13      ! [P: int > $o,Q2: int > $o] :
% 9.25/5.13        ( ( collect_int
% 9.25/5.13          @ ^ [X3: int] :
% 9.25/5.13              ( ( P @ X3 )
% 9.25/5.13             => ( Q2 @ X3 ) ) )
% 9.25/5.13        = ( sup_sup_set_int @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) @ ( collect_int @ Q2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1190_Collect__imp__eq,axiom,
% 9.25/5.13      ! [P: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.13        ( ( collec939566748876313656_nat_o
% 9.25/5.13          @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.13              ( ( P @ X3 )
% 9.25/5.13             => ( Q2 @ X3 ) ) )
% 9.25/5.13        = ( sup_su5209123915105501825_nat_o @ ( uminus5254974436814262692_nat_o @ ( collec939566748876313656_nat_o @ P ) ) @ ( collec939566748876313656_nat_o @ Q2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1191_Collect__imp__eq,axiom,
% 9.25/5.13      ! [P: produc4166570645942440679at_nat > $o,Q2: produc4166570645942440679at_nat > $o] :
% 9.25/5.13        ( ( collec5204685387357076818at_nat
% 9.25/5.13          @ ^ [X3: produc4166570645942440679at_nat] :
% 9.25/5.13              ( ( P @ X3 )
% 9.25/5.13             => ( Q2 @ X3 ) ) )
% 9.25/5.13        = ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ ( collec5204685387357076818at_nat @ P ) ) @ ( collec5204685387357076818at_nat @ Q2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1192_Collect__imp__eq,axiom,
% 9.25/5.13      ! [P: produc3843707927480180839at_nat > $o,Q2: produc3843707927480180839at_nat > $o] :
% 9.25/5.13        ( ( collec6321179662152712658at_nat
% 9.25/5.13          @ ^ [X3: produc3843707927480180839at_nat] :
% 9.25/5.13              ( ( P @ X3 )
% 9.25/5.13             => ( Q2 @ X3 ) ) )
% 9.25/5.13        = ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ ( collec6321179662152712658at_nat @ P ) ) @ ( collec6321179662152712658at_nat @ Q2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1193_Collect__imp__eq,axiom,
% 9.25/5.13      ! [P: nat > $o,Q2: nat > $o] :
% 9.25/5.13        ( ( collect_nat
% 9.25/5.13          @ ^ [X3: nat] :
% 9.25/5.13              ( ( P @ X3 )
% 9.25/5.13             => ( Q2 @ X3 ) ) )
% 9.25/5.13        = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) @ ( collect_nat @ Q2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1194_Collect__disj__eq,axiom,
% 9.25/5.13      ! [P: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.13        ( ( collec5210948495886036740nt_int
% 9.25/5.13          @ ^ [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.13              ( ( P @ X3 )
% 9.25/5.13              | ( Q2 @ X3 ) ) )
% 9.25/5.13        = ( sup_su2047564715030645325nt_int @ ( collec5210948495886036740nt_int @ P ) @ ( collec5210948495886036740nt_int @ Q2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1195_Collect__disj__eq,axiom,
% 9.25/5.13      ! [P: set_nat > $o,Q2: set_nat > $o] :
% 9.25/5.13        ( ( collect_set_nat
% 9.25/5.13          @ ^ [X3: set_nat] :
% 9.25/5.13              ( ( P @ X3 )
% 9.25/5.13              | ( Q2 @ X3 ) ) )
% 9.25/5.13        = ( sup_sup_set_set_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1196_Collect__disj__eq,axiom,
% 9.25/5.13      ! [P: int > $o,Q2: int > $o] :
% 9.25/5.13        ( ( collect_int
% 9.25/5.13          @ ^ [X3: int] :
% 9.25/5.13              ( ( P @ X3 )
% 9.25/5.13              | ( Q2 @ X3 ) ) )
% 9.25/5.13        = ( sup_sup_set_int @ ( collect_int @ P ) @ ( collect_int @ Q2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1197_Collect__disj__eq,axiom,
% 9.25/5.13      ! [P: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.13        ( ( collec939566748876313656_nat_o
% 9.25/5.13          @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.13              ( ( P @ X3 )
% 9.25/5.13              | ( Q2 @ X3 ) ) )
% 9.25/5.13        = ( sup_su5209123915105501825_nat_o @ ( collec939566748876313656_nat_o @ P ) @ ( collec939566748876313656_nat_o @ Q2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1198_Collect__disj__eq,axiom,
% 9.25/5.13      ! [P: produc4166570645942440679at_nat > $o,Q2: produc4166570645942440679at_nat > $o] :
% 9.25/5.13        ( ( collec5204685387357076818at_nat
% 9.25/5.13          @ ^ [X3: produc4166570645942440679at_nat] :
% 9.25/5.13              ( ( P @ X3 )
% 9.25/5.13              | ( Q2 @ X3 ) ) )
% 9.25/5.13        = ( sup_su3035147773818789531at_nat @ ( collec5204685387357076818at_nat @ P ) @ ( collec5204685387357076818at_nat @ Q2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1199_Collect__disj__eq,axiom,
% 9.25/5.13      ! [P: produc3843707927480180839at_nat > $o,Q2: produc3843707927480180839at_nat > $o] :
% 9.25/5.13        ( ( collec6321179662152712658at_nat
% 9.25/5.13          @ ^ [X3: produc3843707927480180839at_nat] :
% 9.25/5.13              ( ( P @ X3 )
% 9.25/5.13              | ( Q2 @ X3 ) ) )
% 9.25/5.13        = ( sup_su5525570899277871387at_nat @ ( collec6321179662152712658at_nat @ P ) @ ( collec6321179662152712658at_nat @ Q2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1200_Collect__disj__eq,axiom,
% 9.25/5.13      ! [P: nat > $o,Q2: nat > $o] :
% 9.25/5.13        ( ( collect_nat
% 9.25/5.13          @ ^ [X3: nat] :
% 9.25/5.13              ( ( P @ X3 )
% 9.25/5.13              | ( Q2 @ X3 ) ) )
% 9.25/5.13        = ( sup_sup_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1201_one__neq__neg__one,axiom,
% 9.25/5.13      ( one_one_int
% 9.25/5.13     != ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1202_one__neq__neg__one,axiom,
% 9.25/5.13      ( one_one_Code_integer
% 9.25/5.13     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1203_one__neq__neg__one,axiom,
% 9.25/5.13      ( one_one_rat
% 9.25/5.13     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1204_Int__emptyI,axiom,
% 9.25/5.13      ! [A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.13        ( ! [X2: set_Pr958786334691620121nt_int] :
% 9.25/5.13            ( ( member2340774599025711042nt_int @ X2 @ A2 )
% 9.25/5.13           => ~ ( member2340774599025711042nt_int @ X2 @ B2 ) )
% 9.25/5.13       => ( ( inf_in8396524679539076455nt_int @ A2 @ B2 )
% 9.25/5.13          = bot_bo1488462491386950373nt_int ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1205_Int__emptyI,axiom,
% 9.25/5.13      ! [A2: set_set_nat,B2: set_set_nat] :
% 9.25/5.13        ( ! [X2: set_nat] :
% 9.25/5.13            ( ( member_set_nat @ X2 @ A2 )
% 9.25/5.13           => ~ ( member_set_nat @ X2 @ B2 ) )
% 9.25/5.13       => ( ( inf_inf_set_set_nat @ A2 @ B2 )
% 9.25/5.13          = bot_bot_set_set_nat ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1206_Int__emptyI,axiom,
% 9.25/5.13      ! [A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13        ( ! [X2: produc3658429121746597890et_nat > $o] :
% 9.25/5.13            ( ( member6576561426505652726_nat_o @ X2 @ A2 )
% 9.25/5.13           => ~ ( member6576561426505652726_nat_o @ X2 @ B2 ) )
% 9.25/5.13       => ( ( inf_in1906310914598751387_nat_o @ A2 @ B2 )
% 9.25/5.13          = bot_bo7824918357723582233_nat_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1207_Int__emptyI,axiom,
% 9.25/5.13      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ! [X2: product_prod_nat_nat] :
% 9.25/5.13            ( ( member8440522571783428010at_nat @ X2 @ A2 )
% 9.25/5.13           => ~ ( member8440522571783428010at_nat @ X2 @ B2 ) )
% 9.25/5.13       => ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 9.25/5.13          = bot_bo2099793752762293965at_nat ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1208_Int__emptyI,axiom,
% 9.25/5.13      ! [A2: set_o,B2: set_o] :
% 9.25/5.13        ( ! [X2: $o] :
% 9.25/5.13            ( ( member_o @ X2 @ A2 )
% 9.25/5.13           => ~ ( member_o @ X2 @ B2 ) )
% 9.25/5.13       => ( ( inf_inf_set_o @ A2 @ B2 )
% 9.25/5.13          = bot_bot_set_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1209_Int__emptyI,axiom,
% 9.25/5.13      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.13        ( ! [X2: nat] :
% 9.25/5.13            ( ( member_nat @ X2 @ A2 )
% 9.25/5.13           => ~ ( member_nat @ X2 @ B2 ) )
% 9.25/5.13       => ( ( inf_inf_set_nat @ A2 @ B2 )
% 9.25/5.13          = bot_bot_set_nat ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1210_Int__emptyI,axiom,
% 9.25/5.13      ! [A2: set_int,B2: set_int] :
% 9.25/5.13        ( ! [X2: int] :
% 9.25/5.13            ( ( member_int @ X2 @ A2 )
% 9.25/5.13           => ~ ( member_int @ X2 @ B2 ) )
% 9.25/5.13       => ( ( inf_inf_set_int @ A2 @ B2 )
% 9.25/5.13          = bot_bot_set_int ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1211_disjoint__iff,axiom,
% 9.25/5.13      ! [A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.13        ( ( ( inf_in8396524679539076455nt_int @ A2 @ B2 )
% 9.25/5.13          = bot_bo1488462491386950373nt_int )
% 9.25/5.13        = ( ! [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.13              ( ( member2340774599025711042nt_int @ X3 @ A2 )
% 9.25/5.13             => ~ ( member2340774599025711042nt_int @ X3 @ B2 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1212_disjoint__iff,axiom,
% 9.25/5.13      ! [A2: set_set_nat,B2: set_set_nat] :
% 9.25/5.13        ( ( ( inf_inf_set_set_nat @ A2 @ B2 )
% 9.25/5.13          = bot_bot_set_set_nat )
% 9.25/5.13        = ( ! [X3: set_nat] :
% 9.25/5.13              ( ( member_set_nat @ X3 @ A2 )
% 9.25/5.13             => ~ ( member_set_nat @ X3 @ B2 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1213_disjoint__iff,axiom,
% 9.25/5.13      ! [A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13        ( ( ( inf_in1906310914598751387_nat_o @ A2 @ B2 )
% 9.25/5.13          = bot_bo7824918357723582233_nat_o )
% 9.25/5.13        = ( ! [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.13              ( ( member6576561426505652726_nat_o @ X3 @ A2 )
% 9.25/5.13             => ~ ( member6576561426505652726_nat_o @ X3 @ B2 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1214_disjoint__iff,axiom,
% 9.25/5.13      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 9.25/5.13          = bot_bo2099793752762293965at_nat )
% 9.25/5.13        = ( ! [X3: product_prod_nat_nat] :
% 9.25/5.13              ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 9.25/5.13             => ~ ( member8440522571783428010at_nat @ X3 @ B2 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1215_disjoint__iff,axiom,
% 9.25/5.13      ! [A2: set_o,B2: set_o] :
% 9.25/5.13        ( ( ( inf_inf_set_o @ A2 @ B2 )
% 9.25/5.13          = bot_bot_set_o )
% 9.25/5.13        = ( ! [X3: $o] :
% 9.25/5.13              ( ( member_o @ X3 @ A2 )
% 9.25/5.13             => ~ ( member_o @ X3 @ B2 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1216_disjoint__iff,axiom,
% 9.25/5.13      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.13        ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 9.25/5.13          = bot_bot_set_nat )
% 9.25/5.13        = ( ! [X3: nat] :
% 9.25/5.13              ( ( member_nat @ X3 @ A2 )
% 9.25/5.13             => ~ ( member_nat @ X3 @ B2 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1217_disjoint__iff,axiom,
% 9.25/5.13      ! [A2: set_int,B2: set_int] :
% 9.25/5.13        ( ( ( inf_inf_set_int @ A2 @ B2 )
% 9.25/5.13          = bot_bot_set_int )
% 9.25/5.13        = ( ! [X3: int] :
% 9.25/5.13              ( ( member_int @ X3 @ A2 )
% 9.25/5.13             => ~ ( member_int @ X3 @ B2 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1218_Int__empty__left,axiom,
% 9.25/5.13      ! [B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( inf_in2572325071724192079at_nat @ bot_bo2099793752762293965at_nat @ B2 )
% 9.25/5.13        = bot_bo2099793752762293965at_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1219_Int__empty__left,axiom,
% 9.25/5.13      ! [B2: set_o] :
% 9.25/5.13        ( ( inf_inf_set_o @ bot_bot_set_o @ B2 )
% 9.25/5.13        = bot_bot_set_o ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1220_Int__empty__left,axiom,
% 9.25/5.13      ! [B2: set_nat] :
% 9.25/5.13        ( ( inf_inf_set_nat @ bot_bot_set_nat @ B2 )
% 9.25/5.13        = bot_bot_set_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1221_Int__empty__left,axiom,
% 9.25/5.13      ! [B2: set_int] :
% 9.25/5.13        ( ( inf_inf_set_int @ bot_bot_set_int @ B2 )
% 9.25/5.13        = bot_bot_set_int ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1222_Int__empty__right,axiom,
% 9.25/5.13      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( inf_in2572325071724192079at_nat @ A2 @ bot_bo2099793752762293965at_nat )
% 9.25/5.13        = bot_bo2099793752762293965at_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1223_Int__empty__right,axiom,
% 9.25/5.13      ! [A2: set_o] :
% 9.25/5.13        ( ( inf_inf_set_o @ A2 @ bot_bot_set_o )
% 9.25/5.13        = bot_bot_set_o ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1224_Int__empty__right,axiom,
% 9.25/5.13      ! [A2: set_nat] :
% 9.25/5.13        ( ( inf_inf_set_nat @ A2 @ bot_bot_set_nat )
% 9.25/5.13        = bot_bot_set_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1225_Int__empty__right,axiom,
% 9.25/5.13      ! [A2: set_int] :
% 9.25/5.13        ( ( inf_inf_set_int @ A2 @ bot_bot_set_int )
% 9.25/5.13        = bot_bot_set_int ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1226_disjoint__iff__not__equal,axiom,
% 9.25/5.13      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 9.25/5.13          = bot_bo2099793752762293965at_nat )
% 9.25/5.13        = ( ! [X3: product_prod_nat_nat] :
% 9.25/5.13              ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 9.25/5.13             => ! [Y3: product_prod_nat_nat] :
% 9.25/5.13                  ( ( member8440522571783428010at_nat @ Y3 @ B2 )
% 9.25/5.13                 => ( X3 != Y3 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1227_disjoint__iff__not__equal,axiom,
% 9.25/5.13      ! [A2: set_o,B2: set_o] :
% 9.25/5.13        ( ( ( inf_inf_set_o @ A2 @ B2 )
% 9.25/5.13          = bot_bot_set_o )
% 9.25/5.13        = ( ! [X3: $o] :
% 9.25/5.13              ( ( member_o @ X3 @ A2 )
% 9.25/5.13             => ! [Y3: $o] :
% 9.25/5.13                  ( ( member_o @ Y3 @ B2 )
% 9.25/5.13                 => ( X3 = ~ Y3 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1228_disjoint__iff__not__equal,axiom,
% 9.25/5.13      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.13        ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 9.25/5.13          = bot_bot_set_nat )
% 9.25/5.13        = ( ! [X3: nat] :
% 9.25/5.13              ( ( member_nat @ X3 @ A2 )
% 9.25/5.13             => ! [Y3: nat] :
% 9.25/5.13                  ( ( member_nat @ Y3 @ B2 )
% 9.25/5.13                 => ( X3 != Y3 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1229_disjoint__iff__not__equal,axiom,
% 9.25/5.13      ! [A2: set_int,B2: set_int] :
% 9.25/5.13        ( ( ( inf_inf_set_int @ A2 @ B2 )
% 9.25/5.13          = bot_bot_set_int )
% 9.25/5.13        = ( ! [X3: int] :
% 9.25/5.13              ( ( member_int @ X3 @ A2 )
% 9.25/5.13             => ! [Y3: int] :
% 9.25/5.13                  ( ( member_int @ Y3 @ B2 )
% 9.25/5.13                 => ( X3 != Y3 ) ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1230_Un__empty__left,axiom,
% 9.25/5.13      ! [B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat @ B2 )
% 9.25/5.13        = B2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1231_Un__empty__left,axiom,
% 9.25/5.13      ! [B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat @ B2 )
% 9.25/5.13        = B2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1232_Un__empty__left,axiom,
% 9.25/5.13      ! [B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat @ B2 )
% 9.25/5.13        = B2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1233_Un__empty__left,axiom,
% 9.25/5.13      ! [B2: set_o] :
% 9.25/5.13        ( ( sup_sup_set_o @ bot_bot_set_o @ B2 )
% 9.25/5.13        = B2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1234_Un__empty__left,axiom,
% 9.25/5.13      ! [B2: set_nat] :
% 9.25/5.13        ( ( sup_sup_set_nat @ bot_bot_set_nat @ B2 )
% 9.25/5.13        = B2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1235_Un__empty__left,axiom,
% 9.25/5.13      ! [B2: set_int] :
% 9.25/5.13        ( ( sup_sup_set_int @ bot_bot_set_int @ B2 )
% 9.25/5.13        = B2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1236_Un__empty__right,axiom,
% 9.25/5.13      ! [A2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( sup_su3035147773818789531at_nat @ A2 @ bot_bo8422036546324065075at_nat )
% 9.25/5.13        = A2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1237_Un__empty__right,axiom,
% 9.25/5.13      ! [A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( sup_su5525570899277871387at_nat @ A2 @ bot_bo228742789529271731at_nat )
% 9.25/5.13        = A2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1238_Un__empty__right,axiom,
% 9.25/5.13      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( sup_su6327502436637775413at_nat @ A2 @ bot_bo2099793752762293965at_nat )
% 9.25/5.13        = A2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1239_Un__empty__right,axiom,
% 9.25/5.13      ! [A2: set_o] :
% 9.25/5.13        ( ( sup_sup_set_o @ A2 @ bot_bot_set_o )
% 9.25/5.13        = A2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1240_Un__empty__right,axiom,
% 9.25/5.13      ! [A2: set_nat] :
% 9.25/5.13        ( ( sup_sup_set_nat @ A2 @ bot_bot_set_nat )
% 9.25/5.13        = A2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1241_Un__empty__right,axiom,
% 9.25/5.13      ! [A2: set_int] :
% 9.25/5.13        ( ( sup_sup_set_int @ A2 @ bot_bot_set_int )
% 9.25/5.13        = A2 ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1242_Compl__Un,axiom,
% 9.25/5.13      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( uminus6524753893492686040at_nat @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 9.25/5.13        = ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ A2 ) @ ( uminus6524753893492686040at_nat @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1243_Compl__Un,axiom,
% 9.25/5.13      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( uminus2330091110623919550at_nat @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 9.25/5.13        = ( inf_in1697001100524423349at_nat @ ( uminus2330091110623919550at_nat @ A2 ) @ ( uminus2330091110623919550at_nat @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1244_Compl__Un,axiom,
% 9.25/5.13      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( uminus935396558254630718at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 9.25/5.13        = ( inf_in7913087082777306421at_nat @ ( uminus935396558254630718at_nat @ A2 ) @ ( uminus935396558254630718at_nat @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1245_Compl__Un,axiom,
% 9.25/5.13      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.13        ( ( uminus5710092332889474511et_nat @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.13        = ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( uminus5710092332889474511et_nat @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1246_Compl__Int,axiom,
% 9.25/5.13      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( uminus6524753893492686040at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 9.25/5.13        = ( sup_su6327502436637775413at_nat @ ( uminus6524753893492686040at_nat @ A2 ) @ ( uminus6524753893492686040at_nat @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1247_Compl__Int,axiom,
% 9.25/5.13      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( uminus2330091110623919550at_nat @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) )
% 9.25/5.13        = ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ A2 ) @ ( uminus2330091110623919550at_nat @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1248_Compl__Int,axiom,
% 9.25/5.13      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( uminus935396558254630718at_nat @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) )
% 9.25/5.13        = ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ A2 ) @ ( uminus935396558254630718at_nat @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1249_Compl__Int,axiom,
% 9.25/5.13      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.13        ( ( uminus5710092332889474511et_nat @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.13        = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( uminus5710092332889474511et_nat @ B2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1250_Un__Int__crazy,axiom,
% 9.25/5.13      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( sup_su6327502436637775413at_nat @ ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) ) @ ( inf_in2572325071724192079at_nat @ C2 @ A2 ) )
% 9.25/5.13        = ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) @ ( sup_su6327502436637775413at_nat @ B2 @ C2 ) ) @ ( sup_su6327502436637775413at_nat @ C2 @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1251_Un__Int__crazy,axiom,
% 9.25/5.13      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) @ ( inf_in1697001100524423349at_nat @ B2 @ C2 ) ) @ ( inf_in1697001100524423349at_nat @ C2 @ A2 ) )
% 9.25/5.13        = ( inf_in1697001100524423349at_nat @ ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) @ ( sup_su3035147773818789531at_nat @ B2 @ C2 ) ) @ ( sup_su3035147773818789531at_nat @ C2 @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1252_Un__Int__crazy,axiom,
% 9.25/5.13      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) @ ( inf_in7913087082777306421at_nat @ B2 @ C2 ) ) @ ( inf_in7913087082777306421at_nat @ C2 @ A2 ) )
% 9.25/5.13        = ( inf_in7913087082777306421at_nat @ ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) ) @ ( sup_su5525570899277871387at_nat @ C2 @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1253_Un__Int__crazy,axiom,
% 9.25/5.13      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 9.25/5.13        ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ ( inf_inf_set_nat @ B2 @ C2 ) ) @ ( inf_inf_set_nat @ C2 @ A2 ) )
% 9.25/5.13        = ( inf_inf_set_nat @ ( inf_inf_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ ( sup_sup_set_nat @ B2 @ C2 ) ) @ ( sup_sup_set_nat @ C2 @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1254_Int__Un__distrib,axiom,
% 9.25/5.13      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( inf_in2572325071724192079at_nat @ A2 @ ( sup_su6327502436637775413at_nat @ B2 @ C2 ) )
% 9.25/5.13        = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ ( inf_in2572325071724192079at_nat @ A2 @ C2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1255_Int__Un__distrib,axiom,
% 9.25/5.13      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( inf_in1697001100524423349at_nat @ A2 @ ( sup_su3035147773818789531at_nat @ B2 @ C2 ) )
% 9.25/5.13        = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) @ ( inf_in1697001100524423349at_nat @ A2 @ C2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1256_Int__Un__distrib,axiom,
% 9.25/5.13      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( inf_in7913087082777306421at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) )
% 9.25/5.13        = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) @ ( inf_in7913087082777306421at_nat @ A2 @ C2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1257_Int__Un__distrib,axiom,
% 9.25/5.13      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 9.25/5.13        ( ( inf_inf_set_nat @ A2 @ ( sup_sup_set_nat @ B2 @ C2 ) )
% 9.25/5.13        = ( sup_sup_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ ( inf_inf_set_nat @ A2 @ C2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1258_Un__Int__distrib,axiom,
% 9.25/5.13      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( sup_su6327502436637775413at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) )
% 9.25/5.13        = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) @ ( sup_su6327502436637775413at_nat @ A2 @ C2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1259_Un__Int__distrib,axiom,
% 9.25/5.13      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( sup_su3035147773818789531at_nat @ A2 @ ( inf_in1697001100524423349at_nat @ B2 @ C2 ) )
% 9.25/5.13        = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) @ ( sup_su3035147773818789531at_nat @ A2 @ C2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1260_Un__Int__distrib,axiom,
% 9.25/5.13      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( sup_su5525570899277871387at_nat @ A2 @ ( inf_in7913087082777306421at_nat @ B2 @ C2 ) )
% 9.25/5.13        = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) @ ( sup_su5525570899277871387at_nat @ A2 @ C2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1261_Un__Int__distrib,axiom,
% 9.25/5.13      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 9.25/5.13        ( ( sup_sup_set_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C2 ) )
% 9.25/5.13        = ( inf_inf_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ ( sup_sup_set_nat @ A2 @ C2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1262_Int__Un__distrib2,axiom,
% 9.25/5.13      ! [B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ B2 @ C2 ) @ A2 )
% 9.25/5.13        = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ B2 @ A2 ) @ ( inf_in2572325071724192079at_nat @ C2 @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1263_Int__Un__distrib2,axiom,
% 9.25/5.13      ! [B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat,A2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ B2 @ C2 ) @ A2 )
% 9.25/5.13        = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ B2 @ A2 ) @ ( inf_in1697001100524423349at_nat @ C2 @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1264_Int__Un__distrib2,axiom,
% 9.25/5.13      ! [B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) @ A2 )
% 9.25/5.13        = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ B2 @ A2 ) @ ( inf_in7913087082777306421at_nat @ C2 @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1265_Int__Un__distrib2,axiom,
% 9.25/5.13      ! [B2: set_nat,C2: set_nat,A2: set_nat] :
% 9.25/5.13        ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ B2 @ C2 ) @ A2 )
% 9.25/5.13        = ( sup_sup_set_nat @ ( inf_inf_set_nat @ B2 @ A2 ) @ ( inf_inf_set_nat @ C2 @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1266_Un__Int__distrib2,axiom,
% 9.25/5.13      ! [B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) @ A2 )
% 9.25/5.13        = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ B2 @ A2 ) @ ( sup_su6327502436637775413at_nat @ C2 @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1267_Un__Int__distrib2,axiom,
% 9.25/5.13      ! [B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat,A2: set_Pr8551490117392284871at_nat] :
% 9.25/5.13        ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ B2 @ C2 ) @ A2 )
% 9.25/5.13        = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ B2 @ A2 ) @ ( sup_su3035147773818789531at_nat @ C2 @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1268_Un__Int__distrib2,axiom,
% 9.25/5.13      ! [B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.13        ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ B2 @ C2 ) @ A2 )
% 9.25/5.13        = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ B2 @ A2 ) @ ( sup_su5525570899277871387at_nat @ C2 @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1269_Un__Int__distrib2,axiom,
% 9.25/5.13      ! [B2: set_nat,C2: set_nat,A2: set_nat] :
% 9.25/5.13        ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ B2 @ C2 ) @ A2 )
% 9.25/5.13        = ( inf_inf_set_nat @ ( sup_sup_set_nat @ B2 @ A2 ) @ ( sup_sup_set_nat @ C2 @ A2 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1270_mult__minus__right,axiom,
% 9.25/5.13      ! [A: int,B: int] :
% 9.25/5.13        ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 9.25/5.13        = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1271_mult__minus__right,axiom,
% 9.25/5.13      ! [A: code_integer,B: code_integer] :
% 9.25/5.13        ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 9.25/5.13        = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1272_mult__minus__right,axiom,
% 9.25/5.13      ! [A: rat,B: rat] :
% 9.25/5.13        ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 9.25/5.13        = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1273_minus__mult__minus,axiom,
% 9.25/5.13      ! [A: int,B: int] :
% 9.25/5.13        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 9.25/5.13        = ( times_times_int @ A @ B ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1274_minus__mult__minus,axiom,
% 9.25/5.13      ! [A: code_integer,B: code_integer] :
% 9.25/5.13        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 9.25/5.13        = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1275_minus__mult__minus,axiom,
% 9.25/5.13      ! [A: rat,B: rat] :
% 9.25/5.13        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 9.25/5.13        = ( times_times_rat @ A @ B ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1276_mult__minus__left,axiom,
% 9.25/5.13      ! [A: int,B: int] :
% 9.25/5.13        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 9.25/5.13        = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1277_mult__minus__left,axiom,
% 9.25/5.13      ! [A: code_integer,B: code_integer] :
% 9.25/5.13        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 9.25/5.13        = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1278_mult__minus__left,axiom,
% 9.25/5.13      ! [A: rat,B: rat] :
% 9.25/5.13        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 9.25/5.13        = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1279_square__eq__1__iff,axiom,
% 9.25/5.13      ! [X: int] :
% 9.25/5.13        ( ( ( times_times_int @ X @ X )
% 9.25/5.13          = one_one_int )
% 9.25/5.13        = ( ( X = one_one_int )
% 9.25/5.13          | ( X
% 9.25/5.13            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1280_square__eq__1__iff,axiom,
% 9.25/5.13      ! [X: code_integer] :
% 9.25/5.13        ( ( ( times_3573771949741848930nteger @ X @ X )
% 9.25/5.13          = one_one_Code_integer )
% 9.25/5.13        = ( ( X = one_one_Code_integer )
% 9.25/5.13          | ( X
% 9.25/5.13            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1281_square__eq__1__iff,axiom,
% 9.25/5.13      ! [X: rat] :
% 9.25/5.13        ( ( ( times_times_rat @ X @ X )
% 9.25/5.13          = one_one_rat )
% 9.25/5.13        = ( ( X = one_one_rat )
% 9.25/5.13          | ( X
% 9.25/5.13            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1282_verit__minus__simplify_I4_J,axiom,
% 9.25/5.13      ! [B: int] :
% 9.25/5.13        ( ( uminus_uminus_int @ ( uminus_uminus_int @ B ) )
% 9.25/5.13        = B ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1283_verit__minus__simplify_I4_J,axiom,
% 9.25/5.13      ! [B: code_integer] :
% 9.25/5.13        ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ B ) )
% 9.25/5.13        = B ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1284_verit__minus__simplify_I4_J,axiom,
% 9.25/5.13      ! [B: rat] :
% 9.25/5.13        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ B ) )
% 9.25/5.13        = B ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1285_old_Oprod_Oinject,axiom,
% 9.25/5.13      ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 9.25/5.13        ( ( ( produc8603105652947943368nteger @ A @ B )
% 9.25/5.13          = ( produc8603105652947943368nteger @ A5 @ B5 ) )
% 9.25/5.13        = ( ( A = A5 )
% 9.25/5.13          & ( B = B5 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1286_old_Oprod_Oinject,axiom,
% 9.25/5.13      ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A5: produc3658429121746597890et_nat > $o,B5: produc3658429121746597890et_nat] :
% 9.25/5.13        ( ( ( produc5001842942810119800et_nat @ A @ B )
% 9.25/5.13          = ( produc5001842942810119800et_nat @ A5 @ B5 ) )
% 9.25/5.13        = ( ( A = A5 )
% 9.25/5.13          & ( B = B5 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1287_old_Oprod_Oinject,axiom,
% 9.25/5.13      ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A5: produc3658429121746597890et_nat > $o,B5: produc3925858234332021118et_nat] :
% 9.25/5.13        ( ( ( produc2245416461498447860et_nat @ A @ B )
% 9.25/5.13          = ( produc2245416461498447860et_nat @ A5 @ B5 ) )
% 9.25/5.13        = ( ( A = A5 )
% 9.25/5.13          & ( B = B5 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1288_old_Oprod_Oinject,axiom,
% 9.25/5.13      ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: product_prod_int_int] :
% 9.25/5.13        ( ( ( produc5700946648718959541nt_int @ A @ B )
% 9.25/5.13          = ( produc5700946648718959541nt_int @ A5 @ B5 ) )
% 9.25/5.13        = ( ( A = A5 )
% 9.25/5.13          & ( B = B5 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1289_old_Oprod_Oinject,axiom,
% 9.25/5.13      ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A5: int > option6357759511663192854e_term,B5: product_prod_int_int] :
% 9.25/5.13        ( ( ( produc4305682042979456191nt_int @ A @ B )
% 9.25/5.13          = ( produc4305682042979456191nt_int @ A5 @ B5 ) )
% 9.25/5.13        = ( ( A = A5 )
% 9.25/5.13          & ( B = B5 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1290_prod_Oinject,axiom,
% 9.25/5.13      ! [X1: produc6241069584506657477e_term > option6357759511663192854e_term,X22: produc8923325533196201883nteger,Y1: produc6241069584506657477e_term > option6357759511663192854e_term,Y22: produc8923325533196201883nteger] :
% 9.25/5.13        ( ( ( produc8603105652947943368nteger @ X1 @ X22 )
% 9.25/5.13          = ( produc8603105652947943368nteger @ Y1 @ Y22 ) )
% 9.25/5.13        = ( ( X1 = Y1 )
% 9.25/5.13          & ( X22 = Y22 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1291_prod_Oinject,axiom,
% 9.25/5.13      ! [X1: produc3658429121746597890et_nat > $o,X22: produc3658429121746597890et_nat,Y1: produc3658429121746597890et_nat > $o,Y22: produc3658429121746597890et_nat] :
% 9.25/5.13        ( ( ( produc5001842942810119800et_nat @ X1 @ X22 )
% 9.25/5.13          = ( produc5001842942810119800et_nat @ Y1 @ Y22 ) )
% 9.25/5.13        = ( ( X1 = Y1 )
% 9.25/5.13          & ( X22 = Y22 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1292_prod_Oinject,axiom,
% 9.25/5.13      ! [X1: produc3658429121746597890et_nat > $o,X22: produc3925858234332021118et_nat,Y1: produc3658429121746597890et_nat > $o,Y22: produc3925858234332021118et_nat] :
% 9.25/5.13        ( ( ( produc2245416461498447860et_nat @ X1 @ X22 )
% 9.25/5.13          = ( produc2245416461498447860et_nat @ Y1 @ Y22 ) )
% 9.25/5.13        = ( ( X1 = Y1 )
% 9.25/5.13          & ( X22 = Y22 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1293_prod_Oinject,axiom,
% 9.25/5.13      ! [X1: produc8551481072490612790e_term > option6357759511663192854e_term,X22: product_prod_int_int,Y1: produc8551481072490612790e_term > option6357759511663192854e_term,Y22: product_prod_int_int] :
% 9.25/5.13        ( ( ( produc5700946648718959541nt_int @ X1 @ X22 )
% 9.25/5.13          = ( produc5700946648718959541nt_int @ Y1 @ Y22 ) )
% 9.25/5.13        = ( ( X1 = Y1 )
% 9.25/5.13          & ( X22 = Y22 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1294_prod_Oinject,axiom,
% 9.25/5.13      ! [X1: int > option6357759511663192854e_term,X22: product_prod_int_int,Y1: int > option6357759511663192854e_term,Y22: product_prod_int_int] :
% 9.25/5.13        ( ( ( produc4305682042979456191nt_int @ X1 @ X22 )
% 9.25/5.13          = ( produc4305682042979456191nt_int @ Y1 @ Y22 ) )
% 9.25/5.13        = ( ( X1 = Y1 )
% 9.25/5.13          & ( X22 = Y22 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1295_lambda__one,axiom,
% 9.25/5.13      ( ( ^ [X3: code_integer] : X3 )
% 9.25/5.13      = ( times_3573771949741848930nteger @ one_one_Code_integer ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1296_lambda__one,axiom,
% 9.25/5.13      ( ( ^ [X3: assn] : X3 )
% 9.25/5.13      = ( times_times_assn @ one_one_assn ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1297_lambda__one,axiom,
% 9.25/5.13      ( ( ^ [X3: rat] : X3 )
% 9.25/5.13      = ( times_times_rat @ one_one_rat ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1298_lambda__one,axiom,
% 9.25/5.13      ( ( ^ [X3: nat] : X3 )
% 9.25/5.13      = ( times_times_nat @ one_one_nat ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1299_lambda__one,axiom,
% 9.25/5.13      ( ( ^ [X3: int] : X3 )
% 9.25/5.13      = ( times_times_int @ one_one_int ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1300_disjointI,axiom,
% 9.25/5.13      ! [A: set_se6260736226359567993nt_int,B: set_se6260736226359567993nt_int] :
% 9.25/5.13        ( ! [X2: set_Pr958786334691620121nt_int] :
% 9.25/5.13            ( ( member2340774599025711042nt_int @ X2 @ A )
% 9.25/5.13           => ~ ( member2340774599025711042nt_int @ X2 @ B ) )
% 9.25/5.13       => ( ( inf_in8396524679539076455nt_int @ A @ B )
% 9.25/5.13          = bot_bo1488462491386950373nt_int ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1301_disjointI,axiom,
% 9.25/5.13      ! [A: set_set_nat,B: set_set_nat] :
% 9.25/5.13        ( ! [X2: set_nat] :
% 9.25/5.13            ( ( member_set_nat @ X2 @ A )
% 9.25/5.13           => ~ ( member_set_nat @ X2 @ B ) )
% 9.25/5.13       => ( ( inf_inf_set_set_nat @ A @ B )
% 9.25/5.13          = bot_bot_set_set_nat ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1302_disjointI,axiom,
% 9.25/5.13      ! [A: set_Pr4532377907799695533_nat_o,B: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13        ( ! [X2: produc3658429121746597890et_nat > $o] :
% 9.25/5.13            ( ( member6576561426505652726_nat_o @ X2 @ A )
% 9.25/5.13           => ~ ( member6576561426505652726_nat_o @ X2 @ B ) )
% 9.25/5.13       => ( ( inf_in1906310914598751387_nat_o @ A @ B )
% 9.25/5.13          = bot_bo7824918357723582233_nat_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1303_disjointI,axiom,
% 9.25/5.13      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ! [X2: product_prod_nat_nat] :
% 9.25/5.13            ( ( member8440522571783428010at_nat @ X2 @ A )
% 9.25/5.13           => ~ ( member8440522571783428010at_nat @ X2 @ B ) )
% 9.25/5.13       => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 9.25/5.13          = bot_bo2099793752762293965at_nat ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1304_disjointI,axiom,
% 9.25/5.13      ! [A: set_o,B: set_o] :
% 9.25/5.13        ( ! [X2: $o] :
% 9.25/5.13            ( ( member_o @ X2 @ A )
% 9.25/5.13           => ~ ( member_o @ X2 @ B ) )
% 9.25/5.13       => ( ( inf_inf_set_o @ A @ B )
% 9.25/5.13          = bot_bot_set_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1305_disjointI,axiom,
% 9.25/5.13      ! [A: set_nat,B: set_nat] :
% 9.25/5.13        ( ! [X2: nat] :
% 9.25/5.13            ( ( member_nat @ X2 @ A )
% 9.25/5.13           => ~ ( member_nat @ X2 @ B ) )
% 9.25/5.13       => ( ( inf_inf_set_nat @ A @ B )
% 9.25/5.13          = bot_bot_set_nat ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1306_disjointI,axiom,
% 9.25/5.13      ! [A: set_int,B: set_int] :
% 9.25/5.13        ( ! [X2: int] :
% 9.25/5.13            ( ( member_int @ X2 @ A )
% 9.25/5.13           => ~ ( member_int @ X2 @ B ) )
% 9.25/5.13       => ( ( inf_inf_set_int @ A @ B )
% 9.25/5.13          = bot_bot_set_int ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1307_minus__mult__commute,axiom,
% 9.25/5.13      ! [A: int,B: int] :
% 9.25/5.13        ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 9.25/5.13        = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1308_minus__mult__commute,axiom,
% 9.25/5.13      ! [A: code_integer,B: code_integer] :
% 9.25/5.13        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 9.25/5.13        = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1309_minus__mult__commute,axiom,
% 9.25/5.13      ! [A: rat,B: rat] :
% 9.25/5.13        ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 9.25/5.13        = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1310_square__eq__iff,axiom,
% 9.25/5.13      ! [A: int,B: int] :
% 9.25/5.13        ( ( ( times_times_int @ A @ A )
% 9.25/5.13          = ( times_times_int @ B @ B ) )
% 9.25/5.13        = ( ( A = B )
% 9.25/5.13          | ( A
% 9.25/5.13            = ( uminus_uminus_int @ B ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1311_square__eq__iff,axiom,
% 9.25/5.13      ! [A: code_integer,B: code_integer] :
% 9.25/5.13        ( ( ( times_3573771949741848930nteger @ A @ A )
% 9.25/5.13          = ( times_3573771949741848930nteger @ B @ B ) )
% 9.25/5.13        = ( ( A = B )
% 9.25/5.13          | ( A
% 9.25/5.13            = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1312_square__eq__iff,axiom,
% 9.25/5.13      ! [A: rat,B: rat] :
% 9.25/5.13        ( ( ( times_times_rat @ A @ A )
% 9.25/5.13          = ( times_times_rat @ B @ B ) )
% 9.25/5.13        = ( ( A = B )
% 9.25/5.13          | ( A
% 9.25/5.13            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1313_UNIV__I,axiom,
% 9.25/5.13      ! [X: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X @ top_to6034159466715884489nt_int ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1314_UNIV__I,axiom,
% 9.25/5.13      ! [X: set_nat] : ( member_set_nat @ X @ top_top_set_set_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1315_UNIV__I,axiom,
% 9.25/5.13      ! [X: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X @ top_to4869887016220417533_nat_o ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1316_UNIV__I,axiom,
% 9.25/5.13      ! [X: list_nat] : ( member_list_nat @ X @ top_top_set_list_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1317_UNIV__I,axiom,
% 9.25/5.13      ! [X: $o] : ( member_o @ X @ top_top_set_o ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1318_UNIV__I,axiom,
% 9.25/5.13      ! [X: rat] : ( member_rat @ X @ top_top_set_rat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1319_UNIV__I,axiom,
% 9.25/5.13      ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1320_UNIV__I,axiom,
% 9.25/5.13      ! [X: int] : ( member_int @ X @ top_top_set_int ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1321_inf1I,axiom,
% 9.25/5.13      ! [A2: product_prod_int_int > $o,X: product_prod_int_int,B2: product_prod_int_int > $o] :
% 9.25/5.13        ( ( A2 @ X )
% 9.25/5.13       => ( ( B2 @ X )
% 9.25/5.13         => ( inf_in3604695632404883862_int_o @ A2 @ B2 @ X ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1322_inf1I,axiom,
% 9.25/5.13      ! [A2: list_char > $o,X: list_char,B2: list_char > $o] :
% 9.25/5.13        ( ( A2 @ X )
% 9.25/5.13       => ( ( B2 @ X )
% 9.25/5.13         => ( inf_inf_list_char_o @ A2 @ B2 @ X ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1323_UNIV__def,axiom,
% 9.25/5.13      ( top_to6034159466715884489nt_int
% 9.25/5.13      = ( collec5210948495886036740nt_int
% 9.25/5.13        @ ^ [X3: set_Pr958786334691620121nt_int] : $true ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1324_UNIV__def,axiom,
% 9.25/5.13      ( top_top_set_set_nat
% 9.25/5.13      = ( collect_set_nat
% 9.25/5.13        @ ^ [X3: set_nat] : $true ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1325_UNIV__def,axiom,
% 9.25/5.13      ( top_to4869887016220417533_nat_o
% 9.25/5.13      = ( collec939566748876313656_nat_o
% 9.25/5.13        @ ^ [X3: produc3658429121746597890et_nat > $o] : $true ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1326_UNIV__def,axiom,
% 9.25/5.13      ( top_top_set_list_nat
% 9.25/5.13      = ( collect_list_nat
% 9.25/5.13        @ ^ [X3: list_nat] : $true ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1327_UNIV__def,axiom,
% 9.25/5.13      ( top_top_set_o
% 9.25/5.13      = ( collect_o
% 9.25/5.13        @ ^ [X3: $o] : $true ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1328_UNIV__def,axiom,
% 9.25/5.13      ( top_top_set_rat
% 9.25/5.13      = ( collect_rat
% 9.25/5.13        @ ^ [X3: rat] : $true ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1329_UNIV__def,axiom,
% 9.25/5.13      ( top_top_set_nat
% 9.25/5.13      = ( collect_nat
% 9.25/5.13        @ ^ [X3: nat] : $true ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1330_UNIV__def,axiom,
% 9.25/5.13      ( top_top_set_int
% 9.25/5.13      = ( collect_int
% 9.25/5.13        @ ^ [X3: int] : $true ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1331_UNIV__eq__I,axiom,
% 9.25/5.13      ! [A2: set_se6260736226359567993nt_int] :
% 9.25/5.13        ( ! [X2: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X2 @ A2 )
% 9.25/5.13       => ( top_to6034159466715884489nt_int = A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1332_UNIV__eq__I,axiom,
% 9.25/5.13      ! [A2: set_set_nat] :
% 9.25/5.13        ( ! [X2: set_nat] : ( member_set_nat @ X2 @ A2 )
% 9.25/5.13       => ( top_top_set_set_nat = A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1333_UNIV__eq__I,axiom,
% 9.25/5.13      ! [A2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13        ( ! [X2: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X2 @ A2 )
% 9.25/5.13       => ( top_to4869887016220417533_nat_o = A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1334_UNIV__eq__I,axiom,
% 9.25/5.13      ! [A2: set_list_nat] :
% 9.25/5.13        ( ! [X2: list_nat] : ( member_list_nat @ X2 @ A2 )
% 9.25/5.13       => ( top_top_set_list_nat = A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1335_UNIV__eq__I,axiom,
% 9.25/5.13      ! [A2: set_o] :
% 9.25/5.13        ( ! [X2: $o] : ( member_o @ X2 @ A2 )
% 9.25/5.13       => ( top_top_set_o = A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1336_UNIV__eq__I,axiom,
% 9.25/5.13      ! [A2: set_rat] :
% 9.25/5.13        ( ! [X2: rat] : ( member_rat @ X2 @ A2 )
% 9.25/5.13       => ( top_top_set_rat = A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1337_UNIV__eq__I,axiom,
% 9.25/5.13      ! [A2: set_nat] :
% 9.25/5.13        ( ! [X2: nat] : ( member_nat @ X2 @ A2 )
% 9.25/5.13       => ( top_top_set_nat = A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1338_UNIV__eq__I,axiom,
% 9.25/5.13      ! [A2: set_int] :
% 9.25/5.13        ( ! [X2: int] : ( member_int @ X2 @ A2 )
% 9.25/5.13       => ( top_top_set_int = A2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1339_top__set__def,axiom,
% 9.25/5.13      ( top_to6034159466715884489nt_int
% 9.25/5.13      = ( collec5210948495886036740nt_int @ top_to6187514276045680724_int_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1340_top__set__def,axiom,
% 9.25/5.13      ( top_top_set_set_nat
% 9.25/5.13      = ( collect_set_nat @ top_top_set_nat_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1341_top__set__def,axiom,
% 9.25/5.13      ( top_to4869887016220417533_nat_o
% 9.25/5.13      = ( collec939566748876313656_nat_o @ top_to2462227307520033056at_o_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1342_top__set__def,axiom,
% 9.25/5.13      ( top_top_set_list_nat
% 9.25/5.13      = ( collect_list_nat @ top_top_list_nat_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1343_top__set__def,axiom,
% 9.25/5.13      ( top_top_set_o
% 9.25/5.13      = ( collect_o @ top_top_o_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1344_top__set__def,axiom,
% 9.25/5.13      ( top_top_set_rat
% 9.25/5.13      = ( collect_rat @ top_top_rat_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1345_top__set__def,axiom,
% 9.25/5.13      ( top_top_set_nat
% 9.25/5.13      = ( collect_nat @ top_top_nat_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1346_top__set__def,axiom,
% 9.25/5.13      ( top_top_set_int
% 9.25/5.13      = ( collect_int @ top_top_int_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1347_UNIV__witness,axiom,
% 9.25/5.13      ? [X2: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X2 @ top_to6034159466715884489nt_int ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1348_UNIV__witness,axiom,
% 9.25/5.13      ? [X2: set_nat] : ( member_set_nat @ X2 @ top_top_set_set_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1349_UNIV__witness,axiom,
% 9.25/5.13      ? [X2: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X2 @ top_to4869887016220417533_nat_o ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1350_UNIV__witness,axiom,
% 9.25/5.13      ? [X2: list_nat] : ( member_list_nat @ X2 @ top_top_set_list_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1351_UNIV__witness,axiom,
% 9.25/5.13      ? [X2: $o] : ( member_o @ X2 @ top_top_set_o ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1352_UNIV__witness,axiom,
% 9.25/5.13      ? [X2: rat] : ( member_rat @ X2 @ top_top_set_rat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1353_UNIV__witness,axiom,
% 9.25/5.13      ? [X2: nat] : ( member_nat @ X2 @ top_top_set_nat ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1354_UNIV__witness,axiom,
% 9.25/5.13      ? [X2: int] : ( member_int @ X2 @ top_top_set_int ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1355_inf1D2,axiom,
% 9.25/5.13      ! [A2: product_prod_int_int > $o,B2: product_prod_int_int > $o,X: product_prod_int_int] :
% 9.25/5.13        ( ( inf_in3604695632404883862_int_o @ A2 @ B2 @ X )
% 9.25/5.13       => ( B2 @ X ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1356_inf1D2,axiom,
% 9.25/5.13      ! [A2: list_char > $o,B2: list_char > $o,X: list_char] :
% 9.25/5.13        ( ( inf_inf_list_char_o @ A2 @ B2 @ X )
% 9.25/5.13       => ( B2 @ X ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1357_inf1D1,axiom,
% 9.25/5.13      ! [A2: product_prod_int_int > $o,B2: product_prod_int_int > $o,X: product_prod_int_int] :
% 9.25/5.13        ( ( inf_in3604695632404883862_int_o @ A2 @ B2 @ X )
% 9.25/5.13       => ( A2 @ X ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1358_inf1D1,axiom,
% 9.25/5.13      ! [A2: list_char > $o,B2: list_char > $o,X: list_char] :
% 9.25/5.13        ( ( inf_inf_list_char_o @ A2 @ B2 @ X )
% 9.25/5.13       => ( A2 @ X ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1359_inf1E,axiom,
% 9.25/5.13      ! [A2: product_prod_int_int > $o,B2: product_prod_int_int > $o,X: product_prod_int_int] :
% 9.25/5.13        ( ( inf_in3604695632404883862_int_o @ A2 @ B2 @ X )
% 9.25/5.13       => ~ ( ( A2 @ X )
% 9.25/5.13           => ~ ( B2 @ X ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1360_inf1E,axiom,
% 9.25/5.13      ! [A2: list_char > $o,B2: list_char > $o,X: list_char] :
% 9.25/5.13        ( ( inf_inf_list_char_o @ A2 @ B2 @ X )
% 9.25/5.13       => ~ ( ( A2 @ X )
% 9.25/5.13           => ~ ( B2 @ X ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1361_times__assn__raw_Ocases,axiom,
% 9.25/5.13      ! [X: produc2732055786443039994et_nat] :
% 9.25/5.13        ~ ! [P3: produc3658429121746597890et_nat > $o,Q3: produc3658429121746597890et_nat > $o,H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 9.25/5.13            ( X
% 9.25/5.13           != ( produc2245416461498447860et_nat @ P3 @ ( produc5001842942810119800et_nat @ Q3 @ ( produc7507926704131184380et_nat @ H @ As4 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1362_pairself_Ocases,axiom,
% 9.25/5.13      ! [X: produc7773217078559923341nt_int] :
% 9.25/5.13        ~ ! [F3: int > option6357759511663192854e_term,A6: int,B6: int] :
% 9.25/5.13            ( X
% 9.25/5.13           != ( produc4305682042979456191nt_int @ F3 @ ( product_Pair_int_int @ A6 @ B6 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1363_old_Oprod_Oexhaust,axiom,
% 9.25/5.13      ! [Y: produc1908205239877642774nteger] :
% 9.25/5.13        ~ ! [A6: produc6241069584506657477e_term > option6357759511663192854e_term,B6: produc8923325533196201883nteger] :
% 9.25/5.13            ( Y
% 9.25/5.13           != ( produc8603105652947943368nteger @ A6 @ B6 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1364_old_Oprod_Oexhaust,axiom,
% 9.25/5.13      ! [Y: produc3925858234332021118et_nat] :
% 9.25/5.13        ~ ! [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat] :
% 9.25/5.13            ( Y
% 9.25/5.13           != ( produc5001842942810119800et_nat @ A6 @ B6 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1365_old_Oprod_Oexhaust,axiom,
% 9.25/5.13      ! [Y: produc2732055786443039994et_nat] :
% 9.25/5.13        ~ ! [A6: produc3658429121746597890et_nat > $o,B6: produc3925858234332021118et_nat] :
% 9.25/5.13            ( Y
% 9.25/5.13           != ( produc2245416461498447860et_nat @ A6 @ B6 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1366_old_Oprod_Oexhaust,axiom,
% 9.25/5.13      ! [Y: produc2285326912895808259nt_int] :
% 9.25/5.13        ~ ! [A6: produc8551481072490612790e_term > option6357759511663192854e_term,B6: product_prod_int_int] :
% 9.25/5.13            ( Y
% 9.25/5.13           != ( produc5700946648718959541nt_int @ A6 @ B6 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1367_old_Oprod_Oexhaust,axiom,
% 9.25/5.13      ! [Y: produc7773217078559923341nt_int] :
% 9.25/5.13        ~ ! [A6: int > option6357759511663192854e_term,B6: product_prod_int_int] :
% 9.25/5.13            ( Y
% 9.25/5.13           != ( produc4305682042979456191nt_int @ A6 @ B6 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1368_bex2I,axiom,
% 9.25/5.13      ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,S: set_Pr1281608226676607948nteger,P: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o] :
% 9.25/5.13        ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A @ B ) @ S )
% 9.25/5.13       => ( ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A @ B ) @ S )
% 9.25/5.13           => ( P @ A @ B ) )
% 9.25/5.13         => ? [A6: produc6241069584506657477e_term > option6357759511663192854e_term,B6: produc8923325533196201883nteger] :
% 9.25/5.13              ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ A6 @ B6 ) @ S )
% 9.25/5.13              & ( P @ A6 @ B6 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1369_bex2I,axiom,
% 9.25/5.13      ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,S: set_Pr3286484037609594932et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 9.25/5.13        ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S )
% 9.25/5.13       => ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S )
% 9.25/5.13           => ( P @ A @ B ) )
% 9.25/5.13         => ? [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat] :
% 9.25/5.13              ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A6 @ B6 ) @ S )
% 9.25/5.13              & ( P @ A6 @ B6 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1370_bex2I,axiom,
% 9.25/5.13      ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,S: set_Pr8536935166611901872et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 9.25/5.13        ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S )
% 9.25/5.13       => ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S )
% 9.25/5.13           => ( P @ A @ B ) )
% 9.25/5.13         => ? [A6: produc3658429121746597890et_nat > $o,B6: produc3925858234332021118et_nat] :
% 9.25/5.13              ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A6 @ B6 ) @ S )
% 9.25/5.13              & ( P @ A6 @ B6 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1371_bex2I,axiom,
% 9.25/5.13      ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,S: set_Pr9222295170931077689nt_int,P: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 9.25/5.13        ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A @ B ) @ S )
% 9.25/5.13       => ( ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A @ B ) @ S )
% 9.25/5.13           => ( P @ A @ B ) )
% 9.25/5.13         => ? [A6: produc8551481072490612790e_term > option6357759511663192854e_term,B6: product_prod_int_int] :
% 9.25/5.13              ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A6 @ B6 ) @ S )
% 9.25/5.13              & ( P @ A6 @ B6 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1372_bex2I,axiom,
% 9.25/5.13      ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,S: set_Pr1872883991513573699nt_int,P: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 9.25/5.13        ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A @ B ) @ S )
% 9.25/5.13       => ( ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A @ B ) @ S )
% 9.25/5.13           => ( P @ A @ B ) )
% 9.25/5.13         => ? [A6: int > option6357759511663192854e_term,B6: product_prod_int_int] :
% 9.25/5.13              ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A6 @ B6 ) @ S )
% 9.25/5.13              & ( P @ A6 @ B6 ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1373_surj__pair,axiom,
% 9.25/5.13      ! [P4: produc1908205239877642774nteger] :
% 9.25/5.13      ? [X2: produc6241069584506657477e_term > option6357759511663192854e_term,Y2: produc8923325533196201883nteger] :
% 9.25/5.13        ( P4
% 9.25/5.13        = ( produc8603105652947943368nteger @ X2 @ Y2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1374_surj__pair,axiom,
% 9.25/5.13      ! [P4: produc3925858234332021118et_nat] :
% 9.25/5.13      ? [X2: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 9.25/5.13        ( P4
% 9.25/5.13        = ( produc5001842942810119800et_nat @ X2 @ Y2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1375_surj__pair,axiom,
% 9.25/5.13      ! [P4: produc2732055786443039994et_nat] :
% 9.25/5.13      ? [X2: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat] :
% 9.25/5.13        ( P4
% 9.25/5.13        = ( produc2245416461498447860et_nat @ X2 @ Y2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1376_surj__pair,axiom,
% 9.25/5.13      ! [P4: produc2285326912895808259nt_int] :
% 9.25/5.13      ? [X2: produc8551481072490612790e_term > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 9.25/5.13        ( P4
% 9.25/5.13        = ( produc5700946648718959541nt_int @ X2 @ Y2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1377_surj__pair,axiom,
% 9.25/5.13      ! [P4: produc7773217078559923341nt_int] :
% 9.25/5.13      ? [X2: int > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 9.25/5.13        ( P4
% 9.25/5.13        = ( produc4305682042979456191nt_int @ X2 @ Y2 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1378_prod__cases,axiom,
% 9.25/5.13      ! [P: produc1908205239877642774nteger > $o,P4: produc1908205239877642774nteger] :
% 9.25/5.13        ( ! [A6: produc6241069584506657477e_term > option6357759511663192854e_term,B6: produc8923325533196201883nteger] : ( P @ ( produc8603105652947943368nteger @ A6 @ B6 ) )
% 9.25/5.13       => ( P @ P4 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1379_prod__cases,axiom,
% 9.25/5.13      ! [P: produc3925858234332021118et_nat > $o,P4: produc3925858234332021118et_nat] :
% 9.25/5.13        ( ! [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat] : ( P @ ( produc5001842942810119800et_nat @ A6 @ B6 ) )
% 9.25/5.13       => ( P @ P4 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1380_prod__cases,axiom,
% 9.25/5.13      ! [P: produc2732055786443039994et_nat > $o,P4: produc2732055786443039994et_nat] :
% 9.25/5.13        ( ! [A6: produc3658429121746597890et_nat > $o,B6: produc3925858234332021118et_nat] : ( P @ ( produc2245416461498447860et_nat @ A6 @ B6 ) )
% 9.25/5.13       => ( P @ P4 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1381_prod__cases,axiom,
% 9.25/5.13      ! [P: produc2285326912895808259nt_int > $o,P4: produc2285326912895808259nt_int] :
% 9.25/5.13        ( ! [A6: produc8551481072490612790e_term > option6357759511663192854e_term,B6: product_prod_int_int] : ( P @ ( produc5700946648718959541nt_int @ A6 @ B6 ) )
% 9.25/5.13       => ( P @ P4 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1382_prod__cases,axiom,
% 9.25/5.13      ! [P: produc7773217078559923341nt_int > $o,P4: produc7773217078559923341nt_int] :
% 9.25/5.13        ( ! [A6: int > option6357759511663192854e_term,B6: product_prod_int_int] : ( P @ ( produc4305682042979456191nt_int @ A6 @ B6 ) )
% 9.25/5.13       => ( P @ P4 ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1383_Pair__inject,axiom,
% 9.25/5.13      ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 9.25/5.13        ( ( ( produc8603105652947943368nteger @ A @ B )
% 9.25/5.13          = ( produc8603105652947943368nteger @ A5 @ B5 ) )
% 9.25/5.13       => ~ ( ( A = A5 )
% 9.25/5.13           => ( B != B5 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1384_Pair__inject,axiom,
% 9.25/5.13      ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A5: produc3658429121746597890et_nat > $o,B5: produc3658429121746597890et_nat] :
% 9.25/5.13        ( ( ( produc5001842942810119800et_nat @ A @ B )
% 9.25/5.13          = ( produc5001842942810119800et_nat @ A5 @ B5 ) )
% 9.25/5.13       => ~ ( ( A = A5 )
% 9.25/5.13           => ( B != B5 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1385_Pair__inject,axiom,
% 9.25/5.13      ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A5: produc3658429121746597890et_nat > $o,B5: produc3925858234332021118et_nat] :
% 9.25/5.13        ( ( ( produc2245416461498447860et_nat @ A @ B )
% 9.25/5.13          = ( produc2245416461498447860et_nat @ A5 @ B5 ) )
% 9.25/5.13       => ~ ( ( A = A5 )
% 9.25/5.13           => ( B != B5 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1386_Pair__inject,axiom,
% 9.25/5.13      ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: product_prod_int_int] :
% 9.25/5.13        ( ( ( produc5700946648718959541nt_int @ A @ B )
% 9.25/5.13          = ( produc5700946648718959541nt_int @ A5 @ B5 ) )
% 9.25/5.13       => ~ ( ( A = A5 )
% 9.25/5.13           => ( B != B5 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1387_Pair__inject,axiom,
% 9.25/5.13      ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A5: int > option6357759511663192854e_term,B5: product_prod_int_int] :
% 9.25/5.13        ( ( ( produc4305682042979456191nt_int @ A @ B )
% 9.25/5.13          = ( produc4305682042979456191nt_int @ A5 @ B5 ) )
% 9.25/5.13       => ~ ( ( A = A5 )
% 9.25/5.13           => ( B != B5 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1388_prod__cases3,axiom,
% 9.25/5.13      ! [Y: produc1908205239877642774nteger] :
% 9.25/5.13        ~ ! [A6: produc6241069584506657477e_term > option6357759511663192854e_term,B6: code_integer,C3: code_integer] :
% 9.25/5.13            ( Y
% 9.25/5.13           != ( produc8603105652947943368nteger @ A6 @ ( produc1086072967326762835nteger @ B6 @ C3 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1389_prod__cases3,axiom,
% 9.25/5.13      ! [Y: produc3925858234332021118et_nat] :
% 9.25/5.13        ~ ! [A6: produc3658429121746597890et_nat > $o,B6: heap_e7401611519738050253t_unit,C3: set_nat] :
% 9.25/5.13            ( Y
% 9.25/5.13           != ( produc5001842942810119800et_nat @ A6 @ ( produc7507926704131184380et_nat @ B6 @ C3 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1390_prod__cases3,axiom,
% 9.25/5.13      ! [Y: produc2732055786443039994et_nat] :
% 9.25/5.13        ~ ! [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat > $o,C3: produc3658429121746597890et_nat] :
% 9.25/5.13            ( Y
% 9.25/5.13           != ( produc2245416461498447860et_nat @ A6 @ ( produc5001842942810119800et_nat @ B6 @ C3 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1391_prod__cases3,axiom,
% 9.25/5.13      ! [Y: produc2285326912895808259nt_int] :
% 9.25/5.13        ~ ! [A6: produc8551481072490612790e_term > option6357759511663192854e_term,B6: int,C3: int] :
% 9.25/5.13            ( Y
% 9.25/5.13           != ( produc5700946648718959541nt_int @ A6 @ ( product_Pair_int_int @ B6 @ C3 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1392_prod__cases3,axiom,
% 9.25/5.13      ! [Y: produc7773217078559923341nt_int] :
% 9.25/5.13        ~ ! [A6: int > option6357759511663192854e_term,B6: int,C3: int] :
% 9.25/5.13            ( Y
% 9.25/5.13           != ( produc4305682042979456191nt_int @ A6 @ ( product_Pair_int_int @ B6 @ C3 ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1393_prod__cases4,axiom,
% 9.25/5.13      ! [Y: produc2732055786443039994et_nat] :
% 9.25/5.13        ~ ! [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat > $o,C3: heap_e7401611519738050253t_unit,D: set_nat] :
% 9.25/5.13            ( Y
% 9.25/5.13           != ( produc2245416461498447860et_nat @ A6 @ ( produc5001842942810119800et_nat @ B6 @ ( produc7507926704131184380et_nat @ C3 @ D ) ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1394_prod__induct3,axiom,
% 9.25/5.13      ! [P: produc1908205239877642774nteger > $o,X: produc1908205239877642774nteger] :
% 9.25/5.13        ( ! [A6: produc6241069584506657477e_term > option6357759511663192854e_term,B6: code_integer,C3: code_integer] : ( P @ ( produc8603105652947943368nteger @ A6 @ ( produc1086072967326762835nteger @ B6 @ C3 ) ) )
% 9.25/5.13       => ( P @ X ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1395_prod__induct3,axiom,
% 9.25/5.13      ! [P: produc3925858234332021118et_nat > $o,X: produc3925858234332021118et_nat] :
% 9.25/5.13        ( ! [A6: produc3658429121746597890et_nat > $o,B6: heap_e7401611519738050253t_unit,C3: set_nat] : ( P @ ( produc5001842942810119800et_nat @ A6 @ ( produc7507926704131184380et_nat @ B6 @ C3 ) ) )
% 9.25/5.13       => ( P @ X ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1396_prod__induct3,axiom,
% 9.25/5.13      ! [P: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 9.25/5.13        ( ! [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat > $o,C3: produc3658429121746597890et_nat] : ( P @ ( produc2245416461498447860et_nat @ A6 @ ( produc5001842942810119800et_nat @ B6 @ C3 ) ) )
% 9.25/5.13       => ( P @ X ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1397_prod__induct3,axiom,
% 9.25/5.13      ! [P: produc2285326912895808259nt_int > $o,X: produc2285326912895808259nt_int] :
% 9.25/5.13        ( ! [A6: produc8551481072490612790e_term > option6357759511663192854e_term,B6: int,C3: int] : ( P @ ( produc5700946648718959541nt_int @ A6 @ ( product_Pair_int_int @ B6 @ C3 ) ) )
% 9.25/5.13       => ( P @ X ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1398_prod__induct3,axiom,
% 9.25/5.13      ! [P: produc7773217078559923341nt_int > $o,X: produc7773217078559923341nt_int] :
% 9.25/5.13        ( ! [A6: int > option6357759511663192854e_term,B6: int,C3: int] : ( P @ ( produc4305682042979456191nt_int @ A6 @ ( product_Pair_int_int @ B6 @ C3 ) ) )
% 9.25/5.13       => ( P @ X ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1399_prod__induct4,axiom,
% 9.25/5.13      ! [P: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 9.25/5.13        ( ! [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat > $o,C3: heap_e7401611519738050253t_unit,D: set_nat] : ( P @ ( produc2245416461498447860et_nat @ A6 @ ( produc5001842942810119800et_nat @ B6 @ ( produc7507926704131184380et_nat @ C3 @ D ) ) ) )
% 9.25/5.13       => ( P @ X ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1400_memb__imp__not__empty,axiom,
% 9.25/5.13      ! [X: set_Pr958786334691620121nt_int,S: set_se6260736226359567993nt_int] :
% 9.25/5.13        ( ( member2340774599025711042nt_int @ X @ S )
% 9.25/5.13       => ( S != bot_bo1488462491386950373nt_int ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1401_memb__imp__not__empty,axiom,
% 9.25/5.13      ! [X: set_nat,S: set_set_nat] :
% 9.25/5.13        ( ( member_set_nat @ X @ S )
% 9.25/5.13       => ( S != bot_bot_set_set_nat ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1402_memb__imp__not__empty,axiom,
% 9.25/5.13      ! [X: produc3658429121746597890et_nat > $o,S: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13        ( ( member6576561426505652726_nat_o @ X @ S )
% 9.25/5.13       => ( S != bot_bo7824918357723582233_nat_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1403_memb__imp__not__empty,axiom,
% 9.25/5.13      ! [X: product_prod_nat_nat,S: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( member8440522571783428010at_nat @ X @ S )
% 9.25/5.13       => ( S != bot_bo2099793752762293965at_nat ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1404_memb__imp__not__empty,axiom,
% 9.25/5.13      ! [X: $o,S: set_o] :
% 9.25/5.13        ( ( member_o @ X @ S )
% 9.25/5.13       => ( S != bot_bot_set_o ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1405_memb__imp__not__empty,axiom,
% 9.25/5.13      ! [X: nat,S: set_nat] :
% 9.25/5.13        ( ( member_nat @ X @ S )
% 9.25/5.13       => ( S != bot_bot_set_nat ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1406_memb__imp__not__empty,axiom,
% 9.25/5.13      ! [X: int,S: set_int] :
% 9.25/5.13        ( ( member_int @ X @ S )
% 9.25/5.13       => ( S != bot_bot_set_int ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1407_set__notEmptyE,axiom,
% 9.25/5.13      ! [S: set_se6260736226359567993nt_int] :
% 9.25/5.13        ( ( S != bot_bo1488462491386950373nt_int )
% 9.25/5.13       => ~ ! [X2: set_Pr958786334691620121nt_int] :
% 9.25/5.13              ~ ( member2340774599025711042nt_int @ X2 @ S ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1408_set__notEmptyE,axiom,
% 9.25/5.13      ! [S: set_set_nat] :
% 9.25/5.13        ( ( S != bot_bot_set_set_nat )
% 9.25/5.13       => ~ ! [X2: set_nat] :
% 9.25/5.13              ~ ( member_set_nat @ X2 @ S ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1409_set__notEmptyE,axiom,
% 9.25/5.13      ! [S: set_Pr4532377907799695533_nat_o] :
% 9.25/5.13        ( ( S != bot_bo7824918357723582233_nat_o )
% 9.25/5.13       => ~ ! [X2: produc3658429121746597890et_nat > $o] :
% 9.25/5.13              ~ ( member6576561426505652726_nat_o @ X2 @ S ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1410_set__notEmptyE,axiom,
% 9.25/5.13      ! [S: set_Pr1261947904930325089at_nat] :
% 9.25/5.13        ( ( S != bot_bo2099793752762293965at_nat )
% 9.25/5.13       => ~ ! [X2: product_prod_nat_nat] :
% 9.25/5.13              ~ ( member8440522571783428010at_nat @ X2 @ S ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1411_set__notEmptyE,axiom,
% 9.25/5.13      ! [S: set_o] :
% 9.25/5.13        ( ( S != bot_bot_set_o )
% 9.25/5.13       => ~ ! [X2: $o] :
% 9.25/5.13              ~ ( member_o @ X2 @ S ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1412_set__notEmptyE,axiom,
% 9.25/5.13      ! [S: set_nat] :
% 9.25/5.13        ( ( S != bot_bot_set_nat )
% 9.25/5.13       => ~ ! [X2: nat] :
% 9.25/5.13              ~ ( member_nat @ X2 @ S ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1413_set__notEmptyE,axiom,
% 9.25/5.13      ! [S: set_int] :
% 9.25/5.13        ( ( S != bot_bot_set_int )
% 9.25/5.13       => ~ ! [X2: int] :
% 9.25/5.13              ~ ( member_int @ X2 @ S ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1414_verit__negate__coefficient_I3_J,axiom,
% 9.25/5.13      ! [A: int,B: int] :
% 9.25/5.13        ( ( A = B )
% 9.25/5.13       => ( ( uminus_uminus_int @ A )
% 9.25/5.13          = ( uminus_uminus_int @ B ) ) ) ).
% 9.25/5.13  
% 9.25/5.13  thf(fact_1415_verit__negate__coefficient_I3_J,axiom,
% 9.25/5.13      ! [A: code_integer,B: code_integer] :
% 9.25/5.13        ( ( A = B )
% 9.25/5.13       => ( ( uminus1351360451143612070nteger @ A )
% 9.25/5.13          = ( uminus1351360451143612070nteger @ B ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1416_verit__negate__coefficient_I3_J,axiom,
% 9.25/5.14      ! [A: rat,B: rat] :
% 9.25/5.14        ( ( A = B )
% 9.25/5.14       => ( ( uminus_uminus_rat @ A )
% 9.25/5.14          = ( uminus_uminus_rat @ B ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1417_sup__Un__eq,axiom,
% 9.25/5.14      ! [R: set_se6260736226359567993nt_int,S: set_se6260736226359567993nt_int] :
% 9.25/5.14        ( ( sup_su1852724690005176016_int_o
% 9.25/5.14          @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ R )
% 9.25/5.14          @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ S ) )
% 9.25/5.14        = ( ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ ( sup_su2047564715030645325nt_int @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1418_sup__Un__eq,axiom,
% 9.25/5.14      ! [R: set_set_nat,S: set_set_nat] :
% 9.25/5.14        ( ( sup_sup_set_nat_o
% 9.25/5.14          @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ R )
% 9.25/5.14          @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ S ) )
% 9.25/5.14        = ( ^ [X3: set_nat] : ( member_set_nat @ X3 @ ( sup_sup_set_set_nat @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1419_sup__Un__eq,axiom,
% 9.25/5.14      ! [R: set_int,S: set_int] :
% 9.25/5.14        ( ( sup_sup_int_o
% 9.25/5.14          @ ^ [X3: int] : ( member_int @ X3 @ R )
% 9.25/5.14          @ ^ [X3: int] : ( member_int @ X3 @ S ) )
% 9.25/5.14        = ( ^ [X3: int] : ( member_int @ X3 @ ( sup_sup_set_int @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1420_sup__Un__eq,axiom,
% 9.25/5.14      ! [R: set_Pr4532377907799695533_nat_o,S: set_Pr4532377907799695533_nat_o] :
% 9.25/5.14        ( ( sup_su8003631835303541148at_o_o
% 9.25/5.14          @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ R )
% 9.25/5.14          @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ S ) )
% 9.25/5.14        = ( ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ ( sup_su5209123915105501825_nat_o @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1421_sup__Un__eq,axiom,
% 9.25/5.14      ! [R: set_Pr8551490117392284871at_nat,S: set_Pr8551490117392284871at_nat] :
% 9.25/5.14        ( ( sup_su6256023009775730178_nat_o
% 9.25/5.14          @ ^ [X3: produc4166570645942440679at_nat] : ( member6689249552917799696at_nat @ X3 @ R )
% 9.25/5.14          @ ^ [X3: produc4166570645942440679at_nat] : ( member6689249552917799696at_nat @ X3 @ S ) )
% 9.25/5.14        = ( ^ [X3: produc4166570645942440679at_nat] : ( member6689249552917799696at_nat @ X3 @ ( sup_su3035147773818789531at_nat @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1422_sup__Un__eq,axiom,
% 9.25/5.14      ! [R: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 9.25/5.14        ( ( sup_su2080679670758317954_nat_o
% 9.25/5.14          @ ^ [X3: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X3 @ R )
% 9.25/5.14          @ ^ [X3: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X3 @ S ) )
% 9.25/5.14        = ( ^ [X3: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X3 @ ( sup_su5525570899277871387at_nat @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1423_sup__Un__eq,axiom,
% 9.25/5.14      ! [R: set_nat,S: set_nat] :
% 9.25/5.14        ( ( sup_sup_nat_o
% 9.25/5.14          @ ^ [X3: nat] : ( member_nat @ X3 @ R )
% 9.25/5.14          @ ^ [X3: nat] : ( member_nat @ X3 @ S ) )
% 9.25/5.14        = ( ^ [X3: nat] : ( member_nat @ X3 @ ( sup_sup_set_nat @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1424_inf__Int__eq,axiom,
% 9.25/5.14      ! [R: set_se6260736226359567993nt_int,S: set_se6260736226359567993nt_int] :
% 9.25/5.14        ( ( inf_in5102985939729578038_int_o
% 9.25/5.14          @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ R )
% 9.25/5.14          @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ S ) )
% 9.25/5.14        = ( ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ ( inf_in8396524679539076455nt_int @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1425_inf__Int__eq,axiom,
% 9.25/5.14      ! [R: set_set_nat,S: set_set_nat] :
% 9.25/5.14        ( ( inf_inf_set_nat_o
% 9.25/5.14          @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ R )
% 9.25/5.14          @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ S ) )
% 9.25/5.14        = ( ^ [X3: set_nat] : ( member_set_nat @ X3 @ ( inf_inf_set_set_nat @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1426_inf__Int__eq,axiom,
% 9.25/5.14      ! [R: set_int,S: set_int] :
% 9.25/5.14        ( ( inf_inf_int_o
% 9.25/5.14          @ ^ [X3: int] : ( member_int @ X3 @ R )
% 9.25/5.14          @ ^ [X3: int] : ( member_int @ X3 @ S ) )
% 9.25/5.14        = ( ^ [X3: int] : ( member_int @ X3 @ ( inf_inf_set_int @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1427_inf__Int__eq,axiom,
% 9.25/5.14      ! [R: set_Pr4532377907799695533_nat_o,S: set_Pr4532377907799695533_nat_o] :
% 9.25/5.14        ( ( inf_in9018898317438245890at_o_o
% 9.25/5.14          @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ R )
% 9.25/5.14          @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ S ) )
% 9.25/5.14        = ( ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ ( inf_in1906310914598751387_nat_o @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1428_inf__Int__eq,axiom,
% 9.25/5.14      ! [R: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 9.25/5.14        ( ( inf_in5163264567034779214_nat_o
% 9.25/5.14          @ ^ [X3: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X3 @ R )
% 9.25/5.14          @ ^ [X3: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X3 @ S ) )
% 9.25/5.14        = ( ^ [X3: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X3 @ ( inf_in2572325071724192079at_nat @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1429_inf__Int__eq,axiom,
% 9.25/5.14      ! [R: set_nat,S: set_nat] :
% 9.25/5.14        ( ( inf_inf_nat_o
% 9.25/5.14          @ ^ [X3: nat] : ( member_nat @ X3 @ R )
% 9.25/5.14          @ ^ [X3: nat] : ( member_nat @ X3 @ S ) )
% 9.25/5.14        = ( ^ [X3: nat] : ( member_nat @ X3 @ ( inf_inf_set_nat @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1430_inf__Int__eq,axiom,
% 9.25/5.14      ! [R: set_Pr958786334691620121nt_int,S: set_Pr958786334691620121nt_int] :
% 9.25/5.14        ( ( inf_in3604695632404883862_int_o
% 9.25/5.14          @ ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ R )
% 9.25/5.14          @ ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ S ) )
% 9.25/5.14        = ( ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ ( inf_in2269163501485487111nt_int @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1431_inf__Int__eq,axiom,
% 9.25/5.14      ! [R: set_list_char,S: set_list_char] :
% 9.25/5.14        ( ( inf_inf_list_char_o
% 9.25/5.14          @ ^ [X3: list_char] : ( member_list_char @ X3 @ R )
% 9.25/5.14          @ ^ [X3: list_char] : ( member_list_char @ X3 @ S ) )
% 9.25/5.14        = ( ^ [X3: list_char] : ( member_list_char @ X3 @ ( inf_in6177012701088388009t_char @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1432_iso__tuple__UNIV__I,axiom,
% 9.25/5.14      ! [X: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X @ top_to6034159466715884489nt_int ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1433_iso__tuple__UNIV__I,axiom,
% 9.25/5.14      ! [X: set_nat] : ( member_set_nat @ X @ top_top_set_set_nat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1434_iso__tuple__UNIV__I,axiom,
% 9.25/5.14      ! [X: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X @ top_to4869887016220417533_nat_o ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1435_iso__tuple__UNIV__I,axiom,
% 9.25/5.14      ! [X: list_nat] : ( member_list_nat @ X @ top_top_set_list_nat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1436_iso__tuple__UNIV__I,axiom,
% 9.25/5.14      ! [X: $o] : ( member_o @ X @ top_top_set_o ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1437_iso__tuple__UNIV__I,axiom,
% 9.25/5.14      ! [X: rat] : ( member_rat @ X @ top_top_set_rat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1438_iso__tuple__UNIV__I,axiom,
% 9.25/5.14      ! [X: nat] : ( member_nat @ X @ top_top_set_nat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1439_iso__tuple__UNIV__I,axiom,
% 9.25/5.14      ! [X: int] : ( member_int @ X @ top_top_set_int ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1440_Collect__empty__eq__bot,axiom,
% 9.25/5.14      ! [P: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.14        ( ( ( collec5210948495886036740nt_int @ P )
% 9.25/5.14          = bot_bo1488462491386950373nt_int )
% 9.25/5.14        = ( P = bot_bo2686080419298087992_int_o ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1441_Collect__empty__eq__bot,axiom,
% 9.25/5.14      ! [P: set_nat > $o] :
% 9.25/5.14        ( ( ( collect_set_nat @ P )
% 9.25/5.14          = bot_bot_set_set_nat )
% 9.25/5.14        = ( P = bot_bot_set_nat_o ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1442_Collect__empty__eq__bot,axiom,
% 9.25/5.14      ! [P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.14        ( ( ( collec939566748876313656_nat_o @ P )
% 9.25/5.14          = bot_bo7824918357723582233_nat_o )
% 9.25/5.14        = ( P = bot_bo7963750851167320836at_o_o ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1443_Collect__empty__eq__bot,axiom,
% 9.25/5.14      ! [P: product_prod_nat_nat > $o] :
% 9.25/5.14        ( ( ( collec3392354462482085612at_nat @ P )
% 9.25/5.14          = bot_bo2099793752762293965at_nat )
% 9.25/5.14        = ( P = bot_bo482883023278783056_nat_o ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1444_Collect__empty__eq__bot,axiom,
% 9.25/5.14      ! [P: $o > $o] :
% 9.25/5.14        ( ( ( collect_o @ P )
% 9.25/5.14          = bot_bot_set_o )
% 9.25/5.14        = ( P = bot_bot_o_o ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1445_Collect__empty__eq__bot,axiom,
% 9.25/5.14      ! [P: nat > $o] :
% 9.25/5.14        ( ( ( collect_nat @ P )
% 9.25/5.14          = bot_bot_set_nat )
% 9.25/5.14        = ( P = bot_bot_nat_o ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1446_Collect__empty__eq__bot,axiom,
% 9.25/5.14      ! [P: int > $o] :
% 9.25/5.14        ( ( ( collect_int @ P )
% 9.25/5.14          = bot_bot_set_int )
% 9.25/5.14        = ( P = bot_bot_int_o ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1447_bot__empty__eq,axiom,
% 9.25/5.14      ( bot_bo2686080419298087992_int_o
% 9.25/5.14      = ( ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ bot_bo1488462491386950373nt_int ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1448_bot__empty__eq,axiom,
% 9.25/5.14      ( bot_bot_set_nat_o
% 9.25/5.14      = ( ^ [X3: set_nat] : ( member_set_nat @ X3 @ bot_bot_set_set_nat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1449_bot__empty__eq,axiom,
% 9.25/5.14      ( bot_bo7963750851167320836at_o_o
% 9.25/5.14      = ( ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ bot_bo7824918357723582233_nat_o ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1450_bot__empty__eq,axiom,
% 9.25/5.14      ( bot_bo482883023278783056_nat_o
% 9.25/5.14      = ( ^ [X3: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X3 @ bot_bo2099793752762293965at_nat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1451_bot__empty__eq,axiom,
% 9.25/5.14      ( bot_bot_o_o
% 9.25/5.14      = ( ^ [X3: $o] : ( member_o @ X3 @ bot_bot_set_o ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1452_bot__empty__eq,axiom,
% 9.25/5.14      ( bot_bot_nat_o
% 9.25/5.14      = ( ^ [X3: nat] : ( member_nat @ X3 @ bot_bot_set_nat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1453_bot__empty__eq,axiom,
% 9.25/5.14      ( bot_bot_int_o
% 9.25/5.14      = ( ^ [X3: int] : ( member_int @ X3 @ bot_bot_set_int ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1454_type__copy__ex__RepI,axiom,
% 9.25/5.14      ! [Rep: product_unit > $o,Abs: $o > product_unit,F4: $o > $o] :
% 9.25/5.14        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ top_top_set_o )
% 9.25/5.14       => ( ( ? [X4: $o] : ( F4 @ X4 ) )
% 9.25/5.14          = ( ? [B3: product_unit] : ( F4 @ ( Rep @ B3 ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1455_type__copy__ex__RepI,axiom,
% 9.25/5.14      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,F4: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.14        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ top_to4869887016220417533_nat_o )
% 9.25/5.14       => ( ( ? [X4: produc3658429121746597890et_nat > $o] : ( F4 @ X4 ) )
% 9.25/5.14          = ( ? [B3: assn] : ( F4 @ ( Rep @ B3 ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1456_type__copy__ex__RepI,axiom,
% 9.25/5.14      ! [Rep: literal > list_char,Abs: list_char > literal,F4: list_char > $o] :
% 9.25/5.14        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ top_to3190553582279535303t_char )
% 9.25/5.14       => ( ( ? [X4: list_char] : ( F4 @ X4 ) )
% 9.25/5.14          = ( ? [B3: literal] : ( F4 @ ( Rep @ B3 ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1457_type__copy__ex__RepI,axiom,
% 9.25/5.14      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,F4: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.14        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ top_to6034159466715884489nt_int )
% 9.25/5.14       => ( ( ? [X4: set_Pr958786334691620121nt_int] : ( F4 @ X4 ) )
% 9.25/5.14          = ( ? [B3: rat] : ( F4 @ ( Rep @ B3 ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1458_type__copy__ex__RepI,axiom,
% 9.25/5.14      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,F4: set_Pr1261947904930325089at_nat > $o] :
% 9.25/5.14        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ top_to7629004291339433233at_nat )
% 9.25/5.14       => ( ( ? [X4: set_Pr1261947904930325089at_nat] : ( F4 @ X4 ) )
% 9.25/5.14          = ( ? [B3: int] : ( F4 @ ( Rep @ B3 ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1459_type__copy__obj__one__point__absE,axiom,
% 9.25/5.14      ! [Rep: product_unit > $o,Abs: $o > product_unit,S3: product_unit] :
% 9.25/5.14        ( ( type_d6188575255521822967unit_o @ Rep @ Abs @ top_top_set_o )
% 9.25/5.14       => ~ ! [X2: $o] :
% 9.25/5.14              ( S3
% 9.25/5.14             != ( Abs @ X2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1460_type__copy__obj__one__point__absE,axiom,
% 9.25/5.14      ! [Rep: assn > produc3658429121746597890et_nat > $o,Abs: ( produc3658429121746597890et_nat > $o ) > assn,S3: assn] :
% 9.25/5.14        ( ( type_d3909072315231072503_nat_o @ Rep @ Abs @ top_to4869887016220417533_nat_o )
% 9.25/5.14       => ~ ! [X2: produc3658429121746597890et_nat > $o] :
% 9.25/5.14              ( S3
% 9.25/5.14             != ( Abs @ X2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1461_type__copy__obj__one__point__absE,axiom,
% 9.25/5.14      ! [Rep: literal > list_char,Abs: list_char > literal,S3: literal] :
% 9.25/5.14        ( ( type_d4752411451802217481t_char @ Rep @ Abs @ top_to3190553582279535303t_char )
% 9.25/5.14       => ~ ! [X2: list_char] :
% 9.25/5.14              ( S3
% 9.25/5.14             != ( Abs @ X2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1462_type__copy__obj__one__point__absE,axiom,
% 9.25/5.14      ! [Rep: rat > set_Pr958786334691620121nt_int,Abs: set_Pr958786334691620121nt_int > rat,S3: rat] :
% 9.25/5.14        ( ( type_d8554052265237484179nt_int @ Rep @ Abs @ top_to6034159466715884489nt_int )
% 9.25/5.14       => ~ ! [X2: set_Pr958786334691620121nt_int] :
% 9.25/5.14              ( S3
% 9.25/5.14             != ( Abs @ X2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1463_type__copy__obj__one__point__absE,axiom,
% 9.25/5.14      ! [Rep: int > set_Pr1261947904930325089at_nat,Abs: set_Pr1261947904930325089at_nat > int,S3: int] :
% 9.25/5.14        ( ( type_d8752208705193531015at_nat @ Rep @ Abs @ top_to7629004291339433233at_nat )
% 9.25/5.14       => ~ ! [X2: set_Pr1261947904930325089at_nat] :
% 9.25/5.14              ( S3
% 9.25/5.14             != ( Abs @ X2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1464_dbl__inc__simps_I4_J,axiom,
% 9.25/5.14      ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.14      = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1465_dbl__inc__simps_I4_J,axiom,
% 9.25/5.14      ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.14      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1466_dbl__inc__simps_I4_J,axiom,
% 9.25/5.14      ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.25/5.14      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1467_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 9.25/5.14      boolea7165431671056489859t_unit @ inf_inf_Product_unit @ sup_sup_Product_unit @ uminus2952777764628376836t_unit @ bot_bot_Product_unit @ top_top_Product_unit ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1468_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 9.25/5.14      boolea379910186789422830_set_o @ inf_inf_set_o @ sup_sup_set_o @ uminus_uminus_set_o @ bot_bot_set_o @ top_top_set_o ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1469_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 9.25/5.14      boolea6493995471900120728et_rat @ inf_inf_set_rat @ sup_sup_set_rat @ uminus2201863774496077783et_rat @ bot_bot_set_rat @ top_top_set_rat ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1470_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 9.25/5.14      boolea778851993438741648et_nat @ inf_inf_set_nat @ sup_sup_set_nat @ uminus5710092332889474511et_nat @ bot_bot_set_nat @ top_top_set_nat ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1471_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 9.25/5.14      boolea5824373010784320748et_int @ inf_inf_set_int @ sup_sup_set_int @ uminus1532241313380277803et_int @ bot_bot_set_int @ top_top_set_int ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1472_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 9.25/5.14      boolea9074081411689916704st_nat @ inf_inf_set_list_nat @ sup_sup_set_list_nat @ uminus3195874150345416415st_nat @ bot_bot_set_list_nat @ top_top_set_list_nat ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1473_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 9.25/5.14      boolea934052484356091300char_o @ inf_inf_list_char_o @ sup_sup_list_char_o @ uminus7154032370948614053char_o @ bot_bot_list_char_o @ top_top_list_char_o ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1474_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 9.25/5.14      boolea949959532490082519at_nat @ inf_in2572325071724192079at_nat @ sup_su6327502436637775413at_nat @ uminus6524753893492686040at_nat @ bot_bo2099793752762293965at_nat @ top_to4669805908274784177at_nat ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1475_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 9.25/5.14      boolea1849928419393854478_int_o @ inf_in3604695632404883862_int_o @ sup_su8463660629351352368_int_o @ uminus7117520113953359693_int_o @ bot_bo8147686125503663512_int_o @ top_to1578927101902068148_int_o ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1476_boolean__algebra_Oabstract__boolean__algebra__axioms,axiom,
% 9.25/5.14      boolea51845251928480829at_nat @ inf_in1697001100524423349at_nat @ sup_su3035147773818789531at_nat @ uminus2330091110623919550at_nat @ bot_bo8422036546324065075at_nat @ top_to8764741339697478167at_nat ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1477_top__empty__eq,axiom,
% 9.25/5.14      ( top_to6187514276045680724_int_o
% 9.25/5.14      = ( ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ top_to6034159466715884489nt_int ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1478_top__empty__eq,axiom,
% 9.25/5.14      ( top_top_set_nat_o
% 9.25/5.14      = ( ^ [X3: set_nat] : ( member_set_nat @ X3 @ top_top_set_set_nat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1479_top__empty__eq,axiom,
% 9.25/5.14      ( top_to2462227307520033056at_o_o
% 9.25/5.14      = ( ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ top_to4869887016220417533_nat_o ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1480_top__empty__eq,axiom,
% 9.25/5.14      ( top_top_list_nat_o
% 9.25/5.14      = ( ^ [X3: list_nat] : ( member_list_nat @ X3 @ top_top_set_list_nat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1481_top__empty__eq,axiom,
% 9.25/5.14      ( top_top_o_o
% 9.25/5.14      = ( ^ [X3: $o] : ( member_o @ X3 @ top_top_set_o ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1482_top__empty__eq,axiom,
% 9.25/5.14      ( top_top_rat_o
% 9.25/5.14      = ( ^ [X3: rat] : ( member_rat @ X3 @ top_top_set_rat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1483_top__empty__eq,axiom,
% 9.25/5.14      ( top_top_nat_o
% 9.25/5.14      = ( ^ [X3: nat] : ( member_nat @ X3 @ top_top_set_nat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1484_top__empty__eq,axiom,
% 9.25/5.14      ( top_top_int_o
% 9.25/5.14      = ( ^ [X3: int] : ( member_int @ X3 @ top_top_set_int ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1485_sup__Un__eq2,axiom,
% 9.25/5.14      ! [R: set_Pr1281608226676607948nteger,S: set_Pr1281608226676607948nteger] :
% 9.25/5.14        ( ( sup_su234547053653886311eger_o
% 9.25/5.14          @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ R )
% 9.25/5.14          @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ S ) )
% 9.25/5.14        = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ ( sup_su4591284015454442744nteger @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1486_sup__Un__eq2,axiom,
% 9.25/5.14      ! [R: set_Pr3286484037609594932et_nat,S: set_Pr3286484037609594932et_nat] :
% 9.25/5.14        ( ( sup_su1630790145277462993_nat_o
% 9.25/5.14          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R )
% 9.25/5.14          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ S ) )
% 9.25/5.14        = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ ( sup_su7128418612487073120et_nat @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1487_sup__Un__eq2,axiom,
% 9.25/5.14      ! [R: set_Pr8536935166611901872et_nat,S: set_Pr8536935166611901872et_nat] :
% 9.25/5.14        ( ( sup_su6535292691877529429_nat_o
% 9.25/5.14          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R )
% 9.25/5.14          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ S ) )
% 9.25/5.14        = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ ( sup_su8975264963432250076et_nat @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1488_sup__Un__eq2,axiom,
% 9.25/5.14      ! [R: set_Pr9222295170931077689nt_int,S: set_Pr9222295170931077689nt_int] :
% 9.25/5.14        ( ( sup_su4182031696650224058_int_o
% 9.25/5.14          @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ R )
% 9.25/5.14          @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ S ) )
% 9.25/5.14        = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ ( sup_su3382966977382714213nt_int @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1489_sup__Un__eq2,axiom,
% 9.25/5.14      ! [R: set_Pr1872883991513573699nt_int,S: set_Pr1872883991513573699nt_int] :
% 9.25/5.14        ( ( sup_su600977994968626096_int_o
% 9.25/5.14          @ ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ R )
% 9.25/5.14          @ ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ S ) )
% 9.25/5.14        = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ ( sup_su3298353300217089135nt_int @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1490_sup__Un__eq2,axiom,
% 9.25/5.14      ! [R: set_Pr8551490117392284871at_nat,S: set_Pr8551490117392284871at_nat] :
% 9.25/5.14        ( ( sup_su2200014604384089602_nat_o
% 9.25/5.14          @ ^ [X3: multis2468970476368604999at_nat,Y3: multis2468970476368604999at_nat] : ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ X3 @ Y3 ) @ R )
% 9.25/5.14          @ ^ [X3: multis2468970476368604999at_nat,Y3: multis2468970476368604999at_nat] : ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ X3 @ Y3 ) @ S ) )
% 9.25/5.14        = ( ^ [X3: multis2468970476368604999at_nat,Y3: multis2468970476368604999at_nat] : ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ X3 @ Y3 ) @ ( sup_su3035147773818789531at_nat @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1491_sup__Un__eq2,axiom,
% 9.25/5.14      ! [R: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 9.25/5.14        ( ( sup_su7519161239522478338_nat_o
% 9.25/5.14          @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ R )
% 9.25/5.14          @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ S ) )
% 9.25/5.14        = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y3 ) @ ( sup_su5525570899277871387at_nat @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1492_inf__Int__eq2,axiom,
% 9.25/5.14      ! [R: set_Pr1281608226676607948nteger,S: set_Pr1281608226676607948nteger] :
% 9.25/5.14        ( ( inf_in3563340378267265229eger_o
% 9.25/5.14          @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ R )
% 9.25/5.14          @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ S ) )
% 9.25/5.14        = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ ( inf_in3408396081536963678nteger @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1493_inf__Int__eq2,axiom,
% 9.25/5.14      ! [R: set_Pr3286484037609594932et_nat,S: set_Pr3286484037609594932et_nat] :
% 9.25/5.14        ( ( inf_in3295504058751909687_nat_o
% 9.25/5.14          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R )
% 9.25/5.14          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ S ) )
% 9.25/5.14        = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ ( inf_in1768905781608824518et_nat @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1494_inf__Int__eq2,axiom,
% 9.25/5.14      ! [R: set_Pr8536935166611901872et_nat,S: set_Pr8536935166611901872et_nat] :
% 9.25/5.14        ( ( inf_in2641120393918057659_nat_o
% 9.25/5.14          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R )
% 9.25/5.14          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ S ) )
% 9.25/5.14        = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ ( inf_in3088352823822785602et_nat @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1495_inf__Int__eq2,axiom,
% 9.25/5.14      ! [R: set_Pr9222295170931077689nt_int,S: set_Pr9222295170931077689nt_int] :
% 9.25/5.14        ( ( inf_in8045883074377559328_int_o
% 9.25/5.14          @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ R )
% 9.25/5.14          @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ S ) )
% 9.25/5.14        = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ ( inf_in2576786181675586251nt_int @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1496_inf__Int__eq2,axiom,
% 9.25/5.14      ! [R: set_Pr1872883991513573699nt_int,S: set_Pr1872883991513573699nt_int] :
% 9.25/5.14        ( ( inf_in8201999774870019094_int_o
% 9.25/5.14          @ ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ R )
% 9.25/5.14          @ ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ S ) )
% 9.25/5.14        = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ ( inf_in8806012763027673301nt_int @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1497_inf__Int__eq2,axiom,
% 9.25/5.14      ! [R: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 9.25/5.14        ( ( inf_inf_nat_nat_o
% 9.25/5.14          @ ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R )
% 9.25/5.14          @ ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ S ) )
% 9.25/5.14        = ( ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ ( inf_in2572325071724192079at_nat @ R @ S ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1498_bot__empty__eq2,axiom,
% 9.25/5.14      ( bot_bo3000040243691356879eger_o
% 9.25/5.14      = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ bot_bo5443222936135328352nteger ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1499_bot__empty__eq2,axiom,
% 9.25/5.14      ( bot_bo5580076615179976505_nat_o
% 9.25/5.14      = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ bot_bo1481135142794719944et_nat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1500_bot__empty__eq2,axiom,
% 9.25/5.14      ( bot_bo3790638025767943357_nat_o
% 9.25/5.14      = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ bot_bo5635537948650799172et_nat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1501_bot__empty__eq2,axiom,
% 9.25/5.14      ( bot_bo8662317086119403298_int_o
% 9.25/5.14      = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ bot_bo572930865798478029nt_int ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1502_bot__empty__eq2,axiom,
% 9.25/5.14      ( bot_bo1403522918969695512_int_o
% 9.25/5.14      = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ bot_bo4508923176915781079nt_int ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1503_bot__empty__eq2,axiom,
% 9.25/5.14      ( bot_bot_nat_nat_o
% 9.25/5.14      = ( ^ [X3: nat,Y3: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ bot_bo2099793752762293965at_nat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1504_pred__equals__eq2,axiom,
% 9.25/5.14      ! [R: set_Pr1281608226676607948nteger,S: set_Pr1281608226676607948nteger] :
% 9.25/5.14        ( ( ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ R ) )
% 9.25/5.14          = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ S ) ) )
% 9.25/5.14        = ( R = S ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1505_pred__equals__eq2,axiom,
% 9.25/5.14      ! [R: set_Pr3286484037609594932et_nat,S: set_Pr3286484037609594932et_nat] :
% 9.25/5.14        ( ( ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R ) )
% 9.25/5.14          = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ S ) ) )
% 9.25/5.14        = ( R = S ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1506_pred__equals__eq2,axiom,
% 9.25/5.14      ! [R: set_Pr8536935166611901872et_nat,S: set_Pr8536935166611901872et_nat] :
% 9.25/5.14        ( ( ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R ) )
% 9.25/5.14          = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ S ) ) )
% 9.25/5.14        = ( R = S ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1507_pred__equals__eq2,axiom,
% 9.25/5.14      ! [R: set_Pr9222295170931077689nt_int,S: set_Pr9222295170931077689nt_int] :
% 9.25/5.14        ( ( ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ R ) )
% 9.25/5.14          = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ S ) ) )
% 9.25/5.14        = ( R = S ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1508_pred__equals__eq2,axiom,
% 9.25/5.14      ! [R: set_Pr1872883991513573699nt_int,S: set_Pr1872883991513573699nt_int] :
% 9.25/5.14        ( ( ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ R ) )
% 9.25/5.14          = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ S ) ) )
% 9.25/5.14        = ( R = S ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1509_top__empty__eq2,axiom,
% 9.25/5.14      ( top_to8112647782992986859eger_o
% 9.25/5.14      = ( ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ top_to7512759353274530428nteger ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1510_top__empty__eq2,axiom,
% 9.25/5.14      ( top_to2428096842796733269_nat_o
% 9.25/5.14      = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ top_to8753217654552796900et_nat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1511_top__empty__eq2,axiom,
% 9.25/5.14      ( top_to7190503160269336793_nat_o
% 9.25/5.14      = ( ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ top_to1599102959340997728et_nat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1512_top__empty__eq2,axiom,
% 9.25/5.14      ( top_to6261655714344447806_int_o
% 9.25/5.14      = ( ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ top_to3181862456159035625nt_int ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1513_top__empty__eq2,axiom,
% 9.25/5.14      ( top_to6513043852502318900_int_o
% 9.25/5.14      = ( ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ top_to2069137843433766899nt_int ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1514_times__assn__raw_Opelims_I3_J,axiom,
% 9.25/5.14      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 9.25/5.14        ( ~ ( times_assn_raw @ X @ Xa @ Xb )
% 9.25/5.14       => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 9.25/5.14         => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 9.25/5.14                ( ( Xb
% 9.25/5.14                  = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.14               => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As4 ) ) ) )
% 9.25/5.14                 => ? [As13: set_nat,As23: set_nat] :
% 9.25/5.14                      ( ( As4
% 9.25/5.14                        = ( sup_sup_set_nat @ As13 @ As23 ) )
% 9.25/5.14                      & ( ( inf_inf_set_nat @ As13 @ As23 )
% 9.25/5.14                        = bot_bot_set_nat )
% 9.25/5.14                      & ( X @ ( produc7507926704131184380et_nat @ H @ As13 ) )
% 9.25/5.14                      & ( Xa @ ( produc7507926704131184380et_nat @ H @ As23 ) ) ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1515_times__assn__raw_Opelims_I2_J,axiom,
% 9.25/5.14      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 9.25/5.14        ( ( times_assn_raw @ X @ Xa @ Xb )
% 9.25/5.14       => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 9.25/5.14         => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 9.25/5.14                ( ( Xb
% 9.25/5.14                  = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.14               => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As4 ) ) ) )
% 9.25/5.14                 => ~ ? [As12: set_nat,As22: set_nat] :
% 9.25/5.14                        ( ( As4
% 9.25/5.14                          = ( sup_sup_set_nat @ As12 @ As22 ) )
% 9.25/5.14                        & ( ( inf_inf_set_nat @ As12 @ As22 )
% 9.25/5.14                          = bot_bot_set_nat )
% 9.25/5.14                        & ( X @ ( produc7507926704131184380et_nat @ H @ As12 ) )
% 9.25/5.14                        & ( Xa @ ( produc7507926704131184380et_nat @ H @ As22 ) ) ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1516_times__assn__raw_Opelims_I1_J,axiom,
% 9.25/5.14      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 9.25/5.14        ( ( ( times_assn_raw @ X @ Xa @ Xb )
% 9.25/5.14          = Y )
% 9.25/5.14       => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 9.25/5.14         => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 9.25/5.14                ( ( Xb
% 9.25/5.14                  = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.14               => ( ( Y
% 9.25/5.14                    = ( ? [As1: set_nat,As2: set_nat] :
% 9.25/5.14                          ( ( As4
% 9.25/5.14                            = ( sup_sup_set_nat @ As1 @ As2 ) )
% 9.25/5.14                          & ( ( inf_inf_set_nat @ As1 @ As2 )
% 9.25/5.14                            = bot_bot_set_nat )
% 9.25/5.14                          & ( X @ ( produc7507926704131184380et_nat @ H @ As1 ) )
% 9.25/5.14                          & ( Xa @ ( produc7507926704131184380et_nat @ H @ As2 ) ) ) ) )
% 9.25/5.14                 => ~ ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As4 ) ) ) ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1517_Set_Ois__empty__def,axiom,
% 9.25/5.14      ( is_emp1662574758705540307at_nat
% 9.25/5.14      = ( ^ [A4: set_Pr1261947904930325089at_nat] : ( A4 = bot_bo2099793752762293965at_nat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1518_Set_Ois__empty__def,axiom,
% 9.25/5.14      ( is_empty_o
% 9.25/5.14      = ( ^ [A4: set_o] : ( A4 = bot_bot_set_o ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1519_Set_Ois__empty__def,axiom,
% 9.25/5.14      ( is_empty_nat
% 9.25/5.14      = ( ^ [A4: set_nat] : ( A4 = bot_bot_set_nat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1520_Set_Ois__empty__def,axiom,
% 9.25/5.14      ( is_empty_int
% 9.25/5.14      = ( ^ [A4: set_int] : ( A4 = bot_bot_set_int ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1521_wand__assnI,axiom,
% 9.25/5.14      ! [H3: heap_e7401611519738050253t_unit,As: set_nat,Q2: assn,R: assn] :
% 9.25/5.14        ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 9.25/5.14       => ( ! [H5: heap_e7401611519738050253t_unit,As5: set_nat] :
% 9.25/5.14              ( ( ( inf_inf_set_nat @ As @ As5 )
% 9.25/5.14                = bot_bot_set_nat )
% 9.25/5.14             => ( ( relH @ As @ H3 @ H5 )
% 9.25/5.14               => ( ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As ) )
% 9.25/5.14                 => ( ( rep_assn @ Q2 @ ( produc7507926704131184380et_nat @ H5 @ As5 ) )
% 9.25/5.14                   => ( rep_assn @ R @ ( produc7507926704131184380et_nat @ H5 @ ( sup_sup_set_nat @ As @ As5 ) ) ) ) ) ) )
% 9.25/5.14         => ( rep_assn @ ( wand_assn @ Q2 @ R ) @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1522_vimage__if,axiom,
% 9.25/5.14      ! [C: nat,A2: set_nat,D2: nat,B2: set_o] :
% 9.25/5.14        ( ( ( member_nat @ C @ A2 )
% 9.25/5.14         => ( ( ( member_nat @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_o_nat
% 9.25/5.14                  @ ^ [X3: $o] : ( if_nat @ ( member_o @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = top_top_set_o ) )
% 9.25/5.14            & ( ~ ( member_nat @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_o_nat
% 9.25/5.14                  @ ^ [X3: $o] : ( if_nat @ ( member_o @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = B2 ) ) ) )
% 9.25/5.14        & ( ~ ( member_nat @ C @ A2 )
% 9.25/5.14         => ( ( ( member_nat @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_o_nat
% 9.25/5.14                  @ ^ [X3: $o] : ( if_nat @ ( member_o @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = ( uminus_uminus_set_o @ B2 ) ) )
% 9.25/5.14            & ( ~ ( member_nat @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_o_nat
% 9.25/5.14                  @ ^ [X3: $o] : ( if_nat @ ( member_o @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = bot_bot_set_o ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1523_vimage__if,axiom,
% 9.25/5.14      ! [C: int,A2: set_int,D2: int,B2: set_o] :
% 9.25/5.14        ( ( ( member_int @ C @ A2 )
% 9.25/5.14         => ( ( ( member_int @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_o_int
% 9.25/5.14                  @ ^ [X3: $o] : ( if_int @ ( member_o @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = top_top_set_o ) )
% 9.25/5.14            & ( ~ ( member_int @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_o_int
% 9.25/5.14                  @ ^ [X3: $o] : ( if_int @ ( member_o @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = B2 ) ) ) )
% 9.25/5.14        & ( ~ ( member_int @ C @ A2 )
% 9.25/5.14         => ( ( ( member_int @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_o_int
% 9.25/5.14                  @ ^ [X3: $o] : ( if_int @ ( member_o @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = ( uminus_uminus_set_o @ B2 ) ) )
% 9.25/5.14            & ( ~ ( member_int @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_o_int
% 9.25/5.14                  @ ^ [X3: $o] : ( if_int @ ( member_o @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = bot_bot_set_o ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1524_vimage__if,axiom,
% 9.25/5.14      ! [C: nat,A2: set_nat,D2: nat,B2: set_rat] :
% 9.25/5.14        ( ( ( member_nat @ C @ A2 )
% 9.25/5.14         => ( ( ( member_nat @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_rat_nat
% 9.25/5.14                  @ ^ [X3: rat] : ( if_nat @ ( member_rat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = top_top_set_rat ) )
% 9.25/5.14            & ( ~ ( member_nat @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_rat_nat
% 9.25/5.14                  @ ^ [X3: rat] : ( if_nat @ ( member_rat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = B2 ) ) ) )
% 9.25/5.14        & ( ~ ( member_nat @ C @ A2 )
% 9.25/5.14         => ( ( ( member_nat @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_rat_nat
% 9.25/5.14                  @ ^ [X3: rat] : ( if_nat @ ( member_rat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = ( uminus2201863774496077783et_rat @ B2 ) ) )
% 9.25/5.14            & ( ~ ( member_nat @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_rat_nat
% 9.25/5.14                  @ ^ [X3: rat] : ( if_nat @ ( member_rat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = bot_bot_set_rat ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1525_vimage__if,axiom,
% 9.25/5.14      ! [C: int,A2: set_int,D2: int,B2: set_rat] :
% 9.25/5.14        ( ( ( member_int @ C @ A2 )
% 9.25/5.14         => ( ( ( member_int @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_rat_int
% 9.25/5.14                  @ ^ [X3: rat] : ( if_int @ ( member_rat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = top_top_set_rat ) )
% 9.25/5.14            & ( ~ ( member_int @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_rat_int
% 9.25/5.14                  @ ^ [X3: rat] : ( if_int @ ( member_rat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = B2 ) ) ) )
% 9.25/5.14        & ( ~ ( member_int @ C @ A2 )
% 9.25/5.14         => ( ( ( member_int @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_rat_int
% 9.25/5.14                  @ ^ [X3: rat] : ( if_int @ ( member_rat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = ( uminus2201863774496077783et_rat @ B2 ) ) )
% 9.25/5.14            & ( ~ ( member_int @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_rat_int
% 9.25/5.14                  @ ^ [X3: rat] : ( if_int @ ( member_rat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = bot_bot_set_rat ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1526_vimage__if,axiom,
% 9.25/5.14      ! [C: nat,A2: set_nat,D2: nat,B2: set_nat] :
% 9.25/5.14        ( ( ( member_nat @ C @ A2 )
% 9.25/5.14         => ( ( ( member_nat @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_nat_nat
% 9.25/5.14                  @ ^ [X3: nat] : ( if_nat @ ( member_nat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = top_top_set_nat ) )
% 9.25/5.14            & ( ~ ( member_nat @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_nat_nat
% 9.25/5.14                  @ ^ [X3: nat] : ( if_nat @ ( member_nat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = B2 ) ) ) )
% 9.25/5.14        & ( ~ ( member_nat @ C @ A2 )
% 9.25/5.14         => ( ( ( member_nat @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_nat_nat
% 9.25/5.14                  @ ^ [X3: nat] : ( if_nat @ ( member_nat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = ( uminus5710092332889474511et_nat @ B2 ) ) )
% 9.25/5.14            & ( ~ ( member_nat @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_nat_nat
% 9.25/5.14                  @ ^ [X3: nat] : ( if_nat @ ( member_nat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = bot_bot_set_nat ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1527_vimage__if,axiom,
% 9.25/5.14      ! [C: int,A2: set_int,D2: int,B2: set_nat] :
% 9.25/5.14        ( ( ( member_int @ C @ A2 )
% 9.25/5.14         => ( ( ( member_int @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_nat_int
% 9.25/5.14                  @ ^ [X3: nat] : ( if_int @ ( member_nat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = top_top_set_nat ) )
% 9.25/5.14            & ( ~ ( member_int @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_nat_int
% 9.25/5.14                  @ ^ [X3: nat] : ( if_int @ ( member_nat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = B2 ) ) ) )
% 9.25/5.14        & ( ~ ( member_int @ C @ A2 )
% 9.25/5.14         => ( ( ( member_int @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_nat_int
% 9.25/5.14                  @ ^ [X3: nat] : ( if_int @ ( member_nat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = ( uminus5710092332889474511et_nat @ B2 ) ) )
% 9.25/5.14            & ( ~ ( member_int @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_nat_int
% 9.25/5.14                  @ ^ [X3: nat] : ( if_int @ ( member_nat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = bot_bot_set_nat ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1528_vimage__if,axiom,
% 9.25/5.14      ! [C: nat,A2: set_nat,D2: nat,B2: set_int] :
% 9.25/5.14        ( ( ( member_nat @ C @ A2 )
% 9.25/5.14         => ( ( ( member_nat @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_int_nat
% 9.25/5.14                  @ ^ [X3: int] : ( if_nat @ ( member_int @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = top_top_set_int ) )
% 9.25/5.14            & ( ~ ( member_nat @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_int_nat
% 9.25/5.14                  @ ^ [X3: int] : ( if_nat @ ( member_int @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = B2 ) ) ) )
% 9.25/5.14        & ( ~ ( member_nat @ C @ A2 )
% 9.25/5.14         => ( ( ( member_nat @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_int_nat
% 9.25/5.14                  @ ^ [X3: int] : ( if_nat @ ( member_int @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = ( uminus1532241313380277803et_int @ B2 ) ) )
% 9.25/5.14            & ( ~ ( member_nat @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_int_nat
% 9.25/5.14                  @ ^ [X3: int] : ( if_nat @ ( member_int @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = bot_bot_set_int ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1529_vimage__if,axiom,
% 9.25/5.14      ! [C: int,A2: set_int,D2: int,B2: set_int] :
% 9.25/5.14        ( ( ( member_int @ C @ A2 )
% 9.25/5.14         => ( ( ( member_int @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_int_int
% 9.25/5.14                  @ ^ [X3: int] : ( if_int @ ( member_int @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = top_top_set_int ) )
% 9.25/5.14            & ( ~ ( member_int @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_int_int
% 9.25/5.14                  @ ^ [X3: int] : ( if_int @ ( member_int @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = B2 ) ) ) )
% 9.25/5.14        & ( ~ ( member_int @ C @ A2 )
% 9.25/5.14         => ( ( ( member_int @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_int_int
% 9.25/5.14                  @ ^ [X3: int] : ( if_int @ ( member_int @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = ( uminus1532241313380277803et_int @ B2 ) ) )
% 9.25/5.14            & ( ~ ( member_int @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_int_int
% 9.25/5.14                  @ ^ [X3: int] : ( if_int @ ( member_int @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = bot_bot_set_int ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1530_vimage__if,axiom,
% 9.25/5.14      ! [C: nat,A2: set_nat,D2: nat,B2: set_set_nat] :
% 9.25/5.14        ( ( ( member_nat @ C @ A2 )
% 9.25/5.14         => ( ( ( member_nat @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_set_nat_nat
% 9.25/5.14                  @ ^ [X3: set_nat] : ( if_nat @ ( member_set_nat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = top_top_set_set_nat ) )
% 9.25/5.14            & ( ~ ( member_nat @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_set_nat_nat
% 9.25/5.14                  @ ^ [X3: set_nat] : ( if_nat @ ( member_set_nat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = B2 ) ) ) )
% 9.25/5.14        & ( ~ ( member_nat @ C @ A2 )
% 9.25/5.14         => ( ( ( member_nat @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_set_nat_nat
% 9.25/5.14                  @ ^ [X3: set_nat] : ( if_nat @ ( member_set_nat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = ( uminus613421341184616069et_nat @ B2 ) ) )
% 9.25/5.14            & ( ~ ( member_nat @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_set_nat_nat
% 9.25/5.14                  @ ^ [X3: set_nat] : ( if_nat @ ( member_set_nat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = bot_bot_set_set_nat ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1531_vimage__if,axiom,
% 9.25/5.14      ! [C: int,A2: set_int,D2: int,B2: set_set_nat] :
% 9.25/5.14        ( ( ( member_int @ C @ A2 )
% 9.25/5.14         => ( ( ( member_int @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_set_nat_int
% 9.25/5.14                  @ ^ [X3: set_nat] : ( if_int @ ( member_set_nat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = top_top_set_set_nat ) )
% 9.25/5.14            & ( ~ ( member_int @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_set_nat_int
% 9.25/5.14                  @ ^ [X3: set_nat] : ( if_int @ ( member_set_nat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = B2 ) ) ) )
% 9.25/5.14        & ( ~ ( member_int @ C @ A2 )
% 9.25/5.14         => ( ( ( member_int @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_set_nat_int
% 9.25/5.14                  @ ^ [X3: set_nat] : ( if_int @ ( member_set_nat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = ( uminus613421341184616069et_nat @ B2 ) ) )
% 9.25/5.14            & ( ~ ( member_int @ D2 @ A2 )
% 9.25/5.14             => ( ( vimage_set_nat_int
% 9.25/5.14                  @ ^ [X3: set_nat] : ( if_int @ ( member_set_nat @ X3 @ B2 ) @ C @ D2 )
% 9.25/5.14                  @ A2 )
% 9.25/5.14                = bot_bot_set_set_nat ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1532_BNF__Composition_Otype__definition__id__bnf__UNIV,axiom,
% 9.25/5.14      type_d5972188401318659438st_nat @ bNF_id_bnf_list_nat @ bNF_id_bnf_list_nat @ top_top_set_list_nat ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1533_BNF__Composition_Otype__definition__id__bnf__UNIV,axiom,
% 9.25/5.14      type_definition_o_o @ bNF_id_bnf_o @ bNF_id_bnf_o @ top_top_set_o ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1534_BNF__Composition_Otype__definition__id__bnf__UNIV,axiom,
% 9.25/5.14      type_d5298809244756387038at_rat @ bNF_id_bnf_rat @ bNF_id_bnf_rat @ top_top_set_rat ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1535_BNF__Composition_Otype__definition__id__bnf__UNIV,axiom,
% 9.25/5.14      type_d6250493948777748686at_nat @ bNF_id_bnf_nat @ bNF_id_bnf_nat @ top_top_set_nat ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1536_BNF__Composition_Otype__definition__id__bnf__UNIV,axiom,
% 9.25/5.14      type_d7247357190169752966nt_int @ bNF_id_bnf_int @ bNF_id_bnf_int @ top_top_set_int ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1537_dbl__dec__simps_I3_J,axiom,
% 9.25/5.14      ( ( neg_nu7757733837767384882nteger @ one_one_Code_integer )
% 9.25/5.14      = one_one_Code_integer ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1538_dbl__dec__simps_I3_J,axiom,
% 9.25/5.14      ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 9.25/5.14      = one_one_rat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1539_dbl__dec__simps_I3_J,axiom,
% 9.25/5.14      ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 9.25/5.14      = one_one_int ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1540_wand__raw_Oelims_I3_J,axiom,
% 9.25/5.14      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 9.25/5.14        ( ~ ( wand_raw @ X @ Xa @ Xb )
% 9.25/5.14       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 9.25/5.14              ( ( Xb
% 9.25/5.14                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.14             => ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.14                & ! [H5: heap_e7401611519738050253t_unit,As5: set_nat] :
% 9.25/5.14                    ( ( ( ( inf_inf_set_nat @ As4 @ As5 )
% 9.25/5.14                        = bot_bot_set_nat )
% 9.25/5.14                      & ( relH @ As4 @ H @ H5 )
% 9.25/5.14                      & ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As4 ) )
% 9.25/5.14                      & ( X @ ( produc7507926704131184380et_nat @ H5 @ As5 ) ) )
% 9.25/5.14                   => ( Xa @ ( produc7507926704131184380et_nat @ H5 @ ( sup_sup_set_nat @ As4 @ As5 ) ) ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1541_wand__raw_Oelims_I2_J,axiom,
% 9.25/5.14      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 9.25/5.14        ( ( wand_raw @ X @ Xa @ Xb )
% 9.25/5.14       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 9.25/5.14              ( ( Xb
% 9.25/5.14                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.14             => ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.14                  & ! [H6: heap_e7401611519738050253t_unit,As6: set_nat] :
% 9.25/5.14                      ( ( ( ( inf_inf_set_nat @ As4 @ As6 )
% 9.25/5.14                          = bot_bot_set_nat )
% 9.25/5.14                        & ( relH @ As4 @ H @ H6 )
% 9.25/5.14                        & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As4 ) )
% 9.25/5.14                        & ( X @ ( produc7507926704131184380et_nat @ H6 @ As6 ) ) )
% 9.25/5.14                     => ( Xa @ ( produc7507926704131184380et_nat @ H6 @ ( sup_sup_set_nat @ As4 @ As6 ) ) ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1542_vimage__Collect__eq,axiom,
% 9.25/5.14      ! [F2: nat > nat,P: nat > $o] :
% 9.25/5.14        ( ( vimage_nat_nat @ F2 @ ( collect_nat @ P ) )
% 9.25/5.14        = ( collect_nat
% 9.25/5.14          @ ^ [Y3: nat] : ( P @ ( F2 @ Y3 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1543_vimage__Collect__eq,axiom,
% 9.25/5.14      ! [F2: int > nat,P: nat > $o] :
% 9.25/5.14        ( ( vimage_int_nat @ F2 @ ( collect_nat @ P ) )
% 9.25/5.14        = ( collect_int
% 9.25/5.14          @ ^ [Y3: int] : ( P @ ( F2 @ Y3 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1544_vimage__Collect__eq,axiom,
% 9.25/5.14      ! [F2: nat > int,P: int > $o] :
% 9.25/5.14        ( ( vimage_nat_int @ F2 @ ( collect_int @ P ) )
% 9.25/5.14        = ( collect_nat
% 9.25/5.14          @ ^ [Y3: nat] : ( P @ ( F2 @ Y3 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1545_vimage__Collect__eq,axiom,
% 9.25/5.14      ! [F2: int > int,P: int > $o] :
% 9.25/5.14        ( ( vimage_int_int @ F2 @ ( collect_int @ P ) )
% 9.25/5.14        = ( collect_int
% 9.25/5.14          @ ^ [Y3: int] : ( P @ ( F2 @ Y3 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1546_vimage__Collect__eq,axiom,
% 9.25/5.14      ! [F2: nat > set_nat,P: set_nat > $o] :
% 9.25/5.14        ( ( vimage_nat_set_nat @ F2 @ ( collect_set_nat @ P ) )
% 9.25/5.14        = ( collect_nat
% 9.25/5.14          @ ^ [Y3: nat] : ( P @ ( F2 @ Y3 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1547_vimage__Collect__eq,axiom,
% 9.25/5.14      ! [F2: int > set_nat,P: set_nat > $o] :
% 9.25/5.14        ( ( vimage_int_set_nat @ F2 @ ( collect_set_nat @ P ) )
% 9.25/5.14        = ( collect_int
% 9.25/5.14          @ ^ [Y3: int] : ( P @ ( F2 @ Y3 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1548_vimage__Collect__eq,axiom,
% 9.25/5.14      ! [F2: set_nat > nat,P: nat > $o] :
% 9.25/5.14        ( ( vimage_set_nat_nat @ F2 @ ( collect_nat @ P ) )
% 9.25/5.14        = ( collect_set_nat
% 9.25/5.14          @ ^ [Y3: set_nat] : ( P @ ( F2 @ Y3 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1549_vimage__Collect__eq,axiom,
% 9.25/5.14      ! [F2: set_nat > int,P: int > $o] :
% 9.25/5.14        ( ( vimage_set_nat_int @ F2 @ ( collect_int @ P ) )
% 9.25/5.14        = ( collect_set_nat
% 9.25/5.14          @ ^ [Y3: set_nat] : ( P @ ( F2 @ Y3 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1550_vimage__Collect__eq,axiom,
% 9.25/5.14      ! [F2: set_nat > set_nat,P: set_nat > $o] :
% 9.25/5.14        ( ( vimage4765135879290611145et_nat @ F2 @ ( collect_set_nat @ P ) )
% 9.25/5.14        = ( collect_set_nat
% 9.25/5.14          @ ^ [Y3: set_nat] : ( P @ ( F2 @ Y3 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1551_vimage__Collect__eq,axiom,
% 9.25/5.14      ! [F2: nat > set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.14        ( ( vimage2935056327143036492nt_int @ F2 @ ( collec5210948495886036740nt_int @ P ) )
% 9.25/5.14        = ( collect_nat
% 9.25/5.14          @ ^ [Y3: nat] : ( P @ ( F2 @ Y3 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1552_vimage__empty,axiom,
% 9.25/5.14      ! [F2: $o > $o] :
% 9.25/5.14        ( ( vimage_o_o @ F2 @ bot_bot_set_o )
% 9.25/5.14        = bot_bot_set_o ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1553_vimage__empty,axiom,
% 9.25/5.14      ! [F2: nat > $o] :
% 9.25/5.14        ( ( vimage_nat_o @ F2 @ bot_bot_set_o )
% 9.25/5.14        = bot_bot_set_nat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1554_vimage__empty,axiom,
% 9.25/5.14      ! [F2: int > $o] :
% 9.25/5.14        ( ( vimage_int_o @ F2 @ bot_bot_set_o )
% 9.25/5.14        = bot_bot_set_int ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1555_vimage__empty,axiom,
% 9.25/5.14      ! [F2: $o > nat] :
% 9.25/5.14        ( ( vimage_o_nat @ F2 @ bot_bot_set_nat )
% 9.25/5.14        = bot_bot_set_o ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1556_vimage__empty,axiom,
% 9.25/5.14      ! [F2: nat > nat] :
% 9.25/5.14        ( ( vimage_nat_nat @ F2 @ bot_bot_set_nat )
% 9.25/5.14        = bot_bot_set_nat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1557_vimage__empty,axiom,
% 9.25/5.14      ! [F2: int > nat] :
% 9.25/5.14        ( ( vimage_int_nat @ F2 @ bot_bot_set_nat )
% 9.25/5.14        = bot_bot_set_int ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1558_vimage__empty,axiom,
% 9.25/5.14      ! [F2: $o > int] :
% 9.25/5.14        ( ( vimage_o_int @ F2 @ bot_bot_set_int )
% 9.25/5.14        = bot_bot_set_o ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1559_vimage__empty,axiom,
% 9.25/5.14      ! [F2: nat > int] :
% 9.25/5.14        ( ( vimage_nat_int @ F2 @ bot_bot_set_int )
% 9.25/5.14        = bot_bot_set_nat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1560_vimage__empty,axiom,
% 9.25/5.14      ! [F2: int > int] :
% 9.25/5.14        ( ( vimage_int_int @ F2 @ bot_bot_set_int )
% 9.25/5.14        = bot_bot_set_int ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1561_vimage__empty,axiom,
% 9.25/5.14      ! [F2: $o > product_prod_nat_nat] :
% 9.25/5.14        ( ( vimage2606541041029201316at_nat @ F2 @ bot_bo2099793752762293965at_nat )
% 9.25/5.14        = bot_bot_set_o ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1562_vimage__UNIV,axiom,
% 9.25/5.14      ! [F2: $o > $o] :
% 9.25/5.14        ( ( vimage_o_o @ F2 @ top_top_set_o )
% 9.25/5.14        = top_top_set_o ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1563_vimage__UNIV,axiom,
% 9.25/5.14      ! [F2: rat > $o] :
% 9.25/5.14        ( ( vimage_rat_o @ F2 @ top_top_set_o )
% 9.25/5.14        = top_top_set_rat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1564_vimage__UNIV,axiom,
% 9.25/5.14      ! [F2: nat > $o] :
% 9.25/5.14        ( ( vimage_nat_o @ F2 @ top_top_set_o )
% 9.25/5.14        = top_top_set_nat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1565_vimage__UNIV,axiom,
% 9.25/5.14      ! [F2: int > $o] :
% 9.25/5.14        ( ( vimage_int_o @ F2 @ top_top_set_o )
% 9.25/5.14        = top_top_set_int ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1566_vimage__UNIV,axiom,
% 9.25/5.14      ! [F2: $o > rat] :
% 9.25/5.14        ( ( vimage_o_rat @ F2 @ top_top_set_rat )
% 9.25/5.14        = top_top_set_o ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1567_vimage__UNIV,axiom,
% 9.25/5.14      ! [F2: rat > rat] :
% 9.25/5.14        ( ( vimage_rat_rat @ F2 @ top_top_set_rat )
% 9.25/5.14        = top_top_set_rat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1568_vimage__UNIV,axiom,
% 9.25/5.14      ! [F2: nat > rat] :
% 9.25/5.14        ( ( vimage_nat_rat @ F2 @ top_top_set_rat )
% 9.25/5.14        = top_top_set_nat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1569_vimage__UNIV,axiom,
% 9.25/5.14      ! [F2: int > rat] :
% 9.25/5.14        ( ( vimage_int_rat @ F2 @ top_top_set_rat )
% 9.25/5.14        = top_top_set_int ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1570_vimage__UNIV,axiom,
% 9.25/5.14      ! [F2: $o > nat] :
% 9.25/5.14        ( ( vimage_o_nat @ F2 @ top_top_set_nat )
% 9.25/5.14        = top_top_set_o ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1571_vimage__UNIV,axiom,
% 9.25/5.14      ! [F2: rat > nat] :
% 9.25/5.14        ( ( vimage_rat_nat @ F2 @ top_top_set_nat )
% 9.25/5.14        = top_top_set_rat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1572_vimage__Int,axiom,
% 9.25/5.14      ! [F2: product_prod_nat_nat > product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.14        ( ( vimage2449269961533847803at_nat @ F2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 9.25/5.14        = ( inf_in2572325071724192079at_nat @ ( vimage2449269961533847803at_nat @ F2 @ A2 ) @ ( vimage2449269961533847803at_nat @ F2 @ B2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1573_vimage__Int,axiom,
% 9.25/5.14      ! [F2: nat > product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.14        ( ( vimage8013328719654469172at_nat @ F2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 9.25/5.14        = ( inf_inf_set_nat @ ( vimage8013328719654469172at_nat @ F2 @ A2 ) @ ( vimage8013328719654469172at_nat @ F2 @ B2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1574_vimage__Int,axiom,
% 9.25/5.14      ! [F2: product_prod_nat_nat > nat,A2: set_nat,B2: set_nat] :
% 9.25/5.14        ( ( vimage4653281326611754070at_nat @ F2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.14        = ( inf_in2572325071724192079at_nat @ ( vimage4653281326611754070at_nat @ F2 @ A2 ) @ ( vimage4653281326611754070at_nat @ F2 @ B2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1575_vimage__Int,axiom,
% 9.25/5.14      ! [F2: nat > nat,A2: set_nat,B2: set_nat] :
% 9.25/5.14        ( ( vimage_nat_nat @ F2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.14        = ( inf_inf_set_nat @ ( vimage_nat_nat @ F2 @ A2 ) @ ( vimage_nat_nat @ F2 @ B2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1576_vimage__Un,axiom,
% 9.25/5.14      ! [F2: produc4166570645942440679at_nat > produc4166570645942440679at_nat,A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.14        ( ( vimage3529983231074640251at_nat @ F2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 9.25/5.14        = ( sup_su3035147773818789531at_nat @ ( vimage3529983231074640251at_nat @ F2 @ A2 ) @ ( vimage3529983231074640251at_nat @ F2 @ B2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1577_vimage__Un,axiom,
% 9.25/5.14      ! [F2: produc3843707927480180839at_nat > produc4166570645942440679at_nat,A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.14        ( ( vimage2716263466903273467at_nat @ F2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 9.25/5.14        = ( sup_su5525570899277871387at_nat @ ( vimage2716263466903273467at_nat @ F2 @ A2 ) @ ( vimage2716263466903273467at_nat @ F2 @ B2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1578_vimage__Un,axiom,
% 9.25/5.14      ! [F2: nat > produc4166570645942440679at_nat,A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.14        ( ( vimage7262694317370708122at_nat @ F2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 9.25/5.14        = ( sup_sup_set_nat @ ( vimage7262694317370708122at_nat @ F2 @ A2 ) @ ( vimage7262694317370708122at_nat @ F2 @ B2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1579_vimage__Un,axiom,
% 9.25/5.14      ! [F2: produc4166570645942440679at_nat > produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.14        ( ( vimage5412736291816116987at_nat @ F2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 9.25/5.14        = ( sup_su3035147773818789531at_nat @ ( vimage5412736291816116987at_nat @ F2 @ A2 ) @ ( vimage5412736291816116987at_nat @ F2 @ B2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1580_vimage__Un,axiom,
% 9.25/5.14      ! [F2: produc3843707927480180839at_nat > produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.14        ( ( vimage6896080417876799867at_nat @ F2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 9.25/5.14        = ( sup_su5525570899277871387at_nat @ ( vimage6896080417876799867at_nat @ F2 @ A2 ) @ ( vimage6896080417876799867at_nat @ F2 @ B2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1581_vimage__Un,axiom,
% 9.25/5.14      ! [F2: nat > produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.14        ( ( vimage6435164912253009178at_nat @ F2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 9.25/5.14        = ( sup_sup_set_nat @ ( vimage6435164912253009178at_nat @ F2 @ A2 ) @ ( vimage6435164912253009178at_nat @ F2 @ B2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1582_vimage__Un,axiom,
% 9.25/5.14      ! [F2: produc4166570645942440679at_nat > nat,A2: set_nat,B2: set_nat] :
% 9.25/5.14        ( ( vimage7952471809483217980at_nat @ F2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.14        = ( sup_su3035147773818789531at_nat @ ( vimage7952471809483217980at_nat @ F2 @ A2 ) @ ( vimage7952471809483217980at_nat @ F2 @ B2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1583_vimage__Un,axiom,
% 9.25/5.14      ! [F2: produc3843707927480180839at_nat > nat,A2: set_nat,B2: set_nat] :
% 9.25/5.14        ( ( vimage7134676753939176892at_nat @ F2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.14        = ( sup_su5525570899277871387at_nat @ ( vimage7134676753939176892at_nat @ F2 @ A2 ) @ ( vimage7134676753939176892at_nat @ F2 @ B2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1584_vimage__Un,axiom,
% 9.25/5.14      ! [F2: nat > nat,A2: set_nat,B2: set_nat] :
% 9.25/5.14        ( ( vimage_nat_nat @ F2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.14        = ( sup_sup_set_nat @ ( vimage_nat_nat @ F2 @ A2 ) @ ( vimage_nat_nat @ F2 @ B2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1585_bool__assn__proper_I1_J,axiom,
% 9.25/5.14      proper @ in_range ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1586_relH__dist__union,axiom,
% 9.25/5.14      ! [As: set_nat,As3: set_nat,H3: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 9.25/5.14        ( ( relH @ ( sup_sup_set_nat @ As @ As3 ) @ H3 @ H4 )
% 9.25/5.14        = ( ( relH @ As @ H3 @ H4 )
% 9.25/5.14          & ( relH @ As3 @ H3 @ H4 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1587_bool__assn__proper_I5_J,axiom,
% 9.25/5.14      ! [P: produc3658429121746597890et_nat > $o] :
% 9.25/5.14        ( ( proper @ P )
% 9.25/5.14       => ( proper
% 9.25/5.14          @ ^ [H2: produc3658429121746597890et_nat] :
% 9.25/5.14              ( ( in_range @ H2 )
% 9.25/5.14              & ~ ( P @ H2 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1588_in__range__empty,axiom,
% 9.25/5.14      ! [H3: heap_e7401611519738050253t_unit] : ( in_range @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1589_vimage__const,axiom,
% 9.25/5.14      ! [C: nat,A2: set_nat] :
% 9.25/5.14        ( ( ( member_nat @ C @ A2 )
% 9.25/5.14         => ( ( vimage_o_nat
% 9.25/5.14              @ ^ [X3: $o] : C
% 9.25/5.14              @ A2 )
% 9.25/5.14            = top_top_set_o ) )
% 9.25/5.14        & ( ~ ( member_nat @ C @ A2 )
% 9.25/5.14         => ( ( vimage_o_nat
% 9.25/5.14              @ ^ [X3: $o] : C
% 9.25/5.14              @ A2 )
% 9.25/5.14            = bot_bot_set_o ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1590_vimage__const,axiom,
% 9.25/5.14      ! [C: int,A2: set_int] :
% 9.25/5.14        ( ( ( member_int @ C @ A2 )
% 9.25/5.14         => ( ( vimage_o_int
% 9.25/5.14              @ ^ [X3: $o] : C
% 9.25/5.14              @ A2 )
% 9.25/5.14            = top_top_set_o ) )
% 9.25/5.14        & ( ~ ( member_int @ C @ A2 )
% 9.25/5.14         => ( ( vimage_o_int
% 9.25/5.14              @ ^ [X3: $o] : C
% 9.25/5.14              @ A2 )
% 9.25/5.14            = bot_bot_set_o ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1591_vimage__const,axiom,
% 9.25/5.14      ! [C: nat,A2: set_nat] :
% 9.25/5.14        ( ( ( member_nat @ C @ A2 )
% 9.25/5.14         => ( ( vimage_rat_nat
% 9.25/5.14              @ ^ [X3: rat] : C
% 9.25/5.14              @ A2 )
% 9.25/5.14            = top_top_set_rat ) )
% 9.25/5.14        & ( ~ ( member_nat @ C @ A2 )
% 9.25/5.14         => ( ( vimage_rat_nat
% 9.25/5.14              @ ^ [X3: rat] : C
% 9.25/5.14              @ A2 )
% 9.25/5.14            = bot_bot_set_rat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1592_vimage__const,axiom,
% 9.25/5.14      ! [C: int,A2: set_int] :
% 9.25/5.14        ( ( ( member_int @ C @ A2 )
% 9.25/5.14         => ( ( vimage_rat_int
% 9.25/5.14              @ ^ [X3: rat] : C
% 9.25/5.14              @ A2 )
% 9.25/5.14            = top_top_set_rat ) )
% 9.25/5.14        & ( ~ ( member_int @ C @ A2 )
% 9.25/5.14         => ( ( vimage_rat_int
% 9.25/5.14              @ ^ [X3: rat] : C
% 9.25/5.14              @ A2 )
% 9.25/5.14            = bot_bot_set_rat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1593_vimage__const,axiom,
% 9.25/5.14      ! [C: nat,A2: set_nat] :
% 9.25/5.14        ( ( ( member_nat @ C @ A2 )
% 9.25/5.14         => ( ( vimage_nat_nat
% 9.25/5.14              @ ^ [X3: nat] : C
% 9.25/5.14              @ A2 )
% 9.25/5.14            = top_top_set_nat ) )
% 9.25/5.14        & ( ~ ( member_nat @ C @ A2 )
% 9.25/5.14         => ( ( vimage_nat_nat
% 9.25/5.14              @ ^ [X3: nat] : C
% 9.25/5.14              @ A2 )
% 9.25/5.14            = bot_bot_set_nat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1594_vimage__const,axiom,
% 9.25/5.14      ! [C: int,A2: set_int] :
% 9.25/5.14        ( ( ( member_int @ C @ A2 )
% 9.25/5.14         => ( ( vimage_nat_int
% 9.25/5.14              @ ^ [X3: nat] : C
% 9.25/5.14              @ A2 )
% 9.25/5.14            = top_top_set_nat ) )
% 9.25/5.14        & ( ~ ( member_int @ C @ A2 )
% 9.25/5.14         => ( ( vimage_nat_int
% 9.25/5.14              @ ^ [X3: nat] : C
% 9.25/5.14              @ A2 )
% 9.25/5.14            = bot_bot_set_nat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1595_vimage__const,axiom,
% 9.25/5.14      ! [C: nat,A2: set_nat] :
% 9.25/5.14        ( ( ( member_nat @ C @ A2 )
% 9.25/5.14         => ( ( vimage_int_nat
% 9.25/5.14              @ ^ [X3: int] : C
% 9.25/5.14              @ A2 )
% 9.25/5.14            = top_top_set_int ) )
% 9.25/5.14        & ( ~ ( member_nat @ C @ A2 )
% 9.25/5.14         => ( ( vimage_int_nat
% 9.25/5.14              @ ^ [X3: int] : C
% 9.25/5.14              @ A2 )
% 9.25/5.14            = bot_bot_set_int ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1596_vimage__const,axiom,
% 9.25/5.14      ! [C: int,A2: set_int] :
% 9.25/5.14        ( ( ( member_int @ C @ A2 )
% 9.25/5.14         => ( ( vimage_int_int
% 9.25/5.14              @ ^ [X3: int] : C
% 9.25/5.14              @ A2 )
% 9.25/5.14            = top_top_set_int ) )
% 9.25/5.14        & ( ~ ( member_int @ C @ A2 )
% 9.25/5.14         => ( ( vimage_int_int
% 9.25/5.14              @ ^ [X3: int] : C
% 9.25/5.14              @ A2 )
% 9.25/5.14            = bot_bot_set_int ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1597_vimage__const,axiom,
% 9.25/5.14      ! [C: nat,A2: set_nat] :
% 9.25/5.14        ( ( ( member_nat @ C @ A2 )
% 9.25/5.14         => ( ( vimage_list_nat_nat
% 9.25/5.14              @ ^ [X3: list_nat] : C
% 9.25/5.14              @ A2 )
% 9.25/5.14            = top_top_set_list_nat ) )
% 9.25/5.14        & ( ~ ( member_nat @ C @ A2 )
% 9.25/5.14         => ( ( vimage_list_nat_nat
% 9.25/5.14              @ ^ [X3: list_nat] : C
% 9.25/5.14              @ A2 )
% 9.25/5.14            = bot_bot_set_list_nat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1598_vimage__const,axiom,
% 9.25/5.14      ! [C: int,A2: set_int] :
% 9.25/5.14        ( ( ( member_int @ C @ A2 )
% 9.25/5.14         => ( ( vimage_list_nat_int
% 9.25/5.14              @ ^ [X3: list_nat] : C
% 9.25/5.14              @ A2 )
% 9.25/5.14            = top_top_set_list_nat ) )
% 9.25/5.14        & ( ~ ( member_int @ C @ A2 )
% 9.25/5.14         => ( ( vimage_list_nat_int
% 9.25/5.14              @ ^ [X3: list_nat] : C
% 9.25/5.14              @ A2 )
% 9.25/5.14            = bot_bot_set_list_nat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1599_in__range__dist__union,axiom,
% 9.25/5.14      ! [H3: heap_e7401611519738050253t_unit,As: set_nat,As3: set_nat] :
% 9.25/5.14        ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ ( sup_sup_set_nat @ As @ As3 ) ) )
% 9.25/5.14        = ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 9.25/5.14          & ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As3 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1600_relH__sym,axiom,
% 9.25/5.14      ! [As: set_nat,H3: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 9.25/5.14        ( ( relH @ As @ H3 @ H4 )
% 9.25/5.14       => ( relH @ As @ H4 @ H3 ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1601_relH__trans,axiom,
% 9.25/5.14      ! [As: set_nat,H12: heap_e7401611519738050253t_unit,H23: heap_e7401611519738050253t_unit,H32: heap_e7401611519738050253t_unit] :
% 9.25/5.14        ( ( relH @ As @ H12 @ H23 )
% 9.25/5.14       => ( ( relH @ As @ H23 @ H32 )
% 9.25/5.14         => ( relH @ As @ H12 @ H32 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1602_vimage__def,axiom,
% 9.25/5.14      ( vimage_nat_nat
% 9.25/5.14      = ( ^ [F: nat > nat,B4: set_nat] :
% 9.25/5.14            ( collect_nat
% 9.25/5.14            @ ^ [X3: nat] : ( member_nat @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1603_vimage__def,axiom,
% 9.25/5.14      ( vimage_nat_int
% 9.25/5.14      = ( ^ [F: nat > int,B4: set_int] :
% 9.25/5.14            ( collect_nat
% 9.25/5.14            @ ^ [X3: nat] : ( member_int @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1604_vimage__def,axiom,
% 9.25/5.14      ( vimage_int_nat
% 9.25/5.14      = ( ^ [F: int > nat,B4: set_nat] :
% 9.25/5.14            ( collect_int
% 9.25/5.14            @ ^ [X3: int] : ( member_nat @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1605_vimage__def,axiom,
% 9.25/5.14      ( vimage_int_int
% 9.25/5.14      = ( ^ [F: int > int,B4: set_int] :
% 9.25/5.14            ( collect_int
% 9.25/5.14            @ ^ [X3: int] : ( member_int @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1606_vimage__def,axiom,
% 9.25/5.14      ( vimage_set_nat_nat
% 9.25/5.14      = ( ^ [F: set_nat > nat,B4: set_nat] :
% 9.25/5.14            ( collect_set_nat
% 9.25/5.14            @ ^ [X3: set_nat] : ( member_nat @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1607_vimage__def,axiom,
% 9.25/5.14      ( vimage_set_nat_int
% 9.25/5.14      = ( ^ [F: set_nat > int,B4: set_int] :
% 9.25/5.14            ( collect_set_nat
% 9.25/5.14            @ ^ [X3: set_nat] : ( member_int @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1608_vimage__def,axiom,
% 9.25/5.14      ( vimage_nat_set_nat
% 9.25/5.14      = ( ^ [F: nat > set_nat,B4: set_set_nat] :
% 9.25/5.14            ( collect_nat
% 9.25/5.14            @ ^ [X3: nat] : ( member_set_nat @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1609_vimage__def,axiom,
% 9.25/5.14      ( vimage_int_set_nat
% 9.25/5.14      = ( ^ [F: int > set_nat,B4: set_set_nat] :
% 9.25/5.14            ( collect_int
% 9.25/5.14            @ ^ [X3: int] : ( member_set_nat @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1610_vimage__def,axiom,
% 9.25/5.14      ( vimage4765135879290611145et_nat
% 9.25/5.14      = ( ^ [F: set_nat > set_nat,B4: set_set_nat] :
% 9.25/5.14            ( collect_set_nat
% 9.25/5.14            @ ^ [X3: set_nat] : ( member_set_nat @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1611_vimage__def,axiom,
% 9.25/5.14      ( vimage928727498438615150nt_nat
% 9.25/5.14      = ( ^ [F: set_Pr958786334691620121nt_int > nat,B4: set_nat] :
% 9.25/5.14            ( collec5210948495886036740nt_int
% 9.25/5.14            @ ^ [X3: set_Pr958786334691620121nt_int] : ( member_nat @ ( F @ X3 ) @ B4 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1612_relH__in__rangeI_I2_J,axiom,
% 9.25/5.14      ! [As: set_nat,H3: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 9.25/5.14        ( ( relH @ As @ H3 @ H4 )
% 9.25/5.14       => ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1613_relH__in__rangeI_I1_J,axiom,
% 9.25/5.14      ! [As: set_nat,H3: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 9.25/5.14        ( ( relH @ As @ H3 @ H4 )
% 9.25/5.14       => ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1614_relH__refl,axiom,
% 9.25/5.14      ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.25/5.14        ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 9.25/5.14       => ( relH @ As @ H3 @ H3 ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1615_proper__iff,axiom,
% 9.25/5.14      ! [P: produc3658429121746597890et_nat > $o,As: set_nat,H3: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit] :
% 9.25/5.14        ( ( proper @ P )
% 9.25/5.14       => ( ( relH @ As @ H3 @ H4 )
% 9.25/5.14         => ( ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As ) )
% 9.25/5.14           => ( ( P @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 9.25/5.14              = ( P @ ( produc7507926704131184380et_nat @ H4 @ As ) ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1616_proper__def,axiom,
% 9.25/5.14      ( proper
% 9.25/5.14      = ( ^ [P2: produc3658429121746597890et_nat > $o] :
% 9.25/5.14          ! [H2: heap_e7401611519738050253t_unit,H7: heap_e7401611519738050253t_unit,As7: set_nat] :
% 9.25/5.14            ( ( ( P2 @ ( produc7507926704131184380et_nat @ H2 @ As7 ) )
% 9.25/5.14             => ( in_range @ ( produc7507926704131184380et_nat @ H2 @ As7 ) ) )
% 9.25/5.14            & ( ( ( P2 @ ( produc7507926704131184380et_nat @ H2 @ As7 ) )
% 9.25/5.14                & ( relH @ As7 @ H2 @ H7 )
% 9.25/5.14                & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As7 ) ) )
% 9.25/5.14             => ( P2 @ ( produc7507926704131184380et_nat @ H7 @ As7 ) ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1617_properD2,axiom,
% 9.25/5.14      ! [P: produc3658429121746597890et_nat > $o,H3: heap_e7401611519738050253t_unit,As: set_nat,H4: heap_e7401611519738050253t_unit] :
% 9.25/5.14        ( ( proper @ P )
% 9.25/5.14       => ( ( P @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 9.25/5.14         => ( ( relH @ As @ H3 @ H4 )
% 9.25/5.14           => ( ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As ) )
% 9.25/5.14             => ( P @ ( produc7507926704131184380et_nat @ H4 @ As ) ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1618_properI,axiom,
% 9.25/5.14      ! [P: produc3658429121746597890et_nat > $o] :
% 9.25/5.14        ( ! [As4: set_nat,H: heap_e7401611519738050253t_unit] :
% 9.25/5.14            ( ( P @ ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.14           => ( in_range @ ( produc7507926704131184380et_nat @ H @ As4 ) ) )
% 9.25/5.14       => ( ! [As4: set_nat,H: heap_e7401611519738050253t_unit,H5: heap_e7401611519738050253t_unit] :
% 9.25/5.14              ( ( P @ ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.14             => ( ( relH @ As4 @ H @ H5 )
% 9.25/5.14               => ( ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As4 ) )
% 9.25/5.14                 => ( P @ ( produc7507926704131184380et_nat @ H5 @ As4 ) ) ) ) )
% 9.25/5.14         => ( proper @ P ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1619_models__in__range,axiom,
% 9.25/5.14      ! [P: assn,H3: produc3658429121746597890et_nat] :
% 9.25/5.14        ( ( rep_assn @ P @ H3 )
% 9.25/5.14       => ( in_range @ H3 ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1620_top__assn__def,axiom,
% 9.25/5.14      ( top_top_assn
% 9.25/5.14      = ( abs_assn @ in_range ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1621_properD1,axiom,
% 9.25/5.14      ! [P: produc3658429121746597890et_nat > $o,H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.25/5.14        ( ( proper @ P )
% 9.25/5.14       => ( ( P @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 9.25/5.14         => ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1622_mod__relH,axiom,
% 9.25/5.14      ! [As: set_nat,H3: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit,P: assn] :
% 9.25/5.14        ( ( relH @ As @ H3 @ H4 )
% 9.25/5.14       => ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 9.25/5.14          = ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H4 @ As ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1623_uminus__assn__def,axiom,
% 9.25/5.14      ( uminus_uminus_assn
% 9.25/5.14      = ( ^ [P2: assn] :
% 9.25/5.14            ( abs_assn
% 9.25/5.14            @ ^ [H2: produc3658429121746597890et_nat] :
% 9.25/5.14                ( ( in_range @ H2 )
% 9.25/5.14                & ~ ( rep_assn @ P2 @ H2 ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1624_wand__raw_Osimps,axiom,
% 9.25/5.14      ! [P: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o,H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.25/5.14        ( ( wand_raw @ P @ Q2 @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 9.25/5.14        = ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 9.25/5.14          & ! [H7: heap_e7401611519738050253t_unit,As8: set_nat] :
% 9.25/5.14              ( ( ( ( inf_inf_set_nat @ As @ As8 )
% 9.25/5.14                  = bot_bot_set_nat )
% 9.25/5.14                & ( relH @ As @ H3 @ H7 )
% 9.25/5.14                & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As ) )
% 9.25/5.14                & ( P @ ( produc7507926704131184380et_nat @ H7 @ As8 ) ) )
% 9.25/5.14             => ( Q2 @ ( produc7507926704131184380et_nat @ H7 @ ( sup_sup_set_nat @ As @ As8 ) ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1625_wand__raw_Oelims_I1_J,axiom,
% 9.25/5.14      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 9.25/5.14        ( ( ( wand_raw @ X @ Xa @ Xb )
% 9.25/5.14          = Y )
% 9.25/5.14       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 9.25/5.14              ( ( Xb
% 9.25/5.14                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.14             => ( Y
% 9.25/5.14                = ( ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.14                      & ! [H7: heap_e7401611519738050253t_unit,As8: set_nat] :
% 9.25/5.14                          ( ( ( ( inf_inf_set_nat @ As4 @ As8 )
% 9.25/5.14                              = bot_bot_set_nat )
% 9.25/5.14                            & ( relH @ As4 @ H @ H7 )
% 9.25/5.14                            & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As4 ) )
% 9.25/5.14                            & ( X @ ( produc7507926704131184380et_nat @ H7 @ As8 ) ) )
% 9.25/5.14                         => ( Xa @ ( produc7507926704131184380et_nat @ H7 @ ( sup_sup_set_nat @ As4 @ As8 ) ) ) ) ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1626_wand__raw_Opelims_I1_J,axiom,
% 9.25/5.14      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 9.25/5.14        ( ( ( wand_raw @ X @ Xa @ Xb )
% 9.25/5.14          = Y )
% 9.25/5.14       => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 9.25/5.14         => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 9.25/5.14                ( ( Xb
% 9.25/5.14                  = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.14               => ( ( Y
% 9.25/5.14                    = ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.14                      & ! [H7: heap_e7401611519738050253t_unit,As8: set_nat] :
% 9.25/5.14                          ( ( ( ( inf_inf_set_nat @ As4 @ As8 )
% 9.25/5.14                              = bot_bot_set_nat )
% 9.25/5.14                            & ( relH @ As4 @ H @ H7 )
% 9.25/5.14                            & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As4 ) )
% 9.25/5.14                            & ( X @ ( produc7507926704131184380et_nat @ H7 @ As8 ) ) )
% 9.25/5.14                         => ( Xa @ ( produc7507926704131184380et_nat @ H7 @ ( sup_sup_set_nat @ As4 @ As8 ) ) ) ) ) )
% 9.25/5.14                 => ~ ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As4 ) ) ) ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1627_wand__raw_Opelims_I2_J,axiom,
% 9.25/5.14      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 9.25/5.14        ( ( wand_raw @ X @ Xa @ Xb )
% 9.25/5.14       => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 9.25/5.14         => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 9.25/5.14                ( ( Xb
% 9.25/5.14                  = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.14               => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As4 ) ) ) )
% 9.25/5.14                 => ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.14                      & ! [H6: heap_e7401611519738050253t_unit,As6: set_nat] :
% 9.25/5.14                          ( ( ( ( inf_inf_set_nat @ As4 @ As6 )
% 9.25/5.14                              = bot_bot_set_nat )
% 9.25/5.14                            & ( relH @ As4 @ H @ H6 )
% 9.25/5.14                            & ( in_range @ ( produc7507926704131184380et_nat @ H6 @ As4 ) )
% 9.25/5.14                            & ( X @ ( produc7507926704131184380et_nat @ H6 @ As6 ) ) )
% 9.25/5.14                         => ( Xa @ ( produc7507926704131184380et_nat @ H6 @ ( sup_sup_set_nat @ As4 @ As6 ) ) ) ) ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1628_wand__raw_Opelims_I3_J,axiom,
% 9.25/5.14      ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 9.25/5.14        ( ~ ( wand_raw @ X @ Xa @ Xb )
% 9.25/5.14       => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 9.25/5.14         => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 9.25/5.14                ( ( Xb
% 9.25/5.14                  = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.14               => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H @ As4 ) ) ) )
% 9.25/5.14                 => ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.14                    & ! [H5: heap_e7401611519738050253t_unit,As5: set_nat] :
% 9.25/5.14                        ( ( ( ( inf_inf_set_nat @ As4 @ As5 )
% 9.25/5.14                            = bot_bot_set_nat )
% 9.25/5.14                          & ( relH @ As4 @ H @ H5 )
% 9.25/5.14                          & ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As4 ) )
% 9.25/5.14                          & ( X @ ( produc7507926704131184380et_nat @ H5 @ As5 ) ) )
% 9.25/5.14                       => ( Xa @ ( produc7507926704131184380et_nat @ H5 @ ( sup_sup_set_nat @ As4 @ As5 ) ) ) ) ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1629_bijective__Empty,axiom,
% 9.25/5.14      bijective_nat_nat @ bot_bo2099793752762293965at_nat ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1630_dbl__inc__simps_I1_J,axiom,
% 9.25/5.14      ! [K: num] :
% 9.25/5.14        ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 9.25/5.14        = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1631_dbl__inc__simps_I1_J,axiom,
% 9.25/5.14      ! [K: num] :
% 9.25/5.14        ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 9.25/5.14        = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1632_dbl__inc__simps_I1_J,axiom,
% 9.25/5.14      ! [K: num] :
% 9.25/5.14        ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 9.25/5.14        = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1633_dbl__dec__simps_I1_J,axiom,
% 9.25/5.14      ! [K: num] :
% 9.25/5.14        ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 9.25/5.14        = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1634_dbl__dec__simps_I1_J,axiom,
% 9.25/5.14      ! [K: num] :
% 9.25/5.14        ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 9.25/5.14        = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1635_dbl__dec__simps_I1_J,axiom,
% 9.25/5.14      ! [K: num] :
% 9.25/5.14        ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 9.25/5.14        = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1636_dbl__dec__simps_I2_J,axiom,
% 9.25/5.14      ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 9.25/5.14      = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1637_dbl__dec__simps_I2_J,axiom,
% 9.25/5.14      ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 9.25/5.14      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1638_dbl__dec__simps_I2_J,axiom,
% 9.25/5.14      ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 9.25/5.14      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1639_pairself_Opelims,axiom,
% 9.25/5.14      ! [X: int > option6357759511663192854e_term,Xa: product_prod_int_int,Y: produc6576344331059438605e_term] :
% 9.25/5.14        ( ( ( pairse3534876335208825186e_term @ X @ Xa )
% 9.25/5.14          = Y )
% 9.25/5.14       => ( ( accp_P8928870874622223812nt_int @ pairse6848479906795794847e_term @ ( produc4305682042979456191nt_int @ X @ Xa ) )
% 9.25/5.14         => ~ ! [A6: int,B6: int] :
% 9.25/5.14                ( ( Xa
% 9.25/5.14                  = ( product_Pair_int_int @ A6 @ B6 ) )
% 9.25/5.14               => ( ( Y
% 9.25/5.14                    = ( produc5950683997804057413e_term @ ( X @ A6 ) @ ( X @ B6 ) ) )
% 9.25/5.14                 => ~ ( accp_P8928870874622223812nt_int @ pairse6848479906795794847e_term @ ( produc4305682042979456191nt_int @ X @ ( product_Pair_int_int @ A6 @ B6 ) ) ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1640_rel__restrict__compl,axiom,
% 9.25/5.14      ! [R: set_Pr1261947904930325089at_nat,A2: set_nat] :
% 9.25/5.14        ( ( inf_in2572325071724192079at_nat @ ( rel_restrict_nat @ R @ A2 ) @ ( rel_restrict_nat @ R @ ( uminus5710092332889474511et_nat @ A2 ) ) )
% 9.25/5.14        = bot_bo2099793752762293965at_nat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1641_Id__on__empty,axiom,
% 9.25/5.14      ( ( id_on_2554058798563519774at_nat @ bot_bo2099793752762293965at_nat )
% 9.25/5.14      = bot_bo5327735625951526323at_nat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1642_Id__on__empty,axiom,
% 9.25/5.14      ( ( id_on_o @ bot_bot_set_o )
% 9.25/5.14      = bot_bo7073875226086086771od_o_o ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1643_Id__on__empty,axiom,
% 9.25/5.14      ( ( id_on_nat @ bot_bot_set_nat )
% 9.25/5.14      = bot_bo2099793752762293965at_nat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1644_Id__on__empty,axiom,
% 9.25/5.14      ( ( id_on_int @ bot_bot_set_int )
% 9.25/5.14      = bot_bo1796632182523588997nt_int ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1645_mult__cancel__right,axiom,
% 9.25/5.14      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.25/5.14        ( ( ( times_3573771949741848930nteger @ A @ C )
% 9.25/5.14          = ( times_3573771949741848930nteger @ B @ C ) )
% 9.25/5.14        = ( ( C = zero_z3403309356797280102nteger )
% 9.25/5.14          | ( A = B ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1646_mult__cancel__right,axiom,
% 9.25/5.14      ! [A: rat,C: rat,B: rat] :
% 9.25/5.14        ( ( ( times_times_rat @ A @ C )
% 9.25/5.14          = ( times_times_rat @ B @ C ) )
% 9.25/5.14        = ( ( C = zero_zero_rat )
% 9.25/5.14          | ( A = B ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1647_mult__cancel__right,axiom,
% 9.25/5.14      ! [A: nat,C: nat,B: nat] :
% 9.25/5.14        ( ( ( times_times_nat @ A @ C )
% 9.25/5.14          = ( times_times_nat @ B @ C ) )
% 9.25/5.14        = ( ( C = zero_zero_nat )
% 9.25/5.14          | ( A = B ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1648_mult__cancel__right,axiom,
% 9.25/5.14      ! [A: int,C: int,B: int] :
% 9.25/5.14        ( ( ( times_times_int @ A @ C )
% 9.25/5.14          = ( times_times_int @ B @ C ) )
% 9.25/5.14        = ( ( C = zero_zero_int )
% 9.25/5.14          | ( A = B ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1649_mult__cancel__left,axiom,
% 9.25/5.14      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.14        ( ( ( times_3573771949741848930nteger @ C @ A )
% 9.25/5.14          = ( times_3573771949741848930nteger @ C @ B ) )
% 9.25/5.14        = ( ( C = zero_z3403309356797280102nteger )
% 9.25/5.14          | ( A = B ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1650_mult__cancel__left,axiom,
% 9.25/5.14      ! [C: rat,A: rat,B: rat] :
% 9.25/5.14        ( ( ( times_times_rat @ C @ A )
% 9.25/5.14          = ( times_times_rat @ C @ B ) )
% 9.25/5.14        = ( ( C = zero_zero_rat )
% 9.25/5.14          | ( A = B ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1651_mult__cancel__left,axiom,
% 9.25/5.14      ! [C: nat,A: nat,B: nat] :
% 9.25/5.14        ( ( ( times_times_nat @ C @ A )
% 9.25/5.14          = ( times_times_nat @ C @ B ) )
% 9.25/5.14        = ( ( C = zero_zero_nat )
% 9.25/5.14          | ( A = B ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1652_mult__cancel__left,axiom,
% 9.25/5.14      ! [C: int,A: int,B: int] :
% 9.25/5.14        ( ( ( times_times_int @ C @ A )
% 9.25/5.14          = ( times_times_int @ C @ B ) )
% 9.25/5.14        = ( ( C = zero_zero_int )
% 9.25/5.14          | ( A = B ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1653_mult__eq__0__iff,axiom,
% 9.25/5.14      ! [A: code_integer,B: code_integer] :
% 9.25/5.14        ( ( ( times_3573771949741848930nteger @ A @ B )
% 9.25/5.14          = zero_z3403309356797280102nteger )
% 9.25/5.14        = ( ( A = zero_z3403309356797280102nteger )
% 9.25/5.14          | ( B = zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1654_mult__eq__0__iff,axiom,
% 9.25/5.14      ! [A: rat,B: rat] :
% 9.25/5.14        ( ( ( times_times_rat @ A @ B )
% 9.25/5.14          = zero_zero_rat )
% 9.25/5.14        = ( ( A = zero_zero_rat )
% 9.25/5.14          | ( B = zero_zero_rat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1655_mult__eq__0__iff,axiom,
% 9.25/5.14      ! [A: nat,B: nat] :
% 9.25/5.14        ( ( ( times_times_nat @ A @ B )
% 9.25/5.14          = zero_zero_nat )
% 9.25/5.14        = ( ( A = zero_zero_nat )
% 9.25/5.14          | ( B = zero_zero_nat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1656_mult__eq__0__iff,axiom,
% 9.25/5.14      ! [A: int,B: int] :
% 9.25/5.14        ( ( ( times_times_int @ A @ B )
% 9.25/5.14          = zero_zero_int )
% 9.25/5.14        = ( ( A = zero_zero_int )
% 9.25/5.14          | ( B = zero_zero_int ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1657_mult__zero__right,axiom,
% 9.25/5.14      ! [A: code_integer] :
% 9.25/5.14        ( ( times_3573771949741848930nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.14        = zero_z3403309356797280102nteger ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1658_mult__zero__right,axiom,
% 9.25/5.14      ! [A: rat] :
% 9.25/5.14        ( ( times_times_rat @ A @ zero_zero_rat )
% 9.25/5.14        = zero_zero_rat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1659_mult__zero__right,axiom,
% 9.25/5.14      ! [A: nat] :
% 9.25/5.14        ( ( times_times_nat @ A @ zero_zero_nat )
% 9.25/5.14        = zero_zero_nat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1660_mult__zero__right,axiom,
% 9.25/5.14      ! [A: int] :
% 9.25/5.14        ( ( times_times_int @ A @ zero_zero_int )
% 9.25/5.14        = zero_zero_int ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1661_mult__zero__left,axiom,
% 9.25/5.14      ! [A: code_integer] :
% 9.25/5.14        ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.14        = zero_z3403309356797280102nteger ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1662_mult__zero__left,axiom,
% 9.25/5.14      ! [A: rat] :
% 9.25/5.14        ( ( times_times_rat @ zero_zero_rat @ A )
% 9.25/5.14        = zero_zero_rat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1663_mult__zero__left,axiom,
% 9.25/5.14      ! [A: nat] :
% 9.25/5.14        ( ( times_times_nat @ zero_zero_nat @ A )
% 9.25/5.14        = zero_zero_nat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1664_mult__zero__left,axiom,
% 9.25/5.14      ! [A: int] :
% 9.25/5.14        ( ( times_times_int @ zero_zero_int @ A )
% 9.25/5.14        = zero_zero_int ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1665_mult__numeral__left__semiring__numeral,axiom,
% 9.25/5.14      ! [V: num,W: num,Z: nat] :
% 9.25/5.14        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 9.25/5.14        = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1666_mult__numeral__left__semiring__numeral,axiom,
% 9.25/5.14      ! [V: num,W: num,Z: int] :
% 9.25/5.14        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 9.25/5.14        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1667_mult__numeral__left__semiring__numeral,axiom,
% 9.25/5.14      ! [V: num,W: num,Z: code_integer] :
% 9.25/5.14        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Z ) )
% 9.25/5.14        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1668_mult__numeral__left__semiring__numeral,axiom,
% 9.25/5.14      ! [V: num,W: num,Z: rat] :
% 9.25/5.14        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 9.25/5.14        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1669_mult__numeral__left__semiring__numeral,axiom,
% 9.25/5.14      ! [V: num,W: num,Z: code_natural] :
% 9.25/5.14        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ W ) @ Z ) )
% 9.25/5.14        = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1670_numeral__times__numeral,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 9.25/5.14        = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1671_numeral__times__numeral,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 9.25/5.14        = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1672_numeral__times__numeral,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 9.25/5.14        = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1673_numeral__times__numeral,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 9.25/5.14        = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1674_numeral__times__numeral,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ M ) @ ( numera5444537566228673987atural @ N ) )
% 9.25/5.14        = ( numera5444537566228673987atural @ ( times_times_num @ M @ N ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1675_neg__equal__zero,axiom,
% 9.25/5.14      ! [A: int] :
% 9.25/5.14        ( ( ( uminus_uminus_int @ A )
% 9.25/5.14          = A )
% 9.25/5.14        = ( A = zero_zero_int ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1676_neg__equal__zero,axiom,
% 9.25/5.14      ! [A: code_integer] :
% 9.25/5.14        ( ( ( uminus1351360451143612070nteger @ A )
% 9.25/5.14          = A )
% 9.25/5.14        = ( A = zero_z3403309356797280102nteger ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1677_neg__equal__zero,axiom,
% 9.25/5.14      ! [A: rat] :
% 9.25/5.14        ( ( ( uminus_uminus_rat @ A )
% 9.25/5.14          = A )
% 9.25/5.14        = ( A = zero_zero_rat ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1678_equal__neg__zero,axiom,
% 9.25/5.14      ! [A: int] :
% 9.25/5.14        ( ( A
% 9.25/5.14          = ( uminus_uminus_int @ A ) )
% 9.25/5.14        = ( A = zero_zero_int ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1679_equal__neg__zero,axiom,
% 9.25/5.14      ! [A: code_integer] :
% 9.25/5.14        ( ( A
% 9.25/5.14          = ( uminus1351360451143612070nteger @ A ) )
% 9.25/5.14        = ( A = zero_z3403309356797280102nteger ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1680_equal__neg__zero,axiom,
% 9.25/5.14      ! [A: rat] :
% 9.25/5.14        ( ( A
% 9.25/5.14          = ( uminus_uminus_rat @ A ) )
% 9.25/5.14        = ( A = zero_zero_rat ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1681_neg__equal__0__iff__equal,axiom,
% 9.25/5.14      ! [A: int] :
% 9.25/5.14        ( ( ( uminus_uminus_int @ A )
% 9.25/5.14          = zero_zero_int )
% 9.25/5.14        = ( A = zero_zero_int ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1682_neg__equal__0__iff__equal,axiom,
% 9.25/5.14      ! [A: code_integer] :
% 9.25/5.14        ( ( ( uminus1351360451143612070nteger @ A )
% 9.25/5.14          = zero_z3403309356797280102nteger )
% 9.25/5.14        = ( A = zero_z3403309356797280102nteger ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1683_neg__equal__0__iff__equal,axiom,
% 9.25/5.14      ! [A: rat] :
% 9.25/5.14        ( ( ( uminus_uminus_rat @ A )
% 9.25/5.14          = zero_zero_rat )
% 9.25/5.14        = ( A = zero_zero_rat ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1684_neg__0__equal__iff__equal,axiom,
% 9.25/5.14      ! [A: int] :
% 9.25/5.14        ( ( zero_zero_int
% 9.25/5.14          = ( uminus_uminus_int @ A ) )
% 9.25/5.14        = ( zero_zero_int = A ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1685_neg__0__equal__iff__equal,axiom,
% 9.25/5.14      ! [A: code_integer] :
% 9.25/5.14        ( ( zero_z3403309356797280102nteger
% 9.25/5.14          = ( uminus1351360451143612070nteger @ A ) )
% 9.25/5.14        = ( zero_z3403309356797280102nteger = A ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1686_neg__0__equal__iff__equal,axiom,
% 9.25/5.14      ! [A: rat] :
% 9.25/5.14        ( ( zero_zero_rat
% 9.25/5.14          = ( uminus_uminus_rat @ A ) )
% 9.25/5.14        = ( zero_zero_rat = A ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1687_add_Oinverse__neutral,axiom,
% 9.25/5.14      ( ( uminus_uminus_int @ zero_zero_int )
% 9.25/5.14      = zero_zero_int ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1688_add_Oinverse__neutral,axiom,
% 9.25/5.14      ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 9.25/5.14      = zero_z3403309356797280102nteger ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1689_add_Oinverse__neutral,axiom,
% 9.25/5.14      ( ( uminus_uminus_rat @ zero_zero_rat )
% 9.25/5.14      = zero_zero_rat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1690_neg__numeral__eq__iff,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 9.25/5.14          = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.14        = ( M = N ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1691_neg__numeral__eq__iff,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 9.25/5.14          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.25/5.14        = ( M = N ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1692_neg__numeral__eq__iff,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 9.25/5.14          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.25/5.14        = ( M = N ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1693_rel__restrict__empty,axiom,
% 9.25/5.14      ! [R: set_Pr8693737435421807431at_nat] :
% 9.25/5.14        ( ( rel_re36662636952045539at_nat @ R @ bot_bo2099793752762293965at_nat )
% 9.25/5.14        = R ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1694_rel__restrict__empty,axiom,
% 9.25/5.14      ! [R: set_Product_prod_o_o] :
% 9.25/5.14        ( ( rel_restrict_o @ R @ bot_bot_set_o )
% 9.25/5.14        = R ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1695_rel__restrict__empty,axiom,
% 9.25/5.14      ! [R: set_Pr1261947904930325089at_nat] :
% 9.25/5.14        ( ( rel_restrict_nat @ R @ bot_bot_set_nat )
% 9.25/5.14        = R ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1696_rel__restrict__empty,axiom,
% 9.25/5.14      ! [R: set_Pr958786334691620121nt_int] :
% 9.25/5.14        ( ( rel_restrict_int @ R @ bot_bot_set_int )
% 9.25/5.14        = R ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1697_Id__onI,axiom,
% 9.25/5.14      ! [A: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int] :
% 9.25/5.14        ( ( member2340774599025711042nt_int @ A @ A2 )
% 9.25/5.14       => ( member5325734588016868240nt_int @ ( produc782388162306416855nt_int @ A @ A ) @ ( id_on_6410342593070439734nt_int @ A2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1698_Id__onI,axiom,
% 9.25/5.14      ! [A: set_nat,A2: set_set_nat] :
% 9.25/5.14        ( ( member_set_nat @ A @ A2 )
% 9.25/5.14       => ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A @ A ) @ ( id_on_set_nat @ A2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1699_Id__onI,axiom,
% 9.25/5.14      ! [A: nat,A2: set_nat] :
% 9.25/5.14        ( ( member_nat @ A @ A2 )
% 9.25/5.14       => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ A ) @ ( id_on_nat @ A2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1700_Id__onI,axiom,
% 9.25/5.14      ! [A: int,A2: set_int] :
% 9.25/5.14        ( ( member_int @ A @ A2 )
% 9.25/5.14       => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ A ) @ ( id_on_int @ A2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1701_Id__onI,axiom,
% 9.25/5.14      ! [A: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.14        ( ( member6576561426505652726_nat_o @ A @ A2 )
% 9.25/5.14       => ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A @ A ) @ ( id_on_7438695062414216554_nat_o @ A2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1702_mult__cancel__right2,axiom,
% 9.25/5.14      ! [A: code_integer,C: code_integer] :
% 9.25/5.14        ( ( ( times_3573771949741848930nteger @ A @ C )
% 9.25/5.14          = C )
% 9.25/5.14        = ( ( C = zero_z3403309356797280102nteger )
% 9.25/5.14          | ( A = one_one_Code_integer ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1703_mult__cancel__right2,axiom,
% 9.25/5.14      ! [A: rat,C: rat] :
% 9.25/5.14        ( ( ( times_times_rat @ A @ C )
% 9.25/5.14          = C )
% 9.25/5.14        = ( ( C = zero_zero_rat )
% 9.25/5.14          | ( A = one_one_rat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1704_mult__cancel__right2,axiom,
% 9.25/5.14      ! [A: int,C: int] :
% 9.25/5.14        ( ( ( times_times_int @ A @ C )
% 9.25/5.14          = C )
% 9.25/5.14        = ( ( C = zero_zero_int )
% 9.25/5.14          | ( A = one_one_int ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1705_mult__cancel__right1,axiom,
% 9.25/5.14      ! [C: code_integer,B: code_integer] :
% 9.25/5.14        ( ( C
% 9.25/5.14          = ( times_3573771949741848930nteger @ B @ C ) )
% 9.25/5.14        = ( ( C = zero_z3403309356797280102nteger )
% 9.25/5.14          | ( B = one_one_Code_integer ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1706_mult__cancel__right1,axiom,
% 9.25/5.14      ! [C: rat,B: rat] :
% 9.25/5.14        ( ( C
% 9.25/5.14          = ( times_times_rat @ B @ C ) )
% 9.25/5.14        = ( ( C = zero_zero_rat )
% 9.25/5.14          | ( B = one_one_rat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1707_mult__cancel__right1,axiom,
% 9.25/5.14      ! [C: int,B: int] :
% 9.25/5.14        ( ( C
% 9.25/5.14          = ( times_times_int @ B @ C ) )
% 9.25/5.14        = ( ( C = zero_zero_int )
% 9.25/5.14          | ( B = one_one_int ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1708_mult__cancel__left2,axiom,
% 9.25/5.14      ! [C: code_integer,A: code_integer] :
% 9.25/5.14        ( ( ( times_3573771949741848930nteger @ C @ A )
% 9.25/5.14          = C )
% 9.25/5.14        = ( ( C = zero_z3403309356797280102nteger )
% 9.25/5.14          | ( A = one_one_Code_integer ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1709_mult__cancel__left2,axiom,
% 9.25/5.14      ! [C: rat,A: rat] :
% 9.25/5.14        ( ( ( times_times_rat @ C @ A )
% 9.25/5.14          = C )
% 9.25/5.14        = ( ( C = zero_zero_rat )
% 9.25/5.14          | ( A = one_one_rat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1710_mult__cancel__left2,axiom,
% 9.25/5.14      ! [C: int,A: int] :
% 9.25/5.14        ( ( ( times_times_int @ C @ A )
% 9.25/5.14          = C )
% 9.25/5.14        = ( ( C = zero_zero_int )
% 9.25/5.14          | ( A = one_one_int ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1711_mult__cancel__left1,axiom,
% 9.25/5.14      ! [C: code_integer,B: code_integer] :
% 9.25/5.14        ( ( C
% 9.25/5.14          = ( times_3573771949741848930nteger @ C @ B ) )
% 9.25/5.14        = ( ( C = zero_z3403309356797280102nteger )
% 9.25/5.14          | ( B = one_one_Code_integer ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1712_mult__cancel__left1,axiom,
% 9.25/5.14      ! [C: rat,B: rat] :
% 9.25/5.14        ( ( C
% 9.25/5.14          = ( times_times_rat @ C @ B ) )
% 9.25/5.14        = ( ( C = zero_zero_rat )
% 9.25/5.14          | ( B = one_one_rat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1713_mult__cancel__left1,axiom,
% 9.25/5.14      ! [C: int,B: int] :
% 9.25/5.14        ( ( C
% 9.25/5.14          = ( times_times_int @ C @ B ) )
% 9.25/5.14        = ( ( C = zero_zero_int )
% 9.25/5.14          | ( B = one_one_int ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1714_mult__neg__numeral__simps_I1_J,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.14        = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1715_mult__neg__numeral__simps_I1_J,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.25/5.14        = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1716_mult__neg__numeral__simps_I1_J,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.25/5.14        = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1717_mult__neg__numeral__simps_I2_J,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 9.25/5.14        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1718_mult__neg__numeral__simps_I2_J,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 9.25/5.14        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1719_mult__neg__numeral__simps_I2_J,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 9.25/5.14        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1720_mult__neg__numeral__simps_I3_J,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.14        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1721_mult__neg__numeral__simps_I3_J,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.25/5.14        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1722_mult__neg__numeral__simps_I3_J,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.25/5.14        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1723_dbl__inc__simps_I2_J,axiom,
% 9.25/5.14      ( ( neg_nu5831290666863070958nteger @ zero_z3403309356797280102nteger )
% 9.25/5.14      = one_one_Code_integer ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1724_dbl__inc__simps_I2_J,axiom,
% 9.25/5.14      ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 9.25/5.14      = one_one_rat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1725_dbl__inc__simps_I2_J,axiom,
% 9.25/5.14      ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 9.25/5.14      = one_one_int ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1726_zero__reorient,axiom,
% 9.25/5.14      ! [X: code_integer] :
% 9.25/5.14        ( ( zero_z3403309356797280102nteger = X )
% 9.25/5.14        = ( X = zero_z3403309356797280102nteger ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1727_zero__reorient,axiom,
% 9.25/5.14      ! [X: multis2468970476368604999at_nat] :
% 9.25/5.14        ( ( zero_z1048942125864253310at_nat = X )
% 9.25/5.14        = ( X = zero_z1048942125864253310at_nat ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1728_zero__reorient,axiom,
% 9.25/5.14      ! [X: rat] :
% 9.25/5.14        ( ( zero_zero_rat = X )
% 9.25/5.14        = ( X = zero_zero_rat ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1729_zero__reorient,axiom,
% 9.25/5.14      ! [X: nat] :
% 9.25/5.14        ( ( zero_zero_nat = X )
% 9.25/5.14        = ( X = zero_zero_nat ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1730_zero__reorient,axiom,
% 9.25/5.14      ! [X: int] :
% 9.25/5.14        ( ( zero_zero_int = X )
% 9.25/5.14        = ( X = zero_zero_int ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1731_zero__neq__neg__numeral,axiom,
% 9.25/5.14      ! [N: num] :
% 9.25/5.14        ( zero_zero_int
% 9.25/5.14       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1732_zero__neq__neg__numeral,axiom,
% 9.25/5.14      ! [N: num] :
% 9.25/5.14        ( zero_z3403309356797280102nteger
% 9.25/5.14       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1733_zero__neq__neg__numeral,axiom,
% 9.25/5.14      ! [N: num] :
% 9.25/5.14        ( zero_zero_rat
% 9.25/5.14       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1734_numeral__neq__neg__numeral,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( numeral_numeral_int @ M )
% 9.25/5.14       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1735_numeral__neq__neg__numeral,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( numera6620942414471956472nteger @ M )
% 9.25/5.14       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1736_numeral__neq__neg__numeral,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( numeral_numeral_rat @ M )
% 9.25/5.14       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1737_neg__numeral__neq__numeral,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 9.25/5.14       != ( numeral_numeral_int @ N ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1738_neg__numeral__neq__numeral,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 9.25/5.14       != ( numera6620942414471956472nteger @ N ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1739_neg__numeral__neq__numeral,axiom,
% 9.25/5.14      ! [M: num,N: num] :
% 9.25/5.14        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 9.25/5.14       != ( numeral_numeral_rat @ N ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1740_mult__right__cancel,axiom,
% 9.25/5.14      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.14        ( ( C != zero_z3403309356797280102nteger )
% 9.25/5.14       => ( ( ( times_3573771949741848930nteger @ A @ C )
% 9.25/5.14            = ( times_3573771949741848930nteger @ B @ C ) )
% 9.25/5.14          = ( A = B ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1741_mult__right__cancel,axiom,
% 9.25/5.14      ! [C: rat,A: rat,B: rat] :
% 9.25/5.14        ( ( C != zero_zero_rat )
% 9.25/5.14       => ( ( ( times_times_rat @ A @ C )
% 9.25/5.14            = ( times_times_rat @ B @ C ) )
% 9.25/5.14          = ( A = B ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1742_mult__right__cancel,axiom,
% 9.25/5.14      ! [C: nat,A: nat,B: nat] :
% 9.25/5.14        ( ( C != zero_zero_nat )
% 9.25/5.14       => ( ( ( times_times_nat @ A @ C )
% 9.25/5.14            = ( times_times_nat @ B @ C ) )
% 9.25/5.14          = ( A = B ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1743_mult__right__cancel,axiom,
% 9.25/5.14      ! [C: int,A: int,B: int] :
% 9.25/5.14        ( ( C != zero_zero_int )
% 9.25/5.14       => ( ( ( times_times_int @ A @ C )
% 9.25/5.14            = ( times_times_int @ B @ C ) )
% 9.25/5.14          = ( A = B ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1744_mult__left__cancel,axiom,
% 9.25/5.14      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.14        ( ( C != zero_z3403309356797280102nteger )
% 9.25/5.14       => ( ( ( times_3573771949741848930nteger @ C @ A )
% 9.25/5.14            = ( times_3573771949741848930nteger @ C @ B ) )
% 9.25/5.14          = ( A = B ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1745_mult__left__cancel,axiom,
% 9.25/5.14      ! [C: rat,A: rat,B: rat] :
% 9.25/5.14        ( ( C != zero_zero_rat )
% 9.25/5.14       => ( ( ( times_times_rat @ C @ A )
% 9.25/5.14            = ( times_times_rat @ C @ B ) )
% 9.25/5.14          = ( A = B ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1746_mult__left__cancel,axiom,
% 9.25/5.14      ! [C: nat,A: nat,B: nat] :
% 9.25/5.14        ( ( C != zero_zero_nat )
% 9.25/5.14       => ( ( ( times_times_nat @ C @ A )
% 9.25/5.14            = ( times_times_nat @ C @ B ) )
% 9.25/5.14          = ( A = B ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1747_mult__left__cancel,axiom,
% 9.25/5.14      ! [C: int,A: int,B: int] :
% 9.25/5.14        ( ( C != zero_zero_int )
% 9.25/5.14       => ( ( ( times_times_int @ C @ A )
% 9.25/5.14            = ( times_times_int @ C @ B ) )
% 9.25/5.14          = ( A = B ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1748_no__zero__divisors,axiom,
% 9.25/5.14      ! [A: code_integer,B: code_integer] :
% 9.25/5.14        ( ( A != zero_z3403309356797280102nteger )
% 9.25/5.14       => ( ( B != zero_z3403309356797280102nteger )
% 9.25/5.14         => ( ( times_3573771949741848930nteger @ A @ B )
% 9.25/5.14           != zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1749_no__zero__divisors,axiom,
% 9.25/5.14      ! [A: rat,B: rat] :
% 9.25/5.14        ( ( A != zero_zero_rat )
% 9.25/5.14       => ( ( B != zero_zero_rat )
% 9.25/5.14         => ( ( times_times_rat @ A @ B )
% 9.25/5.14           != zero_zero_rat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1750_no__zero__divisors,axiom,
% 9.25/5.14      ! [A: nat,B: nat] :
% 9.25/5.14        ( ( A != zero_zero_nat )
% 9.25/5.14       => ( ( B != zero_zero_nat )
% 9.25/5.14         => ( ( times_times_nat @ A @ B )
% 9.25/5.14           != zero_zero_nat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1751_no__zero__divisors,axiom,
% 9.25/5.14      ! [A: int,B: int] :
% 9.25/5.14        ( ( A != zero_zero_int )
% 9.25/5.14       => ( ( B != zero_zero_int )
% 9.25/5.14         => ( ( times_times_int @ A @ B )
% 9.25/5.14           != zero_zero_int ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1752_divisors__zero,axiom,
% 9.25/5.14      ! [A: code_integer,B: code_integer] :
% 9.25/5.14        ( ( ( times_3573771949741848930nteger @ A @ B )
% 9.25/5.14          = zero_z3403309356797280102nteger )
% 9.25/5.14       => ( ( A = zero_z3403309356797280102nteger )
% 9.25/5.14          | ( B = zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1753_divisors__zero,axiom,
% 9.25/5.14      ! [A: rat,B: rat] :
% 9.25/5.14        ( ( ( times_times_rat @ A @ B )
% 9.25/5.14          = zero_zero_rat )
% 9.25/5.14       => ( ( A = zero_zero_rat )
% 9.25/5.14          | ( B = zero_zero_rat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1754_divisors__zero,axiom,
% 9.25/5.14      ! [A: nat,B: nat] :
% 9.25/5.14        ( ( ( times_times_nat @ A @ B )
% 9.25/5.14          = zero_zero_nat )
% 9.25/5.14       => ( ( A = zero_zero_nat )
% 9.25/5.14          | ( B = zero_zero_nat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1755_divisors__zero,axiom,
% 9.25/5.14      ! [A: int,B: int] :
% 9.25/5.14        ( ( ( times_times_int @ A @ B )
% 9.25/5.14          = zero_zero_int )
% 9.25/5.14       => ( ( A = zero_zero_int )
% 9.25/5.14          | ( B = zero_zero_int ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1756_mult__not__zero,axiom,
% 9.25/5.14      ! [A: code_integer,B: code_integer] :
% 9.25/5.14        ( ( ( times_3573771949741848930nteger @ A @ B )
% 9.25/5.14         != zero_z3403309356797280102nteger )
% 9.25/5.14       => ( ( A != zero_z3403309356797280102nteger )
% 9.25/5.14          & ( B != zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1757_mult__not__zero,axiom,
% 9.25/5.14      ! [A: rat,B: rat] :
% 9.25/5.14        ( ( ( times_times_rat @ A @ B )
% 9.25/5.14         != zero_zero_rat )
% 9.25/5.14       => ( ( A != zero_zero_rat )
% 9.25/5.14          & ( B != zero_zero_rat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1758_mult__not__zero,axiom,
% 9.25/5.14      ! [A: nat,B: nat] :
% 9.25/5.14        ( ( ( times_times_nat @ A @ B )
% 9.25/5.14         != zero_zero_nat )
% 9.25/5.14       => ( ( A != zero_zero_nat )
% 9.25/5.14          & ( B != zero_zero_nat ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1759_mult__not__zero,axiom,
% 9.25/5.14      ! [A: int,B: int] :
% 9.25/5.14        ( ( ( times_times_int @ A @ B )
% 9.25/5.14         != zero_zero_int )
% 9.25/5.14       => ( ( A != zero_zero_int )
% 9.25/5.14          & ( B != zero_zero_int ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1760_zero__neq__one,axiom,
% 9.25/5.14      zero_z3403309356797280102nteger != one_one_Code_integer ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1761_zero__neq__one,axiom,
% 9.25/5.14      zero_zero_rat != one_one_rat ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1762_zero__neq__one,axiom,
% 9.25/5.14      zero_zero_nat != one_one_nat ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1763_zero__neq__one,axiom,
% 9.25/5.14      zero_zero_int != one_one_int ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1764_rel__restrictI,axiom,
% 9.25/5.14      ! [X: set_Pr958786334691620121nt_int,R: set_se6260736226359567993nt_int,Y: set_Pr958786334691620121nt_int,E: set_Pr8057934254988874055nt_int] :
% 9.25/5.14        ( ~ ( member2340774599025711042nt_int @ X @ R )
% 9.25/5.14       => ( ~ ( member2340774599025711042nt_int @ Y @ R )
% 9.25/5.14         => ( ( member5325734588016868240nt_int @ ( produc782388162306416855nt_int @ X @ Y ) @ E )
% 9.25/5.14           => ( member5325734588016868240nt_int @ ( produc782388162306416855nt_int @ X @ Y ) @ ( rel_re4349003428253852667nt_int @ E @ R ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1765_rel__restrictI,axiom,
% 9.25/5.14      ! [X: set_nat,R: set_set_nat,Y: set_nat,E: set_Pr5488025237498180813et_nat] :
% 9.25/5.14        ( ~ ( member_set_nat @ X @ R )
% 9.25/5.14       => ( ~ ( member_set_nat @ Y @ R )
% 9.25/5.14         => ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ X @ Y ) @ E )
% 9.25/5.14           => ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ X @ Y ) @ ( rel_restrict_set_nat @ E @ R ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1766_rel__restrictI,axiom,
% 9.25/5.14      ! [X: nat,R: set_nat,Y: nat,E: set_Pr1261947904930325089at_nat] :
% 9.25/5.14        ( ~ ( member_nat @ X @ R )
% 9.25/5.14       => ( ~ ( member_nat @ Y @ R )
% 9.25/5.14         => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ E )
% 9.25/5.14           => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( rel_restrict_nat @ E @ R ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1767_rel__restrictI,axiom,
% 9.25/5.14      ! [X: int,R: set_int,Y: int,E: set_Pr958786334691620121nt_int] :
% 9.25/5.14        ( ~ ( member_int @ X @ R )
% 9.25/5.14       => ( ~ ( member_int @ Y @ R )
% 9.25/5.14         => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ E )
% 9.25/5.14           => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( rel_restrict_int @ E @ R ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1768_rel__restrictI,axiom,
% 9.25/5.14      ! [X: produc3658429121746597890et_nat > $o,R: set_Pr4532377907799695533_nat_o,Y: produc3658429121746597890et_nat > $o,E: set_Pr2161125870931222855_nat_o] :
% 9.25/5.14        ( ~ ( member6576561426505652726_nat_o @ X @ R )
% 9.25/5.14       => ( ~ ( member6576561426505652726_nat_o @ Y @ R )
% 9.25/5.14         => ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ E )
% 9.25/5.14           => ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ ( rel_re3331361160397388719_nat_o @ E @ R ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1769_rel__restrict__notR_I1_J,axiom,
% 9.25/5.14      ! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,A2: set_Pr8057934254988874055nt_int,R: set_se6260736226359567993nt_int] :
% 9.25/5.14        ( ( member5325734588016868240nt_int @ ( produc782388162306416855nt_int @ X @ Y ) @ ( rel_re4349003428253852667nt_int @ A2 @ R ) )
% 9.25/5.14       => ~ ( member2340774599025711042nt_int @ X @ R ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1770_rel__restrict__notR_I1_J,axiom,
% 9.25/5.14      ! [X: set_nat,Y: set_nat,A2: set_Pr5488025237498180813et_nat,R: set_set_nat] :
% 9.25/5.14        ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ X @ Y ) @ ( rel_restrict_set_nat @ A2 @ R ) )
% 9.25/5.14       => ~ ( member_set_nat @ X @ R ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1771_rel__restrict__notR_I1_J,axiom,
% 9.25/5.14      ! [X: nat,Y: nat,A2: set_Pr1261947904930325089at_nat,R: set_nat] :
% 9.25/5.14        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( rel_restrict_nat @ A2 @ R ) )
% 9.25/5.14       => ~ ( member_nat @ X @ R ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1772_rel__restrict__notR_I1_J,axiom,
% 9.25/5.14      ! [X: int,Y: int,A2: set_Pr958786334691620121nt_int,R: set_int] :
% 9.25/5.14        ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( rel_restrict_int @ A2 @ R ) )
% 9.25/5.14       => ~ ( member_int @ X @ R ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1773_rel__restrict__notR_I1_J,axiom,
% 9.25/5.14      ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o,A2: set_Pr2161125870931222855_nat_o,R: set_Pr4532377907799695533_nat_o] :
% 9.25/5.14        ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ ( rel_re3331361160397388719_nat_o @ A2 @ R ) )
% 9.25/5.14       => ~ ( member6576561426505652726_nat_o @ X @ R ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1774_rel__restrict__notR_I2_J,axiom,
% 9.25/5.14      ! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,A2: set_Pr8057934254988874055nt_int,R: set_se6260736226359567993nt_int] :
% 9.25/5.14        ( ( member5325734588016868240nt_int @ ( produc782388162306416855nt_int @ X @ Y ) @ ( rel_re4349003428253852667nt_int @ A2 @ R ) )
% 9.25/5.14       => ~ ( member2340774599025711042nt_int @ Y @ R ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1775_rel__restrict__notR_I2_J,axiom,
% 9.25/5.14      ! [X: set_nat,Y: set_nat,A2: set_Pr5488025237498180813et_nat,R: set_set_nat] :
% 9.25/5.14        ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ X @ Y ) @ ( rel_restrict_set_nat @ A2 @ R ) )
% 9.25/5.14       => ~ ( member_set_nat @ Y @ R ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1776_rel__restrict__notR_I2_J,axiom,
% 9.25/5.14      ! [X: nat,Y: nat,A2: set_Pr1261947904930325089at_nat,R: set_nat] :
% 9.25/5.14        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( rel_restrict_nat @ A2 @ R ) )
% 9.25/5.14       => ~ ( member_nat @ Y @ R ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1777_rel__restrict__notR_I2_J,axiom,
% 9.25/5.14      ! [X: int,Y: int,A2: set_Pr958786334691620121nt_int,R: set_int] :
% 9.25/5.14        ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( rel_restrict_int @ A2 @ R ) )
% 9.25/5.14       => ~ ( member_int @ Y @ R ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1778_rel__restrict__notR_I2_J,axiom,
% 9.25/5.14      ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o,A2: set_Pr2161125870931222855_nat_o,R: set_Pr4532377907799695533_nat_o] :
% 9.25/5.14        ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ ( rel_re3331361160397388719_nat_o @ A2 @ R ) )
% 9.25/5.14       => ~ ( member6576561426505652726_nat_o @ Y @ R ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1779_rel__restrict__union,axiom,
% 9.25/5.14      ! [R: set_Pr4759807026041935047at_nat,A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.14        ( ( rel_re2197483123211154633at_nat @ R @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 9.25/5.14        = ( rel_re2197483123211154633at_nat @ ( rel_re2197483123211154633at_nat @ R @ A2 ) @ B2 ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1780_rel__restrict__union,axiom,
% 9.25/5.14      ! [R: set_Pr5564308138774400199at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.14        ( ( rel_re2767227651283840073at_nat @ R @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 9.25/5.14        = ( rel_re2767227651283840073at_nat @ ( rel_re2767227651283840073at_nat @ R @ A2 ) @ B2 ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1781_rel__restrict__union,axiom,
% 9.25/5.14      ! [R: set_Pr1261947904930325089at_nat,A2: set_nat,B2: set_nat] :
% 9.25/5.14        ( ( rel_restrict_nat @ R @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.14        = ( rel_restrict_nat @ ( rel_restrict_nat @ R @ A2 ) @ B2 ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1782_Id__on__iff,axiom,
% 9.25/5.14      ! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int] :
% 9.25/5.14        ( ( member5325734588016868240nt_int @ ( produc782388162306416855nt_int @ X @ Y ) @ ( id_on_6410342593070439734nt_int @ A2 ) )
% 9.25/5.14        = ( ( X = Y )
% 9.25/5.14          & ( member2340774599025711042nt_int @ X @ A2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1783_Id__on__iff,axiom,
% 9.25/5.14      ! [X: set_nat,Y: set_nat,A2: set_set_nat] :
% 9.25/5.14        ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ X @ Y ) @ ( id_on_set_nat @ A2 ) )
% 9.25/5.14        = ( ( X = Y )
% 9.25/5.14          & ( member_set_nat @ X @ A2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1784_Id__on__iff,axiom,
% 9.25/5.14      ! [X: nat,Y: nat,A2: set_nat] :
% 9.25/5.14        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( id_on_nat @ A2 ) )
% 9.25/5.14        = ( ( X = Y )
% 9.25/5.14          & ( member_nat @ X @ A2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1785_Id__on__iff,axiom,
% 9.25/5.14      ! [X: int,Y: int,A2: set_int] :
% 9.25/5.14        ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( id_on_int @ A2 ) )
% 9.25/5.14        = ( ( X = Y )
% 9.25/5.14          & ( member_int @ X @ A2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1786_Id__on__iff,axiom,
% 9.25/5.14      ! [X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.14        ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ X @ Y ) @ ( id_on_7438695062414216554_nat_o @ A2 ) )
% 9.25/5.14        = ( ( X = Y )
% 9.25/5.14          & ( member6576561426505652726_nat_o @ X @ A2 ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1787_Id__on__eqI,axiom,
% 9.25/5.14      ! [A: set_Pr958786334691620121nt_int,B: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int] :
% 9.25/5.14        ( ( A = B )
% 9.25/5.14       => ( ( member2340774599025711042nt_int @ A @ A2 )
% 9.25/5.14         => ( member5325734588016868240nt_int @ ( produc782388162306416855nt_int @ A @ B ) @ ( id_on_6410342593070439734nt_int @ A2 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1788_Id__on__eqI,axiom,
% 9.25/5.14      ! [A: set_nat,B: set_nat,A2: set_set_nat] :
% 9.25/5.14        ( ( A = B )
% 9.25/5.14       => ( ( member_set_nat @ A @ A2 )
% 9.25/5.14         => ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A @ B ) @ ( id_on_set_nat @ A2 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1789_Id__on__eqI,axiom,
% 9.25/5.14      ! [A: nat,B: nat,A2: set_nat] :
% 9.25/5.14        ( ( A = B )
% 9.25/5.14       => ( ( member_nat @ A @ A2 )
% 9.25/5.14         => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( id_on_nat @ A2 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1790_Id__on__eqI,axiom,
% 9.25/5.14      ! [A: int,B: int,A2: set_int] :
% 9.25/5.14        ( ( A = B )
% 9.25/5.14       => ( ( member_int @ A @ A2 )
% 9.25/5.14         => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( id_on_int @ A2 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1791_Id__on__eqI,axiom,
% 9.25/5.14      ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.14        ( ( A = B )
% 9.25/5.14       => ( ( member6576561426505652726_nat_o @ A @ A2 )
% 9.25/5.14         => ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ A @ B ) @ ( id_on_7438695062414216554_nat_o @ A2 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1792_Id__onE,axiom,
% 9.25/5.14      ! [C: produc412284730452459111nt_int,A2: set_se6260736226359567993nt_int] :
% 9.25/5.14        ( ( member5325734588016868240nt_int @ C @ ( id_on_6410342593070439734nt_int @ A2 ) )
% 9.25/5.14       => ~ ! [X2: set_Pr958786334691620121nt_int] :
% 9.25/5.14              ( ( member2340774599025711042nt_int @ X2 @ A2 )
% 9.25/5.14             => ( C
% 9.25/5.14               != ( produc782388162306416855nt_int @ X2 @ X2 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1793_Id__onE,axiom,
% 9.25/5.14      ! [C: produc7819656566062154093et_nat,A2: set_set_nat] :
% 9.25/5.14        ( ( member8277197624267554838et_nat @ C @ ( id_on_set_nat @ A2 ) )
% 9.25/5.14       => ~ ! [X2: set_nat] :
% 9.25/5.14              ( ( member_set_nat @ X2 @ A2 )
% 9.25/5.14             => ( C
% 9.25/5.14               != ( produc4532415448927165861et_nat @ X2 @ X2 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1794_Id__onE,axiom,
% 9.25/5.14      ! [C: product_prod_nat_nat,A2: set_nat] :
% 9.25/5.14        ( ( member8440522571783428010at_nat @ C @ ( id_on_nat @ A2 ) )
% 9.25/5.14       => ~ ! [X2: nat] :
% 9.25/5.14              ( ( member_nat @ X2 @ A2 )
% 9.25/5.14             => ( C
% 9.25/5.14               != ( product_Pair_nat_nat @ X2 @ X2 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1795_Id__onE,axiom,
% 9.25/5.14      ! [C: product_prod_int_int,A2: set_int] :
% 9.25/5.14        ( ( member5262025264175285858nt_int @ C @ ( id_on_int @ A2 ) )
% 9.25/5.14       => ~ ! [X2: int] :
% 9.25/5.14              ( ( member_int @ X2 @ A2 )
% 9.25/5.14             => ( C
% 9.25/5.14               != ( product_Pair_int_int @ X2 @ X2 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1796_Id__onE,axiom,
% 9.25/5.14      ! [C: produc4928098042776334183_nat_o,A2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.14        ( ( member8781333585448626064_nat_o @ C @ ( id_on_7438695062414216554_nat_o @ A2 ) )
% 9.25/5.14       => ~ ! [X2: produc3658429121746597890et_nat > $o] :
% 9.25/5.14              ( ( member6576561426505652726_nat_o @ X2 @ A2 )
% 9.25/5.14             => ( C
% 9.25/5.14               != ( produc7368190662567826135_nat_o @ X2 @ X2 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1797_lambda__zero,axiom,
% 9.25/5.14      ( ( ^ [H2: code_integer] : zero_z3403309356797280102nteger )
% 9.25/5.14      = ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1798_lambda__zero,axiom,
% 9.25/5.14      ( ( ^ [H2: rat] : zero_zero_rat )
% 9.25/5.14      = ( times_times_rat @ zero_zero_rat ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1799_lambda__zero,axiom,
% 9.25/5.14      ( ( ^ [H2: nat] : zero_zero_nat )
% 9.25/5.14      = ( times_times_nat @ zero_zero_nat ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1800_lambda__zero,axiom,
% 9.25/5.14      ( ( ^ [H2: int] : zero_zero_int )
% 9.25/5.14      = ( times_times_int @ zero_zero_int ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1801_one__neq__neg__numeral,axiom,
% 9.25/5.14      ! [N: num] :
% 9.25/5.14        ( one_one_int
% 9.25/5.14       != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1802_one__neq__neg__numeral,axiom,
% 9.25/5.14      ! [N: num] :
% 9.25/5.14        ( one_one_Code_integer
% 9.25/5.14       != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1803_one__neq__neg__numeral,axiom,
% 9.25/5.14      ! [N: num] :
% 9.25/5.14        ( one_one_rat
% 9.25/5.14       != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1804_numeral__neq__neg__one,axiom,
% 9.25/5.14      ! [N: num] :
% 9.25/5.14        ( ( numeral_numeral_int @ N )
% 9.25/5.14       != ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1805_numeral__neq__neg__one,axiom,
% 9.25/5.14      ! [N: num] :
% 9.25/5.14        ( ( numera6620942414471956472nteger @ N )
% 9.25/5.14       != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1806_numeral__neq__neg__one,axiom,
% 9.25/5.14      ! [N: num] :
% 9.25/5.14        ( ( numeral_numeral_rat @ N )
% 9.25/5.14       != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1807_zero__neq__neg__one,axiom,
% 9.25/5.14      ( zero_zero_int
% 9.25/5.14     != ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1808_zero__neq__neg__one,axiom,
% 9.25/5.14      ( zero_z3403309356797280102nteger
% 9.25/5.14     != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1809_zero__neq__neg__one,axiom,
% 9.25/5.14      ( zero_zero_rat
% 9.25/5.14     != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1810_bijective__def,axiom,
% 9.25/5.14      ( biject9051520373387432658nteger
% 9.25/5.14      = ( ^ [R2: set_Pr1281608226676607948nteger] :
% 9.25/5.14            ( ! [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger,Z3: produc8923325533196201883nteger] :
% 9.25/5.14                ( ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ R2 )
% 9.25/5.14                  & ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Z3 ) @ R2 ) )
% 9.25/5.14               => ( Y3 = Z3 ) )
% 9.25/5.14            & ! [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc6241069584506657477e_term > option6357759511663192854e_term,Z3: produc8923325533196201883nteger] :
% 9.25/5.14                ( ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Z3 ) @ R2 )
% 9.25/5.14                  & ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ Y3 @ Z3 ) @ R2 ) )
% 9.25/5.14               => ( X3 = Y3 ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1811_bijective__def,axiom,
% 9.25/5.14      ( biject2615096655818420098et_nat
% 9.25/5.14      = ( ^ [R2: set_Pr3286484037609594932et_nat] :
% 9.25/5.14            ( ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat,Z3: produc3658429121746597890et_nat] :
% 9.25/5.14                ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R2 )
% 9.25/5.14                  & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Z3 ) @ R2 ) )
% 9.25/5.14               => ( Y3 = Z3 ) )
% 9.25/5.14            & ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat > $o,Z3: produc3658429121746597890et_nat] :
% 9.25/5.14                ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Z3 ) @ R2 )
% 9.25/5.14                  & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ Y3 @ Z3 ) @ R2 ) )
% 9.25/5.14               => ( X3 = Y3 ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1812_bijective__def,axiom,
% 9.25/5.14      ( biject1468766312547416318et_nat
% 9.25/5.14      = ( ^ [R2: set_Pr8536935166611901872et_nat] :
% 9.25/5.14            ( ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat,Z3: produc3925858234332021118et_nat] :
% 9.25/5.14                ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R2 )
% 9.25/5.14                  & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Z3 ) @ R2 ) )
% 9.25/5.14               => ( Y3 = Z3 ) )
% 9.25/5.14            & ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat > $o,Z3: produc3925858234332021118et_nat] :
% 9.25/5.14                ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Z3 ) @ R2 )
% 9.25/5.14                  & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ Y3 @ Z3 ) @ R2 ) )
% 9.25/5.14               => ( X3 = Y3 ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1813_bijective__def,axiom,
% 9.25/5.14      ( biject383251550997737151nt_int
% 9.25/5.14      = ( ^ [R2: set_Pr9222295170931077689nt_int] :
% 9.25/5.14            ( ! [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int,Z3: product_prod_int_int] :
% 9.25/5.14                ( ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ R2 )
% 9.25/5.14                  & ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Z3 ) @ R2 ) )
% 9.25/5.14               => ( Y3 = Z3 ) )
% 9.25/5.14            & ! [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: produc8551481072490612790e_term > option6357759511663192854e_term,Z3: product_prod_int_int] :
% 9.25/5.14                ( ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Z3 ) @ R2 )
% 9.25/5.14                  & ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ Y3 @ Z3 ) @ R2 ) )
% 9.25/5.14               => ( X3 = Y3 ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1814_bijective__def,axiom,
% 9.25/5.14      ( biject576505603616484041nt_int
% 9.25/5.14      = ( ^ [R2: set_Pr1872883991513573699nt_int] :
% 9.25/5.14            ( ! [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int,Z3: product_prod_int_int] :
% 9.25/5.14                ( ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ R2 )
% 9.25/5.14                  & ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Z3 ) @ R2 ) )
% 9.25/5.14               => ( Y3 = Z3 ) )
% 9.25/5.14            & ! [X3: int > option6357759511663192854e_term,Y3: int > option6357759511663192854e_term,Z3: product_prod_int_int] :
% 9.25/5.14                ( ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Z3 ) @ R2 )
% 9.25/5.14                  & ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ Y3 @ Z3 ) @ R2 ) )
% 9.25/5.14               => ( X3 = Y3 ) ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1815_semiring__norm_I170_J,axiom,
% 9.25/5.14      ! [V: num,W: num,Y: int] :
% 9.25/5.14        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y ) )
% 9.25/5.14        = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1816_semiring__norm_I170_J,axiom,
% 9.25/5.14      ! [V: num,W: num,Y: code_integer] :
% 9.25/5.14        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y ) )
% 9.25/5.14        = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1817_semiring__norm_I170_J,axiom,
% 9.25/5.14      ! [V: num,W: num,Y: rat] :
% 9.25/5.14        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y ) )
% 9.25/5.14        = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1818_semiring__norm_I171_J,axiom,
% 9.25/5.14      ! [V: num,W: num,Y: int] :
% 9.25/5.14        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 9.25/5.14        = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1819_semiring__norm_I171_J,axiom,
% 9.25/5.14      ! [V: num,W: num,Y: code_integer] :
% 9.25/5.14        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 9.25/5.14        = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1820_semiring__norm_I171_J,axiom,
% 9.25/5.14      ! [V: num,W: num,Y: rat] :
% 9.25/5.14        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 9.25/5.14        = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1821_semiring__norm_I172_J,axiom,
% 9.25/5.14      ! [V: num,W: num,Y: int] :
% 9.25/5.14        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 9.25/5.14        = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1822_semiring__norm_I172_J,axiom,
% 9.25/5.14      ! [V: num,W: num,Y: code_integer] :
% 9.25/5.14        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 9.25/5.14        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1823_semiring__norm_I172_J,axiom,
% 9.25/5.14      ! [V: num,W: num,Y: rat] :
% 9.25/5.14        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 9.25/5.14        = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1824_numeral__times__minus__swap,axiom,
% 9.25/5.14      ! [W: num,X: int] :
% 9.25/5.14        ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X ) )
% 9.25/5.14        = ( times_times_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1825_numeral__times__minus__swap,axiom,
% 9.25/5.14      ! [W: num,X: code_integer] :
% 9.25/5.14        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X ) )
% 9.25/5.14        = ( times_3573771949741848930nteger @ X @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1826_numeral__times__minus__swap,axiom,
% 9.25/5.14      ! [W: num,X: rat] :
% 9.25/5.14        ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X ) )
% 9.25/5.14        = ( times_times_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1827_dbl__simps_I1_J,axiom,
% 9.25/5.14      ! [K: num] :
% 9.25/5.14        ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 9.25/5.14        = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1828_dbl__simps_I1_J,axiom,
% 9.25/5.14      ! [K: num] :
% 9.25/5.14        ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 9.25/5.14        = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1829_dbl__simps_I1_J,axiom,
% 9.25/5.14      ! [K: num] :
% 9.25/5.14        ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 9.25/5.14        = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1830_eq__divide__eq__numeral1_I2_J,axiom,
% 9.25/5.14      ! [A: rat,B: rat,W: num] :
% 9.25/5.14        ( ( A
% 9.25/5.14          = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 9.25/5.14        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 9.25/5.14             != zero_zero_rat )
% 9.25/5.14           => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 9.25/5.14              = B ) )
% 9.25/5.14          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 9.25/5.14              = zero_zero_rat )
% 9.25/5.14           => ( A = zero_zero_rat ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1831_divide__eq__eq__numeral1_I2_J,axiom,
% 9.25/5.14      ! [B: rat,W: num,A: rat] :
% 9.25/5.14        ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 9.25/5.14          = A )
% 9.25/5.14        = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 9.25/5.14             != zero_zero_rat )
% 9.25/5.14           => ( B
% 9.25/5.14              = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 9.25/5.14          & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 9.25/5.14              = zero_zero_rat )
% 9.25/5.14           => ( A = zero_zero_rat ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1832_eq__numeral__iff__iszero_I12_J,axiom,
% 9.25/5.14      ! [Y: num] :
% 9.25/5.14        ( ( zero_zero_int
% 9.25/5.14          = ( uminus_uminus_int @ ( numeral_numeral_int @ Y ) ) )
% 9.25/5.14        = ( ring_1_iszero_int @ ( numeral_numeral_int @ Y ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1833_eq__numeral__iff__iszero_I12_J,axiom,
% 9.25/5.14      ! [Y: num] :
% 9.25/5.14        ( ( zero_z3403309356797280102nteger
% 9.25/5.14          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ Y ) ) )
% 9.25/5.14        = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ Y ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1834_eq__numeral__iff__iszero_I12_J,axiom,
% 9.25/5.14      ! [Y: num] :
% 9.25/5.14        ( ( zero_zero_rat
% 9.25/5.14          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ Y ) ) )
% 9.25/5.14        = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ Y ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1835_eq__numeral__iff__iszero_I11_J,axiom,
% 9.25/5.14      ! [X: num] :
% 9.25/5.14        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ X ) )
% 9.25/5.14          = zero_zero_int )
% 9.25/5.14        = ( ring_1_iszero_int @ ( numeral_numeral_int @ X ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1836_eq__numeral__iff__iszero_I11_J,axiom,
% 9.25/5.14      ! [X: num] :
% 9.25/5.14        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) )
% 9.25/5.14          = zero_z3403309356797280102nteger )
% 9.25/5.14        = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ X ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1837_eq__numeral__iff__iszero_I11_J,axiom,
% 9.25/5.14      ! [X: num] :
% 9.25/5.14        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) )
% 9.25/5.14          = zero_zero_rat )
% 9.25/5.14        = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ X ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1838_divides__aux__eq,axiom,
% 9.25/5.14      ! [Q4: code_integer,R3: code_integer] :
% 9.25/5.14        ( ( unique5706413561485394159nteger @ ( produc1086072967326762835nteger @ Q4 @ R3 ) )
% 9.25/5.14        = ( R3 = zero_z3403309356797280102nteger ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1839_divides__aux__eq,axiom,
% 9.25/5.14      ! [Q4: nat,R3: nat] :
% 9.25/5.14        ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q4 @ R3 ) )
% 9.25/5.14        = ( R3 = zero_zero_nat ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1840_divides__aux__eq,axiom,
% 9.25/5.14      ! [Q4: int,R3: int] :
% 9.25/5.14        ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 9.25/5.14        = ( R3 = zero_zero_int ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1841_minus__assn__def,axiom,
% 9.25/5.14      ( minus_minus_assn
% 9.25/5.14      = ( ^ [A3: assn,B3: assn] : ( inf_inf_assn @ A3 @ ( uminus_uminus_assn @ B3 ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1842_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 9.25/5.14      ! [A: code_integer] :
% 9.25/5.14        ( ( minus_8373710615458151222nteger @ A @ A )
% 9.25/5.14        = zero_z3403309356797280102nteger ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1843_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 9.25/5.14      ! [A: multis2468970476368604999at_nat] :
% 9.25/5.14        ( ( minus_4286766774447292334at_nat @ A @ A )
% 9.25/5.14        = zero_z1048942125864253310at_nat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1844_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 9.25/5.14      ! [A: rat] :
% 9.25/5.14        ( ( minus_minus_rat @ A @ A )
% 9.25/5.14        = zero_zero_rat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1845_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 9.25/5.14      ! [A: nat] :
% 9.25/5.14        ( ( minus_minus_nat @ A @ A )
% 9.25/5.14        = zero_zero_nat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1846_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 9.25/5.14      ! [A: int] :
% 9.25/5.14        ( ( minus_minus_int @ A @ A )
% 9.25/5.14        = zero_zero_int ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1847_diff__zero,axiom,
% 9.25/5.14      ! [A: code_integer] :
% 9.25/5.14        ( ( minus_8373710615458151222nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.14        = A ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1848_diff__zero,axiom,
% 9.25/5.14      ! [A: multis2468970476368604999at_nat] :
% 9.25/5.14        ( ( minus_4286766774447292334at_nat @ A @ zero_z1048942125864253310at_nat )
% 9.25/5.14        = A ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1849_diff__zero,axiom,
% 9.25/5.14      ! [A: rat] :
% 9.25/5.14        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 9.25/5.14        = A ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1850_diff__zero,axiom,
% 9.25/5.14      ! [A: nat] :
% 9.25/5.14        ( ( minus_minus_nat @ A @ zero_zero_nat )
% 9.25/5.14        = A ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1851_diff__zero,axiom,
% 9.25/5.14      ! [A: int] :
% 9.25/5.14        ( ( minus_minus_int @ A @ zero_zero_int )
% 9.25/5.14        = A ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1852_zero__diff,axiom,
% 9.25/5.14      ! [A: multis2468970476368604999at_nat] :
% 9.25/5.14        ( ( minus_4286766774447292334at_nat @ zero_z1048942125864253310at_nat @ A )
% 9.25/5.14        = zero_z1048942125864253310at_nat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1853_zero__diff,axiom,
% 9.25/5.14      ! [A: nat] :
% 9.25/5.14        ( ( minus_minus_nat @ zero_zero_nat @ A )
% 9.25/5.14        = zero_zero_nat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1854_diff__0__right,axiom,
% 9.25/5.14      ! [A: code_integer] :
% 9.25/5.14        ( ( minus_8373710615458151222nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.14        = A ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1855_diff__0__right,axiom,
% 9.25/5.14      ! [A: rat] :
% 9.25/5.14        ( ( minus_minus_rat @ A @ zero_zero_rat )
% 9.25/5.14        = A ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1856_diff__0__right,axiom,
% 9.25/5.14      ! [A: int] :
% 9.25/5.14        ( ( minus_minus_int @ A @ zero_zero_int )
% 9.25/5.14        = A ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1857_diff__self,axiom,
% 9.25/5.14      ! [A: code_integer] :
% 9.25/5.14        ( ( minus_8373710615458151222nteger @ A @ A )
% 9.25/5.14        = zero_z3403309356797280102nteger ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1858_diff__self,axiom,
% 9.25/5.14      ! [A: rat] :
% 9.25/5.14        ( ( minus_minus_rat @ A @ A )
% 9.25/5.14        = zero_zero_rat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1859_diff__self,axiom,
% 9.25/5.14      ! [A: int] :
% 9.25/5.14        ( ( minus_minus_int @ A @ A )
% 9.25/5.14        = zero_zero_int ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1860_minus__diff__eq,axiom,
% 9.25/5.14      ! [A: int,B: int] :
% 9.25/5.14        ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 9.25/5.14        = ( minus_minus_int @ B @ A ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1861_minus__diff__eq,axiom,
% 9.25/5.14      ! [A: code_integer,B: code_integer] :
% 9.25/5.14        ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 9.25/5.14        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1862_minus__diff__eq,axiom,
% 9.25/5.14      ! [A: rat,B: rat] :
% 9.25/5.14        ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 9.25/5.14        = ( minus_minus_rat @ B @ A ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1863_div__by__1,axiom,
% 9.25/5.14      ! [A: nat] :
% 9.25/5.14        ( ( divide_divide_nat @ A @ one_one_nat )
% 9.25/5.14        = A ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1864_div__by__1,axiom,
% 9.25/5.14      ! [A: int] :
% 9.25/5.14        ( ( divide_divide_int @ A @ one_one_int )
% 9.25/5.14        = A ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1865_div__by__1,axiom,
% 9.25/5.14      ! [A: code_integer] :
% 9.25/5.14        ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 9.25/5.14        = A ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1866_div__by__1,axiom,
% 9.25/5.14      ! [A: rat] :
% 9.25/5.14        ( ( divide_divide_rat @ A @ one_one_rat )
% 9.25/5.14        = A ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1867_div__by__1,axiom,
% 9.25/5.14      ! [A: code_natural] :
% 9.25/5.14        ( ( divide5121882707175180666atural @ A @ one_one_Code_natural )
% 9.25/5.14        = A ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1868_diff__numeral__special_I9_J,axiom,
% 9.25/5.14      ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ one_one_Code_integer )
% 9.25/5.14      = zero_z3403309356797280102nteger ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1869_diff__numeral__special_I9_J,axiom,
% 9.25/5.14      ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 9.25/5.14      = zero_zero_rat ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1870_diff__numeral__special_I9_J,axiom,
% 9.25/5.14      ( ( minus_minus_int @ one_one_int @ one_one_int )
% 9.25/5.14      = zero_zero_int ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1871_left__diff__distrib__numeral,axiom,
% 9.25/5.14      ! [A: int,B: int,V: num] :
% 9.25/5.14        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 9.25/5.14        = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1872_left__diff__distrib__numeral,axiom,
% 9.25/5.14      ! [A: code_integer,B: code_integer,V: num] :
% 9.25/5.14        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V ) )
% 9.25/5.14        = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1873_left__diff__distrib__numeral,axiom,
% 9.25/5.14      ! [A: rat,B: rat,V: num] :
% 9.25/5.14        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 9.25/5.14        = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1874_right__diff__distrib__numeral,axiom,
% 9.25/5.14      ! [V: num,B: int,C: int] :
% 9.25/5.14        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 9.25/5.14        = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1875_right__diff__distrib__numeral,axiom,
% 9.25/5.14      ! [V: num,B: code_integer,C: code_integer] :
% 9.25/5.14        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( minus_8373710615458151222nteger @ B @ C ) )
% 9.25/5.14        = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ C ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1876_right__diff__distrib__numeral,axiom,
% 9.25/5.14      ! [V: num,B: rat,C: rat] :
% 9.25/5.14        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 9.25/5.14        = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1877_verit__minus__simplify_I3_J,axiom,
% 9.25/5.14      ! [B: int] :
% 9.25/5.14        ( ( minus_minus_int @ zero_zero_int @ B )
% 9.25/5.14        = ( uminus_uminus_int @ B ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1878_verit__minus__simplify_I3_J,axiom,
% 9.25/5.14      ! [B: code_integer] :
% 9.25/5.14        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 9.25/5.14        = ( uminus1351360451143612070nteger @ B ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1879_verit__minus__simplify_I3_J,axiom,
% 9.25/5.14      ! [B: rat] :
% 9.25/5.14        ( ( minus_minus_rat @ zero_zero_rat @ B )
% 9.25/5.14        = ( uminus_uminus_rat @ B ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1880_diff__0,axiom,
% 9.25/5.14      ! [A: int] :
% 9.25/5.14        ( ( minus_minus_int @ zero_zero_int @ A )
% 9.25/5.14        = ( uminus_uminus_int @ A ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1881_diff__0,axiom,
% 9.25/5.14      ! [A: code_integer] :
% 9.25/5.14        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.14        = ( uminus1351360451143612070nteger @ A ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1882_diff__0,axiom,
% 9.25/5.14      ! [A: rat] :
% 9.25/5.14        ( ( minus_minus_rat @ zero_zero_rat @ A )
% 9.25/5.14        = ( uminus_uminus_rat @ A ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1883_nonzero__mult__div__cancel__left,axiom,
% 9.25/5.14      ! [A: nat,B: nat] :
% 9.25/5.14        ( ( A != zero_zero_nat )
% 9.25/5.14       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 9.25/5.14          = B ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1884_nonzero__mult__div__cancel__left,axiom,
% 9.25/5.14      ! [A: int,B: int] :
% 9.25/5.14        ( ( A != zero_zero_int )
% 9.25/5.14       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 9.25/5.14          = B ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1885_nonzero__mult__div__cancel__left,axiom,
% 9.25/5.14      ! [A: code_integer,B: code_integer] :
% 9.25/5.14        ( ( A != zero_z3403309356797280102nteger )
% 9.25/5.14       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ A )
% 9.25/5.14          = B ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1886_nonzero__mult__div__cancel__left,axiom,
% 9.25/5.14      ! [A: rat,B: rat] :
% 9.25/5.14        ( ( A != zero_zero_rat )
% 9.25/5.14       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 9.25/5.14          = B ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1887_nonzero__mult__div__cancel__left,axiom,
% 9.25/5.14      ! [A: code_natural,B: code_natural] :
% 9.25/5.14        ( ( A != zero_z2226904508553997617atural )
% 9.25/5.14       => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ A )
% 9.25/5.14          = B ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1888_nonzero__mult__div__cancel__right,axiom,
% 9.25/5.14      ! [B: nat,A: nat] :
% 9.25/5.14        ( ( B != zero_zero_nat )
% 9.25/5.14       => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 9.25/5.14          = A ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1889_nonzero__mult__div__cancel__right,axiom,
% 9.25/5.14      ! [B: int,A: int] :
% 9.25/5.14        ( ( B != zero_zero_int )
% 9.25/5.14       => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 9.25/5.14          = A ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1890_nonzero__mult__div__cancel__right,axiom,
% 9.25/5.14      ! [B: code_integer,A: code_integer] :
% 9.25/5.14        ( ( B != zero_z3403309356797280102nteger )
% 9.25/5.14       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 9.25/5.14          = A ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1891_nonzero__mult__div__cancel__right,axiom,
% 9.25/5.14      ! [B: rat,A: rat] :
% 9.25/5.14        ( ( B != zero_zero_rat )
% 9.25/5.14       => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 9.25/5.14          = A ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1892_nonzero__mult__div__cancel__right,axiom,
% 9.25/5.14      ! [B: code_natural,A: code_natural] :
% 9.25/5.14        ( ( B != zero_z2226904508553997617atural )
% 9.25/5.14       => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ B )
% 9.25/5.14          = A ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1893_div__self,axiom,
% 9.25/5.14      ! [A: nat] :
% 9.25/5.14        ( ( A != zero_zero_nat )
% 9.25/5.14       => ( ( divide_divide_nat @ A @ A )
% 9.25/5.14          = one_one_nat ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1894_div__self,axiom,
% 9.25/5.14      ! [A: int] :
% 9.25/5.14        ( ( A != zero_zero_int )
% 9.25/5.14       => ( ( divide_divide_int @ A @ A )
% 9.25/5.14          = one_one_int ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1895_div__self,axiom,
% 9.25/5.14      ! [A: code_integer] :
% 9.25/5.14        ( ( A != zero_z3403309356797280102nteger )
% 9.25/5.14       => ( ( divide6298287555418463151nteger @ A @ A )
% 9.25/5.14          = one_one_Code_integer ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1896_div__self,axiom,
% 9.25/5.14      ! [A: rat] :
% 9.25/5.14        ( ( A != zero_zero_rat )
% 9.25/5.14       => ( ( divide_divide_rat @ A @ A )
% 9.25/5.14          = one_one_rat ) ) ).
% 9.25/5.14  
% 9.25/5.14  thf(fact_1897_div__self,axiom,
% 9.25/5.14      ! [A: code_natural] :
% 9.25/5.14        ( ( A != zero_z2226904508553997617atural )
% 9.25/5.14       => ( ( divide5121882707175180666atural @ A @ A )
% 9.25/5.15          = one_one_Code_natural ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1898_iszero__neg__numeral,axiom,
% 9.25/5.15      ! [W: num] :
% 9.25/5.15        ( ( ring_1_iszero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) )
% 9.25/5.15        = ( ring_1_iszero_int @ ( numeral_numeral_int @ W ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1899_iszero__neg__numeral,axiom,
% 9.25/5.15      ! [W: num] :
% 9.25/5.15        ( ( ring_16219924574208605041nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) )
% 9.25/5.15        = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ W ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1900_iszero__neg__numeral,axiom,
% 9.25/5.15      ! [W: num] :
% 9.25/5.15        ( ( ring_1_iszero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 9.25/5.15        = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1901_eq__divide__eq__numeral1_I1_J,axiom,
% 9.25/5.15      ! [A: rat,B: rat,W: num] :
% 9.25/5.15        ( ( A
% 9.25/5.15          = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 9.25/5.15        = ( ( ( ( numeral_numeral_rat @ W )
% 9.25/5.15             != zero_zero_rat )
% 9.25/5.15           => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 9.25/5.15              = B ) )
% 9.25/5.15          & ( ( ( numeral_numeral_rat @ W )
% 9.25/5.15              = zero_zero_rat )
% 9.25/5.15           => ( A = zero_zero_rat ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1902_divide__eq__eq__numeral1_I1_J,axiom,
% 9.25/5.15      ! [B: rat,W: num,A: rat] :
% 9.25/5.15        ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 9.25/5.15          = A )
% 9.25/5.15        = ( ( ( ( numeral_numeral_rat @ W )
% 9.25/5.15             != zero_zero_rat )
% 9.25/5.15           => ( B
% 9.25/5.15              = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 9.25/5.15          & ( ( ( numeral_numeral_rat @ W )
% 9.25/5.15              = zero_zero_rat )
% 9.25/5.15           => ( A = zero_zero_rat ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1903_diff__numeral__special_I12_J,axiom,
% 9.25/5.15      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.15      = zero_zero_int ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1904_diff__numeral__special_I12_J,axiom,
% 9.25/5.15      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.15      = zero_z3403309356797280102nteger ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1905_diff__numeral__special_I12_J,axiom,
% 9.25/5.15      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.25/5.15      = zero_zero_rat ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1906_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 9.25/5.15      ! [A: rat,C: rat,B: rat] :
% 9.25/5.15        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 9.25/5.15        = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1907_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 9.25/5.15      ! [A: nat,C: nat,B: nat] :
% 9.25/5.15        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 9.25/5.15        = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1908_cancel__ab__semigroup__add__class_Odiff__right__commute,axiom,
% 9.25/5.15      ! [A: int,C: int,B: int] :
% 9.25/5.15        ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 9.25/5.15        = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1909_diff__eq__diff__eq,axiom,
% 9.25/5.15      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.25/5.15        ( ( ( minus_minus_rat @ A @ B )
% 9.25/5.15          = ( minus_minus_rat @ C @ D2 ) )
% 9.25/5.15       => ( ( A = B )
% 9.25/5.15          = ( C = D2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1910_diff__eq__diff__eq,axiom,
% 9.25/5.15      ! [A: int,B: int,C: int,D2: int] :
% 9.25/5.15        ( ( ( minus_minus_int @ A @ B )
% 9.25/5.15          = ( minus_minus_int @ C @ D2 ) )
% 9.25/5.15       => ( ( A = B )
% 9.25/5.15          = ( C = D2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1911_eq__iff__diff__eq__0,axiom,
% 9.25/5.15      ( ( ^ [Y4: code_integer,Z4: code_integer] : ( Y4 = Z4 ) )
% 9.25/5.15      = ( ^ [A3: code_integer,B3: code_integer] :
% 9.25/5.15            ( ( minus_8373710615458151222nteger @ A3 @ B3 )
% 9.25/5.15            = zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1912_eq__iff__diff__eq__0,axiom,
% 9.25/5.15      ( ( ^ [Y4: rat,Z4: rat] : ( Y4 = Z4 ) )
% 9.25/5.15      = ( ^ [A3: rat,B3: rat] :
% 9.25/5.15            ( ( minus_minus_rat @ A3 @ B3 )
% 9.25/5.15            = zero_zero_rat ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1913_eq__iff__diff__eq__0,axiom,
% 9.25/5.15      ( ( ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 9.25/5.15      = ( ^ [A3: int,B3: int] :
% 9.25/5.15            ( ( minus_minus_int @ A3 @ B3 )
% 9.25/5.15            = zero_zero_int ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1914_left__diff__distrib,axiom,
% 9.25/5.15      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.15        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 9.25/5.15        = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1915_left__diff__distrib,axiom,
% 9.25/5.15      ! [A: rat,B: rat,C: rat] :
% 9.25/5.15        ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 9.25/5.15        = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1916_left__diff__distrib,axiom,
% 9.25/5.15      ! [A: int,B: int,C: int] :
% 9.25/5.15        ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 9.25/5.15        = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1917_right__diff__distrib,axiom,
% 9.25/5.15      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.15        ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 9.25/5.15        = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1918_right__diff__distrib,axiom,
% 9.25/5.15      ! [A: rat,B: rat,C: rat] :
% 9.25/5.15        ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 9.25/5.15        = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1919_right__diff__distrib,axiom,
% 9.25/5.15      ! [A: int,B: int,C: int] :
% 9.25/5.15        ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 9.25/5.15        = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1920_left__diff__distrib_H,axiom,
% 9.25/5.15      ! [B: code_integer,C: code_integer,A: code_integer] :
% 9.25/5.15        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ C ) @ A )
% 9.25/5.15        = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1921_left__diff__distrib_H,axiom,
% 9.25/5.15      ! [B: rat,C: rat,A: rat] :
% 9.25/5.15        ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 9.25/5.15        = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1922_left__diff__distrib_H,axiom,
% 9.25/5.15      ! [B: nat,C: nat,A: nat] :
% 9.25/5.15        ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 9.25/5.15        = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1923_left__diff__distrib_H,axiom,
% 9.25/5.15      ! [B: int,C: int,A: int] :
% 9.25/5.15        ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 9.25/5.15        = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1924_right__diff__distrib_H,axiom,
% 9.25/5.15      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.15        ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 9.25/5.15        = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1925_right__diff__distrib_H,axiom,
% 9.25/5.15      ! [A: rat,B: rat,C: rat] :
% 9.25/5.15        ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 9.25/5.15        = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1926_right__diff__distrib_H,axiom,
% 9.25/5.15      ! [A: nat,B: nat,C: nat] :
% 9.25/5.15        ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 9.25/5.15        = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1927_right__diff__distrib_H,axiom,
% 9.25/5.15      ! [A: int,B: int,C: int] :
% 9.25/5.15        ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 9.25/5.15        = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1928_minus__diff__commute,axiom,
% 9.25/5.15      ! [B: int,A: int] :
% 9.25/5.15        ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 9.25/5.15        = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1929_minus__diff__commute,axiom,
% 9.25/5.15      ! [B: code_integer,A: code_integer] :
% 9.25/5.15        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 9.25/5.15        = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1930_minus__diff__commute,axiom,
% 9.25/5.15      ! [B: rat,A: rat] :
% 9.25/5.15        ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 9.25/5.15        = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1931_not__iszero__1,axiom,
% 9.25/5.15      ~ ( ring_16219924574208605041nteger @ one_one_Code_integer ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1932_not__iszero__1,axiom,
% 9.25/5.15      ~ ( ring_1_iszero_rat @ one_one_rat ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1933_not__iszero__1,axiom,
% 9.25/5.15      ~ ( ring_1_iszero_int @ one_one_int ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1934_diff__eq,axiom,
% 9.25/5.15      ( minus_1356011639430497352at_nat
% 9.25/5.15      = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ X3 @ ( uminus6524753893492686040at_nat @ Y3 ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1935_diff__eq,axiom,
% 9.25/5.15      ( minus_711738161318947805_int_o
% 9.25/5.15      = ( ^ [X3: product_prod_int_int > $o,Y3: product_prod_int_int > $o] : ( inf_in3604695632404883862_int_o @ X3 @ ( uminus7117520113953359693_int_o @ Y3 ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1936_diff__eq,axiom,
% 9.25/5.15      ( minus_6821098565838606101char_o
% 9.25/5.15      = ( ^ [X3: list_char > $o,Y3: list_char > $o] : ( inf_inf_list_char_o @ X3 @ ( uminus7154032370948614053char_o @ Y3 ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1937_diff__eq,axiom,
% 9.25/5.15      ( minus_minus_set_nat
% 9.25/5.15      = ( ^ [X3: set_nat,Y3: set_nat] : ( inf_inf_set_nat @ X3 @ ( uminus5710092332889474511et_nat @ Y3 ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1938_diff__eq,axiom,
% 9.25/5.15      ( minus_3524152463667985524t_unit
% 9.25/5.15      = ( ^ [X3: product_unit,Y3: product_unit] : ( inf_inf_Product_unit @ X3 @ ( uminus2952777764628376836t_unit @ Y3 ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1939_not__iszero__neg__1,axiom,
% 9.25/5.15      ~ ( ring_1_iszero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1940_not__iszero__neg__1,axiom,
% 9.25/5.15      ~ ( ring_16219924574208605041nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1941_not__iszero__neg__1,axiom,
% 9.25/5.15      ~ ( ring_1_iszero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1942_eq__divide__eq__numeral_I1_J,axiom,
% 9.25/5.15      ! [W: num,B: rat,C: rat] :
% 9.25/5.15        ( ( ( numeral_numeral_rat @ W )
% 9.25/5.15          = ( divide_divide_rat @ B @ C ) )
% 9.25/5.15        = ( ( ( C != zero_zero_rat )
% 9.25/5.15           => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 9.25/5.15              = B ) )
% 9.25/5.15          & ( ( C = zero_zero_rat )
% 9.25/5.15           => ( ( numeral_numeral_rat @ W )
% 9.25/5.15              = zero_zero_rat ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1943_divide__eq__eq__numeral_I1_J,axiom,
% 9.25/5.15      ! [B: rat,C: rat,W: num] :
% 9.25/5.15        ( ( ( divide_divide_rat @ B @ C )
% 9.25/5.15          = ( numeral_numeral_rat @ W ) )
% 9.25/5.15        = ( ( ( C != zero_zero_rat )
% 9.25/5.15           => ( B
% 9.25/5.15              = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 9.25/5.15          & ( ( C = zero_zero_rat )
% 9.25/5.15           => ( ( numeral_numeral_rat @ W )
% 9.25/5.15              = zero_zero_rat ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1944_divide__eq__eq__numeral_I2_J,axiom,
% 9.25/5.15      ! [B: rat,C: rat,W: num] :
% 9.25/5.15        ( ( ( divide_divide_rat @ B @ C )
% 9.25/5.15          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 9.25/5.15        = ( ( ( C != zero_zero_rat )
% 9.25/5.15           => ( B
% 9.25/5.15              = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 9.25/5.15          & ( ( C = zero_zero_rat )
% 9.25/5.15           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 9.25/5.15              = zero_zero_rat ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1945_eq__divide__eq__numeral_I2_J,axiom,
% 9.25/5.15      ! [W: num,B: rat,C: rat] :
% 9.25/5.15        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 9.25/5.15          = ( divide_divide_rat @ B @ C ) )
% 9.25/5.15        = ( ( ( C != zero_zero_rat )
% 9.25/5.15           => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 9.25/5.15              = B ) )
% 9.25/5.15          & ( ( C = zero_zero_rat )
% 9.25/5.15           => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 9.25/5.15              = zero_zero_rat ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1946_nonzero__divide__mult__cancel__left,axiom,
% 9.25/5.15      ! [A: rat,B: rat] :
% 9.25/5.15        ( ( A != zero_zero_rat )
% 9.25/5.15       => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 9.25/5.15          = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1947_nonzero__divide__mult__cancel__right,axiom,
% 9.25/5.15      ! [B: rat,A: rat] :
% 9.25/5.15        ( ( B != zero_zero_rat )
% 9.25/5.15       => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 9.25/5.15          = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1948_divide__minus1,axiom,
% 9.25/5.15      ! [X: rat] :
% 9.25/5.15        ( ( divide_divide_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.25/5.15        = ( uminus_uminus_rat @ X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1949_div__minus1__right,axiom,
% 9.25/5.15      ! [A: int] :
% 9.25/5.15        ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.15        = ( uminus_uminus_int @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1950_div__minus1__right,axiom,
% 9.25/5.15      ! [A: code_integer] :
% 9.25/5.15        ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.15        = ( uminus1351360451143612070nteger @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1951_divide__eq__1__iff,axiom,
% 9.25/5.15      ! [A: rat,B: rat] :
% 9.25/5.15        ( ( ( divide_divide_rat @ A @ B )
% 9.25/5.15          = one_one_rat )
% 9.25/5.15        = ( ( B != zero_zero_rat )
% 9.25/5.15          & ( A = B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1952_one__eq__divide__iff,axiom,
% 9.25/5.15      ! [A: rat,B: rat] :
% 9.25/5.15        ( ( one_one_rat
% 9.25/5.15          = ( divide_divide_rat @ A @ B ) )
% 9.25/5.15        = ( ( B != zero_zero_rat )
% 9.25/5.15          & ( A = B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1953_divide__self,axiom,
% 9.25/5.15      ! [A: rat] :
% 9.25/5.15        ( ( A != zero_zero_rat )
% 9.25/5.15       => ( ( divide_divide_rat @ A @ A )
% 9.25/5.15          = one_one_rat ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1954_divide__self__if,axiom,
% 9.25/5.15      ! [A: rat] :
% 9.25/5.15        ( ( ( A = zero_zero_rat )
% 9.25/5.15         => ( ( divide_divide_rat @ A @ A )
% 9.25/5.15            = zero_zero_rat ) )
% 9.25/5.15        & ( ( A != zero_zero_rat )
% 9.25/5.15         => ( ( divide_divide_rat @ A @ A )
% 9.25/5.15            = one_one_rat ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1955_divide__eq__eq__1,axiom,
% 9.25/5.15      ! [B: rat,A: rat] :
% 9.25/5.15        ( ( ( divide_divide_rat @ B @ A )
% 9.25/5.15          = one_one_rat )
% 9.25/5.15        = ( ( A != zero_zero_rat )
% 9.25/5.15          & ( A = B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1956_eq__divide__eq__1,axiom,
% 9.25/5.15      ! [B: rat,A: rat] :
% 9.25/5.15        ( ( one_one_rat
% 9.25/5.15          = ( divide_divide_rat @ B @ A ) )
% 9.25/5.15        = ( ( A != zero_zero_rat )
% 9.25/5.15          & ( A = B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1957_Diff__empty,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( minus_1356011639430497352at_nat @ A2 @ bot_bo2099793752762293965at_nat )
% 9.25/5.15        = A2 ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1958_Diff__empty,axiom,
% 9.25/5.15      ! [A2: set_o] :
% 9.25/5.15        ( ( minus_minus_set_o @ A2 @ bot_bot_set_o )
% 9.25/5.15        = A2 ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1959_Diff__empty,axiom,
% 9.25/5.15      ! [A2: set_int] :
% 9.25/5.15        ( ( minus_minus_set_int @ A2 @ bot_bot_set_int )
% 9.25/5.15        = A2 ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1960_Diff__empty,axiom,
% 9.25/5.15      ! [A2: set_nat] :
% 9.25/5.15        ( ( minus_minus_set_nat @ A2 @ bot_bot_set_nat )
% 9.25/5.15        = A2 ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1961_empty__Diff,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( minus_1356011639430497352at_nat @ bot_bo2099793752762293965at_nat @ A2 )
% 9.25/5.15        = bot_bo2099793752762293965at_nat ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1962_empty__Diff,axiom,
% 9.25/5.15      ! [A2: set_o] :
% 9.25/5.15        ( ( minus_minus_set_o @ bot_bot_set_o @ A2 )
% 9.25/5.15        = bot_bot_set_o ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1963_empty__Diff,axiom,
% 9.25/5.15      ! [A2: set_int] :
% 9.25/5.15        ( ( minus_minus_set_int @ bot_bot_set_int @ A2 )
% 9.25/5.15        = bot_bot_set_int ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1964_empty__Diff,axiom,
% 9.25/5.15      ! [A2: set_nat] :
% 9.25/5.15        ( ( minus_minus_set_nat @ bot_bot_set_nat @ A2 )
% 9.25/5.15        = bot_bot_set_nat ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1965_Diff__cancel,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( minus_1356011639430497352at_nat @ A2 @ A2 )
% 9.25/5.15        = bot_bo2099793752762293965at_nat ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1966_Diff__cancel,axiom,
% 9.25/5.15      ! [A2: set_o] :
% 9.25/5.15        ( ( minus_minus_set_o @ A2 @ A2 )
% 9.25/5.15        = bot_bot_set_o ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1967_Diff__cancel,axiom,
% 9.25/5.15      ! [A2: set_int] :
% 9.25/5.15        ( ( minus_minus_set_int @ A2 @ A2 )
% 9.25/5.15        = bot_bot_set_int ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1968_Diff__cancel,axiom,
% 9.25/5.15      ! [A2: set_nat] :
% 9.25/5.15        ( ( minus_minus_set_nat @ A2 @ A2 )
% 9.25/5.15        = bot_bot_set_nat ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1969_Un__Diff__cancel,axiom,
% 9.25/5.15      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.15        ( ( sup_su3035147773818789531at_nat @ A2 @ ( minus_5060654252129873198at_nat @ B2 @ A2 ) )
% 9.25/5.15        = ( sup_su3035147773818789531at_nat @ A2 @ B2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1970_Un__Diff__cancel,axiom,
% 9.25/5.15      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.15        ( ( sup_su5525570899277871387at_nat @ A2 @ ( minus_3314409938677909166at_nat @ B2 @ A2 ) )
% 9.25/5.15        = ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1971_Un__Diff__cancel,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.15        ( ( sup_sup_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 9.25/5.15        = ( sup_sup_set_nat @ A2 @ B2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1972_Un__Diff__cancel2,axiom,
% 9.25/5.15      ! [B2: set_Pr8551490117392284871at_nat,A2: set_Pr8551490117392284871at_nat] :
% 9.25/5.15        ( ( sup_su3035147773818789531at_nat @ ( minus_5060654252129873198at_nat @ B2 @ A2 ) @ A2 )
% 9.25/5.15        = ( sup_su3035147773818789531at_nat @ B2 @ A2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1973_Un__Diff__cancel2,axiom,
% 9.25/5.15      ! [B2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.15        ( ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ B2 @ A2 ) @ A2 )
% 9.25/5.15        = ( sup_su5525570899277871387at_nat @ B2 @ A2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1974_Un__Diff__cancel2,axiom,
% 9.25/5.15      ! [B2: set_nat,A2: set_nat] :
% 9.25/5.15        ( ( sup_sup_set_nat @ ( minus_minus_set_nat @ B2 @ A2 ) @ A2 )
% 9.25/5.15        = ( sup_sup_set_nat @ B2 @ A2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1975_times__divide__eq__right,axiom,
% 9.25/5.15      ! [A: rat,B: rat,C: rat] :
% 9.25/5.15        ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 9.25/5.15        = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1976_divide__divide__eq__right,axiom,
% 9.25/5.15      ! [A: rat,B: rat,C: rat] :
% 9.25/5.15        ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 9.25/5.15        = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1977_divide__divide__eq__left,axiom,
% 9.25/5.15      ! [A: rat,B: rat,C: rat] :
% 9.25/5.15        ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 9.25/5.15        = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1978_times__divide__eq__left,axiom,
% 9.25/5.15      ! [B: rat,C: rat,A: rat] :
% 9.25/5.15        ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 9.25/5.15        = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1979_Diff__UNIV,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( minus_1356011639430497352at_nat @ A2 @ top_to4669805908274784177at_nat )
% 9.25/5.15        = bot_bo2099793752762293965at_nat ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1980_Diff__UNIV,axiom,
% 9.25/5.15      ! [A2: set_list_nat] :
% 9.25/5.15        ( ( minus_7954133019191499631st_nat @ A2 @ top_top_set_list_nat )
% 9.25/5.15        = bot_bot_set_list_nat ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1981_Diff__UNIV,axiom,
% 9.25/5.15      ! [A2: set_o] :
% 9.25/5.15        ( ( minus_minus_set_o @ A2 @ top_top_set_o )
% 9.25/5.15        = bot_bot_set_o ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1982_Diff__UNIV,axiom,
% 9.25/5.15      ! [A2: set_rat] :
% 9.25/5.15        ( ( minus_minus_set_rat @ A2 @ top_top_set_rat )
% 9.25/5.15        = bot_bot_set_rat ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1983_Diff__UNIV,axiom,
% 9.25/5.15      ! [A2: set_int] :
% 9.25/5.15        ( ( minus_minus_set_int @ A2 @ top_top_set_int )
% 9.25/5.15        = bot_bot_set_int ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1984_Diff__UNIV,axiom,
% 9.25/5.15      ! [A2: set_nat] :
% 9.25/5.15        ( ( minus_minus_set_nat @ A2 @ top_top_set_nat )
% 9.25/5.15        = bot_bot_set_nat ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1985_div__minus__minus,axiom,
% 9.25/5.15      ! [A: int,B: int] :
% 9.25/5.15        ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 9.25/5.15        = ( divide_divide_int @ A @ B ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1986_div__minus__minus,axiom,
% 9.25/5.15      ! [A: code_integer,B: code_integer] :
% 9.25/5.15        ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 9.25/5.15        = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1987_Diff__disjoint,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( inf_in2572325071724192079at_nat @ A2 @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) )
% 9.25/5.15        = bot_bo2099793752762293965at_nat ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1988_Diff__disjoint,axiom,
% 9.25/5.15      ! [A2: set_o,B2: set_o] :
% 9.25/5.15        ( ( inf_inf_set_o @ A2 @ ( minus_minus_set_o @ B2 @ A2 ) )
% 9.25/5.15        = bot_bot_set_o ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1989_Diff__disjoint,axiom,
% 9.25/5.15      ! [A2: set_int,B2: set_int] :
% 9.25/5.15        ( ( inf_inf_set_int @ A2 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 9.25/5.15        = bot_bot_set_int ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1990_Diff__disjoint,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.15        ( ( inf_inf_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 9.25/5.15        = bot_bot_set_nat ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1991_Diff__Compl,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( minus_1356011639430497352at_nat @ A2 @ ( uminus6524753893492686040at_nat @ B2 ) )
% 9.25/5.15        = ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1992_Diff__Compl,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.15        ( ( minus_minus_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ B2 ) )
% 9.25/5.15        = ( inf_inf_set_nat @ A2 @ B2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1993_inter__compl__diff__conv,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( inf_in2572325071724192079at_nat @ A2 @ ( uminus6524753893492686040at_nat @ B2 ) )
% 9.25/5.15        = ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1994_inter__compl__diff__conv,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.15        ( ( inf_inf_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ B2 ) )
% 9.25/5.15        = ( minus_minus_set_nat @ A2 @ B2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1995_Compl__Diff__eq,axiom,
% 9.25/5.15      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.15        ( ( uminus2330091110623919550at_nat @ ( minus_5060654252129873198at_nat @ A2 @ B2 ) )
% 9.25/5.15        = ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ A2 ) @ B2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1996_Compl__Diff__eq,axiom,
% 9.25/5.15      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.15        ( ( uminus935396558254630718at_nat @ ( minus_3314409938677909166at_nat @ A2 @ B2 ) )
% 9.25/5.15        = ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ A2 ) @ B2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1997_Compl__Diff__eq,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.15        ( ( uminus5710092332889474511et_nat @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 9.25/5.15        = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ B2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1998_div__mult__mult1__if,axiom,
% 9.25/5.15      ! [C: nat,A: nat,B: nat] :
% 9.25/5.15        ( ( ( C = zero_zero_nat )
% 9.25/5.15         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 9.25/5.15            = zero_zero_nat ) )
% 9.25/5.15        & ( ( C != zero_zero_nat )
% 9.25/5.15         => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 9.25/5.15            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_1999_div__mult__mult1__if,axiom,
% 9.25/5.15      ! [C: int,A: int,B: int] :
% 9.25/5.15        ( ( ( C = zero_zero_int )
% 9.25/5.15         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.25/5.15            = zero_zero_int ) )
% 9.25/5.15        & ( ( C != zero_zero_int )
% 9.25/5.15         => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.25/5.15            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2000_div__mult__mult1__if,axiom,
% 9.25/5.15      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.15        ( ( ( C = zero_z3403309356797280102nteger )
% 9.25/5.15         => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 9.25/5.15            = zero_z3403309356797280102nteger ) )
% 9.25/5.15        & ( ( C != zero_z3403309356797280102nteger )
% 9.25/5.15         => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 9.25/5.15            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2001_div__mult__mult1__if,axiom,
% 9.25/5.15      ! [C: code_natural,A: code_natural,B: code_natural] :
% 9.25/5.15        ( ( ( C = zero_z2226904508553997617atural )
% 9.25/5.15         => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 9.25/5.15            = zero_z2226904508553997617atural ) )
% 9.25/5.15        & ( ( C != zero_z2226904508553997617atural )
% 9.25/5.15         => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 9.25/5.15            = ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2002_div__mult__mult2,axiom,
% 9.25/5.15      ! [C: nat,A: nat,B: nat] :
% 9.25/5.15        ( ( C != zero_zero_nat )
% 9.25/5.15       => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 9.25/5.15          = ( divide_divide_nat @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2003_div__mult__mult2,axiom,
% 9.25/5.15      ! [C: int,A: int,B: int] :
% 9.25/5.15        ( ( C != zero_zero_int )
% 9.25/5.15       => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 9.25/5.15          = ( divide_divide_int @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2004_div__mult__mult2,axiom,
% 9.25/5.15      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.15        ( ( C != zero_z3403309356797280102nteger )
% 9.25/5.15       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.25/5.15          = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2005_div__mult__mult2,axiom,
% 9.25/5.15      ! [C: code_natural,A: code_natural,B: code_natural] :
% 9.25/5.15        ( ( C != zero_z2226904508553997617atural )
% 9.25/5.15       => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) )
% 9.25/5.15          = ( divide5121882707175180666atural @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2006_div__mult__mult1,axiom,
% 9.25/5.15      ! [C: nat,A: nat,B: nat] :
% 9.25/5.15        ( ( C != zero_zero_nat )
% 9.25/5.15       => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 9.25/5.15          = ( divide_divide_nat @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2007_div__mult__mult1,axiom,
% 9.25/5.15      ! [C: int,A: int,B: int] :
% 9.25/5.15        ( ( C != zero_zero_int )
% 9.25/5.15       => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.25/5.15          = ( divide_divide_int @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2008_div__mult__mult1,axiom,
% 9.25/5.15      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.15        ( ( C != zero_z3403309356797280102nteger )
% 9.25/5.15       => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 9.25/5.15          = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2009_div__mult__mult1,axiom,
% 9.25/5.15      ! [C: code_natural,A: code_natural,B: code_natural] :
% 9.25/5.15        ( ( C != zero_z2226904508553997617atural )
% 9.25/5.15       => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 9.25/5.15          = ( divide5121882707175180666atural @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2010_nonzero__mult__divide__mult__cancel__right2,axiom,
% 9.25/5.15      ! [C: rat,A: rat,B: rat] :
% 9.25/5.15        ( ( C != zero_zero_rat )
% 9.25/5.15       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 9.25/5.15          = ( divide_divide_rat @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2011_nonzero__mult__divide__mult__cancel__right,axiom,
% 9.25/5.15      ! [C: rat,A: rat,B: rat] :
% 9.25/5.15        ( ( C != zero_zero_rat )
% 9.25/5.15       => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 9.25/5.15          = ( divide_divide_rat @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2012_nonzero__mult__divide__mult__cancel__left2,axiom,
% 9.25/5.15      ! [C: rat,A: rat,B: rat] :
% 9.25/5.15        ( ( C != zero_zero_rat )
% 9.25/5.15       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 9.25/5.15          = ( divide_divide_rat @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2013_nonzero__mult__divide__mult__cancel__left,axiom,
% 9.25/5.15      ! [C: rat,A: rat,B: rat] :
% 9.25/5.15        ( ( C != zero_zero_rat )
% 9.25/5.15       => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.25/5.15          = ( divide_divide_rat @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2014_mult__divide__mult__cancel__left__if,axiom,
% 9.25/5.15      ! [C: rat,A: rat,B: rat] :
% 9.25/5.15        ( ( ( C = zero_zero_rat )
% 9.25/5.15         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.25/5.15            = zero_zero_rat ) )
% 9.25/5.15        & ( ( C != zero_zero_rat )
% 9.25/5.15         => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.25/5.15            = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2015_zero__eq__1__divide__iff,axiom,
% 9.25/5.15      ! [A: rat] :
% 9.25/5.15        ( ( zero_zero_rat
% 9.25/5.15          = ( divide_divide_rat @ one_one_rat @ A ) )
% 9.25/5.15        = ( A = zero_zero_rat ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2016_one__divide__eq__0__iff,axiom,
% 9.25/5.15      ! [A: rat] :
% 9.25/5.15        ( ( ( divide_divide_rat @ one_one_rat @ A )
% 9.25/5.15          = zero_zero_rat )
% 9.25/5.15        = ( A = zero_zero_rat ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2017_Int__Diff,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.15        = ( inf_in2572325071724192079at_nat @ A2 @ ( minus_1356011639430497352at_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2018_Int__Diff,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 9.25/5.15        ( ( minus_minus_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.15        = ( inf_inf_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2019_Diff__Int2,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ C2 ) @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) )
% 9.25/5.15        = ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ C2 ) @ B2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2020_Diff__Int2,axiom,
% 9.25/5.15      ! [A2: set_nat,C2: set_nat,B2: set_nat] :
% 9.25/5.15        ( ( minus_minus_set_nat @ ( inf_inf_set_nat @ A2 @ C2 ) @ ( inf_inf_set_nat @ B2 @ C2 ) )
% 9.25/5.15        = ( minus_minus_set_nat @ ( inf_inf_set_nat @ A2 @ C2 ) @ B2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2021_Diff__Diff__Int,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( minus_1356011639430497352at_nat @ A2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 9.25/5.15        = ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2022_Diff__Diff__Int,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.15        ( ( minus_minus_set_nat @ A2 @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 9.25/5.15        = ( inf_inf_set_nat @ A2 @ B2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2023_Diff__Int__distrib,axiom,
% 9.25/5.15      ! [C2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( inf_in2572325071724192079at_nat @ C2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 9.25/5.15        = ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ C2 @ A2 ) @ ( inf_in2572325071724192079at_nat @ C2 @ B2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2024_Diff__Int__distrib,axiom,
% 9.25/5.15      ! [C2: set_nat,A2: set_nat,B2: set_nat] :
% 9.25/5.15        ( ( inf_inf_set_nat @ C2 @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 9.25/5.15        = ( minus_minus_set_nat @ ( inf_inf_set_nat @ C2 @ A2 ) @ ( inf_inf_set_nat @ C2 @ B2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2025_Diff__Int__distrib2,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( inf_in2572325071724192079at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.15        = ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ C2 ) @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2026_Diff__Int__distrib2,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 9.25/5.15        ( ( inf_inf_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.15        = ( minus_minus_set_nat @ ( inf_inf_set_nat @ A2 @ C2 ) @ ( inf_inf_set_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2027_Un__Diff,axiom,
% 9.25/5.15      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 9.25/5.15        ( ( minus_5060654252129873198at_nat @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.15        = ( sup_su3035147773818789531at_nat @ ( minus_5060654252129873198at_nat @ A2 @ C2 ) @ ( minus_5060654252129873198at_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2028_Un__Diff,axiom,
% 9.25/5.15      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 9.25/5.15        ( ( minus_3314409938677909166at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.15        = ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ A2 @ C2 ) @ ( minus_3314409938677909166at_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2029_Un__Diff,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 9.25/5.15        ( ( minus_minus_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.15        = ( sup_sup_set_nat @ ( minus_minus_set_nat @ A2 @ C2 ) @ ( minus_minus_set_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2030_set__diff__diff__left,axiom,
% 9.25/5.15      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 9.25/5.15        ( ( minus_5060654252129873198at_nat @ ( minus_5060654252129873198at_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.15        = ( minus_5060654252129873198at_nat @ A2 @ ( sup_su3035147773818789531at_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2031_set__diff__diff__left,axiom,
% 9.25/5.15      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 9.25/5.15        ( ( minus_3314409938677909166at_nat @ ( minus_3314409938677909166at_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.15        = ( minus_3314409938677909166at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2032_set__diff__diff__left,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 9.25/5.15        ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.15        = ( minus_minus_set_nat @ A2 @ ( sup_sup_set_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2033_Diff__triv,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 9.25/5.15          = bot_bo2099793752762293965at_nat )
% 9.25/5.15       => ( ( minus_1356011639430497352at_nat @ A2 @ B2 )
% 9.25/5.15          = A2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2034_Diff__triv,axiom,
% 9.25/5.15      ! [A2: set_o,B2: set_o] :
% 9.25/5.15        ( ( ( inf_inf_set_o @ A2 @ B2 )
% 9.25/5.15          = bot_bot_set_o )
% 9.25/5.15       => ( ( minus_minus_set_o @ A2 @ B2 )
% 9.25/5.15          = A2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2035_Diff__triv,axiom,
% 9.25/5.15      ! [A2: set_int,B2: set_int] :
% 9.25/5.15        ( ( ( inf_inf_set_int @ A2 @ B2 )
% 9.25/5.15          = bot_bot_set_int )
% 9.25/5.15       => ( ( minus_minus_set_int @ A2 @ B2 )
% 9.25/5.15          = A2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2036_Diff__triv,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.15        ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 9.25/5.15          = bot_bot_set_nat )
% 9.25/5.15       => ( ( minus_minus_set_nat @ A2 @ B2 )
% 9.25/5.15          = A2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2037_Int__Diff__disjoint,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 9.25/5.15        = bot_bo2099793752762293965at_nat ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2038_Int__Diff__disjoint,axiom,
% 9.25/5.15      ! [A2: set_o,B2: set_o] :
% 9.25/5.15        ( ( inf_inf_set_o @ ( inf_inf_set_o @ A2 @ B2 ) @ ( minus_minus_set_o @ A2 @ B2 ) )
% 9.25/5.15        = bot_bot_set_o ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2039_Int__Diff__disjoint,axiom,
% 9.25/5.15      ! [A2: set_int,B2: set_int] :
% 9.25/5.15        ( ( inf_inf_set_int @ ( inf_inf_set_int @ A2 @ B2 ) @ ( minus_minus_set_int @ A2 @ B2 ) )
% 9.25/5.15        = bot_bot_set_int ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2040_Int__Diff__disjoint,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.15        ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 9.25/5.15        = bot_bot_set_nat ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2041_disjoint__alt__simp1,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( ( minus_1356011639430497352at_nat @ A2 @ B2 )
% 9.25/5.15          = A2 )
% 9.25/5.15        = ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 9.25/5.15          = bot_bo2099793752762293965at_nat ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2042_disjoint__alt__simp1,axiom,
% 9.25/5.15      ! [A2: set_o,B2: set_o] :
% 9.25/5.15        ( ( ( minus_minus_set_o @ A2 @ B2 )
% 9.25/5.15          = A2 )
% 9.25/5.15        = ( ( inf_inf_set_o @ A2 @ B2 )
% 9.25/5.15          = bot_bot_set_o ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2043_disjoint__alt__simp1,axiom,
% 9.25/5.15      ! [A2: set_int,B2: set_int] :
% 9.25/5.15        ( ( ( minus_minus_set_int @ A2 @ B2 )
% 9.25/5.15          = A2 )
% 9.25/5.15        = ( ( inf_inf_set_int @ A2 @ B2 )
% 9.25/5.15          = bot_bot_set_int ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2044_disjoint__alt__simp1,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.15        ( ( ( minus_minus_set_nat @ A2 @ B2 )
% 9.25/5.15          = A2 )
% 9.25/5.15        = ( ( inf_inf_set_nat @ A2 @ B2 )
% 9.25/5.15          = bot_bot_set_nat ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2045_disjoint__alt__simp2,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( ( minus_1356011639430497352at_nat @ A2 @ B2 )
% 9.25/5.15         != A2 )
% 9.25/5.15        = ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 9.25/5.15         != bot_bo2099793752762293965at_nat ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2046_disjoint__alt__simp2,axiom,
% 9.25/5.15      ! [A2: set_o,B2: set_o] :
% 9.25/5.15        ( ( ( minus_minus_set_o @ A2 @ B2 )
% 9.25/5.15         != A2 )
% 9.25/5.15        = ( ( inf_inf_set_o @ A2 @ B2 )
% 9.25/5.15         != bot_bot_set_o ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2047_disjoint__alt__simp2,axiom,
% 9.25/5.15      ! [A2: set_int,B2: set_int] :
% 9.25/5.15        ( ( ( minus_minus_set_int @ A2 @ B2 )
% 9.25/5.15         != A2 )
% 9.25/5.15        = ( ( inf_inf_set_int @ A2 @ B2 )
% 9.25/5.15         != bot_bot_set_int ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2048_disjoint__alt__simp2,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.15        ( ( ( minus_minus_set_nat @ A2 @ B2 )
% 9.25/5.15         != A2 )
% 9.25/5.15        = ( ( inf_inf_set_nat @ A2 @ B2 )
% 9.25/5.15         != bot_bot_set_nat ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2049_Diff__Un,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( minus_1356011639430497352at_nat @ A2 @ ( sup_su6327502436637775413at_nat @ B2 @ C2 ) )
% 9.25/5.15        = ( inf_in2572325071724192079at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) @ ( minus_1356011639430497352at_nat @ A2 @ C2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2050_Diff__Un,axiom,
% 9.25/5.15      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 9.25/5.15        ( ( minus_5060654252129873198at_nat @ A2 @ ( sup_su3035147773818789531at_nat @ B2 @ C2 ) )
% 9.25/5.15        = ( inf_in1697001100524423349at_nat @ ( minus_5060654252129873198at_nat @ A2 @ B2 ) @ ( minus_5060654252129873198at_nat @ A2 @ C2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2051_Diff__Un,axiom,
% 9.25/5.15      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 9.25/5.15        ( ( minus_3314409938677909166at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) )
% 9.25/5.15        = ( inf_in7913087082777306421at_nat @ ( minus_3314409938677909166at_nat @ A2 @ B2 ) @ ( minus_3314409938677909166at_nat @ A2 @ C2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2052_Diff__Un,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 9.25/5.15        ( ( minus_minus_set_nat @ A2 @ ( sup_sup_set_nat @ B2 @ C2 ) )
% 9.25/5.15        = ( inf_inf_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ ( minus_minus_set_nat @ A2 @ C2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2053_Diff__Int,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( minus_1356011639430497352at_nat @ A2 @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) )
% 9.25/5.15        = ( sup_su6327502436637775413at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) @ ( minus_1356011639430497352at_nat @ A2 @ C2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2054_Diff__Int,axiom,
% 9.25/5.15      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 9.25/5.15        ( ( minus_5060654252129873198at_nat @ A2 @ ( inf_in1697001100524423349at_nat @ B2 @ C2 ) )
% 9.25/5.15        = ( sup_su3035147773818789531at_nat @ ( minus_5060654252129873198at_nat @ A2 @ B2 ) @ ( minus_5060654252129873198at_nat @ A2 @ C2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2055_Diff__Int,axiom,
% 9.25/5.15      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 9.25/5.15        ( ( minus_3314409938677909166at_nat @ A2 @ ( inf_in7913087082777306421at_nat @ B2 @ C2 ) )
% 9.25/5.15        = ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ A2 @ B2 ) @ ( minus_3314409938677909166at_nat @ A2 @ C2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2056_Diff__Int,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 9.25/5.15        ( ( minus_minus_set_nat @ A2 @ ( inf_inf_set_nat @ B2 @ C2 ) )
% 9.25/5.15        = ( sup_sup_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ ( minus_minus_set_nat @ A2 @ C2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2057_Int__Diff__Un,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) )
% 9.25/5.15        = A2 ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2058_Int__Diff__Un,axiom,
% 9.25/5.15      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.15        ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) @ ( minus_5060654252129873198at_nat @ A2 @ B2 ) )
% 9.25/5.15        = A2 ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2059_Int__Diff__Un,axiom,
% 9.25/5.15      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.15        ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) @ ( minus_3314409938677909166at_nat @ A2 @ B2 ) )
% 9.25/5.15        = A2 ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2060_Int__Diff__Un,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.15        ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ ( minus_minus_set_nat @ A2 @ B2 ) )
% 9.25/5.15        = A2 ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2061_Un__Diff__Int,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( sup_su6327502436637775413at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 9.25/5.15        = A2 ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2062_Un__Diff__Int,axiom,
% 9.25/5.15      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.15        ( ( sup_su3035147773818789531at_nat @ ( minus_5060654252129873198at_nat @ A2 @ B2 ) @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) )
% 9.25/5.15        = A2 ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2063_Un__Diff__Int,axiom,
% 9.25/5.15      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.15        ( ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ A2 @ B2 ) @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) )
% 9.25/5.15        = A2 ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2064_Un__Diff__Int,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.15        ( ( sup_sup_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.15        = A2 ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2065_Compl__eq__Diff__UNIV,axiom,
% 9.25/5.15      ( uminus3195874150345416415st_nat
% 9.25/5.15      = ( minus_7954133019191499631st_nat @ top_top_set_list_nat ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2066_Compl__eq__Diff__UNIV,axiom,
% 9.25/5.15      ( uminus_uminus_set_o
% 9.25/5.15      = ( minus_minus_set_o @ top_top_set_o ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2067_Compl__eq__Diff__UNIV,axiom,
% 9.25/5.15      ( uminus2201863774496077783et_rat
% 9.25/5.15      = ( minus_minus_set_rat @ top_top_set_rat ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2068_Compl__eq__Diff__UNIV,axiom,
% 9.25/5.15      ( uminus1532241313380277803et_int
% 9.25/5.15      = ( minus_minus_set_int @ top_top_set_int ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2069_Compl__eq__Diff__UNIV,axiom,
% 9.25/5.15      ( uminus5710092332889474511et_nat
% 9.25/5.15      = ( minus_minus_set_nat @ top_top_set_nat ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2070_divide__divide__eq__left_H,axiom,
% 9.25/5.15      ! [A: rat,B: rat,C: rat] :
% 9.25/5.15        ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 9.25/5.15        = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2071_divide__divide__times__eq,axiom,
% 9.25/5.15      ! [X: rat,Y: rat,Z: rat,W: rat] :
% 9.25/5.15        ( ( divide_divide_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 9.25/5.15        = ( divide_divide_rat @ ( times_times_rat @ X @ W ) @ ( times_times_rat @ Y @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2072_times__divide__times__eq,axiom,
% 9.25/5.15      ! [X: rat,Y: rat,Z: rat,W: rat] :
% 9.25/5.15        ( ( times_times_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 9.25/5.15        = ( divide_divide_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ W ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2073_div__minus__right,axiom,
% 9.25/5.15      ! [A: int,B: int] :
% 9.25/5.15        ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 9.25/5.15        = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2074_div__minus__right,axiom,
% 9.25/5.15      ! [A: code_integer,B: code_integer] :
% 9.25/5.15        ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 9.25/5.15        = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2075_minus__divide__left,axiom,
% 9.25/5.15      ! [A: rat,B: rat] :
% 9.25/5.15        ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 9.25/5.15        = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2076_minus__divide__divide,axiom,
% 9.25/5.15      ! [A: rat,B: rat] :
% 9.25/5.15        ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 9.25/5.15        = ( divide_divide_rat @ A @ B ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2077_minus__divide__right,axiom,
% 9.25/5.15      ! [A: rat,B: rat] :
% 9.25/5.15        ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 9.25/5.15        = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2078_nonzero__eq__divide__eq,axiom,
% 9.25/5.15      ! [C: rat,A: rat,B: rat] :
% 9.25/5.15        ( ( C != zero_zero_rat )
% 9.25/5.15       => ( ( A
% 9.25/5.15            = ( divide_divide_rat @ B @ C ) )
% 9.25/5.15          = ( ( times_times_rat @ A @ C )
% 9.25/5.15            = B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2079_nonzero__divide__eq__eq,axiom,
% 9.25/5.15      ! [C: rat,B: rat,A: rat] :
% 9.25/5.15        ( ( C != zero_zero_rat )
% 9.25/5.15       => ( ( ( divide_divide_rat @ B @ C )
% 9.25/5.15            = A )
% 9.25/5.15          = ( B
% 9.25/5.15            = ( times_times_rat @ A @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2080_eq__divide__imp,axiom,
% 9.25/5.15      ! [C: rat,A: rat,B: rat] :
% 9.25/5.15        ( ( C != zero_zero_rat )
% 9.25/5.15       => ( ( ( times_times_rat @ A @ C )
% 9.25/5.15            = B )
% 9.25/5.15         => ( A
% 9.25/5.15            = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2081_divide__eq__imp,axiom,
% 9.25/5.15      ! [C: rat,B: rat,A: rat] :
% 9.25/5.15        ( ( C != zero_zero_rat )
% 9.25/5.15       => ( ( B
% 9.25/5.15            = ( times_times_rat @ A @ C ) )
% 9.25/5.15         => ( ( divide_divide_rat @ B @ C )
% 9.25/5.15            = A ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2082_eq__divide__eq,axiom,
% 9.25/5.15      ! [A: rat,B: rat,C: rat] :
% 9.25/5.15        ( ( A
% 9.25/5.15          = ( divide_divide_rat @ B @ C ) )
% 9.25/5.15        = ( ( ( C != zero_zero_rat )
% 9.25/5.15           => ( ( times_times_rat @ A @ C )
% 9.25/5.15              = B ) )
% 9.25/5.15          & ( ( C = zero_zero_rat )
% 9.25/5.15           => ( A = zero_zero_rat ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2083_divide__eq__eq,axiom,
% 9.25/5.15      ! [B: rat,C: rat,A: rat] :
% 9.25/5.15        ( ( ( divide_divide_rat @ B @ C )
% 9.25/5.15          = A )
% 9.25/5.15        = ( ( ( C != zero_zero_rat )
% 9.25/5.15           => ( B
% 9.25/5.15              = ( times_times_rat @ A @ C ) ) )
% 9.25/5.15          & ( ( C = zero_zero_rat )
% 9.25/5.15           => ( A = zero_zero_rat ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2084_frac__eq__eq,axiom,
% 9.25/5.15      ! [Y: rat,Z: rat,X: rat,W: rat] :
% 9.25/5.15        ( ( Y != zero_zero_rat )
% 9.25/5.15       => ( ( Z != zero_zero_rat )
% 9.25/5.15         => ( ( ( divide_divide_rat @ X @ Y )
% 9.25/5.15              = ( divide_divide_rat @ W @ Z ) )
% 9.25/5.15            = ( ( times_times_rat @ X @ Z )
% 9.25/5.15              = ( times_times_rat @ W @ Y ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2085_right__inverse__eq,axiom,
% 9.25/5.15      ! [B: rat,A: rat] :
% 9.25/5.15        ( ( B != zero_zero_rat )
% 9.25/5.15       => ( ( ( divide_divide_rat @ A @ B )
% 9.25/5.15            = one_one_rat )
% 9.25/5.15          = ( A = B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2086_nonzero__minus__divide__right,axiom,
% 9.25/5.15      ! [B: rat,A: rat] :
% 9.25/5.15        ( ( B != zero_zero_rat )
% 9.25/5.15       => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 9.25/5.15          = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2087_nonzero__minus__divide__divide,axiom,
% 9.25/5.15      ! [B: rat,A: rat] :
% 9.25/5.15        ( ( B != zero_zero_rat )
% 9.25/5.15       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 9.25/5.15          = ( divide_divide_rat @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2088_divide__diff__eq__iff,axiom,
% 9.25/5.15      ! [Z: rat,X: rat,Y: rat] :
% 9.25/5.15        ( ( Z != zero_zero_rat )
% 9.25/5.15       => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 9.25/5.15          = ( divide_divide_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2089_diff__divide__eq__iff,axiom,
% 9.25/5.15      ! [Z: rat,X: rat,Y: rat] :
% 9.25/5.15        ( ( Z != zero_zero_rat )
% 9.25/5.15       => ( ( minus_minus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 9.25/5.15          = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2090_diff__frac__eq,axiom,
% 9.25/5.15      ! [Y: rat,Z: rat,X: rat,W: rat] :
% 9.25/5.15        ( ( Y != zero_zero_rat )
% 9.25/5.15       => ( ( Z != zero_zero_rat )
% 9.25/5.15         => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 9.25/5.15            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2091_add__divide__eq__if__simps_I4_J,axiom,
% 9.25/5.15      ! [Z: rat,A: rat,B: rat] :
% 9.25/5.15        ( ( ( Z = zero_zero_rat )
% 9.25/5.15         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 9.25/5.15            = A ) )
% 9.25/5.15        & ( ( Z != zero_zero_rat )
% 9.25/5.15         => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 9.25/5.15            = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2092_nonzero__neg__divide__eq__eq2,axiom,
% 9.25/5.15      ! [B: rat,C: rat,A: rat] :
% 9.25/5.15        ( ( B != zero_zero_rat )
% 9.25/5.15       => ( ( C
% 9.25/5.15            = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 9.25/5.15          = ( ( times_times_rat @ C @ B )
% 9.25/5.15            = ( uminus_uminus_rat @ A ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2093_nonzero__neg__divide__eq__eq,axiom,
% 9.25/5.15      ! [B: rat,A: rat,C: rat] :
% 9.25/5.15        ( ( B != zero_zero_rat )
% 9.25/5.15       => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 9.25/5.15            = C )
% 9.25/5.15          = ( ( uminus_uminus_rat @ A )
% 9.25/5.15            = ( times_times_rat @ C @ B ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2094_minus__divide__eq__eq,axiom,
% 9.25/5.15      ! [B: rat,C: rat,A: rat] :
% 9.25/5.15        ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 9.25/5.15          = A )
% 9.25/5.15        = ( ( ( C != zero_zero_rat )
% 9.25/5.15           => ( ( uminus_uminus_rat @ B )
% 9.25/5.15              = ( times_times_rat @ A @ C ) ) )
% 9.25/5.15          & ( ( C = zero_zero_rat )
% 9.25/5.15           => ( A = zero_zero_rat ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2095_eq__minus__divide__eq,axiom,
% 9.25/5.15      ! [A: rat,B: rat,C: rat] :
% 9.25/5.15        ( ( A
% 9.25/5.15          = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 9.25/5.15        = ( ( ( C != zero_zero_rat )
% 9.25/5.15           => ( ( times_times_rat @ A @ C )
% 9.25/5.15              = ( uminus_uminus_rat @ B ) ) )
% 9.25/5.15          & ( ( C = zero_zero_rat )
% 9.25/5.15           => ( A = zero_zero_rat ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2096_divide__eq__minus__1__iff,axiom,
% 9.25/5.15      ! [A: rat,B: rat] :
% 9.25/5.15        ( ( ( divide_divide_rat @ A @ B )
% 9.25/5.15          = ( uminus_uminus_rat @ one_one_rat ) )
% 9.25/5.15        = ( ( B != zero_zero_rat )
% 9.25/5.15          & ( A
% 9.25/5.15            = ( uminus_uminus_rat @ B ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2097_minus__divide__diff__eq__iff,axiom,
% 9.25/5.15      ! [Z: rat,X: rat,Y: rat] :
% 9.25/5.15        ( ( Z != zero_zero_rat )
% 9.25/5.15       => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 9.25/5.15          = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2098_add__divide__eq__if__simps_I5_J,axiom,
% 9.25/5.15      ! [Z: rat,A: rat,B: rat] :
% 9.25/5.15        ( ( ( Z = zero_zero_rat )
% 9.25/5.15         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 9.25/5.15            = ( uminus_uminus_rat @ B ) ) )
% 9.25/5.15        & ( ( Z != zero_zero_rat )
% 9.25/5.15         => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 9.25/5.15            = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2099_add__divide__eq__if__simps_I6_J,axiom,
% 9.25/5.15      ! [Z: rat,A: rat,B: rat] :
% 9.25/5.15        ( ( ( Z = zero_zero_rat )
% 9.25/5.15         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 9.25/5.15            = ( uminus_uminus_rat @ B ) ) )
% 9.25/5.15        & ( ( Z != zero_zero_rat )
% 9.25/5.15         => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 9.25/5.15            = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2100_bits__div__by__1,axiom,
% 9.25/5.15      ! [A: nat] :
% 9.25/5.15        ( ( divide_divide_nat @ A @ one_one_nat )
% 9.25/5.15        = A ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2101_bits__div__by__1,axiom,
% 9.25/5.15      ! [A: int] :
% 9.25/5.15        ( ( divide_divide_int @ A @ one_one_int )
% 9.25/5.15        = A ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2102_bits__div__by__1,axiom,
% 9.25/5.15      ! [A: code_integer] :
% 9.25/5.15        ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 9.25/5.15        = A ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2103_bits__div__by__1,axiom,
% 9.25/5.15      ! [A: code_natural] :
% 9.25/5.15        ( ( divide5121882707175180666atural @ A @ one_one_Code_natural )
% 9.25/5.15        = A ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2104_inf__period_I1_J,axiom,
% 9.25/5.15      ! [P: code_integer > $o,D3: code_integer,Q2: code_integer > $o] :
% 9.25/5.15        ( ! [X2: code_integer,K2: code_integer] :
% 9.25/5.15            ( ( P @ X2 )
% 9.25/5.15            = ( P @ ( minus_8373710615458151222nteger @ X2 @ ( times_3573771949741848930nteger @ K2 @ D3 ) ) ) )
% 9.25/5.15       => ( ! [X2: code_integer,K2: code_integer] :
% 9.25/5.15              ( ( Q2 @ X2 )
% 9.25/5.15              = ( Q2 @ ( minus_8373710615458151222nteger @ X2 @ ( times_3573771949741848930nteger @ K2 @ D3 ) ) ) )
% 9.25/5.15         => ! [X5: code_integer,K3: code_integer] :
% 9.25/5.15              ( ( ( P @ X5 )
% 9.25/5.15                & ( Q2 @ X5 ) )
% 9.25/5.15              = ( ( P @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K3 @ D3 ) ) )
% 9.25/5.15                & ( Q2 @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K3 @ D3 ) ) ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2105_inf__period_I1_J,axiom,
% 9.25/5.15      ! [P: rat > $o,D3: rat,Q2: rat > $o] :
% 9.25/5.15        ( ! [X2: rat,K2: rat] :
% 9.25/5.15            ( ( P @ X2 )
% 9.25/5.15            = ( P @ ( minus_minus_rat @ X2 @ ( times_times_rat @ K2 @ D3 ) ) ) )
% 9.25/5.15       => ( ! [X2: rat,K2: rat] :
% 9.25/5.15              ( ( Q2 @ X2 )
% 9.25/5.15              = ( Q2 @ ( minus_minus_rat @ X2 @ ( times_times_rat @ K2 @ D3 ) ) ) )
% 9.25/5.15         => ! [X5: rat,K3: rat] :
% 9.25/5.15              ( ( ( P @ X5 )
% 9.25/5.15                & ( Q2 @ X5 ) )
% 9.25/5.15              = ( ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K3 @ D3 ) ) )
% 9.25/5.15                & ( Q2 @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K3 @ D3 ) ) ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2106_inf__period_I1_J,axiom,
% 9.25/5.15      ! [P: int > $o,D3: int,Q2: int > $o] :
% 9.25/5.15        ( ! [X2: int,K2: int] :
% 9.25/5.15            ( ( P @ X2 )
% 9.25/5.15            = ( P @ ( minus_minus_int @ X2 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 9.25/5.15       => ( ! [X2: int,K2: int] :
% 9.25/5.15              ( ( Q2 @ X2 )
% 9.25/5.15              = ( Q2 @ ( minus_minus_int @ X2 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 9.25/5.15         => ! [X5: int,K3: int] :
% 9.25/5.15              ( ( ( P @ X5 )
% 9.25/5.15                & ( Q2 @ X5 ) )
% 9.25/5.15              = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K3 @ D3 ) ) )
% 9.25/5.15                & ( Q2 @ ( minus_minus_int @ X5 @ ( times_times_int @ K3 @ D3 ) ) ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2107_inf__period_I2_J,axiom,
% 9.25/5.15      ! [P: code_integer > $o,D3: code_integer,Q2: code_integer > $o] :
% 9.25/5.15        ( ! [X2: code_integer,K2: code_integer] :
% 9.25/5.15            ( ( P @ X2 )
% 9.25/5.15            = ( P @ ( minus_8373710615458151222nteger @ X2 @ ( times_3573771949741848930nteger @ K2 @ D3 ) ) ) )
% 9.25/5.15       => ( ! [X2: code_integer,K2: code_integer] :
% 9.25/5.15              ( ( Q2 @ X2 )
% 9.25/5.15              = ( Q2 @ ( minus_8373710615458151222nteger @ X2 @ ( times_3573771949741848930nteger @ K2 @ D3 ) ) ) )
% 9.25/5.15         => ! [X5: code_integer,K3: code_integer] :
% 9.25/5.15              ( ( ( P @ X5 )
% 9.25/5.15                | ( Q2 @ X5 ) )
% 9.25/5.15              = ( ( P @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K3 @ D3 ) ) )
% 9.25/5.15                | ( Q2 @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K3 @ D3 ) ) ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2108_inf__period_I2_J,axiom,
% 9.25/5.15      ! [P: rat > $o,D3: rat,Q2: rat > $o] :
% 9.25/5.15        ( ! [X2: rat,K2: rat] :
% 9.25/5.15            ( ( P @ X2 )
% 9.25/5.15            = ( P @ ( minus_minus_rat @ X2 @ ( times_times_rat @ K2 @ D3 ) ) ) )
% 9.25/5.15       => ( ! [X2: rat,K2: rat] :
% 9.25/5.15              ( ( Q2 @ X2 )
% 9.25/5.15              = ( Q2 @ ( minus_minus_rat @ X2 @ ( times_times_rat @ K2 @ D3 ) ) ) )
% 9.25/5.15         => ! [X5: rat,K3: rat] :
% 9.25/5.15              ( ( ( P @ X5 )
% 9.25/5.15                | ( Q2 @ X5 ) )
% 9.25/5.15              = ( ( P @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K3 @ D3 ) ) )
% 9.25/5.15                | ( Q2 @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K3 @ D3 ) ) ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2109_inf__period_I2_J,axiom,
% 9.25/5.15      ! [P: int > $o,D3: int,Q2: int > $o] :
% 9.25/5.15        ( ! [X2: int,K2: int] :
% 9.25/5.15            ( ( P @ X2 )
% 9.25/5.15            = ( P @ ( minus_minus_int @ X2 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 9.25/5.15       => ( ! [X2: int,K2: int] :
% 9.25/5.15              ( ( Q2 @ X2 )
% 9.25/5.15              = ( Q2 @ ( minus_minus_int @ X2 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 9.25/5.15         => ! [X5: int,K3: int] :
% 9.25/5.15              ( ( ( P @ X5 )
% 9.25/5.15                | ( Q2 @ X5 ) )
% 9.25/5.15              = ( ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K3 @ D3 ) ) )
% 9.25/5.15                | ( Q2 @ ( minus_minus_int @ X5 @ ( times_times_int @ K3 @ D3 ) ) ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2110_diff__numeral__special_I5_J,axiom,
% 9.25/5.15      ! [N: num] :
% 9.25/5.15        ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 9.25/5.15        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2111_diff__numeral__special_I5_J,axiom,
% 9.25/5.15      ! [N: num] :
% 9.25/5.15        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 9.25/5.15        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2112_diff__numeral__special_I5_J,axiom,
% 9.25/5.15      ! [N: num] :
% 9.25/5.15        ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 9.25/5.15        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2113_diff__numeral__special_I6_J,axiom,
% 9.25/5.15      ! [M: num] :
% 9.25/5.15        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.15        = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2114_diff__numeral__special_I6_J,axiom,
% 9.25/5.15      ! [M: num] :
% 9.25/5.15        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.15        = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2115_diff__numeral__special_I6_J,axiom,
% 9.25/5.15      ! [M: num] :
% 9.25/5.15        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.25/5.15        = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2116_left__diff__distrib__NO__MATCH,axiom,
% 9.25/5.15      ! [X: nat,Y: nat,C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.15        ( ( nO_MAT8694959213317031834nteger @ ( divide_divide_nat @ X @ Y ) @ C )
% 9.25/5.15       => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 9.25/5.15          = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2117_left__diff__distrib__NO__MATCH,axiom,
% 9.25/5.15      ! [X: nat,Y: nat,C: rat,A: rat,B: rat] :
% 9.25/5.15        ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X @ Y ) @ C )
% 9.25/5.15       => ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 9.25/5.15          = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2118_left__diff__distrib__NO__MATCH,axiom,
% 9.25/5.15      ! [X: nat,Y: nat,C: int,A: int,B: int] :
% 9.25/5.15        ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ C )
% 9.25/5.15       => ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 9.25/5.15          = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2119_left__diff__distrib__NO__MATCH,axiom,
% 9.25/5.15      ! [X: int,Y: int,C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.15        ( ( nO_MAT9066612773553876470nteger @ ( divide_divide_int @ X @ Y ) @ C )
% 9.25/5.15       => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 9.25/5.15          = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2120_left__diff__distrib__NO__MATCH,axiom,
% 9.25/5.15      ! [X: int,Y: int,C: rat,A: rat,B: rat] :
% 9.25/5.15        ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X @ Y ) @ C )
% 9.25/5.15       => ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 9.25/5.15          = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2121_left__diff__distrib__NO__MATCH,axiom,
% 9.25/5.15      ! [X: int,Y: int,C: int,A: int,B: int] :
% 9.25/5.15        ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ C )
% 9.25/5.15       => ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 9.25/5.15          = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2122_left__diff__distrib__NO__MATCH,axiom,
% 9.25/5.15      ! [X: code_integer,Y: code_integer,C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.15        ( ( nO_MAT8252062027627875367nteger @ ( divide6298287555418463151nteger @ X @ Y ) @ C )
% 9.25/5.15       => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 9.25/5.15          = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2123_left__diff__distrib__NO__MATCH,axiom,
% 9.25/5.15      ! [X: code_integer,Y: code_integer,C: rat,A: rat,B: rat] :
% 9.25/5.15        ( ( nO_MAT7795273704451493282er_rat @ ( divide6298287555418463151nteger @ X @ Y ) @ C )
% 9.25/5.15       => ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 9.25/5.15          = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2124_left__diff__distrib__NO__MATCH,axiom,
% 9.25/5.15      ! [X: code_integer,Y: code_integer,C: int,A: int,B: int] :
% 9.25/5.15        ( ( nO_MAT8427913294028938742er_int @ ( divide6298287555418463151nteger @ X @ Y ) @ C )
% 9.25/5.15       => ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 9.25/5.15          = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2125_left__diff__distrib__NO__MATCH,axiom,
% 9.25/5.15      ! [X: rat,Y: rat,C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.15        ( ( nO_MAT243659986023775650nteger @ ( divide_divide_rat @ X @ Y ) @ C )
% 9.25/5.15       => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 9.25/5.15          = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2126_right__diff__distrib__NO__MATCH,axiom,
% 9.25/5.15      ! [X: nat,Y: nat,A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.15        ( ( nO_MAT8694959213317031834nteger @ ( divide_divide_nat @ X @ Y ) @ A )
% 9.25/5.15       => ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 9.25/5.15          = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2127_right__diff__distrib__NO__MATCH,axiom,
% 9.25/5.15      ! [X: nat,Y: nat,A: rat,B: rat,C: rat] :
% 9.25/5.15        ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X @ Y ) @ A )
% 9.25/5.15       => ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 9.25/5.15          = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2128_right__diff__distrib__NO__MATCH,axiom,
% 9.25/5.15      ! [X: nat,Y: nat,A: int,B: int,C: int] :
% 9.25/5.15        ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ A )
% 9.25/5.15       => ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 9.25/5.15          = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2129_right__diff__distrib__NO__MATCH,axiom,
% 9.25/5.15      ! [X: int,Y: int,A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.15        ( ( nO_MAT9066612773553876470nteger @ ( divide_divide_int @ X @ Y ) @ A )
% 9.25/5.15       => ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 9.25/5.15          = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2130_right__diff__distrib__NO__MATCH,axiom,
% 9.25/5.15      ! [X: int,Y: int,A: rat,B: rat,C: rat] :
% 9.25/5.15        ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X @ Y ) @ A )
% 9.25/5.15       => ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 9.25/5.15          = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2131_right__diff__distrib__NO__MATCH,axiom,
% 9.25/5.15      ! [X: int,Y: int,A: int,B: int,C: int] :
% 9.25/5.15        ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ A )
% 9.25/5.15       => ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 9.25/5.15          = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2132_right__diff__distrib__NO__MATCH,axiom,
% 9.25/5.15      ! [X: code_integer,Y: code_integer,A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.15        ( ( nO_MAT8252062027627875367nteger @ ( divide6298287555418463151nteger @ X @ Y ) @ A )
% 9.25/5.15       => ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 9.25/5.15          = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2133_right__diff__distrib__NO__MATCH,axiom,
% 9.25/5.15      ! [X: code_integer,Y: code_integer,A: rat,B: rat,C: rat] :
% 9.25/5.15        ( ( nO_MAT7795273704451493282er_rat @ ( divide6298287555418463151nteger @ X @ Y ) @ A )
% 9.25/5.15       => ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 9.25/5.15          = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2134_right__diff__distrib__NO__MATCH,axiom,
% 9.25/5.15      ! [X: code_integer,Y: code_integer,A: int,B: int,C: int] :
% 9.25/5.15        ( ( nO_MAT8427913294028938742er_int @ ( divide6298287555418463151nteger @ X @ Y ) @ A )
% 9.25/5.15       => ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 9.25/5.15          = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2135_right__diff__distrib__NO__MATCH,axiom,
% 9.25/5.15      ! [X: rat,Y: rat,A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.15        ( ( nO_MAT243659986023775650nteger @ ( divide_divide_rat @ X @ Y ) @ A )
% 9.25/5.15       => ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 9.25/5.15          = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2136_divide__less__eq__numeral_I2_J,axiom,
% 9.25/5.15      ! [B: rat,C: rat,W: num] :
% 9.25/5.15        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 9.25/5.15        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.15           => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 9.25/5.15          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.15           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.15               => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 9.25/5.15              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.15               => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2137_less__divide__eq__numeral_I2_J,axiom,
% 9.25/5.15      ! [W: num,B: rat,C: rat] :
% 9.25/5.15        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 9.25/5.15        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.15           => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 9.25/5.15          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.15           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.15               => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 9.25/5.15              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.15               => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2138_le__divide__eq__numeral1_I2_J,axiom,
% 9.25/5.15      ! [A: rat,B: rat,W: num] :
% 9.25/5.15        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 9.25/5.15        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2139_dual__order_Orefl,axiom,
% 9.25/5.15      ! [A: filter_nat] : ( ord_le2510731241096832064er_nat @ A @ A ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2140_dual__order_Orefl,axiom,
% 9.25/5.15      ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2141_dual__order_Orefl,axiom,
% 9.25/5.15      ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2142_dual__order_Orefl,axiom,
% 9.25/5.15      ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2143_dual__order_Orefl,axiom,
% 9.25/5.15      ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2144_order__refl,axiom,
% 9.25/5.15      ! [X: filter_nat] : ( ord_le2510731241096832064er_nat @ X @ X ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2145_order__refl,axiom,
% 9.25/5.15      ! [X: set_nat] : ( ord_less_eq_set_nat @ X @ X ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2146_order__refl,axiom,
% 9.25/5.15      ! [X: rat] : ( ord_less_eq_rat @ X @ X ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2147_order__refl,axiom,
% 9.25/5.15      ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2148_order__refl,axiom,
% 9.25/5.15      ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2149_empty__subsetI,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ bot_bo2099793752762293965at_nat @ A2 ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2150_empty__subsetI,axiom,
% 9.25/5.15      ! [A2: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A2 ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2151_empty__subsetI,axiom,
% 9.25/5.15      ! [A2: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A2 ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2152_empty__subsetI,axiom,
% 9.25/5.15      ! [A2: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A2 ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2153_subset__empty,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( ord_le3146513528884898305at_nat @ A2 @ bot_bo2099793752762293965at_nat )
% 9.25/5.15        = ( A2 = bot_bo2099793752762293965at_nat ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2154_subset__empty,axiom,
% 9.25/5.15      ! [A2: set_o] :
% 9.25/5.15        ( ( ord_less_eq_set_o @ A2 @ bot_bot_set_o )
% 9.25/5.15        = ( A2 = bot_bot_set_o ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2155_subset__empty,axiom,
% 9.25/5.15      ! [A2: set_int] :
% 9.25/5.15        ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 9.25/5.15        = ( A2 = bot_bot_set_int ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2156_subset__empty,axiom,
% 9.25/5.15      ! [A2: set_nat] :
% 9.25/5.15        ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 9.25/5.15        = ( A2 = bot_bot_set_nat ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2157_Int__subset__iff,axiom,
% 9.25/5.15      ! [C2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( ord_le3146513528884898305at_nat @ C2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 9.25/5.15        = ( ( ord_le3146513528884898305at_nat @ C2 @ A2 )
% 9.25/5.15          & ( ord_le3146513528884898305at_nat @ C2 @ B2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2158_Int__subset__iff,axiom,
% 9.25/5.15      ! [C2: set_nat,A2: set_nat,B2: set_nat] :
% 9.25/5.15        ( ( ord_less_eq_set_nat @ C2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.15        = ( ( ord_less_eq_set_nat @ C2 @ A2 )
% 9.25/5.15          & ( ord_less_eq_set_nat @ C2 @ B2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2159_Un__subset__iff,axiom,
% 9.25/5.15      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 9.25/5.15        ( ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.15        = ( ( ord_le8081472938463900775at_nat @ A2 @ C2 )
% 9.25/5.15          & ( ord_le8081472938463900775at_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2160_Un__subset__iff,axiom,
% 9.25/5.15      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 9.25/5.15        ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.15        = ( ( ord_le1268244103169919719at_nat @ A2 @ C2 )
% 9.25/5.15          & ( ord_le1268244103169919719at_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2161_Un__subset__iff,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 9.25/5.15        ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.15        = ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 9.25/5.15          & ( ord_less_eq_set_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2162_Compl__subset__Compl__iff,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.15        ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( uminus5710092332889474511et_nat @ B2 ) )
% 9.25/5.15        = ( ord_less_eq_set_nat @ B2 @ A2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2163_Compl__anti__mono,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.15        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 9.25/5.15       => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ B2 ) @ ( uminus5710092332889474511et_nat @ A2 ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2164_le__zero__eq,axiom,
% 9.25/5.15      ! [N: nat] :
% 9.25/5.15        ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 9.25/5.15        = ( N = zero_zero_nat ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2165_not__gr__zero,axiom,
% 9.25/5.15      ! [N: nat] :
% 9.25/5.15        ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 9.25/5.15        = ( N = zero_zero_nat ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2166_neg__le__iff__le,axiom,
% 9.25/5.15      ! [B: code_integer,A: code_integer] :
% 9.25/5.15        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 9.25/5.15        = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2167_neg__le__iff__le,axiom,
% 9.25/5.15      ! [B: rat,A: rat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 9.25/5.15        = ( ord_less_eq_rat @ A @ B ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2168_neg__le__iff__le,axiom,
% 9.25/5.15      ! [B: int,A: int] :
% 9.25/5.15        ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 9.25/5.15        = ( ord_less_eq_int @ A @ B ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2169_compl__le__compl__iff,axiom,
% 9.25/5.15      ! [X: product_unit,Y: product_unit] :
% 9.25/5.15        ( ( ord_le3221252021190050221t_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( uminus2952777764628376836t_unit @ Y ) )
% 9.25/5.15        = ( ord_le3221252021190050221t_unit @ Y @ X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2170_compl__le__compl__iff,axiom,
% 9.25/5.15      ! [X: set_nat,Y: set_nat] :
% 9.25/5.15        ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y ) )
% 9.25/5.15        = ( ord_less_eq_set_nat @ Y @ X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2171_neg__less__iff__less,axiom,
% 9.25/5.15      ! [B: int,A: int] :
% 9.25/5.15        ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 9.25/5.15        = ( ord_less_int @ A @ B ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2172_neg__less__iff__less,axiom,
% 9.25/5.15      ! [B: code_integer,A: code_integer] :
% 9.25/5.15        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 9.25/5.15        = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2173_neg__less__iff__less,axiom,
% 9.25/5.15      ! [B: rat,A: rat] :
% 9.25/5.15        ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 9.25/5.15        = ( ord_less_rat @ A @ B ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2174_compl__less__compl__iff,axiom,
% 9.25/5.15      ! [X: product_unit,Y: product_unit] :
% 9.25/5.15        ( ( ord_le361264281704409273t_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( uminus2952777764628376836t_unit @ Y ) )
% 9.25/5.15        = ( ord_le361264281704409273t_unit @ Y @ X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2175_le__inf__iff,axiom,
% 9.25/5.15      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 9.25/5.15        = ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 9.25/5.15          & ( ord_le3146513528884898305at_nat @ X @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2176_le__inf__iff,axiom,
% 9.25/5.15      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 9.25/5.15        ( ( ord_le8369615600986905444_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) )
% 9.25/5.15        = ( ( ord_le8369615600986905444_int_o @ X @ Y )
% 9.25/5.15          & ( ord_le8369615600986905444_int_o @ X @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2177_le__inf__iff,axiom,
% 9.25/5.15      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 9.25/5.15        ( ( ord_le4796328588573674190char_o @ X @ ( inf_inf_list_char_o @ Y @ Z ) )
% 9.25/5.15        = ( ( ord_le4796328588573674190char_o @ X @ Y )
% 9.25/5.15          & ( ord_le4796328588573674190char_o @ X @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2178_le__inf__iff,axiom,
% 9.25/5.15      ! [X: filter_nat,Y: filter_nat,Z: filter_nat] :
% 9.25/5.15        ( ( ord_le2510731241096832064er_nat @ X @ ( inf_inf_filter_nat @ Y @ Z ) )
% 9.25/5.15        = ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 9.25/5.15          & ( ord_le2510731241096832064er_nat @ X @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2179_le__inf__iff,axiom,
% 9.25/5.15      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.25/5.15        ( ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 9.25/5.15        = ( ( ord_less_eq_set_nat @ X @ Y )
% 9.25/5.15          & ( ord_less_eq_set_nat @ X @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2180_le__inf__iff,axiom,
% 9.25/5.15      ! [X: rat,Y: rat,Z: rat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ X @ ( inf_inf_rat @ Y @ Z ) )
% 9.25/5.15        = ( ( ord_less_eq_rat @ X @ Y )
% 9.25/5.15          & ( ord_less_eq_rat @ X @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2181_le__inf__iff,axiom,
% 9.25/5.15      ! [X: nat,Y: nat,Z: nat] :
% 9.25/5.15        ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 9.25/5.15        = ( ( ord_less_eq_nat @ X @ Y )
% 9.25/5.15          & ( ord_less_eq_nat @ X @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2182_le__inf__iff,axiom,
% 9.25/5.15      ! [X: int,Y: int,Z: int] :
% 9.25/5.15        ( ( ord_less_eq_int @ X @ ( inf_inf_int @ Y @ Z ) )
% 9.25/5.15        = ( ( ord_less_eq_int @ X @ Y )
% 9.25/5.15          & ( ord_less_eq_int @ X @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2183_inf_Obounded__iff,axiom,
% 9.25/5.15      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) )
% 9.25/5.15        = ( ( ord_le3146513528884898305at_nat @ A @ B )
% 9.25/5.15          & ( ord_le3146513528884898305at_nat @ A @ C ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2184_inf_Obounded__iff,axiom,
% 9.25/5.15      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o,C: product_prod_int_int > $o] :
% 9.25/5.15        ( ( ord_le8369615600986905444_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C ) )
% 9.25/5.15        = ( ( ord_le8369615600986905444_int_o @ A @ B )
% 9.25/5.15          & ( ord_le8369615600986905444_int_o @ A @ C ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2185_inf_Obounded__iff,axiom,
% 9.25/5.15      ! [A: list_char > $o,B: list_char > $o,C: list_char > $o] :
% 9.25/5.15        ( ( ord_le4796328588573674190char_o @ A @ ( inf_inf_list_char_o @ B @ C ) )
% 9.25/5.15        = ( ( ord_le4796328588573674190char_o @ A @ B )
% 9.25/5.15          & ( ord_le4796328588573674190char_o @ A @ C ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2186_inf_Obounded__iff,axiom,
% 9.25/5.15      ! [A: filter_nat,B: filter_nat,C: filter_nat] :
% 9.25/5.15        ( ( ord_le2510731241096832064er_nat @ A @ ( inf_inf_filter_nat @ B @ C ) )
% 9.25/5.15        = ( ( ord_le2510731241096832064er_nat @ A @ B )
% 9.25/5.15          & ( ord_le2510731241096832064er_nat @ A @ C ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2187_inf_Obounded__iff,axiom,
% 9.25/5.15      ! [A: set_nat,B: set_nat,C: set_nat] :
% 9.25/5.15        ( ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) )
% 9.25/5.15        = ( ( ord_less_eq_set_nat @ A @ B )
% 9.25/5.15          & ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2188_inf_Obounded__iff,axiom,
% 9.25/5.15      ! [A: rat,B: rat,C: rat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C ) )
% 9.25/5.15        = ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.15          & ( ord_less_eq_rat @ A @ C ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2189_inf_Obounded__iff,axiom,
% 9.25/5.15      ! [A: nat,B: nat,C: nat] :
% 9.25/5.15        ( ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C ) )
% 9.25/5.15        = ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.15          & ( ord_less_eq_nat @ A @ C ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2190_inf_Obounded__iff,axiom,
% 9.25/5.15      ! [A: int,B: int,C: int] :
% 9.25/5.15        ( ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C ) )
% 9.25/5.15        = ( ( ord_less_eq_int @ A @ B )
% 9.25/5.15          & ( ord_less_eq_int @ A @ C ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2191_le__sup__iff,axiom,
% 9.25/5.15      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 9.25/5.15        ( ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ Z )
% 9.25/5.15        = ( ( ord_le8081472938463900775at_nat @ X @ Z )
% 9.25/5.15          & ( ord_le8081472938463900775at_nat @ Y @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2192_le__sup__iff,axiom,
% 9.25/5.15      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 9.25/5.15        ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ Z )
% 9.25/5.15        = ( ( ord_le1268244103169919719at_nat @ X @ Z )
% 9.25/5.15          & ( ord_le1268244103169919719at_nat @ Y @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2193_le__sup__iff,axiom,
% 9.25/5.15      ! [X: filter_nat,Y: filter_nat,Z: filter_nat] :
% 9.25/5.15        ( ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ X @ Y ) @ Z )
% 9.25/5.15        = ( ( ord_le2510731241096832064er_nat @ X @ Z )
% 9.25/5.15          & ( ord_le2510731241096832064er_nat @ Y @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2194_le__sup__iff,axiom,
% 9.25/5.15      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.25/5.15        ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z )
% 9.25/5.15        = ( ( ord_less_eq_set_nat @ X @ Z )
% 9.25/5.15          & ( ord_less_eq_set_nat @ Y @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2195_le__sup__iff,axiom,
% 9.25/5.15      ! [X: rat,Y: rat,Z: rat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ ( sup_sup_rat @ X @ Y ) @ Z )
% 9.25/5.15        = ( ( ord_less_eq_rat @ X @ Z )
% 9.25/5.15          & ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2196_le__sup__iff,axiom,
% 9.25/5.15      ! [X: nat,Y: nat,Z: nat] :
% 9.25/5.15        ( ( ord_less_eq_nat @ ( sup_sup_nat @ X @ Y ) @ Z )
% 9.25/5.15        = ( ( ord_less_eq_nat @ X @ Z )
% 9.25/5.15          & ( ord_less_eq_nat @ Y @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2197_le__sup__iff,axiom,
% 9.25/5.15      ! [X: int,Y: int,Z: int] :
% 9.25/5.15        ( ( ord_less_eq_int @ ( sup_sup_int @ X @ Y ) @ Z )
% 9.25/5.15        = ( ( ord_less_eq_int @ X @ Z )
% 9.25/5.15          & ( ord_less_eq_int @ Y @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2198_sup_Obounded__iff,axiom,
% 9.25/5.15      ! [B: set_Pr8551490117392284871at_nat,C: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 9.25/5.15        ( ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ B @ C ) @ A )
% 9.25/5.15        = ( ( ord_le8081472938463900775at_nat @ B @ A )
% 9.25/5.15          & ( ord_le8081472938463900775at_nat @ C @ A ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2199_sup_Obounded__iff,axiom,
% 9.25/5.15      ! [B: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 9.25/5.15        ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ B @ C ) @ A )
% 9.25/5.15        = ( ( ord_le1268244103169919719at_nat @ B @ A )
% 9.25/5.15          & ( ord_le1268244103169919719at_nat @ C @ A ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2200_sup_Obounded__iff,axiom,
% 9.25/5.15      ! [B: filter_nat,C: filter_nat,A: filter_nat] :
% 9.25/5.15        ( ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ B @ C ) @ A )
% 9.25/5.15        = ( ( ord_le2510731241096832064er_nat @ B @ A )
% 9.25/5.15          & ( ord_le2510731241096832064er_nat @ C @ A ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2201_sup_Obounded__iff,axiom,
% 9.25/5.15      ! [B: set_nat,C: set_nat,A: set_nat] :
% 9.25/5.15        ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C ) @ A )
% 9.25/5.15        = ( ( ord_less_eq_set_nat @ B @ A )
% 9.25/5.15          & ( ord_less_eq_set_nat @ C @ A ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2202_sup_Obounded__iff,axiom,
% 9.25/5.15      ! [B: rat,C: rat,A: rat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C ) @ A )
% 9.25/5.15        = ( ( ord_less_eq_rat @ B @ A )
% 9.25/5.15          & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2203_sup_Obounded__iff,axiom,
% 9.25/5.15      ! [B: nat,C: nat,A: nat] :
% 9.25/5.15        ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C ) @ A )
% 9.25/5.15        = ( ( ord_less_eq_nat @ B @ A )
% 9.25/5.15          & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2204_sup_Obounded__iff,axiom,
% 9.25/5.15      ! [B: int,C: int,A: int] :
% 9.25/5.15        ( ( ord_less_eq_int @ ( sup_sup_int @ B @ C ) @ A )
% 9.25/5.15        = ( ( ord_less_eq_int @ B @ A )
% 9.25/5.15          & ( ord_less_eq_int @ C @ A ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2205_Diff__eq__empty__iff,axiom,
% 9.25/5.15      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.15        ( ( ( minus_1356011639430497352at_nat @ A2 @ B2 )
% 9.25/5.15          = bot_bo2099793752762293965at_nat )
% 9.25/5.15        = ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2206_Diff__eq__empty__iff,axiom,
% 9.25/5.15      ! [A2: set_o,B2: set_o] :
% 9.25/5.15        ( ( ( minus_minus_set_o @ A2 @ B2 )
% 9.25/5.15          = bot_bot_set_o )
% 9.25/5.15        = ( ord_less_eq_set_o @ A2 @ B2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2207_Diff__eq__empty__iff,axiom,
% 9.25/5.15      ! [A2: set_int,B2: set_int] :
% 9.25/5.15        ( ( ( minus_minus_set_int @ A2 @ B2 )
% 9.25/5.15          = bot_bot_set_int )
% 9.25/5.15        = ( ord_less_eq_set_int @ A2 @ B2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2208_Diff__eq__empty__iff,axiom,
% 9.25/5.15      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.15        ( ( ( minus_minus_set_nat @ A2 @ B2 )
% 9.25/5.15          = bot_bot_set_nat )
% 9.25/5.15        = ( ord_less_eq_set_nat @ A2 @ B2 ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2209_diff__ge__0__iff__ge,axiom,
% 9.25/5.15      ! [A: code_integer,B: code_integer] :
% 9.25/5.15        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 9.25/5.15        = ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2210_diff__ge__0__iff__ge,axiom,
% 9.25/5.15      ! [A: rat,B: rat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 9.25/5.15        = ( ord_less_eq_rat @ B @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2211_diff__ge__0__iff__ge,axiom,
% 9.25/5.15      ! [A: int,B: int] :
% 9.25/5.15        ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 9.25/5.15        = ( ord_less_eq_int @ B @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2212_diff__gt__0__iff__gt,axiom,
% 9.25/5.15      ! [A: code_integer,B: code_integer] :
% 9.25/5.15        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 9.25/5.15        = ( ord_le6747313008572928689nteger @ B @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2213_diff__gt__0__iff__gt,axiom,
% 9.25/5.15      ! [A: rat,B: rat] :
% 9.25/5.15        ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 9.25/5.15        = ( ord_less_rat @ B @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2214_diff__gt__0__iff__gt,axiom,
% 9.25/5.15      ! [A: int,B: int] :
% 9.25/5.15        ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 9.25/5.15        = ( ord_less_int @ B @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2215_neg__0__le__iff__le,axiom,
% 9.25/5.15      ! [A: code_integer] :
% 9.25/5.15        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 9.25/5.15        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2216_neg__0__le__iff__le,axiom,
% 9.25/5.15      ! [A: rat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 9.25/5.15        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2217_neg__0__le__iff__le,axiom,
% 9.25/5.15      ! [A: int] :
% 9.25/5.15        ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 9.25/5.15        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2218_neg__le__0__iff__le,axiom,
% 9.25/5.15      ! [A: code_integer] :
% 9.25/5.15        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 9.25/5.15        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2219_neg__le__0__iff__le,axiom,
% 9.25/5.15      ! [A: rat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 9.25/5.15        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2220_neg__le__0__iff__le,axiom,
% 9.25/5.15      ! [A: int] :
% 9.25/5.15        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 9.25/5.15        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2221_less__eq__neg__nonpos,axiom,
% 9.25/5.15      ! [A: code_integer] :
% 9.25/5.15        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 9.25/5.15        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2222_less__eq__neg__nonpos,axiom,
% 9.25/5.15      ! [A: rat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 9.25/5.15        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2223_less__eq__neg__nonpos,axiom,
% 9.25/5.15      ! [A: int] :
% 9.25/5.15        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 9.25/5.15        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2224_neg__less__eq__nonneg,axiom,
% 9.25/5.15      ! [A: code_integer] :
% 9.25/5.15        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 9.25/5.15        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2225_neg__less__eq__nonneg,axiom,
% 9.25/5.15      ! [A: rat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 9.25/5.15        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2226_neg__less__eq__nonneg,axiom,
% 9.25/5.15      ! [A: int] :
% 9.25/5.15        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 9.25/5.15        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2227_less__neg__neg,axiom,
% 9.25/5.15      ! [A: int] :
% 9.25/5.15        ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 9.25/5.15        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2228_less__neg__neg,axiom,
% 9.25/5.15      ! [A: code_integer] :
% 9.25/5.15        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 9.25/5.15        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2229_less__neg__neg,axiom,
% 9.25/5.15      ! [A: rat] :
% 9.25/5.15        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 9.25/5.15        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2230_neg__less__pos,axiom,
% 9.25/5.15      ! [A: int] :
% 9.25/5.15        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 9.25/5.15        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2231_neg__less__pos,axiom,
% 9.25/5.15      ! [A: code_integer] :
% 9.25/5.15        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 9.25/5.15        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2232_neg__less__pos,axiom,
% 9.25/5.15      ! [A: rat] :
% 9.25/5.15        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 9.25/5.15        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2233_neg__0__less__iff__less,axiom,
% 9.25/5.15      ! [A: int] :
% 9.25/5.15        ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 9.25/5.15        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2234_neg__0__less__iff__less,axiom,
% 9.25/5.15      ! [A: code_integer] :
% 9.25/5.15        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 9.25/5.15        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2235_neg__0__less__iff__less,axiom,
% 9.25/5.15      ! [A: rat] :
% 9.25/5.15        ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 9.25/5.15        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2236_neg__less__0__iff__less,axiom,
% 9.25/5.15      ! [A: int] :
% 9.25/5.15        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 9.25/5.15        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2237_neg__less__0__iff__less,axiom,
% 9.25/5.15      ! [A: code_integer] :
% 9.25/5.15        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 9.25/5.15        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2238_neg__less__0__iff__less,axiom,
% 9.25/5.15      ! [A: rat] :
% 9.25/5.15        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 9.25/5.15        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2239_neg__numeral__le__iff,axiom,
% 9.25/5.15      ! [M: num,N: num] :
% 9.25/5.15        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.25/5.15        = ( ord_less_eq_num @ N @ M ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2240_neg__numeral__le__iff,axiom,
% 9.25/5.15      ! [M: num,N: num] :
% 9.25/5.15        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.25/5.15        = ( ord_less_eq_num @ N @ M ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2241_neg__numeral__le__iff,axiom,
% 9.25/5.15      ! [M: num,N: num] :
% 9.25/5.15        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.15        = ( ord_less_eq_num @ N @ M ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2242_neg__numeral__less__iff,axiom,
% 9.25/5.15      ! [M: num,N: num] :
% 9.25/5.15        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.15        = ( ord_less_num @ N @ M ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2243_neg__numeral__less__iff,axiom,
% 9.25/5.15      ! [M: num,N: num] :
% 9.25/5.15        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.25/5.15        = ( ord_less_num @ N @ M ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2244_neg__numeral__less__iff,axiom,
% 9.25/5.15      ! [M: num,N: num] :
% 9.25/5.15        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.25/5.15        = ( ord_less_num @ N @ M ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2245_divide__le__0__1__iff,axiom,
% 9.25/5.15      ! [A: rat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 9.25/5.15        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2246_zero__le__divide__1__iff,axiom,
% 9.25/5.15      ! [A: rat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 9.25/5.15        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2247_divide__less__0__1__iff,axiom,
% 9.25/5.15      ! [A: rat] :
% 9.25/5.15        ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 9.25/5.15        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2248_divide__less__eq__1__neg,axiom,
% 9.25/5.15      ! [A: rat,B: rat] :
% 9.25/5.15        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.25/5.15       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 9.25/5.15          = ( ord_less_rat @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2249_divide__less__eq__1__pos,axiom,
% 9.25/5.15      ! [A: rat,B: rat] :
% 9.25/5.15        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.15       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 9.25/5.15          = ( ord_less_rat @ B @ A ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2250_less__divide__eq__1__neg,axiom,
% 9.25/5.15      ! [A: rat,B: rat] :
% 9.25/5.15        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.25/5.15       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 9.25/5.15          = ( ord_less_rat @ B @ A ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2251_less__divide__eq__1__pos,axiom,
% 9.25/5.15      ! [A: rat,B: rat] :
% 9.25/5.15        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.15       => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 9.25/5.15          = ( ord_less_rat @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2252_zero__less__divide__1__iff,axiom,
% 9.25/5.15      ! [A: rat] :
% 9.25/5.15        ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 9.25/5.15        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2253_le__divide__eq__numeral1_I1_J,axiom,
% 9.25/5.15      ! [A: rat,B: rat,W: num] :
% 9.25/5.15        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 9.25/5.15        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2254_divide__le__eq__numeral1_I1_J,axiom,
% 9.25/5.15      ! [B: rat,W: num,A: rat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 9.25/5.15        = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2255_less__divide__eq__numeral1_I1_J,axiom,
% 9.25/5.15      ! [A: rat,B: rat,W: num] :
% 9.25/5.15        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 9.25/5.15        = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2256_divide__less__eq__numeral1_I1_J,axiom,
% 9.25/5.15      ! [B: rat,W: num,A: rat] :
% 9.25/5.15        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 9.25/5.15        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2257_le__divide__eq__1__pos,axiom,
% 9.25/5.15      ! [A: rat,B: rat] :
% 9.25/5.15        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.15       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 9.25/5.15          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2258_le__divide__eq__1__neg,axiom,
% 9.25/5.15      ! [A: rat,B: rat] :
% 9.25/5.15        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.25/5.15       => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 9.25/5.15          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2259_divide__le__eq__1__pos,axiom,
% 9.25/5.15      ! [A: rat,B: rat] :
% 9.25/5.15        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.15       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 9.25/5.15          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2260_divide__le__eq__1__neg,axiom,
% 9.25/5.15      ! [A: rat,B: rat] :
% 9.25/5.15        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.25/5.15       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 9.25/5.15          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2261_divide__le__eq__numeral1_I2_J,axiom,
% 9.25/5.15      ! [B: rat,W: num,A: rat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 9.25/5.15        = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2262_divide__less__eq__numeral1_I2_J,axiom,
% 9.25/5.15      ! [B: rat,W: num,A: rat] :
% 9.25/5.15        ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 9.25/5.15        = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2263_less__divide__eq__numeral1_I2_J,axiom,
% 9.25/5.15      ! [A: rat,B: rat,W: num] :
% 9.25/5.15        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 9.25/5.15        = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2264_minus__set__def,axiom,
% 9.25/5.15      ( minus_2612819937483484256nt_int
% 9.25/5.15      = ( ^ [A4: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
% 9.25/5.15            ( collec5210948495886036740nt_int
% 9.25/5.15            @ ( minus_357216186751819389_int_o
% 9.25/5.15              @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ A4 )
% 9.25/5.15              @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2265_minus__set__def,axiom,
% 9.25/5.15      ( minus_2163939370556025621et_nat
% 9.25/5.15      = ( ^ [A4: set_set_nat,B4: set_set_nat] :
% 9.25/5.15            ( collect_set_nat
% 9.25/5.15            @ ( minus_6910147592129066416_nat_o
% 9.25/5.15              @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A4 )
% 9.25/5.15              @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2266_minus__set__def,axiom,
% 9.25/5.15      ( minus_minus_set_int
% 9.25/5.15      = ( ^ [A4: set_int,B4: set_int] :
% 9.25/5.15            ( collect_int
% 9.25/5.15            @ ( minus_minus_int_o
% 9.25/5.15              @ ^ [X3: int] : ( member_int @ X3 @ A4 )
% 9.25/5.15              @ ^ [X3: int] : ( member_int @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2267_minus__set__def,axiom,
% 9.25/5.15      ( minus_1801376950450012436_nat_o
% 9.25/5.15      = ( ^ [A4: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 9.25/5.15            ( collec939566748876313656_nat_o
% 9.25/5.15            @ ( minus_2803741817741520073at_o_o
% 9.25/5.15              @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ A4 )
% 9.25/5.15              @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2268_minus__set__def,axiom,
% 9.25/5.15      ( minus_minus_set_nat
% 9.25/5.15      = ( ^ [A4: set_nat,B4: set_nat] :
% 9.25/5.15            ( collect_nat
% 9.25/5.15            @ ( minus_minus_nat_o
% 9.25/5.15              @ ^ [X3: nat] : ( member_nat @ X3 @ A4 )
% 9.25/5.15              @ ^ [X3: nat] : ( member_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2269_set__diff__eq,axiom,
% 9.25/5.15      ( minus_2612819937483484256nt_int
% 9.25/5.15      = ( ^ [A4: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
% 9.25/5.15            ( collec5210948495886036740nt_int
% 9.25/5.15            @ ^ [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.15                ( ( member2340774599025711042nt_int @ X3 @ A4 )
% 9.25/5.15                & ~ ( member2340774599025711042nt_int @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2270_set__diff__eq,axiom,
% 9.25/5.15      ( minus_2163939370556025621et_nat
% 9.25/5.15      = ( ^ [A4: set_set_nat,B4: set_set_nat] :
% 9.25/5.15            ( collect_set_nat
% 9.25/5.15            @ ^ [X3: set_nat] :
% 9.25/5.15                ( ( member_set_nat @ X3 @ A4 )
% 9.25/5.15                & ~ ( member_set_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2271_set__diff__eq,axiom,
% 9.25/5.15      ( minus_minus_set_int
% 9.25/5.15      = ( ^ [A4: set_int,B4: set_int] :
% 9.25/5.15            ( collect_int
% 9.25/5.15            @ ^ [X3: int] :
% 9.25/5.15                ( ( member_int @ X3 @ A4 )
% 9.25/5.15                & ~ ( member_int @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2272_set__diff__eq,axiom,
% 9.25/5.15      ( minus_1801376950450012436_nat_o
% 9.25/5.15      = ( ^ [A4: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 9.25/5.15            ( collec939566748876313656_nat_o
% 9.25/5.15            @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.15                ( ( member6576561426505652726_nat_o @ X3 @ A4 )
% 9.25/5.15                & ~ ( member6576561426505652726_nat_o @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2273_set__diff__eq,axiom,
% 9.25/5.15      ( minus_minus_set_nat
% 9.25/5.15      = ( ^ [A4: set_nat,B4: set_nat] :
% 9.25/5.15            ( collect_nat
% 9.25/5.15            @ ^ [X3: nat] :
% 9.25/5.15                ( ( member_nat @ X3 @ A4 )
% 9.25/5.15                & ~ ( member_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2274_order__less__imp__not__less,axiom,
% 9.25/5.15      ! [X: literal,Y: literal] :
% 9.25/5.15        ( ( ord_less_literal @ X @ Y )
% 9.25/5.15       => ~ ( ord_less_literal @ Y @ X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2275_order__less__imp__not__less,axiom,
% 9.25/5.15      ! [X: rat,Y: rat] :
% 9.25/5.15        ( ( ord_less_rat @ X @ Y )
% 9.25/5.15       => ~ ( ord_less_rat @ Y @ X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2276_order__less__imp__not__less,axiom,
% 9.25/5.15      ! [X: nat,Y: nat] :
% 9.25/5.15        ( ( ord_less_nat @ X @ Y )
% 9.25/5.15       => ~ ( ord_less_nat @ Y @ X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2277_order__less__imp__not__less,axiom,
% 9.25/5.15      ! [X: int,Y: int] :
% 9.25/5.15        ( ( ord_less_int @ X @ Y )
% 9.25/5.15       => ~ ( ord_less_int @ Y @ X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2278_order__le__imp__less__or__eq,axiom,
% 9.25/5.15      ! [X: literal,Y: literal] :
% 9.25/5.15        ( ( ord_less_eq_literal @ X @ Y )
% 9.25/5.15       => ( ( ord_less_literal @ X @ Y )
% 9.25/5.15          | ( X = Y ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2279_order__le__imp__less__or__eq,axiom,
% 9.25/5.15      ! [X: filter_nat,Y: filter_nat] :
% 9.25/5.15        ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 9.25/5.15       => ( ( ord_less_filter_nat @ X @ Y )
% 9.25/5.15          | ( X = Y ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2280_order__le__imp__less__or__eq,axiom,
% 9.25/5.15      ! [X: set_nat,Y: set_nat] :
% 9.25/5.15        ( ( ord_less_eq_set_nat @ X @ Y )
% 9.25/5.15       => ( ( ord_less_set_nat @ X @ Y )
% 9.25/5.15          | ( X = Y ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2281_order__le__imp__less__or__eq,axiom,
% 9.25/5.15      ! [X: rat,Y: rat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ X @ Y )
% 9.25/5.15       => ( ( ord_less_rat @ X @ Y )
% 9.25/5.15          | ( X = Y ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2282_order__le__imp__less__or__eq,axiom,
% 9.25/5.15      ! [X: nat,Y: nat] :
% 9.25/5.15        ( ( ord_less_eq_nat @ X @ Y )
% 9.25/5.15       => ( ( ord_less_nat @ X @ Y )
% 9.25/5.15          | ( X = Y ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2283_order__le__imp__less__or__eq,axiom,
% 9.25/5.15      ! [X: int,Y: int] :
% 9.25/5.15        ( ( ord_less_eq_int @ X @ Y )
% 9.25/5.15       => ( ( ord_less_int @ X @ Y )
% 9.25/5.15          | ( X = Y ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2284_linorder__le__less__linear,axiom,
% 9.25/5.15      ! [X: literal,Y: literal] :
% 9.25/5.15        ( ( ord_less_eq_literal @ X @ Y )
% 9.25/5.15        | ( ord_less_literal @ Y @ X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2285_linorder__le__less__linear,axiom,
% 9.25/5.15      ! [X: rat,Y: rat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ X @ Y )
% 9.25/5.15        | ( ord_less_rat @ Y @ X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2286_linorder__le__less__linear,axiom,
% 9.25/5.15      ! [X: nat,Y: nat] :
% 9.25/5.15        ( ( ord_less_eq_nat @ X @ Y )
% 9.25/5.15        | ( ord_less_nat @ Y @ X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2287_linorder__le__less__linear,axiom,
% 9.25/5.15      ! [X: int,Y: int] :
% 9.25/5.15        ( ( ord_less_eq_int @ X @ Y )
% 9.25/5.15        | ( ord_less_int @ Y @ X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2288_order__less__imp__not__eq2,axiom,
% 9.25/5.15      ! [X: literal,Y: literal] :
% 9.25/5.15        ( ( ord_less_literal @ X @ Y )
% 9.25/5.15       => ( Y != X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2289_order__less__imp__not__eq2,axiom,
% 9.25/5.15      ! [X: rat,Y: rat] :
% 9.25/5.15        ( ( ord_less_rat @ X @ Y )
% 9.25/5.15       => ( Y != X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2290_order__less__imp__not__eq2,axiom,
% 9.25/5.15      ! [X: nat,Y: nat] :
% 9.25/5.15        ( ( ord_less_nat @ X @ Y )
% 9.25/5.15       => ( Y != X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2291_order__less__imp__not__eq2,axiom,
% 9.25/5.15      ! [X: int,Y: int] :
% 9.25/5.15        ( ( ord_less_int @ X @ Y )
% 9.25/5.15       => ( Y != X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2292_order__less__imp__not__eq,axiom,
% 9.25/5.15      ! [X: literal,Y: literal] :
% 9.25/5.15        ( ( ord_less_literal @ X @ Y )
% 9.25/5.15       => ( X != Y ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2293_order__less__imp__not__eq,axiom,
% 9.25/5.15      ! [X: rat,Y: rat] :
% 9.25/5.15        ( ( ord_less_rat @ X @ Y )
% 9.25/5.15       => ( X != Y ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2294_order__less__imp__not__eq,axiom,
% 9.25/5.15      ! [X: nat,Y: nat] :
% 9.25/5.15        ( ( ord_less_nat @ X @ Y )
% 9.25/5.15       => ( X != Y ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2295_order__less__imp__not__eq,axiom,
% 9.25/5.15      ! [X: int,Y: int] :
% 9.25/5.15        ( ( ord_less_int @ X @ Y )
% 9.25/5.15       => ( X != Y ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2296_order__less__le__subst2,axiom,
% 9.25/5.15      ! [A: literal,B: literal,F2: literal > literal,C: literal] :
% 9.25/5.15        ( ( ord_less_literal @ A @ B )
% 9.25/5.15       => ( ( ord_less_eq_literal @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: literal,Y2: literal] :
% 9.25/5.15                ( ( ord_less_literal @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2297_order__less__le__subst2,axiom,
% 9.25/5.15      ! [A: rat,B: rat,F2: rat > literal,C: literal] :
% 9.25/5.15        ( ( ord_less_rat @ A @ B )
% 9.25/5.15       => ( ( ord_less_eq_literal @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.15                ( ( ord_less_rat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2298_order__less__le__subst2,axiom,
% 9.25/5.15      ! [A: nat,B: nat,F2: nat > literal,C: literal] :
% 9.25/5.15        ( ( ord_less_nat @ A @ B )
% 9.25/5.15       => ( ( ord_less_eq_literal @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.15                ( ( ord_less_nat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2299_order__less__le__subst2,axiom,
% 9.25/5.15      ! [A: int,B: int,F2: int > literal,C: literal] :
% 9.25/5.15        ( ( ord_less_int @ A @ B )
% 9.25/5.15       => ( ( ord_less_eq_literal @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: int,Y2: int] :
% 9.25/5.15                ( ( ord_less_int @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2300_order__less__le__subst2,axiom,
% 9.25/5.15      ! [A: literal,B: literal,F2: literal > rat,C: rat] :
% 9.25/5.15        ( ( ord_less_literal @ A @ B )
% 9.25/5.15       => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: literal,Y2: literal] :
% 9.25/5.15                ( ( ord_less_literal @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2301_order__less__le__subst2,axiom,
% 9.25/5.15      ! [A: rat,B: rat,F2: rat > rat,C: rat] :
% 9.25/5.15        ( ( ord_less_rat @ A @ B )
% 9.25/5.15       => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.15                ( ( ord_less_rat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2302_order__less__le__subst2,axiom,
% 9.25/5.15      ! [A: nat,B: nat,F2: nat > rat,C: rat] :
% 9.25/5.15        ( ( ord_less_nat @ A @ B )
% 9.25/5.15       => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.15                ( ( ord_less_nat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2303_order__less__le__subst2,axiom,
% 9.25/5.15      ! [A: int,B: int,F2: int > rat,C: rat] :
% 9.25/5.15        ( ( ord_less_int @ A @ B )
% 9.25/5.15       => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: int,Y2: int] :
% 9.25/5.15                ( ( ord_less_int @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2304_order__less__le__subst2,axiom,
% 9.25/5.15      ! [A: literal,B: literal,F2: literal > nat,C: nat] :
% 9.25/5.15        ( ( ord_less_literal @ A @ B )
% 9.25/5.15       => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: literal,Y2: literal] :
% 9.25/5.15                ( ( ord_less_literal @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2305_order__less__le__subst2,axiom,
% 9.25/5.15      ! [A: rat,B: rat,F2: rat > nat,C: nat] :
% 9.25/5.15        ( ( ord_less_rat @ A @ B )
% 9.25/5.15       => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.15                ( ( ord_less_rat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2306_order__less__le__subst1,axiom,
% 9.25/5.15      ! [A: literal,F2: rat > literal,B: rat,C: rat] :
% 9.25/5.15        ( ( ord_less_literal @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_eq_rat @ B @ C )
% 9.25/5.15         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.15                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_eq_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2307_order__less__le__subst1,axiom,
% 9.25/5.15      ! [A: rat,F2: rat > rat,B: rat,C: rat] :
% 9.25/5.15        ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_eq_rat @ B @ C )
% 9.25/5.15         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.15                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2308_order__less__le__subst1,axiom,
% 9.25/5.15      ! [A: nat,F2: rat > nat,B: rat,C: rat] :
% 9.25/5.15        ( ( ord_less_nat @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_eq_rat @ B @ C )
% 9.25/5.15         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.15                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2309_order__less__le__subst1,axiom,
% 9.25/5.15      ! [A: int,F2: rat > int,B: rat,C: rat] :
% 9.25/5.15        ( ( ord_less_int @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_eq_rat @ B @ C )
% 9.25/5.15         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.15                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2310_order__less__le__subst1,axiom,
% 9.25/5.15      ! [A: literal,F2: nat > literal,B: nat,C: nat] :
% 9.25/5.15        ( ( ord_less_literal @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_eq_nat @ B @ C )
% 9.25/5.15         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.15                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_eq_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2311_order__less__le__subst1,axiom,
% 9.25/5.15      ! [A: rat,F2: nat > rat,B: nat,C: nat] :
% 9.25/5.15        ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_eq_nat @ B @ C )
% 9.25/5.15         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.15                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2312_order__less__le__subst1,axiom,
% 9.25/5.15      ! [A: nat,F2: nat > nat,B: nat,C: nat] :
% 9.25/5.15        ( ( ord_less_nat @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_eq_nat @ B @ C )
% 9.25/5.15         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.15                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2313_order__less__le__subst1,axiom,
% 9.25/5.15      ! [A: int,F2: nat > int,B: nat,C: nat] :
% 9.25/5.15        ( ( ord_less_int @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_eq_nat @ B @ C )
% 9.25/5.15         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.15                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2314_order__less__le__subst1,axiom,
% 9.25/5.15      ! [A: literal,F2: int > literal,B: int,C: int] :
% 9.25/5.15        ( ( ord_less_literal @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_eq_int @ B @ C )
% 9.25/5.15         => ( ! [X2: int,Y2: int] :
% 9.25/5.15                ( ( ord_less_eq_int @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_eq_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2315_order__less__le__subst1,axiom,
% 9.25/5.15      ! [A: rat,F2: int > rat,B: int,C: int] :
% 9.25/5.15        ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_eq_int @ B @ C )
% 9.25/5.15         => ( ! [X2: int,Y2: int] :
% 9.25/5.15                ( ( ord_less_eq_int @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2316_order__le__less__subst2,axiom,
% 9.25/5.15      ! [A: rat,B: rat,F2: rat > literal,C: literal] :
% 9.25/5.15        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.15       => ( ( ord_less_literal @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.15                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_eq_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2317_order__le__less__subst2,axiom,
% 9.25/5.15      ! [A: rat,B: rat,F2: rat > rat,C: rat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.15       => ( ( ord_less_rat @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.15                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2318_order__le__less__subst2,axiom,
% 9.25/5.15      ! [A: rat,B: rat,F2: rat > nat,C: nat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.15       => ( ( ord_less_nat @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.15                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2319_order__le__less__subst2,axiom,
% 9.25/5.15      ! [A: rat,B: rat,F2: rat > int,C: int] :
% 9.25/5.15        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.15       => ( ( ord_less_int @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.15                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2320_order__le__less__subst2,axiom,
% 9.25/5.15      ! [A: nat,B: nat,F2: nat > literal,C: literal] :
% 9.25/5.15        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.15       => ( ( ord_less_literal @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.15                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_eq_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2321_order__le__less__subst2,axiom,
% 9.25/5.15      ! [A: nat,B: nat,F2: nat > rat,C: rat] :
% 9.25/5.15        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.15       => ( ( ord_less_rat @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.15                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2322_order__le__less__subst2,axiom,
% 9.25/5.15      ! [A: nat,B: nat,F2: nat > nat,C: nat] :
% 9.25/5.15        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.15       => ( ( ord_less_nat @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.15                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2323_order__le__less__subst2,axiom,
% 9.25/5.15      ! [A: nat,B: nat,F2: nat > int,C: int] :
% 9.25/5.15        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.15       => ( ( ord_less_int @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.15                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2324_order__le__less__subst2,axiom,
% 9.25/5.15      ! [A: int,B: int,F2: int > literal,C: literal] :
% 9.25/5.15        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.15       => ( ( ord_less_literal @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: int,Y2: int] :
% 9.25/5.15                ( ( ord_less_eq_int @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_eq_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2325_order__le__less__subst2,axiom,
% 9.25/5.15      ! [A: int,B: int,F2: int > rat,C: rat] :
% 9.25/5.15        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.15       => ( ( ord_less_rat @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: int,Y2: int] :
% 9.25/5.15                ( ( ord_less_eq_int @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2326_order__le__less__subst1,axiom,
% 9.25/5.15      ! [A: literal,F2: literal > literal,B: literal,C: literal] :
% 9.25/5.15        ( ( ord_less_eq_literal @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_literal @ B @ C )
% 9.25/5.15         => ( ! [X2: literal,Y2: literal] :
% 9.25/5.15                ( ( ord_less_literal @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2327_order__le__less__subst1,axiom,
% 9.25/5.15      ! [A: literal,F2: rat > literal,B: rat,C: rat] :
% 9.25/5.15        ( ( ord_less_eq_literal @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_rat @ B @ C )
% 9.25/5.15         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.15                ( ( ord_less_rat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2328_order__le__less__subst1,axiom,
% 9.25/5.15      ! [A: literal,F2: nat > literal,B: nat,C: nat] :
% 9.25/5.15        ( ( ord_less_eq_literal @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_nat @ B @ C )
% 9.25/5.15         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.15                ( ( ord_less_nat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2329_order__le__less__subst1,axiom,
% 9.25/5.15      ! [A: literal,F2: int > literal,B: int,C: int] :
% 9.25/5.15        ( ( ord_less_eq_literal @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_int @ B @ C )
% 9.25/5.15         => ( ! [X2: int,Y2: int] :
% 9.25/5.15                ( ( ord_less_int @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2330_order__le__less__subst1,axiom,
% 9.25/5.15      ! [A: rat,F2: literal > rat,B: literal,C: literal] :
% 9.25/5.15        ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_literal @ B @ C )
% 9.25/5.15         => ( ! [X2: literal,Y2: literal] :
% 9.25/5.15                ( ( ord_less_literal @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2331_order__le__less__subst1,axiom,
% 9.25/5.15      ! [A: rat,F2: rat > rat,B: rat,C: rat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_rat @ B @ C )
% 9.25/5.15         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.15                ( ( ord_less_rat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2332_order__le__less__subst1,axiom,
% 9.25/5.15      ! [A: rat,F2: nat > rat,B: nat,C: nat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_nat @ B @ C )
% 9.25/5.15         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.15                ( ( ord_less_nat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2333_order__le__less__subst1,axiom,
% 9.25/5.15      ! [A: rat,F2: int > rat,B: int,C: int] :
% 9.25/5.15        ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_int @ B @ C )
% 9.25/5.15         => ( ! [X2: int,Y2: int] :
% 9.25/5.15                ( ( ord_less_int @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2334_order__le__less__subst1,axiom,
% 9.25/5.15      ! [A: nat,F2: literal > nat,B: literal,C: literal] :
% 9.25/5.15        ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_literal @ B @ C )
% 9.25/5.15         => ( ! [X2: literal,Y2: literal] :
% 9.25/5.15                ( ( ord_less_literal @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2335_order__le__less__subst1,axiom,
% 9.25/5.15      ! [A: nat,F2: rat > nat,B: rat,C: rat] :
% 9.25/5.15        ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_rat @ B @ C )
% 9.25/5.15         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.15                ( ( ord_less_rat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2336_linorder__less__linear,axiom,
% 9.25/5.15      ! [X: literal,Y: literal] :
% 9.25/5.15        ( ( ord_less_literal @ X @ Y )
% 9.25/5.15        | ( X = Y )
% 9.25/5.15        | ( ord_less_literal @ Y @ X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2337_linorder__less__linear,axiom,
% 9.25/5.15      ! [X: rat,Y: rat] :
% 9.25/5.15        ( ( ord_less_rat @ X @ Y )
% 9.25/5.15        | ( X = Y )
% 9.25/5.15        | ( ord_less_rat @ Y @ X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2338_linorder__less__linear,axiom,
% 9.25/5.15      ! [X: nat,Y: nat] :
% 9.25/5.15        ( ( ord_less_nat @ X @ Y )
% 9.25/5.15        | ( X = Y )
% 9.25/5.15        | ( ord_less_nat @ Y @ X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2339_linorder__less__linear,axiom,
% 9.25/5.15      ! [X: int,Y: int] :
% 9.25/5.15        ( ( ord_less_int @ X @ Y )
% 9.25/5.15        | ( X = Y )
% 9.25/5.15        | ( ord_less_int @ Y @ X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2340_order__less__le__trans,axiom,
% 9.25/5.15      ! [X: literal,Y: literal,Z: literal] :
% 9.25/5.15        ( ( ord_less_literal @ X @ Y )
% 9.25/5.15       => ( ( ord_less_eq_literal @ Y @ Z )
% 9.25/5.15         => ( ord_less_literal @ X @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2341_order__less__le__trans,axiom,
% 9.25/5.15      ! [X: filter_nat,Y: filter_nat,Z: filter_nat] :
% 9.25/5.15        ( ( ord_less_filter_nat @ X @ Y )
% 9.25/5.15       => ( ( ord_le2510731241096832064er_nat @ Y @ Z )
% 9.25/5.15         => ( ord_less_filter_nat @ X @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2342_order__less__le__trans,axiom,
% 9.25/5.15      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.25/5.15        ( ( ord_less_set_nat @ X @ Y )
% 9.25/5.15       => ( ( ord_less_eq_set_nat @ Y @ Z )
% 9.25/5.15         => ( ord_less_set_nat @ X @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2343_order__less__le__trans,axiom,
% 9.25/5.15      ! [X: rat,Y: rat,Z: rat] :
% 9.25/5.15        ( ( ord_less_rat @ X @ Y )
% 9.25/5.15       => ( ( ord_less_eq_rat @ Y @ Z )
% 9.25/5.15         => ( ord_less_rat @ X @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2344_order__less__le__trans,axiom,
% 9.25/5.15      ! [X: nat,Y: nat,Z: nat] :
% 9.25/5.15        ( ( ord_less_nat @ X @ Y )
% 9.25/5.15       => ( ( ord_less_eq_nat @ Y @ Z )
% 9.25/5.15         => ( ord_less_nat @ X @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2345_order__less__le__trans,axiom,
% 9.25/5.15      ! [X: int,Y: int,Z: int] :
% 9.25/5.15        ( ( ord_less_int @ X @ Y )
% 9.25/5.15       => ( ( ord_less_eq_int @ Y @ Z )
% 9.25/5.15         => ( ord_less_int @ X @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2346_order__less__imp__triv,axiom,
% 9.25/5.15      ! [X: literal,Y: literal,P: $o] :
% 9.25/5.15        ( ( ord_less_literal @ X @ Y )
% 9.25/5.15       => ( ( ord_less_literal @ Y @ X )
% 9.25/5.15         => P ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2347_order__less__imp__triv,axiom,
% 9.25/5.15      ! [X: rat,Y: rat,P: $o] :
% 9.25/5.15        ( ( ord_less_rat @ X @ Y )
% 9.25/5.15       => ( ( ord_less_rat @ Y @ X )
% 9.25/5.15         => P ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2348_order__less__imp__triv,axiom,
% 9.25/5.15      ! [X: nat,Y: nat,P: $o] :
% 9.25/5.15        ( ( ord_less_nat @ X @ Y )
% 9.25/5.15       => ( ( ord_less_nat @ Y @ X )
% 9.25/5.15         => P ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2349_order__less__imp__triv,axiom,
% 9.25/5.15      ! [X: int,Y: int,P: $o] :
% 9.25/5.15        ( ( ord_less_int @ X @ Y )
% 9.25/5.15       => ( ( ord_less_int @ Y @ X )
% 9.25/5.15         => P ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2350_order__le__less__trans,axiom,
% 9.25/5.15      ! [X: literal,Y: literal,Z: literal] :
% 9.25/5.15        ( ( ord_less_eq_literal @ X @ Y )
% 9.25/5.15       => ( ( ord_less_literal @ Y @ Z )
% 9.25/5.15         => ( ord_less_literal @ X @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2351_order__le__less__trans,axiom,
% 9.25/5.15      ! [X: filter_nat,Y: filter_nat,Z: filter_nat] :
% 9.25/5.15        ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 9.25/5.15       => ( ( ord_less_filter_nat @ Y @ Z )
% 9.25/5.15         => ( ord_less_filter_nat @ X @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2352_order__le__less__trans,axiom,
% 9.25/5.15      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.25/5.15        ( ( ord_less_eq_set_nat @ X @ Y )
% 9.25/5.15       => ( ( ord_less_set_nat @ Y @ Z )
% 9.25/5.15         => ( ord_less_set_nat @ X @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2353_order__le__less__trans,axiom,
% 9.25/5.15      ! [X: rat,Y: rat,Z: rat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ X @ Y )
% 9.25/5.15       => ( ( ord_less_rat @ Y @ Z )
% 9.25/5.15         => ( ord_less_rat @ X @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2354_order__le__less__trans,axiom,
% 9.25/5.15      ! [X: nat,Y: nat,Z: nat] :
% 9.25/5.15        ( ( ord_less_eq_nat @ X @ Y )
% 9.25/5.15       => ( ( ord_less_nat @ Y @ Z )
% 9.25/5.15         => ( ord_less_nat @ X @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2355_order__le__less__trans,axiom,
% 9.25/5.15      ! [X: int,Y: int,Z: int] :
% 9.25/5.15        ( ( ord_less_eq_int @ X @ Y )
% 9.25/5.15       => ( ( ord_less_int @ Y @ Z )
% 9.25/5.15         => ( ord_less_int @ X @ Z ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2356_order__neq__le__trans,axiom,
% 9.25/5.15      ! [A: literal,B: literal] :
% 9.25/5.15        ( ( A != B )
% 9.25/5.15       => ( ( ord_less_eq_literal @ A @ B )
% 9.25/5.15         => ( ord_less_literal @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2357_order__neq__le__trans,axiom,
% 9.25/5.15      ! [A: filter_nat,B: filter_nat] :
% 9.25/5.15        ( ( A != B )
% 9.25/5.15       => ( ( ord_le2510731241096832064er_nat @ A @ B )
% 9.25/5.15         => ( ord_less_filter_nat @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2358_order__neq__le__trans,axiom,
% 9.25/5.15      ! [A: set_nat,B: set_nat] :
% 9.25/5.15        ( ( A != B )
% 9.25/5.15       => ( ( ord_less_eq_set_nat @ A @ B )
% 9.25/5.15         => ( ord_less_set_nat @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2359_order__neq__le__trans,axiom,
% 9.25/5.15      ! [A: rat,B: rat] :
% 9.25/5.15        ( ( A != B )
% 9.25/5.15       => ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.15         => ( ord_less_rat @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2360_order__neq__le__trans,axiom,
% 9.25/5.15      ! [A: nat,B: nat] :
% 9.25/5.15        ( ( A != B )
% 9.25/5.15       => ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.15         => ( ord_less_nat @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2361_order__neq__le__trans,axiom,
% 9.25/5.15      ! [A: int,B: int] :
% 9.25/5.15        ( ( A != B )
% 9.25/5.15       => ( ( ord_less_eq_int @ A @ B )
% 9.25/5.15         => ( ord_less_int @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2362_order__less__not__sym,axiom,
% 9.25/5.15      ! [X: literal,Y: literal] :
% 9.25/5.15        ( ( ord_less_literal @ X @ Y )
% 9.25/5.15       => ~ ( ord_less_literal @ Y @ X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2363_order__less__not__sym,axiom,
% 9.25/5.15      ! [X: rat,Y: rat] :
% 9.25/5.15        ( ( ord_less_rat @ X @ Y )
% 9.25/5.15       => ~ ( ord_less_rat @ Y @ X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2364_order__less__not__sym,axiom,
% 9.25/5.15      ! [X: nat,Y: nat] :
% 9.25/5.15        ( ( ord_less_nat @ X @ Y )
% 9.25/5.15       => ~ ( ord_less_nat @ Y @ X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2365_order__less__not__sym,axiom,
% 9.25/5.15      ! [X: int,Y: int] :
% 9.25/5.15        ( ( ord_less_int @ X @ Y )
% 9.25/5.15       => ~ ( ord_less_int @ Y @ X ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2366_order__le__neq__trans,axiom,
% 9.25/5.15      ! [A: literal,B: literal] :
% 9.25/5.15        ( ( ord_less_eq_literal @ A @ B )
% 9.25/5.15       => ( ( A != B )
% 9.25/5.15         => ( ord_less_literal @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2367_order__le__neq__trans,axiom,
% 9.25/5.15      ! [A: filter_nat,B: filter_nat] :
% 9.25/5.15        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 9.25/5.15       => ( ( A != B )
% 9.25/5.15         => ( ord_less_filter_nat @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2368_order__le__neq__trans,axiom,
% 9.25/5.15      ! [A: set_nat,B: set_nat] :
% 9.25/5.15        ( ( ord_less_eq_set_nat @ A @ B )
% 9.25/5.15       => ( ( A != B )
% 9.25/5.15         => ( ord_less_set_nat @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2369_order__le__neq__trans,axiom,
% 9.25/5.15      ! [A: rat,B: rat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.15       => ( ( A != B )
% 9.25/5.15         => ( ord_less_rat @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2370_order__le__neq__trans,axiom,
% 9.25/5.15      ! [A: nat,B: nat] :
% 9.25/5.15        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.15       => ( ( A != B )
% 9.25/5.15         => ( ord_less_nat @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2371_order__le__neq__trans,axiom,
% 9.25/5.15      ! [A: int,B: int] :
% 9.25/5.15        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.15       => ( ( A != B )
% 9.25/5.15         => ( ord_less_int @ A @ B ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2372_order__antisym__conv,axiom,
% 9.25/5.15      ! [Y: filter_nat,X: filter_nat] :
% 9.25/5.15        ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 9.25/5.15       => ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 9.25/5.15          = ( X = Y ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2373_order__antisym__conv,axiom,
% 9.25/5.15      ! [Y: set_nat,X: set_nat] :
% 9.25/5.15        ( ( ord_less_eq_set_nat @ Y @ X )
% 9.25/5.15       => ( ( ord_less_eq_set_nat @ X @ Y )
% 9.25/5.15          = ( X = Y ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2374_order__antisym__conv,axiom,
% 9.25/5.15      ! [Y: rat,X: rat] :
% 9.25/5.15        ( ( ord_less_eq_rat @ Y @ X )
% 9.25/5.15       => ( ( ord_less_eq_rat @ X @ Y )
% 9.25/5.15          = ( X = Y ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2375_order__antisym__conv,axiom,
% 9.25/5.15      ! [Y: nat,X: nat] :
% 9.25/5.15        ( ( ord_less_eq_nat @ Y @ X )
% 9.25/5.15       => ( ( ord_less_eq_nat @ X @ Y )
% 9.25/5.15          = ( X = Y ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2376_order__antisym__conv,axiom,
% 9.25/5.15      ! [Y: int,X: int] :
% 9.25/5.15        ( ( ord_less_eq_int @ Y @ X )
% 9.25/5.15       => ( ( ord_less_eq_int @ X @ Y )
% 9.25/5.15          = ( X = Y ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2377_order__less__subst2,axiom,
% 9.25/5.15      ! [A: literal,B: literal,F2: literal > literal,C: literal] :
% 9.25/5.15        ( ( ord_less_literal @ A @ B )
% 9.25/5.15       => ( ( ord_less_literal @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: literal,Y2: literal] :
% 9.25/5.15                ( ( ord_less_literal @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2378_order__less__subst2,axiom,
% 9.25/5.15      ! [A: literal,B: literal,F2: literal > rat,C: rat] :
% 9.25/5.15        ( ( ord_less_literal @ A @ B )
% 9.25/5.15       => ( ( ord_less_rat @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: literal,Y2: literal] :
% 9.25/5.15                ( ( ord_less_literal @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2379_order__less__subst2,axiom,
% 9.25/5.15      ! [A: literal,B: literal,F2: literal > nat,C: nat] :
% 9.25/5.15        ( ( ord_less_literal @ A @ B )
% 9.25/5.15       => ( ( ord_less_nat @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: literal,Y2: literal] :
% 9.25/5.15                ( ( ord_less_literal @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2380_order__less__subst2,axiom,
% 9.25/5.15      ! [A: literal,B: literal,F2: literal > int,C: int] :
% 9.25/5.15        ( ( ord_less_literal @ A @ B )
% 9.25/5.15       => ( ( ord_less_int @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: literal,Y2: literal] :
% 9.25/5.15                ( ( ord_less_literal @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2381_order__less__subst2,axiom,
% 9.25/5.15      ! [A: rat,B: rat,F2: rat > literal,C: literal] :
% 9.25/5.15        ( ( ord_less_rat @ A @ B )
% 9.25/5.15       => ( ( ord_less_literal @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.15                ( ( ord_less_rat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2382_order__less__subst2,axiom,
% 9.25/5.15      ! [A: rat,B: rat,F2: rat > rat,C: rat] :
% 9.25/5.15        ( ( ord_less_rat @ A @ B )
% 9.25/5.15       => ( ( ord_less_rat @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.15                ( ( ord_less_rat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2383_order__less__subst2,axiom,
% 9.25/5.15      ! [A: rat,B: rat,F2: rat > nat,C: nat] :
% 9.25/5.15        ( ( ord_less_rat @ A @ B )
% 9.25/5.15       => ( ( ord_less_nat @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.15                ( ( ord_less_rat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2384_order__less__subst2,axiom,
% 9.25/5.15      ! [A: rat,B: rat,F2: rat > int,C: int] :
% 9.25/5.15        ( ( ord_less_rat @ A @ B )
% 9.25/5.15       => ( ( ord_less_int @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.15                ( ( ord_less_rat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2385_order__less__subst2,axiom,
% 9.25/5.15      ! [A: nat,B: nat,F2: nat > literal,C: literal] :
% 9.25/5.15        ( ( ord_less_nat @ A @ B )
% 9.25/5.15       => ( ( ord_less_literal @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.15                ( ( ord_less_nat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2386_order__less__subst2,axiom,
% 9.25/5.15      ! [A: nat,B: nat,F2: nat > rat,C: rat] :
% 9.25/5.15        ( ( ord_less_nat @ A @ B )
% 9.25/5.15       => ( ( ord_less_rat @ ( F2 @ B ) @ C )
% 9.25/5.15         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.15                ( ( ord_less_nat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2387_order__less__subst1,axiom,
% 9.25/5.15      ! [A: literal,F2: literal > literal,B: literal,C: literal] :
% 9.25/5.15        ( ( ord_less_literal @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_literal @ B @ C )
% 9.25/5.15         => ( ! [X2: literal,Y2: literal] :
% 9.25/5.15                ( ( ord_less_literal @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2388_order__less__subst1,axiom,
% 9.25/5.15      ! [A: literal,F2: rat > literal,B: rat,C: rat] :
% 9.25/5.15        ( ( ord_less_literal @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_rat @ B @ C )
% 9.25/5.15         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.15                ( ( ord_less_rat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2389_order__less__subst1,axiom,
% 9.25/5.15      ! [A: literal,F2: nat > literal,B: nat,C: nat] :
% 9.25/5.15        ( ( ord_less_literal @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_nat @ B @ C )
% 9.25/5.15         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.15                ( ( ord_less_nat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2390_order__less__subst1,axiom,
% 9.25/5.15      ! [A: literal,F2: int > literal,B: int,C: int] :
% 9.25/5.15        ( ( ord_less_literal @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_int @ B @ C )
% 9.25/5.15         => ( ! [X2: int,Y2: int] :
% 9.25/5.15                ( ( ord_less_int @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2391_order__less__subst1,axiom,
% 9.25/5.15      ! [A: rat,F2: literal > rat,B: literal,C: literal] :
% 9.25/5.15        ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_literal @ B @ C )
% 9.25/5.15         => ( ! [X2: literal,Y2: literal] :
% 9.25/5.15                ( ( ord_less_literal @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2392_order__less__subst1,axiom,
% 9.25/5.15      ! [A: rat,F2: rat > rat,B: rat,C: rat] :
% 9.25/5.15        ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_rat @ B @ C )
% 9.25/5.15         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.15                ( ( ord_less_rat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2393_order__less__subst1,axiom,
% 9.25/5.15      ! [A: rat,F2: nat > rat,B: nat,C: nat] :
% 9.25/5.15        ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 9.25/5.15       => ( ( ord_less_nat @ B @ C )
% 9.25/5.15         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.15                ( ( ord_less_nat @ X2 @ Y2 )
% 9.25/5.15               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.15           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.15  
% 9.25/5.15  thf(fact_2394_order__less__subst1,axiom,
% 9.25/5.15      ! [A: rat,F2: int > rat,B: int,C: int] :
% 9.25/5.16        ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_int @ B @ C )
% 9.25/5.16         => ( ! [X2: int,Y2: int] :
% 9.25/5.16                ( ( ord_less_int @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2395_order__less__subst1,axiom,
% 9.25/5.16      ! [A: nat,F2: literal > nat,B: literal,C: literal] :
% 9.25/5.16        ( ( ord_less_nat @ A @ ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_literal @ B @ C )
% 9.25/5.16         => ( ! [X2: literal,Y2: literal] :
% 9.25/5.16                ( ( ord_less_literal @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2396_order__less__subst1,axiom,
% 9.25/5.16      ! [A: nat,F2: rat > nat,B: rat,C: rat] :
% 9.25/5.16        ( ( ord_less_nat @ A @ ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_rat @ B @ C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2397_order__less__irrefl,axiom,
% 9.25/5.16      ! [X: literal] :
% 9.25/5.16        ~ ( ord_less_literal @ X @ X ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2398_order__less__irrefl,axiom,
% 9.25/5.16      ! [X: rat] :
% 9.25/5.16        ~ ( ord_less_rat @ X @ X ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2399_order__less__irrefl,axiom,
% 9.25/5.16      ! [X: nat] :
% 9.25/5.16        ~ ( ord_less_nat @ X @ X ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2400_order__less__irrefl,axiom,
% 9.25/5.16      ! [X: int] :
% 9.25/5.16        ~ ( ord_less_int @ X @ X ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2401_order__less__imp__le,axiom,
% 9.25/5.16      ! [X: literal,Y: literal] :
% 9.25/5.16        ( ( ord_less_literal @ X @ Y )
% 9.25/5.16       => ( ord_less_eq_literal @ X @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2402_order__less__imp__le,axiom,
% 9.25/5.16      ! [X: filter_nat,Y: filter_nat] :
% 9.25/5.16        ( ( ord_less_filter_nat @ X @ Y )
% 9.25/5.16       => ( ord_le2510731241096832064er_nat @ X @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2403_order__less__imp__le,axiom,
% 9.25/5.16      ! [X: set_nat,Y: set_nat] :
% 9.25/5.16        ( ( ord_less_set_nat @ X @ Y )
% 9.25/5.16       => ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2404_order__less__imp__le,axiom,
% 9.25/5.16      ! [X: rat,Y: rat] :
% 9.25/5.16        ( ( ord_less_rat @ X @ Y )
% 9.25/5.16       => ( ord_less_eq_rat @ X @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2405_order__less__imp__le,axiom,
% 9.25/5.16      ! [X: nat,Y: nat] :
% 9.25/5.16        ( ( ord_less_nat @ X @ Y )
% 9.25/5.16       => ( ord_less_eq_nat @ X @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2406_order__less__imp__le,axiom,
% 9.25/5.16      ! [X: int,Y: int] :
% 9.25/5.16        ( ( ord_less_int @ X @ Y )
% 9.25/5.16       => ( ord_less_eq_int @ X @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2407_ord__less__eq__subst,axiom,
% 9.25/5.16      ! [A: literal,B: literal,F2: literal > literal,C: literal] :
% 9.25/5.16        ( ( ord_less_literal @ A @ B )
% 9.25/5.16       => ( ( ( F2 @ B )
% 9.25/5.16            = C )
% 9.25/5.16         => ( ! [X2: literal,Y2: literal] :
% 9.25/5.16                ( ( ord_less_literal @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2408_ord__less__eq__subst,axiom,
% 9.25/5.16      ! [A: literal,B: literal,F2: literal > rat,C: rat] :
% 9.25/5.16        ( ( ord_less_literal @ A @ B )
% 9.25/5.16       => ( ( ( F2 @ B )
% 9.25/5.16            = C )
% 9.25/5.16         => ( ! [X2: literal,Y2: literal] :
% 9.25/5.16                ( ( ord_less_literal @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2409_ord__less__eq__subst,axiom,
% 9.25/5.16      ! [A: literal,B: literal,F2: literal > nat,C: nat] :
% 9.25/5.16        ( ( ord_less_literal @ A @ B )
% 9.25/5.16       => ( ( ( F2 @ B )
% 9.25/5.16            = C )
% 9.25/5.16         => ( ! [X2: literal,Y2: literal] :
% 9.25/5.16                ( ( ord_less_literal @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2410_ord__less__eq__subst,axiom,
% 9.25/5.16      ! [A: literal,B: literal,F2: literal > int,C: int] :
% 9.25/5.16        ( ( ord_less_literal @ A @ B )
% 9.25/5.16       => ( ( ( F2 @ B )
% 9.25/5.16            = C )
% 9.25/5.16         => ( ! [X2: literal,Y2: literal] :
% 9.25/5.16                ( ( ord_less_literal @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2411_ord__less__eq__subst,axiom,
% 9.25/5.16      ! [A: rat,B: rat,F2: rat > literal,C: literal] :
% 9.25/5.16        ( ( ord_less_rat @ A @ B )
% 9.25/5.16       => ( ( ( F2 @ B )
% 9.25/5.16            = C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2412_ord__less__eq__subst,axiom,
% 9.25/5.16      ! [A: rat,B: rat,F2: rat > rat,C: rat] :
% 9.25/5.16        ( ( ord_less_rat @ A @ B )
% 9.25/5.16       => ( ( ( F2 @ B )
% 9.25/5.16            = C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2413_ord__less__eq__subst,axiom,
% 9.25/5.16      ! [A: rat,B: rat,F2: rat > nat,C: nat] :
% 9.25/5.16        ( ( ord_less_rat @ A @ B )
% 9.25/5.16       => ( ( ( F2 @ B )
% 9.25/5.16            = C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2414_ord__less__eq__subst,axiom,
% 9.25/5.16      ! [A: rat,B: rat,F2: rat > int,C: int] :
% 9.25/5.16        ( ( ord_less_rat @ A @ B )
% 9.25/5.16       => ( ( ( F2 @ B )
% 9.25/5.16            = C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2415_ord__less__eq__subst,axiom,
% 9.25/5.16      ! [A: nat,B: nat,F2: nat > literal,C: literal] :
% 9.25/5.16        ( ( ord_less_nat @ A @ B )
% 9.25/5.16       => ( ( ( F2 @ B )
% 9.25/5.16            = C )
% 9.25/5.16         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.16                ( ( ord_less_nat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_literal @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2416_ord__less__eq__subst,axiom,
% 9.25/5.16      ! [A: nat,B: nat,F2: nat > rat,C: rat] :
% 9.25/5.16        ( ( ord_less_nat @ A @ B )
% 9.25/5.16       => ( ( ( F2 @ B )
% 9.25/5.16            = C )
% 9.25/5.16         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.16                ( ( ord_less_nat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2417_ord__eq__less__subst,axiom,
% 9.25/5.16      ! [A: literal,F2: literal > literal,B: literal,C: literal] :
% 9.25/5.16        ( ( A
% 9.25/5.16          = ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_literal @ B @ C )
% 9.25/5.16         => ( ! [X2: literal,Y2: literal] :
% 9.25/5.16                ( ( ord_less_literal @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2418_ord__eq__less__subst,axiom,
% 9.25/5.16      ! [A: rat,F2: literal > rat,B: literal,C: literal] :
% 9.25/5.16        ( ( A
% 9.25/5.16          = ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_literal @ B @ C )
% 9.25/5.16         => ( ! [X2: literal,Y2: literal] :
% 9.25/5.16                ( ( ord_less_literal @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2419_ord__eq__less__subst,axiom,
% 9.25/5.16      ! [A: nat,F2: literal > nat,B: literal,C: literal] :
% 9.25/5.16        ( ( A
% 9.25/5.16          = ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_literal @ B @ C )
% 9.25/5.16         => ( ! [X2: literal,Y2: literal] :
% 9.25/5.16                ( ( ord_less_literal @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2420_ord__eq__less__subst,axiom,
% 9.25/5.16      ! [A: int,F2: literal > int,B: literal,C: literal] :
% 9.25/5.16        ( ( A
% 9.25/5.16          = ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_literal @ B @ C )
% 9.25/5.16         => ( ! [X2: literal,Y2: literal] :
% 9.25/5.16                ( ( ord_less_literal @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2421_ord__eq__less__subst,axiom,
% 9.25/5.16      ! [A: literal,F2: rat > literal,B: rat,C: rat] :
% 9.25/5.16        ( ( A
% 9.25/5.16          = ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_rat @ B @ C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2422_ord__eq__less__subst,axiom,
% 9.25/5.16      ! [A: rat,F2: rat > rat,B: rat,C: rat] :
% 9.25/5.16        ( ( A
% 9.25/5.16          = ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_rat @ B @ C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2423_ord__eq__less__subst,axiom,
% 9.25/5.16      ! [A: nat,F2: rat > nat,B: rat,C: rat] :
% 9.25/5.16        ( ( A
% 9.25/5.16          = ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_rat @ B @ C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2424_ord__eq__less__subst,axiom,
% 9.25/5.16      ! [A: int,F2: rat > int,B: rat,C: rat] :
% 9.25/5.16        ( ( A
% 9.25/5.16          = ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_rat @ B @ C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2425_ord__eq__less__subst,axiom,
% 9.25/5.16      ! [A: literal,F2: nat > literal,B: nat,C: nat] :
% 9.25/5.16        ( ( A
% 9.25/5.16          = ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_nat @ B @ C )
% 9.25/5.16         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.16                ( ( ord_less_nat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_literal @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_literal @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2426_ord__eq__less__subst,axiom,
% 9.25/5.16      ! [A: rat,F2: nat > rat,B: nat,C: nat] :
% 9.25/5.16        ( ( A
% 9.25/5.16          = ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_nat @ B @ C )
% 9.25/5.16         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.16                ( ( ord_less_nat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2427_linorder__not__less,axiom,
% 9.25/5.16      ! [X: literal,Y: literal] :
% 9.25/5.16        ( ( ~ ( ord_less_literal @ X @ Y ) )
% 9.25/5.16        = ( ord_less_eq_literal @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2428_linorder__not__less,axiom,
% 9.25/5.16      ! [X: rat,Y: rat] :
% 9.25/5.16        ( ( ~ ( ord_less_rat @ X @ Y ) )
% 9.25/5.16        = ( ord_less_eq_rat @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2429_linorder__not__less,axiom,
% 9.25/5.16      ! [X: nat,Y: nat] :
% 9.25/5.16        ( ( ~ ( ord_less_nat @ X @ Y ) )
% 9.25/5.16        = ( ord_less_eq_nat @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2430_linorder__not__less,axiom,
% 9.25/5.16      ! [X: int,Y: int] :
% 9.25/5.16        ( ( ~ ( ord_less_int @ X @ Y ) )
% 9.25/5.16        = ( ord_less_eq_int @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2431_linorder__le__cases,axiom,
% 9.25/5.16      ! [X: rat,Y: rat] :
% 9.25/5.16        ( ~ ( ord_less_eq_rat @ X @ Y )
% 9.25/5.16       => ( ord_less_eq_rat @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2432_linorder__le__cases,axiom,
% 9.25/5.16      ! [X: nat,Y: nat] :
% 9.25/5.16        ( ~ ( ord_less_eq_nat @ X @ Y )
% 9.25/5.16       => ( ord_less_eq_nat @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2433_linorder__le__cases,axiom,
% 9.25/5.16      ! [X: int,Y: int] :
% 9.25/5.16        ( ~ ( ord_less_eq_int @ X @ Y )
% 9.25/5.16       => ( ord_less_eq_int @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2434_order__less__trans,axiom,
% 9.25/5.16      ! [X: literal,Y: literal,Z: literal] :
% 9.25/5.16        ( ( ord_less_literal @ X @ Y )
% 9.25/5.16       => ( ( ord_less_literal @ Y @ Z )
% 9.25/5.16         => ( ord_less_literal @ X @ Z ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2435_order__less__trans,axiom,
% 9.25/5.16      ! [X: rat,Y: rat,Z: rat] :
% 9.25/5.16        ( ( ord_less_rat @ X @ Y )
% 9.25/5.16       => ( ( ord_less_rat @ Y @ Z )
% 9.25/5.16         => ( ord_less_rat @ X @ Z ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2436_order__less__trans,axiom,
% 9.25/5.16      ! [X: nat,Y: nat,Z: nat] :
% 9.25/5.16        ( ( ord_less_nat @ X @ Y )
% 9.25/5.16       => ( ( ord_less_nat @ Y @ Z )
% 9.25/5.16         => ( ord_less_nat @ X @ Z ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2437_order__less__trans,axiom,
% 9.25/5.16      ! [X: int,Y: int,Z: int] :
% 9.25/5.16        ( ( ord_less_int @ X @ Y )
% 9.25/5.16       => ( ( ord_less_int @ Y @ Z )
% 9.25/5.16         => ( ord_less_int @ X @ Z ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2438_order__less__asym_H,axiom,
% 9.25/5.16      ! [A: literal,B: literal] :
% 9.25/5.16        ( ( ord_less_literal @ A @ B )
% 9.25/5.16       => ~ ( ord_less_literal @ B @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2439_order__less__asym_H,axiom,
% 9.25/5.16      ! [A: rat,B: rat] :
% 9.25/5.16        ( ( ord_less_rat @ A @ B )
% 9.25/5.16       => ~ ( ord_less_rat @ B @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2440_order__less__asym_H,axiom,
% 9.25/5.16      ! [A: nat,B: nat] :
% 9.25/5.16        ( ( ord_less_nat @ A @ B )
% 9.25/5.16       => ~ ( ord_less_nat @ B @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2441_order__less__asym_H,axiom,
% 9.25/5.16      ! [A: int,B: int] :
% 9.25/5.16        ( ( ord_less_int @ A @ B )
% 9.25/5.16       => ~ ( ord_less_int @ B @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2442_linorder__neq__iff,axiom,
% 9.25/5.16      ! [X: literal,Y: literal] :
% 9.25/5.16        ( ( X != Y )
% 9.25/5.16        = ( ( ord_less_literal @ X @ Y )
% 9.25/5.16          | ( ord_less_literal @ Y @ X ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2443_linorder__neq__iff,axiom,
% 9.25/5.16      ! [X: rat,Y: rat] :
% 9.25/5.16        ( ( X != Y )
% 9.25/5.16        = ( ( ord_less_rat @ X @ Y )
% 9.25/5.16          | ( ord_less_rat @ Y @ X ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2444_linorder__neq__iff,axiom,
% 9.25/5.16      ! [X: nat,Y: nat] :
% 9.25/5.16        ( ( X != Y )
% 9.25/5.16        = ( ( ord_less_nat @ X @ Y )
% 9.25/5.16          | ( ord_less_nat @ Y @ X ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2445_linorder__neq__iff,axiom,
% 9.25/5.16      ! [X: int,Y: int] :
% 9.25/5.16        ( ( X != Y )
% 9.25/5.16        = ( ( ord_less_int @ X @ Y )
% 9.25/5.16          | ( ord_less_int @ Y @ X ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2446_order__less__asym,axiom,
% 9.25/5.16      ! [X: literal,Y: literal] :
% 9.25/5.16        ( ( ord_less_literal @ X @ Y )
% 9.25/5.16       => ~ ( ord_less_literal @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2447_order__less__asym,axiom,
% 9.25/5.16      ! [X: rat,Y: rat] :
% 9.25/5.16        ( ( ord_less_rat @ X @ Y )
% 9.25/5.16       => ~ ( ord_less_rat @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2448_order__less__asym,axiom,
% 9.25/5.16      ! [X: nat,Y: nat] :
% 9.25/5.16        ( ( ord_less_nat @ X @ Y )
% 9.25/5.16       => ~ ( ord_less_nat @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2449_order__less__asym,axiom,
% 9.25/5.16      ! [X: int,Y: int] :
% 9.25/5.16        ( ( ord_less_int @ X @ Y )
% 9.25/5.16       => ~ ( ord_less_int @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2450_ord__le__eq__subst,axiom,
% 9.25/5.16      ! [A: rat,B: rat,F2: rat > rat,C: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.16       => ( ( ( F2 @ B )
% 9.25/5.16            = C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2451_ord__le__eq__subst,axiom,
% 9.25/5.16      ! [A: rat,B: rat,F2: rat > nat,C: nat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.16       => ( ( ( F2 @ B )
% 9.25/5.16            = C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2452_ord__le__eq__subst,axiom,
% 9.25/5.16      ! [A: rat,B: rat,F2: rat > int,C: int] :
% 9.25/5.16        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.16       => ( ( ( F2 @ B )
% 9.25/5.16            = C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2453_ord__le__eq__subst,axiom,
% 9.25/5.16      ! [A: nat,B: nat,F2: nat > rat,C: rat] :
% 9.25/5.16        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.16       => ( ( ( F2 @ B )
% 9.25/5.16            = C )
% 9.25/5.16         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.16                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2454_ord__le__eq__subst,axiom,
% 9.25/5.16      ! [A: nat,B: nat,F2: nat > nat,C: nat] :
% 9.25/5.16        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.16       => ( ( ( F2 @ B )
% 9.25/5.16            = C )
% 9.25/5.16         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.16                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2455_ord__le__eq__subst,axiom,
% 9.25/5.16      ! [A: nat,B: nat,F2: nat > int,C: int] :
% 9.25/5.16        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.16       => ( ( ( F2 @ B )
% 9.25/5.16            = C )
% 9.25/5.16         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.16                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2456_ord__le__eq__subst,axiom,
% 9.25/5.16      ! [A: int,B: int,F2: int > rat,C: rat] :
% 9.25/5.16        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.16       => ( ( ( F2 @ B )
% 9.25/5.16            = C )
% 9.25/5.16         => ( ! [X2: int,Y2: int] :
% 9.25/5.16                ( ( ord_less_eq_int @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2457_ord__le__eq__subst,axiom,
% 9.25/5.16      ! [A: int,B: int,F2: int > nat,C: nat] :
% 9.25/5.16        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.16       => ( ( ( F2 @ B )
% 9.25/5.16            = C )
% 9.25/5.16         => ( ! [X2: int,Y2: int] :
% 9.25/5.16                ( ( ord_less_eq_int @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2458_ord__le__eq__subst,axiom,
% 9.25/5.16      ! [A: int,B: int,F2: int > int,C: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.16       => ( ( ( F2 @ B )
% 9.25/5.16            = C )
% 9.25/5.16         => ( ! [X2: int,Y2: int] :
% 9.25/5.16                ( ( ord_less_eq_int @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2459_ord__le__eq__subst,axiom,
% 9.25/5.16      ! [A: filter_nat,B: filter_nat,F2: filter_nat > rat,C: rat] :
% 9.25/5.16        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 9.25/5.16       => ( ( ( F2 @ B )
% 9.25/5.16            = C )
% 9.25/5.16         => ( ! [X2: filter_nat,Y2: filter_nat] :
% 9.25/5.16                ( ( ord_le2510731241096832064er_nat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2460_ord__eq__le__subst,axiom,
% 9.25/5.16      ! [A: rat,F2: rat > rat,B: rat,C: rat] :
% 9.25/5.16        ( ( A
% 9.25/5.16          = ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_rat @ B @ C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2461_ord__eq__le__subst,axiom,
% 9.25/5.16      ! [A: nat,F2: rat > nat,B: rat,C: rat] :
% 9.25/5.16        ( ( A
% 9.25/5.16          = ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_rat @ B @ C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2462_ord__eq__le__subst,axiom,
% 9.25/5.16      ! [A: int,F2: rat > int,B: rat,C: rat] :
% 9.25/5.16        ( ( A
% 9.25/5.16          = ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_rat @ B @ C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2463_ord__eq__le__subst,axiom,
% 9.25/5.16      ! [A: rat,F2: nat > rat,B: nat,C: nat] :
% 9.25/5.16        ( ( A
% 9.25/5.16          = ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_nat @ B @ C )
% 9.25/5.16         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.16                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2464_ord__eq__le__subst,axiom,
% 9.25/5.16      ! [A: nat,F2: nat > nat,B: nat,C: nat] :
% 9.25/5.16        ( ( A
% 9.25/5.16          = ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_nat @ B @ C )
% 9.25/5.16         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.16                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2465_ord__eq__le__subst,axiom,
% 9.25/5.16      ! [A: int,F2: nat > int,B: nat,C: nat] :
% 9.25/5.16        ( ( A
% 9.25/5.16          = ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_nat @ B @ C )
% 9.25/5.16         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.16                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2466_ord__eq__le__subst,axiom,
% 9.25/5.16      ! [A: rat,F2: int > rat,B: int,C: int] :
% 9.25/5.16        ( ( A
% 9.25/5.16          = ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_int @ B @ C )
% 9.25/5.16         => ( ! [X2: int,Y2: int] :
% 9.25/5.16                ( ( ord_less_eq_int @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2467_ord__eq__le__subst,axiom,
% 9.25/5.16      ! [A: nat,F2: int > nat,B: int,C: int] :
% 9.25/5.16        ( ( A
% 9.25/5.16          = ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_int @ B @ C )
% 9.25/5.16         => ( ! [X2: int,Y2: int] :
% 9.25/5.16                ( ( ord_less_eq_int @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2468_ord__eq__le__subst,axiom,
% 9.25/5.16      ! [A: int,F2: int > int,B: int,C: int] :
% 9.25/5.16        ( ( A
% 9.25/5.16          = ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_int @ B @ C )
% 9.25/5.16         => ( ! [X2: int,Y2: int] :
% 9.25/5.16                ( ( ord_less_eq_int @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2469_ord__eq__le__subst,axiom,
% 9.25/5.16      ! [A: rat,F2: filter_nat > rat,B: filter_nat,C: filter_nat] :
% 9.25/5.16        ( ( A
% 9.25/5.16          = ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_le2510731241096832064er_nat @ B @ C )
% 9.25/5.16         => ( ! [X2: filter_nat,Y2: filter_nat] :
% 9.25/5.16                ( ( ord_le2510731241096832064er_nat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2470_linorder__not__le,axiom,
% 9.25/5.16      ! [X: literal,Y: literal] :
% 9.25/5.16        ( ( ~ ( ord_less_eq_literal @ X @ Y ) )
% 9.25/5.16        = ( ord_less_literal @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2471_linorder__not__le,axiom,
% 9.25/5.16      ! [X: rat,Y: rat] :
% 9.25/5.16        ( ( ~ ( ord_less_eq_rat @ X @ Y ) )
% 9.25/5.16        = ( ord_less_rat @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2472_linorder__not__le,axiom,
% 9.25/5.16      ! [X: nat,Y: nat] :
% 9.25/5.16        ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 9.25/5.16        = ( ord_less_nat @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2473_linorder__not__le,axiom,
% 9.25/5.16      ! [X: int,Y: int] :
% 9.25/5.16        ( ( ~ ( ord_less_eq_int @ X @ Y ) )
% 9.25/5.16        = ( ord_less_int @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2474_linorder__linear,axiom,
% 9.25/5.16      ! [X: rat,Y: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ X @ Y )
% 9.25/5.16        | ( ord_less_eq_rat @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2475_linorder__linear,axiom,
% 9.25/5.16      ! [X: nat,Y: nat] :
% 9.25/5.16        ( ( ord_less_eq_nat @ X @ Y )
% 9.25/5.16        | ( ord_less_eq_nat @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2476_linorder__linear,axiom,
% 9.25/5.16      ! [X: int,Y: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ X @ Y )
% 9.25/5.16        | ( ord_less_eq_int @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2477_order__less__le,axiom,
% 9.25/5.16      ( ord_less_literal
% 9.25/5.16      = ( ^ [X3: literal,Y3: literal] :
% 9.25/5.16            ( ( ord_less_eq_literal @ X3 @ Y3 )
% 9.25/5.16            & ( X3 != Y3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2478_order__less__le,axiom,
% 9.25/5.16      ( ord_less_filter_nat
% 9.25/5.16      = ( ^ [X3: filter_nat,Y3: filter_nat] :
% 9.25/5.16            ( ( ord_le2510731241096832064er_nat @ X3 @ Y3 )
% 9.25/5.16            & ( X3 != Y3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2479_order__less__le,axiom,
% 9.25/5.16      ( ord_less_set_nat
% 9.25/5.16      = ( ^ [X3: set_nat,Y3: set_nat] :
% 9.25/5.16            ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 9.25/5.16            & ( X3 != Y3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2480_order__less__le,axiom,
% 9.25/5.16      ( ord_less_rat
% 9.25/5.16      = ( ^ [X3: rat,Y3: rat] :
% 9.25/5.16            ( ( ord_less_eq_rat @ X3 @ Y3 )
% 9.25/5.16            & ( X3 != Y3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2481_order__less__le,axiom,
% 9.25/5.16      ( ord_less_nat
% 9.25/5.16      = ( ^ [X3: nat,Y3: nat] :
% 9.25/5.16            ( ( ord_less_eq_nat @ X3 @ Y3 )
% 9.25/5.16            & ( X3 != Y3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2482_order__less__le,axiom,
% 9.25/5.16      ( ord_less_int
% 9.25/5.16      = ( ^ [X3: int,Y3: int] :
% 9.25/5.16            ( ( ord_less_eq_int @ X3 @ Y3 )
% 9.25/5.16            & ( X3 != Y3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2483_order__le__less,axiom,
% 9.25/5.16      ( ord_less_eq_literal
% 9.25/5.16      = ( ^ [X3: literal,Y3: literal] :
% 9.25/5.16            ( ( ord_less_literal @ X3 @ Y3 )
% 9.25/5.16            | ( X3 = Y3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2484_order__le__less,axiom,
% 9.25/5.16      ( ord_le2510731241096832064er_nat
% 9.25/5.16      = ( ^ [X3: filter_nat,Y3: filter_nat] :
% 9.25/5.16            ( ( ord_less_filter_nat @ X3 @ Y3 )
% 9.25/5.16            | ( X3 = Y3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2485_order__le__less,axiom,
% 9.25/5.16      ( ord_less_eq_set_nat
% 9.25/5.16      = ( ^ [X3: set_nat,Y3: set_nat] :
% 9.25/5.16            ( ( ord_less_set_nat @ X3 @ Y3 )
% 9.25/5.16            | ( X3 = Y3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2486_order__le__less,axiom,
% 9.25/5.16      ( ord_less_eq_rat
% 9.25/5.16      = ( ^ [X3: rat,Y3: rat] :
% 9.25/5.16            ( ( ord_less_rat @ X3 @ Y3 )
% 9.25/5.16            | ( X3 = Y3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2487_order__le__less,axiom,
% 9.25/5.16      ( ord_less_eq_nat
% 9.25/5.16      = ( ^ [X3: nat,Y3: nat] :
% 9.25/5.16            ( ( ord_less_nat @ X3 @ Y3 )
% 9.25/5.16            | ( X3 = Y3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2488_order__le__less,axiom,
% 9.25/5.16      ( ord_less_eq_int
% 9.25/5.16      = ( ^ [X3: int,Y3: int] :
% 9.25/5.16            ( ( ord_less_int @ X3 @ Y3 )
% 9.25/5.16            | ( X3 = Y3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2489_order__eq__refl,axiom,
% 9.25/5.16      ! [X: filter_nat,Y: filter_nat] :
% 9.25/5.16        ( ( X = Y )
% 9.25/5.16       => ( ord_le2510731241096832064er_nat @ X @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2490_order__eq__refl,axiom,
% 9.25/5.16      ! [X: set_nat,Y: set_nat] :
% 9.25/5.16        ( ( X = Y )
% 9.25/5.16       => ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2491_order__eq__refl,axiom,
% 9.25/5.16      ! [X: rat,Y: rat] :
% 9.25/5.16        ( ( X = Y )
% 9.25/5.16       => ( ord_less_eq_rat @ X @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2492_order__eq__refl,axiom,
% 9.25/5.16      ! [X: nat,Y: nat] :
% 9.25/5.16        ( ( X = Y )
% 9.25/5.16       => ( ord_less_eq_nat @ X @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2493_order__eq__refl,axiom,
% 9.25/5.16      ! [X: int,Y: int] :
% 9.25/5.16        ( ( X = Y )
% 9.25/5.16       => ( ord_less_eq_int @ X @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2494_linorder__neqE,axiom,
% 9.25/5.16      ! [X: literal,Y: literal] :
% 9.25/5.16        ( ( X != Y )
% 9.25/5.16       => ( ~ ( ord_less_literal @ X @ Y )
% 9.25/5.16         => ( ord_less_literal @ Y @ X ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2495_linorder__neqE,axiom,
% 9.25/5.16      ! [X: rat,Y: rat] :
% 9.25/5.16        ( ( X != Y )
% 9.25/5.16       => ( ~ ( ord_less_rat @ X @ Y )
% 9.25/5.16         => ( ord_less_rat @ Y @ X ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2496_linorder__neqE,axiom,
% 9.25/5.16      ! [X: nat,Y: nat] :
% 9.25/5.16        ( ( X != Y )
% 9.25/5.16       => ( ~ ( ord_less_nat @ X @ Y )
% 9.25/5.16         => ( ord_less_nat @ Y @ X ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2497_linorder__neqE,axiom,
% 9.25/5.16      ! [X: int,Y: int] :
% 9.25/5.16        ( ( X != Y )
% 9.25/5.16       => ( ~ ( ord_less_int @ X @ Y )
% 9.25/5.16         => ( ord_less_int @ Y @ X ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2498_order__subst2,axiom,
% 9.25/5.16      ! [A: rat,B: rat,F2: rat > rat,C: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2499_order__subst2,axiom,
% 9.25/5.16      ! [A: rat,B: rat,F2: rat > nat,C: nat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2500_order__subst2,axiom,
% 9.25/5.16      ! [A: rat,B: rat,F2: rat > int,C: int] :
% 9.25/5.16        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_int @ ( F2 @ B ) @ C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2501_order__subst2,axiom,
% 9.25/5.16      ! [A: nat,B: nat,F2: nat > rat,C: rat] :
% 9.25/5.16        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C )
% 9.25/5.16         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.16                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2502_order__subst2,axiom,
% 9.25/5.16      ! [A: nat,B: nat,F2: nat > nat,C: nat] :
% 9.25/5.16        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
% 9.25/5.16         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.16                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2503_order__subst2,axiom,
% 9.25/5.16      ! [A: nat,B: nat,F2: nat > int,C: int] :
% 9.25/5.16        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_int @ ( F2 @ B ) @ C )
% 9.25/5.16         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.16                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2504_order__subst2,axiom,
% 9.25/5.16      ! [A: int,B: int,F2: int > rat,C: rat] :
% 9.25/5.16        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C )
% 9.25/5.16         => ( ! [X2: int,Y2: int] :
% 9.25/5.16                ( ( ord_less_eq_int @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2505_order__subst2,axiom,
% 9.25/5.16      ! [A: int,B: int,F2: int > nat,C: nat] :
% 9.25/5.16        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C )
% 9.25/5.16         => ( ! [X2: int,Y2: int] :
% 9.25/5.16                ( ( ord_less_eq_int @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_nat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2506_order__subst2,axiom,
% 9.25/5.16      ! [A: int,B: int,F2: int > int,C: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_int @ ( F2 @ B ) @ C )
% 9.25/5.16         => ( ! [X2: int,Y2: int] :
% 9.25/5.16                ( ( ord_less_eq_int @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_int @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2507_order__subst2,axiom,
% 9.25/5.16      ! [A: filter_nat,B: filter_nat,F2: filter_nat > rat,C: rat] :
% 9.25/5.16        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C )
% 9.25/5.16         => ( ! [X2: filter_nat,Y2: filter_nat] :
% 9.25/5.16                ( ( ord_le2510731241096832064er_nat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_rat @ ( F2 @ A ) @ C ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2508_order__subst1,axiom,
% 9.25/5.16      ! [A: rat,F2: rat > rat,B: rat,C: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_rat @ B @ C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2509_order__subst1,axiom,
% 9.25/5.16      ! [A: rat,F2: nat > rat,B: nat,C: nat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_nat @ B @ C )
% 9.25/5.16         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.16                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2510_order__subst1,axiom,
% 9.25/5.16      ! [A: rat,F2: int > rat,B: int,C: int] :
% 9.25/5.16        ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_int @ B @ C )
% 9.25/5.16         => ( ! [X2: int,Y2: int] :
% 9.25/5.16                ( ( ord_less_eq_int @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_rat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_rat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2511_order__subst1,axiom,
% 9.25/5.16      ! [A: nat,F2: rat > nat,B: rat,C: rat] :
% 9.25/5.16        ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_rat @ B @ C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2512_order__subst1,axiom,
% 9.25/5.16      ! [A: nat,F2: nat > nat,B: nat,C: nat] :
% 9.25/5.16        ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_nat @ B @ C )
% 9.25/5.16         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.16                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2513_order__subst1,axiom,
% 9.25/5.16      ! [A: nat,F2: int > nat,B: int,C: int] :
% 9.25/5.16        ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_int @ B @ C )
% 9.25/5.16         => ( ! [X2: int,Y2: int] :
% 9.25/5.16                ( ( ord_less_eq_int @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2514_order__subst1,axiom,
% 9.25/5.16      ! [A: int,F2: rat > int,B: rat,C: rat] :
% 9.25/5.16        ( ( ord_less_eq_int @ A @ ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_rat @ B @ C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2515_order__subst1,axiom,
% 9.25/5.16      ! [A: int,F2: nat > int,B: nat,C: nat] :
% 9.25/5.16        ( ( ord_less_eq_int @ A @ ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_nat @ B @ C )
% 9.25/5.16         => ( ! [X2: nat,Y2: nat] :
% 9.25/5.16                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2516_order__subst1,axiom,
% 9.25/5.16      ! [A: int,F2: int > int,B: int,C: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ A @ ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_int @ B @ C )
% 9.25/5.16         => ( ! [X2: int,Y2: int] :
% 9.25/5.16                ( ( ord_less_eq_int @ X2 @ Y2 )
% 9.25/5.16               => ( ord_less_eq_int @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_less_eq_int @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2517_order__subst1,axiom,
% 9.25/5.16      ! [A: filter_nat,F2: rat > filter_nat,B: rat,C: rat] :
% 9.25/5.16        ( ( ord_le2510731241096832064er_nat @ A @ ( F2 @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_rat @ B @ C )
% 9.25/5.16         => ( ! [X2: rat,Y2: rat] :
% 9.25/5.16                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.16               => ( ord_le2510731241096832064er_nat @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 9.25/5.16           => ( ord_le2510731241096832064er_nat @ A @ ( F2 @ C ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2518_Orderings_Oorder__eq__iff,axiom,
% 9.25/5.16      ( ( ^ [Y4: filter_nat,Z4: filter_nat] : ( Y4 = Z4 ) )
% 9.25/5.16      = ( ^ [A3: filter_nat,B3: filter_nat] :
% 9.25/5.16            ( ( ord_le2510731241096832064er_nat @ A3 @ B3 )
% 9.25/5.16            & ( ord_le2510731241096832064er_nat @ B3 @ A3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2519_Orderings_Oorder__eq__iff,axiom,
% 9.25/5.16      ( ( ^ [Y4: set_nat,Z4: set_nat] : ( Y4 = Z4 ) )
% 9.25/5.16      = ( ^ [A3: set_nat,B3: set_nat] :
% 9.25/5.16            ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 9.25/5.16            & ( ord_less_eq_set_nat @ B3 @ A3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2520_Orderings_Oorder__eq__iff,axiom,
% 9.25/5.16      ( ( ^ [Y4: rat,Z4: rat] : ( Y4 = Z4 ) )
% 9.25/5.16      = ( ^ [A3: rat,B3: rat] :
% 9.25/5.16            ( ( ord_less_eq_rat @ A3 @ B3 )
% 9.25/5.16            & ( ord_less_eq_rat @ B3 @ A3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2521_Orderings_Oorder__eq__iff,axiom,
% 9.25/5.16      ( ( ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 ) )
% 9.25/5.16      = ( ^ [A3: nat,B3: nat] :
% 9.25/5.16            ( ( ord_less_eq_nat @ A3 @ B3 )
% 9.25/5.16            & ( ord_less_eq_nat @ B3 @ A3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2522_Orderings_Oorder__eq__iff,axiom,
% 9.25/5.16      ( ( ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 9.25/5.16      = ( ^ [A3: int,B3: int] :
% 9.25/5.16            ( ( ord_less_eq_int @ A3 @ B3 )
% 9.25/5.16            & ( ord_less_eq_int @ B3 @ A3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2523_antisym,axiom,
% 9.25/5.16      ! [A: filter_nat,B: filter_nat] :
% 9.25/5.16        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 9.25/5.16       => ( ( ord_le2510731241096832064er_nat @ B @ A )
% 9.25/5.16         => ( A = B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2524_antisym,axiom,
% 9.25/5.16      ! [A: set_nat,B: set_nat] :
% 9.25/5.16        ( ( ord_less_eq_set_nat @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_set_nat @ B @ A )
% 9.25/5.16         => ( A = B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2525_antisym,axiom,
% 9.25/5.16      ! [A: rat,B: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_rat @ B @ A )
% 9.25/5.16         => ( A = B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2526_antisym,axiom,
% 9.25/5.16      ! [A: nat,B: nat] :
% 9.25/5.16        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_nat @ B @ A )
% 9.25/5.16         => ( A = B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2527_antisym,axiom,
% 9.25/5.16      ! [A: int,B: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_int @ B @ A )
% 9.25/5.16         => ( A = B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2528_dual__order_Ostrict__implies__order,axiom,
% 9.25/5.16      ! [B: literal,A: literal] :
% 9.25/5.16        ( ( ord_less_literal @ B @ A )
% 9.25/5.16       => ( ord_less_eq_literal @ B @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2529_dual__order_Ostrict__implies__order,axiom,
% 9.25/5.16      ! [B: filter_nat,A: filter_nat] :
% 9.25/5.16        ( ( ord_less_filter_nat @ B @ A )
% 9.25/5.16       => ( ord_le2510731241096832064er_nat @ B @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2530_dual__order_Ostrict__implies__order,axiom,
% 9.25/5.16      ! [B: set_nat,A: set_nat] :
% 9.25/5.16        ( ( ord_less_set_nat @ B @ A )
% 9.25/5.16       => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2531_dual__order_Ostrict__implies__order,axiom,
% 9.25/5.16      ! [B: rat,A: rat] :
% 9.25/5.16        ( ( ord_less_rat @ B @ A )
% 9.25/5.16       => ( ord_less_eq_rat @ B @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2532_dual__order_Ostrict__implies__order,axiom,
% 9.25/5.16      ! [B: nat,A: nat] :
% 9.25/5.16        ( ( ord_less_nat @ B @ A )
% 9.25/5.16       => ( ord_less_eq_nat @ B @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2533_dual__order_Ostrict__implies__order,axiom,
% 9.25/5.16      ! [B: int,A: int] :
% 9.25/5.16        ( ( ord_less_int @ B @ A )
% 9.25/5.16       => ( ord_less_eq_int @ B @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2534_dual__order_Ostrict__implies__not__eq,axiom,
% 9.25/5.16      ! [B: literal,A: literal] :
% 9.25/5.16        ( ( ord_less_literal @ B @ A )
% 9.25/5.16       => ( A != B ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2535_dual__order_Ostrict__implies__not__eq,axiom,
% 9.25/5.16      ! [B: rat,A: rat] :
% 9.25/5.16        ( ( ord_less_rat @ B @ A )
% 9.25/5.16       => ( A != B ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2536_dual__order_Ostrict__implies__not__eq,axiom,
% 9.25/5.16      ! [B: nat,A: nat] :
% 9.25/5.16        ( ( ord_less_nat @ B @ A )
% 9.25/5.16       => ( A != B ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2537_dual__order_Ostrict__implies__not__eq,axiom,
% 9.25/5.16      ! [B: int,A: int] :
% 9.25/5.16        ( ( ord_less_int @ B @ A )
% 9.25/5.16       => ( A != B ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2538_order_Ostrict__implies__order,axiom,
% 9.25/5.16      ! [A: literal,B: literal] :
% 9.25/5.16        ( ( ord_less_literal @ A @ B )
% 9.25/5.16       => ( ord_less_eq_literal @ A @ B ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2539_order_Ostrict__implies__order,axiom,
% 9.25/5.16      ! [A: filter_nat,B: filter_nat] :
% 9.25/5.16        ( ( ord_less_filter_nat @ A @ B )
% 9.25/5.16       => ( ord_le2510731241096832064er_nat @ A @ B ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2540_order_Ostrict__implies__order,axiom,
% 9.25/5.16      ! [A: set_nat,B: set_nat] :
% 9.25/5.16        ( ( ord_less_set_nat @ A @ B )
% 9.25/5.16       => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2541_order_Ostrict__implies__order,axiom,
% 9.25/5.16      ! [A: rat,B: rat] :
% 9.25/5.16        ( ( ord_less_rat @ A @ B )
% 9.25/5.16       => ( ord_less_eq_rat @ A @ B ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2542_order_Ostrict__implies__order,axiom,
% 9.25/5.16      ! [A: nat,B: nat] :
% 9.25/5.16        ( ( ord_less_nat @ A @ B )
% 9.25/5.16       => ( ord_less_eq_nat @ A @ B ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2543_order_Ostrict__implies__order,axiom,
% 9.25/5.16      ! [A: int,B: int] :
% 9.25/5.16        ( ( ord_less_int @ A @ B )
% 9.25/5.16       => ( ord_less_eq_int @ A @ B ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2544_dual__order_Ostrict__iff__not,axiom,
% 9.25/5.16      ( ord_less_literal
% 9.25/5.16      = ( ^ [B3: literal,A3: literal] :
% 9.25/5.16            ( ( ord_less_eq_literal @ B3 @ A3 )
% 9.25/5.16            & ~ ( ord_less_eq_literal @ A3 @ B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2545_dual__order_Ostrict__iff__not,axiom,
% 9.25/5.16      ( ord_less_filter_nat
% 9.25/5.16      = ( ^ [B3: filter_nat,A3: filter_nat] :
% 9.25/5.16            ( ( ord_le2510731241096832064er_nat @ B3 @ A3 )
% 9.25/5.16            & ~ ( ord_le2510731241096832064er_nat @ A3 @ B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2546_dual__order_Ostrict__iff__not,axiom,
% 9.25/5.16      ( ord_less_set_nat
% 9.25/5.16      = ( ^ [B3: set_nat,A3: set_nat] :
% 9.25/5.16            ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 9.25/5.16            & ~ ( ord_less_eq_set_nat @ A3 @ B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2547_dual__order_Ostrict__iff__not,axiom,
% 9.25/5.16      ( ord_less_rat
% 9.25/5.16      = ( ^ [B3: rat,A3: rat] :
% 9.25/5.16            ( ( ord_less_eq_rat @ B3 @ A3 )
% 9.25/5.16            & ~ ( ord_less_eq_rat @ A3 @ B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2548_dual__order_Ostrict__iff__not,axiom,
% 9.25/5.16      ( ord_less_nat
% 9.25/5.16      = ( ^ [B3: nat,A3: nat] :
% 9.25/5.16            ( ( ord_less_eq_nat @ B3 @ A3 )
% 9.25/5.16            & ~ ( ord_less_eq_nat @ A3 @ B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2549_dual__order_Ostrict__iff__not,axiom,
% 9.25/5.16      ( ord_less_int
% 9.25/5.16      = ( ^ [B3: int,A3: int] :
% 9.25/5.16            ( ( ord_less_eq_int @ B3 @ A3 )
% 9.25/5.16            & ~ ( ord_less_eq_int @ A3 @ B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2550_dual__order_Ostrict__trans2,axiom,
% 9.25/5.16      ! [B: literal,A: literal,C: literal] :
% 9.25/5.16        ( ( ord_less_literal @ B @ A )
% 9.25/5.16       => ( ( ord_less_eq_literal @ C @ B )
% 9.25/5.16         => ( ord_less_literal @ C @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2551_dual__order_Ostrict__trans2,axiom,
% 9.25/5.16      ! [B: filter_nat,A: filter_nat,C: filter_nat] :
% 9.25/5.16        ( ( ord_less_filter_nat @ B @ A )
% 9.25/5.16       => ( ( ord_le2510731241096832064er_nat @ C @ B )
% 9.25/5.16         => ( ord_less_filter_nat @ C @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2552_dual__order_Ostrict__trans2,axiom,
% 9.25/5.16      ! [B: set_nat,A: set_nat,C: set_nat] :
% 9.25/5.16        ( ( ord_less_set_nat @ B @ A )
% 9.25/5.16       => ( ( ord_less_eq_set_nat @ C @ B )
% 9.25/5.16         => ( ord_less_set_nat @ C @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2553_dual__order_Ostrict__trans2,axiom,
% 9.25/5.16      ! [B: rat,A: rat,C: rat] :
% 9.25/5.16        ( ( ord_less_rat @ B @ A )
% 9.25/5.16       => ( ( ord_less_eq_rat @ C @ B )
% 9.25/5.16         => ( ord_less_rat @ C @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2554_dual__order_Ostrict__trans2,axiom,
% 9.25/5.16      ! [B: nat,A: nat,C: nat] :
% 9.25/5.16        ( ( ord_less_nat @ B @ A )
% 9.25/5.16       => ( ( ord_less_eq_nat @ C @ B )
% 9.25/5.16         => ( ord_less_nat @ C @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2555_dual__order_Ostrict__trans2,axiom,
% 9.25/5.16      ! [B: int,A: int,C: int] :
% 9.25/5.16        ( ( ord_less_int @ B @ A )
% 9.25/5.16       => ( ( ord_less_eq_int @ C @ B )
% 9.25/5.16         => ( ord_less_int @ C @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2556_dual__order_Ostrict__trans1,axiom,
% 9.25/5.16      ! [B: literal,A: literal,C: literal] :
% 9.25/5.16        ( ( ord_less_eq_literal @ B @ A )
% 9.25/5.16       => ( ( ord_less_literal @ C @ B )
% 9.25/5.16         => ( ord_less_literal @ C @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2557_dual__order_Ostrict__trans1,axiom,
% 9.25/5.16      ! [B: filter_nat,A: filter_nat,C: filter_nat] :
% 9.25/5.16        ( ( ord_le2510731241096832064er_nat @ B @ A )
% 9.25/5.16       => ( ( ord_less_filter_nat @ C @ B )
% 9.25/5.16         => ( ord_less_filter_nat @ C @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2558_dual__order_Ostrict__trans1,axiom,
% 9.25/5.16      ! [B: set_nat,A: set_nat,C: set_nat] :
% 9.25/5.16        ( ( ord_less_eq_set_nat @ B @ A )
% 9.25/5.16       => ( ( ord_less_set_nat @ C @ B )
% 9.25/5.16         => ( ord_less_set_nat @ C @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2559_dual__order_Ostrict__trans1,axiom,
% 9.25/5.16      ! [B: rat,A: rat,C: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ B @ A )
% 9.25/5.16       => ( ( ord_less_rat @ C @ B )
% 9.25/5.16         => ( ord_less_rat @ C @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2560_dual__order_Ostrict__trans1,axiom,
% 9.25/5.16      ! [B: nat,A: nat,C: nat] :
% 9.25/5.16        ( ( ord_less_eq_nat @ B @ A )
% 9.25/5.16       => ( ( ord_less_nat @ C @ B )
% 9.25/5.16         => ( ord_less_nat @ C @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2561_dual__order_Ostrict__trans1,axiom,
% 9.25/5.16      ! [B: int,A: int,C: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ B @ A )
% 9.25/5.16       => ( ( ord_less_int @ C @ B )
% 9.25/5.16         => ( ord_less_int @ C @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2562_order_Ostrict__implies__not__eq,axiom,
% 9.25/5.16      ! [A: literal,B: literal] :
% 9.25/5.16        ( ( ord_less_literal @ A @ B )
% 9.25/5.16       => ( A != B ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2563_order_Ostrict__implies__not__eq,axiom,
% 9.25/5.16      ! [A: rat,B: rat] :
% 9.25/5.16        ( ( ord_less_rat @ A @ B )
% 9.25/5.16       => ( A != B ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2564_order_Ostrict__implies__not__eq,axiom,
% 9.25/5.16      ! [A: nat,B: nat] :
% 9.25/5.16        ( ( ord_less_nat @ A @ B )
% 9.25/5.16       => ( A != B ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2565_order_Ostrict__implies__not__eq,axiom,
% 9.25/5.16      ! [A: int,B: int] :
% 9.25/5.16        ( ( ord_less_int @ A @ B )
% 9.25/5.16       => ( A != B ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2566_dual__order_Ostrict__iff__order,axiom,
% 9.25/5.16      ( ord_less_literal
% 9.25/5.16      = ( ^ [B3: literal,A3: literal] :
% 9.25/5.16            ( ( ord_less_eq_literal @ B3 @ A3 )
% 9.25/5.16            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2567_dual__order_Ostrict__iff__order,axiom,
% 9.25/5.16      ( ord_less_filter_nat
% 9.25/5.16      = ( ^ [B3: filter_nat,A3: filter_nat] :
% 9.25/5.16            ( ( ord_le2510731241096832064er_nat @ B3 @ A3 )
% 9.25/5.16            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2568_dual__order_Ostrict__iff__order,axiom,
% 9.25/5.16      ( ord_less_set_nat
% 9.25/5.16      = ( ^ [B3: set_nat,A3: set_nat] :
% 9.25/5.16            ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 9.25/5.16            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2569_dual__order_Ostrict__iff__order,axiom,
% 9.25/5.16      ( ord_less_rat
% 9.25/5.16      = ( ^ [B3: rat,A3: rat] :
% 9.25/5.16            ( ( ord_less_eq_rat @ B3 @ A3 )
% 9.25/5.16            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2570_dual__order_Ostrict__iff__order,axiom,
% 9.25/5.16      ( ord_less_nat
% 9.25/5.16      = ( ^ [B3: nat,A3: nat] :
% 9.25/5.16            ( ( ord_less_eq_nat @ B3 @ A3 )
% 9.25/5.16            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2571_dual__order_Ostrict__iff__order,axiom,
% 9.25/5.16      ( ord_less_int
% 9.25/5.16      = ( ^ [B3: int,A3: int] :
% 9.25/5.16            ( ( ord_less_eq_int @ B3 @ A3 )
% 9.25/5.16            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2572_dual__order_Oorder__iff__strict,axiom,
% 9.25/5.16      ( ord_less_eq_literal
% 9.25/5.16      = ( ^ [B3: literal,A3: literal] :
% 9.25/5.16            ( ( ord_less_literal @ B3 @ A3 )
% 9.25/5.16            | ( A3 = B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2573_dual__order_Oorder__iff__strict,axiom,
% 9.25/5.16      ( ord_le2510731241096832064er_nat
% 9.25/5.16      = ( ^ [B3: filter_nat,A3: filter_nat] :
% 9.25/5.16            ( ( ord_less_filter_nat @ B3 @ A3 )
% 9.25/5.16            | ( A3 = B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2574_dual__order_Oorder__iff__strict,axiom,
% 9.25/5.16      ( ord_less_eq_set_nat
% 9.25/5.16      = ( ^ [B3: set_nat,A3: set_nat] :
% 9.25/5.16            ( ( ord_less_set_nat @ B3 @ A3 )
% 9.25/5.16            | ( A3 = B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2575_dual__order_Oorder__iff__strict,axiom,
% 9.25/5.16      ( ord_less_eq_rat
% 9.25/5.16      = ( ^ [B3: rat,A3: rat] :
% 9.25/5.16            ( ( ord_less_rat @ B3 @ A3 )
% 9.25/5.16            | ( A3 = B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2576_dual__order_Oorder__iff__strict,axiom,
% 9.25/5.16      ( ord_less_eq_nat
% 9.25/5.16      = ( ^ [B3: nat,A3: nat] :
% 9.25/5.16            ( ( ord_less_nat @ B3 @ A3 )
% 9.25/5.16            | ( A3 = B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2577_dual__order_Oorder__iff__strict,axiom,
% 9.25/5.16      ( ord_less_eq_int
% 9.25/5.16      = ( ^ [B3: int,A3: int] :
% 9.25/5.16            ( ( ord_less_int @ B3 @ A3 )
% 9.25/5.16            | ( A3 = B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2578_dual__order_Ostrict__trans,axiom,
% 9.25/5.16      ! [B: literal,A: literal,C: literal] :
% 9.25/5.16        ( ( ord_less_literal @ B @ A )
% 9.25/5.16       => ( ( ord_less_literal @ C @ B )
% 9.25/5.16         => ( ord_less_literal @ C @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2579_dual__order_Ostrict__trans,axiom,
% 9.25/5.16      ! [B: rat,A: rat,C: rat] :
% 9.25/5.16        ( ( ord_less_rat @ B @ A )
% 9.25/5.16       => ( ( ord_less_rat @ C @ B )
% 9.25/5.16         => ( ord_less_rat @ C @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2580_dual__order_Ostrict__trans,axiom,
% 9.25/5.16      ! [B: nat,A: nat,C: nat] :
% 9.25/5.16        ( ( ord_less_nat @ B @ A )
% 9.25/5.16       => ( ( ord_less_nat @ C @ B )
% 9.25/5.16         => ( ord_less_nat @ C @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2581_dual__order_Ostrict__trans,axiom,
% 9.25/5.16      ! [B: int,A: int,C: int] :
% 9.25/5.16        ( ( ord_less_int @ B @ A )
% 9.25/5.16       => ( ( ord_less_int @ C @ B )
% 9.25/5.16         => ( ord_less_int @ C @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2582_dense__le__bounded,axiom,
% 9.25/5.16      ! [X: rat,Y: rat,Z: rat] :
% 9.25/5.16        ( ( ord_less_rat @ X @ Y )
% 9.25/5.16       => ( ! [W2: rat] :
% 9.25/5.16              ( ( ord_less_rat @ X @ W2 )
% 9.25/5.16             => ( ( ord_less_rat @ W2 @ Y )
% 9.25/5.16               => ( ord_less_eq_rat @ W2 @ Z ) ) )
% 9.25/5.16         => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2583_dense__ge__bounded,axiom,
% 9.25/5.16      ! [Z: rat,X: rat,Y: rat] :
% 9.25/5.16        ( ( ord_less_rat @ Z @ X )
% 9.25/5.16       => ( ! [W2: rat] :
% 9.25/5.16              ( ( ord_less_rat @ Z @ W2 )
% 9.25/5.16             => ( ( ord_less_rat @ W2 @ X )
% 9.25/5.16               => ( ord_less_eq_rat @ Y @ W2 ) ) )
% 9.25/5.16         => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2584_not__less__iff__gr__or__eq,axiom,
% 9.25/5.16      ! [X: literal,Y: literal] :
% 9.25/5.16        ( ( ~ ( ord_less_literal @ X @ Y ) )
% 9.25/5.16        = ( ( ord_less_literal @ Y @ X )
% 9.25/5.16          | ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2585_not__less__iff__gr__or__eq,axiom,
% 9.25/5.16      ! [X: rat,Y: rat] :
% 9.25/5.16        ( ( ~ ( ord_less_rat @ X @ Y ) )
% 9.25/5.16        = ( ( ord_less_rat @ Y @ X )
% 9.25/5.16          | ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2586_not__less__iff__gr__or__eq,axiom,
% 9.25/5.16      ! [X: nat,Y: nat] :
% 9.25/5.16        ( ( ~ ( ord_less_nat @ X @ Y ) )
% 9.25/5.16        = ( ( ord_less_nat @ Y @ X )
% 9.25/5.16          | ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2587_not__less__iff__gr__or__eq,axiom,
% 9.25/5.16      ! [X: int,Y: int] :
% 9.25/5.16        ( ( ~ ( ord_less_int @ X @ Y ) )
% 9.25/5.16        = ( ( ord_less_int @ Y @ X )
% 9.25/5.16          | ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2588_order_Ostrict__iff__not,axiom,
% 9.25/5.16      ( ord_less_literal
% 9.25/5.16      = ( ^ [A3: literal,B3: literal] :
% 9.25/5.16            ( ( ord_less_eq_literal @ A3 @ B3 )
% 9.25/5.16            & ~ ( ord_less_eq_literal @ B3 @ A3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2589_order_Ostrict__iff__not,axiom,
% 9.25/5.16      ( ord_less_filter_nat
% 9.25/5.16      = ( ^ [A3: filter_nat,B3: filter_nat] :
% 9.25/5.16            ( ( ord_le2510731241096832064er_nat @ A3 @ B3 )
% 9.25/5.16            & ~ ( ord_le2510731241096832064er_nat @ B3 @ A3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2590_order_Ostrict__iff__not,axiom,
% 9.25/5.16      ( ord_less_set_nat
% 9.25/5.16      = ( ^ [A3: set_nat,B3: set_nat] :
% 9.25/5.16            ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 9.25/5.16            & ~ ( ord_less_eq_set_nat @ B3 @ A3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2591_order_Ostrict__iff__not,axiom,
% 9.25/5.16      ( ord_less_rat
% 9.25/5.16      = ( ^ [A3: rat,B3: rat] :
% 9.25/5.16            ( ( ord_less_eq_rat @ A3 @ B3 )
% 9.25/5.16            & ~ ( ord_less_eq_rat @ B3 @ A3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2592_order_Ostrict__iff__not,axiom,
% 9.25/5.16      ( ord_less_nat
% 9.25/5.16      = ( ^ [A3: nat,B3: nat] :
% 9.25/5.16            ( ( ord_less_eq_nat @ A3 @ B3 )
% 9.25/5.16            & ~ ( ord_less_eq_nat @ B3 @ A3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2593_order_Ostrict__iff__not,axiom,
% 9.25/5.16      ( ord_less_int
% 9.25/5.16      = ( ^ [A3: int,B3: int] :
% 9.25/5.16            ( ( ord_less_eq_int @ A3 @ B3 )
% 9.25/5.16            & ~ ( ord_less_eq_int @ B3 @ A3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2594_order_Ostrict__trans2,axiom,
% 9.25/5.16      ! [A: literal,B: literal,C: literal] :
% 9.25/5.16        ( ( ord_less_literal @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_literal @ B @ C )
% 9.25/5.16         => ( ord_less_literal @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2595_order_Ostrict__trans2,axiom,
% 9.25/5.16      ! [A: filter_nat,B: filter_nat,C: filter_nat] :
% 9.25/5.16        ( ( ord_less_filter_nat @ A @ B )
% 9.25/5.16       => ( ( ord_le2510731241096832064er_nat @ B @ C )
% 9.25/5.16         => ( ord_less_filter_nat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2596_order_Ostrict__trans2,axiom,
% 9.25/5.16      ! [A: set_nat,B: set_nat,C: set_nat] :
% 9.25/5.16        ( ( ord_less_set_nat @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_set_nat @ B @ C )
% 9.25/5.16         => ( ord_less_set_nat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2597_order_Ostrict__trans2,axiom,
% 9.25/5.16      ! [A: rat,B: rat,C: rat] :
% 9.25/5.16        ( ( ord_less_rat @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_rat @ B @ C )
% 9.25/5.16         => ( ord_less_rat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2598_order_Ostrict__trans2,axiom,
% 9.25/5.16      ! [A: nat,B: nat,C: nat] :
% 9.25/5.16        ( ( ord_less_nat @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_nat @ B @ C )
% 9.25/5.16         => ( ord_less_nat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2599_order_Ostrict__trans2,axiom,
% 9.25/5.16      ! [A: int,B: int,C: int] :
% 9.25/5.16        ( ( ord_less_int @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_int @ B @ C )
% 9.25/5.16         => ( ord_less_int @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2600_order_Ostrict__trans1,axiom,
% 9.25/5.16      ! [A: literal,B: literal,C: literal] :
% 9.25/5.16        ( ( ord_less_eq_literal @ A @ B )
% 9.25/5.16       => ( ( ord_less_literal @ B @ C )
% 9.25/5.16         => ( ord_less_literal @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2601_order_Ostrict__trans1,axiom,
% 9.25/5.16      ! [A: filter_nat,B: filter_nat,C: filter_nat] :
% 9.25/5.16        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 9.25/5.16       => ( ( ord_less_filter_nat @ B @ C )
% 9.25/5.16         => ( ord_less_filter_nat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2602_order_Ostrict__trans1,axiom,
% 9.25/5.16      ! [A: set_nat,B: set_nat,C: set_nat] :
% 9.25/5.16        ( ( ord_less_eq_set_nat @ A @ B )
% 9.25/5.16       => ( ( ord_less_set_nat @ B @ C )
% 9.25/5.16         => ( ord_less_set_nat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2603_order_Ostrict__trans1,axiom,
% 9.25/5.16      ! [A: rat,B: rat,C: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.16       => ( ( ord_less_rat @ B @ C )
% 9.25/5.16         => ( ord_less_rat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2604_order_Ostrict__trans1,axiom,
% 9.25/5.16      ! [A: nat,B: nat,C: nat] :
% 9.25/5.16        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.16       => ( ( ord_less_nat @ B @ C )
% 9.25/5.16         => ( ord_less_nat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2605_order_Ostrict__trans1,axiom,
% 9.25/5.16      ! [A: int,B: int,C: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.16       => ( ( ord_less_int @ B @ C )
% 9.25/5.16         => ( ord_less_int @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2606_order_Ostrict__iff__order,axiom,
% 9.25/5.16      ( ord_less_literal
% 9.25/5.16      = ( ^ [A3: literal,B3: literal] :
% 9.25/5.16            ( ( ord_less_eq_literal @ A3 @ B3 )
% 9.25/5.16            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2607_order_Ostrict__iff__order,axiom,
% 9.25/5.16      ( ord_less_filter_nat
% 9.25/5.16      = ( ^ [A3: filter_nat,B3: filter_nat] :
% 9.25/5.16            ( ( ord_le2510731241096832064er_nat @ A3 @ B3 )
% 9.25/5.16            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2608_order_Ostrict__iff__order,axiom,
% 9.25/5.16      ( ord_less_set_nat
% 9.25/5.16      = ( ^ [A3: set_nat,B3: set_nat] :
% 9.25/5.16            ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 9.25/5.16            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2609_order_Ostrict__iff__order,axiom,
% 9.25/5.16      ( ord_less_rat
% 9.25/5.16      = ( ^ [A3: rat,B3: rat] :
% 9.25/5.16            ( ( ord_less_eq_rat @ A3 @ B3 )
% 9.25/5.16            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2610_order_Ostrict__iff__order,axiom,
% 9.25/5.16      ( ord_less_nat
% 9.25/5.16      = ( ^ [A3: nat,B3: nat] :
% 9.25/5.16            ( ( ord_less_eq_nat @ A3 @ B3 )
% 9.25/5.16            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2611_order_Ostrict__iff__order,axiom,
% 9.25/5.16      ( ord_less_int
% 9.25/5.16      = ( ^ [A3: int,B3: int] :
% 9.25/5.16            ( ( ord_less_eq_int @ A3 @ B3 )
% 9.25/5.16            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2612_order_Oorder__iff__strict,axiom,
% 9.25/5.16      ( ord_less_eq_literal
% 9.25/5.16      = ( ^ [A3: literal,B3: literal] :
% 9.25/5.16            ( ( ord_less_literal @ A3 @ B3 )
% 9.25/5.16            | ( A3 = B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2613_order_Oorder__iff__strict,axiom,
% 9.25/5.16      ( ord_le2510731241096832064er_nat
% 9.25/5.16      = ( ^ [A3: filter_nat,B3: filter_nat] :
% 9.25/5.16            ( ( ord_less_filter_nat @ A3 @ B3 )
% 9.25/5.16            | ( A3 = B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2614_order_Oorder__iff__strict,axiom,
% 9.25/5.16      ( ord_less_eq_set_nat
% 9.25/5.16      = ( ^ [A3: set_nat,B3: set_nat] :
% 9.25/5.16            ( ( ord_less_set_nat @ A3 @ B3 )
% 9.25/5.16            | ( A3 = B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2615_order_Oorder__iff__strict,axiom,
% 9.25/5.16      ( ord_less_eq_rat
% 9.25/5.16      = ( ^ [A3: rat,B3: rat] :
% 9.25/5.16            ( ( ord_less_rat @ A3 @ B3 )
% 9.25/5.16            | ( A3 = B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2616_order_Oorder__iff__strict,axiom,
% 9.25/5.16      ( ord_less_eq_nat
% 9.25/5.16      = ( ^ [A3: nat,B3: nat] :
% 9.25/5.16            ( ( ord_less_nat @ A3 @ B3 )
% 9.25/5.16            | ( A3 = B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2617_order_Oorder__iff__strict,axiom,
% 9.25/5.16      ( ord_less_eq_int
% 9.25/5.16      = ( ^ [A3: int,B3: int] :
% 9.25/5.16            ( ( ord_less_int @ A3 @ B3 )
% 9.25/5.16            | ( A3 = B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2618_order_Ostrict__trans,axiom,
% 9.25/5.16      ! [A: literal,B: literal,C: literal] :
% 9.25/5.16        ( ( ord_less_literal @ A @ B )
% 9.25/5.16       => ( ( ord_less_literal @ B @ C )
% 9.25/5.16         => ( ord_less_literal @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2619_order_Ostrict__trans,axiom,
% 9.25/5.16      ! [A: rat,B: rat,C: rat] :
% 9.25/5.16        ( ( ord_less_rat @ A @ B )
% 9.25/5.16       => ( ( ord_less_rat @ B @ C )
% 9.25/5.16         => ( ord_less_rat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2620_order_Ostrict__trans,axiom,
% 9.25/5.16      ! [A: nat,B: nat,C: nat] :
% 9.25/5.16        ( ( ord_less_nat @ A @ B )
% 9.25/5.16       => ( ( ord_less_nat @ B @ C )
% 9.25/5.16         => ( ord_less_nat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2621_order_Ostrict__trans,axiom,
% 9.25/5.16      ! [A: int,B: int,C: int] :
% 9.25/5.16        ( ( ord_less_int @ A @ B )
% 9.25/5.16       => ( ( ord_less_int @ B @ C )
% 9.25/5.16         => ( ord_less_int @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2622_linorder__less__wlog,axiom,
% 9.25/5.16      ! [P: literal > literal > $o,A: literal,B: literal] :
% 9.25/5.16        ( ! [A6: literal,B6: literal] :
% 9.25/5.16            ( ( ord_less_literal @ A6 @ B6 )
% 9.25/5.16           => ( P @ A6 @ B6 ) )
% 9.25/5.16       => ( ! [A6: literal] : ( P @ A6 @ A6 )
% 9.25/5.16         => ( ! [A6: literal,B6: literal] :
% 9.25/5.16                ( ( P @ B6 @ A6 )
% 9.25/5.16               => ( P @ A6 @ B6 ) )
% 9.25/5.16           => ( P @ A @ B ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2623_linorder__less__wlog,axiom,
% 9.25/5.16      ! [P: rat > rat > $o,A: rat,B: rat] :
% 9.25/5.16        ( ! [A6: rat,B6: rat] :
% 9.25/5.16            ( ( ord_less_rat @ A6 @ B6 )
% 9.25/5.16           => ( P @ A6 @ B6 ) )
% 9.25/5.16       => ( ! [A6: rat] : ( P @ A6 @ A6 )
% 9.25/5.16         => ( ! [A6: rat,B6: rat] :
% 9.25/5.16                ( ( P @ B6 @ A6 )
% 9.25/5.16               => ( P @ A6 @ B6 ) )
% 9.25/5.16           => ( P @ A @ B ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2624_linorder__less__wlog,axiom,
% 9.25/5.16      ! [P: nat > nat > $o,A: nat,B: nat] :
% 9.25/5.16        ( ! [A6: nat,B6: nat] :
% 9.25/5.16            ( ( ord_less_nat @ A6 @ B6 )
% 9.25/5.16           => ( P @ A6 @ B6 ) )
% 9.25/5.16       => ( ! [A6: nat] : ( P @ A6 @ A6 )
% 9.25/5.16         => ( ! [A6: nat,B6: nat] :
% 9.25/5.16                ( ( P @ B6 @ A6 )
% 9.25/5.16               => ( P @ A6 @ B6 ) )
% 9.25/5.16           => ( P @ A @ B ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2625_linorder__less__wlog,axiom,
% 9.25/5.16      ! [P: int > int > $o,A: int,B: int] :
% 9.25/5.16        ( ! [A6: int,B6: int] :
% 9.25/5.16            ( ( ord_less_int @ A6 @ B6 )
% 9.25/5.16           => ( P @ A6 @ B6 ) )
% 9.25/5.16       => ( ! [A6: int] : ( P @ A6 @ A6 )
% 9.25/5.16         => ( ! [A6: int,B6: int] :
% 9.25/5.16                ( ( P @ B6 @ A6 )
% 9.25/5.16               => ( P @ A6 @ B6 ) )
% 9.25/5.16           => ( P @ A @ B ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2626_exists__least__iff,axiom,
% 9.25/5.16      ( ( ^ [P5: nat > $o] :
% 9.25/5.16          ? [X6: nat] : ( P5 @ X6 ) )
% 9.25/5.16      = ( ^ [P2: nat > $o] :
% 9.25/5.16          ? [N2: nat] :
% 9.25/5.16            ( ( P2 @ N2 )
% 9.25/5.16            & ! [M2: nat] :
% 9.25/5.16                ( ( ord_less_nat @ M2 @ N2 )
% 9.25/5.16               => ~ ( P2 @ M2 ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2627_dual__order_Oirrefl,axiom,
% 9.25/5.16      ! [A: literal] :
% 9.25/5.16        ~ ( ord_less_literal @ A @ A ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2628_dual__order_Oirrefl,axiom,
% 9.25/5.16      ! [A: rat] :
% 9.25/5.16        ~ ( ord_less_rat @ A @ A ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2629_dual__order_Oirrefl,axiom,
% 9.25/5.16      ! [A: nat] :
% 9.25/5.16        ~ ( ord_less_nat @ A @ A ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2630_dual__order_Oirrefl,axiom,
% 9.25/5.16      ! [A: int] :
% 9.25/5.16        ~ ( ord_less_int @ A @ A ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2631_dual__order_Otrans,axiom,
% 9.25/5.16      ! [B: filter_nat,A: filter_nat,C: filter_nat] :
% 9.25/5.16        ( ( ord_le2510731241096832064er_nat @ B @ A )
% 9.25/5.16       => ( ( ord_le2510731241096832064er_nat @ C @ B )
% 9.25/5.16         => ( ord_le2510731241096832064er_nat @ C @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2632_dual__order_Otrans,axiom,
% 9.25/5.16      ! [B: set_nat,A: set_nat,C: set_nat] :
% 9.25/5.16        ( ( ord_less_eq_set_nat @ B @ A )
% 9.25/5.16       => ( ( ord_less_eq_set_nat @ C @ B )
% 9.25/5.16         => ( ord_less_eq_set_nat @ C @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2633_dual__order_Otrans,axiom,
% 9.25/5.16      ! [B: rat,A: rat,C: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ B @ A )
% 9.25/5.16       => ( ( ord_less_eq_rat @ C @ B )
% 9.25/5.16         => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2634_dual__order_Otrans,axiom,
% 9.25/5.16      ! [B: nat,A: nat,C: nat] :
% 9.25/5.16        ( ( ord_less_eq_nat @ B @ A )
% 9.25/5.16       => ( ( ord_less_eq_nat @ C @ B )
% 9.25/5.16         => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2635_dual__order_Otrans,axiom,
% 9.25/5.16      ! [B: int,A: int,C: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ B @ A )
% 9.25/5.16       => ( ( ord_less_eq_int @ C @ B )
% 9.25/5.16         => ( ord_less_eq_int @ C @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2636_dual__order_Oasym,axiom,
% 9.25/5.16      ! [B: literal,A: literal] :
% 9.25/5.16        ( ( ord_less_literal @ B @ A )
% 9.25/5.16       => ~ ( ord_less_literal @ A @ B ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2637_dual__order_Oasym,axiom,
% 9.25/5.16      ! [B: rat,A: rat] :
% 9.25/5.16        ( ( ord_less_rat @ B @ A )
% 9.25/5.16       => ~ ( ord_less_rat @ A @ B ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2638_dual__order_Oasym,axiom,
% 9.25/5.16      ! [B: nat,A: nat] :
% 9.25/5.16        ( ( ord_less_nat @ B @ A )
% 9.25/5.16       => ~ ( ord_less_nat @ A @ B ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2639_dual__order_Oasym,axiom,
% 9.25/5.16      ! [B: int,A: int] :
% 9.25/5.16        ( ( ord_less_int @ B @ A )
% 9.25/5.16       => ~ ( ord_less_int @ A @ B ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2640_dual__order_Oantisym,axiom,
% 9.25/5.16      ! [B: filter_nat,A: filter_nat] :
% 9.25/5.16        ( ( ord_le2510731241096832064er_nat @ B @ A )
% 9.25/5.16       => ( ( ord_le2510731241096832064er_nat @ A @ B )
% 9.25/5.16         => ( A = B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2641_dual__order_Oantisym,axiom,
% 9.25/5.16      ! [B: set_nat,A: set_nat] :
% 9.25/5.16        ( ( ord_less_eq_set_nat @ B @ A )
% 9.25/5.16       => ( ( ord_less_eq_set_nat @ A @ B )
% 9.25/5.16         => ( A = B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2642_dual__order_Oantisym,axiom,
% 9.25/5.16      ! [B: rat,A: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ B @ A )
% 9.25/5.16       => ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.16         => ( A = B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2643_dual__order_Oantisym,axiom,
% 9.25/5.16      ! [B: nat,A: nat] :
% 9.25/5.16        ( ( ord_less_eq_nat @ B @ A )
% 9.25/5.16       => ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.16         => ( A = B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2644_dual__order_Oantisym,axiom,
% 9.25/5.16      ! [B: int,A: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ B @ A )
% 9.25/5.16       => ( ( ord_less_eq_int @ A @ B )
% 9.25/5.16         => ( A = B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2645_not__le__imp__less,axiom,
% 9.25/5.16      ! [Y: literal,X: literal] :
% 9.25/5.16        ( ~ ( ord_less_eq_literal @ Y @ X )
% 9.25/5.16       => ( ord_less_literal @ X @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2646_not__le__imp__less,axiom,
% 9.25/5.16      ! [Y: rat,X: rat] :
% 9.25/5.16        ( ~ ( ord_less_eq_rat @ Y @ X )
% 9.25/5.16       => ( ord_less_rat @ X @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2647_not__le__imp__less,axiom,
% 9.25/5.16      ! [Y: nat,X: nat] :
% 9.25/5.16        ( ~ ( ord_less_eq_nat @ Y @ X )
% 9.25/5.16       => ( ord_less_nat @ X @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2648_not__le__imp__less,axiom,
% 9.25/5.16      ! [Y: int,X: int] :
% 9.25/5.16        ( ~ ( ord_less_eq_int @ Y @ X )
% 9.25/5.16       => ( ord_less_int @ X @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2649_less__le__not__le,axiom,
% 9.25/5.16      ( ord_less_literal
% 9.25/5.16      = ( ^ [X3: literal,Y3: literal] :
% 9.25/5.16            ( ( ord_less_eq_literal @ X3 @ Y3 )
% 9.25/5.16            & ~ ( ord_less_eq_literal @ Y3 @ X3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2650_less__le__not__le,axiom,
% 9.25/5.16      ( ord_less_filter_nat
% 9.25/5.16      = ( ^ [X3: filter_nat,Y3: filter_nat] :
% 9.25/5.16            ( ( ord_le2510731241096832064er_nat @ X3 @ Y3 )
% 9.25/5.16            & ~ ( ord_le2510731241096832064er_nat @ Y3 @ X3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2651_less__le__not__le,axiom,
% 9.25/5.16      ( ord_less_set_nat
% 9.25/5.16      = ( ^ [X3: set_nat,Y3: set_nat] :
% 9.25/5.16            ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 9.25/5.16            & ~ ( ord_less_eq_set_nat @ Y3 @ X3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2652_less__le__not__le,axiom,
% 9.25/5.16      ( ord_less_rat
% 9.25/5.16      = ( ^ [X3: rat,Y3: rat] :
% 9.25/5.16            ( ( ord_less_eq_rat @ X3 @ Y3 )
% 9.25/5.16            & ~ ( ord_less_eq_rat @ Y3 @ X3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2653_less__le__not__le,axiom,
% 9.25/5.16      ( ord_less_nat
% 9.25/5.16      = ( ^ [X3: nat,Y3: nat] :
% 9.25/5.16            ( ( ord_less_eq_nat @ X3 @ Y3 )
% 9.25/5.16            & ~ ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2654_less__le__not__le,axiom,
% 9.25/5.16      ( ord_less_int
% 9.25/5.16      = ( ^ [X3: int,Y3: int] :
% 9.25/5.16            ( ( ord_less_eq_int @ X3 @ Y3 )
% 9.25/5.16            & ~ ( ord_less_eq_int @ Y3 @ X3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2655_dual__order_Oeq__iff,axiom,
% 9.25/5.16      ( ( ^ [Y4: filter_nat,Z4: filter_nat] : ( Y4 = Z4 ) )
% 9.25/5.16      = ( ^ [A3: filter_nat,B3: filter_nat] :
% 9.25/5.16            ( ( ord_le2510731241096832064er_nat @ B3 @ A3 )
% 9.25/5.16            & ( ord_le2510731241096832064er_nat @ A3 @ B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2656_dual__order_Oeq__iff,axiom,
% 9.25/5.16      ( ( ^ [Y4: set_nat,Z4: set_nat] : ( Y4 = Z4 ) )
% 9.25/5.16      = ( ^ [A3: set_nat,B3: set_nat] :
% 9.25/5.16            ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 9.25/5.16            & ( ord_less_eq_set_nat @ A3 @ B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2657_dual__order_Oeq__iff,axiom,
% 9.25/5.16      ( ( ^ [Y4: rat,Z4: rat] : ( Y4 = Z4 ) )
% 9.25/5.16      = ( ^ [A3: rat,B3: rat] :
% 9.25/5.16            ( ( ord_less_eq_rat @ B3 @ A3 )
% 9.25/5.16            & ( ord_less_eq_rat @ A3 @ B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2658_dual__order_Oeq__iff,axiom,
% 9.25/5.16      ( ( ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 ) )
% 9.25/5.16      = ( ^ [A3: nat,B3: nat] :
% 9.25/5.16            ( ( ord_less_eq_nat @ B3 @ A3 )
% 9.25/5.16            & ( ord_less_eq_nat @ A3 @ B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2659_dual__order_Oeq__iff,axiom,
% 9.25/5.16      ( ( ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 9.25/5.16      = ( ^ [A3: int,B3: int] :
% 9.25/5.16            ( ( ord_less_eq_int @ B3 @ A3 )
% 9.25/5.16            & ( ord_less_eq_int @ A3 @ B3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2660_linorder__cases,axiom,
% 9.25/5.16      ! [X: literal,Y: literal] :
% 9.25/5.16        ( ~ ( ord_less_literal @ X @ Y )
% 9.25/5.16       => ( ( X != Y )
% 9.25/5.16         => ( ord_less_literal @ Y @ X ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2661_linorder__cases,axiom,
% 9.25/5.16      ! [X: rat,Y: rat] :
% 9.25/5.16        ( ~ ( ord_less_rat @ X @ Y )
% 9.25/5.16       => ( ( X != Y )
% 9.25/5.16         => ( ord_less_rat @ Y @ X ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2662_linorder__cases,axiom,
% 9.25/5.16      ! [X: nat,Y: nat] :
% 9.25/5.16        ( ~ ( ord_less_nat @ X @ Y )
% 9.25/5.16       => ( ( X != Y )
% 9.25/5.16         => ( ord_less_nat @ Y @ X ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2663_linorder__cases,axiom,
% 9.25/5.16      ! [X: int,Y: int] :
% 9.25/5.16        ( ~ ( ord_less_int @ X @ Y )
% 9.25/5.16       => ( ( X != Y )
% 9.25/5.16         => ( ord_less_int @ Y @ X ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2664_dense__le,axiom,
% 9.25/5.16      ! [Y: rat,Z: rat] :
% 9.25/5.16        ( ! [X2: rat] :
% 9.25/5.16            ( ( ord_less_rat @ X2 @ Y )
% 9.25/5.16           => ( ord_less_eq_rat @ X2 @ Z ) )
% 9.25/5.16       => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2665_dense__ge,axiom,
% 9.25/5.16      ! [Z: rat,Y: rat] :
% 9.25/5.16        ( ! [X2: rat] :
% 9.25/5.16            ( ( ord_less_rat @ Z @ X2 )
% 9.25/5.16           => ( ord_less_eq_rat @ Y @ X2 ) )
% 9.25/5.16       => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2666_linorder__wlog,axiom,
% 9.25/5.16      ! [P: rat > rat > $o,A: rat,B: rat] :
% 9.25/5.16        ( ! [A6: rat,B6: rat] :
% 9.25/5.16            ( ( ord_less_eq_rat @ A6 @ B6 )
% 9.25/5.16           => ( P @ A6 @ B6 ) )
% 9.25/5.16       => ( ! [A6: rat,B6: rat] :
% 9.25/5.16              ( ( P @ B6 @ A6 )
% 9.25/5.16             => ( P @ A6 @ B6 ) )
% 9.25/5.16         => ( P @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2667_linorder__wlog,axiom,
% 9.25/5.16      ! [P: nat > nat > $o,A: nat,B: nat] :
% 9.25/5.16        ( ! [A6: nat,B6: nat] :
% 9.25/5.16            ( ( ord_less_eq_nat @ A6 @ B6 )
% 9.25/5.16           => ( P @ A6 @ B6 ) )
% 9.25/5.16       => ( ! [A6: nat,B6: nat] :
% 9.25/5.16              ( ( P @ B6 @ A6 )
% 9.25/5.16             => ( P @ A6 @ B6 ) )
% 9.25/5.16         => ( P @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2668_linorder__wlog,axiom,
% 9.25/5.16      ! [P: int > int > $o,A: int,B: int] :
% 9.25/5.16        ( ! [A6: int,B6: int] :
% 9.25/5.16            ( ( ord_less_eq_int @ A6 @ B6 )
% 9.25/5.16           => ( P @ A6 @ B6 ) )
% 9.25/5.16       => ( ! [A6: int,B6: int] :
% 9.25/5.16              ( ( P @ B6 @ A6 )
% 9.25/5.16             => ( P @ A6 @ B6 ) )
% 9.25/5.16         => ( P @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2669_antisym__conv3,axiom,
% 9.25/5.16      ! [Y: literal,X: literal] :
% 9.25/5.16        ( ~ ( ord_less_literal @ Y @ X )
% 9.25/5.16       => ( ( ~ ( ord_less_literal @ X @ Y ) )
% 9.25/5.16          = ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2670_antisym__conv3,axiom,
% 9.25/5.16      ! [Y: rat,X: rat] :
% 9.25/5.16        ( ~ ( ord_less_rat @ Y @ X )
% 9.25/5.16       => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 9.25/5.16          = ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2671_antisym__conv3,axiom,
% 9.25/5.16      ! [Y: nat,X: nat] :
% 9.25/5.16        ( ~ ( ord_less_nat @ Y @ X )
% 9.25/5.16       => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 9.25/5.16          = ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2672_antisym__conv3,axiom,
% 9.25/5.16      ! [Y: int,X: int] :
% 9.25/5.16        ( ~ ( ord_less_int @ Y @ X )
% 9.25/5.16       => ( ( ~ ( ord_less_int @ X @ Y ) )
% 9.25/5.16          = ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2673_less__induct,axiom,
% 9.25/5.16      ! [P: nat > $o,A: nat] :
% 9.25/5.16        ( ! [X2: nat] :
% 9.25/5.16            ( ! [Y5: nat] :
% 9.25/5.16                ( ( ord_less_nat @ Y5 @ X2 )
% 9.25/5.16               => ( P @ Y5 ) )
% 9.25/5.16           => ( P @ X2 ) )
% 9.25/5.16       => ( P @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2674_ord__less__eq__trans,axiom,
% 9.25/5.16      ! [A: literal,B: literal,C: literal] :
% 9.25/5.16        ( ( ord_less_literal @ A @ B )
% 9.25/5.16       => ( ( B = C )
% 9.25/5.16         => ( ord_less_literal @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2675_ord__less__eq__trans,axiom,
% 9.25/5.16      ! [A: rat,B: rat,C: rat] :
% 9.25/5.16        ( ( ord_less_rat @ A @ B )
% 9.25/5.16       => ( ( B = C )
% 9.25/5.16         => ( ord_less_rat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2676_ord__less__eq__trans,axiom,
% 9.25/5.16      ! [A: nat,B: nat,C: nat] :
% 9.25/5.16        ( ( ord_less_nat @ A @ B )
% 9.25/5.16       => ( ( B = C )
% 9.25/5.16         => ( ord_less_nat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2677_ord__less__eq__trans,axiom,
% 9.25/5.16      ! [A: int,B: int,C: int] :
% 9.25/5.16        ( ( ord_less_int @ A @ B )
% 9.25/5.16       => ( ( B = C )
% 9.25/5.16         => ( ord_less_int @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2678_ord__eq__less__trans,axiom,
% 9.25/5.16      ! [A: literal,B: literal,C: literal] :
% 9.25/5.16        ( ( A = B )
% 9.25/5.16       => ( ( ord_less_literal @ B @ C )
% 9.25/5.16         => ( ord_less_literal @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2679_ord__eq__less__trans,axiom,
% 9.25/5.16      ! [A: rat,B: rat,C: rat] :
% 9.25/5.16        ( ( A = B )
% 9.25/5.16       => ( ( ord_less_rat @ B @ C )
% 9.25/5.16         => ( ord_less_rat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2680_ord__eq__less__trans,axiom,
% 9.25/5.16      ! [A: nat,B: nat,C: nat] :
% 9.25/5.16        ( ( A = B )
% 9.25/5.16       => ( ( ord_less_nat @ B @ C )
% 9.25/5.16         => ( ord_less_nat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2681_ord__eq__less__trans,axiom,
% 9.25/5.16      ! [A: int,B: int,C: int] :
% 9.25/5.16        ( ( A = B )
% 9.25/5.16       => ( ( ord_less_int @ B @ C )
% 9.25/5.16         => ( ord_less_int @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2682_order__trans,axiom,
% 9.25/5.16      ! [X: filter_nat,Y: filter_nat,Z: filter_nat] :
% 9.25/5.16        ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 9.25/5.16       => ( ( ord_le2510731241096832064er_nat @ Y @ Z )
% 9.25/5.16         => ( ord_le2510731241096832064er_nat @ X @ Z ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2683_order__trans,axiom,
% 9.25/5.16      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.25/5.16        ( ( ord_less_eq_set_nat @ X @ Y )
% 9.25/5.16       => ( ( ord_less_eq_set_nat @ Y @ Z )
% 9.25/5.16         => ( ord_less_eq_set_nat @ X @ Z ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2684_order__trans,axiom,
% 9.25/5.16      ! [X: rat,Y: rat,Z: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ X @ Y )
% 9.25/5.16       => ( ( ord_less_eq_rat @ Y @ Z )
% 9.25/5.16         => ( ord_less_eq_rat @ X @ Z ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2685_order__trans,axiom,
% 9.25/5.16      ! [X: nat,Y: nat,Z: nat] :
% 9.25/5.16        ( ( ord_less_eq_nat @ X @ Y )
% 9.25/5.16       => ( ( ord_less_eq_nat @ Y @ Z )
% 9.25/5.16         => ( ord_less_eq_nat @ X @ Z ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2686_order__trans,axiom,
% 9.25/5.16      ! [X: int,Y: int,Z: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ X @ Y )
% 9.25/5.16       => ( ( ord_less_eq_int @ Y @ Z )
% 9.25/5.16         => ( ord_less_eq_int @ X @ Z ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2687_order_Otrans,axiom,
% 9.25/5.16      ! [A: filter_nat,B: filter_nat,C: filter_nat] :
% 9.25/5.16        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 9.25/5.16       => ( ( ord_le2510731241096832064er_nat @ B @ C )
% 9.25/5.16         => ( ord_le2510731241096832064er_nat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2688_order_Otrans,axiom,
% 9.25/5.16      ! [A: set_nat,B: set_nat,C: set_nat] :
% 9.25/5.16        ( ( ord_less_eq_set_nat @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_set_nat @ B @ C )
% 9.25/5.16         => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2689_order_Otrans,axiom,
% 9.25/5.16      ! [A: rat,B: rat,C: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_rat @ B @ C )
% 9.25/5.16         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2690_order_Otrans,axiom,
% 9.25/5.16      ! [A: nat,B: nat,C: nat] :
% 9.25/5.16        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_nat @ B @ C )
% 9.25/5.16         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2691_order_Otrans,axiom,
% 9.25/5.16      ! [A: int,B: int,C: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_int @ B @ C )
% 9.25/5.16         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2692_order_Oasym,axiom,
% 9.25/5.16      ! [A: literal,B: literal] :
% 9.25/5.16        ( ( ord_less_literal @ A @ B )
% 9.25/5.16       => ~ ( ord_less_literal @ B @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2693_order_Oasym,axiom,
% 9.25/5.16      ! [A: rat,B: rat] :
% 9.25/5.16        ( ( ord_less_rat @ A @ B )
% 9.25/5.16       => ~ ( ord_less_rat @ B @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2694_order_Oasym,axiom,
% 9.25/5.16      ! [A: nat,B: nat] :
% 9.25/5.16        ( ( ord_less_nat @ A @ B )
% 9.25/5.16       => ~ ( ord_less_nat @ B @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2695_order_Oasym,axiom,
% 9.25/5.16      ! [A: int,B: int] :
% 9.25/5.16        ( ( ord_less_int @ A @ B )
% 9.25/5.16       => ~ ( ord_less_int @ B @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2696_order__antisym,axiom,
% 9.25/5.16      ! [X: filter_nat,Y: filter_nat] :
% 9.25/5.16        ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 9.25/5.16       => ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 9.25/5.16         => ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2697_order__antisym,axiom,
% 9.25/5.16      ! [X: set_nat,Y: set_nat] :
% 9.25/5.16        ( ( ord_less_eq_set_nat @ X @ Y )
% 9.25/5.16       => ( ( ord_less_eq_set_nat @ Y @ X )
% 9.25/5.16         => ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2698_order__antisym,axiom,
% 9.25/5.16      ! [X: rat,Y: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ X @ Y )
% 9.25/5.16       => ( ( ord_less_eq_rat @ Y @ X )
% 9.25/5.16         => ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2699_order__antisym,axiom,
% 9.25/5.16      ! [X: nat,Y: nat] :
% 9.25/5.16        ( ( ord_less_eq_nat @ X @ Y )
% 9.25/5.16       => ( ( ord_less_eq_nat @ Y @ X )
% 9.25/5.16         => ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2700_order__antisym,axiom,
% 9.25/5.16      ! [X: int,Y: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ X @ Y )
% 9.25/5.16       => ( ( ord_less_eq_int @ Y @ X )
% 9.25/5.16         => ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2701_antisym__conv2,axiom,
% 9.25/5.16      ! [X: literal,Y: literal] :
% 9.25/5.16        ( ( ord_less_eq_literal @ X @ Y )
% 9.25/5.16       => ( ( ~ ( ord_less_literal @ X @ Y ) )
% 9.25/5.16          = ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2702_antisym__conv2,axiom,
% 9.25/5.16      ! [X: filter_nat,Y: filter_nat] :
% 9.25/5.16        ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 9.25/5.16       => ( ( ~ ( ord_less_filter_nat @ X @ Y ) )
% 9.25/5.16          = ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2703_antisym__conv2,axiom,
% 9.25/5.16      ! [X: set_nat,Y: set_nat] :
% 9.25/5.16        ( ( ord_less_eq_set_nat @ X @ Y )
% 9.25/5.16       => ( ( ~ ( ord_less_set_nat @ X @ Y ) )
% 9.25/5.16          = ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2704_antisym__conv2,axiom,
% 9.25/5.16      ! [X: rat,Y: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ X @ Y )
% 9.25/5.16       => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 9.25/5.16          = ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2705_antisym__conv2,axiom,
% 9.25/5.16      ! [X: nat,Y: nat] :
% 9.25/5.16        ( ( ord_less_eq_nat @ X @ Y )
% 9.25/5.16       => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 9.25/5.16          = ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2706_antisym__conv2,axiom,
% 9.25/5.16      ! [X: int,Y: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ X @ Y )
% 9.25/5.16       => ( ( ~ ( ord_less_int @ X @ Y ) )
% 9.25/5.16          = ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2707_antisym__conv1,axiom,
% 9.25/5.16      ! [X: literal,Y: literal] :
% 9.25/5.16        ( ~ ( ord_less_literal @ X @ Y )
% 9.25/5.16       => ( ( ord_less_eq_literal @ X @ Y )
% 9.25/5.16          = ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2708_antisym__conv1,axiom,
% 9.25/5.16      ! [X: filter_nat,Y: filter_nat] :
% 9.25/5.16        ( ~ ( ord_less_filter_nat @ X @ Y )
% 9.25/5.16       => ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 9.25/5.16          = ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2709_antisym__conv1,axiom,
% 9.25/5.16      ! [X: set_nat,Y: set_nat] :
% 9.25/5.16        ( ~ ( ord_less_set_nat @ X @ Y )
% 9.25/5.16       => ( ( ord_less_eq_set_nat @ X @ Y )
% 9.25/5.16          = ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2710_antisym__conv1,axiom,
% 9.25/5.16      ! [X: rat,Y: rat] :
% 9.25/5.16        ( ~ ( ord_less_rat @ X @ Y )
% 9.25/5.16       => ( ( ord_less_eq_rat @ X @ Y )
% 9.25/5.16          = ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2711_antisym__conv1,axiom,
% 9.25/5.16      ! [X: nat,Y: nat] :
% 9.25/5.16        ( ~ ( ord_less_nat @ X @ Y )
% 9.25/5.16       => ( ( ord_less_eq_nat @ X @ Y )
% 9.25/5.16          = ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2712_antisym__conv1,axiom,
% 9.25/5.16      ! [X: int,Y: int] :
% 9.25/5.16        ( ~ ( ord_less_int @ X @ Y )
% 9.25/5.16       => ( ( ord_less_eq_int @ X @ Y )
% 9.25/5.16          = ( X = Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2713_ord__le__eq__trans,axiom,
% 9.25/5.16      ! [A: filter_nat,B: filter_nat,C: filter_nat] :
% 9.25/5.16        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 9.25/5.16       => ( ( B = C )
% 9.25/5.16         => ( ord_le2510731241096832064er_nat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2714_ord__le__eq__trans,axiom,
% 9.25/5.16      ! [A: set_nat,B: set_nat,C: set_nat] :
% 9.25/5.16        ( ( ord_less_eq_set_nat @ A @ B )
% 9.25/5.16       => ( ( B = C )
% 9.25/5.16         => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2715_ord__le__eq__trans,axiom,
% 9.25/5.16      ! [A: rat,B: rat,C: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.16       => ( ( B = C )
% 9.25/5.16         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2716_ord__le__eq__trans,axiom,
% 9.25/5.16      ! [A: nat,B: nat,C: nat] :
% 9.25/5.16        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.16       => ( ( B = C )
% 9.25/5.16         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2717_ord__le__eq__trans,axiom,
% 9.25/5.16      ! [A: int,B: int,C: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.16       => ( ( B = C )
% 9.25/5.16         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2718_ord__eq__le__trans,axiom,
% 9.25/5.16      ! [A: filter_nat,B: filter_nat,C: filter_nat] :
% 9.25/5.16        ( ( A = B )
% 9.25/5.16       => ( ( ord_le2510731241096832064er_nat @ B @ C )
% 9.25/5.16         => ( ord_le2510731241096832064er_nat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2719_ord__eq__le__trans,axiom,
% 9.25/5.16      ! [A: set_nat,B: set_nat,C: set_nat] :
% 9.25/5.16        ( ( A = B )
% 9.25/5.16       => ( ( ord_less_eq_set_nat @ B @ C )
% 9.25/5.16         => ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2720_ord__eq__le__trans,axiom,
% 9.25/5.16      ! [A: rat,B: rat,C: rat] :
% 9.25/5.16        ( ( A = B )
% 9.25/5.16       => ( ( ord_less_eq_rat @ B @ C )
% 9.25/5.16         => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2721_ord__eq__le__trans,axiom,
% 9.25/5.16      ! [A: nat,B: nat,C: nat] :
% 9.25/5.16        ( ( A = B )
% 9.25/5.16       => ( ( ord_less_eq_nat @ B @ C )
% 9.25/5.16         => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2722_ord__eq__le__trans,axiom,
% 9.25/5.16      ! [A: int,B: int,C: int] :
% 9.25/5.16        ( ( A = B )
% 9.25/5.16       => ( ( ord_less_eq_int @ B @ C )
% 9.25/5.16         => ( ord_less_eq_int @ A @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2723_order__class_Oorder__eq__iff,axiom,
% 9.25/5.16      ( ( ^ [Y4: filter_nat,Z4: filter_nat] : ( Y4 = Z4 ) )
% 9.25/5.16      = ( ^ [X3: filter_nat,Y3: filter_nat] :
% 9.25/5.16            ( ( ord_le2510731241096832064er_nat @ X3 @ Y3 )
% 9.25/5.16            & ( ord_le2510731241096832064er_nat @ Y3 @ X3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2724_order__class_Oorder__eq__iff,axiom,
% 9.25/5.16      ( ( ^ [Y4: set_nat,Z4: set_nat] : ( Y4 = Z4 ) )
% 9.25/5.16      = ( ^ [X3: set_nat,Y3: set_nat] :
% 9.25/5.16            ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 9.25/5.16            & ( ord_less_eq_set_nat @ Y3 @ X3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2725_order__class_Oorder__eq__iff,axiom,
% 9.25/5.16      ( ( ^ [Y4: rat,Z4: rat] : ( Y4 = Z4 ) )
% 9.25/5.16      = ( ^ [X3: rat,Y3: rat] :
% 9.25/5.16            ( ( ord_less_eq_rat @ X3 @ Y3 )
% 9.25/5.16            & ( ord_less_eq_rat @ Y3 @ X3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2726_order__class_Oorder__eq__iff,axiom,
% 9.25/5.16      ( ( ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 ) )
% 9.25/5.16      = ( ^ [X3: nat,Y3: nat] :
% 9.25/5.16            ( ( ord_less_eq_nat @ X3 @ Y3 )
% 9.25/5.16            & ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2727_order__class_Oorder__eq__iff,axiom,
% 9.25/5.16      ( ( ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 9.25/5.16      = ( ^ [X3: int,Y3: int] :
% 9.25/5.16            ( ( ord_less_eq_int @ X3 @ Y3 )
% 9.25/5.16            & ( ord_less_eq_int @ Y3 @ X3 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2728_less__imp__neq,axiom,
% 9.25/5.16      ! [X: literal,Y: literal] :
% 9.25/5.16        ( ( ord_less_literal @ X @ Y )
% 9.25/5.16       => ( X != Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2729_less__imp__neq,axiom,
% 9.25/5.16      ! [X: rat,Y: rat] :
% 9.25/5.16        ( ( ord_less_rat @ X @ Y )
% 9.25/5.16       => ( X != Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2730_less__imp__neq,axiom,
% 9.25/5.16      ! [X: nat,Y: nat] :
% 9.25/5.16        ( ( ord_less_nat @ X @ Y )
% 9.25/5.16       => ( X != Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2731_less__imp__neq,axiom,
% 9.25/5.16      ! [X: int,Y: int] :
% 9.25/5.16        ( ( ord_less_int @ X @ Y )
% 9.25/5.16       => ( X != Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2732_le__cases3,axiom,
% 9.25/5.16      ! [X: rat,Y: rat,Z: rat] :
% 9.25/5.16        ( ( ( ord_less_eq_rat @ X @ Y )
% 9.25/5.16         => ~ ( ord_less_eq_rat @ Y @ Z ) )
% 9.25/5.16       => ( ( ( ord_less_eq_rat @ Y @ X )
% 9.25/5.16           => ~ ( ord_less_eq_rat @ X @ Z ) )
% 9.25/5.16         => ( ( ( ord_less_eq_rat @ X @ Z )
% 9.25/5.16             => ~ ( ord_less_eq_rat @ Z @ Y ) )
% 9.25/5.16           => ( ( ( ord_less_eq_rat @ Z @ Y )
% 9.25/5.16               => ~ ( ord_less_eq_rat @ Y @ X ) )
% 9.25/5.16             => ( ( ( ord_less_eq_rat @ Y @ Z )
% 9.25/5.16                 => ~ ( ord_less_eq_rat @ Z @ X ) )
% 9.25/5.16               => ~ ( ( ord_less_eq_rat @ Z @ X )
% 9.25/5.16                   => ~ ( ord_less_eq_rat @ X @ Y ) ) ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2733_le__cases3,axiom,
% 9.25/5.16      ! [X: nat,Y: nat,Z: nat] :
% 9.25/5.16        ( ( ( ord_less_eq_nat @ X @ Y )
% 9.25/5.16         => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 9.25/5.16       => ( ( ( ord_less_eq_nat @ Y @ X )
% 9.25/5.16           => ~ ( ord_less_eq_nat @ X @ Z ) )
% 9.25/5.16         => ( ( ( ord_less_eq_nat @ X @ Z )
% 9.25/5.16             => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 9.25/5.16           => ( ( ( ord_less_eq_nat @ Z @ Y )
% 9.25/5.16               => ~ ( ord_less_eq_nat @ Y @ X ) )
% 9.25/5.16             => ( ( ( ord_less_eq_nat @ Y @ Z )
% 9.25/5.16                 => ~ ( ord_less_eq_nat @ Z @ X ) )
% 9.25/5.16               => ~ ( ( ord_less_eq_nat @ Z @ X )
% 9.25/5.16                   => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2734_le__cases3,axiom,
% 9.25/5.16      ! [X: int,Y: int,Z: int] :
% 9.25/5.16        ( ( ( ord_less_eq_int @ X @ Y )
% 9.25/5.16         => ~ ( ord_less_eq_int @ Y @ Z ) )
% 9.25/5.16       => ( ( ( ord_less_eq_int @ Y @ X )
% 9.25/5.16           => ~ ( ord_less_eq_int @ X @ Z ) )
% 9.25/5.16         => ( ( ( ord_less_eq_int @ X @ Z )
% 9.25/5.16             => ~ ( ord_less_eq_int @ Z @ Y ) )
% 9.25/5.16           => ( ( ( ord_less_eq_int @ Z @ Y )
% 9.25/5.16               => ~ ( ord_less_eq_int @ Y @ X ) )
% 9.25/5.16             => ( ( ( ord_less_eq_int @ Y @ Z )
% 9.25/5.16                 => ~ ( ord_less_eq_int @ Z @ X ) )
% 9.25/5.16               => ~ ( ( ord_less_eq_int @ Z @ X )
% 9.25/5.16                   => ~ ( ord_less_eq_int @ X @ Y ) ) ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2735_dense,axiom,
% 9.25/5.16      ! [X: rat,Y: rat] :
% 9.25/5.16        ( ( ord_less_rat @ X @ Y )
% 9.25/5.16       => ? [Z2: rat] :
% 9.25/5.16            ( ( ord_less_rat @ X @ Z2 )
% 9.25/5.16            & ( ord_less_rat @ Z2 @ Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2736_nle__le,axiom,
% 9.25/5.16      ! [A: rat,B: rat] :
% 9.25/5.16        ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 9.25/5.16        = ( ( ord_less_eq_rat @ B @ A )
% 9.25/5.16          & ( B != A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2737_nle__le,axiom,
% 9.25/5.16      ! [A: nat,B: nat] :
% 9.25/5.16        ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 9.25/5.16        = ( ( ord_less_eq_nat @ B @ A )
% 9.25/5.16          & ( B != A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2738_nle__le,axiom,
% 9.25/5.16      ! [A: int,B: int] :
% 9.25/5.16        ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 9.25/5.16        = ( ( ord_less_eq_int @ B @ A )
% 9.25/5.16          & ( B != A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2739_nless__le,axiom,
% 9.25/5.16      ! [A: literal,B: literal] :
% 9.25/5.16        ( ( ~ ( ord_less_literal @ A @ B ) )
% 9.25/5.16        = ( ~ ( ord_less_eq_literal @ A @ B )
% 9.25/5.16          | ( A = B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2740_nless__le,axiom,
% 9.25/5.16      ! [A: filter_nat,B: filter_nat] :
% 9.25/5.16        ( ( ~ ( ord_less_filter_nat @ A @ B ) )
% 9.25/5.16        = ( ~ ( ord_le2510731241096832064er_nat @ A @ B )
% 9.25/5.16          | ( A = B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2741_nless__le,axiom,
% 9.25/5.16      ! [A: set_nat,B: set_nat] :
% 9.25/5.16        ( ( ~ ( ord_less_set_nat @ A @ B ) )
% 9.25/5.16        = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 9.25/5.16          | ( A = B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2742_nless__le,axiom,
% 9.25/5.16      ! [A: rat,B: rat] :
% 9.25/5.16        ( ( ~ ( ord_less_rat @ A @ B ) )
% 9.25/5.16        = ( ~ ( ord_less_eq_rat @ A @ B )
% 9.25/5.16          | ( A = B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2743_nless__le,axiom,
% 9.25/5.16      ! [A: nat,B: nat] :
% 9.25/5.16        ( ( ~ ( ord_less_nat @ A @ B ) )
% 9.25/5.16        = ( ~ ( ord_less_eq_nat @ A @ B )
% 9.25/5.16          | ( A = B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2744_nless__le,axiom,
% 9.25/5.16      ! [A: int,B: int] :
% 9.25/5.16        ( ( ~ ( ord_less_int @ A @ B ) )
% 9.25/5.16        = ( ~ ( ord_less_eq_int @ A @ B )
% 9.25/5.16          | ( A = B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2745_gt__ex,axiom,
% 9.25/5.16      ! [X: rat] :
% 9.25/5.16      ? [X_1: rat] : ( ord_less_rat @ X @ X_1 ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2746_gt__ex,axiom,
% 9.25/5.16      ! [X: nat] :
% 9.25/5.16      ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2747_gt__ex,axiom,
% 9.25/5.16      ! [X: int] :
% 9.25/5.16      ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2748_lt__ex,axiom,
% 9.25/5.16      ! [X: rat] :
% 9.25/5.16      ? [Y2: rat] : ( ord_less_rat @ Y2 @ X ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2749_lt__ex,axiom,
% 9.25/5.16      ! [X: int] :
% 9.25/5.16      ? [Y2: int] : ( ord_less_int @ Y2 @ X ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2750_leI,axiom,
% 9.25/5.16      ! [X: literal,Y: literal] :
% 9.25/5.16        ( ~ ( ord_less_literal @ X @ Y )
% 9.25/5.16       => ( ord_less_eq_literal @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2751_leI,axiom,
% 9.25/5.16      ! [X: rat,Y: rat] :
% 9.25/5.16        ( ~ ( ord_less_rat @ X @ Y )
% 9.25/5.16       => ( ord_less_eq_rat @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2752_leI,axiom,
% 9.25/5.16      ! [X: nat,Y: nat] :
% 9.25/5.16        ( ~ ( ord_less_nat @ X @ Y )
% 9.25/5.16       => ( ord_less_eq_nat @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2753_leI,axiom,
% 9.25/5.16      ! [X: int,Y: int] :
% 9.25/5.16        ( ~ ( ord_less_int @ X @ Y )
% 9.25/5.16       => ( ord_less_eq_int @ Y @ X ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2754_leD,axiom,
% 9.25/5.16      ! [Y: literal,X: literal] :
% 9.25/5.16        ( ( ord_less_eq_literal @ Y @ X )
% 9.25/5.16       => ~ ( ord_less_literal @ X @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2755_leD,axiom,
% 9.25/5.16      ! [Y: filter_nat,X: filter_nat] :
% 9.25/5.16        ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 9.25/5.16       => ~ ( ord_less_filter_nat @ X @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2756_leD,axiom,
% 9.25/5.16      ! [Y: set_nat,X: set_nat] :
% 9.25/5.16        ( ( ord_less_eq_set_nat @ Y @ X )
% 9.25/5.16       => ~ ( ord_less_set_nat @ X @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2757_leD,axiom,
% 9.25/5.16      ! [Y: rat,X: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ Y @ X )
% 9.25/5.16       => ~ ( ord_less_rat @ X @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2758_leD,axiom,
% 9.25/5.16      ! [Y: nat,X: nat] :
% 9.25/5.16        ( ( ord_less_eq_nat @ Y @ X )
% 9.25/5.16       => ~ ( ord_less_nat @ X @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2759_leD,axiom,
% 9.25/5.16      ! [Y: int,X: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ Y @ X )
% 9.25/5.16       => ~ ( ord_less_int @ X @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2760_pred__subset__eq2,axiom,
% 9.25/5.16      ! [R: set_Pr1281608226676607948nteger,S: set_Pr1281608226676607948nteger] :
% 9.25/5.16        ( ( ord_le4340812435750786203eger_o
% 9.25/5.16          @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ R )
% 9.25/5.16          @ ^ [X3: produc6241069584506657477e_term > option6357759511663192854e_term,Y3: produc8923325533196201883nteger] : ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X3 @ Y3 ) @ S ) )
% 9.25/5.16        = ( ord_le653643898420964396nteger @ R @ S ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2761_pred__subset__eq2,axiom,
% 9.25/5.16      ! [R: set_Pr3286484037609594932et_nat,S: set_Pr3286484037609594932et_nat] :
% 9.25/5.16        ( ( ord_le8000401564054156549_nat_o
% 9.25/5.16          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R )
% 9.25/5.16          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ S ) )
% 9.25/5.16        = ( ord_le5966269811547037844et_nat @ R @ S ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2762_pred__subset__eq2,axiom,
% 9.25/5.16      ! [R: set_Pr8536935166611901872et_nat,S: set_Pr8536935166611901872et_nat] :
% 9.25/5.16        ( ( ord_le6753239538765779593_nat_o
% 9.25/5.16          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R )
% 9.25/5.16          @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ S ) )
% 9.25/5.16        = ( ord_le4763372923235995152et_nat @ R @ S ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2763_pred__subset__eq2,axiom,
% 9.25/5.16      ! [R: set_Pr9222295170931077689nt_int,S: set_Pr9222295170931077689nt_int] :
% 9.25/5.16        ( ( ord_le5643404153117327598_int_o
% 9.25/5.16          @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ R )
% 9.25/5.16          @ ^ [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ S ) )
% 9.25/5.16        = ( ord_le8725513860283290265nt_int @ R @ S ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2764_pred__subset__eq2,axiom,
% 9.25/5.16      ! [R: set_Pr1872883991513573699nt_int,S: set_Pr1872883991513573699nt_int] :
% 9.25/5.16        ( ( ord_le2124322318746777828_int_o
% 9.25/5.16          @ ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ R )
% 9.25/5.16          @ ^ [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ S ) )
% 9.25/5.16        = ( ord_le135402666524580259nt_int @ R @ S ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2765_mult__less__le__imp__less,axiom,
% 9.25/5.16      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.25/5.16        ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.25/5.16       => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 9.25/5.16         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.16           => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.16             => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2766_mult__less__le__imp__less,axiom,
% 9.25/5.16      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.25/5.16        ( ( ord_less_rat @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_rat @ C @ D2 )
% 9.25/5.16         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.16           => ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.16             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2767_mult__less__le__imp__less,axiom,
% 9.25/5.16      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.25/5.16        ( ( ord_less_nat @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_nat @ C @ D2 )
% 9.25/5.16         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.25/5.16           => ( ( ord_less_nat @ zero_zero_nat @ C )
% 9.25/5.16             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2768_mult__less__le__imp__less,axiom,
% 9.25/5.16      ! [A: int,B: int,C: int,D2: int] :
% 9.25/5.16        ( ( ord_less_int @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_int @ C @ D2 )
% 9.25/5.16         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.16           => ( ( ord_less_int @ zero_zero_int @ C )
% 9.25/5.16             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2769_mult__le__less__imp__less,axiom,
% 9.25/5.16      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.25/5.16        ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.25/5.16       => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 9.25/5.16         => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.16           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.16             => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2770_mult__le__less__imp__less,axiom,
% 9.25/5.16      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.16       => ( ( ord_less_rat @ C @ D2 )
% 9.25/5.16         => ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.16           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.25/5.16             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2771_mult__le__less__imp__less,axiom,
% 9.25/5.16      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.25/5.16        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.16       => ( ( ord_less_nat @ C @ D2 )
% 9.25/5.16         => ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.25/5.16           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.25/5.16             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2772_mult__le__less__imp__less,axiom,
% 9.25/5.16      ! [A: int,B: int,C: int,D2: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.16       => ( ( ord_less_int @ C @ D2 )
% 9.25/5.16         => ( ( ord_less_int @ zero_zero_int @ A )
% 9.25/5.16           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.25/5.16             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2773_mult__right__le__imp__le,axiom,
% 9.25/5.16      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.25/5.16        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.25/5.16       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.16         => ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2774_mult__right__le__imp__le,axiom,
% 9.25/5.16      ! [A: rat,C: rat,B: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 9.25/5.16       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.16         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2775_mult__right__le__imp__le,axiom,
% 9.25/5.16      ! [A: nat,C: nat,B: nat] :
% 9.25/5.16        ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 9.25/5.16       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 9.25/5.16         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2776_mult__right__le__imp__le,axiom,
% 9.25/5.16      ! [A: int,C: int,B: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 9.25/5.16       => ( ( ord_less_int @ zero_zero_int @ C )
% 9.25/5.16         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2777_mult__left__le__imp__le,axiom,
% 9.25/5.16      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.16        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 9.25/5.16       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.16         => ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2778_mult__left__le__imp__le,axiom,
% 9.25/5.16      ! [C: rat,A: rat,B: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.25/5.16       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.16         => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2779_mult__left__le__imp__le,axiom,
% 9.25/5.16      ! [C: nat,A: nat,B: nat] :
% 9.25/5.16        ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 9.25/5.16       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 9.25/5.16         => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2780_mult__left__le__imp__le,axiom,
% 9.25/5.16      ! [C: int,A: int,B: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.25/5.16       => ( ( ord_less_int @ zero_zero_int @ C )
% 9.25/5.16         => ( ord_less_eq_int @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2781_mult__le__cancel__left__pos,axiom,
% 9.25/5.16      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.16        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.16       => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 9.25/5.16          = ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2782_mult__le__cancel__left__pos,axiom,
% 9.25/5.16      ! [C: rat,A: rat,B: rat] :
% 9.25/5.16        ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.16       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.25/5.16          = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2783_mult__le__cancel__left__pos,axiom,
% 9.25/5.16      ! [C: int,A: int,B: int] :
% 9.25/5.16        ( ( ord_less_int @ zero_zero_int @ C )
% 9.25/5.16       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.25/5.16          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2784_mult__le__cancel__left__neg,axiom,
% 9.25/5.16      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.16        ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 9.25/5.16       => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 9.25/5.16          = ( ord_le3102999989581377725nteger @ B @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2785_mult__le__cancel__left__neg,axiom,
% 9.25/5.16      ! [C: rat,A: rat,B: rat] :
% 9.25/5.16        ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.16       => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.25/5.16          = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2786_mult__le__cancel__left__neg,axiom,
% 9.25/5.16      ! [C: int,A: int,B: int] :
% 9.25/5.16        ( ( ord_less_int @ C @ zero_zero_int )
% 9.25/5.16       => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.25/5.16          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2787_mult__less__cancel__right,axiom,
% 9.25/5.16      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.25/5.16        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.25/5.16        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.16           => ( ord_le6747313008572928689nteger @ A @ B ) )
% 9.25/5.16          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 9.25/5.16           => ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2788_mult__less__cancel__right,axiom,
% 9.25/5.16      ! [A: rat,C: rat,B: rat] :
% 9.25/5.16        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 9.25/5.16        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.25/5.16           => ( ord_less_rat @ A @ B ) )
% 9.25/5.16          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.25/5.16           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2789_mult__less__cancel__right,axiom,
% 9.25/5.16      ! [A: int,C: int,B: int] :
% 9.25/5.16        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 9.25/5.16        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.25/5.16           => ( ord_less_int @ A @ B ) )
% 9.25/5.16          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.25/5.16           => ( ord_less_int @ B @ A ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2790_mult__strict__mono_H,axiom,
% 9.25/5.16      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.25/5.16        ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.25/5.16       => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 9.25/5.16         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.16           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.16             => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2791_mult__strict__mono_H,axiom,
% 9.25/5.16      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.25/5.16        ( ( ord_less_rat @ A @ B )
% 9.25/5.16       => ( ( ord_less_rat @ C @ D2 )
% 9.25/5.16         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.16           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.25/5.16             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2792_mult__strict__mono_H,axiom,
% 9.25/5.16      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.25/5.16        ( ( ord_less_nat @ A @ B )
% 9.25/5.16       => ( ( ord_less_nat @ C @ D2 )
% 9.25/5.16         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.25/5.16           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.25/5.16             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2793_mult__strict__mono_H,axiom,
% 9.25/5.16      ! [A: int,B: int,C: int,D2: int] :
% 9.25/5.16        ( ( ord_less_int @ A @ B )
% 9.25/5.16       => ( ( ord_less_int @ C @ D2 )
% 9.25/5.16         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.16           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.25/5.16             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2794_mult__right__less__imp__less,axiom,
% 9.25/5.16      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.25/5.16        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.25/5.16       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.16         => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2795_mult__right__less__imp__less,axiom,
% 9.25/5.16      ! [A: rat,C: rat,B: rat] :
% 9.25/5.16        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 9.25/5.16       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.25/5.16         => ( ord_less_rat @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2796_mult__right__less__imp__less,axiom,
% 9.25/5.16      ! [A: nat,C: nat,B: nat] :
% 9.25/5.16        ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 9.25/5.16       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.25/5.16         => ( ord_less_nat @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2797_mult__right__less__imp__less,axiom,
% 9.25/5.16      ! [A: int,C: int,B: int] :
% 9.25/5.16        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 9.25/5.16       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.25/5.16         => ( ord_less_int @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2798_mult__less__cancel__left,axiom,
% 9.25/5.16      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.16        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 9.25/5.16        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.16           => ( ord_le6747313008572928689nteger @ A @ B ) )
% 9.25/5.16          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 9.25/5.16           => ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2799_mult__less__cancel__left,axiom,
% 9.25/5.16      ! [C: rat,A: rat,B: rat] :
% 9.25/5.16        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.25/5.16        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.25/5.16           => ( ord_less_rat @ A @ B ) )
% 9.25/5.16          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.25/5.16           => ( ord_less_rat @ B @ A ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2800_mult__less__cancel__left,axiom,
% 9.25/5.16      ! [C: int,A: int,B: int] :
% 9.25/5.16        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.25/5.16        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.25/5.16           => ( ord_less_int @ A @ B ) )
% 9.25/5.16          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.25/5.16           => ( ord_less_int @ B @ A ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2801_mult__strict__mono,axiom,
% 9.25/5.16      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.25/5.16        ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.25/5.16       => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 9.25/5.16         => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 9.25/5.16           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.16             => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2802_mult__strict__mono,axiom,
% 9.25/5.16      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.25/5.16        ( ( ord_less_rat @ A @ B )
% 9.25/5.16       => ( ( ord_less_rat @ C @ D2 )
% 9.25/5.16         => ( ( ord_less_rat @ zero_zero_rat @ B )
% 9.25/5.16           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.25/5.16             => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2803_mult__strict__mono,axiom,
% 9.25/5.16      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.25/5.16        ( ( ord_less_nat @ A @ B )
% 9.25/5.16       => ( ( ord_less_nat @ C @ D2 )
% 9.25/5.16         => ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.25/5.16           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.25/5.16             => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2804_mult__strict__mono,axiom,
% 9.25/5.16      ! [A: int,B: int,C: int,D2: int] :
% 9.25/5.16        ( ( ord_less_int @ A @ B )
% 9.25/5.16       => ( ( ord_less_int @ C @ D2 )
% 9.25/5.16         => ( ( ord_less_int @ zero_zero_int @ B )
% 9.25/5.16           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.25/5.16             => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2805_mult__left__less__imp__less,axiom,
% 9.25/5.16      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.16        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 9.25/5.16       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.16         => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2806_mult__left__less__imp__less,axiom,
% 9.25/5.16      ! [C: rat,A: rat,B: rat] :
% 9.25/5.16        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.25/5.16         => ( ord_less_rat @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2807_mult__left__less__imp__less,axiom,
% 9.25/5.16      ! [C: nat,A: nat,B: nat] :
% 9.25/5.16        ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.25/5.16         => ( ord_less_nat @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2808_mult__left__less__imp__less,axiom,
% 9.25/5.16      ! [C: int,A: int,B: int] :
% 9.25/5.16        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.25/5.16       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.25/5.16         => ( ord_less_int @ A @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2809_mult__le__cancel__right,axiom,
% 9.25/5.16      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.25/5.16        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.25/5.16        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.16           => ( ord_le3102999989581377725nteger @ A @ B ) )
% 9.25/5.16          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 9.25/5.16           => ( ord_le3102999989581377725nteger @ B @ A ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2810_mult__le__cancel__right,axiom,
% 9.25/5.16      ! [A: rat,C: rat,B: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 9.25/5.16        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.16           => ( ord_less_eq_rat @ A @ B ) )
% 9.25/5.16          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.16           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2811_mult__le__cancel__right,axiom,
% 9.25/5.16      ! [A: int,C: int,B: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 9.25/5.16        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 9.25/5.16           => ( ord_less_eq_int @ A @ B ) )
% 9.25/5.16          & ( ( ord_less_int @ C @ zero_zero_int )
% 9.25/5.16           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2812_mult__le__cancel__left,axiom,
% 9.25/5.16      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.16        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 9.25/5.16        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.16           => ( ord_le3102999989581377725nteger @ A @ B ) )
% 9.25/5.16          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 9.25/5.16           => ( ord_le3102999989581377725nteger @ B @ A ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2813_mult__le__cancel__left,axiom,
% 9.25/5.16      ! [C: rat,A: rat,B: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.25/5.16        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.16           => ( ord_less_eq_rat @ A @ B ) )
% 9.25/5.16          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.16           => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2814_mult__le__cancel__left,axiom,
% 9.25/5.16      ! [C: int,A: int,B: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.25/5.16        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 9.25/5.16           => ( ord_less_eq_int @ A @ B ) )
% 9.25/5.16          & ( ( ord_less_int @ C @ zero_zero_int )
% 9.25/5.16           => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2815_zero__less__iff__neq__zero,axiom,
% 9.25/5.16      ! [N: nat] :
% 9.25/5.16        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.16        = ( N != zero_zero_nat ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2816_gr__implies__not__zero,axiom,
% 9.25/5.16      ! [M: nat,N: nat] :
% 9.25/5.16        ( ( ord_less_nat @ M @ N )
% 9.25/5.16       => ( N != zero_zero_nat ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2817_not__less__zero,axiom,
% 9.25/5.16      ! [N: nat] :
% 9.25/5.16        ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2818_gr__zeroI,axiom,
% 9.25/5.16      ! [N: nat] :
% 9.25/5.16        ( ( N != zero_zero_nat )
% 9.25/5.16       => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2819_zero__le,axiom,
% 9.25/5.16      ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2820_less__numeral__extra_I4_J,axiom,
% 9.25/5.16      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2821_less__numeral__extra_I4_J,axiom,
% 9.25/5.16      ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2822_less__numeral__extra_I4_J,axiom,
% 9.25/5.16      ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2823_less__numeral__extra_I4_J,axiom,
% 9.25/5.16      ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2824_diff__strict__right__mono,axiom,
% 9.25/5.16      ! [A: rat,B: rat,C: rat] :
% 9.25/5.16        ( ( ord_less_rat @ A @ B )
% 9.25/5.16       => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2825_diff__strict__right__mono,axiom,
% 9.25/5.16      ! [A: int,B: int,C: int] :
% 9.25/5.16        ( ( ord_less_int @ A @ B )
% 9.25/5.16       => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2826_diff__strict__left__mono,axiom,
% 9.25/5.16      ! [B: rat,A: rat,C: rat] :
% 9.25/5.16        ( ( ord_less_rat @ B @ A )
% 9.25/5.16       => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2827_diff__strict__left__mono,axiom,
% 9.25/5.16      ! [B: int,A: int,C: int] :
% 9.25/5.16        ( ( ord_less_int @ B @ A )
% 9.25/5.16       => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2828_diff__eq__diff__less,axiom,
% 9.25/5.16      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.25/5.16        ( ( ( minus_minus_rat @ A @ B )
% 9.25/5.16          = ( minus_minus_rat @ C @ D2 ) )
% 9.25/5.16       => ( ( ord_less_rat @ A @ B )
% 9.25/5.16          = ( ord_less_rat @ C @ D2 ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2829_diff__eq__diff__less,axiom,
% 9.25/5.16      ! [A: int,B: int,C: int,D2: int] :
% 9.25/5.16        ( ( ( minus_minus_int @ A @ B )
% 9.25/5.16          = ( minus_minus_int @ C @ D2 ) )
% 9.25/5.16       => ( ( ord_less_int @ A @ B )
% 9.25/5.16          = ( ord_less_int @ C @ D2 ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2830_diff__strict__mono,axiom,
% 9.25/5.16      ! [A: rat,B: rat,D2: rat,C: rat] :
% 9.25/5.16        ( ( ord_less_rat @ A @ B )
% 9.25/5.16       => ( ( ord_less_rat @ D2 @ C )
% 9.25/5.16         => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2831_diff__strict__mono,axiom,
% 9.25/5.16      ! [A: int,B: int,D2: int,C: int] :
% 9.25/5.16        ( ( ord_less_int @ A @ B )
% 9.25/5.16       => ( ( ord_less_int @ D2 @ C )
% 9.25/5.16         => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2832_bot_Oextremum__strict,axiom,
% 9.25/5.16      ! [A: set_Pr1261947904930325089at_nat] :
% 9.25/5.16        ~ ( ord_le7866589430770878221at_nat @ A @ bot_bo2099793752762293965at_nat ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2833_bot_Oextremum__strict,axiom,
% 9.25/5.16      ! [A: set_o] :
% 9.25/5.16        ~ ( ord_less_set_o @ A @ bot_bot_set_o ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2834_bot_Oextremum__strict,axiom,
% 9.25/5.16      ! [A: set_nat] :
% 9.25/5.16        ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2835_bot_Oextremum__strict,axiom,
% 9.25/5.16      ! [A: set_int] :
% 9.25/5.16        ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2836_bot_Oextremum__strict,axiom,
% 9.25/5.16      ! [A: nat] :
% 9.25/5.16        ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2837_bot_Onot__eq__extremum,axiom,
% 9.25/5.16      ! [A: set_Pr1261947904930325089at_nat] :
% 9.25/5.16        ( ( A != bot_bo2099793752762293965at_nat )
% 9.25/5.16        = ( ord_le7866589430770878221at_nat @ bot_bo2099793752762293965at_nat @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2838_bot_Onot__eq__extremum,axiom,
% 9.25/5.16      ! [A: set_o] :
% 9.25/5.16        ( ( A != bot_bot_set_o )
% 9.25/5.16        = ( ord_less_set_o @ bot_bot_set_o @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2839_bot_Onot__eq__extremum,axiom,
% 9.25/5.16      ! [A: set_nat] :
% 9.25/5.16        ( ( A != bot_bot_set_nat )
% 9.25/5.16        = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2840_bot_Onot__eq__extremum,axiom,
% 9.25/5.16      ! [A: set_int] :
% 9.25/5.16        ( ( A != bot_bot_set_int )
% 9.25/5.16        = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2841_bot_Onot__eq__extremum,axiom,
% 9.25/5.16      ! [A: nat] :
% 9.25/5.16        ( ( A != bot_bot_nat )
% 9.25/5.16        = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2842_not__psubset__empty,axiom,
% 9.25/5.16      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.16        ~ ( ord_le7866589430770878221at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2843_not__psubset__empty,axiom,
% 9.25/5.16      ! [A2: set_o] :
% 9.25/5.16        ~ ( ord_less_set_o @ A2 @ bot_bot_set_o ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2844_not__psubset__empty,axiom,
% 9.25/5.16      ! [A2: set_nat] :
% 9.25/5.16        ~ ( ord_less_set_nat @ A2 @ bot_bot_set_nat ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2845_not__psubset__empty,axiom,
% 9.25/5.16      ! [A2: set_int] :
% 9.25/5.16        ~ ( ord_less_set_int @ A2 @ bot_bot_set_int ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2846_verit__negate__coefficient_I2_J,axiom,
% 9.25/5.16      ! [A: int,B: int] :
% 9.25/5.16        ( ( ord_less_int @ A @ B )
% 9.25/5.16       => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2847_verit__negate__coefficient_I2_J,axiom,
% 9.25/5.16      ! [A: code_integer,B: code_integer] :
% 9.25/5.16        ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.25/5.16       => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2848_verit__negate__coefficient_I2_J,axiom,
% 9.25/5.16      ! [A: rat,B: rat] :
% 9.25/5.16        ( ( ord_less_rat @ A @ B )
% 9.25/5.16       => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2849_less__minus__iff,axiom,
% 9.25/5.16      ! [A: int,B: int] :
% 9.25/5.16        ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 9.25/5.16        = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2850_less__minus__iff,axiom,
% 9.25/5.16      ! [A: code_integer,B: code_integer] :
% 9.25/5.16        ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 9.25/5.16        = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2851_less__minus__iff,axiom,
% 9.25/5.16      ! [A: rat,B: rat] :
% 9.25/5.16        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 9.25/5.16        = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2852_minus__less__iff,axiom,
% 9.25/5.16      ! [A: int,B: int] :
% 9.25/5.16        ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 9.25/5.16        = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2853_minus__less__iff,axiom,
% 9.25/5.16      ! [A: code_integer,B: code_integer] :
% 9.25/5.16        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 9.25/5.16        = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2854_minus__less__iff,axiom,
% 9.25/5.16      ! [A: rat,B: rat] :
% 9.25/5.16        ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 9.25/5.16        = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2855_compl__less__swap2,axiom,
% 9.25/5.16      ! [Y: product_unit,X: product_unit] :
% 9.25/5.16        ( ( ord_le361264281704409273t_unit @ ( uminus2952777764628376836t_unit @ Y ) @ X )
% 9.25/5.16       => ( ord_le361264281704409273t_unit @ ( uminus2952777764628376836t_unit @ X ) @ Y ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2856_compl__less__swap1,axiom,
% 9.25/5.16      ! [Y: product_unit,X: product_unit] :
% 9.25/5.16        ( ( ord_le361264281704409273t_unit @ Y @ ( uminus2952777764628376836t_unit @ X ) )
% 9.25/5.16       => ( ord_le361264281704409273t_unit @ X @ ( uminus2952777764628376836t_unit @ Y ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2857_le__numeral__extra_I4_J,axiom,
% 9.25/5.16      ord_le3102999989581377725nteger @ one_one_Code_integer @ one_one_Code_integer ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2858_le__numeral__extra_I4_J,axiom,
% 9.25/5.16      ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2859_le__numeral__extra_I4_J,axiom,
% 9.25/5.16      ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2860_le__numeral__extra_I4_J,axiom,
% 9.25/5.16      ord_less_eq_int @ one_one_int @ one_one_int ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2861_diff__eq__diff__less__eq,axiom,
% 9.25/5.16      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.25/5.16        ( ( ( minus_minus_rat @ A @ B )
% 9.25/5.16          = ( minus_minus_rat @ C @ D2 ) )
% 9.25/5.16       => ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.16          = ( ord_less_eq_rat @ C @ D2 ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2862_diff__eq__diff__less__eq,axiom,
% 9.25/5.16      ! [A: int,B: int,C: int,D2: int] :
% 9.25/5.16        ( ( ( minus_minus_int @ A @ B )
% 9.25/5.16          = ( minus_minus_int @ C @ D2 ) )
% 9.25/5.16       => ( ( ord_less_eq_int @ A @ B )
% 9.25/5.16          = ( ord_less_eq_int @ C @ D2 ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2863_diff__right__mono,axiom,
% 9.25/5.16      ! [A: rat,B: rat,C: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.16       => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2864_diff__right__mono,axiom,
% 9.25/5.16      ! [A: int,B: int,C: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.16       => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2865_diff__left__mono,axiom,
% 9.25/5.16      ! [B: rat,A: rat,C: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ B @ A )
% 9.25/5.16       => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2866_diff__left__mono,axiom,
% 9.25/5.16      ! [B: int,A: int,C: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ B @ A )
% 9.25/5.16       => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2867_diff__mono,axiom,
% 9.25/5.16      ! [A: rat,B: rat,D2: rat,C: rat] :
% 9.25/5.16        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_rat @ D2 @ C )
% 9.25/5.16         => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2868_diff__mono,axiom,
% 9.25/5.16      ! [A: int,B: int,D2: int,C: int] :
% 9.25/5.16        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.16       => ( ( ord_less_eq_int @ D2 @ C )
% 9.25/5.16         => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2869_subrelI,axiom,
% 9.25/5.16      ! [R3: set_Pr1281608226676607948nteger,S3: set_Pr1281608226676607948nteger] :
% 9.25/5.16        ( ! [X2: produc6241069584506657477e_term > option6357759511663192854e_term,Y2: produc8923325533196201883nteger] :
% 9.25/5.16            ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X2 @ Y2 ) @ R3 )
% 9.25/5.16           => ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ X2 @ Y2 ) @ S3 ) )
% 9.25/5.16       => ( ord_le653643898420964396nteger @ R3 @ S3 ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2870_subrelI,axiom,
% 9.25/5.16      ! [R3: set_Pr3286484037609594932et_nat,S3: set_Pr3286484037609594932et_nat] :
% 9.25/5.16        ( ! [X2: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 9.25/5.16            ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X2 @ Y2 ) @ R3 )
% 9.25/5.16           => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X2 @ Y2 ) @ S3 ) )
% 9.25/5.16       => ( ord_le5966269811547037844et_nat @ R3 @ S3 ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2871_subrelI,axiom,
% 9.25/5.16      ! [R3: set_Pr8536935166611901872et_nat,S3: set_Pr8536935166611901872et_nat] :
% 9.25/5.16        ( ! [X2: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat] :
% 9.25/5.16            ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X2 @ Y2 ) @ R3 )
% 9.25/5.16           => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X2 @ Y2 ) @ S3 ) )
% 9.25/5.16       => ( ord_le4763372923235995152et_nat @ R3 @ S3 ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2872_subrelI,axiom,
% 9.25/5.16      ! [R3: set_Pr9222295170931077689nt_int,S3: set_Pr9222295170931077689nt_int] :
% 9.25/5.16        ( ! [X2: produc8551481072490612790e_term > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 9.25/5.16            ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X2 @ Y2 ) @ R3 )
% 9.25/5.16           => ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X2 @ Y2 ) @ S3 ) )
% 9.25/5.16       => ( ord_le8725513860283290265nt_int @ R3 @ S3 ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2873_subrelI,axiom,
% 9.25/5.16      ! [R3: set_Pr1872883991513573699nt_int,S3: set_Pr1872883991513573699nt_int] :
% 9.25/5.16        ( ! [X2: int > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 9.25/5.16            ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X2 @ Y2 ) @ R3 )
% 9.25/5.16           => ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X2 @ Y2 ) @ S3 ) )
% 9.25/5.16       => ( ord_le135402666524580259nt_int @ R3 @ S3 ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2874_bot_Oextremum,axiom,
% 9.25/5.16      ! [A: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ bot_bo2099793752762293965at_nat @ A ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2875_bot_Oextremum,axiom,
% 9.25/5.16      ! [A: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2876_bot_Oextremum,axiom,
% 9.25/5.16      ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2877_bot_Oextremum,axiom,
% 9.25/5.16      ! [A: filter_nat] : ( ord_le2510731241096832064er_nat @ bot_bot_filter_nat @ A ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2878_bot_Oextremum,axiom,
% 9.25/5.16      ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2879_bot_Oextremum,axiom,
% 9.25/5.16      ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2880_bot_Oextremum__unique,axiom,
% 9.25/5.16      ! [A: set_Pr1261947904930325089at_nat] :
% 9.25/5.16        ( ( ord_le3146513528884898305at_nat @ A @ bot_bo2099793752762293965at_nat )
% 9.25/5.16        = ( A = bot_bo2099793752762293965at_nat ) ) ).
% 9.25/5.16  
% 9.25/5.16  thf(fact_2881_bot_Oextremum__unique,axiom,
% 9.25/5.17      ! [A: set_o] :
% 9.25/5.17        ( ( ord_less_eq_set_o @ A @ bot_bot_set_o )
% 9.25/5.17        = ( A = bot_bot_set_o ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2882_bot_Oextremum__unique,axiom,
% 9.25/5.17      ! [A: set_int] :
% 9.25/5.17        ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 9.25/5.17        = ( A = bot_bot_set_int ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2883_bot_Oextremum__unique,axiom,
% 9.25/5.17      ! [A: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ A @ bot_bot_filter_nat )
% 9.25/5.17        = ( A = bot_bot_filter_nat ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2884_bot_Oextremum__unique,axiom,
% 9.25/5.17      ! [A: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 9.25/5.17        = ( A = bot_bot_set_nat ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2885_bot_Oextremum__unique,axiom,
% 9.25/5.17      ! [A: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 9.25/5.17        = ( A = bot_bot_nat ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2886_bot_Oextremum__uniqueI,axiom,
% 9.25/5.17      ! [A: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le3146513528884898305at_nat @ A @ bot_bo2099793752762293965at_nat )
% 9.25/5.17       => ( A = bot_bo2099793752762293965at_nat ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2887_bot_Oextremum__uniqueI,axiom,
% 9.25/5.17      ! [A: set_o] :
% 9.25/5.17        ( ( ord_less_eq_set_o @ A @ bot_bot_set_o )
% 9.25/5.17       => ( A = bot_bot_set_o ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2888_bot_Oextremum__uniqueI,axiom,
% 9.25/5.17      ! [A: set_int] :
% 9.25/5.17        ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 9.25/5.17       => ( A = bot_bot_set_int ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2889_bot_Oextremum__uniqueI,axiom,
% 9.25/5.17      ! [A: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ A @ bot_bot_filter_nat )
% 9.25/5.17       => ( A = bot_bot_filter_nat ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2890_bot_Oextremum__uniqueI,axiom,
% 9.25/5.17      ! [A: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 9.25/5.17       => ( A = bot_bot_set_nat ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2891_bot_Oextremum__uniqueI,axiom,
% 9.25/5.17      ! [A: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 9.25/5.17       => ( A = bot_bot_nat ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2892_top_Onot__eq__extremum,axiom,
% 9.25/5.17      ! [A: set_list_nat] :
% 9.25/5.17        ( ( A != top_top_set_list_nat )
% 9.25/5.17        = ( ord_le1190675801316882794st_nat @ A @ top_top_set_list_nat ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2893_top_Onot__eq__extremum,axiom,
% 9.25/5.17      ! [A: set_o] :
% 9.25/5.17        ( ( A != top_top_set_o )
% 9.25/5.17        = ( ord_less_set_o @ A @ top_top_set_o ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2894_top_Onot__eq__extremum,axiom,
% 9.25/5.17      ! [A: set_rat] :
% 9.25/5.17        ( ( A != top_top_set_rat )
% 9.25/5.17        = ( ord_less_set_rat @ A @ top_top_set_rat ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2895_top_Onot__eq__extremum,axiom,
% 9.25/5.17      ! [A: set_nat] :
% 9.25/5.17        ( ( A != top_top_set_nat )
% 9.25/5.17        = ( ord_less_set_nat @ A @ top_top_set_nat ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2896_top_Onot__eq__extremum,axiom,
% 9.25/5.17      ! [A: set_int] :
% 9.25/5.17        ( ( A != top_top_set_int )
% 9.25/5.17        = ( ord_less_set_int @ A @ top_top_set_int ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2897_top_Oextremum__strict,axiom,
% 9.25/5.17      ! [A: set_list_nat] :
% 9.25/5.17        ~ ( ord_le1190675801316882794st_nat @ top_top_set_list_nat @ A ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2898_top_Oextremum__strict,axiom,
% 9.25/5.17      ! [A: set_o] :
% 9.25/5.17        ~ ( ord_less_set_o @ top_top_set_o @ A ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2899_top_Oextremum__strict,axiom,
% 9.25/5.17      ! [A: set_rat] :
% 9.25/5.17        ~ ( ord_less_set_rat @ top_top_set_rat @ A ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2900_top_Oextremum__strict,axiom,
% 9.25/5.17      ! [A: set_nat] :
% 9.25/5.17        ~ ( ord_less_set_nat @ top_top_set_nat @ A ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2901_top_Oextremum__strict,axiom,
% 9.25/5.17      ! [A: set_int] :
% 9.25/5.17        ~ ( ord_less_set_int @ top_top_set_int @ A ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2902_less__infI1,axiom,
% 9.25/5.17      ! [A: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le7866589430770878221at_nat @ A @ X )
% 9.25/5.17       => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2903_less__infI1,axiom,
% 9.25/5.17      ! [A: set_nat,X: set_nat,B: set_nat] :
% 9.25/5.17        ( ( ord_less_set_nat @ A @ X )
% 9.25/5.17       => ( ord_less_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2904_less__infI1,axiom,
% 9.25/5.17      ! [A: product_prod_int_int > $o,X: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8213806771718485336_int_o @ A @ X )
% 9.25/5.17       => ( ord_le8213806771718485336_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2905_less__infI1,axiom,
% 9.25/5.17      ! [A: list_char > $o,X: list_char > $o,B: list_char > $o] :
% 9.25/5.17        ( ( ord_less_list_char_o @ A @ X )
% 9.25/5.17       => ( ord_less_list_char_o @ ( inf_inf_list_char_o @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2906_less__infI1,axiom,
% 9.25/5.17      ! [A: rat,X: rat,B: rat] :
% 9.25/5.17        ( ( ord_less_rat @ A @ X )
% 9.25/5.17       => ( ord_less_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2907_less__infI1,axiom,
% 9.25/5.17      ! [A: nat,X: nat,B: nat] :
% 9.25/5.17        ( ( ord_less_nat @ A @ X )
% 9.25/5.17       => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2908_less__infI1,axiom,
% 9.25/5.17      ! [A: int,X: int,B: int] :
% 9.25/5.17        ( ( ord_less_int @ A @ X )
% 9.25/5.17       => ( ord_less_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2909_less__infI2,axiom,
% 9.25/5.17      ! [B: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le7866589430770878221at_nat @ B @ X )
% 9.25/5.17       => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2910_less__infI2,axiom,
% 9.25/5.17      ! [B: set_nat,X: set_nat,A: set_nat] :
% 9.25/5.17        ( ( ord_less_set_nat @ B @ X )
% 9.25/5.17       => ( ord_less_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2911_less__infI2,axiom,
% 9.25/5.17      ! [B: product_prod_int_int > $o,X: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8213806771718485336_int_o @ B @ X )
% 9.25/5.17       => ( ord_le8213806771718485336_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2912_less__infI2,axiom,
% 9.25/5.17      ! [B: list_char > $o,X: list_char > $o,A: list_char > $o] :
% 9.25/5.17        ( ( ord_less_list_char_o @ B @ X )
% 9.25/5.17       => ( ord_less_list_char_o @ ( inf_inf_list_char_o @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2913_less__infI2,axiom,
% 9.25/5.17      ! [B: rat,X: rat,A: rat] :
% 9.25/5.17        ( ( ord_less_rat @ B @ X )
% 9.25/5.17       => ( ord_less_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2914_less__infI2,axiom,
% 9.25/5.17      ! [B: nat,X: nat,A: nat] :
% 9.25/5.17        ( ( ord_less_nat @ B @ X )
% 9.25/5.17       => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2915_less__infI2,axiom,
% 9.25/5.17      ! [B: int,X: int,A: int] :
% 9.25/5.17        ( ( ord_less_int @ B @ X )
% 9.25/5.17       => ( ord_less_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2916_inf_Oabsorb3,axiom,
% 9.25/5.17      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le7866589430770878221at_nat @ A @ B )
% 9.25/5.17       => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2917_inf_Oabsorb3,axiom,
% 9.25/5.17      ! [A: set_nat,B: set_nat] :
% 9.25/5.17        ( ( ord_less_set_nat @ A @ B )
% 9.25/5.17       => ( ( inf_inf_set_nat @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2918_inf_Oabsorb3,axiom,
% 9.25/5.17      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8213806771718485336_int_o @ A @ B )
% 9.25/5.17       => ( ( inf_in3604695632404883862_int_o @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2919_inf_Oabsorb3,axiom,
% 9.25/5.17      ! [A: list_char > $o,B: list_char > $o] :
% 9.25/5.17        ( ( ord_less_list_char_o @ A @ B )
% 9.25/5.17       => ( ( inf_inf_list_char_o @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2920_inf_Oabsorb3,axiom,
% 9.25/5.17      ! [A: rat,B: rat] :
% 9.25/5.17        ( ( ord_less_rat @ A @ B )
% 9.25/5.17       => ( ( inf_inf_rat @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2921_inf_Oabsorb3,axiom,
% 9.25/5.17      ! [A: nat,B: nat] :
% 9.25/5.17        ( ( ord_less_nat @ A @ B )
% 9.25/5.17       => ( ( inf_inf_nat @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2922_inf_Oabsorb3,axiom,
% 9.25/5.17      ! [A: int,B: int] :
% 9.25/5.17        ( ( ord_less_int @ A @ B )
% 9.25/5.17       => ( ( inf_inf_int @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2923_inf_Oabsorb4,axiom,
% 9.25/5.17      ! [B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le7866589430770878221at_nat @ B @ A )
% 9.25/5.17       => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2924_inf_Oabsorb4,axiom,
% 9.25/5.17      ! [B: set_nat,A: set_nat] :
% 9.25/5.17        ( ( ord_less_set_nat @ B @ A )
% 9.25/5.17       => ( ( inf_inf_set_nat @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2925_inf_Oabsorb4,axiom,
% 9.25/5.17      ! [B: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8213806771718485336_int_o @ B @ A )
% 9.25/5.17       => ( ( inf_in3604695632404883862_int_o @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2926_inf_Oabsorb4,axiom,
% 9.25/5.17      ! [B: list_char > $o,A: list_char > $o] :
% 9.25/5.17        ( ( ord_less_list_char_o @ B @ A )
% 9.25/5.17       => ( ( inf_inf_list_char_o @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2927_inf_Oabsorb4,axiom,
% 9.25/5.17      ! [B: rat,A: rat] :
% 9.25/5.17        ( ( ord_less_rat @ B @ A )
% 9.25/5.17       => ( ( inf_inf_rat @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2928_inf_Oabsorb4,axiom,
% 9.25/5.17      ! [B: nat,A: nat] :
% 9.25/5.17        ( ( ord_less_nat @ B @ A )
% 9.25/5.17       => ( ( inf_inf_nat @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2929_inf_Oabsorb4,axiom,
% 9.25/5.17      ! [B: int,A: int] :
% 9.25/5.17        ( ( ord_less_int @ B @ A )
% 9.25/5.17       => ( ( inf_inf_int @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2930_inf_Ostrict__boundedE,axiom,
% 9.25/5.17      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le7866589430770878221at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) )
% 9.25/5.17       => ~ ( ( ord_le7866589430770878221at_nat @ A @ B )
% 9.25/5.17           => ~ ( ord_le7866589430770878221at_nat @ A @ C ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2931_inf_Ostrict__boundedE,axiom,
% 9.25/5.17      ! [A: set_nat,B: set_nat,C: set_nat] :
% 9.25/5.17        ( ( ord_less_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) )
% 9.25/5.17       => ~ ( ( ord_less_set_nat @ A @ B )
% 9.25/5.17           => ~ ( ord_less_set_nat @ A @ C ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2932_inf_Ostrict__boundedE,axiom,
% 9.25/5.17      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o,C: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8213806771718485336_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C ) )
% 9.25/5.17       => ~ ( ( ord_le8213806771718485336_int_o @ A @ B )
% 9.25/5.17           => ~ ( ord_le8213806771718485336_int_o @ A @ C ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2933_inf_Ostrict__boundedE,axiom,
% 9.25/5.17      ! [A: list_char > $o,B: list_char > $o,C: list_char > $o] :
% 9.25/5.17        ( ( ord_less_list_char_o @ A @ ( inf_inf_list_char_o @ B @ C ) )
% 9.25/5.17       => ~ ( ( ord_less_list_char_o @ A @ B )
% 9.25/5.17           => ~ ( ord_less_list_char_o @ A @ C ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2934_inf_Ostrict__boundedE,axiom,
% 9.25/5.17      ! [A: rat,B: rat,C: rat] :
% 9.25/5.17        ( ( ord_less_rat @ A @ ( inf_inf_rat @ B @ C ) )
% 9.25/5.17       => ~ ( ( ord_less_rat @ A @ B )
% 9.25/5.17           => ~ ( ord_less_rat @ A @ C ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2935_inf_Ostrict__boundedE,axiom,
% 9.25/5.17      ! [A: nat,B: nat,C: nat] :
% 9.25/5.17        ( ( ord_less_nat @ A @ ( inf_inf_nat @ B @ C ) )
% 9.25/5.17       => ~ ( ( ord_less_nat @ A @ B )
% 9.25/5.17           => ~ ( ord_less_nat @ A @ C ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2936_inf_Ostrict__boundedE,axiom,
% 9.25/5.17      ! [A: int,B: int,C: int] :
% 9.25/5.17        ( ( ord_less_int @ A @ ( inf_inf_int @ B @ C ) )
% 9.25/5.17       => ~ ( ( ord_less_int @ A @ B )
% 9.25/5.17           => ~ ( ord_less_int @ A @ C ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2937_inf_Ostrict__order__iff,axiom,
% 9.25/5.17      ( ord_le7866589430770878221at_nat
% 9.25/5.17      = ( ^ [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 9.25/5.17            ( ( A3
% 9.25/5.17              = ( inf_in2572325071724192079at_nat @ A3 @ B3 ) )
% 9.25/5.17            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2938_inf_Ostrict__order__iff,axiom,
% 9.25/5.17      ( ord_less_set_nat
% 9.25/5.17      = ( ^ [A3: set_nat,B3: set_nat] :
% 9.25/5.17            ( ( A3
% 9.25/5.17              = ( inf_inf_set_nat @ A3 @ B3 ) )
% 9.25/5.17            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2939_inf_Ostrict__order__iff,axiom,
% 9.25/5.17      ( ord_le8213806771718485336_int_o
% 9.25/5.17      = ( ^ [A3: product_prod_int_int > $o,B3: product_prod_int_int > $o] :
% 9.25/5.17            ( ( A3
% 9.25/5.17              = ( inf_in3604695632404883862_int_o @ A3 @ B3 ) )
% 9.25/5.17            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2940_inf_Ostrict__order__iff,axiom,
% 9.25/5.17      ( ord_less_list_char_o
% 9.25/5.17      = ( ^ [A3: list_char > $o,B3: list_char > $o] :
% 9.25/5.17            ( ( A3
% 9.25/5.17              = ( inf_inf_list_char_o @ A3 @ B3 ) )
% 9.25/5.17            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2941_inf_Ostrict__order__iff,axiom,
% 9.25/5.17      ( ord_less_rat
% 9.25/5.17      = ( ^ [A3: rat,B3: rat] :
% 9.25/5.17            ( ( A3
% 9.25/5.17              = ( inf_inf_rat @ A3 @ B3 ) )
% 9.25/5.17            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2942_inf_Ostrict__order__iff,axiom,
% 9.25/5.17      ( ord_less_nat
% 9.25/5.17      = ( ^ [A3: nat,B3: nat] :
% 9.25/5.17            ( ( A3
% 9.25/5.17              = ( inf_inf_nat @ A3 @ B3 ) )
% 9.25/5.17            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2943_inf_Ostrict__order__iff,axiom,
% 9.25/5.17      ( ord_less_int
% 9.25/5.17      = ( ^ [A3: int,B3: int] :
% 9.25/5.17            ( ( A3
% 9.25/5.17              = ( inf_inf_int @ A3 @ B3 ) )
% 9.25/5.17            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2944_inf_Ostrict__coboundedI1,axiom,
% 9.25/5.17      ! [A: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le7866589430770878221at_nat @ A @ C )
% 9.25/5.17       => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2945_inf_Ostrict__coboundedI1,axiom,
% 9.25/5.17      ! [A: set_nat,C: set_nat,B: set_nat] :
% 9.25/5.17        ( ( ord_less_set_nat @ A @ C )
% 9.25/5.17       => ( ord_less_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2946_inf_Ostrict__coboundedI1,axiom,
% 9.25/5.17      ! [A: product_prod_int_int > $o,C: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8213806771718485336_int_o @ A @ C )
% 9.25/5.17       => ( ord_le8213806771718485336_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2947_inf_Ostrict__coboundedI1,axiom,
% 9.25/5.17      ! [A: list_char > $o,C: list_char > $o,B: list_char > $o] :
% 9.25/5.17        ( ( ord_less_list_char_o @ A @ C )
% 9.25/5.17       => ( ord_less_list_char_o @ ( inf_inf_list_char_o @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2948_inf_Ostrict__coboundedI1,axiom,
% 9.25/5.17      ! [A: rat,C: rat,B: rat] :
% 9.25/5.17        ( ( ord_less_rat @ A @ C )
% 9.25/5.17       => ( ord_less_rat @ ( inf_inf_rat @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2949_inf_Ostrict__coboundedI1,axiom,
% 9.25/5.17      ! [A: nat,C: nat,B: nat] :
% 9.25/5.17        ( ( ord_less_nat @ A @ C )
% 9.25/5.17       => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2950_inf_Ostrict__coboundedI1,axiom,
% 9.25/5.17      ! [A: int,C: int,B: int] :
% 9.25/5.17        ( ( ord_less_int @ A @ C )
% 9.25/5.17       => ( ord_less_int @ ( inf_inf_int @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2951_inf_Ostrict__coboundedI2,axiom,
% 9.25/5.17      ! [B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le7866589430770878221at_nat @ B @ C )
% 9.25/5.17       => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2952_inf_Ostrict__coboundedI2,axiom,
% 9.25/5.17      ! [B: set_nat,C: set_nat,A: set_nat] :
% 9.25/5.17        ( ( ord_less_set_nat @ B @ C )
% 9.25/5.17       => ( ord_less_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2953_inf_Ostrict__coboundedI2,axiom,
% 9.25/5.17      ! [B: product_prod_int_int > $o,C: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8213806771718485336_int_o @ B @ C )
% 9.25/5.17       => ( ord_le8213806771718485336_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2954_inf_Ostrict__coboundedI2,axiom,
% 9.25/5.17      ! [B: list_char > $o,C: list_char > $o,A: list_char > $o] :
% 9.25/5.17        ( ( ord_less_list_char_o @ B @ C )
% 9.25/5.17       => ( ord_less_list_char_o @ ( inf_inf_list_char_o @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2955_inf_Ostrict__coboundedI2,axiom,
% 9.25/5.17      ! [B: rat,C: rat,A: rat] :
% 9.25/5.17        ( ( ord_less_rat @ B @ C )
% 9.25/5.17       => ( ord_less_rat @ ( inf_inf_rat @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2956_inf_Ostrict__coboundedI2,axiom,
% 9.25/5.17      ! [B: nat,C: nat,A: nat] :
% 9.25/5.17        ( ( ord_less_nat @ B @ C )
% 9.25/5.17       => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2957_inf_Ostrict__coboundedI2,axiom,
% 9.25/5.17      ! [B: int,C: int,A: int] :
% 9.25/5.17        ( ( ord_less_int @ B @ C )
% 9.25/5.17       => ( ord_less_int @ ( inf_inf_int @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2958_less__supI1,axiom,
% 9.25/5.17      ! [X: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le7642048601412989811at_nat @ X @ A )
% 9.25/5.17       => ( ord_le7642048601412989811at_nat @ X @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2959_less__supI1,axiom,
% 9.25/5.17      ! [X: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le2604355607129572851at_nat @ X @ A )
% 9.25/5.17       => ( ord_le2604355607129572851at_nat @ X @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2960_less__supI1,axiom,
% 9.25/5.17      ! [X: set_nat,A: set_nat,B: set_nat] :
% 9.25/5.17        ( ( ord_less_set_nat @ X @ A )
% 9.25/5.17       => ( ord_less_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2961_less__supI1,axiom,
% 9.25/5.17      ! [X: rat,A: rat,B: rat] :
% 9.25/5.17        ( ( ord_less_rat @ X @ A )
% 9.25/5.17       => ( ord_less_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2962_less__supI1,axiom,
% 9.25/5.17      ! [X: nat,A: nat,B: nat] :
% 9.25/5.17        ( ( ord_less_nat @ X @ A )
% 9.25/5.17       => ( ord_less_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2963_less__supI1,axiom,
% 9.25/5.17      ! [X: int,A: int,B: int] :
% 9.25/5.17        ( ( ord_less_int @ X @ A )
% 9.25/5.17       => ( ord_less_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2964_less__supI2,axiom,
% 9.25/5.17      ! [X: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le7642048601412989811at_nat @ X @ B )
% 9.25/5.17       => ( ord_le7642048601412989811at_nat @ X @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2965_less__supI2,axiom,
% 9.25/5.17      ! [X: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le2604355607129572851at_nat @ X @ B )
% 9.25/5.17       => ( ord_le2604355607129572851at_nat @ X @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2966_less__supI2,axiom,
% 9.25/5.17      ! [X: set_nat,B: set_nat,A: set_nat] :
% 9.25/5.17        ( ( ord_less_set_nat @ X @ B )
% 9.25/5.17       => ( ord_less_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2967_less__supI2,axiom,
% 9.25/5.17      ! [X: rat,B: rat,A: rat] :
% 9.25/5.17        ( ( ord_less_rat @ X @ B )
% 9.25/5.17       => ( ord_less_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2968_less__supI2,axiom,
% 9.25/5.17      ! [X: nat,B: nat,A: nat] :
% 9.25/5.17        ( ( ord_less_nat @ X @ B )
% 9.25/5.17       => ( ord_less_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2969_less__supI2,axiom,
% 9.25/5.17      ! [X: int,B: int,A: int] :
% 9.25/5.17        ( ( ord_less_int @ X @ B )
% 9.25/5.17       => ( ord_less_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2970_sup_Oabsorb3,axiom,
% 9.25/5.17      ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le7642048601412989811at_nat @ B @ A )
% 9.25/5.17       => ( ( sup_su3035147773818789531at_nat @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2971_sup_Oabsorb3,axiom,
% 9.25/5.17      ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le2604355607129572851at_nat @ B @ A )
% 9.25/5.17       => ( ( sup_su5525570899277871387at_nat @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2972_sup_Oabsorb3,axiom,
% 9.25/5.17      ! [B: set_nat,A: set_nat] :
% 9.25/5.17        ( ( ord_less_set_nat @ B @ A )
% 9.25/5.17       => ( ( sup_sup_set_nat @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2973_sup_Oabsorb3,axiom,
% 9.25/5.17      ! [B: rat,A: rat] :
% 9.25/5.17        ( ( ord_less_rat @ B @ A )
% 9.25/5.17       => ( ( sup_sup_rat @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2974_sup_Oabsorb3,axiom,
% 9.25/5.17      ! [B: nat,A: nat] :
% 9.25/5.17        ( ( ord_less_nat @ B @ A )
% 9.25/5.17       => ( ( sup_sup_nat @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2975_sup_Oabsorb3,axiom,
% 9.25/5.17      ! [B: int,A: int] :
% 9.25/5.17        ( ( ord_less_int @ B @ A )
% 9.25/5.17       => ( ( sup_sup_int @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2976_sup_Oabsorb4,axiom,
% 9.25/5.17      ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le7642048601412989811at_nat @ A @ B )
% 9.25/5.17       => ( ( sup_su3035147773818789531at_nat @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2977_sup_Oabsorb4,axiom,
% 9.25/5.17      ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le2604355607129572851at_nat @ A @ B )
% 9.25/5.17       => ( ( sup_su5525570899277871387at_nat @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2978_sup_Oabsorb4,axiom,
% 9.25/5.17      ! [A: set_nat,B: set_nat] :
% 9.25/5.17        ( ( ord_less_set_nat @ A @ B )
% 9.25/5.17       => ( ( sup_sup_set_nat @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2979_sup_Oabsorb4,axiom,
% 9.25/5.17      ! [A: rat,B: rat] :
% 9.25/5.17        ( ( ord_less_rat @ A @ B )
% 9.25/5.17       => ( ( sup_sup_rat @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2980_sup_Oabsorb4,axiom,
% 9.25/5.17      ! [A: nat,B: nat] :
% 9.25/5.17        ( ( ord_less_nat @ A @ B )
% 9.25/5.17       => ( ( sup_sup_nat @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2981_sup_Oabsorb4,axiom,
% 9.25/5.17      ! [A: int,B: int] :
% 9.25/5.17        ( ( ord_less_int @ A @ B )
% 9.25/5.17       => ( ( sup_sup_int @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2982_sup_Ostrict__boundedE,axiom,
% 9.25/5.17      ! [B: set_Pr8551490117392284871at_nat,C: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le7642048601412989811at_nat @ ( sup_su3035147773818789531at_nat @ B @ C ) @ A )
% 9.25/5.17       => ~ ( ( ord_le7642048601412989811at_nat @ B @ A )
% 9.25/5.17           => ~ ( ord_le7642048601412989811at_nat @ C @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2983_sup_Ostrict__boundedE,axiom,
% 9.25/5.17      ! [B: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le2604355607129572851at_nat @ ( sup_su5525570899277871387at_nat @ B @ C ) @ A )
% 9.25/5.17       => ~ ( ( ord_le2604355607129572851at_nat @ B @ A )
% 9.25/5.17           => ~ ( ord_le2604355607129572851at_nat @ C @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2984_sup_Ostrict__boundedE,axiom,
% 9.25/5.17      ! [B: set_nat,C: set_nat,A: set_nat] :
% 9.25/5.17        ( ( ord_less_set_nat @ ( sup_sup_set_nat @ B @ C ) @ A )
% 9.25/5.17       => ~ ( ( ord_less_set_nat @ B @ A )
% 9.25/5.17           => ~ ( ord_less_set_nat @ C @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2985_sup_Ostrict__boundedE,axiom,
% 9.25/5.17      ! [B: rat,C: rat,A: rat] :
% 9.25/5.17        ( ( ord_less_rat @ ( sup_sup_rat @ B @ C ) @ A )
% 9.25/5.17       => ~ ( ( ord_less_rat @ B @ A )
% 9.25/5.17           => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2986_sup_Ostrict__boundedE,axiom,
% 9.25/5.17      ! [B: nat,C: nat,A: nat] :
% 9.25/5.17        ( ( ord_less_nat @ ( sup_sup_nat @ B @ C ) @ A )
% 9.25/5.17       => ~ ( ( ord_less_nat @ B @ A )
% 9.25/5.17           => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2987_sup_Ostrict__boundedE,axiom,
% 9.25/5.17      ! [B: int,C: int,A: int] :
% 9.25/5.17        ( ( ord_less_int @ ( sup_sup_int @ B @ C ) @ A )
% 9.25/5.17       => ~ ( ( ord_less_int @ B @ A )
% 9.25/5.17           => ~ ( ord_less_int @ C @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2988_sup_Ostrict__order__iff,axiom,
% 9.25/5.17      ( ord_le7642048601412989811at_nat
% 9.25/5.17      = ( ^ [B3: set_Pr8551490117392284871at_nat,A3: set_Pr8551490117392284871at_nat] :
% 9.25/5.17            ( ( A3
% 9.25/5.17              = ( sup_su3035147773818789531at_nat @ A3 @ B3 ) )
% 9.25/5.17            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2989_sup_Ostrict__order__iff,axiom,
% 9.25/5.17      ( ord_le2604355607129572851at_nat
% 9.25/5.17      = ( ^ [B3: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] :
% 9.25/5.17            ( ( A3
% 9.25/5.17              = ( sup_su5525570899277871387at_nat @ A3 @ B3 ) )
% 9.25/5.17            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2990_sup_Ostrict__order__iff,axiom,
% 9.25/5.17      ( ord_less_set_nat
% 9.25/5.17      = ( ^ [B3: set_nat,A3: set_nat] :
% 9.25/5.17            ( ( A3
% 9.25/5.17              = ( sup_sup_set_nat @ A3 @ B3 ) )
% 9.25/5.17            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2991_sup_Ostrict__order__iff,axiom,
% 9.25/5.17      ( ord_less_rat
% 9.25/5.17      = ( ^ [B3: rat,A3: rat] :
% 9.25/5.17            ( ( A3
% 9.25/5.17              = ( sup_sup_rat @ A3 @ B3 ) )
% 9.25/5.17            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2992_sup_Ostrict__order__iff,axiom,
% 9.25/5.17      ( ord_less_nat
% 9.25/5.17      = ( ^ [B3: nat,A3: nat] :
% 9.25/5.17            ( ( A3
% 9.25/5.17              = ( sup_sup_nat @ A3 @ B3 ) )
% 9.25/5.17            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2993_sup_Ostrict__order__iff,axiom,
% 9.25/5.17      ( ord_less_int
% 9.25/5.17      = ( ^ [B3: int,A3: int] :
% 9.25/5.17            ( ( A3
% 9.25/5.17              = ( sup_sup_int @ A3 @ B3 ) )
% 9.25/5.17            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2994_sup_Ostrict__coboundedI1,axiom,
% 9.25/5.17      ! [C: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le7642048601412989811at_nat @ C @ A )
% 9.25/5.17       => ( ord_le7642048601412989811at_nat @ C @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2995_sup_Ostrict__coboundedI1,axiom,
% 9.25/5.17      ! [C: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le2604355607129572851at_nat @ C @ A )
% 9.25/5.17       => ( ord_le2604355607129572851at_nat @ C @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2996_sup_Ostrict__coboundedI1,axiom,
% 9.25/5.17      ! [C: set_nat,A: set_nat,B: set_nat] :
% 9.25/5.17        ( ( ord_less_set_nat @ C @ A )
% 9.25/5.17       => ( ord_less_set_nat @ C @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2997_sup_Ostrict__coboundedI1,axiom,
% 9.25/5.17      ! [C: rat,A: rat,B: rat] :
% 9.25/5.17        ( ( ord_less_rat @ C @ A )
% 9.25/5.17       => ( ord_less_rat @ C @ ( sup_sup_rat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2998_sup_Ostrict__coboundedI1,axiom,
% 9.25/5.17      ! [C: nat,A: nat,B: nat] :
% 9.25/5.17        ( ( ord_less_nat @ C @ A )
% 9.25/5.17       => ( ord_less_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_2999_sup_Ostrict__coboundedI1,axiom,
% 9.25/5.17      ! [C: int,A: int,B: int] :
% 9.25/5.17        ( ( ord_less_int @ C @ A )
% 9.25/5.17       => ( ord_less_int @ C @ ( sup_sup_int @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3000_sup_Ostrict__coboundedI2,axiom,
% 9.25/5.17      ! [C: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le7642048601412989811at_nat @ C @ B )
% 9.25/5.17       => ( ord_le7642048601412989811at_nat @ C @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3001_sup_Ostrict__coboundedI2,axiom,
% 9.25/5.17      ! [C: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le2604355607129572851at_nat @ C @ B )
% 9.25/5.17       => ( ord_le2604355607129572851at_nat @ C @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3002_sup_Ostrict__coboundedI2,axiom,
% 9.25/5.17      ! [C: set_nat,B: set_nat,A: set_nat] :
% 9.25/5.17        ( ( ord_less_set_nat @ C @ B )
% 9.25/5.17       => ( ord_less_set_nat @ C @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3003_sup_Ostrict__coboundedI2,axiom,
% 9.25/5.17      ! [C: rat,B: rat,A: rat] :
% 9.25/5.17        ( ( ord_less_rat @ C @ B )
% 9.25/5.17       => ( ord_less_rat @ C @ ( sup_sup_rat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3004_sup_Ostrict__coboundedI2,axiom,
% 9.25/5.17      ! [C: nat,B: nat,A: nat] :
% 9.25/5.17        ( ( ord_less_nat @ C @ B )
% 9.25/5.17       => ( ord_less_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3005_sup_Ostrict__coboundedI2,axiom,
% 9.25/5.17      ! [C: int,B: int,A: int] :
% 9.25/5.17        ( ( ord_less_int @ C @ B )
% 9.25/5.17       => ( ord_less_int @ C @ ( sup_sup_int @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3006_le__minus__iff,axiom,
% 9.25/5.17      ! [A: code_integer,B: code_integer] :
% 9.25/5.17        ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 9.25/5.17        = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3007_le__minus__iff,axiom,
% 9.25/5.17      ! [A: rat,B: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 9.25/5.17        = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3008_le__minus__iff,axiom,
% 9.25/5.17      ! [A: int,B: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 9.25/5.17        = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3009_minus__le__iff,axiom,
% 9.25/5.17      ! [A: code_integer,B: code_integer] :
% 9.25/5.17        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 9.25/5.17        = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3010_minus__le__iff,axiom,
% 9.25/5.17      ! [A: rat,B: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 9.25/5.17        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3011_minus__le__iff,axiom,
% 9.25/5.17      ! [A: int,B: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 9.25/5.17        = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3012_le__imp__neg__le,axiom,
% 9.25/5.17      ! [A: code_integer,B: code_integer] :
% 9.25/5.17        ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.25/5.17       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3013_le__imp__neg__le,axiom,
% 9.25/5.17      ! [A: rat,B: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.17       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3014_le__imp__neg__le,axiom,
% 9.25/5.17      ! [A: int,B: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.17       => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3015_compl__le__swap2,axiom,
% 9.25/5.17      ! [Y: product_unit,X: product_unit] :
% 9.25/5.17        ( ( ord_le3221252021190050221t_unit @ ( uminus2952777764628376836t_unit @ Y ) @ X )
% 9.25/5.17       => ( ord_le3221252021190050221t_unit @ ( uminus2952777764628376836t_unit @ X ) @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3016_compl__le__swap2,axiom,
% 9.25/5.17      ! [Y: set_nat,X: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ X )
% 9.25/5.17       => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3017_compl__le__swap1,axiom,
% 9.25/5.17      ! [Y: product_unit,X: product_unit] :
% 9.25/5.17        ( ( ord_le3221252021190050221t_unit @ Y @ ( uminus2952777764628376836t_unit @ X ) )
% 9.25/5.17       => ( ord_le3221252021190050221t_unit @ X @ ( uminus2952777764628376836t_unit @ Y ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3018_compl__le__swap1,axiom,
% 9.25/5.17      ! [Y: set_nat,X: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ Y @ ( uminus5710092332889474511et_nat @ X ) )
% 9.25/5.17       => ( ord_less_eq_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3019_compl__mono,axiom,
% 9.25/5.17      ! [X: product_unit,Y: product_unit] :
% 9.25/5.17        ( ( ord_le3221252021190050221t_unit @ X @ Y )
% 9.25/5.17       => ( ord_le3221252021190050221t_unit @ ( uminus2952777764628376836t_unit @ Y ) @ ( uminus2952777764628376836t_unit @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3020_compl__mono,axiom,
% 9.25/5.17      ! [X: set_nat,Y: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ X @ Y )
% 9.25/5.17       => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ ( uminus5710092332889474511et_nat @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3021_subset__minus__empty,axiom,
% 9.25/5.17      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 9.25/5.17       => ( ( minus_1356011639430497352at_nat @ A2 @ B2 )
% 9.25/5.17          = bot_bo2099793752762293965at_nat ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3022_subset__minus__empty,axiom,
% 9.25/5.17      ! [A2: set_o,B2: set_o] :
% 9.25/5.17        ( ( ord_less_eq_set_o @ A2 @ B2 )
% 9.25/5.17       => ( ( minus_minus_set_o @ A2 @ B2 )
% 9.25/5.17          = bot_bot_set_o ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3023_subset__minus__empty,axiom,
% 9.25/5.17      ! [A2: set_int,B2: set_int] :
% 9.25/5.17        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 9.25/5.17       => ( ( minus_minus_set_int @ A2 @ B2 )
% 9.25/5.17          = bot_bot_set_int ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3024_subset__minus__empty,axiom,
% 9.25/5.17      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 9.25/5.17       => ( ( minus_minus_set_nat @ A2 @ B2 )
% 9.25/5.17          = bot_bot_set_nat ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3025_top_Oextremum__uniqueI,axiom,
% 9.25/5.17      ! [A: set_list_nat] :
% 9.25/5.17        ( ( ord_le6045566169113846134st_nat @ top_top_set_list_nat @ A )
% 9.25/5.17       => ( A = top_top_set_list_nat ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3026_top_Oextremum__uniqueI,axiom,
% 9.25/5.17      ! [A: set_o] :
% 9.25/5.17        ( ( ord_less_eq_set_o @ top_top_set_o @ A )
% 9.25/5.17       => ( A = top_top_set_o ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3027_top_Oextremum__uniqueI,axiom,
% 9.25/5.17      ! [A: set_rat] :
% 9.25/5.17        ( ( ord_less_eq_set_rat @ top_top_set_rat @ A )
% 9.25/5.17       => ( A = top_top_set_rat ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3028_top_Oextremum__uniqueI,axiom,
% 9.25/5.17      ! [A: set_int] :
% 9.25/5.17        ( ( ord_less_eq_set_int @ top_top_set_int @ A )
% 9.25/5.17       => ( A = top_top_set_int ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3029_top_Oextremum__uniqueI,axiom,
% 9.25/5.17      ! [A: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ top_top_filter_nat @ A )
% 9.25/5.17       => ( A = top_top_filter_nat ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3030_top_Oextremum__uniqueI,axiom,
% 9.25/5.17      ! [A: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ top_top_set_nat @ A )
% 9.25/5.17       => ( A = top_top_set_nat ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3031_top_Oextremum__unique,axiom,
% 9.25/5.17      ! [A: set_list_nat] :
% 9.25/5.17        ( ( ord_le6045566169113846134st_nat @ top_top_set_list_nat @ A )
% 9.25/5.17        = ( A = top_top_set_list_nat ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3032_top_Oextremum__unique,axiom,
% 9.25/5.17      ! [A: set_o] :
% 9.25/5.17        ( ( ord_less_eq_set_o @ top_top_set_o @ A )
% 9.25/5.17        = ( A = top_top_set_o ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3033_top_Oextremum__unique,axiom,
% 9.25/5.17      ! [A: set_rat] :
% 9.25/5.17        ( ( ord_less_eq_set_rat @ top_top_set_rat @ A )
% 9.25/5.17        = ( A = top_top_set_rat ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3034_top_Oextremum__unique,axiom,
% 9.25/5.17      ! [A: set_int] :
% 9.25/5.17        ( ( ord_less_eq_set_int @ top_top_set_int @ A )
% 9.25/5.17        = ( A = top_top_set_int ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3035_top_Oextremum__unique,axiom,
% 9.25/5.17      ! [A: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ top_top_filter_nat @ A )
% 9.25/5.17        = ( A = top_top_filter_nat ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3036_top_Oextremum__unique,axiom,
% 9.25/5.17      ! [A: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ top_top_set_nat @ A )
% 9.25/5.17        = ( A = top_top_set_nat ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3037_top__greatest,axiom,
% 9.25/5.17      ! [A: set_list_nat] : ( ord_le6045566169113846134st_nat @ A @ top_top_set_list_nat ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3038_top__greatest,axiom,
% 9.25/5.17      ! [A: set_o] : ( ord_less_eq_set_o @ A @ top_top_set_o ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3039_top__greatest,axiom,
% 9.25/5.17      ! [A: set_rat] : ( ord_less_eq_set_rat @ A @ top_top_set_rat ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3040_top__greatest,axiom,
% 9.25/5.17      ! [A: set_int] : ( ord_less_eq_set_int @ A @ top_top_set_int ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3041_top__greatest,axiom,
% 9.25/5.17      ! [A: filter_nat] : ( ord_le2510731241096832064er_nat @ A @ top_top_filter_nat ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3042_top__greatest,axiom,
% 9.25/5.17      ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ top_top_set_nat ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3043_inf__sup__ord_I2_J,axiom,
% 9.25/5.17      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3044_inf__sup__ord_I2_J,axiom,
% 9.25/5.17      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ Y ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3045_inf__sup__ord_I2_J,axiom,
% 9.25/5.17      ! [X: list_char > $o,Y: list_char > $o] : ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ X @ Y ) @ Y ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3046_inf__sup__ord_I2_J,axiom,
% 9.25/5.17      ! [X: filter_nat,Y: filter_nat] : ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ X @ Y ) @ Y ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3047_inf__sup__ord_I2_J,axiom,
% 9.25/5.17      ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3048_inf__sup__ord_I2_J,axiom,
% 9.25/5.17      ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ Y ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3049_inf__sup__ord_I2_J,axiom,
% 9.25/5.17      ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3050_inf__sup__ord_I2_J,axiom,
% 9.25/5.17      ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ Y ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3051_inf__sup__ord_I1_J,axiom,
% 9.25/5.17      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ X ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3052_inf__sup__ord_I1_J,axiom,
% 9.25/5.17      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ X ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3053_inf__sup__ord_I1_J,axiom,
% 9.25/5.17      ! [X: list_char > $o,Y: list_char > $o] : ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ X @ Y ) @ X ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3054_inf__sup__ord_I1_J,axiom,
% 9.25/5.17      ! [X: filter_nat,Y: filter_nat] : ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ X @ Y ) @ X ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3055_inf__sup__ord_I1_J,axiom,
% 9.25/5.17      ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ X ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3056_inf__sup__ord_I1_J,axiom,
% 9.25/5.17      ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ X ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3057_inf__sup__ord_I1_J,axiom,
% 9.25/5.17      ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3058_inf__sup__ord_I1_J,axiom,
% 9.25/5.17      ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ X ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3059_inf__le1,axiom,
% 9.25/5.17      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ X ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3060_inf__le1,axiom,
% 9.25/5.17      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ X ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3061_inf__le1,axiom,
% 9.25/5.17      ! [X: list_char > $o,Y: list_char > $o] : ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ X @ Y ) @ X ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3062_inf__le1,axiom,
% 9.25/5.17      ! [X: filter_nat,Y: filter_nat] : ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ X @ Y ) @ X ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3063_inf__le1,axiom,
% 9.25/5.17      ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ X ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3064_inf__le1,axiom,
% 9.25/5.17      ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ X ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3065_inf__le1,axiom,
% 9.25/5.17      ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3066_inf__le1,axiom,
% 9.25/5.17      ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ X ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3067_inf__le2,axiom,
% 9.25/5.17      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3068_inf__le2,axiom,
% 9.25/5.17      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ Y ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3069_inf__le2,axiom,
% 9.25/5.17      ! [X: list_char > $o,Y: list_char > $o] : ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ X @ Y ) @ Y ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3070_inf__le2,axiom,
% 9.25/5.17      ! [X: filter_nat,Y: filter_nat] : ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ X @ Y ) @ Y ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3071_inf__le2,axiom,
% 9.25/5.17      ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3072_inf__le2,axiom,
% 9.25/5.17      ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ Y ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3073_inf__le2,axiom,
% 9.25/5.17      ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3074_inf__le2,axiom,
% 9.25/5.17      ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ Y ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3075_le__infE,axiom,
% 9.25/5.17      ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ A @ B ) )
% 9.25/5.17       => ~ ( ( ord_le3146513528884898305at_nat @ X @ A )
% 9.25/5.17           => ~ ( ord_le3146513528884898305at_nat @ X @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3076_le__infE,axiom,
% 9.25/5.17      ! [X: product_prod_int_int > $o,A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8369615600986905444_int_o @ X @ ( inf_in3604695632404883862_int_o @ A @ B ) )
% 9.25/5.17       => ~ ( ( ord_le8369615600986905444_int_o @ X @ A )
% 9.25/5.17           => ~ ( ord_le8369615600986905444_int_o @ X @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3077_le__infE,axiom,
% 9.25/5.17      ! [X: list_char > $o,A: list_char > $o,B: list_char > $o] :
% 9.25/5.17        ( ( ord_le4796328588573674190char_o @ X @ ( inf_inf_list_char_o @ A @ B ) )
% 9.25/5.17       => ~ ( ( ord_le4796328588573674190char_o @ X @ A )
% 9.25/5.17           => ~ ( ord_le4796328588573674190char_o @ X @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3078_le__infE,axiom,
% 9.25/5.17      ! [X: filter_nat,A: filter_nat,B: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ X @ ( inf_inf_filter_nat @ A @ B ) )
% 9.25/5.17       => ~ ( ( ord_le2510731241096832064er_nat @ X @ A )
% 9.25/5.17           => ~ ( ord_le2510731241096832064er_nat @ X @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3079_le__infE,axiom,
% 9.25/5.17      ! [X: set_nat,A: set_nat,B: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ A @ B ) )
% 9.25/5.17       => ~ ( ( ord_less_eq_set_nat @ X @ A )
% 9.25/5.17           => ~ ( ord_less_eq_set_nat @ X @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3080_le__infE,axiom,
% 9.25/5.17      ! [X: rat,A: rat,B: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ X @ ( inf_inf_rat @ A @ B ) )
% 9.25/5.17       => ~ ( ( ord_less_eq_rat @ X @ A )
% 9.25/5.17           => ~ ( ord_less_eq_rat @ X @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3081_le__infE,axiom,
% 9.25/5.17      ! [X: nat,A: nat,B: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A @ B ) )
% 9.25/5.17       => ~ ( ( ord_less_eq_nat @ X @ A )
% 9.25/5.17           => ~ ( ord_less_eq_nat @ X @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3082_le__infE,axiom,
% 9.25/5.17      ! [X: int,A: int,B: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ X @ ( inf_inf_int @ A @ B ) )
% 9.25/5.17       => ~ ( ( ord_less_eq_int @ X @ A )
% 9.25/5.17           => ~ ( ord_less_eq_int @ X @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3083_le__infI,axiom,
% 9.25/5.17      ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le3146513528884898305at_nat @ X @ A )
% 9.25/5.17       => ( ( ord_le3146513528884898305at_nat @ X @ B )
% 9.25/5.17         => ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3084_le__infI,axiom,
% 9.25/5.17      ! [X: product_prod_int_int > $o,A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8369615600986905444_int_o @ X @ A )
% 9.25/5.17       => ( ( ord_le8369615600986905444_int_o @ X @ B )
% 9.25/5.17         => ( ord_le8369615600986905444_int_o @ X @ ( inf_in3604695632404883862_int_o @ A @ B ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3085_le__infI,axiom,
% 9.25/5.17      ! [X: list_char > $o,A: list_char > $o,B: list_char > $o] :
% 9.25/5.17        ( ( ord_le4796328588573674190char_o @ X @ A )
% 9.25/5.17       => ( ( ord_le4796328588573674190char_o @ X @ B )
% 9.25/5.17         => ( ord_le4796328588573674190char_o @ X @ ( inf_inf_list_char_o @ A @ B ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3086_le__infI,axiom,
% 9.25/5.17      ! [X: filter_nat,A: filter_nat,B: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ X @ A )
% 9.25/5.17       => ( ( ord_le2510731241096832064er_nat @ X @ B )
% 9.25/5.17         => ( ord_le2510731241096832064er_nat @ X @ ( inf_inf_filter_nat @ A @ B ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3087_le__infI,axiom,
% 9.25/5.17      ! [X: set_nat,A: set_nat,B: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ X @ A )
% 9.25/5.17       => ( ( ord_less_eq_set_nat @ X @ B )
% 9.25/5.17         => ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3088_le__infI,axiom,
% 9.25/5.17      ! [X: rat,A: rat,B: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ X @ A )
% 9.25/5.17       => ( ( ord_less_eq_rat @ X @ B )
% 9.25/5.17         => ( ord_less_eq_rat @ X @ ( inf_inf_rat @ A @ B ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3089_le__infI,axiom,
% 9.25/5.17      ! [X: nat,A: nat,B: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ X @ A )
% 9.25/5.17       => ( ( ord_less_eq_nat @ X @ B )
% 9.25/5.17         => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A @ B ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3090_le__infI,axiom,
% 9.25/5.17      ! [X: int,A: int,B: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ X @ A )
% 9.25/5.17       => ( ( ord_less_eq_int @ X @ B )
% 9.25/5.17         => ( ord_less_eq_int @ X @ ( inf_inf_int @ A @ B ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3091_inf__mono,axiom,
% 9.25/5.17      ! [A: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,D2: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le3146513528884898305at_nat @ A @ C )
% 9.25/5.17       => ( ( ord_le3146513528884898305at_nat @ B @ D2 )
% 9.25/5.17         => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ ( inf_in2572325071724192079at_nat @ C @ D2 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3092_inf__mono,axiom,
% 9.25/5.17      ! [A: product_prod_int_int > $o,C: product_prod_int_int > $o,B: product_prod_int_int > $o,D2: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8369615600986905444_int_o @ A @ C )
% 9.25/5.17       => ( ( ord_le8369615600986905444_int_o @ B @ D2 )
% 9.25/5.17         => ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ ( inf_in3604695632404883862_int_o @ C @ D2 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3093_inf__mono,axiom,
% 9.25/5.17      ! [A: list_char > $o,C: list_char > $o,B: list_char > $o,D2: list_char > $o] :
% 9.25/5.17        ( ( ord_le4796328588573674190char_o @ A @ C )
% 9.25/5.17       => ( ( ord_le4796328588573674190char_o @ B @ D2 )
% 9.25/5.17         => ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ A @ B ) @ ( inf_inf_list_char_o @ C @ D2 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3094_inf__mono,axiom,
% 9.25/5.17      ! [A: filter_nat,C: filter_nat,B: filter_nat,D2: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ A @ C )
% 9.25/5.17       => ( ( ord_le2510731241096832064er_nat @ B @ D2 )
% 9.25/5.17         => ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ A @ B ) @ ( inf_inf_filter_nat @ C @ D2 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3095_inf__mono,axiom,
% 9.25/5.17      ! [A: set_nat,C: set_nat,B: set_nat,D2: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ A @ C )
% 9.25/5.17       => ( ( ord_less_eq_set_nat @ B @ D2 )
% 9.25/5.17         => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ ( inf_inf_set_nat @ C @ D2 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3096_inf__mono,axiom,
% 9.25/5.17      ! [A: rat,C: rat,B: rat,D2: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ A @ C )
% 9.25/5.17       => ( ( ord_less_eq_rat @ B @ D2 )
% 9.25/5.17         => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ ( inf_inf_rat @ C @ D2 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3097_inf__mono,axiom,
% 9.25/5.17      ! [A: nat,C: nat,B: nat,D2: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ A @ C )
% 9.25/5.17       => ( ( ord_less_eq_nat @ B @ D2 )
% 9.25/5.17         => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ ( inf_inf_nat @ C @ D2 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3098_inf__mono,axiom,
% 9.25/5.17      ! [A: int,C: int,B: int,D2: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ A @ C )
% 9.25/5.17       => ( ( ord_less_eq_int @ B @ D2 )
% 9.25/5.17         => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ ( inf_inf_int @ C @ D2 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3099_le__infI1,axiom,
% 9.25/5.17      ! [A: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le3146513528884898305at_nat @ A @ X )
% 9.25/5.17       => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3100_le__infI1,axiom,
% 9.25/5.17      ! [A: product_prod_int_int > $o,X: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8369615600986905444_int_o @ A @ X )
% 9.25/5.17       => ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3101_le__infI1,axiom,
% 9.25/5.17      ! [A: list_char > $o,X: list_char > $o,B: list_char > $o] :
% 9.25/5.17        ( ( ord_le4796328588573674190char_o @ A @ X )
% 9.25/5.17       => ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3102_le__infI1,axiom,
% 9.25/5.17      ! [A: filter_nat,X: filter_nat,B: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ A @ X )
% 9.25/5.17       => ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3103_le__infI1,axiom,
% 9.25/5.17      ! [A: set_nat,X: set_nat,B: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ A @ X )
% 9.25/5.17       => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3104_le__infI1,axiom,
% 9.25/5.17      ! [A: rat,X: rat,B: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ A @ X )
% 9.25/5.17       => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3105_le__infI1,axiom,
% 9.25/5.17      ! [A: nat,X: nat,B: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ A @ X )
% 9.25/5.17       => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3106_le__infI1,axiom,
% 9.25/5.17      ! [A: int,X: int,B: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ A @ X )
% 9.25/5.17       => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3107_le__infI2,axiom,
% 9.25/5.17      ! [B: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le3146513528884898305at_nat @ B @ X )
% 9.25/5.17       => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3108_le__infI2,axiom,
% 9.25/5.17      ! [B: product_prod_int_int > $o,X: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8369615600986905444_int_o @ B @ X )
% 9.25/5.17       => ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3109_le__infI2,axiom,
% 9.25/5.17      ! [B: list_char > $o,X: list_char > $o,A: list_char > $o] :
% 9.25/5.17        ( ( ord_le4796328588573674190char_o @ B @ X )
% 9.25/5.17       => ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3110_le__infI2,axiom,
% 9.25/5.17      ! [B: filter_nat,X: filter_nat,A: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ B @ X )
% 9.25/5.17       => ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3111_le__infI2,axiom,
% 9.25/5.17      ! [B: set_nat,X: set_nat,A: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ B @ X )
% 9.25/5.17       => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3112_le__infI2,axiom,
% 9.25/5.17      ! [B: rat,X: rat,A: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ B @ X )
% 9.25/5.17       => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3113_le__infI2,axiom,
% 9.25/5.17      ! [B: nat,X: nat,A: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ B @ X )
% 9.25/5.17       => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3114_le__infI2,axiom,
% 9.25/5.17      ! [B: int,X: int,A: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ B @ X )
% 9.25/5.17       => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3115_inf_OorderE,axiom,
% 9.25/5.17      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le3146513528884898305at_nat @ A @ B )
% 9.25/5.17       => ( A
% 9.25/5.17          = ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3116_inf_OorderE,axiom,
% 9.25/5.17      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8369615600986905444_int_o @ A @ B )
% 9.25/5.17       => ( A
% 9.25/5.17          = ( inf_in3604695632404883862_int_o @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3117_inf_OorderE,axiom,
% 9.25/5.17      ! [A: list_char > $o,B: list_char > $o] :
% 9.25/5.17        ( ( ord_le4796328588573674190char_o @ A @ B )
% 9.25/5.17       => ( A
% 9.25/5.17          = ( inf_inf_list_char_o @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3118_inf_OorderE,axiom,
% 9.25/5.17      ! [A: filter_nat,B: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 9.25/5.17       => ( A
% 9.25/5.17          = ( inf_inf_filter_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3119_inf_OorderE,axiom,
% 9.25/5.17      ! [A: set_nat,B: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ A @ B )
% 9.25/5.17       => ( A
% 9.25/5.17          = ( inf_inf_set_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3120_inf_OorderE,axiom,
% 9.25/5.17      ! [A: rat,B: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.17       => ( A
% 9.25/5.17          = ( inf_inf_rat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3121_inf_OorderE,axiom,
% 9.25/5.17      ! [A: nat,B: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.17       => ( A
% 9.25/5.17          = ( inf_inf_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3122_inf_OorderE,axiom,
% 9.25/5.17      ! [A: int,B: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.17       => ( A
% 9.25/5.17          = ( inf_inf_int @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3123_inf_OorderI,axiom,
% 9.25/5.17      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( A
% 9.25/5.17          = ( inf_in2572325071724192079at_nat @ A @ B ) )
% 9.25/5.17       => ( ord_le3146513528884898305at_nat @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3124_inf_OorderI,axiom,
% 9.25/5.17      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 9.25/5.17        ( ( A
% 9.25/5.17          = ( inf_in3604695632404883862_int_o @ A @ B ) )
% 9.25/5.17       => ( ord_le8369615600986905444_int_o @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3125_inf_OorderI,axiom,
% 9.25/5.17      ! [A: list_char > $o,B: list_char > $o] :
% 9.25/5.17        ( ( A
% 9.25/5.17          = ( inf_inf_list_char_o @ A @ B ) )
% 9.25/5.17       => ( ord_le4796328588573674190char_o @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3126_inf_OorderI,axiom,
% 9.25/5.17      ! [A: filter_nat,B: filter_nat] :
% 9.25/5.17        ( ( A
% 9.25/5.17          = ( inf_inf_filter_nat @ A @ B ) )
% 9.25/5.17       => ( ord_le2510731241096832064er_nat @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3127_inf_OorderI,axiom,
% 9.25/5.17      ! [A: set_nat,B: set_nat] :
% 9.25/5.17        ( ( A
% 9.25/5.17          = ( inf_inf_set_nat @ A @ B ) )
% 9.25/5.17       => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3128_inf_OorderI,axiom,
% 9.25/5.17      ! [A: rat,B: rat] :
% 9.25/5.17        ( ( A
% 9.25/5.17          = ( inf_inf_rat @ A @ B ) )
% 9.25/5.17       => ( ord_less_eq_rat @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3129_inf_OorderI,axiom,
% 9.25/5.17      ! [A: nat,B: nat] :
% 9.25/5.17        ( ( A
% 9.25/5.17          = ( inf_inf_nat @ A @ B ) )
% 9.25/5.17       => ( ord_less_eq_nat @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3130_inf_OorderI,axiom,
% 9.25/5.17      ! [A: int,B: int] :
% 9.25/5.17        ( ( A
% 9.25/5.17          = ( inf_inf_int @ A @ B ) )
% 9.25/5.17       => ( ord_less_eq_int @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3131_inf__unique,axiom,
% 9.25/5.17      ! [F2: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ! [X2: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( F2 @ X2 @ Y2 ) @ X2 )
% 9.25/5.17       => ( ! [X2: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( F2 @ X2 @ Y2 ) @ Y2 )
% 9.25/5.17         => ( ! [X2: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
% 9.25/5.17                ( ( ord_le3146513528884898305at_nat @ X2 @ Y2 )
% 9.25/5.17               => ( ( ord_le3146513528884898305at_nat @ X2 @ Z2 )
% 9.25/5.17                 => ( ord_le3146513528884898305at_nat @ X2 @ ( F2 @ Y2 @ Z2 ) ) ) )
% 9.25/5.17           => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 9.25/5.17              = ( F2 @ X @ Y ) ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3132_inf__unique,axiom,
% 9.25/5.17      ! [F2: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o,X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 9.25/5.17        ( ! [X2: product_prod_int_int > $o,Y2: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( F2 @ X2 @ Y2 ) @ X2 )
% 9.25/5.17       => ( ! [X2: product_prod_int_int > $o,Y2: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( F2 @ X2 @ Y2 ) @ Y2 )
% 9.25/5.17         => ( ! [X2: product_prod_int_int > $o,Y2: product_prod_int_int > $o,Z2: product_prod_int_int > $o] :
% 9.25/5.17                ( ( ord_le8369615600986905444_int_o @ X2 @ Y2 )
% 9.25/5.17               => ( ( ord_le8369615600986905444_int_o @ X2 @ Z2 )
% 9.25/5.17                 => ( ord_le8369615600986905444_int_o @ X2 @ ( F2 @ Y2 @ Z2 ) ) ) )
% 9.25/5.17           => ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 9.25/5.17              = ( F2 @ X @ Y ) ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3133_inf__unique,axiom,
% 9.25/5.17      ! [F2: ( list_char > $o ) > ( list_char > $o ) > list_char > $o,X: list_char > $o,Y: list_char > $o] :
% 9.25/5.17        ( ! [X2: list_char > $o,Y2: list_char > $o] : ( ord_le4796328588573674190char_o @ ( F2 @ X2 @ Y2 ) @ X2 )
% 9.25/5.17       => ( ! [X2: list_char > $o,Y2: list_char > $o] : ( ord_le4796328588573674190char_o @ ( F2 @ X2 @ Y2 ) @ Y2 )
% 9.25/5.17         => ( ! [X2: list_char > $o,Y2: list_char > $o,Z2: list_char > $o] :
% 9.25/5.17                ( ( ord_le4796328588573674190char_o @ X2 @ Y2 )
% 9.25/5.17               => ( ( ord_le4796328588573674190char_o @ X2 @ Z2 )
% 9.25/5.17                 => ( ord_le4796328588573674190char_o @ X2 @ ( F2 @ Y2 @ Z2 ) ) ) )
% 9.25/5.17           => ( ( inf_inf_list_char_o @ X @ Y )
% 9.25/5.17              = ( F2 @ X @ Y ) ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3134_inf__unique,axiom,
% 9.25/5.17      ! [F2: filter_nat > filter_nat > filter_nat,X: filter_nat,Y: filter_nat] :
% 9.25/5.17        ( ! [X2: filter_nat,Y2: filter_nat] : ( ord_le2510731241096832064er_nat @ ( F2 @ X2 @ Y2 ) @ X2 )
% 9.25/5.17       => ( ! [X2: filter_nat,Y2: filter_nat] : ( ord_le2510731241096832064er_nat @ ( F2 @ X2 @ Y2 ) @ Y2 )
% 9.25/5.17         => ( ! [X2: filter_nat,Y2: filter_nat,Z2: filter_nat] :
% 9.25/5.17                ( ( ord_le2510731241096832064er_nat @ X2 @ Y2 )
% 9.25/5.17               => ( ( ord_le2510731241096832064er_nat @ X2 @ Z2 )
% 9.25/5.17                 => ( ord_le2510731241096832064er_nat @ X2 @ ( F2 @ Y2 @ Z2 ) ) ) )
% 9.25/5.17           => ( ( inf_inf_filter_nat @ X @ Y )
% 9.25/5.17              = ( F2 @ X @ Y ) ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3135_inf__unique,axiom,
% 9.25/5.17      ! [F2: set_nat > set_nat > set_nat,X: set_nat,Y: set_nat] :
% 9.25/5.17        ( ! [X2: set_nat,Y2: set_nat] : ( ord_less_eq_set_nat @ ( F2 @ X2 @ Y2 ) @ X2 )
% 9.25/5.17       => ( ! [X2: set_nat,Y2: set_nat] : ( ord_less_eq_set_nat @ ( F2 @ X2 @ Y2 ) @ Y2 )
% 9.25/5.17         => ( ! [X2: set_nat,Y2: set_nat,Z2: set_nat] :
% 9.25/5.17                ( ( ord_less_eq_set_nat @ X2 @ Y2 )
% 9.25/5.17               => ( ( ord_less_eq_set_nat @ X2 @ Z2 )
% 9.25/5.17                 => ( ord_less_eq_set_nat @ X2 @ ( F2 @ Y2 @ Z2 ) ) ) )
% 9.25/5.17           => ( ( inf_inf_set_nat @ X @ Y )
% 9.25/5.17              = ( F2 @ X @ Y ) ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3136_inf__unique,axiom,
% 9.25/5.17      ! [F2: rat > rat > rat,X: rat,Y: rat] :
% 9.25/5.17        ( ! [X2: rat,Y2: rat] : ( ord_less_eq_rat @ ( F2 @ X2 @ Y2 ) @ X2 )
% 9.25/5.17       => ( ! [X2: rat,Y2: rat] : ( ord_less_eq_rat @ ( F2 @ X2 @ Y2 ) @ Y2 )
% 9.25/5.17         => ( ! [X2: rat,Y2: rat,Z2: rat] :
% 9.25/5.17                ( ( ord_less_eq_rat @ X2 @ Y2 )
% 9.25/5.17               => ( ( ord_less_eq_rat @ X2 @ Z2 )
% 9.25/5.17                 => ( ord_less_eq_rat @ X2 @ ( F2 @ Y2 @ Z2 ) ) ) )
% 9.25/5.17           => ( ( inf_inf_rat @ X @ Y )
% 9.25/5.17              = ( F2 @ X @ Y ) ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3137_inf__unique,axiom,
% 9.25/5.17      ! [F2: nat > nat > nat,X: nat,Y: nat] :
% 9.25/5.17        ( ! [X2: nat,Y2: nat] : ( ord_less_eq_nat @ ( F2 @ X2 @ Y2 ) @ X2 )
% 9.25/5.17       => ( ! [X2: nat,Y2: nat] : ( ord_less_eq_nat @ ( F2 @ X2 @ Y2 ) @ Y2 )
% 9.25/5.17         => ( ! [X2: nat,Y2: nat,Z2: nat] :
% 9.25/5.17                ( ( ord_less_eq_nat @ X2 @ Y2 )
% 9.25/5.17               => ( ( ord_less_eq_nat @ X2 @ Z2 )
% 9.25/5.17                 => ( ord_less_eq_nat @ X2 @ ( F2 @ Y2 @ Z2 ) ) ) )
% 9.25/5.17           => ( ( inf_inf_nat @ X @ Y )
% 9.25/5.17              = ( F2 @ X @ Y ) ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3138_inf__unique,axiom,
% 9.25/5.17      ! [F2: int > int > int,X: int,Y: int] :
% 9.25/5.17        ( ! [X2: int,Y2: int] : ( ord_less_eq_int @ ( F2 @ X2 @ Y2 ) @ X2 )
% 9.25/5.17       => ( ! [X2: int,Y2: int] : ( ord_less_eq_int @ ( F2 @ X2 @ Y2 ) @ Y2 )
% 9.25/5.17         => ( ! [X2: int,Y2: int,Z2: int] :
% 9.25/5.17                ( ( ord_less_eq_int @ X2 @ Y2 )
% 9.25/5.17               => ( ( ord_less_eq_int @ X2 @ Z2 )
% 9.25/5.17                 => ( ord_less_eq_int @ X2 @ ( F2 @ Y2 @ Z2 ) ) ) )
% 9.25/5.17           => ( ( inf_inf_int @ X @ Y )
% 9.25/5.17              = ( F2 @ X @ Y ) ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3139_le__iff__inf,axiom,
% 9.25/5.17      ( ord_le3146513528884898305at_nat
% 9.25/5.17      = ( ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 9.25/5.17            ( ( inf_in2572325071724192079at_nat @ X3 @ Y3 )
% 9.25/5.17            = X3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3140_le__iff__inf,axiom,
% 9.25/5.17      ( ord_le8369615600986905444_int_o
% 9.25/5.17      = ( ^ [X3: product_prod_int_int > $o,Y3: product_prod_int_int > $o] :
% 9.25/5.17            ( ( inf_in3604695632404883862_int_o @ X3 @ Y3 )
% 9.25/5.17            = X3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3141_le__iff__inf,axiom,
% 9.25/5.17      ( ord_le4796328588573674190char_o
% 9.25/5.17      = ( ^ [X3: list_char > $o,Y3: list_char > $o] :
% 9.25/5.17            ( ( inf_inf_list_char_o @ X3 @ Y3 )
% 9.25/5.17            = X3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3142_le__iff__inf,axiom,
% 9.25/5.17      ( ord_le2510731241096832064er_nat
% 9.25/5.17      = ( ^ [X3: filter_nat,Y3: filter_nat] :
% 9.25/5.17            ( ( inf_inf_filter_nat @ X3 @ Y3 )
% 9.25/5.17            = X3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3143_le__iff__inf,axiom,
% 9.25/5.17      ( ord_less_eq_set_nat
% 9.25/5.17      = ( ^ [X3: set_nat,Y3: set_nat] :
% 9.25/5.17            ( ( inf_inf_set_nat @ X3 @ Y3 )
% 9.25/5.17            = X3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3144_le__iff__inf,axiom,
% 9.25/5.17      ( ord_less_eq_rat
% 9.25/5.17      = ( ^ [X3: rat,Y3: rat] :
% 9.25/5.17            ( ( inf_inf_rat @ X3 @ Y3 )
% 9.25/5.17            = X3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3145_le__iff__inf,axiom,
% 9.25/5.17      ( ord_less_eq_nat
% 9.25/5.17      = ( ^ [X3: nat,Y3: nat] :
% 9.25/5.17            ( ( inf_inf_nat @ X3 @ Y3 )
% 9.25/5.17            = X3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3146_le__iff__inf,axiom,
% 9.25/5.17      ( ord_less_eq_int
% 9.25/5.17      = ( ^ [X3: int,Y3: int] :
% 9.25/5.17            ( ( inf_inf_int @ X3 @ Y3 )
% 9.25/5.17            = X3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3147_inf_Oabsorb1,axiom,
% 9.25/5.17      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le3146513528884898305at_nat @ A @ B )
% 9.25/5.17       => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3148_inf_Oabsorb1,axiom,
% 9.25/5.17      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8369615600986905444_int_o @ A @ B )
% 9.25/5.17       => ( ( inf_in3604695632404883862_int_o @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3149_inf_Oabsorb1,axiom,
% 9.25/5.17      ! [A: list_char > $o,B: list_char > $o] :
% 9.25/5.17        ( ( ord_le4796328588573674190char_o @ A @ B )
% 9.25/5.17       => ( ( inf_inf_list_char_o @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3150_inf_Oabsorb1,axiom,
% 9.25/5.17      ! [A: filter_nat,B: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 9.25/5.17       => ( ( inf_inf_filter_nat @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3151_inf_Oabsorb1,axiom,
% 9.25/5.17      ! [A: set_nat,B: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ A @ B )
% 9.25/5.17       => ( ( inf_inf_set_nat @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3152_inf_Oabsorb1,axiom,
% 9.25/5.17      ! [A: rat,B: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.17       => ( ( inf_inf_rat @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3153_inf_Oabsorb1,axiom,
% 9.25/5.17      ! [A: nat,B: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.17       => ( ( inf_inf_nat @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3154_inf_Oabsorb1,axiom,
% 9.25/5.17      ! [A: int,B: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.17       => ( ( inf_inf_int @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3155_inf_Oabsorb2,axiom,
% 9.25/5.17      ! [B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le3146513528884898305at_nat @ B @ A )
% 9.25/5.17       => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3156_inf_Oabsorb2,axiom,
% 9.25/5.17      ! [B: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8369615600986905444_int_o @ B @ A )
% 9.25/5.17       => ( ( inf_in3604695632404883862_int_o @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3157_inf_Oabsorb2,axiom,
% 9.25/5.17      ! [B: list_char > $o,A: list_char > $o] :
% 9.25/5.17        ( ( ord_le4796328588573674190char_o @ B @ A )
% 9.25/5.17       => ( ( inf_inf_list_char_o @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3158_inf_Oabsorb2,axiom,
% 9.25/5.17      ! [B: filter_nat,A: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ B @ A )
% 9.25/5.17       => ( ( inf_inf_filter_nat @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3159_inf_Oabsorb2,axiom,
% 9.25/5.17      ! [B: set_nat,A: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ B @ A )
% 9.25/5.17       => ( ( inf_inf_set_nat @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3160_inf_Oabsorb2,axiom,
% 9.25/5.17      ! [B: rat,A: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ B @ A )
% 9.25/5.17       => ( ( inf_inf_rat @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3161_inf_Oabsorb2,axiom,
% 9.25/5.17      ! [B: nat,A: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ B @ A )
% 9.25/5.17       => ( ( inf_inf_nat @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3162_inf_Oabsorb2,axiom,
% 9.25/5.17      ! [B: int,A: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ B @ A )
% 9.25/5.17       => ( ( inf_inf_int @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3163_inf__absorb1,axiom,
% 9.25/5.17      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 9.25/5.17       => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 9.25/5.17          = X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3164_inf__absorb1,axiom,
% 9.25/5.17      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8369615600986905444_int_o @ X @ Y )
% 9.25/5.17       => ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 9.25/5.17          = X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3165_inf__absorb1,axiom,
% 9.25/5.17      ! [X: list_char > $o,Y: list_char > $o] :
% 9.25/5.17        ( ( ord_le4796328588573674190char_o @ X @ Y )
% 9.25/5.17       => ( ( inf_inf_list_char_o @ X @ Y )
% 9.25/5.17          = X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3166_inf__absorb1,axiom,
% 9.25/5.17      ! [X: filter_nat,Y: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 9.25/5.17       => ( ( inf_inf_filter_nat @ X @ Y )
% 9.25/5.17          = X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3167_inf__absorb1,axiom,
% 9.25/5.17      ! [X: set_nat,Y: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ X @ Y )
% 9.25/5.17       => ( ( inf_inf_set_nat @ X @ Y )
% 9.25/5.17          = X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3168_inf__absorb1,axiom,
% 9.25/5.17      ! [X: rat,Y: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ X @ Y )
% 9.25/5.17       => ( ( inf_inf_rat @ X @ Y )
% 9.25/5.17          = X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3169_inf__absorb1,axiom,
% 9.25/5.17      ! [X: nat,Y: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ X @ Y )
% 9.25/5.17       => ( ( inf_inf_nat @ X @ Y )
% 9.25/5.17          = X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3170_inf__absorb1,axiom,
% 9.25/5.17      ! [X: int,Y: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ X @ Y )
% 9.25/5.17       => ( ( inf_inf_int @ X @ Y )
% 9.25/5.17          = X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3171_inf__absorb2,axiom,
% 9.25/5.17      ! [Y: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le3146513528884898305at_nat @ Y @ X )
% 9.25/5.17       => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 9.25/5.17          = Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3172_inf__absorb2,axiom,
% 9.25/5.17      ! [Y: product_prod_int_int > $o,X: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8369615600986905444_int_o @ Y @ X )
% 9.25/5.17       => ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 9.25/5.17          = Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3173_inf__absorb2,axiom,
% 9.25/5.17      ! [Y: list_char > $o,X: list_char > $o] :
% 9.25/5.17        ( ( ord_le4796328588573674190char_o @ Y @ X )
% 9.25/5.17       => ( ( inf_inf_list_char_o @ X @ Y )
% 9.25/5.17          = Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3174_inf__absorb2,axiom,
% 9.25/5.17      ! [Y: filter_nat,X: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 9.25/5.17       => ( ( inf_inf_filter_nat @ X @ Y )
% 9.25/5.17          = Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3175_inf__absorb2,axiom,
% 9.25/5.17      ! [Y: set_nat,X: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ Y @ X )
% 9.25/5.17       => ( ( inf_inf_set_nat @ X @ Y )
% 9.25/5.17          = Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3176_inf__absorb2,axiom,
% 9.25/5.17      ! [Y: rat,X: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ Y @ X )
% 9.25/5.17       => ( ( inf_inf_rat @ X @ Y )
% 9.25/5.17          = Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3177_inf__absorb2,axiom,
% 9.25/5.17      ! [Y: nat,X: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ Y @ X )
% 9.25/5.17       => ( ( inf_inf_nat @ X @ Y )
% 9.25/5.17          = Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3178_inf__absorb2,axiom,
% 9.25/5.17      ! [Y: int,X: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ Y @ X )
% 9.25/5.17       => ( ( inf_inf_int @ X @ Y )
% 9.25/5.17          = Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3179_inf_OboundedE,axiom,
% 9.25/5.17      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) )
% 9.25/5.17       => ~ ( ( ord_le3146513528884898305at_nat @ A @ B )
% 9.25/5.17           => ~ ( ord_le3146513528884898305at_nat @ A @ C ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3180_inf_OboundedE,axiom,
% 9.25/5.17      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o,C: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8369615600986905444_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C ) )
% 9.25/5.17       => ~ ( ( ord_le8369615600986905444_int_o @ A @ B )
% 9.25/5.17           => ~ ( ord_le8369615600986905444_int_o @ A @ C ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3181_inf_OboundedE,axiom,
% 9.25/5.17      ! [A: list_char > $o,B: list_char > $o,C: list_char > $o] :
% 9.25/5.17        ( ( ord_le4796328588573674190char_o @ A @ ( inf_inf_list_char_o @ B @ C ) )
% 9.25/5.17       => ~ ( ( ord_le4796328588573674190char_o @ A @ B )
% 9.25/5.17           => ~ ( ord_le4796328588573674190char_o @ A @ C ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3182_inf_OboundedE,axiom,
% 9.25/5.17      ! [A: filter_nat,B: filter_nat,C: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ A @ ( inf_inf_filter_nat @ B @ C ) )
% 9.25/5.17       => ~ ( ( ord_le2510731241096832064er_nat @ A @ B )
% 9.25/5.17           => ~ ( ord_le2510731241096832064er_nat @ A @ C ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3183_inf_OboundedE,axiom,
% 9.25/5.17      ! [A: set_nat,B: set_nat,C: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) )
% 9.25/5.17       => ~ ( ( ord_less_eq_set_nat @ A @ B )
% 9.25/5.17           => ~ ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3184_inf_OboundedE,axiom,
% 9.25/5.17      ! [A: rat,B: rat,C: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C ) )
% 9.25/5.17       => ~ ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.17           => ~ ( ord_less_eq_rat @ A @ C ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3185_inf_OboundedE,axiom,
% 9.25/5.17      ! [A: nat,B: nat,C: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C ) )
% 9.25/5.17       => ~ ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.17           => ~ ( ord_less_eq_nat @ A @ C ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3186_inf_OboundedE,axiom,
% 9.25/5.17      ! [A: int,B: int,C: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C ) )
% 9.25/5.17       => ~ ( ( ord_less_eq_int @ A @ B )
% 9.25/5.17           => ~ ( ord_less_eq_int @ A @ C ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3187_inf_OboundedI,axiom,
% 9.25/5.17      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le3146513528884898305at_nat @ A @ B )
% 9.25/5.17       => ( ( ord_le3146513528884898305at_nat @ A @ C )
% 9.25/5.17         => ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3188_inf_OboundedI,axiom,
% 9.25/5.17      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o,C: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8369615600986905444_int_o @ A @ B )
% 9.25/5.17       => ( ( ord_le8369615600986905444_int_o @ A @ C )
% 9.25/5.17         => ( ord_le8369615600986905444_int_o @ A @ ( inf_in3604695632404883862_int_o @ B @ C ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3189_inf_OboundedI,axiom,
% 9.25/5.17      ! [A: list_char > $o,B: list_char > $o,C: list_char > $o] :
% 9.25/5.17        ( ( ord_le4796328588573674190char_o @ A @ B )
% 9.25/5.17       => ( ( ord_le4796328588573674190char_o @ A @ C )
% 9.25/5.17         => ( ord_le4796328588573674190char_o @ A @ ( inf_inf_list_char_o @ B @ C ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3190_inf_OboundedI,axiom,
% 9.25/5.17      ! [A: filter_nat,B: filter_nat,C: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 9.25/5.17       => ( ( ord_le2510731241096832064er_nat @ A @ C )
% 9.25/5.17         => ( ord_le2510731241096832064er_nat @ A @ ( inf_inf_filter_nat @ B @ C ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3191_inf_OboundedI,axiom,
% 9.25/5.17      ! [A: set_nat,B: set_nat,C: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ A @ B )
% 9.25/5.17       => ( ( ord_less_eq_set_nat @ A @ C )
% 9.25/5.17         => ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3192_inf_OboundedI,axiom,
% 9.25/5.17      ! [A: rat,B: rat,C: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.17       => ( ( ord_less_eq_rat @ A @ C )
% 9.25/5.17         => ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3193_inf_OboundedI,axiom,
% 9.25/5.17      ! [A: nat,B: nat,C: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.17       => ( ( ord_less_eq_nat @ A @ C )
% 9.25/5.17         => ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3194_inf_OboundedI,axiom,
% 9.25/5.17      ! [A: int,B: int,C: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.17       => ( ( ord_less_eq_int @ A @ C )
% 9.25/5.17         => ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3195_inf__greatest,axiom,
% 9.25/5.17      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 9.25/5.17       => ( ( ord_le3146513528884898305at_nat @ X @ Z )
% 9.25/5.17         => ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3196_inf__greatest,axiom,
% 9.25/5.17      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8369615600986905444_int_o @ X @ Y )
% 9.25/5.17       => ( ( ord_le8369615600986905444_int_o @ X @ Z )
% 9.25/5.17         => ( ord_le8369615600986905444_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3197_inf__greatest,axiom,
% 9.25/5.17      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 9.25/5.17        ( ( ord_le4796328588573674190char_o @ X @ Y )
% 9.25/5.17       => ( ( ord_le4796328588573674190char_o @ X @ Z )
% 9.25/5.17         => ( ord_le4796328588573674190char_o @ X @ ( inf_inf_list_char_o @ Y @ Z ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3198_inf__greatest,axiom,
% 9.25/5.17      ! [X: filter_nat,Y: filter_nat,Z: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 9.25/5.17       => ( ( ord_le2510731241096832064er_nat @ X @ Z )
% 9.25/5.17         => ( ord_le2510731241096832064er_nat @ X @ ( inf_inf_filter_nat @ Y @ Z ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3199_inf__greatest,axiom,
% 9.25/5.17      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ X @ Y )
% 9.25/5.17       => ( ( ord_less_eq_set_nat @ X @ Z )
% 9.25/5.17         => ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3200_inf__greatest,axiom,
% 9.25/5.17      ! [X: rat,Y: rat,Z: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ X @ Y )
% 9.25/5.17       => ( ( ord_less_eq_rat @ X @ Z )
% 9.25/5.17         => ( ord_less_eq_rat @ X @ ( inf_inf_rat @ Y @ Z ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3201_inf__greatest,axiom,
% 9.25/5.17      ! [X: nat,Y: nat,Z: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ X @ Y )
% 9.25/5.17       => ( ( ord_less_eq_nat @ X @ Z )
% 9.25/5.17         => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3202_inf__greatest,axiom,
% 9.25/5.17      ! [X: int,Y: int,Z: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ X @ Y )
% 9.25/5.17       => ( ( ord_less_eq_int @ X @ Z )
% 9.25/5.17         => ( ord_less_eq_int @ X @ ( inf_inf_int @ Y @ Z ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3203_inf_Oorder__iff,axiom,
% 9.25/5.17      ( ord_le3146513528884898305at_nat
% 9.25/5.17      = ( ^ [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 9.25/5.17            ( A3
% 9.25/5.17            = ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3204_inf_Oorder__iff,axiom,
% 9.25/5.17      ( ord_le8369615600986905444_int_o
% 9.25/5.17      = ( ^ [A3: product_prod_int_int > $o,B3: product_prod_int_int > $o] :
% 9.25/5.17            ( A3
% 9.25/5.17            = ( inf_in3604695632404883862_int_o @ A3 @ B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3205_inf_Oorder__iff,axiom,
% 9.25/5.17      ( ord_le4796328588573674190char_o
% 9.25/5.17      = ( ^ [A3: list_char > $o,B3: list_char > $o] :
% 9.25/5.17            ( A3
% 9.25/5.17            = ( inf_inf_list_char_o @ A3 @ B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3206_inf_Oorder__iff,axiom,
% 9.25/5.17      ( ord_le2510731241096832064er_nat
% 9.25/5.17      = ( ^ [A3: filter_nat,B3: filter_nat] :
% 9.25/5.17            ( A3
% 9.25/5.17            = ( inf_inf_filter_nat @ A3 @ B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3207_inf_Oorder__iff,axiom,
% 9.25/5.17      ( ord_less_eq_set_nat
% 9.25/5.17      = ( ^ [A3: set_nat,B3: set_nat] :
% 9.25/5.17            ( A3
% 9.25/5.17            = ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3208_inf_Oorder__iff,axiom,
% 9.25/5.17      ( ord_less_eq_rat
% 9.25/5.17      = ( ^ [A3: rat,B3: rat] :
% 9.25/5.17            ( A3
% 9.25/5.17            = ( inf_inf_rat @ A3 @ B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3209_inf_Oorder__iff,axiom,
% 9.25/5.17      ( ord_less_eq_nat
% 9.25/5.17      = ( ^ [A3: nat,B3: nat] :
% 9.25/5.17            ( A3
% 9.25/5.17            = ( inf_inf_nat @ A3 @ B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3210_inf_Oorder__iff,axiom,
% 9.25/5.17      ( ord_less_eq_int
% 9.25/5.17      = ( ^ [A3: int,B3: int] :
% 9.25/5.17            ( A3
% 9.25/5.17            = ( inf_inf_int @ A3 @ B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3211_inf_Ocobounded1,axiom,
% 9.25/5.17      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ A ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3212_inf_Ocobounded1,axiom,
% 9.25/5.17      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ A ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3213_inf_Ocobounded1,axiom,
% 9.25/5.17      ! [A: list_char > $o,B: list_char > $o] : ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ A @ B ) @ A ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3214_inf_Ocobounded1,axiom,
% 9.25/5.17      ! [A: filter_nat,B: filter_nat] : ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ A @ B ) @ A ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3215_inf_Ocobounded1,axiom,
% 9.25/5.17      ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ A ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3216_inf_Ocobounded1,axiom,
% 9.25/5.17      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ A ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3217_inf_Ocobounded1,axiom,
% 9.25/5.17      ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ A ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3218_inf_Ocobounded1,axiom,
% 9.25/5.17      ! [A: int,B: int] : ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ A ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3219_inf_Ocobounded2,axiom,
% 9.25/5.17      ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ B ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3220_inf_Ocobounded2,axiom,
% 9.25/5.17      ! [A: product_prod_int_int > $o,B: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ B ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3221_inf_Ocobounded2,axiom,
% 9.25/5.17      ! [A: list_char > $o,B: list_char > $o] : ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ A @ B ) @ B ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3222_inf_Ocobounded2,axiom,
% 9.25/5.17      ! [A: filter_nat,B: filter_nat] : ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ A @ B ) @ B ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3223_inf_Ocobounded2,axiom,
% 9.25/5.17      ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ B ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3224_inf_Ocobounded2,axiom,
% 9.25/5.17      ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ B ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3225_inf_Ocobounded2,axiom,
% 9.25/5.17      ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ B ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3226_inf_Ocobounded2,axiom,
% 9.25/5.17      ! [A: int,B: int] : ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ B ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3227_inf_Oabsorb__iff1,axiom,
% 9.25/5.17      ( ord_le3146513528884898305at_nat
% 9.25/5.17      = ( ^ [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 9.25/5.17            ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 9.25/5.17            = A3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3228_inf_Oabsorb__iff1,axiom,
% 9.25/5.17      ( ord_le8369615600986905444_int_o
% 9.25/5.17      = ( ^ [A3: product_prod_int_int > $o,B3: product_prod_int_int > $o] :
% 9.25/5.17            ( ( inf_in3604695632404883862_int_o @ A3 @ B3 )
% 9.25/5.17            = A3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3229_inf_Oabsorb__iff1,axiom,
% 9.25/5.17      ( ord_le4796328588573674190char_o
% 9.25/5.17      = ( ^ [A3: list_char > $o,B3: list_char > $o] :
% 9.25/5.17            ( ( inf_inf_list_char_o @ A3 @ B3 )
% 9.25/5.17            = A3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3230_inf_Oabsorb__iff1,axiom,
% 9.25/5.17      ( ord_le2510731241096832064er_nat
% 9.25/5.17      = ( ^ [A3: filter_nat,B3: filter_nat] :
% 9.25/5.17            ( ( inf_inf_filter_nat @ A3 @ B3 )
% 9.25/5.17            = A3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3231_inf_Oabsorb__iff1,axiom,
% 9.25/5.17      ( ord_less_eq_set_nat
% 9.25/5.17      = ( ^ [A3: set_nat,B3: set_nat] :
% 9.25/5.17            ( ( inf_inf_set_nat @ A3 @ B3 )
% 9.25/5.17            = A3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3232_inf_Oabsorb__iff1,axiom,
% 9.25/5.17      ( ord_less_eq_rat
% 9.25/5.17      = ( ^ [A3: rat,B3: rat] :
% 9.25/5.17            ( ( inf_inf_rat @ A3 @ B3 )
% 9.25/5.17            = A3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3233_inf_Oabsorb__iff1,axiom,
% 9.25/5.17      ( ord_less_eq_nat
% 9.25/5.17      = ( ^ [A3: nat,B3: nat] :
% 9.25/5.17            ( ( inf_inf_nat @ A3 @ B3 )
% 9.25/5.17            = A3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3234_inf_Oabsorb__iff1,axiom,
% 9.25/5.17      ( ord_less_eq_int
% 9.25/5.17      = ( ^ [A3: int,B3: int] :
% 9.25/5.17            ( ( inf_inf_int @ A3 @ B3 )
% 9.25/5.17            = A3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3235_inf_Oabsorb__iff2,axiom,
% 9.25/5.17      ( ord_le3146513528884898305at_nat
% 9.25/5.17      = ( ^ [B3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 9.25/5.17            ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 9.25/5.17            = B3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3236_inf_Oabsorb__iff2,axiom,
% 9.25/5.17      ( ord_le8369615600986905444_int_o
% 9.25/5.17      = ( ^ [B3: product_prod_int_int > $o,A3: product_prod_int_int > $o] :
% 9.25/5.17            ( ( inf_in3604695632404883862_int_o @ A3 @ B3 )
% 9.25/5.17            = B3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3237_inf_Oabsorb__iff2,axiom,
% 9.25/5.17      ( ord_le4796328588573674190char_o
% 9.25/5.17      = ( ^ [B3: list_char > $o,A3: list_char > $o] :
% 9.25/5.17            ( ( inf_inf_list_char_o @ A3 @ B3 )
% 9.25/5.17            = B3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3238_inf_Oabsorb__iff2,axiom,
% 9.25/5.17      ( ord_le2510731241096832064er_nat
% 9.25/5.17      = ( ^ [B3: filter_nat,A3: filter_nat] :
% 9.25/5.17            ( ( inf_inf_filter_nat @ A3 @ B3 )
% 9.25/5.17            = B3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3239_inf_Oabsorb__iff2,axiom,
% 9.25/5.17      ( ord_less_eq_set_nat
% 9.25/5.17      = ( ^ [B3: set_nat,A3: set_nat] :
% 9.25/5.17            ( ( inf_inf_set_nat @ A3 @ B3 )
% 9.25/5.17            = B3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3240_inf_Oabsorb__iff2,axiom,
% 9.25/5.17      ( ord_less_eq_rat
% 9.25/5.17      = ( ^ [B3: rat,A3: rat] :
% 9.25/5.17            ( ( inf_inf_rat @ A3 @ B3 )
% 9.25/5.17            = B3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3241_inf_Oabsorb__iff2,axiom,
% 9.25/5.17      ( ord_less_eq_nat
% 9.25/5.17      = ( ^ [B3: nat,A3: nat] :
% 9.25/5.17            ( ( inf_inf_nat @ A3 @ B3 )
% 9.25/5.17            = B3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3242_inf_Oabsorb__iff2,axiom,
% 9.25/5.17      ( ord_less_eq_int
% 9.25/5.17      = ( ^ [B3: int,A3: int] :
% 9.25/5.17            ( ( inf_inf_int @ A3 @ B3 )
% 9.25/5.17            = B3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3243_inf_OcoboundedI1,axiom,
% 9.25/5.17      ! [A: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le3146513528884898305at_nat @ A @ C )
% 9.25/5.17       => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3244_inf_OcoboundedI1,axiom,
% 9.25/5.17      ! [A: product_prod_int_int > $o,C: product_prod_int_int > $o,B: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8369615600986905444_int_o @ A @ C )
% 9.25/5.17       => ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3245_inf_OcoboundedI1,axiom,
% 9.25/5.17      ! [A: list_char > $o,C: list_char > $o,B: list_char > $o] :
% 9.25/5.17        ( ( ord_le4796328588573674190char_o @ A @ C )
% 9.25/5.17       => ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3246_inf_OcoboundedI1,axiom,
% 9.25/5.17      ! [A: filter_nat,C: filter_nat,B: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ A @ C )
% 9.25/5.17       => ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3247_inf_OcoboundedI1,axiom,
% 9.25/5.17      ! [A: set_nat,C: set_nat,B: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ A @ C )
% 9.25/5.17       => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3248_inf_OcoboundedI1,axiom,
% 9.25/5.17      ! [A: rat,C: rat,B: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ A @ C )
% 9.25/5.17       => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3249_inf_OcoboundedI1,axiom,
% 9.25/5.17      ! [A: nat,C: nat,B: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ A @ C )
% 9.25/5.17       => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3250_inf_OcoboundedI1,axiom,
% 9.25/5.17      ! [A: int,C: int,B: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ A @ C )
% 9.25/5.17       => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3251_inf_OcoboundedI2,axiom,
% 9.25/5.17      ! [B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 9.25/5.17        ( ( ord_le3146513528884898305at_nat @ B @ C )
% 9.25/5.17       => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3252_inf_OcoboundedI2,axiom,
% 9.25/5.17      ! [B: product_prod_int_int > $o,C: product_prod_int_int > $o,A: product_prod_int_int > $o] :
% 9.25/5.17        ( ( ord_le8369615600986905444_int_o @ B @ C )
% 9.25/5.17       => ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3253_inf_OcoboundedI2,axiom,
% 9.25/5.17      ! [B: list_char > $o,C: list_char > $o,A: list_char > $o] :
% 9.25/5.17        ( ( ord_le4796328588573674190char_o @ B @ C )
% 9.25/5.17       => ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3254_inf_OcoboundedI2,axiom,
% 9.25/5.17      ! [B: filter_nat,C: filter_nat,A: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ B @ C )
% 9.25/5.17       => ( ord_le2510731241096832064er_nat @ ( inf_inf_filter_nat @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3255_inf_OcoboundedI2,axiom,
% 9.25/5.17      ! [B: set_nat,C: set_nat,A: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ B @ C )
% 9.25/5.17       => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3256_inf_OcoboundedI2,axiom,
% 9.25/5.17      ! [B: rat,C: rat,A: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ B @ C )
% 9.25/5.17       => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3257_inf_OcoboundedI2,axiom,
% 9.25/5.17      ! [B: nat,C: nat,A: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ B @ C )
% 9.25/5.17       => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3258_inf_OcoboundedI2,axiom,
% 9.25/5.17      ! [B: int,C: int,A: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ B @ C )
% 9.25/5.17       => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ C ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3259_inf__sup__ord_I4_J,axiom,
% 9.25/5.17      ! [Y: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ Y @ ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3260_inf__sup__ord_I4_J,axiom,
% 9.25/5.17      ! [Y: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3261_inf__sup__ord_I4_J,axiom,
% 9.25/5.17      ! [Y: filter_nat,X: filter_nat] : ( ord_le2510731241096832064er_nat @ Y @ ( sup_sup_filter_nat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3262_inf__sup__ord_I4_J,axiom,
% 9.25/5.17      ! [Y: set_nat,X: set_nat] : ( ord_less_eq_set_nat @ Y @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3263_inf__sup__ord_I4_J,axiom,
% 9.25/5.17      ! [Y: rat,X: rat] : ( ord_less_eq_rat @ Y @ ( sup_sup_rat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3264_inf__sup__ord_I4_J,axiom,
% 9.25/5.17      ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3265_inf__sup__ord_I4_J,axiom,
% 9.25/5.17      ! [Y: int,X: int] : ( ord_less_eq_int @ Y @ ( sup_sup_int @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3266_inf__sup__ord_I3_J,axiom,
% 9.25/5.17      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3267_inf__sup__ord_I3_J,axiom,
% 9.25/5.17      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3268_inf__sup__ord_I3_J,axiom,
% 9.25/5.17      ! [X: filter_nat,Y: filter_nat] : ( ord_le2510731241096832064er_nat @ X @ ( sup_sup_filter_nat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3269_inf__sup__ord_I3_J,axiom,
% 9.25/5.17      ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3270_inf__sup__ord_I3_J,axiom,
% 9.25/5.17      ! [X: rat,Y: rat] : ( ord_less_eq_rat @ X @ ( sup_sup_rat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3271_inf__sup__ord_I3_J,axiom,
% 9.25/5.17      ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3272_inf__sup__ord_I3_J,axiom,
% 9.25/5.17      ! [X: int,Y: int] : ( ord_less_eq_int @ X @ ( sup_sup_int @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3273_le__supE,axiom,
% 9.25/5.17      ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A @ B ) @ X )
% 9.25/5.17       => ~ ( ( ord_le8081472938463900775at_nat @ A @ X )
% 9.25/5.17           => ~ ( ord_le8081472938463900775at_nat @ B @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3274_le__supE,axiom,
% 9.25/5.17      ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ X )
% 9.25/5.17       => ~ ( ( ord_le1268244103169919719at_nat @ A @ X )
% 9.25/5.17           => ~ ( ord_le1268244103169919719at_nat @ B @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3275_le__supE,axiom,
% 9.25/5.17      ! [A: filter_nat,B: filter_nat,X: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ A @ B ) @ X )
% 9.25/5.17       => ~ ( ( ord_le2510731241096832064er_nat @ A @ X )
% 9.25/5.17           => ~ ( ord_le2510731241096832064er_nat @ B @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3276_le__supE,axiom,
% 9.25/5.17      ! [A: set_nat,B: set_nat,X: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ X )
% 9.25/5.17       => ~ ( ( ord_less_eq_set_nat @ A @ X )
% 9.25/5.17           => ~ ( ord_less_eq_set_nat @ B @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3277_le__supE,axiom,
% 9.25/5.17      ! [A: rat,B: rat,X: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ X )
% 9.25/5.17       => ~ ( ( ord_less_eq_rat @ A @ X )
% 9.25/5.17           => ~ ( ord_less_eq_rat @ B @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3278_le__supE,axiom,
% 9.25/5.17      ! [A: nat,B: nat,X: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X )
% 9.25/5.17       => ~ ( ( ord_less_eq_nat @ A @ X )
% 9.25/5.17           => ~ ( ord_less_eq_nat @ B @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3279_le__supE,axiom,
% 9.25/5.17      ! [A: int,B: int,X: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ X )
% 9.25/5.17       => ~ ( ( ord_less_eq_int @ A @ X )
% 9.25/5.17           => ~ ( ord_less_eq_int @ B @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3280_le__supI,axiom,
% 9.25/5.17      ! [A: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le8081472938463900775at_nat @ A @ X )
% 9.25/5.17       => ( ( ord_le8081472938463900775at_nat @ B @ X )
% 9.25/5.17         => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A @ B ) @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3281_le__supI,axiom,
% 9.25/5.17      ! [A: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le1268244103169919719at_nat @ A @ X )
% 9.25/5.17       => ( ( ord_le1268244103169919719at_nat @ B @ X )
% 9.25/5.17         => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3282_le__supI,axiom,
% 9.25/5.17      ! [A: filter_nat,X: filter_nat,B: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ A @ X )
% 9.25/5.17       => ( ( ord_le2510731241096832064er_nat @ B @ X )
% 9.25/5.17         => ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ A @ B ) @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3283_le__supI,axiom,
% 9.25/5.17      ! [A: set_nat,X: set_nat,B: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ A @ X )
% 9.25/5.17       => ( ( ord_less_eq_set_nat @ B @ X )
% 9.25/5.17         => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3284_le__supI,axiom,
% 9.25/5.17      ! [A: rat,X: rat,B: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ A @ X )
% 9.25/5.17       => ( ( ord_less_eq_rat @ B @ X )
% 9.25/5.17         => ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3285_le__supI,axiom,
% 9.25/5.17      ! [A: nat,X: nat,B: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ A @ X )
% 9.25/5.17       => ( ( ord_less_eq_nat @ B @ X )
% 9.25/5.17         => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3286_le__supI,axiom,
% 9.25/5.17      ! [A: int,X: int,B: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ A @ X )
% 9.25/5.17       => ( ( ord_less_eq_int @ B @ X )
% 9.25/5.17         => ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3287_sup__ge1,axiom,
% 9.25/5.17      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3288_sup__ge1,axiom,
% 9.25/5.17      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3289_sup__ge1,axiom,
% 9.25/5.17      ! [X: filter_nat,Y: filter_nat] : ( ord_le2510731241096832064er_nat @ X @ ( sup_sup_filter_nat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3290_sup__ge1,axiom,
% 9.25/5.17      ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3291_sup__ge1,axiom,
% 9.25/5.17      ! [X: rat,Y: rat] : ( ord_less_eq_rat @ X @ ( sup_sup_rat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3292_sup__ge1,axiom,
% 9.25/5.17      ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3293_sup__ge1,axiom,
% 9.25/5.17      ! [X: int,Y: int] : ( ord_less_eq_int @ X @ ( sup_sup_int @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3294_sup__ge2,axiom,
% 9.25/5.17      ! [Y: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ Y @ ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3295_sup__ge2,axiom,
% 9.25/5.17      ! [Y: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3296_sup__ge2,axiom,
% 9.25/5.17      ! [Y: filter_nat,X: filter_nat] : ( ord_le2510731241096832064er_nat @ Y @ ( sup_sup_filter_nat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3297_sup__ge2,axiom,
% 9.25/5.17      ! [Y: set_nat,X: set_nat] : ( ord_less_eq_set_nat @ Y @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3298_sup__ge2,axiom,
% 9.25/5.17      ! [Y: rat,X: rat] : ( ord_less_eq_rat @ Y @ ( sup_sup_rat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3299_sup__ge2,axiom,
% 9.25/5.17      ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3300_sup__ge2,axiom,
% 9.25/5.17      ! [Y: int,X: int] : ( ord_less_eq_int @ Y @ ( sup_sup_int @ X @ Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3301_le__supI1,axiom,
% 9.25/5.17      ! [X: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le8081472938463900775at_nat @ X @ A )
% 9.25/5.17       => ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3302_le__supI1,axiom,
% 9.25/5.17      ! [X: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le1268244103169919719at_nat @ X @ A )
% 9.25/5.17       => ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3303_le__supI1,axiom,
% 9.25/5.17      ! [X: filter_nat,A: filter_nat,B: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ X @ A )
% 9.25/5.17       => ( ord_le2510731241096832064er_nat @ X @ ( sup_sup_filter_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3304_le__supI1,axiom,
% 9.25/5.17      ! [X: set_nat,A: set_nat,B: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ X @ A )
% 9.25/5.17       => ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3305_le__supI1,axiom,
% 9.25/5.17      ! [X: rat,A: rat,B: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ X @ A )
% 9.25/5.17       => ( ord_less_eq_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3306_le__supI1,axiom,
% 9.25/5.17      ! [X: nat,A: nat,B: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ X @ A )
% 9.25/5.17       => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3307_le__supI1,axiom,
% 9.25/5.17      ! [X: int,A: int,B: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ X @ A )
% 9.25/5.17       => ( ord_less_eq_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3308_le__supI2,axiom,
% 9.25/5.17      ! [X: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le8081472938463900775at_nat @ X @ B )
% 9.25/5.17       => ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3309_le__supI2,axiom,
% 9.25/5.17      ! [X: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le1268244103169919719at_nat @ X @ B )
% 9.25/5.17       => ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3310_le__supI2,axiom,
% 9.25/5.17      ! [X: filter_nat,B: filter_nat,A: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ X @ B )
% 9.25/5.17       => ( ord_le2510731241096832064er_nat @ X @ ( sup_sup_filter_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3311_le__supI2,axiom,
% 9.25/5.17      ! [X: set_nat,B: set_nat,A: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ X @ B )
% 9.25/5.17       => ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3312_le__supI2,axiom,
% 9.25/5.17      ! [X: rat,B: rat,A: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ X @ B )
% 9.25/5.17       => ( ord_less_eq_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3313_le__supI2,axiom,
% 9.25/5.17      ! [X: nat,B: nat,A: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ X @ B )
% 9.25/5.17       => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3314_le__supI2,axiom,
% 9.25/5.17      ! [X: int,B: int,A: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ X @ B )
% 9.25/5.17       => ( ord_less_eq_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3315_sup_Omono,axiom,
% 9.25/5.17      ! [C: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,D2: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le8081472938463900775at_nat @ C @ A )
% 9.25/5.17       => ( ( ord_le8081472938463900775at_nat @ D2 @ B )
% 9.25/5.17         => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ C @ D2 ) @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3316_sup_Omono,axiom,
% 9.25/5.17      ! [C: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,D2: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le1268244103169919719at_nat @ C @ A )
% 9.25/5.17       => ( ( ord_le1268244103169919719at_nat @ D2 @ B )
% 9.25/5.17         => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ C @ D2 ) @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3317_sup_Omono,axiom,
% 9.25/5.17      ! [C: filter_nat,A: filter_nat,D2: filter_nat,B: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ C @ A )
% 9.25/5.17       => ( ( ord_le2510731241096832064er_nat @ D2 @ B )
% 9.25/5.17         => ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ C @ D2 ) @ ( sup_sup_filter_nat @ A @ B ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3318_sup_Omono,axiom,
% 9.25/5.17      ! [C: set_nat,A: set_nat,D2: set_nat,B: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ C @ A )
% 9.25/5.17       => ( ( ord_less_eq_set_nat @ D2 @ B )
% 9.25/5.17         => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ C @ D2 ) @ ( sup_sup_set_nat @ A @ B ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3319_sup_Omono,axiom,
% 9.25/5.17      ! [C: rat,A: rat,D2: rat,B: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ C @ A )
% 9.25/5.17       => ( ( ord_less_eq_rat @ D2 @ B )
% 9.25/5.17         => ( ord_less_eq_rat @ ( sup_sup_rat @ C @ D2 ) @ ( sup_sup_rat @ A @ B ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3320_sup_Omono,axiom,
% 9.25/5.17      ! [C: nat,A: nat,D2: nat,B: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ C @ A )
% 9.25/5.17       => ( ( ord_less_eq_nat @ D2 @ B )
% 9.25/5.17         => ( ord_less_eq_nat @ ( sup_sup_nat @ C @ D2 ) @ ( sup_sup_nat @ A @ B ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3321_sup_Omono,axiom,
% 9.25/5.17      ! [C: int,A: int,D2: int,B: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ C @ A )
% 9.25/5.17       => ( ( ord_less_eq_int @ D2 @ B )
% 9.25/5.17         => ( ord_less_eq_int @ ( sup_sup_int @ C @ D2 ) @ ( sup_sup_int @ A @ B ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3322_sup__mono,axiom,
% 9.25/5.17      ! [A: set_Pr8551490117392284871at_nat,C: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,D2: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le8081472938463900775at_nat @ A @ C )
% 9.25/5.17       => ( ( ord_le8081472938463900775at_nat @ B @ D2 )
% 9.25/5.17         => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A @ B ) @ ( sup_su3035147773818789531at_nat @ C @ D2 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3323_sup__mono,axiom,
% 9.25/5.17      ! [A: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,D2: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le1268244103169919719at_nat @ A @ C )
% 9.25/5.17       => ( ( ord_le1268244103169919719at_nat @ B @ D2 )
% 9.25/5.17         => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ ( sup_su5525570899277871387at_nat @ C @ D2 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3324_sup__mono,axiom,
% 9.25/5.17      ! [A: filter_nat,C: filter_nat,B: filter_nat,D2: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ A @ C )
% 9.25/5.17       => ( ( ord_le2510731241096832064er_nat @ B @ D2 )
% 9.25/5.17         => ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ A @ B ) @ ( sup_sup_filter_nat @ C @ D2 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3325_sup__mono,axiom,
% 9.25/5.17      ! [A: set_nat,C: set_nat,B: set_nat,D2: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ A @ C )
% 9.25/5.17       => ( ( ord_less_eq_set_nat @ B @ D2 )
% 9.25/5.17         => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ ( sup_sup_set_nat @ C @ D2 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3326_sup__mono,axiom,
% 9.25/5.17      ! [A: rat,C: rat,B: rat,D2: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ A @ C )
% 9.25/5.17       => ( ( ord_less_eq_rat @ B @ D2 )
% 9.25/5.17         => ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ ( sup_sup_rat @ C @ D2 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3327_sup__mono,axiom,
% 9.25/5.17      ! [A: nat,C: nat,B: nat,D2: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ A @ C )
% 9.25/5.17       => ( ( ord_less_eq_nat @ B @ D2 )
% 9.25/5.17         => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ ( sup_sup_nat @ C @ D2 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3328_sup__mono,axiom,
% 9.25/5.17      ! [A: int,C: int,B: int,D2: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ A @ C )
% 9.25/5.17       => ( ( ord_less_eq_int @ B @ D2 )
% 9.25/5.17         => ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ ( sup_sup_int @ C @ D2 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3329_sup__least,axiom,
% 9.25/5.17      ! [Y: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le8081472938463900775at_nat @ Y @ X )
% 9.25/5.17       => ( ( ord_le8081472938463900775at_nat @ Z @ X )
% 9.25/5.17         => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ Y @ Z ) @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3330_sup__least,axiom,
% 9.25/5.17      ! [Y: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le1268244103169919719at_nat @ Y @ X )
% 9.25/5.17       => ( ( ord_le1268244103169919719at_nat @ Z @ X )
% 9.25/5.17         => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ Y @ Z ) @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3331_sup__least,axiom,
% 9.25/5.17      ! [Y: filter_nat,X: filter_nat,Z: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 9.25/5.17       => ( ( ord_le2510731241096832064er_nat @ Z @ X )
% 9.25/5.17         => ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ Y @ Z ) @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3332_sup__least,axiom,
% 9.25/5.17      ! [Y: set_nat,X: set_nat,Z: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ Y @ X )
% 9.25/5.17       => ( ( ord_less_eq_set_nat @ Z @ X )
% 9.25/5.17         => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ Y @ Z ) @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3333_sup__least,axiom,
% 9.25/5.17      ! [Y: rat,X: rat,Z: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ Y @ X )
% 9.25/5.17       => ( ( ord_less_eq_rat @ Z @ X )
% 9.25/5.17         => ( ord_less_eq_rat @ ( sup_sup_rat @ Y @ Z ) @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3334_sup__least,axiom,
% 9.25/5.17      ! [Y: nat,X: nat,Z: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ Y @ X )
% 9.25/5.17       => ( ( ord_less_eq_nat @ Z @ X )
% 9.25/5.17         => ( ord_less_eq_nat @ ( sup_sup_nat @ Y @ Z ) @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3335_sup__least,axiom,
% 9.25/5.17      ! [Y: int,X: int,Z: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ Y @ X )
% 9.25/5.17       => ( ( ord_less_eq_int @ Z @ X )
% 9.25/5.17         => ( ord_less_eq_int @ ( sup_sup_int @ Y @ Z ) @ X ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3336_le__iff__sup,axiom,
% 9.25/5.17      ( ord_le8081472938463900775at_nat
% 9.25/5.17      = ( ^ [X3: set_Pr8551490117392284871at_nat,Y3: set_Pr8551490117392284871at_nat] :
% 9.25/5.17            ( ( sup_su3035147773818789531at_nat @ X3 @ Y3 )
% 9.25/5.17            = Y3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3337_le__iff__sup,axiom,
% 9.25/5.17      ( ord_le1268244103169919719at_nat
% 9.25/5.17      = ( ^ [X3: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] :
% 9.25/5.17            ( ( sup_su5525570899277871387at_nat @ X3 @ Y3 )
% 9.25/5.17            = Y3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3338_le__iff__sup,axiom,
% 9.25/5.17      ( ord_le2510731241096832064er_nat
% 9.25/5.17      = ( ^ [X3: filter_nat,Y3: filter_nat] :
% 9.25/5.17            ( ( sup_sup_filter_nat @ X3 @ Y3 )
% 9.25/5.17            = Y3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3339_le__iff__sup,axiom,
% 9.25/5.17      ( ord_less_eq_set_nat
% 9.25/5.17      = ( ^ [X3: set_nat,Y3: set_nat] :
% 9.25/5.17            ( ( sup_sup_set_nat @ X3 @ Y3 )
% 9.25/5.17            = Y3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3340_le__iff__sup,axiom,
% 9.25/5.17      ( ord_less_eq_rat
% 9.25/5.17      = ( ^ [X3: rat,Y3: rat] :
% 9.25/5.17            ( ( sup_sup_rat @ X3 @ Y3 )
% 9.25/5.17            = Y3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3341_le__iff__sup,axiom,
% 9.25/5.17      ( ord_less_eq_nat
% 9.25/5.17      = ( ^ [X3: nat,Y3: nat] :
% 9.25/5.17            ( ( sup_sup_nat @ X3 @ Y3 )
% 9.25/5.17            = Y3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3342_le__iff__sup,axiom,
% 9.25/5.17      ( ord_less_eq_int
% 9.25/5.17      = ( ^ [X3: int,Y3: int] :
% 9.25/5.17            ( ( sup_sup_int @ X3 @ Y3 )
% 9.25/5.17            = Y3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3343_sup_OorderE,axiom,
% 9.25/5.17      ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le8081472938463900775at_nat @ B @ A )
% 9.25/5.17       => ( A
% 9.25/5.17          = ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3344_sup_OorderE,axiom,
% 9.25/5.17      ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le1268244103169919719at_nat @ B @ A )
% 9.25/5.17       => ( A
% 9.25/5.17          = ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3345_sup_OorderE,axiom,
% 9.25/5.17      ! [B: filter_nat,A: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ B @ A )
% 9.25/5.17       => ( A
% 9.25/5.17          = ( sup_sup_filter_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3346_sup_OorderE,axiom,
% 9.25/5.17      ! [B: set_nat,A: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ B @ A )
% 9.25/5.17       => ( A
% 9.25/5.17          = ( sup_sup_set_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3347_sup_OorderE,axiom,
% 9.25/5.17      ! [B: rat,A: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ B @ A )
% 9.25/5.17       => ( A
% 9.25/5.17          = ( sup_sup_rat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3348_sup_OorderE,axiom,
% 9.25/5.17      ! [B: nat,A: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ B @ A )
% 9.25/5.17       => ( A
% 9.25/5.17          = ( sup_sup_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3349_sup_OorderE,axiom,
% 9.25/5.17      ! [B: int,A: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ B @ A )
% 9.25/5.17       => ( A
% 9.25/5.17          = ( sup_sup_int @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3350_sup_OorderI,axiom,
% 9.25/5.17      ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( A
% 9.25/5.17          = ( sup_su3035147773818789531at_nat @ A @ B ) )
% 9.25/5.17       => ( ord_le8081472938463900775at_nat @ B @ A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3351_sup_OorderI,axiom,
% 9.25/5.17      ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( A
% 9.25/5.17          = ( sup_su5525570899277871387at_nat @ A @ B ) )
% 9.25/5.17       => ( ord_le1268244103169919719at_nat @ B @ A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3352_sup_OorderI,axiom,
% 9.25/5.17      ! [A: filter_nat,B: filter_nat] :
% 9.25/5.17        ( ( A
% 9.25/5.17          = ( sup_sup_filter_nat @ A @ B ) )
% 9.25/5.17       => ( ord_le2510731241096832064er_nat @ B @ A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3353_sup_OorderI,axiom,
% 9.25/5.17      ! [A: set_nat,B: set_nat] :
% 9.25/5.17        ( ( A
% 9.25/5.17          = ( sup_sup_set_nat @ A @ B ) )
% 9.25/5.17       => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3354_sup_OorderI,axiom,
% 9.25/5.17      ! [A: rat,B: rat] :
% 9.25/5.17        ( ( A
% 9.25/5.17          = ( sup_sup_rat @ A @ B ) )
% 9.25/5.17       => ( ord_less_eq_rat @ B @ A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3355_sup_OorderI,axiom,
% 9.25/5.17      ! [A: nat,B: nat] :
% 9.25/5.17        ( ( A
% 9.25/5.17          = ( sup_sup_nat @ A @ B ) )
% 9.25/5.17       => ( ord_less_eq_nat @ B @ A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3356_sup_OorderI,axiom,
% 9.25/5.17      ! [A: int,B: int] :
% 9.25/5.17        ( ( A
% 9.25/5.17          = ( sup_sup_int @ A @ B ) )
% 9.25/5.17       => ( ord_less_eq_int @ B @ A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3357_sup__unique,axiom,
% 9.25/5.17      ! [F2: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ! [X2: set_Pr8551490117392284871at_nat,Y2: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ X2 @ ( F2 @ X2 @ Y2 ) )
% 9.25/5.17       => ( ! [X2: set_Pr8551490117392284871at_nat,Y2: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ Y2 @ ( F2 @ X2 @ Y2 ) )
% 9.25/5.17         => ( ! [X2: set_Pr8551490117392284871at_nat,Y2: set_Pr8551490117392284871at_nat,Z2: set_Pr8551490117392284871at_nat] :
% 9.25/5.17                ( ( ord_le8081472938463900775at_nat @ Y2 @ X2 )
% 9.25/5.17               => ( ( ord_le8081472938463900775at_nat @ Z2 @ X2 )
% 9.25/5.17                 => ( ord_le8081472938463900775at_nat @ ( F2 @ Y2 @ Z2 ) @ X2 ) ) )
% 9.25/5.17           => ( ( sup_su3035147773818789531at_nat @ X @ Y )
% 9.25/5.17              = ( F2 @ X @ Y ) ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3358_sup__unique,axiom,
% 9.25/5.17      ! [F2: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ! [X2: set_Pr4329608150637261639at_nat,Y2: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ X2 @ ( F2 @ X2 @ Y2 ) )
% 9.25/5.17       => ( ! [X2: set_Pr4329608150637261639at_nat,Y2: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y2 @ ( F2 @ X2 @ Y2 ) )
% 9.25/5.17         => ( ! [X2: set_Pr4329608150637261639at_nat,Y2: set_Pr4329608150637261639at_nat,Z2: set_Pr4329608150637261639at_nat] :
% 9.25/5.17                ( ( ord_le1268244103169919719at_nat @ Y2 @ X2 )
% 9.25/5.17               => ( ( ord_le1268244103169919719at_nat @ Z2 @ X2 )
% 9.25/5.17                 => ( ord_le1268244103169919719at_nat @ ( F2 @ Y2 @ Z2 ) @ X2 ) ) )
% 9.25/5.17           => ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 9.25/5.17              = ( F2 @ X @ Y ) ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3359_sup__unique,axiom,
% 9.25/5.17      ! [F2: filter_nat > filter_nat > filter_nat,X: filter_nat,Y: filter_nat] :
% 9.25/5.17        ( ! [X2: filter_nat,Y2: filter_nat] : ( ord_le2510731241096832064er_nat @ X2 @ ( F2 @ X2 @ Y2 ) )
% 9.25/5.17       => ( ! [X2: filter_nat,Y2: filter_nat] : ( ord_le2510731241096832064er_nat @ Y2 @ ( F2 @ X2 @ Y2 ) )
% 9.25/5.17         => ( ! [X2: filter_nat,Y2: filter_nat,Z2: filter_nat] :
% 9.25/5.17                ( ( ord_le2510731241096832064er_nat @ Y2 @ X2 )
% 9.25/5.17               => ( ( ord_le2510731241096832064er_nat @ Z2 @ X2 )
% 9.25/5.17                 => ( ord_le2510731241096832064er_nat @ ( F2 @ Y2 @ Z2 ) @ X2 ) ) )
% 9.25/5.17           => ( ( sup_sup_filter_nat @ X @ Y )
% 9.25/5.17              = ( F2 @ X @ Y ) ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3360_sup__unique,axiom,
% 9.25/5.17      ! [F2: set_nat > set_nat > set_nat,X: set_nat,Y: set_nat] :
% 9.25/5.17        ( ! [X2: set_nat,Y2: set_nat] : ( ord_less_eq_set_nat @ X2 @ ( F2 @ X2 @ Y2 ) )
% 9.25/5.17       => ( ! [X2: set_nat,Y2: set_nat] : ( ord_less_eq_set_nat @ Y2 @ ( F2 @ X2 @ Y2 ) )
% 9.25/5.17         => ( ! [X2: set_nat,Y2: set_nat,Z2: set_nat] :
% 9.25/5.17                ( ( ord_less_eq_set_nat @ Y2 @ X2 )
% 9.25/5.17               => ( ( ord_less_eq_set_nat @ Z2 @ X2 )
% 9.25/5.17                 => ( ord_less_eq_set_nat @ ( F2 @ Y2 @ Z2 ) @ X2 ) ) )
% 9.25/5.17           => ( ( sup_sup_set_nat @ X @ Y )
% 9.25/5.17              = ( F2 @ X @ Y ) ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3361_sup__unique,axiom,
% 9.25/5.17      ! [F2: rat > rat > rat,X: rat,Y: rat] :
% 9.25/5.17        ( ! [X2: rat,Y2: rat] : ( ord_less_eq_rat @ X2 @ ( F2 @ X2 @ Y2 ) )
% 9.25/5.17       => ( ! [X2: rat,Y2: rat] : ( ord_less_eq_rat @ Y2 @ ( F2 @ X2 @ Y2 ) )
% 9.25/5.17         => ( ! [X2: rat,Y2: rat,Z2: rat] :
% 9.25/5.17                ( ( ord_less_eq_rat @ Y2 @ X2 )
% 9.25/5.17               => ( ( ord_less_eq_rat @ Z2 @ X2 )
% 9.25/5.17                 => ( ord_less_eq_rat @ ( F2 @ Y2 @ Z2 ) @ X2 ) ) )
% 9.25/5.17           => ( ( sup_sup_rat @ X @ Y )
% 9.25/5.17              = ( F2 @ X @ Y ) ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3362_sup__unique,axiom,
% 9.25/5.17      ! [F2: nat > nat > nat,X: nat,Y: nat] :
% 9.25/5.17        ( ! [X2: nat,Y2: nat] : ( ord_less_eq_nat @ X2 @ ( F2 @ X2 @ Y2 ) )
% 9.25/5.17       => ( ! [X2: nat,Y2: nat] : ( ord_less_eq_nat @ Y2 @ ( F2 @ X2 @ Y2 ) )
% 9.25/5.17         => ( ! [X2: nat,Y2: nat,Z2: nat] :
% 9.25/5.17                ( ( ord_less_eq_nat @ Y2 @ X2 )
% 9.25/5.17               => ( ( ord_less_eq_nat @ Z2 @ X2 )
% 9.25/5.17                 => ( ord_less_eq_nat @ ( F2 @ Y2 @ Z2 ) @ X2 ) ) )
% 9.25/5.17           => ( ( sup_sup_nat @ X @ Y )
% 9.25/5.17              = ( F2 @ X @ Y ) ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3363_sup__unique,axiom,
% 9.25/5.17      ! [F2: int > int > int,X: int,Y: int] :
% 9.25/5.17        ( ! [X2: int,Y2: int] : ( ord_less_eq_int @ X2 @ ( F2 @ X2 @ Y2 ) )
% 9.25/5.17       => ( ! [X2: int,Y2: int] : ( ord_less_eq_int @ Y2 @ ( F2 @ X2 @ Y2 ) )
% 9.25/5.17         => ( ! [X2: int,Y2: int,Z2: int] :
% 9.25/5.17                ( ( ord_less_eq_int @ Y2 @ X2 )
% 9.25/5.17               => ( ( ord_less_eq_int @ Z2 @ X2 )
% 9.25/5.17                 => ( ord_less_eq_int @ ( F2 @ Y2 @ Z2 ) @ X2 ) ) )
% 9.25/5.17           => ( ( sup_sup_int @ X @ Y )
% 9.25/5.17              = ( F2 @ X @ Y ) ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3364_sup_Oabsorb1,axiom,
% 9.25/5.17      ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le8081472938463900775at_nat @ B @ A )
% 9.25/5.17       => ( ( sup_su3035147773818789531at_nat @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3365_sup_Oabsorb1,axiom,
% 9.25/5.17      ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le1268244103169919719at_nat @ B @ A )
% 9.25/5.17       => ( ( sup_su5525570899277871387at_nat @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3366_sup_Oabsorb1,axiom,
% 9.25/5.17      ! [B: filter_nat,A: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ B @ A )
% 9.25/5.17       => ( ( sup_sup_filter_nat @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3367_sup_Oabsorb1,axiom,
% 9.25/5.17      ! [B: set_nat,A: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ B @ A )
% 9.25/5.17       => ( ( sup_sup_set_nat @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3368_sup_Oabsorb1,axiom,
% 9.25/5.17      ! [B: rat,A: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ B @ A )
% 9.25/5.17       => ( ( sup_sup_rat @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3369_sup_Oabsorb1,axiom,
% 9.25/5.17      ! [B: nat,A: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ B @ A )
% 9.25/5.17       => ( ( sup_sup_nat @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3370_sup_Oabsorb1,axiom,
% 9.25/5.17      ! [B: int,A: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ B @ A )
% 9.25/5.17       => ( ( sup_sup_int @ A @ B )
% 9.25/5.17          = A ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3371_sup_Oabsorb2,axiom,
% 9.25/5.17      ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le8081472938463900775at_nat @ A @ B )
% 9.25/5.17       => ( ( sup_su3035147773818789531at_nat @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3372_sup_Oabsorb2,axiom,
% 9.25/5.17      ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le1268244103169919719at_nat @ A @ B )
% 9.25/5.17       => ( ( sup_su5525570899277871387at_nat @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3373_sup_Oabsorb2,axiom,
% 9.25/5.17      ! [A: filter_nat,B: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ A @ B )
% 9.25/5.17       => ( ( sup_sup_filter_nat @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3374_sup_Oabsorb2,axiom,
% 9.25/5.17      ! [A: set_nat,B: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ A @ B )
% 9.25/5.17       => ( ( sup_sup_set_nat @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3375_sup_Oabsorb2,axiom,
% 9.25/5.17      ! [A: rat,B: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.17       => ( ( sup_sup_rat @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3376_sup_Oabsorb2,axiom,
% 9.25/5.17      ! [A: nat,B: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.17       => ( ( sup_sup_nat @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3377_sup_Oabsorb2,axiom,
% 9.25/5.17      ! [A: int,B: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.17       => ( ( sup_sup_int @ A @ B )
% 9.25/5.17          = B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3378_sup__absorb1,axiom,
% 9.25/5.17      ! [Y: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le8081472938463900775at_nat @ Y @ X )
% 9.25/5.17       => ( ( sup_su3035147773818789531at_nat @ X @ Y )
% 9.25/5.17          = X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3379_sup__absorb1,axiom,
% 9.25/5.17      ! [Y: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le1268244103169919719at_nat @ Y @ X )
% 9.25/5.17       => ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 9.25/5.17          = X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3380_sup__absorb1,axiom,
% 9.25/5.17      ! [Y: filter_nat,X: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ Y @ X )
% 9.25/5.17       => ( ( sup_sup_filter_nat @ X @ Y )
% 9.25/5.17          = X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3381_sup__absorb1,axiom,
% 9.25/5.17      ! [Y: set_nat,X: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ Y @ X )
% 9.25/5.17       => ( ( sup_sup_set_nat @ X @ Y )
% 9.25/5.17          = X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3382_sup__absorb1,axiom,
% 9.25/5.17      ! [Y: rat,X: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ Y @ X )
% 9.25/5.17       => ( ( sup_sup_rat @ X @ Y )
% 9.25/5.17          = X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3383_sup__absorb1,axiom,
% 9.25/5.17      ! [Y: nat,X: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ Y @ X )
% 9.25/5.17       => ( ( sup_sup_nat @ X @ Y )
% 9.25/5.17          = X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3384_sup__absorb1,axiom,
% 9.25/5.17      ! [Y: int,X: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ Y @ X )
% 9.25/5.17       => ( ( sup_sup_int @ X @ Y )
% 9.25/5.17          = X ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3385_sup__absorb2,axiom,
% 9.25/5.17      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le8081472938463900775at_nat @ X @ Y )
% 9.25/5.17       => ( ( sup_su3035147773818789531at_nat @ X @ Y )
% 9.25/5.17          = Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3386_sup__absorb2,axiom,
% 9.25/5.17      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le1268244103169919719at_nat @ X @ Y )
% 9.25/5.17       => ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 9.25/5.17          = Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3387_sup__absorb2,axiom,
% 9.25/5.17      ! [X: filter_nat,Y: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ X @ Y )
% 9.25/5.17       => ( ( sup_sup_filter_nat @ X @ Y )
% 9.25/5.17          = Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3388_sup__absorb2,axiom,
% 9.25/5.17      ! [X: set_nat,Y: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ X @ Y )
% 9.25/5.17       => ( ( sup_sup_set_nat @ X @ Y )
% 9.25/5.17          = Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3389_sup__absorb2,axiom,
% 9.25/5.17      ! [X: rat,Y: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ X @ Y )
% 9.25/5.17       => ( ( sup_sup_rat @ X @ Y )
% 9.25/5.17          = Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3390_sup__absorb2,axiom,
% 9.25/5.17      ! [X: nat,Y: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ X @ Y )
% 9.25/5.17       => ( ( sup_sup_nat @ X @ Y )
% 9.25/5.17          = Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3391_sup__absorb2,axiom,
% 9.25/5.17      ! [X: int,Y: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ X @ Y )
% 9.25/5.17       => ( ( sup_sup_int @ X @ Y )
% 9.25/5.17          = Y ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3392_sup_OboundedE,axiom,
% 9.25/5.17      ! [B: set_Pr8551490117392284871at_nat,C: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ B @ C ) @ A )
% 9.25/5.17       => ~ ( ( ord_le8081472938463900775at_nat @ B @ A )
% 9.25/5.17           => ~ ( ord_le8081472938463900775at_nat @ C @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3393_sup_OboundedE,axiom,
% 9.25/5.17      ! [B: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ B @ C ) @ A )
% 9.25/5.17       => ~ ( ( ord_le1268244103169919719at_nat @ B @ A )
% 9.25/5.17           => ~ ( ord_le1268244103169919719at_nat @ C @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3394_sup_OboundedE,axiom,
% 9.25/5.17      ! [B: filter_nat,C: filter_nat,A: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ B @ C ) @ A )
% 9.25/5.17       => ~ ( ( ord_le2510731241096832064er_nat @ B @ A )
% 9.25/5.17           => ~ ( ord_le2510731241096832064er_nat @ C @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3395_sup_OboundedE,axiom,
% 9.25/5.17      ! [B: set_nat,C: set_nat,A: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C ) @ A )
% 9.25/5.17       => ~ ( ( ord_less_eq_set_nat @ B @ A )
% 9.25/5.17           => ~ ( ord_less_eq_set_nat @ C @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3396_sup_OboundedE,axiom,
% 9.25/5.17      ! [B: rat,C: rat,A: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C ) @ A )
% 9.25/5.17       => ~ ( ( ord_less_eq_rat @ B @ A )
% 9.25/5.17           => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3397_sup_OboundedE,axiom,
% 9.25/5.17      ! [B: nat,C: nat,A: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C ) @ A )
% 9.25/5.17       => ~ ( ( ord_less_eq_nat @ B @ A )
% 9.25/5.17           => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3398_sup_OboundedE,axiom,
% 9.25/5.17      ! [B: int,C: int,A: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ ( sup_sup_int @ B @ C ) @ A )
% 9.25/5.17       => ~ ( ( ord_less_eq_int @ B @ A )
% 9.25/5.17           => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3399_sup_OboundedI,axiom,
% 9.25/5.17      ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,C: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le8081472938463900775at_nat @ B @ A )
% 9.25/5.17       => ( ( ord_le8081472938463900775at_nat @ C @ A )
% 9.25/5.17         => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ B @ C ) @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3400_sup_OboundedI,axiom,
% 9.25/5.17      ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le1268244103169919719at_nat @ B @ A )
% 9.25/5.17       => ( ( ord_le1268244103169919719at_nat @ C @ A )
% 9.25/5.17         => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ B @ C ) @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3401_sup_OboundedI,axiom,
% 9.25/5.17      ! [B: filter_nat,A: filter_nat,C: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ B @ A )
% 9.25/5.17       => ( ( ord_le2510731241096832064er_nat @ C @ A )
% 9.25/5.17         => ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ B @ C ) @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3402_sup_OboundedI,axiom,
% 9.25/5.17      ! [B: set_nat,A: set_nat,C: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ B @ A )
% 9.25/5.17       => ( ( ord_less_eq_set_nat @ C @ A )
% 9.25/5.17         => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C ) @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3403_sup_OboundedI,axiom,
% 9.25/5.17      ! [B: rat,A: rat,C: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ B @ A )
% 9.25/5.17       => ( ( ord_less_eq_rat @ C @ A )
% 9.25/5.17         => ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C ) @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3404_sup_OboundedI,axiom,
% 9.25/5.17      ! [B: nat,A: nat,C: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ B @ A )
% 9.25/5.17       => ( ( ord_less_eq_nat @ C @ A )
% 9.25/5.17         => ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C ) @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3405_sup_OboundedI,axiom,
% 9.25/5.17      ! [B: int,A: int,C: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ B @ A )
% 9.25/5.17       => ( ( ord_less_eq_int @ C @ A )
% 9.25/5.17         => ( ord_less_eq_int @ ( sup_sup_int @ B @ C ) @ A ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3406_sup_Oorder__iff,axiom,
% 9.25/5.17      ( ord_le8081472938463900775at_nat
% 9.25/5.17      = ( ^ [B3: set_Pr8551490117392284871at_nat,A3: set_Pr8551490117392284871at_nat] :
% 9.25/5.17            ( A3
% 9.25/5.17            = ( sup_su3035147773818789531at_nat @ A3 @ B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3407_sup_Oorder__iff,axiom,
% 9.25/5.17      ( ord_le1268244103169919719at_nat
% 9.25/5.17      = ( ^ [B3: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] :
% 9.25/5.17            ( A3
% 9.25/5.17            = ( sup_su5525570899277871387at_nat @ A3 @ B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3408_sup_Oorder__iff,axiom,
% 9.25/5.17      ( ord_le2510731241096832064er_nat
% 9.25/5.17      = ( ^ [B3: filter_nat,A3: filter_nat] :
% 9.25/5.17            ( A3
% 9.25/5.17            = ( sup_sup_filter_nat @ A3 @ B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3409_sup_Oorder__iff,axiom,
% 9.25/5.17      ( ord_less_eq_set_nat
% 9.25/5.17      = ( ^ [B3: set_nat,A3: set_nat] :
% 9.25/5.17            ( A3
% 9.25/5.17            = ( sup_sup_set_nat @ A3 @ B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3410_sup_Oorder__iff,axiom,
% 9.25/5.17      ( ord_less_eq_rat
% 9.25/5.17      = ( ^ [B3: rat,A3: rat] :
% 9.25/5.17            ( A3
% 9.25/5.17            = ( sup_sup_rat @ A3 @ B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3411_sup_Oorder__iff,axiom,
% 9.25/5.17      ( ord_less_eq_nat
% 9.25/5.17      = ( ^ [B3: nat,A3: nat] :
% 9.25/5.17            ( A3
% 9.25/5.17            = ( sup_sup_nat @ A3 @ B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3412_sup_Oorder__iff,axiom,
% 9.25/5.17      ( ord_less_eq_int
% 9.25/5.17      = ( ^ [B3: int,A3: int] :
% 9.25/5.17            ( A3
% 9.25/5.17            = ( sup_sup_int @ A3 @ B3 ) ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3413_sup_Ocobounded1,axiom,
% 9.25/5.17      ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ A @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3414_sup_Ocobounded1,axiom,
% 9.25/5.17      ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ A @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3415_sup_Ocobounded1,axiom,
% 9.25/5.17      ! [A: filter_nat,B: filter_nat] : ( ord_le2510731241096832064er_nat @ A @ ( sup_sup_filter_nat @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3416_sup_Ocobounded1,axiom,
% 9.25/5.17      ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ A @ ( sup_sup_set_nat @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3417_sup_Ocobounded1,axiom,
% 9.25/5.17      ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( sup_sup_rat @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3418_sup_Ocobounded1,axiom,
% 9.25/5.17      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( sup_sup_nat @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3419_sup_Ocobounded1,axiom,
% 9.25/5.17      ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( sup_sup_int @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3420_sup_Ocobounded2,axiom,
% 9.25/5.17      ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ B @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3421_sup_Ocobounded2,axiom,
% 9.25/5.17      ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ B @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3422_sup_Ocobounded2,axiom,
% 9.25/5.17      ! [B: filter_nat,A: filter_nat] : ( ord_le2510731241096832064er_nat @ B @ ( sup_sup_filter_nat @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3423_sup_Ocobounded2,axiom,
% 9.25/5.17      ! [B: set_nat,A: set_nat] : ( ord_less_eq_set_nat @ B @ ( sup_sup_set_nat @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3424_sup_Ocobounded2,axiom,
% 9.25/5.17      ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( sup_sup_rat @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3425_sup_Ocobounded2,axiom,
% 9.25/5.17      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( sup_sup_nat @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3426_sup_Ocobounded2,axiom,
% 9.25/5.17      ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( sup_sup_int @ A @ B ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3427_sup_Oabsorb__iff1,axiom,
% 9.25/5.17      ( ord_le8081472938463900775at_nat
% 9.25/5.17      = ( ^ [B3: set_Pr8551490117392284871at_nat,A3: set_Pr8551490117392284871at_nat] :
% 9.25/5.17            ( ( sup_su3035147773818789531at_nat @ A3 @ B3 )
% 9.25/5.17            = A3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3428_sup_Oabsorb__iff1,axiom,
% 9.25/5.17      ( ord_le1268244103169919719at_nat
% 9.25/5.17      = ( ^ [B3: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] :
% 9.25/5.17            ( ( sup_su5525570899277871387at_nat @ A3 @ B3 )
% 9.25/5.17            = A3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3429_sup_Oabsorb__iff1,axiom,
% 9.25/5.17      ( ord_le2510731241096832064er_nat
% 9.25/5.17      = ( ^ [B3: filter_nat,A3: filter_nat] :
% 9.25/5.17            ( ( sup_sup_filter_nat @ A3 @ B3 )
% 9.25/5.17            = A3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3430_sup_Oabsorb__iff1,axiom,
% 9.25/5.17      ( ord_less_eq_set_nat
% 9.25/5.17      = ( ^ [B3: set_nat,A3: set_nat] :
% 9.25/5.17            ( ( sup_sup_set_nat @ A3 @ B3 )
% 9.25/5.17            = A3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3431_sup_Oabsorb__iff1,axiom,
% 9.25/5.17      ( ord_less_eq_rat
% 9.25/5.17      = ( ^ [B3: rat,A3: rat] :
% 9.25/5.17            ( ( sup_sup_rat @ A3 @ B3 )
% 9.25/5.17            = A3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3432_sup_Oabsorb__iff1,axiom,
% 9.25/5.17      ( ord_less_eq_nat
% 9.25/5.17      = ( ^ [B3: nat,A3: nat] :
% 9.25/5.17            ( ( sup_sup_nat @ A3 @ B3 )
% 9.25/5.17            = A3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3433_sup_Oabsorb__iff1,axiom,
% 9.25/5.17      ( ord_less_eq_int
% 9.25/5.17      = ( ^ [B3: int,A3: int] :
% 9.25/5.17            ( ( sup_sup_int @ A3 @ B3 )
% 9.25/5.17            = A3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3434_sup_Oabsorb__iff2,axiom,
% 9.25/5.17      ( ord_le8081472938463900775at_nat
% 9.25/5.17      = ( ^ [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] :
% 9.25/5.17            ( ( sup_su3035147773818789531at_nat @ A3 @ B3 )
% 9.25/5.17            = B3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3435_sup_Oabsorb__iff2,axiom,
% 9.25/5.17      ( ord_le1268244103169919719at_nat
% 9.25/5.17      = ( ^ [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 9.25/5.17            ( ( sup_su5525570899277871387at_nat @ A3 @ B3 )
% 9.25/5.17            = B3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3436_sup_Oabsorb__iff2,axiom,
% 9.25/5.17      ( ord_le2510731241096832064er_nat
% 9.25/5.17      = ( ^ [A3: filter_nat,B3: filter_nat] :
% 9.25/5.17            ( ( sup_sup_filter_nat @ A3 @ B3 )
% 9.25/5.17            = B3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3437_sup_Oabsorb__iff2,axiom,
% 9.25/5.17      ( ord_less_eq_set_nat
% 9.25/5.17      = ( ^ [A3: set_nat,B3: set_nat] :
% 9.25/5.17            ( ( sup_sup_set_nat @ A3 @ B3 )
% 9.25/5.17            = B3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3438_sup_Oabsorb__iff2,axiom,
% 9.25/5.17      ( ord_less_eq_rat
% 9.25/5.17      = ( ^ [A3: rat,B3: rat] :
% 9.25/5.17            ( ( sup_sup_rat @ A3 @ B3 )
% 9.25/5.17            = B3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3439_sup_Oabsorb__iff2,axiom,
% 9.25/5.17      ( ord_less_eq_nat
% 9.25/5.17      = ( ^ [A3: nat,B3: nat] :
% 9.25/5.17            ( ( sup_sup_nat @ A3 @ B3 )
% 9.25/5.17            = B3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3440_sup_Oabsorb__iff2,axiom,
% 9.25/5.17      ( ord_less_eq_int
% 9.25/5.17      = ( ^ [A3: int,B3: int] :
% 9.25/5.17            ( ( sup_sup_int @ A3 @ B3 )
% 9.25/5.17            = B3 ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3441_sup_OcoboundedI1,axiom,
% 9.25/5.17      ! [C: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le8081472938463900775at_nat @ C @ A )
% 9.25/5.17       => ( ord_le8081472938463900775at_nat @ C @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3442_sup_OcoboundedI1,axiom,
% 9.25/5.17      ! [C: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le1268244103169919719at_nat @ C @ A )
% 9.25/5.17       => ( ord_le1268244103169919719at_nat @ C @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3443_sup_OcoboundedI1,axiom,
% 9.25/5.17      ! [C: filter_nat,A: filter_nat,B: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ C @ A )
% 9.25/5.17       => ( ord_le2510731241096832064er_nat @ C @ ( sup_sup_filter_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3444_sup_OcoboundedI1,axiom,
% 9.25/5.17      ! [C: set_nat,A: set_nat,B: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ C @ A )
% 9.25/5.17       => ( ord_less_eq_set_nat @ C @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3445_sup_OcoboundedI1,axiom,
% 9.25/5.17      ! [C: rat,A: rat,B: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ C @ A )
% 9.25/5.17       => ( ord_less_eq_rat @ C @ ( sup_sup_rat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3446_sup_OcoboundedI1,axiom,
% 9.25/5.17      ! [C: nat,A: nat,B: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ C @ A )
% 9.25/5.17       => ( ord_less_eq_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3447_sup_OcoboundedI1,axiom,
% 9.25/5.17      ! [C: int,A: int,B: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ C @ A )
% 9.25/5.17       => ( ord_less_eq_int @ C @ ( sup_sup_int @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3448_sup_OcoboundedI2,axiom,
% 9.25/5.17      ! [C: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 9.25/5.17        ( ( ord_le8081472938463900775at_nat @ C @ B )
% 9.25/5.17       => ( ord_le8081472938463900775at_nat @ C @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3449_sup_OcoboundedI2,axiom,
% 9.25/5.17      ! [C: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 9.25/5.17        ( ( ord_le1268244103169919719at_nat @ C @ B )
% 9.25/5.17       => ( ord_le1268244103169919719at_nat @ C @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3450_sup_OcoboundedI2,axiom,
% 9.25/5.17      ! [C: filter_nat,B: filter_nat,A: filter_nat] :
% 9.25/5.17        ( ( ord_le2510731241096832064er_nat @ C @ B )
% 9.25/5.17       => ( ord_le2510731241096832064er_nat @ C @ ( sup_sup_filter_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3451_sup_OcoboundedI2,axiom,
% 9.25/5.17      ! [C: set_nat,B: set_nat,A: set_nat] :
% 9.25/5.17        ( ( ord_less_eq_set_nat @ C @ B )
% 9.25/5.17       => ( ord_less_eq_set_nat @ C @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3452_sup_OcoboundedI2,axiom,
% 9.25/5.17      ! [C: rat,B: rat,A: rat] :
% 9.25/5.17        ( ( ord_less_eq_rat @ C @ B )
% 9.25/5.17       => ( ord_less_eq_rat @ C @ ( sup_sup_rat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3453_sup_OcoboundedI2,axiom,
% 9.25/5.17      ! [C: nat,B: nat,A: nat] :
% 9.25/5.17        ( ( ord_less_eq_nat @ C @ B )
% 9.25/5.17       => ( ord_less_eq_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).
% 9.25/5.17  
% 9.25/5.17  thf(fact_3454_sup_OcoboundedI2,axiom,
% 9.25/5.17      ! [C: int,B: int,A: int] :
% 9.25/5.17        ( ( ord_less_eq_int @ C @ B )
% 9.25/5.18       => ( ord_less_eq_int @ C @ ( sup_sup_int @ A @ B ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3455_subset__UNIV,axiom,
% 9.25/5.18      ! [A2: set_list_nat] : ( ord_le6045566169113846134st_nat @ A2 @ top_top_set_list_nat ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3456_subset__UNIV,axiom,
% 9.25/5.18      ! [A2: set_o] : ( ord_less_eq_set_o @ A2 @ top_top_set_o ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3457_subset__UNIV,axiom,
% 9.25/5.18      ! [A2: set_rat] : ( ord_less_eq_set_rat @ A2 @ top_top_set_rat ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3458_subset__UNIV,axiom,
% 9.25/5.18      ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ top_top_set_int ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3459_subset__UNIV,axiom,
% 9.25/5.18      ! [A2: set_nat] : ( ord_less_eq_set_nat @ A2 @ top_top_set_nat ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3460_inter__eq__subsetI,axiom,
% 9.25/5.18      ! [S: set_Pr1261947904930325089at_nat,S4: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.18        ( ( ord_le3146513528884898305at_nat @ S @ S4 )
% 9.25/5.18       => ( ( ( inf_in2572325071724192079at_nat @ A2 @ S4 )
% 9.25/5.18            = ( inf_in2572325071724192079at_nat @ B2 @ S4 ) )
% 9.25/5.18         => ( ( inf_in2572325071724192079at_nat @ A2 @ S )
% 9.25/5.18            = ( inf_in2572325071724192079at_nat @ B2 @ S ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3461_inter__eq__subsetI,axiom,
% 9.25/5.18      ! [S: set_nat,S4: set_nat,A2: set_nat,B2: set_nat] :
% 9.25/5.18        ( ( ord_less_eq_set_nat @ S @ S4 )
% 9.25/5.18       => ( ( ( inf_inf_set_nat @ A2 @ S4 )
% 9.25/5.18            = ( inf_inf_set_nat @ B2 @ S4 ) )
% 9.25/5.18         => ( ( inf_inf_set_nat @ A2 @ S )
% 9.25/5.18            = ( inf_inf_set_nat @ B2 @ S ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3462_Int__Collect__mono,axiom,
% 9.25/5.18      ! [A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int,P: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.18        ( ( ord_le483042692224249369nt_int @ A2 @ B2 )
% 9.25/5.18       => ( ! [X2: set_Pr958786334691620121nt_int] :
% 9.25/5.18              ( ( member2340774599025711042nt_int @ X2 @ A2 )
% 9.25/5.18             => ( ( P @ X2 )
% 9.25/5.18               => ( Q2 @ X2 ) ) )
% 9.25/5.18         => ( ord_le483042692224249369nt_int @ ( inf_in8396524679539076455nt_int @ A2 @ ( collec5210948495886036740nt_int @ P ) ) @ ( inf_in8396524679539076455nt_int @ B2 @ ( collec5210948495886036740nt_int @ Q2 ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3463_Int__Collect__mono,axiom,
% 9.25/5.18      ! [A2: set_set_nat,B2: set_set_nat,P: set_nat > $o,Q2: set_nat > $o] :
% 9.25/5.18        ( ( ord_le6893508408891458716et_nat @ A2 @ B2 )
% 9.25/5.18       => ( ! [X2: set_nat] :
% 9.25/5.18              ( ( member_set_nat @ X2 @ A2 )
% 9.25/5.18             => ( ( P @ X2 )
% 9.25/5.18               => ( Q2 @ X2 ) ) )
% 9.25/5.18         => ( ord_le6893508408891458716et_nat @ ( inf_inf_set_set_nat @ A2 @ ( collect_set_nat @ P ) ) @ ( inf_inf_set_set_nat @ B2 @ ( collect_set_nat @ Q2 ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3464_Int__Collect__mono,axiom,
% 9.25/5.18      ! [A2: set_int,B2: set_int,P: int > $o,Q2: int > $o] :
% 9.25/5.18        ( ( ord_less_eq_set_int @ A2 @ B2 )
% 9.25/5.18       => ( ! [X2: int] :
% 9.25/5.18              ( ( member_int @ X2 @ A2 )
% 9.25/5.18             => ( ( P @ X2 )
% 9.25/5.18               => ( Q2 @ X2 ) ) )
% 9.25/5.18         => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) @ ( inf_inf_set_int @ B2 @ ( collect_int @ Q2 ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3465_Int__Collect__mono,axiom,
% 9.25/5.18      ! [A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o,P: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.18        ( ( ord_le2965882846123202637_nat_o @ A2 @ B2 )
% 9.25/5.18       => ( ! [X2: produc3658429121746597890et_nat > $o] :
% 9.25/5.18              ( ( member6576561426505652726_nat_o @ X2 @ A2 )
% 9.25/5.18             => ( ( P @ X2 )
% 9.25/5.18               => ( Q2 @ X2 ) ) )
% 9.25/5.18         => ( ord_le2965882846123202637_nat_o @ ( inf_in1906310914598751387_nat_o @ A2 @ ( collec939566748876313656_nat_o @ P ) ) @ ( inf_in1906310914598751387_nat_o @ B2 @ ( collec939566748876313656_nat_o @ Q2 ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3466_Int__Collect__mono,axiom,
% 9.25/5.18      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > $o] :
% 9.25/5.18        ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 9.25/5.18       => ( ! [X2: product_prod_nat_nat] :
% 9.25/5.18              ( ( member8440522571783428010at_nat @ X2 @ A2 )
% 9.25/5.18             => ( ( P @ X2 )
% 9.25/5.18               => ( Q2 @ X2 ) ) )
% 9.25/5.18         => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ ( collec3392354462482085612at_nat @ P ) ) @ ( inf_in2572325071724192079at_nat @ B2 @ ( collec3392354462482085612at_nat @ Q2 ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3467_Int__Collect__mono,axiom,
% 9.25/5.18      ! [A2: set_nat,B2: set_nat,P: nat > $o,Q2: nat > $o] :
% 9.25/5.18        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 9.25/5.18       => ( ! [X2: nat] :
% 9.25/5.18              ( ( member_nat @ X2 @ A2 )
% 9.25/5.18             => ( ( P @ X2 )
% 9.25/5.18               => ( Q2 @ X2 ) ) )
% 9.25/5.18         => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) @ ( inf_inf_set_nat @ B2 @ ( collect_nat @ Q2 ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3468_Int__greatest,axiom,
% 9.25/5.18      ! [C2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.18        ( ( ord_le3146513528884898305at_nat @ C2 @ A2 )
% 9.25/5.18       => ( ( ord_le3146513528884898305at_nat @ C2 @ B2 )
% 9.25/5.18         => ( ord_le3146513528884898305at_nat @ C2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3469_Int__greatest,axiom,
% 9.25/5.18      ! [C2: set_nat,A2: set_nat,B2: set_nat] :
% 9.25/5.18        ( ( ord_less_eq_set_nat @ C2 @ A2 )
% 9.25/5.18       => ( ( ord_less_eq_set_nat @ C2 @ B2 )
% 9.25/5.18         => ( ord_less_eq_set_nat @ C2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3470_Int__absorb2,axiom,
% 9.25/5.18      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.18        ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 9.25/5.18       => ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 9.25/5.18          = A2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3471_Int__absorb2,axiom,
% 9.25/5.18      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.18        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 9.25/5.18       => ( ( inf_inf_set_nat @ A2 @ B2 )
% 9.25/5.18          = A2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3472_Int__absorb1,axiom,
% 9.25/5.18      ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.18        ( ( ord_le3146513528884898305at_nat @ B2 @ A2 )
% 9.25/5.18       => ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 9.25/5.18          = B2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3473_Int__absorb1,axiom,
% 9.25/5.18      ! [B2: set_nat,A2: set_nat] :
% 9.25/5.18        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 9.25/5.18       => ( ( inf_inf_set_nat @ A2 @ B2 )
% 9.25/5.18          = B2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3474_Int__lower2,axiom,
% 9.25/5.18      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ B2 ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3475_Int__lower2,axiom,
% 9.25/5.18      ! [A2: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ B2 ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3476_Int__lower1,axiom,
% 9.25/5.18      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ A2 ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3477_Int__lower1,axiom,
% 9.25/5.18      ! [A2: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ A2 ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3478_Int__mono,axiom,
% 9.25/5.18      ! [A2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,D3: set_Pr1261947904930325089at_nat] :
% 9.25/5.18        ( ( ord_le3146513528884898305at_nat @ A2 @ C2 )
% 9.25/5.18       => ( ( ord_le3146513528884898305at_nat @ B2 @ D3 )
% 9.25/5.18         => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ ( inf_in2572325071724192079at_nat @ C2 @ D3 ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3479_Int__mono,axiom,
% 9.25/5.18      ! [A2: set_nat,C2: set_nat,B2: set_nat,D3: set_nat] :
% 9.25/5.18        ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 9.25/5.18       => ( ( ord_less_eq_set_nat @ B2 @ D3 )
% 9.25/5.18         => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ ( inf_inf_set_nat @ C2 @ D3 ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3480_subset__Un__eq,axiom,
% 9.25/5.18      ( ord_le8081472938463900775at_nat
% 9.25/5.18      = ( ^ [A4: set_Pr8551490117392284871at_nat,B4: set_Pr8551490117392284871at_nat] :
% 9.25/5.18            ( ( sup_su3035147773818789531at_nat @ A4 @ B4 )
% 9.25/5.18            = B4 ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3481_subset__Un__eq,axiom,
% 9.25/5.18      ( ord_le1268244103169919719at_nat
% 9.25/5.18      = ( ^ [A4: set_Pr4329608150637261639at_nat,B4: set_Pr4329608150637261639at_nat] :
% 9.25/5.18            ( ( sup_su5525570899277871387at_nat @ A4 @ B4 )
% 9.25/5.18            = B4 ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3482_subset__Un__eq,axiom,
% 9.25/5.18      ( ord_less_eq_set_nat
% 9.25/5.18      = ( ^ [A4: set_nat,B4: set_nat] :
% 9.25/5.18            ( ( sup_sup_set_nat @ A4 @ B4 )
% 9.25/5.18            = B4 ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3483_subset__UnE,axiom,
% 9.25/5.18      ! [C2: set_Pr8551490117392284871at_nat,A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.18        ( ( ord_le8081472938463900775at_nat @ C2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 9.25/5.18       => ~ ! [A7: set_Pr8551490117392284871at_nat] :
% 9.25/5.18              ( ( ord_le8081472938463900775at_nat @ A7 @ A2 )
% 9.25/5.18             => ! [B7: set_Pr8551490117392284871at_nat] :
% 9.25/5.18                  ( ( ord_le8081472938463900775at_nat @ B7 @ B2 )
% 9.25/5.18                 => ( C2
% 9.25/5.18                   != ( sup_su3035147773818789531at_nat @ A7 @ B7 ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3484_subset__UnE,axiom,
% 9.25/5.18      ! [C2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.18        ( ( ord_le1268244103169919719at_nat @ C2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 9.25/5.18       => ~ ! [A7: set_Pr4329608150637261639at_nat] :
% 9.25/5.18              ( ( ord_le1268244103169919719at_nat @ A7 @ A2 )
% 9.25/5.18             => ! [B7: set_Pr4329608150637261639at_nat] :
% 9.25/5.18                  ( ( ord_le1268244103169919719at_nat @ B7 @ B2 )
% 9.25/5.18                 => ( C2
% 9.25/5.18                   != ( sup_su5525570899277871387at_nat @ A7 @ B7 ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3485_subset__UnE,axiom,
% 9.25/5.18      ! [C2: set_nat,A2: set_nat,B2: set_nat] :
% 9.25/5.18        ( ( ord_less_eq_set_nat @ C2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.18       => ~ ! [A7: set_nat] :
% 9.25/5.18              ( ( ord_less_eq_set_nat @ A7 @ A2 )
% 9.25/5.18             => ! [B7: set_nat] :
% 9.25/5.18                  ( ( ord_less_eq_set_nat @ B7 @ B2 )
% 9.25/5.18                 => ( C2
% 9.25/5.18                   != ( sup_sup_set_nat @ A7 @ B7 ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3486_Un__absorb2,axiom,
% 9.25/5.18      ! [B2: set_Pr8551490117392284871at_nat,A2: set_Pr8551490117392284871at_nat] :
% 9.25/5.18        ( ( ord_le8081472938463900775at_nat @ B2 @ A2 )
% 9.25/5.18       => ( ( sup_su3035147773818789531at_nat @ A2 @ B2 )
% 9.25/5.18          = A2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3487_Un__absorb2,axiom,
% 9.25/5.18      ! [B2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.18        ( ( ord_le1268244103169919719at_nat @ B2 @ A2 )
% 9.25/5.18       => ( ( sup_su5525570899277871387at_nat @ A2 @ B2 )
% 9.25/5.18          = A2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3488_Un__absorb2,axiom,
% 9.25/5.18      ! [B2: set_nat,A2: set_nat] :
% 9.25/5.18        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 9.25/5.18       => ( ( sup_sup_set_nat @ A2 @ B2 )
% 9.25/5.18          = A2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3489_Un__absorb1,axiom,
% 9.25/5.18      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.18        ( ( ord_le8081472938463900775at_nat @ A2 @ B2 )
% 9.25/5.18       => ( ( sup_su3035147773818789531at_nat @ A2 @ B2 )
% 9.25/5.18          = B2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3490_Un__absorb1,axiom,
% 9.25/5.18      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.18        ( ( ord_le1268244103169919719at_nat @ A2 @ B2 )
% 9.25/5.18       => ( ( sup_su5525570899277871387at_nat @ A2 @ B2 )
% 9.25/5.18          = B2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3491_Un__absorb1,axiom,
% 9.25/5.18      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.18        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 9.25/5.18       => ( ( sup_sup_set_nat @ A2 @ B2 )
% 9.25/5.18          = B2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3492_Un__upper2,axiom,
% 9.25/5.18      ! [B2: set_Pr8551490117392284871at_nat,A2: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ B2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3493_Un__upper2,axiom,
% 9.25/5.18      ! [B2: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ B2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3494_Un__upper2,axiom,
% 9.25/5.18      ! [B2: set_nat,A2: set_nat] : ( ord_less_eq_set_nat @ B2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3495_Un__upper1,axiom,
% 9.25/5.18      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ A2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3496_Un__upper1,axiom,
% 9.25/5.18      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3497_Un__upper1,axiom,
% 9.25/5.18      ! [A2: set_nat,B2: set_nat] : ( ord_less_eq_set_nat @ A2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3498_Un__least,axiom,
% 9.25/5.18      ! [A2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.18        ( ( ord_le8081472938463900775at_nat @ A2 @ C2 )
% 9.25/5.18       => ( ( ord_le8081472938463900775at_nat @ B2 @ C2 )
% 9.25/5.18         => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) @ C2 ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3499_Un__least,axiom,
% 9.25/5.18      ! [A2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.18        ( ( ord_le1268244103169919719at_nat @ A2 @ C2 )
% 9.25/5.18       => ( ( ord_le1268244103169919719at_nat @ B2 @ C2 )
% 9.25/5.18         => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) @ C2 ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3500_Un__least,axiom,
% 9.25/5.18      ! [A2: set_nat,C2: set_nat,B2: set_nat] :
% 9.25/5.18        ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 9.25/5.18       => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 9.25/5.18         => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ C2 ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3501_Un__mono,axiom,
% 9.25/5.18      ! [A2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,D3: set_Pr8551490117392284871at_nat] :
% 9.25/5.18        ( ( ord_le8081472938463900775at_nat @ A2 @ C2 )
% 9.25/5.18       => ( ( ord_le8081472938463900775at_nat @ B2 @ D3 )
% 9.25/5.18         => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) @ ( sup_su3035147773818789531at_nat @ C2 @ D3 ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3502_Un__mono,axiom,
% 9.25/5.18      ! [A2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,D3: set_Pr4329608150637261639at_nat] :
% 9.25/5.18        ( ( ord_le1268244103169919719at_nat @ A2 @ C2 )
% 9.25/5.18       => ( ( ord_le1268244103169919719at_nat @ B2 @ D3 )
% 9.25/5.18         => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) @ ( sup_su5525570899277871387at_nat @ C2 @ D3 ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3503_Un__mono,axiom,
% 9.25/5.18      ! [A2: set_nat,C2: set_nat,B2: set_nat,D3: set_nat] :
% 9.25/5.18        ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 9.25/5.18       => ( ( ord_less_eq_set_nat @ B2 @ D3 )
% 9.25/5.18         => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A2 @ B2 ) @ ( sup_sup_set_nat @ C2 @ D3 ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3504_Diff__partition,axiom,
% 9.25/5.18      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.18        ( ( ord_le8081472938463900775at_nat @ A2 @ B2 )
% 9.25/5.18       => ( ( sup_su3035147773818789531at_nat @ A2 @ ( minus_5060654252129873198at_nat @ B2 @ A2 ) )
% 9.25/5.18          = B2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3505_Diff__partition,axiom,
% 9.25/5.18      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.18        ( ( ord_le1268244103169919719at_nat @ A2 @ B2 )
% 9.25/5.18       => ( ( sup_su5525570899277871387at_nat @ A2 @ ( minus_3314409938677909166at_nat @ B2 @ A2 ) )
% 9.25/5.18          = B2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3506_Diff__partition,axiom,
% 9.25/5.18      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.18        ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 9.25/5.18       => ( ( sup_sup_set_nat @ A2 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 9.25/5.18          = B2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3507_Diff__subset__conv,axiom,
% 9.25/5.18      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 9.25/5.18        ( ( ord_le8081472938463900775at_nat @ ( minus_5060654252129873198at_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.18        = ( ord_le8081472938463900775at_nat @ A2 @ ( sup_su3035147773818789531at_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3508_Diff__subset__conv,axiom,
% 9.25/5.18      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 9.25/5.18        ( ( ord_le1268244103169919719at_nat @ ( minus_3314409938677909166at_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.18        = ( ord_le1268244103169919719at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3509_Diff__subset__conv,axiom,
% 9.25/5.18      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 9.25/5.18        ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.18        = ( ord_less_eq_set_nat @ A2 @ ( sup_sup_set_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3510_relH__subset,axiom,
% 9.25/5.18      ! [Bs: set_nat,H3: heap_e7401611519738050253t_unit,H4: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.25/5.18        ( ( relH @ Bs @ H3 @ H4 )
% 9.25/5.18       => ( ( ord_less_eq_set_nat @ As @ Bs )
% 9.25/5.18         => ( relH @ As @ H3 @ H4 ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3511_mult__le__cancel__left1,axiom,
% 9.25/5.18      ! [C: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ C @ B ) )
% 9.25/5.18        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.18           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 9.25/5.18          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 9.25/5.18           => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3512_mult__le__cancel__left1,axiom,
% 9.25/5.18      ! [C: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 9.25/5.18          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3513_mult__le__cancel__left1,axiom,
% 9.25/5.18      ! [C: int,B: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 9.25/5.18        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 9.25/5.18           => ( ord_less_eq_int @ one_one_int @ B ) )
% 9.25/5.18          & ( ( ord_less_int @ C @ zero_zero_int )
% 9.25/5.18           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3514_mult__le__cancel__left2,axiom,
% 9.25/5.18      ! [C: code_integer,A: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ C )
% 9.25/5.18        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.18           => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 9.25/5.18          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 9.25/5.18           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3515_mult__le__cancel__left2,axiom,
% 9.25/5.18      ! [C: rat,A: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 9.25/5.18          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3516_mult__le__cancel__left2,axiom,
% 9.25/5.18      ! [C: int,A: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 9.25/5.18        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 9.25/5.18           => ( ord_less_eq_int @ A @ one_one_int ) )
% 9.25/5.18          & ( ( ord_less_int @ C @ zero_zero_int )
% 9.25/5.18           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3517_mult__le__cancel__right1,axiom,
% 9.25/5.18      ! [C: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.25/5.18        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.18           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 9.25/5.18          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 9.25/5.18           => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3518_mult__le__cancel__right1,axiom,
% 9.25/5.18      ! [C: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 9.25/5.18          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18           => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3519_mult__le__cancel__right1,axiom,
% 9.25/5.18      ! [C: int,B: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 9.25/5.18        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 9.25/5.18           => ( ord_less_eq_int @ one_one_int @ B ) )
% 9.25/5.18          & ( ( ord_less_int @ C @ zero_zero_int )
% 9.25/5.18           => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3520_mult__le__cancel__right2,axiom,
% 9.25/5.18      ! [A: code_integer,C: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ C )
% 9.25/5.18        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.18           => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 9.25/5.18          & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 9.25/5.18           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3521_mult__le__cancel__right2,axiom,
% 9.25/5.18      ! [A: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 9.25/5.18          & ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18           => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3522_mult__le__cancel__right2,axiom,
% 9.25/5.18      ! [A: int,C: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 9.25/5.18        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 9.25/5.18           => ( ord_less_eq_int @ A @ one_one_int ) )
% 9.25/5.18          & ( ( ord_less_int @ C @ zero_zero_int )
% 9.25/5.18           => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3523_mult__less__cancel__left1,axiom,
% 9.25/5.18      ! [C: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ C @ B ) )
% 9.25/5.18        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.18           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 9.25/5.18          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 9.25/5.18           => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3524_mult__less__cancel__left1,axiom,
% 9.25/5.18      ! [C: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 9.25/5.18        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_rat @ one_one_rat @ B ) )
% 9.25/5.18          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.25/5.18           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3525_mult__less__cancel__left1,axiom,
% 9.25/5.18      ! [C: int,B: int] :
% 9.25/5.18        ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 9.25/5.18        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.25/5.18           => ( ord_less_int @ one_one_int @ B ) )
% 9.25/5.18          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.25/5.18           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3526_mult__less__cancel__left2,axiom,
% 9.25/5.18      ! [C: code_integer,A: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ C )
% 9.25/5.18        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.18           => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 9.25/5.18          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 9.25/5.18           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3527_mult__less__cancel__left2,axiom,
% 9.25/5.18      ! [C: rat,A: rat] :
% 9.25/5.18        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 9.25/5.18        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_rat @ A @ one_one_rat ) )
% 9.25/5.18          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.25/5.18           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3528_mult__less__cancel__left2,axiom,
% 9.25/5.18      ! [C: int,A: int] :
% 9.25/5.18        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 9.25/5.18        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.25/5.18           => ( ord_less_int @ A @ one_one_int ) )
% 9.25/5.18          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.25/5.18           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3529_mult__less__cancel__right1,axiom,
% 9.25/5.18      ! [C: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.25/5.18        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.18           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 9.25/5.18          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 9.25/5.18           => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3530_mult__less__cancel__right1,axiom,
% 9.25/5.18      ! [C: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 9.25/5.18        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_rat @ one_one_rat @ B ) )
% 9.25/5.18          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.25/5.18           => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3531_mult__less__cancel__right1,axiom,
% 9.25/5.18      ! [C: int,B: int] :
% 9.25/5.18        ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 9.25/5.18        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.25/5.18           => ( ord_less_int @ one_one_int @ B ) )
% 9.25/5.18          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.25/5.18           => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3532_mult__less__cancel__right2,axiom,
% 9.25/5.18      ! [A: code_integer,C: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ C )
% 9.25/5.18        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.18           => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 9.25/5.18          & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 9.25/5.18           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3533_mult__less__cancel__right2,axiom,
% 9.25/5.18      ! [A: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 9.25/5.18        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_rat @ A @ one_one_rat ) )
% 9.25/5.18          & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.25/5.18           => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3534_mult__less__cancel__right2,axiom,
% 9.25/5.18      ! [A: int,C: int] :
% 9.25/5.18        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 9.25/5.18        = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.25/5.18           => ( ord_less_int @ A @ one_one_int ) )
% 9.25/5.18          & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.25/5.18           => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3535_field__le__mult__one__interval,axiom,
% 9.25/5.18      ! [X: rat,Y: rat] :
% 9.25/5.18        ( ! [Z2: rat] :
% 9.25/5.18            ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 9.25/5.18           => ( ( ord_less_rat @ Z2 @ one_one_rat )
% 9.25/5.18             => ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ X ) @ Y ) ) )
% 9.25/5.18       => ( ord_less_eq_rat @ X @ Y ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3536_divide__left__mono__neg,axiom,
% 9.25/5.18      ! [A: rat,B: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.18       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.25/5.18         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 9.25/5.18           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3537_mult__imp__le__div__pos,axiom,
% 9.25/5.18      ! [Y: rat,Z: rat,X: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 9.25/5.18       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 9.25/5.18         => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3538_mult__imp__div__pos__le,axiom,
% 9.25/5.18      ! [Y: rat,X: rat,Z: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 9.25/5.18       => ( ( ord_less_eq_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 9.25/5.18         => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3539_pos__le__divide__eq,axiom,
% 9.25/5.18      ! [C: rat,A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 9.25/5.18          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3540_pos__divide__le__eq,axiom,
% 9.25/5.18      ! [C: rat,B: rat,A: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 9.25/5.18          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3541_neg__le__divide__eq,axiom,
% 9.25/5.18      ! [C: rat,A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18       => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 9.25/5.18          = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3542_neg__divide__le__eq,axiom,
% 9.25/5.18      ! [C: rat,B: rat,A: rat] :
% 9.25/5.18        ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18       => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 9.25/5.18          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3543_divide__left__mono,axiom,
% 9.25/5.18      ! [B: rat,A: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ B @ A )
% 9.25/5.18       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.25/5.18         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 9.25/5.18           => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3544_le__divide__eq,axiom,
% 9.25/5.18      ! [A: rat,B: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 9.25/5.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 9.25/5.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3545_divide__le__eq,axiom,
% 9.25/5.18      ! [B: rat,C: rat,A: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 9.25/5.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 9.25/5.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3546_le__divide__eq__1,axiom,
% 9.25/5.18      ! [B: rat,A: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.18            & ( ord_less_eq_rat @ A @ B ) )
% 9.25/5.18          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.25/5.18            & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3547_divide__le__eq__1,axiom,
% 9.25/5.18      ! [B: rat,A: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.18            & ( ord_less_eq_rat @ B @ A ) )
% 9.25/5.18          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.25/5.18            & ( ord_less_eq_rat @ A @ B ) )
% 9.25/5.18          | ( A = zero_zero_rat ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3548_le__divide__eq__numeral_I1_J,axiom,
% 9.25/5.18      ! [W: num,B: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 9.25/5.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 9.25/5.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3549_divide__le__eq__numeral_I1_J,axiom,
% 9.25/5.18      ! [B: rat,C: rat,W: num] :
% 9.25/5.18        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 9.25/5.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 9.25/5.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3550_pos__minus__divide__le__eq,axiom,
% 9.25/5.18      ! [C: rat,B: rat,A: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 9.25/5.18          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3551_pos__le__minus__divide__eq,axiom,
% 9.25/5.18      ! [C: rat,A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 9.25/5.18          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3552_neg__minus__divide__le__eq,axiom,
% 9.25/5.18      ! [C: rat,B: rat,A: rat] :
% 9.25/5.18        ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 9.25/5.18          = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3553_neg__le__minus__divide__eq,axiom,
% 9.25/5.18      ! [C: rat,A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18       => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 9.25/5.18          = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3554_minus__divide__le__eq,axiom,
% 9.25/5.18      ! [B: rat,C: rat,A: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 9.25/5.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 9.25/5.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3555_le__minus__divide__eq,axiom,
% 9.25/5.18      ! [A: rat,B: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 9.25/5.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 9.25/5.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3556_less__eq__assn__def,axiom,
% 9.25/5.18      ( ord_less_eq_assn
% 9.25/5.18      = ( ^ [A3: assn,B3: assn] :
% 9.25/5.18            ( A3
% 9.25/5.18            = ( inf_inf_assn @ A3 @ B3 ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3557_mult__neg__neg,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.18       => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 9.25/5.18         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3558_mult__neg__neg,axiom,
% 9.25/5.18      ! [A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.25/5.18       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 9.25/5.18         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3559_mult__neg__neg,axiom,
% 9.25/5.18      ! [A: int,B: int] :
% 9.25/5.18        ( ( ord_less_int @ A @ zero_zero_int )
% 9.25/5.18       => ( ( ord_less_int @ B @ zero_zero_int )
% 9.25/5.18         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3560_not__square__less__zero,axiom,
% 9.25/5.18      ! [A: code_integer] :
% 9.25/5.18        ~ ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ A ) @ zero_z3403309356797280102nteger ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3561_not__square__less__zero,axiom,
% 9.25/5.18      ! [A: rat] :
% 9.25/5.18        ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3562_not__square__less__zero,axiom,
% 9.25/5.18      ! [A: int] :
% 9.25/5.18        ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3563_mult__less__0__iff,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger )
% 9.25/5.18        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.18            & ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger ) )
% 9.25/5.18          | ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.18            & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3564_mult__less__0__iff,axiom,
% 9.25/5.18      ! [A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.18            & ( ord_less_rat @ B @ zero_zero_rat ) )
% 9.25/5.18          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.25/5.18            & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3565_mult__less__0__iff,axiom,
% 9.25/5.18      ! [A: int,B: int] :
% 9.25/5.18        ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 9.25/5.18        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 9.25/5.18            & ( ord_less_int @ B @ zero_zero_int ) )
% 9.25/5.18          | ( ( ord_less_int @ A @ zero_zero_int )
% 9.25/5.18            & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3566_mult__neg__pos,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.18       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 9.25/5.18         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3567_mult__neg__pos,axiom,
% 9.25/5.18      ! [A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.25/5.18       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 9.25/5.18         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3568_mult__neg__pos,axiom,
% 9.25/5.18      ! [A: nat,B: nat] :
% 9.25/5.18        ( ( ord_less_nat @ A @ zero_zero_nat )
% 9.25/5.18       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.25/5.18         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3569_mult__neg__pos,axiom,
% 9.25/5.18      ! [A: int,B: int] :
% 9.25/5.18        ( ( ord_less_int @ A @ zero_zero_int )
% 9.25/5.18       => ( ( ord_less_int @ zero_zero_int @ B )
% 9.25/5.18         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3570_mult__pos__neg,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.18       => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 9.25/5.18         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3571_mult__pos__neg,axiom,
% 9.25/5.18      ! [A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.18       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 9.25/5.18         => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3572_mult__pos__neg,axiom,
% 9.25/5.18      ! [A: nat,B: nat] :
% 9.25/5.18        ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.25/5.18       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 9.25/5.18         => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3573_mult__pos__neg,axiom,
% 9.25/5.18      ! [A: int,B: int] :
% 9.25/5.18        ( ( ord_less_int @ zero_zero_int @ A )
% 9.25/5.18       => ( ( ord_less_int @ B @ zero_zero_int )
% 9.25/5.18         => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3574_mult__pos__pos,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.18       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 9.25/5.18         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3575_mult__pos__pos,axiom,
% 9.25/5.18      ! [A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.18       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 9.25/5.18         => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3576_mult__pos__pos,axiom,
% 9.25/5.18      ! [A: nat,B: nat] :
% 9.25/5.18        ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.25/5.18       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.25/5.18         => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3577_mult__pos__pos,axiom,
% 9.25/5.18      ! [A: int,B: int] :
% 9.25/5.18        ( ( ord_less_int @ zero_zero_int @ A )
% 9.25/5.18       => ( ( ord_less_int @ zero_zero_int @ B )
% 9.25/5.18         => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3578_mult__pos__neg2,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.18       => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 9.25/5.18         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ B @ A ) @ zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3579_mult__pos__neg2,axiom,
% 9.25/5.18      ! [A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.18       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 9.25/5.18         => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3580_mult__pos__neg2,axiom,
% 9.25/5.18      ! [A: nat,B: nat] :
% 9.25/5.18        ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.25/5.18       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 9.25/5.18         => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3581_mult__pos__neg2,axiom,
% 9.25/5.18      ! [A: int,B: int] :
% 9.25/5.18        ( ( ord_less_int @ zero_zero_int @ A )
% 9.25/5.18       => ( ( ord_less_int @ B @ zero_zero_int )
% 9.25/5.18         => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3582_zero__less__mult__iff,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 9.25/5.18        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.18            & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) )
% 9.25/5.18          | ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.18            & ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3583_zero__less__mult__iff,axiom,
% 9.25/5.18      ! [A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.18            & ( ord_less_rat @ zero_zero_rat @ B ) )
% 9.25/5.18          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.25/5.18            & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3584_zero__less__mult__iff,axiom,
% 9.25/5.18      ! [A: int,B: int] :
% 9.25/5.18        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 9.25/5.18        = ( ( ( ord_less_int @ zero_zero_int @ A )
% 9.25/5.18            & ( ord_less_int @ zero_zero_int @ B ) )
% 9.25/5.18          | ( ( ord_less_int @ A @ zero_zero_int )
% 9.25/5.18            & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3585_zero__less__mult__pos,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 9.25/5.18       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.18         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3586_zero__less__mult__pos,axiom,
% 9.25/5.18      ! [A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 9.25/5.18       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.18         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3587_zero__less__mult__pos,axiom,
% 9.25/5.18      ! [A: nat,B: nat] :
% 9.25/5.18        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 9.25/5.18       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.25/5.18         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3588_zero__less__mult__pos,axiom,
% 9.25/5.18      ! [A: int,B: int] :
% 9.25/5.18        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 9.25/5.18       => ( ( ord_less_int @ zero_zero_int @ A )
% 9.25/5.18         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3589_zero__less__mult__pos2,axiom,
% 9.25/5.18      ! [B: code_integer,A: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ B @ A ) )
% 9.25/5.18       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.18         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3590_zero__less__mult__pos2,axiom,
% 9.25/5.18      ! [B: rat,A: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 9.25/5.18       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.18         => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3591_zero__less__mult__pos2,axiom,
% 9.25/5.18      ! [B: nat,A: nat] :
% 9.25/5.18        ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 9.25/5.18       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.25/5.18         => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3592_zero__less__mult__pos2,axiom,
% 9.25/5.18      ! [B: int,A: int] :
% 9.25/5.18        ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 9.25/5.18       => ( ( ord_less_int @ zero_zero_int @ A )
% 9.25/5.18         => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3593_mult__less__cancel__left__neg,axiom,
% 9.25/5.18      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 9.25/5.18       => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 9.25/5.18          = ( ord_le6747313008572928689nteger @ B @ A ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3594_mult__less__cancel__left__neg,axiom,
% 9.25/5.18      ! [C: rat,A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.25/5.18          = ( ord_less_rat @ B @ A ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3595_mult__less__cancel__left__neg,axiom,
% 9.25/5.18      ! [C: int,A: int,B: int] :
% 9.25/5.18        ( ( ord_less_int @ C @ zero_zero_int )
% 9.25/5.18       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.25/5.18          = ( ord_less_int @ B @ A ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3596_mult__less__cancel__left__pos,axiom,
% 9.25/5.18      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.18       => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 9.25/5.18          = ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3597_mult__less__cancel__left__pos,axiom,
% 9.25/5.18      ! [C: rat,A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18       => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.25/5.18          = ( ord_less_rat @ A @ B ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3598_mult__less__cancel__left__pos,axiom,
% 9.25/5.18      ! [C: int,A: int,B: int] :
% 9.25/5.18        ( ( ord_less_int @ zero_zero_int @ C )
% 9.25/5.18       => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.25/5.18          = ( ord_less_int @ A @ B ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3599_mult__strict__left__mono__neg,axiom,
% 9.25/5.18      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ B @ A )
% 9.25/5.18       => ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 9.25/5.18         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3600_mult__strict__left__mono__neg,axiom,
% 9.25/5.18      ! [B: rat,A: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_rat @ B @ A )
% 9.25/5.18       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3601_mult__strict__left__mono__neg,axiom,
% 9.25/5.18      ! [B: int,A: int,C: int] :
% 9.25/5.18        ( ( ord_less_int @ B @ A )
% 9.25/5.18       => ( ( ord_less_int @ C @ zero_zero_int )
% 9.25/5.18         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3602_mult__strict__left__mono,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.25/5.18       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.18         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3603_mult__strict__left__mono,axiom,
% 9.25/5.18      ! [A: rat,B: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_rat @ A @ B )
% 9.25/5.18       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3604_mult__strict__left__mono,axiom,
% 9.25/5.18      ! [A: nat,B: nat,C: nat] :
% 9.25/5.18        ( ( ord_less_nat @ A @ B )
% 9.25/5.18       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 9.25/5.18         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3605_mult__strict__left__mono,axiom,
% 9.25/5.18      ! [A: int,B: int,C: int] :
% 9.25/5.18        ( ( ord_less_int @ A @ B )
% 9.25/5.18       => ( ( ord_less_int @ zero_zero_int @ C )
% 9.25/5.18         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3606_mult__less__cancel__left__disj,axiom,
% 9.25/5.18      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 9.25/5.18        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.18            & ( ord_le6747313008572928689nteger @ A @ B ) )
% 9.25/5.18          | ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 9.25/5.18            & ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3607_mult__less__cancel__left__disj,axiom,
% 9.25/5.18      ! [C: rat,A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18            & ( ord_less_rat @ A @ B ) )
% 9.25/5.18          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3608_mult__less__cancel__left__disj,axiom,
% 9.25/5.18      ! [C: int,A: int,B: int] :
% 9.25/5.18        ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.25/5.18        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 9.25/5.18            & ( ord_less_int @ A @ B ) )
% 9.25/5.18          | ( ( ord_less_int @ C @ zero_zero_int )
% 9.25/5.18            & ( ord_less_int @ B @ A ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3609_mult__strict__right__mono__neg,axiom,
% 9.25/5.18      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ B @ A )
% 9.25/5.18       => ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 9.25/5.18         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3610_mult__strict__right__mono__neg,axiom,
% 9.25/5.18      ! [B: rat,A: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_rat @ B @ A )
% 9.25/5.18       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3611_mult__strict__right__mono__neg,axiom,
% 9.25/5.18      ! [B: int,A: int,C: int] :
% 9.25/5.18        ( ( ord_less_int @ B @ A )
% 9.25/5.18       => ( ( ord_less_int @ C @ zero_zero_int )
% 9.25/5.18         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3612_mult__strict__right__mono,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.25/5.18       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.18         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3613_mult__strict__right__mono,axiom,
% 9.25/5.18      ! [A: rat,B: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_rat @ A @ B )
% 9.25/5.18       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18         => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3614_mult__strict__right__mono,axiom,
% 9.25/5.18      ! [A: nat,B: nat,C: nat] :
% 9.25/5.18        ( ( ord_less_nat @ A @ B )
% 9.25/5.18       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 9.25/5.18         => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3615_mult__strict__right__mono,axiom,
% 9.25/5.18      ! [A: int,B: int,C: int] :
% 9.25/5.18        ( ( ord_less_int @ A @ B )
% 9.25/5.18       => ( ( ord_less_int @ zero_zero_int @ C )
% 9.25/5.18         => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3616_mult__less__cancel__right__disj,axiom,
% 9.25/5.18      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.25/5.18        = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.18            & ( ord_le6747313008572928689nteger @ A @ B ) )
% 9.25/5.18          | ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 9.25/5.18            & ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3617_mult__less__cancel__right__disj,axiom,
% 9.25/5.18      ! [A: rat,C: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18            & ( ord_less_rat @ A @ B ) )
% 9.25/5.18          | ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3618_mult__less__cancel__right__disj,axiom,
% 9.25/5.18      ! [A: int,C: int,B: int] :
% 9.25/5.18        ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 9.25/5.18        = ( ( ( ord_less_int @ zero_zero_int @ C )
% 9.25/5.18            & ( ord_less_int @ A @ B ) )
% 9.25/5.18          | ( ( ord_less_int @ C @ zero_zero_int )
% 9.25/5.18            & ( ord_less_int @ B @ A ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3619_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.25/5.18       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.18         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3620_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 9.25/5.18      ! [A: rat,B: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_rat @ A @ B )
% 9.25/5.18       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18         => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3621_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 9.25/5.18      ! [A: nat,B: nat,C: nat] :
% 9.25/5.18        ( ( ord_less_nat @ A @ B )
% 9.25/5.18       => ( ( ord_less_nat @ zero_zero_nat @ C )
% 9.25/5.18         => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3622_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 9.25/5.18      ! [A: int,B: int,C: int] :
% 9.25/5.18        ( ( ord_less_int @ A @ B )
% 9.25/5.18       => ( ( ord_less_int @ zero_zero_int @ C )
% 9.25/5.18         => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3623_zero__less__one,axiom,
% 9.25/5.18      ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3624_zero__less__one,axiom,
% 9.25/5.18      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3625_zero__less__one,axiom,
% 9.25/5.18      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3626_zero__less__one,axiom,
% 9.25/5.18      ord_less_int @ zero_zero_int @ one_one_int ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3627_not__one__less__zero,axiom,
% 9.25/5.18      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3628_not__one__less__zero,axiom,
% 9.25/5.18      ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3629_not__one__less__zero,axiom,
% 9.25/5.18      ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3630_not__one__less__zero,axiom,
% 9.25/5.18      ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3631_less__numeral__extra_I1_J,axiom,
% 9.25/5.18      ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3632_less__numeral__extra_I1_J,axiom,
% 9.25/5.18      ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3633_less__numeral__extra_I1_J,axiom,
% 9.25/5.18      ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3634_less__numeral__extra_I1_J,axiom,
% 9.25/5.18      ord_less_int @ zero_zero_int @ one_one_int ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3635_less__iff__diff__less__0,axiom,
% 9.25/5.18      ( ord_le6747313008572928689nteger
% 9.25/5.18      = ( ^ [A3: code_integer,B3: code_integer] : ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A3 @ B3 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3636_less__iff__diff__less__0,axiom,
% 9.25/5.18      ( ord_less_rat
% 9.25/5.18      = ( ^ [A3: rat,B3: rat] : ( ord_less_rat @ ( minus_minus_rat @ A3 @ B3 ) @ zero_zero_rat ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3637_less__iff__diff__less__0,axiom,
% 9.25/5.18      ( ord_less_int
% 9.25/5.18      = ( ^ [A3: int,B3: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B3 ) @ zero_zero_int ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3638_not__numeral__less__one,axiom,
% 9.25/5.18      ! [N: num] :
% 9.25/5.18        ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3639_not__numeral__less__one,axiom,
% 9.25/5.18      ! [N: num] :
% 9.25/5.18        ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3640_not__numeral__less__one,axiom,
% 9.25/5.18      ! [N: num] :
% 9.25/5.18        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3641_not__numeral__less__one,axiom,
% 9.25/5.18      ! [N: num] :
% 9.25/5.18        ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3642_not__numeral__less__one,axiom,
% 9.25/5.18      ! [N: num] :
% 9.25/5.18        ~ ( ord_le5570908160329646204atural @ ( numera5444537566228673987atural @ N ) @ one_one_Code_natural ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3643_less__1__mult,axiom,
% 9.25/5.18      ! [M: code_integer,N: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ M )
% 9.25/5.18       => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ N )
% 9.25/5.18         => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ M @ N ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3644_less__1__mult,axiom,
% 9.25/5.18      ! [M: rat,N: rat] :
% 9.25/5.18        ( ( ord_less_rat @ one_one_rat @ M )
% 9.25/5.18       => ( ( ord_less_rat @ one_one_rat @ N )
% 9.25/5.18         => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3645_less__1__mult,axiom,
% 9.25/5.18      ! [M: nat,N: nat] :
% 9.25/5.18        ( ( ord_less_nat @ one_one_nat @ M )
% 9.25/5.18       => ( ( ord_less_nat @ one_one_nat @ N )
% 9.25/5.18         => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3646_less__1__mult,axiom,
% 9.25/5.18      ! [M: int,N: int] :
% 9.25/5.18        ( ( ord_less_int @ one_one_int @ M )
% 9.25/5.18       => ( ( ord_less_int @ one_one_int @ N )
% 9.25/5.18         => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3647_mult__mono,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.25/5.18       => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 9.25/5.18         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 9.25/5.18           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.18             => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3648_mult__mono,axiom,
% 9.25/5.18      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.18       => ( ( ord_less_eq_rat @ C @ D2 )
% 9.25/5.18         => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.25/5.18           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.25/5.18             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3649_mult__mono,axiom,
% 9.25/5.18      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.25/5.18        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.18       => ( ( ord_less_eq_nat @ C @ D2 )
% 9.25/5.18         => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 9.25/5.18           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.25/5.18             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3650_mult__mono,axiom,
% 9.25/5.18      ! [A: int,B: int,C: int,D2: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.18       => ( ( ord_less_eq_int @ C @ D2 )
% 9.25/5.18         => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.25/5.18           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.25/5.18             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3651_mult__mono_H,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.25/5.18       => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 9.25/5.18         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.18           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.18             => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3652_mult__mono_H,axiom,
% 9.25/5.18      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.18       => ( ( ord_less_eq_rat @ C @ D2 )
% 9.25/5.18         => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.18           => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.25/5.18             => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3653_mult__mono_H,axiom,
% 9.25/5.18      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.25/5.18        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.18       => ( ( ord_less_eq_nat @ C @ D2 )
% 9.25/5.18         => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.25/5.18           => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.25/5.18             => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3654_mult__mono_H,axiom,
% 9.25/5.18      ! [A: int,B: int,C: int,D2: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.18       => ( ( ord_less_eq_int @ C @ D2 )
% 9.25/5.18         => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.18           => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.25/5.18             => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3655_zero__le__square,axiom,
% 9.25/5.18      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ A ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3656_zero__le__square,axiom,
% 9.25/5.18      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3657_zero__le__square,axiom,
% 9.25/5.18      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3658_split__mult__pos__le,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.18            & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) )
% 9.25/5.18          | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.18            & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 9.25/5.18       => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3659_split__mult__pos__le,axiom,
% 9.25/5.18      ! [A: rat,B: rat] :
% 9.25/5.18        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.18            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 9.25/5.18          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.25/5.18            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 9.25/5.18       => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3660_split__mult__pos__le,axiom,
% 9.25/5.18      ! [A: int,B: int] :
% 9.25/5.18        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.18            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 9.25/5.18          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.25/5.18            & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 9.25/5.18       => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3661_mult__left__mono__neg,axiom,
% 9.25/5.18      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ B @ A )
% 9.25/5.18       => ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 9.25/5.18         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3662_mult__left__mono__neg,axiom,
% 9.25/5.18      ! [B: rat,A: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ B @ A )
% 9.25/5.18       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.25/5.18         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3663_mult__left__mono__neg,axiom,
% 9.25/5.18      ! [B: int,A: int,C: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ B @ A )
% 9.25/5.18       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.25/5.18         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3664_mult__nonpos__nonpos,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.18       => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 9.25/5.18         => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3665_mult__nonpos__nonpos,axiom,
% 9.25/5.18      ! [A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.25/5.18       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 9.25/5.18         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3666_mult__nonpos__nonpos,axiom,
% 9.25/5.18      ! [A: int,B: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.25/5.18       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 9.25/5.18         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3667_mult__left__mono,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.25/5.18       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.18         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3668_mult__left__mono,axiom,
% 9.25/5.18      ! [A: rat,B: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.18       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.25/5.18         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3669_mult__left__mono,axiom,
% 9.25/5.18      ! [A: nat,B: nat,C: nat] :
% 9.25/5.18        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.18       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.25/5.18         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3670_mult__left__mono,axiom,
% 9.25/5.18      ! [A: int,B: int,C: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.18       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.25/5.18         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3671_mult__right__mono__neg,axiom,
% 9.25/5.18      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ B @ A )
% 9.25/5.18       => ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 9.25/5.18         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3672_mult__right__mono__neg,axiom,
% 9.25/5.18      ! [B: rat,A: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ B @ A )
% 9.25/5.18       => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.25/5.18         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3673_mult__right__mono__neg,axiom,
% 9.25/5.18      ! [B: int,A: int,C: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ B @ A )
% 9.25/5.18       => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.25/5.18         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3674_mult__right__mono,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.25/5.18       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.18         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3675_mult__right__mono,axiom,
% 9.25/5.18      ! [A: rat,B: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.18       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.25/5.18         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3676_mult__right__mono,axiom,
% 9.25/5.18      ! [A: nat,B: nat,C: nat] :
% 9.25/5.18        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.18       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.25/5.18         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3677_mult__right__mono,axiom,
% 9.25/5.18      ! [A: int,B: int,C: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.18       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.25/5.18         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3678_mult__le__0__iff,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger )
% 9.25/5.18        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.18            & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) )
% 9.25/5.18          | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.18            & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3679_mult__le__0__iff,axiom,
% 9.25/5.18      ! [A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 9.25/5.18        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.18            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 9.25/5.18          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.25/5.18            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3680_mult__le__0__iff,axiom,
% 9.25/5.18      ! [A: int,B: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 9.25/5.18        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.18            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 9.25/5.18          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.25/5.18            & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3681_split__mult__neg__le,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.18            & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) )
% 9.25/5.18          | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.18            & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) )
% 9.25/5.18       => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3682_split__mult__neg__le,axiom,
% 9.25/5.18      ! [A: rat,B: rat] :
% 9.25/5.18        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.18            & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 9.25/5.18          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.25/5.18            & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 9.25/5.18       => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3683_split__mult__neg__le,axiom,
% 9.25/5.18      ! [A: nat,B: nat] :
% 9.25/5.18        ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.25/5.18            & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 9.25/5.18          | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 9.25/5.18            & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 9.25/5.18       => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3684_split__mult__neg__le,axiom,
% 9.25/5.18      ! [A: int,B: int] :
% 9.25/5.18        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.18            & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 9.25/5.18          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.25/5.18            & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 9.25/5.18       => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3685_mult__nonneg__nonneg,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.18       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 9.25/5.18         => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3686_mult__nonneg__nonneg,axiom,
% 9.25/5.18      ! [A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.18       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.25/5.18         => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3687_mult__nonneg__nonneg,axiom,
% 9.25/5.18      ! [A: nat,B: nat] :
% 9.25/5.18        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.25/5.18       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 9.25/5.18         => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3688_mult__nonneg__nonneg,axiom,
% 9.25/5.18      ! [A: int,B: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.18       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.25/5.18         => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3689_mult__nonneg__nonpos,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.18       => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 9.25/5.18         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3690_mult__nonneg__nonpos,axiom,
% 9.25/5.18      ! [A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.18       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 9.25/5.18         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3691_mult__nonneg__nonpos,axiom,
% 9.25/5.18      ! [A: nat,B: nat] :
% 9.25/5.18        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.25/5.18       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 9.25/5.18         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3692_mult__nonneg__nonpos,axiom,
% 9.25/5.18      ! [A: int,B: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.18       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 9.25/5.18         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3693_mult__nonpos__nonneg,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.18       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 9.25/5.18         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3694_mult__nonpos__nonneg,axiom,
% 9.25/5.18      ! [A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.25/5.18       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.25/5.18         => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3695_mult__nonpos__nonneg,axiom,
% 9.25/5.18      ! [A: nat,B: nat] :
% 9.25/5.18        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 9.25/5.18       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 9.25/5.18         => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3696_mult__nonpos__nonneg,axiom,
% 9.25/5.18      ! [A: int,B: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.25/5.18       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.25/5.18         => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3697_mult__nonneg__nonpos2,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.18       => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 9.25/5.18         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ B @ A ) @ zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3698_mult__nonneg__nonpos2,axiom,
% 9.25/5.18      ! [A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.18       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 9.25/5.18         => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3699_mult__nonneg__nonpos2,axiom,
% 9.25/5.18      ! [A: nat,B: nat] :
% 9.25/5.18        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.25/5.18       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 9.25/5.18         => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3700_mult__nonneg__nonpos2,axiom,
% 9.25/5.18      ! [A: int,B: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.18       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 9.25/5.18         => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3701_zero__le__mult__iff,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 9.25/5.18        = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.18            & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) )
% 9.25/5.18          | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.18            & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3702_zero__le__mult__iff,axiom,
% 9.25/5.18      ! [A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 9.25/5.18        = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.18            & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 9.25/5.18          | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.25/5.18            & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3703_zero__le__mult__iff,axiom,
% 9.25/5.18      ! [A: int,B: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 9.25/5.18        = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.18            & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 9.25/5.18          | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.25/5.18            & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3704_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.25/5.18       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.18         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3705_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 9.25/5.18      ! [A: rat,B: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.18       => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.25/5.18         => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3706_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 9.25/5.18      ! [A: nat,B: nat,C: nat] :
% 9.25/5.18        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.18       => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.25/5.18         => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3707_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 9.25/5.18      ! [A: int,B: int,C: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.18       => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.25/5.18         => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3708_zero__less__one__class_Ozero__le__one,axiom,
% 9.25/5.18      ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3709_zero__less__one__class_Ozero__le__one,axiom,
% 9.25/5.18      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3710_zero__less__one__class_Ozero__le__one,axiom,
% 9.25/5.18      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3711_zero__less__one__class_Ozero__le__one,axiom,
% 9.25/5.18      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3712_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 9.25/5.18      ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3713_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 9.25/5.18      ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3714_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 9.25/5.18      ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3715_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 9.25/5.18      ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3716_not__one__le__zero,axiom,
% 9.25/5.18      ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3717_not__one__le__zero,axiom,
% 9.25/5.18      ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3718_not__one__le__zero,axiom,
% 9.25/5.18      ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3719_not__one__le__zero,axiom,
% 9.25/5.18      ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3720_le__iff__diff__le__0,axiom,
% 9.25/5.18      ( ord_le3102999989581377725nteger
% 9.25/5.18      = ( ^ [A3: code_integer,B3: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A3 @ B3 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3721_le__iff__diff__le__0,axiom,
% 9.25/5.18      ( ord_less_eq_rat
% 9.25/5.18      = ( ^ [A3: rat,B3: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A3 @ B3 ) @ zero_zero_rat ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3722_le__iff__diff__le__0,axiom,
% 9.25/5.18      ( ord_less_eq_int
% 9.25/5.18      = ( ^ [A3: int,B3: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B3 ) @ zero_zero_int ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3723_not__numeral__less__neg__numeral,axiom,
% 9.25/5.18      ! [M: num,N: num] :
% 9.25/5.18        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3724_not__numeral__less__neg__numeral,axiom,
% 9.25/5.18      ! [M: num,N: num] :
% 9.25/5.18        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3725_not__numeral__less__neg__numeral,axiom,
% 9.25/5.18      ! [M: num,N: num] :
% 9.25/5.18        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3726_neg__numeral__less__numeral,axiom,
% 9.25/5.18      ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3727_neg__numeral__less__numeral,axiom,
% 9.25/5.18      ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3728_neg__numeral__less__numeral,axiom,
% 9.25/5.18      ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3729_less__minus__one__simps_I4_J,axiom,
% 9.25/5.18      ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3730_less__minus__one__simps_I4_J,axiom,
% 9.25/5.18      ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3731_less__minus__one__simps_I4_J,axiom,
% 9.25/5.18      ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3732_less__minus__one__simps_I2_J,axiom,
% 9.25/5.18      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3733_less__minus__one__simps_I2_J,axiom,
% 9.25/5.18      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3734_less__minus__one__simps_I2_J,axiom,
% 9.25/5.18      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3735_one__le__numeral,axiom,
% 9.25/5.18      ! [N: num] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3736_one__le__numeral,axiom,
% 9.25/5.18      ! [N: num] : ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3737_one__le__numeral,axiom,
% 9.25/5.18      ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3738_one__le__numeral,axiom,
% 9.25/5.18      ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3739_one__le__numeral,axiom,
% 9.25/5.18      ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3740_diff__shunt__var,axiom,
% 9.25/5.18      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.25/5.18        ( ( ( minus_1356011639430497352at_nat @ X @ Y )
% 9.25/5.18          = bot_bo2099793752762293965at_nat )
% 9.25/5.18        = ( ord_le3146513528884898305at_nat @ X @ Y ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3741_diff__shunt__var,axiom,
% 9.25/5.18      ! [X: set_o,Y: set_o] :
% 9.25/5.18        ( ( ( minus_minus_set_o @ X @ Y )
% 9.25/5.18          = bot_bot_set_o )
% 9.25/5.18        = ( ord_less_eq_set_o @ X @ Y ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3742_diff__shunt__var,axiom,
% 9.25/5.18      ! [X: set_int,Y: set_int] :
% 9.25/5.18        ( ( ( minus_minus_set_int @ X @ Y )
% 9.25/5.18          = bot_bot_set_int )
% 9.25/5.18        = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3743_diff__shunt__var,axiom,
% 9.25/5.18      ! [X: set_nat,Y: set_nat] :
% 9.25/5.18        ( ( ( minus_minus_set_nat @ X @ Y )
% 9.25/5.18          = bot_bot_set_nat )
% 9.25/5.18        = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3744_not__numeral__le__neg__numeral,axiom,
% 9.25/5.18      ! [M: num,N: num] :
% 9.25/5.18        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3745_not__numeral__le__neg__numeral,axiom,
% 9.25/5.18      ! [M: num,N: num] :
% 9.25/5.18        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3746_not__numeral__le__neg__numeral,axiom,
% 9.25/5.18      ! [M: num,N: num] :
% 9.25/5.18        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3747_neg__numeral__le__numeral,axiom,
% 9.25/5.18      ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3748_neg__numeral__le__numeral,axiom,
% 9.25/5.18      ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3749_neg__numeral__le__numeral,axiom,
% 9.25/5.18      ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3750_le__minus__one__simps_I4_J,axiom,
% 9.25/5.18      ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3751_le__minus__one__simps_I4_J,axiom,
% 9.25/5.18      ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3752_le__minus__one__simps_I4_J,axiom,
% 9.25/5.18      ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3753_le__minus__one__simps_I2_J,axiom,
% 9.25/5.18      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3754_le__minus__one__simps_I2_J,axiom,
% 9.25/5.18      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3755_le__minus__one__simps_I2_J,axiom,
% 9.25/5.18      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3756_disjoint__alt__simp3,axiom,
% 9.25/5.18      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.18        ( ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) @ A2 )
% 9.25/5.18        = ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 9.25/5.18         != bot_bo2099793752762293965at_nat ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3757_disjoint__alt__simp3,axiom,
% 9.25/5.18      ! [A2: set_o,B2: set_o] :
% 9.25/5.18        ( ( ord_less_set_o @ ( minus_minus_set_o @ A2 @ B2 ) @ A2 )
% 9.25/5.18        = ( ( inf_inf_set_o @ A2 @ B2 )
% 9.25/5.18         != bot_bot_set_o ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3758_disjoint__alt__simp3,axiom,
% 9.25/5.18      ! [A2: set_int,B2: set_int] :
% 9.25/5.18        ( ( ord_less_set_int @ ( minus_minus_set_int @ A2 @ B2 ) @ A2 )
% 9.25/5.18        = ( ( inf_inf_set_int @ A2 @ B2 )
% 9.25/5.18         != bot_bot_set_int ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3759_disjoint__alt__simp3,axiom,
% 9.25/5.18      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.18        ( ( ord_less_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ A2 )
% 9.25/5.18        = ( ( inf_inf_set_nat @ A2 @ B2 )
% 9.25/5.18         != bot_bot_set_nat ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3760_distrib__inf__le,axiom,
% 9.25/5.18      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) @ ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3761_distrib__inf__le,axiom,
% 9.25/5.18      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( sup_su8463660629351352368_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ ( inf_in3604695632404883862_int_o @ X @ Z ) ) @ ( inf_in3604695632404883862_int_o @ X @ ( sup_su8463660629351352368_int_o @ Y @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3762_distrib__inf__le,axiom,
% 9.25/5.18      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] : ( ord_le4796328588573674190char_o @ ( sup_sup_list_char_o @ ( inf_inf_list_char_o @ X @ Y ) @ ( inf_inf_list_char_o @ X @ Z ) ) @ ( inf_inf_list_char_o @ X @ ( sup_sup_list_char_o @ Y @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3763_distrib__inf__le,axiom,
% 9.25/5.18      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) @ ( inf_in1697001100524423349at_nat @ X @ Z ) ) @ ( inf_in1697001100524423349at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3764_distrib__inf__le,axiom,
% 9.25/5.18      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ ( inf_in7913087082777306421at_nat @ X @ Z ) ) @ ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3765_distrib__inf__le,axiom,
% 9.25/5.18      ! [X: filter_nat,Y: filter_nat,Z: filter_nat] : ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ ( inf_inf_filter_nat @ X @ Y ) @ ( inf_inf_filter_nat @ X @ Z ) ) @ ( inf_inf_filter_nat @ X @ ( sup_sup_filter_nat @ Y @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3766_distrib__inf__le,axiom,
% 9.25/5.18      ! [X: set_nat,Y: set_nat,Z: set_nat] : ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z ) ) @ ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3767_distrib__inf__le,axiom,
% 9.25/5.18      ! [X: rat,Y: rat,Z: rat] : ( ord_less_eq_rat @ ( sup_sup_rat @ ( inf_inf_rat @ X @ Y ) @ ( inf_inf_rat @ X @ Z ) ) @ ( inf_inf_rat @ X @ ( sup_sup_rat @ Y @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3768_distrib__inf__le,axiom,
% 9.25/5.18      ! [X: nat,Y: nat,Z: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z ) ) @ ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3769_distrib__inf__le,axiom,
% 9.25/5.18      ! [X: int,Y: int,Z: int] : ( ord_less_eq_int @ ( sup_sup_int @ ( inf_inf_int @ X @ Y ) @ ( inf_inf_int @ X @ Z ) ) @ ( inf_inf_int @ X @ ( sup_sup_int @ Y @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3770_distrib__sup__le,axiom,
% 9.25/5.18      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) ) @ ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3771_distrib__sup__le,axiom,
% 9.25/5.18      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] : ( ord_le8369615600986905444_int_o @ ( sup_su8463660629351352368_int_o @ X @ ( inf_in3604695632404883862_int_o @ Y @ Z ) ) @ ( inf_in3604695632404883862_int_o @ ( sup_su8463660629351352368_int_o @ X @ Y ) @ ( sup_su8463660629351352368_int_o @ X @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3772_distrib__sup__le,axiom,
% 9.25/5.18      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] : ( ord_le4796328588573674190char_o @ ( sup_sup_list_char_o @ X @ ( inf_inf_list_char_o @ Y @ Z ) ) @ ( inf_inf_list_char_o @ ( sup_sup_list_char_o @ X @ Y ) @ ( sup_sup_list_char_o @ X @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3773_distrib__sup__le,axiom,
% 9.25/5.18      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ X @ ( inf_in1697001100524423349at_nat @ Y @ Z ) ) @ ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ ( sup_su3035147773818789531at_nat @ X @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3774_distrib__sup__le,axiom,
% 9.25/5.18      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ Y @ Z ) ) @ ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3775_distrib__sup__le,axiom,
% 9.25/5.18      ! [X: filter_nat,Y: filter_nat,Z: filter_nat] : ( ord_le2510731241096832064er_nat @ ( sup_sup_filter_nat @ X @ ( inf_inf_filter_nat @ Y @ Z ) ) @ ( inf_inf_filter_nat @ ( sup_sup_filter_nat @ X @ Y ) @ ( sup_sup_filter_nat @ X @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3776_distrib__sup__le,axiom,
% 9.25/5.18      ! [X: set_nat,Y: set_nat,Z: set_nat] : ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) ) @ ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3777_distrib__sup__le,axiom,
% 9.25/5.18      ! [X: rat,Y: rat,Z: rat] : ( ord_less_eq_rat @ ( sup_sup_rat @ X @ ( inf_inf_rat @ Y @ Z ) ) @ ( inf_inf_rat @ ( sup_sup_rat @ X @ Y ) @ ( sup_sup_rat @ X @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3778_distrib__sup__le,axiom,
% 9.25/5.18      ! [X: nat,Y: nat,Z: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) @ ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3779_distrib__sup__le,axiom,
% 9.25/5.18      ! [X: int,Y: int,Z: int] : ( ord_less_eq_int @ ( sup_sup_int @ X @ ( inf_inf_int @ Y @ Z ) ) @ ( inf_inf_int @ ( sup_sup_int @ X @ Y ) @ ( sup_sup_int @ X @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3780_disjoint__mono,axiom,
% 9.25/5.18      ! [A: set_Pr1261947904930325089at_nat,A5: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 9.25/5.18        ( ( ord_le3146513528884898305at_nat @ A @ A5 )
% 9.25/5.18       => ( ( ord_le3146513528884898305at_nat @ B @ B5 )
% 9.25/5.18         => ( ( ( inf_in2572325071724192079at_nat @ A5 @ B5 )
% 9.25/5.18              = bot_bo2099793752762293965at_nat )
% 9.25/5.18           => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 9.25/5.18              = bot_bo2099793752762293965at_nat ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3781_disjoint__mono,axiom,
% 9.25/5.18      ! [A: set_o,A5: set_o,B: set_o,B5: set_o] :
% 9.25/5.18        ( ( ord_less_eq_set_o @ A @ A5 )
% 9.25/5.18       => ( ( ord_less_eq_set_o @ B @ B5 )
% 9.25/5.18         => ( ( ( inf_inf_set_o @ A5 @ B5 )
% 9.25/5.18              = bot_bot_set_o )
% 9.25/5.18           => ( ( inf_inf_set_o @ A @ B )
% 9.25/5.18              = bot_bot_set_o ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3782_disjoint__mono,axiom,
% 9.25/5.18      ! [A: set_int,A5: set_int,B: set_int,B5: set_int] :
% 9.25/5.18        ( ( ord_less_eq_set_int @ A @ A5 )
% 9.25/5.18       => ( ( ord_less_eq_set_int @ B @ B5 )
% 9.25/5.18         => ( ( ( inf_inf_set_int @ A5 @ B5 )
% 9.25/5.18              = bot_bot_set_int )
% 9.25/5.18           => ( ( inf_inf_set_int @ A @ B )
% 9.25/5.18              = bot_bot_set_int ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3783_disjoint__mono,axiom,
% 9.25/5.18      ! [A: set_nat,A5: set_nat,B: set_nat,B5: set_nat] :
% 9.25/5.18        ( ( ord_less_eq_set_nat @ A @ A5 )
% 9.25/5.18       => ( ( ord_less_eq_set_nat @ B @ B5 )
% 9.25/5.18         => ( ( ( inf_inf_set_nat @ A5 @ B5 )
% 9.25/5.18              = bot_bot_set_nat )
% 9.25/5.18           => ( ( inf_inf_set_nat @ A @ B )
% 9.25/5.18              = bot_bot_set_nat ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3784_Un__Int__assoc__eq,axiom,
% 9.25/5.18      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 9.25/5.18        ( ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.18          = ( inf_in2572325071724192079at_nat @ A2 @ ( sup_su6327502436637775413at_nat @ B2 @ C2 ) ) )
% 9.25/5.18        = ( ord_le3146513528884898305at_nat @ C2 @ A2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3785_Un__Int__assoc__eq,axiom,
% 9.25/5.18      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 9.25/5.18        ( ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.18          = ( inf_in1697001100524423349at_nat @ A2 @ ( sup_su3035147773818789531at_nat @ B2 @ C2 ) ) )
% 9.25/5.18        = ( ord_le8081472938463900775at_nat @ C2 @ A2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3786_Un__Int__assoc__eq,axiom,
% 9.25/5.18      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 9.25/5.18        ( ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.18          = ( inf_in7913087082777306421at_nat @ A2 @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) ) )
% 9.25/5.18        = ( ord_le1268244103169919719at_nat @ C2 @ A2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3787_Un__Int__assoc__eq,axiom,
% 9.25/5.18      ! [A2: set_nat,B2: set_nat,C2: set_nat] :
% 9.25/5.18        ( ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ A2 @ B2 ) @ C2 )
% 9.25/5.18          = ( inf_inf_set_nat @ A2 @ ( sup_sup_set_nat @ B2 @ C2 ) ) )
% 9.25/5.18        = ( ord_less_eq_set_nat @ C2 @ A2 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3788_subset__Compl__self__eq,axiom,
% 9.25/5.18      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.18        ( ( ord_le3146513528884898305at_nat @ A2 @ ( uminus6524753893492686040at_nat @ A2 ) )
% 9.25/5.18        = ( A2 = bot_bo2099793752762293965at_nat ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3789_subset__Compl__self__eq,axiom,
% 9.25/5.18      ! [A2: set_o] :
% 9.25/5.18        ( ( ord_less_eq_set_o @ A2 @ ( uminus_uminus_set_o @ A2 ) )
% 9.25/5.18        = ( A2 = bot_bot_set_o ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3790_subset__Compl__self__eq,axiom,
% 9.25/5.18      ! [A2: set_int] :
% 9.25/5.18        ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ A2 ) )
% 9.25/5.18        = ( A2 = bot_bot_set_int ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3791_subset__Compl__self__eq,axiom,
% 9.25/5.18      ! [A2: set_nat] :
% 9.25/5.18        ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ A2 ) )
% 9.25/5.18        = ( A2 = bot_bot_set_nat ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3792_le__divide__eq__numeral_I2_J,axiom,
% 9.25/5.18      ! [W: num,B: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 9.25/5.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 9.25/5.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3793_divide__le__eq__numeral_I2_J,axiom,
% 9.25/5.18      ! [B: rat,C: rat,W: num] :
% 9.25/5.18        ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 9.25/5.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 9.25/5.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3794_in__range__subset,axiom,
% 9.25/5.18      ! [As: set_nat,As3: set_nat,H3: heap_e7401611519738050253t_unit] :
% 9.25/5.18        ( ( ord_less_eq_set_nat @ As @ As3 )
% 9.25/5.18       => ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As3 ) )
% 9.25/5.18         => ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3795_not__zero__less__neg__numeral,axiom,
% 9.25/5.18      ! [N: num] :
% 9.25/5.18        ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3796_not__zero__less__neg__numeral,axiom,
% 9.25/5.18      ! [N: num] :
% 9.25/5.18        ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3797_not__zero__less__neg__numeral,axiom,
% 9.25/5.18      ! [N: num] :
% 9.25/5.18        ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3798_neg__numeral__less__zero,axiom,
% 9.25/5.18      ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3799_neg__numeral__less__zero,axiom,
% 9.25/5.18      ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3800_neg__numeral__less__zero,axiom,
% 9.25/5.18      ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3801_less__minus__one__simps_I3_J,axiom,
% 9.25/5.18      ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3802_less__minus__one__simps_I3_J,axiom,
% 9.25/5.18      ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3803_less__minus__one__simps_I3_J,axiom,
% 9.25/5.18      ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3804_less__minus__one__simps_I1_J,axiom,
% 9.25/5.18      ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3805_less__minus__one__simps_I1_J,axiom,
% 9.25/5.18      ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3806_less__minus__one__simps_I1_J,axiom,
% 9.25/5.18      ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3807_divide__less__eq,axiom,
% 9.25/5.18      ! [B: rat,C: rat,A: rat] :
% 9.25/5.18        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 9.25/5.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 9.25/5.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3808_less__divide__eq,axiom,
% 9.25/5.18      ! [A: rat,B: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 9.25/5.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 9.25/5.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3809_neg__divide__less__eq,axiom,
% 9.25/5.18      ! [C: rat,B: rat,A: rat] :
% 9.25/5.18        ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 9.25/5.18          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3810_neg__less__divide__eq,axiom,
% 9.25/5.18      ! [C: rat,A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 9.25/5.18          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3811_pos__divide__less__eq,axiom,
% 9.25/5.18      ! [C: rat,B: rat,A: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18       => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 9.25/5.18          = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3812_pos__less__divide__eq,axiom,
% 9.25/5.18      ! [C: rat,A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18       => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 9.25/5.18          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3813_mult__imp__div__pos__less,axiom,
% 9.25/5.18      ! [Y: rat,X: rat,Z: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 9.25/5.18       => ( ( ord_less_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 9.25/5.18         => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3814_mult__imp__less__div__pos,axiom,
% 9.25/5.18      ! [Y: rat,Z: rat,X: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ Y )
% 9.25/5.18       => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 9.25/5.18         => ( ord_less_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3815_divide__strict__left__mono,axiom,
% 9.25/5.18      ! [B: rat,A: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_rat @ B @ A )
% 9.25/5.18       => ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 9.25/5.18           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3816_divide__strict__left__mono__neg,axiom,
% 9.25/5.18      ! [A: rat,B: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_rat @ A @ B )
% 9.25/5.18       => ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18         => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 9.25/5.18           => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3817_divide__less__eq__1,axiom,
% 9.25/5.18      ! [B: rat,A: rat] :
% 9.25/5.18        ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.18            & ( ord_less_rat @ B @ A ) )
% 9.25/5.18          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.25/5.18            & ( ord_less_rat @ A @ B ) )
% 9.25/5.18          | ( A = zero_zero_rat ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3818_less__divide__eq__1,axiom,
% 9.25/5.18      ! [B: rat,A: rat] :
% 9.25/5.18        ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.18            & ( ord_less_rat @ A @ B ) )
% 9.25/5.18          | ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.25/5.18            & ( ord_less_rat @ B @ A ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3819_neg__numeral__less__one,axiom,
% 9.25/5.18      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3820_neg__numeral__less__one,axiom,
% 9.25/5.18      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3821_neg__numeral__less__one,axiom,
% 9.25/5.18      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3822_neg__one__less__numeral,axiom,
% 9.25/5.18      ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3823_neg__one__less__numeral,axiom,
% 9.25/5.18      ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3824_neg__one__less__numeral,axiom,
% 9.25/5.18      ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3825_not__numeral__less__neg__one,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3826_not__numeral__less__neg__one,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3827_not__numeral__less__neg__one,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3828_not__one__less__neg__numeral,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3829_not__one__less__neg__numeral,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3830_not__one__less__neg__numeral,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3831_not__neg__one__less__neg__numeral,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3832_not__neg__one__less__neg__numeral,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3833_not__neg__one__less__neg__numeral,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3834_mult__left__le__one__le,axiom,
% 9.25/5.18      ! [X: code_integer,Y: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 9.25/5.18       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 9.25/5.18         => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 9.25/5.18           => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Y @ X ) @ X ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3835_mult__left__le__one__le,axiom,
% 9.25/5.18      ! [X: rat,Y: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.25/5.18       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 9.25/5.18         => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 9.25/5.18           => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3836_mult__left__le__one__le,axiom,
% 9.25/5.18      ! [X: int,Y: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.25/5.18       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 9.25/5.18         => ( ( ord_less_eq_int @ Y @ one_one_int )
% 9.25/5.18           => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3837_mult__right__le__one__le,axiom,
% 9.25/5.18      ! [X: code_integer,Y: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 9.25/5.18       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 9.25/5.18         => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 9.25/5.18           => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X @ Y ) @ X ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3838_mult__right__le__one__le,axiom,
% 9.25/5.18      ! [X: rat,Y: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.25/5.18       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 9.25/5.18         => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 9.25/5.18           => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3839_mult__right__le__one__le,axiom,
% 9.25/5.18      ! [X: int,Y: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.25/5.18       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 9.25/5.18         => ( ( ord_less_eq_int @ Y @ one_one_int )
% 9.25/5.18           => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3840_mult__le__one,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 9.25/5.18       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 9.25/5.18         => ( ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer )
% 9.25/5.18           => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3841_mult__le__one,axiom,
% 9.25/5.18      ! [A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ A @ one_one_rat )
% 9.25/5.18       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.25/5.18         => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 9.25/5.18           => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3842_mult__le__one,axiom,
% 9.25/5.18      ! [A: nat,B: nat] :
% 9.25/5.18        ( ( ord_less_eq_nat @ A @ one_one_nat )
% 9.25/5.18       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 9.25/5.18         => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 9.25/5.18           => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3843_mult__le__one,axiom,
% 9.25/5.18      ! [A: int,B: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ A @ one_one_int )
% 9.25/5.18       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.25/5.18         => ( ( ord_less_eq_int @ B @ one_one_int )
% 9.25/5.18           => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3844_mult__left__le,axiom,
% 9.25/5.18      ! [C: code_integer,A: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ C @ one_one_Code_integer )
% 9.25/5.18       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.18         => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ A ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3845_mult__left__le,axiom,
% 9.25/5.18      ! [C: rat,A: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ C @ one_one_rat )
% 9.25/5.18       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.18         => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3846_mult__left__le,axiom,
% 9.25/5.18      ! [C: nat,A: nat] :
% 9.25/5.18        ( ( ord_less_eq_nat @ C @ one_one_nat )
% 9.25/5.18       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.25/5.18         => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3847_mult__left__le,axiom,
% 9.25/5.18      ! [C: int,A: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ C @ one_one_int )
% 9.25/5.18       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.18         => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3848_not__zero__le__neg__numeral,axiom,
% 9.25/5.18      ! [N: num] :
% 9.25/5.18        ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3849_not__zero__le__neg__numeral,axiom,
% 9.25/5.18      ! [N: num] :
% 9.25/5.18        ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3850_not__zero__le__neg__numeral,axiom,
% 9.25/5.18      ! [N: num] :
% 9.25/5.18        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3851_neg__numeral__le__zero,axiom,
% 9.25/5.18      ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3852_neg__numeral__le__zero,axiom,
% 9.25/5.18      ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3853_neg__numeral__le__zero,axiom,
% 9.25/5.18      ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3854_le__minus__one__simps_I3_J,axiom,
% 9.25/5.18      ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3855_le__minus__one__simps_I3_J,axiom,
% 9.25/5.18      ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3856_le__minus__one__simps_I3_J,axiom,
% 9.25/5.18      ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3857_le__minus__one__simps_I1_J,axiom,
% 9.25/5.18      ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3858_le__minus__one__simps_I1_J,axiom,
% 9.25/5.18      ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3859_le__minus__one__simps_I1_J,axiom,
% 9.25/5.18      ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3860_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 9.25/5.18      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.18       => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.25/5.18          = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3861_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 9.25/5.18      ! [C: nat,A: nat,B: nat] :
% 9.25/5.18        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.25/5.18       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 9.25/5.18          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3862_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 9.25/5.18      ! [C: int,A: int,B: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.25/5.18       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 9.25/5.18          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3863_neg__numeral__le__one,axiom,
% 9.25/5.18      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3864_neg__numeral__le__one,axiom,
% 9.25/5.18      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3865_neg__numeral__le__one,axiom,
% 9.25/5.18      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3866_neg__one__le__numeral,axiom,
% 9.25/5.18      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3867_neg__one__le__numeral,axiom,
% 9.25/5.18      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3868_neg__one__le__numeral,axiom,
% 9.25/5.18      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3869_neg__numeral__le__neg__one,axiom,
% 9.25/5.18      ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3870_neg__numeral__le__neg__one,axiom,
% 9.25/5.18      ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3871_neg__numeral__le__neg__one,axiom,
% 9.25/5.18      ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3872_not__numeral__le__neg__one,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3873_not__numeral__le__neg__one,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3874_not__numeral__le__neg__one,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3875_not__one__le__neg__numeral,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3876_not__one__le__neg__numeral,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3877_not__one__le__neg__numeral,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3878_inf__shunt,axiom,
% 9.25/5.18      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o] :
% 9.25/5.18        ( ( ( inf_in3604695632404883862_int_o @ X @ Y )
% 9.25/5.18          = bot_bo8147686125503663512_int_o )
% 9.25/5.18        = ( ord_le8369615600986905444_int_o @ X @ ( uminus7117520113953359693_int_o @ Y ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3879_inf__shunt,axiom,
% 9.25/5.18      ! [X: list_char > $o,Y: list_char > $o] :
% 9.25/5.18        ( ( ( inf_inf_list_char_o @ X @ Y )
% 9.25/5.18          = bot_bot_list_char_o )
% 9.25/5.18        = ( ord_le4796328588573674190char_o @ X @ ( uminus7154032370948614053char_o @ Y ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3880_inf__shunt,axiom,
% 9.25/5.18      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.25/5.18        ( ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 9.25/5.18          = bot_bo2099793752762293965at_nat )
% 9.25/5.18        = ( ord_le3146513528884898305at_nat @ X @ ( uminus6524753893492686040at_nat @ Y ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3881_inf__shunt,axiom,
% 9.25/5.18      ! [X: set_o,Y: set_o] :
% 9.25/5.18        ( ( ( inf_inf_set_o @ X @ Y )
% 9.25/5.18          = bot_bot_set_o )
% 9.25/5.18        = ( ord_less_eq_set_o @ X @ ( uminus_uminus_set_o @ Y ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3882_inf__shunt,axiom,
% 9.25/5.18      ! [X: set_int,Y: set_int] :
% 9.25/5.18        ( ( ( inf_inf_set_int @ X @ Y )
% 9.25/5.18          = bot_bot_set_int )
% 9.25/5.18        = ( ord_less_eq_set_int @ X @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3883_inf__shunt,axiom,
% 9.25/5.18      ! [X: product_unit,Y: product_unit] :
% 9.25/5.18        ( ( ( inf_inf_Product_unit @ X @ Y )
% 9.25/5.18          = bot_bot_Product_unit )
% 9.25/5.18        = ( ord_le3221252021190050221t_unit @ X @ ( uminus2952777764628376836t_unit @ Y ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3884_inf__shunt,axiom,
% 9.25/5.18      ! [X: set_nat,Y: set_nat] :
% 9.25/5.18        ( ( ( inf_inf_set_nat @ X @ Y )
% 9.25/5.18          = bot_bot_set_nat )
% 9.25/5.18        = ( ord_less_eq_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3885_sup__shunt,axiom,
% 9.25/5.18      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 9.25/5.18        ( ( ( sup_su3035147773818789531at_nat @ X @ Y )
% 9.25/5.18          = top_to8764741339697478167at_nat )
% 9.25/5.18        = ( ord_le8081472938463900775at_nat @ ( uminus2330091110623919550at_nat @ X ) @ Y ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3886_sup__shunt,axiom,
% 9.25/5.18      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 9.25/5.18        ( ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 9.25/5.18          = top_to6833984726390702231at_nat )
% 9.25/5.18        = ( ord_le1268244103169919719at_nat @ ( uminus935396558254630718at_nat @ X ) @ Y ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3887_sup__shunt,axiom,
% 9.25/5.18      ! [X: set_list_nat,Y: set_list_nat] :
% 9.25/5.18        ( ( ( sup_sup_set_list_nat @ X @ Y )
% 9.25/5.18          = top_top_set_list_nat )
% 9.25/5.18        = ( ord_le6045566169113846134st_nat @ ( uminus3195874150345416415st_nat @ X ) @ Y ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3888_sup__shunt,axiom,
% 9.25/5.18      ! [X: set_o,Y: set_o] :
% 9.25/5.18        ( ( ( sup_sup_set_o @ X @ Y )
% 9.25/5.18          = top_top_set_o )
% 9.25/5.18        = ( ord_less_eq_set_o @ ( uminus_uminus_set_o @ X ) @ Y ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3889_sup__shunt,axiom,
% 9.25/5.18      ! [X: set_rat,Y: set_rat] :
% 9.25/5.18        ( ( ( sup_sup_set_rat @ X @ Y )
% 9.25/5.18          = top_top_set_rat )
% 9.25/5.18        = ( ord_less_eq_set_rat @ ( uminus2201863774496077783et_rat @ X ) @ Y ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3890_sup__shunt,axiom,
% 9.25/5.18      ! [X: set_int,Y: set_int] :
% 9.25/5.18        ( ( ( sup_sup_set_int @ X @ Y )
% 9.25/5.18          = top_top_set_int )
% 9.25/5.18        = ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ Y ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3891_sup__shunt,axiom,
% 9.25/5.18      ! [X: product_unit,Y: product_unit] :
% 9.25/5.18        ( ( ( sup_sup_Product_unit @ X @ Y )
% 9.25/5.18          = top_top_Product_unit )
% 9.25/5.18        = ( ord_le3221252021190050221t_unit @ ( uminus2952777764628376836t_unit @ X ) @ Y ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3892_sup__shunt,axiom,
% 9.25/5.18      ! [X: set_nat,Y: set_nat] :
% 9.25/5.18        ( ( ( sup_sup_set_nat @ X @ Y )
% 9.25/5.18          = top_top_set_nat )
% 9.25/5.18        = ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ Y ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3893_shunt1,axiom,
% 9.25/5.18      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 9.25/5.18        ( ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Z )
% 9.25/5.18        = ( ord_le3146513528884898305at_nat @ X @ ( sup_su6327502436637775413at_nat @ ( uminus6524753893492686040at_nat @ Y ) @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3894_shunt1,axiom,
% 9.25/5.18      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 9.25/5.18        ( ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ Y ) @ Z )
% 9.25/5.18        = ( ord_le8369615600986905444_int_o @ X @ ( sup_su8463660629351352368_int_o @ ( uminus7117520113953359693_int_o @ Y ) @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3895_shunt1,axiom,
% 9.25/5.18      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 9.25/5.18        ( ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ X @ Y ) @ Z )
% 9.25/5.18        = ( ord_le4796328588573674190char_o @ X @ ( sup_sup_list_char_o @ ( uminus7154032370948614053char_o @ Y ) @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3896_shunt1,axiom,
% 9.25/5.18      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 9.25/5.18        ( ( ord_le8081472938463900775at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) @ Z )
% 9.25/5.18        = ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ Y ) @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3897_shunt1,axiom,
% 9.25/5.18      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 9.25/5.18        ( ( ord_le1268244103169919719at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ Z )
% 9.25/5.18        = ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ Y ) @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3898_shunt1,axiom,
% 9.25/5.18      ! [X: product_unit,Y: product_unit,Z: product_unit] :
% 9.25/5.18        ( ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ X @ Y ) @ Z )
% 9.25/5.18        = ( ord_le3221252021190050221t_unit @ X @ ( sup_sup_Product_unit @ ( uminus2952777764628376836t_unit @ Y ) @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3899_shunt1,axiom,
% 9.25/5.18      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.25/5.18        ( ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Z )
% 9.25/5.18        = ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3900_shunt2,axiom,
% 9.25/5.18      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 9.25/5.18        ( ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ ( uminus6524753893492686040at_nat @ Y ) ) @ Z )
% 9.25/5.18        = ( ord_le3146513528884898305at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3901_shunt2,axiom,
% 9.25/5.18      ! [X: product_prod_int_int > $o,Y: product_prod_int_int > $o,Z: product_prod_int_int > $o] :
% 9.25/5.18        ( ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ X @ ( uminus7117520113953359693_int_o @ Y ) ) @ Z )
% 9.25/5.18        = ( ord_le8369615600986905444_int_o @ X @ ( sup_su8463660629351352368_int_o @ Y @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3902_shunt2,axiom,
% 9.25/5.18      ! [X: list_char > $o,Y: list_char > $o,Z: list_char > $o] :
% 9.25/5.18        ( ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ X @ ( uminus7154032370948614053char_o @ Y ) ) @ Z )
% 9.25/5.18        = ( ord_le4796328588573674190char_o @ X @ ( sup_sup_list_char_o @ Y @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3903_shunt2,axiom,
% 9.25/5.18      ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 9.25/5.18        ( ( ord_le8081472938463900775at_nat @ ( inf_in1697001100524423349at_nat @ X @ ( uminus2330091110623919550at_nat @ Y ) ) @ Z )
% 9.25/5.18        = ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3904_shunt2,axiom,
% 9.25/5.18      ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 9.25/5.18        ( ( ord_le1268244103169919719at_nat @ ( inf_in7913087082777306421at_nat @ X @ ( uminus935396558254630718at_nat @ Y ) ) @ Z )
% 9.25/5.18        = ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3905_shunt2,axiom,
% 9.25/5.18      ! [X: product_unit,Y: product_unit,Z: product_unit] :
% 9.25/5.18        ( ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ X @ ( uminus2952777764628376836t_unit @ Y ) ) @ Z )
% 9.25/5.18        = ( ord_le3221252021190050221t_unit @ X @ ( sup_sup_Product_unit @ Y @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3906_shunt2,axiom,
% 9.25/5.18      ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 9.25/5.18        ( ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) @ Z )
% 9.25/5.18        = ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3907_sup__neg__inf,axiom,
% 9.25/5.18      ! [P4: set_Pr1261947904930325089at_nat,Q4: set_Pr1261947904930325089at_nat,R3: set_Pr1261947904930325089at_nat] :
% 9.25/5.18        ( ( ord_le3146513528884898305at_nat @ P4 @ ( sup_su6327502436637775413at_nat @ Q4 @ R3 ) )
% 9.25/5.18        = ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ P4 @ ( uminus6524753893492686040at_nat @ Q4 ) ) @ R3 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3908_sup__neg__inf,axiom,
% 9.25/5.18      ! [P4: product_prod_int_int > $o,Q4: product_prod_int_int > $o,R3: product_prod_int_int > $o] :
% 9.25/5.18        ( ( ord_le8369615600986905444_int_o @ P4 @ ( sup_su8463660629351352368_int_o @ Q4 @ R3 ) )
% 9.25/5.18        = ( ord_le8369615600986905444_int_o @ ( inf_in3604695632404883862_int_o @ P4 @ ( uminus7117520113953359693_int_o @ Q4 ) ) @ R3 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3909_sup__neg__inf,axiom,
% 9.25/5.18      ! [P4: list_char > $o,Q4: list_char > $o,R3: list_char > $o] :
% 9.25/5.18        ( ( ord_le4796328588573674190char_o @ P4 @ ( sup_sup_list_char_o @ Q4 @ R3 ) )
% 9.25/5.18        = ( ord_le4796328588573674190char_o @ ( inf_inf_list_char_o @ P4 @ ( uminus7154032370948614053char_o @ Q4 ) ) @ R3 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3910_sup__neg__inf,axiom,
% 9.25/5.18      ! [P4: set_Pr8551490117392284871at_nat,Q4: set_Pr8551490117392284871at_nat,R3: set_Pr8551490117392284871at_nat] :
% 9.25/5.18        ( ( ord_le8081472938463900775at_nat @ P4 @ ( sup_su3035147773818789531at_nat @ Q4 @ R3 ) )
% 9.25/5.18        = ( ord_le8081472938463900775at_nat @ ( inf_in1697001100524423349at_nat @ P4 @ ( uminus2330091110623919550at_nat @ Q4 ) ) @ R3 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3911_sup__neg__inf,axiom,
% 9.25/5.18      ! [P4: set_Pr4329608150637261639at_nat,Q4: set_Pr4329608150637261639at_nat,R3: set_Pr4329608150637261639at_nat] :
% 9.25/5.18        ( ( ord_le1268244103169919719at_nat @ P4 @ ( sup_su5525570899277871387at_nat @ Q4 @ R3 ) )
% 9.25/5.18        = ( ord_le1268244103169919719at_nat @ ( inf_in7913087082777306421at_nat @ P4 @ ( uminus935396558254630718at_nat @ Q4 ) ) @ R3 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3912_sup__neg__inf,axiom,
% 9.25/5.18      ! [P4: product_unit,Q4: product_unit,R3: product_unit] :
% 9.25/5.18        ( ( ord_le3221252021190050221t_unit @ P4 @ ( sup_sup_Product_unit @ Q4 @ R3 ) )
% 9.25/5.18        = ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ P4 @ ( uminus2952777764628376836t_unit @ Q4 ) ) @ R3 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3913_sup__neg__inf,axiom,
% 9.25/5.18      ! [P4: set_nat,Q4: set_nat,R3: set_nat] :
% 9.25/5.18        ( ( ord_less_eq_set_nat @ P4 @ ( sup_sup_set_nat @ Q4 @ R3 ) )
% 9.25/5.18        = ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ P4 @ ( uminus5710092332889474511et_nat @ Q4 ) ) @ R3 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3914_disjoint__eq__subset__Compl,axiom,
% 9.25/5.18      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.18        ( ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 9.25/5.18          = bot_bo2099793752762293965at_nat )
% 9.25/5.18        = ( ord_le3146513528884898305at_nat @ A2 @ ( uminus6524753893492686040at_nat @ B2 ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3915_disjoint__eq__subset__Compl,axiom,
% 9.25/5.18      ! [A2: set_o,B2: set_o] :
% 9.25/5.18        ( ( ( inf_inf_set_o @ A2 @ B2 )
% 9.25/5.18          = bot_bot_set_o )
% 9.25/5.18        = ( ord_less_eq_set_o @ A2 @ ( uminus_uminus_set_o @ B2 ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3916_disjoint__eq__subset__Compl,axiom,
% 9.25/5.18      ! [A2: set_int,B2: set_int] :
% 9.25/5.18        ( ( ( inf_inf_set_int @ A2 @ B2 )
% 9.25/5.18          = bot_bot_set_int )
% 9.25/5.18        = ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ B2 ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3917_disjoint__eq__subset__Compl,axiom,
% 9.25/5.18      ! [A2: set_nat,B2: set_nat] :
% 9.25/5.18        ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 9.25/5.18          = bot_bot_set_nat )
% 9.25/5.18        = ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ B2 ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3918_less__divide__eq__numeral_I1_J,axiom,
% 9.25/5.18      ! [W: num,B: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 9.25/5.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 9.25/5.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3919_divide__less__eq__numeral_I1_J,axiom,
% 9.25/5.18      ! [B: rat,C: rat,W: num] :
% 9.25/5.18        ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 9.25/5.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 9.25/5.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3920_frac__less__eq,axiom,
% 9.25/5.18      ! [Y: rat,Z: rat,X: rat,W: rat] :
% 9.25/5.18        ( ( Y != zero_zero_rat )
% 9.25/5.18       => ( ( Z != zero_zero_rat )
% 9.25/5.18         => ( ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 9.25/5.18            = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3921_pos__minus__divide__less__eq,axiom,
% 9.25/5.18      ! [C: rat,B: rat,A: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 9.25/5.18          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3922_pos__less__minus__divide__eq,axiom,
% 9.25/5.18      ! [C: rat,A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 9.25/5.18          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3923_neg__minus__divide__less__eq,axiom,
% 9.25/5.18      ! [C: rat,B: rat,A: rat] :
% 9.25/5.18        ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18       => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 9.25/5.18          = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3924_neg__less__minus__divide__eq,axiom,
% 9.25/5.18      ! [C: rat,A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18       => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 9.25/5.18          = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3925_minus__divide__less__eq,axiom,
% 9.25/5.18      ! [B: rat,C: rat,A: rat] :
% 9.25/5.18        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 9.25/5.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 9.25/5.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3926_less__minus__divide__eq,axiom,
% 9.25/5.18      ! [A: rat,B: rat,C: rat] :
% 9.25/5.18        ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 9.25/5.18        = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 9.25/5.18          & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 9.25/5.18           => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 9.25/5.18              & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 9.25/5.18               => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3927_frac__le__eq,axiom,
% 9.25/5.18      ! [Y: rat,Z: rat,X: rat,W: rat] :
% 9.25/5.18        ( ( Y != zero_zero_rat )
% 9.25/5.18       => ( ( Z != zero_zero_rat )
% 9.25/5.18         => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 9.25/5.18            = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3928_mult__le__cancel__iff1,axiom,
% 9.25/5.18      ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z )
% 9.25/5.18       => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X @ Z ) @ ( times_3573771949741848930nteger @ Y @ Z ) )
% 9.25/5.18          = ( ord_le3102999989581377725nteger @ X @ Y ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3929_mult__le__cancel__iff1,axiom,
% 9.25/5.18      ! [Z: rat,X: rat,Y: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 9.25/5.18       => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 9.25/5.18          = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3930_mult__le__cancel__iff1,axiom,
% 9.25/5.18      ! [Z: int,X: int,Y: int] :
% 9.25/5.18        ( ( ord_less_int @ zero_zero_int @ Z )
% 9.25/5.18       => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 9.25/5.18          = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3931_mult__le__cancel__iff2,axiom,
% 9.25/5.18      ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z )
% 9.25/5.18       => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Z @ X ) @ ( times_3573771949741848930nteger @ Z @ Y ) )
% 9.25/5.18          = ( ord_le3102999989581377725nteger @ X @ Y ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3932_mult__le__cancel__iff2,axiom,
% 9.25/5.18      ! [Z: rat,X: rat,Y: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 9.25/5.18       => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ ( times_times_rat @ Z @ Y ) )
% 9.25/5.18          = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3933_mult__le__cancel__iff2,axiom,
% 9.25/5.18      ! [Z: int,X: int,Y: int] :
% 9.25/5.18        ( ( ord_less_int @ zero_zero_int @ Z )
% 9.25/5.18       => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X ) @ ( times_times_int @ Z @ Y ) )
% 9.25/5.18          = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3934_mult__less__iff1,axiom,
% 9.25/5.18      ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z )
% 9.25/5.18       => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ X @ Z ) @ ( times_3573771949741848930nteger @ Y @ Z ) )
% 9.25/5.18          = ( ord_le6747313008572928689nteger @ X @ Y ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3935_mult__less__iff1,axiom,
% 9.25/5.18      ! [Z: rat,X: rat,Y: rat] :
% 9.25/5.18        ( ( ord_less_rat @ zero_zero_rat @ Z )
% 9.25/5.18       => ( ( ord_less_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 9.25/5.18          = ( ord_less_rat @ X @ Y ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3936_mult__less__iff1,axiom,
% 9.25/5.18      ! [Z: int,X: int,Y: int] :
% 9.25/5.18        ( ( ord_less_int @ zero_zero_int @ Z )
% 9.25/5.18       => ( ( ord_less_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 9.25/5.18          = ( ord_less_int @ X @ Y ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3937_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 9.25/5.18      ( semila5207306265035627125at_nat @ sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat
% 9.25/5.18      @ ^ [X3: set_Pr8551490117392284871at_nat,Y3: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ Y3 @ X3 )
% 9.25/5.18      @ ^ [X3: set_Pr8551490117392284871at_nat,Y3: set_Pr8551490117392284871at_nat] : ( ord_le7642048601412989811at_nat @ Y3 @ X3 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3938_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 9.25/5.18      ( semila6534579987270727413at_nat @ sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat
% 9.25/5.18      @ ^ [X3: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y3 @ X3 )
% 9.25/5.18      @ ^ [X3: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] : ( ord_le2604355607129572851at_nat @ Y3 @ X3 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3939_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 9.25/5.18      ( semila4918476307565957903at_nat @ sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat
% 9.25/5.18      @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ Y3 @ X3 )
% 9.25/5.18      @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le7866589430770878221at_nat @ Y3 @ X3 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3940_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 9.25/5.18      ( semila2554085542299052326_set_o @ sup_sup_set_o @ bot_bot_set_o
% 9.25/5.18      @ ^ [X3: set_o,Y3: set_o] : ( ord_less_eq_set_o @ Y3 @ X3 )
% 9.25/5.18      @ ^ [X3: set_o,Y3: set_o] : ( ord_less_set_o @ Y3 @ X3 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3941_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 9.25/5.18      ( semila6712789903965657268et_int @ sup_sup_set_int @ bot_bot_set_int
% 9.25/5.18      @ ^ [X3: set_int,Y3: set_int] : ( ord_less_eq_set_int @ Y3 @ X3 )
% 9.25/5.18      @ ^ [X3: set_int,Y3: set_int] : ( ord_less_set_int @ Y3 @ X3 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3942_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 9.25/5.18      ( semila5926144314033625522er_nat @ sup_sup_filter_nat @ bot_bot_filter_nat
% 9.25/5.18      @ ^ [X3: filter_nat,Y3: filter_nat] : ( ord_le2510731241096832064er_nat @ Y3 @ X3 )
% 9.25/5.18      @ ^ [X3: filter_nat,Y3: filter_nat] : ( ord_less_filter_nat @ Y3 @ X3 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3943_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 9.25/5.18      ( semila1667268886620078168et_nat @ sup_sup_set_nat @ bot_bot_set_nat
% 9.25/5.18      @ ^ [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ Y3 @ X3 )
% 9.25/5.18      @ ^ [X3: set_nat,Y3: set_nat] : ( ord_less_set_nat @ Y3 @ X3 ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3944_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 9.25/5.18      semila4918476307565957903at_nat @ inf_in2572325071724192079at_nat @ top_to4669805908274784177at_nat @ ord_le3146513528884898305at_nat @ ord_le7866589430770878221at_nat ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3945_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 9.25/5.18      semila8052717425514686422_int_o @ inf_in3604695632404883862_int_o @ top_to1578927101902068148_int_o @ ord_le8369615600986905444_int_o @ ord_le8213806771718485336_int_o ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3946_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 9.25/5.18      semila3134969884451571676char_o @ inf_inf_list_char_o @ top_top_list_char_o @ ord_le4796328588573674190char_o @ ord_less_list_char_o ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3947_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 9.25/5.18      semila2613578647866687720st_nat @ inf_inf_set_list_nat @ top_top_set_list_nat @ ord_le6045566169113846134st_nat @ ord_le1190675801316882794st_nat ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3948_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 9.25/5.18      semila2554085542299052326_set_o @ inf_inf_set_o @ top_top_set_o @ ord_less_eq_set_o @ ord_less_set_o ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3949_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 9.25/5.18      semila7382412365081457248et_rat @ inf_inf_set_rat @ top_top_set_rat @ ord_less_eq_set_rat @ ord_less_set_rat ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3950_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 9.25/5.18      semila6712789903965657268et_int @ inf_inf_set_int @ top_top_set_int @ ord_less_eq_set_int @ ord_less_set_int ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3951_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 9.25/5.18      semila5926144314033625522er_nat @ inf_inf_filter_nat @ top_top_filter_nat @ ord_le2510731241096832064er_nat @ ord_less_filter_nat ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3952_inf__top_Osemilattice__neutr__order__axioms,axiom,
% 9.25/5.18      semila1667268886620078168et_nat @ inf_inf_set_nat @ top_top_set_nat @ ord_less_eq_set_nat @ ord_less_set_nat ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3953_bot_Oordering__top__axioms,axiom,
% 9.25/5.18      ( orderi2172309028950807442at_nat
% 9.25/5.18      @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ Y3 @ X3 )
% 9.25/5.18      @ ^ [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le7866589430770878221at_nat @ Y3 @ X3 )
% 9.25/5.18      @ bot_bo2099793752762293965at_nat ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3954_bot_Oordering__top__axioms,axiom,
% 9.25/5.18      ( ordering_top_set_o
% 9.25/5.18      @ ^ [X3: set_o,Y3: set_o] : ( ord_less_eq_set_o @ Y3 @ X3 )
% 9.25/5.18      @ ^ [X3: set_o,Y3: set_o] : ( ord_less_set_o @ Y3 @ X3 )
% 9.25/5.18      @ bot_bot_set_o ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3955_bot_Oordering__top__axioms,axiom,
% 9.25/5.18      ( ordering_top_set_int
% 9.25/5.18      @ ^ [X3: set_int,Y3: set_int] : ( ord_less_eq_set_int @ Y3 @ X3 )
% 9.25/5.18      @ ^ [X3: set_int,Y3: set_int] : ( ord_less_set_int @ Y3 @ X3 )
% 9.25/5.18      @ bot_bot_set_int ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3956_bot_Oordering__top__axioms,axiom,
% 9.25/5.18      ( orderi2807725203697798511er_nat
% 9.25/5.18      @ ^ [X3: filter_nat,Y3: filter_nat] : ( ord_le2510731241096832064er_nat @ Y3 @ X3 )
% 9.25/5.18      @ ^ [X3: filter_nat,Y3: filter_nat] : ( ord_less_filter_nat @ Y3 @ X3 )
% 9.25/5.18      @ bot_bot_filter_nat ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3957_bot_Oordering__top__axioms,axiom,
% 9.25/5.18      ( ordering_top_set_nat
% 9.25/5.18      @ ^ [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ Y3 @ X3 )
% 9.25/5.18      @ ^ [X3: set_nat,Y3: set_nat] : ( ord_less_set_nat @ Y3 @ X3 )
% 9.25/5.18      @ bot_bot_set_nat ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3958_bot_Oordering__top__axioms,axiom,
% 9.25/5.18      ( ordering_top_nat
% 9.25/5.18      @ ^ [X3: nat,Y3: nat] : ( ord_less_eq_nat @ Y3 @ X3 )
% 9.25/5.18      @ ^ [X3: nat,Y3: nat] : ( ord_less_nat @ Y3 @ X3 )
% 9.25/5.18      @ bot_bot_nat ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3959_neg__numeral__less__neg__one__iff,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.18        = ( M != one ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3960_neg__numeral__less__neg__one__iff,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.18        = ( M != one ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3961_neg__numeral__less__neg__one__iff,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.25/5.18        = ( M != one ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3962_not__neg__one__le__neg__numeral__iff,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 9.25/5.18        = ( M != one ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3963_not__neg__one__le__neg__numeral__iff,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 9.25/5.18        = ( M != one ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3964_not__neg__one__le__neg__numeral__iff,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 9.25/5.18        = ( M != one ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3965_add__neg__numeral__special_I6_J,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.18        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3966_add__neg__numeral__special_I6_J,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.18        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3967_add__neg__numeral__special_I6_J,axiom,
% 9.25/5.18      ! [M: num] :
% 9.25/5.18        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.25/5.18        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3968_add__neg__numeral__special_I5_J,axiom,
% 9.25/5.18      ! [N: num] :
% 9.25/5.18        ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.18        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3969_add__neg__numeral__special_I5_J,axiom,
% 9.25/5.18      ! [N: num] :
% 9.25/5.18        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.25/5.18        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3970_add__neg__numeral__special_I5_J,axiom,
% 9.25/5.18      ! [N: num] :
% 9.25/5.18        ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.25/5.18        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3971_add__left__cancel,axiom,
% 9.25/5.18      ! [A: rat,B: rat,C: rat] :
% 9.25/5.18        ( ( ( plus_plus_rat @ A @ B )
% 9.25/5.18          = ( plus_plus_rat @ A @ C ) )
% 9.25/5.18        = ( B = C ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3972_add__left__cancel,axiom,
% 9.25/5.18      ! [A: nat,B: nat,C: nat] :
% 9.25/5.18        ( ( ( plus_plus_nat @ A @ B )
% 9.25/5.18          = ( plus_plus_nat @ A @ C ) )
% 9.25/5.18        = ( B = C ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3973_add__left__cancel,axiom,
% 9.25/5.18      ! [A: int,B: int,C: int] :
% 9.25/5.18        ( ( ( plus_plus_int @ A @ B )
% 9.25/5.18          = ( plus_plus_int @ A @ C ) )
% 9.25/5.18        = ( B = C ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3974_add__right__cancel,axiom,
% 9.25/5.18      ! [B: rat,A: rat,C: rat] :
% 9.25/5.18        ( ( ( plus_plus_rat @ B @ A )
% 9.25/5.18          = ( plus_plus_rat @ C @ A ) )
% 9.25/5.18        = ( B = C ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3975_add__right__cancel,axiom,
% 9.25/5.18      ! [B: nat,A: nat,C: nat] :
% 9.25/5.18        ( ( ( plus_plus_nat @ B @ A )
% 9.25/5.18          = ( plus_plus_nat @ C @ A ) )
% 9.25/5.18        = ( B = C ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3976_add__right__cancel,axiom,
% 9.25/5.18      ! [B: int,A: int,C: int] :
% 9.25/5.18        ( ( ( plus_plus_int @ B @ A )
% 9.25/5.18          = ( plus_plus_int @ C @ A ) )
% 9.25/5.18        = ( B = C ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3977_add__le__cancel__left,axiom,
% 9.25/5.18      ! [C: rat,A: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 9.25/5.18        = ( ord_less_eq_rat @ A @ B ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3978_add__le__cancel__left,axiom,
% 9.25/5.18      ! [C: nat,A: nat,B: nat] :
% 9.25/5.18        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 9.25/5.18        = ( ord_less_eq_nat @ A @ B ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3979_add__le__cancel__left,axiom,
% 9.25/5.18      ! [C: int,A: int,B: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 9.25/5.18        = ( ord_less_eq_int @ A @ B ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3980_add__le__cancel__right,axiom,
% 9.25/5.18      ! [A: rat,C: rat,B: rat] :
% 9.25/5.18        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 9.25/5.18        = ( ord_less_eq_rat @ A @ B ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3981_add__le__cancel__right,axiom,
% 9.25/5.18      ! [A: nat,C: nat,B: nat] :
% 9.25/5.18        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 9.25/5.18        = ( ord_less_eq_nat @ A @ B ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3982_add__le__cancel__right,axiom,
% 9.25/5.18      ! [A: int,C: int,B: int] :
% 9.25/5.18        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 9.25/5.18        = ( ord_less_eq_int @ A @ B ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3983_add_Oright__neutral,axiom,
% 9.25/5.18      ! [A: literal] :
% 9.25/5.18        ( ( plus_plus_literal @ A @ zero_zero_literal )
% 9.25/5.18        = A ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3984_add_Oright__neutral,axiom,
% 9.25/5.18      ! [A: code_integer] :
% 9.25/5.18        ( ( plus_p5714425477246183910nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.18        = A ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3985_add_Oright__neutral,axiom,
% 9.25/5.18      ! [A: multis2468970476368604999at_nat] :
% 9.25/5.18        ( ( plus_p7104986032573967614at_nat @ A @ zero_z1048942125864253310at_nat )
% 9.25/5.18        = A ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3986_add_Oright__neutral,axiom,
% 9.25/5.18      ! [A: rat] :
% 9.25/5.18        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 9.25/5.18        = A ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3987_add_Oright__neutral,axiom,
% 9.25/5.18      ! [A: nat] :
% 9.25/5.18        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 9.25/5.18        = A ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3988_add_Oright__neutral,axiom,
% 9.25/5.18      ! [A: int] :
% 9.25/5.18        ( ( plus_plus_int @ A @ zero_zero_int )
% 9.25/5.18        = A ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3989_double__zero__sym,axiom,
% 9.25/5.18      ! [A: code_integer] :
% 9.25/5.18        ( ( zero_z3403309356797280102nteger
% 9.25/5.18          = ( plus_p5714425477246183910nteger @ A @ A ) )
% 9.25/5.18        = ( A = zero_z3403309356797280102nteger ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3990_double__zero__sym,axiom,
% 9.25/5.18      ! [A: rat] :
% 9.25/5.18        ( ( zero_zero_rat
% 9.25/5.18          = ( plus_plus_rat @ A @ A ) )
% 9.25/5.18        = ( A = zero_zero_rat ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3991_double__zero__sym,axiom,
% 9.25/5.18      ! [A: int] :
% 9.25/5.18        ( ( zero_zero_int
% 9.25/5.18          = ( plus_plus_int @ A @ A ) )
% 9.25/5.18        = ( A = zero_zero_int ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3992_add__cancel__left__left,axiom,
% 9.25/5.18      ! [B: code_integer,A: code_integer] :
% 9.25/5.18        ( ( ( plus_p5714425477246183910nteger @ B @ A )
% 9.25/5.18          = A )
% 9.25/5.18        = ( B = zero_z3403309356797280102nteger ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3993_add__cancel__left__left,axiom,
% 9.25/5.18      ! [B: multis2468970476368604999at_nat,A: multis2468970476368604999at_nat] :
% 9.25/5.18        ( ( ( plus_p7104986032573967614at_nat @ B @ A )
% 9.25/5.18          = A )
% 9.25/5.18        = ( B = zero_z1048942125864253310at_nat ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3994_add__cancel__left__left,axiom,
% 9.25/5.18      ! [B: rat,A: rat] :
% 9.25/5.18        ( ( ( plus_plus_rat @ B @ A )
% 9.25/5.18          = A )
% 9.25/5.18        = ( B = zero_zero_rat ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3995_add__cancel__left__left,axiom,
% 9.25/5.18      ! [B: nat,A: nat] :
% 9.25/5.18        ( ( ( plus_plus_nat @ B @ A )
% 9.25/5.18          = A )
% 9.25/5.18        = ( B = zero_zero_nat ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3996_add__cancel__left__left,axiom,
% 9.25/5.18      ! [B: int,A: int] :
% 9.25/5.18        ( ( ( plus_plus_int @ B @ A )
% 9.25/5.18          = A )
% 9.25/5.18        = ( B = zero_zero_int ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3997_add__cancel__left__right,axiom,
% 9.25/5.18      ! [A: code_integer,B: code_integer] :
% 9.25/5.18        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 9.25/5.18          = A )
% 9.25/5.18        = ( B = zero_z3403309356797280102nteger ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3998_add__cancel__left__right,axiom,
% 9.25/5.18      ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 9.25/5.18        ( ( ( plus_p7104986032573967614at_nat @ A @ B )
% 9.25/5.18          = A )
% 9.25/5.18        = ( B = zero_z1048942125864253310at_nat ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_3999_add__cancel__left__right,axiom,
% 9.25/5.18      ! [A: rat,B: rat] :
% 9.25/5.18        ( ( ( plus_plus_rat @ A @ B )
% 9.25/5.18          = A )
% 9.25/5.18        = ( B = zero_zero_rat ) ) ).
% 9.25/5.18  
% 9.25/5.18  thf(fact_4000_add__cancel__left__right,axiom,
% 9.25/5.18      ! [A: nat,B: nat] :
% 9.25/5.18        ( ( ( plus_plus_nat @ A @ B )
% 9.25/5.18          = A )
% 9.25/5.18        = ( B = zero_zero_nat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4001_add__cancel__left__right,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( ( plus_plus_int @ A @ B )
% 9.25/5.19          = A )
% 9.25/5.19        = ( B = zero_zero_int ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4002_add__cancel__right__left,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( A
% 9.25/5.19          = ( plus_p5714425477246183910nteger @ B @ A ) )
% 9.25/5.19        = ( B = zero_z3403309356797280102nteger ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4003_add__cancel__right__left,axiom,
% 9.25/5.19      ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 9.25/5.19        ( ( A
% 9.25/5.19          = ( plus_p7104986032573967614at_nat @ B @ A ) )
% 9.25/5.19        = ( B = zero_z1048942125864253310at_nat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4004_add__cancel__right__left,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( A
% 9.25/5.19          = ( plus_plus_rat @ B @ A ) )
% 9.25/5.19        = ( B = zero_zero_rat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4005_add__cancel__right__left,axiom,
% 9.25/5.19      ! [A: nat,B: nat] :
% 9.25/5.19        ( ( A
% 9.25/5.19          = ( plus_plus_nat @ B @ A ) )
% 9.25/5.19        = ( B = zero_zero_nat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4006_add__cancel__right__left,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( A
% 9.25/5.19          = ( plus_plus_int @ B @ A ) )
% 9.25/5.19        = ( B = zero_zero_int ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4007_add__cancel__right__right,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( A
% 9.25/5.19          = ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.25/5.19        = ( B = zero_z3403309356797280102nteger ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4008_add__cancel__right__right,axiom,
% 9.25/5.19      ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 9.25/5.19        ( ( A
% 9.25/5.19          = ( plus_p7104986032573967614at_nat @ A @ B ) )
% 9.25/5.19        = ( B = zero_z1048942125864253310at_nat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4009_add__cancel__right__right,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( A
% 9.25/5.19          = ( plus_plus_rat @ A @ B ) )
% 9.25/5.19        = ( B = zero_zero_rat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4010_add__cancel__right__right,axiom,
% 9.25/5.19      ! [A: nat,B: nat] :
% 9.25/5.19        ( ( A
% 9.25/5.19          = ( plus_plus_nat @ A @ B ) )
% 9.25/5.19        = ( B = zero_zero_nat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4011_add__cancel__right__right,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( A
% 9.25/5.19          = ( plus_plus_int @ A @ B ) )
% 9.25/5.19        = ( B = zero_zero_int ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4012_add__eq__0__iff__both__eq__0,axiom,
% 9.25/5.19      ! [X: nat,Y: nat] :
% 9.25/5.19        ( ( ( plus_plus_nat @ X @ Y )
% 9.25/5.19          = zero_zero_nat )
% 9.25/5.19        = ( ( X = zero_zero_nat )
% 9.25/5.19          & ( Y = zero_zero_nat ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4013_zero__eq__add__iff__both__eq__0,axiom,
% 9.25/5.19      ! [X: nat,Y: nat] :
% 9.25/5.19        ( ( zero_zero_nat
% 9.25/5.19          = ( plus_plus_nat @ X @ Y ) )
% 9.25/5.19        = ( ( X = zero_zero_nat )
% 9.25/5.19          & ( Y = zero_zero_nat ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4014_add__0,axiom,
% 9.25/5.19      ! [A: literal] :
% 9.25/5.19        ( ( plus_plus_literal @ zero_zero_literal @ A )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4015_add__0,axiom,
% 9.25/5.19      ! [A: code_integer] :
% 9.25/5.19        ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4016_add__0,axiom,
% 9.25/5.19      ! [A: multis2468970476368604999at_nat] :
% 9.25/5.19        ( ( plus_p7104986032573967614at_nat @ zero_z1048942125864253310at_nat @ A )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4017_add__0,axiom,
% 9.25/5.19      ! [A: rat] :
% 9.25/5.19        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4018_add__0,axiom,
% 9.25/5.19      ! [A: nat] :
% 9.25/5.19        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4019_add__0,axiom,
% 9.25/5.19      ! [A: int] :
% 9.25/5.19        ( ( plus_plus_int @ zero_zero_int @ A )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4020_add__less__cancel__left,axiom,
% 9.25/5.19      ! [C: rat,A: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 9.25/5.19        = ( ord_less_rat @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4021_add__less__cancel__left,axiom,
% 9.25/5.19      ! [C: nat,A: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 9.25/5.19        = ( ord_less_nat @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4022_add__less__cancel__left,axiom,
% 9.25/5.19      ! [C: int,A: int,B: int] :
% 9.25/5.19        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 9.25/5.19        = ( ord_less_int @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4023_add__less__cancel__right,axiom,
% 9.25/5.19      ! [A: rat,C: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 9.25/5.19        = ( ord_less_rat @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4024_add__less__cancel__right,axiom,
% 9.25/5.19      ! [A: nat,C: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 9.25/5.19        = ( ord_less_nat @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4025_add__less__cancel__right,axiom,
% 9.25/5.19      ! [A: int,C: int,B: int] :
% 9.25/5.19        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 9.25/5.19        = ( ord_less_int @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4026_add__diff__cancel,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4027_add__diff__cancel,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4028_diff__add__cancel,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4029_diff__add__cancel,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4030_add__diff__cancel__left,axiom,
% 9.25/5.19      ! [C: rat,A: rat,B: rat] :
% 9.25/5.19        ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 9.25/5.19        = ( minus_minus_rat @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4031_add__diff__cancel__left,axiom,
% 9.25/5.19      ! [C: nat,A: nat,B: nat] :
% 9.25/5.19        ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 9.25/5.19        = ( minus_minus_nat @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4032_add__diff__cancel__left,axiom,
% 9.25/5.19      ! [C: int,A: int,B: int] :
% 9.25/5.19        ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 9.25/5.19        = ( minus_minus_int @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4033_add__diff__cancel__left_H,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 9.25/5.19        = B ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4034_add__diff__cancel__left_H,axiom,
% 9.25/5.19      ! [A: nat,B: nat] :
% 9.25/5.19        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 9.25/5.19        = B ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4035_add__diff__cancel__left_H,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 9.25/5.19        = B ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4036_add__diff__cancel__right,axiom,
% 9.25/5.19      ! [A: rat,C: rat,B: rat] :
% 9.25/5.19        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 9.25/5.19        = ( minus_minus_rat @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4037_add__diff__cancel__right,axiom,
% 9.25/5.19      ! [A: nat,C: nat,B: nat] :
% 9.25/5.19        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 9.25/5.19        = ( minus_minus_nat @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4038_add__diff__cancel__right,axiom,
% 9.25/5.19      ! [A: int,C: int,B: int] :
% 9.25/5.19        ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 9.25/5.19        = ( minus_minus_int @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4039_add__diff__cancel__right_H,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4040_add__diff__cancel__right_H,axiom,
% 9.25/5.19      ! [A: nat,B: nat] :
% 9.25/5.19        ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4041_add__diff__cancel__right_H,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4042_minus__add__distrib,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 9.25/5.19        = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4043_minus__add__distrib,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.25/5.19        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4044_minus__add__distrib,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 9.25/5.19        = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4045_minus__add__cancel,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 9.25/5.19        = B ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4046_minus__add__cancel,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.25/5.19        = B ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4047_minus__add__cancel,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 9.25/5.19        = B ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4048_add__minus__cancel,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 9.25/5.19        = B ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4049_add__minus__cancel,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 9.25/5.19        = B ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4050_add__minus__cancel,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 9.25/5.19        = B ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4051_add__le__same__cancel1,axiom,
% 9.25/5.19      ! [B: code_integer,A: code_integer] :
% 9.25/5.19        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 9.25/5.19        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4052_add__le__same__cancel1,axiom,
% 9.25/5.19      ! [B: rat,A: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 9.25/5.19        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4053_add__le__same__cancel1,axiom,
% 9.25/5.19      ! [B: nat,A: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 9.25/5.19        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4054_add__le__same__cancel1,axiom,
% 9.25/5.19      ! [B: int,A: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 9.25/5.19        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4055_add__le__same__cancel2,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 9.25/5.19        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4056_add__le__same__cancel2,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 9.25/5.19        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4057_add__le__same__cancel2,axiom,
% 9.25/5.19      ! [A: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 9.25/5.19        = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4058_add__le__same__cancel2,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 9.25/5.19        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4059_le__add__same__cancel1,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.25/5.19        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4060_le__add__same__cancel1,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 9.25/5.19        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4061_le__add__same__cancel1,axiom,
% 9.25/5.19      ! [A: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 9.25/5.19        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4062_le__add__same__cancel1,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 9.25/5.19        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4063_le__add__same__cancel2,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 9.25/5.19        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4064_le__add__same__cancel2,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 9.25/5.19        = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4065_le__add__same__cancel2,axiom,
% 9.25/5.19      ! [A: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 9.25/5.19        = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4066_le__add__same__cancel2,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 9.25/5.19        = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4067_double__add__le__zero__iff__single__add__le__zero,axiom,
% 9.25/5.19      ! [A: code_integer] :
% 9.25/5.19        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ A ) @ zero_z3403309356797280102nteger )
% 9.25/5.19        = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4068_double__add__le__zero__iff__single__add__le__zero,axiom,
% 9.25/5.19      ! [A: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 9.25/5.19        = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4069_double__add__le__zero__iff__single__add__le__zero,axiom,
% 9.25/5.19      ! [A: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 9.25/5.19        = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4070_zero__le__double__add__iff__zero__le__single__add,axiom,
% 9.25/5.19      ! [A: code_integer] :
% 9.25/5.19        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ A ) )
% 9.25/5.19        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4071_zero__le__double__add__iff__zero__le__single__add,axiom,
% 9.25/5.19      ! [A: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 9.25/5.19        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4072_zero__le__double__add__iff__zero__le__single__add,axiom,
% 9.25/5.19      ! [A: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 9.25/5.19        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4073_add__less__same__cancel1,axiom,
% 9.25/5.19      ! [B: code_integer,A: code_integer] :
% 9.25/5.19        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 9.25/5.19        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4074_add__less__same__cancel1,axiom,
% 9.25/5.19      ! [B: rat,A: rat] :
% 9.25/5.19        ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 9.25/5.19        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4075_add__less__same__cancel1,axiom,
% 9.25/5.19      ! [B: nat,A: nat] :
% 9.25/5.19        ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 9.25/5.19        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4076_add__less__same__cancel1,axiom,
% 9.25/5.19      ! [B: int,A: int] :
% 9.25/5.19        ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 9.25/5.19        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4077_add__less__same__cancel2,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 9.25/5.19        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4078_add__less__same__cancel2,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 9.25/5.19        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4079_add__less__same__cancel2,axiom,
% 9.25/5.19      ! [A: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 9.25/5.19        = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4080_add__less__same__cancel2,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 9.25/5.19        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4081_less__add__same__cancel1,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.25/5.19        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4082_less__add__same__cancel1,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 9.25/5.19        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4083_less__add__same__cancel1,axiom,
% 9.25/5.19      ! [A: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 9.25/5.19        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4084_less__add__same__cancel1,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 9.25/5.19        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4085_less__add__same__cancel2,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 9.25/5.19        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4086_less__add__same__cancel2,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 9.25/5.19        = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4087_less__add__same__cancel2,axiom,
% 9.25/5.19      ! [A: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 9.25/5.19        = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4088_less__add__same__cancel2,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 9.25/5.19        = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4089_double__add__less__zero__iff__single__add__less__zero,axiom,
% 9.25/5.19      ! [A: code_integer] :
% 9.25/5.19        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ A ) @ zero_z3403309356797280102nteger )
% 9.25/5.19        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4090_double__add__less__zero__iff__single__add__less__zero,axiom,
% 9.25/5.19      ! [A: rat] :
% 9.25/5.19        ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 9.25/5.19        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4091_double__add__less__zero__iff__single__add__less__zero,axiom,
% 9.25/5.19      ! [A: int] :
% 9.25/5.19        ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 9.25/5.19        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4092_zero__less__double__add__iff__zero__less__single__add,axiom,
% 9.25/5.19      ! [A: code_integer] :
% 9.25/5.19        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ A ) )
% 9.25/5.19        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4093_zero__less__double__add__iff__zero__less__single__add,axiom,
% 9.25/5.19      ! [A: rat] :
% 9.25/5.19        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 9.25/5.19        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4094_zero__less__double__add__iff__zero__less__single__add,axiom,
% 9.25/5.19      ! [A: int] :
% 9.25/5.19        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 9.25/5.19        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4095_diff__add__zero,axiom,
% 9.25/5.19      ! [A: multis2468970476368604999at_nat,B: multis2468970476368604999at_nat] :
% 9.25/5.19        ( ( minus_4286766774447292334at_nat @ A @ ( plus_p7104986032573967614at_nat @ A @ B ) )
% 9.25/5.19        = zero_z1048942125864253310at_nat ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4096_diff__add__zero,axiom,
% 9.25/5.19      ! [A: nat,B: nat] :
% 9.25/5.19        ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 9.25/5.19        = zero_zero_nat ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4097_distrib__right__numeral,axiom,
% 9.25/5.19      ! [A: nat,B: nat,V: num] :
% 9.25/5.19        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 9.25/5.19        = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4098_distrib__right__numeral,axiom,
% 9.25/5.19      ! [A: int,B: int,V: num] :
% 9.25/5.19        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 9.25/5.19        = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4099_distrib__right__numeral,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer,V: num] :
% 9.25/5.19        ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V ) )
% 9.25/5.19        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4100_distrib__right__numeral,axiom,
% 9.25/5.19      ! [A: rat,B: rat,V: num] :
% 9.25/5.19        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 9.25/5.19        = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4101_distrib__right__numeral,axiom,
% 9.25/5.19      ! [A: code_natural,B: code_natural,V: num] :
% 9.25/5.19        ( ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ A @ B ) @ ( numera5444537566228673987atural @ V ) )
% 9.25/5.19        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( numera5444537566228673987atural @ V ) ) @ ( times_2397367101498566445atural @ B @ ( numera5444537566228673987atural @ V ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4102_distrib__left__numeral,axiom,
% 9.25/5.19      ! [V: num,B: nat,C: nat] :
% 9.25/5.19        ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 9.25/5.19        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4103_distrib__left__numeral,axiom,
% 9.25/5.19      ! [V: num,B: int,C: int] :
% 9.25/5.19        ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 9.25/5.19        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4104_distrib__left__numeral,axiom,
% 9.25/5.19      ! [V: num,B: code_integer,C: code_integer] :
% 9.25/5.19        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 9.25/5.19        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4105_distrib__left__numeral,axiom,
% 9.25/5.19      ! [V: num,B: rat,C: rat] :
% 9.25/5.19        ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 9.25/5.19        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4106_distrib__left__numeral,axiom,
% 9.25/5.19      ! [V: num,B: code_natural,C: code_natural] :
% 9.25/5.19        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ ( plus_p4538020629002901425atural @ B @ C ) )
% 9.25/5.19        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ B ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4107_ab__left__minus,axiom,
% 9.25/5.19      ! [A: int] :
% 9.25/5.19        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 9.25/5.19        = zero_zero_int ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4108_ab__left__minus,axiom,
% 9.25/5.19      ! [A: code_integer] :
% 9.25/5.19        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 9.25/5.19        = zero_z3403309356797280102nteger ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4109_ab__left__minus,axiom,
% 9.25/5.19      ! [A: rat] :
% 9.25/5.19        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 9.25/5.19        = zero_zero_rat ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4110_add_Oright__inverse,axiom,
% 9.25/5.19      ! [A: int] :
% 9.25/5.19        ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 9.25/5.19        = zero_zero_int ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4111_add_Oright__inverse,axiom,
% 9.25/5.19      ! [A: code_integer] :
% 9.25/5.19        ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 9.25/5.19        = zero_z3403309356797280102nteger ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4112_add_Oright__inverse,axiom,
% 9.25/5.19      ! [A: rat] :
% 9.25/5.19        ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 9.25/5.19        = zero_zero_rat ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4113_semiring__norm_I168_J,axiom,
% 9.25/5.19      ! [V: num,W: num,Y: int] :
% 9.25/5.19        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 9.25/5.19        = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4114_semiring__norm_I168_J,axiom,
% 9.25/5.19      ! [V: num,W: num,Y: code_integer] :
% 9.25/5.19        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 9.25/5.19        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4115_semiring__norm_I168_J,axiom,
% 9.25/5.19      ! [V: num,W: num,Y: rat] :
% 9.25/5.19        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 9.25/5.19        = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4116_add__neg__numeral__simps_I3_J,axiom,
% 9.25/5.19      ! [M: num,N: num] :
% 9.25/5.19        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.19        = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4117_add__neg__numeral__simps_I3_J,axiom,
% 9.25/5.19      ! [M: num,N: num] :
% 9.25/5.19        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.25/5.19        = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4118_add__neg__numeral__simps_I3_J,axiom,
% 9.25/5.19      ! [M: num,N: num] :
% 9.25/5.19        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.25/5.19        = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4119_numeral__eq__one__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( ( numeral_numeral_nat @ N )
% 9.25/5.19          = one_one_nat )
% 9.25/5.19        = ( N = one ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4120_numeral__eq__one__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( ( numeral_numeral_int @ N )
% 9.25/5.19          = one_one_int )
% 9.25/5.19        = ( N = one ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4121_numeral__eq__one__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( ( numera6620942414471956472nteger @ N )
% 9.25/5.19          = one_one_Code_integer )
% 9.25/5.19        = ( N = one ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4122_numeral__eq__one__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( ( numeral_numeral_rat @ N )
% 9.25/5.19          = one_one_rat )
% 9.25/5.19        = ( N = one ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4123_numeral__eq__one__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( ( numera5444537566228673987atural @ N )
% 9.25/5.19          = one_one_Code_natural )
% 9.25/5.19        = ( N = one ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4124_one__eq__numeral__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( one_one_nat
% 9.25/5.19          = ( numeral_numeral_nat @ N ) )
% 9.25/5.19        = ( one = N ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4125_one__eq__numeral__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( one_one_int
% 9.25/5.19          = ( numeral_numeral_int @ N ) )
% 9.25/5.19        = ( one = N ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4126_one__eq__numeral__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( one_one_Code_integer
% 9.25/5.19          = ( numera6620942414471956472nteger @ N ) )
% 9.25/5.19        = ( one = N ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4127_one__eq__numeral__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( one_one_rat
% 9.25/5.19          = ( numeral_numeral_rat @ N ) )
% 9.25/5.19        = ( one = N ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4128_one__eq__numeral__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( one_one_Code_natural
% 9.25/5.19          = ( numera5444537566228673987atural @ N ) )
% 9.25/5.19        = ( one = N ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4129_diff__numeral__simps_I3_J,axiom,
% 9.25/5.19      ! [M: num,N: num] :
% 9.25/5.19        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 9.25/5.19        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4130_diff__numeral__simps_I3_J,axiom,
% 9.25/5.19      ! [M: num,N: num] :
% 9.25/5.19        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 9.25/5.19        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4131_diff__numeral__simps_I3_J,axiom,
% 9.25/5.19      ! [M: num,N: num] :
% 9.25/5.19        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 9.25/5.19        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4132_diff__numeral__simps_I2_J,axiom,
% 9.25/5.19      ! [M: num,N: num] :
% 9.25/5.19        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.19        = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4133_diff__numeral__simps_I2_J,axiom,
% 9.25/5.19      ! [M: num,N: num] :
% 9.25/5.19        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.25/5.19        = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4134_diff__numeral__simps_I2_J,axiom,
% 9.25/5.19      ! [M: num,N: num] :
% 9.25/5.19        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.25/5.19        = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4135_uminus__add__conv__diff,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 9.25/5.19        = ( minus_minus_int @ B @ A ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4136_uminus__add__conv__diff,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 9.25/5.19        = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4137_uminus__add__conv__diff,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 9.25/5.19        = ( minus_minus_rat @ B @ A ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4138_diff__minus__eq__add,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 9.25/5.19        = ( plus_plus_int @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4139_diff__minus__eq__add,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 9.25/5.19        = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4140_diff__minus__eq__add,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 9.25/5.19        = ( plus_plus_rat @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4141_add__neg__numeral__special_I7_J,axiom,
% 9.25/5.19      ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.19      = zero_zero_int ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4142_add__neg__numeral__special_I7_J,axiom,
% 9.25/5.19      ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.19      = zero_z3403309356797280102nteger ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4143_add__neg__numeral__special_I7_J,axiom,
% 9.25/5.19      ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.25/5.19      = zero_zero_rat ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4144_add__neg__numeral__special_I8_J,axiom,
% 9.25/5.19      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 9.25/5.19      = zero_zero_int ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4145_add__neg__numeral__special_I8_J,axiom,
% 9.25/5.19      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 9.25/5.19      = zero_z3403309356797280102nteger ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4146_add__neg__numeral__special_I8_J,axiom,
% 9.25/5.19      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 9.25/5.19      = zero_zero_rat ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4147_div__mult__self4,axiom,
% 9.25/5.19      ! [B: nat,C: nat,A: nat] :
% 9.25/5.19        ( ( B != zero_zero_nat )
% 9.25/5.19       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 9.25/5.19          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4148_div__mult__self4,axiom,
% 9.25/5.19      ! [B: int,C: int,A: int] :
% 9.25/5.19        ( ( B != zero_zero_int )
% 9.25/5.19       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 9.25/5.19          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4149_div__mult__self4,axiom,
% 9.25/5.19      ! [B: code_integer,C: code_integer,A: code_integer] :
% 9.25/5.19        ( ( B != zero_z3403309356797280102nteger )
% 9.25/5.19       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 9.25/5.19          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4150_div__mult__self4,axiom,
% 9.25/5.19      ! [B: code_natural,C: code_natural,A: code_natural] :
% 9.25/5.19        ( ( B != zero_z2226904508553997617atural )
% 9.25/5.19       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ C ) @ A ) @ B )
% 9.25/5.19          = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4151_div__mult__self3,axiom,
% 9.25/5.19      ! [B: nat,C: nat,A: nat] :
% 9.25/5.19        ( ( B != zero_zero_nat )
% 9.25/5.19       => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 9.25/5.19          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4152_div__mult__self3,axiom,
% 9.25/5.19      ! [B: int,C: int,A: int] :
% 9.25/5.19        ( ( B != zero_zero_int )
% 9.25/5.19       => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 9.25/5.19          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4153_div__mult__self3,axiom,
% 9.25/5.19      ! [B: code_integer,C: code_integer,A: code_integer] :
% 9.25/5.19        ( ( B != zero_z3403309356797280102nteger )
% 9.25/5.19       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 9.25/5.19          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4154_div__mult__self3,axiom,
% 9.25/5.19      ! [B: code_natural,C: code_natural,A: code_natural] :
% 9.25/5.19        ( ( B != zero_z2226904508553997617atural )
% 9.25/5.19       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C @ B ) @ A ) @ B )
% 9.25/5.19          = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4155_div__mult__self2,axiom,
% 9.25/5.19      ! [B: nat,A: nat,C: nat] :
% 9.25/5.19        ( ( B != zero_zero_nat )
% 9.25/5.19       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 9.25/5.19          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4156_div__mult__self2,axiom,
% 9.25/5.19      ! [B: int,A: int,C: int] :
% 9.25/5.19        ( ( B != zero_zero_int )
% 9.25/5.19       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 9.25/5.19          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4157_div__mult__self2,axiom,
% 9.25/5.19      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.25/5.19        ( ( B != zero_z3403309356797280102nteger )
% 9.25/5.19       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 9.25/5.19          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4158_div__mult__self2,axiom,
% 9.25/5.19      ! [B: code_natural,A: code_natural,C: code_natural] :
% 9.25/5.19        ( ( B != zero_z2226904508553997617atural )
% 9.25/5.19       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ B @ C ) ) @ B )
% 9.25/5.19          = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4159_div__mult__self1,axiom,
% 9.25/5.19      ! [B: nat,A: nat,C: nat] :
% 9.25/5.19        ( ( B != zero_zero_nat )
% 9.25/5.19       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 9.25/5.19          = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4160_div__mult__self1,axiom,
% 9.25/5.19      ! [B: int,A: int,C: int] :
% 9.25/5.19        ( ( B != zero_zero_int )
% 9.25/5.19       => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 9.25/5.19          = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4161_div__mult__self1,axiom,
% 9.25/5.19      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.25/5.19        ( ( B != zero_z3403309356797280102nteger )
% 9.25/5.19       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 9.25/5.19          = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4162_div__mult__self1,axiom,
% 9.25/5.19      ! [B: code_natural,A: code_natural,C: code_natural] :
% 9.25/5.19        ( ( B != zero_z2226904508553997617atural )
% 9.25/5.19       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ C @ B ) ) @ B )
% 9.25/5.19          = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4163_one__plus__numeral,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 9.25/5.19        = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4164_one__plus__numeral,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 9.25/5.19        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4165_one__plus__numeral,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 9.25/5.19        = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4166_one__plus__numeral,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 9.25/5.19        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4167_one__plus__numeral,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N ) )
% 9.25/5.19        = ( numera5444537566228673987atural @ ( plus_plus_num @ one @ N ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4168_numeral__plus__one,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 9.25/5.19        = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4169_numeral__plus__one,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 9.25/5.19        = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4170_numeral__plus__one,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer )
% 9.25/5.19        = ( numera6620942414471956472nteger @ ( plus_plus_num @ N @ one ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4171_numeral__plus__one,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 9.25/5.19        = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4172_numeral__plus__one,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N ) @ one_one_Code_natural )
% 9.25/5.19        = ( numera5444537566228673987atural @ ( plus_plus_num @ N @ one ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4173_numeral__eq__neg__one__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 9.25/5.19          = ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.19        = ( N = one ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4174_numeral__eq__neg__one__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 9.25/5.19          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.19        = ( N = one ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4175_numeral__eq__neg__one__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 9.25/5.19          = ( uminus_uminus_rat @ one_one_rat ) )
% 9.25/5.19        = ( N = one ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4176_neg__one__eq__numeral__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( ( uminus_uminus_int @ one_one_int )
% 9.25/5.19          = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.19        = ( N = one ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4177_neg__one__eq__numeral__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 9.25/5.19          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.25/5.19        = ( N = one ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4178_neg__one__eq__numeral__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( ( uminus_uminus_rat @ one_one_rat )
% 9.25/5.19          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.25/5.19        = ( N = one ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4179_diff__numeral__special_I3_J,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.19        = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4180_diff__numeral__special_I3_J,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.25/5.19        = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4181_diff__numeral__special_I3_J,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.25/5.19        = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4182_diff__numeral__special_I4_J,axiom,
% 9.25/5.19      ! [M: num] :
% 9.25/5.19        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 9.25/5.19        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4183_diff__numeral__special_I4_J,axiom,
% 9.25/5.19      ! [M: num] :
% 9.25/5.19        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 9.25/5.19        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4184_diff__numeral__special_I4_J,axiom,
% 9.25/5.19      ! [M: num] :
% 9.25/5.19        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 9.25/5.19        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4185_numeral__le__one__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer )
% 9.25/5.19        = ( ord_less_eq_num @ N @ one ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4186_numeral__le__one__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( ord_le1926595141338095240atural @ ( numera5444537566228673987atural @ N ) @ one_one_Code_natural )
% 9.25/5.19        = ( ord_less_eq_num @ N @ one ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4187_numeral__le__one__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 9.25/5.19        = ( ord_less_eq_num @ N @ one ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4188_numeral__le__one__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 9.25/5.19        = ( ord_less_eq_num @ N @ one ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4189_numeral__le__one__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 9.25/5.19        = ( ord_less_eq_num @ N @ one ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4190_one__less__numeral__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 9.25/5.19        = ( ord_less_num @ one @ N ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4191_one__less__numeral__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 9.25/5.19        = ( ord_less_num @ one @ N ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4192_one__less__numeral__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 9.25/5.19        = ( ord_less_num @ one @ N ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4193_one__less__numeral__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 9.25/5.19        = ( ord_less_num @ one @ N ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4194_one__less__numeral__iff,axiom,
% 9.25/5.19      ! [N: num] :
% 9.25/5.19        ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N ) )
% 9.25/5.19        = ( ord_less_num @ one @ N ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4195_pred__subset__eq,axiom,
% 9.25/5.19      ! [R: set_se6260736226359567993nt_int,S: set_se6260736226359567993nt_int] :
% 9.25/5.19        ( ( ord_le8334417538754933252_int_o
% 9.25/5.19          @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ R )
% 9.25/5.19          @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ S ) )
% 9.25/5.19        = ( ord_le483042692224249369nt_int @ R @ S ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4196_pred__subset__eq,axiom,
% 9.25/5.19      ! [R: set_set_nat,S: set_set_nat] :
% 9.25/5.19        ( ( ord_le3964352015994296041_nat_o
% 9.25/5.19          @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ R )
% 9.25/5.19          @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ S ) )
% 9.25/5.19        = ( ord_le6893508408891458716et_nat @ R @ S ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4197_pred__subset__eq,axiom,
% 9.25/5.19      ! [R: set_int,S: set_int] :
% 9.25/5.19        ( ( ord_less_eq_int_o
% 9.25/5.19          @ ^ [X3: int] : ( member_int @ X3 @ R )
% 9.25/5.19          @ ^ [X3: int] : ( member_int @ X3 @ S ) )
% 9.25/5.19        = ( ord_less_eq_set_int @ R @ S ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4198_pred__subset__eq,axiom,
% 9.25/5.19      ! [R: set_Pr4532377907799695533_nat_o,S: set_Pr4532377907799695533_nat_o] :
% 9.25/5.19        ( ( ord_le1304494283415849680at_o_o
% 9.25/5.19          @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ R )
% 9.25/5.19          @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ S ) )
% 9.25/5.19        = ( ord_le2965882846123202637_nat_o @ R @ S ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4199_pred__subset__eq,axiom,
% 9.25/5.19      ! [R: set_nat,S: set_nat] :
% 9.25/5.19        ( ( ord_less_eq_nat_o
% 9.25/5.19          @ ^ [X3: nat] : ( member_nat @ X3 @ R )
% 9.25/5.19          @ ^ [X3: nat] : ( member_nat @ X3 @ S ) )
% 9.25/5.19        = ( ord_less_eq_set_nat @ R @ S ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4200_less__eq__set__def,axiom,
% 9.25/5.19      ( ord_le483042692224249369nt_int
% 9.25/5.19      = ( ^ [A4: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
% 9.25/5.19            ( ord_le8334417538754933252_int_o
% 9.25/5.19            @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ A4 )
% 9.25/5.19            @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ B4 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4201_less__eq__set__def,axiom,
% 9.25/5.19      ( ord_le6893508408891458716et_nat
% 9.25/5.19      = ( ^ [A4: set_set_nat,B4: set_set_nat] :
% 9.25/5.19            ( ord_le3964352015994296041_nat_o
% 9.25/5.19            @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A4 )
% 9.25/5.19            @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ B4 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4202_less__eq__set__def,axiom,
% 9.25/5.19      ( ord_less_eq_set_int
% 9.25/5.19      = ( ^ [A4: set_int,B4: set_int] :
% 9.25/5.19            ( ord_less_eq_int_o
% 9.25/5.19            @ ^ [X3: int] : ( member_int @ X3 @ A4 )
% 9.25/5.19            @ ^ [X3: int] : ( member_int @ X3 @ B4 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4203_less__eq__set__def,axiom,
% 9.25/5.19      ( ord_le2965882846123202637_nat_o
% 9.25/5.19      = ( ^ [A4: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 9.25/5.19            ( ord_le1304494283415849680at_o_o
% 9.25/5.19            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ A4 )
% 9.25/5.19            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ B4 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4204_less__eq__set__def,axiom,
% 9.25/5.19      ( ord_less_eq_set_nat
% 9.25/5.19      = ( ^ [A4: set_nat,B4: set_nat] :
% 9.25/5.19            ( ord_less_eq_nat_o
% 9.25/5.19            @ ^ [X3: nat] : ( member_nat @ X3 @ A4 )
% 9.25/5.19            @ ^ [X3: nat] : ( member_nat @ X3 @ B4 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4205_less__set__def,axiom,
% 9.25/5.19      ( ord_le1924305788584680229nt_int
% 9.25/5.19      = ( ^ [A4: set_se6260736226359567993nt_int,B4: set_se6260736226359567993nt_int] :
% 9.25/5.19            ( ord_le2688692977766382584_int_o
% 9.25/5.19            @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ A4 )
% 9.25/5.19            @ ^ [X3: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ X3 @ B4 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4206_less__set__def,axiom,
% 9.25/5.19      ( ord_less_set_set_nat
% 9.25/5.19      = ( ^ [A4: set_set_nat,B4: set_set_nat] :
% 9.25/5.19            ( ord_less_set_nat_o
% 9.25/5.19            @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A4 )
% 9.25/5.19            @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ B4 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4207_less__set__def,axiom,
% 9.25/5.19      ( ord_less_set_nat
% 9.25/5.19      = ( ^ [A4: set_nat,B4: set_nat] :
% 9.25/5.19            ( ord_less_nat_o
% 9.25/5.19            @ ^ [X3: nat] : ( member_nat @ X3 @ A4 )
% 9.25/5.19            @ ^ [X3: nat] : ( member_nat @ X3 @ B4 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4208_less__set__def,axiom,
% 9.25/5.19      ( ord_less_set_int
% 9.25/5.19      = ( ^ [A4: set_int,B4: set_int] :
% 9.25/5.19            ( ord_less_int_o
% 9.25/5.19            @ ^ [X3: int] : ( member_int @ X3 @ A4 )
% 9.25/5.19            @ ^ [X3: int] : ( member_int @ X3 @ B4 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4209_less__set__def,axiom,
% 9.25/5.19      ( ord_le2453136405763929_nat_o
% 9.25/5.19      = ( ^ [A4: set_Pr4532377907799695533_nat_o,B4: set_Pr4532377907799695533_nat_o] :
% 9.25/5.19            ( ord_le5728734702541193924at_o_o
% 9.25/5.19            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ A4 )
% 9.25/5.19            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ X3 @ B4 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4210_less__assn__def,axiom,
% 9.25/5.19      ( ord_less_assn
% 9.25/5.19      = ( ^ [A3: assn,B3: assn] :
% 9.25/5.19            ( ( ord_less_eq_assn @ A3 @ B3 )
% 9.25/5.19            & ( A3 != B3 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4211_Collect__subset,axiom,
% 9.25/5.19      ! [A2: set_se6260736226359567993nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.19        ( ord_le483042692224249369nt_int
% 9.25/5.19        @ ( collec5210948495886036740nt_int
% 9.25/5.19          @ ^ [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.19              ( ( member2340774599025711042nt_int @ X3 @ A2 )
% 9.25/5.19              & ( P @ X3 ) ) )
% 9.25/5.19        @ A2 ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4212_Collect__subset,axiom,
% 9.25/5.19      ! [A2: set_set_nat,P: set_nat > $o] :
% 9.25/5.19        ( ord_le6893508408891458716et_nat
% 9.25/5.19        @ ( collect_set_nat
% 9.25/5.19          @ ^ [X3: set_nat] :
% 9.25/5.19              ( ( member_set_nat @ X3 @ A2 )
% 9.25/5.19              & ( P @ X3 ) ) )
% 9.25/5.19        @ A2 ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4213_Collect__subset,axiom,
% 9.25/5.19      ! [A2: set_int,P: int > $o] :
% 9.25/5.19        ( ord_less_eq_set_int
% 9.25/5.19        @ ( collect_int
% 9.25/5.19          @ ^ [X3: int] :
% 9.25/5.19              ( ( member_int @ X3 @ A2 )
% 9.25/5.19              & ( P @ X3 ) ) )
% 9.25/5.19        @ A2 ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4214_Collect__subset,axiom,
% 9.25/5.19      ! [A2: set_Pr4532377907799695533_nat_o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.19        ( ord_le2965882846123202637_nat_o
% 9.25/5.19        @ ( collec939566748876313656_nat_o
% 9.25/5.19          @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.19              ( ( member6576561426505652726_nat_o @ X3 @ A2 )
% 9.25/5.19              & ( P @ X3 ) ) )
% 9.25/5.19        @ A2 ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4215_Collect__subset,axiom,
% 9.25/5.19      ! [A2: set_nat,P: nat > $o] :
% 9.25/5.19        ( ord_less_eq_set_nat
% 9.25/5.19        @ ( collect_nat
% 9.25/5.19          @ ^ [X3: nat] :
% 9.25/5.19              ( ( member_nat @ X3 @ A2 )
% 9.25/5.19              & ( P @ X3 ) ) )
% 9.25/5.19        @ A2 ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4216_conj__subset__def,axiom,
% 9.25/5.19      ! [A2: set_se6260736226359567993nt_int,P: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.19        ( ( ord_le483042692224249369nt_int @ A2
% 9.25/5.19          @ ( collec5210948495886036740nt_int
% 9.25/5.19            @ ^ [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.19                ( ( P @ X3 )
% 9.25/5.19                & ( Q2 @ X3 ) ) ) )
% 9.25/5.19        = ( ( ord_le483042692224249369nt_int @ A2 @ ( collec5210948495886036740nt_int @ P ) )
% 9.25/5.19          & ( ord_le483042692224249369nt_int @ A2 @ ( collec5210948495886036740nt_int @ Q2 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4217_conj__subset__def,axiom,
% 9.25/5.19      ! [A2: set_set_nat,P: set_nat > $o,Q2: set_nat > $o] :
% 9.25/5.19        ( ( ord_le6893508408891458716et_nat @ A2
% 9.25/5.19          @ ( collect_set_nat
% 9.25/5.19            @ ^ [X3: set_nat] :
% 9.25/5.19                ( ( P @ X3 )
% 9.25/5.19                & ( Q2 @ X3 ) ) ) )
% 9.25/5.19        = ( ( ord_le6893508408891458716et_nat @ A2 @ ( collect_set_nat @ P ) )
% 9.25/5.19          & ( ord_le6893508408891458716et_nat @ A2 @ ( collect_set_nat @ Q2 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4218_conj__subset__def,axiom,
% 9.25/5.19      ! [A2: set_int,P: int > $o,Q2: int > $o] :
% 9.25/5.19        ( ( ord_less_eq_set_int @ A2
% 9.25/5.19          @ ( collect_int
% 9.25/5.19            @ ^ [X3: int] :
% 9.25/5.19                ( ( P @ X3 )
% 9.25/5.19                & ( Q2 @ X3 ) ) ) )
% 9.25/5.19        = ( ( ord_less_eq_set_int @ A2 @ ( collect_int @ P ) )
% 9.25/5.19          & ( ord_less_eq_set_int @ A2 @ ( collect_int @ Q2 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4219_conj__subset__def,axiom,
% 9.25/5.19      ! [A2: set_Pr4532377907799695533_nat_o,P: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.19        ( ( ord_le2965882846123202637_nat_o @ A2
% 9.25/5.19          @ ( collec939566748876313656_nat_o
% 9.25/5.19            @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.19                ( ( P @ X3 )
% 9.25/5.19                & ( Q2 @ X3 ) ) ) )
% 9.25/5.19        = ( ( ord_le2965882846123202637_nat_o @ A2 @ ( collec939566748876313656_nat_o @ P ) )
% 9.25/5.19          & ( ord_le2965882846123202637_nat_o @ A2 @ ( collec939566748876313656_nat_o @ Q2 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4220_conj__subset__def,axiom,
% 9.25/5.19      ! [A2: set_nat,P: nat > $o,Q2: nat > $o] :
% 9.25/5.19        ( ( ord_less_eq_set_nat @ A2
% 9.25/5.19          @ ( collect_nat
% 9.25/5.19            @ ^ [X3: nat] :
% 9.25/5.19                ( ( P @ X3 )
% 9.25/5.19                & ( Q2 @ X3 ) ) ) )
% 9.25/5.19        = ( ( ord_less_eq_set_nat @ A2 @ ( collect_nat @ P ) )
% 9.25/5.19          & ( ord_less_eq_set_nat @ A2 @ ( collect_nat @ Q2 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4221_ordering__top_Oextremum,axiom,
% 9.25/5.19      ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 9.25/5.19        ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 9.25/5.19       => ( Less_eq @ A @ Top ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4222_ordering__top_Oextremum__strict,axiom,
% 9.25/5.19      ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 9.25/5.19        ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 9.25/5.19       => ~ ( Less @ Top @ A ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4223_ordering__top_Oextremum__unique,axiom,
% 9.25/5.19      ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 9.25/5.19        ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 9.25/5.19       => ( ( Less_eq @ Top @ A )
% 9.25/5.19          = ( A = Top ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4224_ordering__top_Onot__eq__extremum,axiom,
% 9.25/5.19      ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 9.25/5.19        ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 9.25/5.19       => ( ( A != Top )
% 9.25/5.19          = ( Less @ A @ Top ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4225_ordering__top_Oextremum__uniqueI,axiom,
% 9.25/5.19      ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 9.25/5.19        ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 9.25/5.19       => ( ( Less_eq @ Top @ A )
% 9.25/5.19         => ( A = Top ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4226_semilattice__neutr__order_Oeq__neutr__iff,axiom,
% 9.25/5.19      ! [F2: nat > nat > nat,Z: nat,Less_eq: nat > nat > $o,Less: nat > nat > $o,A: nat,B: nat] :
% 9.25/5.19        ( ( semila1623282765462674594er_nat @ F2 @ Z @ Less_eq @ Less )
% 9.25/5.19       => ( ( ( F2 @ A @ B )
% 9.25/5.19            = Z )
% 9.25/5.19          = ( ( A = Z )
% 9.25/5.19            & ( B = Z ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4227_semilattice__neutr__order_Oneutr__eq__iff,axiom,
% 9.25/5.19      ! [F2: nat > nat > nat,Z: nat,Less_eq: nat > nat > $o,Less: nat > nat > $o,A: nat,B: nat] :
% 9.25/5.19        ( ( semila1623282765462674594er_nat @ F2 @ Z @ Less_eq @ Less )
% 9.25/5.19       => ( ( Z
% 9.25/5.19            = ( F2 @ A @ B ) )
% 9.25/5.19          = ( ( A = Z )
% 9.25/5.19            & ( B = Z ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4228_add__mono__thms__linordered__semiring_I4_J,axiom,
% 9.25/5.19      ! [I: rat,J: rat,K: rat,L: rat] :
% 9.25/5.19        ( ( ( I = J )
% 9.25/5.19          & ( K = L ) )
% 9.25/5.19       => ( ( plus_plus_rat @ I @ K )
% 9.25/5.19          = ( plus_plus_rat @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4229_add__mono__thms__linordered__semiring_I4_J,axiom,
% 9.25/5.19      ! [I: nat,J: nat,K: nat,L: nat] :
% 9.25/5.19        ( ( ( I = J )
% 9.25/5.19          & ( K = L ) )
% 9.25/5.19       => ( ( plus_plus_nat @ I @ K )
% 9.25/5.19          = ( plus_plus_nat @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4230_add__mono__thms__linordered__semiring_I4_J,axiom,
% 9.25/5.19      ! [I: int,J: int,K: int,L: int] :
% 9.25/5.19        ( ( ( I = J )
% 9.25/5.19          & ( K = L ) )
% 9.25/5.19       => ( ( plus_plus_int @ I @ K )
% 9.25/5.19          = ( plus_plus_int @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4231_group__cancel_Oadd1,axiom,
% 9.25/5.19      ! [A2: rat,K: rat,A: rat,B: rat] :
% 9.25/5.19        ( ( A2
% 9.25/5.19          = ( plus_plus_rat @ K @ A ) )
% 9.25/5.19       => ( ( plus_plus_rat @ A2 @ B )
% 9.25/5.19          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4232_group__cancel_Oadd1,axiom,
% 9.25/5.19      ! [A2: nat,K: nat,A: nat,B: nat] :
% 9.25/5.19        ( ( A2
% 9.25/5.19          = ( plus_plus_nat @ K @ A ) )
% 9.25/5.19       => ( ( plus_plus_nat @ A2 @ B )
% 9.25/5.19          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4233_group__cancel_Oadd1,axiom,
% 9.25/5.19      ! [A2: int,K: int,A: int,B: int] :
% 9.25/5.19        ( ( A2
% 9.25/5.19          = ( plus_plus_int @ K @ A ) )
% 9.25/5.19       => ( ( plus_plus_int @ A2 @ B )
% 9.25/5.19          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4234_group__cancel_Oadd2,axiom,
% 9.25/5.19      ! [B2: rat,K: rat,B: rat,A: rat] :
% 9.25/5.19        ( ( B2
% 9.25/5.19          = ( plus_plus_rat @ K @ B ) )
% 9.25/5.19       => ( ( plus_plus_rat @ A @ B2 )
% 9.25/5.19          = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4235_group__cancel_Oadd2,axiom,
% 9.25/5.19      ! [B2: nat,K: nat,B: nat,A: nat] :
% 9.25/5.19        ( ( B2
% 9.25/5.19          = ( plus_plus_nat @ K @ B ) )
% 9.25/5.19       => ( ( plus_plus_nat @ A @ B2 )
% 9.25/5.19          = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4236_group__cancel_Oadd2,axiom,
% 9.25/5.19      ! [B2: int,K: int,B: int,A: int] :
% 9.25/5.19        ( ( B2
% 9.25/5.19          = ( plus_plus_int @ K @ B ) )
% 9.25/5.19       => ( ( plus_plus_int @ A @ B2 )
% 9.25/5.19          = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4237_add_Oassoc,axiom,
% 9.25/5.19      ! [A: literal,B: literal,C: literal] :
% 9.25/5.19        ( ( plus_plus_literal @ ( plus_plus_literal @ A @ B ) @ C )
% 9.25/5.19        = ( plus_plus_literal @ A @ ( plus_plus_literal @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4238_add_Oassoc,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.25/5.19        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4239_add_Oassoc,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.25/5.19        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4240_add_Oassoc,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.25/5.19        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4241_add_Oleft__cancel,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( ( plus_plus_rat @ A @ B )
% 9.25/5.19          = ( plus_plus_rat @ A @ C ) )
% 9.25/5.19        = ( B = C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4242_add_Oleft__cancel,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( ( plus_plus_int @ A @ B )
% 9.25/5.19          = ( plus_plus_int @ A @ C ) )
% 9.25/5.19        = ( B = C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4243_add_Oright__cancel,axiom,
% 9.25/5.19      ! [B: rat,A: rat,C: rat] :
% 9.25/5.19        ( ( ( plus_plus_rat @ B @ A )
% 9.25/5.19          = ( plus_plus_rat @ C @ A ) )
% 9.25/5.19        = ( B = C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4244_add_Oright__cancel,axiom,
% 9.25/5.19      ! [B: int,A: int,C: int] :
% 9.25/5.19        ( ( ( plus_plus_int @ B @ A )
% 9.25/5.19          = ( plus_plus_int @ C @ A ) )
% 9.25/5.19        = ( B = C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4245_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 9.25/5.19      ( plus_plus_rat
% 9.25/5.19      = ( ^ [A3: rat,B3: rat] : ( plus_plus_rat @ B3 @ A3 ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4246_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 9.25/5.19      ( plus_plus_nat
% 9.25/5.19      = ( ^ [A3: nat,B3: nat] : ( plus_plus_nat @ B3 @ A3 ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4247_ab__semigroup__add__class_Oadd_Ocommute,axiom,
% 9.25/5.19      ( plus_plus_int
% 9.25/5.19      = ( ^ [A3: int,B3: int] : ( plus_plus_int @ B3 @ A3 ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4248_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 9.25/5.19      ! [B: rat,A: rat,C: rat] :
% 9.25/5.19        ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 9.25/5.19        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4249_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 9.25/5.19      ! [B: nat,A: nat,C: nat] :
% 9.25/5.19        ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 9.25/5.19        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4250_ab__semigroup__add__class_Oadd_Oleft__commute,axiom,
% 9.25/5.19      ! [B: int,A: int,C: int] :
% 9.25/5.19        ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 9.25/5.19        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4251_add__left__imp__eq,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( ( plus_plus_rat @ A @ B )
% 9.25/5.19          = ( plus_plus_rat @ A @ C ) )
% 9.25/5.19       => ( B = C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4252_add__left__imp__eq,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( ( plus_plus_nat @ A @ B )
% 9.25/5.19          = ( plus_plus_nat @ A @ C ) )
% 9.25/5.19       => ( B = C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4253_add__left__imp__eq,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( ( plus_plus_int @ A @ B )
% 9.25/5.19          = ( plus_plus_int @ A @ C ) )
% 9.25/5.19       => ( B = C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4254_add__right__imp__eq,axiom,
% 9.25/5.19      ! [B: rat,A: rat,C: rat] :
% 9.25/5.19        ( ( ( plus_plus_rat @ B @ A )
% 9.25/5.19          = ( plus_plus_rat @ C @ A ) )
% 9.25/5.19       => ( B = C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4255_add__right__imp__eq,axiom,
% 9.25/5.19      ! [B: nat,A: nat,C: nat] :
% 9.25/5.19        ( ( ( plus_plus_nat @ B @ A )
% 9.25/5.19          = ( plus_plus_nat @ C @ A ) )
% 9.25/5.19       => ( B = C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4256_add__right__imp__eq,axiom,
% 9.25/5.19      ! [B: int,A: int,C: int] :
% 9.25/5.19        ( ( ( plus_plus_int @ B @ A )
% 9.25/5.19          = ( plus_plus_int @ C @ A ) )
% 9.25/5.19       => ( B = C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4257_add_Oright__assoc,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.25/5.19        = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4258_add_Oright__assoc,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.25/5.19        = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4259_add_Oright__assoc,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.25/5.19        = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4260_add_Oright__commute,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.25/5.19        = ( plus_plus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4261_add_Oright__commute,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.25/5.19        = ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4262_add_Oright__commute,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.25/5.19        = ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4263_numerals_I1_J,axiom,
% 9.25/5.19      ( ( numeral_numeral_nat @ one )
% 9.25/5.19      = one_one_nat ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4264_add__mono__thms__linordered__semiring_I3_J,axiom,
% 9.25/5.19      ! [I: rat,J: rat,K: rat,L: rat] :
% 9.25/5.19        ( ( ( ord_less_eq_rat @ I @ J )
% 9.25/5.19          & ( K = L ) )
% 9.25/5.19       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4265_add__mono__thms__linordered__semiring_I3_J,axiom,
% 9.25/5.19      ! [I: nat,J: nat,K: nat,L: nat] :
% 9.25/5.19        ( ( ( ord_less_eq_nat @ I @ J )
% 9.25/5.19          & ( K = L ) )
% 9.25/5.19       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4266_add__mono__thms__linordered__semiring_I3_J,axiom,
% 9.25/5.19      ! [I: int,J: int,K: int,L: int] :
% 9.25/5.19        ( ( ( ord_less_eq_int @ I @ J )
% 9.25/5.19          & ( K = L ) )
% 9.25/5.19       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4267_add__mono__thms__linordered__semiring_I2_J,axiom,
% 9.25/5.19      ! [I: rat,J: rat,K: rat,L: rat] :
% 9.25/5.19        ( ( ( I = J )
% 9.25/5.19          & ( ord_less_eq_rat @ K @ L ) )
% 9.25/5.19       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4268_add__mono__thms__linordered__semiring_I2_J,axiom,
% 9.25/5.19      ! [I: nat,J: nat,K: nat,L: nat] :
% 9.25/5.19        ( ( ( I = J )
% 9.25/5.19          & ( ord_less_eq_nat @ K @ L ) )
% 9.25/5.19       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4269_add__mono__thms__linordered__semiring_I2_J,axiom,
% 9.25/5.19      ! [I: int,J: int,K: int,L: int] :
% 9.25/5.19        ( ( ( I = J )
% 9.25/5.19          & ( ord_less_eq_int @ K @ L ) )
% 9.25/5.19       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4270_add__mono__thms__linordered__semiring_I1_J,axiom,
% 9.25/5.19      ! [I: rat,J: rat,K: rat,L: rat] :
% 9.25/5.19        ( ( ( ord_less_eq_rat @ I @ J )
% 9.25/5.19          & ( ord_less_eq_rat @ K @ L ) )
% 9.25/5.19       => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4271_add__mono__thms__linordered__semiring_I1_J,axiom,
% 9.25/5.19      ! [I: nat,J: nat,K: nat,L: nat] :
% 9.25/5.19        ( ( ( ord_less_eq_nat @ I @ J )
% 9.25/5.19          & ( ord_less_eq_nat @ K @ L ) )
% 9.25/5.19       => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4272_add__mono__thms__linordered__semiring_I1_J,axiom,
% 9.25/5.19      ! [I: int,J: int,K: int,L: int] :
% 9.25/5.19        ( ( ( ord_less_eq_int @ I @ J )
% 9.25/5.19          & ( ord_less_eq_int @ K @ L ) )
% 9.25/5.19       => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4273_add__mono,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.19       => ( ( ord_less_eq_rat @ C @ D2 )
% 9.25/5.19         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4274_add__mono,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.19       => ( ( ord_less_eq_nat @ C @ D2 )
% 9.25/5.19         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4275_add__mono,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int,D2: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.19       => ( ( ord_less_eq_int @ C @ D2 )
% 9.25/5.19         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4276_add__left__mono,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.19       => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4277_add__left__mono,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.19       => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4278_add__left__mono,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.19       => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4279_less__eqE,axiom,
% 9.25/5.19      ! [A: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.19       => ~ ! [C3: nat] :
% 9.25/5.19              ( B
% 9.25/5.19             != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4280_add__right__mono,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.19       => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4281_add__right__mono,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.19       => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4282_add__right__mono,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.19       => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4283_le__iff__add,axiom,
% 9.25/5.19      ( ord_less_eq_nat
% 9.25/5.19      = ( ^ [A3: nat,B3: nat] :
% 9.25/5.19          ? [C4: nat] :
% 9.25/5.19            ( B3
% 9.25/5.19            = ( plus_plus_nat @ A3 @ C4 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4284_add__le__imp__le__left,axiom,
% 9.25/5.19      ! [C: rat,A: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 9.25/5.19       => ( ord_less_eq_rat @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4285_add__le__imp__le__left,axiom,
% 9.25/5.19      ! [C: nat,A: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 9.25/5.19       => ( ord_less_eq_nat @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4286_add__le__imp__le__left,axiom,
% 9.25/5.19      ! [C: int,A: int,B: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 9.25/5.19       => ( ord_less_eq_int @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4287_add__le__imp__le__right,axiom,
% 9.25/5.19      ! [A: rat,C: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 9.25/5.19       => ( ord_less_eq_rat @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4288_add__le__imp__le__right,axiom,
% 9.25/5.19      ! [A: nat,C: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 9.25/5.19       => ( ord_less_eq_nat @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4289_add__le__imp__le__right,axiom,
% 9.25/5.19      ! [A: int,C: int,B: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 9.25/5.19       => ( ord_less_eq_int @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4290_comm__monoid__add__class_Oadd__0,axiom,
% 9.25/5.19      ! [A: code_integer] :
% 9.25/5.19        ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4291_comm__monoid__add__class_Oadd__0,axiom,
% 9.25/5.19      ! [A: multis2468970476368604999at_nat] :
% 9.25/5.19        ( ( plus_p7104986032573967614at_nat @ zero_z1048942125864253310at_nat @ A )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4292_comm__monoid__add__class_Oadd__0,axiom,
% 9.25/5.19      ! [A: rat] :
% 9.25/5.19        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4293_comm__monoid__add__class_Oadd__0,axiom,
% 9.25/5.19      ! [A: nat] :
% 9.25/5.19        ( ( plus_plus_nat @ zero_zero_nat @ A )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4294_comm__monoid__add__class_Oadd__0,axiom,
% 9.25/5.19      ! [A: int] :
% 9.25/5.19        ( ( plus_plus_int @ zero_zero_int @ A )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4295_add_Ocomm__neutral,axiom,
% 9.25/5.19      ! [A: code_integer] :
% 9.25/5.19        ( ( plus_p5714425477246183910nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4296_add_Ocomm__neutral,axiom,
% 9.25/5.19      ! [A: multis2468970476368604999at_nat] :
% 9.25/5.19        ( ( plus_p7104986032573967614at_nat @ A @ zero_z1048942125864253310at_nat )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4297_add_Ocomm__neutral,axiom,
% 9.25/5.19      ! [A: rat] :
% 9.25/5.19        ( ( plus_plus_rat @ A @ zero_zero_rat )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4298_add_Ocomm__neutral,axiom,
% 9.25/5.19      ! [A: nat] :
% 9.25/5.19        ( ( plus_plus_nat @ A @ zero_zero_nat )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4299_add_Ocomm__neutral,axiom,
% 9.25/5.19      ! [A: int] :
% 9.25/5.19        ( ( plus_plus_int @ A @ zero_zero_int )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4300_add_Ogroup__left__neutral,axiom,
% 9.25/5.19      ! [A: code_integer] :
% 9.25/5.19        ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4301_add_Ogroup__left__neutral,axiom,
% 9.25/5.19      ! [A: rat] :
% 9.25/5.19        ( ( plus_plus_rat @ zero_zero_rat @ A )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4302_add_Ogroup__left__neutral,axiom,
% 9.25/5.19      ! [A: int] :
% 9.25/5.19        ( ( plus_plus_int @ zero_zero_int @ A )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4303_add__mono__thms__linordered__field_I5_J,axiom,
% 9.25/5.19      ! [I: rat,J: rat,K: rat,L: rat] :
% 9.25/5.19        ( ( ( ord_less_rat @ I @ J )
% 9.25/5.19          & ( ord_less_rat @ K @ L ) )
% 9.25/5.19       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4304_add__mono__thms__linordered__field_I5_J,axiom,
% 9.25/5.19      ! [I: nat,J: nat,K: nat,L: nat] :
% 9.25/5.19        ( ( ( ord_less_nat @ I @ J )
% 9.25/5.19          & ( ord_less_nat @ K @ L ) )
% 9.25/5.19       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4305_add__mono__thms__linordered__field_I5_J,axiom,
% 9.25/5.19      ! [I: int,J: int,K: int,L: int] :
% 9.25/5.19        ( ( ( ord_less_int @ I @ J )
% 9.25/5.19          & ( ord_less_int @ K @ L ) )
% 9.25/5.19       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4306_add__mono__thms__linordered__field_I2_J,axiom,
% 9.25/5.19      ! [I: rat,J: rat,K: rat,L: rat] :
% 9.25/5.19        ( ( ( I = J )
% 9.25/5.19          & ( ord_less_rat @ K @ L ) )
% 9.25/5.19       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4307_add__mono__thms__linordered__field_I2_J,axiom,
% 9.25/5.19      ! [I: nat,J: nat,K: nat,L: nat] :
% 9.25/5.19        ( ( ( I = J )
% 9.25/5.19          & ( ord_less_nat @ K @ L ) )
% 9.25/5.19       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4308_add__mono__thms__linordered__field_I2_J,axiom,
% 9.25/5.19      ! [I: int,J: int,K: int,L: int] :
% 9.25/5.19        ( ( ( I = J )
% 9.25/5.19          & ( ord_less_int @ K @ L ) )
% 9.25/5.19       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4309_add__mono__thms__linordered__field_I1_J,axiom,
% 9.25/5.19      ! [I: rat,J: rat,K: rat,L: rat] :
% 9.25/5.19        ( ( ( ord_less_rat @ I @ J )
% 9.25/5.19          & ( K = L ) )
% 9.25/5.19       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4310_add__mono__thms__linordered__field_I1_J,axiom,
% 9.25/5.19      ! [I: nat,J: nat,K: nat,L: nat] :
% 9.25/5.19        ( ( ( ord_less_nat @ I @ J )
% 9.25/5.19          & ( K = L ) )
% 9.25/5.19       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4311_add__mono__thms__linordered__field_I1_J,axiom,
% 9.25/5.19      ! [I: int,J: int,K: int,L: int] :
% 9.25/5.19        ( ( ( ord_less_int @ I @ J )
% 9.25/5.19          & ( K = L ) )
% 9.25/5.19       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4312_add__strict__mono,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.25/5.19        ( ( ord_less_rat @ A @ B )
% 9.25/5.19       => ( ( ord_less_rat @ C @ D2 )
% 9.25/5.19         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4313_add__strict__mono,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.25/5.19        ( ( ord_less_nat @ A @ B )
% 9.25/5.19       => ( ( ord_less_nat @ C @ D2 )
% 9.25/5.19         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4314_add__strict__mono,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int,D2: int] :
% 9.25/5.19        ( ( ord_less_int @ A @ B )
% 9.25/5.19       => ( ( ord_less_int @ C @ D2 )
% 9.25/5.19         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4315_add__strict__left__mono,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( ord_less_rat @ A @ B )
% 9.25/5.19       => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4316_add__strict__left__mono,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( ord_less_nat @ A @ B )
% 9.25/5.19       => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4317_add__strict__left__mono,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( ord_less_int @ A @ B )
% 9.25/5.19       => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4318_add__strict__right__mono,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( ord_less_rat @ A @ B )
% 9.25/5.19       => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4319_add__strict__right__mono,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( ord_less_nat @ A @ B )
% 9.25/5.19       => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4320_add__strict__right__mono,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( ord_less_int @ A @ B )
% 9.25/5.19       => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4321_add__less__imp__less__left,axiom,
% 9.25/5.19      ! [C: rat,A: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 9.25/5.19       => ( ord_less_rat @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4322_add__less__imp__less__left,axiom,
% 9.25/5.19      ! [C: nat,A: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 9.25/5.19       => ( ord_less_nat @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4323_add__less__imp__less__left,axiom,
% 9.25/5.19      ! [C: int,A: int,B: int] :
% 9.25/5.19        ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 9.25/5.19       => ( ord_less_int @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4324_add__less__imp__less__right,axiom,
% 9.25/5.19      ! [A: rat,C: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 9.25/5.19       => ( ord_less_rat @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4325_add__less__imp__less__right,axiom,
% 9.25/5.19      ! [A: nat,C: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 9.25/5.19       => ( ord_less_nat @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4326_add__less__imp__less__right,axiom,
% 9.25/5.19      ! [A: int,C: int,B: int] :
% 9.25/5.19        ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 9.25/5.19       => ( ord_less_int @ A @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4327_combine__common__factor,axiom,
% 9.25/5.19      ! [A: code_integer,E2: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.19        ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E2 ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ C ) )
% 9.25/5.19        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ E2 ) @ C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4328_combine__common__factor,axiom,
% 9.25/5.19      ! [A: rat,E2: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ C ) )
% 9.25/5.19        = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E2 ) @ C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4329_combine__common__factor,axiom,
% 9.25/5.19      ! [A: nat,E2: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( plus_plus_nat @ ( times_times_nat @ A @ E2 ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E2 ) @ C ) )
% 9.25/5.19        = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E2 ) @ C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4330_combine__common__factor,axiom,
% 9.25/5.19      ! [A: int,E2: int,B: int,C: int] :
% 9.25/5.19        ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ C ) )
% 9.25/5.19        = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E2 ) @ C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4331_distrib__right,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.19        ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 9.25/5.19        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4332_distrib__right,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.25/5.19        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4333_distrib__right,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.25/5.19        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4334_distrib__right,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.25/5.19        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4335_distrib__left,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.19        ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 9.25/5.19        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4336_distrib__left,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 9.25/5.19        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4337_distrib__left,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 9.25/5.19        = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4338_distrib__left,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 9.25/5.19        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4339_comm__semiring__class_Odistrib,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.19        ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 9.25/5.19        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4340_comm__semiring__class_Odistrib,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.25/5.19        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4341_comm__semiring__class_Odistrib,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.25/5.19        = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4342_comm__semiring__class_Odistrib,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.25/5.19        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4343_ring__class_Oring__distribs_I1_J,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.19        ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 9.25/5.19        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4344_ring__class_Oring__distribs_I1_J,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 9.25/5.19        = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4345_ring__class_Oring__distribs_I1_J,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 9.25/5.19        = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4346_ring__class_Oring__distribs_I2_J,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.19        ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 9.25/5.19        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4347_ring__class_Oring__distribs_I2_J,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.25/5.19        = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4348_ring__class_Oring__distribs_I2_J,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.25/5.19        = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4349_group__cancel_Osub1,axiom,
% 9.25/5.19      ! [A2: rat,K: rat,A: rat,B: rat] :
% 9.25/5.19        ( ( A2
% 9.25/5.19          = ( plus_plus_rat @ K @ A ) )
% 9.25/5.19       => ( ( minus_minus_rat @ A2 @ B )
% 9.25/5.19          = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4350_group__cancel_Osub1,axiom,
% 9.25/5.19      ! [A2: int,K: int,A: int,B: int] :
% 9.25/5.19        ( ( A2
% 9.25/5.19          = ( plus_plus_int @ K @ A ) )
% 9.25/5.19       => ( ( minus_minus_int @ A2 @ B )
% 9.25/5.19          = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4351_diff__eq__eq,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( ( minus_minus_rat @ A @ B )
% 9.25/5.19          = C )
% 9.25/5.19        = ( A
% 9.25/5.19          = ( plus_plus_rat @ C @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4352_diff__eq__eq,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( ( minus_minus_int @ A @ B )
% 9.25/5.19          = C )
% 9.25/5.19        = ( A
% 9.25/5.19          = ( plus_plus_int @ C @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4353_eq__diff__eq,axiom,
% 9.25/5.19      ! [A: rat,C: rat,B: rat] :
% 9.25/5.19        ( ( A
% 9.25/5.19          = ( minus_minus_rat @ C @ B ) )
% 9.25/5.19        = ( ( plus_plus_rat @ A @ B )
% 9.25/5.19          = C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4354_eq__diff__eq,axiom,
% 9.25/5.19      ! [A: int,C: int,B: int] :
% 9.25/5.19        ( ( A
% 9.25/5.19          = ( minus_minus_int @ C @ B ) )
% 9.25/5.19        = ( ( plus_plus_int @ A @ B )
% 9.25/5.19          = C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4355_add__diff__eq,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 9.25/5.19        = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4356_add__diff__eq,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 9.25/5.19        = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4357_diff__diff__eq2,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 9.25/5.19        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4358_diff__diff__eq2,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 9.25/5.19        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4359_diff__add__eq,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 9.25/5.19        = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4360_diff__add__eq,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 9.25/5.19        = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4361_diff__add__eq__diff__diff__swap,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 9.25/5.19        = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4362_diff__add__eq__diff__diff__swap,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 9.25/5.19        = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4363_add__implies__diff,axiom,
% 9.25/5.19      ! [C: rat,B: rat,A: rat] :
% 9.25/5.19        ( ( ( plus_plus_rat @ C @ B )
% 9.25/5.19          = A )
% 9.25/5.19       => ( C
% 9.25/5.19          = ( minus_minus_rat @ A @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4364_add__implies__diff,axiom,
% 9.25/5.19      ! [C: nat,B: nat,A: nat] :
% 9.25/5.19        ( ( ( plus_plus_nat @ C @ B )
% 9.25/5.19          = A )
% 9.25/5.19       => ( C
% 9.25/5.19          = ( minus_minus_nat @ A @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4365_add__implies__diff,axiom,
% 9.25/5.19      ! [C: int,B: int,A: int] :
% 9.25/5.19        ( ( ( plus_plus_int @ C @ B )
% 9.25/5.19          = A )
% 9.25/5.19       => ( C
% 9.25/5.19          = ( minus_minus_int @ A @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4366_diff__diff__eq,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 9.25/5.19        = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4367_diff__diff__eq,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 9.25/5.19        = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4368_diff__diff__eq,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 9.25/5.19        = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4369_is__num__normalize_I8_J,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 9.25/5.19        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4370_is__num__normalize_I8_J,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.25/5.19        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4371_is__num__normalize_I8_J,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 9.25/5.19        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4372_add_Oinverse__distrib__swap,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 9.25/5.19        = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4373_add_Oinverse__distrib__swap,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.25/5.19        = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4374_add_Oinverse__distrib__swap,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 9.25/5.19        = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4375_group__cancel_Oneg1,axiom,
% 9.25/5.19      ! [A2: int,K: int,A: int] :
% 9.25/5.19        ( ( A2
% 9.25/5.19          = ( plus_plus_int @ K @ A ) )
% 9.25/5.19       => ( ( uminus_uminus_int @ A2 )
% 9.25/5.19          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4376_group__cancel_Oneg1,axiom,
% 9.25/5.19      ! [A2: code_integer,K: code_integer,A: code_integer] :
% 9.25/5.19        ( ( A2
% 9.25/5.19          = ( plus_p5714425477246183910nteger @ K @ A ) )
% 9.25/5.19       => ( ( uminus1351360451143612070nteger @ A2 )
% 9.25/5.19          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4377_group__cancel_Oneg1,axiom,
% 9.25/5.19      ! [A2: rat,K: rat,A: rat] :
% 9.25/5.19        ( ( A2
% 9.25/5.19          = ( plus_plus_rat @ K @ A ) )
% 9.25/5.19       => ( ( uminus_uminus_rat @ A2 )
% 9.25/5.19          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4378_add_Osafe__commute,axiom,
% 9.25/5.19      ! [X: rat,Y: rat,A: rat,B: rat] :
% 9.25/5.19        ( ( syntax3730441303064801268at_rat @ ( plus_plus_rat @ X @ Y ) @ A )
% 9.25/5.19       => ( ( plus_plus_rat @ A @ B )
% 9.25/5.19          = ( plus_plus_rat @ B @ A ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4379_add_Osafe__commute,axiom,
% 9.25/5.19      ! [X: nat,Y: nat,A: nat,B: nat] :
% 9.25/5.19        ( ( syntax4682126007086162916at_nat @ ( plus_plus_nat @ X @ Y ) @ A )
% 9.25/5.19       => ( ( plus_plus_nat @ A @ B )
% 9.25/5.19          = ( plus_plus_nat @ B @ A ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4380_add_Osafe__commute,axiom,
% 9.25/5.19      ! [X: int,Y: int,A: int,B: int] :
% 9.25/5.19        ( ( syntax5678989248478167196nt_int @ ( plus_plus_int @ X @ Y ) @ A )
% 9.25/5.19       => ( ( plus_plus_int @ A @ B )
% 9.25/5.19          = ( plus_plus_int @ B @ A ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4381_add__nonpos__eq__0__iff,axiom,
% 9.25/5.19      ! [X: code_integer,Y: code_integer] :
% 9.25/5.19        ( ( ord_le3102999989581377725nteger @ X @ zero_z3403309356797280102nteger )
% 9.25/5.19       => ( ( ord_le3102999989581377725nteger @ Y @ zero_z3403309356797280102nteger )
% 9.25/5.19         => ( ( ( plus_p5714425477246183910nteger @ X @ Y )
% 9.25/5.19              = zero_z3403309356797280102nteger )
% 9.25/5.19            = ( ( X = zero_z3403309356797280102nteger )
% 9.25/5.19              & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4382_add__nonpos__eq__0__iff,axiom,
% 9.25/5.19      ! [X: rat,Y: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 9.25/5.19       => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 9.25/5.19         => ( ( ( plus_plus_rat @ X @ Y )
% 9.25/5.19              = zero_zero_rat )
% 9.25/5.19            = ( ( X = zero_zero_rat )
% 9.25/5.19              & ( Y = zero_zero_rat ) ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4383_add__nonpos__eq__0__iff,axiom,
% 9.25/5.19      ! [X: nat,Y: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 9.25/5.19       => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 9.25/5.19         => ( ( ( plus_plus_nat @ X @ Y )
% 9.25/5.19              = zero_zero_nat )
% 9.25/5.19            = ( ( X = zero_zero_nat )
% 9.25/5.19              & ( Y = zero_zero_nat ) ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4384_add__nonpos__eq__0__iff,axiom,
% 9.25/5.19      ! [X: int,Y: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ X @ zero_zero_int )
% 9.25/5.19       => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 9.25/5.19         => ( ( ( plus_plus_int @ X @ Y )
% 9.25/5.19              = zero_zero_int )
% 9.25/5.19            = ( ( X = zero_zero_int )
% 9.25/5.19              & ( Y = zero_zero_int ) ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4385_add__nonneg__eq__0__iff,axiom,
% 9.25/5.19      ! [X: code_integer,Y: code_integer] :
% 9.25/5.19        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 9.25/5.19       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 9.25/5.19         => ( ( ( plus_p5714425477246183910nteger @ X @ Y )
% 9.25/5.19              = zero_z3403309356797280102nteger )
% 9.25/5.19            = ( ( X = zero_z3403309356797280102nteger )
% 9.25/5.19              & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4386_add__nonneg__eq__0__iff,axiom,
% 9.25/5.19      ! [X: rat,Y: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.25/5.19       => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 9.25/5.19         => ( ( ( plus_plus_rat @ X @ Y )
% 9.25/5.19              = zero_zero_rat )
% 9.25/5.19            = ( ( X = zero_zero_rat )
% 9.25/5.19              & ( Y = zero_zero_rat ) ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4387_add__nonneg__eq__0__iff,axiom,
% 9.25/5.19      ! [X: nat,Y: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 9.25/5.19       => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 9.25/5.19         => ( ( ( plus_plus_nat @ X @ Y )
% 9.25/5.19              = zero_zero_nat )
% 9.25/5.19            = ( ( X = zero_zero_nat )
% 9.25/5.19              & ( Y = zero_zero_nat ) ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4388_add__nonneg__eq__0__iff,axiom,
% 9.25/5.19      ! [X: int,Y: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.25/5.19       => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 9.25/5.19         => ( ( ( plus_plus_int @ X @ Y )
% 9.25/5.19              = zero_zero_int )
% 9.25/5.19            = ( ( X = zero_zero_int )
% 9.25/5.19              & ( Y = zero_zero_int ) ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4389_add__nonpos__nonpos,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.19       => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 9.25/5.19         => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4390_add__nonpos__nonpos,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.25/5.19       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 9.25/5.19         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4391_add__nonpos__nonpos,axiom,
% 9.25/5.19      ! [A: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 9.25/5.19       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 9.25/5.19         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4392_add__nonpos__nonpos,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.25/5.19       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 9.25/5.19         => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4393_add__nonneg__nonneg,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.19       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 9.25/5.19         => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4394_add__nonneg__nonneg,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.19       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.25/5.19         => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4395_add__nonneg__nonneg,axiom,
% 9.25/5.19      ! [A: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.25/5.19       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 9.25/5.19         => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4396_add__nonneg__nonneg,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.19       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.25/5.19         => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4397_add__increasing2,axiom,
% 9.25/5.19      ! [C: code_integer,B: code_integer,A: code_integer] :
% 9.25/5.19        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.19       => ( ( ord_le3102999989581377725nteger @ B @ A )
% 9.25/5.19         => ( ord_le3102999989581377725nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4398_add__increasing2,axiom,
% 9.25/5.19      ! [C: rat,B: rat,A: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 9.25/5.19       => ( ( ord_less_eq_rat @ B @ A )
% 9.25/5.19         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4399_add__increasing2,axiom,
% 9.25/5.19      ! [C: nat,B: nat,A: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.25/5.19       => ( ( ord_less_eq_nat @ B @ A )
% 9.25/5.19         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4400_add__increasing2,axiom,
% 9.25/5.19      ! [C: int,B: int,A: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.25/5.19       => ( ( ord_less_eq_int @ B @ A )
% 9.25/5.19         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4401_add__decreasing2,axiom,
% 9.25/5.19      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 9.25/5.19       => ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.25/5.19         => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4402_add__decreasing2,axiom,
% 9.25/5.19      ! [C: rat,A: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 9.25/5.19       => ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.19         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4403_add__decreasing2,axiom,
% 9.25/5.19      ! [C: nat,A: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 9.25/5.19       => ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.19         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4404_add__decreasing2,axiom,
% 9.25/5.19      ! [C: int,A: int,B: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ C @ zero_zero_int )
% 9.25/5.19       => ( ( ord_less_eq_int @ A @ B )
% 9.25/5.19         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4405_add__increasing,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.19        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.19       => ( ( ord_le3102999989581377725nteger @ B @ C )
% 9.25/5.19         => ( ord_le3102999989581377725nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4406_add__increasing,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.19       => ( ( ord_less_eq_rat @ B @ C )
% 9.25/5.19         => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4407_add__increasing,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.25/5.19       => ( ( ord_less_eq_nat @ B @ C )
% 9.25/5.19         => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4408_add__increasing,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.19       => ( ( ord_less_eq_int @ B @ C )
% 9.25/5.19         => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4409_add__decreasing,axiom,
% 9.25/5.19      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.25/5.19        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.19       => ( ( ord_le3102999989581377725nteger @ C @ B )
% 9.25/5.19         => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4410_add__decreasing,axiom,
% 9.25/5.19      ! [A: rat,C: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.25/5.19       => ( ( ord_less_eq_rat @ C @ B )
% 9.25/5.19         => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4411_add__decreasing,axiom,
% 9.25/5.19      ! [A: nat,C: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 9.25/5.19       => ( ( ord_less_eq_nat @ C @ B )
% 9.25/5.19         => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4412_add__decreasing,axiom,
% 9.25/5.19      ! [A: int,C: int,B: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.25/5.19       => ( ( ord_less_eq_int @ C @ B )
% 9.25/5.19         => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4413_add__mono__thms__linordered__field_I4_J,axiom,
% 9.25/5.19      ! [I: rat,J: rat,K: rat,L: rat] :
% 9.25/5.19        ( ( ( ord_less_eq_rat @ I @ J )
% 9.25/5.19          & ( ord_less_rat @ K @ L ) )
% 9.25/5.19       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4414_add__mono__thms__linordered__field_I4_J,axiom,
% 9.25/5.19      ! [I: nat,J: nat,K: nat,L: nat] :
% 9.25/5.19        ( ( ( ord_less_eq_nat @ I @ J )
% 9.25/5.19          & ( ord_less_nat @ K @ L ) )
% 9.25/5.19       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4415_add__mono__thms__linordered__field_I4_J,axiom,
% 9.25/5.19      ! [I: int,J: int,K: int,L: int] :
% 9.25/5.19        ( ( ( ord_less_eq_int @ I @ J )
% 9.25/5.19          & ( ord_less_int @ K @ L ) )
% 9.25/5.19       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4416_add__mono__thms__linordered__field_I3_J,axiom,
% 9.25/5.19      ! [I: rat,J: rat,K: rat,L: rat] :
% 9.25/5.19        ( ( ( ord_less_rat @ I @ J )
% 9.25/5.19          & ( ord_less_eq_rat @ K @ L ) )
% 9.25/5.19       => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4417_add__mono__thms__linordered__field_I3_J,axiom,
% 9.25/5.19      ! [I: nat,J: nat,K: nat,L: nat] :
% 9.25/5.19        ( ( ( ord_less_nat @ I @ J )
% 9.25/5.19          & ( ord_less_eq_nat @ K @ L ) )
% 9.25/5.19       => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4418_add__mono__thms__linordered__field_I3_J,axiom,
% 9.25/5.19      ! [I: int,J: int,K: int,L: int] :
% 9.25/5.19        ( ( ( ord_less_int @ I @ J )
% 9.25/5.19          & ( ord_less_eq_int @ K @ L ) )
% 9.25/5.19       => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4419_add__le__less__mono,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.19       => ( ( ord_less_rat @ C @ D2 )
% 9.25/5.19         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4420_add__le__less__mono,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.19       => ( ( ord_less_nat @ C @ D2 )
% 9.25/5.19         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4421_add__le__less__mono,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int,D2: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.19       => ( ( ord_less_int @ C @ D2 )
% 9.25/5.19         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4422_add__less__le__mono,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.25/5.19        ( ( ord_less_rat @ A @ B )
% 9.25/5.19       => ( ( ord_less_eq_rat @ C @ D2 )
% 9.25/5.19         => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4423_add__less__le__mono,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.25/5.19        ( ( ord_less_nat @ A @ B )
% 9.25/5.19       => ( ( ord_less_eq_nat @ C @ D2 )
% 9.25/5.19         => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4424_add__less__le__mono,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int,D2: int] :
% 9.25/5.19        ( ( ord_less_int @ A @ B )
% 9.25/5.19       => ( ( ord_less_eq_int @ C @ D2 )
% 9.25/5.19         => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4425_pos__add__strict,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.19        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.19       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 9.25/5.19         => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4426_pos__add__strict,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.19       => ( ( ord_less_rat @ B @ C )
% 9.25/5.19         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4427_pos__add__strict,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.25/5.19       => ( ( ord_less_nat @ B @ C )
% 9.25/5.19         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4428_pos__add__strict,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( ord_less_int @ zero_zero_int @ A )
% 9.25/5.19       => ( ( ord_less_int @ B @ C )
% 9.25/5.19         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4429_canonically__ordered__monoid__add__class_OlessE,axiom,
% 9.25/5.19      ! [A: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_nat @ A @ B )
% 9.25/5.19       => ~ ! [C3: nat] :
% 9.25/5.19              ( ( B
% 9.25/5.19                = ( plus_plus_nat @ A @ C3 ) )
% 9.25/5.19             => ( C3 = zero_zero_nat ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4430_add__pos__pos,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.19       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 9.25/5.19         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4431_add__pos__pos,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.19       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 9.25/5.19         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4432_add__pos__pos,axiom,
% 9.25/5.19      ! [A: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.25/5.19       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.25/5.19         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4433_add__pos__pos,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( ord_less_int @ zero_zero_int @ A )
% 9.25/5.19       => ( ( ord_less_int @ zero_zero_int @ B )
% 9.25/5.19         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4434_add__neg__neg,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.19       => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 9.25/5.19         => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4435_add__neg__neg,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.25/5.19       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 9.25/5.19         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4436_add__neg__neg,axiom,
% 9.25/5.19      ! [A: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_nat @ A @ zero_zero_nat )
% 9.25/5.19       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 9.25/5.19         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4437_add__neg__neg,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( ord_less_int @ A @ zero_zero_int )
% 9.25/5.19       => ( ( ord_less_int @ B @ zero_zero_int )
% 9.25/5.19         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4438_diff__le__eq,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 9.25/5.19        = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4439_diff__le__eq,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 9.25/5.19        = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4440_le__diff__eq,axiom,
% 9.25/5.19      ! [A: rat,C: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 9.25/5.19        = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4441_le__diff__eq,axiom,
% 9.25/5.19      ! [A: int,C: int,B: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 9.25/5.19        = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4442_ordered__cancel__comm__monoid__diff__class_Odiff__add,axiom,
% 9.25/5.19      ! [A: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.19       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 9.25/5.19          = B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4443_le__add__diff,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.19       => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4444_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.19       => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 9.25/5.19          = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4445_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.19       => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 9.25/5.19          = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4446_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.19       => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 9.25/5.19          = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4447_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.19       => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 9.25/5.19          = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4448_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.19       => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 9.25/5.19          = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4449_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.19       => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 9.25/5.19          = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4450_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 9.25/5.19      ! [A: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.19       => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 9.25/5.19          = B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4451_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.19       => ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.19         => ( ( ( minus_minus_nat @ B @ A )
% 9.25/5.19              = C )
% 9.25/5.19            = ( B
% 9.25/5.19              = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4452_add__mono1,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.25/5.19       => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ B @ one_one_Code_integer ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4453_add__mono1,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_rat @ A @ B )
% 9.25/5.19       => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4454_add__mono1,axiom,
% 9.25/5.19      ! [A: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_nat @ A @ B )
% 9.25/5.19       => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4455_add__mono1,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( ord_less_int @ A @ B )
% 9.25/5.19       => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4456_less__add__one,axiom,
% 9.25/5.19      ! [A: code_integer] : ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4457_less__add__one,axiom,
% 9.25/5.19      ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4458_less__add__one,axiom,
% 9.25/5.19      ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4459_less__add__one,axiom,
% 9.25/5.19      ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4460_diff__less__eq,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 9.25/5.19        = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4461_diff__less__eq,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 9.25/5.19        = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4462_less__diff__eq,axiom,
% 9.25/5.19      ! [A: rat,C: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 9.25/5.19        = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4463_less__diff__eq,axiom,
% 9.25/5.19      ! [A: int,C: int,B: int] :
% 9.25/5.19        ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 9.25/5.19        = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4464_neg__eq__iff__add__eq__0,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( ( uminus_uminus_int @ A )
% 9.25/5.19          = B )
% 9.25/5.19        = ( ( plus_plus_int @ A @ B )
% 9.25/5.19          = zero_zero_int ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4465_neg__eq__iff__add__eq__0,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( ( uminus1351360451143612070nteger @ A )
% 9.25/5.19          = B )
% 9.25/5.19        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 9.25/5.19          = zero_z3403309356797280102nteger ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4466_neg__eq__iff__add__eq__0,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( ( uminus_uminus_rat @ A )
% 9.25/5.19          = B )
% 9.25/5.19        = ( ( plus_plus_rat @ A @ B )
% 9.25/5.19          = zero_zero_rat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4467_eq__neg__iff__add__eq__0,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( A
% 9.25/5.19          = ( uminus_uminus_int @ B ) )
% 9.25/5.19        = ( ( plus_plus_int @ A @ B )
% 9.25/5.19          = zero_zero_int ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4468_eq__neg__iff__add__eq__0,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( A
% 9.25/5.19          = ( uminus1351360451143612070nteger @ B ) )
% 9.25/5.19        = ( ( plus_p5714425477246183910nteger @ A @ B )
% 9.25/5.19          = zero_z3403309356797280102nteger ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4469_eq__neg__iff__add__eq__0,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( A
% 9.25/5.19          = ( uminus_uminus_rat @ B ) )
% 9.25/5.19        = ( ( plus_plus_rat @ A @ B )
% 9.25/5.19          = zero_zero_rat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4470_add_Oinverse__unique,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( ( plus_plus_int @ A @ B )
% 9.25/5.19          = zero_zero_int )
% 9.25/5.19       => ( ( uminus_uminus_int @ A )
% 9.25/5.19          = B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4471_add_Oinverse__unique,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 9.25/5.19          = zero_z3403309356797280102nteger )
% 9.25/5.19       => ( ( uminus1351360451143612070nteger @ A )
% 9.25/5.19          = B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4472_add_Oinverse__unique,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( ( plus_plus_rat @ A @ B )
% 9.25/5.19          = zero_zero_rat )
% 9.25/5.19       => ( ( uminus_uminus_rat @ A )
% 9.25/5.19          = B ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4473_ab__group__add__class_Oab__left__minus,axiom,
% 9.25/5.19      ! [A: int] :
% 9.25/5.19        ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 9.25/5.19        = zero_zero_int ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4474_ab__group__add__class_Oab__left__minus,axiom,
% 9.25/5.19      ! [A: code_integer] :
% 9.25/5.19        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 9.25/5.19        = zero_z3403309356797280102nteger ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4475_ab__group__add__class_Oab__left__minus,axiom,
% 9.25/5.19      ! [A: rat] :
% 9.25/5.19        ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 9.25/5.19        = zero_zero_rat ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4476_add__eq__0__iff,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( ( plus_plus_int @ A @ B )
% 9.25/5.19          = zero_zero_int )
% 9.25/5.19        = ( B
% 9.25/5.19          = ( uminus_uminus_int @ A ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4477_add__eq__0__iff,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 9.25/5.19          = zero_z3403309356797280102nteger )
% 9.25/5.19        = ( B
% 9.25/5.19          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4478_add__eq__0__iff,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( ( plus_plus_rat @ A @ B )
% 9.25/5.19          = zero_zero_rat )
% 9.25/5.19        = ( B
% 9.25/5.19          = ( uminus_uminus_rat @ A ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4479_one__plus__numeral__commute,axiom,
% 9.25/5.19      ! [X: num] :
% 9.25/5.19        ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 9.25/5.19        = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4480_one__plus__numeral__commute,axiom,
% 9.25/5.19      ! [X: num] :
% 9.25/5.19        ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 9.25/5.19        = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4481_one__plus__numeral__commute,axiom,
% 9.25/5.19      ! [X: num] :
% 9.25/5.19        ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 9.25/5.19        = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4482_one__plus__numeral__commute,axiom,
% 9.25/5.19      ! [X: num] :
% 9.25/5.19        ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 9.25/5.19        = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4483_one__plus__numeral__commute,axiom,
% 9.25/5.19      ! [X: num] :
% 9.25/5.19        ( ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ X ) )
% 9.25/5.19        = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ X ) @ one_one_Code_natural ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4484_square__diff__square__factored,axiom,
% 9.25/5.19      ! [X: code_integer,Y: code_integer] :
% 9.25/5.19        ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 9.25/5.19        = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( minus_8373710615458151222nteger @ X @ Y ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4485_square__diff__square__factored,axiom,
% 9.25/5.19      ! [X: rat,Y: rat] :
% 9.25/5.19        ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 9.25/5.19        = ( times_times_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_rat @ X @ Y ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4486_square__diff__square__factored,axiom,
% 9.25/5.19      ! [X: int,Y: int] :
% 9.25/5.19        ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 9.25/5.19        = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4487_eq__add__iff2,axiom,
% 9.25/5.19      ! [A: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 9.25/5.19        ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E2 ) @ C )
% 9.25/5.19          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 9.25/5.19        = ( C
% 9.25/5.19          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4488_eq__add__iff2,axiom,
% 9.25/5.19      ! [A: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 9.25/5.19        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 9.25/5.19          = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 9.25/5.19        = ( C
% 9.25/5.19          = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4489_eq__add__iff2,axiom,
% 9.25/5.19      ! [A: int,E2: int,C: int,B: int,D2: int] :
% 9.25/5.19        ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 9.25/5.19          = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 9.25/5.19        = ( C
% 9.25/5.19          = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4490_eq__add__iff1,axiom,
% 9.25/5.19      ! [A: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 9.25/5.19        ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E2 ) @ C )
% 9.25/5.19          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 9.25/5.19        = ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E2 ) @ C )
% 9.25/5.19          = D2 ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4491_eq__add__iff1,axiom,
% 9.25/5.19      ! [A: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 9.25/5.19        ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 9.25/5.19          = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 9.25/5.19        = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C )
% 9.25/5.19          = D2 ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4492_eq__add__iff1,axiom,
% 9.25/5.19      ! [A: int,E2: int,C: int,B: int,D2: int] :
% 9.25/5.19        ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 9.25/5.19          = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 9.25/5.19        = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C )
% 9.25/5.19          = D2 ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4493_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 9.25/5.19      ( minus_minus_int
% 9.25/5.19      = ( ^ [A3: int,B3: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4494_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 9.25/5.19      ( minus_8373710615458151222nteger
% 9.25/5.19      = ( ^ [A3: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4495_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 9.25/5.19      ( minus_minus_rat
% 9.25/5.19      = ( ^ [A3: rat,B3: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4496_diff__conv__add__uminus,axiom,
% 9.25/5.19      ( minus_minus_int
% 9.25/5.19      = ( ^ [A3: int,B3: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B3 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4497_diff__conv__add__uminus,axiom,
% 9.25/5.19      ( minus_8373710615458151222nteger
% 9.25/5.19      = ( ^ [A3: code_integer,B3: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B3 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4498_diff__conv__add__uminus,axiom,
% 9.25/5.19      ( minus_minus_rat
% 9.25/5.19      = ( ^ [A3: rat,B3: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B3 ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4499_group__cancel_Osub2,axiom,
% 9.25/5.19      ! [B2: int,K: int,B: int,A: int] :
% 9.25/5.19        ( ( B2
% 9.25/5.19          = ( plus_plus_int @ K @ B ) )
% 9.25/5.19       => ( ( minus_minus_int @ A @ B2 )
% 9.25/5.19          = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4500_group__cancel_Osub2,axiom,
% 9.25/5.19      ! [B2: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 9.25/5.19        ( ( B2
% 9.25/5.19          = ( plus_p5714425477246183910nteger @ K @ B ) )
% 9.25/5.19       => ( ( minus_8373710615458151222nteger @ A @ B2 )
% 9.25/5.19          = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4501_group__cancel_Osub2,axiom,
% 9.25/5.19      ! [B2: rat,K: rat,B: rat,A: rat] :
% 9.25/5.19        ( ( B2
% 9.25/5.19          = ( plus_plus_rat @ K @ B ) )
% 9.25/5.19       => ( ( minus_minus_rat @ A @ B2 )
% 9.25/5.19          = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4502_eq__numeral__iff__iszero_I7_J,axiom,
% 9.25/5.19      ! [X: num] :
% 9.25/5.19        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ X ) )
% 9.25/5.19          = one_one_int )
% 9.25/5.19        = ( ring_1_iszero_int @ ( numeral_numeral_int @ ( plus_plus_num @ X @ one ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4503_eq__numeral__iff__iszero_I7_J,axiom,
% 9.25/5.19      ! [X: num] :
% 9.25/5.19        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) )
% 9.25/5.19          = one_one_Code_integer )
% 9.25/5.19        = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ X @ one ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4504_eq__numeral__iff__iszero_I7_J,axiom,
% 9.25/5.19      ! [X: num] :
% 9.25/5.19        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) )
% 9.25/5.19          = one_one_rat )
% 9.25/5.19        = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ X @ one ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4505_eq__numeral__iff__iszero_I8_J,axiom,
% 9.25/5.19      ! [Y: num] :
% 9.25/5.19        ( ( one_one_int
% 9.25/5.19          = ( uminus_uminus_int @ ( numeral_numeral_int @ Y ) ) )
% 9.25/5.19        = ( ring_1_iszero_int @ ( numeral_numeral_int @ ( plus_plus_num @ one @ Y ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4506_eq__numeral__iff__iszero_I8_J,axiom,
% 9.25/5.19      ! [Y: num] :
% 9.25/5.19        ( ( one_one_Code_integer
% 9.25/5.19          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ Y ) ) )
% 9.25/5.19        = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ Y ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4507_eq__numeral__iff__iszero_I8_J,axiom,
% 9.25/5.19      ! [Y: num] :
% 9.25/5.19        ( ( one_one_rat
% 9.25/5.19          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ Y ) ) )
% 9.25/5.19        = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ one @ Y ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4508_mult__numeral__1__right,axiom,
% 9.25/5.19      ! [A: nat] :
% 9.25/5.19        ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4509_mult__numeral__1__right,axiom,
% 9.25/5.19      ! [A: int] :
% 9.25/5.19        ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4510_mult__numeral__1__right,axiom,
% 9.25/5.19      ! [A: code_integer] :
% 9.25/5.19        ( ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ one ) )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4511_mult__numeral__1__right,axiom,
% 9.25/5.19      ! [A: rat] :
% 9.25/5.19        ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4512_mult__numeral__1__right,axiom,
% 9.25/5.19      ! [A: code_natural] :
% 9.25/5.19        ( ( times_2397367101498566445atural @ A @ ( numera5444537566228673987atural @ one ) )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4513_mult__numeral__1,axiom,
% 9.25/5.19      ! [A: nat] :
% 9.25/5.19        ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4514_mult__numeral__1,axiom,
% 9.25/5.19      ! [A: int] :
% 9.25/5.19        ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4515_mult__numeral__1,axiom,
% 9.25/5.19      ! [A: code_integer] :
% 9.25/5.19        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ one ) @ A )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4516_mult__numeral__1,axiom,
% 9.25/5.19      ! [A: rat] :
% 9.25/5.19        ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4517_mult__numeral__1,axiom,
% 9.25/5.19      ! [A: code_natural] :
% 9.25/5.19        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ one ) @ A )
% 9.25/5.19        = A ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4518_numeral__One,axiom,
% 9.25/5.19      ( ( numeral_numeral_nat @ one )
% 9.25/5.19      = one_one_nat ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4519_numeral__One,axiom,
% 9.25/5.19      ( ( numeral_numeral_int @ one )
% 9.25/5.19      = one_one_int ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4520_numeral__One,axiom,
% 9.25/5.19      ( ( numera6620942414471956472nteger @ one )
% 9.25/5.19      = one_one_Code_integer ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4521_numeral__One,axiom,
% 9.25/5.19      ( ( numeral_numeral_rat @ one )
% 9.25/5.19      = one_one_rat ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4522_numeral__One,axiom,
% 9.25/5.19      ( ( numera5444537566228673987atural @ one )
% 9.25/5.19      = one_one_Code_natural ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4523_add_Ocomm__monoid__axioms,axiom,
% 9.25/5.19      comm_m1654649897431166824nteger @ plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4524_add_Ocomm__monoid__axioms,axiom,
% 9.25/5.19      comm_m1862543879040115196at_nat @ plus_p7104986032573967614at_nat @ zero_z1048942125864253310at_nat ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4525_add_Ocomm__monoid__axioms,axiom,
% 9.25/5.19      comm_monoid_rat @ plus_plus_rat @ zero_zero_rat ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4526_add_Ocomm__monoid__axioms,axiom,
% 9.25/5.19      comm_monoid_nat @ plus_plus_nat @ zero_zero_nat ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4527_add_Ocomm__monoid__axioms,axiom,
% 9.25/5.19      comm_monoid_int @ plus_plus_int @ zero_zero_int ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4528_add_Omonoid__axioms,axiom,
% 9.25/5.19      monoid_literal @ plus_plus_literal @ zero_zero_literal ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4529_add_Omonoid__axioms,axiom,
% 9.25/5.19      monoid_Code_integer @ plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4530_add_Omonoid__axioms,axiom,
% 9.25/5.19      monoid66256789251010760at_nat @ plus_p7104986032573967614at_nat @ zero_z1048942125864253310at_nat ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4531_add_Omonoid__axioms,axiom,
% 9.25/5.19      monoid_rat @ plus_plus_rat @ zero_zero_rat ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4532_add_Omonoid__axioms,axiom,
% 9.25/5.19      monoid_nat @ plus_plus_nat @ zero_zero_nat ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4533_add_Omonoid__axioms,axiom,
% 9.25/5.19      monoid_int @ plus_plus_int @ zero_zero_int ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4534_semilattice__neutr__order_Oaxioms_I1_J,axiom,
% 9.25/5.19      ! [F2: nat > nat > nat,Z: nat,Less_eq: nat > nat > $o,Less: nat > nat > $o] :
% 9.25/5.19        ( ( semila1623282765462674594er_nat @ F2 @ Z @ Less_eq @ Less )
% 9.25/5.19       => ( semila9081495762789891438tr_nat @ F2 @ Z ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4535_dbl__inc__def,axiom,
% 9.25/5.19      ( neg_nu5831290666863070958nteger
% 9.25/5.19      = ( ^ [X3: code_integer] : ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ X3 @ X3 ) @ one_one_Code_integer ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4536_dbl__inc__def,axiom,
% 9.25/5.19      ( neg_nu5219082963157363817nc_rat
% 9.25/5.19      = ( ^ [X3: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X3 @ X3 ) @ one_one_rat ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4537_dbl__inc__def,axiom,
% 9.25/5.19      ( neg_nu5851722552734809277nc_int
% 9.25/5.19      = ( ^ [X3: int] : ( plus_plus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4538_add__strict__increasing2,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.19        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.19       => ( ( ord_le6747313008572928689nteger @ B @ C )
% 9.25/5.19         => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4539_add__strict__increasing2,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.19       => ( ( ord_less_rat @ B @ C )
% 9.25/5.19         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4540_add__strict__increasing2,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.25/5.19       => ( ( ord_less_nat @ B @ C )
% 9.25/5.19         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4541_add__strict__increasing2,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.19       => ( ( ord_less_int @ B @ C )
% 9.25/5.19         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4542_add__strict__increasing,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.19        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.19       => ( ( ord_le3102999989581377725nteger @ B @ C )
% 9.25/5.19         => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4543_add__strict__increasing,axiom,
% 9.25/5.19      ! [A: rat,B: rat,C: rat] :
% 9.25/5.19        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.19       => ( ( ord_less_eq_rat @ B @ C )
% 9.25/5.19         => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4544_add__strict__increasing,axiom,
% 9.25/5.19      ! [A: nat,B: nat,C: nat] :
% 9.25/5.19        ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.25/5.19       => ( ( ord_less_eq_nat @ B @ C )
% 9.25/5.19         => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4545_add__strict__increasing,axiom,
% 9.25/5.19      ! [A: int,B: int,C: int] :
% 9.25/5.19        ( ( ord_less_int @ zero_zero_int @ A )
% 9.25/5.19       => ( ( ord_less_eq_int @ B @ C )
% 9.25/5.19         => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4546_add__pos__nonneg,axiom,
% 9.25/5.19      ! [A: code_integer,B: code_integer] :
% 9.25/5.19        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.19       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 9.25/5.19         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4547_add__pos__nonneg,axiom,
% 9.25/5.19      ! [A: rat,B: rat] :
% 9.25/5.19        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.19       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.25/5.19         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4548_add__pos__nonneg,axiom,
% 9.25/5.19      ! [A: nat,B: nat] :
% 9.25/5.19        ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.25/5.19       => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 9.25/5.19         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 9.25/5.19  
% 9.25/5.19  thf(fact_4549_add__pos__nonneg,axiom,
% 9.25/5.19      ! [A: int,B: int] :
% 9.25/5.19        ( ( ord_less_int @ zero_zero_int @ A )
% 9.25/5.19       => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.25/5.19         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4550_add__nonpos__neg,axiom,
% 9.25/5.20      ! [A: code_integer,B: code_integer] :
% 9.25/5.20        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.20       => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 9.25/5.20         => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4551_add__nonpos__neg,axiom,
% 9.25/5.20      ! [A: rat,B: rat] :
% 9.25/5.20        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.25/5.20       => ( ( ord_less_rat @ B @ zero_zero_rat )
% 9.25/5.20         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4552_add__nonpos__neg,axiom,
% 9.25/5.20      ! [A: nat,B: nat] :
% 9.25/5.20        ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 9.25/5.20       => ( ( ord_less_nat @ B @ zero_zero_nat )
% 9.25/5.20         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4553_add__nonpos__neg,axiom,
% 9.25/5.20      ! [A: int,B: int] :
% 9.25/5.20        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.25/5.20       => ( ( ord_less_int @ B @ zero_zero_int )
% 9.25/5.20         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4554_add__nonneg__pos,axiom,
% 9.25/5.20      ! [A: code_integer,B: code_integer] :
% 9.25/5.20        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.20       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 9.25/5.20         => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4555_add__nonneg__pos,axiom,
% 9.25/5.20      ! [A: rat,B: rat] :
% 9.25/5.20        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.20       => ( ( ord_less_rat @ zero_zero_rat @ B )
% 9.25/5.20         => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4556_add__nonneg__pos,axiom,
% 9.25/5.20      ! [A: nat,B: nat] :
% 9.25/5.20        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.25/5.20       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.25/5.20         => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4557_add__nonneg__pos,axiom,
% 9.25/5.20      ! [A: int,B: int] :
% 9.25/5.20        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.20       => ( ( ord_less_int @ zero_zero_int @ B )
% 9.25/5.20         => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4558_add__neg__nonpos,axiom,
% 9.25/5.20      ! [A: code_integer,B: code_integer] :
% 9.25/5.20        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.20       => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 9.25/5.20         => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4559_add__neg__nonpos,axiom,
% 9.25/5.20      ! [A: rat,B: rat] :
% 9.25/5.20        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.25/5.20       => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 9.25/5.20         => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4560_add__neg__nonpos,axiom,
% 9.25/5.20      ! [A: nat,B: nat] :
% 9.25/5.20        ( ( ord_less_nat @ A @ zero_zero_nat )
% 9.25/5.20       => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 9.25/5.20         => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4561_add__neg__nonpos,axiom,
% 9.25/5.20      ! [A: int,B: int] :
% 9.25/5.20        ( ( ord_less_int @ A @ zero_zero_int )
% 9.25/5.20       => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 9.25/5.20         => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4562_sum__squares__ge__zero,axiom,
% 9.25/5.20      ! [X: code_integer,Y: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4563_sum__squares__ge__zero,axiom,
% 9.25/5.20      ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4564_sum__squares__ge__zero,axiom,
% 9.25/5.20      ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4565_not__sum__squares__lt__zero,axiom,
% 9.25/5.20      ! [X: code_integer,Y: code_integer] :
% 9.25/5.20        ~ ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4566_not__sum__squares__lt__zero,axiom,
% 9.25/5.20      ! [X: rat,Y: rat] :
% 9.25/5.20        ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4567_not__sum__squares__lt__zero,axiom,
% 9.25/5.20      ! [X: int,Y: int] :
% 9.25/5.20        ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4568_discrete,axiom,
% 9.25/5.20      ( ord_le6747313008572928689nteger
% 9.25/5.20      = ( ^ [A3: code_integer] : ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A3 @ one_one_Code_integer ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4569_discrete,axiom,
% 9.25/5.20      ( ord_less_nat
% 9.25/5.20      = ( ^ [A3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A3 @ one_one_nat ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4570_discrete,axiom,
% 9.25/5.20      ( ord_less_int
% 9.25/5.20      = ( ^ [A3: int] : ( ord_less_eq_int @ ( plus_plus_int @ A3 @ one_one_int ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4571_zero__less__two,axiom,
% 9.25/5.20      ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4572_zero__less__two,axiom,
% 9.25/5.20      ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4573_zero__less__two,axiom,
% 9.25/5.20      ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4574_zero__less__two,axiom,
% 9.25/5.20      ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4575_le__add__iff1,axiom,
% 9.25/5.20      ! [A: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 9.25/5.20        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E2 ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 9.25/5.20        = ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4576_le__add__iff1,axiom,
% 9.25/5.20      ! [A: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 9.25/5.20        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 9.25/5.20        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4577_le__add__iff1,axiom,
% 9.25/5.20      ! [A: int,E2: int,C: int,B: int,D2: int] :
% 9.25/5.20        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 9.25/5.20        = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4578_le__add__iff2,axiom,
% 9.25/5.20      ! [A: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 9.25/5.20        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E2 ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 9.25/5.20        = ( ord_le3102999989581377725nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4579_le__add__iff2,axiom,
% 9.25/5.20      ! [A: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 9.25/5.20        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 9.25/5.20        = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4580_le__add__iff2,axiom,
% 9.25/5.20      ! [A: int,E2: int,C: int,B: int,D2: int] :
% 9.25/5.20        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 9.25/5.20        = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4581_less__add__iff1,axiom,
% 9.25/5.20      ! [A: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 9.25/5.20        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E2 ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 9.25/5.20        = ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4582_less__add__iff1,axiom,
% 9.25/5.20      ! [A: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 9.25/5.20        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 9.25/5.20        = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4583_less__add__iff1,axiom,
% 9.25/5.20      ! [A: int,E2: int,C: int,B: int,D2: int] :
% 9.25/5.20        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 9.25/5.20        = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D2 ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4584_less__add__iff2,axiom,
% 9.25/5.20      ! [A: code_integer,E2: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 9.25/5.20        ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E2 ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E2 ) @ D2 ) )
% 9.25/5.20        = ( ord_le6747313008572928689nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4585_less__add__iff2,axiom,
% 9.25/5.20      ! [A: rat,E2: rat,C: rat,B: rat,D2: rat] :
% 9.25/5.20        ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D2 ) )
% 9.25/5.20        = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4586_less__add__iff2,axiom,
% 9.25/5.20      ! [A: int,E2: int,C: int,B: int,D2: int] :
% 9.25/5.20        ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D2 ) )
% 9.25/5.20        = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D2 ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4587_divide__add__eq__iff,axiom,
% 9.25/5.20      ! [Z: rat,X: rat,Y: rat] :
% 9.25/5.20        ( ( Z != zero_zero_rat )
% 9.25/5.20       => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 9.25/5.20          = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4588_add__divide__eq__iff,axiom,
% 9.25/5.20      ! [Z: rat,X: rat,Y: rat] :
% 9.25/5.20        ( ( Z != zero_zero_rat )
% 9.25/5.20       => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 9.25/5.20          = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4589_add__num__frac,axiom,
% 9.25/5.20      ! [Y: rat,Z: rat,X: rat] :
% 9.25/5.20        ( ( Y != zero_zero_rat )
% 9.25/5.20       => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X @ Y ) )
% 9.25/5.20          = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4590_add__frac__num,axiom,
% 9.25/5.20      ! [Y: rat,X: rat,Z: rat] :
% 9.25/5.20        ( ( Y != zero_zero_rat )
% 9.25/5.20       => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ Z )
% 9.25/5.20          = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4591_add__frac__eq,axiom,
% 9.25/5.20      ! [Y: rat,Z: rat,X: rat,W: rat] :
% 9.25/5.20        ( ( Y != zero_zero_rat )
% 9.25/5.20       => ( ( Z != zero_zero_rat )
% 9.25/5.20         => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 9.25/5.20            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4592_add__divide__eq__if__simps_I1_J,axiom,
% 9.25/5.20      ! [Z: rat,A: rat,B: rat] :
% 9.25/5.20        ( ( ( Z = zero_zero_rat )
% 9.25/5.20         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 9.25/5.20            = A ) )
% 9.25/5.20        & ( ( Z != zero_zero_rat )
% 9.25/5.20         => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 9.25/5.20            = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4593_add__divide__eq__if__simps_I2_J,axiom,
% 9.25/5.20      ! [Z: rat,A: rat,B: rat] :
% 9.25/5.20        ( ( ( Z = zero_zero_rat )
% 9.25/5.20         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 9.25/5.20            = B ) )
% 9.25/5.20        & ( ( Z != zero_zero_rat )
% 9.25/5.20         => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 9.25/5.20            = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4594_square__diff__one__factored,axiom,
% 9.25/5.20      ! [X: code_integer] :
% 9.25/5.20        ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ one_one_Code_integer )
% 9.25/5.20        = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4595_square__diff__one__factored,axiom,
% 9.25/5.20      ! [X: rat] :
% 9.25/5.20        ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 9.25/5.20        = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4596_square__diff__one__factored,axiom,
% 9.25/5.20      ! [X: int] :
% 9.25/5.20        ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 9.25/5.20        = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4597_div__add__self2,axiom,
% 9.25/5.20      ! [B: nat,A: nat] :
% 9.25/5.20        ( ( B != zero_zero_nat )
% 9.25/5.20       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 9.25/5.20          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4598_div__add__self2,axiom,
% 9.25/5.20      ! [B: int,A: int] :
% 9.25/5.20        ( ( B != zero_zero_int )
% 9.25/5.20       => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 9.25/5.20          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4599_div__add__self2,axiom,
% 9.25/5.20      ! [B: code_integer,A: code_integer] :
% 9.25/5.20        ( ( B != zero_z3403309356797280102nteger )
% 9.25/5.20       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 9.25/5.20          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4600_div__add__self2,axiom,
% 9.25/5.20      ! [B: code_natural,A: code_natural] :
% 9.25/5.20        ( ( B != zero_z2226904508553997617atural )
% 9.25/5.20       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ B ) @ B )
% 9.25/5.20          = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4601_div__add__self1,axiom,
% 9.25/5.20      ! [B: nat,A: nat] :
% 9.25/5.20        ( ( B != zero_zero_nat )
% 9.25/5.20       => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 9.25/5.20          = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4602_div__add__self1,axiom,
% 9.25/5.20      ! [B: int,A: int] :
% 9.25/5.20        ( ( B != zero_zero_int )
% 9.25/5.20       => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 9.25/5.20          = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4603_div__add__self1,axiom,
% 9.25/5.20      ! [B: code_integer,A: code_integer] :
% 9.25/5.20        ( ( B != zero_z3403309356797280102nteger )
% 9.25/5.20       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 9.25/5.20          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4604_div__add__self1,axiom,
% 9.25/5.20      ! [B: code_natural,A: code_natural] :
% 9.25/5.20        ( ( B != zero_z2226904508553997617atural )
% 9.25/5.20       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ B @ A ) @ B )
% 9.25/5.20          = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4605_less__half__sum,axiom,
% 9.25/5.20      ! [A: rat,B: rat] :
% 9.25/5.20        ( ( ord_less_rat @ A @ B )
% 9.25/5.20       => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4606_gt__half__sum,axiom,
% 9.25/5.20      ! [A: rat,B: rat] :
% 9.25/5.20        ( ( ord_less_rat @ A @ B )
% 9.25/5.20       => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4607_mult__1s__ring__1_I1_J,axiom,
% 9.25/5.20      ! [B: int] :
% 9.25/5.20        ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 9.25/5.20        = ( uminus_uminus_int @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4608_mult__1s__ring__1_I1_J,axiom,
% 9.25/5.20      ! [B: code_integer] :
% 9.25/5.20        ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 9.25/5.20        = ( uminus1351360451143612070nteger @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4609_mult__1s__ring__1_I1_J,axiom,
% 9.25/5.20      ! [B: rat] :
% 9.25/5.20        ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 9.25/5.20        = ( uminus_uminus_rat @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4610_mult__1s__ring__1_I2_J,axiom,
% 9.25/5.20      ! [B: int] :
% 9.25/5.20        ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 9.25/5.20        = ( uminus_uminus_int @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4611_mult__1s__ring__1_I2_J,axiom,
% 9.25/5.20      ! [B: code_integer] :
% 9.25/5.20        ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 9.25/5.20        = ( uminus1351360451143612070nteger @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4612_mult__1s__ring__1_I2_J,axiom,
% 9.25/5.20      ! [B: rat] :
% 9.25/5.20        ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 9.25/5.20        = ( uminus_uminus_rat @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4613_uminus__numeral__One,axiom,
% 9.25/5.20      ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 9.25/5.20      = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4614_uminus__numeral__One,axiom,
% 9.25/5.20      ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 9.25/5.20      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4615_uminus__numeral__One,axiom,
% 9.25/5.20      ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 9.25/5.20      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4616_numeral__inc,axiom,
% 9.25/5.20      ! [X: num] :
% 9.25/5.20        ( ( numeral_numeral_nat @ ( inc @ X ) )
% 9.25/5.20        = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4617_numeral__inc,axiom,
% 9.25/5.20      ! [X: num] :
% 9.25/5.20        ( ( numeral_numeral_int @ ( inc @ X ) )
% 9.25/5.20        = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4618_numeral__inc,axiom,
% 9.25/5.20      ! [X: num] :
% 9.25/5.20        ( ( numera6620942414471956472nteger @ ( inc @ X ) )
% 9.25/5.20        = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4619_numeral__inc,axiom,
% 9.25/5.20      ! [X: num] :
% 9.25/5.20        ( ( numeral_numeral_rat @ ( inc @ X ) )
% 9.25/5.20        = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4620_numeral__inc,axiom,
% 9.25/5.20      ! [X: num] :
% 9.25/5.20        ( ( numera5444537566228673987atural @ ( inc @ X ) )
% 9.25/5.20        = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ X ) @ one_one_Code_natural ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4621_eq__numeral__iff__iszero_I3_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ X ) )
% 9.25/5.20          = ( numeral_numeral_int @ Y ) )
% 9.25/5.20        = ( ring_1_iszero_int @ ( numeral_numeral_int @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4622_eq__numeral__iff__iszero_I3_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) )
% 9.25/5.20          = ( numera6620942414471956472nteger @ Y ) )
% 9.25/5.20        = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4623_eq__numeral__iff__iszero_I3_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) )
% 9.25/5.20          = ( numeral_numeral_rat @ Y ) )
% 9.25/5.20        = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4624_eq__numeral__iff__iszero_I2_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( ( numeral_numeral_int @ X )
% 9.25/5.20          = ( uminus_uminus_int @ ( numeral_numeral_int @ Y ) ) )
% 9.25/5.20        = ( ring_1_iszero_int @ ( numeral_numeral_int @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4625_eq__numeral__iff__iszero_I2_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( ( numera6620942414471956472nteger @ X )
% 9.25/5.20          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ Y ) ) )
% 9.25/5.20        = ( ring_16219924574208605041nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4626_eq__numeral__iff__iszero_I2_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( ( numeral_numeral_rat @ X )
% 9.25/5.20          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ Y ) ) )
% 9.25/5.20        = ( ring_1_iszero_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ X @ Y ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4627_distrib__left__NO__MATCH,axiom,
% 9.25/5.20      ! [X: nat,Y: nat,A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.20        ( ( nO_MAT8694959213317031834nteger @ ( divide_divide_nat @ X @ Y ) @ A )
% 9.25/5.20       => ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 9.25/5.20          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4628_distrib__left__NO__MATCH,axiom,
% 9.25/5.20      ! [X: nat,Y: nat,A: rat,B: rat,C: rat] :
% 9.25/5.20        ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X @ Y ) @ A )
% 9.25/5.20       => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 9.25/5.20          = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4629_distrib__left__NO__MATCH,axiom,
% 9.25/5.20      ! [X: nat,Y: nat,A: nat,B: nat,C: nat] :
% 9.25/5.20        ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X @ Y ) @ A )
% 9.25/5.20       => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 9.25/5.20          = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4630_distrib__left__NO__MATCH,axiom,
% 9.25/5.20      ! [X: nat,Y: nat,A: int,B: int,C: int] :
% 9.25/5.20        ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ A )
% 9.25/5.20       => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 9.25/5.20          = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4631_distrib__left__NO__MATCH,axiom,
% 9.25/5.20      ! [X: int,Y: int,A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.20        ( ( nO_MAT9066612773553876470nteger @ ( divide_divide_int @ X @ Y ) @ A )
% 9.25/5.20       => ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 9.25/5.20          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4632_distrib__left__NO__MATCH,axiom,
% 9.25/5.20      ! [X: int,Y: int,A: rat,B: rat,C: rat] :
% 9.25/5.20        ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X @ Y ) @ A )
% 9.25/5.20       => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 9.25/5.20          = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4633_distrib__left__NO__MATCH,axiom,
% 9.25/5.20      ! [X: int,Y: int,A: nat,B: nat,C: nat] :
% 9.25/5.20        ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X @ Y ) @ A )
% 9.25/5.20       => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 9.25/5.20          = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4634_distrib__left__NO__MATCH,axiom,
% 9.25/5.20      ! [X: int,Y: int,A: int,B: int,C: int] :
% 9.25/5.20        ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ A )
% 9.25/5.20       => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 9.25/5.20          = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4635_distrib__left__NO__MATCH,axiom,
% 9.25/5.20      ! [X: code_integer,Y: code_integer,A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.20        ( ( nO_MAT8252062027627875367nteger @ ( divide6298287555418463151nteger @ X @ Y ) @ A )
% 9.25/5.20       => ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 9.25/5.20          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4636_distrib__left__NO__MATCH,axiom,
% 9.25/5.20      ! [X: code_integer,Y: code_integer,A: rat,B: rat,C: rat] :
% 9.25/5.20        ( ( nO_MAT7795273704451493282er_rat @ ( divide6298287555418463151nteger @ X @ Y ) @ A )
% 9.25/5.20       => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 9.25/5.20          = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4637_distrib__right__NO__MATCH,axiom,
% 9.25/5.20      ! [X: nat,Y: nat,C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.20        ( ( nO_MAT8694959213317031834nteger @ ( divide_divide_nat @ X @ Y ) @ C )
% 9.25/5.20       => ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 9.25/5.20          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4638_distrib__right__NO__MATCH,axiom,
% 9.25/5.20      ! [X: nat,Y: nat,C: rat,A: rat,B: rat] :
% 9.25/5.20        ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X @ Y ) @ C )
% 9.25/5.20       => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.25/5.20          = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4639_distrib__right__NO__MATCH,axiom,
% 9.25/5.20      ! [X: nat,Y: nat,C: nat,A: nat,B: nat] :
% 9.25/5.20        ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X @ Y ) @ C )
% 9.25/5.20       => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.25/5.20          = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4640_distrib__right__NO__MATCH,axiom,
% 9.25/5.20      ! [X: nat,Y: nat,C: int,A: int,B: int] :
% 9.25/5.20        ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ C )
% 9.25/5.20       => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.25/5.20          = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4641_distrib__right__NO__MATCH,axiom,
% 9.25/5.20      ! [X: int,Y: int,C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.20        ( ( nO_MAT9066612773553876470nteger @ ( divide_divide_int @ X @ Y ) @ C )
% 9.25/5.20       => ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 9.25/5.20          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4642_distrib__right__NO__MATCH,axiom,
% 9.25/5.20      ! [X: int,Y: int,C: rat,A: rat,B: rat] :
% 9.25/5.20        ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X @ Y ) @ C )
% 9.25/5.20       => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.25/5.20          = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4643_distrib__right__NO__MATCH,axiom,
% 9.25/5.20      ! [X: int,Y: int,C: nat,A: nat,B: nat] :
% 9.25/5.20        ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X @ Y ) @ C )
% 9.25/5.20       => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 9.25/5.20          = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4644_distrib__right__NO__MATCH,axiom,
% 9.25/5.20      ! [X: int,Y: int,C: int,A: int,B: int] :
% 9.25/5.20        ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ C )
% 9.25/5.20       => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 9.25/5.20          = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4645_distrib__right__NO__MATCH,axiom,
% 9.25/5.20      ! [X: code_integer,Y: code_integer,C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.20        ( ( nO_MAT8252062027627875367nteger @ ( divide6298287555418463151nteger @ X @ Y ) @ C )
% 9.25/5.20       => ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 9.25/5.20          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4646_distrib__right__NO__MATCH,axiom,
% 9.25/5.20      ! [X: code_integer,Y: code_integer,C: rat,A: rat,B: rat] :
% 9.25/5.20        ( ( nO_MAT7795273704451493282er_rat @ ( divide6298287555418463151nteger @ X @ Y ) @ C )
% 9.25/5.20       => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 9.25/5.20          = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4647_dbl__dec__def,axiom,
% 9.25/5.20      ( neg_nu7757733837767384882nteger
% 9.25/5.20      = ( ^ [X3: code_integer] : ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ X3 @ X3 ) @ one_one_Code_integer ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4648_dbl__dec__def,axiom,
% 9.25/5.20      ( neg_nu3179335615603231917ec_rat
% 9.25/5.20      = ( ^ [X3: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X3 @ X3 ) @ one_one_rat ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4649_dbl__dec__def,axiom,
% 9.25/5.20      ( neg_nu3811975205180677377ec_int
% 9.25/5.20      = ( ^ [X3: int] : ( minus_minus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4650_not__iszero__neg__Numeral1,axiom,
% 9.25/5.20      ~ ( ring_1_iszero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4651_not__iszero__neg__Numeral1,axiom,
% 9.25/5.20      ~ ( ring_16219924574208605041nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4652_not__iszero__neg__Numeral1,axiom,
% 9.25/5.20      ~ ( ring_1_iszero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4653_convex__bound__le,axiom,
% 9.25/5.20      ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
% 9.25/5.20        ( ( ord_le3102999989581377725nteger @ X @ A )
% 9.25/5.20       => ( ( ord_le3102999989581377725nteger @ Y @ A )
% 9.25/5.20         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 9.25/5.20           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V )
% 9.25/5.20             => ( ( ( plus_p5714425477246183910nteger @ U @ V )
% 9.25/5.20                  = one_one_Code_integer )
% 9.25/5.20               => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4654_convex__bound__le,axiom,
% 9.25/5.20      ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 9.25/5.20        ( ( ord_less_eq_rat @ X @ A )
% 9.25/5.20       => ( ( ord_less_eq_rat @ Y @ A )
% 9.25/5.20         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 9.25/5.20           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 9.25/5.20             => ( ( ( plus_plus_rat @ U @ V )
% 9.25/5.20                  = one_one_rat )
% 9.25/5.20               => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4655_convex__bound__le,axiom,
% 9.25/5.20      ! [X: int,A: int,Y: int,U: int,V: int] :
% 9.25/5.20        ( ( ord_less_eq_int @ X @ A )
% 9.25/5.20       => ( ( ord_less_eq_int @ Y @ A )
% 9.25/5.20         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 9.25/5.20           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 9.25/5.20             => ( ( ( plus_plus_int @ U @ V )
% 9.25/5.20                  = one_one_int )
% 9.25/5.20               => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4656_minus__divide__add__eq__iff,axiom,
% 9.25/5.20      ! [Z: rat,X: rat,Y: rat] :
% 9.25/5.20        ( ( Z != zero_zero_rat )
% 9.25/5.20       => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 9.25/5.20          = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4657_add__divide__eq__if__simps_I3_J,axiom,
% 9.25/5.20      ! [Z: rat,A: rat,B: rat] :
% 9.25/5.20        ( ( ( Z = zero_zero_rat )
% 9.25/5.20         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 9.25/5.20            = B ) )
% 9.25/5.20        & ( ( Z != zero_zero_rat )
% 9.25/5.20         => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 9.25/5.20            = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4658_convex__bound__lt,axiom,
% 9.25/5.20      ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
% 9.25/5.20        ( ( ord_le6747313008572928689nteger @ X @ A )
% 9.25/5.20       => ( ( ord_le6747313008572928689nteger @ Y @ A )
% 9.25/5.20         => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 9.25/5.20           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V )
% 9.25/5.20             => ( ( ( plus_p5714425477246183910nteger @ U @ V )
% 9.25/5.20                  = one_one_Code_integer )
% 9.25/5.20               => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4659_convex__bound__lt,axiom,
% 9.25/5.20      ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 9.25/5.20        ( ( ord_less_rat @ X @ A )
% 9.25/5.20       => ( ( ord_less_rat @ Y @ A )
% 9.25/5.20         => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 9.25/5.20           => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 9.25/5.20             => ( ( ( plus_plus_rat @ U @ V )
% 9.25/5.20                  = one_one_rat )
% 9.25/5.20               => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4660_convex__bound__lt,axiom,
% 9.25/5.20      ! [X: int,A: int,Y: int,U: int,V: int] :
% 9.25/5.20        ( ( ord_less_int @ X @ A )
% 9.25/5.20       => ( ( ord_less_int @ Y @ A )
% 9.25/5.20         => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 9.25/5.20           => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 9.25/5.20             => ( ( ( plus_plus_int @ U @ V )
% 9.25/5.20                  = one_one_int )
% 9.25/5.20               => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4661_scaling__mono,axiom,
% 9.25/5.20      ! [U: rat,V: rat,R3: rat,S3: rat] :
% 9.25/5.20        ( ( ord_less_eq_rat @ U @ V )
% 9.25/5.20       => ( ( ord_less_eq_rat @ zero_zero_rat @ R3 )
% 9.25/5.20         => ( ( ord_less_eq_rat @ R3 @ S3 )
% 9.25/5.20           => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R3 @ ( minus_minus_rat @ V @ U ) ) @ S3 ) ) @ V ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4662_top_Oordering__top__axioms,axiom,
% 9.25/5.20      orderi7613023277850353061st_nat @ ord_le6045566169113846134st_nat @ ord_le1190675801316882794st_nat @ top_top_set_list_nat ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4663_top_Oordering__top__axioms,axiom,
% 9.25/5.20      ordering_top_set_o @ ord_less_eq_set_o @ ord_less_set_o @ top_top_set_o ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4664_top_Oordering__top__axioms,axiom,
% 9.25/5.20      ordering_top_set_rat @ ord_less_eq_set_rat @ ord_less_set_rat @ top_top_set_rat ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4665_top_Oordering__top__axioms,axiom,
% 9.25/5.20      ordering_top_set_int @ ord_less_eq_set_int @ ord_less_set_int @ top_top_set_int ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4666_top_Oordering__top__axioms,axiom,
% 9.25/5.20      orderi2807725203697798511er_nat @ ord_le2510731241096832064er_nat @ ord_less_filter_nat @ top_top_filter_nat ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4667_top_Oordering__top__axioms,axiom,
% 9.25/5.20      ordering_top_set_nat @ ord_less_eq_set_nat @ ord_less_set_nat @ top_top_set_nat ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4668_sum__squares__gt__zero__iff,axiom,
% 9.25/5.20      ! [X: code_integer,Y: code_integer] :
% 9.25/5.20        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) )
% 9.25/5.20        = ( ( X != zero_z3403309356797280102nteger )
% 9.25/5.20          | ( Y != zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4669_sum__squares__gt__zero__iff,axiom,
% 9.25/5.20      ! [X: rat,Y: rat] :
% 9.25/5.20        ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 9.25/5.20        = ( ( X != zero_zero_rat )
% 9.25/5.20          | ( Y != zero_zero_rat ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4670_sum__squares__gt__zero__iff,axiom,
% 9.25/5.20      ! [X: int,Y: int] :
% 9.25/5.20        ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 9.25/5.20        = ( ( X != zero_zero_int )
% 9.25/5.20          | ( Y != zero_zero_int ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4671_sum__squares__le__zero__iff,axiom,
% 9.25/5.20      ! [X: code_integer,Y: code_integer] :
% 9.25/5.20        ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger )
% 9.25/5.20        = ( ( X = zero_z3403309356797280102nteger )
% 9.25/5.20          & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4672_sum__squares__le__zero__iff,axiom,
% 9.25/5.20      ! [X: rat,Y: rat] :
% 9.25/5.20        ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 9.25/5.20        = ( ( X = zero_zero_rat )
% 9.25/5.20          & ( Y = zero_zero_rat ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4673_sum__squares__le__zero__iff,axiom,
% 9.25/5.20      ! [X: int,Y: int] :
% 9.25/5.20        ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 9.25/5.20        = ( ( X = zero_zero_int )
% 9.25/5.20          & ( Y = zero_zero_int ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4674_add__scale__eq__noteq,axiom,
% 9.25/5.20      ! [R3: code_integer,A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.25/5.20        ( ( R3 != zero_z3403309356797280102nteger )
% 9.25/5.20       => ( ( ( A = B )
% 9.25/5.20            & ( C != D2 ) )
% 9.25/5.20         => ( ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ R3 @ C ) )
% 9.25/5.20           != ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ R3 @ D2 ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4675_add__scale__eq__noteq,axiom,
% 9.25/5.20      ! [R3: rat,A: rat,B: rat,C: rat,D2: rat] :
% 9.25/5.20        ( ( R3 != zero_zero_rat )
% 9.25/5.20       => ( ( ( A = B )
% 9.25/5.20            & ( C != D2 ) )
% 9.25/5.20         => ( ( plus_plus_rat @ A @ ( times_times_rat @ R3 @ C ) )
% 9.25/5.20           != ( plus_plus_rat @ B @ ( times_times_rat @ R3 @ D2 ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4676_add__scale__eq__noteq,axiom,
% 9.25/5.20      ! [R3: nat,A: nat,B: nat,C: nat,D2: nat] :
% 9.25/5.20        ( ( R3 != zero_zero_nat )
% 9.25/5.20       => ( ( ( A = B )
% 9.25/5.20            & ( C != D2 ) )
% 9.25/5.20         => ( ( plus_plus_nat @ A @ ( times_times_nat @ R3 @ C ) )
% 9.25/5.20           != ( plus_plus_nat @ B @ ( times_times_nat @ R3 @ D2 ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4677_add__scale__eq__noteq,axiom,
% 9.25/5.20      ! [R3: int,A: int,B: int,C: int,D2: int] :
% 9.25/5.20        ( ( R3 != zero_zero_int )
% 9.25/5.20       => ( ( ( A = B )
% 9.25/5.20            & ( C != D2 ) )
% 9.25/5.20         => ( ( plus_plus_int @ A @ ( times_times_int @ R3 @ C ) )
% 9.25/5.20           != ( plus_plus_int @ B @ ( times_times_int @ R3 @ D2 ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4678_sum__squares__eq__zero__iff,axiom,
% 9.25/5.20      ! [X: code_integer,Y: code_integer] :
% 9.25/5.20        ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 9.25/5.20          = zero_z3403309356797280102nteger )
% 9.25/5.20        = ( ( X = zero_z3403309356797280102nteger )
% 9.25/5.20          & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4679_sum__squares__eq__zero__iff,axiom,
% 9.25/5.20      ! [X: rat,Y: rat] :
% 9.25/5.20        ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 9.25/5.20          = zero_zero_rat )
% 9.25/5.20        = ( ( X = zero_zero_rat )
% 9.25/5.20          & ( Y = zero_zero_rat ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4680_sum__squares__eq__zero__iff,axiom,
% 9.25/5.20      ! [X: int,Y: int] :
% 9.25/5.20        ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 9.25/5.20          = zero_zero_int )
% 9.25/5.20        = ( ( X = zero_zero_int )
% 9.25/5.20          & ( Y = zero_zero_int ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4681_less__by__empty,axiom,
% 9.25/5.20      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.20        ( ( A2 = bot_bo2099793752762293965at_nat )
% 9.25/5.20       => ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4682_divmod__algorithm__code_I2_J,axiom,
% 9.25/5.20      ! [M: num] :
% 9.25/5.20        ( ( unique5052692396658037445od_int @ M @ one )
% 9.25/5.20        = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4683_divmod__algorithm__code_I2_J,axiom,
% 9.25/5.20      ! [M: num] :
% 9.25/5.20        ( ( unique5055182867167087721od_nat @ M @ one )
% 9.25/5.20        = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4684_divmod__algorithm__code_I2_J,axiom,
% 9.25/5.20      ! [M: num] :
% 9.25/5.20        ( ( unique3479559517661332726nteger @ M @ one )
% 9.25/5.20        = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4685_minus__sub__one__diff__one,axiom,
% 9.25/5.20      ! [M: num] :
% 9.25/5.20        ( ( minus_minus_int @ ( uminus_uminus_int @ ( neg_numeral_sub_int @ M @ one ) ) @ one_one_int )
% 9.25/5.20        = ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4686_minus__sub__one__diff__one,axiom,
% 9.25/5.20      ! [M: num] :
% 9.25/5.20        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( neg_nu5755505904847501662nteger @ M @ one ) ) @ one_one_Code_integer )
% 9.25/5.20        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4687_minus__sub__one__diff__one,axiom,
% 9.25/5.20      ! [M: num] :
% 9.25/5.20        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( neg_numeral_sub_rat @ M @ one ) ) @ one_one_rat )
% 9.25/5.20        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4688_semiring__norm_I166_J,axiom,
% 9.25/5.20      ! [V: num,W: num,Y: int] :
% 9.25/5.20        ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 9.25/5.20        = ( plus_plus_int @ ( neg_numeral_sub_int @ V @ W ) @ Y ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4689_semiring__norm_I166_J,axiom,
% 9.25/5.20      ! [V: num,W: num,Y: code_integer] :
% 9.25/5.20        ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 9.25/5.20        = ( plus_p5714425477246183910nteger @ ( neg_nu5755505904847501662nteger @ V @ W ) @ Y ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4690_semiring__norm_I166_J,axiom,
% 9.25/5.20      ! [V: num,W: num,Y: rat] :
% 9.25/5.20        ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 9.25/5.20        = ( plus_plus_rat @ ( neg_numeral_sub_rat @ V @ W ) @ Y ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4691_semiring__norm_I167_J,axiom,
% 9.25/5.20      ! [V: num,W: num,Y: int] :
% 9.25/5.20        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Y ) )
% 9.25/5.20        = ( plus_plus_int @ ( neg_numeral_sub_int @ W @ V ) @ Y ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4692_semiring__norm_I167_J,axiom,
% 9.25/5.20      ! [V: num,W: num,Y: code_integer] :
% 9.25/5.20        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ W ) @ Y ) )
% 9.25/5.20        = ( plus_p5714425477246183910nteger @ ( neg_nu5755505904847501662nteger @ W @ V ) @ Y ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4693_semiring__norm_I167_J,axiom,
% 9.25/5.20      ! [V: num,W: num,Y: rat] :
% 9.25/5.20        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Y ) )
% 9.25/5.20        = ( plus_plus_rat @ ( neg_numeral_sub_rat @ W @ V ) @ Y ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4694_add__neg__numeral__simps_I1_J,axiom,
% 9.25/5.20      ! [M: num,N: num] :
% 9.25/5.20        ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.20        = ( neg_numeral_sub_int @ M @ N ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4695_add__neg__numeral__simps_I1_J,axiom,
% 9.25/5.20      ! [M: num,N: num] :
% 9.25/5.20        ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.25/5.20        = ( neg_nu5755505904847501662nteger @ M @ N ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4696_add__neg__numeral__simps_I1_J,axiom,
% 9.25/5.20      ! [M: num,N: num] :
% 9.25/5.20        ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.25/5.20        = ( neg_numeral_sub_rat @ M @ N ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4697_add__neg__numeral__simps_I2_J,axiom,
% 9.25/5.20      ! [M: num,N: num] :
% 9.25/5.20        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 9.25/5.20        = ( neg_numeral_sub_int @ N @ M ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4698_add__neg__numeral__simps_I2_J,axiom,
% 9.25/5.20      ! [M: num,N: num] :
% 9.25/5.20        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 9.25/5.20        = ( neg_nu5755505904847501662nteger @ N @ M ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4699_add__neg__numeral__simps_I2_J,axiom,
% 9.25/5.20      ! [M: num,N: num] :
% 9.25/5.20        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 9.25/5.20        = ( neg_numeral_sub_rat @ N @ M ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4700_diff__numeral__simps_I4_J,axiom,
% 9.25/5.20      ! [M: num,N: num] :
% 9.25/5.20        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.20        = ( neg_numeral_sub_int @ N @ M ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4701_diff__numeral__simps_I4_J,axiom,
% 9.25/5.20      ! [M: num,N: num] :
% 9.25/5.20        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.25/5.20        = ( neg_nu5755505904847501662nteger @ N @ M ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4702_diff__numeral__simps_I4_J,axiom,
% 9.25/5.20      ! [M: num,N: num] :
% 9.25/5.20        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.25/5.20        = ( neg_numeral_sub_rat @ N @ M ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4703_diff__numeral__special_I2_J,axiom,
% 9.25/5.20      ! [M: num] :
% 9.25/5.20        ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int )
% 9.25/5.20        = ( neg_numeral_sub_int @ M @ one ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4704_diff__numeral__special_I2_J,axiom,
% 9.25/5.20      ! [M: num] :
% 9.25/5.20        ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ one_one_Code_integer )
% 9.25/5.20        = ( neg_nu5755505904847501662nteger @ M @ one ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4705_diff__numeral__special_I2_J,axiom,
% 9.25/5.20      ! [M: num] :
% 9.25/5.20        ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ one_one_rat )
% 9.25/5.20        = ( neg_numeral_sub_rat @ M @ one ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4706_diff__numeral__special_I1_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( minus_minus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 9.25/5.20        = ( neg_numeral_sub_int @ one @ N ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4707_diff__numeral__special_I1_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 9.25/5.20        = ( neg_nu5755505904847501662nteger @ one @ N ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4708_diff__numeral__special_I1_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( minus_minus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 9.25/5.20        = ( neg_numeral_sub_rat @ one @ N ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4709_add__neg__numeral__special_I4_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 9.25/5.20        = ( neg_numeral_sub_int @ N @ one ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4710_add__neg__numeral__special_I4_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 9.25/5.20        = ( neg_nu5755505904847501662nteger @ N @ one ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4711_add__neg__numeral__special_I4_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 9.25/5.20        = ( neg_numeral_sub_rat @ N @ one ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4712_add__neg__numeral__special_I3_J,axiom,
% 9.25/5.20      ! [M: num] :
% 9.25/5.20        ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.20        = ( neg_numeral_sub_int @ M @ one ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4713_add__neg__numeral__special_I3_J,axiom,
% 9.25/5.20      ! [M: num] :
% 9.25/5.20        ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.20        = ( neg_nu5755505904847501662nteger @ M @ one ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4714_add__neg__numeral__special_I3_J,axiom,
% 9.25/5.20      ! [M: num] :
% 9.25/5.20        ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.25/5.20        = ( neg_numeral_sub_rat @ M @ one ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4715_add__neg__numeral__special_I2_J,axiom,
% 9.25/5.20      ! [M: num] :
% 9.25/5.20        ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 9.25/5.20        = ( neg_numeral_sub_int @ one @ M ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4716_add__neg__numeral__special_I2_J,axiom,
% 9.25/5.20      ! [M: num] :
% 9.25/5.20        ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 9.25/5.20        = ( neg_nu5755505904847501662nteger @ one @ M ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4717_add__neg__numeral__special_I2_J,axiom,
% 9.25/5.20      ! [M: num] :
% 9.25/5.20        ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 9.25/5.20        = ( neg_numeral_sub_rat @ one @ M ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4718_add__neg__numeral__special_I1_J,axiom,
% 9.25/5.20      ! [M: num] :
% 9.25/5.20        ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) )
% 9.25/5.20        = ( neg_numeral_sub_int @ one @ M ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4719_add__neg__numeral__special_I1_J,axiom,
% 9.25/5.20      ! [M: num] :
% 9.25/5.20        ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) )
% 9.25/5.20        = ( neg_nu5755505904847501662nteger @ one @ M ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4720_add__neg__numeral__special_I1_J,axiom,
% 9.25/5.20      ! [M: num] :
% 9.25/5.20        ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) )
% 9.25/5.20        = ( neg_numeral_sub_rat @ one @ M ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4721_diff__numeral__special_I8_J,axiom,
% 9.25/5.20      ! [M: num] :
% 9.25/5.20        ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.20        = ( neg_numeral_sub_int @ one @ M ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4722_diff__numeral__special_I8_J,axiom,
% 9.25/5.20      ! [M: num] :
% 9.25/5.20        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.20        = ( neg_nu5755505904847501662nteger @ one @ M ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4723_diff__numeral__special_I8_J,axiom,
% 9.25/5.20      ! [M: num] :
% 9.25/5.20        ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.25/5.20        = ( neg_numeral_sub_rat @ one @ M ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4724_diff__numeral__special_I7_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.20        = ( neg_numeral_sub_int @ N @ one ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4725_diff__numeral__special_I7_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.25/5.20        = ( neg_nu5755505904847501662nteger @ N @ one ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4726_diff__numeral__special_I7_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.25/5.20        = ( neg_numeral_sub_rat @ N @ one ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4727_div__eq__dividend__iff,axiom,
% 9.25/5.20      ! [M: nat,N: nat] :
% 9.25/5.20        ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.25/5.20       => ( ( ( divide_divide_nat @ M @ N )
% 9.25/5.20            = M )
% 9.25/5.20          = ( N = one_one_nat ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4728_div__less__dividend,axiom,
% 9.25/5.20      ! [N: nat,M: nat] :
% 9.25/5.20        ( ( ord_less_nat @ one_one_nat @ N )
% 9.25/5.20       => ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.25/5.20         => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4729_nat__geq__1__eq__neqz,axiom,
% 9.25/5.20      ! [X: nat] :
% 9.25/5.20        ( ( ord_less_eq_nat @ one_one_nat @ X )
% 9.25/5.20        = ( X != zero_zero_nat ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4730_eq__numeral__iff__iszero_I4_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ X ) )
% 9.25/5.20          = ( uminus_uminus_int @ ( numeral_numeral_int @ Y ) ) )
% 9.25/5.20        = ( ring_1_iszero_int @ ( neg_numeral_sub_int @ Y @ X ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4731_eq__numeral__iff__iszero_I4_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) )
% 9.25/5.20          = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ Y ) ) )
% 9.25/5.20        = ( ring_16219924574208605041nteger @ ( neg_nu5755505904847501662nteger @ Y @ X ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4732_eq__numeral__iff__iszero_I4_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) )
% 9.25/5.20          = ( uminus_uminus_rat @ ( numeral_numeral_rat @ Y ) ) )
% 9.25/5.20        = ( ring_1_iszero_rat @ ( neg_numeral_sub_rat @ Y @ X ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4733_eq__numeral__iff__iszero_I6_J,axiom,
% 9.25/5.20      ! [Y: num] :
% 9.25/5.20        ( ( one_one_int
% 9.25/5.20          = ( numeral_numeral_int @ Y ) )
% 9.25/5.20        = ( ring_1_iszero_int @ ( neg_numeral_sub_int @ one @ Y ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4734_eq__numeral__iff__iszero_I6_J,axiom,
% 9.25/5.20      ! [Y: num] :
% 9.25/5.20        ( ( one_one_Code_integer
% 9.25/5.20          = ( numera6620942414471956472nteger @ Y ) )
% 9.25/5.20        = ( ring_16219924574208605041nteger @ ( neg_nu5755505904847501662nteger @ one @ Y ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4735_eq__numeral__iff__iszero_I6_J,axiom,
% 9.25/5.20      ! [Y: num] :
% 9.25/5.20        ( ( one_one_rat
% 9.25/5.20          = ( numeral_numeral_rat @ Y ) )
% 9.25/5.20        = ( ring_1_iszero_rat @ ( neg_numeral_sub_rat @ one @ Y ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4736_eq__numeral__iff__iszero_I5_J,axiom,
% 9.25/5.20      ! [X: num] :
% 9.25/5.20        ( ( ( numeral_numeral_int @ X )
% 9.25/5.20          = one_one_int )
% 9.25/5.20        = ( ring_1_iszero_int @ ( neg_numeral_sub_int @ X @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4737_eq__numeral__iff__iszero_I5_J,axiom,
% 9.25/5.20      ! [X: num] :
% 9.25/5.20        ( ( ( numera6620942414471956472nteger @ X )
% 9.25/5.20          = one_one_Code_integer )
% 9.25/5.20        = ( ring_16219924574208605041nteger @ ( neg_nu5755505904847501662nteger @ X @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4738_eq__numeral__iff__iszero_I5_J,axiom,
% 9.25/5.20      ! [X: num] :
% 9.25/5.20        ( ( ( numeral_numeral_rat @ X )
% 9.25/5.20          = one_one_rat )
% 9.25/5.20        = ( ring_1_iszero_rat @ ( neg_numeral_sub_rat @ X @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4739_crossproduct__eq,axiom,
% 9.25/5.20      ! [W: code_integer,Y: code_integer,X: code_integer,Z: code_integer] :
% 9.25/5.20        ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ W @ Y ) @ ( times_3573771949741848930nteger @ X @ Z ) )
% 9.25/5.20          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ W @ Z ) @ ( times_3573771949741848930nteger @ X @ Y ) ) )
% 9.25/5.20        = ( ( W = X )
% 9.25/5.20          | ( Y = Z ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4740_crossproduct__eq,axiom,
% 9.25/5.20      ! [W: rat,Y: rat,X: rat,Z: rat] :
% 9.25/5.20        ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y ) @ ( times_times_rat @ X @ Z ) )
% 9.25/5.20          = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X @ Y ) ) )
% 9.25/5.20        = ( ( W = X )
% 9.25/5.20          | ( Y = Z ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4741_crossproduct__eq,axiom,
% 9.25/5.20      ! [W: nat,Y: nat,X: nat,Z: nat] :
% 9.25/5.20        ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z ) )
% 9.25/5.20          = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y ) ) )
% 9.25/5.20        = ( ( W = X )
% 9.25/5.20          | ( Y = Z ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4742_crossproduct__eq,axiom,
% 9.25/5.20      ! [W: int,Y: int,X: int,Z: int] :
% 9.25/5.20        ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X @ Z ) )
% 9.25/5.20          = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X @ Y ) ) )
% 9.25/5.20        = ( ( W = X )
% 9.25/5.20          | ( Y = Z ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4743_crossproduct__noteq,axiom,
% 9.25/5.20      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.25/5.20        ( ( ( A != B )
% 9.25/5.20          & ( C != D2 ) )
% 9.25/5.20        = ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) )
% 9.25/5.20         != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ D2 ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4744_crossproduct__noteq,axiom,
% 9.25/5.20      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.25/5.20        ( ( ( A != B )
% 9.25/5.20          & ( C != D2 ) )
% 9.25/5.20        = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) )
% 9.25/5.20         != ( plus_plus_rat @ ( times_times_rat @ A @ D2 ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4745_crossproduct__noteq,axiom,
% 9.25/5.20      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.25/5.20        ( ( ( A != B )
% 9.25/5.20          & ( C != D2 ) )
% 9.25/5.20        = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) )
% 9.25/5.20         != ( plus_plus_nat @ ( times_times_nat @ A @ D2 ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4746_crossproduct__noteq,axiom,
% 9.25/5.20      ! [A: int,B: int,C: int,D2: int] :
% 9.25/5.20        ( ( ( A != B )
% 9.25/5.20          & ( C != D2 ) )
% 9.25/5.20        = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) )
% 9.25/5.20         != ( plus_plus_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4747_less__one,axiom,
% 9.25/5.20      ! [N: nat] :
% 9.25/5.20        ( ( ord_less_nat @ N @ one_one_nat )
% 9.25/5.20        = ( N = zero_zero_nat ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4748_nat__mult__eq__1__iff,axiom,
% 9.25/5.20      ! [M: nat,N: nat] :
% 9.25/5.20        ( ( ( times_times_nat @ M @ N )
% 9.25/5.20          = one_one_nat )
% 9.25/5.20        = ( ( M = one_one_nat )
% 9.25/5.20          & ( N = one_one_nat ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4749_nat__1__eq__mult__iff,axiom,
% 9.25/5.20      ! [M: nat,N: nat] :
% 9.25/5.20        ( ( one_one_nat
% 9.25/5.20          = ( times_times_nat @ M @ N ) )
% 9.25/5.20        = ( ( M = one_one_nat )
% 9.25/5.20          & ( N = one_one_nat ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4750_subset__emptyI,axiom,
% 9.25/5.20      ! [A2: set_se6260736226359567993nt_int] :
% 9.25/5.20        ( ! [X2: set_Pr958786334691620121nt_int] :
% 9.25/5.20            ~ ( member2340774599025711042nt_int @ X2 @ A2 )
% 9.25/5.20       => ( ord_le483042692224249369nt_int @ A2 @ bot_bo1488462491386950373nt_int ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4751_subset__emptyI,axiom,
% 9.25/5.20      ! [A2: set_set_nat] :
% 9.25/5.20        ( ! [X2: set_nat] :
% 9.25/5.20            ~ ( member_set_nat @ X2 @ A2 )
% 9.25/5.20       => ( ord_le6893508408891458716et_nat @ A2 @ bot_bot_set_set_nat ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4752_subset__emptyI,axiom,
% 9.25/5.20      ! [A2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.20        ( ! [X2: produc3658429121746597890et_nat > $o] :
% 9.25/5.20            ~ ( member6576561426505652726_nat_o @ X2 @ A2 )
% 9.25/5.20       => ( ord_le2965882846123202637_nat_o @ A2 @ bot_bo7824918357723582233_nat_o ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4753_subset__emptyI,axiom,
% 9.25/5.20      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.20        ( ! [X2: product_prod_nat_nat] :
% 9.25/5.20            ~ ( member8440522571783428010at_nat @ X2 @ A2 )
% 9.25/5.20       => ( ord_le3146513528884898305at_nat @ A2 @ bot_bo2099793752762293965at_nat ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4754_subset__emptyI,axiom,
% 9.25/5.20      ! [A2: set_o] :
% 9.25/5.20        ( ! [X2: $o] :
% 9.25/5.20            ~ ( member_o @ X2 @ A2 )
% 9.25/5.20       => ( ord_less_eq_set_o @ A2 @ bot_bot_set_o ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4755_subset__emptyI,axiom,
% 9.25/5.20      ! [A2: set_int] :
% 9.25/5.20        ( ! [X2: int] :
% 9.25/5.20            ~ ( member_int @ X2 @ A2 )
% 9.25/5.20       => ( ord_less_eq_set_int @ A2 @ bot_bot_set_int ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4756_subset__emptyI,axiom,
% 9.25/5.20      ! [A2: set_nat] :
% 9.25/5.20        ( ! [X2: nat] :
% 9.25/5.20            ~ ( member_nat @ X2 @ A2 )
% 9.25/5.20       => ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4757_dbl__simps_I4_J,axiom,
% 9.25/5.20      ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.20      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4758_dbl__simps_I4_J,axiom,
% 9.25/5.20      ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.20      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4759_dbl__simps_I4_J,axiom,
% 9.25/5.20      ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.25/5.20      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4760_dbl__dec__simps_I4_J,axiom,
% 9.25/5.20      ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.20      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4761_dbl__dec__simps_I4_J,axiom,
% 9.25/5.20      ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.20      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4762_dbl__dec__simps_I4_J,axiom,
% 9.25/5.20      ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.25/5.20      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4763_divmod__algorithm__code_I3_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 9.25/5.20        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4764_divmod__algorithm__code_I3_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 9.25/5.20        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4765_divmod__algorithm__code_I3_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N ) )
% 9.25/5.20        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4766_divmod__step__eq,axiom,
% 9.25/5.20      ! [L: num,R3: int,Q4: int] :
% 9.25/5.20        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R3 )
% 9.25/5.20         => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 9.25/5.20            = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ one_one_int ) @ ( minus_minus_int @ R3 @ ( numeral_numeral_int @ L ) ) ) ) )
% 9.25/5.20        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R3 )
% 9.25/5.20         => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 9.25/5.20            = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q4 ) @ R3 ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4767_divmod__step__eq,axiom,
% 9.25/5.20      ! [L: num,R3: nat,Q4: nat] :
% 9.25/5.20        ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R3 )
% 9.25/5.20         => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q4 @ R3 ) )
% 9.25/5.20            = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ one_one_nat ) @ ( minus_minus_nat @ R3 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 9.25/5.20        & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R3 )
% 9.25/5.20         => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q4 @ R3 ) )
% 9.25/5.20            = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q4 ) @ R3 ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4768_divmod__step__eq,axiom,
% 9.25/5.20      ! [L: num,R3: code_integer,Q4: code_integer] :
% 9.25/5.20        ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R3 )
% 9.25/5.20         => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q4 @ R3 ) )
% 9.25/5.20            = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R3 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 9.25/5.20        & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R3 )
% 9.25/5.20         => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q4 @ R3 ) )
% 9.25/5.20            = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q4 ) @ R3 ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4769_one__add__one,axiom,
% 9.25/5.20      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 9.25/5.20      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4770_one__add__one,axiom,
% 9.25/5.20      ( ( plus_plus_int @ one_one_int @ one_one_int )
% 9.25/5.20      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4771_one__add__one,axiom,
% 9.25/5.20      ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer )
% 9.25/5.20      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4772_one__add__one,axiom,
% 9.25/5.20      ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 9.25/5.20      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4773_one__add__one,axiom,
% 9.25/5.20      ( ( plus_p4538020629002901425atural @ one_one_Code_natural @ one_one_Code_natural )
% 9.25/5.20      = ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4774_dbl__simps_I3_J,axiom,
% 9.25/5.20      ( ( neg_numeral_dbl_int @ one_one_int )
% 9.25/5.20      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4775_dbl__simps_I3_J,axiom,
% 9.25/5.20      ( ( neg_nu8804712462038260780nteger @ one_one_Code_integer )
% 9.25/5.20      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4776_dbl__simps_I3_J,axiom,
% 9.25/5.20      ( ( neg_numeral_dbl_rat @ one_one_rat )
% 9.25/5.20      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4777_dbl__inc__simps_I3_J,axiom,
% 9.25/5.20      ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 9.25/5.20      = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4778_dbl__inc__simps_I3_J,axiom,
% 9.25/5.20      ( ( neg_nu5831290666863070958nteger @ one_one_Code_integer )
% 9.25/5.20      = ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4779_dbl__inc__simps_I3_J,axiom,
% 9.25/5.20      ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 9.25/5.20      = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4780_one__div__two__eq__zero,axiom,
% 9.25/5.20      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.20      = zero_zero_nat ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4781_one__div__two__eq__zero,axiom,
% 9.25/5.20      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.20      = zero_zero_int ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4782_one__div__two__eq__zero,axiom,
% 9.25/5.20      ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.20      = zero_z3403309356797280102nteger ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4783_one__div__two__eq__zero,axiom,
% 9.25/5.20      ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.20      = zero_z2226904508553997617atural ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4784_bits__1__div__2,axiom,
% 9.25/5.20      ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.20      = zero_zero_nat ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4785_bits__1__div__2,axiom,
% 9.25/5.20      ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.20      = zero_zero_int ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4786_bits__1__div__2,axiom,
% 9.25/5.20      ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.20      = zero_z3403309356797280102nteger ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4787_bits__1__div__2,axiom,
% 9.25/5.20      ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.20      = zero_z2226904508553997617atural ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4788_add__neg__numeral__special_I9_J,axiom,
% 9.25/5.20      ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.20      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4789_add__neg__numeral__special_I9_J,axiom,
% 9.25/5.20      ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.20      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4790_add__neg__numeral__special_I9_J,axiom,
% 9.25/5.20      ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.25/5.20      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4791_diff__numeral__special_I10_J,axiom,
% 9.25/5.20      ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 9.25/5.20      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4792_diff__numeral__special_I10_J,axiom,
% 9.25/5.20      ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 9.25/5.20      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4793_diff__numeral__special_I10_J,axiom,
% 9.25/5.20      ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 9.25/5.20      = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4794_diff__numeral__special_I11_J,axiom,
% 9.25/5.20      ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.20      = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4795_diff__numeral__special_I11_J,axiom,
% 9.25/5.20      ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.20      = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4796_diff__numeral__special_I11_J,axiom,
% 9.25/5.20      ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.25/5.20      = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4797_divmod__algorithm__code_I4_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 9.25/5.20        = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4798_divmod__algorithm__code_I4_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 9.25/5.20        = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4799_divmod__algorithm__code_I4_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N ) )
% 9.25/5.20        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4800_sub__num__simps_I3_J,axiom,
% 9.25/5.20      ! [L: num] :
% 9.25/5.20        ( ( neg_numeral_sub_int @ one @ ( bit1 @ L ) )
% 9.25/5.20        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ L ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4801_sub__num__simps_I3_J,axiom,
% 9.25/5.20      ! [L: num] :
% 9.25/5.20        ( ( neg_nu5755505904847501662nteger @ one @ ( bit1 @ L ) )
% 9.25/5.20        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ L ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4802_sub__num__simps_I3_J,axiom,
% 9.25/5.20      ! [L: num] :
% 9.25/5.20        ( ( neg_numeral_sub_rat @ one @ ( bit1 @ L ) )
% 9.25/5.20        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ L ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4803_divmod__algorithm__code_I7_J,axiom,
% 9.25/5.20      ! [M: num,N: num] :
% 9.25/5.20        ( ( ( ord_less_eq_num @ M @ N )
% 9.25/5.20         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 9.25/5.20            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 9.25/5.20        & ( ~ ( ord_less_eq_num @ M @ N )
% 9.25/5.20         => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 9.25/5.20            = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4804_divmod__algorithm__code_I7_J,axiom,
% 9.25/5.20      ! [M: num,N: num] :
% 9.25/5.20        ( ( ( ord_less_eq_num @ M @ N )
% 9.25/5.20         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 9.25/5.20            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 9.25/5.20        & ( ~ ( ord_less_eq_num @ M @ N )
% 9.25/5.20         => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 9.25/5.20            = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4805_divmod__algorithm__code_I7_J,axiom,
% 9.25/5.20      ! [M: num,N: num] :
% 9.25/5.20        ( ( ( ord_less_eq_num @ M @ N )
% 9.25/5.20         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 9.25/5.20            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 9.25/5.20        & ( ~ ( ord_less_eq_num @ M @ N )
% 9.25/5.20         => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 9.25/5.20            = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4806_divmod__algorithm__code_I8_J,axiom,
% 9.25/5.20      ! [M: num,N: num] :
% 9.25/5.20        ( ( ( ord_less_num @ M @ N )
% 9.25/5.20         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 9.25/5.20            = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 9.25/5.20        & ( ~ ( ord_less_num @ M @ N )
% 9.25/5.20         => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 9.25/5.20            = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4807_divmod__algorithm__code_I8_J,axiom,
% 9.25/5.20      ! [M: num,N: num] :
% 9.25/5.20        ( ( ( ord_less_num @ M @ N )
% 9.25/5.20         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 9.25/5.20            = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 9.25/5.20        & ( ~ ( ord_less_num @ M @ N )
% 9.25/5.20         => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 9.25/5.20            = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4808_divmod__algorithm__code_I8_J,axiom,
% 9.25/5.20      ! [M: num,N: num] :
% 9.25/5.20        ( ( ( ord_less_num @ M @ N )
% 9.25/5.20         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 9.25/5.20            = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 9.25/5.20        & ( ~ ( ord_less_num @ M @ N )
% 9.25/5.20         => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 9.25/5.20            = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4809_bot__nat__0_Oordering__top__axioms,axiom,
% 9.25/5.20      ( ordering_top_nat
% 9.25/5.20      @ ^ [X3: nat,Y3: nat] : ( ord_less_eq_nat @ Y3 @ X3 )
% 9.25/5.20      @ ^ [X3: nat,Y3: nat] : ( ord_less_nat @ Y3 @ X3 )
% 9.25/5.20      @ zero_zero_nat ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4810_bot__nat__def,axiom,
% 9.25/5.20      bot_bot_nat = zero_zero_nat ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4811_xor__num_Ocases,axiom,
% 9.25/5.20      ! [X: product_prod_num_num] :
% 9.25/5.20        ( ( X
% 9.25/5.20         != ( product_Pair_num_num @ one @ one ) )
% 9.25/5.20       => ( ! [N3: num] :
% 9.25/5.20              ( X
% 9.25/5.20             != ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) )
% 9.25/5.20         => ( ! [N3: num] :
% 9.25/5.20                ( X
% 9.25/5.20               != ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) )
% 9.25/5.20           => ( ! [M3: num] :
% 9.25/5.20                  ( X
% 9.25/5.20                 != ( product_Pair_num_num @ ( bit0 @ M3 ) @ one ) )
% 9.25/5.20             => ( ! [M3: num,N3: num] :
% 9.25/5.20                    ( X
% 9.25/5.20                   != ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit0 @ N3 ) ) )
% 9.25/5.20               => ( ! [M3: num,N3: num] :
% 9.25/5.20                      ( X
% 9.25/5.20                     != ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit1 @ N3 ) ) )
% 9.25/5.20                 => ( ! [M3: num] :
% 9.25/5.20                        ( X
% 9.25/5.20                       != ( product_Pair_num_num @ ( bit1 @ M3 ) @ one ) )
% 9.25/5.20                   => ( ! [M3: num,N3: num] :
% 9.25/5.20                          ( X
% 9.25/5.20                         != ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit0 @ N3 ) ) )
% 9.25/5.20                     => ~ ! [M3: num,N3: num] :
% 9.25/5.20                            ( X
% 9.25/5.20                           != ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4812_neg__zdiv__mult__2,axiom,
% 9.25/5.20      ! [A: int,B: int] :
% 9.25/5.20        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.25/5.20       => ( ( 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 ) )
% 9.25/5.20          = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4813_pos__zdiv__mult__2,axiom,
% 9.25/5.20      ! [A: int,B: int] :
% 9.25/5.20        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.20       => ( ( 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 ) )
% 9.25/5.20          = ( divide_divide_int @ B @ A ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4814_int__bit__induct,axiom,
% 9.25/5.20      ! [P: int > $o,K: int] :
% 9.25/5.20        ( ( P @ zero_zero_int )
% 9.25/5.20       => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.20         => ( ! [K2: int] :
% 9.25/5.20                ( ( P @ K2 )
% 9.25/5.20               => ( ( K2 != zero_zero_int )
% 9.25/5.20                 => ( P @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 9.25/5.20           => ( ! [K2: int] :
% 9.25/5.20                  ( ( P @ K2 )
% 9.25/5.20                 => ( ( K2
% 9.25/5.20                     != ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.20                   => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 9.25/5.20             => ( P @ K ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4815_numeral__code_I2_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 9.25/5.20        = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4816_numeral__code_I2_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 9.25/5.20        = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4817_numeral__code_I2_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( numera6620942414471956472nteger @ ( bit0 @ N ) )
% 9.25/5.20        = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4818_numeral__code_I2_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 9.25/5.20        = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4819_numeral__code_I2_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( numera5444537566228673987atural @ ( bit0 @ N ) )
% 9.25/5.20        = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N ) @ ( numera5444537566228673987atural @ N ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4820_numeral__Bit1,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 9.25/5.20        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4821_numeral__Bit1,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 9.25/5.20        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4822_numeral__Bit1,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( numera6620942414471956472nteger @ ( bit1 @ N ) )
% 9.25/5.20        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ N ) ) @ one_one_Code_integer ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4823_numeral__Bit1,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 9.25/5.20        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4824_numeral__Bit1,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( numera5444537566228673987atural @ ( bit1 @ N ) )
% 9.25/5.20        = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N ) @ ( numera5444537566228673987atural @ N ) ) @ one_one_Code_natural ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4825_nat__1__add__1,axiom,
% 9.25/5.20      ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 9.25/5.20      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4826_ssubst__Pair__rhs,axiom,
% 9.25/5.20      ! [R3: produc6241069584506657477e_term > option6357759511663192854e_term,S3: produc8923325533196201883nteger,R: set_Pr1281608226676607948nteger,S5: produc8923325533196201883nteger] :
% 9.25/5.20        ( ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ R3 @ S3 ) @ R )
% 9.25/5.20       => ( ( S5 = S3 )
% 9.25/5.20         => ( member4164122664394876845nteger @ ( produc8603105652947943368nteger @ R3 @ S5 ) @ R ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4827_ssubst__Pair__rhs,axiom,
% 9.25/5.20      ! [R3: produc3658429121746597890et_nat > $o,S3: produc3658429121746597890et_nat,R: set_Pr3286484037609594932et_nat,S5: produc3658429121746597890et_nat] :
% 9.25/5.20        ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R3 @ S3 ) @ R )
% 9.25/5.20       => ( ( S5 = S3 )
% 9.25/5.20         => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R3 @ S5 ) @ R ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4828_ssubst__Pair__rhs,axiom,
% 9.25/5.20      ! [R3: produc3658429121746597890et_nat > $o,S3: produc3925858234332021118et_nat,R: set_Pr8536935166611901872et_nat,S5: produc3925858234332021118et_nat] :
% 9.25/5.20        ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R3 @ S3 ) @ R )
% 9.25/5.20       => ( ( S5 = S3 )
% 9.25/5.20         => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R3 @ S5 ) @ R ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4829_ssubst__Pair__rhs,axiom,
% 9.25/5.20      ! [R3: produc8551481072490612790e_term > option6357759511663192854e_term,S3: product_prod_int_int,R: set_Pr9222295170931077689nt_int,S5: product_prod_int_int] :
% 9.25/5.20        ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ R3 @ S3 ) @ R )
% 9.25/5.20       => ( ( S5 = S3 )
% 9.25/5.20         => ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ R3 @ S5 ) @ R ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4830_ssubst__Pair__rhs,axiom,
% 9.25/5.20      ! [R3: int > option6357759511663192854e_term,S3: product_prod_int_int,R: set_Pr1872883991513573699nt_int,S5: product_prod_int_int] :
% 9.25/5.20        ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ R3 @ S3 ) @ R )
% 9.25/5.20       => ( ( S5 = S3 )
% 9.25/5.20         => ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ R3 @ S5 ) @ R ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4831_numeral__code_I3_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 9.25/5.20        = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4832_numeral__code_I3_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 9.25/5.20        = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4833_numeral__code_I3_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( numera6620942414471956472nteger @ ( bit1 @ N ) )
% 9.25/5.20        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ N ) ) @ one_one_Code_integer ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4834_numeral__code_I3_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 9.25/5.20        = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4835_numeral__code_I3_J,axiom,
% 9.25/5.20      ! [N: num] :
% 9.25/5.20        ( ( numera5444537566228673987atural @ ( bit1 @ N ) )
% 9.25/5.20        = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N ) @ ( numera5444537566228673987atural @ N ) ) @ one_one_Code_natural ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4836_mult__eq__self__implies__10,axiom,
% 9.25/5.20      ! [M: nat,N: nat] :
% 9.25/5.20        ( ( M
% 9.25/5.20          = ( times_times_nat @ M @ N ) )
% 9.25/5.20       => ( ( N = one_one_nat )
% 9.25/5.20          | ( M = zero_zero_nat ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4837_nat__mult__1,axiom,
% 9.25/5.20      ! [N: nat] :
% 9.25/5.20        ( ( times_times_nat @ one_one_nat @ N )
% 9.25/5.20        = N ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4838_nat__mult__1__right,axiom,
% 9.25/5.20      ! [N: nat] :
% 9.25/5.20        ( ( times_times_nat @ N @ one_one_nat )
% 9.25/5.20        = N ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4839_mult__eq__if,axiom,
% 9.25/5.20      ( times_times_nat
% 9.25/5.20      = ( ^ [M2: nat,N2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4840_divmod__divmod__step,axiom,
% 9.25/5.20      ( unique5052692396658037445od_int
% 9.25/5.20      = ( ^ [M2: num,N2: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M2 @ N2 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M2 ) ) @ ( unique5024387138958732305ep_int @ N2 @ ( unique5052692396658037445od_int @ M2 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4841_divmod__divmod__step,axiom,
% 9.25/5.20      ( unique5055182867167087721od_nat
% 9.25/5.20      = ( ^ [M2: num,N2: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M2 @ N2 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M2 ) ) @ ( unique5026877609467782581ep_nat @ N2 @ ( unique5055182867167087721od_nat @ M2 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4842_divmod__divmod__step,axiom,
% 9.25/5.20      ( unique3479559517661332726nteger
% 9.25/5.20      = ( ^ [M2: num,N2: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M2 @ N2 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( unique4921790084139445826nteger @ N2 @ ( unique3479559517661332726nteger @ M2 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4843_mult__2,axiom,
% 9.25/5.20      ! [Z: nat] :
% 9.25/5.20        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 9.25/5.20        = ( plus_plus_nat @ Z @ Z ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4844_mult__2,axiom,
% 9.25/5.20      ! [Z: int] :
% 9.25/5.20        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 9.25/5.20        = ( plus_plus_int @ Z @ Z ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4845_mult__2,axiom,
% 9.25/5.20      ! [Z: code_integer] :
% 9.25/5.20        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Z )
% 9.25/5.20        = ( plus_p5714425477246183910nteger @ Z @ Z ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4846_mult__2,axiom,
% 9.25/5.20      ! [Z: rat] :
% 9.25/5.20        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 9.25/5.20        = ( plus_plus_rat @ Z @ Z ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4847_mult__2,axiom,
% 9.25/5.20      ! [Z: code_natural] :
% 9.25/5.20        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ Z )
% 9.25/5.20        = ( plus_p4538020629002901425atural @ Z @ Z ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4848_mult__2__right,axiom,
% 9.25/5.20      ! [Z: nat] :
% 9.25/5.20        ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.20        = ( plus_plus_nat @ Z @ Z ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4849_mult__2__right,axiom,
% 9.25/5.20      ! [Z: int] :
% 9.25/5.20        ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.20        = ( plus_plus_int @ Z @ Z ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4850_mult__2__right,axiom,
% 9.25/5.20      ! [Z: code_integer] :
% 9.25/5.20        ( ( times_3573771949741848930nteger @ Z @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.20        = ( plus_p5714425477246183910nteger @ Z @ Z ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4851_mult__2__right,axiom,
% 9.25/5.20      ! [Z: rat] :
% 9.25/5.20        ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 9.25/5.20        = ( plus_plus_rat @ Z @ Z ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4852_mult__2__right,axiom,
% 9.25/5.20      ! [Z: code_natural] :
% 9.25/5.20        ( ( times_2397367101498566445atural @ Z @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.20        = ( plus_p4538020629002901425atural @ Z @ Z ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4853_left__add__twice,axiom,
% 9.25/5.20      ! [A: nat,B: nat] :
% 9.25/5.20        ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 9.25/5.20        = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4854_left__add__twice,axiom,
% 9.25/5.20      ! [A: int,B: int] :
% 9.25/5.20        ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 9.25/5.20        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4855_left__add__twice,axiom,
% 9.25/5.20      ! [A: code_integer,B: code_integer] :
% 9.25/5.20        ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 9.25/5.20        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4856_left__add__twice,axiom,
% 9.25/5.20      ! [A: rat,B: rat] :
% 9.25/5.20        ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 9.25/5.20        = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4857_left__add__twice,axiom,
% 9.25/5.20      ! [A: code_natural,B: code_natural] :
% 9.25/5.20        ( ( plus_p4538020629002901425atural @ A @ ( plus_p4538020629002901425atural @ A @ B ) )
% 9.25/5.20        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4858_prop__restrict,axiom,
% 9.25/5.20      ! [X: set_Pr958786334691620121nt_int,Z5: set_se6260736226359567993nt_int,X7: set_se6260736226359567993nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.20        ( ( member2340774599025711042nt_int @ X @ Z5 )
% 9.25/5.20       => ( ( ord_le483042692224249369nt_int @ Z5
% 9.25/5.20            @ ( collec5210948495886036740nt_int
% 9.25/5.20              @ ^ [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.20                  ( ( member2340774599025711042nt_int @ X3 @ X7 )
% 9.25/5.20                  & ( P @ X3 ) ) ) )
% 9.25/5.20         => ( P @ X ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4859_prop__restrict,axiom,
% 9.25/5.20      ! [X: set_nat,Z5: set_set_nat,X7: set_set_nat,P: set_nat > $o] :
% 9.25/5.20        ( ( member_set_nat @ X @ Z5 )
% 9.25/5.20       => ( ( ord_le6893508408891458716et_nat @ Z5
% 9.25/5.20            @ ( collect_set_nat
% 9.25/5.20              @ ^ [X3: set_nat] :
% 9.25/5.20                  ( ( member_set_nat @ X3 @ X7 )
% 9.25/5.20                  & ( P @ X3 ) ) ) )
% 9.25/5.20         => ( P @ X ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4860_prop__restrict,axiom,
% 9.25/5.20      ! [X: int,Z5: set_int,X7: set_int,P: int > $o] :
% 9.25/5.20        ( ( member_int @ X @ Z5 )
% 9.25/5.20       => ( ( ord_less_eq_set_int @ Z5
% 9.25/5.20            @ ( collect_int
% 9.25/5.20              @ ^ [X3: int] :
% 9.25/5.20                  ( ( member_int @ X3 @ X7 )
% 9.25/5.20                  & ( P @ X3 ) ) ) )
% 9.25/5.20         => ( P @ X ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4861_prop__restrict,axiom,
% 9.25/5.20      ! [X: produc3658429121746597890et_nat > $o,Z5: set_Pr4532377907799695533_nat_o,X7: set_Pr4532377907799695533_nat_o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.20        ( ( member6576561426505652726_nat_o @ X @ Z5 )
% 9.25/5.20       => ( ( ord_le2965882846123202637_nat_o @ Z5
% 9.25/5.20            @ ( collec939566748876313656_nat_o
% 9.25/5.20              @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.20                  ( ( member6576561426505652726_nat_o @ X3 @ X7 )
% 9.25/5.20                  & ( P @ X3 ) ) ) )
% 9.25/5.20         => ( P @ X ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4862_prop__restrict,axiom,
% 9.25/5.20      ! [X: nat,Z5: set_nat,X7: set_nat,P: nat > $o] :
% 9.25/5.20        ( ( member_nat @ X @ Z5 )
% 9.25/5.20       => ( ( ord_less_eq_set_nat @ Z5
% 9.25/5.20            @ ( collect_nat
% 9.25/5.20              @ ^ [X3: nat] :
% 9.25/5.20                  ( ( member_nat @ X3 @ X7 )
% 9.25/5.20                  & ( P @ X3 ) ) ) )
% 9.25/5.20         => ( P @ X ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4863_Collect__restrict,axiom,
% 9.25/5.20      ! [X7: set_se6260736226359567993nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.20        ( ord_le483042692224249369nt_int
% 9.25/5.20        @ ( collec5210948495886036740nt_int
% 9.25/5.20          @ ^ [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.20              ( ( member2340774599025711042nt_int @ X3 @ X7 )
% 9.25/5.20              & ( P @ X3 ) ) )
% 9.25/5.20        @ X7 ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4864_Collect__restrict,axiom,
% 9.25/5.20      ! [X7: set_set_nat,P: set_nat > $o] :
% 9.25/5.20        ( ord_le6893508408891458716et_nat
% 9.25/5.20        @ ( collect_set_nat
% 9.25/5.20          @ ^ [X3: set_nat] :
% 9.25/5.20              ( ( member_set_nat @ X3 @ X7 )
% 9.25/5.20              & ( P @ X3 ) ) )
% 9.25/5.20        @ X7 ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4865_Collect__restrict,axiom,
% 9.25/5.20      ! [X7: set_int,P: int > $o] :
% 9.25/5.20        ( ord_less_eq_set_int
% 9.25/5.20        @ ( collect_int
% 9.25/5.20          @ ^ [X3: int] :
% 9.25/5.20              ( ( member_int @ X3 @ X7 )
% 9.25/5.20              & ( P @ X3 ) ) )
% 9.25/5.20        @ X7 ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4866_Collect__restrict,axiom,
% 9.25/5.20      ! [X7: set_Pr4532377907799695533_nat_o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.20        ( ord_le2965882846123202637_nat_o
% 9.25/5.20        @ ( collec939566748876313656_nat_o
% 9.25/5.20          @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.20              ( ( member6576561426505652726_nat_o @ X3 @ X7 )
% 9.25/5.20              & ( P @ X3 ) ) )
% 9.25/5.20        @ X7 ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4867_Collect__restrict,axiom,
% 9.25/5.20      ! [X7: set_nat,P: nat > $o] :
% 9.25/5.20        ( ord_less_eq_set_nat
% 9.25/5.20        @ ( collect_nat
% 9.25/5.20          @ ^ [X3: nat] :
% 9.25/5.20              ( ( member_nat @ X3 @ X7 )
% 9.25/5.20              & ( P @ X3 ) ) )
% 9.25/5.20        @ X7 ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4868_minus__1__div__2__eq,axiom,
% 9.25/5.20      ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.20      = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4869_minus__1__div__2__eq,axiom,
% 9.25/5.20      ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.20      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4870_set__bit__0,axiom,
% 9.25/5.20      ! [A: code_integer] :
% 9.25/5.20        ( ( bit_se2793503036327961859nteger @ zero_zero_nat @ A )
% 9.25/5.20        = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4871_set__bit__0,axiom,
% 9.25/5.20      ! [A: code_natural] :
% 9.25/5.20        ( ( bit_se1617098188084679374atural @ zero_zero_nat @ A )
% 9.25/5.20        = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4872_set__bit__0,axiom,
% 9.25/5.20      ! [A: int] :
% 9.25/5.20        ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 9.25/5.20        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4873_set__bit__0,axiom,
% 9.25/5.20      ! [A: nat] :
% 9.25/5.20        ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 9.25/5.20        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4874_nat__induct2,axiom,
% 9.25/5.20      ! [P: nat > $o,N: nat] :
% 9.25/5.20        ( ( P @ zero_zero_nat )
% 9.25/5.20       => ( ( P @ one_one_nat )
% 9.25/5.20         => ( ! [N3: nat] :
% 9.25/5.20                ( ( P @ N3 )
% 9.25/5.20               => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 9.25/5.20           => ( P @ N ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4875_unset__bit__0,axiom,
% 9.25/5.20      ! [A: nat] :
% 9.25/5.20        ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 9.25/5.20        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4876_unset__bit__0,axiom,
% 9.25/5.20      ! [A: code_integer] :
% 9.25/5.20        ( ( bit_se8260200283734997820nteger @ zero_zero_nat @ A )
% 9.25/5.20        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4877_unset__bit__0,axiom,
% 9.25/5.20      ! [A: code_natural] :
% 9.25/5.20        ( ( bit_se7083795435491715335atural @ zero_zero_nat @ A )
% 9.25/5.20        = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4878_unset__bit__0,axiom,
% 9.25/5.20      ! [A: int] :
% 9.25/5.20        ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 9.25/5.20        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4879_divmod__algorithm__code_I6_J,axiom,
% 9.25/5.20      ! [M: num,N: num] :
% 9.25/5.20        ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 9.25/5.20        = ( produc4245557441103728435nt_int
% 9.25/5.20          @ ^ [Q5: int,R4: int] : ( product_Pair_int_int @ Q5 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R4 ) @ one_one_int ) )
% 9.25/5.20          @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4880_divmod__algorithm__code_I6_J,axiom,
% 9.25/5.20      ! [M: num,N: num] :
% 9.25/5.20        ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 9.25/5.20        = ( produc2626176000494625587at_nat
% 9.25/5.20          @ ^ [Q5: nat,R4: nat] : ( product_Pair_nat_nat @ Q5 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R4 ) @ one_one_nat ) )
% 9.25/5.20          @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4881_divmod__algorithm__code_I6_J,axiom,
% 9.25/5.20      ! [M: num,N: num] :
% 9.25/5.20        ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 9.25/5.20        = ( produc6916734918728496179nteger
% 9.25/5.20          @ ^ [Q5: code_integer,R4: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R4 ) @ one_one_Code_integer ) )
% 9.25/5.20          @ ( unique3479559517661332726nteger @ M @ N ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4882_divmod__step__def,axiom,
% 9.25/5.20      ( unique5024387138958732305ep_int
% 9.25/5.20      = ( ^ [L2: num] :
% 9.25/5.20            ( produc4245557441103728435nt_int
% 9.25/5.20            @ ^ [Q5: int,R4: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R4 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R4 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R4 ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4883_divmod__step__def,axiom,
% 9.25/5.20      ( unique5026877609467782581ep_nat
% 9.25/5.20      = ( ^ [L2: num] :
% 9.25/5.20            ( produc2626176000494625587at_nat
% 9.25/5.20            @ ^ [Q5: nat,R4: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R4 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R4 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R4 ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4884_divmod__step__def,axiom,
% 9.25/5.20      ( unique4921790084139445826nteger
% 9.25/5.20      = ( ^ [L2: num] :
% 9.25/5.20            ( produc6916734918728496179nteger
% 9.25/5.20            @ ^ [Q5: code_integer,R4: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R4 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R4 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R4 ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4885_divmod__digit__1_I1_J,axiom,
% 9.25/5.20      ! [A: code_integer,B: code_integer] :
% 9.25/5.20        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.20       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 9.25/5.20         => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 9.25/5.20           => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 9.25/5.20              = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4886_divmod__digit__1_I1_J,axiom,
% 9.25/5.20      ! [A: nat,B: nat] :
% 9.25/5.20        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.25/5.20       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.25/5.20         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 9.25/5.20           => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_nat )
% 9.25/5.20              = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4887_divmod__digit__1_I1_J,axiom,
% 9.25/5.20      ! [A: int,B: int] :
% 9.25/5.20        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.20       => ( ( ord_less_int @ zero_zero_int @ B )
% 9.25/5.20         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 9.25/5.20           => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_int )
% 9.25/5.20              = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4888_xor__numerals_I6_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 9.25/5.20        = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4889_xor__numerals_I6_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 9.25/5.20        = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4890_xor__numerals_I6_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 9.25/5.20        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4891_xor__numerals_I6_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 9.25/5.20        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4892_mod__minus__minus,axiom,
% 9.25/5.20      ! [A: int,B: int] :
% 9.25/5.20        ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 9.25/5.20        = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4893_mod__minus__minus,axiom,
% 9.25/5.20      ! [A: code_integer,B: code_integer] :
% 9.25/5.20        ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 9.25/5.20        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4894_case__prod__conv,axiom,
% 9.25/5.20      ! [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 9.25/5.20        ( ( produc27273713700761075at_nat @ F2 @ ( product_Pair_nat_nat @ A @ B ) )
% 9.25/5.20        = ( F2 @ A @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4895_case__prod__conv,axiom,
% 9.25/5.20      ! [F2: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 9.25/5.20        ( ( produc8739625826339149834_nat_o @ F2 @ ( product_Pair_nat_nat @ A @ B ) )
% 9.25/5.20        = ( F2 @ A @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4896_case__prod__conv,axiom,
% 9.25/5.20      ! [F2: int > int > product_prod_int_int,A: int,B: int] :
% 9.25/5.20        ( ( produc4245557441103728435nt_int @ F2 @ ( product_Pair_int_int @ A @ B ) )
% 9.25/5.20        = ( F2 @ A @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4897_case__prod__conv,axiom,
% 9.25/5.20      ! [F2: int > int > $o,A: int,B: int] :
% 9.25/5.20        ( ( produc4947309494688390418_int_o @ F2 @ ( product_Pair_int_int @ A @ B ) )
% 9.25/5.20        = ( F2 @ A @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4898_case__prod__conv,axiom,
% 9.25/5.20      ! [F2: int > int > int,A: int,B: int] :
% 9.25/5.20        ( ( produc8211389475949308722nt_int @ F2 @ ( product_Pair_int_int @ A @ B ) )
% 9.25/5.20        = ( F2 @ A @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4899_mod__mult__self1__is__0,axiom,
% 9.25/5.20      ! [B: nat,A: nat] :
% 9.25/5.20        ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 9.25/5.20        = zero_zero_nat ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4900_mod__mult__self1__is__0,axiom,
% 9.25/5.20      ! [B: int,A: int] :
% 9.25/5.20        ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 9.25/5.20        = zero_zero_int ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4901_mod__mult__self1__is__0,axiom,
% 9.25/5.20      ! [B: code_integer,A: code_integer] :
% 9.25/5.20        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 9.25/5.20        = zero_z3403309356797280102nteger ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4902_mod__mult__self1__is__0,axiom,
% 9.25/5.20      ! [B: code_natural,A: code_natural] :
% 9.25/5.20        ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ B @ A ) @ B )
% 9.25/5.20        = zero_z2226904508553997617atural ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4903_mod__mult__self2__is__0,axiom,
% 9.25/5.20      ! [A: nat,B: nat] :
% 9.25/5.20        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 9.25/5.20        = zero_zero_nat ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4904_mod__mult__self2__is__0,axiom,
% 9.25/5.20      ! [A: int,B: int] :
% 9.25/5.20        ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 9.25/5.20        = zero_zero_int ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4905_mod__mult__self2__is__0,axiom,
% 9.25/5.20      ! [A: code_integer,B: code_integer] :
% 9.25/5.20        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 9.25/5.20        = zero_z3403309356797280102nteger ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4906_mod__mult__self2__is__0,axiom,
% 9.25/5.20      ! [A: code_natural,B: code_natural] :
% 9.25/5.20        ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ B )
% 9.25/5.20        = zero_z2226904508553997617atural ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4907_bits__mod__by__1,axiom,
% 9.25/5.20      ! [A: nat] :
% 9.25/5.20        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 9.25/5.20        = zero_zero_nat ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4908_bits__mod__by__1,axiom,
% 9.25/5.20      ! [A: int] :
% 9.25/5.20        ( ( modulo_modulo_int @ A @ one_one_int )
% 9.25/5.20        = zero_zero_int ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4909_bits__mod__by__1,axiom,
% 9.25/5.20      ! [A: code_integer] :
% 9.25/5.20        ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 9.25/5.20        = zero_z3403309356797280102nteger ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4910_bits__mod__by__1,axiom,
% 9.25/5.20      ! [A: code_natural] :
% 9.25/5.20        ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 9.25/5.20        = zero_z2226904508553997617atural ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4911_mod__by__1,axiom,
% 9.25/5.20      ! [A: nat] :
% 9.25/5.20        ( ( modulo_modulo_nat @ A @ one_one_nat )
% 9.25/5.20        = zero_zero_nat ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4912_mod__by__1,axiom,
% 9.25/5.20      ! [A: int] :
% 9.25/5.20        ( ( modulo_modulo_int @ A @ one_one_int )
% 9.25/5.20        = zero_zero_int ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4913_mod__by__1,axiom,
% 9.25/5.20      ! [A: code_integer] :
% 9.25/5.20        ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 9.25/5.20        = zero_z3403309356797280102nteger ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4914_mod__by__1,axiom,
% 9.25/5.20      ! [A: code_natural] :
% 9.25/5.20        ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 9.25/5.20        = zero_z2226904508553997617atural ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4915_mod__mult__self4,axiom,
% 9.25/5.20      ! [B: nat,C: nat,A: nat] :
% 9.25/5.20        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 9.25/5.20        = ( modulo_modulo_nat @ A @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4916_mod__mult__self4,axiom,
% 9.25/5.20      ! [B: int,C: int,A: int] :
% 9.25/5.20        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 9.25/5.20        = ( modulo_modulo_int @ A @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4917_mod__mult__self4,axiom,
% 9.25/5.20      ! [B: code_integer,C: code_integer,A: code_integer] :
% 9.25/5.20        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 9.25/5.20        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4918_mod__mult__self4,axiom,
% 9.25/5.20      ! [B: code_natural,C: code_natural,A: code_natural] :
% 9.25/5.20        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ C ) @ A ) @ B )
% 9.25/5.20        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4919_mod__mult__self3,axiom,
% 9.25/5.20      ! [C: nat,B: nat,A: nat] :
% 9.25/5.20        ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 9.25/5.20        = ( modulo_modulo_nat @ A @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4920_mod__mult__self3,axiom,
% 9.25/5.20      ! [C: int,B: int,A: int] :
% 9.25/5.20        ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 9.25/5.20        = ( modulo_modulo_int @ A @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4921_mod__mult__self3,axiom,
% 9.25/5.20      ! [C: code_integer,B: code_integer,A: code_integer] :
% 9.25/5.20        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 9.25/5.20        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4922_mod__mult__self3,axiom,
% 9.25/5.20      ! [C: code_natural,B: code_natural,A: code_natural] :
% 9.25/5.20        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C @ B ) @ A ) @ B )
% 9.25/5.20        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4923_mod__mult__self2,axiom,
% 9.25/5.20      ! [A: nat,B: nat,C: nat] :
% 9.25/5.20        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 9.25/5.20        = ( modulo_modulo_nat @ A @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4924_mod__mult__self2,axiom,
% 9.25/5.20      ! [A: int,B: int,C: int] :
% 9.25/5.20        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 9.25/5.20        = ( modulo_modulo_int @ A @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4925_mod__mult__self2,axiom,
% 9.25/5.20      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.20        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 9.25/5.20        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4926_mod__mult__self2,axiom,
% 9.25/5.20      ! [A: code_natural,B: code_natural,C: code_natural] :
% 9.25/5.20        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ B @ C ) ) @ B )
% 9.25/5.20        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4927_mod__mult__self1,axiom,
% 9.25/5.20      ! [A: nat,C: nat,B: nat] :
% 9.25/5.20        ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 9.25/5.20        = ( modulo_modulo_nat @ A @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4928_mod__mult__self1,axiom,
% 9.25/5.20      ! [A: int,C: int,B: int] :
% 9.25/5.20        ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 9.25/5.20        = ( modulo_modulo_int @ A @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4929_mod__mult__self1,axiom,
% 9.25/5.20      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.25/5.20        ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 9.25/5.20        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4930_mod__mult__self1,axiom,
% 9.25/5.20      ! [A: code_natural,C: code_natural,B: code_natural] :
% 9.25/5.20        ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ C @ B ) ) @ B )
% 9.25/5.20        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4931_minus__mod__self1,axiom,
% 9.25/5.20      ! [B: int,A: int] :
% 9.25/5.20        ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 9.25/5.20        = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4932_minus__mod__self1,axiom,
% 9.25/5.20      ! [B: code_integer,A: code_integer] :
% 9.25/5.20        ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 9.25/5.20        = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4933_mod__minus1__right,axiom,
% 9.25/5.20      ! [A: int] :
% 9.25/5.20        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.20        = zero_zero_int ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4934_mod__minus1__right,axiom,
% 9.25/5.20      ! [A: code_integer] :
% 9.25/5.20        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.20        = zero_z3403309356797280102nteger ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4935_bits__one__mod__two__eq__one,axiom,
% 9.25/5.20      ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.20      = one_one_nat ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4936_bits__one__mod__two__eq__one,axiom,
% 9.25/5.20      ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.20      = one_one_int ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4937_bits__one__mod__two__eq__one,axiom,
% 9.25/5.20      ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.20      = one_one_Code_integer ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4938_bits__one__mod__two__eq__one,axiom,
% 9.25/5.20      ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.20      = one_one_Code_natural ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4939_one__mod__two__eq__one,axiom,
% 9.25/5.20      ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.20      = one_one_nat ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4940_one__mod__two__eq__one,axiom,
% 9.25/5.20      ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.20      = one_one_int ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4941_one__mod__two__eq__one,axiom,
% 9.25/5.20      ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.20      = one_one_Code_integer ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4942_one__mod__two__eq__one,axiom,
% 9.25/5.20      ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.20      = one_one_Code_natural ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4943_xor__numerals_I3_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 9.25/5.20        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4944_xor__numerals_I3_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 9.25/5.20        = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4945_xor__numerals_I3_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 9.25/5.20        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4946_xor__numerals_I3_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 9.25/5.20        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4947_xor__numerals_I8_J,axiom,
% 9.25/5.20      ! [X: num] :
% 9.25/5.20        ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ one_one_Code_integer )
% 9.25/5.20        = ( numera6620942414471956472nteger @ ( bit0 @ X ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4948_xor__numerals_I8_J,axiom,
% 9.25/5.20      ! [X: num] :
% 9.25/5.20        ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ one_one_Code_natural )
% 9.25/5.20        = ( numera5444537566228673987atural @ ( bit0 @ X ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4949_xor__numerals_I8_J,axiom,
% 9.25/5.20      ! [X: num] :
% 9.25/5.20        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 9.25/5.20        = ( numeral_numeral_int @ ( bit0 @ X ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4950_xor__numerals_I8_J,axiom,
% 9.25/5.20      ! [X: num] :
% 9.25/5.20        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 9.25/5.20        = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4951_xor__numerals_I5_J,axiom,
% 9.25/5.20      ! [X: num] :
% 9.25/5.20        ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ one_one_Code_integer )
% 9.25/5.20        = ( numera6620942414471956472nteger @ ( bit1 @ X ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4952_xor__numerals_I5_J,axiom,
% 9.25/5.20      ! [X: num] :
% 9.25/5.20        ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ one_one_Code_natural )
% 9.25/5.20        = ( numera5444537566228673987atural @ ( bit1 @ X ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4953_xor__numerals_I5_J,axiom,
% 9.25/5.20      ! [X: num] :
% 9.25/5.20        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 9.25/5.20        = ( numeral_numeral_int @ ( bit1 @ X ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4954_xor__numerals_I5_J,axiom,
% 9.25/5.20      ! [X: num] :
% 9.25/5.20        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 9.25/5.20        = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4955_xor__numerals_I2_J,axiom,
% 9.25/5.20      ! [Y: num] :
% 9.25/5.20        ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 9.25/5.20        = ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4956_xor__numerals_I2_J,axiom,
% 9.25/5.20      ! [Y: num] :
% 9.25/5.20        ( ( bit_se2046307713759805098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 9.25/5.20        = ( numera5444537566228673987atural @ ( bit0 @ Y ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4957_xor__numerals_I2_J,axiom,
% 9.25/5.20      ! [Y: num] :
% 9.25/5.20        ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 9.25/5.20        = ( numeral_numeral_int @ ( bit0 @ Y ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4958_xor__numerals_I2_J,axiom,
% 9.25/5.20      ! [Y: num] :
% 9.25/5.20        ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 9.25/5.20        = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4959_xor__numerals_I1_J,axiom,
% 9.25/5.20      ! [Y: num] :
% 9.25/5.20        ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 9.25/5.20        = ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4960_xor__numerals_I1_J,axiom,
% 9.25/5.20      ! [Y: num] :
% 9.25/5.20        ( ( bit_se2046307713759805098atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 9.25/5.20        = ( numera5444537566228673987atural @ ( bit1 @ Y ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4961_xor__numerals_I1_J,axiom,
% 9.25/5.20      ! [Y: num] :
% 9.25/5.20        ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 9.25/5.20        = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4962_xor__numerals_I1_J,axiom,
% 9.25/5.20      ! [Y: num] :
% 9.25/5.20        ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 9.25/5.20        = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4963_not__mod__2__eq__0__eq__1,axiom,
% 9.25/5.20      ! [A: nat] :
% 9.25/5.20        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.20         != zero_zero_nat )
% 9.25/5.20        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.20          = one_one_nat ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4964_not__mod__2__eq__0__eq__1,axiom,
% 9.25/5.20      ! [A: int] :
% 9.25/5.20        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.20         != zero_zero_int )
% 9.25/5.20        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.20          = one_one_int ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4965_not__mod__2__eq__0__eq__1,axiom,
% 9.25/5.20      ! [A: code_integer] :
% 9.25/5.20        ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.20         != zero_z3403309356797280102nteger )
% 9.25/5.20        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.20          = one_one_Code_integer ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4966_not__mod__2__eq__0__eq__1,axiom,
% 9.25/5.20      ! [A: code_natural] :
% 9.25/5.20        ( ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.20         != zero_z2226904508553997617atural )
% 9.25/5.20        = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.20          = one_one_Code_natural ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4967_not__mod__2__eq__1__eq__0,axiom,
% 9.25/5.20      ! [A: nat] :
% 9.25/5.20        ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.20         != one_one_nat )
% 9.25/5.20        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.20          = zero_zero_nat ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4968_not__mod__2__eq__1__eq__0,axiom,
% 9.25/5.20      ! [A: int] :
% 9.25/5.20        ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.20         != one_one_int )
% 9.25/5.20        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.20          = zero_zero_int ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4969_not__mod__2__eq__1__eq__0,axiom,
% 9.25/5.20      ! [A: code_integer] :
% 9.25/5.20        ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.20         != one_one_Code_integer )
% 9.25/5.20        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.20          = zero_z3403309356797280102nteger ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4970_not__mod__2__eq__1__eq__0,axiom,
% 9.25/5.20      ! [A: code_natural] :
% 9.25/5.20        ( ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.20         != one_one_Code_natural )
% 9.25/5.20        = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.20          = zero_z2226904508553997617atural ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4971_minus__1__mod__2__eq,axiom,
% 9.25/5.20      ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.20      = one_one_int ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4972_minus__1__mod__2__eq,axiom,
% 9.25/5.20      ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.20      = one_one_Code_integer ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4973_bits__minus__1__mod__2__eq,axiom,
% 9.25/5.20      ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.20      = one_one_int ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4974_bits__minus__1__mod__2__eq,axiom,
% 9.25/5.20      ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.20      = one_one_Code_integer ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4975_mod2__gr__0,axiom,
% 9.25/5.20      ! [M: nat] :
% 9.25/5.20        ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.25/5.20        = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.20          = one_one_nat ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4976_xor__numerals_I7_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 9.25/5.20        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4977_xor__numerals_I7_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 9.25/5.20        = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4978_xor__numerals_I7_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 9.25/5.20        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4979_xor__numerals_I7_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 9.25/5.20        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4980_zmod__numeral__Bit1,axiom,
% 9.25/5.20      ! [V: num,W: num] :
% 9.25/5.20        ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 9.25/5.20        = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) @ one_one_int ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4981_divmod__algorithm__code_I5_J,axiom,
% 9.25/5.20      ! [M: num,N: num] :
% 9.25/5.20        ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 9.25/5.20        = ( produc4245557441103728435nt_int
% 9.25/5.20          @ ^ [Q5: int,R4: int] : ( product_Pair_int_int @ Q5 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R4 ) )
% 9.25/5.20          @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4982_divmod__algorithm__code_I5_J,axiom,
% 9.25/5.20      ! [M: num,N: num] :
% 9.25/5.20        ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 9.25/5.20        = ( produc2626176000494625587at_nat
% 9.25/5.20          @ ^ [Q5: nat,R4: nat] : ( product_Pair_nat_nat @ Q5 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R4 ) )
% 9.25/5.20          @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4983_divmod__algorithm__code_I5_J,axiom,
% 9.25/5.20      ! [M: num,N: num] :
% 9.25/5.20        ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 9.25/5.20        = ( produc6916734918728496179nteger
% 9.25/5.20          @ ^ [Q5: code_integer,R4: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R4 ) )
% 9.25/5.20          @ ( unique3479559517661332726nteger @ M @ N ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4984_xor__numerals_I4_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 9.25/5.20        = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4985_xor__numerals_I4_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 9.25/5.20        = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4986_xor__numerals_I4_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 9.25/5.20        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4987_xor__numerals_I4_J,axiom,
% 9.25/5.20      ! [X: num,Y: num] :
% 9.25/5.20        ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 9.25/5.20        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4988_zmod__minus1,axiom,
% 9.25/5.20      ! [B: int] :
% 9.25/5.20        ( ( ord_less_int @ zero_zero_int @ B )
% 9.25/5.20       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 9.25/5.20          = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4989_minus__mod__int__eq,axiom,
% 9.25/5.20      ! [L: int,K: int] :
% 9.25/5.20        ( ( ord_less_eq_int @ zero_zero_int @ L )
% 9.25/5.20       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 9.25/5.20          = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4990_zdiv__zminus1__eq__if,axiom,
% 9.25/5.20      ! [B: int,A: int] :
% 9.25/5.20        ( ( B != zero_zero_int )
% 9.25/5.20       => ( ( ( ( modulo_modulo_int @ A @ B )
% 9.25/5.20              = zero_zero_int )
% 9.25/5.20           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 9.25/5.20              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 9.25/5.20          & ( ( ( modulo_modulo_int @ A @ B )
% 9.25/5.20             != zero_zero_int )
% 9.25/5.20           => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 9.25/5.20              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4991_zdiv__zminus2__eq__if,axiom,
% 9.25/5.20      ! [B: int,A: int] :
% 9.25/5.20        ( ( B != zero_zero_int )
% 9.25/5.20       => ( ( ( ( modulo_modulo_int @ A @ B )
% 9.25/5.20              = zero_zero_int )
% 9.25/5.20           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 9.25/5.20              = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 9.25/5.20          & ( ( ( modulo_modulo_int @ A @ B )
% 9.25/5.20             != zero_zero_int )
% 9.25/5.20           => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 9.25/5.20              = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4992_div__pos__neg__trivial,axiom,
% 9.25/5.20      ! [K: int,L: int] :
% 9.25/5.20        ( ( ord_less_int @ zero_zero_int @ K )
% 9.25/5.20       => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 9.25/5.20         => ( ( divide_divide_int @ K @ L )
% 9.25/5.20            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4993_div__pos__geq,axiom,
% 9.25/5.20      ! [L: int,K: int] :
% 9.25/5.20        ( ( ord_less_int @ zero_zero_int @ L )
% 9.25/5.20       => ( ( ord_less_eq_int @ L @ K )
% 9.25/5.20         => ( ( divide_divide_int @ K @ L )
% 9.25/5.20            = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4994_int__div__less__self,axiom,
% 9.25/5.20      ! [X: int,K: int] :
% 9.25/5.20        ( ( ord_less_int @ zero_zero_int @ X )
% 9.25/5.20       => ( ( ord_less_int @ one_one_int @ K )
% 9.25/5.20         => ( ord_less_int @ ( divide_divide_int @ X @ K ) @ X ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4995_verit__less__mono__div__int2,axiom,
% 9.25/5.20      ! [A2: int,B2: int,N: int] :
% 9.25/5.20        ( ( ord_less_eq_int @ A2 @ B2 )
% 9.25/5.20       => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 9.25/5.20         => ( ord_less_eq_int @ ( divide_divide_int @ B2 @ N ) @ ( divide_divide_int @ A2 @ N ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4996_verit__le__mono__div__int,axiom,
% 9.25/5.20      ! [A2: int,B2: int,N: int] :
% 9.25/5.20        ( ( ord_less_int @ A2 @ B2 )
% 9.25/5.20       => ( ( ord_less_int @ zero_zero_int @ N )
% 9.25/5.20         => ( ord_less_eq_int
% 9.25/5.20            @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N )
% 9.25/5.20              @ ( if_int
% 9.25/5.20                @ ( ( modulo_modulo_int @ B2 @ N )
% 9.25/5.20                  = zero_zero_int )
% 9.25/5.20                @ one_one_int
% 9.25/5.20                @ zero_zero_int ) )
% 9.25/5.20            @ ( divide_divide_int @ B2 @ N ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4997_div__eq__minus1,axiom,
% 9.25/5.20      ! [B: int] :
% 9.25/5.20        ( ( ord_less_int @ zero_zero_int @ B )
% 9.25/5.20       => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 9.25/5.20          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4998_divmod__int__def,axiom,
% 9.25/5.20      ( unique5052692396658037445od_int
% 9.25/5.20      = ( ^ [M2: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_4999_zmod__zminus1__not__zero,axiom,
% 9.25/5.20      ! [K: int,L: int] :
% 9.25/5.20        ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 9.25/5.20         != zero_zero_int )
% 9.25/5.20       => ( ( modulo_modulo_int @ K @ L )
% 9.25/5.20         != zero_zero_int ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5000_zmod__zminus2__not__zero,axiom,
% 9.25/5.20      ! [K: int,L: int] :
% 9.25/5.20        ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L ) )
% 9.25/5.20         != zero_zero_int )
% 9.25/5.20       => ( ( modulo_modulo_int @ K @ L )
% 9.25/5.20         != zero_zero_int ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5001_zmod__zminus2__eq__if,axiom,
% 9.25/5.20      ! [A: int,B: int] :
% 9.25/5.20        ( ( ( ( modulo_modulo_int @ A @ B )
% 9.25/5.20            = zero_zero_int )
% 9.25/5.20         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 9.25/5.20            = zero_zero_int ) )
% 9.25/5.20        & ( ( ( modulo_modulo_int @ A @ B )
% 9.25/5.20           != zero_zero_int )
% 9.25/5.20         => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 9.25/5.20            = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5002_zmod__zminus1__eq__if,axiom,
% 9.25/5.20      ! [A: int,B: int] :
% 9.25/5.20        ( ( ( ( modulo_modulo_int @ A @ B )
% 9.25/5.20            = zero_zero_int )
% 9.25/5.20         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 9.25/5.20            = zero_zero_int ) )
% 9.25/5.20        & ( ( ( modulo_modulo_int @ A @ B )
% 9.25/5.20           != zero_zero_int )
% 9.25/5.20         => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 9.25/5.20            = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5003_prod_Ocase__distrib,axiom,
% 9.25/5.20      ! [H3: $o > $o,F2: int > int > $o,Prod: product_prod_int_int] :
% 9.25/5.20        ( ( H3 @ ( produc4947309494688390418_int_o @ F2 @ Prod ) )
% 9.25/5.20        = ( produc4947309494688390418_int_o
% 9.25/5.20          @ ^ [X12: int,X23: int] : ( H3 @ ( F2 @ X12 @ X23 ) )
% 9.25/5.20          @ Prod ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5004_prod_Ocase__distrib,axiom,
% 9.25/5.20      ! [H3: $o > int,F2: int > int > $o,Prod: product_prod_int_int] :
% 9.25/5.20        ( ( H3 @ ( produc4947309494688390418_int_o @ F2 @ Prod ) )
% 9.25/5.20        = ( produc8211389475949308722nt_int
% 9.25/5.20          @ ^ [X12: int,X23: int] : ( H3 @ ( F2 @ X12 @ X23 ) )
% 9.25/5.20          @ Prod ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5005_prod_Ocase__distrib,axiom,
% 9.25/5.20      ! [H3: int > $o,F2: int > int > int,Prod: product_prod_int_int] :
% 9.25/5.20        ( ( H3 @ ( produc8211389475949308722nt_int @ F2 @ Prod ) )
% 9.25/5.20        = ( produc4947309494688390418_int_o
% 9.25/5.20          @ ^ [X12: int,X23: int] : ( H3 @ ( F2 @ X12 @ X23 ) )
% 9.25/5.20          @ Prod ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5006_prod_Ocase__distrib,axiom,
% 9.25/5.20      ! [H3: int > int,F2: int > int > int,Prod: product_prod_int_int] :
% 9.25/5.20        ( ( H3 @ ( produc8211389475949308722nt_int @ F2 @ Prod ) )
% 9.25/5.20        = ( produc8211389475949308722nt_int
% 9.25/5.20          @ ^ [X12: int,X23: int] : ( H3 @ ( F2 @ X12 @ X23 ) )
% 9.25/5.20          @ Prod ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5007_prod_Ocase__distrib,axiom,
% 9.25/5.20      ! [H3: product_prod_int_int > $o,F2: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 9.25/5.20        ( ( H3 @ ( produc4245557441103728435nt_int @ F2 @ Prod ) )
% 9.25/5.20        = ( produc4947309494688390418_int_o
% 9.25/5.20          @ ^ [X12: int,X23: int] : ( H3 @ ( F2 @ X12 @ X23 ) )
% 9.25/5.20          @ Prod ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5008_prod_Ocase__distrib,axiom,
% 9.25/5.20      ! [H3: product_prod_int_int > int,F2: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 9.25/5.20        ( ( H3 @ ( produc4245557441103728435nt_int @ F2 @ Prod ) )
% 9.25/5.20        = ( produc8211389475949308722nt_int
% 9.25/5.20          @ ^ [X12: int,X23: int] : ( H3 @ ( F2 @ X12 @ X23 ) )
% 9.25/5.20          @ Prod ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5009_prod_Ocase__distrib,axiom,
% 9.25/5.20      ! [H3: $o > product_prod_int_int,F2: int > int > $o,Prod: product_prod_int_int] :
% 9.25/5.20        ( ( H3 @ ( produc4947309494688390418_int_o @ F2 @ Prod ) )
% 9.25/5.20        = ( produc4245557441103728435nt_int
% 9.25/5.20          @ ^ [X12: int,X23: int] : ( H3 @ ( F2 @ X12 @ X23 ) )
% 9.25/5.20          @ Prod ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5010_prod_Ocase__distrib,axiom,
% 9.25/5.20      ! [H3: int > product_prod_int_int,F2: int > int > int,Prod: product_prod_int_int] :
% 9.25/5.20        ( ( H3 @ ( produc8211389475949308722nt_int @ F2 @ Prod ) )
% 9.25/5.20        = ( produc4245557441103728435nt_int
% 9.25/5.20          @ ^ [X12: int,X23: int] : ( H3 @ ( F2 @ X12 @ X23 ) )
% 9.25/5.20          @ Prod ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5011_prod_Ocase__distrib,axiom,
% 9.25/5.20      ! [H3: product_prod_int_int > product_prod_int_int,F2: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 9.25/5.20        ( ( H3 @ ( produc4245557441103728435nt_int @ F2 @ Prod ) )
% 9.25/5.20        = ( produc4245557441103728435nt_int
% 9.25/5.20          @ ^ [X12: int,X23: int] : ( H3 @ ( F2 @ X12 @ X23 ) )
% 9.25/5.20          @ Prod ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5012_prod_Ocase__distrib,axiom,
% 9.25/5.20      ! [H3: ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o,F2: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 9.25/5.20        ( ( H3 @ ( produc8739625826339149834_nat_o @ F2 @ Prod ) )
% 9.25/5.20        = ( produc8739625826339149834_nat_o
% 9.25/5.20          @ ^ [X12: nat,X23: nat] : ( H3 @ ( F2 @ X12 @ X23 ) )
% 9.25/5.20          @ Prod ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5013_case__prod__app,axiom,
% 9.25/5.20      ( produc27273713700761075at_nat
% 9.25/5.20      = ( ^ [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 9.25/5.20            ( produc2626176000494625587at_nat
% 9.25/5.20            @ ^ [L2: nat,R4: nat] : ( F @ L2 @ R4 @ Y3 )
% 9.25/5.20            @ X3 ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5014_case__prod__app,axiom,
% 9.25/5.20      ( produc8739625826339149834_nat_o
% 9.25/5.20      = ( ^ [F: nat > nat > product_prod_nat_nat > $o,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 9.25/5.20            ( produc6081775807080527818_nat_o
% 9.25/5.20            @ ^ [L2: nat,R4: nat] : ( F @ L2 @ R4 @ Y3 )
% 9.25/5.20            @ X3 ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5015_nested__case__prod__simp,axiom,
% 9.25/5.20      ( produc27273713700761075at_nat
% 9.25/5.20      = ( ^ [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 9.25/5.20            ( produc2626176000494625587at_nat
% 9.25/5.20            @ ^ [A3: nat,B3: nat] : ( F @ A3 @ B3 @ Y3 )
% 9.25/5.20            @ X3 ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5016_nested__case__prod__simp,axiom,
% 9.25/5.20      ( produc8739625826339149834_nat_o
% 9.25/5.20      = ( ^ [F: nat > nat > product_prod_nat_nat > $o,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 9.25/5.20            ( produc6081775807080527818_nat_o
% 9.25/5.20            @ ^ [A3: nat,B3: nat] : ( F @ A3 @ B3 @ Y3 )
% 9.25/5.20            @ X3 ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5017_mod__mult__eq,axiom,
% 9.25/5.20      ! [A: nat,C: nat,B: nat] :
% 9.25/5.20        ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 9.25/5.20        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5018_mod__mult__eq,axiom,
% 9.25/5.20      ! [A: int,C: int,B: int] :
% 9.25/5.20        ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 9.25/5.20        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5019_mod__mult__eq,axiom,
% 9.25/5.20      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.25/5.20        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 9.25/5.20        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5020_mod__mult__eq,axiom,
% 9.25/5.20      ! [A: code_natural,C: code_natural,B: code_natural] :
% 9.25/5.20        ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ C ) @ ( modulo8411746178871703098atural @ B @ C ) ) @ C )
% 9.25/5.20        = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5021_mod__mult__cong,axiom,
% 9.25/5.20      ! [A: nat,C: nat,A5: nat,B: nat,B5: nat] :
% 9.25/5.20        ( ( ( modulo_modulo_nat @ A @ C )
% 9.25/5.20          = ( modulo_modulo_nat @ A5 @ C ) )
% 9.25/5.20       => ( ( ( modulo_modulo_nat @ B @ C )
% 9.25/5.20            = ( modulo_modulo_nat @ B5 @ C ) )
% 9.25/5.20         => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 9.25/5.20            = ( modulo_modulo_nat @ ( times_times_nat @ A5 @ B5 ) @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5022_mod__mult__cong,axiom,
% 9.25/5.20      ! [A: int,C: int,A5: int,B: int,B5: int] :
% 9.25/5.20        ( ( ( modulo_modulo_int @ A @ C )
% 9.25/5.20          = ( modulo_modulo_int @ A5 @ C ) )
% 9.25/5.20       => ( ( ( modulo_modulo_int @ B @ C )
% 9.25/5.20            = ( modulo_modulo_int @ B5 @ C ) )
% 9.25/5.20         => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 9.25/5.20            = ( modulo_modulo_int @ ( times_times_int @ A5 @ B5 ) @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5023_mod__mult__cong,axiom,
% 9.25/5.20      ! [A: code_integer,C: code_integer,A5: code_integer,B: code_integer,B5: code_integer] :
% 9.25/5.20        ( ( ( modulo364778990260209775nteger @ A @ C )
% 9.25/5.20          = ( modulo364778990260209775nteger @ A5 @ C ) )
% 9.25/5.20       => ( ( ( modulo364778990260209775nteger @ B @ C )
% 9.25/5.20            = ( modulo364778990260209775nteger @ B5 @ C ) )
% 9.25/5.20         => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 9.25/5.20            = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A5 @ B5 ) @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5024_mod__mult__cong,axiom,
% 9.25/5.20      ! [A: code_natural,C: code_natural,A5: code_natural,B: code_natural,B5: code_natural] :
% 9.25/5.20        ( ( ( modulo8411746178871703098atural @ A @ C )
% 9.25/5.20          = ( modulo8411746178871703098atural @ A5 @ C ) )
% 9.25/5.20       => ( ( ( modulo8411746178871703098atural @ B @ C )
% 9.25/5.20            = ( modulo8411746178871703098atural @ B5 @ C ) )
% 9.25/5.20         => ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C )
% 9.25/5.20            = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A5 @ B5 ) @ C ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5025_mod__mult__mult2,axiom,
% 9.25/5.20      ! [A: nat,C: nat,B: nat] :
% 9.25/5.20        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 9.25/5.20        = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5026_mod__mult__mult2,axiom,
% 9.25/5.20      ! [A: int,C: int,B: int] :
% 9.25/5.20        ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 9.25/5.20        = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5027_mod__mult__mult2,axiom,
% 9.25/5.20      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.25/5.20        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.25/5.20        = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5028_mod__mult__mult2,axiom,
% 9.25/5.20      ! [A: code_natural,C: code_natural,B: code_natural] :
% 9.25/5.20        ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) )
% 9.25/5.20        = ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ B ) @ C ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5029_mult__mod__right,axiom,
% 9.25/5.20      ! [C: nat,A: nat,B: nat] :
% 9.25/5.20        ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 9.25/5.20        = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5030_mult__mod__right,axiom,
% 9.25/5.20      ! [C: int,A: int,B: int] :
% 9.25/5.20        ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 9.25/5.20        = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5031_mult__mod__right,axiom,
% 9.25/5.20      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.20        ( ( times_3573771949741848930nteger @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 9.25/5.20        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5032_mult__mod__right,axiom,
% 9.25/5.20      ! [C: code_natural,A: code_natural,B: code_natural] :
% 9.25/5.20        ( ( times_2397367101498566445atural @ C @ ( modulo8411746178871703098atural @ A @ B ) )
% 9.25/5.20        = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5033_mod__mult__left__eq,axiom,
% 9.25/5.20      ! [A: nat,C: nat,B: nat] :
% 9.25/5.20        ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 9.25/5.20        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5034_mod__mult__left__eq,axiom,
% 9.25/5.20      ! [A: int,C: int,B: int] :
% 9.25/5.20        ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 9.25/5.20        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5035_mod__mult__left__eq,axiom,
% 9.25/5.20      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.25/5.20        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 9.25/5.20        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5036_mod__mult__left__eq,axiom,
% 9.25/5.20      ! [A: code_natural,C: code_natural,B: code_natural] :
% 9.25/5.20        ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ C ) @ B ) @ C )
% 9.25/5.20        = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5037_mod__mult__right__eq,axiom,
% 9.25/5.20      ! [A: nat,B: nat,C: nat] :
% 9.25/5.20        ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 9.25/5.20        = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5038_mod__mult__right__eq,axiom,
% 9.25/5.20      ! [A: int,B: int,C: int] :
% 9.25/5.20        ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 9.25/5.20        = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5039_mod__mult__right__eq,axiom,
% 9.25/5.20      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.20        ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 9.25/5.20        = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5040_mod__mult__right__eq,axiom,
% 9.25/5.20      ! [A: code_natural,B: code_natural,C: code_natural] :
% 9.25/5.20        ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ ( modulo8411746178871703098atural @ B @ C ) ) @ C )
% 9.25/5.20        = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5041_mod__minus__eq,axiom,
% 9.25/5.20      ! [A: int,B: int] :
% 9.25/5.20        ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 9.25/5.20        = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5042_mod__minus__eq,axiom,
% 9.25/5.20      ! [A: code_integer,B: code_integer] :
% 9.25/5.20        ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 9.25/5.20        = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5043_mod__minus__cong,axiom,
% 9.25/5.20      ! [A: int,B: int,A5: int] :
% 9.25/5.20        ( ( ( modulo_modulo_int @ A @ B )
% 9.25/5.20          = ( modulo_modulo_int @ A5 @ B ) )
% 9.25/5.20       => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 9.25/5.20          = ( modulo_modulo_int @ ( uminus_uminus_int @ A5 ) @ B ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5044_mod__minus__cong,axiom,
% 9.25/5.20      ! [A: code_integer,B: code_integer,A5: code_integer] :
% 9.25/5.20        ( ( ( modulo364778990260209775nteger @ A @ B )
% 9.25/5.20          = ( modulo364778990260209775nteger @ A5 @ B ) )
% 9.25/5.20       => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 9.25/5.20          = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A5 ) @ B ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5045_mod__minus__right,axiom,
% 9.25/5.20      ! [A: int,B: int] :
% 9.25/5.20        ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 9.25/5.20        = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5046_mod__minus__right,axiom,
% 9.25/5.20      ! [A: code_integer,B: code_integer] :
% 9.25/5.20        ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 9.25/5.20        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5047_split__cong,axiom,
% 9.25/5.20      ! [Q4: product_prod_nat_nat,F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,P4: product_prod_nat_nat] :
% 9.25/5.20        ( ! [X2: nat,Y2: nat] :
% 9.25/5.20            ( ( ( product_Pair_nat_nat @ X2 @ Y2 )
% 9.25/5.20              = Q4 )
% 9.25/5.20           => ( ( F2 @ X2 @ Y2 )
% 9.25/5.20              = ( G2 @ X2 @ Y2 ) ) )
% 9.25/5.20       => ( ( P4 = Q4 )
% 9.25/5.20         => ( ( produc27273713700761075at_nat @ F2 @ P4 )
% 9.25/5.20            = ( produc27273713700761075at_nat @ G2 @ Q4 ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5048_split__cong,axiom,
% 9.25/5.20      ! [Q4: product_prod_nat_nat,F2: nat > nat > product_prod_nat_nat > $o,G2: nat > nat > product_prod_nat_nat > $o,P4: product_prod_nat_nat] :
% 9.25/5.20        ( ! [X2: nat,Y2: nat] :
% 9.25/5.20            ( ( ( product_Pair_nat_nat @ X2 @ Y2 )
% 9.25/5.20              = Q4 )
% 9.25/5.20           => ( ( F2 @ X2 @ Y2 )
% 9.25/5.20              = ( G2 @ X2 @ Y2 ) ) )
% 9.25/5.20       => ( ( P4 = Q4 )
% 9.25/5.20         => ( ( produc8739625826339149834_nat_o @ F2 @ P4 )
% 9.25/5.20            = ( produc8739625826339149834_nat_o @ G2 @ Q4 ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5049_split__cong,axiom,
% 9.25/5.20      ! [Q4: product_prod_int_int,F2: int > int > product_prod_int_int,G2: int > int > product_prod_int_int,P4: product_prod_int_int] :
% 9.25/5.20        ( ! [X2: int,Y2: int] :
% 9.25/5.20            ( ( ( product_Pair_int_int @ X2 @ Y2 )
% 9.25/5.20              = Q4 )
% 9.25/5.20           => ( ( F2 @ X2 @ Y2 )
% 9.25/5.20              = ( G2 @ X2 @ Y2 ) ) )
% 9.25/5.20       => ( ( P4 = Q4 )
% 9.25/5.20         => ( ( produc4245557441103728435nt_int @ F2 @ P4 )
% 9.25/5.20            = ( produc4245557441103728435nt_int @ G2 @ Q4 ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5050_split__cong,axiom,
% 9.25/5.20      ! [Q4: product_prod_int_int,F2: int > int > $o,G2: int > int > $o,P4: product_prod_int_int] :
% 9.25/5.20        ( ! [X2: int,Y2: int] :
% 9.25/5.20            ( ( ( product_Pair_int_int @ X2 @ Y2 )
% 9.25/5.20              = Q4 )
% 9.25/5.20           => ( ( F2 @ X2 @ Y2 )
% 9.25/5.20              = ( G2 @ X2 @ Y2 ) ) )
% 9.25/5.20       => ( ( P4 = Q4 )
% 9.25/5.20         => ( ( produc4947309494688390418_int_o @ F2 @ P4 )
% 9.25/5.20            = ( produc4947309494688390418_int_o @ G2 @ Q4 ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5051_split__cong,axiom,
% 9.25/5.20      ! [Q4: product_prod_int_int,F2: int > int > int,G2: int > int > int,P4: product_prod_int_int] :
% 9.25/5.20        ( ! [X2: int,Y2: int] :
% 9.25/5.20            ( ( ( product_Pair_int_int @ X2 @ Y2 )
% 9.25/5.20              = Q4 )
% 9.25/5.20           => ( ( F2 @ X2 @ Y2 )
% 9.25/5.20              = ( G2 @ X2 @ Y2 ) ) )
% 9.25/5.20       => ( ( P4 = Q4 )
% 9.25/5.20         => ( ( produc8211389475949308722nt_int @ F2 @ P4 )
% 9.25/5.20            = ( produc8211389475949308722nt_int @ G2 @ Q4 ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5052_old_Oprod_Ocase,axiom,
% 9.25/5.20      ! [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X22: nat] :
% 9.25/5.20        ( ( produc27273713700761075at_nat @ F2 @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 9.25/5.20        = ( F2 @ X1 @ X22 ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5053_old_Oprod_Ocase,axiom,
% 9.25/5.20      ! [F2: nat > nat > product_prod_nat_nat > $o,X1: nat,X22: nat] :
% 9.25/5.20        ( ( produc8739625826339149834_nat_o @ F2 @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 9.25/5.20        = ( F2 @ X1 @ X22 ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5054_old_Oprod_Ocase,axiom,
% 9.25/5.20      ! [F2: int > int > product_prod_int_int,X1: int,X22: int] :
% 9.25/5.20        ( ( produc4245557441103728435nt_int @ F2 @ ( product_Pair_int_int @ X1 @ X22 ) )
% 9.25/5.20        = ( F2 @ X1 @ X22 ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5055_old_Oprod_Ocase,axiom,
% 9.25/5.20      ! [F2: int > int > $o,X1: int,X22: int] :
% 9.25/5.20        ( ( produc4947309494688390418_int_o @ F2 @ ( product_Pair_int_int @ X1 @ X22 ) )
% 9.25/5.20        = ( F2 @ X1 @ X22 ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5056_old_Oprod_Ocase,axiom,
% 9.25/5.20      ! [F2: int > int > int,X1: int,X22: int] :
% 9.25/5.20        ( ( produc8211389475949308722nt_int @ F2 @ ( product_Pair_int_int @ X1 @ X22 ) )
% 9.25/5.20        = ( F2 @ X1 @ X22 ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5057_case__prod__Pair__iden,axiom,
% 9.25/5.20      ! [P4: produc1908205239877642774nteger] :
% 9.25/5.20        ( ( produc6512950862096126219nteger @ produc8603105652947943368nteger @ P4 )
% 9.25/5.20        = P4 ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5058_case__prod__Pair__iden,axiom,
% 9.25/5.20      ! [P4: produc3925858234332021118et_nat] :
% 9.25/5.20        ( ( produc4058941399401191971et_nat @ produc5001842942810119800et_nat @ P4 )
% 9.25/5.20        = P4 ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5059_case__prod__Pair__iden,axiom,
% 9.25/5.20      ! [P4: produc2732055786443039994et_nat] :
% 9.25/5.20        ( ( produc2377985495875741467et_nat @ produc2245416461498447860et_nat @ P4 )
% 9.25/5.20        = P4 ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5060_case__prod__Pair__iden,axiom,
% 9.25/5.20      ! [P4: produc2285326912895808259nt_int] :
% 9.25/5.20        ( ( produc8492565224438309093nt_int @ produc5700946648718959541nt_int @ P4 )
% 9.25/5.20        = P4 ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5061_case__prod__Pair__iden,axiom,
% 9.25/5.20      ! [P4: produc7773217078559923341nt_int] :
% 9.25/5.20        ( ( produc5122537100556696953nt_int @ produc4305682042979456191nt_int @ P4 )
% 9.25/5.20        = P4 ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5062_case__prod__Pair__iden,axiom,
% 9.25/5.20      ! [P4: product_prod_int_int] :
% 9.25/5.20        ( ( produc4245557441103728435nt_int @ product_Pair_int_int @ P4 )
% 9.25/5.20        = P4 ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5063_case__prodE2,axiom,
% 9.25/5.20      ! [Q2: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,P: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Z: product_prod_nat_nat] :
% 9.25/5.20        ( ( Q2 @ ( produc27273713700761075at_nat @ P @ Z ) )
% 9.25/5.20       => ~ ! [X2: nat,Y2: nat] :
% 9.25/5.20              ( ( Z
% 9.25/5.20                = ( product_Pair_nat_nat @ X2 @ Y2 ) )
% 9.25/5.20             => ~ ( Q2 @ ( P @ X2 @ Y2 ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5064_case__prodE2,axiom,
% 9.25/5.20      ! [Q2: ( product_prod_nat_nat > $o ) > $o,P: nat > nat > product_prod_nat_nat > $o,Z: product_prod_nat_nat] :
% 9.25/5.20        ( ( Q2 @ ( produc8739625826339149834_nat_o @ P @ Z ) )
% 9.25/5.20       => ~ ! [X2: nat,Y2: nat] :
% 9.25/5.20              ( ( Z
% 9.25/5.20                = ( product_Pair_nat_nat @ X2 @ Y2 ) )
% 9.25/5.20             => ~ ( Q2 @ ( P @ X2 @ Y2 ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5065_case__prodE2,axiom,
% 9.25/5.20      ! [Q2: product_prod_int_int > $o,P: int > int > product_prod_int_int,Z: product_prod_int_int] :
% 9.25/5.20        ( ( Q2 @ ( produc4245557441103728435nt_int @ P @ Z ) )
% 9.25/5.20       => ~ ! [X2: int,Y2: int] :
% 9.25/5.20              ( ( Z
% 9.25/5.20                = ( product_Pair_int_int @ X2 @ Y2 ) )
% 9.25/5.20             => ~ ( Q2 @ ( P @ X2 @ Y2 ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5066_case__prodE2,axiom,
% 9.25/5.20      ! [Q2: $o > $o,P: int > int > $o,Z: product_prod_int_int] :
% 9.25/5.20        ( ( Q2 @ ( produc4947309494688390418_int_o @ P @ Z ) )
% 9.25/5.20       => ~ ! [X2: int,Y2: int] :
% 9.25/5.20              ( ( Z
% 9.25/5.20                = ( product_Pair_int_int @ X2 @ Y2 ) )
% 9.25/5.20             => ~ ( Q2 @ ( P @ X2 @ Y2 ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5067_case__prodE2,axiom,
% 9.25/5.20      ! [Q2: int > $o,P: int > int > int,Z: product_prod_int_int] :
% 9.25/5.20        ( ( Q2 @ ( produc8211389475949308722nt_int @ P @ Z ) )
% 9.25/5.20       => ~ ! [X2: int,Y2: int] :
% 9.25/5.20              ( ( Z
% 9.25/5.20                = ( product_Pair_int_int @ X2 @ Y2 ) )
% 9.25/5.20             => ~ ( Q2 @ ( P @ X2 @ Y2 ) ) ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5068_case__prod__eta,axiom,
% 9.25/5.20      ! [F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 9.25/5.20        ( ( produc27273713700761075at_nat
% 9.25/5.20          @ ^ [X3: nat,Y3: nat] : ( F2 @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 9.25/5.20        = F2 ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5069_case__prod__eta,axiom,
% 9.25/5.20      ! [F2: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 9.25/5.20        ( ( produc8739625826339149834_nat_o
% 9.25/5.20          @ ^ [X3: nat,Y3: nat] : ( F2 @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 9.25/5.20        = F2 ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5070_case__prod__eta,axiom,
% 9.25/5.20      ! [F2: product_prod_int_int > product_prod_int_int] :
% 9.25/5.20        ( ( produc4245557441103728435nt_int
% 9.25/5.20          @ ^ [X3: int,Y3: int] : ( F2 @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 9.25/5.20        = F2 ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5071_case__prod__eta,axiom,
% 9.25/5.20      ! [F2: product_prod_int_int > $o] :
% 9.25/5.20        ( ( produc4947309494688390418_int_o
% 9.25/5.20          @ ^ [X3: int,Y3: int] : ( F2 @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 9.25/5.20        = F2 ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5072_case__prod__eta,axiom,
% 9.25/5.20      ! [F2: product_prod_int_int > int] :
% 9.25/5.20        ( ( produc8211389475949308722nt_int
% 9.25/5.20          @ ^ [X3: int,Y3: int] : ( F2 @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 9.25/5.20        = F2 ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5073_cond__case__prod__eta,axiom,
% 9.25/5.20      ! [F2: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 9.25/5.20        ( ! [X2: nat,Y2: nat] :
% 9.25/5.20            ( ( F2 @ X2 @ Y2 )
% 9.25/5.20            = ( G2 @ ( product_Pair_nat_nat @ X2 @ Y2 ) ) )
% 9.25/5.20       => ( ( produc27273713700761075at_nat @ F2 )
% 9.25/5.20          = G2 ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5074_cond__case__prod__eta,axiom,
% 9.25/5.20      ! [F2: nat > nat > product_prod_nat_nat > $o,G2: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 9.25/5.20        ( ! [X2: nat,Y2: nat] :
% 9.25/5.20            ( ( F2 @ X2 @ Y2 )
% 9.25/5.20            = ( G2 @ ( product_Pair_nat_nat @ X2 @ Y2 ) ) )
% 9.25/5.20       => ( ( produc8739625826339149834_nat_o @ F2 )
% 9.25/5.20          = G2 ) ) ).
% 9.25/5.20  
% 9.25/5.20  thf(fact_5075_cond__case__prod__eta,axiom,
% 9.25/5.20      ! [F2: int > int > product_prod_int_int,G2: product_prod_int_int > product_prod_int_int] :
% 9.25/5.20        ( ! [X2: int,Y2: int] :
% 9.25/5.20            ( ( F2 @ X2 @ Y2 )
% 9.25/5.20            = ( G2 @ ( product_Pair_int_int @ X2 @ Y2 ) ) )
% 9.25/5.20       => ( ( produc4245557441103728435nt_int @ F2 )
% 9.25/5.21          = G2 ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5076_cond__case__prod__eta,axiom,
% 9.25/5.21      ! [F2: int > int > $o,G2: product_prod_int_int > $o] :
% 9.25/5.21        ( ! [X2: int,Y2: int] :
% 9.25/5.21            ( ( F2 @ X2 @ Y2 )
% 9.25/5.21            = ( G2 @ ( product_Pair_int_int @ X2 @ Y2 ) ) )
% 9.25/5.21       => ( ( produc4947309494688390418_int_o @ F2 )
% 9.25/5.21          = G2 ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5077_cond__case__prod__eta,axiom,
% 9.25/5.21      ! [F2: int > int > int,G2: product_prod_int_int > int] :
% 9.25/5.21        ( ! [X2: int,Y2: int] :
% 9.25/5.21            ( ( F2 @ X2 @ Y2 )
% 9.25/5.21            = ( G2 @ ( product_Pair_int_int @ X2 @ Y2 ) ) )
% 9.25/5.21       => ( ( produc8211389475949308722nt_int @ F2 )
% 9.25/5.21          = G2 ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5078_mod__eqE,axiom,
% 9.25/5.21      ! [A: int,C: int,B: int] :
% 9.25/5.21        ( ( ( modulo_modulo_int @ A @ C )
% 9.25/5.21          = ( modulo_modulo_int @ B @ C ) )
% 9.25/5.21       => ~ ! [D: int] :
% 9.25/5.21              ( B
% 9.25/5.21             != ( plus_plus_int @ A @ ( times_times_int @ C @ D ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5079_mod__eqE,axiom,
% 9.25/5.21      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.25/5.21        ( ( ( modulo364778990260209775nteger @ A @ C )
% 9.25/5.21          = ( modulo364778990260209775nteger @ B @ C ) )
% 9.25/5.21       => ~ ! [D: code_integer] :
% 9.25/5.21              ( B
% 9.25/5.21             != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5080_pos__zmod__mult__2,axiom,
% 9.25/5.21      ! [A: int,B: int] :
% 9.25/5.21        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.21       => ( ( 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 ) )
% 9.25/5.21          = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5081_neg__zmod__mult__2,axiom,
% 9.25/5.21      ! [A: int,B: int] :
% 9.25/5.21        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.25/5.21       => ( ( 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 ) )
% 9.25/5.21          = ( 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 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5082_divmod_H__nat__def,axiom,
% 9.25/5.21      ( unique5055182867167087721od_nat
% 9.25/5.21      = ( ^ [M2: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5083_divmod__step__int__def,axiom,
% 9.25/5.21      ( unique5024387138958732305ep_int
% 9.25/5.21      = ( ^ [L2: num] :
% 9.25/5.21            ( produc4245557441103728435nt_int
% 9.25/5.21            @ ^ [Q5: int,R4: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R4 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R4 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R4 ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5084_uncurry__def,axiom,
% 9.25/5.21      uncurr8011562610307062878at_nat = produc27273713700761075at_nat ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5085_uncurry__def,axiom,
% 9.25/5.21      uncurr7511940902602773877_nat_o = produc8739625826339149834_nat_o ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5086_uncurry__def,axiom,
% 9.25/5.21      uncurr7650761721940715016nt_int = produc4245557441103728435nt_int ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5087_uncurry__def,axiom,
% 9.25/5.21      uncurry_int_int_o = produc4947309494688390418_int_o ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5088_uncurry__def,axiom,
% 9.25/5.21      uncurry_int_int_int = produc8211389475949308722nt_int ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5089_xor_Ocomm__monoid__axioms,axiom,
% 9.25/5.21      comm_m1654649897431166824nteger @ bit_se3222712562003087583nteger @ zero_z3403309356797280102nteger ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5090_xor_Ocomm__monoid__axioms,axiom,
% 9.25/5.21      comm_monoid_int @ bit_se6526347334894502574or_int @ zero_zero_int ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5091_xor_Ocomm__monoid__axioms,axiom,
% 9.25/5.21      comm_monoid_nat @ bit_se6528837805403552850or_nat @ zero_zero_nat ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5092_xor_Omonoid__axioms,axiom,
% 9.25/5.21      monoid_Code_integer @ bit_se3222712562003087583nteger @ zero_z3403309356797280102nteger ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5093_xor_Omonoid__axioms,axiom,
% 9.25/5.21      monoid_int @ bit_se6526347334894502574or_int @ zero_zero_int ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5094_xor_Omonoid__axioms,axiom,
% 9.25/5.21      monoid_nat @ bit_se6528837805403552850or_nat @ zero_zero_nat ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5095_mult__div__mod__eq,axiom,
% 9.25/5.21      ! [B: nat,A: nat] :
% 9.25/5.21        ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5096_mult__div__mod__eq,axiom,
% 9.25/5.21      ! [B: int,A: int] :
% 9.25/5.21        ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5097_mult__div__mod__eq,axiom,
% 9.25/5.21      ! [B: code_integer,A: code_integer] :
% 9.25/5.21        ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5098_mult__div__mod__eq,axiom,
% 9.25/5.21      ! [B: code_natural,A: code_natural] :
% 9.25/5.21        ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5099_mod__mult__div__eq,axiom,
% 9.25/5.21      ! [A: nat,B: nat] :
% 9.25/5.21        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5100_mod__mult__div__eq,axiom,
% 9.25/5.21      ! [A: int,B: int] :
% 9.25/5.21        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5101_mod__mult__div__eq,axiom,
% 9.25/5.21      ! [A: code_integer,B: code_integer] :
% 9.25/5.21        ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5102_mod__mult__div__eq,axiom,
% 9.25/5.21      ! [A: code_natural,B: code_natural] :
% 9.25/5.21        ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5103_mod__div__mult__eq,axiom,
% 9.25/5.21      ! [A: nat,B: nat] :
% 9.25/5.21        ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5104_mod__div__mult__eq,axiom,
% 9.25/5.21      ! [A: int,B: int] :
% 9.25/5.21        ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5105_mod__div__mult__eq,axiom,
% 9.25/5.21      ! [A: code_integer,B: code_integer] :
% 9.25/5.21        ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5106_mod__div__mult__eq,axiom,
% 9.25/5.21      ! [A: code_natural,B: code_natural] :
% 9.25/5.21        ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5107_div__mult__mod__eq,axiom,
% 9.25/5.21      ! [A: nat,B: nat] :
% 9.25/5.21        ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5108_div__mult__mod__eq,axiom,
% 9.25/5.21      ! [A: int,B: int] :
% 9.25/5.21        ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5109_div__mult__mod__eq,axiom,
% 9.25/5.21      ! [A: code_integer,B: code_integer] :
% 9.25/5.21        ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5110_div__mult__mod__eq,axiom,
% 9.25/5.21      ! [A: code_natural,B: code_natural] :
% 9.25/5.21        ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5111_mod__div__decomp,axiom,
% 9.25/5.21      ! [A: nat,B: nat] :
% 9.25/5.21        ( A
% 9.25/5.21        = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5112_mod__div__decomp,axiom,
% 9.25/5.21      ! [A: int,B: int] :
% 9.25/5.21        ( A
% 9.25/5.21        = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5113_mod__div__decomp,axiom,
% 9.25/5.21      ! [A: code_integer,B: code_integer] :
% 9.25/5.21        ( A
% 9.25/5.21        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5114_mod__div__decomp,axiom,
% 9.25/5.21      ! [A: code_natural,B: code_natural] :
% 9.25/5.21        ( A
% 9.25/5.21        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5115_cancel__div__mod__rules_I1_J,axiom,
% 9.25/5.21      ! [A: nat,B: nat,C: nat] :
% 9.25/5.21        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 9.25/5.21        = ( plus_plus_nat @ A @ C ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5116_cancel__div__mod__rules_I1_J,axiom,
% 9.25/5.21      ! [A: int,B: int,C: int] :
% 9.25/5.21        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 9.25/5.21        = ( plus_plus_int @ A @ C ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5117_cancel__div__mod__rules_I1_J,axiom,
% 9.25/5.21      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.21        ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 9.25/5.21        = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5118_cancel__div__mod__rules_I1_J,axiom,
% 9.25/5.21      ! [A: code_natural,B: code_natural,C: code_natural] :
% 9.25/5.21        ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C )
% 9.25/5.21        = ( plus_p4538020629002901425atural @ A @ C ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5119_cancel__div__mod__rules_I2_J,axiom,
% 9.25/5.21      ! [B: nat,A: nat,C: nat] :
% 9.25/5.21        ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 9.25/5.21        = ( plus_plus_nat @ A @ C ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5120_cancel__div__mod__rules_I2_J,axiom,
% 9.25/5.21      ! [B: int,A: int,C: int] :
% 9.25/5.21        ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 9.25/5.21        = ( plus_plus_int @ A @ C ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5121_cancel__div__mod__rules_I2_J,axiom,
% 9.25/5.21      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.25/5.21        ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 9.25/5.21        = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5122_cancel__div__mod__rules_I2_J,axiom,
% 9.25/5.21      ! [B: code_natural,A: code_natural,C: code_natural] :
% 9.25/5.21        ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C )
% 9.25/5.21        = ( plus_p4538020629002901425atural @ A @ C ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5123_div__mult1__eq,axiom,
% 9.25/5.21      ! [A: nat,B: nat,C: nat] :
% 9.25/5.21        ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 9.25/5.21        = ( 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 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5124_div__mult1__eq,axiom,
% 9.25/5.21      ! [A: int,B: int,C: int] :
% 9.25/5.21        ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 9.25/5.21        = ( 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 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5125_div__mult1__eq,axiom,
% 9.25/5.21      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.21        ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 9.25/5.21        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5126_div__mult1__eq,axiom,
% 9.25/5.21      ! [A: code_natural,B: code_natural,C: code_natural] :
% 9.25/5.21        ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C )
% 9.25/5.21        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C ) ) @ ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ ( modulo8411746178871703098atural @ B @ C ) ) @ C ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5127_minus__mult__div__eq__mod,axiom,
% 9.25/5.21      ! [A: nat,B: nat] :
% 9.25/5.21        ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 9.25/5.21        = ( modulo_modulo_nat @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5128_minus__mult__div__eq__mod,axiom,
% 9.25/5.21      ! [A: int,B: int] :
% 9.25/5.21        ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 9.25/5.21        = ( modulo_modulo_int @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5129_minus__mult__div__eq__mod,axiom,
% 9.25/5.21      ! [A: code_integer,B: code_integer] :
% 9.25/5.21        ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 9.25/5.21        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5130_minus__mult__div__eq__mod,axiom,
% 9.25/5.21      ! [A: code_natural,B: code_natural] :
% 9.25/5.21        ( ( minus_7197305767214868737atural @ A @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) )
% 9.25/5.21        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5131_minus__mod__eq__mult__div,axiom,
% 9.25/5.21      ! [A: nat,B: nat] :
% 9.25/5.21        ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 9.25/5.21        = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5132_minus__mod__eq__mult__div,axiom,
% 9.25/5.21      ! [A: int,B: int] :
% 9.25/5.21        ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 9.25/5.21        = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5133_minus__mod__eq__mult__div,axiom,
% 9.25/5.21      ! [A: code_integer,B: code_integer] :
% 9.25/5.21        ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 9.25/5.21        = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5134_minus__mod__eq__mult__div,axiom,
% 9.25/5.21      ! [A: code_natural,B: code_natural] :
% 9.25/5.21        ( ( minus_7197305767214868737atural @ A @ ( modulo8411746178871703098atural @ A @ B ) )
% 9.25/5.21        = ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5135_minus__mod__eq__div__mult,axiom,
% 9.25/5.21      ! [A: nat,B: nat] :
% 9.25/5.21        ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 9.25/5.21        = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5136_minus__mod__eq__div__mult,axiom,
% 9.25/5.21      ! [A: int,B: int] :
% 9.25/5.21        ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 9.25/5.21        = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5137_minus__mod__eq__div__mult,axiom,
% 9.25/5.21      ! [A: code_integer,B: code_integer] :
% 9.25/5.21        ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 9.25/5.21        = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5138_minus__mod__eq__div__mult,axiom,
% 9.25/5.21      ! [A: code_natural,B: code_natural] :
% 9.25/5.21        ( ( minus_7197305767214868737atural @ A @ ( modulo8411746178871703098atural @ A @ B ) )
% 9.25/5.21        = ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5139_minus__div__mult__eq__mod,axiom,
% 9.25/5.21      ! [A: nat,B: nat] :
% 9.25/5.21        ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 9.25/5.21        = ( modulo_modulo_nat @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5140_minus__div__mult__eq__mod,axiom,
% 9.25/5.21      ! [A: int,B: int] :
% 9.25/5.21        ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 9.25/5.21        = ( modulo_modulo_int @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5141_minus__div__mult__eq__mod,axiom,
% 9.25/5.21      ! [A: code_integer,B: code_integer] :
% 9.25/5.21        ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 9.25/5.21        = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5142_minus__div__mult__eq__mod,axiom,
% 9.25/5.21      ! [A: code_natural,B: code_natural] :
% 9.25/5.21        ( ( minus_7197305767214868737atural @ A @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) )
% 9.25/5.21        = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5143_divmod__def,axiom,
% 9.25/5.21      ( unique5052692396658037445od_int
% 9.25/5.21      = ( ^ [M2: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5144_divmod__def,axiom,
% 9.25/5.21      ( unique5055182867167087721od_nat
% 9.25/5.21      = ( ^ [M2: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5145_divmod__def,axiom,
% 9.25/5.21      ( unique3479559517661332726nteger
% 9.25/5.21      = ( ^ [M2: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5146_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 9.25/5.21      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.21        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 9.25/5.21       => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.25/5.21          = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5147_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 9.25/5.21      ! [C: nat,A: nat,B: nat] :
% 9.25/5.21        ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 9.25/5.21       => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 9.25/5.21          = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5148_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 9.25/5.21      ! [C: int,A: int,B: int] :
% 9.25/5.21        ( ( ord_less_eq_int @ zero_zero_int @ C )
% 9.25/5.21       => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 9.25/5.21          = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5149_verit__le__mono__div,axiom,
% 9.25/5.21      ! [A2: nat,B2: nat,N: nat] :
% 9.25/5.21        ( ( ord_less_nat @ A2 @ B2 )
% 9.25/5.21       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.21         => ( ord_less_eq_nat
% 9.25/5.21            @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N )
% 9.25/5.21              @ ( if_nat
% 9.25/5.21                @ ( ( modulo_modulo_nat @ B2 @ N )
% 9.25/5.21                  = zero_zero_nat )
% 9.25/5.21                @ one_one_nat
% 9.25/5.21                @ zero_zero_nat ) )
% 9.25/5.21            @ ( divide_divide_nat @ B2 @ N ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5150_divmod__step__nat__def,axiom,
% 9.25/5.21      ( unique5026877609467782581ep_nat
% 9.25/5.21      = ( ^ [L2: num] :
% 9.25/5.21            ( produc2626176000494625587at_nat
% 9.25/5.21            @ ^ [Q5: nat,R4: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R4 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R4 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R4 ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5151_divmod__digit__0_I2_J,axiom,
% 9.25/5.21      ! [B: nat,A: nat] :
% 9.25/5.21        ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.25/5.21       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 9.25/5.21         => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 9.25/5.21            = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5152_divmod__digit__0_I2_J,axiom,
% 9.25/5.21      ! [B: int,A: int] :
% 9.25/5.21        ( ( ord_less_int @ zero_zero_int @ B )
% 9.25/5.21       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 9.25/5.21         => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 9.25/5.21            = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5153_divmod__digit__0_I2_J,axiom,
% 9.25/5.21      ! [B: code_integer,A: code_integer] :
% 9.25/5.21        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 9.25/5.21       => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 9.25/5.21         => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 9.25/5.21            = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5154_divmod__digit__0_I1_J,axiom,
% 9.25/5.21      ! [B: nat,A: nat] :
% 9.25/5.21        ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.25/5.21       => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 9.25/5.21         => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 9.25/5.21            = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5155_divmod__digit__0_I1_J,axiom,
% 9.25/5.21      ! [B: int,A: int] :
% 9.25/5.21        ( ( ord_less_int @ zero_zero_int @ B )
% 9.25/5.21       => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 9.25/5.21         => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 9.25/5.21            = ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5156_divmod__digit__0_I1_J,axiom,
% 9.25/5.21      ! [B: code_integer,A: code_integer] :
% 9.25/5.21        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 9.25/5.21       => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 9.25/5.21         => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 9.25/5.21            = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5157_mod__double__modulus,axiom,
% 9.25/5.21      ! [M: code_integer,X: code_integer] :
% 9.25/5.21        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 9.25/5.21       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 9.25/5.21         => ( ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 9.25/5.21              = ( modulo364778990260209775nteger @ X @ M ) )
% 9.25/5.21            | ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 9.25/5.21              = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X @ M ) @ M ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5158_mod__double__modulus,axiom,
% 9.25/5.21      ! [M: nat,X: nat] :
% 9.25/5.21        ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.25/5.21       => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 9.25/5.21         => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 9.25/5.21              = ( modulo_modulo_nat @ X @ M ) )
% 9.25/5.21            | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 9.25/5.21              = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M ) @ M ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5159_mod__double__modulus,axiom,
% 9.25/5.21      ! [M: int,X: int] :
% 9.25/5.21        ( ( ord_less_int @ zero_zero_int @ M )
% 9.25/5.21       => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.25/5.21         => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 9.25/5.21              = ( modulo_modulo_int @ X @ M ) )
% 9.25/5.21            | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 9.25/5.21              = ( plus_plus_int @ ( modulo_modulo_int @ X @ M ) @ M ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5160_divmod__digit__1_I2_J,axiom,
% 9.25/5.21      ! [A: code_integer,B: code_integer] :
% 9.25/5.21        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.21       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 9.25/5.21         => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 9.25/5.21           => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 9.25/5.21              = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5161_divmod__digit__1_I2_J,axiom,
% 9.25/5.21      ! [A: nat,B: nat] :
% 9.25/5.21        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.25/5.21       => ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.25/5.21         => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 9.25/5.21           => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 9.25/5.21              = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5162_divmod__digit__1_I2_J,axiom,
% 9.25/5.21      ! [A: int,B: int] :
% 9.25/5.21        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.21       => ( ( ord_less_int @ zero_zero_int @ B )
% 9.25/5.21         => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 9.25/5.21           => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 9.25/5.21              = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5163_zle__add1__eq__le,axiom,
% 9.25/5.21      ! [W: int,Z: int] :
% 9.25/5.21        ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 9.25/5.21        = ( ord_less_eq_int @ W @ Z ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5164_zle__diff1__eq,axiom,
% 9.25/5.21      ! [W: int,Z: int] :
% 9.25/5.21        ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 9.25/5.21        = ( ord_less_int @ W @ Z ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5165_one__div__minus__numeral,axiom,
% 9.25/5.21      ! [N: num] :
% 9.25/5.21        ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.21        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5166_minus__one__div__numeral,axiom,
% 9.25/5.21      ! [N: num] :
% 9.25/5.21        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 9.25/5.21        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5167_le__imp__0__less,axiom,
% 9.25/5.21      ! [Z: int] :
% 9.25/5.21        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 9.25/5.21       => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5168_signed__take__bit__rec,axiom,
% 9.25/5.21      ( bit_ri6519982836138164636nteger
% 9.25/5.21      = ( ^ [N2: nat,A3: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5169_signed__take__bit__rec,axiom,
% 9.25/5.21      ( bit_ri631733984087533419it_int
% 9.25/5.21      = ( ^ [N2: nat,A3: int] : ( if_int @ ( N2 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5170_numeral__div__minus__numeral,axiom,
% 9.25/5.21      ! [M: num,N: num] :
% 9.25/5.21        ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.21        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5171_minus__numeral__div__numeral,axiom,
% 9.25/5.21      ! [M: num,N: num] :
% 9.25/5.21        ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 9.25/5.21        = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5172_case__prodI2,axiom,
% 9.25/5.21      ! [P4: produc1908205239877642774nteger,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o] :
% 9.25/5.21        ( ! [A6: produc6241069584506657477e_term > option6357759511663192854e_term,B6: produc8923325533196201883nteger] :
% 9.25/5.21            ( ( P4
% 9.25/5.21              = ( produc8603105652947943368nteger @ A6 @ B6 ) )
% 9.25/5.21           => ( C @ A6 @ B6 ) )
% 9.25/5.21       => ( produc6253627499356882019eger_o @ C @ P4 ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5173_case__prodI2,axiom,
% 9.25/5.21      ! [P4: produc3925858234332021118et_nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 9.25/5.21        ( ! [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat] :
% 9.25/5.21            ( ( P4
% 9.25/5.21              = ( produc5001842942810119800et_nat @ A6 @ B6 ) )
% 9.25/5.21           => ( C @ A6 @ B6 ) )
% 9.25/5.21       => ( produc1437786849005270451_nat_o @ C @ P4 ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5174_case__prodI2,axiom,
% 9.25/5.21      ! [P4: produc2732055786443039994et_nat,C: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 9.25/5.21        ( ! [A6: produc3658429121746597890et_nat > $o,B6: produc3925858234332021118et_nat] :
% 9.25/5.21            ( ( P4
% 9.25/5.21              = ( produc2245416461498447860et_nat @ A6 @ B6 ) )
% 9.25/5.21           => ( C @ A6 @ B6 ) )
% 9.25/5.21       => ( produc838355143741117751_nat_o @ C @ P4 ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5175_case__prodI2,axiom,
% 9.25/5.21      ! [P4: produc2285326912895808259nt_int,C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 9.25/5.21        ( ! [A6: produc8551481072490612790e_term > option6357759511663192854e_term,B6: product_prod_int_int] :
% 9.25/5.21            ( ( P4
% 9.25/5.21              = ( produc5700946648718959541nt_int @ A6 @ B6 ) )
% 9.25/5.21           => ( C @ A6 @ B6 ) )
% 9.25/5.21       => ( produc1573362020775583542_int_o @ C @ P4 ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5176_case__prodI2,axiom,
% 9.25/5.21      ! [P4: produc7773217078559923341nt_int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 9.25/5.21        ( ! [A6: int > option6357759511663192854e_term,B6: product_prod_int_int] :
% 9.25/5.21            ( ( P4
% 9.25/5.21              = ( produc4305682042979456191nt_int @ A6 @ B6 ) )
% 9.25/5.21           => ( C @ A6 @ B6 ) )
% 9.25/5.21       => ( produc2558449545302689196_int_o @ C @ P4 ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5177_case__prodI2,axiom,
% 9.25/5.21      ! [P4: product_prod_int_int,C: int > int > $o] :
% 9.25/5.21        ( ! [A6: int,B6: int] :
% 9.25/5.21            ( ( P4
% 9.25/5.21              = ( product_Pair_int_int @ A6 @ B6 ) )
% 9.25/5.21           => ( C @ A6 @ B6 ) )
% 9.25/5.21       => ( produc4947309494688390418_int_o @ C @ P4 ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5178_case__prodI,axiom,
% 9.25/5.21      ! [F2: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 9.25/5.21        ( ( F2 @ A @ B )
% 9.25/5.21       => ( produc6253627499356882019eger_o @ F2 @ ( produc8603105652947943368nteger @ A @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5179_case__prodI,axiom,
% 9.25/5.21      ! [F2: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 9.25/5.21        ( ( F2 @ A @ B )
% 9.25/5.21       => ( produc1437786849005270451_nat_o @ F2 @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5180_case__prodI,axiom,
% 9.25/5.21      ! [F2: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 9.25/5.21        ( ( F2 @ A @ B )
% 9.25/5.21       => ( produc838355143741117751_nat_o @ F2 @ ( produc2245416461498447860et_nat @ A @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5181_case__prodI,axiom,
% 9.25/5.21      ! [F2: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.25/5.21        ( ( F2 @ A @ B )
% 9.25/5.21       => ( produc1573362020775583542_int_o @ F2 @ ( produc5700946648718959541nt_int @ A @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5182_case__prodI,axiom,
% 9.25/5.21      ! [F2: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.25/5.21        ( ( F2 @ A @ B )
% 9.25/5.21       => ( produc2558449545302689196_int_o @ F2 @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5183_case__prodI,axiom,
% 9.25/5.21      ! [F2: int > int > $o,A: int,B: int] :
% 9.25/5.21        ( ( F2 @ A @ B )
% 9.25/5.21       => ( produc4947309494688390418_int_o @ F2 @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5184_mem__case__prodI2,axiom,
% 9.25/5.21      ! [P4: produc7773217078559923341nt_int,Z: nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat] :
% 9.25/5.21        ( ! [A6: int > option6357759511663192854e_term,B6: product_prod_int_int] :
% 9.25/5.21            ( ( P4
% 9.25/5.21              = ( produc4305682042979456191nt_int @ A6 @ B6 ) )
% 9.25/5.21           => ( member_nat @ Z @ ( C @ A6 @ B6 ) ) )
% 9.25/5.21       => ( member_nat @ Z @ ( produc8289552606927098482et_nat @ C @ P4 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5185_mem__case__prodI2,axiom,
% 9.25/5.21      ! [P4: produc7773217078559923341nt_int,Z: int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_int] :
% 9.25/5.21        ( ! [A6: int > option6357759511663192854e_term,B6: product_prod_int_int] :
% 9.25/5.21            ( ( P4
% 9.25/5.21              = ( produc4305682042979456191nt_int @ A6 @ B6 ) )
% 9.25/5.21           => ( member_int @ Z @ ( C @ A6 @ B6 ) ) )
% 9.25/5.21       => ( member_int @ Z @ ( produc4111701587417901774et_int @ C @ P4 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5186_mem__case__prodI2,axiom,
% 9.25/5.21      ! [P4: produc7773217078559923341nt_int,Z: set_nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_set_nat] :
% 9.25/5.21        ( ! [A6: int > option6357759511663192854e_term,B6: product_prod_int_int] :
% 9.25/5.21            ( ( P4
% 9.25/5.21              = ( produc4305682042979456191nt_int @ A6 @ B6 ) )
% 9.25/5.21           => ( member_set_nat @ Z @ ( C @ A6 @ B6 ) ) )
% 9.25/5.21       => ( member_set_nat @ Z @ ( produc3577156405726439208et_nat @ C @ P4 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5187_mem__case__prodI2,axiom,
% 9.25/5.21      ! [P4: produc3925858234332021118et_nat,Z: nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_nat] :
% 9.25/5.21        ( ! [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat] :
% 9.25/5.21            ( ( P4
% 9.25/5.21              = ( produc5001842942810119800et_nat @ A6 @ B6 ) )
% 9.25/5.21           => ( member_nat @ Z @ ( C @ A6 @ B6 ) ) )
% 9.25/5.21       => ( member_nat @ Z @ ( produc8805491454895738411et_nat @ C @ P4 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5188_mem__case__prodI2,axiom,
% 9.25/5.21      ! [P4: produc3925858234332021118et_nat,Z: int,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_int] :
% 9.25/5.21        ( ! [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat] :
% 9.25/5.21            ( ( P4
% 9.25/5.21              = ( produc5001842942810119800et_nat @ A6 @ B6 ) )
% 9.25/5.21           => ( member_int @ Z @ ( C @ A6 @ B6 ) ) )
% 9.25/5.21       => ( member_int @ Z @ ( produc4627640435386541703et_int @ C @ P4 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5189_mem__case__prodI2,axiom,
% 9.25/5.21      ! [P4: produc3925858234332021118et_nat,Z: set_nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_set_nat] :
% 9.25/5.21        ( ! [A6: produc3658429121746597890et_nat > $o,B6: produc3658429121746597890et_nat] :
% 9.25/5.21            ( ( P4
% 9.25/5.21              = ( produc5001842942810119800et_nat @ A6 @ B6 ) )
% 9.25/5.21           => ( member_set_nat @ Z @ ( C @ A6 @ B6 ) ) )
% 9.25/5.21       => ( member_set_nat @ Z @ ( produc2333231157791014625et_nat @ C @ P4 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5190_mem__case__prodI2,axiom,
% 9.25/5.21      ! [P4: produc7773217078559923341nt_int,Z: set_Pr958786334691620121nt_int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_se6260736226359567993nt_int] :
% 9.25/5.21        ( ! [A6: int > option6357759511663192854e_term,B6: product_prod_int_int] :
% 9.25/5.21            ( ( P4
% 9.25/5.21              = ( produc4305682042979456191nt_int @ A6 @ B6 ) )
% 9.25/5.21           => ( member2340774599025711042nt_int @ Z @ ( C @ A6 @ B6 ) ) )
% 9.25/5.21       => ( member2340774599025711042nt_int @ Z @ ( produc575502675617541261nt_int @ C @ P4 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5191_mem__case__prodI2,axiom,
% 9.25/5.21      ! [P4: produc1908205239877642774nteger,Z: nat,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat] :
% 9.25/5.21        ( ! [A6: produc6241069584506657477e_term > option6357759511663192854e_term,B6: produc8923325533196201883nteger] :
% 9.25/5.21            ( ( P4
% 9.25/5.21              = ( produc8603105652947943368nteger @ A6 @ B6 ) )
% 9.25/5.21           => ( member_nat @ Z @ ( C @ A6 @ B6 ) ) )
% 9.25/5.21       => ( member_nat @ Z @ ( produc654622801845291899et_nat @ C @ P4 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5192_mem__case__prodI2,axiom,
% 9.25/5.21      ! [P4: produc1908205239877642774nteger,Z: int,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int] :
% 9.25/5.21        ( ! [A6: produc6241069584506657477e_term > option6357759511663192854e_term,B6: produc8923325533196201883nteger] :
% 9.25/5.21            ( ( P4
% 9.25/5.21              = ( produc8603105652947943368nteger @ A6 @ B6 ) )
% 9.25/5.21           => ( member_int @ Z @ ( C @ A6 @ B6 ) ) )
% 9.25/5.21       => ( member_int @ Z @ ( produc5700143819190870999et_int @ C @ P4 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5193_mem__case__prodI2,axiom,
% 9.25/5.21      ! [P4: produc2285326912895808259nt_int,Z: nat,C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > set_nat] :
% 9.25/5.21        ( ! [A6: produc8551481072490612790e_term > option6357759511663192854e_term,B6: product_prod_int_int] :
% 9.25/5.21            ( ( P4
% 9.25/5.21              = ( produc5700946648718959541nt_int @ A6 @ B6 ) )
% 9.25/5.21           => ( member_nat @ Z @ ( C @ A6 @ B6 ) ) )
% 9.25/5.21       => ( member_nat @ Z @ ( produc3619988815162578792et_nat @ C @ P4 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5194_mem__case__prodI,axiom,
% 9.25/5.21      ! [Z: nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.25/5.21        ( ( member_nat @ Z @ ( C @ A @ B ) )
% 9.25/5.21       => ( member_nat @ Z @ ( produc8289552606927098482et_nat @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5195_mem__case__prodI,axiom,
% 9.25/5.21      ! [Z: int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_int,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.25/5.21        ( ( member_int @ Z @ ( C @ A @ B ) )
% 9.25/5.21       => ( member_int @ Z @ ( produc4111701587417901774et_int @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5196_mem__case__prodI,axiom,
% 9.25/5.21      ! [Z: set_nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_set_nat,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.25/5.21        ( ( member_set_nat @ Z @ ( C @ A @ B ) )
% 9.25/5.21       => ( member_set_nat @ Z @ ( produc3577156405726439208et_nat @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5197_mem__case__prodI,axiom,
% 9.25/5.21      ! [Z: nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_nat,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 9.25/5.21        ( ( member_nat @ Z @ ( C @ A @ B ) )
% 9.25/5.21       => ( member_nat @ Z @ ( produc8805491454895738411et_nat @ C @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5198_mem__case__prodI,axiom,
% 9.25/5.21      ! [Z: int,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_int,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 9.25/5.21        ( ( member_int @ Z @ ( C @ A @ B ) )
% 9.25/5.21       => ( member_int @ Z @ ( produc4627640435386541703et_int @ C @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5199_mem__case__prodI,axiom,
% 9.25/5.21      ! [Z: set_nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_set_nat,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 9.25/5.21        ( ( member_set_nat @ Z @ ( C @ A @ B ) )
% 9.25/5.21       => ( member_set_nat @ Z @ ( produc2333231157791014625et_nat @ C @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5200_mem__case__prodI,axiom,
% 9.25/5.21      ! [Z: set_Pr958786334691620121nt_int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_se6260736226359567993nt_int,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.25/5.21        ( ( member2340774599025711042nt_int @ Z @ ( C @ A @ B ) )
% 9.25/5.21       => ( member2340774599025711042nt_int @ Z @ ( produc575502675617541261nt_int @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5201_mem__case__prodI,axiom,
% 9.25/5.21      ! [Z: nat,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 9.25/5.21        ( ( member_nat @ Z @ ( C @ A @ B ) )
% 9.25/5.21       => ( member_nat @ Z @ ( produc654622801845291899et_nat @ C @ ( produc8603105652947943368nteger @ A @ B ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5202_mem__case__prodI,axiom,
% 9.25/5.21      ! [Z: int,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 9.25/5.21        ( ( member_int @ Z @ ( C @ A @ B ) )
% 9.25/5.21       => ( member_int @ Z @ ( produc5700143819190870999et_int @ C @ ( produc8603105652947943368nteger @ A @ B ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5203_mem__case__prodI,axiom,
% 9.25/5.21      ! [Z: nat,C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > set_nat,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.25/5.21        ( ( member_nat @ Z @ ( C @ A @ B ) )
% 9.25/5.21       => ( member_nat @ Z @ ( produc3619988815162578792et_nat @ C @ ( produc5700946648718959541nt_int @ A @ B ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5204_case__prodI2_H,axiom,
% 9.25/5.21      ! [P4: product_prod_nat_nat,C: nat > nat > product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 9.25/5.21        ( ! [A6: nat,B6: nat] :
% 9.25/5.21            ( ( ( product_Pair_nat_nat @ A6 @ B6 )
% 9.25/5.21              = P4 )
% 9.25/5.21           => ( C @ A6 @ B6 @ X ) )
% 9.25/5.21       => ( produc8739625826339149834_nat_o @ C @ P4 @ X ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5205_Collect__const__case__prod,axiom,
% 9.25/5.21      ! [P: $o] :
% 9.25/5.21        ( ( P
% 9.25/5.21         => ( ( collec3392354462482085612at_nat
% 9.25/5.21              @ ( produc6081775807080527818_nat_o
% 9.25/5.21                @ ^ [A3: nat,B3: nat] : P ) )
% 9.25/5.21            = top_to4669805908274784177at_nat ) )
% 9.25/5.21        & ( ~ P
% 9.25/5.21         => ( ( collec3392354462482085612at_nat
% 9.25/5.21              @ ( produc6081775807080527818_nat_o
% 9.25/5.21                @ ^ [A3: nat,B3: nat] : P ) )
% 9.25/5.21            = bot_bo2099793752762293965at_nat ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5206_Collect__const__case__prod,axiom,
% 9.25/5.21      ! [P: $o] :
% 9.25/5.21        ( ( P
% 9.25/5.21         => ( ( collec213857154873943460nt_int
% 9.25/5.21              @ ( produc4947309494688390418_int_o
% 9.25/5.21                @ ^ [A3: int,B3: int] : P ) )
% 9.25/5.21            = top_to4366644338036079209nt_int ) )
% 9.25/5.21        & ( ~ P
% 9.25/5.21         => ( ( collec213857154873943460nt_int
% 9.25/5.21              @ ( produc4947309494688390418_int_o
% 9.25/5.21                @ ^ [A3: int,B3: int] : P ) )
% 9.25/5.21            = bot_bo1796632182523588997nt_int ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5207_signed__take__bit__of__minus__1,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( bit_ri6519982836138164636nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.21        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5208_signed__take__bit__of__minus__1,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.21        = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5209_signed__take__bit__numeral__of__1,axiom,
% 9.25/5.21      ! [K: num] :
% 9.25/5.21        ( ( bit_ri6519982836138164636nteger @ ( numeral_numeral_nat @ K ) @ one_one_Code_integer )
% 9.25/5.21        = one_one_Code_integer ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5210_signed__take__bit__numeral__of__1,axiom,
% 9.25/5.21      ! [K: num] :
% 9.25/5.21        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 9.25/5.21        = one_one_int ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5211_signed__take__bit__0,axiom,
% 9.25/5.21      ! [A: code_integer] :
% 9.25/5.21        ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 9.25/5.21        = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5212_signed__take__bit__0,axiom,
% 9.25/5.21      ! [A: int] :
% 9.25/5.21        ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 9.25/5.21        = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5213_mem__case__prodE,axiom,
% 9.25/5.21      ! [Z: nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat,P4: produc7773217078559923341nt_int] :
% 9.25/5.21        ( ( member_nat @ Z @ ( produc8289552606927098482et_nat @ C @ P4 ) )
% 9.25/5.21       => ~ ! [X2: int > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 9.25/5.21              ( ( P4
% 9.25/5.21                = ( produc4305682042979456191nt_int @ X2 @ Y2 ) )
% 9.25/5.21             => ~ ( member_nat @ Z @ ( C @ X2 @ Y2 ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5214_mem__case__prodE,axiom,
% 9.25/5.21      ! [Z: int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_int,P4: produc7773217078559923341nt_int] :
% 9.25/5.21        ( ( member_int @ Z @ ( produc4111701587417901774et_int @ C @ P4 ) )
% 9.25/5.21       => ~ ! [X2: int > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 9.25/5.21              ( ( P4
% 9.25/5.21                = ( produc4305682042979456191nt_int @ X2 @ Y2 ) )
% 9.25/5.21             => ~ ( member_int @ Z @ ( C @ X2 @ Y2 ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5215_mem__case__prodE,axiom,
% 9.25/5.21      ! [Z: set_nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_set_nat,P4: produc7773217078559923341nt_int] :
% 9.25/5.21        ( ( member_set_nat @ Z @ ( produc3577156405726439208et_nat @ C @ P4 ) )
% 9.25/5.21       => ~ ! [X2: int > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 9.25/5.21              ( ( P4
% 9.25/5.21                = ( produc4305682042979456191nt_int @ X2 @ Y2 ) )
% 9.25/5.21             => ~ ( member_set_nat @ Z @ ( C @ X2 @ Y2 ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5216_mem__case__prodE,axiom,
% 9.25/5.21      ! [Z: nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_nat,P4: produc3925858234332021118et_nat] :
% 9.25/5.21        ( ( member_nat @ Z @ ( produc8805491454895738411et_nat @ C @ P4 ) )
% 9.25/5.21       => ~ ! [X2: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 9.25/5.21              ( ( P4
% 9.25/5.21                = ( produc5001842942810119800et_nat @ X2 @ Y2 ) )
% 9.25/5.21             => ~ ( member_nat @ Z @ ( C @ X2 @ Y2 ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5217_mem__case__prodE,axiom,
% 9.25/5.21      ! [Z: int,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_int,P4: produc3925858234332021118et_nat] :
% 9.25/5.21        ( ( member_int @ Z @ ( produc4627640435386541703et_int @ C @ P4 ) )
% 9.25/5.21       => ~ ! [X2: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 9.25/5.21              ( ( P4
% 9.25/5.21                = ( produc5001842942810119800et_nat @ X2 @ Y2 ) )
% 9.25/5.21             => ~ ( member_int @ Z @ ( C @ X2 @ Y2 ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5218_mem__case__prodE,axiom,
% 9.25/5.21      ! [Z: set_nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_set_nat,P4: produc3925858234332021118et_nat] :
% 9.25/5.21        ( ( member_set_nat @ Z @ ( produc2333231157791014625et_nat @ C @ P4 ) )
% 9.25/5.21       => ~ ! [X2: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 9.25/5.21              ( ( P4
% 9.25/5.21                = ( produc5001842942810119800et_nat @ X2 @ Y2 ) )
% 9.25/5.21             => ~ ( member_set_nat @ Z @ ( C @ X2 @ Y2 ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5219_mem__case__prodE,axiom,
% 9.25/5.21      ! [Z: set_Pr958786334691620121nt_int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_se6260736226359567993nt_int,P4: produc7773217078559923341nt_int] :
% 9.25/5.21        ( ( member2340774599025711042nt_int @ Z @ ( produc575502675617541261nt_int @ C @ P4 ) )
% 9.25/5.21       => ~ ! [X2: int > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 9.25/5.21              ( ( P4
% 9.25/5.21                = ( produc4305682042979456191nt_int @ X2 @ Y2 ) )
% 9.25/5.21             => ~ ( member2340774599025711042nt_int @ Z @ ( C @ X2 @ Y2 ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5220_mem__case__prodE,axiom,
% 9.25/5.21      ! [Z: nat,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat,P4: produc1908205239877642774nteger] :
% 9.25/5.21        ( ( member_nat @ Z @ ( produc654622801845291899et_nat @ C @ P4 ) )
% 9.25/5.21       => ~ ! [X2: produc6241069584506657477e_term > option6357759511663192854e_term,Y2: produc8923325533196201883nteger] :
% 9.25/5.21              ( ( P4
% 9.25/5.21                = ( produc8603105652947943368nteger @ X2 @ Y2 ) )
% 9.25/5.21             => ~ ( member_nat @ Z @ ( C @ X2 @ Y2 ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5221_mem__case__prodE,axiom,
% 9.25/5.21      ! [Z: int,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int,P4: produc1908205239877642774nteger] :
% 9.25/5.21        ( ( member_int @ Z @ ( produc5700143819190870999et_int @ C @ P4 ) )
% 9.25/5.21       => ~ ! [X2: produc6241069584506657477e_term > option6357759511663192854e_term,Y2: produc8923325533196201883nteger] :
% 9.25/5.21              ( ( P4
% 9.25/5.21                = ( produc8603105652947943368nteger @ X2 @ Y2 ) )
% 9.25/5.21             => ~ ( member_int @ Z @ ( C @ X2 @ Y2 ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5222_mem__case__prodE,axiom,
% 9.25/5.21      ! [Z: nat,C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > set_nat,P4: produc2285326912895808259nt_int] :
% 9.25/5.21        ( ( member_nat @ Z @ ( produc3619988815162578792et_nat @ C @ P4 ) )
% 9.25/5.21       => ~ ! [X2: produc8551481072490612790e_term > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 9.25/5.21              ( ( P4
% 9.25/5.21                = ( produc5700946648718959541nt_int @ X2 @ Y2 ) )
% 9.25/5.21             => ~ ( member_nat @ Z @ ( C @ X2 @ Y2 ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5223_signed__take__bit__minus,axiom,
% 9.25/5.21      ! [N: nat,K: int] :
% 9.25/5.21        ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N @ K ) ) )
% 9.25/5.21        = ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5224_case__prodE,axiom,
% 9.25/5.21      ! [C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,P4: produc1908205239877642774nteger] :
% 9.25/5.21        ( ( produc6253627499356882019eger_o @ C @ P4 )
% 9.25/5.21       => ~ ! [X2: produc6241069584506657477e_term > option6357759511663192854e_term,Y2: produc8923325533196201883nteger] :
% 9.25/5.21              ( ( P4
% 9.25/5.21                = ( produc8603105652947943368nteger @ X2 @ Y2 ) )
% 9.25/5.21             => ~ ( C @ X2 @ Y2 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5225_case__prodE,axiom,
% 9.25/5.21      ! [C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,P4: produc3925858234332021118et_nat] :
% 9.25/5.21        ( ( produc1437786849005270451_nat_o @ C @ P4 )
% 9.25/5.21       => ~ ! [X2: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 9.25/5.21              ( ( P4
% 9.25/5.21                = ( produc5001842942810119800et_nat @ X2 @ Y2 ) )
% 9.25/5.21             => ~ ( C @ X2 @ Y2 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5226_case__prodE,axiom,
% 9.25/5.21      ! [C: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o,P4: produc2732055786443039994et_nat] :
% 9.25/5.21        ( ( produc838355143741117751_nat_o @ C @ P4 )
% 9.25/5.21       => ~ ! [X2: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat] :
% 9.25/5.21              ( ( P4
% 9.25/5.21                = ( produc2245416461498447860et_nat @ X2 @ Y2 ) )
% 9.25/5.21             => ~ ( C @ X2 @ Y2 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5227_case__prodE,axiom,
% 9.25/5.21      ! [C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,P4: produc2285326912895808259nt_int] :
% 9.25/5.21        ( ( produc1573362020775583542_int_o @ C @ P4 )
% 9.25/5.21       => ~ ! [X2: produc8551481072490612790e_term > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 9.25/5.21              ( ( P4
% 9.25/5.21                = ( produc5700946648718959541nt_int @ X2 @ Y2 ) )
% 9.25/5.21             => ~ ( C @ X2 @ Y2 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5228_case__prodE,axiom,
% 9.25/5.21      ! [C: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,P4: produc7773217078559923341nt_int] :
% 9.25/5.21        ( ( produc2558449545302689196_int_o @ C @ P4 )
% 9.25/5.21       => ~ ! [X2: int > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 9.25/5.21              ( ( P4
% 9.25/5.21                = ( produc4305682042979456191nt_int @ X2 @ Y2 ) )
% 9.25/5.21             => ~ ( C @ X2 @ Y2 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5229_case__prodE,axiom,
% 9.25/5.21      ! [C: int > int > $o,P4: product_prod_int_int] :
% 9.25/5.21        ( ( produc4947309494688390418_int_o @ C @ P4 )
% 9.25/5.21       => ~ ! [X2: int,Y2: int] :
% 9.25/5.21              ( ( P4
% 9.25/5.21                = ( product_Pair_int_int @ X2 @ Y2 ) )
% 9.25/5.21             => ~ ( C @ X2 @ Y2 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5230_case__prodD,axiom,
% 9.25/5.21      ! [F2: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 9.25/5.21        ( ( produc6253627499356882019eger_o @ F2 @ ( produc8603105652947943368nteger @ A @ B ) )
% 9.25/5.21       => ( F2 @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5231_case__prodD,axiom,
% 9.25/5.21      ! [F2: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 9.25/5.21        ( ( produc1437786849005270451_nat_o @ F2 @ ( produc5001842942810119800et_nat @ A @ B ) )
% 9.25/5.21       => ( F2 @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5232_case__prodD,axiom,
% 9.25/5.21      ! [F2: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 9.25/5.21        ( ( produc838355143741117751_nat_o @ F2 @ ( produc2245416461498447860et_nat @ A @ B ) )
% 9.25/5.21       => ( F2 @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5233_case__prodD,axiom,
% 9.25/5.21      ! [F2: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.25/5.21        ( ( produc1573362020775583542_int_o @ F2 @ ( produc5700946648718959541nt_int @ A @ B ) )
% 9.25/5.21       => ( F2 @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5234_case__prodD,axiom,
% 9.25/5.21      ! [F2: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 9.25/5.21        ( ( produc2558449545302689196_int_o @ F2 @ ( produc4305682042979456191nt_int @ A @ B ) )
% 9.25/5.21       => ( F2 @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5235_case__prodD,axiom,
% 9.25/5.21      ! [F2: int > int > $o,A: int,B: int] :
% 9.25/5.21        ( ( produc4947309494688390418_int_o @ F2 @ ( product_Pair_int_int @ A @ B ) )
% 9.25/5.21       => ( F2 @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5236_case__prodE_H,axiom,
% 9.25/5.21      ! [C: nat > nat > product_prod_nat_nat > $o,P4: product_prod_nat_nat,Z: product_prod_nat_nat] :
% 9.25/5.21        ( ( produc8739625826339149834_nat_o @ C @ P4 @ Z )
% 9.25/5.21       => ~ ! [X2: nat,Y2: nat] :
% 9.25/5.21              ( ( P4
% 9.25/5.21                = ( product_Pair_nat_nat @ X2 @ Y2 ) )
% 9.25/5.21             => ~ ( C @ X2 @ Y2 @ Z ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5237_case__prodD_H,axiom,
% 9.25/5.21      ! [R: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C: product_prod_nat_nat] :
% 9.25/5.21        ( ( produc8739625826339149834_nat_o @ R @ ( product_Pair_nat_nat @ A @ B ) @ C )
% 9.25/5.21       => ( R @ A @ B @ C ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5238_Id__on__def_H,axiom,
% 9.25/5.21      ! [A2: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.21        ( ( id_on_6410342593070439734nt_int @ ( collec5210948495886036740nt_int @ A2 ) )
% 9.25/5.21        = ( collec2889756465124990930nt_int
% 9.25/5.21          @ ( produc1547782455048856492_int_o
% 9.25/5.21            @ ^ [X3: set_Pr958786334691620121nt_int,Y3: set_Pr958786334691620121nt_int] :
% 9.25/5.21                ( ( X3 = Y3 )
% 9.25/5.21                & ( A2 @ X3 ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5239_Id__on__def_H,axiom,
% 9.25/5.21      ! [A2: set_nat > $o] :
% 9.25/5.21        ( ( id_on_set_nat @ ( collect_set_nat @ A2 ) )
% 9.25/5.21        = ( collec6662362479098859352et_nat
% 9.25/5.21          @ ( produc6247414631856714078_nat_o
% 9.25/5.21            @ ^ [X3: set_nat,Y3: set_nat] :
% 9.25/5.21                ( ( X3 = Y3 )
% 9.25/5.21                & ( A2 @ X3 ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5240_Id__on__def_H,axiom,
% 9.25/5.21      ! [A2: nat > $o] :
% 9.25/5.21        ( ( id_on_nat @ ( collect_nat @ A2 ) )
% 9.25/5.21        = ( collec3392354462482085612at_nat
% 9.25/5.21          @ ( produc6081775807080527818_nat_o
% 9.25/5.21            @ ^ [X3: nat,Y3: nat] :
% 9.25/5.21                ( ( X3 = Y3 )
% 9.25/5.21                & ( A2 @ X3 ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5241_Id__on__def_H,axiom,
% 9.25/5.21      ! [A2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.21        ( ( id_on_7438695062414216554_nat_o @ ( collec939566748876313656_nat_o @ A2 ) )
% 9.25/5.21        = ( collec7086185654880424402_nat_o
% 9.25/5.21          @ ( produc5150382289251079596at_o_o
% 9.25/5.21            @ ^ [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat > $o] :
% 9.25/5.21                ( ( X3 = Y3 )
% 9.25/5.21                & ( A2 @ X3 ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5242_Id__on__def_H,axiom,
% 9.25/5.21      ! [A2: int > $o] :
% 9.25/5.21        ( ( id_on_int @ ( collect_int @ A2 ) )
% 9.25/5.21        = ( collec213857154873943460nt_int
% 9.25/5.21          @ ( produc4947309494688390418_int_o
% 9.25/5.21            @ ^ [X3: int,Y3: int] :
% 9.25/5.21                ( ( X3 = Y3 )
% 9.25/5.21                & ( A2 @ X3 ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5243_rel__restrict__def,axiom,
% 9.25/5.21      ( rel_re4349003428253852667nt_int
% 9.25/5.21      = ( ^ [R2: set_Pr8057934254988874055nt_int,A4: set_se6260736226359567993nt_int] :
% 9.25/5.21            ( collec2889756465124990930nt_int
% 9.25/5.21            @ ( produc1547782455048856492_int_o
% 9.25/5.21              @ ^ [V2: set_Pr958786334691620121nt_int,W3: set_Pr958786334691620121nt_int] :
% 9.25/5.21                  ( ( member5325734588016868240nt_int @ ( produc782388162306416855nt_int @ V2 @ W3 ) @ R2 )
% 9.25/5.21                  & ~ ( member2340774599025711042nt_int @ V2 @ A4 )
% 9.25/5.21                  & ~ ( member2340774599025711042nt_int @ W3 @ A4 ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5244_rel__restrict__def,axiom,
% 9.25/5.21      ( rel_restrict_set_nat
% 9.25/5.21      = ( ^ [R2: set_Pr5488025237498180813et_nat,A4: set_set_nat] :
% 9.25/5.21            ( collec6662362479098859352et_nat
% 9.25/5.21            @ ( produc6247414631856714078_nat_o
% 9.25/5.21              @ ^ [V2: set_nat,W3: set_nat] :
% 9.25/5.21                  ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ V2 @ W3 ) @ R2 )
% 9.25/5.21                  & ~ ( member_set_nat @ V2 @ A4 )
% 9.25/5.21                  & ~ ( member_set_nat @ W3 @ A4 ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5245_rel__restrict__def,axiom,
% 9.25/5.21      ( rel_restrict_nat
% 9.25/5.21      = ( ^ [R2: set_Pr1261947904930325089at_nat,A4: set_nat] :
% 9.25/5.21            ( collec3392354462482085612at_nat
% 9.25/5.21            @ ( produc6081775807080527818_nat_o
% 9.25/5.21              @ ^ [V2: nat,W3: nat] :
% 9.25/5.21                  ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ V2 @ W3 ) @ R2 )
% 9.25/5.21                  & ~ ( member_nat @ V2 @ A4 )
% 9.25/5.21                  & ~ ( member_nat @ W3 @ A4 ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5246_rel__restrict__def,axiom,
% 9.25/5.21      ( rel_re3331361160397388719_nat_o
% 9.25/5.21      = ( ^ [R2: set_Pr2161125870931222855_nat_o,A4: set_Pr4532377907799695533_nat_o] :
% 9.25/5.21            ( collec7086185654880424402_nat_o
% 9.25/5.21            @ ( produc5150382289251079596at_o_o
% 9.25/5.21              @ ^ [V2: produc3658429121746597890et_nat > $o,W3: produc3658429121746597890et_nat > $o] :
% 9.25/5.21                  ( ( member8781333585448626064_nat_o @ ( produc7368190662567826135_nat_o @ V2 @ W3 ) @ R2 )
% 9.25/5.21                  & ~ ( member6576561426505652726_nat_o @ V2 @ A4 )
% 9.25/5.21                  & ~ ( member6576561426505652726_nat_o @ W3 @ A4 ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5247_rel__restrict__def,axiom,
% 9.25/5.21      ( rel_restrict_int
% 9.25/5.21      = ( ^ [R2: set_Pr958786334691620121nt_int,A4: set_int] :
% 9.25/5.21            ( collec213857154873943460nt_int
% 9.25/5.21            @ ( produc4947309494688390418_int_o
% 9.25/5.21              @ ^ [V2: int,W3: int] :
% 9.25/5.21                  ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ V2 @ W3 ) @ R2 )
% 9.25/5.21                  & ~ ( member_int @ V2 @ A4 )
% 9.25/5.21                  & ~ ( member_int @ W3 @ A4 ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5248_int__less__induct,axiom,
% 9.25/5.21      ! [I: int,K: int,P: int > $o] :
% 9.25/5.21        ( ( ord_less_int @ I @ K )
% 9.25/5.21       => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 9.25/5.21         => ( ! [I2: int] :
% 9.25/5.21                ( ( ord_less_int @ I2 @ K )
% 9.25/5.21               => ( ( P @ I2 )
% 9.25/5.21                 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 9.25/5.21           => ( P @ I ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5249_minus__int__code_I2_J,axiom,
% 9.25/5.21      ! [L: int] :
% 9.25/5.21        ( ( minus_minus_int @ zero_zero_int @ L )
% 9.25/5.21        = ( uminus_uminus_int @ L ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5250_uminus__int__code_I1_J,axiom,
% 9.25/5.21      ( ( uminus_uminus_int @ zero_zero_int )
% 9.25/5.21      = zero_zero_int ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5251_int__le__induct,axiom,
% 9.25/5.21      ! [I: int,K: int,P: int > $o] :
% 9.25/5.21        ( ( ord_less_eq_int @ I @ K )
% 9.25/5.21       => ( ( P @ K )
% 9.25/5.21         => ( ! [I2: int] :
% 9.25/5.21                ( ( ord_less_eq_int @ I2 @ K )
% 9.25/5.21               => ( ( P @ I2 )
% 9.25/5.21                 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 9.25/5.21           => ( P @ I ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5252_zless__add1__eq,axiom,
% 9.25/5.21      ! [W: int,Z: int] :
% 9.25/5.21        ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 9.25/5.21        = ( ( ord_less_int @ W @ Z )
% 9.25/5.21          | ( W = Z ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5253_int__gr__induct,axiom,
% 9.25/5.21      ! [K: int,I: int,P: int > $o] :
% 9.25/5.21        ( ( ord_less_int @ K @ I )
% 9.25/5.21       => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 9.25/5.21         => ( ! [I2: int] :
% 9.25/5.21                ( ( ord_less_int @ K @ I2 )
% 9.25/5.21               => ( ( P @ I2 )
% 9.25/5.21                 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 9.25/5.21           => ( P @ I ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5254_int__one__le__iff__zero__less,axiom,
% 9.25/5.21      ! [Z: int] :
% 9.25/5.21        ( ( ord_less_eq_int @ one_one_int @ Z )
% 9.25/5.21        = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5255_pos__zmult__eq__1__iff,axiom,
% 9.25/5.21      ! [M: int,N: int] :
% 9.25/5.21        ( ( ord_less_int @ zero_zero_int @ M )
% 9.25/5.21       => ( ( ( times_times_int @ M @ N )
% 9.25/5.21            = one_one_int )
% 9.25/5.21          = ( ( M = one_one_int )
% 9.25/5.21            & ( N = one_one_int ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5256_odd__nonzero,axiom,
% 9.25/5.21      ! [Z: int] :
% 9.25/5.21        ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 9.25/5.21       != zero_zero_int ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5257_odd__less__0__iff,axiom,
% 9.25/5.21      ! [Z: int] :
% 9.25/5.21        ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 9.25/5.21        = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5258_zless__imp__add1__zle,axiom,
% 9.25/5.21      ! [W: int,Z: int] :
% 9.25/5.21        ( ( ord_less_int @ W @ Z )
% 9.25/5.21       => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5259_int__ge__induct,axiom,
% 9.25/5.21      ! [K: int,I: int,P: int > $o] :
% 9.25/5.21        ( ( ord_less_eq_int @ K @ I )
% 9.25/5.21       => ( ( P @ K )
% 9.25/5.21         => ( ! [I2: int] :
% 9.25/5.21                ( ( ord_less_eq_int @ K @ I2 )
% 9.25/5.21               => ( ( P @ I2 )
% 9.25/5.21                 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 9.25/5.21           => ( P @ I ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5260_add1__zle__eq,axiom,
% 9.25/5.21      ! [W: int,Z: int] :
% 9.25/5.21        ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 9.25/5.21        = ( ord_less_int @ W @ Z ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5261_int__induct,axiom,
% 9.25/5.21      ! [P: int > $o,K: int,I: int] :
% 9.25/5.21        ( ( P @ K )
% 9.25/5.21       => ( ! [I2: int] :
% 9.25/5.21              ( ( ord_less_eq_int @ K @ I2 )
% 9.25/5.21             => ( ( P @ I2 )
% 9.25/5.21               => ( P @ ( plus_plus_int @ I2 @ one_one_int ) ) ) )
% 9.25/5.21         => ( ! [I2: int] :
% 9.25/5.21                ( ( ord_less_eq_int @ I2 @ K )
% 9.25/5.21               => ( ( P @ I2 )
% 9.25/5.21                 => ( P @ ( minus_minus_int @ I2 @ one_one_int ) ) ) )
% 9.25/5.21           => ( P @ I ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5262_zmult__eq__1__iff,axiom,
% 9.25/5.21      ! [M: int,N: int] :
% 9.25/5.21        ( ( ( times_times_int @ M @ N )
% 9.25/5.21          = one_one_int )
% 9.25/5.21        = ( ( ( M = one_one_int )
% 9.25/5.21            & ( N = one_one_int ) )
% 9.25/5.21          | ( ( M
% 9.25/5.21              = ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.21            & ( N
% 9.25/5.21              = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5263_pos__zmult__eq__1__iff__lemma,axiom,
% 9.25/5.21      ! [M: int,N: int] :
% 9.25/5.21        ( ( ( times_times_int @ M @ N )
% 9.25/5.21          = one_one_int )
% 9.25/5.21       => ( ( M = one_one_int )
% 9.25/5.21          | ( M
% 9.25/5.21            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5264_neg__eucl__rel__int__mult__2,axiom,
% 9.25/5.21      ! [B: int,A: int,Q4: int,R3: int] :
% 9.25/5.21        ( ( ord_less_eq_int @ B @ zero_zero_int )
% 9.25/5.21       => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 9.25/5.21         => ( 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 @ Q4 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R3 ) @ one_one_int ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5265_signed__take__bit__numeral__minus__bit1,axiom,
% 9.25/5.21      ! [L: num,K: num] :
% 9.25/5.21        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 9.25/5.21        = ( 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 ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5266_pos__eucl__rel__int__mult__2,axiom,
% 9.25/5.21      ! [B: int,A: int,Q4: int,R3: int] :
% 9.25/5.21        ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.25/5.21       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 9.25/5.21         => ( 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 @ Q4 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R3 ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5267_signed__take__bit__Suc__minus__bit1,axiom,
% 9.25/5.21      ! [N: nat,K: num] :
% 9.25/5.21        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 9.25/5.21        = ( 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 ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5268_divmod__BitM__2__eq,axiom,
% 9.25/5.21      ! [M: num] :
% 9.25/5.21        ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 9.25/5.21        = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5269_split__part,axiom,
% 9.25/5.21      ! [P: $o,Q2: int > int > $o] :
% 9.25/5.21        ( ( produc4947309494688390418_int_o
% 9.25/5.21          @ ^ [A3: int,B3: int] :
% 9.25/5.21              ( P
% 9.25/5.21              & ( Q2 @ A3 @ B3 ) ) )
% 9.25/5.21        = ( ^ [Ab: product_prod_int_int] :
% 9.25/5.21              ( P
% 9.25/5.21              & ( produc4947309494688390418_int_o @ Q2 @ Ab ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5270_diff__Suc__1,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 9.25/5.21        = N ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5271_signed__take__bit__Suc__1,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ one_one_Code_integer )
% 9.25/5.21        = one_one_Code_integer ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5272_signed__take__bit__Suc__1,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 9.25/5.21        = one_one_int ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5273_Suc__diff,axiom,
% 9.25/5.21      ! [M: nat,N: nat] :
% 9.25/5.21        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.21       => ( ( ord_less_eq_nat @ one_one_nat @ M )
% 9.25/5.21         => ( ( suc @ ( minus_minus_nat @ N @ M ) )
% 9.25/5.21            = ( minus_minus_nat @ N @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5274_Suc__1,axiom,
% 9.25/5.21      ( ( suc @ one_one_nat )
% 9.25/5.21      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5275_Suc__diff__1,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.21       => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 9.25/5.21          = N ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5276_Suc__times__numeral__mod__eq,axiom,
% 9.25/5.21      ! [K: num,N: nat] :
% 9.25/5.21        ( ( ( numeral_numeral_nat @ K )
% 9.25/5.21         != one_one_nat )
% 9.25/5.21       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 9.25/5.21          = one_one_nat ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5277_sub__num__simps_I2_J,axiom,
% 9.25/5.21      ! [L: num] :
% 9.25/5.21        ( ( neg_numeral_sub_int @ one @ ( bit0 @ L ) )
% 9.25/5.21        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bitM @ L ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5278_sub__num__simps_I2_J,axiom,
% 9.25/5.21      ! [L: num] :
% 9.25/5.21        ( ( neg_nu5755505904847501662nteger @ one @ ( bit0 @ L ) )
% 9.25/5.21        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bitM @ L ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5279_sub__num__simps_I2_J,axiom,
% 9.25/5.21      ! [L: num] :
% 9.25/5.21        ( ( neg_numeral_sub_rat @ one @ ( bit0 @ L ) )
% 9.25/5.21        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bitM @ L ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5280_signed__take__bit__Suc__minus__bit0,axiom,
% 9.25/5.21      ! [N: nat,K: num] :
% 9.25/5.21        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 9.25/5.21        = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5281_signed__take__bit__numeral__minus__bit0,axiom,
% 9.25/5.21      ! [L: num,K: num] :
% 9.25/5.21        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 9.25/5.21        = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5282_signed__take__bit__Suc__bit1,axiom,
% 9.25/5.21      ! [N: nat,K: num] :
% 9.25/5.21        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 9.25/5.21        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5283_signed__take__bit__numeral__bit1,axiom,
% 9.25/5.21      ! [L: num,K: num] :
% 9.25/5.21        ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 9.25/5.21        = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5284_prod_Odisc__eq__case,axiom,
% 9.25/5.21      ! [Prod: product_prod_int_int] :
% 9.25/5.21        ( produc4947309494688390418_int_o
% 9.25/5.21        @ ^ [Uu: int,Uv: int] : $true
% 9.25/5.21        @ Prod ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5285_unique__remainder,axiom,
% 9.25/5.21      ! [A: int,B: int,Q4: int,R3: int,Q6: int,R5: int] :
% 9.25/5.21        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 9.25/5.21       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q6 @ R5 ) )
% 9.25/5.21         => ( R3 = R5 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5286_unique__quotient,axiom,
% 9.25/5.21      ! [A: int,B: int,Q4: int,R3: int,Q6: int,R5: int] :
% 9.25/5.21        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 9.25/5.21       => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q6 @ R5 ) )
% 9.25/5.21         => ( Q4 = Q6 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5287_One__nat__def,axiom,
% 9.25/5.21      ( one_one_nat
% 9.25/5.21      = ( suc @ zero_zero_nat ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5288_Suc__eq__plus1,axiom,
% 9.25/5.21      ( suc
% 9.25/5.21      = ( ^ [N2: nat] : ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5289_plus__1__eq__Suc,axiom,
% 9.25/5.21      ( ( plus_plus_nat @ one_one_nat )
% 9.25/5.21      = suc ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5290_Suc__eq__plus1__left,axiom,
% 9.25/5.21      ( suc
% 9.25/5.21      = ( plus_plus_nat @ one_one_nat ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5291_diff__Suc__eq__diff__pred,axiom,
% 9.25/5.21      ! [M: nat,N: nat] :
% 9.25/5.21        ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 9.25/5.21        = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5292_eucl__rel__int__by0,axiom,
% 9.25/5.21      ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5293_nat__induct__non__zero,axiom,
% 9.25/5.21      ! [N: nat,P: nat > $o] :
% 9.25/5.21        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.21       => ( ( P @ one_one_nat )
% 9.25/5.21         => ( ! [N3: nat] :
% 9.25/5.21                ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 9.25/5.21               => ( ( P @ N3 )
% 9.25/5.21                 => ( P @ ( suc @ N3 ) ) ) )
% 9.25/5.21           => ( P @ N ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5294_div__int__unique,axiom,
% 9.25/5.21      ! [K: int,L: int,Q4: int,R3: int] :
% 9.25/5.21        ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 9.25/5.21       => ( ( divide_divide_int @ K @ L )
% 9.25/5.21          = Q4 ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5295_mod__int__unique,axiom,
% 9.25/5.21      ! [K: int,L: int,Q4: int,R3: int] :
% 9.25/5.21        ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 9.25/5.21       => ( ( modulo_modulo_int @ K @ L )
% 9.25/5.21          = R3 ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5296_pred__numeral__def,axiom,
% 9.25/5.21      ( pred_numeral
% 9.25/5.21      = ( ^ [K4: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K4 ) @ one_one_nat ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5297_small__lazy_H_Ocases,axiom,
% 9.25/5.21      ! [X: product_prod_int_int] :
% 9.25/5.21        ~ ! [D: int,I2: int] :
% 9.25/5.21            ( X
% 9.25/5.21           != ( product_Pair_int_int @ D @ I2 ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5298_exhaustive__int_H_Ocases,axiom,
% 9.25/5.21      ! [X: produc7773217078559923341nt_int] :
% 9.25/5.21        ~ ! [F3: int > option6357759511663192854e_term,D: int,I2: int] :
% 9.25/5.21            ( X
% 9.25/5.21           != ( produc4305682042979456191nt_int @ F3 @ ( product_Pair_int_int @ D @ I2 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5299_full__exhaustive__int_H_Ocases,axiom,
% 9.25/5.21      ! [X: produc2285326912895808259nt_int] :
% 9.25/5.21        ~ ! [F3: produc8551481072490612790e_term > option6357759511663192854e_term,D: int,I2: int] :
% 9.25/5.21            ( X
% 9.25/5.21           != ( produc5700946648718959541nt_int @ F3 @ ( product_Pair_int_int @ D @ I2 ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5300_Suc__pred_H,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.21       => ( N
% 9.25/5.21          = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5301_Suc__diff__eq__diff__pred,axiom,
% 9.25/5.21      ! [N: nat,M: nat] :
% 9.25/5.21        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.21       => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 9.25/5.21          = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5302_add__eq__if,axiom,
% 9.25/5.21      ( plus_plus_nat
% 9.25/5.21      = ( ^ [M2: nat,N2: nat] : ( if_nat @ ( M2 = zero_zero_nat ) @ N2 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5303_Suc__n__minus__m__eq,axiom,
% 9.25/5.21      ! [M: nat,N: nat] :
% 9.25/5.21        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.21       => ( ( ord_less_nat @ one_one_nat @ M )
% 9.25/5.21         => ( ( suc @ ( minus_minus_nat @ N @ M ) )
% 9.25/5.21            = ( minus_minus_nat @ N @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5304_eucl__rel__int__dividesI,axiom,
% 9.25/5.21      ! [L: int,K: int,Q4: int] :
% 9.25/5.21        ( ( L != zero_zero_int )
% 9.25/5.21       => ( ( K
% 9.25/5.21            = ( times_times_int @ Q4 @ L ) )
% 9.25/5.21         => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q4 @ zero_zero_int ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5305_numeral__BitM,axiom,
% 9.25/5.21      ! [N: num] :
% 9.25/5.21        ( ( numeral_numeral_int @ ( bitM @ N ) )
% 9.25/5.21        = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ one_one_int ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5306_numeral__BitM,axiom,
% 9.25/5.21      ! [N: num] :
% 9.25/5.21        ( ( numera6620942414471956472nteger @ ( bitM @ N ) )
% 9.25/5.21        = ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ one_one_Code_integer ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5307_numeral__BitM,axiom,
% 9.25/5.21      ! [N: num] :
% 9.25/5.21        ( ( numeral_numeral_rat @ ( bitM @ N ) )
% 9.25/5.21        = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N ) ) @ one_one_rat ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5308_eucl__rel__int,axiom,
% 9.25/5.21      ! [K: int,L: int] : ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L ) @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5309_Suc__times__mod__eq,axiom,
% 9.25/5.21      ! [M: nat,N: nat] :
% 9.25/5.21        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 9.25/5.21       => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 9.25/5.21          = one_one_nat ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5310_zminus1__lemma,axiom,
% 9.25/5.21      ! [A: int,B: int,Q4: int,R3: int] :
% 9.25/5.21        ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 9.25/5.21       => ( ( B != zero_zero_int )
% 9.25/5.21         => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R3 = zero_zero_int ) @ ( uminus_uminus_int @ Q4 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q4 ) @ one_one_int ) ) @ ( if_int @ ( R3 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R3 ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5311_signed__take__bit__Suc,axiom,
% 9.25/5.21      ! [N: nat,A: code_integer] :
% 9.25/5.21        ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ A )
% 9.25/5.21        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5312_signed__take__bit__Suc,axiom,
% 9.25/5.21      ! [N: nat,A: int] :
% 9.25/5.21        ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 9.25/5.21        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5313_unset__bit__Suc,axiom,
% 9.25/5.21      ! [N: nat,A: nat] :
% 9.25/5.21        ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 9.25/5.21        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5314_unset__bit__Suc,axiom,
% 9.25/5.21      ! [N: nat,A: code_integer] :
% 9.25/5.21        ( ( bit_se8260200283734997820nteger @ ( suc @ N ) @ A )
% 9.25/5.21        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5315_unset__bit__Suc,axiom,
% 9.25/5.21      ! [N: nat,A: code_natural] :
% 9.25/5.21        ( ( bit_se7083795435491715335atural @ ( suc @ N ) @ A )
% 9.25/5.21        = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se7083795435491715335atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5316_unset__bit__Suc,axiom,
% 9.25/5.21      ! [N: nat,A: int] :
% 9.25/5.21        ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 9.25/5.21        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5317_set__bit__Suc,axiom,
% 9.25/5.21      ! [N: nat,A: code_integer] :
% 9.25/5.21        ( ( bit_se2793503036327961859nteger @ ( suc @ N ) @ A )
% 9.25/5.21        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5318_set__bit__Suc,axiom,
% 9.25/5.21      ! [N: nat,A: code_natural] :
% 9.25/5.21        ( ( bit_se1617098188084679374atural @ ( suc @ N ) @ A )
% 9.25/5.21        = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se1617098188084679374atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5319_set__bit__Suc,axiom,
% 9.25/5.21      ! [N: nat,A: int] :
% 9.25/5.21        ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 9.25/5.21        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5320_set__bit__Suc,axiom,
% 9.25/5.21      ! [N: nat,A: nat] :
% 9.25/5.21        ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 9.25/5.21        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5321_eucl__rel__int__iff,axiom,
% 9.25/5.21      ! [K: int,L: int,Q4: int,R3: int] :
% 9.25/5.21        ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 9.25/5.21        = ( ( K
% 9.25/5.21            = ( plus_plus_int @ ( times_times_int @ L @ Q4 ) @ R3 ) )
% 9.25/5.21          & ( ( ord_less_int @ zero_zero_int @ L )
% 9.25/5.21           => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 9.25/5.21              & ( ord_less_int @ R3 @ L ) ) )
% 9.25/5.21          & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 9.25/5.21           => ( ( ( ord_less_int @ L @ zero_zero_int )
% 9.25/5.21               => ( ( ord_less_int @ L @ R3 )
% 9.25/5.21                  & ( ord_less_eq_int @ R3 @ zero_zero_int ) ) )
% 9.25/5.21              & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 9.25/5.21               => ( Q4 = zero_zero_int ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5322_divmod__nat__if,axiom,
% 9.25/5.21      ( divmod_nat
% 9.25/5.21      = ( ^ [M2: nat,N2: nat] :
% 9.25/5.21            ( if_Pro6206227464963214023at_nat
% 9.25/5.21            @ ( ( N2 = zero_zero_nat )
% 9.25/5.21              | ( ord_less_nat @ M2 @ N2 ) )
% 9.25/5.21            @ ( product_Pair_nat_nat @ zero_zero_nat @ M2 )
% 9.25/5.21            @ ( produc2626176000494625587at_nat
% 9.25/5.21              @ ^ [Q5: nat] : ( product_Pair_nat_nat @ ( suc @ Q5 ) )
% 9.25/5.21              @ ( divmod_nat @ ( minus_minus_nat @ M2 @ N2 ) @ N2 ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5323_flip__bit__Suc,axiom,
% 9.25/5.21      ! [N: nat,A: code_integer] :
% 9.25/5.21        ( ( bit_se1345352211410354436nteger @ ( suc @ N ) @ A )
% 9.25/5.21        = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5324_flip__bit__Suc,axiom,
% 9.25/5.21      ! [N: nat,A: code_natural] :
% 9.25/5.21        ( ( bit_se168947363167071951atural @ ( suc @ N ) @ A )
% 9.25/5.21        = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se168947363167071951atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5325_flip__bit__Suc,axiom,
% 9.25/5.21      ! [N: nat,A: int] :
% 9.25/5.21        ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 9.25/5.21        = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5326_flip__bit__Suc,axiom,
% 9.25/5.21      ! [N: nat,A: nat] :
% 9.25/5.21        ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 9.25/5.21        = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5327_take__bit__numeral__minus__bit1,axiom,
% 9.25/5.21      ! [L: num,K: num] :
% 9.25/5.21        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 9.25/5.21        = ( 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 ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5328_int__ge__less__than2__def,axiom,
% 9.25/5.21      ( int_ge_less_than2
% 9.25/5.21      = ( ^ [D4: int] :
% 9.25/5.21            ( collec213857154873943460nt_int
% 9.25/5.21            @ ( produc4947309494688390418_int_o
% 9.25/5.21              @ ^ [Z6: int,Z3: int] :
% 9.25/5.21                  ( ( ord_less_eq_int @ D4 @ Z3 )
% 9.25/5.21                  & ( ord_less_int @ Z6 @ Z3 ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5329_int__ge__less__than__def,axiom,
% 9.25/5.21      ( int_ge_less_than
% 9.25/5.21      = ( ^ [D4: int] :
% 9.25/5.21            ( collec213857154873943460nt_int
% 9.25/5.21            @ ( produc4947309494688390418_int_o
% 9.25/5.21              @ ^ [Z6: int,Z3: int] :
% 9.25/5.21                  ( ( ord_less_eq_int @ D4 @ Z6 )
% 9.25/5.21                  & ( ord_less_int @ Z6 @ Z3 ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5330_take__bit__Suc__1,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ one_one_Code_integer )
% 9.25/5.21        = one_one_Code_integer ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5331_take__bit__Suc__1,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ one_one_nat )
% 9.25/5.21        = one_one_nat ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5332_take__bit__Suc__1,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ one_one_int )
% 9.25/5.21        = one_one_int ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5333_take__bit__numeral__1,axiom,
% 9.25/5.21      ! [L: num] :
% 9.25/5.21        ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ L ) @ one_one_Code_integer )
% 9.25/5.21        = one_one_Code_integer ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5334_take__bit__numeral__1,axiom,
% 9.25/5.21      ! [L: num] :
% 9.25/5.21        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ one_one_nat )
% 9.25/5.21        = one_one_nat ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5335_take__bit__numeral__1,axiom,
% 9.25/5.21      ! [L: num] :
% 9.25/5.21        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ one_one_int )
% 9.25/5.21        = one_one_int ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5336_take__bit__of__1__eq__0__iff,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( ( bit_se1745604003318907178nteger @ N @ one_one_Code_integer )
% 9.25/5.21          = zero_z3403309356797280102nteger )
% 9.25/5.21        = ( N = zero_zero_nat ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5337_take__bit__of__1__eq__0__iff,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 9.25/5.21          = zero_zero_nat )
% 9.25/5.21        = ( N = zero_zero_nat ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5338_take__bit__of__1__eq__0__iff,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 9.25/5.21          = zero_zero_int )
% 9.25/5.21        = ( N = zero_zero_nat ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5339_take__bit__minus,axiom,
% 9.25/5.21      ! [N: nat,K: int] :
% 9.25/5.21        ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 9.25/5.21        = ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5340_take__bit__decr__eq,axiom,
% 9.25/5.21      ! [N: nat,K: int] :
% 9.25/5.21        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 9.25/5.21         != zero_zero_int )
% 9.25/5.21       => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 9.25/5.21          = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5341_take__bit__Suc__bit0,axiom,
% 9.25/5.21      ! [N: nat,K: num] :
% 9.25/5.21        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 9.25/5.21        = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5342_take__bit__Suc__bit0,axiom,
% 9.25/5.21      ! [N: nat,K: num] :
% 9.25/5.21        ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) )
% 9.25/5.21        = ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5343_take__bit__Suc__bit0,axiom,
% 9.25/5.21      ! [N: nat,K: num] :
% 9.25/5.21        ( ( bit_se569199155075624693atural @ ( suc @ N ) @ ( numera5444537566228673987atural @ ( bit0 @ K ) ) )
% 9.25/5.21        = ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ N @ ( numera5444537566228673987atural @ K ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5344_take__bit__Suc__bit0,axiom,
% 9.25/5.21      ! [N: nat,K: num] :
% 9.25/5.21        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 9.25/5.21        = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5345_take__bit__numeral__bit0,axiom,
% 9.25/5.21      ! [L: num,K: num] :
% 9.25/5.21        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 9.25/5.21        = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5346_take__bit__numeral__bit0,axiom,
% 9.25/5.21      ! [L: num,K: num] :
% 9.25/5.21        ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ L ) @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) )
% 9.25/5.21        = ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( pred_numeral @ L ) @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5347_take__bit__numeral__bit0,axiom,
% 9.25/5.21      ! [L: num,K: num] :
% 9.25/5.21        ( ( bit_se569199155075624693atural @ ( numeral_numeral_nat @ L ) @ ( numera5444537566228673987atural @ ( bit0 @ K ) ) )
% 9.25/5.21        = ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ ( pred_numeral @ L ) @ ( numera5444537566228673987atural @ K ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5348_take__bit__numeral__bit0,axiom,
% 9.25/5.21      ! [L: num,K: num] :
% 9.25/5.21        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 9.25/5.21        = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5349_take__bit__Suc__minus__bit0,axiom,
% 9.25/5.21      ! [N: nat,K: num] :
% 9.25/5.21        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 9.25/5.21        = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5350_take__bit__numeral__minus__bit0,axiom,
% 9.25/5.21      ! [L: num,K: num] :
% 9.25/5.21        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 9.25/5.21        = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5351_take__bit__Suc__bit1,axiom,
% 9.25/5.21      ! [N: nat,K: num] :
% 9.25/5.21        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 9.25/5.21        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5352_take__bit__Suc__bit1,axiom,
% 9.25/5.21      ! [N: nat,K: num] :
% 9.25/5.21        ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( numera6620942414471956472nteger @ ( bit1 @ K ) ) )
% 9.25/5.21        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5353_take__bit__Suc__bit1,axiom,
% 9.25/5.21      ! [N: nat,K: num] :
% 9.25/5.21        ( ( bit_se569199155075624693atural @ ( suc @ N ) @ ( numera5444537566228673987atural @ ( bit1 @ K ) ) )
% 9.25/5.21        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ N @ ( numera5444537566228673987atural @ K ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ one_one_Code_natural ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5354_take__bit__Suc__bit1,axiom,
% 9.25/5.21      ! [N: nat,K: num] :
% 9.25/5.21        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 9.25/5.21        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5355_take__bit__Suc,axiom,
% 9.25/5.21      ! [N: nat,A: nat] :
% 9.25/5.21        ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ A )
% 9.25/5.21        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5356_take__bit__Suc,axiom,
% 9.25/5.21      ! [N: nat,A: code_integer] :
% 9.25/5.21        ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A )
% 9.25/5.21        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5357_take__bit__Suc,axiom,
% 9.25/5.21      ! [N: nat,A: code_natural] :
% 9.25/5.21        ( ( bit_se569199155075624693atural @ ( suc @ N ) @ A )
% 9.25/5.21        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5358_take__bit__Suc,axiom,
% 9.25/5.21      ! [N: nat,A: int] :
% 9.25/5.21        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 9.25/5.21        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5359_take__bit__numeral__bit1,axiom,
% 9.25/5.21      ! [L: num,K: num] :
% 9.25/5.21        ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 9.25/5.21        = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5360_take__bit__numeral__bit1,axiom,
% 9.25/5.21      ! [L: num,K: num] :
% 9.25/5.21        ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ L ) @ ( numera6620942414471956472nteger @ ( bit1 @ K ) ) )
% 9.25/5.21        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( pred_numeral @ L ) @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5361_take__bit__numeral__bit1,axiom,
% 9.25/5.21      ! [L: num,K: num] :
% 9.25/5.21        ( ( bit_se569199155075624693atural @ ( numeral_numeral_nat @ L ) @ ( numera5444537566228673987atural @ ( bit1 @ K ) ) )
% 9.25/5.21        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ ( pred_numeral @ L ) @ ( numera5444537566228673987atural @ K ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ one_one_Code_natural ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5362_take__bit__numeral__bit1,axiom,
% 9.25/5.21      ! [L: num,K: num] :
% 9.25/5.21        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 9.25/5.21        = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5363_divmod__nat__def,axiom,
% 9.25/5.21      ( divmod_nat
% 9.25/5.21      = ( ^ [M2: nat,N2: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M2 @ N2 ) @ ( modulo_modulo_nat @ M2 @ N2 ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5364_take__bit__Suc__minus__bit1,axiom,
% 9.25/5.21      ! [N: nat,K: num] :
% 9.25/5.21        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 9.25/5.21        = ( 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 ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5365_take__bit__rec,axiom,
% 9.25/5.21      ( bit_se2925701944663578781it_nat
% 9.25/5.21      = ( ^ [N2: nat,A3: nat] : ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5366_take__bit__rec,axiom,
% 9.25/5.21      ( bit_se1745604003318907178nteger
% 9.25/5.21      = ( ^ [N2: nat,A3: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5367_take__bit__rec,axiom,
% 9.25/5.21      ( bit_se569199155075624693atural
% 9.25/5.21      = ( ^ [N2: nat,A3: code_natural] : ( if_Code_natural @ ( N2 = zero_zero_nat ) @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide5121882707175180666atural @ A3 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( modulo8411746178871703098atural @ A3 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5368_take__bit__rec,axiom,
% 9.25/5.21      ( bit_se2923211474154528505it_int
% 9.25/5.21      = ( ^ [N2: nat,A3: int] : ( if_int @ ( N2 = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5369_mask__numeral,axiom,
% 9.25/5.21      ! [N: num] :
% 9.25/5.21        ( ( bit_se2119862282449309892nteger @ ( numeral_numeral_nat @ N ) )
% 9.25/5.21        = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ ( pred_numeral @ N ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5370_mask__numeral,axiom,
% 9.25/5.21      ! [N: num] :
% 9.25/5.21        ( ( bit_se943457434206027407atural @ ( numeral_numeral_nat @ N ) )
% 9.25/5.21        = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se943457434206027407atural @ ( pred_numeral @ N ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5371_mask__numeral,axiom,
% 9.25/5.21      ! [N: num] :
% 9.25/5.21        ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N ) )
% 9.25/5.21        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5372_mask__numeral,axiom,
% 9.25/5.21      ! [N: num] :
% 9.25/5.21        ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N ) )
% 9.25/5.21        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5373_and__int__unfold,axiom,
% 9.25/5.21      ( bit_se725231765392027082nd_int
% 9.25/5.21      = ( ^ [K4: int,L2: int] :
% 9.25/5.21            ( if_int
% 9.25/5.21            @ ( ( K4 = zero_zero_int )
% 9.25/5.21              | ( L2 = zero_zero_int ) )
% 9.25/5.21            @ zero_zero_int
% 9.25/5.21            @ ( if_int
% 9.25/5.21              @ ( K4
% 9.25/5.21                = ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.21              @ L2
% 9.25/5.21              @ ( if_int
% 9.25/5.21                @ ( L2
% 9.25/5.21                  = ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.21                @ K4
% 9.25/5.21                @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K4 @ ( 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 @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5374_take__bit__minus__small__eq,axiom,
% 9.25/5.21      ! [K: int,N: nat] :
% 9.25/5.21        ( ( ord_less_int @ zero_zero_int @ K )
% 9.25/5.21       => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.21         => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 9.25/5.21            = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5375_signed__take__bit__int__greater__eq,axiom,
% 9.25/5.21      ! [K: int,N: nat] :
% 9.25/5.21        ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 9.25/5.21       => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5376_normalize__negative,axiom,
% 9.25/5.21      ! [Q4: int,P4: int] :
% 9.25/5.21        ( ( ord_less_int @ Q4 @ zero_zero_int )
% 9.25/5.21       => ( ( normalize @ ( product_Pair_int_int @ P4 @ Q4 ) )
% 9.25/5.21          = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P4 ) @ ( uminus_uminus_int @ Q4 ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5377_odd__two__times__div__two__nat,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.21       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.25/5.21          = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5378_odd__two__times__div__two__succ,axiom,
% 9.25/5.21      ! [A: nat] :
% 9.25/5.21        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 9.25/5.21          = A ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5379_odd__two__times__div__two__succ,axiom,
% 9.25/5.21      ! [A: int] :
% 9.25/5.21        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 9.25/5.21          = A ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5380_odd__two__times__div__two__succ,axiom,
% 9.25/5.21      ! [A: code_integer] :
% 9.25/5.21        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 9.25/5.21          = A ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5381_odd__two__times__div__two__succ,axiom,
% 9.25/5.21      ! [A: code_natural] :
% 9.25/5.21        ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ one_one_Code_natural )
% 9.25/5.21          = A ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5382_dvd__minus__iff,axiom,
% 9.25/5.21      ! [X: int,Y: int] :
% 9.25/5.21        ( ( dvd_dvd_int @ X @ ( uminus_uminus_int @ Y ) )
% 9.25/5.21        = ( dvd_dvd_int @ X @ Y ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5383_dvd__minus__iff,axiom,
% 9.25/5.21      ! [X: code_integer,Y: code_integer] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ X @ ( uminus1351360451143612070nteger @ Y ) )
% 9.25/5.21        = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5384_dvd__minus__iff,axiom,
% 9.25/5.21      ! [X: rat,Y: rat] :
% 9.25/5.21        ( ( dvd_dvd_rat @ X @ ( uminus_uminus_rat @ Y ) )
% 9.25/5.21        = ( dvd_dvd_rat @ X @ Y ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5385_minus__dvd__iff,axiom,
% 9.25/5.21      ! [X: int,Y: int] :
% 9.25/5.21        ( ( dvd_dvd_int @ ( uminus_uminus_int @ X ) @ Y )
% 9.25/5.21        = ( dvd_dvd_int @ X @ Y ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5386_minus__dvd__iff,axiom,
% 9.25/5.21      ! [X: code_integer,Y: code_integer] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X ) @ Y )
% 9.25/5.21        = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5387_minus__dvd__iff,axiom,
% 9.25/5.21      ! [X: rat,Y: rat] :
% 9.25/5.21        ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X ) @ Y )
% 9.25/5.21        = ( dvd_dvd_rat @ X @ Y ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5388_power__one,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( power_8256067586552552935nteger @ one_one_Code_integer @ N )
% 9.25/5.21        = one_one_Code_integer ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5389_power__one,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( power_power_assn @ one_one_assn @ N )
% 9.25/5.21        = one_one_assn ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5390_power__one,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( power_power_rat @ one_one_rat @ N )
% 9.25/5.21        = one_one_rat ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5391_power__one,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( power_power_int @ one_one_int @ N )
% 9.25/5.21        = one_one_int ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5392_power__one,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( power_power_nat @ one_one_nat @ N )
% 9.25/5.21        = one_one_nat ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5393_power__one__right,axiom,
% 9.25/5.21      ! [A: int] :
% 9.25/5.21        ( ( power_power_int @ A @ one_one_nat )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5394_power__one__right,axiom,
% 9.25/5.21      ! [A: nat] :
% 9.25/5.21        ( ( power_power_nat @ A @ one_one_nat )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5395_nat__dvd__1__iff__1,axiom,
% 9.25/5.21      ! [M: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ M @ one_one_nat )
% 9.25/5.21        = ( M = one_one_nat ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5396_dvd__mult__cancel__left,axiom,
% 9.25/5.21      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 9.25/5.21        = ( ( C = zero_z3403309356797280102nteger )
% 9.25/5.21          | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5397_dvd__mult__cancel__left,axiom,
% 9.25/5.21      ! [C: rat,A: rat,B: rat] :
% 9.25/5.21        ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 9.25/5.21        = ( ( C = zero_zero_rat )
% 9.25/5.21          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5398_dvd__mult__cancel__left,axiom,
% 9.25/5.21      ! [C: int,A: int,B: int] :
% 9.25/5.21        ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 9.25/5.21        = ( ( C = zero_zero_int )
% 9.25/5.21          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5399_dvd__mult__cancel__right,axiom,
% 9.25/5.21      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.25/5.21        = ( ( C = zero_z3403309356797280102nteger )
% 9.25/5.21          | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5400_dvd__mult__cancel__right,axiom,
% 9.25/5.21      ! [A: rat,C: rat,B: rat] :
% 9.25/5.21        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 9.25/5.21        = ( ( C = zero_zero_rat )
% 9.25/5.21          | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5401_dvd__mult__cancel__right,axiom,
% 9.25/5.21      ! [A: int,C: int,B: int] :
% 9.25/5.21        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 9.25/5.21        = ( ( C = zero_zero_int )
% 9.25/5.21          | ( dvd_dvd_int @ A @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5402_dvd__times__left__cancel__iff,axiom,
% 9.25/5.21      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.21        ( ( A != zero_z3403309356797280102nteger )
% 9.25/5.21       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 9.25/5.21          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5403_dvd__times__left__cancel__iff,axiom,
% 9.25/5.21      ! [A: nat,B: nat,C: nat] :
% 9.25/5.21        ( ( A != zero_zero_nat )
% 9.25/5.21       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 9.25/5.21          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5404_dvd__times__left__cancel__iff,axiom,
% 9.25/5.21      ! [A: int,B: int,C: int] :
% 9.25/5.21        ( ( A != zero_zero_int )
% 9.25/5.21       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 9.25/5.21          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5405_dvd__times__right__cancel__iff,axiom,
% 9.25/5.21      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.21        ( ( A != zero_z3403309356797280102nteger )
% 9.25/5.21       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 9.25/5.21          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5406_dvd__times__right__cancel__iff,axiom,
% 9.25/5.21      ! [A: nat,B: nat,C: nat] :
% 9.25/5.21        ( ( A != zero_zero_nat )
% 9.25/5.21       => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 9.25/5.21          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5407_dvd__times__right__cancel__iff,axiom,
% 9.25/5.21      ! [A: int,B: int,C: int] :
% 9.25/5.21        ( ( A != zero_zero_int )
% 9.25/5.21       => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 9.25/5.21          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5408_dvd__add__times__triv__left__iff,axiom,
% 9.25/5.21      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 9.25/5.21        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5409_dvd__add__times__triv__left__iff,axiom,
% 9.25/5.21      ! [A: rat,C: rat,B: rat] :
% 9.25/5.21        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 9.25/5.21        = ( dvd_dvd_rat @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5410_dvd__add__times__triv__left__iff,axiom,
% 9.25/5.21      ! [A: nat,C: nat,B: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 9.25/5.21        = ( dvd_dvd_nat @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5411_dvd__add__times__triv__left__iff,axiom,
% 9.25/5.21      ! [A: int,C: int,B: int] :
% 9.25/5.21        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 9.25/5.21        = ( dvd_dvd_int @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5412_dvd__add__times__triv__right__iff,axiom,
% 9.25/5.21      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 9.25/5.21        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5413_dvd__add__times__triv__right__iff,axiom,
% 9.25/5.21      ! [A: rat,B: rat,C: rat] :
% 9.25/5.21        ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 9.25/5.21        = ( dvd_dvd_rat @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5414_dvd__add__times__triv__right__iff,axiom,
% 9.25/5.21      ! [A: nat,B: nat,C: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 9.25/5.21        = ( dvd_dvd_nat @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5415_dvd__add__times__triv__right__iff,axiom,
% 9.25/5.21      ! [A: int,B: int,C: int] :
% 9.25/5.21        ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 9.25/5.21        = ( dvd_dvd_int @ A @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5416_unit__prod,axiom,
% 9.25/5.21      ! [A: code_integer,B: code_integer] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.25/5.21       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.25/5.21         => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5417_unit__prod,axiom,
% 9.25/5.21      ! [A: nat,B: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.25/5.21       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.25/5.21         => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5418_unit__prod,axiom,
% 9.25/5.21      ! [A: int,B: int] :
% 9.25/5.21        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.25/5.21       => ( ( dvd_dvd_int @ B @ one_one_int )
% 9.25/5.21         => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5419_power__inject__exp,axiom,
% 9.25/5.21      ! [A: code_integer,M: nat,N: nat] :
% 9.25/5.21        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 9.25/5.21       => ( ( ( power_8256067586552552935nteger @ A @ M )
% 9.25/5.21            = ( power_8256067586552552935nteger @ A @ N ) )
% 9.25/5.21          = ( M = N ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5420_power__inject__exp,axiom,
% 9.25/5.21      ! [A: rat,M: nat,N: nat] :
% 9.25/5.21        ( ( ord_less_rat @ one_one_rat @ A )
% 9.25/5.21       => ( ( ( power_power_rat @ A @ M )
% 9.25/5.21            = ( power_power_rat @ A @ N ) )
% 9.25/5.21          = ( M = N ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5421_power__inject__exp,axiom,
% 9.25/5.21      ! [A: nat,M: nat,N: nat] :
% 9.25/5.21        ( ( ord_less_nat @ one_one_nat @ A )
% 9.25/5.21       => ( ( ( power_power_nat @ A @ M )
% 9.25/5.21            = ( power_power_nat @ A @ N ) )
% 9.25/5.21          = ( M = N ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5422_power__inject__exp,axiom,
% 9.25/5.21      ! [A: int,M: nat,N: nat] :
% 9.25/5.21        ( ( ord_less_int @ one_one_int @ A )
% 9.25/5.21       => ( ( ( power_power_int @ A @ M )
% 9.25/5.21            = ( power_power_int @ A @ N ) )
% 9.25/5.21          = ( M = N ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5423_dvd__div__mult__self,axiom,
% 9.25/5.21      ! [A: nat,B: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ A @ B )
% 9.25/5.21       => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 9.25/5.21          = B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5424_dvd__div__mult__self,axiom,
% 9.25/5.21      ! [A: int,B: int] :
% 9.25/5.21        ( ( dvd_dvd_int @ A @ B )
% 9.25/5.21       => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 9.25/5.21          = B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5425_dvd__div__mult__self,axiom,
% 9.25/5.21      ! [A: code_integer,B: code_integer] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ A @ B )
% 9.25/5.21       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 9.25/5.21          = B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5426_dvd__div__mult__self,axiom,
% 9.25/5.21      ! [A: code_natural,B: code_natural] :
% 9.25/5.21        ( ( dvd_dvd_Code_natural @ A @ B )
% 9.25/5.21       => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ B @ A ) @ A )
% 9.25/5.21          = B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5427_dvd__mult__div__cancel,axiom,
% 9.25/5.21      ! [A: nat,B: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ A @ B )
% 9.25/5.21       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 9.25/5.21          = B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5428_dvd__mult__div__cancel,axiom,
% 9.25/5.21      ! [A: int,B: int] :
% 9.25/5.21        ( ( dvd_dvd_int @ A @ B )
% 9.25/5.21       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 9.25/5.21          = B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5429_dvd__mult__div__cancel,axiom,
% 9.25/5.21      ! [A: code_integer,B: code_integer] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ A @ B )
% 9.25/5.21       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 9.25/5.21          = B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5430_dvd__mult__div__cancel,axiom,
% 9.25/5.21      ! [A: code_natural,B: code_natural] :
% 9.25/5.21        ( ( dvd_dvd_Code_natural @ A @ B )
% 9.25/5.21       => ( ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ A ) )
% 9.25/5.21          = B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5431_unit__div,axiom,
% 9.25/5.21      ! [A: nat,B: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.25/5.21       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.25/5.21         => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5432_unit__div,axiom,
% 9.25/5.21      ! [A: int,B: int] :
% 9.25/5.21        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.25/5.21       => ( ( dvd_dvd_int @ B @ one_one_int )
% 9.25/5.21         => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5433_unit__div,axiom,
% 9.25/5.21      ! [A: code_integer,B: code_integer] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.25/5.21       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.25/5.21         => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5434_unit__div,axiom,
% 9.25/5.21      ! [A: code_natural,B: code_natural] :
% 9.25/5.21        ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 9.25/5.21       => ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.25/5.21         => ( dvd_dvd_Code_natural @ ( divide5121882707175180666atural @ A @ B ) @ one_one_Code_natural ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5435_unit__div__1__unit,axiom,
% 9.25/5.21      ! [A: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.25/5.21       => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5436_unit__div__1__unit,axiom,
% 9.25/5.21      ! [A: int] :
% 9.25/5.21        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.25/5.21       => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5437_unit__div__1__unit,axiom,
% 9.25/5.21      ! [A: code_integer] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.25/5.21       => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5438_unit__div__1__unit,axiom,
% 9.25/5.21      ! [A: code_natural] :
% 9.25/5.21        ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 9.25/5.21       => ( dvd_dvd_Code_natural @ ( divide5121882707175180666atural @ one_one_Code_natural @ A ) @ one_one_Code_natural ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5439_unit__div__1__div__1,axiom,
% 9.25/5.21      ! [A: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.25/5.21       => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 9.25/5.21          = A ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5440_unit__div__1__div__1,axiom,
% 9.25/5.21      ! [A: int] :
% 9.25/5.21        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.25/5.21       => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 9.25/5.21          = A ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5441_unit__div__1__div__1,axiom,
% 9.25/5.21      ! [A: code_integer] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.25/5.21       => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 9.25/5.21          = A ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5442_unit__div__1__div__1,axiom,
% 9.25/5.21      ! [A: code_natural] :
% 9.25/5.21        ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 9.25/5.21       => ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( divide5121882707175180666atural @ one_one_Code_natural @ A ) )
% 9.25/5.21          = A ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5443_and_Oleft__neutral,axiom,
% 9.25/5.21      ! [A: code_integer] :
% 9.25/5.21        ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5444_and_Oleft__neutral,axiom,
% 9.25/5.21      ! [A: int] :
% 9.25/5.21        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5445_and_Oright__neutral,axiom,
% 9.25/5.21      ! [A: code_integer] :
% 9.25/5.21        ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5446_and_Oright__neutral,axiom,
% 9.25/5.21      ! [A: int] :
% 9.25/5.21        ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5447_bit_Oconj__one__right,axiom,
% 9.25/5.21      ! [X: code_integer] :
% 9.25/5.21        ( ( bit_se3949692690581998587nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.21        = X ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5448_bit_Oconj__one__right,axiom,
% 9.25/5.21      ! [X: int] :
% 9.25/5.21        ( ( bit_se725231765392027082nd_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.21        = X ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5449_unit__mult__div__div,axiom,
% 9.25/5.21      ! [A: nat,B: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.25/5.21       => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 9.25/5.21          = ( divide_divide_nat @ B @ A ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5450_unit__mult__div__div,axiom,
% 9.25/5.21      ! [A: int,B: int] :
% 9.25/5.21        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.25/5.21       => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 9.25/5.21          = ( divide_divide_int @ B @ A ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5451_unit__mult__div__div,axiom,
% 9.25/5.21      ! [A: code_integer,B: code_integer] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.25/5.21       => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 9.25/5.21          = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5452_unit__mult__div__div,axiom,
% 9.25/5.21      ! [A: code_natural,B: code_natural] :
% 9.25/5.21        ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 9.25/5.21       => ( ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ one_one_Code_natural @ A ) )
% 9.25/5.21          = ( divide5121882707175180666atural @ B @ A ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5453_unit__div__mult__self,axiom,
% 9.25/5.21      ! [A: nat,B: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.25/5.21       => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 9.25/5.21          = B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5454_unit__div__mult__self,axiom,
% 9.25/5.21      ! [A: int,B: int] :
% 9.25/5.21        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.25/5.21       => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 9.25/5.21          = B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5455_unit__div__mult__self,axiom,
% 9.25/5.21      ! [A: code_integer,B: code_integer] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.25/5.21       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 9.25/5.21          = B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5456_unit__div__mult__self,axiom,
% 9.25/5.21      ! [A: code_natural,B: code_natural] :
% 9.25/5.21        ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 9.25/5.21       => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ B @ A ) @ A )
% 9.25/5.21          = B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5457_power__strict__increasing__iff,axiom,
% 9.25/5.21      ! [B: code_integer,X: nat,Y: nat] :
% 9.25/5.21        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 9.25/5.21       => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ X ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 9.25/5.21          = ( ord_less_nat @ X @ Y ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5458_power__strict__increasing__iff,axiom,
% 9.25/5.21      ! [B: rat,X: nat,Y: nat] :
% 9.25/5.21        ( ( ord_less_rat @ one_one_rat @ B )
% 9.25/5.21       => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 9.25/5.21          = ( ord_less_nat @ X @ Y ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5459_power__strict__increasing__iff,axiom,
% 9.25/5.21      ! [B: nat,X: nat,Y: nat] :
% 9.25/5.21        ( ( ord_less_nat @ one_one_nat @ B )
% 9.25/5.21       => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 9.25/5.21          = ( ord_less_nat @ X @ Y ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5460_power__strict__increasing__iff,axiom,
% 9.25/5.21      ! [B: int,X: nat,Y: nat] :
% 9.25/5.21        ( ( ord_less_int @ one_one_int @ B )
% 9.25/5.21       => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 9.25/5.21          = ( ord_less_nat @ X @ Y ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5461_minus__one__mult__self,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 9.25/5.21        = one_one_int ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5462_minus__one__mult__self,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 9.25/5.21        = one_one_Code_integer ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5463_minus__one__mult__self,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 9.25/5.21        = one_one_rat ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5464_left__minus__one__mult__self,axiom,
% 9.25/5.21      ! [N: nat,A: int] :
% 9.25/5.21        ( ( 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 ) )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5465_left__minus__one__mult__self,axiom,
% 9.25/5.21      ! [N: nat,A: code_integer] :
% 9.25/5.21        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5466_left__minus__one__mult__self,axiom,
% 9.25/5.21      ! [N: nat,A: rat] :
% 9.25/5.21        ( ( 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 ) )
% 9.25/5.21        = A ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5467_and__numerals_I8_J,axiom,
% 9.25/5.21      ! [X: num] :
% 9.25/5.21        ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ one_one_Code_integer )
% 9.25/5.21        = one_one_Code_integer ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5468_and__numerals_I8_J,axiom,
% 9.25/5.21      ! [X: num] :
% 9.25/5.21        ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ one_one_Code_natural )
% 9.25/5.21        = one_one_Code_natural ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5469_and__numerals_I8_J,axiom,
% 9.25/5.21      ! [X: num] :
% 9.25/5.21        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 9.25/5.21        = one_one_int ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5470_and__numerals_I8_J,axiom,
% 9.25/5.21      ! [X: num] :
% 9.25/5.21        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 9.25/5.21        = one_one_nat ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5471_and__numerals_I2_J,axiom,
% 9.25/5.21      ! [Y: num] :
% 9.25/5.21        ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 9.25/5.21        = one_one_Code_integer ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5472_and__numerals_I2_J,axiom,
% 9.25/5.21      ! [Y: num] :
% 9.25/5.21        ( ( bit_se2773287842338716102atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 9.25/5.21        = one_one_Code_natural ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5473_and__numerals_I2_J,axiom,
% 9.25/5.21      ! [Y: num] :
% 9.25/5.21        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 9.25/5.21        = one_one_int ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5474_and__numerals_I2_J,axiom,
% 9.25/5.21      ! [Y: num] :
% 9.25/5.21        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 9.25/5.21        = one_one_nat ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5475_mask__Suc__0,axiom,
% 9.25/5.21      ( ( bit_se2119862282449309892nteger @ ( suc @ zero_zero_nat ) )
% 9.25/5.21      = one_one_Code_integer ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5476_mask__Suc__0,axiom,
% 9.25/5.21      ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 9.25/5.21      = one_one_int ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5477_mask__Suc__0,axiom,
% 9.25/5.21      ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 9.25/5.21      = one_one_nat ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5478_power__add__numeral,axiom,
% 9.25/5.21      ! [A: code_integer,M: num,N: num] :
% 9.25/5.21        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ N ) ) )
% 9.25/5.21        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5479_power__add__numeral,axiom,
% 9.25/5.21      ! [A: assn,M: num,N: num] :
% 9.25/5.21        ( ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_assn @ A @ ( numeral_numeral_nat @ N ) ) )
% 9.25/5.21        = ( power_power_assn @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5480_power__add__numeral,axiom,
% 9.25/5.21      ! [A: rat,M: num,N: num] :
% 9.25/5.21        ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) )
% 9.25/5.21        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5481_power__add__numeral,axiom,
% 9.25/5.21      ! [A: nat,M: num,N: num] :
% 9.25/5.21        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 9.25/5.21        = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5482_power__add__numeral,axiom,
% 9.25/5.21      ! [A: int,M: num,N: num] :
% 9.25/5.21        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 9.25/5.21        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5483_power__add__numeral2,axiom,
% 9.25/5.21      ! [A: code_integer,M: num,N: num,B: code_integer] :
% 9.25/5.21        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 9.25/5.21        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5484_power__add__numeral2,axiom,
% 9.25/5.21      ! [A: assn,M: num,N: num,B: assn] :
% 9.25/5.21        ( ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 9.25/5.21        = ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5485_power__add__numeral2,axiom,
% 9.25/5.21      ! [A: rat,M: num,N: num,B: rat] :
% 9.25/5.21        ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 9.25/5.21        = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5486_power__add__numeral2,axiom,
% 9.25/5.21      ! [A: nat,M: num,N: num,B: nat] :
% 9.25/5.21        ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 9.25/5.21        = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5487_power__add__numeral2,axiom,
% 9.25/5.21      ! [A: int,M: num,N: num,B: int] :
% 9.25/5.21        ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 9.25/5.21        = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5488_take__bit__minus__one__eq__mask,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( bit_se1745604003318907178nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.21        = ( bit_se2119862282449309892nteger @ N ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5489_take__bit__minus__one__eq__mask,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.21        = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5490_normalize__denom__zero,axiom,
% 9.25/5.21      ! [P4: int] :
% 9.25/5.21        ( ( normalize @ ( product_Pair_int_int @ P4 @ zero_zero_int ) )
% 9.25/5.21        = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5491_power__strict__decreasing__iff,axiom,
% 9.25/5.21      ! [B: code_integer,M: nat,N: nat] :
% 9.25/5.21        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 9.25/5.21       => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 9.25/5.21         => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ M ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 9.25/5.21            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5492_power__strict__decreasing__iff,axiom,
% 9.25/5.21      ! [B: rat,M: nat,N: nat] :
% 9.25/5.21        ( ( ord_less_rat @ zero_zero_rat @ B )
% 9.25/5.21       => ( ( ord_less_rat @ B @ one_one_rat )
% 9.25/5.21         => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 9.25/5.21            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5493_power__strict__decreasing__iff,axiom,
% 9.25/5.21      ! [B: nat,M: nat,N: nat] :
% 9.25/5.21        ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.25/5.21       => ( ( ord_less_nat @ B @ one_one_nat )
% 9.25/5.21         => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 9.25/5.21            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5494_power__strict__decreasing__iff,axiom,
% 9.25/5.21      ! [B: int,M: nat,N: nat] :
% 9.25/5.21        ( ( ord_less_int @ zero_zero_int @ B )
% 9.25/5.21       => ( ( ord_less_int @ B @ one_one_int )
% 9.25/5.21         => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 9.25/5.21            = ( ord_less_nat @ N @ M ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5495_even__mult__iff,axiom,
% 9.25/5.21      ! [A: nat,B: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 9.25/5.21        = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.25/5.21          | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5496_even__mult__iff,axiom,
% 9.25/5.21      ! [A: int,B: int] :
% 9.25/5.21        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 9.25/5.21        = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.25/5.21          | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5497_even__mult__iff,axiom,
% 9.25/5.21      ! [A: code_integer,B: code_integer] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 9.25/5.21        = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.25/5.21          | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5498_even__mult__iff,axiom,
% 9.25/5.21      ! [A: code_natural,B: code_natural] :
% 9.25/5.21        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( times_2397367101498566445atural @ A @ B ) )
% 9.25/5.21        = ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.25/5.21          | ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5499_power__increasing__iff,axiom,
% 9.25/5.21      ! [B: code_integer,X: nat,Y: nat] :
% 9.25/5.21        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 9.25/5.21       => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ X ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 9.25/5.21          = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5500_power__increasing__iff,axiom,
% 9.25/5.21      ! [B: rat,X: nat,Y: nat] :
% 9.25/5.21        ( ( ord_less_rat @ one_one_rat @ B )
% 9.25/5.21       => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 9.25/5.21          = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5501_power__increasing__iff,axiom,
% 9.25/5.21      ! [B: nat,X: nat,Y: nat] :
% 9.25/5.21        ( ( ord_less_nat @ one_one_nat @ B )
% 9.25/5.21       => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 9.25/5.21          = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5502_power__increasing__iff,axiom,
% 9.25/5.21      ! [B: int,X: nat,Y: nat] :
% 9.25/5.21        ( ( ord_less_int @ one_one_int @ B )
% 9.25/5.21       => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 9.25/5.21          = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5503_and__numerals_I5_J,axiom,
% 9.25/5.21      ! [X: num] :
% 9.25/5.21        ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ one_one_Code_integer )
% 9.25/5.21        = zero_z3403309356797280102nteger ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5504_and__numerals_I5_J,axiom,
% 9.25/5.21      ! [X: num] :
% 9.25/5.21        ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ one_one_Code_natural )
% 9.25/5.21        = zero_z2226904508553997617atural ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5505_and__numerals_I5_J,axiom,
% 9.25/5.21      ! [X: num] :
% 9.25/5.21        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 9.25/5.21        = zero_zero_int ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5506_and__numerals_I5_J,axiom,
% 9.25/5.21      ! [X: num] :
% 9.25/5.21        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 9.25/5.21        = zero_zero_nat ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5507_and__numerals_I1_J,axiom,
% 9.25/5.21      ! [Y: num] :
% 9.25/5.21        ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 9.25/5.21        = zero_z3403309356797280102nteger ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5508_and__numerals_I1_J,axiom,
% 9.25/5.21      ! [Y: num] :
% 9.25/5.21        ( ( bit_se2773287842338716102atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 9.25/5.21        = zero_z2226904508553997617atural ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5509_and__numerals_I1_J,axiom,
% 9.25/5.21      ! [Y: num] :
% 9.25/5.21        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 9.25/5.21        = zero_zero_int ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5510_and__numerals_I1_J,axiom,
% 9.25/5.21      ! [Y: num] :
% 9.25/5.21        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 9.25/5.21        = zero_zero_nat ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5511_and__numerals_I3_J,axiom,
% 9.25/5.21      ! [X: num,Y: num] :
% 9.25/5.21        ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 9.25/5.21        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5512_and__numerals_I3_J,axiom,
% 9.25/5.21      ! [X: num,Y: num] :
% 9.25/5.21        ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 9.25/5.21        = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5513_and__numerals_I3_J,axiom,
% 9.25/5.21      ! [X: num,Y: num] :
% 9.25/5.21        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 9.25/5.21        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5514_and__numerals_I3_J,axiom,
% 9.25/5.21      ! [X: num,Y: num] :
% 9.25/5.21        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 9.25/5.21        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5515_power2__minus,axiom,
% 9.25/5.21      ! [A: int] :
% 9.25/5.21        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.21        = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5516_power2__minus,axiom,
% 9.25/5.21      ! [A: code_integer] :
% 9.25/5.21        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.21        = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5517_power2__minus,axiom,
% 9.25/5.21      ! [A: rat] :
% 9.25/5.21        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.21        = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5518_and__minus__numerals_I6_J,axiom,
% 9.25/5.21      ! [N: num] :
% 9.25/5.21        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 9.25/5.21        = one_one_int ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5519_and__minus__numerals_I2_J,axiom,
% 9.25/5.21      ! [N: num] :
% 9.25/5.21        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 9.25/5.21        = one_one_int ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5520_power__decreasing__iff,axiom,
% 9.25/5.21      ! [B: code_integer,M: nat,N: nat] :
% 9.25/5.21        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 9.25/5.21       => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 9.25/5.21         => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ M ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 9.25/5.21            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5521_power__decreasing__iff,axiom,
% 9.25/5.21      ! [B: rat,M: nat,N: nat] :
% 9.25/5.21        ( ( ord_less_rat @ zero_zero_rat @ B )
% 9.25/5.21       => ( ( ord_less_rat @ B @ one_one_rat )
% 9.25/5.21         => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 9.25/5.21            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5522_power__decreasing__iff,axiom,
% 9.25/5.21      ! [B: nat,M: nat,N: nat] :
% 9.25/5.21        ( ( ord_less_nat @ zero_zero_nat @ B )
% 9.25/5.21       => ( ( ord_less_nat @ B @ one_one_nat )
% 9.25/5.21         => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 9.25/5.21            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5523_power__decreasing__iff,axiom,
% 9.25/5.21      ! [B: int,M: nat,N: nat] :
% 9.25/5.21        ( ( ord_less_int @ zero_zero_int @ B )
% 9.25/5.21       => ( ( ord_less_int @ B @ one_one_int )
% 9.25/5.21         => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 9.25/5.21            = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5524_even__plus__one__iff,axiom,
% 9.25/5.21      ! [A: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 9.25/5.21        = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5525_even__plus__one__iff,axiom,
% 9.25/5.21      ! [A: int] :
% 9.25/5.21        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 9.25/5.21        = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5526_even__plus__one__iff,axiom,
% 9.25/5.21      ! [A: code_integer] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 9.25/5.21        = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5527_even__plus__one__iff,axiom,
% 9.25/5.21      ! [A: code_natural] :
% 9.25/5.21        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) )
% 9.25/5.21        = ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5528_and__numerals_I4_J,axiom,
% 9.25/5.21      ! [X: num,Y: num] :
% 9.25/5.21        ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 9.25/5.21        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5529_and__numerals_I4_J,axiom,
% 9.25/5.21      ! [X: num,Y: num] :
% 9.25/5.21        ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 9.25/5.21        = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5530_and__numerals_I4_J,axiom,
% 9.25/5.21      ! [X: num,Y: num] :
% 9.25/5.21        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 9.25/5.21        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5531_and__numerals_I4_J,axiom,
% 9.25/5.21      ! [X: num,Y: num] :
% 9.25/5.21        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 9.25/5.21        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5532_and__numerals_I6_J,axiom,
% 9.25/5.21      ! [X: num,Y: num] :
% 9.25/5.21        ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 9.25/5.21        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5533_and__numerals_I6_J,axiom,
% 9.25/5.21      ! [X: num,Y: num] :
% 9.25/5.21        ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 9.25/5.21        = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5534_and__numerals_I6_J,axiom,
% 9.25/5.21      ! [X: num,Y: num] :
% 9.25/5.21        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 9.25/5.21        = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5535_and__numerals_I6_J,axiom,
% 9.25/5.21      ! [X: num,Y: num] :
% 9.25/5.21        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 9.25/5.21        = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5536_Power_Oring__1__class_Opower__minus__even,axiom,
% 9.25/5.21      ! [A: int,N: nat] :
% 9.25/5.21        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.21        = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5537_Power_Oring__1__class_Opower__minus__even,axiom,
% 9.25/5.21      ! [A: code_integer,N: nat] :
% 9.25/5.21        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.21        = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5538_Power_Oring__1__class_Opower__minus__even,axiom,
% 9.25/5.21      ! [A: rat,N: nat] :
% 9.25/5.21        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.21        = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5539_Parity_Oring__1__class_Opower__minus__even,axiom,
% 9.25/5.21      ! [N: nat,A: int] :
% 9.25/5.21        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.21       => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 9.25/5.21          = ( power_power_int @ A @ N ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5540_Parity_Oring__1__class_Opower__minus__even,axiom,
% 9.25/5.21      ! [N: nat,A: code_integer] :
% 9.25/5.21        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.21       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 9.25/5.21          = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5541_Parity_Oring__1__class_Opower__minus__even,axiom,
% 9.25/5.21      ! [N: nat,A: rat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.21       => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 9.25/5.21          = ( power_power_rat @ A @ N ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5542_power__minus__odd,axiom,
% 9.25/5.21      ! [N: nat,A: int] :
% 9.25/5.21        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.21       => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 9.25/5.21          = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5543_power__minus__odd,axiom,
% 9.25/5.21      ! [N: nat,A: code_integer] :
% 9.25/5.21        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.21       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 9.25/5.21          = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5544_power__minus__odd,axiom,
% 9.25/5.21      ! [N: nat,A: rat] :
% 9.25/5.21        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.21       => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 9.25/5.21          = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5545_and__minus__numerals_I5_J,axiom,
% 9.25/5.21      ! [N: num] :
% 9.25/5.21        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 9.25/5.21        = zero_zero_int ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5546_and__minus__numerals_I1_J,axiom,
% 9.25/5.21      ! [N: num] :
% 9.25/5.21        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 9.25/5.21        = zero_zero_int ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5547_even__succ__div__two,axiom,
% 9.25/5.21      ! [A: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.21          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5548_even__succ__div__two,axiom,
% 9.25/5.21      ! [A: int] :
% 9.25/5.21        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.21          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5549_even__succ__div__two,axiom,
% 9.25/5.21      ! [A: code_integer] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.21          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5550_even__succ__div__two,axiom,
% 9.25/5.21      ! [A: code_natural] :
% 9.25/5.21        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.21          = ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5551_odd__succ__div__two,axiom,
% 9.25/5.21      ! [A: nat] :
% 9.25/5.21        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.21          = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5552_odd__succ__div__two,axiom,
% 9.25/5.21      ! [A: int] :
% 9.25/5.21        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.21          = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5553_odd__succ__div__two,axiom,
% 9.25/5.21      ! [A: code_integer] :
% 9.25/5.21        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.21          = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5554_odd__succ__div__two,axiom,
% 9.25/5.21      ! [A: code_natural] :
% 9.25/5.21        ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ one_one_Code_natural ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.21          = ( plus_p4538020629002901425atural @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ one_one_Code_natural ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5555_even__succ__div__2,axiom,
% 9.25/5.21      ! [A: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.21          = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5556_even__succ__div__2,axiom,
% 9.25/5.21      ! [A: int] :
% 9.25/5.21        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.21          = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5557_even__succ__div__2,axiom,
% 9.25/5.21      ! [A: code_integer] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.21          = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5558_even__succ__div__2,axiom,
% 9.25/5.21      ! [A: code_natural] :
% 9.25/5.21        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.21          = ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5559_power__minus1__even,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.21        = one_one_int ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5560_power__minus1__even,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.21        = one_one_Code_integer ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5561_power__minus1__even,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.21        = one_one_rat ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5562_neg__one__odd__power,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.21       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 9.25/5.21          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5563_neg__one__odd__power,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.21       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 9.25/5.21          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5564_neg__one__odd__power,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.21       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 9.25/5.21          = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5565_neg__one__even__power,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.21       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 9.25/5.21          = one_one_int ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5566_neg__one__even__power,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.21       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 9.25/5.21          = one_one_Code_integer ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5567_neg__one__even__power,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.21       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 9.25/5.21          = one_one_rat ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5568_semiring__parity__class_Oeven__mask__iff,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 9.25/5.21        = ( N = zero_zero_nat ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5569_semiring__parity__class_Oeven__mask__iff,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 9.25/5.21        = ( N = zero_zero_nat ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5570_semiring__parity__class_Oeven__mask__iff,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 9.25/5.21        = ( N = zero_zero_nat ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5571_semiring__parity__class_Oeven__mask__iff,axiom,
% 9.25/5.21      ! [N: nat] :
% 9.25/5.21        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) @ one_one_Code_natural ) )
% 9.25/5.21        = ( N = zero_zero_nat ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5572_and__numerals_I7_J,axiom,
% 9.25/5.21      ! [X: num,Y: num] :
% 9.25/5.21        ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 9.25/5.21        = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5573_and__numerals_I7_J,axiom,
% 9.25/5.21      ! [X: num,Y: num] :
% 9.25/5.21        ( ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 9.25/5.21        = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2773287842338716102atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5574_and__numerals_I7_J,axiom,
% 9.25/5.21      ! [X: num,Y: num] :
% 9.25/5.21        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 9.25/5.21        = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5575_and__numerals_I7_J,axiom,
% 9.25/5.21      ! [X: num,Y: num] :
% 9.25/5.21        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 9.25/5.21        = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5576_even__succ__div__exp,axiom,
% 9.25/5.21      ! [A: nat,N: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.21         => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.21            = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5577_even__succ__div__exp,axiom,
% 9.25/5.21      ! [A: int,N: nat] :
% 9.25/5.21        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.21         => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.21            = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5578_even__succ__div__exp,axiom,
% 9.25/5.21      ! [A: code_integer,N: nat] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.21         => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.21            = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5579_even__succ__div__exp,axiom,
% 9.25/5.21      ! [A: code_natural,N: nat] :
% 9.25/5.21        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.21         => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.21            = ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5580_even__succ__mod__exp,axiom,
% 9.25/5.21      ! [A: nat,N: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.21         => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.21            = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5581_even__succ__mod__exp,axiom,
% 9.25/5.21      ! [A: int,N: nat] :
% 9.25/5.21        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.21         => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.21            = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5582_even__succ__mod__exp,axiom,
% 9.25/5.21      ! [A: code_integer,N: nat] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.21         => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.21            = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5583_even__succ__mod__exp,axiom,
% 9.25/5.21      ! [A: code_natural,N: nat] :
% 9.25/5.21        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.25/5.21       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.21         => ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.21            = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5584_is__unit__power__iff,axiom,
% 9.25/5.21      ! [A: code_integer,N: nat] :
% 9.25/5.21        ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 9.25/5.21        = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.25/5.21          | ( N = zero_zero_nat ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5585_is__unit__power__iff,axiom,
% 9.25/5.21      ! [A: int,N: nat] :
% 9.25/5.21        ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 9.25/5.21        = ( ( dvd_dvd_int @ A @ one_one_int )
% 9.25/5.21          | ( N = zero_zero_nat ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5586_is__unit__power__iff,axiom,
% 9.25/5.21      ! [A: nat,N: nat] :
% 9.25/5.21        ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 9.25/5.21        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.25/5.21          | ( N = zero_zero_nat ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5587_power__commuting__commutes,axiom,
% 9.25/5.21      ! [X: code_integer,Y: code_integer,N: nat] :
% 9.25/5.21        ( ( ( times_3573771949741848930nteger @ X @ Y )
% 9.25/5.21          = ( times_3573771949741848930nteger @ Y @ X ) )
% 9.25/5.21       => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ N ) @ Y )
% 9.25/5.21          = ( times_3573771949741848930nteger @ Y @ ( power_8256067586552552935nteger @ X @ N ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5588_power__commuting__commutes,axiom,
% 9.25/5.21      ! [X: assn,Y: assn,N: nat] :
% 9.25/5.21        ( ( ( times_times_assn @ X @ Y )
% 9.25/5.21          = ( times_times_assn @ Y @ X ) )
% 9.25/5.21       => ( ( times_times_assn @ ( power_power_assn @ X @ N ) @ Y )
% 9.25/5.21          = ( times_times_assn @ Y @ ( power_power_assn @ X @ N ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5589_power__commuting__commutes,axiom,
% 9.25/5.21      ! [X: rat,Y: rat,N: nat] :
% 9.25/5.21        ( ( ( times_times_rat @ X @ Y )
% 9.25/5.21          = ( times_times_rat @ Y @ X ) )
% 9.25/5.21       => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ Y )
% 9.25/5.21          = ( times_times_rat @ Y @ ( power_power_rat @ X @ N ) ) ) ) ).
% 9.25/5.21  
% 9.25/5.21  thf(fact_5590_power__commuting__commutes,axiom,
% 9.25/5.21      ! [X: nat,Y: nat,N: nat] :
% 9.25/5.21        ( ( ( times_times_nat @ X @ Y )
% 9.25/5.21          = ( times_times_nat @ Y @ X ) )
% 9.25/5.22       => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ Y )
% 9.25/5.22          = ( times_times_nat @ Y @ ( power_power_nat @ X @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5591_power__commuting__commutes,axiom,
% 9.25/5.22      ! [X: int,Y: int,N: nat] :
% 9.25/5.22        ( ( ( times_times_int @ X @ Y )
% 9.25/5.22          = ( times_times_int @ Y @ X ) )
% 9.25/5.22       => ( ( times_times_int @ ( power_power_int @ X @ N ) @ Y )
% 9.25/5.22          = ( times_times_int @ Y @ ( power_power_int @ X @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5592_power__mult__distrib,axiom,
% 9.25/5.22      ! [A: code_integer,B: code_integer,N: nat] :
% 9.25/5.22        ( ( power_8256067586552552935nteger @ ( times_3573771949741848930nteger @ A @ B ) @ N )
% 9.25/5.22        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5593_power__mult__distrib,axiom,
% 9.25/5.22      ! [A: assn,B: assn,N: nat] :
% 9.25/5.22        ( ( power_power_assn @ ( times_times_assn @ A @ B ) @ N )
% 9.25/5.22        = ( times_times_assn @ ( power_power_assn @ A @ N ) @ ( power_power_assn @ B @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5594_power__mult__distrib,axiom,
% 9.25/5.22      ! [A: rat,B: rat,N: nat] :
% 9.25/5.22        ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N )
% 9.25/5.22        = ( times_times_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5595_power__mult__distrib,axiom,
% 9.25/5.22      ! [A: nat,B: nat,N: nat] :
% 9.25/5.22        ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 9.25/5.22        = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5596_power__mult__distrib,axiom,
% 9.25/5.22      ! [A: int,B: int,N: nat] :
% 9.25/5.22        ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 9.25/5.22        = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5597_power__commutes,axiom,
% 9.25/5.22      ! [A: code_integer,N: nat] :
% 9.25/5.22        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ N ) @ A )
% 9.25/5.22        = ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5598_power__commutes,axiom,
% 9.25/5.22      ! [A: assn,N: nat] :
% 9.25/5.22        ( ( times_times_assn @ ( power_power_assn @ A @ N ) @ A )
% 9.25/5.22        = ( times_times_assn @ A @ ( power_power_assn @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5599_power__commutes,axiom,
% 9.25/5.22      ! [A: rat,N: nat] :
% 9.25/5.22        ( ( times_times_rat @ ( power_power_rat @ A @ N ) @ A )
% 9.25/5.22        = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5600_power__commutes,axiom,
% 9.25/5.22      ! [A: nat,N: nat] :
% 9.25/5.22        ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 9.25/5.22        = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5601_power__commutes,axiom,
% 9.25/5.22      ! [A: int,N: nat] :
% 9.25/5.22        ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 9.25/5.22        = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5602_dvdE,axiom,
% 9.25/5.22      ! [B: code_integer,A: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ B @ A )
% 9.25/5.22       => ~ ! [K2: code_integer] :
% 9.25/5.22              ( A
% 9.25/5.22             != ( times_3573771949741848930nteger @ B @ K2 ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5603_dvdE,axiom,
% 9.25/5.22      ! [B: assn,A: assn] :
% 9.25/5.22        ( ( dvd_dvd_assn @ B @ A )
% 9.25/5.22       => ~ ! [K2: assn] :
% 9.25/5.22              ( A
% 9.25/5.22             != ( times_times_assn @ B @ K2 ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5604_dvdE,axiom,
% 9.25/5.22      ! [B: rat,A: rat] :
% 9.25/5.22        ( ( dvd_dvd_rat @ B @ A )
% 9.25/5.22       => ~ ! [K2: rat] :
% 9.25/5.22              ( A
% 9.25/5.22             != ( times_times_rat @ B @ K2 ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5605_dvdE,axiom,
% 9.25/5.22      ! [B: nat,A: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ B @ A )
% 9.25/5.22       => ~ ! [K2: nat] :
% 9.25/5.22              ( A
% 9.25/5.22             != ( times_times_nat @ B @ K2 ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5606_dvdE,axiom,
% 9.25/5.22      ! [B: int,A: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ B @ A )
% 9.25/5.22       => ~ ! [K2: int] :
% 9.25/5.22              ( A
% 9.25/5.22             != ( times_times_int @ B @ K2 ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5607_dvdI,axiom,
% 9.25/5.22      ! [A: code_integer,B: code_integer,K: code_integer] :
% 9.25/5.22        ( ( A
% 9.25/5.22          = ( times_3573771949741848930nteger @ B @ K ) )
% 9.25/5.22       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5608_dvdI,axiom,
% 9.25/5.22      ! [A: assn,B: assn,K: assn] :
% 9.25/5.22        ( ( A
% 9.25/5.22          = ( times_times_assn @ B @ K ) )
% 9.25/5.22       => ( dvd_dvd_assn @ B @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5609_dvdI,axiom,
% 9.25/5.22      ! [A: rat,B: rat,K: rat] :
% 9.25/5.22        ( ( A
% 9.25/5.22          = ( times_times_rat @ B @ K ) )
% 9.25/5.22       => ( dvd_dvd_rat @ B @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5610_dvdI,axiom,
% 9.25/5.22      ! [A: nat,B: nat,K: nat] :
% 9.25/5.22        ( ( A
% 9.25/5.22          = ( times_times_nat @ B @ K ) )
% 9.25/5.22       => ( dvd_dvd_nat @ B @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5611_dvdI,axiom,
% 9.25/5.22      ! [A: int,B: int,K: int] :
% 9.25/5.22        ( ( A
% 9.25/5.22          = ( times_times_int @ B @ K ) )
% 9.25/5.22       => ( dvd_dvd_int @ B @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5612_dvd__def,axiom,
% 9.25/5.22      ( dvd_dvd_Code_integer
% 9.25/5.22      = ( ^ [B3: code_integer,A3: code_integer] :
% 9.25/5.22          ? [K4: code_integer] :
% 9.25/5.22            ( A3
% 9.25/5.22            = ( times_3573771949741848930nteger @ B3 @ K4 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5613_dvd__def,axiom,
% 9.25/5.22      ( dvd_dvd_assn
% 9.25/5.22      = ( ^ [B3: assn,A3: assn] :
% 9.25/5.22          ? [K4: assn] :
% 9.25/5.22            ( A3
% 9.25/5.22            = ( times_times_assn @ B3 @ K4 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5614_dvd__def,axiom,
% 9.25/5.22      ( dvd_dvd_rat
% 9.25/5.22      = ( ^ [B3: rat,A3: rat] :
% 9.25/5.22          ? [K4: rat] :
% 9.25/5.22            ( A3
% 9.25/5.22            = ( times_times_rat @ B3 @ K4 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5615_dvd__def,axiom,
% 9.25/5.22      ( dvd_dvd_nat
% 9.25/5.22      = ( ^ [B3: nat,A3: nat] :
% 9.25/5.22          ? [K4: nat] :
% 9.25/5.22            ( A3
% 9.25/5.22            = ( times_times_nat @ B3 @ K4 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5616_dvd__def,axiom,
% 9.25/5.22      ( dvd_dvd_int
% 9.25/5.22      = ( ^ [B3: int,A3: int] :
% 9.25/5.22          ? [K4: int] :
% 9.25/5.22            ( A3
% 9.25/5.22            = ( times_times_int @ B3 @ K4 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5617_dvd__mult,axiom,
% 9.25/5.22      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ A @ C )
% 9.25/5.22       => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5618_dvd__mult,axiom,
% 9.25/5.22      ! [A: assn,C: assn,B: assn] :
% 9.25/5.22        ( ( dvd_dvd_assn @ A @ C )
% 9.25/5.22       => ( dvd_dvd_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5619_dvd__mult,axiom,
% 9.25/5.22      ! [A: rat,C: rat,B: rat] :
% 9.25/5.22        ( ( dvd_dvd_rat @ A @ C )
% 9.25/5.22       => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5620_dvd__mult,axiom,
% 9.25/5.22      ! [A: nat,C: nat,B: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ A @ C )
% 9.25/5.22       => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5621_dvd__mult,axiom,
% 9.25/5.22      ! [A: int,C: int,B: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ A @ C )
% 9.25/5.22       => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5622_dvd__mult2,axiom,
% 9.25/5.22      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ A @ B )
% 9.25/5.22       => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5623_dvd__mult2,axiom,
% 9.25/5.22      ! [A: assn,B: assn,C: assn] :
% 9.25/5.22        ( ( dvd_dvd_assn @ A @ B )
% 9.25/5.22       => ( dvd_dvd_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5624_dvd__mult2,axiom,
% 9.25/5.22      ! [A: rat,B: rat,C: rat] :
% 9.25/5.22        ( ( dvd_dvd_rat @ A @ B )
% 9.25/5.22       => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5625_dvd__mult2,axiom,
% 9.25/5.22      ! [A: nat,B: nat,C: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ A @ B )
% 9.25/5.22       => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5626_dvd__mult2,axiom,
% 9.25/5.22      ! [A: int,B: int,C: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ A @ B )
% 9.25/5.22       => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5627_dvd__mult__left,axiom,
% 9.25/5.22      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 9.25/5.22       => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5628_dvd__mult__left,axiom,
% 9.25/5.22      ! [A: assn,B: assn,C: assn] :
% 9.25/5.22        ( ( dvd_dvd_assn @ ( times_times_assn @ A @ B ) @ C )
% 9.25/5.22       => ( dvd_dvd_assn @ A @ C ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5629_dvd__mult__left,axiom,
% 9.25/5.22      ! [A: rat,B: rat,C: rat] :
% 9.25/5.22        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 9.25/5.22       => ( dvd_dvd_rat @ A @ C ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5630_dvd__mult__left,axiom,
% 9.25/5.22      ! [A: nat,B: nat,C: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 9.25/5.22       => ( dvd_dvd_nat @ A @ C ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5631_dvd__mult__left,axiom,
% 9.25/5.22      ! [A: int,B: int,C: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 9.25/5.22       => ( dvd_dvd_int @ A @ C ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5632_dvd__triv__left,axiom,
% 9.25/5.22      ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5633_dvd__triv__left,axiom,
% 9.25/5.22      ! [A: assn,B: assn] : ( dvd_dvd_assn @ A @ ( times_times_assn @ A @ B ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5634_dvd__triv__left,axiom,
% 9.25/5.22      ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5635_dvd__triv__left,axiom,
% 9.25/5.22      ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5636_dvd__triv__left,axiom,
% 9.25/5.22      ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5637_mult__dvd__mono,axiom,
% 9.25/5.22      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ A @ B )
% 9.25/5.22       => ( ( dvd_dvd_Code_integer @ C @ D2 )
% 9.25/5.22         => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5638_mult__dvd__mono,axiom,
% 9.25/5.22      ! [A: assn,B: assn,C: assn,D2: assn] :
% 9.25/5.22        ( ( dvd_dvd_assn @ A @ B )
% 9.25/5.22       => ( ( dvd_dvd_assn @ C @ D2 )
% 9.25/5.22         => ( dvd_dvd_assn @ ( times_times_assn @ A @ C ) @ ( times_times_assn @ B @ D2 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5639_mult__dvd__mono,axiom,
% 9.25/5.22      ! [A: rat,B: rat,C: rat,D2: rat] :
% 9.25/5.22        ( ( dvd_dvd_rat @ A @ B )
% 9.25/5.22       => ( ( dvd_dvd_rat @ C @ D2 )
% 9.25/5.22         => ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5640_mult__dvd__mono,axiom,
% 9.25/5.22      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ A @ B )
% 9.25/5.22       => ( ( dvd_dvd_nat @ C @ D2 )
% 9.25/5.22         => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5641_mult__dvd__mono,axiom,
% 9.25/5.22      ! [A: int,B: int,C: int,D2: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ A @ B )
% 9.25/5.22       => ( ( dvd_dvd_int @ C @ D2 )
% 9.25/5.22         => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5642_dvd__mult__right,axiom,
% 9.25/5.22      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 9.25/5.22       => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5643_dvd__mult__right,axiom,
% 9.25/5.22      ! [A: assn,B: assn,C: assn] :
% 9.25/5.22        ( ( dvd_dvd_assn @ ( times_times_assn @ A @ B ) @ C )
% 9.25/5.22       => ( dvd_dvd_assn @ B @ C ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5644_dvd__mult__right,axiom,
% 9.25/5.22      ! [A: rat,B: rat,C: rat] :
% 9.25/5.22        ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 9.25/5.22       => ( dvd_dvd_rat @ B @ C ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5645_dvd__mult__right,axiom,
% 9.25/5.22      ! [A: nat,B: nat,C: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 9.25/5.22       => ( dvd_dvd_nat @ B @ C ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5646_dvd__mult__right,axiom,
% 9.25/5.22      ! [A: int,B: int,C: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 9.25/5.22       => ( dvd_dvd_int @ B @ C ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5647_dvd__triv__right,axiom,
% 9.25/5.22      ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5648_dvd__triv__right,axiom,
% 9.25/5.22      ! [A: assn,B: assn] : ( dvd_dvd_assn @ A @ ( times_times_assn @ B @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5649_dvd__triv__right,axiom,
% 9.25/5.22      ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5650_dvd__triv__right,axiom,
% 9.25/5.22      ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5651_dvd__triv__right,axiom,
% 9.25/5.22      ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5652_one__dvd,axiom,
% 9.25/5.22      ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5653_one__dvd,axiom,
% 9.25/5.22      ! [A: assn] : ( dvd_dvd_assn @ one_one_assn @ A ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5654_one__dvd,axiom,
% 9.25/5.22      ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5655_one__dvd,axiom,
% 9.25/5.22      ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5656_one__dvd,axiom,
% 9.25/5.22      ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5657_unit__imp__dvd,axiom,
% 9.25/5.22      ! [B: code_integer,A: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.25/5.22       => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5658_unit__imp__dvd,axiom,
% 9.25/5.22      ! [B: nat,A: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.25/5.22       => ( dvd_dvd_nat @ B @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5659_unit__imp__dvd,axiom,
% 9.25/5.22      ! [B: int,A: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.25/5.22       => ( dvd_dvd_int @ B @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5660_dvd__unit__imp__unit,axiom,
% 9.25/5.22      ! [A: code_integer,B: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ A @ B )
% 9.25/5.22       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.25/5.22         => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5661_dvd__unit__imp__unit,axiom,
% 9.25/5.22      ! [A: nat,B: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ A @ B )
% 9.25/5.22       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.25/5.22         => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5662_dvd__unit__imp__unit,axiom,
% 9.25/5.22      ! [A: int,B: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ A @ B )
% 9.25/5.22       => ( ( dvd_dvd_int @ B @ one_one_int )
% 9.25/5.22         => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5663_uminus__dvd__conv_I1_J,axiom,
% 9.25/5.22      ( dvd_dvd_int
% 9.25/5.22      = ( ^ [D4: int] : ( dvd_dvd_int @ ( uminus_uminus_int @ D4 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5664_uminus__dvd__conv_I2_J,axiom,
% 9.25/5.22      ( dvd_dvd_int
% 9.25/5.22      = ( ^ [D4: int,T2: int] : ( dvd_dvd_int @ D4 @ ( uminus_uminus_int @ T2 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5665_dvd__power__iff,axiom,
% 9.25/5.22      ! [X: code_integer,M: nat,N: nat] :
% 9.25/5.22        ( ( X != zero_z3403309356797280102nteger )
% 9.25/5.22       => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M ) @ ( power_8256067586552552935nteger @ X @ N ) )
% 9.25/5.22          = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 9.25/5.22            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5666_dvd__power__iff,axiom,
% 9.25/5.22      ! [X: int,M: nat,N: nat] :
% 9.25/5.22        ( ( X != zero_zero_int )
% 9.25/5.22       => ( ( dvd_dvd_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ N ) )
% 9.25/5.22          = ( ( dvd_dvd_int @ X @ one_one_int )
% 9.25/5.22            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5667_dvd__power__iff,axiom,
% 9.25/5.22      ! [X: nat,M: nat,N: nat] :
% 9.25/5.22        ( ( X != zero_zero_nat )
% 9.25/5.22       => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M ) @ ( power_power_nat @ X @ N ) )
% 9.25/5.22          = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 9.25/5.22            | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5668_dvd__power,axiom,
% 9.25/5.22      ! [N: nat,X: code_integer] :
% 9.25/5.22        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.22          | ( X = one_one_Code_integer ) )
% 9.25/5.22       => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5669_dvd__power,axiom,
% 9.25/5.22      ! [N: nat,X: rat] :
% 9.25/5.22        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.22          | ( X = one_one_rat ) )
% 9.25/5.22       => ( dvd_dvd_rat @ X @ ( power_power_rat @ X @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5670_dvd__power,axiom,
% 9.25/5.22      ! [N: nat,X: int] :
% 9.25/5.22        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.22          | ( X = one_one_int ) )
% 9.25/5.22       => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5671_dvd__power,axiom,
% 9.25/5.22      ! [N: nat,X: nat] :
% 9.25/5.22        ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.22          | ( X = one_one_nat ) )
% 9.25/5.22       => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5672_subset__divisors__dvd,axiom,
% 9.25/5.22      ! [A: int,B: int] :
% 9.25/5.22        ( ( ord_less_eq_set_int
% 9.25/5.22          @ ( collect_int
% 9.25/5.22            @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ A ) )
% 9.25/5.22          @ ( collect_int
% 9.25/5.22            @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ B ) ) )
% 9.25/5.22        = ( dvd_dvd_int @ A @ B ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5673_subset__divisors__dvd,axiom,
% 9.25/5.22      ! [A: code_integer,B: code_integer] :
% 9.25/5.22        ( ( ord_le7084787975880047091nteger
% 9.25/5.22          @ ( collect_Code_integer
% 9.25/5.22            @ ^ [C4: code_integer] : ( dvd_dvd_Code_integer @ C4 @ A ) )
% 9.25/5.22          @ ( collect_Code_integer
% 9.25/5.22            @ ^ [C4: code_integer] : ( dvd_dvd_Code_integer @ C4 @ B ) ) )
% 9.25/5.22        = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5674_subset__divisors__dvd,axiom,
% 9.25/5.22      ! [A: nat,B: nat] :
% 9.25/5.22        ( ( ord_less_eq_set_nat
% 9.25/5.22          @ ( collect_nat
% 9.25/5.22            @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ A ) )
% 9.25/5.22          @ ( collect_nat
% 9.25/5.22            @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ B ) ) )
% 9.25/5.22        = ( dvd_dvd_nat @ A @ B ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5675_strict__subset__divisors__dvd,axiom,
% 9.25/5.22      ! [A: nat,B: nat] :
% 9.25/5.22        ( ( ord_less_set_nat
% 9.25/5.22          @ ( collect_nat
% 9.25/5.22            @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ A ) )
% 9.25/5.22          @ ( collect_nat
% 9.25/5.22            @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ B ) ) )
% 9.25/5.22        = ( ( dvd_dvd_nat @ A @ B )
% 9.25/5.22          & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5676_strict__subset__divisors__dvd,axiom,
% 9.25/5.22      ! [A: int,B: int] :
% 9.25/5.22        ( ( ord_less_set_int
% 9.25/5.22          @ ( collect_int
% 9.25/5.22            @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ A ) )
% 9.25/5.22          @ ( collect_int
% 9.25/5.22            @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ B ) ) )
% 9.25/5.22        = ( ( dvd_dvd_int @ A @ B )
% 9.25/5.22          & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5677_strict__subset__divisors__dvd,axiom,
% 9.25/5.22      ! [A: code_integer,B: code_integer] :
% 9.25/5.22        ( ( ord_le1307284697595431911nteger
% 9.25/5.22          @ ( collect_Code_integer
% 9.25/5.22            @ ^ [C4: code_integer] : ( dvd_dvd_Code_integer @ C4 @ A ) )
% 9.25/5.22          @ ( collect_Code_integer
% 9.25/5.22            @ ^ [C4: code_integer] : ( dvd_dvd_Code_integer @ C4 @ B ) ) )
% 9.25/5.22        = ( ( dvd_dvd_Code_integer @ A @ B )
% 9.25/5.22          & ~ ( dvd_dvd_Code_integer @ B @ A ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5678_and__eq__minus__1__iff,axiom,
% 9.25/5.22      ! [A: code_integer,B: code_integer] :
% 9.25/5.22        ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 9.25/5.22          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.22        = ( ( A
% 9.25/5.22            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.22          & ( B
% 9.25/5.22            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5679_and__eq__minus__1__iff,axiom,
% 9.25/5.22      ! [A: int,B: int] :
% 9.25/5.22        ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 9.25/5.22          = ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.22        = ( ( A
% 9.25/5.22            = ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.22          & ( B
% 9.25/5.22            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5680_uminus__power__if,axiom,
% 9.25/5.22      ! [N: nat,A: int] :
% 9.25/5.22        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.22         => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 9.25/5.22            = ( power_power_int @ A @ N ) ) )
% 9.25/5.22        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.22         => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 9.25/5.22            = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5681_uminus__power__if,axiom,
% 9.25/5.22      ! [N: nat,A: code_integer] :
% 9.25/5.22        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.22         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 9.25/5.22            = ( power_8256067586552552935nteger @ A @ N ) ) )
% 9.25/5.22        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.22         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 9.25/5.22            = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5682_uminus__power__if,axiom,
% 9.25/5.22      ! [N: nat,A: rat] :
% 9.25/5.22        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.22         => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 9.25/5.22            = ( power_power_rat @ A @ N ) ) )
% 9.25/5.22        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.22         => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 9.25/5.22            = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5683_take__bit__eq__mask__iff__exp__dvd,axiom,
% 9.25/5.22      ! [N: nat,K: int] :
% 9.25/5.22        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 9.25/5.22          = ( bit_se2000444600071755411sk_int @ N ) )
% 9.25/5.22        = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5684_one__le__power,axiom,
% 9.25/5.22      ! [A: code_integer,N: nat] :
% 9.25/5.22        ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 9.25/5.22       => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5685_one__le__power,axiom,
% 9.25/5.22      ! [A: rat,N: nat] :
% 9.25/5.22        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 9.25/5.22       => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5686_one__le__power,axiom,
% 9.25/5.22      ! [A: nat,N: nat] :
% 9.25/5.22        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 9.25/5.22       => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5687_one__le__power,axiom,
% 9.25/5.22      ! [A: int,N: nat] :
% 9.25/5.22        ( ( ord_less_eq_int @ one_one_int @ A )
% 9.25/5.22       => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5688_not__is__unit__0,axiom,
% 9.25/5.22      ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5689_not__is__unit__0,axiom,
% 9.25/5.22      ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5690_not__is__unit__0,axiom,
% 9.25/5.22      ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5691_left__right__inverse__power,axiom,
% 9.25/5.22      ! [X: code_integer,Y: code_integer,N: nat] :
% 9.25/5.22        ( ( ( times_3573771949741848930nteger @ X @ Y )
% 9.25/5.22          = one_one_Code_integer )
% 9.25/5.22       => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y @ N ) )
% 9.25/5.22          = one_one_Code_integer ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5692_left__right__inverse__power,axiom,
% 9.25/5.22      ! [X: assn,Y: assn,N: nat] :
% 9.25/5.22        ( ( ( times_times_assn @ X @ Y )
% 9.25/5.22          = one_one_assn )
% 9.25/5.22       => ( ( times_times_assn @ ( power_power_assn @ X @ N ) @ ( power_power_assn @ Y @ N ) )
% 9.25/5.22          = one_one_assn ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5693_left__right__inverse__power,axiom,
% 9.25/5.22      ! [X: rat,Y: rat,N: nat] :
% 9.25/5.22        ( ( ( times_times_rat @ X @ Y )
% 9.25/5.22          = one_one_rat )
% 9.25/5.22       => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y @ N ) )
% 9.25/5.22          = one_one_rat ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5694_left__right__inverse__power,axiom,
% 9.25/5.22      ! [X: nat,Y: nat,N: nat] :
% 9.25/5.22        ( ( ( times_times_nat @ X @ Y )
% 9.25/5.22          = one_one_nat )
% 9.25/5.22       => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) )
% 9.25/5.22          = one_one_nat ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5695_left__right__inverse__power,axiom,
% 9.25/5.22      ! [X: int,Y: int,N: nat] :
% 9.25/5.22        ( ( ( times_times_int @ X @ Y )
% 9.25/5.22          = one_one_int )
% 9.25/5.22       => ( ( times_times_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 9.25/5.22          = one_one_int ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5696_power__Suc,axiom,
% 9.25/5.22      ! [A: code_integer,N: nat] :
% 9.25/5.22        ( ( power_8256067586552552935nteger @ A @ ( suc @ N ) )
% 9.25/5.22        = ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5697_power__Suc,axiom,
% 9.25/5.22      ! [A: assn,N: nat] :
% 9.25/5.22        ( ( power_power_assn @ A @ ( suc @ N ) )
% 9.25/5.22        = ( times_times_assn @ A @ ( power_power_assn @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5698_power__Suc,axiom,
% 9.25/5.22      ! [A: rat,N: nat] :
% 9.25/5.22        ( ( power_power_rat @ A @ ( suc @ N ) )
% 9.25/5.22        = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5699_power__Suc,axiom,
% 9.25/5.22      ! [A: nat,N: nat] :
% 9.25/5.22        ( ( power_power_nat @ A @ ( suc @ N ) )
% 9.25/5.22        = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5700_power__Suc,axiom,
% 9.25/5.22      ! [A: int,N: nat] :
% 9.25/5.22        ( ( power_power_int @ A @ ( suc @ N ) )
% 9.25/5.22        = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5701_power__Suc2,axiom,
% 9.25/5.22      ! [A: code_integer,N: nat] :
% 9.25/5.22        ( ( power_8256067586552552935nteger @ A @ ( suc @ N ) )
% 9.25/5.22        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ N ) @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5702_power__Suc2,axiom,
% 9.25/5.22      ! [A: assn,N: nat] :
% 9.25/5.22        ( ( power_power_assn @ A @ ( suc @ N ) )
% 9.25/5.22        = ( times_times_assn @ ( power_power_assn @ A @ N ) @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5703_power__Suc2,axiom,
% 9.25/5.22      ! [A: rat,N: nat] :
% 9.25/5.22        ( ( power_power_rat @ A @ ( suc @ N ) )
% 9.25/5.22        = ( times_times_rat @ ( power_power_rat @ A @ N ) @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5704_power__Suc2,axiom,
% 9.25/5.22      ! [A: nat,N: nat] :
% 9.25/5.22        ( ( power_power_nat @ A @ ( suc @ N ) )
% 9.25/5.22        = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5705_power__Suc2,axiom,
% 9.25/5.22      ! [A: int,N: nat] :
% 9.25/5.22        ( ( power_power_int @ A @ ( suc @ N ) )
% 9.25/5.22        = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5706_is__unit__mult__iff,axiom,
% 9.25/5.22      ! [A: code_integer,B: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 9.25/5.22        = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.25/5.22          & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5707_is__unit__mult__iff,axiom,
% 9.25/5.22      ! [A: nat,B: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 9.25/5.22        = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.25/5.22          & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5708_is__unit__mult__iff,axiom,
% 9.25/5.22      ! [A: int,B: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 9.25/5.22        = ( ( dvd_dvd_int @ A @ one_one_int )
% 9.25/5.22          & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5709_dvd__mult__unit__iff,axiom,
% 9.25/5.22      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.25/5.22       => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 9.25/5.22          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5710_dvd__mult__unit__iff,axiom,
% 9.25/5.22      ! [B: nat,A: nat,C: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.25/5.22       => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 9.25/5.22          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5711_dvd__mult__unit__iff,axiom,
% 9.25/5.22      ! [B: int,A: int,C: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.25/5.22       => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 9.25/5.22          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5712_mult__unit__dvd__iff,axiom,
% 9.25/5.22      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.25/5.22       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 9.25/5.22          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5713_mult__unit__dvd__iff,axiom,
% 9.25/5.22      ! [B: nat,A: nat,C: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.25/5.22       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 9.25/5.22          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5714_mult__unit__dvd__iff,axiom,
% 9.25/5.22      ! [B: int,A: int,C: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.25/5.22       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 9.25/5.22          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5715_dvd__mult__unit__iff_H,axiom,
% 9.25/5.22      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.25/5.22       => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.25/5.22          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5716_dvd__mult__unit__iff_H,axiom,
% 9.25/5.22      ! [B: nat,A: nat,C: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.25/5.22       => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 9.25/5.22          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5717_dvd__mult__unit__iff_H,axiom,
% 9.25/5.22      ! [B: int,A: int,C: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.25/5.22       => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 9.25/5.22          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5718_mult__unit__dvd__iff_H,axiom,
% 9.25/5.22      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.25/5.22       => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 9.25/5.22          = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5719_mult__unit__dvd__iff_H,axiom,
% 9.25/5.22      ! [A: nat,B: nat,C: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.25/5.22       => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 9.25/5.22          = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5720_mult__unit__dvd__iff_H,axiom,
% 9.25/5.22      ! [A: int,B: int,C: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.25/5.22       => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 9.25/5.22          = ( dvd_dvd_int @ B @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5721_unit__mult__left__cancel,axiom,
% 9.25/5.22      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.25/5.22       => ( ( ( times_3573771949741848930nteger @ A @ B )
% 9.25/5.22            = ( times_3573771949741848930nteger @ A @ C ) )
% 9.25/5.22          = ( B = C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5722_unit__mult__left__cancel,axiom,
% 9.25/5.22      ! [A: nat,B: nat,C: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.25/5.22       => ( ( ( times_times_nat @ A @ B )
% 9.25/5.22            = ( times_times_nat @ A @ C ) )
% 9.25/5.22          = ( B = C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5723_unit__mult__left__cancel,axiom,
% 9.25/5.22      ! [A: int,B: int,C: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.25/5.22       => ( ( ( times_times_int @ A @ B )
% 9.25/5.22            = ( times_times_int @ A @ C ) )
% 9.25/5.22          = ( B = C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5724_unit__mult__right__cancel,axiom,
% 9.25/5.22      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.25/5.22       => ( ( ( times_3573771949741848930nteger @ B @ A )
% 9.25/5.22            = ( times_3573771949741848930nteger @ C @ A ) )
% 9.25/5.22          = ( B = C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5725_unit__mult__right__cancel,axiom,
% 9.25/5.22      ! [A: nat,B: nat,C: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.25/5.22       => ( ( ( times_times_nat @ B @ A )
% 9.25/5.22            = ( times_times_nat @ C @ A ) )
% 9.25/5.22          = ( B = C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5726_unit__mult__right__cancel,axiom,
% 9.25/5.22      ! [A: int,B: int,C: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.25/5.22       => ( ( ( times_times_int @ B @ A )
% 9.25/5.22            = ( times_times_int @ C @ A ) )
% 9.25/5.22          = ( B = C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5727_power__0,axiom,
% 9.25/5.22      ! [A: code_integer] :
% 9.25/5.22        ( ( power_8256067586552552935nteger @ A @ zero_zero_nat )
% 9.25/5.22        = one_one_Code_integer ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5728_power__0,axiom,
% 9.25/5.22      ! [A: assn] :
% 9.25/5.22        ( ( power_power_assn @ A @ zero_zero_nat )
% 9.25/5.22        = one_one_assn ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5729_power__0,axiom,
% 9.25/5.22      ! [A: rat] :
% 9.25/5.22        ( ( power_power_rat @ A @ zero_zero_nat )
% 9.25/5.22        = one_one_rat ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5730_power__0,axiom,
% 9.25/5.22      ! [A: int] :
% 9.25/5.22        ( ( power_power_int @ A @ zero_zero_nat )
% 9.25/5.22        = one_one_int ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5731_power__0,axiom,
% 9.25/5.22      ! [A: nat] :
% 9.25/5.22        ( ( power_power_nat @ A @ zero_zero_nat )
% 9.25/5.22        = one_one_nat ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5732_power__one__over,axiom,
% 9.25/5.22      ! [A: rat,N: nat] :
% 9.25/5.22        ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 9.25/5.22        = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5733_dvd__div__mult,axiom,
% 9.25/5.22      ! [C: nat,B: nat,A: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ C @ B )
% 9.25/5.22       => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 9.25/5.22          = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5734_dvd__div__mult,axiom,
% 9.25/5.22      ! [C: int,B: int,A: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ C @ B )
% 9.25/5.22       => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 9.25/5.22          = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5735_dvd__div__mult,axiom,
% 9.25/5.22      ! [C: code_integer,B: code_integer,A: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ C @ B )
% 9.25/5.22       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 9.25/5.22          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5736_dvd__div__mult,axiom,
% 9.25/5.22      ! [C: code_natural,B: code_natural,A: code_natural] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ C @ B )
% 9.25/5.22       => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ B @ C ) @ A )
% 9.25/5.22          = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ B @ A ) @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5737_div__mult__swap,axiom,
% 9.25/5.22      ! [C: nat,B: nat,A: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ C @ B )
% 9.25/5.22       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 9.25/5.22          = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5738_div__mult__swap,axiom,
% 9.25/5.22      ! [C: int,B: int,A: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ C @ B )
% 9.25/5.22       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 9.25/5.22          = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5739_div__mult__swap,axiom,
% 9.25/5.22      ! [C: code_integer,B: code_integer,A: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ C @ B )
% 9.25/5.22       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 9.25/5.22          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5740_div__mult__swap,axiom,
% 9.25/5.22      ! [C: code_natural,B: code_natural,A: code_natural] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ C @ B )
% 9.25/5.22       => ( ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C ) )
% 9.25/5.22          = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5741_div__div__eq__right,axiom,
% 9.25/5.22      ! [C: nat,B: nat,A: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ C @ B )
% 9.25/5.22       => ( ( dvd_dvd_nat @ B @ A )
% 9.25/5.22         => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 9.25/5.22            = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5742_div__div__eq__right,axiom,
% 9.25/5.22      ! [C: int,B: int,A: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ C @ B )
% 9.25/5.22       => ( ( dvd_dvd_int @ B @ A )
% 9.25/5.22         => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 9.25/5.22            = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5743_div__div__eq__right,axiom,
% 9.25/5.22      ! [C: code_integer,B: code_integer,A: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ C @ B )
% 9.25/5.22       => ( ( dvd_dvd_Code_integer @ B @ A )
% 9.25/5.22         => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 9.25/5.22            = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5744_div__div__eq__right,axiom,
% 9.25/5.22      ! [C: code_natural,B: code_natural,A: code_natural] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ C @ B )
% 9.25/5.22       => ( ( dvd_dvd_Code_natural @ B @ A )
% 9.25/5.22         => ( ( divide5121882707175180666atural @ A @ ( divide5121882707175180666atural @ B @ C ) )
% 9.25/5.22            = ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ C ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5745_dvd__div__mult2__eq,axiom,
% 9.25/5.22      ! [B: nat,C: nat,A: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 9.25/5.22       => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 9.25/5.22          = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5746_dvd__div__mult2__eq,axiom,
% 9.25/5.22      ! [B: int,C: int,A: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 9.25/5.22       => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 9.25/5.22          = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5747_dvd__div__mult2__eq,axiom,
% 9.25/5.22      ! [B: code_integer,C: code_integer,A: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 9.25/5.22       => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.25/5.22          = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5748_dvd__div__mult2__eq,axiom,
% 9.25/5.22      ! [B: code_natural,C: code_natural,A: code_natural] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ B @ C ) @ A )
% 9.25/5.22       => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ C ) )
% 9.25/5.22          = ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ B ) @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5749_dvd__mult__imp__div,axiom,
% 9.25/5.22      ! [A: nat,C: nat,B: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 9.25/5.22       => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5750_dvd__mult__imp__div,axiom,
% 9.25/5.22      ! [A: int,C: int,B: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 9.25/5.22       => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5751_dvd__mult__imp__div,axiom,
% 9.25/5.22      ! [A: code_integer,C: code_integer,B: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 9.25/5.22       => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5752_dvd__mult__imp__div,axiom,
% 9.25/5.22      ! [A: code_natural,C: code_natural,B: code_natural] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ A @ C ) @ B )
% 9.25/5.22       => ( dvd_dvd_Code_natural @ A @ ( divide5121882707175180666atural @ B @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5753_div__mult__div__if__dvd,axiom,
% 9.25/5.22      ! [B: nat,A: nat,D2: nat,C: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ B @ A )
% 9.25/5.22       => ( ( dvd_dvd_nat @ D2 @ C )
% 9.25/5.22         => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D2 ) )
% 9.25/5.22            = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5754_div__mult__div__if__dvd,axiom,
% 9.25/5.22      ! [B: int,A: int,D2: int,C: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ B @ A )
% 9.25/5.22       => ( ( dvd_dvd_int @ D2 @ C )
% 9.25/5.22         => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D2 ) )
% 9.25/5.22            = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5755_div__mult__div__if__dvd,axiom,
% 9.25/5.22      ! [B: code_integer,A: code_integer,D2: code_integer,C: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ B @ A )
% 9.25/5.22       => ( ( dvd_dvd_Code_integer @ D2 @ C )
% 9.25/5.22         => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D2 ) )
% 9.25/5.22            = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5756_div__mult__div__if__dvd,axiom,
% 9.25/5.22      ! [B: code_natural,A: code_natural,D2: code_natural,C: code_natural] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ B @ A )
% 9.25/5.22       => ( ( dvd_dvd_Code_natural @ D2 @ C )
% 9.25/5.22         => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ ( divide5121882707175180666atural @ C @ D2 ) )
% 9.25/5.22            = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D2 ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5757_power__add,axiom,
% 9.25/5.22      ! [A: code_integer,M: nat,N: nat] :
% 9.25/5.22        ( ( power_8256067586552552935nteger @ A @ ( plus_plus_nat @ M @ N ) )
% 9.25/5.22        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5758_power__add,axiom,
% 9.25/5.22      ! [A: assn,M: nat,N: nat] :
% 9.25/5.22        ( ( power_power_assn @ A @ ( plus_plus_nat @ M @ N ) )
% 9.25/5.22        = ( times_times_assn @ ( power_power_assn @ A @ M ) @ ( power_power_assn @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5759_power__add,axiom,
% 9.25/5.22      ! [A: rat,M: nat,N: nat] :
% 9.25/5.22        ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N ) )
% 9.25/5.22        = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5760_power__add,axiom,
% 9.25/5.22      ! [A: nat,M: nat,N: nat] :
% 9.25/5.22        ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 9.25/5.22        = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5761_power__add,axiom,
% 9.25/5.22      ! [A: int,M: nat,N: nat] :
% 9.25/5.22        ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 9.25/5.22        = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5762_unit__div__cancel,axiom,
% 9.25/5.22      ! [A: nat,B: nat,C: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.25/5.22       => ( ( ( divide_divide_nat @ B @ A )
% 9.25/5.22            = ( divide_divide_nat @ C @ A ) )
% 9.25/5.22          = ( B = C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5763_unit__div__cancel,axiom,
% 9.25/5.22      ! [A: int,B: int,C: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.25/5.22       => ( ( ( divide_divide_int @ B @ A )
% 9.25/5.22            = ( divide_divide_int @ C @ A ) )
% 9.25/5.22          = ( B = C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5764_unit__div__cancel,axiom,
% 9.25/5.22      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.25/5.22       => ( ( ( divide6298287555418463151nteger @ B @ A )
% 9.25/5.22            = ( divide6298287555418463151nteger @ C @ A ) )
% 9.25/5.22          = ( B = C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5765_unit__div__cancel,axiom,
% 9.25/5.22      ! [A: code_natural,B: code_natural,C: code_natural] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 9.25/5.22       => ( ( ( divide5121882707175180666atural @ B @ A )
% 9.25/5.22            = ( divide5121882707175180666atural @ C @ A ) )
% 9.25/5.22          = ( B = C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5766_div__unit__dvd__iff,axiom,
% 9.25/5.22      ! [B: nat,A: nat,C: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.25/5.22       => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 9.25/5.22          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5767_div__unit__dvd__iff,axiom,
% 9.25/5.22      ! [B: int,A: int,C: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.25/5.22       => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 9.25/5.22          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5768_div__unit__dvd__iff,axiom,
% 9.25/5.22      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.25/5.22       => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 9.25/5.22          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5769_div__unit__dvd__iff,axiom,
% 9.25/5.22      ! [B: code_natural,A: code_natural,C: code_natural] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.25/5.22       => ( ( dvd_dvd_Code_natural @ ( divide5121882707175180666atural @ A @ B ) @ C )
% 9.25/5.22          = ( dvd_dvd_Code_natural @ A @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5770_dvd__div__unit__iff,axiom,
% 9.25/5.22      ! [B: nat,A: nat,C: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.25/5.22       => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 9.25/5.22          = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5771_dvd__div__unit__iff,axiom,
% 9.25/5.22      ! [B: int,A: int,C: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.25/5.22       => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 9.25/5.22          = ( dvd_dvd_int @ A @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5772_dvd__div__unit__iff,axiom,
% 9.25/5.22      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.25/5.22       => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 9.25/5.22          = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5773_dvd__div__unit__iff,axiom,
% 9.25/5.22      ! [B: code_natural,A: code_natural,C: code_natural] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.25/5.22       => ( ( dvd_dvd_Code_natural @ A @ ( divide5121882707175180666atural @ C @ B ) )
% 9.25/5.22          = ( dvd_dvd_Code_natural @ A @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5774_dvd__div__neg,axiom,
% 9.25/5.22      ! [B: int,A: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ B @ A )
% 9.25/5.22       => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 9.25/5.22          = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5775_dvd__div__neg,axiom,
% 9.25/5.22      ! [B: code_integer,A: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ B @ A )
% 9.25/5.22       => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 9.25/5.22          = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5776_dvd__div__neg,axiom,
% 9.25/5.22      ! [B: rat,A: rat] :
% 9.25/5.22        ( ( dvd_dvd_rat @ B @ A )
% 9.25/5.22       => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 9.25/5.22          = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5777_dvd__neg__div,axiom,
% 9.25/5.22      ! [B: int,A: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ B @ A )
% 9.25/5.22       => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 9.25/5.22          = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5778_dvd__neg__div,axiom,
% 9.25/5.22      ! [B: code_integer,A: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ B @ A )
% 9.25/5.22       => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 9.25/5.22          = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5779_dvd__neg__div,axiom,
% 9.25/5.22      ! [B: rat,A: rat] :
% 9.25/5.22        ( ( dvd_dvd_rat @ B @ A )
% 9.25/5.22       => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 9.25/5.22          = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5780_minus__one__power__iff,axiom,
% 9.25/5.22      ! [N: nat] :
% 9.25/5.22        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.22         => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 9.25/5.22            = one_one_int ) )
% 9.25/5.22        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.22         => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 9.25/5.22            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5781_minus__one__power__iff,axiom,
% 9.25/5.22      ! [N: nat] :
% 9.25/5.22        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.22         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 9.25/5.22            = one_one_Code_integer ) )
% 9.25/5.22        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.22         => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 9.25/5.22            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5782_minus__one__power__iff,axiom,
% 9.25/5.22      ! [N: nat] :
% 9.25/5.22        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.22         => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 9.25/5.22            = one_one_rat ) )
% 9.25/5.22        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.22         => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 9.25/5.22            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5783_mask__int__def,axiom,
% 9.25/5.22      ( bit_se2000444600071755411sk_int
% 9.25/5.22      = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5784_mask__eq__exp__minus__1,axiom,
% 9.25/5.22      ( bit_se2119862282449309892nteger
% 9.25/5.22      = ( ^ [N2: nat] : ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5785_mask__eq__exp__minus__1,axiom,
% 9.25/5.22      ( bit_se943457434206027407atural
% 9.25/5.22      = ( ^ [N2: nat] : ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_natural ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5786_mask__eq__exp__minus__1,axiom,
% 9.25/5.22      ( bit_se2000444600071755411sk_int
% 9.25/5.22      = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5787_mask__eq__exp__minus__1,axiom,
% 9.25/5.22      ( bit_se2002935070580805687sk_nat
% 9.25/5.22      = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5788_power__le__one,axiom,
% 9.25/5.22      ! [A: code_integer,N: nat] :
% 9.25/5.22        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.22       => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 9.25/5.22         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5789_power__le__one,axiom,
% 9.25/5.22      ! [A: rat,N: nat] :
% 9.25/5.22        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.22       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 9.25/5.22         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5790_power__le__one,axiom,
% 9.25/5.22      ! [A: nat,N: nat] :
% 9.25/5.22        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.25/5.22       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 9.25/5.22         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5791_power__le__one,axiom,
% 9.25/5.22      ! [A: int,N: nat] :
% 9.25/5.22        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.22       => ( ( ord_less_eq_int @ A @ one_one_int )
% 9.25/5.22         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5792_power__gt1__lemma,axiom,
% 9.25/5.22      ! [A: code_integer,N: nat] :
% 9.25/5.22        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 9.25/5.22       => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5793_power__gt1__lemma,axiom,
% 9.25/5.22      ! [A: rat,N: nat] :
% 9.25/5.22        ( ( ord_less_rat @ one_one_rat @ A )
% 9.25/5.22       => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5794_power__gt1__lemma,axiom,
% 9.25/5.22      ! [A: nat,N: nat] :
% 9.25/5.22        ( ( ord_less_nat @ one_one_nat @ A )
% 9.25/5.22       => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5795_power__gt1__lemma,axiom,
% 9.25/5.22      ! [A: int,N: nat] :
% 9.25/5.22        ( ( ord_less_int @ one_one_int @ A )
% 9.25/5.22       => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5796_power__less__power__Suc,axiom,
% 9.25/5.22      ! [A: code_integer,N: nat] :
% 9.25/5.22        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 9.25/5.22       => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5797_power__less__power__Suc,axiom,
% 9.25/5.22      ! [A: rat,N: nat] :
% 9.25/5.22        ( ( ord_less_rat @ one_one_rat @ A )
% 9.25/5.22       => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5798_power__less__power__Suc,axiom,
% 9.25/5.22      ! [A: nat,N: nat] :
% 9.25/5.22        ( ( ord_less_nat @ one_one_nat @ A )
% 9.25/5.22       => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5799_power__less__power__Suc,axiom,
% 9.25/5.22      ! [A: int,N: nat] :
% 9.25/5.22        ( ( ord_less_int @ one_one_int @ A )
% 9.25/5.22       => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5800_unity__coeff__ex,axiom,
% 9.25/5.22      ! [P: code_integer > $o,L: code_integer] :
% 9.25/5.22        ( ( ? [X3: code_integer] : ( P @ ( times_3573771949741848930nteger @ L @ X3 ) ) )
% 9.25/5.22        = ( ? [X3: code_integer] :
% 9.25/5.22              ( ( dvd_dvd_Code_integer @ L @ ( plus_p5714425477246183910nteger @ X3 @ zero_z3403309356797280102nteger ) )
% 9.25/5.22              & ( P @ X3 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5801_unity__coeff__ex,axiom,
% 9.25/5.22      ! [P: rat > $o,L: rat] :
% 9.25/5.22        ( ( ? [X3: rat] : ( P @ ( times_times_rat @ L @ X3 ) ) )
% 9.25/5.22        = ( ? [X3: rat] :
% 9.25/5.22              ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X3 @ zero_zero_rat ) )
% 9.25/5.22              & ( P @ X3 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5802_unity__coeff__ex,axiom,
% 9.25/5.22      ! [P: nat > $o,L: nat] :
% 9.25/5.22        ( ( ? [X3: nat] : ( P @ ( times_times_nat @ L @ X3 ) ) )
% 9.25/5.22        = ( ? [X3: nat] :
% 9.25/5.22              ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X3 @ zero_zero_nat ) )
% 9.25/5.22              & ( P @ X3 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5803_unity__coeff__ex,axiom,
% 9.25/5.22      ! [P: int > $o,L: int] :
% 9.25/5.22        ( ( ? [X3: int] : ( P @ ( times_times_int @ L @ X3 ) ) )
% 9.25/5.22        = ( ? [X3: int] :
% 9.25/5.22              ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X3 @ zero_zero_int ) )
% 9.25/5.22              & ( P @ X3 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5804_power__0__left,axiom,
% 9.25/5.22      ! [N: nat] :
% 9.25/5.22        ( ( ( N = zero_zero_nat )
% 9.25/5.22         => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 9.25/5.22            = one_one_Code_integer ) )
% 9.25/5.22        & ( ( N != zero_zero_nat )
% 9.25/5.22         => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 9.25/5.22            = zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5805_power__0__left,axiom,
% 9.25/5.22      ! [N: nat] :
% 9.25/5.22        ( ( ( N = zero_zero_nat )
% 9.25/5.22         => ( ( power_power_rat @ zero_zero_rat @ N )
% 9.25/5.22            = one_one_rat ) )
% 9.25/5.22        & ( ( N != zero_zero_nat )
% 9.25/5.22         => ( ( power_power_rat @ zero_zero_rat @ N )
% 9.25/5.22            = zero_zero_rat ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5806_power__0__left,axiom,
% 9.25/5.22      ! [N: nat] :
% 9.25/5.22        ( ( ( N = zero_zero_nat )
% 9.25/5.22         => ( ( power_power_int @ zero_zero_int @ N )
% 9.25/5.22            = one_one_int ) )
% 9.25/5.22        & ( ( N != zero_zero_nat )
% 9.25/5.22         => ( ( power_power_int @ zero_zero_int @ N )
% 9.25/5.22            = zero_zero_int ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5807_power__0__left,axiom,
% 9.25/5.22      ! [N: nat] :
% 9.25/5.22        ( ( ( N = zero_zero_nat )
% 9.25/5.22         => ( ( power_power_nat @ zero_zero_nat @ N )
% 9.25/5.22            = one_one_nat ) )
% 9.25/5.22        & ( ( N != zero_zero_nat )
% 9.25/5.22         => ( ( power_power_nat @ zero_zero_nat @ N )
% 9.25/5.22            = zero_zero_nat ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5808_unit__dvdE,axiom,
% 9.25/5.22      ! [A: code_integer,B: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.25/5.22       => ~ ( ( A != zero_z3403309356797280102nteger )
% 9.25/5.22           => ! [C3: code_integer] :
% 9.25/5.22                ( B
% 9.25/5.22               != ( times_3573771949741848930nteger @ A @ C3 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5809_unit__dvdE,axiom,
% 9.25/5.22      ! [A: nat,B: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.25/5.22       => ~ ( ( A != zero_zero_nat )
% 9.25/5.22           => ! [C3: nat] :
% 9.25/5.22                ( B
% 9.25/5.22               != ( times_times_nat @ A @ C3 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5810_unit__dvdE,axiom,
% 9.25/5.22      ! [A: int,B: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.25/5.22       => ~ ( ( A != zero_zero_int )
% 9.25/5.22           => ! [C3: int] :
% 9.25/5.22                ( B
% 9.25/5.22               != ( times_times_int @ A @ C3 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5811_power__gt1,axiom,
% 9.25/5.22      ! [A: code_integer,N: nat] :
% 9.25/5.22        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 9.25/5.22       => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5812_power__gt1,axiom,
% 9.25/5.22      ! [A: rat,N: nat] :
% 9.25/5.22        ( ( ord_less_rat @ one_one_rat @ A )
% 9.25/5.22       => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5813_power__gt1,axiom,
% 9.25/5.22      ! [A: nat,N: nat] :
% 9.25/5.22        ( ( ord_less_nat @ one_one_nat @ A )
% 9.25/5.22       => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5814_power__gt1,axiom,
% 9.25/5.22      ! [A: int,N: nat] :
% 9.25/5.22        ( ( ord_less_int @ one_one_int @ A )
% 9.25/5.22       => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5815_and_Ocomm__monoid__axioms,axiom,
% 9.25/5.22      comm_m1654649897431166824nteger @ bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5816_and_Ocomm__monoid__axioms,axiom,
% 9.25/5.22      comm_monoid_int @ bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5817_power__less__imp__less__exp,axiom,
% 9.25/5.22      ! [A: code_integer,M: nat,N: nat] :
% 9.25/5.22        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 9.25/5.22       => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 9.25/5.22         => ( ord_less_nat @ M @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5818_power__less__imp__less__exp,axiom,
% 9.25/5.22      ! [A: rat,M: nat,N: nat] :
% 9.25/5.22        ( ( ord_less_rat @ one_one_rat @ A )
% 9.25/5.22       => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 9.25/5.22         => ( ord_less_nat @ M @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5819_power__less__imp__less__exp,axiom,
% 9.25/5.22      ! [A: nat,M: nat,N: nat] :
% 9.25/5.22        ( ( ord_less_nat @ one_one_nat @ A )
% 9.25/5.22       => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 9.25/5.22         => ( ord_less_nat @ M @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5820_power__less__imp__less__exp,axiom,
% 9.25/5.22      ! [A: int,M: nat,N: nat] :
% 9.25/5.22        ( ( ord_less_int @ one_one_int @ A )
% 9.25/5.22       => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 9.25/5.22         => ( ord_less_nat @ M @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5821_power__strict__increasing,axiom,
% 9.25/5.22      ! [N: nat,N4: nat,A: code_integer] :
% 9.25/5.22        ( ( ord_less_nat @ N @ N4 )
% 9.25/5.22       => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 9.25/5.22         => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ A @ N4 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5822_power__strict__increasing,axiom,
% 9.25/5.22      ! [N: nat,N4: nat,A: rat] :
% 9.25/5.22        ( ( ord_less_nat @ N @ N4 )
% 9.25/5.22       => ( ( ord_less_rat @ one_one_rat @ A )
% 9.25/5.22         => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5823_power__strict__increasing,axiom,
% 9.25/5.22      ! [N: nat,N4: nat,A: nat] :
% 9.25/5.22        ( ( ord_less_nat @ N @ N4 )
% 9.25/5.22       => ( ( ord_less_nat @ one_one_nat @ A )
% 9.25/5.22         => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5824_power__strict__increasing,axiom,
% 9.25/5.22      ! [N: nat,N4: nat,A: int] :
% 9.25/5.22        ( ( ord_less_nat @ N @ N4 )
% 9.25/5.22       => ( ( ord_less_int @ one_one_int @ A )
% 9.25/5.22         => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5825_power__increasing,axiom,
% 9.25/5.22      ! [N: nat,N4: nat,A: code_integer] :
% 9.25/5.22        ( ( ord_less_eq_nat @ N @ N4 )
% 9.25/5.22       => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 9.25/5.22         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ A @ N4 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5826_power__increasing,axiom,
% 9.25/5.22      ! [N: nat,N4: nat,A: rat] :
% 9.25/5.22        ( ( ord_less_eq_nat @ N @ N4 )
% 9.25/5.22       => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 9.25/5.22         => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5827_power__increasing,axiom,
% 9.25/5.22      ! [N: nat,N4: nat,A: nat] :
% 9.25/5.22        ( ( ord_less_eq_nat @ N @ N4 )
% 9.25/5.22       => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 9.25/5.22         => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5828_power__increasing,axiom,
% 9.25/5.22      ! [N: nat,N4: nat,A: int] :
% 9.25/5.22        ( ( ord_less_eq_nat @ N @ N4 )
% 9.25/5.22       => ( ( ord_less_eq_int @ one_one_int @ A )
% 9.25/5.22         => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5829_power__minus,axiom,
% 9.25/5.22      ! [A: int,N: nat] :
% 9.25/5.22        ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 9.25/5.22        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5830_power__minus,axiom,
% 9.25/5.22      ! [A: code_integer,N: nat] :
% 9.25/5.22        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 9.25/5.22        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5831_power__minus,axiom,
% 9.25/5.22      ! [A: rat,N: nat] :
% 9.25/5.22        ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 9.25/5.22        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5832_inf__period_I4_J,axiom,
% 9.25/5.22      ! [D2: code_integer,D3: code_integer,T3: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ D2 @ D3 )
% 9.25/5.22       => ! [X5: code_integer,K3: code_integer] :
% 9.25/5.22            ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ T3 ) ) )
% 9.25/5.22            = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K3 @ D3 ) ) @ T3 ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5833_inf__period_I4_J,axiom,
% 9.25/5.22      ! [D2: rat,D3: rat,T3: rat] :
% 9.25/5.22        ( ( dvd_dvd_rat @ D2 @ D3 )
% 9.25/5.22       => ! [X5: rat,K3: rat] :
% 9.25/5.22            ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ T3 ) ) )
% 9.25/5.22            = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K3 @ D3 ) ) @ T3 ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5834_inf__period_I4_J,axiom,
% 9.25/5.22      ! [D2: int,D3: int,T3: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ D2 @ D3 )
% 9.25/5.22       => ! [X5: int,K3: int] :
% 9.25/5.22            ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T3 ) ) )
% 9.25/5.22            = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K3 @ D3 ) ) @ T3 ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5835_inf__period_I3_J,axiom,
% 9.25/5.22      ! [D2: code_integer,D3: code_integer,T3: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ D2 @ D3 )
% 9.25/5.22       => ! [X5: code_integer,K3: code_integer] :
% 9.25/5.22            ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X5 @ T3 ) )
% 9.25/5.22            = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X5 @ ( times_3573771949741848930nteger @ K3 @ D3 ) ) @ T3 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5836_inf__period_I3_J,axiom,
% 9.25/5.22      ! [D2: rat,D3: rat,T3: rat] :
% 9.25/5.22        ( ( dvd_dvd_rat @ D2 @ D3 )
% 9.25/5.22       => ! [X5: rat,K3: rat] :
% 9.25/5.22            ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X5 @ T3 ) )
% 9.25/5.22            = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K3 @ D3 ) ) @ T3 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5837_inf__period_I3_J,axiom,
% 9.25/5.22      ! [D2: int,D3: int,T3: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ D2 @ D3 )
% 9.25/5.22       => ! [X5: int,K3: int] :
% 9.25/5.22            ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T3 ) )
% 9.25/5.22            = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K3 @ D3 ) ) @ T3 ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5838_dvd__div__div__eq__mult,axiom,
% 9.25/5.22      ! [A: nat,C: nat,B: nat,D2: nat] :
% 9.25/5.22        ( ( A != zero_zero_nat )
% 9.25/5.22       => ( ( C != zero_zero_nat )
% 9.25/5.22         => ( ( dvd_dvd_nat @ A @ B )
% 9.25/5.22           => ( ( dvd_dvd_nat @ C @ D2 )
% 9.25/5.22             => ( ( ( divide_divide_nat @ B @ A )
% 9.25/5.22                  = ( divide_divide_nat @ D2 @ C ) )
% 9.25/5.22                = ( ( times_times_nat @ B @ C )
% 9.25/5.22                  = ( times_times_nat @ A @ D2 ) ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5839_dvd__div__div__eq__mult,axiom,
% 9.25/5.22      ! [A: int,C: int,B: int,D2: int] :
% 9.25/5.22        ( ( A != zero_zero_int )
% 9.25/5.22       => ( ( C != zero_zero_int )
% 9.25/5.22         => ( ( dvd_dvd_int @ A @ B )
% 9.25/5.22           => ( ( dvd_dvd_int @ C @ D2 )
% 9.25/5.22             => ( ( ( divide_divide_int @ B @ A )
% 9.25/5.22                  = ( divide_divide_int @ D2 @ C ) )
% 9.25/5.22                = ( ( times_times_int @ B @ C )
% 9.25/5.22                  = ( times_times_int @ A @ D2 ) ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5840_dvd__div__div__eq__mult,axiom,
% 9.25/5.22      ! [A: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 9.25/5.22        ( ( A != zero_z3403309356797280102nteger )
% 9.25/5.22       => ( ( C != zero_z3403309356797280102nteger )
% 9.25/5.22         => ( ( dvd_dvd_Code_integer @ A @ B )
% 9.25/5.22           => ( ( dvd_dvd_Code_integer @ C @ D2 )
% 9.25/5.22             => ( ( ( divide6298287555418463151nteger @ B @ A )
% 9.25/5.22                  = ( divide6298287555418463151nteger @ D2 @ C ) )
% 9.25/5.22                = ( ( times_3573771949741848930nteger @ B @ C )
% 9.25/5.22                  = ( times_3573771949741848930nteger @ A @ D2 ) ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5841_dvd__div__div__eq__mult,axiom,
% 9.25/5.22      ! [A: code_natural,C: code_natural,B: code_natural,D2: code_natural] :
% 9.25/5.22        ( ( A != zero_z2226904508553997617atural )
% 9.25/5.22       => ( ( C != zero_z2226904508553997617atural )
% 9.25/5.22         => ( ( dvd_dvd_Code_natural @ A @ B )
% 9.25/5.22           => ( ( dvd_dvd_Code_natural @ C @ D2 )
% 9.25/5.22             => ( ( ( divide5121882707175180666atural @ B @ A )
% 9.25/5.22                  = ( divide5121882707175180666atural @ D2 @ C ) )
% 9.25/5.22                = ( ( times_2397367101498566445atural @ B @ C )
% 9.25/5.22                  = ( times_2397367101498566445atural @ A @ D2 ) ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5842_dvd__div__iff__mult,axiom,
% 9.25/5.22      ! [C: nat,B: nat,A: nat] :
% 9.25/5.22        ( ( C != zero_zero_nat )
% 9.25/5.22       => ( ( dvd_dvd_nat @ C @ B )
% 9.25/5.22         => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 9.25/5.22            = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5843_dvd__div__iff__mult,axiom,
% 9.25/5.22      ! [C: int,B: int,A: int] :
% 9.25/5.22        ( ( C != zero_zero_int )
% 9.25/5.22       => ( ( dvd_dvd_int @ C @ B )
% 9.25/5.22         => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 9.25/5.22            = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5844_dvd__div__iff__mult,axiom,
% 9.25/5.22      ! [C: code_integer,B: code_integer,A: code_integer] :
% 9.25/5.22        ( ( C != zero_z3403309356797280102nteger )
% 9.25/5.22       => ( ( dvd_dvd_Code_integer @ C @ B )
% 9.25/5.22         => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 9.25/5.22            = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5845_dvd__div__iff__mult,axiom,
% 9.25/5.22      ! [C: code_natural,B: code_natural,A: code_natural] :
% 9.25/5.22        ( ( C != zero_z2226904508553997617atural )
% 9.25/5.22       => ( ( dvd_dvd_Code_natural @ C @ B )
% 9.25/5.22         => ( ( dvd_dvd_Code_natural @ A @ ( divide5121882707175180666atural @ B @ C ) )
% 9.25/5.22            = ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ A @ C ) @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5846_div__dvd__iff__mult,axiom,
% 9.25/5.22      ! [B: nat,A: nat,C: nat] :
% 9.25/5.22        ( ( B != zero_zero_nat )
% 9.25/5.22       => ( ( dvd_dvd_nat @ B @ A )
% 9.25/5.22         => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 9.25/5.22            = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5847_div__dvd__iff__mult,axiom,
% 9.25/5.22      ! [B: int,A: int,C: int] :
% 9.25/5.22        ( ( B != zero_zero_int )
% 9.25/5.22       => ( ( dvd_dvd_int @ B @ A )
% 9.25/5.22         => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 9.25/5.22            = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5848_div__dvd__iff__mult,axiom,
% 9.25/5.22      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.25/5.22        ( ( B != zero_z3403309356797280102nteger )
% 9.25/5.22       => ( ( dvd_dvd_Code_integer @ B @ A )
% 9.25/5.22         => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 9.25/5.22            = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5849_div__dvd__iff__mult,axiom,
% 9.25/5.22      ! [B: code_natural,A: code_natural,C: code_natural] :
% 9.25/5.22        ( ( B != zero_z2226904508553997617atural )
% 9.25/5.22       => ( ( dvd_dvd_Code_natural @ B @ A )
% 9.25/5.22         => ( ( dvd_dvd_Code_natural @ ( divide5121882707175180666atural @ A @ B ) @ C )
% 9.25/5.22            = ( dvd_dvd_Code_natural @ A @ ( times_2397367101498566445atural @ C @ B ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5850_dvd__div__eq__mult,axiom,
% 9.25/5.22      ! [A: nat,B: nat,C: nat] :
% 9.25/5.22        ( ( A != zero_zero_nat )
% 9.25/5.22       => ( ( dvd_dvd_nat @ A @ B )
% 9.25/5.22         => ( ( ( divide_divide_nat @ B @ A )
% 9.25/5.22              = C )
% 9.25/5.22            = ( B
% 9.25/5.22              = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5851_dvd__div__eq__mult,axiom,
% 9.25/5.22      ! [A: int,B: int,C: int] :
% 9.25/5.22        ( ( A != zero_zero_int )
% 9.25/5.22       => ( ( dvd_dvd_int @ A @ B )
% 9.25/5.22         => ( ( ( divide_divide_int @ B @ A )
% 9.25/5.22              = C )
% 9.25/5.22            = ( B
% 9.25/5.22              = ( times_times_int @ C @ A ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5852_dvd__div__eq__mult,axiom,
% 9.25/5.22      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.22        ( ( A != zero_z3403309356797280102nteger )
% 9.25/5.22       => ( ( dvd_dvd_Code_integer @ A @ B )
% 9.25/5.22         => ( ( ( divide6298287555418463151nteger @ B @ A )
% 9.25/5.22              = C )
% 9.25/5.22            = ( B
% 9.25/5.22              = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5853_dvd__div__eq__mult,axiom,
% 9.25/5.22      ! [A: code_natural,B: code_natural,C: code_natural] :
% 9.25/5.22        ( ( A != zero_z2226904508553997617atural )
% 9.25/5.22       => ( ( dvd_dvd_Code_natural @ A @ B )
% 9.25/5.22         => ( ( ( divide5121882707175180666atural @ B @ A )
% 9.25/5.22              = C )
% 9.25/5.22            = ( B
% 9.25/5.22              = ( times_2397367101498566445atural @ C @ A ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5854_unit__div__eq__0__iff,axiom,
% 9.25/5.22      ! [B: nat,A: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.25/5.22       => ( ( ( divide_divide_nat @ A @ B )
% 9.25/5.22            = zero_zero_nat )
% 9.25/5.22          = ( A = zero_zero_nat ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5855_unit__div__eq__0__iff,axiom,
% 9.25/5.22      ! [B: int,A: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.25/5.22       => ( ( ( divide_divide_int @ A @ B )
% 9.25/5.22            = zero_zero_int )
% 9.25/5.22          = ( A = zero_zero_int ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5856_unit__div__eq__0__iff,axiom,
% 9.25/5.22      ! [B: code_integer,A: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.25/5.22       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 9.25/5.22            = zero_z3403309356797280102nteger )
% 9.25/5.22          = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5857_unit__div__eq__0__iff,axiom,
% 9.25/5.22      ! [B: code_natural,A: code_natural] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.25/5.22       => ( ( ( divide5121882707175180666atural @ A @ B )
% 9.25/5.22            = zero_z2226904508553997617atural )
% 9.25/5.22          = ( A = zero_z2226904508553997617atural ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5858_and_Omonoid__axioms,axiom,
% 9.25/5.22      monoid_Code_integer @ bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5859_and_Omonoid__axioms,axiom,
% 9.25/5.22      monoid_int @ bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5860_unit__eq__div1,axiom,
% 9.25/5.22      ! [B: nat,A: nat,C: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.25/5.22       => ( ( ( divide_divide_nat @ A @ B )
% 9.25/5.22            = C )
% 9.25/5.22          = ( A
% 9.25/5.22            = ( times_times_nat @ C @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5861_unit__eq__div1,axiom,
% 9.25/5.22      ! [B: int,A: int,C: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.25/5.22       => ( ( ( divide_divide_int @ A @ B )
% 9.25/5.22            = C )
% 9.25/5.22          = ( A
% 9.25/5.22            = ( times_times_int @ C @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5862_unit__eq__div1,axiom,
% 9.25/5.22      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.25/5.22       => ( ( ( divide6298287555418463151nteger @ A @ B )
% 9.25/5.22            = C )
% 9.25/5.22          = ( A
% 9.25/5.22            = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5863_unit__eq__div1,axiom,
% 9.25/5.22      ! [B: code_natural,A: code_natural,C: code_natural] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.25/5.22       => ( ( ( divide5121882707175180666atural @ A @ B )
% 9.25/5.22            = C )
% 9.25/5.22          = ( A
% 9.25/5.22            = ( times_2397367101498566445atural @ C @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5864_unit__eq__div2,axiom,
% 9.25/5.22      ! [B: nat,A: nat,C: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.25/5.22       => ( ( A
% 9.25/5.22            = ( divide_divide_nat @ C @ B ) )
% 9.25/5.22          = ( ( times_times_nat @ A @ B )
% 9.25/5.22            = C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5865_unit__eq__div2,axiom,
% 9.25/5.22      ! [B: int,A: int,C: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.25/5.22       => ( ( A
% 9.25/5.22            = ( divide_divide_int @ C @ B ) )
% 9.25/5.22          = ( ( times_times_int @ A @ B )
% 9.25/5.22            = C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5866_unit__eq__div2,axiom,
% 9.25/5.22      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.25/5.22       => ( ( A
% 9.25/5.22            = ( divide6298287555418463151nteger @ C @ B ) )
% 9.25/5.22          = ( ( times_3573771949741848930nteger @ A @ B )
% 9.25/5.22            = C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5867_unit__eq__div2,axiom,
% 9.25/5.22      ! [B: code_natural,A: code_natural,C: code_natural] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.25/5.22       => ( ( A
% 9.25/5.22            = ( divide5121882707175180666atural @ C @ B ) )
% 9.25/5.22          = ( ( times_2397367101498566445atural @ A @ B )
% 9.25/5.22            = C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5868_div__mult__unit2,axiom,
% 9.25/5.22      ! [C: nat,B: nat,A: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ C @ one_one_nat )
% 9.25/5.22       => ( ( dvd_dvd_nat @ B @ A )
% 9.25/5.22         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 9.25/5.22            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5869_div__mult__unit2,axiom,
% 9.25/5.22      ! [C: int,B: int,A: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ C @ one_one_int )
% 9.25/5.22       => ( ( dvd_dvd_int @ B @ A )
% 9.25/5.22         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 9.25/5.22            = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5870_div__mult__unit2,axiom,
% 9.25/5.22      ! [C: code_integer,B: code_integer,A: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 9.25/5.22       => ( ( dvd_dvd_Code_integer @ B @ A )
% 9.25/5.22         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.25/5.22            = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5871_div__mult__unit2,axiom,
% 9.25/5.22      ! [C: code_natural,B: code_natural,A: code_natural] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ C @ one_one_Code_natural )
% 9.25/5.22       => ( ( dvd_dvd_Code_natural @ B @ A )
% 9.25/5.22         => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ C ) )
% 9.25/5.22            = ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ B ) @ C ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5872_unit__div__commute,axiom,
% 9.25/5.22      ! [B: nat,A: nat,C: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.25/5.22       => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 9.25/5.22          = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5873_unit__div__commute,axiom,
% 9.25/5.22      ! [B: int,A: int,C: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.25/5.22       => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 9.25/5.22          = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5874_unit__div__commute,axiom,
% 9.25/5.22      ! [B: code_integer,A: code_integer,C: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.25/5.22       => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 9.25/5.22          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5875_unit__div__commute,axiom,
% 9.25/5.22      ! [B: code_natural,A: code_natural,C: code_natural] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.25/5.22       => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ C )
% 9.25/5.22          = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ C ) @ B ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5876_unit__div__mult__swap,axiom,
% 9.25/5.22      ! [C: nat,A: nat,B: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ C @ one_one_nat )
% 9.25/5.22       => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 9.25/5.22          = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5877_unit__div__mult__swap,axiom,
% 9.25/5.22      ! [C: int,A: int,B: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ C @ one_one_int )
% 9.25/5.22       => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 9.25/5.22          = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5878_unit__div__mult__swap,axiom,
% 9.25/5.22      ! [C: code_integer,A: code_integer,B: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 9.25/5.22       => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 9.25/5.22          = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5879_unit__div__mult__swap,axiom,
% 9.25/5.22      ! [C: code_natural,A: code_natural,B: code_natural] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ C @ one_one_Code_natural )
% 9.25/5.22       => ( ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C ) )
% 9.25/5.22          = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5880_is__unit__div__mult2__eq,axiom,
% 9.25/5.22      ! [B: nat,C: nat,A: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.25/5.22       => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 9.25/5.22         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 9.25/5.22            = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5881_is__unit__div__mult2__eq,axiom,
% 9.25/5.22      ! [B: int,C: int,A: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.25/5.22       => ( ( dvd_dvd_int @ C @ one_one_int )
% 9.25/5.22         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 9.25/5.22            = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5882_is__unit__div__mult2__eq,axiom,
% 9.25/5.22      ! [B: code_integer,C: code_integer,A: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.25/5.22       => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 9.25/5.22         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 9.25/5.22            = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5883_is__unit__div__mult2__eq,axiom,
% 9.25/5.22      ! [B: code_natural,C: code_natural,A: code_natural] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.25/5.22       => ( ( dvd_dvd_Code_natural @ C @ one_one_Code_natural )
% 9.25/5.22         => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ C ) )
% 9.25/5.22            = ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ B ) @ C ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5884_unit__imp__mod__eq__0,axiom,
% 9.25/5.22      ! [B: nat,A: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.25/5.22       => ( ( modulo_modulo_nat @ A @ B )
% 9.25/5.22          = zero_zero_nat ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5885_unit__imp__mod__eq__0,axiom,
% 9.25/5.22      ! [B: int,A: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ B @ one_one_int )
% 9.25/5.22       => ( ( modulo_modulo_int @ A @ B )
% 9.25/5.22          = zero_zero_int ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5886_unit__imp__mod__eq__0,axiom,
% 9.25/5.22      ! [B: code_integer,A: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.25/5.22       => ( ( modulo364778990260209775nteger @ A @ B )
% 9.25/5.22          = zero_z3403309356797280102nteger ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5887_unit__imp__mod__eq__0,axiom,
% 9.25/5.22      ! [B: code_natural,A: code_natural] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.25/5.22       => ( ( modulo8411746178871703098atural @ A @ B )
% 9.25/5.22          = zero_z2226904508553997617atural ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5888_power__minus__Bit0,axiom,
% 9.25/5.22      ! [X: int,K: num] :
% 9.25/5.22        ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 9.25/5.22        = ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5889_power__minus__Bit0,axiom,
% 9.25/5.22      ! [X: code_integer,K: num] :
% 9.25/5.22        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 9.25/5.22        = ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5890_power__minus__Bit0,axiom,
% 9.25/5.22      ! [X: rat,K: num] :
% 9.25/5.22        ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 9.25/5.22        = ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5891_and_Osemilattice__neutr__axioms,axiom,
% 9.25/5.22      semila6106414119144251899nteger @ bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5892_and_Osemilattice__neutr__axioms,axiom,
% 9.25/5.22      semila9079005292280841162tr_int @ bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5893_power__minus__Bit1,axiom,
% 9.25/5.22      ! [X: int,K: num] :
% 9.25/5.22        ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 9.25/5.22        = ( uminus_uminus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5894_power__minus__Bit1,axiom,
% 9.25/5.22      ! [X: code_integer,K: num] :
% 9.25/5.22        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 9.25/5.22        = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5895_power__minus__Bit1,axiom,
% 9.25/5.22      ! [X: rat,K: num] :
% 9.25/5.22        ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 9.25/5.22        = ( uminus_uminus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5896_even__mask__div__iff_H,axiom,
% 9.25/5.22      ! [M: nat,N: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.25/5.22        = ( ord_less_eq_nat @ M @ N ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5897_even__mask__div__iff_H,axiom,
% 9.25/5.22      ! [M: nat,N: nat] :
% 9.25/5.22        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 9.25/5.22        = ( ord_less_eq_nat @ M @ N ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5898_even__mask__div__iff_H,axiom,
% 9.25/5.22      ! [M: nat,N: nat] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 9.25/5.22        = ( ord_less_eq_nat @ M @ N ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5899_even__mask__div__iff_H,axiom,
% 9.25/5.22      ! [M: nat,N: nat] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) @ one_one_Code_natural ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) )
% 9.25/5.22        = ( ord_less_eq_nat @ M @ N ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5900_power__numeral__even,axiom,
% 9.25/5.22      ! [Z: code_integer,W: num] :
% 9.25/5.22        ( ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 9.25/5.22        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5901_power__numeral__even,axiom,
% 9.25/5.22      ! [Z: assn,W: num] :
% 9.25/5.22        ( ( power_power_assn @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 9.25/5.22        = ( times_times_assn @ ( power_power_assn @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_assn @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5902_power__numeral__even,axiom,
% 9.25/5.22      ! [Z: rat,W: num] :
% 9.25/5.22        ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 9.25/5.22        = ( times_times_rat @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5903_power__numeral__even,axiom,
% 9.25/5.22      ! [Z: nat,W: num] :
% 9.25/5.22        ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 9.25/5.22        = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5904_power__numeral__even,axiom,
% 9.25/5.22      ! [Z: int,W: num] :
% 9.25/5.22        ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 9.25/5.22        = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5905_power__numeral__odd,axiom,
% 9.25/5.22      ! [Z: code_integer,W: num] :
% 9.25/5.22        ( ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 9.25/5.22        = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ Z @ ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5906_power__numeral__odd,axiom,
% 9.25/5.22      ! [Z: assn,W: num] :
% 9.25/5.22        ( ( power_power_assn @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 9.25/5.22        = ( times_times_assn @ ( times_times_assn @ Z @ ( power_power_assn @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_assn @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5907_power__numeral__odd,axiom,
% 9.25/5.22      ! [Z: rat,W: num] :
% 9.25/5.22        ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 9.25/5.22        = ( times_times_rat @ ( times_times_rat @ Z @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5908_power__numeral__odd,axiom,
% 9.25/5.22      ! [Z: nat,W: num] :
% 9.25/5.22        ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 9.25/5.22        = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5909_power__numeral__odd,axiom,
% 9.25/5.22      ! [Z: int,W: num] :
% 9.25/5.22        ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 9.25/5.22        = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5910_even__mask__div__iff,axiom,
% 9.25/5.22      ! [M: nat,N: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.25/5.22        = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.22            = zero_zero_nat )
% 9.25/5.22          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5911_even__mask__div__iff,axiom,
% 9.25/5.22      ! [M: nat,N: nat] :
% 9.25/5.22        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 9.25/5.22        = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 9.25/5.22            = zero_zero_int )
% 9.25/5.22          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5912_even__mask__div__iff,axiom,
% 9.25/5.22      ! [M: nat,N: nat] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 9.25/5.22        = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 9.25/5.22            = zero_z3403309356797280102nteger )
% 9.25/5.22          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5913_even__mask__div__iff,axiom,
% 9.25/5.22      ! [M: nat,N: nat] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) @ one_one_Code_natural ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) )
% 9.25/5.22        = ( ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N )
% 9.25/5.22            = zero_z2226904508553997617atural )
% 9.25/5.22          | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5914_stable__imp__take__bit__eq,axiom,
% 9.25/5.22      ! [A: nat,N: nat] :
% 9.25/5.22        ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22          = A )
% 9.25/5.22       => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.25/5.22           => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 9.25/5.22              = zero_zero_nat ) )
% 9.25/5.22          & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.25/5.22           => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 9.25/5.22              = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5915_stable__imp__take__bit__eq,axiom,
% 9.25/5.22      ! [A: code_integer,N: nat] :
% 9.25/5.22        ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.22          = A )
% 9.25/5.22       => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.25/5.22           => ( ( bit_se1745604003318907178nteger @ N @ A )
% 9.25/5.22              = zero_z3403309356797280102nteger ) )
% 9.25/5.22          & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.25/5.22           => ( ( bit_se1745604003318907178nteger @ N @ A )
% 9.25/5.22              = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5916_stable__imp__take__bit__eq,axiom,
% 9.25/5.22      ! [A: code_natural,N: nat] :
% 9.25/5.22        ( ( ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.22          = A )
% 9.25/5.22       => ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.25/5.22           => ( ( bit_se569199155075624693atural @ N @ A )
% 9.25/5.22              = zero_z2226904508553997617atural ) )
% 9.25/5.22          & ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.25/5.22           => ( ( bit_se569199155075624693atural @ N @ A )
% 9.25/5.22              = ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) @ one_one_Code_natural ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5917_stable__imp__take__bit__eq,axiom,
% 9.25/5.22      ! [A: int,N: nat] :
% 9.25/5.22        ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.22          = A )
% 9.25/5.22       => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.25/5.22           => ( ( bit_se2923211474154528505it_int @ N @ A )
% 9.25/5.22              = zero_zero_int ) )
% 9.25/5.22          & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.25/5.22           => ( ( bit_se2923211474154528505it_int @ N @ A )
% 9.25/5.22              = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5918_power__Suc__less,axiom,
% 9.25/5.22      ! [A: code_integer,N: nat] :
% 9.25/5.22        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.22       => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 9.25/5.22         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5919_power__Suc__less,axiom,
% 9.25/5.22      ! [A: rat,N: nat] :
% 9.25/5.22        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.22       => ( ( ord_less_rat @ A @ one_one_rat )
% 9.25/5.22         => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5920_power__Suc__less,axiom,
% 9.25/5.22      ! [A: nat,N: nat] :
% 9.25/5.22        ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.25/5.22       => ( ( ord_less_nat @ A @ one_one_nat )
% 9.25/5.22         => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5921_power__Suc__less,axiom,
% 9.25/5.22      ! [A: int,N: nat] :
% 9.25/5.22        ( ( ord_less_int @ zero_zero_int @ A )
% 9.25/5.22       => ( ( ord_less_int @ A @ one_one_int )
% 9.25/5.22         => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5922_power__Suc__le__self,axiom,
% 9.25/5.22      ! [A: code_integer,N: nat] :
% 9.25/5.22        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.22       => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 9.25/5.22         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5923_power__Suc__le__self,axiom,
% 9.25/5.22      ! [A: rat,N: nat] :
% 9.25/5.22        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.22       => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 9.25/5.22         => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5924_power__Suc__le__self,axiom,
% 9.25/5.22      ! [A: nat,N: nat] :
% 9.25/5.22        ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.25/5.22       => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 9.25/5.22         => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5925_power__Suc__le__self,axiom,
% 9.25/5.22      ! [A: int,N: nat] :
% 9.25/5.22        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.22       => ( ( ord_less_eq_int @ A @ one_one_int )
% 9.25/5.22         => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5926_power__Suc__less__one,axiom,
% 9.25/5.22      ! [A: code_integer,N: nat] :
% 9.25/5.22        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.22       => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 9.25/5.22         => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) @ one_one_Code_integer ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5927_power__Suc__less__one,axiom,
% 9.25/5.22      ! [A: rat,N: nat] :
% 9.25/5.22        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.22       => ( ( ord_less_rat @ A @ one_one_rat )
% 9.25/5.22         => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5928_power__Suc__less__one,axiom,
% 9.25/5.22      ! [A: nat,N: nat] :
% 9.25/5.22        ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.25/5.22       => ( ( ord_less_nat @ A @ one_one_nat )
% 9.25/5.22         => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5929_power__Suc__less__one,axiom,
% 9.25/5.22      ! [A: int,N: nat] :
% 9.25/5.22        ( ( ord_less_int @ zero_zero_int @ A )
% 9.25/5.22       => ( ( ord_less_int @ A @ one_one_int )
% 9.25/5.22         => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5930_power__strict__decreasing,axiom,
% 9.25/5.22      ! [N: nat,N4: nat,A: code_integer] :
% 9.25/5.22        ( ( ord_less_nat @ N @ N4 )
% 9.25/5.22       => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.22         => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 9.25/5.22           => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N4 ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5931_power__strict__decreasing,axiom,
% 9.25/5.22      ! [N: nat,N4: nat,A: rat] :
% 9.25/5.22        ( ( ord_less_nat @ N @ N4 )
% 9.25/5.22       => ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.22         => ( ( ord_less_rat @ A @ one_one_rat )
% 9.25/5.22           => ( ord_less_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5932_power__strict__decreasing,axiom,
% 9.25/5.22      ! [N: nat,N4: nat,A: nat] :
% 9.25/5.22        ( ( ord_less_nat @ N @ N4 )
% 9.25/5.22       => ( ( ord_less_nat @ zero_zero_nat @ A )
% 9.25/5.22         => ( ( ord_less_nat @ A @ one_one_nat )
% 9.25/5.22           => ( ord_less_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5933_power__strict__decreasing,axiom,
% 9.25/5.22      ! [N: nat,N4: nat,A: int] :
% 9.25/5.22        ( ( ord_less_nat @ N @ N4 )
% 9.25/5.22       => ( ( ord_less_int @ zero_zero_int @ A )
% 9.25/5.22         => ( ( ord_less_int @ A @ one_one_int )
% 9.25/5.22           => ( ord_less_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5934_power__decreasing,axiom,
% 9.25/5.22      ! [N: nat,N4: nat,A: code_integer] :
% 9.25/5.22        ( ( ord_less_eq_nat @ N @ N4 )
% 9.25/5.22       => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.22         => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 9.25/5.22           => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N4 ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5935_power__decreasing,axiom,
% 9.25/5.22      ! [N: nat,N4: nat,A: rat] :
% 9.25/5.22        ( ( ord_less_eq_nat @ N @ N4 )
% 9.25/5.22       => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.22         => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 9.25/5.22           => ( ord_less_eq_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5936_power__decreasing,axiom,
% 9.25/5.22      ! [N: nat,N4: nat,A: nat] :
% 9.25/5.22        ( ( ord_less_eq_nat @ N @ N4 )
% 9.25/5.22       => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 9.25/5.22         => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 9.25/5.22           => ( ord_less_eq_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5937_power__decreasing,axiom,
% 9.25/5.22      ! [N: nat,N4: nat,A: int] :
% 9.25/5.22        ( ( ord_less_eq_nat @ N @ N4 )
% 9.25/5.22       => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.22         => ( ( ord_less_eq_int @ A @ one_one_int )
% 9.25/5.22           => ( ord_less_eq_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5938_power__le__imp__le__exp,axiom,
% 9.25/5.22      ! [A: code_integer,M: nat,N: nat] :
% 9.25/5.22        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 9.25/5.22       => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 9.25/5.22         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5939_power__le__imp__le__exp,axiom,
% 9.25/5.22      ! [A: rat,M: nat,N: nat] :
% 9.25/5.22        ( ( ord_less_rat @ one_one_rat @ A )
% 9.25/5.22       => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 9.25/5.22         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5940_power__le__imp__le__exp,axiom,
% 9.25/5.22      ! [A: nat,M: nat,N: nat] :
% 9.25/5.22        ( ( ord_less_nat @ one_one_nat @ A )
% 9.25/5.22       => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 9.25/5.22         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5941_power__le__imp__le__exp,axiom,
% 9.25/5.22      ! [A: int,M: nat,N: nat] :
% 9.25/5.22        ( ( ord_less_int @ one_one_int @ A )
% 9.25/5.22       => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 9.25/5.22         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5942_self__le__power,axiom,
% 9.25/5.22      ! [A: code_integer,N: nat] :
% 9.25/5.22        ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 9.25/5.22       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.22         => ( ord_le3102999989581377725nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5943_self__le__power,axiom,
% 9.25/5.22      ! [A: rat,N: nat] :
% 9.25/5.22        ( ( ord_less_eq_rat @ one_one_rat @ A )
% 9.25/5.22       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.22         => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5944_self__le__power,axiom,
% 9.25/5.22      ! [A: nat,N: nat] :
% 9.25/5.22        ( ( ord_less_eq_nat @ one_one_nat @ A )
% 9.25/5.22       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.22         => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5945_self__le__power,axiom,
% 9.25/5.22      ! [A: int,N: nat] :
% 9.25/5.22        ( ( ord_less_eq_int @ one_one_int @ A )
% 9.25/5.22       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.22         => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5946_one__less__power,axiom,
% 9.25/5.22      ! [A: code_integer,N: nat] :
% 9.25/5.22        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 9.25/5.22       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.22         => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5947_one__less__power,axiom,
% 9.25/5.22      ! [A: rat,N: nat] :
% 9.25/5.22        ( ( ord_less_rat @ one_one_rat @ A )
% 9.25/5.22       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.22         => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5948_one__less__power,axiom,
% 9.25/5.22      ! [A: nat,N: nat] :
% 9.25/5.22        ( ( ord_less_nat @ one_one_nat @ A )
% 9.25/5.22       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.22         => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5949_one__less__power,axiom,
% 9.25/5.22      ! [A: int,N: nat] :
% 9.25/5.22        ( ( ord_less_int @ one_one_int @ A )
% 9.25/5.22       => ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.22         => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5950_is__unit__div__mult__cancel__right,axiom,
% 9.25/5.22      ! [A: nat,B: nat] :
% 9.25/5.22        ( ( A != zero_zero_nat )
% 9.25/5.22       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.25/5.22         => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 9.25/5.22            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5951_is__unit__div__mult__cancel__right,axiom,
% 9.25/5.22      ! [A: int,B: int] :
% 9.25/5.22        ( ( A != zero_zero_int )
% 9.25/5.22       => ( ( dvd_dvd_int @ B @ one_one_int )
% 9.25/5.22         => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 9.25/5.22            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5952_is__unit__div__mult__cancel__right,axiom,
% 9.25/5.22      ! [A: code_integer,B: code_integer] :
% 9.25/5.22        ( ( A != zero_z3403309356797280102nteger )
% 9.25/5.22       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.25/5.22         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 9.25/5.22            = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5953_is__unit__div__mult__cancel__right,axiom,
% 9.25/5.22      ! [A: code_natural,B: code_natural] :
% 9.25/5.22        ( ( A != zero_z2226904508553997617atural )
% 9.25/5.22       => ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.25/5.22         => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ A ) )
% 9.25/5.22            = ( divide5121882707175180666atural @ one_one_Code_natural @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5954_is__unit__div__mult__cancel__left,axiom,
% 9.25/5.22      ! [A: nat,B: nat] :
% 9.25/5.22        ( ( A != zero_zero_nat )
% 9.25/5.22       => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 9.25/5.22         => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 9.25/5.22            = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5955_is__unit__div__mult__cancel__left,axiom,
% 9.25/5.22      ! [A: int,B: int] :
% 9.25/5.22        ( ( A != zero_zero_int )
% 9.25/5.22       => ( ( dvd_dvd_int @ B @ one_one_int )
% 9.25/5.22         => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 9.25/5.22            = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5956_is__unit__div__mult__cancel__left,axiom,
% 9.25/5.22      ! [A: code_integer,B: code_integer] :
% 9.25/5.22        ( ( A != zero_z3403309356797280102nteger )
% 9.25/5.22       => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 9.25/5.22         => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 9.25/5.22            = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5957_is__unit__div__mult__cancel__left,axiom,
% 9.25/5.22      ! [A: code_natural,B: code_natural] :
% 9.25/5.22        ( ( A != zero_z2226904508553997617atural )
% 9.25/5.22       => ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 9.25/5.22         => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ A @ B ) )
% 9.25/5.22            = ( divide5121882707175180666atural @ one_one_Code_natural @ B ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5958_is__unitE,axiom,
% 9.25/5.22      ! [A: nat,C: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ A @ one_one_nat )
% 9.25/5.22       => ~ ( ( A != zero_zero_nat )
% 9.25/5.22           => ! [B6: nat] :
% 9.25/5.22                ( ( B6 != zero_zero_nat )
% 9.25/5.22               => ( ( dvd_dvd_nat @ B6 @ one_one_nat )
% 9.25/5.22                 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 9.25/5.22                      = B6 )
% 9.25/5.22                   => ( ( ( divide_divide_nat @ one_one_nat @ B6 )
% 9.25/5.22                        = A )
% 9.25/5.22                     => ( ( ( times_times_nat @ A @ B6 )
% 9.25/5.22                          = one_one_nat )
% 9.25/5.22                       => ( ( divide_divide_nat @ C @ A )
% 9.25/5.22                         != ( times_times_nat @ C @ B6 ) ) ) ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5959_is__unitE,axiom,
% 9.25/5.22      ! [A: int,C: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ A @ one_one_int )
% 9.25/5.22       => ~ ( ( A != zero_zero_int )
% 9.25/5.22           => ! [B6: int] :
% 9.25/5.22                ( ( B6 != zero_zero_int )
% 9.25/5.22               => ( ( dvd_dvd_int @ B6 @ one_one_int )
% 9.25/5.22                 => ( ( ( divide_divide_int @ one_one_int @ A )
% 9.25/5.22                      = B6 )
% 9.25/5.22                   => ( ( ( divide_divide_int @ one_one_int @ B6 )
% 9.25/5.22                        = A )
% 9.25/5.22                     => ( ( ( times_times_int @ A @ B6 )
% 9.25/5.22                          = one_one_int )
% 9.25/5.22                       => ( ( divide_divide_int @ C @ A )
% 9.25/5.22                         != ( times_times_int @ C @ B6 ) ) ) ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5960_is__unitE,axiom,
% 9.25/5.22      ! [A: code_integer,C: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 9.25/5.22       => ~ ( ( A != zero_z3403309356797280102nteger )
% 9.25/5.22           => ! [B6: code_integer] :
% 9.25/5.22                ( ( B6 != zero_z3403309356797280102nteger )
% 9.25/5.22               => ( ( dvd_dvd_Code_integer @ B6 @ one_one_Code_integer )
% 9.25/5.22                 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 9.25/5.22                      = B6 )
% 9.25/5.22                   => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B6 )
% 9.25/5.22                        = A )
% 9.25/5.22                     => ( ( ( times_3573771949741848930nteger @ A @ B6 )
% 9.25/5.22                          = one_one_Code_integer )
% 9.25/5.22                       => ( ( divide6298287555418463151nteger @ C @ A )
% 9.25/5.22                         != ( times_3573771949741848930nteger @ C @ B6 ) ) ) ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5961_is__unitE,axiom,
% 9.25/5.22      ! [A: code_natural,C: code_natural] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 9.25/5.22       => ~ ( ( A != zero_z2226904508553997617atural )
% 9.25/5.22           => ! [B6: code_natural] :
% 9.25/5.22                ( ( B6 != zero_z2226904508553997617atural )
% 9.25/5.22               => ( ( dvd_dvd_Code_natural @ B6 @ one_one_Code_natural )
% 9.25/5.22                 => ( ( ( divide5121882707175180666atural @ one_one_Code_natural @ A )
% 9.25/5.22                      = B6 )
% 9.25/5.22                   => ( ( ( divide5121882707175180666atural @ one_one_Code_natural @ B6 )
% 9.25/5.22                        = A )
% 9.25/5.22                     => ( ( ( times_2397367101498566445atural @ A @ B6 )
% 9.25/5.22                          = one_one_Code_natural )
% 9.25/5.22                       => ( ( divide5121882707175180666atural @ C @ A )
% 9.25/5.22                         != ( times_2397367101498566445atural @ C @ B6 ) ) ) ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5962_evenE,axiom,
% 9.25/5.22      ! [A: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.25/5.22       => ~ ! [B6: nat] :
% 9.25/5.22              ( A
% 9.25/5.22             != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B6 ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5963_evenE,axiom,
% 9.25/5.22      ! [A: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.25/5.22       => ~ ! [B6: int] :
% 9.25/5.22              ( A
% 9.25/5.22             != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B6 ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5964_evenE,axiom,
% 9.25/5.22      ! [A: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.25/5.22       => ~ ! [B6: code_integer] :
% 9.25/5.22              ( A
% 9.25/5.22             != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B6 ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5965_evenE,axiom,
% 9.25/5.22      ! [A: code_natural] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.25/5.22       => ~ ! [B6: code_natural] :
% 9.25/5.22              ( A
% 9.25/5.22             != ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B6 ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5966_odd__one,axiom,
% 9.25/5.22      ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5967_odd__one,axiom,
% 9.25/5.22      ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5968_odd__one,axiom,
% 9.25/5.22      ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5969_odd__one,axiom,
% 9.25/5.22      ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ one_one_Code_natural ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5970_even__minus,axiom,
% 9.25/5.22      ! [A: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 9.25/5.22        = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5971_even__minus,axiom,
% 9.25/5.22      ! [A: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 9.25/5.22        = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5972_power4__eq__xxxx,axiom,
% 9.25/5.22      ! [X: code_integer] :
% 9.25/5.22        ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 9.25/5.22        = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ X @ X ) @ X ) @ X ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5973_power4__eq__xxxx,axiom,
% 9.25/5.22      ! [X: assn] :
% 9.25/5.22        ( ( power_power_assn @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 9.25/5.22        = ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ X @ X ) @ X ) @ X ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5974_power4__eq__xxxx,axiom,
% 9.25/5.22      ! [X: rat] :
% 9.25/5.22        ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 9.25/5.22        = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X @ X ) @ X ) @ X ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5975_power4__eq__xxxx,axiom,
% 9.25/5.22      ! [X: nat] :
% 9.25/5.22        ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 9.25/5.22        = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5976_power4__eq__xxxx,axiom,
% 9.25/5.22      ! [X: int] :
% 9.25/5.22        ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 9.25/5.22        = ( times_times_int @ ( times_times_int @ ( times_times_int @ X @ X ) @ X ) @ X ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5977_power2__eq__square,axiom,
% 9.25/5.22      ! [A: code_integer] :
% 9.25/5.22        ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22        = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5978_power2__eq__square,axiom,
% 9.25/5.22      ! [A: assn] :
% 9.25/5.22        ( ( power_power_assn @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22        = ( times_times_assn @ A @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5979_power2__eq__square,axiom,
% 9.25/5.22      ! [A: rat] :
% 9.25/5.22        ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22        = ( times_times_rat @ A @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5980_power2__eq__square,axiom,
% 9.25/5.22      ! [A: nat] :
% 9.25/5.22        ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22        = ( times_times_nat @ A @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5981_power2__eq__square,axiom,
% 9.25/5.22      ! [A: int] :
% 9.25/5.22        ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22        = ( times_times_int @ A @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5982_one__power2,axiom,
% 9.25/5.22      ( ( power_8256067586552552935nteger @ one_one_Code_integer @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22      = one_one_Code_integer ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5983_one__power2,axiom,
% 9.25/5.22      ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22      = one_one_rat ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5984_one__power2,axiom,
% 9.25/5.22      ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22      = one_one_int ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5985_one__power2,axiom,
% 9.25/5.22      ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22      = one_one_nat ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5986_power2__eq__iff,axiom,
% 9.25/5.22      ! [X: int,Y: int] :
% 9.25/5.22        ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22          = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.25/5.22        = ( ( X = Y )
% 9.25/5.22          | ( X
% 9.25/5.22            = ( uminus_uminus_int @ Y ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5987_power2__eq__iff,axiom,
% 9.25/5.22      ! [X: code_integer,Y: code_integer] :
% 9.25/5.22        ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22          = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.25/5.22        = ( ( X = Y )
% 9.25/5.22          | ( X
% 9.25/5.22            = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5988_power2__eq__iff,axiom,
% 9.25/5.22      ! [X: rat,Y: rat] :
% 9.25/5.22        ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22          = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.25/5.22        = ( ( X = Y )
% 9.25/5.22          | ( X
% 9.25/5.22            = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5989_power3__eq__cube,axiom,
% 9.25/5.22      ! [A: code_integer] :
% 9.25/5.22        ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 9.25/5.22        = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A @ A ) @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5990_power3__eq__cube,axiom,
% 9.25/5.22      ! [A: assn] :
% 9.25/5.22        ( ( power_power_assn @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 9.25/5.22        = ( times_times_assn @ ( times_times_assn @ A @ A ) @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5991_power3__eq__cube,axiom,
% 9.25/5.22      ! [A: rat] :
% 9.25/5.22        ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 9.25/5.22        = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5992_power3__eq__cube,axiom,
% 9.25/5.22      ! [A: nat] :
% 9.25/5.22        ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 9.25/5.22        = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5993_power3__eq__cube,axiom,
% 9.25/5.22      ! [A: int] :
% 9.25/5.22        ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 9.25/5.22        = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5994_dvd__mult__cancel2,axiom,
% 9.25/5.22      ! [M: nat,N: nat] :
% 9.25/5.22        ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.25/5.22       => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 9.25/5.22          = ( N = one_one_nat ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5995_dvd__mult__cancel1,axiom,
% 9.25/5.22      ! [M: nat,N: nat] :
% 9.25/5.22        ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.25/5.22       => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 9.25/5.22          = ( N = one_one_nat ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5996_even__mult__exp__div__exp__iff,axiom,
% 9.25/5.22      ! [A: nat,M: nat,N: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.25/5.22        = ( ( ord_less_nat @ N @ M )
% 9.25/5.22          | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 9.25/5.22            = zero_zero_nat )
% 9.25/5.22          | ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.22            & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5997_even__mult__exp__div__exp__iff,axiom,
% 9.25/5.22      ! [A: int,M: nat,N: nat] :
% 9.25/5.22        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 9.25/5.22        = ( ( ord_less_nat @ N @ M )
% 9.25/5.22          | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 9.25/5.22            = zero_zero_int )
% 9.25/5.22          | ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.22            & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5998_even__mult__exp__div__exp__iff,axiom,
% 9.25/5.22      ! [A: code_integer,M: nat,N: nat] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 9.25/5.22        = ( ( ord_less_nat @ N @ M )
% 9.25/5.22          | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 9.25/5.22            = zero_z3403309356797280102nteger )
% 9.25/5.22          | ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.22            & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_5999_even__mult__exp__div__exp__iff,axiom,
% 9.25/5.22      ! [A: code_natural,M: nat,N: nat] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) )
% 9.25/5.22        = ( ( ord_less_nat @ N @ M )
% 9.25/5.22          | ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N )
% 9.25/5.22            = zero_z2226904508553997617atural )
% 9.25/5.22          | ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.22            & ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6000_power__minus_H,axiom,
% 9.25/5.22      ! [X: int,N: nat] :
% 9.25/5.22        ( ( nO_MATCH_int_int @ one_one_int @ X )
% 9.25/5.22       => ( ( power_power_int @ ( uminus_uminus_int @ X ) @ N )
% 9.25/5.22          = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ X @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6001_power__minus_H,axiom,
% 9.25/5.22      ! [X: code_integer,N: nat] :
% 9.25/5.22        ( ( nO_MAT8252062027627875367nteger @ one_one_Code_integer @ X )
% 9.25/5.22       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ N )
% 9.25/5.22          = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ X @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6002_power__minus_H,axiom,
% 9.25/5.22      ! [X: rat,N: nat] :
% 9.25/5.22        ( ( nO_MATCH_rat_rat @ one_one_rat @ X )
% 9.25/5.22       => ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ N )
% 9.25/5.22          = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ X @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6003_and__one__eq,axiom,
% 9.25/5.22      ! [A: code_integer] :
% 9.25/5.22        ( ( bit_se3949692690581998587nteger @ A @ one_one_Code_integer )
% 9.25/5.22        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6004_and__one__eq,axiom,
% 9.25/5.22      ! [A: code_natural] :
% 9.25/5.22        ( ( bit_se2773287842338716102atural @ A @ one_one_Code_natural )
% 9.25/5.22        = ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6005_and__one__eq,axiom,
% 9.25/5.22      ! [A: int] :
% 9.25/5.22        ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 9.25/5.22        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6006_and__one__eq,axiom,
% 9.25/5.22      ! [A: nat] :
% 9.25/5.22        ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 9.25/5.22        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6007_one__and__eq,axiom,
% 9.25/5.22      ! [A: code_integer] :
% 9.25/5.22        ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ A )
% 9.25/5.22        = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6008_one__and__eq,axiom,
% 9.25/5.22      ! [A: code_natural] :
% 9.25/5.22        ( ( bit_se2773287842338716102atural @ one_one_Code_natural @ A )
% 9.25/5.22        = ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6009_one__and__eq,axiom,
% 9.25/5.22      ! [A: int] :
% 9.25/5.22        ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 9.25/5.22        = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6010_one__and__eq,axiom,
% 9.25/5.22      ! [A: nat] :
% 9.25/5.22        ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 9.25/5.22        = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6011_take__bit__eq__mask__iff,axiom,
% 9.25/5.22      ! [N: nat,K: int] :
% 9.25/5.22        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 9.25/5.22          = ( bit_se2000444600071755411sk_int @ N ) )
% 9.25/5.22        = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 9.25/5.22          = zero_zero_int ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6012_even__two__times__div__two,axiom,
% 9.25/5.22      ! [A: nat] :
% 9.25/5.22        ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.25/5.22       => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.25/5.22          = A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6013_even__two__times__div__two,axiom,
% 9.25/5.22      ! [A: int] :
% 9.25/5.22        ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.25/5.22       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 9.25/5.22          = A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6014_even__two__times__div__two,axiom,
% 9.25/5.22      ! [A: code_integer] :
% 9.25/5.22        ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.25/5.22       => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 9.25/5.22          = A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6015_even__two__times__div__two,axiom,
% 9.25/5.22      ! [A: code_natural] :
% 9.25/5.22        ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.25/5.22       => ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) )
% 9.25/5.22          = A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6016_power2__eq__1__iff,axiom,
% 9.25/5.22      ! [A: int] :
% 9.25/5.22        ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22          = one_one_int )
% 9.25/5.22        = ( ( A = one_one_int )
% 9.25/5.22          | ( A
% 9.25/5.22            = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6017_power2__eq__1__iff,axiom,
% 9.25/5.22      ! [A: code_integer] :
% 9.25/5.22        ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22          = one_one_Code_integer )
% 9.25/5.22        = ( ( A = one_one_Code_integer )
% 9.25/5.22          | ( A
% 9.25/5.22            = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6018_power2__eq__1__iff,axiom,
% 9.25/5.22      ! [A: rat] :
% 9.25/5.22        ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22          = one_one_rat )
% 9.25/5.22        = ( ( A = one_one_rat )
% 9.25/5.22          | ( A
% 9.25/5.22            = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6019_power__diff__power__eq,axiom,
% 9.25/5.22      ! [A: nat,N: nat,M: nat] :
% 9.25/5.22        ( ( A != zero_zero_nat )
% 9.25/5.22       => ( ( ( ord_less_eq_nat @ N @ M )
% 9.25/5.22           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 9.25/5.22              = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 9.25/5.22          & ( ~ ( ord_less_eq_nat @ N @ M )
% 9.25/5.22           => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 9.25/5.22              = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6020_power__diff__power__eq,axiom,
% 9.25/5.22      ! [A: int,N: nat,M: nat] :
% 9.25/5.22        ( ( A != zero_zero_int )
% 9.25/5.22       => ( ( ( ord_less_eq_nat @ N @ M )
% 9.25/5.22           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 9.25/5.22              = ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 9.25/5.22          & ( ~ ( ord_less_eq_nat @ N @ M )
% 9.25/5.22           => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 9.25/5.22              = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6021_power__diff__power__eq,axiom,
% 9.25/5.22      ! [A: code_integer,N: nat,M: nat] :
% 9.25/5.22        ( ( A != zero_z3403309356797280102nteger )
% 9.25/5.22       => ( ( ( ord_less_eq_nat @ N @ M )
% 9.25/5.22           => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 9.25/5.22              = ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 9.25/5.22          & ( ~ ( ord_less_eq_nat @ N @ M )
% 9.25/5.22           => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 9.25/5.22              = ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6022_power__diff__power__eq,axiom,
% 9.25/5.22      ! [A: code_natural,N: nat,M: nat] :
% 9.25/5.22        ( ( A != zero_z2226904508553997617atural )
% 9.25/5.22       => ( ( ( ord_less_eq_nat @ N @ M )
% 9.25/5.22           => ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M ) @ ( power_7079662738309270450atural @ A @ N ) )
% 9.25/5.22              = ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 9.25/5.22          & ( ~ ( ord_less_eq_nat @ N @ M )
% 9.25/5.22           => ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M ) @ ( power_7079662738309270450atural @ A @ N ) )
% 9.25/5.22              = ( divide5121882707175180666atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6023_odd__iff__mod__2__eq__one,axiom,
% 9.25/5.22      ! [A: nat] :
% 9.25/5.22        ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 9.25/5.22        = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22          = one_one_nat ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6024_odd__iff__mod__2__eq__one,axiom,
% 9.25/5.22      ! [A: int] :
% 9.25/5.22        ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 9.25/5.22        = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.22          = one_one_int ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6025_odd__iff__mod__2__eq__one,axiom,
% 9.25/5.22      ! [A: code_integer] :
% 9.25/5.22        ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 9.25/5.22        = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.22          = one_one_Code_integer ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6026_odd__iff__mod__2__eq__one,axiom,
% 9.25/5.22      ! [A: code_natural] :
% 9.25/5.22        ( ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) )
% 9.25/5.22        = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.22          = one_one_Code_natural ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6027_normalize__denom__pos,axiom,
% 9.25/5.22      ! [R3: product_prod_int_int,P4: int,Q4: int] :
% 9.25/5.22        ( ( ( normalize @ R3 )
% 9.25/5.22          = ( product_Pair_int_int @ P4 @ Q4 ) )
% 9.25/5.22       => ( ord_less_int @ zero_zero_int @ Q4 ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6028_power__eq__if,axiom,
% 9.25/5.22      ( power_8256067586552552935nteger
% 9.25/5.22      = ( ^ [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 ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6029_power__eq__if,axiom,
% 9.25/5.22      ( power_power_assn
% 9.25/5.22      = ( ^ [P6: assn,M2: nat] : ( if_assn @ ( M2 = zero_zero_nat ) @ one_one_assn @ ( times_times_assn @ P6 @ ( power_power_assn @ P6 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6030_power__eq__if,axiom,
% 9.25/5.22      ( power_power_rat
% 9.25/5.22      = ( ^ [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 ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6031_power__eq__if,axiom,
% 9.25/5.22      ( power_power_nat
% 9.25/5.22      = ( ^ [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 ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6032_power__eq__if,axiom,
% 9.25/5.22      ( power_power_int
% 9.25/5.22      = ( ^ [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 ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6033_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 9.25/5.22      ! [K: nat,N: nat] :
% 9.25/5.22        ( ( ord_less_eq_nat @ K @ N )
% 9.25/5.22       => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 9.25/5.22          = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6034_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 9.25/5.22      ! [K: nat,N: nat] :
% 9.25/5.22        ( ( ord_less_eq_nat @ K @ N )
% 9.25/5.22       => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 9.25/5.22          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6035_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 9.25/5.22      ! [K: nat,N: nat] :
% 9.25/5.22        ( ( ord_less_eq_nat @ K @ N )
% 9.25/5.22       => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 9.25/5.22          = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6036_normalize__crossproduct,axiom,
% 9.25/5.22      ! [Q4: int,S3: int,P4: int,R3: int] :
% 9.25/5.22        ( ( Q4 != zero_zero_int )
% 9.25/5.22       => ( ( S3 != zero_zero_int )
% 9.25/5.22         => ( ( ( normalize @ ( product_Pair_int_int @ P4 @ Q4 ) )
% 9.25/5.22              = ( normalize @ ( product_Pair_int_int @ R3 @ S3 ) ) )
% 9.25/5.22           => ( ( times_times_int @ P4 @ S3 )
% 9.25/5.22              = ( times_times_int @ R3 @ Q4 ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6037_power__minus__mult,axiom,
% 9.25/5.22      ! [N: nat,A: code_integer] :
% 9.25/5.22        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.22       => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 9.25/5.22          = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6038_power__minus__mult,axiom,
% 9.25/5.22      ! [N: nat,A: assn] :
% 9.25/5.22        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.22       => ( ( times_times_assn @ ( power_power_assn @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 9.25/5.22          = ( power_power_assn @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6039_power__minus__mult,axiom,
% 9.25/5.22      ! [N: nat,A: rat] :
% 9.25/5.22        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.22       => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 9.25/5.22          = ( power_power_rat @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6040_power__minus__mult,axiom,
% 9.25/5.22      ! [N: nat,A: nat] :
% 9.25/5.22        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.22       => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 9.25/5.22          = ( power_power_nat @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6041_power__minus__mult,axiom,
% 9.25/5.22      ! [N: nat,A: int] :
% 9.25/5.22        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.22       => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 9.25/5.22          = ( power_power_int @ A @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6042_power2__sum,axiom,
% 9.25/5.22      ! [X: nat,Y: nat] :
% 9.25/5.22        ( ( power_power_nat @ ( plus_plus_nat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22        = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6043_power2__sum,axiom,
% 9.25/5.22      ! [X: int,Y: int] :
% 9.25/5.22        ( ( power_power_int @ ( plus_plus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22        = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6044_power2__sum,axiom,
% 9.25/5.22      ! [X: code_integer,Y: code_integer] :
% 9.25/5.22        ( ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6045_power2__sum,axiom,
% 9.25/5.22      ! [X: rat,Y: rat] :
% 9.25/5.22        ( ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22        = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6046_power2__sum,axiom,
% 9.25/5.22      ! [X: code_natural,Y: code_natural] :
% 9.25/5.22        ( ( power_7079662738309270450atural @ ( plus_p4538020629002901425atural @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22        = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( power_7079662738309270450atural @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_7079662738309270450atural @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_2397367101498566445atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6047_oddE,axiom,
% 9.25/5.22      ! [A: nat] :
% 9.25/5.22        ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.25/5.22       => ~ ! [B6: nat] :
% 9.25/5.22              ( A
% 9.25/5.22             != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B6 ) @ one_one_nat ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6048_oddE,axiom,
% 9.25/5.22      ! [A: int] :
% 9.25/5.22        ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.25/5.22       => ~ ! [B6: int] :
% 9.25/5.22              ( A
% 9.25/5.22             != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B6 ) @ one_one_int ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6049_oddE,axiom,
% 9.25/5.22      ! [A: code_integer] :
% 9.25/5.22        ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.25/5.22       => ~ ! [B6: code_integer] :
% 9.25/5.22              ( A
% 9.25/5.22             != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B6 ) @ one_one_Code_integer ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6050_oddE,axiom,
% 9.25/5.22      ! [A: code_natural] :
% 9.25/5.22        ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.25/5.22       => ~ ! [B6: code_natural] :
% 9.25/5.22              ( A
% 9.25/5.22             != ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B6 ) @ one_one_Code_natural ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6051_square__le__1,axiom,
% 9.25/5.22      ! [X: code_integer] :
% 9.25/5.22        ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 9.25/5.22       => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 9.25/5.22         => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6052_square__le__1,axiom,
% 9.25/5.22      ! [X: rat] :
% 9.25/5.22        ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 9.25/5.22       => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 9.25/5.22         => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6053_square__le__1,axiom,
% 9.25/5.22      ! [X: int] :
% 9.25/5.22        ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 9.25/5.22       => ( ( ord_less_eq_int @ X @ one_one_int )
% 9.25/5.22         => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6054_parity__cases,axiom,
% 9.25/5.22      ! [A: nat] :
% 9.25/5.22        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.25/5.22         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22           != zero_zero_nat ) )
% 9.25/5.22       => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.25/5.22           => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22             != one_one_nat ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6055_parity__cases,axiom,
% 9.25/5.22      ! [A: int] :
% 9.25/5.22        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.25/5.22         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.22           != zero_zero_int ) )
% 9.25/5.22       => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.25/5.22           => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.22             != one_one_int ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6056_parity__cases,axiom,
% 9.25/5.22      ! [A: code_integer] :
% 9.25/5.22        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.25/5.22         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.22           != zero_z3403309356797280102nteger ) )
% 9.25/5.22       => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.25/5.22           => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.22             != one_one_Code_integer ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6057_parity__cases,axiom,
% 9.25/5.22      ! [A: code_natural] :
% 9.25/5.22        ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.25/5.22         => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.22           != zero_z2226904508553997617atural ) )
% 9.25/5.22       => ~ ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.25/5.22           => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.22             != one_one_Code_natural ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6058_mod2__eq__if,axiom,
% 9.25/5.22      ! [A: nat] :
% 9.25/5.22        ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.25/5.22         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22            = zero_zero_nat ) )
% 9.25/5.22        & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 9.25/5.22         => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22            = one_one_nat ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6059_mod2__eq__if,axiom,
% 9.25/5.22      ! [A: int] :
% 9.25/5.22        ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.25/5.22         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.22            = zero_zero_int ) )
% 9.25/5.22        & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 9.25/5.22         => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.22            = one_one_int ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6060_mod2__eq__if,axiom,
% 9.25/5.22      ! [A: code_integer] :
% 9.25/5.22        ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.25/5.22         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.22            = zero_z3403309356797280102nteger ) )
% 9.25/5.22        & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 9.25/5.22         => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.22            = one_one_Code_integer ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6061_mod2__eq__if,axiom,
% 9.25/5.22      ! [A: code_natural] :
% 9.25/5.22        ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.25/5.22         => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.22            = zero_z2226904508553997617atural ) )
% 9.25/5.22        & ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 9.25/5.22         => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.22            = one_one_Code_natural ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6062_minus__power__mult__self,axiom,
% 9.25/5.22      ! [A: int,N: nat] :
% 9.25/5.22        ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 9.25/5.22        = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6063_minus__power__mult__self,axiom,
% 9.25/5.22      ! [A: code_integer,N: nat] :
% 9.25/5.22        ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 9.25/5.22        = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6064_minus__power__mult__self,axiom,
% 9.25/5.22      ! [A: rat,N: nat] :
% 9.25/5.22        ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 9.25/5.22        = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6065_power__odd__eq,axiom,
% 9.25/5.22      ! [A: code_integer,N: nat] :
% 9.25/5.22        ( ( power_8256067586552552935nteger @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.25/5.22        = ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6066_power__odd__eq,axiom,
% 9.25/5.22      ! [A: assn,N: nat] :
% 9.25/5.22        ( ( power_power_assn @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.25/5.22        = ( times_times_assn @ A @ ( power_power_assn @ ( power_power_assn @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6067_power__odd__eq,axiom,
% 9.25/5.22      ! [A: rat,N: nat] :
% 9.25/5.22        ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.25/5.22        = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6068_power__odd__eq,axiom,
% 9.25/5.22      ! [A: nat,N: nat] :
% 9.25/5.22        ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.25/5.22        = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6069_power__odd__eq,axiom,
% 9.25/5.22      ! [A: int,N: nat] :
% 9.25/5.22        ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.25/5.22        = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6070_minus__1__div__exp__eq__int,axiom,
% 9.25/5.22      ! [N: nat] :
% 9.25/5.22        ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.22        = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6071_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 9.25/5.22      ! [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 ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6072_signed__take__bit__int__less__eq__self__iff,axiom,
% 9.25/5.22      ! [N: nat,K: int] :
% 9.25/5.22        ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 9.25/5.22        = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6073_signed__take__bit__int__greater__self__iff,axiom,
% 9.25/5.22      ! [K: int,N: nat] :
% 9.25/5.22        ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 9.25/5.22        = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6074_power2__diff,axiom,
% 9.25/5.22      ! [X: int,Y: int] :
% 9.25/5.22        ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22        = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6075_power2__diff,axiom,
% 9.25/5.22      ! [X: code_integer,Y: code_integer] :
% 9.25/5.22        ( ( power_8256067586552552935nteger @ ( minus_8373710615458151222nteger @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22        = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6076_power2__diff,axiom,
% 9.25/5.22      ! [X: rat,Y: rat] :
% 9.25/5.22        ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.22        = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6077_mask__half__int,axiom,
% 9.25/5.22      ! [N: nat] :
% 9.25/5.22        ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.22        = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6078_mult__exp__mod__exp__eq,axiom,
% 9.25/5.22      ! [M: nat,N: nat,A: nat] :
% 9.25/5.22        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.22       => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.22          = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6079_mult__exp__mod__exp__eq,axiom,
% 9.25/5.22      ! [M: nat,N: nat,A: int] :
% 9.25/5.22        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.22       => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.22          = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6080_mult__exp__mod__exp__eq,axiom,
% 9.25/5.22      ! [M: nat,N: nat,A: code_integer] :
% 9.25/5.22        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.22       => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.22          = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6081_mult__exp__mod__exp__eq,axiom,
% 9.25/5.22      ! [M: nat,N: nat,A: code_natural] :
% 9.25/5.22        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.22       => ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.22          = ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6082_power__minus1__odd,axiom,
% 9.25/5.22      ! [N: nat] :
% 9.25/5.22        ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.25/5.22        = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6083_power__minus1__odd,axiom,
% 9.25/5.22      ! [N: nat] :
% 9.25/5.22        ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.25/5.22        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6084_power__minus1__odd,axiom,
% 9.25/5.22      ! [N: nat] :
% 9.25/5.22        ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 9.25/5.22        = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6085_signed__take__bit__int__eq__self__iff,axiom,
% 9.25/5.22      ! [N: nat,K: int] :
% 9.25/5.22        ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 9.25/5.22          = K )
% 9.25/5.22        = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 9.25/5.22          & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6086_signed__take__bit__int__eq__self,axiom,
% 9.25/5.22      ! [N: nat,K: int] :
% 9.25/5.22        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 9.25/5.22       => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.22         => ( ( bit_ri631733984087533419it_int @ N @ K )
% 9.25/5.22            = K ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6087_take__bit__incr__eq,axiom,
% 9.25/5.22      ! [N: nat,K: int] :
% 9.25/5.22        ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 9.25/5.22         != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 9.25/5.22       => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 9.25/5.22          = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6088_take__bit__Suc__minus__1__eq,axiom,
% 9.25/5.22      ! [N: nat] :
% 9.25/5.22        ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.22        = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_Code_integer ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6089_take__bit__Suc__minus__1__eq,axiom,
% 9.25/5.22      ! [N: nat] :
% 9.25/5.22        ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.22        = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_int ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6090_take__bit__numeral__minus__1__eq,axiom,
% 9.25/5.22      ! [K: num] :
% 9.25/5.22        ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.22        = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6091_take__bit__numeral__minus__1__eq,axiom,
% 9.25/5.22      ! [K: num] :
% 9.25/5.22        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.22        = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6092_gcd__nat_Oordering__top__axioms,axiom,
% 9.25/5.22      ( ordering_top_nat @ dvd_dvd_nat
% 9.25/5.22      @ ^ [M2: nat,N2: nat] :
% 9.25/5.22          ( ( dvd_dvd_nat @ M2 @ N2 )
% 9.25/5.22          & ( M2 != N2 ) )
% 9.25/5.22      @ zero_zero_nat ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6093_fold__atLeastAtMost__nat_Opsimps,axiom,
% 9.25/5.22      ! [F2: nat > nat > nat,A: nat,B: nat,Acc: nat] :
% 9.25/5.22        ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ F2 @ ( produc487386426758144856at_nat @ A @ ( product_Pair_nat_nat @ B @ Acc ) ) ) )
% 9.25/5.22       => ( ( ( ord_less_nat @ B @ A )
% 9.25/5.22           => ( ( set_fo2584398358068434914at_nat @ F2 @ A @ B @ Acc )
% 9.25/5.22              = Acc ) )
% 9.25/5.22          & ( ~ ( ord_less_nat @ B @ A )
% 9.25/5.22           => ( ( set_fo2584398358068434914at_nat @ F2 @ A @ B @ Acc )
% 9.25/5.22              = ( set_fo2584398358068434914at_nat @ F2 @ ( plus_plus_nat @ A @ one_one_nat ) @ B @ ( F2 @ A @ Acc ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6094_fold__atLeastAtMost__nat_Opelims,axiom,
% 9.25/5.22      ! [X: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y: nat] :
% 9.25/5.22        ( ( ( set_fo2584398358068434914at_nat @ X @ Xa @ Xb @ Xc )
% 9.25/5.22          = Y )
% 9.25/5.22       => ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ X @ ( produc487386426758144856at_nat @ Xa @ ( product_Pair_nat_nat @ Xb @ Xc ) ) ) )
% 9.25/5.22         => ~ ( ( ( ( ord_less_nat @ Xb @ Xa )
% 9.25/5.22                 => ( Y = Xc ) )
% 9.25/5.22                & ( ~ ( ord_less_nat @ Xb @ Xa )
% 9.25/5.22                 => ( Y
% 9.25/5.22                    = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X @ Xa @ Xc ) ) ) ) )
% 9.25/5.22             => ~ ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ X @ ( produc487386426758144856at_nat @ Xa @ ( product_Pair_nat_nat @ Xb @ Xc ) ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6095_flip__bit__0,axiom,
% 9.25/5.22      ! [A: code_integer] :
% 9.25/5.22        ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 9.25/5.22        = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6096_flip__bit__0,axiom,
% 9.25/5.22      ! [A: code_natural] :
% 9.25/5.22        ( ( bit_se168947363167071951atural @ zero_zero_nat @ A )
% 9.25/5.22        = ( plus_p4538020629002901425atural @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6097_flip__bit__0,axiom,
% 9.25/5.22      ! [A: int] :
% 9.25/5.22        ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 9.25/5.22        = ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6098_flip__bit__0,axiom,
% 9.25/5.22      ! [A: nat] :
% 9.25/5.22        ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 9.25/5.22        = ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6099_one__mod__2__pow__eq,axiom,
% 9.25/5.22      ! [N: nat] :
% 9.25/5.22        ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.22        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6100_one__mod__2__pow__eq,axiom,
% 9.25/5.22      ! [N: nat] :
% 9.25/5.22        ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.22        = ( zero_n8403883297036319079atural @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6101_one__mod__2__pow__eq,axiom,
% 9.25/5.22      ! [N: nat] :
% 9.25/5.22        ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.22        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6102_one__mod__2__pow__eq,axiom,
% 9.25/5.22      ! [N: nat] :
% 9.25/5.22        ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.22        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6103_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 9.25/5.22      ! [X: num,N: nat,A: int] :
% 9.25/5.22        ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 9.25/5.22        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6104_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 9.25/5.22      ! [X: num,N: nat,A: int] :
% 9.25/5.22        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 9.25/5.22        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6105_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 9.25/5.22      ! [X: num,N: nat,A: int] :
% 9.25/5.22        ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 9.25/5.22        = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6106_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 9.25/5.22      ! [A: int,X: num,N: nat] :
% 9.25/5.22        ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 9.25/5.22        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6107_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 9.25/5.22      ! [A: int,X: num,N: nat] :
% 9.25/5.22        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 9.25/5.22        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6108_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 9.25/5.22      ! [A: int,X: num,N: nat] :
% 9.25/5.22        ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 9.25/5.22        = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6109_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 9.25/5.22      ! [X: num,N: nat,A: int] :
% 9.25/5.22        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 9.25/5.22        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6110_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 9.25/5.22      ! [X: num,N: nat,A: int] :
% 9.25/5.22        ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 9.25/5.22        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6111_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 9.25/5.22      ! [X: num,N: nat,A: int] :
% 9.25/5.22        ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 9.25/5.22        = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6112_of__bool__eq__1__iff,axiom,
% 9.25/5.22      ! [P: $o] :
% 9.25/5.22        ( ( ( zero_n356916108424825756nteger @ P )
% 9.25/5.22          = one_one_Code_integer )
% 9.25/5.22        = P ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6113_of__bool__eq__1__iff,axiom,
% 9.25/5.22      ! [P: $o] :
% 9.25/5.22        ( ( ( zero_n2052037380579107095ol_rat @ P )
% 9.25/5.22          = one_one_rat )
% 9.25/5.22        = P ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6114_of__bool__eq__1__iff,axiom,
% 9.25/5.22      ! [P: $o] :
% 9.25/5.22        ( ( ( zero_n2684676970156552555ol_int @ P )
% 9.25/5.22          = one_one_int )
% 9.25/5.22        = P ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6115_of__bool__eq__1__iff,axiom,
% 9.25/5.22      ! [P: $o] :
% 9.25/5.22        ( ( ( zero_n2687167440665602831ol_nat @ P )
% 9.25/5.22          = one_one_nat )
% 9.25/5.22        = P ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6116_of__bool__eq_I2_J,axiom,
% 9.25/5.22      ( ( zero_n356916108424825756nteger @ $true )
% 9.25/5.22      = one_one_Code_integer ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6117_of__bool__eq_I2_J,axiom,
% 9.25/5.22      ( ( zero_n2052037380579107095ol_rat @ $true )
% 9.25/5.22      = one_one_rat ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6118_of__bool__eq_I2_J,axiom,
% 9.25/5.22      ( ( zero_n2684676970156552555ol_int @ $true )
% 9.25/5.22      = one_one_int ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6119_of__bool__eq_I2_J,axiom,
% 9.25/5.22      ( ( zero_n2687167440665602831ol_nat @ $true )
% 9.25/5.22      = one_one_nat ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6120_of__bool__less__one__iff,axiom,
% 9.25/5.22      ! [P: $o] :
% 9.25/5.22        ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 9.25/5.22        = ~ P ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6121_of__bool__less__one__iff,axiom,
% 9.25/5.22      ! [P: $o] :
% 9.25/5.22        ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 9.25/5.22        = ~ P ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6122_of__bool__less__one__iff,axiom,
% 9.25/5.22      ! [P: $o] :
% 9.25/5.22        ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 9.25/5.22        = ~ P ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6123_of__bool__less__one__iff,axiom,
% 9.25/5.22      ! [P: $o] :
% 9.25/5.22        ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 9.25/5.22        = ~ P ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6124_of__bool__not__iff,axiom,
% 9.25/5.22      ! [P: $o] :
% 9.25/5.22        ( ( zero_n356916108424825756nteger @ ~ P )
% 9.25/5.22        = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6125_of__bool__not__iff,axiom,
% 9.25/5.22      ! [P: $o] :
% 9.25/5.22        ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 9.25/5.22        = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6126_of__bool__not__iff,axiom,
% 9.25/5.22      ! [P: $o] :
% 9.25/5.22        ( ( zero_n2684676970156552555ol_int @ ~ P )
% 9.25/5.22        = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6127_of__int__1,axiom,
% 9.25/5.22      ( ( ring_18347121197199848620nteger @ one_one_int )
% 9.25/5.22      = one_one_Code_integer ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6128_of__int__1,axiom,
% 9.25/5.22      ( ( ring_1_of_int_int @ one_one_int )
% 9.25/5.22      = one_one_int ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6129_of__int__1,axiom,
% 9.25/5.22      ( ( ring_1_of_int_rat @ one_one_int )
% 9.25/5.22      = one_one_rat ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6130_of__int__eq__1__iff,axiom,
% 9.25/5.22      ! [Z: int] :
% 9.25/5.22        ( ( ( ring_18347121197199848620nteger @ Z )
% 9.25/5.22          = one_one_Code_integer )
% 9.25/5.22        = ( Z = one_one_int ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6131_of__int__eq__1__iff,axiom,
% 9.25/5.22      ! [Z: int] :
% 9.25/5.22        ( ( ( ring_1_of_int_int @ Z )
% 9.25/5.22          = one_one_int )
% 9.25/5.22        = ( Z = one_one_int ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6132_of__int__eq__1__iff,axiom,
% 9.25/5.22      ! [Z: int] :
% 9.25/5.22        ( ( ( ring_1_of_int_rat @ Z )
% 9.25/5.22          = one_one_rat )
% 9.25/5.22        = ( Z = one_one_int ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6133_of__int__mult,axiom,
% 9.25/5.22      ! [W: int,Z: int] :
% 9.25/5.22        ( ( ring_18347121197199848620nteger @ ( times_times_int @ W @ Z ) )
% 9.25/5.22        = ( times_3573771949741848930nteger @ ( ring_18347121197199848620nteger @ W ) @ ( ring_18347121197199848620nteger @ Z ) ) ) ).
% 9.25/5.22  
% 9.25/5.22  thf(fact_6134_of__int__mult,axiom,
% 9.25/5.22      ! [W: int,Z: int] :
% 9.25/5.23        ( ( ring_1_of_int_rat @ ( times_times_int @ W @ Z ) )
% 9.25/5.23        = ( times_times_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6135_of__int__mult,axiom,
% 9.25/5.23      ! [W: int,Z: int] :
% 9.25/5.23        ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 9.25/5.23        = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6136_of__int__minus,axiom,
% 9.25/5.23      ! [Z: int] :
% 9.25/5.23        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ Z ) )
% 9.25/5.23        = ( uminus_uminus_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6137_of__int__minus,axiom,
% 9.25/5.23      ! [Z: int] :
% 9.25/5.23        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ Z ) )
% 9.25/5.23        = ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ Z ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6138_of__int__minus,axiom,
% 9.25/5.23      ! [Z: int] :
% 9.25/5.23        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ Z ) )
% 9.25/5.23        = ( uminus_uminus_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6139_Divides_Oadjust__div__eq,axiom,
% 9.25/5.23      ! [Q4: int,R3: int] :
% 9.25/5.23        ( ( adjust_div @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 9.25/5.23        = ( plus_plus_int @ Q4 @ ( zero_n2684676970156552555ol_int @ ( R3 != zero_zero_int ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6140_and__nat__numerals_I4_J,axiom,
% 9.25/5.23      ! [X: num] :
% 9.25/5.23        ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 9.25/5.23        = one_one_nat ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6141_and__nat__numerals_I2_J,axiom,
% 9.25/5.23      ! [Y: num] :
% 9.25/5.23        ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 9.25/5.23        = one_one_nat ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6142_of__int__le__1__iff,axiom,
% 9.25/5.23      ! [Z: int] :
% 9.25/5.23        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ Z ) @ one_one_Code_integer )
% 9.25/5.23        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6143_of__int__le__1__iff,axiom,
% 9.25/5.23      ! [Z: int] :
% 9.25/5.23        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 9.25/5.23        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6144_of__int__le__1__iff,axiom,
% 9.25/5.23      ! [Z: int] :
% 9.25/5.23        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 9.25/5.23        = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6145_of__int__1__le__iff,axiom,
% 9.25/5.23      ! [Z: int] :
% 9.25/5.23        ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( ring_18347121197199848620nteger @ Z ) )
% 9.25/5.23        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6146_of__int__1__le__iff,axiom,
% 9.25/5.23      ! [Z: int] :
% 9.25/5.23        ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 9.25/5.23        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6147_of__int__1__le__iff,axiom,
% 9.25/5.23      ! [Z: int] :
% 9.25/5.23        ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 9.25/5.23        = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6148_of__int__less__1__iff,axiom,
% 9.25/5.23      ! [Z: int] :
% 9.25/5.23        ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ Z ) @ one_one_Code_integer )
% 9.25/5.23        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6149_of__int__less__1__iff,axiom,
% 9.25/5.23      ! [Z: int] :
% 9.25/5.23        ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 9.25/5.23        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6150_of__int__less__1__iff,axiom,
% 9.25/5.23      ! [Z: int] :
% 9.25/5.23        ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 9.25/5.23        = ( ord_less_int @ Z @ one_one_int ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6151_of__int__1__less__iff,axiom,
% 9.25/5.23      ! [Z: int] :
% 9.25/5.23        ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( ring_18347121197199848620nteger @ Z ) )
% 9.25/5.23        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6152_of__int__1__less__iff,axiom,
% 9.25/5.23      ! [Z: int] :
% 9.25/5.23        ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 9.25/5.23        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6153_of__int__1__less__iff,axiom,
% 9.25/5.23      ! [Z: int] :
% 9.25/5.23        ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 9.25/5.23        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6154_take__bit__of__1,axiom,
% 9.25/5.23      ! [N: nat] :
% 9.25/5.23        ( ( bit_se1745604003318907178nteger @ N @ one_one_Code_integer )
% 9.25/5.23        = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6155_take__bit__of__1,axiom,
% 9.25/5.23      ! [N: nat] :
% 9.25/5.23        ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 9.25/5.23        = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6156_take__bit__of__1,axiom,
% 9.25/5.23      ! [N: nat] :
% 9.25/5.23        ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 9.25/5.23        = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6157_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 9.25/5.23      ! [X: num,N: nat,Y: int] :
% 9.25/5.23        ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 9.25/5.23          = ( ring_1_of_int_int @ Y ) )
% 9.25/5.23        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 9.25/5.23          = Y ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6158_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 9.25/5.23      ! [X: num,N: nat,Y: int] :
% 9.25/5.23        ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N )
% 9.25/5.23          = ( ring_18347121197199848620nteger @ Y ) )
% 9.25/5.23        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 9.25/5.23          = Y ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6159_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 9.25/5.23      ! [X: num,N: nat,Y: int] :
% 9.25/5.23        ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N )
% 9.25/5.23          = ( ring_1_of_int_rat @ Y ) )
% 9.25/5.23        = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 9.25/5.23          = Y ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6160_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 9.25/5.23      ! [Y: int,X: num,N: nat] :
% 9.25/5.23        ( ( ( ring_1_of_int_int @ Y )
% 9.25/5.23          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 9.25/5.23        = ( Y
% 9.25/5.23          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6161_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 9.25/5.23      ! [Y: int,X: num,N: nat] :
% 9.25/5.23        ( ( ( ring_18347121197199848620nteger @ Y )
% 9.25/5.23          = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 9.25/5.23        = ( Y
% 9.25/5.23          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6162_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 9.25/5.23      ! [Y: int,X: num,N: nat] :
% 9.25/5.23        ( ( ( ring_1_of_int_rat @ Y )
% 9.25/5.23          = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 9.25/5.23        = ( Y
% 9.25/5.23          = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6163_one__div__2__pow__eq,axiom,
% 9.25/5.23      ! [N: nat] :
% 9.25/5.23        ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.23        = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6164_one__div__2__pow__eq,axiom,
% 9.25/5.23      ! [N: nat] :
% 9.25/5.23        ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.23        = ( zero_n8403883297036319079atural @ ( N = zero_zero_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6165_one__div__2__pow__eq,axiom,
% 9.25/5.23      ! [N: nat] :
% 9.25/5.23        ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.23        = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6166_one__div__2__pow__eq,axiom,
% 9.25/5.23      ! [N: nat] :
% 9.25/5.23        ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.23        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6167_bits__1__div__exp,axiom,
% 9.25/5.23      ! [N: nat] :
% 9.25/5.23        ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.23        = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6168_bits__1__div__exp,axiom,
% 9.25/5.23      ! [N: nat] :
% 9.25/5.23        ( ( divide5121882707175180666atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.23        = ( zero_n8403883297036319079atural @ ( N = zero_zero_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6169_bits__1__div__exp,axiom,
% 9.25/5.23      ! [N: nat] :
% 9.25/5.23        ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.23        = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6170_bits__1__div__exp,axiom,
% 9.25/5.23      ! [N: nat] :
% 9.25/5.23        ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.23        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6171_take__bit__of__exp,axiom,
% 9.25/5.23      ! [M: nat,N: nat] :
% 9.25/5.23        ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.23        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6172_take__bit__of__exp,axiom,
% 9.25/5.23      ! [M: nat,N: nat] :
% 9.25/5.23        ( ( bit_se569199155075624693atural @ M @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.23        = ( times_2397367101498566445atural @ ( zero_n8403883297036319079atural @ ( ord_less_nat @ N @ M ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6173_take__bit__of__exp,axiom,
% 9.25/5.23      ! [M: nat,N: nat] :
% 9.25/5.23        ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.23        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6174_take__bit__of__exp,axiom,
% 9.25/5.23      ! [M: nat,N: nat] :
% 9.25/5.23        ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.23        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6175_take__bit__of__2,axiom,
% 9.25/5.23      ! [N: nat] :
% 9.25/5.23        ( ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.23        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6176_take__bit__of__2,axiom,
% 9.25/5.23      ! [N: nat] :
% 9.25/5.23        ( ( bit_se569199155075624693atural @ N @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.23        = ( times_2397367101498566445atural @ ( zero_n8403883297036319079atural @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6177_take__bit__of__2,axiom,
% 9.25/5.23      ! [N: nat] :
% 9.25/5.23        ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.23        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6178_take__bit__of__2,axiom,
% 9.25/5.23      ! [N: nat] :
% 9.25/5.23        ( ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.23        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6179_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 9.25/5.23      ! [A: int,X: num,N: nat] :
% 9.25/5.23        ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 9.25/5.23        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6180_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 9.25/5.23      ! [A: int,X: num,N: nat] :
% 9.25/5.23        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 9.25/5.23        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6181_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 9.25/5.23      ! [A: int,X: num,N: nat] :
% 9.25/5.23        ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 9.25/5.23        = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6182_mult__of__int__commute,axiom,
% 9.25/5.23      ! [X: int,Y: code_integer] :
% 9.25/5.23        ( ( times_3573771949741848930nteger @ ( ring_18347121197199848620nteger @ X ) @ Y )
% 9.25/5.23        = ( times_3573771949741848930nteger @ Y @ ( ring_18347121197199848620nteger @ X ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6183_mult__of__int__commute,axiom,
% 9.25/5.23      ! [X: int,Y: rat] :
% 9.25/5.23        ( ( times_times_rat @ ( ring_1_of_int_rat @ X ) @ Y )
% 9.25/5.23        = ( times_times_rat @ Y @ ( ring_1_of_int_rat @ X ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6184_mult__of__int__commute,axiom,
% 9.25/5.23      ! [X: int,Y: int] :
% 9.25/5.23        ( ( times_times_int @ ( ring_1_of_int_int @ X ) @ Y )
% 9.25/5.23        = ( times_times_int @ Y @ ( ring_1_of_int_int @ X ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6185_of__bool__conj,axiom,
% 9.25/5.23      ! [P: $o,Q2: $o] :
% 9.25/5.23        ( ( zero_n356916108424825756nteger
% 9.25/5.23          @ ( P
% 9.25/5.23            & Q2 ) )
% 9.25/5.23        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6186_of__bool__conj,axiom,
% 9.25/5.23      ! [P: $o,Q2: $o] :
% 9.25/5.23        ( ( zero_n2052037380579107095ol_rat
% 9.25/5.23          @ ( P
% 9.25/5.23            & Q2 ) )
% 9.25/5.23        = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6187_of__bool__conj,axiom,
% 9.25/5.23      ! [P: $o,Q2: $o] :
% 9.25/5.23        ( ( zero_n2684676970156552555ol_int
% 9.25/5.23          @ ( P
% 9.25/5.23            & Q2 ) )
% 9.25/5.23        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6188_of__bool__conj,axiom,
% 9.25/5.23      ! [P: $o,Q2: $o] :
% 9.25/5.23        ( ( zero_n2687167440665602831ol_nat
% 9.25/5.23          @ ( P
% 9.25/5.23            & Q2 ) )
% 9.25/5.23        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6189_of__bool__less__eq__one,axiom,
% 9.25/5.23      ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6190_of__bool__less__eq__one,axiom,
% 9.25/5.23      ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6191_of__bool__less__eq__one,axiom,
% 9.25/5.23      ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6192_of__bool__less__eq__one,axiom,
% 9.25/5.23      ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6193_split__of__bool__asm,axiom,
% 9.25/5.23      ! [P: code_integer > $o,P4: $o] :
% 9.25/5.23        ( ( P @ ( zero_n356916108424825756nteger @ P4 ) )
% 9.25/5.23        = ( ~ ( ( P4
% 9.25/5.23                & ~ ( P @ one_one_Code_integer ) )
% 9.25/5.23              | ( ~ P4
% 9.25/5.23                & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6194_split__of__bool__asm,axiom,
% 9.25/5.23      ! [P: rat > $o,P4: $o] :
% 9.25/5.23        ( ( P @ ( zero_n2052037380579107095ol_rat @ P4 ) )
% 9.25/5.23        = ( ~ ( ( P4
% 9.25/5.23                & ~ ( P @ one_one_rat ) )
% 9.25/5.23              | ( ~ P4
% 9.25/5.23                & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6195_split__of__bool__asm,axiom,
% 9.25/5.23      ! [P: int > $o,P4: $o] :
% 9.25/5.23        ( ( P @ ( zero_n2684676970156552555ol_int @ P4 ) )
% 9.25/5.23        = ( ~ ( ( P4
% 9.25/5.23                & ~ ( P @ one_one_int ) )
% 9.25/5.23              | ( ~ P4
% 9.25/5.23                & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6196_split__of__bool__asm,axiom,
% 9.25/5.23      ! [P: nat > $o,P4: $o] :
% 9.25/5.23        ( ( P @ ( zero_n2687167440665602831ol_nat @ P4 ) )
% 9.25/5.23        = ( ~ ( ( P4
% 9.25/5.23                & ~ ( P @ one_one_nat ) )
% 9.25/5.23              | ( ~ P4
% 9.25/5.23                & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6197_split__of__bool,axiom,
% 9.25/5.23      ! [P: code_integer > $o,P4: $o] :
% 9.25/5.23        ( ( P @ ( zero_n356916108424825756nteger @ P4 ) )
% 9.25/5.23        = ( ( P4
% 9.25/5.23           => ( P @ one_one_Code_integer ) )
% 9.25/5.23          & ( ~ P4
% 9.25/5.23           => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6198_split__of__bool,axiom,
% 9.25/5.23      ! [P: rat > $o,P4: $o] :
% 9.25/5.23        ( ( P @ ( zero_n2052037380579107095ol_rat @ P4 ) )
% 9.25/5.23        = ( ( P4
% 9.25/5.23           => ( P @ one_one_rat ) )
% 9.25/5.23          & ( ~ P4
% 9.25/5.23           => ( P @ zero_zero_rat ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6199_split__of__bool,axiom,
% 9.25/5.23      ! [P: int > $o,P4: $o] :
% 9.25/5.23        ( ( P @ ( zero_n2684676970156552555ol_int @ P4 ) )
% 9.25/5.23        = ( ( P4
% 9.25/5.23           => ( P @ one_one_int ) )
% 9.25/5.23          & ( ~ P4
% 9.25/5.23           => ( P @ zero_zero_int ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6200_split__of__bool,axiom,
% 9.25/5.23      ! [P: nat > $o,P4: $o] :
% 9.25/5.23        ( ( P @ ( zero_n2687167440665602831ol_nat @ P4 ) )
% 9.25/5.23        = ( ( P4
% 9.25/5.23           => ( P @ one_one_nat ) )
% 9.25/5.23          & ( ~ P4
% 9.25/5.23           => ( P @ zero_zero_nat ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6201_of__bool__def,axiom,
% 9.25/5.23      ( zero_n356916108424825756nteger
% 9.25/5.23      = ( ^ [P6: $o] : ( if_Code_integer @ P6 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6202_of__bool__def,axiom,
% 9.25/5.23      ( zero_n2052037380579107095ol_rat
% 9.25/5.23      = ( ^ [P6: $o] : ( if_rat @ P6 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6203_of__bool__def,axiom,
% 9.25/5.23      ( zero_n2684676970156552555ol_int
% 9.25/5.23      = ( ^ [P6: $o] : ( if_int @ P6 @ one_one_int @ zero_zero_int ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6204_of__bool__def,axiom,
% 9.25/5.23      ( zero_n2687167440665602831ol_nat
% 9.25/5.23      = ( ^ [P6: $o] : ( if_nat @ P6 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6205_Divides_Oadjust__div__def,axiom,
% 9.25/5.23      ( adjust_div
% 9.25/5.23      = ( produc8211389475949308722nt_int
% 9.25/5.23        @ ^ [Q5: int,R4: int] : ( plus_plus_int @ Q5 @ ( zero_n2684676970156552555ol_int @ ( R4 != zero_zero_int ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6206_of__int__neg__numeral,axiom,
% 9.25/5.23      ! [K: num] :
% 9.25/5.23        ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 9.25/5.23        = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6207_of__int__neg__numeral,axiom,
% 9.25/5.23      ! [K: num] :
% 9.25/5.23        ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 9.25/5.23        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6208_of__int__neg__numeral,axiom,
% 9.25/5.23      ! [K: num] :
% 9.25/5.23        ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 9.25/5.23        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6209_power__dvd__imp__le,axiom,
% 9.25/5.23      ! [I: nat,M: nat,N: nat] :
% 9.25/5.23        ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 9.25/5.23       => ( ( ord_less_nat @ one_one_nat @ I )
% 9.25/5.23         => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6210_fold__atLeastAtMost__nat_Osimps,axiom,
% 9.25/5.23      ( set_fo2584398358068434914at_nat
% 9.25/5.23      = ( ^ [F: nat > nat > nat,A3: nat,B3: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B3 @ A3 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F @ ( plus_plus_nat @ A3 @ one_one_nat ) @ B3 @ ( F @ A3 @ Acc2 ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6211_fold__atLeastAtMost__nat_Oelims,axiom,
% 9.25/5.23      ! [X: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y: nat] :
% 9.25/5.23        ( ( ( set_fo2584398358068434914at_nat @ X @ Xa @ Xb @ Xc )
% 9.25/5.23          = Y )
% 9.25/5.23       => ( ( ( ord_less_nat @ Xb @ Xa )
% 9.25/5.23           => ( Y = Xc ) )
% 9.25/5.23          & ( ~ ( ord_less_nat @ Xb @ Xa )
% 9.25/5.23           => ( Y
% 9.25/5.23              = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X @ Xa @ Xc ) ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6212_mask__nat__def,axiom,
% 9.25/5.23      ( bit_se2002935070580805687sk_nat
% 9.25/5.23      = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6213_bits__induct,axiom,
% 9.25/5.23      ! [P: code_integer > $o,A: code_integer] :
% 9.25/5.23        ( ! [A6: code_integer] :
% 9.25/5.23            ( ( ( divide6298287555418463151nteger @ A6 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.23              = A6 )
% 9.25/5.23           => ( P @ A6 ) )
% 9.25/5.23       => ( ! [A6: code_integer,B6: $o] :
% 9.25/5.23              ( ( P @ A6 )
% 9.25/5.23             => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B6 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A6 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.23                  = A6 )
% 9.25/5.23               => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B6 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A6 ) ) ) ) )
% 9.25/5.23         => ( P @ A ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6214_bits__induct,axiom,
% 9.25/5.23      ! [P: code_natural > $o,A: code_natural] :
% 9.25/5.23        ( ! [A6: code_natural] :
% 9.25/5.23            ( ( ( divide5121882707175180666atural @ A6 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.23              = A6 )
% 9.25/5.23           => ( P @ A6 ) )
% 9.25/5.23       => ( ! [A6: code_natural,B6: $o] :
% 9.25/5.23              ( ( P @ A6 )
% 9.25/5.23             => ( ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( zero_n8403883297036319079atural @ B6 ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A6 ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.23                  = A6 )
% 9.25/5.23               => ( P @ ( plus_p4538020629002901425atural @ ( zero_n8403883297036319079atural @ B6 ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A6 ) ) ) ) )
% 9.25/5.23         => ( P @ A ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6215_bits__induct,axiom,
% 9.25/5.23      ! [P: int > $o,A: int] :
% 9.25/5.23        ( ! [A6: int] :
% 9.25/5.23            ( ( ( divide_divide_int @ A6 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.23              = A6 )
% 9.25/5.23           => ( P @ A6 ) )
% 9.25/5.23       => ( ! [A6: int,B6: $o] :
% 9.25/5.23              ( ( P @ A6 )
% 9.25/5.23             => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B6 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A6 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.23                  = A6 )
% 9.25/5.23               => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B6 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A6 ) ) ) ) )
% 9.25/5.23         => ( P @ A ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6216_bits__induct,axiom,
% 9.25/5.23      ! [P: nat > $o,A: nat] :
% 9.25/5.23        ( ! [A6: nat] :
% 9.25/5.23            ( ( ( divide_divide_nat @ A6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.23              = A6 )
% 9.25/5.23           => ( P @ A6 ) )
% 9.25/5.23       => ( ! [A6: nat,B6: $o] :
% 9.25/5.23              ( ( P @ A6 )
% 9.25/5.23             => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B6 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A6 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.23                  = A6 )
% 9.25/5.23               => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B6 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A6 ) ) ) ) )
% 9.25/5.23         => ( P @ A ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6217_exp__mod__exp,axiom,
% 9.25/5.23      ! [M: nat,N: nat] :
% 9.25/5.23        ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.23        = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6218_exp__mod__exp,axiom,
% 9.25/5.23      ! [M: nat,N: nat] :
% 9.25/5.23        ( ( modulo8411746178871703098atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.23        = ( times_2397367101498566445atural @ ( zero_n8403883297036319079atural @ ( ord_less_nat @ M @ N ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6219_exp__mod__exp,axiom,
% 9.25/5.23      ! [M: nat,N: nat] :
% 9.25/5.23        ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.23        = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6220_exp__mod__exp,axiom,
% 9.25/5.23      ! [M: nat,N: nat] :
% 9.25/5.23        ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.23        = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6221_dvd__productE,axiom,
% 9.25/5.23      ! [P4: nat,A: nat,B: nat] :
% 9.25/5.23        ( ( dvd_dvd_nat @ P4 @ ( times_times_nat @ A @ B ) )
% 9.25/5.23       => ~ ! [X2: nat,Y2: nat] :
% 9.25/5.23              ( ( P4
% 9.25/5.23                = ( times_times_nat @ X2 @ Y2 ) )
% 9.25/5.23             => ( ( dvd_dvd_nat @ X2 @ A )
% 9.25/5.23               => ~ ( dvd_dvd_nat @ Y2 @ B ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6222_dvd__productE,axiom,
% 9.25/5.23      ! [P4: int,A: int,B: int] :
% 9.25/5.23        ( ( dvd_dvd_int @ P4 @ ( times_times_int @ A @ B ) )
% 9.25/5.23       => ~ ! [X2: int,Y2: int] :
% 9.25/5.23              ( ( P4
% 9.25/5.23                = ( times_times_int @ X2 @ Y2 ) )
% 9.25/5.23             => ( ( dvd_dvd_int @ X2 @ A )
% 9.25/5.23               => ~ ( dvd_dvd_int @ Y2 @ B ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6223_division__decomp,axiom,
% 9.25/5.23      ! [A: nat,B: nat,C: nat] :
% 9.25/5.23        ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 9.25/5.23       => ? [B8: nat,C5: nat] :
% 9.25/5.23            ( ( A
% 9.25/5.23              = ( times_times_nat @ B8 @ C5 ) )
% 9.25/5.23            & ( dvd_dvd_nat @ B8 @ B )
% 9.25/5.23            & ( dvd_dvd_nat @ C5 @ C ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6224_division__decomp,axiom,
% 9.25/5.23      ! [A: int,B: int,C: int] :
% 9.25/5.23        ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 9.25/5.23       => ? [B8: int,C5: int] :
% 9.25/5.23            ( ( A
% 9.25/5.23              = ( times_times_int @ B8 @ C5 ) )
% 9.25/5.23            & ( dvd_dvd_int @ B8 @ B )
% 9.25/5.23            & ( dvd_dvd_int @ C5 @ C ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6225_ex__power__ivl1,axiom,
% 9.25/5.23      ! [B: nat,K: nat] :
% 9.25/5.23        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 9.25/5.23       => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 9.25/5.23         => ? [N3: nat] :
% 9.25/5.23              ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 9.25/5.23              & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6226_ex__power__ivl2,axiom,
% 9.25/5.23      ! [B: nat,K: nat] :
% 9.25/5.23        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 9.25/5.23       => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 9.25/5.23         => ? [N3: nat] :
% 9.25/5.23              ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 9.25/5.23              & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6227_xor__one__eq,axiom,
% 9.25/5.23      ! [A: code_integer] :
% 9.25/5.23        ( ( bit_se3222712562003087583nteger @ A @ one_one_Code_integer )
% 9.25/5.23        = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 9.25/5.23          @ ( zero_n356916108424825756nteger
% 9.25/5.23            @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6228_xor__one__eq,axiom,
% 9.25/5.23      ! [A: code_natural] :
% 9.25/5.23        ( ( bit_se2046307713759805098atural @ A @ one_one_Code_natural )
% 9.25/5.23        = ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ A @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) )
% 9.25/5.23          @ ( zero_n8403883297036319079atural
% 9.25/5.23            @ ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6229_xor__one__eq,axiom,
% 9.25/5.23      ! [A: int] :
% 9.25/5.23        ( ( bit_se6526347334894502574or_int @ A @ one_one_int )
% 9.25/5.23        = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 9.25/5.23          @ ( zero_n2684676970156552555ol_int
% 9.25/5.23            @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6230_xor__one__eq,axiom,
% 9.25/5.23      ! [A: nat] :
% 9.25/5.23        ( ( bit_se6528837805403552850or_nat @ A @ one_one_nat )
% 9.25/5.23        = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 9.25/5.23          @ ( zero_n2687167440665602831ol_nat
% 9.25/5.23            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6231_one__xor__eq,axiom,
% 9.25/5.23      ! [A: code_integer] :
% 9.25/5.23        ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ A )
% 9.25/5.23        = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 9.25/5.23          @ ( zero_n356916108424825756nteger
% 9.25/5.23            @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6232_one__xor__eq,axiom,
% 9.25/5.23      ! [A: code_natural] :
% 9.25/5.23        ( ( bit_se2046307713759805098atural @ one_one_Code_natural @ A )
% 9.25/5.23        = ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ A @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) )
% 9.25/5.23          @ ( zero_n8403883297036319079atural
% 9.25/5.23            @ ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6233_one__xor__eq,axiom,
% 9.25/5.23      ! [A: int] :
% 9.25/5.23        ( ( bit_se6526347334894502574or_int @ one_one_int @ A )
% 9.25/5.23        = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 9.25/5.23          @ ( zero_n2684676970156552555ol_int
% 9.25/5.23            @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6234_one__xor__eq,axiom,
% 9.25/5.23      ! [A: nat] :
% 9.25/5.23        ( ( bit_se6528837805403552850or_nat @ one_one_nat @ A )
% 9.25/5.23        = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 9.25/5.23          @ ( zero_n2687167440665602831ol_nat
% 9.25/5.23            @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6235_exp__div__exp__eq,axiom,
% 9.25/5.23      ! [M: nat,N: nat] :
% 9.25/5.23        ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.23        = ( times_3573771949741848930nteger
% 9.25/5.23          @ ( zero_n356916108424825756nteger
% 9.25/5.23            @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 9.25/5.23               != zero_z3403309356797280102nteger )
% 9.25/5.23              & ( ord_less_eq_nat @ N @ M ) ) )
% 9.25/5.23          @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6236_exp__div__exp__eq,axiom,
% 9.25/5.23      ! [M: nat,N: nat] :
% 9.25/5.23        ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.23        = ( times_2397367101498566445atural
% 9.25/5.23          @ ( zero_n8403883297036319079atural
% 9.25/5.23            @ ( ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M )
% 9.25/5.23               != zero_z2226904508553997617atural )
% 9.25/5.23              & ( ord_less_eq_nat @ N @ M ) ) )
% 9.25/5.23          @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6237_exp__div__exp__eq,axiom,
% 9.25/5.23      ! [M: nat,N: nat] :
% 9.25/5.23        ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.23        = ( times_times_int
% 9.25/5.23          @ ( zero_n2684676970156552555ol_int
% 9.25/5.23            @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 9.25/5.23               != zero_zero_int )
% 9.25/5.23              & ( ord_less_eq_nat @ N @ M ) ) )
% 9.25/5.23          @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6238_exp__div__exp__eq,axiom,
% 9.25/5.23      ! [M: nat,N: nat] :
% 9.25/5.23        ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.23        = ( times_times_nat
% 9.25/5.23          @ ( zero_n2687167440665602831ol_nat
% 9.25/5.23            @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 9.25/5.23               != zero_zero_nat )
% 9.25/5.23              & ( ord_less_eq_nat @ N @ M ) ) )
% 9.25/5.23          @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6239_floor__exists1,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23      ? [X2: int] :
% 9.25/5.23        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X2 ) @ X )
% 9.25/5.23        & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ X2 @ one_one_int ) ) )
% 9.25/5.23        & ! [Y5: int] :
% 9.25/5.23            ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y5 ) @ X )
% 9.25/5.23              & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y5 @ one_one_int ) ) ) )
% 9.25/5.23           => ( Y5 = X2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6240_floor__exists,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23      ? [Z2: int] :
% 9.25/5.23        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X )
% 9.25/5.23        & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6241_and__int_Osimps,axiom,
% 9.25/5.23      ( bit_se725231765392027082nd_int
% 9.25/5.23      = ( ^ [K4: int,L2: int] :
% 9.25/5.23            ( if_int
% 9.25/5.23            @ ( ( member_int @ K4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.25/5.23              & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.25/5.23            @ ( uminus_uminus_int
% 9.25/5.23              @ ( zero_n2684676970156552555ol_int
% 9.25/5.23                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K4 )
% 9.25/5.23                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 9.25/5.23            @ ( plus_plus_int
% 9.25/5.23              @ ( zero_n2684676970156552555ol_int
% 9.25/5.23                @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K4 )
% 9.25/5.23                  & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 9.25/5.23              @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6242_and__int_Oelims,axiom,
% 9.25/5.23      ! [X: int,Xa: int,Y: int] :
% 9.25/5.23        ( ( ( bit_se725231765392027082nd_int @ X @ Xa )
% 9.25/5.23          = Y )
% 9.25/5.23       => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.25/5.23              & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.25/5.23           => ( Y
% 9.25/5.23              = ( uminus_uminus_int
% 9.25/5.23                @ ( zero_n2684676970156552555ol_int
% 9.25/5.23                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 9.25/5.23                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 9.25/5.23          & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.25/5.23                & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.25/5.23           => ( Y
% 9.25/5.23              = ( plus_plus_int
% 9.25/5.23                @ ( zero_n2684676970156552555ol_int
% 9.25/5.23                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 9.25/5.23                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 9.25/5.23                @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6243_round__unique,axiom,
% 9.25/5.23      ! [X: rat,Y: int] :
% 9.25/5.23        ( ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y ) )
% 9.25/5.23       => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 9.25/5.23         => ( ( archim7778729529865785530nd_rat @ X )
% 9.25/5.23            = Y ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6244_push__bit__numeral__minus__1,axiom,
% 9.25/5.23      ! [N: num] :
% 9.25/5.23        ( ( bit_se7788150548672797655nteger @ ( numeral_numeral_nat @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.23        = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6245_push__bit__numeral__minus__1,axiom,
% 9.25/5.23      ! [N: num] :
% 9.25/5.23        ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.23        = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6246_divmod__step__integer__def,axiom,
% 9.25/5.23      ( unique4921790084139445826nteger
% 9.25/5.23      = ( ^ [L2: num] :
% 9.25/5.23            ( produc6916734918728496179nteger
% 9.25/5.23            @ ^ [Q5: code_integer,R4: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R4 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R4 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R4 ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6247_singletonI,axiom,
% 9.25/5.23      ! [A: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ A @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6248_singletonI,axiom,
% 9.25/5.23      ! [A: set_Pr958786334691620121nt_int] : ( member2340774599025711042nt_int @ A @ ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6249_singletonI,axiom,
% 9.25/5.23      ! [A: set_nat] : ( member_set_nat @ A @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6250_singletonI,axiom,
% 9.25/5.23      ! [A: produc3658429121746597890et_nat > $o] : ( member6576561426505652726_nat_o @ A @ ( insert5175938949040314269_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6251_singletonI,axiom,
% 9.25/5.23      ! [A: product_prod_nat_nat] : ( member8440522571783428010at_nat @ A @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6252_singletonI,axiom,
% 9.25/5.23      ! [A: $o] : ( member_o @ A @ ( insert_o @ A @ bot_bot_set_o ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6253_singletonI,axiom,
% 9.25/5.23      ! [A: nat] : ( member_nat @ A @ ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6254_singletonI,axiom,
% 9.25/5.23      ! [A: int] : ( member_int @ A @ ( insert_int @ A @ bot_bot_set_int ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6255_Int__insert__right__if1,axiom,
% 9.25/5.23      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( member8757157785044589968at_nat @ A @ A2 )
% 9.25/5.23       => ( ( inf_in7913087082777306421at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ B2 ) )
% 9.25/5.23          = ( insert9069300056098147895at_nat @ A @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6256_Int__insert__right__if1,axiom,
% 9.25/5.23      ! [A: $o,A2: set_o,B2: set_o] :
% 9.25/5.23        ( ( member_o @ A @ A2 )
% 9.25/5.23       => ( ( inf_inf_set_o @ A2 @ ( insert_o @ A @ B2 ) )
% 9.25/5.23          = ( insert_o @ A @ ( inf_inf_set_o @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6257_Int__insert__right__if1,axiom,
% 9.25/5.23      ! [A: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.23        ( ( member2340774599025711042nt_int @ A @ A2 )
% 9.25/5.23       => ( ( inf_in8396524679539076455nt_int @ A2 @ ( insert8897473484851387113nt_int @ A @ B2 ) )
% 9.25/5.23          = ( insert8897473484851387113nt_int @ A @ ( inf_in8396524679539076455nt_int @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6258_Int__insert__right__if1,axiom,
% 9.25/5.23      ! [A: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 9.25/5.23        ( ( member_set_nat @ A @ A2 )
% 9.25/5.23       => ( ( inf_inf_set_set_nat @ A2 @ ( insert_set_nat @ A @ B2 ) )
% 9.25/5.23          = ( insert_set_nat @ A @ ( inf_inf_set_set_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6259_Int__insert__right__if1,axiom,
% 9.25/5.23      ! [A: int,A2: set_int,B2: set_int] :
% 9.25/5.23        ( ( member_int @ A @ A2 )
% 9.25/5.23       => ( ( inf_inf_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 9.25/5.23          = ( insert_int @ A @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6260_Int__insert__right__if1,axiom,
% 9.25/5.23      ! [A: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.23        ( ( member6576561426505652726_nat_o @ A @ A2 )
% 9.25/5.23       => ( ( inf_in1906310914598751387_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ A @ B2 ) )
% 9.25/5.23          = ( insert5175938949040314269_nat_o @ A @ ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6261_Int__insert__right__if1,axiom,
% 9.25/5.23      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( member8440522571783428010at_nat @ A @ A2 )
% 9.25/5.23       => ( ( inf_in2572325071724192079at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 9.25/5.23          = ( insert8211810215607154385at_nat @ A @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6262_Int__insert__right__if1,axiom,
% 9.25/5.23      ! [A: nat,A2: set_nat,B2: set_nat] :
% 9.25/5.23        ( ( member_nat @ A @ A2 )
% 9.25/5.23       => ( ( inf_inf_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 9.25/5.23          = ( insert_nat @ A @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6263_Int__insert__right__if0,axiom,
% 9.25/5.23      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ~ ( member8757157785044589968at_nat @ A @ A2 )
% 9.25/5.23       => ( ( inf_in7913087082777306421at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ B2 ) )
% 9.25/5.23          = ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6264_Int__insert__right__if0,axiom,
% 9.25/5.23      ! [A: $o,A2: set_o,B2: set_o] :
% 9.25/5.23        ( ~ ( member_o @ A @ A2 )
% 9.25/5.23       => ( ( inf_inf_set_o @ A2 @ ( insert_o @ A @ B2 ) )
% 9.25/5.23          = ( inf_inf_set_o @ A2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6265_Int__insert__right__if0,axiom,
% 9.25/5.23      ! [A: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.23        ( ~ ( member2340774599025711042nt_int @ A @ A2 )
% 9.25/5.23       => ( ( inf_in8396524679539076455nt_int @ A2 @ ( insert8897473484851387113nt_int @ A @ B2 ) )
% 9.25/5.23          = ( inf_in8396524679539076455nt_int @ A2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6266_Int__insert__right__if0,axiom,
% 9.25/5.23      ! [A: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 9.25/5.23        ( ~ ( member_set_nat @ A @ A2 )
% 9.25/5.23       => ( ( inf_inf_set_set_nat @ A2 @ ( insert_set_nat @ A @ B2 ) )
% 9.25/5.23          = ( inf_inf_set_set_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6267_Int__insert__right__if0,axiom,
% 9.25/5.23      ! [A: int,A2: set_int,B2: set_int] :
% 9.25/5.23        ( ~ ( member_int @ A @ A2 )
% 9.25/5.23       => ( ( inf_inf_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 9.25/5.23          = ( inf_inf_set_int @ A2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6268_Int__insert__right__if0,axiom,
% 9.25/5.23      ! [A: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.23        ( ~ ( member6576561426505652726_nat_o @ A @ A2 )
% 9.25/5.23       => ( ( inf_in1906310914598751387_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ A @ B2 ) )
% 9.25/5.23          = ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6269_Int__insert__right__if0,axiom,
% 9.25/5.23      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ~ ( member8440522571783428010at_nat @ A @ A2 )
% 9.25/5.23       => ( ( inf_in2572325071724192079at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 9.25/5.23          = ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6270_Int__insert__right__if0,axiom,
% 9.25/5.23      ! [A: nat,A2: set_nat,B2: set_nat] :
% 9.25/5.23        ( ~ ( member_nat @ A @ A2 )
% 9.25/5.23       => ( ( inf_inf_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 9.25/5.23          = ( inf_inf_set_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6271_insert__inter__insert,axiom,
% 9.25/5.23      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A @ A2 ) @ ( insert9069300056098147895at_nat @ A @ B2 ) )
% 9.25/5.23        = ( insert9069300056098147895at_nat @ A @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6272_insert__inter__insert,axiom,
% 9.25/5.23      ! [A: $o,A2: set_o,B2: set_o] :
% 9.25/5.23        ( ( inf_inf_set_o @ ( insert_o @ A @ A2 ) @ ( insert_o @ A @ B2 ) )
% 9.25/5.23        = ( insert_o @ A @ ( inf_inf_set_o @ A2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6273_insert__inter__insert,axiom,
% 9.25/5.23      ! [A: int,A2: set_int,B2: set_int] :
% 9.25/5.23        ( ( inf_inf_set_int @ ( insert_int @ A @ A2 ) @ ( insert_int @ A @ B2 ) )
% 9.25/5.23        = ( insert_int @ A @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6274_insert__inter__insert,axiom,
% 9.25/5.23      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ A2 ) @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 9.25/5.23        = ( insert8211810215607154385at_nat @ A @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6275_insert__inter__insert,axiom,
% 9.25/5.23      ! [A: nat,A2: set_nat,B2: set_nat] :
% 9.25/5.23        ( ( inf_inf_set_nat @ ( insert_nat @ A @ A2 ) @ ( insert_nat @ A @ B2 ) )
% 9.25/5.23        = ( insert_nat @ A @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6276_Int__insert__left__if1,axiom,
% 9.25/5.23      ! [A: produc3843707927480180839at_nat,C2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( member8757157785044589968at_nat @ A @ C2 )
% 9.25/5.23       => ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A @ B2 ) @ C2 )
% 9.25/5.23          = ( insert9069300056098147895at_nat @ A @ ( inf_in7913087082777306421at_nat @ B2 @ C2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6277_Int__insert__left__if1,axiom,
% 9.25/5.23      ! [A: $o,C2: set_o,B2: set_o] :
% 9.25/5.23        ( ( member_o @ A @ C2 )
% 9.25/5.23       => ( ( inf_inf_set_o @ ( insert_o @ A @ B2 ) @ C2 )
% 9.25/5.23          = ( insert_o @ A @ ( inf_inf_set_o @ B2 @ C2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6278_Int__insert__left__if1,axiom,
% 9.25/5.23      ! [A: set_Pr958786334691620121nt_int,C2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.23        ( ( member2340774599025711042nt_int @ A @ C2 )
% 9.25/5.23       => ( ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ B2 ) @ C2 )
% 9.25/5.23          = ( insert8897473484851387113nt_int @ A @ ( inf_in8396524679539076455nt_int @ B2 @ C2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6279_Int__insert__left__if1,axiom,
% 9.25/5.23      ! [A: set_nat,C2: set_set_nat,B2: set_set_nat] :
% 9.25/5.23        ( ( member_set_nat @ A @ C2 )
% 9.25/5.23       => ( ( inf_inf_set_set_nat @ ( insert_set_nat @ A @ B2 ) @ C2 )
% 9.25/5.23          = ( insert_set_nat @ A @ ( inf_inf_set_set_nat @ B2 @ C2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6280_Int__insert__left__if1,axiom,
% 9.25/5.23      ! [A: int,C2: set_int,B2: set_int] :
% 9.25/5.23        ( ( member_int @ A @ C2 )
% 9.25/5.23       => ( ( inf_inf_set_int @ ( insert_int @ A @ B2 ) @ C2 )
% 9.25/5.23          = ( insert_int @ A @ ( inf_inf_set_int @ B2 @ C2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6281_Int__insert__left__if1,axiom,
% 9.25/5.23      ! [A: produc3658429121746597890et_nat > $o,C2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.23        ( ( member6576561426505652726_nat_o @ A @ C2 )
% 9.25/5.23       => ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A @ B2 ) @ C2 )
% 9.25/5.23          = ( insert5175938949040314269_nat_o @ A @ ( inf_in1906310914598751387_nat_o @ B2 @ C2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6282_Int__insert__left__if1,axiom,
% 9.25/5.23      ! [A: product_prod_nat_nat,C2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( member8440522571783428010at_nat @ A @ C2 )
% 9.25/5.23       => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ B2 ) @ C2 )
% 9.25/5.23          = ( insert8211810215607154385at_nat @ A @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6283_Int__insert__left__if1,axiom,
% 9.25/5.23      ! [A: nat,C2: set_nat,B2: set_nat] :
% 9.25/5.23        ( ( member_nat @ A @ C2 )
% 9.25/5.23       => ( ( inf_inf_set_nat @ ( insert_nat @ A @ B2 ) @ C2 )
% 9.25/5.23          = ( insert_nat @ A @ ( inf_inf_set_nat @ B2 @ C2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6284_Int__insert__left__if0,axiom,
% 9.25/5.23      ! [A: produc3843707927480180839at_nat,C2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ~ ( member8757157785044589968at_nat @ A @ C2 )
% 9.25/5.23       => ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A @ B2 ) @ C2 )
% 9.25/5.23          = ( inf_in7913087082777306421at_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6285_Int__insert__left__if0,axiom,
% 9.25/5.23      ! [A: $o,C2: set_o,B2: set_o] :
% 9.25/5.23        ( ~ ( member_o @ A @ C2 )
% 9.25/5.23       => ( ( inf_inf_set_o @ ( insert_o @ A @ B2 ) @ C2 )
% 9.25/5.23          = ( inf_inf_set_o @ B2 @ C2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6286_Int__insert__left__if0,axiom,
% 9.25/5.23      ! [A: set_Pr958786334691620121nt_int,C2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.23        ( ~ ( member2340774599025711042nt_int @ A @ C2 )
% 9.25/5.23       => ( ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ B2 ) @ C2 )
% 9.25/5.23          = ( inf_in8396524679539076455nt_int @ B2 @ C2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6287_Int__insert__left__if0,axiom,
% 9.25/5.23      ! [A: set_nat,C2: set_set_nat,B2: set_set_nat] :
% 9.25/5.23        ( ~ ( member_set_nat @ A @ C2 )
% 9.25/5.23       => ( ( inf_inf_set_set_nat @ ( insert_set_nat @ A @ B2 ) @ C2 )
% 9.25/5.23          = ( inf_inf_set_set_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6288_Int__insert__left__if0,axiom,
% 9.25/5.23      ! [A: int,C2: set_int,B2: set_int] :
% 9.25/5.23        ( ~ ( member_int @ A @ C2 )
% 9.25/5.23       => ( ( inf_inf_set_int @ ( insert_int @ A @ B2 ) @ C2 )
% 9.25/5.23          = ( inf_inf_set_int @ B2 @ C2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6289_Int__insert__left__if0,axiom,
% 9.25/5.23      ! [A: produc3658429121746597890et_nat > $o,C2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.23        ( ~ ( member6576561426505652726_nat_o @ A @ C2 )
% 9.25/5.23       => ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A @ B2 ) @ C2 )
% 9.25/5.23          = ( inf_in1906310914598751387_nat_o @ B2 @ C2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6290_Int__insert__left__if0,axiom,
% 9.25/5.23      ! [A: product_prod_nat_nat,C2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ~ ( member8440522571783428010at_nat @ A @ C2 )
% 9.25/5.23       => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ B2 ) @ C2 )
% 9.25/5.23          = ( inf_in2572325071724192079at_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6291_Int__insert__left__if0,axiom,
% 9.25/5.23      ! [A: nat,C2: set_nat,B2: set_nat] :
% 9.25/5.23        ( ~ ( member_nat @ A @ C2 )
% 9.25/5.23       => ( ( inf_inf_set_nat @ ( insert_nat @ A @ B2 ) @ C2 )
% 9.25/5.23          = ( inf_inf_set_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6292_Un__insert__right,axiom,
% 9.25/5.23      ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( sup_su6327502436637775413at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 9.25/5.23        = ( insert8211810215607154385at_nat @ A @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6293_Un__insert__right,axiom,
% 9.25/5.23      ! [A2: set_o,A: $o,B2: set_o] :
% 9.25/5.23        ( ( sup_sup_set_o @ A2 @ ( insert_o @ A @ B2 ) )
% 9.25/5.23        = ( insert_o @ A @ ( sup_sup_set_o @ A2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6294_Un__insert__right,axiom,
% 9.25/5.23      ! [A2: set_int,A: int,B2: set_int] :
% 9.25/5.23        ( ( sup_sup_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 9.25/5.23        = ( insert_int @ A @ ( sup_sup_set_int @ A2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6295_Un__insert__right,axiom,
% 9.25/5.23      ! [A2: set_Pr8551490117392284871at_nat,A: produc4166570645942440679at_nat,B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.23        ( ( sup_su3035147773818789531at_nat @ A2 @ ( insert6337962749363155127at_nat @ A @ B2 ) )
% 9.25/5.23        = ( insert6337962749363155127at_nat @ A @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6296_Un__insert__right,axiom,
% 9.25/5.23      ! [A2: set_Pr4329608150637261639at_nat,A: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( sup_su5525570899277871387at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ B2 ) )
% 9.25/5.23        = ( insert9069300056098147895at_nat @ A @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6297_Un__insert__right,axiom,
% 9.25/5.23      ! [A2: set_nat,A: nat,B2: set_nat] :
% 9.25/5.23        ( ( sup_sup_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 9.25/5.23        = ( insert_nat @ A @ ( sup_sup_set_nat @ A2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6298_Un__insert__left,axiom,
% 9.25/5.23      ! [A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( sup_su6327502436637775413at_nat @ ( insert8211810215607154385at_nat @ A @ B2 ) @ C2 )
% 9.25/5.23        = ( insert8211810215607154385at_nat @ A @ ( sup_su6327502436637775413at_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6299_Un__insert__left,axiom,
% 9.25/5.23      ! [A: $o,B2: set_o,C2: set_o] :
% 9.25/5.23        ( ( sup_sup_set_o @ ( insert_o @ A @ B2 ) @ C2 )
% 9.25/5.23        = ( insert_o @ A @ ( sup_sup_set_o @ B2 @ C2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6300_Un__insert__left,axiom,
% 9.25/5.23      ! [A: int,B2: set_int,C2: set_int] :
% 9.25/5.23        ( ( sup_sup_set_int @ ( insert_int @ A @ B2 ) @ C2 )
% 9.25/5.23        = ( insert_int @ A @ ( sup_sup_set_int @ B2 @ C2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6301_Un__insert__left,axiom,
% 9.25/5.23      ! [A: produc4166570645942440679at_nat,B2: set_Pr8551490117392284871at_nat,C2: set_Pr8551490117392284871at_nat] :
% 9.25/5.23        ( ( sup_su3035147773818789531at_nat @ ( insert6337962749363155127at_nat @ A @ B2 ) @ C2 )
% 9.25/5.23        = ( insert6337962749363155127at_nat @ A @ ( sup_su3035147773818789531at_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6302_Un__insert__left,axiom,
% 9.25/5.23      ! [A: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat,C2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( sup_su5525570899277871387at_nat @ ( insert9069300056098147895at_nat @ A @ B2 ) @ C2 )
% 9.25/5.23        = ( insert9069300056098147895at_nat @ A @ ( sup_su5525570899277871387at_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6303_Un__insert__left,axiom,
% 9.25/5.23      ! [A: nat,B2: set_nat,C2: set_nat] :
% 9.25/5.23        ( ( sup_sup_set_nat @ ( insert_nat @ A @ B2 ) @ C2 )
% 9.25/5.23        = ( insert_nat @ A @ ( sup_sup_set_nat @ B2 @ C2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6304_singleton__conv2,axiom,
% 9.25/5.23      ! [A: produc3843707927480180839at_nat] :
% 9.25/5.23        ( ( collec6321179662152712658at_nat
% 9.25/5.23          @ ( ^ [Y4: produc3843707927480180839at_nat,Z4: produc3843707927480180839at_nat] : ( Y4 = Z4 )
% 9.25/5.23            @ A ) )
% 9.25/5.23        = ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6305_singleton__conv2,axiom,
% 9.25/5.23      ! [A: set_Pr958786334691620121nt_int] :
% 9.25/5.23        ( ( collec5210948495886036740nt_int
% 9.25/5.23          @ ( ^ [Y4: set_Pr958786334691620121nt_int,Z4: set_Pr958786334691620121nt_int] : ( Y4 = Z4 )
% 9.25/5.23            @ A ) )
% 9.25/5.23        = ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6306_singleton__conv2,axiom,
% 9.25/5.23      ! [A: set_nat] :
% 9.25/5.23        ( ( collect_set_nat
% 9.25/5.23          @ ( ^ [Y4: set_nat,Z4: set_nat] : ( Y4 = Z4 )
% 9.25/5.23            @ A ) )
% 9.25/5.23        = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6307_singleton__conv2,axiom,
% 9.25/5.23      ! [A: produc3658429121746597890et_nat > $o] :
% 9.25/5.23        ( ( collec939566748876313656_nat_o
% 9.25/5.23          @ ( ^ [Y4: produc3658429121746597890et_nat > $o,Z4: produc3658429121746597890et_nat > $o] : ( Y4 = Z4 )
% 9.25/5.23            @ A ) )
% 9.25/5.23        = ( insert5175938949040314269_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6308_singleton__conv2,axiom,
% 9.25/5.23      ! [A: product_prod_nat_nat] :
% 9.25/5.23        ( ( collec3392354462482085612at_nat
% 9.25/5.23          @ ( ^ [Y4: product_prod_nat_nat,Z4: product_prod_nat_nat] : ( Y4 = Z4 )
% 9.25/5.23            @ A ) )
% 9.25/5.23        = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6309_singleton__conv2,axiom,
% 9.25/5.23      ! [A: $o] :
% 9.25/5.23        ( ( collect_o
% 9.25/5.23          @ ( ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 9.25/5.23            @ A ) )
% 9.25/5.23        = ( insert_o @ A @ bot_bot_set_o ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6310_singleton__conv2,axiom,
% 9.25/5.23      ! [A: nat] :
% 9.25/5.23        ( ( collect_nat
% 9.25/5.23          @ ( ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 )
% 9.25/5.23            @ A ) )
% 9.25/5.23        = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6311_singleton__conv2,axiom,
% 9.25/5.23      ! [A: int] :
% 9.25/5.23        ( ( collect_int
% 9.25/5.23          @ ( ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 9.25/5.23            @ A ) )
% 9.25/5.23        = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6312_singleton__conv,axiom,
% 9.25/5.23      ! [A: produc3843707927480180839at_nat] :
% 9.25/5.23        ( ( collec6321179662152712658at_nat
% 9.25/5.23          @ ^ [X3: produc3843707927480180839at_nat] : ( X3 = A ) )
% 9.25/5.23        = ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6313_singleton__conv,axiom,
% 9.25/5.23      ! [A: set_Pr958786334691620121nt_int] :
% 9.25/5.23        ( ( collec5210948495886036740nt_int
% 9.25/5.23          @ ^ [X3: set_Pr958786334691620121nt_int] : ( X3 = A ) )
% 9.25/5.23        = ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6314_singleton__conv,axiom,
% 9.25/5.23      ! [A: set_nat] :
% 9.25/5.23        ( ( collect_set_nat
% 9.25/5.23          @ ^ [X3: set_nat] : ( X3 = A ) )
% 9.25/5.23        = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6315_singleton__conv,axiom,
% 9.25/5.23      ! [A: produc3658429121746597890et_nat > $o] :
% 9.25/5.23        ( ( collec939566748876313656_nat_o
% 9.25/5.23          @ ^ [X3: produc3658429121746597890et_nat > $o] : ( X3 = A ) )
% 9.25/5.23        = ( insert5175938949040314269_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6316_singleton__conv,axiom,
% 9.25/5.23      ! [A: product_prod_nat_nat] :
% 9.25/5.23        ( ( collec3392354462482085612at_nat
% 9.25/5.23          @ ^ [X3: product_prod_nat_nat] : ( X3 = A ) )
% 9.25/5.23        = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6317_singleton__conv,axiom,
% 9.25/5.23      ! [A: $o] :
% 9.25/5.23        ( ( collect_o
% 9.25/5.23          @ ^ [X3: $o] : ( X3 = A ) )
% 9.25/5.23        = ( insert_o @ A @ bot_bot_set_o ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6318_singleton__conv,axiom,
% 9.25/5.23      ! [A: nat] :
% 9.25/5.23        ( ( collect_nat
% 9.25/5.23          @ ^ [X3: nat] : ( X3 = A ) )
% 9.25/5.23        = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6319_singleton__conv,axiom,
% 9.25/5.23      ! [A: int] :
% 9.25/5.23        ( ( collect_int
% 9.25/5.23          @ ^ [X3: int] : ( X3 = A ) )
% 9.25/5.23        = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6320_singleton__insert__inj__eq,axiom,
% 9.25/5.23      ! [B: produc3843707927480180839at_nat,A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat )
% 9.25/5.23          = ( insert9069300056098147895at_nat @ A @ A2 ) )
% 9.25/5.23        = ( ( A = B )
% 9.25/5.23          & ( ord_le1268244103169919719at_nat @ A2 @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6321_singleton__insert__inj__eq,axiom,
% 9.25/5.23      ! [B: product_prod_nat_nat,A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat )
% 9.25/5.23          = ( insert8211810215607154385at_nat @ A @ A2 ) )
% 9.25/5.23        = ( ( A = B )
% 9.25/5.23          & ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6322_singleton__insert__inj__eq,axiom,
% 9.25/5.23      ! [B: $o,A: $o,A2: set_o] :
% 9.25/5.23        ( ( ( insert_o @ B @ bot_bot_set_o )
% 9.25/5.23          = ( insert_o @ A @ A2 ) )
% 9.25/5.23        = ( ( A = B )
% 9.25/5.23          & ( ord_less_eq_set_o @ A2 @ ( insert_o @ B @ bot_bot_set_o ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6323_singleton__insert__inj__eq,axiom,
% 9.25/5.23      ! [B: int,A: int,A2: set_int] :
% 9.25/5.23        ( ( ( insert_int @ B @ bot_bot_set_int )
% 9.25/5.23          = ( insert_int @ A @ A2 ) )
% 9.25/5.23        = ( ( A = B )
% 9.25/5.23          & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6324_singleton__insert__inj__eq,axiom,
% 9.25/5.23      ! [B: nat,A: nat,A2: set_nat] :
% 9.25/5.23        ( ( ( insert_nat @ B @ bot_bot_set_nat )
% 9.25/5.23          = ( insert_nat @ A @ A2 ) )
% 9.25/5.23        = ( ( A = B )
% 9.25/5.23          & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6325_singleton__insert__inj__eq_H,axiom,
% 9.25/5.23      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B: produc3843707927480180839at_nat] :
% 9.25/5.23        ( ( ( insert9069300056098147895at_nat @ A @ A2 )
% 9.25/5.23          = ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) )
% 9.25/5.23        = ( ( A = B )
% 9.25/5.23          & ( ord_le1268244103169919719at_nat @ A2 @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6326_singleton__insert__inj__eq_H,axiom,
% 9.25/5.23      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat] :
% 9.25/5.23        ( ( ( insert8211810215607154385at_nat @ A @ A2 )
% 9.25/5.23          = ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) )
% 9.25/5.23        = ( ( A = B )
% 9.25/5.23          & ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6327_singleton__insert__inj__eq_H,axiom,
% 9.25/5.23      ! [A: $o,A2: set_o,B: $o] :
% 9.25/5.23        ( ( ( insert_o @ A @ A2 )
% 9.25/5.23          = ( insert_o @ B @ bot_bot_set_o ) )
% 9.25/5.23        = ( ( A = B )
% 9.25/5.23          & ( ord_less_eq_set_o @ A2 @ ( insert_o @ B @ bot_bot_set_o ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6328_singleton__insert__inj__eq_H,axiom,
% 9.25/5.23      ! [A: int,A2: set_int,B: int] :
% 9.25/5.23        ( ( ( insert_int @ A @ A2 )
% 9.25/5.23          = ( insert_int @ B @ bot_bot_set_int ) )
% 9.25/5.23        = ( ( A = B )
% 9.25/5.23          & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6329_singleton__insert__inj__eq_H,axiom,
% 9.25/5.23      ! [A: nat,A2: set_nat,B: nat] :
% 9.25/5.23        ( ( ( insert_nat @ A @ A2 )
% 9.25/5.23          = ( insert_nat @ B @ bot_bot_set_nat ) )
% 9.25/5.23        = ( ( A = B )
% 9.25/5.23          & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6330_insert__disjoint_I1_J,axiom,
% 9.25/5.23      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A @ A2 ) @ B2 )
% 9.25/5.23          = bot_bo228742789529271731at_nat )
% 9.25/5.23        = ( ~ ( member8757157785044589968at_nat @ A @ B2 )
% 9.25/5.23          & ( ( inf_in7913087082777306421at_nat @ A2 @ B2 )
% 9.25/5.23            = bot_bo228742789529271731at_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6331_insert__disjoint_I1_J,axiom,
% 9.25/5.23      ! [A: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.23        ( ( ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ A2 ) @ B2 )
% 9.25/5.23          = bot_bo1488462491386950373nt_int )
% 9.25/5.23        = ( ~ ( member2340774599025711042nt_int @ A @ B2 )
% 9.25/5.23          & ( ( inf_in8396524679539076455nt_int @ A2 @ B2 )
% 9.25/5.23            = bot_bo1488462491386950373nt_int ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6332_insert__disjoint_I1_J,axiom,
% 9.25/5.23      ! [A: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 9.25/5.23        ( ( ( inf_inf_set_set_nat @ ( insert_set_nat @ A @ A2 ) @ B2 )
% 9.25/5.23          = bot_bot_set_set_nat )
% 9.25/5.23        = ( ~ ( member_set_nat @ A @ B2 )
% 9.25/5.23          & ( ( inf_inf_set_set_nat @ A2 @ B2 )
% 9.25/5.23            = bot_bot_set_set_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6333_insert__disjoint_I1_J,axiom,
% 9.25/5.23      ! [A: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.23        ( ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A @ A2 ) @ B2 )
% 9.25/5.23          = bot_bo7824918357723582233_nat_o )
% 9.25/5.23        = ( ~ ( member6576561426505652726_nat_o @ A @ B2 )
% 9.25/5.23          & ( ( inf_in1906310914598751387_nat_o @ A2 @ B2 )
% 9.25/5.23            = bot_bo7824918357723582233_nat_o ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6334_insert__disjoint_I1_J,axiom,
% 9.25/5.23      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ A2 ) @ B2 )
% 9.25/5.23          = bot_bo2099793752762293965at_nat )
% 9.25/5.23        = ( ~ ( member8440522571783428010at_nat @ A @ B2 )
% 9.25/5.23          & ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 9.25/5.23            = bot_bo2099793752762293965at_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6335_insert__disjoint_I1_J,axiom,
% 9.25/5.23      ! [A: $o,A2: set_o,B2: set_o] :
% 9.25/5.23        ( ( ( inf_inf_set_o @ ( insert_o @ A @ A2 ) @ B2 )
% 9.25/5.23          = bot_bot_set_o )
% 9.25/5.23        = ( ~ ( member_o @ A @ B2 )
% 9.25/5.23          & ( ( inf_inf_set_o @ A2 @ B2 )
% 9.25/5.23            = bot_bot_set_o ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6336_insert__disjoint_I1_J,axiom,
% 9.25/5.23      ! [A: nat,A2: set_nat,B2: set_nat] :
% 9.25/5.23        ( ( ( inf_inf_set_nat @ ( insert_nat @ A @ A2 ) @ B2 )
% 9.25/5.23          = bot_bot_set_nat )
% 9.25/5.23        = ( ~ ( member_nat @ A @ B2 )
% 9.25/5.23          & ( ( inf_inf_set_nat @ A2 @ B2 )
% 9.25/5.23            = bot_bot_set_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6337_insert__disjoint_I1_J,axiom,
% 9.25/5.23      ! [A: int,A2: set_int,B2: set_int] :
% 9.25/5.23        ( ( ( inf_inf_set_int @ ( insert_int @ A @ A2 ) @ B2 )
% 9.25/5.23          = bot_bot_set_int )
% 9.25/5.23        = ( ~ ( member_int @ A @ B2 )
% 9.25/5.23          & ( ( inf_inf_set_int @ A2 @ B2 )
% 9.25/5.23            = bot_bot_set_int ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6338_insert__disjoint_I2_J,axiom,
% 9.25/5.23      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( bot_bo228742789529271731at_nat
% 9.25/5.23          = ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A @ A2 ) @ B2 ) )
% 9.25/5.23        = ( ~ ( member8757157785044589968at_nat @ A @ B2 )
% 9.25/5.23          & ( bot_bo228742789529271731at_nat
% 9.25/5.23            = ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6339_insert__disjoint_I2_J,axiom,
% 9.25/5.23      ! [A: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.23        ( ( bot_bo1488462491386950373nt_int
% 9.25/5.23          = ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ A2 ) @ B2 ) )
% 9.25/5.23        = ( ~ ( member2340774599025711042nt_int @ A @ B2 )
% 9.25/5.23          & ( bot_bo1488462491386950373nt_int
% 9.25/5.23            = ( inf_in8396524679539076455nt_int @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6340_insert__disjoint_I2_J,axiom,
% 9.25/5.23      ! [A: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 9.25/5.23        ( ( bot_bot_set_set_nat
% 9.25/5.23          = ( inf_inf_set_set_nat @ ( insert_set_nat @ A @ A2 ) @ B2 ) )
% 9.25/5.23        = ( ~ ( member_set_nat @ A @ B2 )
% 9.25/5.23          & ( bot_bot_set_set_nat
% 9.25/5.23            = ( inf_inf_set_set_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6341_insert__disjoint_I2_J,axiom,
% 9.25/5.23      ! [A: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.23        ( ( bot_bo7824918357723582233_nat_o
% 9.25/5.23          = ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A @ A2 ) @ B2 ) )
% 9.25/5.23        = ( ~ ( member6576561426505652726_nat_o @ A @ B2 )
% 9.25/5.23          & ( bot_bo7824918357723582233_nat_o
% 9.25/5.23            = ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6342_insert__disjoint_I2_J,axiom,
% 9.25/5.23      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( bot_bo2099793752762293965at_nat
% 9.25/5.23          = ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ A2 ) @ B2 ) )
% 9.25/5.23        = ( ~ ( member8440522571783428010at_nat @ A @ B2 )
% 9.25/5.23          & ( bot_bo2099793752762293965at_nat
% 9.25/5.23            = ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6343_insert__disjoint_I2_J,axiom,
% 9.25/5.23      ! [A: $o,A2: set_o,B2: set_o] :
% 9.25/5.23        ( ( bot_bot_set_o
% 9.25/5.23          = ( inf_inf_set_o @ ( insert_o @ A @ A2 ) @ B2 ) )
% 9.25/5.23        = ( ~ ( member_o @ A @ B2 )
% 9.25/5.23          & ( bot_bot_set_o
% 9.25/5.23            = ( inf_inf_set_o @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6344_insert__disjoint_I2_J,axiom,
% 9.25/5.23      ! [A: nat,A2: set_nat,B2: set_nat] :
% 9.25/5.23        ( ( bot_bot_set_nat
% 9.25/5.23          = ( inf_inf_set_nat @ ( insert_nat @ A @ A2 ) @ B2 ) )
% 9.25/5.23        = ( ~ ( member_nat @ A @ B2 )
% 9.25/5.23          & ( bot_bot_set_nat
% 9.25/5.23            = ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6345_insert__disjoint_I2_J,axiom,
% 9.25/5.23      ! [A: int,A2: set_int,B2: set_int] :
% 9.25/5.23        ( ( bot_bot_set_int
% 9.25/5.23          = ( inf_inf_set_int @ ( insert_int @ A @ A2 ) @ B2 ) )
% 9.25/5.23        = ( ~ ( member_int @ A @ B2 )
% 9.25/5.23          & ( bot_bot_set_int
% 9.25/5.23            = ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6346_disjoint__insert_I1_J,axiom,
% 9.25/5.23      ! [B2: set_Pr4329608150637261639at_nat,A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( ( inf_in7913087082777306421at_nat @ B2 @ ( insert9069300056098147895at_nat @ A @ A2 ) )
% 9.25/5.23          = bot_bo228742789529271731at_nat )
% 9.25/5.23        = ( ~ ( member8757157785044589968at_nat @ A @ B2 )
% 9.25/5.23          & ( ( inf_in7913087082777306421at_nat @ B2 @ A2 )
% 9.25/5.23            = bot_bo228742789529271731at_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6347_disjoint__insert_I1_J,axiom,
% 9.25/5.23      ! [B2: set_se6260736226359567993nt_int,A: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int] :
% 9.25/5.23        ( ( ( inf_in8396524679539076455nt_int @ B2 @ ( insert8897473484851387113nt_int @ A @ A2 ) )
% 9.25/5.23          = bot_bo1488462491386950373nt_int )
% 9.25/5.23        = ( ~ ( member2340774599025711042nt_int @ A @ B2 )
% 9.25/5.23          & ( ( inf_in8396524679539076455nt_int @ B2 @ A2 )
% 9.25/5.23            = bot_bo1488462491386950373nt_int ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6348_disjoint__insert_I1_J,axiom,
% 9.25/5.23      ! [B2: set_set_nat,A: set_nat,A2: set_set_nat] :
% 9.25/5.23        ( ( ( inf_inf_set_set_nat @ B2 @ ( insert_set_nat @ A @ A2 ) )
% 9.25/5.23          = bot_bot_set_set_nat )
% 9.25/5.23        = ( ~ ( member_set_nat @ A @ B2 )
% 9.25/5.23          & ( ( inf_inf_set_set_nat @ B2 @ A2 )
% 9.25/5.23            = bot_bot_set_set_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6349_disjoint__insert_I1_J,axiom,
% 9.25/5.23      ! [B2: set_Pr4532377907799695533_nat_o,A: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.23        ( ( ( inf_in1906310914598751387_nat_o @ B2 @ ( insert5175938949040314269_nat_o @ A @ A2 ) )
% 9.25/5.23          = bot_bo7824918357723582233_nat_o )
% 9.25/5.23        = ( ~ ( member6576561426505652726_nat_o @ A @ B2 )
% 9.25/5.23          & ( ( inf_in1906310914598751387_nat_o @ B2 @ A2 )
% 9.25/5.23            = bot_bo7824918357723582233_nat_o ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6350_disjoint__insert_I1_J,axiom,
% 9.25/5.23      ! [B2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( ( inf_in2572325071724192079at_nat @ B2 @ ( insert8211810215607154385at_nat @ A @ A2 ) )
% 9.25/5.23          = bot_bo2099793752762293965at_nat )
% 9.25/5.23        = ( ~ ( member8440522571783428010at_nat @ A @ B2 )
% 9.25/5.23          & ( ( inf_in2572325071724192079at_nat @ B2 @ A2 )
% 9.25/5.23            = bot_bo2099793752762293965at_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6351_disjoint__insert_I1_J,axiom,
% 9.25/5.23      ! [B2: set_o,A: $o,A2: set_o] :
% 9.25/5.23        ( ( ( inf_inf_set_o @ B2 @ ( insert_o @ A @ A2 ) )
% 9.25/5.23          = bot_bot_set_o )
% 9.25/5.23        = ( ~ ( member_o @ A @ B2 )
% 9.25/5.23          & ( ( inf_inf_set_o @ B2 @ A2 )
% 9.25/5.23            = bot_bot_set_o ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6352_disjoint__insert_I1_J,axiom,
% 9.25/5.23      ! [B2: set_nat,A: nat,A2: set_nat] :
% 9.25/5.23        ( ( ( inf_inf_set_nat @ B2 @ ( insert_nat @ A @ A2 ) )
% 9.25/5.23          = bot_bot_set_nat )
% 9.25/5.23        = ( ~ ( member_nat @ A @ B2 )
% 9.25/5.23          & ( ( inf_inf_set_nat @ B2 @ A2 )
% 9.25/5.23            = bot_bot_set_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6353_disjoint__insert_I1_J,axiom,
% 9.25/5.23      ! [B2: set_int,A: int,A2: set_int] :
% 9.25/5.23        ( ( ( inf_inf_set_int @ B2 @ ( insert_int @ A @ A2 ) )
% 9.25/5.23          = bot_bot_set_int )
% 9.25/5.23        = ( ~ ( member_int @ A @ B2 )
% 9.25/5.23          & ( ( inf_inf_set_int @ B2 @ A2 )
% 9.25/5.23            = bot_bot_set_int ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6354_disjoint__insert_I2_J,axiom,
% 9.25/5.23      ! [A2: set_Pr4329608150637261639at_nat,B: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( bot_bo228742789529271731at_nat
% 9.25/5.23          = ( inf_in7913087082777306421at_nat @ A2 @ ( insert9069300056098147895at_nat @ B @ B2 ) ) )
% 9.25/5.23        = ( ~ ( member8757157785044589968at_nat @ B @ A2 )
% 9.25/5.23          & ( bot_bo228742789529271731at_nat
% 9.25/5.23            = ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6355_disjoint__insert_I2_J,axiom,
% 9.25/5.23      ! [A2: set_se6260736226359567993nt_int,B: set_Pr958786334691620121nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.23        ( ( bot_bo1488462491386950373nt_int
% 9.25/5.23          = ( inf_in8396524679539076455nt_int @ A2 @ ( insert8897473484851387113nt_int @ B @ B2 ) ) )
% 9.25/5.23        = ( ~ ( member2340774599025711042nt_int @ B @ A2 )
% 9.25/5.23          & ( bot_bo1488462491386950373nt_int
% 9.25/5.23            = ( inf_in8396524679539076455nt_int @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6356_disjoint__insert_I2_J,axiom,
% 9.25/5.23      ! [A2: set_set_nat,B: set_nat,B2: set_set_nat] :
% 9.25/5.23        ( ( bot_bot_set_set_nat
% 9.25/5.23          = ( inf_inf_set_set_nat @ A2 @ ( insert_set_nat @ B @ B2 ) ) )
% 9.25/5.23        = ( ~ ( member_set_nat @ B @ A2 )
% 9.25/5.23          & ( bot_bot_set_set_nat
% 9.25/5.23            = ( inf_inf_set_set_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6357_disjoint__insert_I2_J,axiom,
% 9.25/5.23      ! [A2: set_Pr4532377907799695533_nat_o,B: produc3658429121746597890et_nat > $o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.23        ( ( bot_bo7824918357723582233_nat_o
% 9.25/5.23          = ( inf_in1906310914598751387_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ B @ B2 ) ) )
% 9.25/5.23        = ( ~ ( member6576561426505652726_nat_o @ B @ A2 )
% 9.25/5.23          & ( bot_bo7824918357723582233_nat_o
% 9.25/5.23            = ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6358_disjoint__insert_I2_J,axiom,
% 9.25/5.23      ! [A2: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( bot_bo2099793752762293965at_nat
% 9.25/5.23          = ( inf_in2572325071724192079at_nat @ A2 @ ( insert8211810215607154385at_nat @ B @ B2 ) ) )
% 9.25/5.23        = ( ~ ( member8440522571783428010at_nat @ B @ A2 )
% 9.25/5.23          & ( bot_bo2099793752762293965at_nat
% 9.25/5.23            = ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6359_disjoint__insert_I2_J,axiom,
% 9.25/5.23      ! [A2: set_o,B: $o,B2: set_o] :
% 9.25/5.23        ( ( bot_bot_set_o
% 9.25/5.23          = ( inf_inf_set_o @ A2 @ ( insert_o @ B @ B2 ) ) )
% 9.25/5.23        = ( ~ ( member_o @ B @ A2 )
% 9.25/5.23          & ( bot_bot_set_o
% 9.25/5.23            = ( inf_inf_set_o @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6360_disjoint__insert_I2_J,axiom,
% 9.25/5.23      ! [A2: set_nat,B: nat,B2: set_nat] :
% 9.25/5.23        ( ( bot_bot_set_nat
% 9.25/5.23          = ( inf_inf_set_nat @ A2 @ ( insert_nat @ B @ B2 ) ) )
% 9.25/5.23        = ( ~ ( member_nat @ B @ A2 )
% 9.25/5.23          & ( bot_bot_set_nat
% 9.25/5.23            = ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6361_disjoint__insert_I2_J,axiom,
% 9.25/5.23      ! [A2: set_int,B: int,B2: set_int] :
% 9.25/5.23        ( ( bot_bot_set_int
% 9.25/5.23          = ( inf_inf_set_int @ A2 @ ( insert_int @ B @ B2 ) ) )
% 9.25/5.23        = ( ~ ( member_int @ B @ A2 )
% 9.25/5.23          & ( bot_bot_set_int
% 9.25/5.23            = ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6362_insert__Diff__single,axiom,
% 9.25/5.23      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( insert9069300056098147895at_nat @ A @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) )
% 9.25/5.23        = ( insert9069300056098147895at_nat @ A @ A2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6363_insert__Diff__single,axiom,
% 9.25/5.23      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( insert8211810215607154385at_nat @ A @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 9.25/5.23        = ( insert8211810215607154385at_nat @ A @ A2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6364_insert__Diff__single,axiom,
% 9.25/5.23      ! [A: $o,A2: set_o] :
% 9.25/5.23        ( ( insert_o @ A @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 9.25/5.23        = ( insert_o @ A @ A2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6365_insert__Diff__single,axiom,
% 9.25/5.23      ! [A: int,A2: set_int] :
% 9.25/5.23        ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.25/5.23        = ( insert_int @ A @ A2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6366_insert__Diff__single,axiom,
% 9.25/5.23      ! [A: nat,A2: set_nat] :
% 9.25/5.23        ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.25/5.23        = ( insert_nat @ A @ A2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6367_round__1,axiom,
% 9.25/5.23      ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 9.25/5.23      = one_one_int ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6368_subset__Compl__singleton,axiom,
% 9.25/5.23      ! [A2: set_Pr4329608150637261639at_nat,B: produc3843707927480180839at_nat] :
% 9.25/5.23        ( ( ord_le1268244103169919719at_nat @ A2 @ ( uminus935396558254630718at_nat @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) )
% 9.25/5.23        = ( ~ ( member8757157785044589968at_nat @ B @ A2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6369_subset__Compl__singleton,axiom,
% 9.25/5.23      ! [A2: set_se6260736226359567993nt_int,B: set_Pr958786334691620121nt_int] :
% 9.25/5.23        ( ( ord_le483042692224249369nt_int @ A2 @ ( uminus6423885277529793776nt_int @ ( insert8897473484851387113nt_int @ B @ bot_bo1488462491386950373nt_int ) ) )
% 9.25/5.23        = ( ~ ( member2340774599025711042nt_int @ B @ A2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6370_subset__Compl__singleton,axiom,
% 9.25/5.23      ! [A2: set_set_nat,B: set_nat] :
% 9.25/5.23        ( ( ord_le6893508408891458716et_nat @ A2 @ ( uminus613421341184616069et_nat @ ( insert_set_nat @ B @ bot_bot_set_set_nat ) ) )
% 9.25/5.23        = ( ~ ( member_set_nat @ B @ A2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6371_subset__Compl__singleton,axiom,
% 9.25/5.23      ! [A2: set_Pr4532377907799695533_nat_o,B: produc3658429121746597890et_nat > $o] :
% 9.25/5.23        ( ( ord_le2965882846123202637_nat_o @ A2 @ ( uminus5254974436814262692_nat_o @ ( insert5175938949040314269_nat_o @ B @ bot_bo7824918357723582233_nat_o ) ) )
% 9.25/5.23        = ( ~ ( member6576561426505652726_nat_o @ B @ A2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6372_subset__Compl__singleton,axiom,
% 9.25/5.23      ! [A2: set_Pr1261947904930325089at_nat,B: product_prod_nat_nat] :
% 9.25/5.23        ( ( ord_le3146513528884898305at_nat @ A2 @ ( uminus6524753893492686040at_nat @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) )
% 9.25/5.23        = ( ~ ( member8440522571783428010at_nat @ B @ A2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6373_subset__Compl__singleton,axiom,
% 9.25/5.23      ! [A2: set_o,B: $o] :
% 9.25/5.23        ( ( ord_less_eq_set_o @ A2 @ ( uminus_uminus_set_o @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 9.25/5.23        = ( ~ ( member_o @ B @ A2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6374_subset__Compl__singleton,axiom,
% 9.25/5.23      ! [A2: set_int,B: int] :
% 9.25/5.23        ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 9.25/5.23        = ( ~ ( member_int @ B @ A2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6375_subset__Compl__singleton,axiom,
% 9.25/5.23      ! [A2: set_nat,B: nat] :
% 9.25/5.23        ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 9.25/5.23        = ( ~ ( member_nat @ B @ A2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6376_push__bit__Suc__minus__numeral,axiom,
% 9.25/5.23      ! [N: nat,K: num] :
% 9.25/5.23        ( ( bit_se7788150548672797655nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 9.25/5.23        = ( bit_se7788150548672797655nteger @ N @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6377_push__bit__Suc__minus__numeral,axiom,
% 9.25/5.23      ! [N: nat,K: num] :
% 9.25/5.23        ( ( bit_se545348938243370406it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 9.25/5.23        = ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6378_round__neg__numeral,axiom,
% 9.25/5.23      ! [N: num] :
% 9.25/5.23        ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.25/5.23        = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6379_push__bit__Suc,axiom,
% 9.25/5.23      ! [N: nat,A: code_integer] :
% 9.25/5.23        ( ( bit_se7788150548672797655nteger @ ( suc @ N ) @ A )
% 9.25/5.23        = ( bit_se7788150548672797655nteger @ N @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6380_push__bit__Suc,axiom,
% 9.25/5.23      ! [N: nat,A: code_natural] :
% 9.25/5.23        ( ( bit_se6611745700429515170atural @ ( suc @ N ) @ A )
% 9.25/5.23        = ( bit_se6611745700429515170atural @ N @ ( times_2397367101498566445atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6381_push__bit__Suc,axiom,
% 9.25/5.23      ! [N: nat,A: int] :
% 9.25/5.23        ( ( bit_se545348938243370406it_int @ ( suc @ N ) @ A )
% 9.25/5.23        = ( bit_se545348938243370406it_int @ N @ ( times_times_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6382_push__bit__Suc,axiom,
% 9.25/5.23      ! [N: nat,A: nat] :
% 9.25/5.23        ( ( bit_se547839408752420682it_nat @ ( suc @ N ) @ A )
% 9.25/5.23        = ( bit_se547839408752420682it_nat @ N @ ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6383_push__bit__of__1,axiom,
% 9.25/5.23      ! [N: nat] :
% 9.25/5.23        ( ( bit_se7788150548672797655nteger @ N @ one_one_Code_integer )
% 9.25/5.23        = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6384_push__bit__of__1,axiom,
% 9.25/5.23      ! [N: nat] :
% 9.25/5.23        ( ( bit_se6611745700429515170atural @ N @ one_one_Code_natural )
% 9.25/5.23        = ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6385_push__bit__of__1,axiom,
% 9.25/5.23      ! [N: nat] :
% 9.25/5.23        ( ( bit_se545348938243370406it_int @ N @ one_one_int )
% 9.25/5.23        = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6386_push__bit__of__1,axiom,
% 9.25/5.23      ! [N: nat] :
% 9.25/5.23        ( ( bit_se547839408752420682it_nat @ N @ one_one_nat )
% 9.25/5.23        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6387_push__bit__minus__numeral,axiom,
% 9.25/5.23      ! [L: num,K: num] :
% 9.25/5.23        ( ( bit_se7788150548672797655nteger @ ( numeral_numeral_nat @ L ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 9.25/5.23        = ( bit_se7788150548672797655nteger @ ( pred_numeral @ L ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6388_push__bit__minus__numeral,axiom,
% 9.25/5.23      ! [L: num,K: num] :
% 9.25/5.23        ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 9.25/5.23        = ( bit_se545348938243370406it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6389_minus__integer__code_I2_J,axiom,
% 9.25/5.23      ! [L: code_integer] :
% 9.25/5.23        ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L )
% 9.25/5.23        = ( uminus1351360451143612070nteger @ L ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6390_insert__Collect,axiom,
% 9.25/5.23      ! [A: produc3843707927480180839at_nat,P: produc3843707927480180839at_nat > $o] :
% 9.25/5.23        ( ( insert9069300056098147895at_nat @ A @ ( collec6321179662152712658at_nat @ P ) )
% 9.25/5.23        = ( collec6321179662152712658at_nat
% 9.25/5.23          @ ^ [U2: produc3843707927480180839at_nat] :
% 9.25/5.23              ( ( U2 != A )
% 9.25/5.23             => ( P @ U2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6391_insert__Collect,axiom,
% 9.25/5.23      ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 9.25/5.23        ( ( insert8211810215607154385at_nat @ A @ ( collec3392354462482085612at_nat @ P ) )
% 9.25/5.23        = ( collec3392354462482085612at_nat
% 9.25/5.23          @ ^ [U2: product_prod_nat_nat] :
% 9.25/5.23              ( ( U2 != A )
% 9.25/5.23             => ( P @ U2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6392_insert__Collect,axiom,
% 9.25/5.23      ! [A: $o,P: $o > $o] :
% 9.25/5.23        ( ( insert_o @ A @ ( collect_o @ P ) )
% 9.25/5.23        = ( collect_o
% 9.25/5.23          @ ^ [U2: $o] :
% 9.25/5.23              ( ( U2 != A )
% 9.25/5.23             => ( P @ U2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6393_insert__Collect,axiom,
% 9.25/5.23      ! [A: set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.23        ( ( insert8897473484851387113nt_int @ A @ ( collec5210948495886036740nt_int @ P ) )
% 9.25/5.23        = ( collec5210948495886036740nt_int
% 9.25/5.23          @ ^ [U2: set_Pr958786334691620121nt_int] :
% 9.25/5.23              ( ( U2 != A )
% 9.25/5.23             => ( P @ U2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6394_insert__Collect,axiom,
% 9.25/5.23      ! [A: set_nat,P: set_nat > $o] :
% 9.25/5.23        ( ( insert_set_nat @ A @ ( collect_set_nat @ P ) )
% 9.25/5.23        = ( collect_set_nat
% 9.25/5.23          @ ^ [U2: set_nat] :
% 9.25/5.23              ( ( U2 != A )
% 9.25/5.23             => ( P @ U2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6395_insert__Collect,axiom,
% 9.25/5.23      ! [A: nat,P: nat > $o] :
% 9.25/5.23        ( ( insert_nat @ A @ ( collect_nat @ P ) )
% 9.25/5.23        = ( collect_nat
% 9.25/5.23          @ ^ [U2: nat] :
% 9.25/5.23              ( ( U2 != A )
% 9.25/5.23             => ( P @ U2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6396_insert__Collect,axiom,
% 9.25/5.23      ! [A: int,P: int > $o] :
% 9.25/5.23        ( ( insert_int @ A @ ( collect_int @ P ) )
% 9.25/5.23        = ( collect_int
% 9.25/5.23          @ ^ [U2: int] :
% 9.25/5.23              ( ( U2 != A )
% 9.25/5.23             => ( P @ U2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6397_insert__Collect,axiom,
% 9.25/5.23      ! [A: produc3658429121746597890et_nat > $o,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.23        ( ( insert5175938949040314269_nat_o @ A @ ( collec939566748876313656_nat_o @ P ) )
% 9.25/5.23        = ( collec939566748876313656_nat_o
% 9.25/5.23          @ ^ [U2: produc3658429121746597890et_nat > $o] :
% 9.25/5.23              ( ( U2 != A )
% 9.25/5.23             => ( P @ U2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6398_insert__compr,axiom,
% 9.25/5.23      ( insert9069300056098147895at_nat
% 9.25/5.23      = ( ^ [A3: produc3843707927480180839at_nat,B4: set_Pr4329608150637261639at_nat] :
% 9.25/5.23            ( collec6321179662152712658at_nat
% 9.25/5.23            @ ^ [X3: produc3843707927480180839at_nat] :
% 9.25/5.23                ( ( X3 = A3 )
% 9.25/5.23                | ( member8757157785044589968at_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6399_insert__compr,axiom,
% 9.25/5.23      ( insert8211810215607154385at_nat
% 9.25/5.23      = ( ^ [A3: product_prod_nat_nat,B4: set_Pr1261947904930325089at_nat] :
% 9.25/5.23            ( collec3392354462482085612at_nat
% 9.25/5.23            @ ^ [X3: product_prod_nat_nat] :
% 9.25/5.23                ( ( X3 = A3 )
% 9.25/5.23                | ( member8440522571783428010at_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6400_insert__compr,axiom,
% 9.25/5.23      ( insert_o
% 9.25/5.23      = ( ^ [A3: $o,B4: set_o] :
% 9.25/5.23            ( collect_o
% 9.25/5.23            @ ^ [X3: $o] :
% 9.25/5.23                ( ( X3 = A3 )
% 9.25/5.23                | ( member_o @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6401_insert__compr,axiom,
% 9.25/5.23      ( insert8897473484851387113nt_int
% 9.25/5.23      = ( ^ [A3: set_Pr958786334691620121nt_int,B4: set_se6260736226359567993nt_int] :
% 9.25/5.23            ( collec5210948495886036740nt_int
% 9.25/5.23            @ ^ [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.23                ( ( X3 = A3 )
% 9.25/5.23                | ( member2340774599025711042nt_int @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6402_insert__compr,axiom,
% 9.25/5.23      ( insert_set_nat
% 9.25/5.23      = ( ^ [A3: set_nat,B4: set_set_nat] :
% 9.25/5.23            ( collect_set_nat
% 9.25/5.23            @ ^ [X3: set_nat] :
% 9.25/5.23                ( ( X3 = A3 )
% 9.25/5.23                | ( member_set_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6403_insert__compr,axiom,
% 9.25/5.23      ( insert_nat
% 9.25/5.23      = ( ^ [A3: nat,B4: set_nat] :
% 9.25/5.23            ( collect_nat
% 9.25/5.23            @ ^ [X3: nat] :
% 9.25/5.23                ( ( X3 = A3 )
% 9.25/5.23                | ( member_nat @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6404_insert__compr,axiom,
% 9.25/5.23      ( insert_int
% 9.25/5.23      = ( ^ [A3: int,B4: set_int] :
% 9.25/5.23            ( collect_int
% 9.25/5.23            @ ^ [X3: int] :
% 9.25/5.23                ( ( X3 = A3 )
% 9.25/5.23                | ( member_int @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6405_insert__compr,axiom,
% 9.25/5.23      ( insert5175938949040314269_nat_o
% 9.25/5.23      = ( ^ [A3: produc3658429121746597890et_nat > $o,B4: set_Pr4532377907799695533_nat_o] :
% 9.25/5.23            ( collec939566748876313656_nat_o
% 9.25/5.23            @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.23                ( ( X3 = A3 )
% 9.25/5.23                | ( member6576561426505652726_nat_o @ X3 @ B4 ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6406_divmod__integer_H__def,axiom,
% 9.25/5.23      ( unique3479559517661332726nteger
% 9.25/5.23      = ( ^ [M2: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6407_exhaustive__integer_H_Ocases,axiom,
% 9.25/5.23      ! [X: produc8763457246119570046nteger] :
% 9.25/5.23        ~ ! [F3: code_integer > option6357759511663192854e_term,D: code_integer,I2: code_integer] :
% 9.25/5.23            ( X
% 9.25/5.23           != ( produc6137756002093451184nteger @ F3 @ ( produc1086072967326762835nteger @ D @ I2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6408_full__exhaustive__integer_H_Ocases,axiom,
% 9.25/5.23      ! [X: produc1908205239877642774nteger] :
% 9.25/5.23        ~ ! [F3: produc6241069584506657477e_term > option6357759511663192854e_term,D: code_integer,I2: code_integer] :
% 9.25/5.23            ( X
% 9.25/5.23           != ( produc8603105652947943368nteger @ F3 @ ( produc1086072967326762835nteger @ D @ I2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6409_ID_Opred__cong,axiom,
% 9.25/5.23      ! [X: produc3843707927480180839at_nat,Ya: produc3843707927480180839at_nat,P: produc3843707927480180839at_nat > $o,Pa: produc3843707927480180839at_nat > $o] :
% 9.25/5.23        ( ( X = Ya )
% 9.25/5.23       => ( ! [Z2: produc3843707927480180839at_nat] :
% 9.25/5.23              ( ( member8757157785044589968at_nat @ Z2 @ ( insert9069300056098147895at_nat @ Ya @ bot_bo228742789529271731at_nat ) )
% 9.25/5.23             => ( ( P @ Z2 )
% 9.25/5.23                = ( Pa @ Z2 ) ) )
% 9.25/5.23         => ( ( bNF_id1044457264471098170_nat_o @ P @ X )
% 9.25/5.23            = ( bNF_id1044457264471098170_nat_o @ Pa @ Ya ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6410_ID_Opred__cong,axiom,
% 9.25/5.23      ! [X: set_Pr958786334691620121nt_int,Ya: set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o,Pa: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.23        ( ( X = Ya )
% 9.25/5.23       => ( ! [Z2: set_Pr958786334691620121nt_int] :
% 9.25/5.23              ( ( member2340774599025711042nt_int @ Z2 @ ( insert8897473484851387113nt_int @ Ya @ bot_bo1488462491386950373nt_int ) )
% 9.25/5.23             => ( ( P @ Z2 )
% 9.25/5.23                = ( Pa @ Z2 ) ) )
% 9.25/5.23         => ( ( bNF_id9176111459293603464_int_o @ P @ X )
% 9.25/5.23            = ( bNF_id9176111459293603464_int_o @ Pa @ Ya ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6411_ID_Opred__cong,axiom,
% 9.25/5.23      ! [X: set_nat,Ya: set_nat,P: set_nat > $o,Pa: set_nat > $o] :
% 9.25/5.23        ( ( X = Ya )
% 9.25/5.23       => ( ! [Z2: set_nat] :
% 9.25/5.23              ( ( member_set_nat @ Z2 @ ( insert_set_nat @ Ya @ bot_bot_set_set_nat ) )
% 9.25/5.23             => ( ( P @ Z2 )
% 9.25/5.23                = ( Pa @ Z2 ) ) )
% 9.25/5.23         => ( ( bNF_id_bnf_set_nat_o @ P @ X )
% 9.25/5.23            = ( bNF_id_bnf_set_nat_o @ Pa @ Ya ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6412_ID_Opred__cong,axiom,
% 9.25/5.23      ! [X: produc3658429121746597890et_nat > $o,Ya: produc3658429121746597890et_nat > $o,P: ( produc3658429121746597890et_nat > $o ) > $o,Pa: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.23        ( ( X = Ya )
% 9.25/5.23       => ( ! [Z2: produc3658429121746597890et_nat > $o] :
% 9.25/5.23              ( ( member6576561426505652726_nat_o @ Z2 @ ( insert5175938949040314269_nat_o @ Ya @ bot_bo7824918357723582233_nat_o ) )
% 9.25/5.23             => ( ( P @ Z2 )
% 9.25/5.23                = ( Pa @ Z2 ) ) )
% 9.25/5.23         => ( ( bNF_id4470576313039291732at_o_o @ P @ X )
% 9.25/5.23            = ( bNF_id4470576313039291732at_o_o @ Pa @ Ya ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6413_ID_Opred__cong,axiom,
% 9.25/5.23      ! [X: product_prod_nat_nat,Ya: product_prod_nat_nat,P: product_prod_nat_nat > $o,Pa: product_prod_nat_nat > $o] :
% 9.25/5.23        ( ( X = Ya )
% 9.25/5.23       => ( ! [Z2: product_prod_nat_nat] :
% 9.25/5.23              ( ( member8440522571783428010at_nat @ Z2 @ ( insert8211810215607154385at_nat @ Ya @ bot_bo2099793752762293965at_nat ) )
% 9.25/5.23             => ( ( P @ Z2 )
% 9.25/5.23                = ( Pa @ Z2 ) ) )
% 9.25/5.23         => ( ( bNF_id5045731369644952736_nat_o @ P @ X )
% 9.25/5.23            = ( bNF_id5045731369644952736_nat_o @ Pa @ Ya ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6414_ID_Opred__cong,axiom,
% 9.25/5.23      ! [X: $o,Ya: $o,P: $o > $o,Pa: $o > $o] :
% 9.25/5.23        ( ( X = Ya )
% 9.25/5.23       => ( ! [Z2: $o] :
% 9.25/5.23              ( ( member_o @ Z2 @ ( insert_o @ Ya @ bot_bot_set_o ) )
% 9.25/5.23             => ( ( P @ Z2 )
% 9.25/5.23                = ( Pa @ Z2 ) ) )
% 9.25/5.23         => ( ( bNF_id_bnf_o_o @ P @ X )
% 9.25/5.23            = ( bNF_id_bnf_o_o @ Pa @ Ya ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6415_ID_Opred__cong,axiom,
% 9.25/5.23      ! [X: nat,Ya: nat,P: nat > $o,Pa: nat > $o] :
% 9.25/5.23        ( ( X = Ya )
% 9.25/5.23       => ( ! [Z2: nat] :
% 9.25/5.23              ( ( member_nat @ Z2 @ ( insert_nat @ Ya @ bot_bot_set_nat ) )
% 9.25/5.23             => ( ( P @ Z2 )
% 9.25/5.23                = ( Pa @ Z2 ) ) )
% 9.25/5.23         => ( ( bNF_id_bnf_nat_o @ P @ X )
% 9.25/5.23            = ( bNF_id_bnf_nat_o @ Pa @ Ya ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6416_ID_Opred__cong,axiom,
% 9.25/5.23      ! [X: int,Ya: int,P: int > $o,Pa: int > $o] :
% 9.25/5.23        ( ( X = Ya )
% 9.25/5.23       => ( ! [Z2: int] :
% 9.25/5.23              ( ( member_int @ Z2 @ ( insert_int @ Ya @ bot_bot_set_int ) )
% 9.25/5.23             => ( ( P @ Z2 )
% 9.25/5.23                = ( Pa @ Z2 ) ) )
% 9.25/5.23         => ( ( bNF_id_bnf_int_o @ P @ X )
% 9.25/5.23            = ( bNF_id_bnf_int_o @ Pa @ Ya ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6417_ID_Opred__mono__strong,axiom,
% 9.25/5.23      ! [P: produc3843707927480180839at_nat > $o,X: produc3843707927480180839at_nat,Pa: produc3843707927480180839at_nat > $o] :
% 9.25/5.23        ( ( bNF_id1044457264471098170_nat_o @ P @ X )
% 9.25/5.23       => ( ! [Z2: produc3843707927480180839at_nat] :
% 9.25/5.23              ( ( member8757157785044589968at_nat @ Z2 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 9.25/5.23             => ( ( P @ Z2 )
% 9.25/5.23               => ( Pa @ Z2 ) ) )
% 9.25/5.23         => ( bNF_id1044457264471098170_nat_o @ Pa @ X ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6418_ID_Opred__mono__strong,axiom,
% 9.25/5.23      ! [P: set_Pr958786334691620121nt_int > $o,X: set_Pr958786334691620121nt_int,Pa: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.23        ( ( bNF_id9176111459293603464_int_o @ P @ X )
% 9.25/5.23       => ( ! [Z2: set_Pr958786334691620121nt_int] :
% 9.25/5.23              ( ( member2340774599025711042nt_int @ Z2 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
% 9.25/5.23             => ( ( P @ Z2 )
% 9.25/5.23               => ( Pa @ Z2 ) ) )
% 9.25/5.23         => ( bNF_id9176111459293603464_int_o @ Pa @ X ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6419_ID_Opred__mono__strong,axiom,
% 9.25/5.23      ! [P: set_nat > $o,X: set_nat,Pa: set_nat > $o] :
% 9.25/5.23        ( ( bNF_id_bnf_set_nat_o @ P @ X )
% 9.25/5.23       => ( ! [Z2: set_nat] :
% 9.25/5.23              ( ( member_set_nat @ Z2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 9.25/5.23             => ( ( P @ Z2 )
% 9.25/5.23               => ( Pa @ Z2 ) ) )
% 9.25/5.23         => ( bNF_id_bnf_set_nat_o @ Pa @ X ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6420_ID_Opred__mono__strong,axiom,
% 9.25/5.23      ! [P: ( produc3658429121746597890et_nat > $o ) > $o,X: produc3658429121746597890et_nat > $o,Pa: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.23        ( ( bNF_id4470576313039291732at_o_o @ P @ X )
% 9.25/5.23       => ( ! [Z2: produc3658429121746597890et_nat > $o] :
% 9.25/5.23              ( ( member6576561426505652726_nat_o @ Z2 @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 9.25/5.23             => ( ( P @ Z2 )
% 9.25/5.23               => ( Pa @ Z2 ) ) )
% 9.25/5.23         => ( bNF_id4470576313039291732at_o_o @ Pa @ X ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6421_ID_Opred__mono__strong,axiom,
% 9.25/5.23      ! [P: product_prod_nat_nat > $o,X: product_prod_nat_nat,Pa: product_prod_nat_nat > $o] :
% 9.25/5.23        ( ( bNF_id5045731369644952736_nat_o @ P @ X )
% 9.25/5.23       => ( ! [Z2: product_prod_nat_nat] :
% 9.25/5.23              ( ( member8440522571783428010at_nat @ Z2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 9.25/5.23             => ( ( P @ Z2 )
% 9.25/5.23               => ( Pa @ Z2 ) ) )
% 9.25/5.23         => ( bNF_id5045731369644952736_nat_o @ Pa @ X ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6422_ID_Opred__mono__strong,axiom,
% 9.25/5.23      ! [P: $o > $o,X: $o,Pa: $o > $o] :
% 9.25/5.23        ( ( bNF_id_bnf_o_o @ P @ X )
% 9.25/5.23       => ( ! [Z2: $o] :
% 9.25/5.23              ( ( member_o @ Z2 @ ( insert_o @ X @ bot_bot_set_o ) )
% 9.25/5.23             => ( ( P @ Z2 )
% 9.25/5.23               => ( Pa @ Z2 ) ) )
% 9.25/5.23         => ( bNF_id_bnf_o_o @ Pa @ X ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6423_ID_Opred__mono__strong,axiom,
% 9.25/5.23      ! [P: nat > $o,X: nat,Pa: nat > $o] :
% 9.25/5.23        ( ( bNF_id_bnf_nat_o @ P @ X )
% 9.25/5.23       => ( ! [Z2: nat] :
% 9.25/5.23              ( ( member_nat @ Z2 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 9.25/5.23             => ( ( P @ Z2 )
% 9.25/5.23               => ( Pa @ Z2 ) ) )
% 9.25/5.23         => ( bNF_id_bnf_nat_o @ Pa @ X ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6424_ID_Opred__mono__strong,axiom,
% 9.25/5.23      ! [P: int > $o,X: int,Pa: int > $o] :
% 9.25/5.23        ( ( bNF_id_bnf_int_o @ P @ X )
% 9.25/5.23       => ( ! [Z2: int] :
% 9.25/5.23              ( ( member_int @ Z2 @ ( insert_int @ X @ bot_bot_set_int ) )
% 9.25/5.23             => ( ( P @ Z2 )
% 9.25/5.23               => ( Pa @ Z2 ) ) )
% 9.25/5.23         => ( bNF_id_bnf_int_o @ Pa @ X ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6425_ID_Orel__cong,axiom,
% 9.25/5.23      ! [X: $o,Ya: $o,Y: $o,Xa: $o,R: $o > $o > $o,Ra: $o > $o > $o] :
% 9.25/5.23        ( ( X = Ya )
% 9.25/5.23       => ( ( Y = Xa )
% 9.25/5.23         => ( ! [Z2: $o,Yb: $o] :
% 9.25/5.23                ( ( member_o @ Z2 @ ( insert_o @ Ya @ bot_bot_set_o ) )
% 9.25/5.23               => ( ( member_o @ Yb @ ( insert_o @ Xa @ bot_bot_set_o ) )
% 9.25/5.23                 => ( ( R @ Z2 @ Yb )
% 9.25/5.23                    = ( Ra @ Z2 @ Yb ) ) ) )
% 9.25/5.23           => ( ( bNF_id_bnf_o_o_o @ R @ X @ Y )
% 9.25/5.23              = ( bNF_id_bnf_o_o_o @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6426_ID_Orel__cong,axiom,
% 9.25/5.23      ! [X: $o,Ya: $o,Y: nat,Xa: nat,R: $o > nat > $o,Ra: $o > nat > $o] :
% 9.25/5.23        ( ( X = Ya )
% 9.25/5.23       => ( ( Y = Xa )
% 9.25/5.23         => ( ! [Z2: $o,Yb: nat] :
% 9.25/5.23                ( ( member_o @ Z2 @ ( insert_o @ Ya @ bot_bot_set_o ) )
% 9.25/5.23               => ( ( member_nat @ Yb @ ( insert_nat @ Xa @ bot_bot_set_nat ) )
% 9.25/5.23                 => ( ( R @ Z2 @ Yb )
% 9.25/5.23                    = ( Ra @ Z2 @ Yb ) ) ) )
% 9.25/5.23           => ( ( bNF_id_bnf_o_nat_o @ R @ X @ Y )
% 9.25/5.23              = ( bNF_id_bnf_o_nat_o @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6427_ID_Orel__cong,axiom,
% 9.25/5.23      ! [X: $o,Ya: $o,Y: int,Xa: int,R: $o > int > $o,Ra: $o > int > $o] :
% 9.25/5.23        ( ( X = Ya )
% 9.25/5.23       => ( ( Y = Xa )
% 9.25/5.23         => ( ! [Z2: $o,Yb: int] :
% 9.25/5.23                ( ( member_o @ Z2 @ ( insert_o @ Ya @ bot_bot_set_o ) )
% 9.25/5.23               => ( ( member_int @ Yb @ ( insert_int @ Xa @ bot_bot_set_int ) )
% 9.25/5.23                 => ( ( R @ Z2 @ Yb )
% 9.25/5.23                    = ( Ra @ Z2 @ Yb ) ) ) )
% 9.25/5.23           => ( ( bNF_id_bnf_o_int_o @ R @ X @ Y )
% 9.25/5.23              = ( bNF_id_bnf_o_int_o @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6428_ID_Orel__cong,axiom,
% 9.25/5.23      ! [X: nat,Ya: nat,Y: $o,Xa: $o,R: nat > $o > $o,Ra: nat > $o > $o] :
% 9.25/5.23        ( ( X = Ya )
% 9.25/5.23       => ( ( Y = Xa )
% 9.25/5.23         => ( ! [Z2: nat,Yb: $o] :
% 9.25/5.23                ( ( member_nat @ Z2 @ ( insert_nat @ Ya @ bot_bot_set_nat ) )
% 9.25/5.23               => ( ( member_o @ Yb @ ( insert_o @ Xa @ bot_bot_set_o ) )
% 9.25/5.23                 => ( ( R @ Z2 @ Yb )
% 9.25/5.23                    = ( Ra @ Z2 @ Yb ) ) ) )
% 9.25/5.23           => ( ( bNF_id_bnf_nat_o_o @ R @ X @ Y )
% 9.25/5.23              = ( bNF_id_bnf_nat_o_o @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6429_ID_Orel__cong,axiom,
% 9.25/5.23      ! [X: nat,Ya: nat,Y: nat,Xa: nat,R: nat > nat > $o,Ra: nat > nat > $o] :
% 9.25/5.23        ( ( X = Ya )
% 9.25/5.23       => ( ( Y = Xa )
% 9.25/5.23         => ( ! [Z2: nat,Yb: nat] :
% 9.25/5.23                ( ( member_nat @ Z2 @ ( insert_nat @ Ya @ bot_bot_set_nat ) )
% 9.25/5.23               => ( ( member_nat @ Yb @ ( insert_nat @ Xa @ bot_bot_set_nat ) )
% 9.25/5.23                 => ( ( R @ Z2 @ Yb )
% 9.25/5.23                    = ( Ra @ Z2 @ Yb ) ) ) )
% 9.25/5.23           => ( ( bNF_id_bnf_nat_nat_o @ R @ X @ Y )
% 9.25/5.23              = ( bNF_id_bnf_nat_nat_o @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6430_ID_Orel__cong,axiom,
% 9.25/5.23      ! [X: nat,Ya: nat,Y: int,Xa: int,R: nat > int > $o,Ra: nat > int > $o] :
% 9.25/5.23        ( ( X = Ya )
% 9.25/5.23       => ( ( Y = Xa )
% 9.25/5.23         => ( ! [Z2: nat,Yb: int] :
% 9.25/5.23                ( ( member_nat @ Z2 @ ( insert_nat @ Ya @ bot_bot_set_nat ) )
% 9.25/5.23               => ( ( member_int @ Yb @ ( insert_int @ Xa @ bot_bot_set_int ) )
% 9.25/5.23                 => ( ( R @ Z2 @ Yb )
% 9.25/5.23                    = ( Ra @ Z2 @ Yb ) ) ) )
% 9.25/5.23           => ( ( bNF_id_bnf_nat_int_o @ R @ X @ Y )
% 9.25/5.23              = ( bNF_id_bnf_nat_int_o @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6431_ID_Orel__cong,axiom,
% 9.25/5.23      ! [X: int,Ya: int,Y: $o,Xa: $o,R: int > $o > $o,Ra: int > $o > $o] :
% 9.25/5.23        ( ( X = Ya )
% 9.25/5.23       => ( ( Y = Xa )
% 9.25/5.23         => ( ! [Z2: int,Yb: $o] :
% 9.25/5.23                ( ( member_int @ Z2 @ ( insert_int @ Ya @ bot_bot_set_int ) )
% 9.25/5.23               => ( ( member_o @ Yb @ ( insert_o @ Xa @ bot_bot_set_o ) )
% 9.25/5.23                 => ( ( R @ Z2 @ Yb )
% 9.25/5.23                    = ( Ra @ Z2 @ Yb ) ) ) )
% 9.25/5.23           => ( ( bNF_id_bnf_int_o_o @ R @ X @ Y )
% 9.25/5.23              = ( bNF_id_bnf_int_o_o @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6432_ID_Orel__cong,axiom,
% 9.25/5.23      ! [X: int,Ya: int,Y: nat,Xa: nat,R: int > nat > $o,Ra: int > nat > $o] :
% 9.25/5.23        ( ( X = Ya )
% 9.25/5.23       => ( ( Y = Xa )
% 9.25/5.23         => ( ! [Z2: int,Yb: nat] :
% 9.25/5.23                ( ( member_int @ Z2 @ ( insert_int @ Ya @ bot_bot_set_int ) )
% 9.25/5.23               => ( ( member_nat @ Yb @ ( insert_nat @ Xa @ bot_bot_set_nat ) )
% 9.25/5.23                 => ( ( R @ Z2 @ Yb )
% 9.25/5.23                    = ( Ra @ Z2 @ Yb ) ) ) )
% 9.25/5.23           => ( ( bNF_id_bnf_int_nat_o @ R @ X @ Y )
% 9.25/5.23              = ( bNF_id_bnf_int_nat_o @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6433_ID_Orel__cong,axiom,
% 9.25/5.23      ! [X: int,Ya: int,Y: int,Xa: int,R: int > int > $o,Ra: int > int > $o] :
% 9.25/5.23        ( ( X = Ya )
% 9.25/5.23       => ( ( Y = Xa )
% 9.25/5.23         => ( ! [Z2: int,Yb: int] :
% 9.25/5.23                ( ( member_int @ Z2 @ ( insert_int @ Ya @ bot_bot_set_int ) )
% 9.25/5.23               => ( ( member_int @ Yb @ ( insert_int @ Xa @ bot_bot_set_int ) )
% 9.25/5.23                 => ( ( R @ Z2 @ Yb )
% 9.25/5.23                    = ( Ra @ Z2 @ Yb ) ) ) )
% 9.25/5.23           => ( ( bNF_id_bnf_int_int_o @ R @ X @ Y )
% 9.25/5.23              = ( bNF_id_bnf_int_int_o @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6434_ID_Orel__cong,axiom,
% 9.25/5.23      ! [X: set_nat,Ya: set_nat,Y: $o,Xa: $o,R: set_nat > $o > $o,Ra: set_nat > $o > $o] :
% 9.25/5.23        ( ( X = Ya )
% 9.25/5.23       => ( ( Y = Xa )
% 9.25/5.23         => ( ! [Z2: set_nat,Yb: $o] :
% 9.25/5.23                ( ( member_set_nat @ Z2 @ ( insert_set_nat @ Ya @ bot_bot_set_set_nat ) )
% 9.25/5.23               => ( ( member_o @ Yb @ ( insert_o @ Xa @ bot_bot_set_o ) )
% 9.25/5.23                 => ( ( R @ Z2 @ Yb )
% 9.25/5.23                    = ( Ra @ Z2 @ Yb ) ) ) )
% 9.25/5.23           => ( ( bNF_id1382368747416007662at_o_o @ R @ X @ Y )
% 9.25/5.23              = ( bNF_id1382368747416007662at_o_o @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6435_ID_Orel__mono__strong,axiom,
% 9.25/5.23      ! [R: $o > $o > $o,X: $o,Y: $o,Ra: $o > $o > $o] :
% 9.25/5.23        ( ( bNF_id_bnf_o_o_o @ R @ X @ Y )
% 9.25/5.23       => ( ! [Z2: $o,Yb: $o] :
% 9.25/5.23              ( ( member_o @ Z2 @ ( insert_o @ X @ bot_bot_set_o ) )
% 9.25/5.23             => ( ( member_o @ Yb @ ( insert_o @ Y @ bot_bot_set_o ) )
% 9.25/5.23               => ( ( R @ Z2 @ Yb )
% 9.25/5.23                 => ( Ra @ Z2 @ Yb ) ) ) )
% 9.25/5.23         => ( bNF_id_bnf_o_o_o @ Ra @ X @ Y ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6436_ID_Orel__mono__strong,axiom,
% 9.25/5.23      ! [R: $o > nat > $o,X: $o,Y: nat,Ra: $o > nat > $o] :
% 9.25/5.23        ( ( bNF_id_bnf_o_nat_o @ R @ X @ Y )
% 9.25/5.23       => ( ! [Z2: $o,Yb: nat] :
% 9.25/5.23              ( ( member_o @ Z2 @ ( insert_o @ X @ bot_bot_set_o ) )
% 9.25/5.23             => ( ( member_nat @ Yb @ ( insert_nat @ Y @ bot_bot_set_nat ) )
% 9.25/5.23               => ( ( R @ Z2 @ Yb )
% 9.25/5.23                 => ( Ra @ Z2 @ Yb ) ) ) )
% 9.25/5.23         => ( bNF_id_bnf_o_nat_o @ Ra @ X @ Y ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6437_ID_Orel__mono__strong,axiom,
% 9.25/5.23      ! [R: $o > int > $o,X: $o,Y: int,Ra: $o > int > $o] :
% 9.25/5.23        ( ( bNF_id_bnf_o_int_o @ R @ X @ Y )
% 9.25/5.23       => ( ! [Z2: $o,Yb: int] :
% 9.25/5.23              ( ( member_o @ Z2 @ ( insert_o @ X @ bot_bot_set_o ) )
% 9.25/5.23             => ( ( member_int @ Yb @ ( insert_int @ Y @ bot_bot_set_int ) )
% 9.25/5.23               => ( ( R @ Z2 @ Yb )
% 9.25/5.23                 => ( Ra @ Z2 @ Yb ) ) ) )
% 9.25/5.23         => ( bNF_id_bnf_o_int_o @ Ra @ X @ Y ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6438_ID_Orel__mono__strong,axiom,
% 9.25/5.23      ! [R: nat > $o > $o,X: nat,Y: $o,Ra: nat > $o > $o] :
% 9.25/5.23        ( ( bNF_id_bnf_nat_o_o @ R @ X @ Y )
% 9.25/5.23       => ( ! [Z2: nat,Yb: $o] :
% 9.25/5.23              ( ( member_nat @ Z2 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 9.25/5.23             => ( ( member_o @ Yb @ ( insert_o @ Y @ bot_bot_set_o ) )
% 9.25/5.23               => ( ( R @ Z2 @ Yb )
% 9.25/5.23                 => ( Ra @ Z2 @ Yb ) ) ) )
% 9.25/5.23         => ( bNF_id_bnf_nat_o_o @ Ra @ X @ Y ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6439_ID_Orel__mono__strong,axiom,
% 9.25/5.23      ! [R: nat > nat > $o,X: nat,Y: nat,Ra: nat > nat > $o] :
% 9.25/5.23        ( ( bNF_id_bnf_nat_nat_o @ R @ X @ Y )
% 9.25/5.23       => ( ! [Z2: nat,Yb: nat] :
% 9.25/5.23              ( ( member_nat @ Z2 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 9.25/5.23             => ( ( member_nat @ Yb @ ( insert_nat @ Y @ bot_bot_set_nat ) )
% 9.25/5.23               => ( ( R @ Z2 @ Yb )
% 9.25/5.23                 => ( Ra @ Z2 @ Yb ) ) ) )
% 9.25/5.23         => ( bNF_id_bnf_nat_nat_o @ Ra @ X @ Y ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6440_ID_Orel__mono__strong,axiom,
% 9.25/5.23      ! [R: nat > int > $o,X: nat,Y: int,Ra: nat > int > $o] :
% 9.25/5.23        ( ( bNF_id_bnf_nat_int_o @ R @ X @ Y )
% 9.25/5.23       => ( ! [Z2: nat,Yb: int] :
% 9.25/5.23              ( ( member_nat @ Z2 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 9.25/5.23             => ( ( member_int @ Yb @ ( insert_int @ Y @ bot_bot_set_int ) )
% 9.25/5.23               => ( ( R @ Z2 @ Yb )
% 9.25/5.23                 => ( Ra @ Z2 @ Yb ) ) ) )
% 9.25/5.23         => ( bNF_id_bnf_nat_int_o @ Ra @ X @ Y ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6441_ID_Orel__mono__strong,axiom,
% 9.25/5.23      ! [R: int > $o > $o,X: int,Y: $o,Ra: int > $o > $o] :
% 9.25/5.23        ( ( bNF_id_bnf_int_o_o @ R @ X @ Y )
% 9.25/5.23       => ( ! [Z2: int,Yb: $o] :
% 9.25/5.23              ( ( member_int @ Z2 @ ( insert_int @ X @ bot_bot_set_int ) )
% 9.25/5.23             => ( ( member_o @ Yb @ ( insert_o @ Y @ bot_bot_set_o ) )
% 9.25/5.23               => ( ( R @ Z2 @ Yb )
% 9.25/5.23                 => ( Ra @ Z2 @ Yb ) ) ) )
% 9.25/5.23         => ( bNF_id_bnf_int_o_o @ Ra @ X @ Y ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6442_ID_Orel__mono__strong,axiom,
% 9.25/5.23      ! [R: int > nat > $o,X: int,Y: nat,Ra: int > nat > $o] :
% 9.25/5.23        ( ( bNF_id_bnf_int_nat_o @ R @ X @ Y )
% 9.25/5.23       => ( ! [Z2: int,Yb: nat] :
% 9.25/5.23              ( ( member_int @ Z2 @ ( insert_int @ X @ bot_bot_set_int ) )
% 9.25/5.23             => ( ( member_nat @ Yb @ ( insert_nat @ Y @ bot_bot_set_nat ) )
% 9.25/5.23               => ( ( R @ Z2 @ Yb )
% 9.25/5.23                 => ( Ra @ Z2 @ Yb ) ) ) )
% 9.25/5.23         => ( bNF_id_bnf_int_nat_o @ Ra @ X @ Y ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6443_ID_Orel__mono__strong,axiom,
% 9.25/5.23      ! [R: int > int > $o,X: int,Y: int,Ra: int > int > $o] :
% 9.25/5.23        ( ( bNF_id_bnf_int_int_o @ R @ X @ Y )
% 9.25/5.23       => ( ! [Z2: int,Yb: int] :
% 9.25/5.23              ( ( member_int @ Z2 @ ( insert_int @ X @ bot_bot_set_int ) )
% 9.25/5.23             => ( ( member_int @ Yb @ ( insert_int @ Y @ bot_bot_set_int ) )
% 9.25/5.23               => ( ( R @ Z2 @ Yb )
% 9.25/5.23                 => ( Ra @ Z2 @ Yb ) ) ) )
% 9.25/5.23         => ( bNF_id_bnf_int_int_o @ Ra @ X @ Y ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6444_ID_Orel__mono__strong,axiom,
% 9.25/5.23      ! [R: set_nat > $o > $o,X: set_nat,Y: $o,Ra: set_nat > $o > $o] :
% 9.25/5.23        ( ( bNF_id1382368747416007662at_o_o @ R @ X @ Y )
% 9.25/5.23       => ( ! [Z2: set_nat,Yb: $o] :
% 9.25/5.23              ( ( member_set_nat @ Z2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 9.25/5.23             => ( ( member_o @ Yb @ ( insert_o @ Y @ bot_bot_set_o ) )
% 9.25/5.23               => ( ( R @ Z2 @ Yb )
% 9.25/5.23                 => ( Ra @ Z2 @ Yb ) ) ) )
% 9.25/5.23         => ( bNF_id1382368747416007662at_o_o @ Ra @ X @ Y ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6445_ID_Orel__refl__strong,axiom,
% 9.25/5.23      ! [X: produc3843707927480180839at_nat,Ra: produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o] :
% 9.25/5.23        ( ! [Z2: produc3843707927480180839at_nat] :
% 9.25/5.23            ( ( member8757157785044589968at_nat @ Z2 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 9.25/5.23           => ( Ra @ Z2 @ Z2 ) )
% 9.25/5.23       => ( bNF_id5557877041440844106_nat_o @ Ra @ X @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6446_ID_Orel__refl__strong,axiom,
% 9.25/5.23      ! [X: set_Pr958786334691620121nt_int,Ra: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o] :
% 9.25/5.23        ( ! [Z2: set_Pr958786334691620121nt_int] :
% 9.25/5.23            ( ( member2340774599025711042nt_int @ Z2 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
% 9.25/5.23           => ( Ra @ Z2 @ Z2 ) )
% 9.25/5.23       => ( bNF_id745042670895148362_int_o @ Ra @ X @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6447_ID_Orel__refl__strong,axiom,
% 9.25/5.23      ! [X: set_nat,Ra: set_nat > set_nat > $o] :
% 9.25/5.23        ( ! [Z2: set_nat] :
% 9.25/5.23            ( ( member_set_nat @ Z2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 9.25/5.23           => ( Ra @ Z2 @ Z2 ) )
% 9.25/5.23       => ( bNF_id293821497076346774_nat_o @ Ra @ X @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6448_ID_Orel__refl__strong,axiom,
% 9.25/5.23      ! [X: produc3658429121746597890et_nat > $o,Ra: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.23        ( ! [Z2: produc3658429121746597890et_nat > $o] :
% 9.25/5.23            ( ( member6576561426505652726_nat_o @ Z2 @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 9.25/5.23           => ( Ra @ Z2 @ Z2 ) )
% 9.25/5.23       => ( bNF_id2059982186938784458at_o_o @ Ra @ X @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6449_ID_Orel__refl__strong,axiom,
% 9.25/5.23      ! [X: product_prod_nat_nat,Ra: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 9.25/5.23        ( ! [Z2: product_prod_nat_nat] :
% 9.25/5.23            ( ( member8440522571783428010at_nat @ Z2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 9.25/5.23           => ( Ra @ Z2 @ Z2 ) )
% 9.25/5.23       => ( bNF_id146787821168362314_nat_o @ Ra @ X @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6450_ID_Orel__refl__strong,axiom,
% 9.25/5.23      ! [X: $o,Ra: $o > $o > $o] :
% 9.25/5.23        ( ! [Z2: $o] :
% 9.25/5.23            ( ( member_o @ Z2 @ ( insert_o @ X @ bot_bot_set_o ) )
% 9.25/5.23           => ( Ra @ Z2 @ Z2 ) )
% 9.25/5.23       => ( bNF_id_bnf_o_o_o @ Ra @ X @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6451_ID_Orel__refl__strong,axiom,
% 9.25/5.23      ! [X: nat,Ra: nat > nat > $o] :
% 9.25/5.23        ( ! [Z2: nat] :
% 9.25/5.23            ( ( member_nat @ Z2 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 9.25/5.23           => ( Ra @ Z2 @ Z2 ) )
% 9.25/5.23       => ( bNF_id_bnf_nat_nat_o @ Ra @ X @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6452_ID_Orel__refl__strong,axiom,
% 9.25/5.23      ! [X: int,Ra: int > int > $o] :
% 9.25/5.23        ( ! [Z2: int] :
% 9.25/5.23            ( ( member_int @ Z2 @ ( insert_int @ X @ bot_bot_set_int ) )
% 9.25/5.23           => ( Ra @ Z2 @ Z2 ) )
% 9.25/5.23       => ( bNF_id_bnf_int_int_o @ Ra @ X @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6453_singleton__inject,axiom,
% 9.25/5.23      ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
% 9.25/5.23        ( ( ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat )
% 9.25/5.23          = ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) )
% 9.25/5.23       => ( A = B ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6454_singleton__inject,axiom,
% 9.25/5.23      ! [A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 9.25/5.23        ( ( ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat )
% 9.25/5.23          = ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) )
% 9.25/5.23       => ( A = B ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6455_singleton__inject,axiom,
% 9.25/5.23      ! [A: $o,B: $o] :
% 9.25/5.23        ( ( ( insert_o @ A @ bot_bot_set_o )
% 9.25/5.23          = ( insert_o @ B @ bot_bot_set_o ) )
% 9.25/5.23       => ( A = B ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6456_singleton__inject,axiom,
% 9.25/5.23      ! [A: nat,B: nat] :
% 9.25/5.23        ( ( ( insert_nat @ A @ bot_bot_set_nat )
% 9.25/5.23          = ( insert_nat @ B @ bot_bot_set_nat ) )
% 9.25/5.23       => ( A = B ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6457_singleton__inject,axiom,
% 9.25/5.23      ! [A: int,B: int] :
% 9.25/5.23        ( ( ( insert_int @ A @ bot_bot_set_int )
% 9.25/5.23          = ( insert_int @ B @ bot_bot_set_int ) )
% 9.25/5.23       => ( A = B ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6458_insert__not__empty,axiom,
% 9.25/5.23      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( insert9069300056098147895at_nat @ A @ A2 )
% 9.25/5.23       != bot_bo228742789529271731at_nat ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6459_insert__not__empty,axiom,
% 9.25/5.23      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( insert8211810215607154385at_nat @ A @ A2 )
% 9.25/5.23       != bot_bo2099793752762293965at_nat ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6460_insert__not__empty,axiom,
% 9.25/5.23      ! [A: $o,A2: set_o] :
% 9.25/5.23        ( ( insert_o @ A @ A2 )
% 9.25/5.23       != bot_bot_set_o ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6461_insert__not__empty,axiom,
% 9.25/5.23      ! [A: nat,A2: set_nat] :
% 9.25/5.23        ( ( insert_nat @ A @ A2 )
% 9.25/5.23       != bot_bot_set_nat ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6462_insert__not__empty,axiom,
% 9.25/5.23      ! [A: int,A2: set_int] :
% 9.25/5.23        ( ( insert_int @ A @ A2 )
% 9.25/5.23       != bot_bot_set_int ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6463_doubleton__eq__iff,axiom,
% 9.25/5.23      ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat,C: produc3843707927480180839at_nat,D2: produc3843707927480180839at_nat] :
% 9.25/5.23        ( ( ( insert9069300056098147895at_nat @ A @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) )
% 9.25/5.23          = ( insert9069300056098147895at_nat @ C @ ( insert9069300056098147895at_nat @ D2 @ bot_bo228742789529271731at_nat ) ) )
% 9.25/5.23        = ( ( ( A = C )
% 9.25/5.23            & ( B = D2 ) )
% 9.25/5.23          | ( ( A = D2 )
% 9.25/5.23            & ( B = C ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6464_doubleton__eq__iff,axiom,
% 9.25/5.23      ! [A: product_prod_nat_nat,B: product_prod_nat_nat,C: product_prod_nat_nat,D2: product_prod_nat_nat] :
% 9.25/5.23        ( ( ( insert8211810215607154385at_nat @ A @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) )
% 9.25/5.23          = ( insert8211810215607154385at_nat @ C @ ( insert8211810215607154385at_nat @ D2 @ bot_bo2099793752762293965at_nat ) ) )
% 9.25/5.23        = ( ( ( A = C )
% 9.25/5.23            & ( B = D2 ) )
% 9.25/5.23          | ( ( A = D2 )
% 9.25/5.23            & ( B = C ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6465_doubleton__eq__iff,axiom,
% 9.25/5.23      ! [A: $o,B: $o,C: $o,D2: $o] :
% 9.25/5.23        ( ( ( insert_o @ A @ ( insert_o @ B @ bot_bot_set_o ) )
% 9.25/5.23          = ( insert_o @ C @ ( insert_o @ D2 @ bot_bot_set_o ) ) )
% 9.25/5.23        = ( ( ( A = C )
% 9.25/5.23            & ( B = D2 ) )
% 9.25/5.23          | ( ( A = D2 )
% 9.25/5.23            & ( B = C ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6466_doubleton__eq__iff,axiom,
% 9.25/5.23      ! [A: nat,B: nat,C: nat,D2: nat] :
% 9.25/5.23        ( ( ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) )
% 9.25/5.23          = ( insert_nat @ C @ ( insert_nat @ D2 @ bot_bot_set_nat ) ) )
% 9.25/5.23        = ( ( ( A = C )
% 9.25/5.23            & ( B = D2 ) )
% 9.25/5.23          | ( ( A = D2 )
% 9.25/5.23            & ( B = C ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6467_doubleton__eq__iff,axiom,
% 9.25/5.23      ! [A: int,B: int,C: int,D2: int] :
% 9.25/5.23        ( ( ( insert_int @ A @ ( insert_int @ B @ bot_bot_set_int ) )
% 9.25/5.23          = ( insert_int @ C @ ( insert_int @ D2 @ bot_bot_set_int ) ) )
% 9.25/5.23        = ( ( ( A = C )
% 9.25/5.23            & ( B = D2 ) )
% 9.25/5.23          | ( ( A = D2 )
% 9.25/5.23            & ( B = C ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6468_singleton__iff,axiom,
% 9.25/5.23      ! [B: produc3843707927480180839at_nat,A: produc3843707927480180839at_nat] :
% 9.25/5.23        ( ( member8757157785044589968at_nat @ B @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) )
% 9.25/5.23        = ( B = A ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6469_singleton__iff,axiom,
% 9.25/5.23      ! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
% 9.25/5.23        ( ( member2340774599025711042nt_int @ B @ ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) )
% 9.25/5.23        = ( B = A ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6470_singleton__iff,axiom,
% 9.25/5.23      ! [B: set_nat,A: set_nat] :
% 9.25/5.23        ( ( member_set_nat @ B @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) )
% 9.25/5.23        = ( B = A ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6471_singleton__iff,axiom,
% 9.25/5.23      ! [B: produc3658429121746597890et_nat > $o,A: produc3658429121746597890et_nat > $o] :
% 9.25/5.23        ( ( member6576561426505652726_nat_o @ B @ ( insert5175938949040314269_nat_o @ A @ bot_bo7824918357723582233_nat_o ) )
% 9.25/5.23        = ( B = A ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6472_singleton__iff,axiom,
% 9.25/5.23      ! [B: product_prod_nat_nat,A: product_prod_nat_nat] :
% 9.25/5.23        ( ( member8440522571783428010at_nat @ B @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) )
% 9.25/5.23        = ( B = A ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6473_singleton__iff,axiom,
% 9.25/5.23      ! [B: $o,A: $o] :
% 9.25/5.23        ( ( member_o @ B @ ( insert_o @ A @ bot_bot_set_o ) )
% 9.25/5.23        = ( B = A ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6474_singleton__iff,axiom,
% 9.25/5.23      ! [B: nat,A: nat] :
% 9.25/5.23        ( ( member_nat @ B @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 9.25/5.23        = ( B = A ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6475_singleton__iff,axiom,
% 9.25/5.23      ! [B: int,A: int] :
% 9.25/5.23        ( ( member_int @ B @ ( insert_int @ A @ bot_bot_set_int ) )
% 9.25/5.23        = ( B = A ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6476_singletonD,axiom,
% 9.25/5.23      ! [B: produc3843707927480180839at_nat,A: produc3843707927480180839at_nat] :
% 9.25/5.23        ( ( member8757157785044589968at_nat @ B @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) )
% 9.25/5.23       => ( B = A ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6477_singletonD,axiom,
% 9.25/5.23      ! [B: set_Pr958786334691620121nt_int,A: set_Pr958786334691620121nt_int] :
% 9.25/5.23        ( ( member2340774599025711042nt_int @ B @ ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) )
% 9.25/5.23       => ( B = A ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6478_singletonD,axiom,
% 9.25/5.23      ! [B: set_nat,A: set_nat] :
% 9.25/5.23        ( ( member_set_nat @ B @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) )
% 9.25/5.23       => ( B = A ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6479_singletonD,axiom,
% 9.25/5.23      ! [B: produc3658429121746597890et_nat > $o,A: produc3658429121746597890et_nat > $o] :
% 9.25/5.23        ( ( member6576561426505652726_nat_o @ B @ ( insert5175938949040314269_nat_o @ A @ bot_bo7824918357723582233_nat_o ) )
% 9.25/5.23       => ( B = A ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6480_singletonD,axiom,
% 9.25/5.23      ! [B: product_prod_nat_nat,A: product_prod_nat_nat] :
% 9.25/5.23        ( ( member8440522571783428010at_nat @ B @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) )
% 9.25/5.23       => ( B = A ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6481_singletonD,axiom,
% 9.25/5.23      ! [B: $o,A: $o] :
% 9.25/5.23        ( ( member_o @ B @ ( insert_o @ A @ bot_bot_set_o ) )
% 9.25/5.23       => ( B = A ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6482_singletonD,axiom,
% 9.25/5.23      ! [B: nat,A: nat] :
% 9.25/5.23        ( ( member_nat @ B @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 9.25/5.23       => ( B = A ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6483_singletonD,axiom,
% 9.25/5.23      ! [B: int,A: int] :
% 9.25/5.23        ( ( member_int @ B @ ( insert_int @ A @ bot_bot_set_int ) )
% 9.25/5.23       => ( B = A ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6484_flip__bit__int__def,axiom,
% 9.25/5.23      ( bit_se2159334234014336723it_int
% 9.25/5.23      = ( ^ [N2: nat,K4: int] : ( bit_se6526347334894502574or_int @ K4 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6485_insert__UNIV,axiom,
% 9.25/5.23      ! [X: produc3843707927480180839at_nat] :
% 9.25/5.23        ( ( insert9069300056098147895at_nat @ X @ top_to6833984726390702231at_nat )
% 9.25/5.23        = top_to6833984726390702231at_nat ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6486_insert__UNIV,axiom,
% 9.25/5.23      ! [X: product_prod_nat_nat] :
% 9.25/5.23        ( ( insert8211810215607154385at_nat @ X @ top_to4669805908274784177at_nat )
% 9.25/5.23        = top_to4669805908274784177at_nat ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6487_insert__UNIV,axiom,
% 9.25/5.23      ! [X: list_nat] :
% 9.25/5.23        ( ( insert_list_nat @ X @ top_top_set_list_nat )
% 9.25/5.23        = top_top_set_list_nat ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6488_insert__UNIV,axiom,
% 9.25/5.23      ! [X: $o] :
% 9.25/5.23        ( ( insert_o @ X @ top_top_set_o )
% 9.25/5.23        = top_top_set_o ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6489_insert__UNIV,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23        ( ( insert_rat @ X @ top_top_set_rat )
% 9.25/5.23        = top_top_set_rat ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6490_insert__UNIV,axiom,
% 9.25/5.23      ! [X: nat] :
% 9.25/5.23        ( ( insert_nat @ X @ top_top_set_nat )
% 9.25/5.23        = top_top_set_nat ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6491_insert__UNIV,axiom,
% 9.25/5.23      ! [X: int] :
% 9.25/5.23        ( ( insert_int @ X @ top_top_set_int )
% 9.25/5.23        = top_top_set_int ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6492_Int__insert__right,axiom,
% 9.25/5.23      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( ( member8757157785044589968at_nat @ A @ A2 )
% 9.25/5.23         => ( ( inf_in7913087082777306421at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ B2 ) )
% 9.25/5.23            = ( insert9069300056098147895at_nat @ A @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) )
% 9.25/5.23        & ( ~ ( member8757157785044589968at_nat @ A @ A2 )
% 9.25/5.23         => ( ( inf_in7913087082777306421at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ B2 ) )
% 9.25/5.23            = ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6493_Int__insert__right,axiom,
% 9.25/5.23      ! [A: $o,A2: set_o,B2: set_o] :
% 9.25/5.23        ( ( ( member_o @ A @ A2 )
% 9.25/5.23         => ( ( inf_inf_set_o @ A2 @ ( insert_o @ A @ B2 ) )
% 9.25/5.23            = ( insert_o @ A @ ( inf_inf_set_o @ A2 @ B2 ) ) ) )
% 9.25/5.23        & ( ~ ( member_o @ A @ A2 )
% 9.25/5.23         => ( ( inf_inf_set_o @ A2 @ ( insert_o @ A @ B2 ) )
% 9.25/5.23            = ( inf_inf_set_o @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6494_Int__insert__right,axiom,
% 9.25/5.23      ! [A: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.23        ( ( ( member2340774599025711042nt_int @ A @ A2 )
% 9.25/5.23         => ( ( inf_in8396524679539076455nt_int @ A2 @ ( insert8897473484851387113nt_int @ A @ B2 ) )
% 9.25/5.23            = ( insert8897473484851387113nt_int @ A @ ( inf_in8396524679539076455nt_int @ A2 @ B2 ) ) ) )
% 9.25/5.23        & ( ~ ( member2340774599025711042nt_int @ A @ A2 )
% 9.25/5.23         => ( ( inf_in8396524679539076455nt_int @ A2 @ ( insert8897473484851387113nt_int @ A @ B2 ) )
% 9.25/5.23            = ( inf_in8396524679539076455nt_int @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6495_Int__insert__right,axiom,
% 9.25/5.23      ! [A: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 9.25/5.23        ( ( ( member_set_nat @ A @ A2 )
% 9.25/5.23         => ( ( inf_inf_set_set_nat @ A2 @ ( insert_set_nat @ A @ B2 ) )
% 9.25/5.23            = ( insert_set_nat @ A @ ( inf_inf_set_set_nat @ A2 @ B2 ) ) ) )
% 9.25/5.23        & ( ~ ( member_set_nat @ A @ A2 )
% 9.25/5.23         => ( ( inf_inf_set_set_nat @ A2 @ ( insert_set_nat @ A @ B2 ) )
% 9.25/5.23            = ( inf_inf_set_set_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6496_Int__insert__right,axiom,
% 9.25/5.23      ! [A: int,A2: set_int,B2: set_int] :
% 9.25/5.23        ( ( ( member_int @ A @ A2 )
% 9.25/5.23         => ( ( inf_inf_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 9.25/5.23            = ( insert_int @ A @ ( inf_inf_set_int @ A2 @ B2 ) ) ) )
% 9.25/5.23        & ( ~ ( member_int @ A @ A2 )
% 9.25/5.23         => ( ( inf_inf_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 9.25/5.23            = ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6497_Int__insert__right,axiom,
% 9.25/5.23      ! [A: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.23        ( ( ( member6576561426505652726_nat_o @ A @ A2 )
% 9.25/5.23         => ( ( inf_in1906310914598751387_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ A @ B2 ) )
% 9.25/5.23            = ( insert5175938949040314269_nat_o @ A @ ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) ) ) )
% 9.25/5.23        & ( ~ ( member6576561426505652726_nat_o @ A @ A2 )
% 9.25/5.23         => ( ( inf_in1906310914598751387_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ A @ B2 ) )
% 9.25/5.23            = ( inf_in1906310914598751387_nat_o @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6498_Int__insert__right,axiom,
% 9.25/5.23      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( ( member8440522571783428010at_nat @ A @ A2 )
% 9.25/5.23         => ( ( inf_in2572325071724192079at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 9.25/5.23            = ( insert8211810215607154385at_nat @ A @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) )
% 9.25/5.23        & ( ~ ( member8440522571783428010at_nat @ A @ A2 )
% 9.25/5.23         => ( ( inf_in2572325071724192079at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 9.25/5.23            = ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6499_Int__insert__right,axiom,
% 9.25/5.23      ! [A: nat,A2: set_nat,B2: set_nat] :
% 9.25/5.23        ( ( ( member_nat @ A @ A2 )
% 9.25/5.23         => ( ( inf_inf_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 9.25/5.23            = ( insert_nat @ A @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) )
% 9.25/5.23        & ( ~ ( member_nat @ A @ A2 )
% 9.25/5.23         => ( ( inf_inf_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 9.25/5.23            = ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6500_Int__insert__left,axiom,
% 9.25/5.23      ! [A: produc3843707927480180839at_nat,C2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( ( member8757157785044589968at_nat @ A @ C2 )
% 9.25/5.23         => ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A @ B2 ) @ C2 )
% 9.25/5.23            = ( insert9069300056098147895at_nat @ A @ ( inf_in7913087082777306421at_nat @ B2 @ C2 ) ) ) )
% 9.25/5.23        & ( ~ ( member8757157785044589968at_nat @ A @ C2 )
% 9.25/5.23         => ( ( inf_in7913087082777306421at_nat @ ( insert9069300056098147895at_nat @ A @ B2 ) @ C2 )
% 9.25/5.23            = ( inf_in7913087082777306421at_nat @ B2 @ C2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6501_Int__insert__left,axiom,
% 9.25/5.23      ! [A: $o,C2: set_o,B2: set_o] :
% 9.25/5.23        ( ( ( member_o @ A @ C2 )
% 9.25/5.23         => ( ( inf_inf_set_o @ ( insert_o @ A @ B2 ) @ C2 )
% 9.25/5.23            = ( insert_o @ A @ ( inf_inf_set_o @ B2 @ C2 ) ) ) )
% 9.25/5.23        & ( ~ ( member_o @ A @ C2 )
% 9.25/5.23         => ( ( inf_inf_set_o @ ( insert_o @ A @ B2 ) @ C2 )
% 9.25/5.23            = ( inf_inf_set_o @ B2 @ C2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6502_Int__insert__left,axiom,
% 9.25/5.23      ! [A: set_Pr958786334691620121nt_int,C2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.23        ( ( ( member2340774599025711042nt_int @ A @ C2 )
% 9.25/5.23         => ( ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ B2 ) @ C2 )
% 9.25/5.23            = ( insert8897473484851387113nt_int @ A @ ( inf_in8396524679539076455nt_int @ B2 @ C2 ) ) ) )
% 9.25/5.23        & ( ~ ( member2340774599025711042nt_int @ A @ C2 )
% 9.25/5.23         => ( ( inf_in8396524679539076455nt_int @ ( insert8897473484851387113nt_int @ A @ B2 ) @ C2 )
% 9.25/5.23            = ( inf_in8396524679539076455nt_int @ B2 @ C2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6503_Int__insert__left,axiom,
% 9.25/5.23      ! [A: set_nat,C2: set_set_nat,B2: set_set_nat] :
% 9.25/5.23        ( ( ( member_set_nat @ A @ C2 )
% 9.25/5.23         => ( ( inf_inf_set_set_nat @ ( insert_set_nat @ A @ B2 ) @ C2 )
% 9.25/5.23            = ( insert_set_nat @ A @ ( inf_inf_set_set_nat @ B2 @ C2 ) ) ) )
% 9.25/5.23        & ( ~ ( member_set_nat @ A @ C2 )
% 9.25/5.23         => ( ( inf_inf_set_set_nat @ ( insert_set_nat @ A @ B2 ) @ C2 )
% 9.25/5.23            = ( inf_inf_set_set_nat @ B2 @ C2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6504_Int__insert__left,axiom,
% 9.25/5.23      ! [A: int,C2: set_int,B2: set_int] :
% 9.25/5.23        ( ( ( member_int @ A @ C2 )
% 9.25/5.23         => ( ( inf_inf_set_int @ ( insert_int @ A @ B2 ) @ C2 )
% 9.25/5.23            = ( insert_int @ A @ ( inf_inf_set_int @ B2 @ C2 ) ) ) )
% 9.25/5.23        & ( ~ ( member_int @ A @ C2 )
% 9.25/5.23         => ( ( inf_inf_set_int @ ( insert_int @ A @ B2 ) @ C2 )
% 9.25/5.23            = ( inf_inf_set_int @ B2 @ C2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6505_Int__insert__left,axiom,
% 9.25/5.23      ! [A: produc3658429121746597890et_nat > $o,C2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.23        ( ( ( member6576561426505652726_nat_o @ A @ C2 )
% 9.25/5.23         => ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A @ B2 ) @ C2 )
% 9.25/5.23            = ( insert5175938949040314269_nat_o @ A @ ( inf_in1906310914598751387_nat_o @ B2 @ C2 ) ) ) )
% 9.25/5.23        & ( ~ ( member6576561426505652726_nat_o @ A @ C2 )
% 9.25/5.23         => ( ( inf_in1906310914598751387_nat_o @ ( insert5175938949040314269_nat_o @ A @ B2 ) @ C2 )
% 9.25/5.23            = ( inf_in1906310914598751387_nat_o @ B2 @ C2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6506_Int__insert__left,axiom,
% 9.25/5.23      ! [A: product_prod_nat_nat,C2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( ( member8440522571783428010at_nat @ A @ C2 )
% 9.25/5.23         => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ B2 ) @ C2 )
% 9.25/5.23            = ( insert8211810215607154385at_nat @ A @ ( inf_in2572325071724192079at_nat @ B2 @ C2 ) ) ) )
% 9.25/5.23        & ( ~ ( member8440522571783428010at_nat @ A @ C2 )
% 9.25/5.23         => ( ( inf_in2572325071724192079at_nat @ ( insert8211810215607154385at_nat @ A @ B2 ) @ C2 )
% 9.25/5.23            = ( inf_in2572325071724192079at_nat @ B2 @ C2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6507_Int__insert__left,axiom,
% 9.25/5.23      ! [A: nat,C2: set_nat,B2: set_nat] :
% 9.25/5.23        ( ( ( member_nat @ A @ C2 )
% 9.25/5.23         => ( ( inf_inf_set_nat @ ( insert_nat @ A @ B2 ) @ C2 )
% 9.25/5.23            = ( insert_nat @ A @ ( inf_inf_set_nat @ B2 @ C2 ) ) ) )
% 9.25/5.23        & ( ~ ( member_nat @ A @ C2 )
% 9.25/5.23         => ( ( inf_inf_set_nat @ ( insert_nat @ A @ B2 ) @ C2 )
% 9.25/5.23            = ( inf_inf_set_nat @ B2 @ C2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6508_flip__bit__nat__def,axiom,
% 9.25/5.23      ( bit_se2161824704523386999it_nat
% 9.25/5.23      = ( ^ [M2: nat,N2: nat] : ( bit_se6528837805403552850or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M2 @ one_one_nat ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6509_push__bit__minus,axiom,
% 9.25/5.23      ! [N: nat,A: code_integer] :
% 9.25/5.23        ( ( bit_se7788150548672797655nteger @ N @ ( uminus1351360451143612070nteger @ A ) )
% 9.25/5.23        = ( uminus1351360451143612070nteger @ ( bit_se7788150548672797655nteger @ N @ A ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6510_push__bit__minus,axiom,
% 9.25/5.23      ! [N: nat,A: int] :
% 9.25/5.23        ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ A ) )
% 9.25/5.23        = ( uminus_uminus_int @ ( bit_se545348938243370406it_int @ N @ A ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6511_Collect__conv__if2,axiom,
% 9.25/5.23      ! [P: produc3843707927480180839at_nat > $o,A: produc3843707927480180839at_nat] :
% 9.25/5.23        ( ( ( P @ A )
% 9.25/5.23         => ( ( collec6321179662152712658at_nat
% 9.25/5.23              @ ^ [X3: produc3843707927480180839at_nat] :
% 9.25/5.23                  ( ( A = X3 )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) )
% 9.25/5.23        & ( ~ ( P @ A )
% 9.25/5.23         => ( ( collec6321179662152712658at_nat
% 9.25/5.23              @ ^ [X3: produc3843707927480180839at_nat] :
% 9.25/5.23                  ( ( A = X3 )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = bot_bo228742789529271731at_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6512_Collect__conv__if2,axiom,
% 9.25/5.23      ! [P: set_Pr958786334691620121nt_int > $o,A: set_Pr958786334691620121nt_int] :
% 9.25/5.23        ( ( ( P @ A )
% 9.25/5.23         => ( ( collec5210948495886036740nt_int
% 9.25/5.23              @ ^ [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.23                  ( ( A = X3 )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) )
% 9.25/5.23        & ( ~ ( P @ A )
% 9.25/5.23         => ( ( collec5210948495886036740nt_int
% 9.25/5.23              @ ^ [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.23                  ( ( A = X3 )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = bot_bo1488462491386950373nt_int ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6513_Collect__conv__if2,axiom,
% 9.25/5.23      ! [P: set_nat > $o,A: set_nat] :
% 9.25/5.23        ( ( ( P @ A )
% 9.25/5.23         => ( ( collect_set_nat
% 9.25/5.23              @ ^ [X3: set_nat] :
% 9.25/5.23                  ( ( A = X3 )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 9.25/5.23        & ( ~ ( P @ A )
% 9.25/5.23         => ( ( collect_set_nat
% 9.25/5.23              @ ^ [X3: set_nat] :
% 9.25/5.23                  ( ( A = X3 )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = bot_bot_set_set_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6514_Collect__conv__if2,axiom,
% 9.25/5.23      ! [P: ( produc3658429121746597890et_nat > $o ) > $o,A: produc3658429121746597890et_nat > $o] :
% 9.25/5.23        ( ( ( P @ A )
% 9.25/5.23         => ( ( collec939566748876313656_nat_o
% 9.25/5.23              @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.23                  ( ( A = X3 )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = ( insert5175938949040314269_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ) )
% 9.25/5.23        & ( ~ ( P @ A )
% 9.25/5.23         => ( ( collec939566748876313656_nat_o
% 9.25/5.23              @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.23                  ( ( A = X3 )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = bot_bo7824918357723582233_nat_o ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6515_Collect__conv__if2,axiom,
% 9.25/5.23      ! [P: product_prod_nat_nat > $o,A: product_prod_nat_nat] :
% 9.25/5.23        ( ( ( P @ A )
% 9.25/5.23         => ( ( collec3392354462482085612at_nat
% 9.25/5.23              @ ^ [X3: product_prod_nat_nat] :
% 9.25/5.23                  ( ( A = X3 )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 9.25/5.23        & ( ~ ( P @ A )
% 9.25/5.23         => ( ( collec3392354462482085612at_nat
% 9.25/5.23              @ ^ [X3: product_prod_nat_nat] :
% 9.25/5.23                  ( ( A = X3 )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = bot_bo2099793752762293965at_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6516_Collect__conv__if2,axiom,
% 9.25/5.23      ! [P: $o > $o,A: $o] :
% 9.25/5.23        ( ( ( P @ A )
% 9.25/5.23         => ( ( collect_o
% 9.25/5.23              @ ^ [X3: $o] :
% 9.25/5.23                  ( ( A = X3 )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = ( insert_o @ A @ bot_bot_set_o ) ) )
% 9.25/5.23        & ( ~ ( P @ A )
% 9.25/5.23         => ( ( collect_o
% 9.25/5.23              @ ^ [X3: $o] :
% 9.25/5.23                  ( ( A = X3 )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = bot_bot_set_o ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6517_Collect__conv__if2,axiom,
% 9.25/5.23      ! [P: nat > $o,A: nat] :
% 9.25/5.23        ( ( ( P @ A )
% 9.25/5.23         => ( ( collect_nat
% 9.25/5.23              @ ^ [X3: nat] :
% 9.25/5.23                  ( ( A = X3 )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.25/5.23        & ( ~ ( P @ A )
% 9.25/5.23         => ( ( collect_nat
% 9.25/5.23              @ ^ [X3: nat] :
% 9.25/5.23                  ( ( A = X3 )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = bot_bot_set_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6518_Collect__conv__if2,axiom,
% 9.25/5.23      ! [P: int > $o,A: int] :
% 9.25/5.23        ( ( ( P @ A )
% 9.25/5.23         => ( ( collect_int
% 9.25/5.23              @ ^ [X3: int] :
% 9.25/5.23                  ( ( A = X3 )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.25/5.23        & ( ~ ( P @ A )
% 9.25/5.23         => ( ( collect_int
% 9.25/5.23              @ ^ [X3: int] :
% 9.25/5.23                  ( ( A = X3 )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = bot_bot_set_int ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6519_Collect__conv__if,axiom,
% 9.25/5.23      ! [P: produc3843707927480180839at_nat > $o,A: produc3843707927480180839at_nat] :
% 9.25/5.23        ( ( ( P @ A )
% 9.25/5.23         => ( ( collec6321179662152712658at_nat
% 9.25/5.23              @ ^ [X3: produc3843707927480180839at_nat] :
% 9.25/5.23                  ( ( X3 = A )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) )
% 9.25/5.23        & ( ~ ( P @ A )
% 9.25/5.23         => ( ( collec6321179662152712658at_nat
% 9.25/5.23              @ ^ [X3: produc3843707927480180839at_nat] :
% 9.25/5.23                  ( ( X3 = A )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = bot_bo228742789529271731at_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6520_Collect__conv__if,axiom,
% 9.25/5.23      ! [P: set_Pr958786334691620121nt_int > $o,A: set_Pr958786334691620121nt_int] :
% 9.25/5.23        ( ( ( P @ A )
% 9.25/5.23         => ( ( collec5210948495886036740nt_int
% 9.25/5.23              @ ^ [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.23                  ( ( X3 = A )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) )
% 9.25/5.23        & ( ~ ( P @ A )
% 9.25/5.23         => ( ( collec5210948495886036740nt_int
% 9.25/5.23              @ ^ [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.23                  ( ( X3 = A )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = bot_bo1488462491386950373nt_int ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6521_Collect__conv__if,axiom,
% 9.25/5.23      ! [P: set_nat > $o,A: set_nat] :
% 9.25/5.23        ( ( ( P @ A )
% 9.25/5.23         => ( ( collect_set_nat
% 9.25/5.23              @ ^ [X3: set_nat] :
% 9.25/5.23                  ( ( X3 = A )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 9.25/5.23        & ( ~ ( P @ A )
% 9.25/5.23         => ( ( collect_set_nat
% 9.25/5.23              @ ^ [X3: set_nat] :
% 9.25/5.23                  ( ( X3 = A )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = bot_bot_set_set_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6522_Collect__conv__if,axiom,
% 9.25/5.23      ! [P: ( produc3658429121746597890et_nat > $o ) > $o,A: produc3658429121746597890et_nat > $o] :
% 9.25/5.23        ( ( ( P @ A )
% 9.25/5.23         => ( ( collec939566748876313656_nat_o
% 9.25/5.23              @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.23                  ( ( X3 = A )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = ( insert5175938949040314269_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ) )
% 9.25/5.23        & ( ~ ( P @ A )
% 9.25/5.23         => ( ( collec939566748876313656_nat_o
% 9.25/5.23              @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.23                  ( ( X3 = A )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = bot_bo7824918357723582233_nat_o ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6523_Collect__conv__if,axiom,
% 9.25/5.23      ! [P: product_prod_nat_nat > $o,A: product_prod_nat_nat] :
% 9.25/5.23        ( ( ( P @ A )
% 9.25/5.23         => ( ( collec3392354462482085612at_nat
% 9.25/5.23              @ ^ [X3: product_prod_nat_nat] :
% 9.25/5.23                  ( ( X3 = A )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 9.25/5.23        & ( ~ ( P @ A )
% 9.25/5.23         => ( ( collec3392354462482085612at_nat
% 9.25/5.23              @ ^ [X3: product_prod_nat_nat] :
% 9.25/5.23                  ( ( X3 = A )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = bot_bo2099793752762293965at_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6524_Collect__conv__if,axiom,
% 9.25/5.23      ! [P: $o > $o,A: $o] :
% 9.25/5.23        ( ( ( P @ A )
% 9.25/5.23         => ( ( collect_o
% 9.25/5.23              @ ^ [X3: $o] :
% 9.25/5.23                  ( ( X3 = A )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = ( insert_o @ A @ bot_bot_set_o ) ) )
% 9.25/5.23        & ( ~ ( P @ A )
% 9.25/5.23         => ( ( collect_o
% 9.25/5.23              @ ^ [X3: $o] :
% 9.25/5.23                  ( ( X3 = A )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = bot_bot_set_o ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6525_Collect__conv__if,axiom,
% 9.25/5.23      ! [P: nat > $o,A: nat] :
% 9.25/5.23        ( ( ( P @ A )
% 9.25/5.23         => ( ( collect_nat
% 9.25/5.23              @ ^ [X3: nat] :
% 9.25/5.23                  ( ( X3 = A )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.25/5.23        & ( ~ ( P @ A )
% 9.25/5.23         => ( ( collect_nat
% 9.25/5.23              @ ^ [X3: nat] :
% 9.25/5.23                  ( ( X3 = A )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = bot_bot_set_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6526_Collect__conv__if,axiom,
% 9.25/5.23      ! [P: int > $o,A: int] :
% 9.25/5.23        ( ( ( P @ A )
% 9.25/5.23         => ( ( collect_int
% 9.25/5.23              @ ^ [X3: int] :
% 9.25/5.23                  ( ( X3 = A )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.25/5.23        & ( ~ ( P @ A )
% 9.25/5.23         => ( ( collect_int
% 9.25/5.23              @ ^ [X3: int] :
% 9.25/5.23                  ( ( X3 = A )
% 9.25/5.23                  & ( P @ X3 ) ) )
% 9.25/5.23            = bot_bot_set_int ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6527_insert__def,axiom,
% 9.25/5.23      ( insert8211810215607154385at_nat
% 9.25/5.23      = ( ^ [A3: product_prod_nat_nat] :
% 9.25/5.23            ( sup_su6327502436637775413at_nat
% 9.25/5.23            @ ( collec3392354462482085612at_nat
% 9.25/5.23              @ ^ [X3: product_prod_nat_nat] : ( X3 = A3 ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6528_insert__def,axiom,
% 9.25/5.23      ( insert_o
% 9.25/5.23      = ( ^ [A3: $o] :
% 9.25/5.23            ( sup_sup_set_o
% 9.25/5.23            @ ( collect_o
% 9.25/5.23              @ ^ [X3: $o] : ( X3 = A3 ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6529_insert__def,axiom,
% 9.25/5.23      ( insert8897473484851387113nt_int
% 9.25/5.23      = ( ^ [A3: set_Pr958786334691620121nt_int] :
% 9.25/5.23            ( sup_su2047564715030645325nt_int
% 9.25/5.23            @ ( collec5210948495886036740nt_int
% 9.25/5.23              @ ^ [X3: set_Pr958786334691620121nt_int] : ( X3 = A3 ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6530_insert__def,axiom,
% 9.25/5.23      ( insert_set_nat
% 9.25/5.23      = ( ^ [A3: set_nat] :
% 9.25/5.23            ( sup_sup_set_set_nat
% 9.25/5.23            @ ( collect_set_nat
% 9.25/5.23              @ ^ [X3: set_nat] : ( X3 = A3 ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6531_insert__def,axiom,
% 9.25/5.23      ( insert_int
% 9.25/5.23      = ( ^ [A3: int] :
% 9.25/5.23            ( sup_sup_set_int
% 9.25/5.23            @ ( collect_int
% 9.25/5.23              @ ^ [X3: int] : ( X3 = A3 ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6532_insert__def,axiom,
% 9.25/5.23      ( insert5175938949040314269_nat_o
% 9.25/5.23      = ( ^ [A3: produc3658429121746597890et_nat > $o] :
% 9.25/5.23            ( sup_su5209123915105501825_nat_o
% 9.25/5.23            @ ( collec939566748876313656_nat_o
% 9.25/5.23              @ ^ [X3: produc3658429121746597890et_nat > $o] : ( X3 = A3 ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6533_insert__def,axiom,
% 9.25/5.23      ( insert6337962749363155127at_nat
% 9.25/5.23      = ( ^ [A3: produc4166570645942440679at_nat] :
% 9.25/5.23            ( sup_su3035147773818789531at_nat
% 9.25/5.23            @ ( collec5204685387357076818at_nat
% 9.25/5.23              @ ^ [X3: produc4166570645942440679at_nat] : ( X3 = A3 ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6534_insert__def,axiom,
% 9.25/5.23      ( insert9069300056098147895at_nat
% 9.25/5.23      = ( ^ [A3: produc3843707927480180839at_nat] :
% 9.25/5.23            ( sup_su5525570899277871387at_nat
% 9.25/5.23            @ ( collec6321179662152712658at_nat
% 9.25/5.23              @ ^ [X3: produc3843707927480180839at_nat] : ( X3 = A3 ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6535_insert__def,axiom,
% 9.25/5.23      ( insert_nat
% 9.25/5.23      = ( ^ [A3: nat] :
% 9.25/5.23            ( sup_sup_set_nat
% 9.25/5.23            @ ( collect_nat
% 9.25/5.23              @ ^ [X3: nat] : ( X3 = A3 ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6536_subset__singletonD,axiom,
% 9.25/5.23      ! [A2: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat] :
% 9.25/5.23        ( ( ord_le1268244103169919719at_nat @ A2 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 9.25/5.23       => ( ( A2 = bot_bo228742789529271731at_nat )
% 9.25/5.23          | ( A2
% 9.25/5.23            = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6537_subset__singletonD,axiom,
% 9.25/5.23      ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 9.25/5.23        ( ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 9.25/5.23       => ( ( A2 = bot_bo2099793752762293965at_nat )
% 9.25/5.23          | ( A2
% 9.25/5.23            = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6538_subset__singletonD,axiom,
% 9.25/5.23      ! [A2: set_o,X: $o] :
% 9.25/5.23        ( ( ord_less_eq_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) )
% 9.25/5.23       => ( ( A2 = bot_bot_set_o )
% 9.25/5.23          | ( A2
% 9.25/5.23            = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6539_subset__singletonD,axiom,
% 9.25/5.23      ! [A2: set_int,X: int] :
% 9.25/5.23        ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) )
% 9.25/5.23       => ( ( A2 = bot_bot_set_int )
% 9.25/5.23          | ( A2
% 9.25/5.23            = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6540_subset__singletonD,axiom,
% 9.25/5.23      ! [A2: set_nat,X: nat] :
% 9.25/5.23        ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 9.25/5.23       => ( ( A2 = bot_bot_set_nat )
% 9.25/5.23          | ( A2
% 9.25/5.23            = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6541_subset__singleton__iff,axiom,
% 9.25/5.23      ! [X7: set_Pr4329608150637261639at_nat,A: produc3843707927480180839at_nat] :
% 9.25/5.23        ( ( ord_le1268244103169919719at_nat @ X7 @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) )
% 9.25/5.23        = ( ( X7 = bot_bo228742789529271731at_nat )
% 9.25/5.23          | ( X7
% 9.25/5.23            = ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6542_subset__singleton__iff,axiom,
% 9.25/5.23      ! [X7: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
% 9.25/5.23        ( ( ord_le3146513528884898305at_nat @ X7 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) )
% 9.25/5.23        = ( ( X7 = bot_bo2099793752762293965at_nat )
% 9.25/5.23          | ( X7
% 9.25/5.23            = ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6543_subset__singleton__iff,axiom,
% 9.25/5.23      ! [X7: set_o,A: $o] :
% 9.25/5.23        ( ( ord_less_eq_set_o @ X7 @ ( insert_o @ A @ bot_bot_set_o ) )
% 9.25/5.23        = ( ( X7 = bot_bot_set_o )
% 9.25/5.23          | ( X7
% 9.25/5.23            = ( insert_o @ A @ bot_bot_set_o ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6544_subset__singleton__iff,axiom,
% 9.25/5.23      ! [X7: set_int,A: int] :
% 9.25/5.23        ( ( ord_less_eq_set_int @ X7 @ ( insert_int @ A @ bot_bot_set_int ) )
% 9.25/5.23        = ( ( X7 = bot_bot_set_int )
% 9.25/5.23          | ( X7
% 9.25/5.23            = ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6545_subset__singleton__iff,axiom,
% 9.25/5.23      ! [X7: set_nat,A: nat] :
% 9.25/5.23        ( ( ord_less_eq_set_nat @ X7 @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 9.25/5.23        = ( ( X7 = bot_bot_set_nat )
% 9.25/5.23          | ( X7
% 9.25/5.23            = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6546_singleton__Un__iff,axiom,
% 9.25/5.23      ! [X: produc4166570645942440679at_nat,A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat] :
% 9.25/5.23        ( ( ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat )
% 9.25/5.23          = ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 9.25/5.23        = ( ( ( A2 = bot_bo8422036546324065075at_nat )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) )
% 9.25/5.23            & ( B2 = bot_bo8422036546324065075at_nat ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6547_singleton__Un__iff,axiom,
% 9.25/5.23      ! [X: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat )
% 9.25/5.23          = ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 9.25/5.23        = ( ( ( A2 = bot_bo228742789529271731at_nat )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 9.25/5.23            & ( B2 = bot_bo228742789529271731at_nat ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6548_singleton__Un__iff,axiom,
% 9.25/5.23      ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat )
% 9.25/5.23          = ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 9.25/5.23        = ( ( ( A2 = bot_bo2099793752762293965at_nat )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 9.25/5.23            & ( B2 = bot_bo2099793752762293965at_nat ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6549_singleton__Un__iff,axiom,
% 9.25/5.23      ! [X: $o,A2: set_o,B2: set_o] :
% 9.25/5.23        ( ( ( insert_o @ X @ bot_bot_set_o )
% 9.25/5.23          = ( sup_sup_set_o @ A2 @ B2 ) )
% 9.25/5.23        = ( ( ( A2 = bot_bot_set_o )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert_o @ X @ bot_bot_set_o ) ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert_o @ X @ bot_bot_set_o ) )
% 9.25/5.23            & ( B2 = bot_bot_set_o ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert_o @ X @ bot_bot_set_o ) )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6550_singleton__Un__iff,axiom,
% 9.25/5.23      ! [X: nat,A2: set_nat,B2: set_nat] :
% 9.25/5.23        ( ( ( insert_nat @ X @ bot_bot_set_nat )
% 9.25/5.23          = ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.23        = ( ( ( A2 = bot_bot_set_nat )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert_nat @ X @ bot_bot_set_nat ) )
% 9.25/5.23            & ( B2 = bot_bot_set_nat ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert_nat @ X @ bot_bot_set_nat ) )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6551_singleton__Un__iff,axiom,
% 9.25/5.23      ! [X: int,A2: set_int,B2: set_int] :
% 9.25/5.23        ( ( ( insert_int @ X @ bot_bot_set_int )
% 9.25/5.23          = ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.23        = ( ( ( A2 = bot_bot_set_int )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert_int @ X @ bot_bot_set_int ) ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert_int @ X @ bot_bot_set_int ) )
% 9.25/5.23            & ( B2 = bot_bot_set_int ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert_int @ X @ bot_bot_set_int ) )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6552_Un__singleton__iff,axiom,
% 9.25/5.23      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,X: produc4166570645942440679at_nat] :
% 9.25/5.23        ( ( ( sup_su3035147773818789531at_nat @ A2 @ B2 )
% 9.25/5.23          = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) )
% 9.25/5.23        = ( ( ( A2 = bot_bo8422036546324065075at_nat )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) )
% 9.25/5.23            & ( B2 = bot_bo8422036546324065075at_nat ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert6337962749363155127at_nat @ X @ bot_bo8422036546324065075at_nat ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6553_Un__singleton__iff,axiom,
% 9.25/5.23      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat] :
% 9.25/5.23        ( ( ( sup_su5525570899277871387at_nat @ A2 @ B2 )
% 9.25/5.23          = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 9.25/5.23        = ( ( ( A2 = bot_bo228742789529271731at_nat )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 9.25/5.23            & ( B2 = bot_bo228742789529271731at_nat ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6554_Un__singleton__iff,axiom,
% 9.25/5.23      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 9.25/5.23        ( ( ( sup_su6327502436637775413at_nat @ A2 @ B2 )
% 9.25/5.23          = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 9.25/5.23        = ( ( ( A2 = bot_bo2099793752762293965at_nat )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 9.25/5.23            & ( B2 = bot_bo2099793752762293965at_nat ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6555_Un__singleton__iff,axiom,
% 9.25/5.23      ! [A2: set_o,B2: set_o,X: $o] :
% 9.25/5.23        ( ( ( sup_sup_set_o @ A2 @ B2 )
% 9.25/5.23          = ( insert_o @ X @ bot_bot_set_o ) )
% 9.25/5.23        = ( ( ( A2 = bot_bot_set_o )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert_o @ X @ bot_bot_set_o ) ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert_o @ X @ bot_bot_set_o ) )
% 9.25/5.23            & ( B2 = bot_bot_set_o ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert_o @ X @ bot_bot_set_o ) )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6556_Un__singleton__iff,axiom,
% 9.25/5.23      ! [A2: set_nat,B2: set_nat,X: nat] :
% 9.25/5.23        ( ( ( sup_sup_set_nat @ A2 @ B2 )
% 9.25/5.23          = ( insert_nat @ X @ bot_bot_set_nat ) )
% 9.25/5.23        = ( ( ( A2 = bot_bot_set_nat )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert_nat @ X @ bot_bot_set_nat ) )
% 9.25/5.23            & ( B2 = bot_bot_set_nat ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert_nat @ X @ bot_bot_set_nat ) )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6557_Un__singleton__iff,axiom,
% 9.25/5.23      ! [A2: set_int,B2: set_int,X: int] :
% 9.25/5.23        ( ( ( sup_sup_set_int @ A2 @ B2 )
% 9.25/5.23          = ( insert_int @ X @ bot_bot_set_int ) )
% 9.25/5.23        = ( ( ( A2 = bot_bot_set_int )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert_int @ X @ bot_bot_set_int ) ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert_int @ X @ bot_bot_set_int ) )
% 9.25/5.23            & ( B2 = bot_bot_set_int ) )
% 9.25/5.23          | ( ( A2
% 9.25/5.23              = ( insert_int @ X @ bot_bot_set_int ) )
% 9.25/5.23            & ( B2
% 9.25/5.23              = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6558_insert__is__Un,axiom,
% 9.25/5.23      ( insert6337962749363155127at_nat
% 9.25/5.23      = ( ^ [A3: produc4166570645942440679at_nat] : ( sup_su3035147773818789531at_nat @ ( insert6337962749363155127at_nat @ A3 @ bot_bo8422036546324065075at_nat ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6559_insert__is__Un,axiom,
% 9.25/5.23      ( insert9069300056098147895at_nat
% 9.25/5.23      = ( ^ [A3: produc3843707927480180839at_nat] : ( sup_su5525570899277871387at_nat @ ( insert9069300056098147895at_nat @ A3 @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6560_insert__is__Un,axiom,
% 9.25/5.23      ( insert8211810215607154385at_nat
% 9.25/5.23      = ( ^ [A3: product_prod_nat_nat] : ( sup_su6327502436637775413at_nat @ ( insert8211810215607154385at_nat @ A3 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6561_insert__is__Un,axiom,
% 9.25/5.23      ( insert_o
% 9.25/5.23      = ( ^ [A3: $o] : ( sup_sup_set_o @ ( insert_o @ A3 @ bot_bot_set_o ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6562_insert__is__Un,axiom,
% 9.25/5.23      ( insert_nat
% 9.25/5.23      = ( ^ [A3: nat] : ( sup_sup_set_nat @ ( insert_nat @ A3 @ bot_bot_set_nat ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6563_insert__is__Un,axiom,
% 9.25/5.23      ( insert_int
% 9.25/5.23      = ( ^ [A3: int] : ( sup_sup_set_int @ ( insert_int @ A3 @ bot_bot_set_int ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6564_set__minus__singleton__eq,axiom,
% 9.25/5.23      ! [X: produc3843707927480180839at_nat,X7: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ~ ( member8757157785044589968at_nat @ X @ X7 )
% 9.25/5.23       => ( ( minus_3314409938677909166at_nat @ X7 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 9.25/5.23          = X7 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6565_set__minus__singleton__eq,axiom,
% 9.25/5.23      ! [X: set_Pr958786334691620121nt_int,X7: set_se6260736226359567993nt_int] :
% 9.25/5.23        ( ~ ( member2340774599025711042nt_int @ X @ X7 )
% 9.25/5.23       => ( ( minus_2612819937483484256nt_int @ X7 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
% 9.25/5.23          = X7 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6566_set__minus__singleton__eq,axiom,
% 9.25/5.23      ! [X: set_nat,X7: set_set_nat] :
% 9.25/5.23        ( ~ ( member_set_nat @ X @ X7 )
% 9.25/5.23       => ( ( minus_2163939370556025621et_nat @ X7 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 9.25/5.23          = X7 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6567_set__minus__singleton__eq,axiom,
% 9.25/5.23      ! [X: produc3658429121746597890et_nat > $o,X7: set_Pr4532377907799695533_nat_o] :
% 9.25/5.23        ( ~ ( member6576561426505652726_nat_o @ X @ X7 )
% 9.25/5.23       => ( ( minus_1801376950450012436_nat_o @ X7 @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 9.25/5.23          = X7 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6568_set__minus__singleton__eq,axiom,
% 9.25/5.23      ! [X: product_prod_nat_nat,X7: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ~ ( member8440522571783428010at_nat @ X @ X7 )
% 9.25/5.23       => ( ( minus_1356011639430497352at_nat @ X7 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 9.25/5.23          = X7 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6569_set__minus__singleton__eq,axiom,
% 9.25/5.23      ! [X: $o,X7: set_o] :
% 9.25/5.23        ( ~ ( member_o @ X @ X7 )
% 9.25/5.23       => ( ( minus_minus_set_o @ X7 @ ( insert_o @ X @ bot_bot_set_o ) )
% 9.25/5.23          = X7 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6570_set__minus__singleton__eq,axiom,
% 9.25/5.23      ! [X: int,X7: set_int] :
% 9.25/5.23        ( ~ ( member_int @ X @ X7 )
% 9.25/5.23       => ( ( minus_minus_set_int @ X7 @ ( insert_int @ X @ bot_bot_set_int ) )
% 9.25/5.23          = X7 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6571_set__minus__singleton__eq,axiom,
% 9.25/5.23      ! [X: nat,X7: set_nat] :
% 9.25/5.23        ( ~ ( member_nat @ X @ X7 )
% 9.25/5.23       => ( ( minus_minus_set_nat @ X7 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 9.25/5.23          = X7 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6572_insert__minus__eq,axiom,
% 9.25/5.23      ! [X: produc3843707927480180839at_nat,Y: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( X != Y )
% 9.25/5.23       => ( ( minus_3314409938677909166at_nat @ ( insert9069300056098147895at_nat @ X @ A2 ) @ ( insert9069300056098147895at_nat @ Y @ bot_bo228742789529271731at_nat ) )
% 9.25/5.23          = ( insert9069300056098147895at_nat @ X @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ Y @ bot_bo228742789529271731at_nat ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6573_insert__minus__eq,axiom,
% 9.25/5.23      ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( X != Y )
% 9.25/5.23       => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ ( insert8211810215607154385at_nat @ Y @ bot_bo2099793752762293965at_nat ) )
% 9.25/5.23          = ( insert8211810215607154385at_nat @ X @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ Y @ bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6574_insert__minus__eq,axiom,
% 9.25/5.23      ! [X: $o,Y: $o,A2: set_o] :
% 9.25/5.23        ( ( X != Y )
% 9.25/5.23       => ( ( minus_minus_set_o @ ( insert_o @ X @ A2 ) @ ( insert_o @ Y @ bot_bot_set_o ) )
% 9.25/5.23          = ( insert_o @ X @ ( minus_minus_set_o @ A2 @ ( insert_o @ Y @ bot_bot_set_o ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6575_insert__minus__eq,axiom,
% 9.25/5.23      ! [X: int,Y: int,A2: set_int] :
% 9.25/5.23        ( ( X != Y )
% 9.25/5.23       => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ ( insert_int @ Y @ bot_bot_set_int ) )
% 9.25/5.23          = ( insert_int @ X @ ( minus_minus_set_int @ A2 @ ( insert_int @ Y @ bot_bot_set_int ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6576_insert__minus__eq,axiom,
% 9.25/5.23      ! [X: nat,Y: nat,A2: set_nat] :
% 9.25/5.23        ( ( X != Y )
% 9.25/5.23       => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ ( insert_nat @ Y @ bot_bot_set_nat ) )
% 9.25/5.23          = ( insert_nat @ X @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ Y @ bot_bot_set_nat ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6577_Diff__insert,axiom,
% 9.25/5.23      ! [A2: set_Pr4329608150637261639at_nat,A: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ B2 ) )
% 9.25/5.23        = ( minus_3314409938677909166at_nat @ ( minus_3314409938677909166at_nat @ A2 @ B2 ) @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6578_Diff__insert,axiom,
% 9.25/5.23      ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 9.25/5.23        = ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6579_Diff__insert,axiom,
% 9.25/5.23      ! [A2: set_o,A: $o,B2: set_o] :
% 9.25/5.23        ( ( minus_minus_set_o @ A2 @ ( insert_o @ A @ B2 ) )
% 9.25/5.23        = ( minus_minus_set_o @ ( minus_minus_set_o @ A2 @ B2 ) @ ( insert_o @ A @ bot_bot_set_o ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6580_Diff__insert,axiom,
% 9.25/5.23      ! [A2: set_int,A: int,B2: set_int] :
% 9.25/5.23        ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 9.25/5.23        = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ B2 ) @ ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6581_Diff__insert,axiom,
% 9.25/5.23      ! [A2: set_nat,A: nat,B2: set_nat] :
% 9.25/5.23        ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 9.25/5.23        = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B2 ) @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6582_insert__Diff,axiom,
% 9.25/5.23      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( member8757157785044589968at_nat @ A @ A2 )
% 9.25/5.23       => ( ( insert9069300056098147895at_nat @ A @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) )
% 9.25/5.23          = A2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6583_insert__Diff,axiom,
% 9.25/5.23      ! [A: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int] :
% 9.25/5.23        ( ( member2340774599025711042nt_int @ A @ A2 )
% 9.25/5.23       => ( ( insert8897473484851387113nt_int @ A @ ( minus_2612819937483484256nt_int @ A2 @ ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) )
% 9.25/5.23          = A2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6584_insert__Diff,axiom,
% 9.25/5.23      ! [A: set_nat,A2: set_set_nat] :
% 9.25/5.23        ( ( member_set_nat @ A @ A2 )
% 9.25/5.23       => ( ( insert_set_nat @ A @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 9.25/5.23          = A2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6585_insert__Diff,axiom,
% 9.25/5.23      ! [A: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.23        ( ( member6576561426505652726_nat_o @ A @ A2 )
% 9.25/5.23       => ( ( insert5175938949040314269_nat_o @ A @ ( minus_1801376950450012436_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ) )
% 9.25/5.23          = A2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6586_insert__Diff,axiom,
% 9.25/5.23      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( member8440522571783428010at_nat @ A @ A2 )
% 9.25/5.23       => ( ( insert8211810215607154385at_nat @ A @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 9.25/5.23          = A2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6587_insert__Diff,axiom,
% 9.25/5.23      ! [A: $o,A2: set_o] :
% 9.25/5.23        ( ( member_o @ A @ A2 )
% 9.25/5.23       => ( ( insert_o @ A @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 9.25/5.23          = A2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6588_insert__Diff,axiom,
% 9.25/5.23      ! [A: int,A2: set_int] :
% 9.25/5.23        ( ( member_int @ A @ A2 )
% 9.25/5.23       => ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.25/5.23          = A2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6589_insert__Diff,axiom,
% 9.25/5.23      ! [A: nat,A2: set_nat] :
% 9.25/5.23        ( ( member_nat @ A @ A2 )
% 9.25/5.23       => ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.25/5.23          = A2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6590_Diff__insert2,axiom,
% 9.25/5.23      ! [A2: set_Pr4329608150637261639at_nat,A: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ B2 ) )
% 9.25/5.23        = ( minus_3314409938677909166at_nat @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) @ B2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6591_Diff__insert2,axiom,
% 9.25/5.23      ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 9.25/5.23        = ( minus_1356011639430497352at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) @ B2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6592_Diff__insert2,axiom,
% 9.25/5.23      ! [A2: set_o,A: $o,B2: set_o] :
% 9.25/5.23        ( ( minus_minus_set_o @ A2 @ ( insert_o @ A @ B2 ) )
% 9.25/5.23        = ( minus_minus_set_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) @ B2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6593_Diff__insert2,axiom,
% 9.25/5.23      ! [A2: set_int,A: int,B2: set_int] :
% 9.25/5.23        ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) )
% 9.25/5.23        = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) @ B2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6594_Diff__insert2,axiom,
% 9.25/5.23      ! [A2: set_nat,A: nat,B2: set_nat] :
% 9.25/5.23        ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) )
% 9.25/5.23        = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ B2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6595_Diff__insert__absorb,axiom,
% 9.25/5.23      ! [X: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ~ ( member8757157785044589968at_nat @ X @ A2 )
% 9.25/5.23       => ( ( minus_3314409938677909166at_nat @ ( insert9069300056098147895at_nat @ X @ A2 ) @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 9.25/5.23          = A2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6596_Diff__insert__absorb,axiom,
% 9.25/5.23      ! [X: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int] :
% 9.25/5.23        ( ~ ( member2340774599025711042nt_int @ X @ A2 )
% 9.25/5.23       => ( ( minus_2612819937483484256nt_int @ ( insert8897473484851387113nt_int @ X @ A2 ) @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) )
% 9.25/5.23          = A2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6597_Diff__insert__absorb,axiom,
% 9.25/5.23      ! [X: set_nat,A2: set_set_nat] :
% 9.25/5.23        ( ~ ( member_set_nat @ X @ A2 )
% 9.25/5.23       => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 9.25/5.23          = A2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6598_Diff__insert__absorb,axiom,
% 9.25/5.23      ! [X: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.23        ( ~ ( member6576561426505652726_nat_o @ X @ A2 )
% 9.25/5.23       => ( ( minus_1801376950450012436_nat_o @ ( insert5175938949040314269_nat_o @ X @ A2 ) @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) )
% 9.25/5.23          = A2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6599_Diff__insert__absorb,axiom,
% 9.25/5.23      ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 9.25/5.23       => ( ( minus_1356011639430497352at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 9.25/5.23          = A2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6600_Diff__insert__absorb,axiom,
% 9.25/5.23      ! [X: $o,A2: set_o] :
% 9.25/5.23        ( ~ ( member_o @ X @ A2 )
% 9.25/5.23       => ( ( minus_minus_set_o @ ( insert_o @ X @ A2 ) @ ( insert_o @ X @ bot_bot_set_o ) )
% 9.25/5.23          = A2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6601_Diff__insert__absorb,axiom,
% 9.25/5.23      ! [X: int,A2: set_int] :
% 9.25/5.23        ( ~ ( member_int @ X @ A2 )
% 9.25/5.23       => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 9.25/5.23          = A2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6602_Diff__insert__absorb,axiom,
% 9.25/5.23      ! [X: nat,A2: set_nat] :
% 9.25/5.23        ( ~ ( member_nat @ X @ A2 )
% 9.25/5.23       => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 9.25/5.23          = A2 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6603_vimage__singleton__eq,axiom,
% 9.25/5.23      ! [A: nat,F2: nat > $o,B: $o] :
% 9.25/5.23        ( ( member_nat @ A @ ( vimage_nat_o @ F2 @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 9.25/5.23        = ( ( F2 @ A )
% 9.25/5.23          = B ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6604_vimage__singleton__eq,axiom,
% 9.25/5.23      ! [A: int,F2: int > $o,B: $o] :
% 9.25/5.23        ( ( member_int @ A @ ( vimage_int_o @ F2 @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 9.25/5.23        = ( ( F2 @ A )
% 9.25/5.23          = B ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6605_vimage__singleton__eq,axiom,
% 9.25/5.23      ! [A: nat,F2: nat > nat,B: nat] :
% 9.25/5.23        ( ( member_nat @ A @ ( vimage_nat_nat @ F2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 9.25/5.23        = ( ( F2 @ A )
% 9.25/5.23          = B ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6606_vimage__singleton__eq,axiom,
% 9.25/5.23      ! [A: int,F2: int > nat,B: nat] :
% 9.25/5.23        ( ( member_int @ A @ ( vimage_int_nat @ F2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 9.25/5.23        = ( ( F2 @ A )
% 9.25/5.23          = B ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6607_vimage__singleton__eq,axiom,
% 9.25/5.23      ! [A: nat,F2: nat > int,B: int] :
% 9.25/5.23        ( ( member_nat @ A @ ( vimage_nat_int @ F2 @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 9.25/5.23        = ( ( F2 @ A )
% 9.25/5.23          = B ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6608_vimage__singleton__eq,axiom,
% 9.25/5.23      ! [A: int,F2: int > int,B: int] :
% 9.25/5.23        ( ( member_int @ A @ ( vimage_int_int @ F2 @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 9.25/5.23        = ( ( F2 @ A )
% 9.25/5.23          = B ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6609_vimage__singleton__eq,axiom,
% 9.25/5.23      ! [A: set_nat,F2: set_nat > $o,B: $o] :
% 9.25/5.23        ( ( member_set_nat @ A @ ( vimage_set_nat_o @ F2 @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 9.25/5.23        = ( ( F2 @ A )
% 9.25/5.23          = B ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6610_vimage__singleton__eq,axiom,
% 9.25/5.23      ! [A: set_nat,F2: set_nat > nat,B: nat] :
% 9.25/5.23        ( ( member_set_nat @ A @ ( vimage_set_nat_nat @ F2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 9.25/5.23        = ( ( F2 @ A )
% 9.25/5.23          = B ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6611_vimage__singleton__eq,axiom,
% 9.25/5.23      ! [A: set_nat,F2: set_nat > int,B: int] :
% 9.25/5.23        ( ( member_set_nat @ A @ ( vimage_set_nat_int @ F2 @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 9.25/5.23        = ( ( F2 @ A )
% 9.25/5.23          = B ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6612_vimage__singleton__eq,axiom,
% 9.25/5.23      ! [A: nat,F2: nat > product_prod_nat_nat,B: product_prod_nat_nat] :
% 9.25/5.23        ( ( member_nat @ A @ ( vimage8013328719654469172at_nat @ F2 @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) )
% 9.25/5.23        = ( ( F2 @ A )
% 9.25/5.23          = B ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6613_subset__insert__iff,axiom,
% 9.25/5.23      ! [A2: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( ord_le1268244103169919719at_nat @ A2 @ ( insert9069300056098147895at_nat @ X @ B2 ) )
% 9.25/5.23        = ( ( ( member8757157785044589968at_nat @ X @ A2 )
% 9.25/5.23           => ( ord_le1268244103169919719at_nat @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) @ B2 ) )
% 9.25/5.23          & ( ~ ( member8757157785044589968at_nat @ X @ A2 )
% 9.25/5.23           => ( ord_le1268244103169919719at_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6614_subset__insert__iff,axiom,
% 9.25/5.23      ! [A2: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.23        ( ( ord_le483042692224249369nt_int @ A2 @ ( insert8897473484851387113nt_int @ X @ B2 ) )
% 9.25/5.23        = ( ( ( member2340774599025711042nt_int @ X @ A2 )
% 9.25/5.23           => ( ord_le483042692224249369nt_int @ ( minus_2612819937483484256nt_int @ A2 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) ) @ B2 ) )
% 9.25/5.23          & ( ~ ( member2340774599025711042nt_int @ X @ A2 )
% 9.25/5.23           => ( ord_le483042692224249369nt_int @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6615_subset__insert__iff,axiom,
% 9.25/5.23      ! [A2: set_set_nat,X: set_nat,B2: set_set_nat] :
% 9.25/5.23        ( ( ord_le6893508408891458716et_nat @ A2 @ ( insert_set_nat @ X @ B2 ) )
% 9.25/5.23        = ( ( ( member_set_nat @ X @ A2 )
% 9.25/5.23           => ( ord_le6893508408891458716et_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B2 ) )
% 9.25/5.23          & ( ~ ( member_set_nat @ X @ A2 )
% 9.25/5.23           => ( ord_le6893508408891458716et_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6616_subset__insert__iff,axiom,
% 9.25/5.23      ! [A2: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.23        ( ( ord_le2965882846123202637_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ X @ B2 ) )
% 9.25/5.23        = ( ( ( member6576561426505652726_nat_o @ X @ A2 )
% 9.25/5.23           => ( ord_le2965882846123202637_nat_o @ ( minus_1801376950450012436_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) @ B2 ) )
% 9.25/5.23          & ( ~ ( member6576561426505652726_nat_o @ X @ A2 )
% 9.25/5.23           => ( ord_le2965882846123202637_nat_o @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6617_subset__insert__iff,axiom,
% 9.25/5.23      ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) )
% 9.25/5.23        = ( ( ( member8440522571783428010at_nat @ X @ A2 )
% 9.25/5.23           => ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B2 ) )
% 9.25/5.23          & ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 9.25/5.23           => ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6618_subset__insert__iff,axiom,
% 9.25/5.23      ! [A2: set_o,X: $o,B2: set_o] :
% 9.25/5.23        ( ( ord_less_eq_set_o @ A2 @ ( insert_o @ X @ B2 ) )
% 9.25/5.23        = ( ( ( member_o @ X @ A2 )
% 9.25/5.23           => ( ord_less_eq_set_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) @ B2 ) )
% 9.25/5.23          & ( ~ ( member_o @ X @ A2 )
% 9.25/5.23           => ( ord_less_eq_set_o @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6619_subset__insert__iff,axiom,
% 9.25/5.23      ! [A2: set_int,X: int,B2: set_int] :
% 9.25/5.23        ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B2 ) )
% 9.25/5.23        = ( ( ( member_int @ X @ A2 )
% 9.25/5.23           => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B2 ) )
% 9.25/5.23          & ( ~ ( member_int @ X @ A2 )
% 9.25/5.23           => ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6620_subset__insert__iff,axiom,
% 9.25/5.23      ! [A2: set_nat,X: nat,B2: set_nat] :
% 9.25/5.23        ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B2 ) )
% 9.25/5.23        = ( ( ( member_nat @ X @ A2 )
% 9.25/5.23           => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B2 ) )
% 9.25/5.23          & ( ~ ( member_nat @ X @ A2 )
% 9.25/5.23           => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6621_Diff__single__insert,axiom,
% 9.25/5.23      ! [A2: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( ord_le1268244103169919719at_nat @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) @ B2 )
% 9.25/5.23       => ( ord_le1268244103169919719at_nat @ A2 @ ( insert9069300056098147895at_nat @ X @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6622_Diff__single__insert,axiom,
% 9.25/5.23      ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( ord_le3146513528884898305at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B2 )
% 9.25/5.23       => ( ord_le3146513528884898305at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6623_Diff__single__insert,axiom,
% 9.25/5.23      ! [A2: set_o,X: $o,B2: set_o] :
% 9.25/5.23        ( ( ord_less_eq_set_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) @ B2 )
% 9.25/5.23       => ( ord_less_eq_set_o @ A2 @ ( insert_o @ X @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6624_Diff__single__insert,axiom,
% 9.25/5.23      ! [A2: set_int,X: int,B2: set_int] :
% 9.25/5.23        ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B2 )
% 9.25/5.23       => ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6625_Diff__single__insert,axiom,
% 9.25/5.23      ! [A2: set_nat,X: nat,B2: set_nat] :
% 9.25/5.23        ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B2 )
% 9.25/5.23       => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6626_remove__subset,axiom,
% 9.25/5.23      ! [X: produc3843707927480180839at_nat,S: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( member8757157785044589968at_nat @ X @ S )
% 9.25/5.23       => ( ord_le2604355607129572851at_nat @ ( minus_3314409938677909166at_nat @ S @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) @ S ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6627_remove__subset,axiom,
% 9.25/5.23      ! [X: set_Pr958786334691620121nt_int,S: set_se6260736226359567993nt_int] :
% 9.25/5.23        ( ( member2340774599025711042nt_int @ X @ S )
% 9.25/5.23       => ( ord_le1924305788584680229nt_int @ ( minus_2612819937483484256nt_int @ S @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) ) @ S ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6628_remove__subset,axiom,
% 9.25/5.23      ! [X: set_nat,S: set_set_nat] :
% 9.25/5.23        ( ( member_set_nat @ X @ S )
% 9.25/5.23       => ( ord_less_set_set_nat @ ( minus_2163939370556025621et_nat @ S @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ S ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6629_remove__subset,axiom,
% 9.25/5.23      ! [X: produc3658429121746597890et_nat > $o,S: set_Pr4532377907799695533_nat_o] :
% 9.25/5.23        ( ( member6576561426505652726_nat_o @ X @ S )
% 9.25/5.23       => ( ord_le2453136405763929_nat_o @ ( minus_1801376950450012436_nat_o @ S @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) @ S ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6630_remove__subset,axiom,
% 9.25/5.23      ! [X: product_prod_nat_nat,S: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( member8440522571783428010at_nat @ X @ S )
% 9.25/5.23       => ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ S @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ S ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6631_remove__subset,axiom,
% 9.25/5.23      ! [X: $o,S: set_o] :
% 9.25/5.23        ( ( member_o @ X @ S )
% 9.25/5.23       => ( ord_less_set_o @ ( minus_minus_set_o @ S @ ( insert_o @ X @ bot_bot_set_o ) ) @ S ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6632_remove__subset,axiom,
% 9.25/5.23      ! [X: int,S: set_int] :
% 9.25/5.23        ( ( member_int @ X @ S )
% 9.25/5.23       => ( ord_less_set_int @ ( minus_minus_set_int @ S @ ( insert_int @ X @ bot_bot_set_int ) ) @ S ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6633_remove__subset,axiom,
% 9.25/5.23      ! [X: nat,S: set_nat] :
% 9.25/5.23        ( ( member_nat @ X @ S )
% 9.25/5.23       => ( ord_less_set_nat @ ( minus_minus_set_nat @ S @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ S ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6634_vimage__insert,axiom,
% 9.25/5.23      ! [F2: nat > $o,A: $o,B2: set_o] :
% 9.25/5.23        ( ( vimage_nat_o @ F2 @ ( insert_o @ A @ B2 ) )
% 9.25/5.23        = ( sup_sup_set_nat @ ( vimage_nat_o @ F2 @ ( insert_o @ A @ bot_bot_set_o ) ) @ ( vimage_nat_o @ F2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6635_vimage__insert,axiom,
% 9.25/5.23      ! [F2: nat > nat,A: nat,B2: set_nat] :
% 9.25/5.23        ( ( vimage_nat_nat @ F2 @ ( insert_nat @ A @ B2 ) )
% 9.25/5.23        = ( sup_sup_set_nat @ ( vimage_nat_nat @ F2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ ( vimage_nat_nat @ F2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6636_vimage__insert,axiom,
% 9.25/5.23      ! [F2: nat > int,A: int,B2: set_int] :
% 9.25/5.23        ( ( vimage_nat_int @ F2 @ ( insert_int @ A @ B2 ) )
% 9.25/5.23        = ( sup_sup_set_nat @ ( vimage_nat_int @ F2 @ ( insert_int @ A @ bot_bot_set_int ) ) @ ( vimage_nat_int @ F2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6637_vimage__insert,axiom,
% 9.25/5.23      ! [F2: nat > product_prod_nat_nat,A: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( vimage8013328719654469172at_nat @ F2 @ ( insert8211810215607154385at_nat @ A @ B2 ) )
% 9.25/5.23        = ( sup_sup_set_nat @ ( vimage8013328719654469172at_nat @ F2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) @ ( vimage8013328719654469172at_nat @ F2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6638_vimage__insert,axiom,
% 9.25/5.23      ! [F2: nat > produc3843707927480180839at_nat,A: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( vimage6435164912253009178at_nat @ F2 @ ( insert9069300056098147895at_nat @ A @ B2 ) )
% 9.25/5.23        = ( sup_sup_set_nat @ ( vimage6435164912253009178at_nat @ F2 @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) @ ( vimage6435164912253009178at_nat @ F2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6639_vimage__insert,axiom,
% 9.25/5.23      ! [F2: produc4166570645942440679at_nat > $o,A: $o,B2: set_o] :
% 9.25/5.23        ( ( vimage2280073292226551852_nat_o @ F2 @ ( insert_o @ A @ B2 ) )
% 9.25/5.23        = ( sup_su3035147773818789531at_nat @ ( vimage2280073292226551852_nat_o @ F2 @ ( insert_o @ A @ bot_bot_set_o ) ) @ ( vimage2280073292226551852_nat_o @ F2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6640_vimage__insert,axiom,
% 9.25/5.23      ! [F2: produc3843707927480180839at_nat > $o,A: $o,B2: set_o] :
% 9.25/5.23        ( ( vimage3307185822755684012_nat_o @ F2 @ ( insert_o @ A @ B2 ) )
% 9.25/5.23        = ( sup_su5525570899277871387at_nat @ ( vimage3307185822755684012_nat_o @ F2 @ ( insert_o @ A @ bot_bot_set_o ) ) @ ( vimage3307185822755684012_nat_o @ F2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6641_vimage__insert,axiom,
% 9.25/5.23      ! [F2: produc4166570645942440679at_nat > nat,A: nat,B2: set_nat] :
% 9.25/5.23        ( ( vimage7952471809483217980at_nat @ F2 @ ( insert_nat @ A @ B2 ) )
% 9.25/5.23        = ( sup_su3035147773818789531at_nat @ ( vimage7952471809483217980at_nat @ F2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ ( vimage7952471809483217980at_nat @ F2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6642_vimage__insert,axiom,
% 9.25/5.23      ! [F2: produc3843707927480180839at_nat > nat,A: nat,B2: set_nat] :
% 9.25/5.23        ( ( vimage7134676753939176892at_nat @ F2 @ ( insert_nat @ A @ B2 ) )
% 9.25/5.23        = ( sup_su5525570899277871387at_nat @ ( vimage7134676753939176892at_nat @ F2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ ( vimage7134676753939176892at_nat @ F2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6643_vimage__insert,axiom,
% 9.25/5.23      ! [F2: produc4166570645942440679at_nat > int,A: int,B2: set_int] :
% 9.25/5.23        ( ( vimage7949981338974167704at_int @ F2 @ ( insert_int @ A @ B2 ) )
% 9.25/5.23        = ( sup_su3035147773818789531at_nat @ ( vimage7949981338974167704at_int @ F2 @ ( insert_int @ A @ bot_bot_set_int ) ) @ ( vimage7949981338974167704at_int @ F2 @ B2 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6644_Compl__insert,axiom,
% 9.25/5.23      ! [X: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( uminus935396558254630718at_nat @ ( insert9069300056098147895at_nat @ X @ A2 ) )
% 9.25/5.23        = ( minus_3314409938677909166at_nat @ ( uminus935396558254630718at_nat @ A2 ) @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6645_Compl__insert,axiom,
% 9.25/5.23      ! [X: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( uminus6524753893492686040at_nat @ ( insert8211810215607154385at_nat @ X @ A2 ) )
% 9.25/5.23        = ( minus_1356011639430497352at_nat @ ( uminus6524753893492686040at_nat @ A2 ) @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6646_Compl__insert,axiom,
% 9.25/5.23      ! [X: $o,A2: set_o] :
% 9.25/5.23        ( ( uminus_uminus_set_o @ ( insert_o @ X @ A2 ) )
% 9.25/5.23        = ( minus_minus_set_o @ ( uminus_uminus_set_o @ A2 ) @ ( insert_o @ X @ bot_bot_set_o ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6647_Compl__insert,axiom,
% 9.25/5.23      ! [X: int,A2: set_int] :
% 9.25/5.23        ( ( uminus1532241313380277803et_int @ ( insert_int @ X @ A2 ) )
% 9.25/5.23        = ( minus_minus_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6648_Compl__insert,axiom,
% 9.25/5.23      ! [X: nat,A2: set_nat] :
% 9.25/5.23        ( ( uminus5710092332889474511et_nat @ ( insert_nat @ X @ A2 ) )
% 9.25/5.23        = ( minus_minus_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6649_one__integer_Orsp,axiom,
% 9.25/5.23      one_one_int = one_one_int ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6650_one__natural_Orsp,axiom,
% 9.25/5.23      one_one_nat = one_one_nat ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6651_flip__bit__eq__xor,axiom,
% 9.25/5.23      ( bit_se1345352211410354436nteger
% 9.25/5.23      = ( ^ [N2: nat,A3: code_integer] : ( bit_se3222712562003087583nteger @ A3 @ ( bit_se7788150548672797655nteger @ N2 @ one_one_Code_integer ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6652_flip__bit__eq__xor,axiom,
% 9.25/5.23      ( bit_se2159334234014336723it_int
% 9.25/5.23      = ( ^ [N2: nat,A3: int] : ( bit_se6526347334894502574or_int @ A3 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6653_flip__bit__eq__xor,axiom,
% 9.25/5.23      ( bit_se2161824704523386999it_nat
% 9.25/5.23      = ( ^ [N2: nat,A3: nat] : ( bit_se6528837805403552850or_nat @ A3 @ ( bit_se547839408752420682it_nat @ N2 @ one_one_nat ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6654_psubset__insert__iff,axiom,
% 9.25/5.23      ! [A2: set_Pr4329608150637261639at_nat,X: produc3843707927480180839at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.23        ( ( ord_le2604355607129572851at_nat @ A2 @ ( insert9069300056098147895at_nat @ X @ B2 ) )
% 9.25/5.23        = ( ( ( member8757157785044589968at_nat @ X @ B2 )
% 9.25/5.23           => ( ord_le2604355607129572851at_nat @ A2 @ B2 ) )
% 9.25/5.23          & ( ~ ( member8757157785044589968at_nat @ X @ B2 )
% 9.25/5.23           => ( ( ( member8757157785044589968at_nat @ X @ A2 )
% 9.25/5.23               => ( ord_le2604355607129572851at_nat @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) @ B2 ) )
% 9.25/5.23              & ( ~ ( member8757157785044589968at_nat @ X @ A2 )
% 9.25/5.23               => ( ord_le1268244103169919719at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6655_psubset__insert__iff,axiom,
% 9.25/5.23      ! [A2: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.23        ( ( ord_le1924305788584680229nt_int @ A2 @ ( insert8897473484851387113nt_int @ X @ B2 ) )
% 9.25/5.23        = ( ( ( member2340774599025711042nt_int @ X @ B2 )
% 9.25/5.23           => ( ord_le1924305788584680229nt_int @ A2 @ B2 ) )
% 9.25/5.23          & ( ~ ( member2340774599025711042nt_int @ X @ B2 )
% 9.25/5.23           => ( ( ( member2340774599025711042nt_int @ X @ A2 )
% 9.25/5.23               => ( ord_le1924305788584680229nt_int @ ( minus_2612819937483484256nt_int @ A2 @ ( insert8897473484851387113nt_int @ X @ bot_bo1488462491386950373nt_int ) ) @ B2 ) )
% 9.25/5.23              & ( ~ ( member2340774599025711042nt_int @ X @ A2 )
% 9.25/5.23               => ( ord_le483042692224249369nt_int @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6656_psubset__insert__iff,axiom,
% 9.25/5.23      ! [A2: set_set_nat,X: set_nat,B2: set_set_nat] :
% 9.25/5.23        ( ( ord_less_set_set_nat @ A2 @ ( insert_set_nat @ X @ B2 ) )
% 9.25/5.23        = ( ( ( member_set_nat @ X @ B2 )
% 9.25/5.23           => ( ord_less_set_set_nat @ A2 @ B2 ) )
% 9.25/5.23          & ( ~ ( member_set_nat @ X @ B2 )
% 9.25/5.23           => ( ( ( member_set_nat @ X @ A2 )
% 9.25/5.23               => ( ord_less_set_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B2 ) )
% 9.25/5.23              & ( ~ ( member_set_nat @ X @ A2 )
% 9.25/5.23               => ( ord_le6893508408891458716et_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6657_psubset__insert__iff,axiom,
% 9.25/5.23      ! [A2: set_Pr4532377907799695533_nat_o,X: produc3658429121746597890et_nat > $o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.23        ( ( ord_le2453136405763929_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ X @ B2 ) )
% 9.25/5.23        = ( ( ( member6576561426505652726_nat_o @ X @ B2 )
% 9.25/5.23           => ( ord_le2453136405763929_nat_o @ A2 @ B2 ) )
% 9.25/5.23          & ( ~ ( member6576561426505652726_nat_o @ X @ B2 )
% 9.25/5.23           => ( ( ( member6576561426505652726_nat_o @ X @ A2 )
% 9.25/5.23               => ( ord_le2453136405763929_nat_o @ ( minus_1801376950450012436_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ X @ bot_bo7824918357723582233_nat_o ) ) @ B2 ) )
% 9.25/5.23              & ( ~ ( member6576561426505652726_nat_o @ X @ A2 )
% 9.25/5.23               => ( ord_le2965882846123202637_nat_o @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6658_psubset__insert__iff,axiom,
% 9.25/5.23      ! [A2: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.23        ( ( ord_le7866589430770878221at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ B2 ) )
% 9.25/5.23        = ( ( ( member8440522571783428010at_nat @ X @ B2 )
% 9.25/5.23           => ( ord_le7866589430770878221at_nat @ A2 @ B2 ) )
% 9.25/5.23          & ( ~ ( member8440522571783428010at_nat @ X @ B2 )
% 9.25/5.23           => ( ( ( member8440522571783428010at_nat @ X @ A2 )
% 9.25/5.23               => ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) @ B2 ) )
% 9.25/5.23              & ( ~ ( member8440522571783428010at_nat @ X @ A2 )
% 9.25/5.23               => ( ord_le3146513528884898305at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6659_psubset__insert__iff,axiom,
% 9.25/5.23      ! [A2: set_o,X: $o,B2: set_o] :
% 9.25/5.23        ( ( ord_less_set_o @ A2 @ ( insert_o @ X @ B2 ) )
% 9.25/5.23        = ( ( ( member_o @ X @ B2 )
% 9.25/5.23           => ( ord_less_set_o @ A2 @ B2 ) )
% 9.25/5.23          & ( ~ ( member_o @ X @ B2 )
% 9.25/5.23           => ( ( ( member_o @ X @ A2 )
% 9.25/5.23               => ( ord_less_set_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) @ B2 ) )
% 9.25/5.23              & ( ~ ( member_o @ X @ A2 )
% 9.25/5.23               => ( ord_less_eq_set_o @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6660_psubset__insert__iff,axiom,
% 9.25/5.23      ! [A2: set_int,X: int,B2: set_int] :
% 9.25/5.23        ( ( ord_less_set_int @ A2 @ ( insert_int @ X @ B2 ) )
% 9.25/5.23        = ( ( ( member_int @ X @ B2 )
% 9.25/5.23           => ( ord_less_set_int @ A2 @ B2 ) )
% 9.25/5.23          & ( ~ ( member_int @ X @ B2 )
% 9.25/5.23           => ( ( ( member_int @ X @ A2 )
% 9.25/5.23               => ( ord_less_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B2 ) )
% 9.25/5.23              & ( ~ ( member_int @ X @ A2 )
% 9.25/5.23               => ( ord_less_eq_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6661_psubset__insert__iff,axiom,
% 9.25/5.23      ! [A2: set_nat,X: nat,B2: set_nat] :
% 9.25/5.23        ( ( ord_less_set_nat @ A2 @ ( insert_nat @ X @ B2 ) )
% 9.25/5.23        = ( ( ( member_nat @ X @ B2 )
% 9.25/5.23           => ( ord_less_set_nat @ A2 @ B2 ) )
% 9.25/5.23          & ( ~ ( member_nat @ X @ B2 )
% 9.25/5.23           => ( ( ( member_nat @ X @ A2 )
% 9.25/5.23               => ( ord_less_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B2 ) )
% 9.25/5.23              & ( ~ ( member_nat @ X @ A2 )
% 9.25/5.23               => ( ord_less_eq_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6662_push__bit__double,axiom,
% 9.25/5.23      ! [N: nat,A: code_integer] :
% 9.25/5.23        ( ( bit_se7788150548672797655nteger @ N @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 9.25/5.23        = ( times_3573771949741848930nteger @ ( bit_se7788150548672797655nteger @ N @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6663_push__bit__double,axiom,
% 9.25/5.23      ! [N: nat,A: code_natural] :
% 9.25/5.23        ( ( bit_se6611745700429515170atural @ N @ ( times_2397367101498566445atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) )
% 9.25/5.23        = ( times_2397367101498566445atural @ ( bit_se6611745700429515170atural @ N @ A ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6664_push__bit__double,axiom,
% 9.25/5.23      ! [N: nat,A: int] :
% 9.25/5.23        ( ( bit_se545348938243370406it_int @ N @ ( times_times_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 9.25/5.23        = ( times_times_int @ ( bit_se545348938243370406it_int @ N @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6665_push__bit__double,axiom,
% 9.25/5.23      ! [N: nat,A: nat] :
% 9.25/5.23        ( ( bit_se547839408752420682it_nat @ N @ ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 9.25/5.23        = ( times_times_nat @ ( bit_se547839408752420682it_nat @ N @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6666_push__bit__eq__mult,axiom,
% 9.25/5.23      ( bit_se7788150548672797655nteger
% 9.25/5.23      = ( ^ [N2: nat,A3: code_integer] : ( times_3573771949741848930nteger @ A3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6667_push__bit__eq__mult,axiom,
% 9.25/5.23      ( bit_se6611745700429515170atural
% 9.25/5.23      = ( ^ [N2: nat,A3: code_natural] : ( times_2397367101498566445atural @ A3 @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6668_push__bit__eq__mult,axiom,
% 9.25/5.23      ( bit_se545348938243370406it_int
% 9.25/5.23      = ( ^ [N2: nat,A3: int] : ( times_times_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6669_push__bit__eq__mult,axiom,
% 9.25/5.23      ( bit_se547839408752420682it_nat
% 9.25/5.23      = ( ^ [N2: nat,A3: nat] : ( times_times_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6670_push__bit__minus__one,axiom,
% 9.25/5.23      ! [N: nat] :
% 9.25/5.23        ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.23        = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6671_of__int__round__le,axiom,
% 9.25/5.23      ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6672_of__int__round__ge,axiom,
% 9.25/5.23      ! [X: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6673_of__int__round__gt,axiom,
% 9.25/5.23      ! [X: rat] : ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6674_integer__of__int__code,axiom,
% 9.25/5.23      ( code_integer_of_int
% 9.25/5.23      = ( ^ [K4: int] :
% 9.25/5.23            ( if_Code_integer @ ( ord_less_int @ K4 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K4 ) ) )
% 9.25/5.23            @ ( if_Code_integer @ ( K4 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 9.25/5.23              @ ( if_Code_integer
% 9.25/5.23                @ ( ( modulo_modulo_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.23                  = zero_zero_int )
% 9.25/5.23                @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 9.25/5.23                @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6675_and__int_Opsimps,axiom,
% 9.25/5.23      ! [K: int,L: int] :
% 9.25/5.23        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 9.25/5.23       => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.25/5.23              & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.25/5.23           => ( ( bit_se725231765392027082nd_int @ K @ L )
% 9.25/5.23              = ( uminus_uminus_int
% 9.25/5.23                @ ( zero_n2684676970156552555ol_int
% 9.25/5.23                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 9.25/5.23                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 9.25/5.23          & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.25/5.23                & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.25/5.23           => ( ( bit_se725231765392027082nd_int @ K @ L )
% 9.25/5.23              = ( plus_plus_int
% 9.25/5.23                @ ( zero_n2684676970156552555ol_int
% 9.25/5.23                  @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 9.25/5.23                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 9.25/5.23                @ ( 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 ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6676_and__int_Opelims,axiom,
% 9.25/5.23      ! [X: int,Xa: int,Y: int] :
% 9.25/5.23        ( ( ( bit_se725231765392027082nd_int @ X @ Xa )
% 9.25/5.23          = Y )
% 9.25/5.23       => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) )
% 9.25/5.23         => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.25/5.23                    & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.25/5.23                 => ( Y
% 9.25/5.23                    = ( uminus_uminus_int
% 9.25/5.23                      @ ( zero_n2684676970156552555ol_int
% 9.25/5.23                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 9.25/5.23                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 9.25/5.23                & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.25/5.23                      & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.25/5.23                 => ( Y
% 9.25/5.23                    = ( plus_plus_int
% 9.25/5.23                      @ ( zero_n2684676970156552555ol_int
% 9.25/5.23                        @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 9.25/5.23                          & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 9.25/5.23                      @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 9.25/5.23             => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6677_neg__numeral__le__ceiling,axiom,
% 9.25/5.23      ! [V: num,X: rat] :
% 9.25/5.23        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 9.25/5.23        = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6678_ceiling__less__neg__numeral,axiom,
% 9.25/5.23      ! [X: rat,V: num] :
% 9.25/5.23        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.25/5.23        = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6679_floor__le__neg__numeral,axiom,
% 9.25/5.23      ! [X: rat,V: num] :
% 9.25/5.23        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.25/5.23        = ( ord_less_rat @ X @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6680_neg__numeral__less__floor,axiom,
% 9.25/5.23      ! [V: num,X: rat] :
% 9.25/5.23        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 9.25/5.23        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6681_floor__one,axiom,
% 9.25/5.23      ( ( archim3151403230148437115or_rat @ one_one_rat )
% 9.25/5.23      = one_one_int ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6682_ceiling__one,axiom,
% 9.25/5.23      ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 9.25/5.23      = one_one_int ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6683_floor__uminus__of__int,axiom,
% 9.25/5.23      ! [Z: int] :
% 9.25/5.23        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ Z ) ) )
% 9.25/5.23        = ( uminus_uminus_int @ Z ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6684_zero__less__floor,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23        ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 9.25/5.23        = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6685_floor__le__zero,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 9.25/5.23        = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6686_one__le__floor,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23        ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 9.25/5.23        = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6687_ceiling__less__one,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 9.25/5.23        = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6688_one__le__ceiling,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23        ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 9.25/5.23        = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6689_floor__less__one,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 9.25/5.23        = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6690_ceiling__le__one,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 9.25/5.23        = ( ord_less_eq_rat @ X @ one_one_rat ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6691_one__less__ceiling,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23        ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 9.25/5.23        = ( ord_less_rat @ one_one_rat @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6692_floor__neg__numeral,axiom,
% 9.25/5.23      ! [V: num] :
% 9.25/5.23        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 9.25/5.23        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6693_ceiling__neg__numeral,axiom,
% 9.25/5.23      ! [V: num] :
% 9.25/5.23        ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 9.25/5.23        = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6694_ceiling__add__one,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23        ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 9.25/5.23        = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6695_floor__diff__one,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23        ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 9.25/5.23        = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6696_ceiling__diff__one,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23        ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X @ one_one_rat ) )
% 9.25/5.23        = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6697_ceiling__less__zero,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 9.25/5.23        = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6698_zero__le__ceiling,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23        ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 9.25/5.23        = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6699_numeral__less__floor,axiom,
% 9.25/5.23      ! [V: num,X: rat] :
% 9.25/5.23        ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 9.25/5.23        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6700_floor__le__numeral,axiom,
% 9.25/5.23      ! [X: rat,V: num] :
% 9.25/5.23        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 9.25/5.23        = ( ord_less_rat @ X @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6701_ceiling__less__numeral,axiom,
% 9.25/5.23      ! [X: rat,V: num] :
% 9.25/5.23        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 9.25/5.23        = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6702_numeral__le__ceiling,axiom,
% 9.25/5.23      ! [V: num,X: rat] :
% 9.25/5.23        ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 9.25/5.23        = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6703_one__less__floor,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23        ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 9.25/5.23        = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6704_floor__le__one,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 9.25/5.23        = ( ord_less_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6705_neg__numeral__le__floor,axiom,
% 9.25/5.23      ! [V: num,X: rat] :
% 9.25/5.23        ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 9.25/5.23        = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6706_floor__less__neg__numeral,axiom,
% 9.25/5.23      ! [X: rat,V: num] :
% 9.25/5.23        ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.25/5.23        = ( ord_less_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6707_ceiling__le__neg__numeral,axiom,
% 9.25/5.23      ! [X: rat,V: num] :
% 9.25/5.23        ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 9.25/5.23        = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6708_neg__numeral__less__ceiling,axiom,
% 9.25/5.23      ! [V: num,X: rat] :
% 9.25/5.23        ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 9.25/5.23        = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6709_integer__of__int__cases,axiom,
% 9.25/5.23      ! [X: code_integer] :
% 9.25/5.23        ~ ! [Y2: int] :
% 9.25/5.23            ( ( X
% 9.25/5.23              = ( code_integer_of_int @ Y2 ) )
% 9.25/5.23           => ~ ( member_int @ Y2 @ top_top_set_int ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6710_integer__of__int__induct,axiom,
% 9.25/5.23      ! [P: code_integer > $o,X: code_integer] :
% 9.25/5.23        ( ! [Y2: int] :
% 9.25/5.23            ( ( member_int @ Y2 @ top_top_set_int )
% 9.25/5.23           => ( P @ ( code_integer_of_int @ Y2 ) ) )
% 9.25/5.23       => ( P @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6711_integer__of__int__inject,axiom,
% 9.25/5.23      ! [X: int,Y: int] :
% 9.25/5.23        ( ( member_int @ X @ top_top_set_int )
% 9.25/5.23       => ( ( member_int @ Y @ top_top_set_int )
% 9.25/5.23         => ( ( ( code_integer_of_int @ X )
% 9.25/5.23              = ( code_integer_of_int @ Y ) )
% 9.25/5.23            = ( X = Y ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6712_uminus__integer__code_I1_J,axiom,
% 9.25/5.23      ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 9.25/5.23      = zero_z3403309356797280102nteger ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6713_ceiling__def,axiom,
% 9.25/5.23      ( archim2889992004027027881ng_rat
% 9.25/5.23      = ( ^ [X3: rat] : ( uminus_uminus_int @ ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ X3 ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6714_floor__minus,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23        ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ X ) )
% 9.25/5.23        = ( uminus_uminus_int @ ( archim2889992004027027881ng_rat @ X ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6715_ceiling__minus,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23        ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ X ) )
% 9.25/5.23        = ( uminus_uminus_int @ ( archim3151403230148437115or_rat @ X ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6716_uminus__integer_Oabs__eq,axiom,
% 9.25/5.23      ! [X: int] :
% 9.25/5.23        ( ( uminus1351360451143612070nteger @ ( code_integer_of_int @ X ) )
% 9.25/5.23        = ( code_integer_of_int @ ( uminus_uminus_int @ X ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6717_ceiling__diff__floor__le__1,axiom,
% 9.25/5.23      ! [X: rat] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim3151403230148437115or_rat @ X ) ) @ one_one_int ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6718_ceiling__altdef,axiom,
% 9.25/5.23      ( archim2889992004027027881ng_rat
% 9.25/5.23      = ( ^ [X3: rat] :
% 9.25/5.23            ( if_int
% 9.25/5.23            @ ( X3
% 9.25/5.23              = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X3 ) ) )
% 9.25/5.23            @ ( archim3151403230148437115or_rat @ X3 )
% 9.25/5.23            @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X3 ) @ one_one_int ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6719_one__integer__def,axiom,
% 9.25/5.23      ( one_one_Code_integer
% 9.25/5.23      = ( code_integer_of_int @ one_one_int ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6720_one__add__floor,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23        ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 9.25/5.23        = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ one_one_rat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6721_floor__unique,axiom,
% 9.25/5.23      ! [Z: int,X: rat] :
% 9.25/5.23        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X )
% 9.25/5.23       => ( ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 9.25/5.23         => ( ( archim3151403230148437115or_rat @ X )
% 9.25/5.23            = Z ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6722_floor__eq__iff,axiom,
% 9.25/5.23      ! [X: rat,A: int] :
% 9.25/5.23        ( ( ( archim3151403230148437115or_rat @ X )
% 9.25/5.23          = A )
% 9.25/5.23        = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X )
% 9.25/5.23          & ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6723_floor__split,axiom,
% 9.25/5.23      ! [P: int > $o,T3: rat] :
% 9.25/5.23        ( ( P @ ( archim3151403230148437115or_rat @ T3 ) )
% 9.25/5.23        = ( ! [I3: int] :
% 9.25/5.23              ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I3 ) @ T3 )
% 9.25/5.23                & ( ord_less_rat @ T3 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I3 ) @ one_one_rat ) ) )
% 9.25/5.23             => ( P @ I3 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6724_le__mult__floor,axiom,
% 9.25/5.23      ! [A: rat,B: rat] :
% 9.25/5.23        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.23       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.25/5.23         => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6725_less__floor__iff,axiom,
% 9.25/5.23      ! [Z: int,X: rat] :
% 9.25/5.23        ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 9.25/5.23        = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6726_floor__le__iff,axiom,
% 9.25/5.23      ! [X: rat,Z: int] :
% 9.25/5.23        ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 9.25/5.23        = ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6727_floor__correct,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) @ X )
% 9.25/5.23        & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6728_ceiling__correct,axiom,
% 9.25/5.23      ! [X: rat] :
% 9.25/5.23        ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) @ one_one_rat ) @ X )
% 9.25/5.23        & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6729_ceiling__unique,axiom,
% 9.25/5.23      ! [Z: int,X: rat] :
% 9.25/5.23        ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X )
% 9.25/5.23       => ( ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z ) )
% 9.25/5.23         => ( ( archim2889992004027027881ng_rat @ X )
% 9.25/5.23            = Z ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6730_ceiling__eq__iff,axiom,
% 9.25/5.23      ! [X: rat,A: int] :
% 9.25/5.23        ( ( ( archim2889992004027027881ng_rat @ X )
% 9.25/5.23          = A )
% 9.25/5.23        = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X )
% 9.25/5.23          & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6731_ceiling__split,axiom,
% 9.25/5.23      ! [P: int > $o,T3: rat] :
% 9.25/5.23        ( ( P @ ( archim2889992004027027881ng_rat @ T3 ) )
% 9.25/5.23        = ( ! [I3: int] :
% 9.25/5.23              ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I3 ) @ one_one_rat ) @ T3 )
% 9.25/5.23                & ( ord_less_eq_rat @ T3 @ ( ring_1_of_int_rat @ I3 ) ) )
% 9.25/5.23             => ( P @ I3 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6732_mult__ceiling__le,axiom,
% 9.25/5.23      ! [A: rat,B: rat] :
% 9.25/5.23        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.23       => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.25/5.23         => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6733_ceiling__less__iff,axiom,
% 9.25/5.23      ! [X: rat,Z: int] :
% 9.25/5.23        ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ Z )
% 9.25/5.23        = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6734_le__ceiling__iff,axiom,
% 9.25/5.23      ! [Z: int,X: rat] :
% 9.25/5.23        ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X ) )
% 9.25/5.23        = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6735_floor__divide__lower,axiom,
% 9.25/5.23      ! [Q4: rat,P4: rat] :
% 9.25/5.23        ( ( ord_less_rat @ zero_zero_rat @ Q4 )
% 9.25/5.23       => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P4 @ Q4 ) ) ) @ Q4 ) @ P4 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6736_ceiling__divide__upper,axiom,
% 9.25/5.23      ! [Q4: rat,P4: rat] :
% 9.25/5.23        ( ( ord_less_rat @ zero_zero_rat @ Q4 )
% 9.25/5.23       => ( ord_less_eq_rat @ P4 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P4 @ Q4 ) ) ) @ Q4 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6737_floor__divide__upper,axiom,
% 9.25/5.23      ! [Q4: rat,P4: rat] :
% 9.25/5.23        ( ( ord_less_rat @ zero_zero_rat @ Q4 )
% 9.25/5.23       => ( ord_less_rat @ P4 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P4 @ Q4 ) ) ) @ one_one_rat ) @ Q4 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6738_round__def,axiom,
% 9.25/5.23      ( archim7778729529865785530nd_rat
% 9.25/5.23      = ( ^ [X3: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6739_ceiling__divide__lower,axiom,
% 9.25/5.23      ! [Q4: rat,P4: rat] :
% 9.25/5.23        ( ( ord_less_rat @ zero_zero_rat @ Q4 )
% 9.25/5.23       => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P4 @ Q4 ) ) ) @ one_one_rat ) @ Q4 ) @ P4 ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6740_and__int_Opinduct,axiom,
% 9.25/5.23      ! [A0: int,A1: int,P: int > int > $o] :
% 9.25/5.23        ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 9.25/5.23       => ( ! [K2: int,L3: int] :
% 9.25/5.23              ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L3 ) )
% 9.25/5.23             => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 9.25/5.23                      & ( member_int @ L3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 9.25/5.23                 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 9.25/5.23               => ( P @ K2 @ L3 ) ) )
% 9.25/5.23         => ( P @ A0 @ A1 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6741_upto_Opinduct,axiom,
% 9.25/5.23      ! [A0: int,A1: int,P: int > int > $o] :
% 9.25/5.23        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 9.25/5.23       => ( ! [I2: int,J2: int] :
% 9.25/5.23              ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J2 ) )
% 9.25/5.23             => ( ( ( ord_less_eq_int @ I2 @ J2 )
% 9.25/5.23                 => ( P @ ( plus_plus_int @ I2 @ one_one_int ) @ J2 ) )
% 9.25/5.23               => ( P @ I2 @ J2 ) ) )
% 9.25/5.23         => ( P @ A0 @ A1 ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6742_round__altdef,axiom,
% 9.25/5.23      ( archim7778729529865785530nd_rat
% 9.25/5.23      = ( ^ [X3: rat] : ( if_int @ ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( archimedean_frac_rat @ X3 ) ) @ ( archim2889992004027027881ng_rat @ X3 ) @ ( archim3151403230148437115or_rat @ X3 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6743_the__elem__eq,axiom,
% 9.25/5.23      ! [X: produc3843707927480180839at_nat] :
% 9.25/5.23        ( ( the_el221668144340439132at_nat @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) )
% 9.25/5.23        = X ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6744_the__elem__eq,axiom,
% 9.25/5.23      ! [X: product_prod_nat_nat] :
% 9.25/5.23        ( ( the_el2281957884133575798at_nat @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) )
% 9.25/5.23        = X ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6745_the__elem__eq,axiom,
% 9.25/5.23      ! [X: $o] :
% 9.25/5.23        ( ( the_elem_o @ ( insert_o @ X @ bot_bot_set_o ) )
% 9.25/5.23        = X ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6746_the__elem__eq,axiom,
% 9.25/5.23      ! [X: nat] :
% 9.25/5.23        ( ( the_elem_nat @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 9.25/5.23        = X ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6747_the__elem__eq,axiom,
% 9.25/5.23      ! [X: int] :
% 9.25/5.23        ( ( the_elem_int @ ( insert_int @ X @ bot_bot_set_int ) )
% 9.25/5.23        = X ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6748_round__unique_H,axiom,
% 9.25/5.23      ! [X: rat,N: int] :
% 9.25/5.23        ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ N ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 9.25/5.23       => ( ( archim7778729529865785530nd_rat @ X )
% 9.25/5.23          = N ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6749_of__int__round__abs__le,axiom,
% 9.25/5.23      ! [X: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ X ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6750_num__of__integer__code,axiom,
% 9.25/5.23      ( code_num_of_integer
% 9.25/5.23      = ( ^ [K4: code_integer] :
% 9.25/5.23            ( if_num @ ( ord_le3102999989581377725nteger @ K4 @ one_one_Code_integer ) @ one
% 9.25/5.23            @ ( produc7336495610019696514er_num
% 9.25/5.23              @ ^ [L2: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ one ) )
% 9.25/5.23              @ ( code_divmod_integer @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6751_bit__cut__integer__def,axiom,
% 9.25/5.23      ( code_bit_cut_integer
% 9.25/5.23      = ( ^ [K4: code_integer] :
% 9.25/5.23            ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.23            @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K4 ) ) ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6752_abs__idempotent,axiom,
% 9.25/5.23      ! [A: int] :
% 9.25/5.23        ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 9.25/5.23        = ( abs_abs_int @ A ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6753_abs__idempotent,axiom,
% 9.25/5.23      ! [A: code_integer] :
% 9.25/5.23        ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 9.25/5.23        = ( abs_abs_Code_integer @ A ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6754_abs__idempotent,axiom,
% 9.25/5.23      ! [A: rat] :
% 9.25/5.23        ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 9.25/5.23        = ( abs_abs_rat @ A ) ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6755_abs__zero,axiom,
% 9.25/5.23      ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 9.25/5.23      = zero_z3403309356797280102nteger ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6756_abs__zero,axiom,
% 9.25/5.23      ( ( abs_abs_rat @ zero_zero_rat )
% 9.25/5.23      = zero_zero_rat ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6757_abs__zero,axiom,
% 9.25/5.23      ( ( abs_abs_int @ zero_zero_int )
% 9.25/5.23      = zero_zero_int ) ).
% 9.25/5.23  
% 9.25/5.23  thf(fact_6758_abs__eq__0,axiom,
% 9.25/5.23      ! [A: code_integer] :
% 9.25/5.24        ( ( ( abs_abs_Code_integer @ A )
% 9.25/5.24          = zero_z3403309356797280102nteger )
% 9.25/5.24        = ( A = zero_z3403309356797280102nteger ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6759_abs__eq__0,axiom,
% 9.25/5.24      ! [A: rat] :
% 9.25/5.24        ( ( ( abs_abs_rat @ A )
% 9.25/5.24          = zero_zero_rat )
% 9.25/5.24        = ( A = zero_zero_rat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6760_abs__eq__0,axiom,
% 9.25/5.24      ! [A: int] :
% 9.25/5.24        ( ( ( abs_abs_int @ A )
% 9.25/5.24          = zero_zero_int )
% 9.25/5.24        = ( A = zero_zero_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6761_abs__0__eq,axiom,
% 9.25/5.24      ! [A: code_integer] :
% 9.25/5.24        ( ( zero_z3403309356797280102nteger
% 9.25/5.24          = ( abs_abs_Code_integer @ A ) )
% 9.25/5.24        = ( A = zero_z3403309356797280102nteger ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6762_abs__0__eq,axiom,
% 9.25/5.24      ! [A: rat] :
% 9.25/5.24        ( ( zero_zero_rat
% 9.25/5.24          = ( abs_abs_rat @ A ) )
% 9.25/5.24        = ( A = zero_zero_rat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6763_abs__0__eq,axiom,
% 9.25/5.24      ! [A: int] :
% 9.25/5.24        ( ( zero_zero_int
% 9.25/5.24          = ( abs_abs_int @ A ) )
% 9.25/5.24        = ( A = zero_zero_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6764_abs__add__abs,axiom,
% 9.25/5.24      ! [A: code_integer,B: code_integer] :
% 9.25/5.24        ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 9.25/5.24        = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6765_abs__add__abs,axiom,
% 9.25/5.24      ! [A: rat,B: rat] :
% 9.25/5.24        ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 9.25/5.24        = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6766_abs__add__abs,axiom,
% 9.25/5.24      ! [A: int,B: int] :
% 9.25/5.24        ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 9.25/5.24        = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6767_abs__mult__self__eq,axiom,
% 9.25/5.24      ! [A: code_integer] :
% 9.25/5.24        ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 9.25/5.24        = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6768_abs__mult__self__eq,axiom,
% 9.25/5.24      ! [A: rat] :
% 9.25/5.24        ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 9.25/5.24        = ( times_times_rat @ A @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6769_abs__mult__self__eq,axiom,
% 9.25/5.24      ! [A: int] :
% 9.25/5.24        ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 9.25/5.24        = ( times_times_int @ A @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6770_abs__1,axiom,
% 9.25/5.24      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 9.25/5.24      = one_one_Code_integer ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6771_abs__1,axiom,
% 9.25/5.24      ( ( abs_abs_rat @ one_one_rat )
% 9.25/5.24      = one_one_rat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6772_abs__1,axiom,
% 9.25/5.24      ( ( abs_abs_int @ one_one_int )
% 9.25/5.24      = one_one_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6773_abs__minus,axiom,
% 9.25/5.24      ! [A: int] :
% 9.25/5.24        ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 9.25/5.24        = ( abs_abs_int @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6774_abs__minus,axiom,
% 9.25/5.24      ! [A: code_integer] :
% 9.25/5.24        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 9.25/5.24        = ( abs_abs_Code_integer @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6775_abs__minus,axiom,
% 9.25/5.24      ! [A: rat] :
% 9.25/5.24        ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 9.25/5.24        = ( abs_abs_rat @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6776_abs__minus__cancel,axiom,
% 9.25/5.24      ! [A: int] :
% 9.25/5.24        ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 9.25/5.24        = ( abs_abs_int @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6777_abs__minus__cancel,axiom,
% 9.25/5.24      ! [A: code_integer] :
% 9.25/5.24        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 9.25/5.24        = ( abs_abs_Code_integer @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6778_abs__minus__cancel,axiom,
% 9.25/5.24      ! [A: rat] :
% 9.25/5.24        ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 9.25/5.24        = ( abs_abs_rat @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6779_zdvd1__eq,axiom,
% 9.25/5.24      ! [X: int] :
% 9.25/5.24        ( ( dvd_dvd_int @ X @ one_one_int )
% 9.25/5.24        = ( ( abs_abs_int @ X )
% 9.25/5.24          = one_one_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6780_abs__le__zero__iff,axiom,
% 9.25/5.24      ! [A: code_integer] :
% 9.25/5.24        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 9.25/5.24        = ( A = zero_z3403309356797280102nteger ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6781_abs__le__zero__iff,axiom,
% 9.25/5.24      ! [A: rat] :
% 9.25/5.24        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 9.25/5.24        = ( A = zero_zero_rat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6782_abs__le__zero__iff,axiom,
% 9.25/5.24      ! [A: int] :
% 9.25/5.24        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 9.25/5.24        = ( A = zero_zero_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6783_abs__le__self__iff,axiom,
% 9.25/5.24      ! [A: code_integer] :
% 9.25/5.24        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 9.25/5.24        = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6784_abs__le__self__iff,axiom,
% 9.25/5.24      ! [A: rat] :
% 9.25/5.24        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 9.25/5.24        = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6785_abs__le__self__iff,axiom,
% 9.25/5.24      ! [A: int] :
% 9.25/5.24        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 9.25/5.24        = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6786_abs__of__nonneg,axiom,
% 9.25/5.24      ! [A: code_integer] :
% 9.25/5.24        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.24       => ( ( abs_abs_Code_integer @ A )
% 9.25/5.24          = A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6787_abs__of__nonneg,axiom,
% 9.25/5.24      ! [A: rat] :
% 9.25/5.24        ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.24       => ( ( abs_abs_rat @ A )
% 9.25/5.24          = A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6788_abs__of__nonneg,axiom,
% 9.25/5.24      ! [A: int] :
% 9.25/5.24        ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.24       => ( ( abs_abs_int @ A )
% 9.25/5.24          = A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6789_zero__less__abs__iff,axiom,
% 9.25/5.24      ! [A: code_integer] :
% 9.25/5.24        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 9.25/5.24        = ( A != zero_z3403309356797280102nteger ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6790_zero__less__abs__iff,axiom,
% 9.25/5.24      ! [A: rat] :
% 9.25/5.24        ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 9.25/5.24        = ( A != zero_zero_rat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6791_zero__less__abs__iff,axiom,
% 9.25/5.24      ! [A: int] :
% 9.25/5.24        ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 9.25/5.24        = ( A != zero_zero_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6792_abs__neg__numeral,axiom,
% 9.25/5.24      ! [N: num] :
% 9.25/5.24        ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.24        = ( numeral_numeral_int @ N ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6793_abs__neg__numeral,axiom,
% 9.25/5.24      ! [N: num] :
% 9.25/5.24        ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.25/5.24        = ( numera6620942414471956472nteger @ N ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6794_abs__neg__numeral,axiom,
% 9.25/5.24      ! [N: num] :
% 9.25/5.24        ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 9.25/5.24        = ( numeral_numeral_rat @ N ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6795_abs__neg__one,axiom,
% 9.25/5.24      ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.24      = one_one_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6796_abs__neg__one,axiom,
% 9.25/5.24      ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.24      = one_one_Code_integer ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6797_abs__neg__one,axiom,
% 9.25/5.24      ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.25/5.24      = one_one_rat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6798_abs__power__minus,axiom,
% 9.25/5.24      ! [A: int,N: nat] :
% 9.25/5.24        ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 9.25/5.24        = ( abs_abs_int @ ( power_power_int @ A @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6799_abs__power__minus,axiom,
% 9.25/5.24      ! [A: code_integer,N: nat] :
% 9.25/5.24        ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 9.25/5.24        = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6800_abs__power__minus,axiom,
% 9.25/5.24      ! [A: rat,N: nat] :
% 9.25/5.24        ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 9.25/5.24        = ( abs_abs_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6801_zabs__less__one__iff,axiom,
% 9.25/5.24      ! [Z: int] :
% 9.25/5.24        ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 9.25/5.24        = ( Z = zero_zero_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6802_abs__of__nonpos,axiom,
% 9.25/5.24      ! [A: code_integer] :
% 9.25/5.24        ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.24       => ( ( abs_abs_Code_integer @ A )
% 9.25/5.24          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6803_abs__of__nonpos,axiom,
% 9.25/5.24      ! [A: rat] :
% 9.25/5.24        ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 9.25/5.24       => ( ( abs_abs_rat @ A )
% 9.25/5.24          = ( uminus_uminus_rat @ A ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6804_abs__of__nonpos,axiom,
% 9.25/5.24      ! [A: int] :
% 9.25/5.24        ( ( ord_less_eq_int @ A @ zero_zero_int )
% 9.25/5.24       => ( ( abs_abs_int @ A )
% 9.25/5.24          = ( uminus_uminus_int @ A ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6805_abs__ge__self,axiom,
% 9.25/5.24      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6806_abs__ge__self,axiom,
% 9.25/5.24      ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6807_abs__ge__self,axiom,
% 9.25/5.24      ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6808_abs__le__D1,axiom,
% 9.25/5.24      ! [A: code_integer,B: code_integer] :
% 9.25/5.24        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 9.25/5.24       => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6809_abs__le__D1,axiom,
% 9.25/5.24      ! [A: rat,B: rat] :
% 9.25/5.24        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 9.25/5.24       => ( ord_less_eq_rat @ A @ B ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6810_abs__le__D1,axiom,
% 9.25/5.24      ! [A: int,B: int] :
% 9.25/5.24        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 9.25/5.24       => ( ord_less_eq_int @ A @ B ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6811_abs__mult,axiom,
% 9.25/5.24      ! [A: code_integer,B: code_integer] :
% 9.25/5.24        ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 9.25/5.24        = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6812_abs__mult,axiom,
% 9.25/5.24      ! [A: rat,B: rat] :
% 9.25/5.24        ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 9.25/5.24        = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6813_abs__mult,axiom,
% 9.25/5.24      ! [A: int,B: int] :
% 9.25/5.24        ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 9.25/5.24        = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6814_abs__one,axiom,
% 9.25/5.24      ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 9.25/5.24      = one_one_Code_integer ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6815_abs__one,axiom,
% 9.25/5.24      ( ( abs_abs_rat @ one_one_rat )
% 9.25/5.24      = one_one_rat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6816_abs__one,axiom,
% 9.25/5.24      ( ( abs_abs_int @ one_one_int )
% 9.25/5.24      = one_one_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6817_abs__minus__commute,axiom,
% 9.25/5.24      ! [A: code_integer,B: code_integer] :
% 9.25/5.24        ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 9.25/5.24        = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6818_abs__minus__commute,axiom,
% 9.25/5.24      ! [A: rat,B: rat] :
% 9.25/5.24        ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 9.25/5.24        = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6819_abs__minus__commute,axiom,
% 9.25/5.24      ! [A: int,B: int] :
% 9.25/5.24        ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 9.25/5.24        = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6820_abs__eq__iff,axiom,
% 9.25/5.24      ! [X: int,Y: int] :
% 9.25/5.24        ( ( ( abs_abs_int @ X )
% 9.25/5.24          = ( abs_abs_int @ Y ) )
% 9.25/5.24        = ( ( X = Y )
% 9.25/5.24          | ( X
% 9.25/5.24            = ( uminus_uminus_int @ Y ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6821_abs__eq__iff,axiom,
% 9.25/5.24      ! [X: code_integer,Y: code_integer] :
% 9.25/5.24        ( ( ( abs_abs_Code_integer @ X )
% 9.25/5.24          = ( abs_abs_Code_integer @ Y ) )
% 9.25/5.24        = ( ( X = Y )
% 9.25/5.24          | ( X
% 9.25/5.24            = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6822_abs__eq__iff,axiom,
% 9.25/5.24      ! [X: rat,Y: rat] :
% 9.25/5.24        ( ( ( abs_abs_rat @ X )
% 9.25/5.24          = ( abs_abs_rat @ Y ) )
% 9.25/5.24        = ( ( X = Y )
% 9.25/5.24          | ( X
% 9.25/5.24            = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6823_abs__ge__zero,axiom,
% 9.25/5.24      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6824_abs__ge__zero,axiom,
% 9.25/5.24      ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6825_abs__ge__zero,axiom,
% 9.25/5.24      ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6826_abs__of__pos,axiom,
% 9.25/5.24      ! [A: code_integer] :
% 9.25/5.24        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.24       => ( ( abs_abs_Code_integer @ A )
% 9.25/5.24          = A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6827_abs__of__pos,axiom,
% 9.25/5.24      ! [A: rat] :
% 9.25/5.24        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.24       => ( ( abs_abs_rat @ A )
% 9.25/5.24          = A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6828_abs__of__pos,axiom,
% 9.25/5.24      ! [A: int] :
% 9.25/5.24        ( ( ord_less_int @ zero_zero_int @ A )
% 9.25/5.24       => ( ( abs_abs_int @ A )
% 9.25/5.24          = A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6829_abs__not__less__zero,axiom,
% 9.25/5.24      ! [A: code_integer] :
% 9.25/5.24        ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6830_abs__not__less__zero,axiom,
% 9.25/5.24      ! [A: rat] :
% 9.25/5.24        ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6831_abs__not__less__zero,axiom,
% 9.25/5.24      ! [A: int] :
% 9.25/5.24        ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6832_abs__triangle__ineq,axiom,
% 9.25/5.24      ! [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 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6833_abs__triangle__ineq,axiom,
% 9.25/5.24      ! [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 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6834_abs__triangle__ineq,axiom,
% 9.25/5.24      ! [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 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6835_abs__triangle__ineq2__sym,axiom,
% 9.25/5.24      ! [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 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6836_abs__triangle__ineq2__sym,axiom,
% 9.25/5.24      ! [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 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6837_abs__triangle__ineq2__sym,axiom,
% 9.25/5.24      ! [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 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6838_abs__triangle__ineq3,axiom,
% 9.25/5.24      ! [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 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6839_abs__triangle__ineq3,axiom,
% 9.25/5.24      ! [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 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6840_abs__triangle__ineq3,axiom,
% 9.25/5.24      ! [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 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6841_abs__triangle__ineq2,axiom,
% 9.25/5.24      ! [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 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6842_abs__triangle__ineq2,axiom,
% 9.25/5.24      ! [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 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6843_abs__triangle__ineq2,axiom,
% 9.25/5.24      ! [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 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6844_abs__mult__less,axiom,
% 9.25/5.24      ! [A: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 9.25/5.24        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 9.25/5.24       => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D2 )
% 9.25/5.24         => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6845_abs__mult__less,axiom,
% 9.25/5.24      ! [A: rat,C: rat,B: rat,D2: rat] :
% 9.25/5.24        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 9.25/5.24       => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D2 )
% 9.25/5.24         => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6846_abs__mult__less,axiom,
% 9.25/5.24      ! [A: int,C: int,B: int,D2: int] :
% 9.25/5.24        ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 9.25/5.24       => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D2 )
% 9.25/5.24         => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6847_abs__ge__minus__self,axiom,
% 9.25/5.24      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6848_abs__ge__minus__self,axiom,
% 9.25/5.24      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6849_abs__ge__minus__self,axiom,
% 9.25/5.24      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6850_abs__le__iff,axiom,
% 9.25/5.24      ! [A: code_integer,B: code_integer] :
% 9.25/5.24        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 9.25/5.24        = ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.25/5.24          & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6851_abs__le__iff,axiom,
% 9.25/5.24      ! [A: rat,B: rat] :
% 9.25/5.24        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 9.25/5.24        = ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.24          & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6852_abs__le__iff,axiom,
% 9.25/5.24      ! [A: int,B: int] :
% 9.25/5.24        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 9.25/5.24        = ( ( ord_less_eq_int @ A @ B )
% 9.25/5.24          & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6853_abs__le__D2,axiom,
% 9.25/5.24      ! [A: code_integer,B: code_integer] :
% 9.25/5.24        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 9.25/5.24       => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6854_abs__le__D2,axiom,
% 9.25/5.24      ! [A: rat,B: rat] :
% 9.25/5.24        ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 9.25/5.24       => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6855_abs__le__D2,axiom,
% 9.25/5.24      ! [A: int,B: int] :
% 9.25/5.24        ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 9.25/5.24       => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6856_abs__leI,axiom,
% 9.25/5.24      ! [A: code_integer,B: code_integer] :
% 9.25/5.24        ( ( ord_le3102999989581377725nteger @ A @ B )
% 9.25/5.24       => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 9.25/5.24         => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6857_abs__leI,axiom,
% 9.25/5.24      ! [A: rat,B: rat] :
% 9.25/5.24        ( ( ord_less_eq_rat @ A @ B )
% 9.25/5.24       => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 9.25/5.24         => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6858_abs__leI,axiom,
% 9.25/5.24      ! [A: int,B: int] :
% 9.25/5.24        ( ( ord_less_eq_int @ A @ B )
% 9.25/5.24       => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 9.25/5.24         => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6859_abs__less__iff,axiom,
% 9.25/5.24      ! [A: int,B: int] :
% 9.25/5.24        ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 9.25/5.24        = ( ( ord_less_int @ A @ B )
% 9.25/5.24          & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6860_abs__less__iff,axiom,
% 9.25/5.24      ! [A: code_integer,B: code_integer] :
% 9.25/5.24        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 9.25/5.24        = ( ( ord_le6747313008572928689nteger @ A @ B )
% 9.25/5.24          & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6861_abs__less__iff,axiom,
% 9.25/5.24      ! [A: rat,B: rat] :
% 9.25/5.24        ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 9.25/5.24        = ( ( ord_less_rat @ A @ B )
% 9.25/5.24          & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6862_abs__zmult__eq__1,axiom,
% 9.25/5.24      ! [M: int,N: int] :
% 9.25/5.24        ( ( ( abs_abs_int @ ( times_times_int @ M @ N ) )
% 9.25/5.24          = one_one_int )
% 9.25/5.24       => ( ( abs_abs_int @ M )
% 9.25/5.24          = one_one_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6863_frac__lt__1,axiom,
% 9.25/5.24      ! [X: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X ) @ one_one_rat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6864_frac__1__eq,axiom,
% 9.25/5.24      ! [X: rat] :
% 9.25/5.24        ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ one_one_rat ) )
% 9.25/5.24        = ( archimedean_frac_rat @ X ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6865_dense__eq0__I,axiom,
% 9.25/5.24      ! [X: rat] :
% 9.25/5.24        ( ! [E3: rat] :
% 9.25/5.24            ( ( ord_less_rat @ zero_zero_rat @ E3 )
% 9.25/5.24           => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E3 ) )
% 9.25/5.24       => ( X = zero_zero_rat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6866_abs__eq__mult,axiom,
% 9.25/5.24      ! [A: code_integer,B: code_integer] :
% 9.25/5.24        ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.24            | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 9.25/5.24          & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 9.25/5.24            | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 9.25/5.24       => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 9.25/5.24          = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6867_abs__eq__mult,axiom,
% 9.25/5.24      ! [A: rat,B: rat] :
% 9.25/5.24        ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.24            | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 9.25/5.24          & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.25/5.24            | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 9.25/5.24       => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 9.25/5.24          = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6868_abs__eq__mult,axiom,
% 9.25/5.24      ! [A: int,B: int] :
% 9.25/5.24        ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.24            | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 9.25/5.24          & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.25/5.24            | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 9.25/5.24       => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 9.25/5.24          = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6869_abs__mult__pos,axiom,
% 9.25/5.24      ! [X: code_integer,Y: code_integer] :
% 9.25/5.24        ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 9.25/5.24       => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X )
% 9.25/5.24          = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6870_abs__mult__pos,axiom,
% 9.25/5.24      ! [X: rat,Y: rat] :
% 9.25/5.24        ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.25/5.24       => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X )
% 9.25/5.24          = ( abs_abs_rat @ ( times_times_rat @ Y @ X ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6871_abs__mult__pos,axiom,
% 9.25/5.24      ! [X: int,Y: int] :
% 9.25/5.24        ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.25/5.24       => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X )
% 9.25/5.24          = ( abs_abs_int @ ( times_times_int @ Y @ X ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6872_abs__minus__le__zero,axiom,
% 9.25/5.24      ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6873_abs__minus__le__zero,axiom,
% 9.25/5.24      ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6874_abs__minus__le__zero,axiom,
% 9.25/5.24      ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6875_eq__abs__iff_H,axiom,
% 9.25/5.24      ! [A: code_integer,B: code_integer] :
% 9.25/5.24        ( ( A
% 9.25/5.24          = ( abs_abs_Code_integer @ B ) )
% 9.25/5.24        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.24          & ( ( B = A )
% 9.25/5.24            | ( B
% 9.25/5.24              = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6876_eq__abs__iff_H,axiom,
% 9.25/5.24      ! [A: rat,B: rat] :
% 9.25/5.24        ( ( A
% 9.25/5.24          = ( abs_abs_rat @ B ) )
% 9.25/5.24        = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 9.25/5.24          & ( ( B = A )
% 9.25/5.24            | ( B
% 9.25/5.24              = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6877_eq__abs__iff_H,axiom,
% 9.25/5.24      ! [A: int,B: int] :
% 9.25/5.24        ( ( A
% 9.25/5.24          = ( abs_abs_int @ B ) )
% 9.25/5.24        = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 9.25/5.24          & ( ( B = A )
% 9.25/5.24            | ( B
% 9.25/5.24              = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6878_abs__eq__iff_H,axiom,
% 9.25/5.24      ! [A: code_integer,B: code_integer] :
% 9.25/5.24        ( ( ( abs_abs_Code_integer @ A )
% 9.25/5.24          = B )
% 9.25/5.24        = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 9.25/5.24          & ( ( A = B )
% 9.25/5.24            | ( A
% 9.25/5.24              = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6879_abs__eq__iff_H,axiom,
% 9.25/5.24      ! [A: rat,B: rat] :
% 9.25/5.24        ( ( ( abs_abs_rat @ A )
% 9.25/5.24          = B )
% 9.25/5.24        = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 9.25/5.24          & ( ( A = B )
% 9.25/5.24            | ( A
% 9.25/5.24              = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6880_abs__eq__iff_H,axiom,
% 9.25/5.24      ! [A: int,B: int] :
% 9.25/5.24        ( ( ( abs_abs_int @ A )
% 9.25/5.24          = B )
% 9.25/5.24        = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 9.25/5.24          & ( ( A = B )
% 9.25/5.24            | ( A
% 9.25/5.24              = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6881_abs__diff__triangle__ineq,axiom,
% 9.25/5.24      ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D2 ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6882_abs__diff__triangle__ineq,axiom,
% 9.25/5.24      ! [A: rat,B: rat,C: rat,D2: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D2 ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6883_abs__diff__triangle__ineq,axiom,
% 9.25/5.24      ! [A: int,B: int,C: int,D2: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D2 ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6884_abs__triangle__ineq4,axiom,
% 9.25/5.24      ! [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 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6885_abs__triangle__ineq4,axiom,
% 9.25/5.24      ! [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 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6886_abs__triangle__ineq4,axiom,
% 9.25/5.24      ! [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 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6887_abs__if__raw,axiom,
% 9.25/5.24      ( abs_abs_int
% 9.25/5.24      = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6888_abs__if__raw,axiom,
% 9.25/5.24      ( abs_abs_Code_integer
% 9.25/5.24      = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6889_abs__if__raw,axiom,
% 9.25/5.24      ( abs_abs_rat
% 9.25/5.24      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6890_abs__of__neg,axiom,
% 9.25/5.24      ! [A: int] :
% 9.25/5.24        ( ( ord_less_int @ A @ zero_zero_int )
% 9.25/5.24       => ( ( abs_abs_int @ A )
% 9.25/5.24          = ( uminus_uminus_int @ A ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6891_abs__of__neg,axiom,
% 9.25/5.24      ! [A: code_integer] :
% 9.25/5.24        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.24       => ( ( abs_abs_Code_integer @ A )
% 9.25/5.24          = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6892_abs__of__neg,axiom,
% 9.25/5.24      ! [A: rat] :
% 9.25/5.24        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.25/5.24       => ( ( abs_abs_rat @ A )
% 9.25/5.24          = ( uminus_uminus_rat @ A ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6893_abs__if,axiom,
% 9.25/5.24      ( abs_abs_int
% 9.25/5.24      = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6894_abs__if,axiom,
% 9.25/5.24      ( abs_abs_Code_integer
% 9.25/5.24      = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6895_abs__if,axiom,
% 9.25/5.24      ( abs_abs_rat
% 9.25/5.24      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6896_zabs__def,axiom,
% 9.25/5.24      ( abs_abs_int
% 9.25/5.24      = ( ^ [I3: int] : ( if_int @ ( ord_less_int @ I3 @ zero_zero_int ) @ ( uminus_uminus_int @ I3 ) @ I3 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6897_abs__integer__code,axiom,
% 9.25/5.24      ( abs_abs_Code_integer
% 9.25/5.24      = ( ^ [K4: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K4 ) @ K4 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6898_abs__add__one__gt__zero,axiom,
% 9.25/5.24      ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6899_abs__add__one__gt__zero,axiom,
% 9.25/5.24      ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6900_abs__add__one__gt__zero,axiom,
% 9.25/5.24      ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6901_of__int__leD,axiom,
% 9.25/5.24      ! [N: int,X: code_integer] :
% 9.25/5.24        ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 9.25/5.24       => ( ( N = zero_zero_int )
% 9.25/5.24          | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6902_of__int__leD,axiom,
% 9.25/5.24      ! [N: int,X: rat] :
% 9.25/5.24        ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 9.25/5.24       => ( ( N = zero_zero_int )
% 9.25/5.24          | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6903_of__int__leD,axiom,
% 9.25/5.24      ! [N: int,X: int] :
% 9.25/5.24        ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 9.25/5.24       => ( ( N = zero_zero_int )
% 9.25/5.24          | ( ord_less_eq_int @ one_one_int @ X ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6904_of__int__lessD,axiom,
% 9.25/5.24      ! [N: int,X: code_integer] :
% 9.25/5.24        ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 9.25/5.24       => ( ( N = zero_zero_int )
% 9.25/5.24          | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6905_of__int__lessD,axiom,
% 9.25/5.24      ! [N: int,X: rat] :
% 9.25/5.24        ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 9.25/5.24       => ( ( N = zero_zero_int )
% 9.25/5.24          | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6906_of__int__lessD,axiom,
% 9.25/5.24      ! [N: int,X: int] :
% 9.25/5.24        ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 9.25/5.24       => ( ( N = zero_zero_int )
% 9.25/5.24          | ( ord_less_int @ one_one_int @ X ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6907_zdvd__mult__cancel1,axiom,
% 9.25/5.24      ! [M: int,N: int] :
% 9.25/5.24        ( ( M != zero_zero_int )
% 9.25/5.24       => ( ( dvd_dvd_int @ ( times_times_int @ M @ N ) @ M )
% 9.25/5.24          = ( ( abs_abs_int @ N )
% 9.25/5.24            = one_one_int ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6908_abs__square__eq__1,axiom,
% 9.25/5.24      ! [X: code_integer] :
% 9.25/5.24        ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.24          = one_one_Code_integer )
% 9.25/5.24        = ( ( abs_abs_Code_integer @ X )
% 9.25/5.24          = one_one_Code_integer ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6909_abs__square__eq__1,axiom,
% 9.25/5.24      ! [X: rat] :
% 9.25/5.24        ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.24          = one_one_rat )
% 9.25/5.24        = ( ( abs_abs_rat @ X )
% 9.25/5.24          = one_one_rat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6910_abs__square__eq__1,axiom,
% 9.25/5.24      ! [X: int] :
% 9.25/5.24        ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.24          = one_one_int )
% 9.25/5.24        = ( ( abs_abs_int @ X )
% 9.25/5.24          = one_one_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6911_frac__eq,axiom,
% 9.25/5.24      ! [X: rat] :
% 9.25/5.24        ( ( ( archimedean_frac_rat @ X )
% 9.25/5.24          = X )
% 9.25/5.24        = ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 9.25/5.24          & ( ord_less_rat @ X @ one_one_rat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6912_frac__add,axiom,
% 9.25/5.24      ! [X: rat,Y: rat] :
% 9.25/5.24        ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 9.25/5.24         => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 9.25/5.24            = ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) ) )
% 9.25/5.24        & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 9.25/5.24         => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 9.25/5.24            = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6913_abs__square__le__1,axiom,
% 9.25/5.24      ! [X: code_integer] :
% 9.25/5.24        ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 9.25/5.24        = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6914_abs__square__le__1,axiom,
% 9.25/5.24      ! [X: rat] :
% 9.25/5.24        ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 9.25/5.24        = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6915_abs__square__le__1,axiom,
% 9.25/5.24      ! [X: int] :
% 9.25/5.24        ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 9.25/5.24        = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6916_abs__square__less__1,axiom,
% 9.25/5.24      ! [X: code_integer] :
% 9.25/5.24        ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 9.25/5.24        = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6917_abs__square__less__1,axiom,
% 9.25/5.24      ! [X: rat] :
% 9.25/5.24        ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 9.25/5.24        = ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6918_abs__square__less__1,axiom,
% 9.25/5.24      ! [X: int] :
% 9.25/5.24        ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 9.25/5.24        = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6919_nat__intermed__int__val,axiom,
% 9.25/5.24      ! [M: nat,N: nat,F2: nat > int,K: int] :
% 9.25/5.24        ( ! [I2: nat] :
% 9.25/5.24            ( ( ( ord_less_eq_nat @ M @ I2 )
% 9.25/5.24              & ( ord_less_nat @ I2 @ N ) )
% 9.25/5.24           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F2 @ ( suc @ I2 ) ) @ ( F2 @ I2 ) ) ) @ one_one_int ) )
% 9.25/5.24       => ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24         => ( ( ord_less_eq_int @ ( F2 @ M ) @ K )
% 9.25/5.24           => ( ( ord_less_eq_int @ K @ ( F2 @ N ) )
% 9.25/5.24             => ? [I2: nat] :
% 9.25/5.24                  ( ( ord_less_eq_nat @ M @ I2 )
% 9.25/5.24                  & ( ord_less_eq_nat @ I2 @ N )
% 9.25/5.24                  & ( ( F2 @ I2 )
% 9.25/5.24                    = K ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6920_incr__lemma,axiom,
% 9.25/5.24      ! [D2: int,Z: int,X: int] :
% 9.25/5.24        ( ( ord_less_int @ zero_zero_int @ D2 )
% 9.25/5.24       => ( ord_less_int @ Z @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6921_decr__lemma,axiom,
% 9.25/5.24      ! [D2: int,X: int,Z: int] :
% 9.25/5.24        ( ( ord_less_int @ zero_zero_int @ D2 )
% 9.25/5.24       => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D2 ) ) @ Z ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6922_nat__ivt__aux,axiom,
% 9.25/5.24      ! [N: nat,F2: nat > int,K: int] :
% 9.25/5.24        ( ! [I2: nat] :
% 9.25/5.24            ( ( ord_less_nat @ I2 @ N )
% 9.25/5.24           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F2 @ ( suc @ I2 ) ) @ ( F2 @ I2 ) ) ) @ one_one_int ) )
% 9.25/5.24       => ( ( ord_less_eq_int @ ( F2 @ zero_zero_nat ) @ K )
% 9.25/5.24         => ( ( ord_less_eq_int @ K @ ( F2 @ N ) )
% 9.25/5.24           => ? [I2: nat] :
% 9.25/5.24                ( ( ord_less_eq_nat @ I2 @ N )
% 9.25/5.24                & ( ( F2 @ I2 )
% 9.25/5.24                  = K ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6923_floor__add,axiom,
% 9.25/5.24      ! [X: rat,Y: rat] :
% 9.25/5.24        ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 9.25/5.24         => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 9.25/5.24            = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) ) )
% 9.25/5.24        & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 9.25/5.24         => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 9.25/5.24            = ( plus_plus_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) @ one_one_int ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6924_nat0__intermed__int__val,axiom,
% 9.25/5.24      ! [N: nat,F2: nat > int,K: int] :
% 9.25/5.24        ( ! [I2: nat] :
% 9.25/5.24            ( ( ord_less_nat @ I2 @ N )
% 9.25/5.24           => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F2 @ ( plus_plus_nat @ I2 @ one_one_nat ) ) @ ( F2 @ I2 ) ) ) @ one_one_int ) )
% 9.25/5.24       => ( ( ord_less_eq_int @ ( F2 @ zero_zero_nat ) @ K )
% 9.25/5.24         => ( ( ord_less_eq_int @ K @ ( F2 @ N ) )
% 9.25/5.24           => ? [I2: nat] :
% 9.25/5.24                ( ( ord_less_eq_nat @ I2 @ N )
% 9.25/5.24                & ( ( F2 @ I2 )
% 9.25/5.24                  = K ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6925_divmod__integer__def,axiom,
% 9.25/5.24      ( code_divmod_integer
% 9.25/5.24      = ( ^ [K4: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K4 @ L2 ) @ ( modulo364778990260209775nteger @ K4 @ L2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6926_bit__cut__integer__code,axiom,
% 9.25/5.24      ( code_bit_cut_integer
% 9.25/5.24      = ( ^ [K4: code_integer] :
% 9.25/5.24            ( if_Pro5737122678794959658eger_o @ ( K4 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 9.25/5.24            @ ( produc9125791028180074456eger_o
% 9.25/5.24              @ ^ [R4: code_integer,S2: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K4 ) @ R4 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ S2 ) ) @ ( S2 = one_one_Code_integer ) )
% 9.25/5.24              @ ( code_divmod_abs @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6927_nat__of__integer__code,axiom,
% 9.25/5.24      ( code_nat_of_integer
% 9.25/5.24      = ( ^ [K4: code_integer] :
% 9.25/5.24            ( if_nat @ ( ord_le3102999989581377725nteger @ K4 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 9.25/5.24            @ ( produc1555791787009142072er_nat
% 9.25/5.24              @ ^ [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 ) )
% 9.25/5.24              @ ( code_divmod_integer @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6928_int__of__integer__code,axiom,
% 9.25/5.24      ( code_int_of_integer
% 9.25/5.24      = ( ^ [K4: code_integer] :
% 9.25/5.24            ( if_int @ ( ord_le6747313008572928689nteger @ K4 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K4 ) ) )
% 9.25/5.24            @ ( if_int @ ( K4 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 9.25/5.24              @ ( produc1553301316500091796er_int
% 9.25/5.24                @ ^ [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 ) )
% 9.25/5.24                @ ( code_divmod_integer @ K4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6929_xor__int__unfold,axiom,
% 9.25/5.24      ( bit_se6526347334894502574or_int
% 9.25/5.24      = ( ^ [K4: int,L2: int] :
% 9.25/5.24            ( if_int
% 9.25/5.24            @ ( K4
% 9.25/5.24              = ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.24            @ ( bit_ri7919022796975470100ot_int @ L2 )
% 9.25/5.24            @ ( if_int
% 9.25/5.24              @ ( L2
% 9.25/5.24                = ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.24              @ ( bit_ri7919022796975470100ot_int @ K4 )
% 9.25/5.24              @ ( if_int @ ( K4 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K4 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K4 @ ( 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 @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6930_is__singleton__the__elem,axiom,
% 9.25/5.24      ( is_sin2937591304547752795at_nat
% 9.25/5.24      = ( ^ [A4: set_Pr4329608150637261639at_nat] :
% 9.25/5.24            ( A4
% 9.25/5.24            = ( insert9069300056098147895at_nat @ ( the_el221668144340439132at_nat @ A4 ) @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6931_is__singleton__the__elem,axiom,
% 9.25/5.24      ( is_sin2850979758926227957at_nat
% 9.25/5.24      = ( ^ [A4: set_Pr1261947904930325089at_nat] :
% 9.25/5.24            ( A4
% 9.25/5.24            = ( insert8211810215607154385at_nat @ ( the_el2281957884133575798at_nat @ A4 ) @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6932_is__singleton__the__elem,axiom,
% 9.25/5.24      ( is_singleton_o
% 9.25/5.24      = ( ^ [A4: set_o] :
% 9.25/5.24            ( A4
% 9.25/5.24            = ( insert_o @ ( the_elem_o @ A4 ) @ bot_bot_set_o ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6933_is__singleton__the__elem,axiom,
% 9.25/5.24      ( is_singleton_nat
% 9.25/5.24      = ( ^ [A4: set_nat] :
% 9.25/5.24            ( A4
% 9.25/5.24            = ( insert_nat @ ( the_elem_nat @ A4 ) @ bot_bot_set_nat ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6934_is__singleton__the__elem,axiom,
% 9.25/5.24      ( is_singleton_int
% 9.25/5.24      = ( ^ [A4: set_int] :
% 9.25/5.24            ( A4
% 9.25/5.24            = ( insert_int @ ( the_elem_int @ A4 ) @ bot_bot_set_int ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6935_integer__of__num_I3_J,axiom,
% 9.25/5.24      ! [N: num] :
% 9.25/5.24        ( ( code_integer_of_num @ ( bit1 @ N ) )
% 9.25/5.24        = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6936_mask__eq__sum__exp__nat,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 9.25/5.24        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.24          @ ( collect_nat
% 9.25/5.24            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6937_of__int__sum,axiom,
% 9.25/5.24      ! [F2: int > int,A2: set_int] :
% 9.25/5.24        ( ( ring_1_of_int_rat @ ( groups4538972089207619220nt_int @ F2 @ A2 ) )
% 9.25/5.24        = ( groups3906332499630173760nt_rat
% 9.25/5.24          @ ^ [X3: int] : ( ring_1_of_int_rat @ ( F2 @ X3 ) )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6938_of__int__sum,axiom,
% 9.25/5.24      ! [F2: int > int,A2: set_int] :
% 9.25/5.24        ( ( ring_1_of_int_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) )
% 9.25/5.24        = ( groups4538972089207619220nt_int
% 9.25/5.24          @ ^ [X3: int] : ( ring_1_of_int_int @ ( F2 @ X3 ) )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6939_one__integer_Orep__eq,axiom,
% 9.25/5.24      ( ( code_int_of_integer @ one_one_Code_integer )
% 9.25/5.24      = one_one_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6940_uminus__integer_Orep__eq,axiom,
% 9.25/5.24      ! [X: code_integer] :
% 9.25/5.24        ( ( code_int_of_integer @ ( uminus1351360451143612070nteger @ X ) )
% 9.25/5.24        = ( uminus_uminus_int @ ( code_int_of_integer @ X ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6941_is__singletonI,axiom,
% 9.25/5.24      ! [X: produc3843707927480180839at_nat] : ( is_sin2937591304547752795at_nat @ ( insert9069300056098147895at_nat @ X @ bot_bo228742789529271731at_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6942_is__singletonI,axiom,
% 9.25/5.24      ! [X: product_prod_nat_nat] : ( is_sin2850979758926227957at_nat @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6943_is__singletonI,axiom,
% 9.25/5.24      ! [X: $o] : ( is_singleton_o @ ( insert_o @ X @ bot_bot_set_o ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6944_is__singletonI,axiom,
% 9.25/5.24      ! [X: nat] : ( is_singleton_nat @ ( insert_nat @ X @ bot_bot_set_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6945_is__singletonI,axiom,
% 9.25/5.24      ! [X: int] : ( is_singleton_int @ ( insert_int @ X @ bot_bot_set_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6946_bit_Ocompl__zero,axiom,
% 9.25/5.24      ( ( bit_ri7632146776885996613nteger @ zero_z3403309356797280102nteger )
% 9.25/5.24      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6947_bit_Ocompl__zero,axiom,
% 9.25/5.24      ( ( bit_ri7919022796975470100ot_int @ zero_zero_int )
% 9.25/5.24      = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6948_bit_Ocompl__one,axiom,
% 9.25/5.24      ( ( bit_ri7632146776885996613nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.24      = zero_z3403309356797280102nteger ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6949_bit_Ocompl__one,axiom,
% 9.25/5.24      ( ( bit_ri7919022796975470100ot_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.24      = zero_zero_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6950_bit_Oxor__cancel__right,axiom,
% 9.25/5.24      ! [X: code_integer] :
% 9.25/5.24        ( ( bit_se3222712562003087583nteger @ X @ ( bit_ri7632146776885996613nteger @ X ) )
% 9.25/5.24        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6951_bit_Oxor__cancel__right,axiom,
% 9.25/5.24      ! [X: int] :
% 9.25/5.24        ( ( bit_se6526347334894502574or_int @ X @ ( bit_ri7919022796975470100ot_int @ X ) )
% 9.25/5.24        = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6952_bit_Oxor__cancel__left,axiom,
% 9.25/5.24      ! [X: code_integer] :
% 9.25/5.24        ( ( bit_se3222712562003087583nteger @ ( bit_ri7632146776885996613nteger @ X ) @ X )
% 9.25/5.24        = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6953_bit_Oxor__cancel__left,axiom,
% 9.25/5.24      ! [X: int] :
% 9.25/5.24        ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X ) @ X )
% 9.25/5.24        = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6954_bit_Oxor__one__right,axiom,
% 9.25/5.24      ! [X: code_integer] :
% 9.25/5.24        ( ( bit_se3222712562003087583nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.24        = ( bit_ri7632146776885996613nteger @ X ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6955_bit_Oxor__one__right,axiom,
% 9.25/5.24      ! [X: int] :
% 9.25/5.24        ( ( bit_se6526347334894502574or_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.24        = ( bit_ri7919022796975470100ot_int @ X ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6956_bit_Oxor__one__left,axiom,
% 9.25/5.24      ! [X: code_integer] :
% 9.25/5.24        ( ( bit_se3222712562003087583nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 9.25/5.24        = ( bit_ri7632146776885996613nteger @ X ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6957_bit_Oxor__one__left,axiom,
% 9.25/5.24      ! [X: int] :
% 9.25/5.24        ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 9.25/5.24        = ( bit_ri7919022796975470100ot_int @ X ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6958_minus__not__numeral__eq,axiom,
% 9.25/5.24      ! [N: num] :
% 9.25/5.24        ( ( uminus1351360451143612070nteger @ ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.25/5.24        = ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6959_minus__not__numeral__eq,axiom,
% 9.25/5.24      ! [N: num] :
% 9.25/5.24        ( ( uminus_uminus_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.24        = ( numeral_numeral_int @ ( inc @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6960_not__minus__numeral__eq,axiom,
% 9.25/5.24      ! [N: num] :
% 9.25/5.24        ( ( bit_ri7632146776885996613nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 9.25/5.24        = ( neg_nu5755505904847501662nteger @ N @ one ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6961_not__minus__numeral__eq,axiom,
% 9.25/5.24      ! [N: num] :
% 9.25/5.24        ( ( bit_ri7919022796975470100ot_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.24        = ( neg_numeral_sub_int @ N @ one ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6962_push__bit__minus__one__eq__not__mask,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( bit_se7788150548672797655nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.24        = ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6963_push__bit__minus__one__eq__not__mask,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.24        = ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6964_xor__minus__numerals_I2_J,axiom,
% 9.25/5.24      ! [K: int,N: num] :
% 9.25/5.24        ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.24        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N @ one ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6965_xor__minus__numerals_I1_J,axiom,
% 9.25/5.24      ! [N: num,K: int] :
% 9.25/5.24        ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ K )
% 9.25/5.24        = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N @ one ) @ K ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6966_not__one__eq,axiom,
% 9.25/5.24      ( ( bit_ri7632146776885996613nteger @ one_one_Code_integer )
% 9.25/5.24      = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6967_not__one__eq,axiom,
% 9.25/5.24      ( ( bit_ri7919022796975470100ot_int @ one_one_int )
% 9.25/5.24      = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6968_int__of__integer,axiom,
% 9.25/5.24      ! [X: code_integer] : ( member_int @ ( code_int_of_integer @ X ) @ top_top_set_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6969_int__of__integer__cases,axiom,
% 9.25/5.24      ! [Y: int] :
% 9.25/5.24        ( ( member_int @ Y @ top_top_set_int )
% 9.25/5.24       => ~ ! [X2: code_integer] :
% 9.25/5.24              ( Y
% 9.25/5.24             != ( code_int_of_integer @ X2 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6970_int__of__integer__induct,axiom,
% 9.25/5.24      ! [Y: int,P: int > $o] :
% 9.25/5.24        ( ( member_int @ Y @ top_top_set_int )
% 9.25/5.24       => ( ! [X2: code_integer] : ( P @ ( code_int_of_integer @ X2 ) )
% 9.25/5.24         => ( P @ Y ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6971_mod__sum__eq,axiom,
% 9.25/5.24      ! [F2: nat > nat,A: nat,A2: set_nat] :
% 9.25/5.24        ( ( modulo_modulo_nat
% 9.25/5.24          @ ( groups3542108847815614940at_nat
% 9.25/5.24            @ ^ [I3: nat] : ( modulo_modulo_nat @ ( F2 @ I3 ) @ A )
% 9.25/5.24            @ A2 )
% 9.25/5.24          @ A )
% 9.25/5.24        = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F2 @ A2 ) @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6972_mod__sum__eq,axiom,
% 9.25/5.24      ! [F2: int > int,A: int,A2: set_int] :
% 9.25/5.24        ( ( modulo_modulo_int
% 9.25/5.24          @ ( groups4538972089207619220nt_int
% 9.25/5.24            @ ^ [I3: int] : ( modulo_modulo_int @ ( F2 @ I3 ) @ A )
% 9.25/5.24            @ A2 )
% 9.25/5.24          @ A )
% 9.25/5.24        = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) @ A ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6973_type__definition__integer,axiom,
% 9.25/5.24      type_d8366093980585677751er_int @ code_int_of_integer @ code_integer_of_int @ top_top_set_int ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6974_integer__of__int__inverse,axiom,
% 9.25/5.24      ! [Y: int] :
% 9.25/5.24        ( ( member_int @ Y @ top_top_set_int )
% 9.25/5.24       => ( ( code_int_of_integer @ ( code_integer_of_int @ Y ) )
% 9.25/5.24          = Y ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6975_is__singletonI_H,axiom,
% 9.25/5.24      ! [A2: set_se6260736226359567993nt_int] :
% 9.25/5.24        ( ( A2 != bot_bo1488462491386950373nt_int )
% 9.25/5.24       => ( ! [X2: set_Pr958786334691620121nt_int,Y2: set_Pr958786334691620121nt_int] :
% 9.25/5.24              ( ( member2340774599025711042nt_int @ X2 @ A2 )
% 9.25/5.24             => ( ( member2340774599025711042nt_int @ Y2 @ A2 )
% 9.25/5.24               => ( X2 = Y2 ) ) )
% 9.25/5.24         => ( is_sin6299389887212142093nt_int @ A2 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6976_is__singletonI_H,axiom,
% 9.25/5.24      ! [A2: set_set_nat] :
% 9.25/5.24        ( ( A2 != bot_bot_set_set_nat )
% 9.25/5.24       => ( ! [X2: set_nat,Y2: set_nat] :
% 9.25/5.24              ( ( member_set_nat @ X2 @ A2 )
% 9.25/5.24             => ( ( member_set_nat @ Y2 @ A2 )
% 9.25/5.24               => ( X2 = Y2 ) ) )
% 9.25/5.24         => ( is_singleton_set_nat @ A2 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6977_is__singletonI_H,axiom,
% 9.25/5.24      ! [A2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.24        ( ( A2 != bot_bo7824918357723582233_nat_o )
% 9.25/5.24       => ( ! [X2: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat > $o] :
% 9.25/5.24              ( ( member6576561426505652726_nat_o @ X2 @ A2 )
% 9.25/5.24             => ( ( member6576561426505652726_nat_o @ Y2 @ A2 )
% 9.25/5.24               => ( X2 = Y2 ) ) )
% 9.25/5.24         => ( is_sin5180296473474724033_nat_o @ A2 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6978_is__singletonI_H,axiom,
% 9.25/5.24      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.24        ( ( A2 != bot_bo2099793752762293965at_nat )
% 9.25/5.24       => ( ! [X2: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 9.25/5.24              ( ( member8440522571783428010at_nat @ X2 @ A2 )
% 9.25/5.24             => ( ( member8440522571783428010at_nat @ Y2 @ A2 )
% 9.25/5.24               => ( X2 = Y2 ) ) )
% 9.25/5.24         => ( is_sin2850979758926227957at_nat @ A2 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6979_is__singletonI_H,axiom,
% 9.25/5.24      ! [A2: set_o] :
% 9.25/5.24        ( ( A2 != bot_bot_set_o )
% 9.25/5.24       => ( ! [X2: $o,Y2: $o] :
% 9.25/5.24              ( ( member_o @ X2 @ A2 )
% 9.25/5.24             => ( ( member_o @ Y2 @ A2 )
% 9.25/5.24               => ( X2 = Y2 ) ) )
% 9.25/5.24         => ( is_singleton_o @ A2 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6980_is__singletonI_H,axiom,
% 9.25/5.24      ! [A2: set_nat] :
% 9.25/5.24        ( ( A2 != bot_bot_set_nat )
% 9.25/5.24       => ( ! [X2: nat,Y2: nat] :
% 9.25/5.24              ( ( member_nat @ X2 @ A2 )
% 9.25/5.24             => ( ( member_nat @ Y2 @ A2 )
% 9.25/5.24               => ( X2 = Y2 ) ) )
% 9.25/5.24         => ( is_singleton_nat @ A2 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6981_is__singletonI_H,axiom,
% 9.25/5.24      ! [A2: set_int] :
% 9.25/5.24        ( ( A2 != bot_bot_set_int )
% 9.25/5.24       => ( ! [X2: int,Y2: int] :
% 9.25/5.24              ( ( member_int @ X2 @ A2 )
% 9.25/5.24             => ( ( member_int @ Y2 @ A2 )
% 9.25/5.24               => ( X2 = Y2 ) ) )
% 9.25/5.24         => ( is_singleton_int @ A2 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6982_minus__eq__not__plus__1,axiom,
% 9.25/5.24      ( uminus1351360451143612070nteger
% 9.25/5.24      = ( ^ [A3: code_integer] : ( plus_p5714425477246183910nteger @ ( bit_ri7632146776885996613nteger @ A3 ) @ one_one_Code_integer ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6983_minus__eq__not__plus__1,axiom,
% 9.25/5.24      ( uminus_uminus_int
% 9.25/5.24      = ( ^ [A3: int] : ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A3 ) @ one_one_int ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6984_minus__eq__not__minus__1,axiom,
% 9.25/5.24      ( uminus1351360451143612070nteger
% 9.25/5.24      = ( ^ [A3: code_integer] : ( bit_ri7632146776885996613nteger @ ( minus_8373710615458151222nteger @ A3 @ one_one_Code_integer ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6985_minus__eq__not__minus__1,axiom,
% 9.25/5.24      ( uminus_uminus_int
% 9.25/5.24      = ( ^ [A3: int] : ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A3 @ one_one_int ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6986_not__eq__complement,axiom,
% 9.25/5.24      ( bit_ri7632146776885996613nteger
% 9.25/5.24      = ( ^ [A3: code_integer] : ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A3 ) @ one_one_Code_integer ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6987_not__eq__complement,axiom,
% 9.25/5.24      ( bit_ri7919022796975470100ot_int
% 9.25/5.24      = ( ^ [A3: int] : ( minus_minus_int @ ( uminus_uminus_int @ A3 ) @ one_one_int ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6988_not__int__def,axiom,
% 9.25/5.24      ( bit_ri7919022796975470100ot_int
% 9.25/5.24      = ( ^ [K4: int] : ( minus_minus_int @ ( uminus_uminus_int @ K4 ) @ one_one_int ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6989_and__not__numerals_I1_J,axiom,
% 9.25/5.24      ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 9.25/5.24      = zero_zero_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6990_sum__power__add,axiom,
% 9.25/5.24      ! [X: code_integer,M: nat,I4: set_nat] :
% 9.25/5.24        ( ( groups7501900531339628137nteger
% 9.25/5.24          @ ^ [I3: nat] : ( power_8256067586552552935nteger @ X @ ( plus_plus_nat @ M @ I3 ) )
% 9.25/5.24          @ I4 )
% 9.25/5.24        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ M ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ I4 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6991_sum__power__add,axiom,
% 9.25/5.24      ! [X: rat,M: nat,I4: set_nat] :
% 9.25/5.24        ( ( groups2906978787729119204at_rat
% 9.25/5.24          @ ^ [I3: nat] : ( power_power_rat @ X @ ( plus_plus_nat @ M @ I3 ) )
% 9.25/5.24          @ I4 )
% 9.25/5.24        = ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ I4 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6992_sum__power__add,axiom,
% 9.25/5.24      ! [X: int,M: nat,I4: set_nat] :
% 9.25/5.24        ( ( groups3539618377306564664at_int
% 9.25/5.24          @ ^ [I3: nat] : ( power_power_int @ X @ ( plus_plus_nat @ M @ I3 ) )
% 9.25/5.24          @ I4 )
% 9.25/5.24        = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ I4 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6993_minus__numeral__inc__eq,axiom,
% 9.25/5.24      ! [N: num] :
% 9.25/5.24        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) )
% 9.25/5.24        = ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6994_minus__numeral__inc__eq,axiom,
% 9.25/5.24      ! [N: num] :
% 9.25/5.24        ( ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) )
% 9.25/5.24        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6995_unset__bit__int__def,axiom,
% 9.25/5.24      ( bit_se4203085406695923979it_int
% 9.25/5.24      = ( ^ [N2: nat,K4: int] : ( bit_se725231765392027082nd_int @ K4 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6996_divmod__abs__code_I6_J,axiom,
% 9.25/5.24      ! [J: code_integer] :
% 9.25/5.24        ( ( code_divmod_abs @ zero_z3403309356797280102nteger @ J )
% 9.25/5.24        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6997_divmod__abs__code_I5_J,axiom,
% 9.25/5.24      ! [J: code_integer] :
% 9.25/5.24        ( ( code_divmod_abs @ J @ zero_z3403309356797280102nteger )
% 9.25/5.24        = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ J ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6998_and__not__numerals_I2_J,axiom,
% 9.25/5.24      ! [N: num] :
% 9.25/5.24        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 9.25/5.24        = one_one_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_6999_and__not__numerals_I4_J,axiom,
% 9.25/5.24      ! [M: num] :
% 9.25/5.24        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 9.25/5.24        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7000_not__numeral__Bit0__eq,axiom,
% 9.25/5.24      ! [N: num] :
% 9.25/5.24        ( ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) )
% 9.25/5.24        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7001_not__numeral__Bit0__eq,axiom,
% 9.25/5.24      ! [N: num] :
% 9.25/5.24        ( ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) )
% 9.25/5.24        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7002_minus__numeral__eq__not__sub__one,axiom,
% 9.25/5.24      ! [N: num] :
% 9.25/5.24        ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 9.25/5.24        = ( bit_ri7632146776885996613nteger @ ( neg_nu5755505904847501662nteger @ N @ one ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7003_minus__numeral__eq__not__sub__one,axiom,
% 9.25/5.24      ! [N: num] :
% 9.25/5.24        ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 9.25/5.24        = ( bit_ri7919022796975470100ot_int @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7004_not__numeral__BitM__eq,axiom,
% 9.25/5.24      ! [N: num] :
% 9.25/5.24        ( ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ ( bitM @ N ) ) )
% 9.25/5.24        = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7005_not__numeral__BitM__eq,axiom,
% 9.25/5.24      ! [N: num] :
% 9.25/5.24        ( ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bitM @ N ) ) )
% 9.25/5.24        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7006_unset__bit__eq__and__not,axiom,
% 9.25/5.24      ( bit_se8260200283734997820nteger
% 9.25/5.24      = ( ^ [N2: nat,A3: code_integer] : ( bit_se3949692690581998587nteger @ A3 @ ( bit_ri7632146776885996613nteger @ ( bit_se7788150548672797655nteger @ N2 @ one_one_Code_integer ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7007_unset__bit__eq__and__not,axiom,
% 9.25/5.24      ( bit_se4203085406695923979it_int
% 9.25/5.24      = ( ^ [N2: nat,A3: int] : ( bit_se725231765392027082nd_int @ A3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7008_is__singletonE,axiom,
% 9.25/5.24      ! [A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.24        ( ( is_sin2937591304547752795at_nat @ A2 )
% 9.25/5.24       => ~ ! [X2: produc3843707927480180839at_nat] :
% 9.25/5.24              ( A2
% 9.25/5.24             != ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7009_is__singletonE,axiom,
% 9.25/5.24      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.24        ( ( is_sin2850979758926227957at_nat @ A2 )
% 9.25/5.24       => ~ ! [X2: product_prod_nat_nat] :
% 9.25/5.24              ( A2
% 9.25/5.24             != ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7010_is__singletonE,axiom,
% 9.25/5.24      ! [A2: set_o] :
% 9.25/5.24        ( ( is_singleton_o @ A2 )
% 9.25/5.24       => ~ ! [X2: $o] :
% 9.25/5.24              ( A2
% 9.25/5.24             != ( insert_o @ X2 @ bot_bot_set_o ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7011_is__singletonE,axiom,
% 9.25/5.24      ! [A2: set_nat] :
% 9.25/5.24        ( ( is_singleton_nat @ A2 )
% 9.25/5.24       => ~ ! [X2: nat] :
% 9.25/5.24              ( A2
% 9.25/5.24             != ( insert_nat @ X2 @ bot_bot_set_nat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7012_is__singletonE,axiom,
% 9.25/5.24      ! [A2: set_int] :
% 9.25/5.24        ( ( is_singleton_int @ A2 )
% 9.25/5.24       => ~ ! [X2: int] :
% 9.25/5.24              ( A2
% 9.25/5.24             != ( insert_int @ X2 @ bot_bot_set_int ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7013_is__singleton__def,axiom,
% 9.25/5.24      ( is_sin2937591304547752795at_nat
% 9.25/5.24      = ( ^ [A4: set_Pr4329608150637261639at_nat] :
% 9.25/5.24          ? [X3: produc3843707927480180839at_nat] :
% 9.25/5.24            ( A4
% 9.25/5.24            = ( insert9069300056098147895at_nat @ X3 @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7014_is__singleton__def,axiom,
% 9.25/5.24      ( is_sin2850979758926227957at_nat
% 9.25/5.24      = ( ^ [A4: set_Pr1261947904930325089at_nat] :
% 9.25/5.24          ? [X3: product_prod_nat_nat] :
% 9.25/5.24            ( A4
% 9.25/5.24            = ( insert8211810215607154385at_nat @ X3 @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7015_is__singleton__def,axiom,
% 9.25/5.24      ( is_singleton_o
% 9.25/5.24      = ( ^ [A4: set_o] :
% 9.25/5.24          ? [X3: $o] :
% 9.25/5.24            ( A4
% 9.25/5.24            = ( insert_o @ X3 @ bot_bot_set_o ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7016_is__singleton__def,axiom,
% 9.25/5.24      ( is_singleton_nat
% 9.25/5.24      = ( ^ [A4: set_nat] :
% 9.25/5.24          ? [X3: nat] :
% 9.25/5.24            ( A4
% 9.25/5.24            = ( insert_nat @ X3 @ bot_bot_set_nat ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7017_is__singleton__def,axiom,
% 9.25/5.24      ( is_singleton_int
% 9.25/5.24      = ( ^ [A4: set_int] :
% 9.25/5.24          ? [X3: int] :
% 9.25/5.24            ( A4
% 9.25/5.24            = ( insert_int @ X3 @ bot_bot_set_int ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7018_and__not__numerals_I7_J,axiom,
% 9.25/5.24      ! [M: num] :
% 9.25/5.24        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 9.25/5.24        = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7019_and__not__numerals_I3_J,axiom,
% 9.25/5.24      ! [N: num] :
% 9.25/5.24        ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 9.25/5.24        = zero_zero_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7020_integer__of__num__triv_I1_J,axiom,
% 9.25/5.24      ( ( code_integer_of_num @ one )
% 9.25/5.24      = one_one_Code_integer ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7021_integer__of__num_I2_J,axiom,
% 9.25/5.24      ! [N: num] :
% 9.25/5.24        ( ( code_integer_of_num @ ( bit0 @ N ) )
% 9.25/5.24        = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7022_minus__exp__eq__not__mask,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.24        = ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7023_minus__exp__eq__not__mask,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.24        = ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7024_divmod__abs__def,axiom,
% 9.25/5.24      ( code_divmod_abs
% 9.25/5.24      = ( ^ [K4: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K4 ) @ ( abs_abs_Code_integer @ L2 ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K4 ) @ ( abs_abs_Code_integer @ L2 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7025_mask__eq__sum__exp,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int )
% 9.25/5.24        = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 9.25/5.24          @ ( collect_nat
% 9.25/5.24            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7026_mask__eq__sum__exp,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer )
% 9.25/5.24        = ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 9.25/5.24          @ ( collect_nat
% 9.25/5.24            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7027_mask__eq__sum__exp,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) @ one_one_Code_natural )
% 9.25/5.24        = ( groups6325495683096345652atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 9.25/5.24          @ ( collect_nat
% 9.25/5.24            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7028_mask__eq__sum__exp,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat )
% 9.25/5.24        = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.24          @ ( collect_nat
% 9.25/5.24            @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7029_and__not__numerals_I8_J,axiom,
% 9.25/5.24      ! [M: num,N: num] :
% 9.25/5.24        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 9.25/5.24        = ( 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 ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7030_sum__abs__ge__zero,axiom,
% 9.25/5.24      ! [F2: int > int,A2: set_int] :
% 9.25/5.24        ( ord_less_eq_int @ zero_zero_int
% 9.25/5.24        @ ( groups4538972089207619220nt_int
% 9.25/5.24          @ ^ [I3: int] : ( abs_abs_int @ ( F2 @ I3 ) )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7031_sum__abs,axiom,
% 9.25/5.24      ! [F2: int > int,A2: set_int] :
% 9.25/5.24        ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) )
% 9.25/5.24        @ ( groups4538972089207619220nt_int
% 9.25/5.24          @ ^ [I3: int] : ( abs_abs_int @ ( F2 @ I3 ) )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7032_sum_Oempty,axiom,
% 9.25/5.24      ! [G2: $o > code_integer] :
% 9.25/5.24        ( ( groups4406642042086082107nteger @ G2 @ bot_bot_set_o )
% 9.25/5.24        = zero_z3403309356797280102nteger ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7033_sum_Oempty,axiom,
% 9.25/5.24      ! [G2: $o > rat] :
% 9.25/5.24        ( ( groups7872700643590313910_o_rat @ G2 @ bot_bot_set_o )
% 9.25/5.24        = zero_zero_rat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7034_sum_Oempty,axiom,
% 9.25/5.24      ! [G2: $o > nat] :
% 9.25/5.24        ( ( groups8507830703676809646_o_nat @ G2 @ bot_bot_set_o )
% 9.25/5.24        = zero_zero_nat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7035_sum_Oempty,axiom,
% 9.25/5.24      ! [G2: $o > int] :
% 9.25/5.24        ( ( groups8505340233167759370_o_int @ G2 @ bot_bot_set_o )
% 9.25/5.24        = zero_zero_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7036_sum_Oempty,axiom,
% 9.25/5.24      ! [G2: nat > code_integer] :
% 9.25/5.24        ( ( groups7501900531339628137nteger @ G2 @ bot_bot_set_nat )
% 9.25/5.24        = zero_z3403309356797280102nteger ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7037_sum_Oempty,axiom,
% 9.25/5.24      ! [G2: nat > rat] :
% 9.25/5.24        ( ( groups2906978787729119204at_rat @ G2 @ bot_bot_set_nat )
% 9.25/5.24        = zero_zero_rat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7038_sum_Oempty,axiom,
% 9.25/5.24      ! [G2: nat > int] :
% 9.25/5.24        ( ( groups3539618377306564664at_int @ G2 @ bot_bot_set_nat )
% 9.25/5.24        = zero_zero_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7039_sum_Oempty,axiom,
% 9.25/5.24      ! [G2: int > code_integer] :
% 9.25/5.24        ( ( groups7873554091576472773nteger @ G2 @ bot_bot_set_int )
% 9.25/5.24        = zero_z3403309356797280102nteger ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7040_sum_Oempty,axiom,
% 9.25/5.24      ! [G2: int > rat] :
% 9.25/5.24        ( ( groups3906332499630173760nt_rat @ G2 @ bot_bot_set_int )
% 9.25/5.24        = zero_zero_rat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7041_sum_Oempty,axiom,
% 9.25/5.24      ! [G2: int > nat] :
% 9.25/5.24        ( ( groups4541462559716669496nt_nat @ G2 @ bot_bot_set_int )
% 9.25/5.24        = zero_zero_nat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7042_convex__sum__bound__le,axiom,
% 9.25/5.24      ! [I4: set_nat,X: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 9.25/5.24        ( ! [I2: nat] :
% 9.25/5.24            ( ( member_nat @ I2 @ I4 )
% 9.25/5.24           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I2 ) ) )
% 9.25/5.24       => ( ( ( groups7501900531339628137nteger @ X @ I4 )
% 9.25/5.24            = one_one_Code_integer )
% 9.25/5.24         => ( ! [I2: nat] :
% 9.25/5.24                ( ( member_nat @ I2 @ I4 )
% 9.25/5.24               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 9.25/5.24           => ( ord_le3102999989581377725nteger
% 9.25/5.24              @ ( abs_abs_Code_integer
% 9.25/5.24                @ ( minus_8373710615458151222nteger
% 9.25/5.24                  @ ( groups7501900531339628137nteger
% 9.25/5.24                    @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.25/5.24                    @ I4 )
% 9.25/5.24                  @ B ) )
% 9.25/5.24              @ Delta ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7043_convex__sum__bound__le,axiom,
% 9.25/5.24      ! [I4: set_int,X: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 9.25/5.24        ( ! [I2: int] :
% 9.25/5.24            ( ( member_int @ I2 @ I4 )
% 9.25/5.24           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I2 ) ) )
% 9.25/5.24       => ( ( ( groups7873554091576472773nteger @ X @ I4 )
% 9.25/5.24            = one_one_Code_integer )
% 9.25/5.24         => ( ! [I2: int] :
% 9.25/5.24                ( ( member_int @ I2 @ I4 )
% 9.25/5.24               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 9.25/5.24           => ( ord_le3102999989581377725nteger
% 9.25/5.24              @ ( abs_abs_Code_integer
% 9.25/5.24                @ ( minus_8373710615458151222nteger
% 9.25/5.24                  @ ( groups7873554091576472773nteger
% 9.25/5.24                    @ ^ [I3: int] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.25/5.24                    @ I4 )
% 9.25/5.24                  @ B ) )
% 9.25/5.24              @ Delta ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7044_convex__sum__bound__le,axiom,
% 9.25/5.24      ! [I4: set_nat,X: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 9.25/5.24        ( ! [I2: nat] :
% 9.25/5.24            ( ( member_nat @ I2 @ I4 )
% 9.25/5.24           => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I2 ) ) )
% 9.25/5.24       => ( ( ( groups2906978787729119204at_rat @ X @ I4 )
% 9.25/5.24            = one_one_rat )
% 9.25/5.24         => ( ! [I2: nat] :
% 9.25/5.24                ( ( member_nat @ I2 @ I4 )
% 9.25/5.24               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 9.25/5.24           => ( ord_less_eq_rat
% 9.25/5.24              @ ( abs_abs_rat
% 9.25/5.24                @ ( minus_minus_rat
% 9.25/5.24                  @ ( groups2906978787729119204at_rat
% 9.25/5.24                    @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.25/5.24                    @ I4 )
% 9.25/5.24                  @ B ) )
% 9.25/5.24              @ Delta ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7045_convex__sum__bound__le,axiom,
% 9.25/5.24      ! [I4: set_int,X: int > rat,A: int > rat,B: rat,Delta: rat] :
% 9.25/5.24        ( ! [I2: int] :
% 9.25/5.24            ( ( member_int @ I2 @ I4 )
% 9.25/5.24           => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I2 ) ) )
% 9.25/5.24       => ( ( ( groups3906332499630173760nt_rat @ X @ I4 )
% 9.25/5.24            = one_one_rat )
% 9.25/5.24         => ( ! [I2: int] :
% 9.25/5.24                ( ( member_int @ I2 @ I4 )
% 9.25/5.24               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 9.25/5.24           => ( ord_less_eq_rat
% 9.25/5.24              @ ( abs_abs_rat
% 9.25/5.24                @ ( minus_minus_rat
% 9.25/5.24                  @ ( groups3906332499630173760nt_rat
% 9.25/5.24                    @ ^ [I3: int] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.25/5.24                    @ I4 )
% 9.25/5.24                  @ B ) )
% 9.25/5.24              @ Delta ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7046_convex__sum__bound__le,axiom,
% 9.25/5.24      ! [I4: set_nat,X: nat > int,A: nat > int,B: int,Delta: int] :
% 9.25/5.24        ( ! [I2: nat] :
% 9.25/5.24            ( ( member_nat @ I2 @ I4 )
% 9.25/5.24           => ( ord_less_eq_int @ zero_zero_int @ ( X @ I2 ) ) )
% 9.25/5.24       => ( ( ( groups3539618377306564664at_int @ X @ I4 )
% 9.25/5.24            = one_one_int )
% 9.25/5.24         => ( ! [I2: nat] :
% 9.25/5.24                ( ( member_nat @ I2 @ I4 )
% 9.25/5.24               => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 9.25/5.24           => ( ord_less_eq_int
% 9.25/5.24              @ ( abs_abs_int
% 9.25/5.24                @ ( minus_minus_int
% 9.25/5.24                  @ ( groups3539618377306564664at_int
% 9.25/5.24                    @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.25/5.24                    @ I4 )
% 9.25/5.24                  @ B ) )
% 9.25/5.24              @ Delta ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7047_convex__sum__bound__le,axiom,
% 9.25/5.24      ! [I4: set_int,X: int > int,A: int > int,B: int,Delta: int] :
% 9.25/5.24        ( ! [I2: int] :
% 9.25/5.24            ( ( member_int @ I2 @ I4 )
% 9.25/5.24           => ( ord_less_eq_int @ zero_zero_int @ ( X @ I2 ) ) )
% 9.25/5.24       => ( ( ( groups4538972089207619220nt_int @ X @ I4 )
% 9.25/5.24            = one_one_int )
% 9.25/5.24         => ( ! [I2: int] :
% 9.25/5.24                ( ( member_int @ I2 @ I4 )
% 9.25/5.24               => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 9.25/5.24           => ( ord_less_eq_int
% 9.25/5.24              @ ( abs_abs_int
% 9.25/5.24                @ ( minus_minus_int
% 9.25/5.24                  @ ( groups4538972089207619220nt_int
% 9.25/5.24                    @ ^ [I3: int] : ( times_times_int @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.25/5.24                    @ I4 )
% 9.25/5.24                  @ B ) )
% 9.25/5.24              @ Delta ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7048_convex__sum__bound__le,axiom,
% 9.25/5.24      ! [I4: set_set_nat,X: set_nat > code_integer,A: set_nat > code_integer,B: code_integer,Delta: code_integer] :
% 9.25/5.24        ( ! [I2: set_nat] :
% 9.25/5.24            ( ( member_set_nat @ I2 @ I4 )
% 9.25/5.24           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I2 ) ) )
% 9.25/5.24       => ( ( ( groups9190459664516455967nteger @ X @ I4 )
% 9.25/5.24            = one_one_Code_integer )
% 9.25/5.24         => ( ! [I2: set_nat] :
% 9.25/5.24                ( ( member_set_nat @ I2 @ I4 )
% 9.25/5.24               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 9.25/5.24           => ( ord_le3102999989581377725nteger
% 9.25/5.24              @ ( abs_abs_Code_integer
% 9.25/5.24                @ ( minus_8373710615458151222nteger
% 9.25/5.24                  @ ( groups9190459664516455967nteger
% 9.25/5.24                    @ ^ [I3: set_nat] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.25/5.24                    @ I4 )
% 9.25/5.24                  @ B ) )
% 9.25/5.24              @ Delta ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7049_convex__sum__bound__le,axiom,
% 9.25/5.24      ! [I4: set_set_nat,X: set_nat > rat,A: set_nat > rat,B: rat,Delta: rat] :
% 9.25/5.24        ( ! [I2: set_nat] :
% 9.25/5.24            ( ( member_set_nat @ I2 @ I4 )
% 9.25/5.24           => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I2 ) ) )
% 9.25/5.24       => ( ( ( groups7659867448343625626at_rat @ X @ I4 )
% 9.25/5.24            = one_one_rat )
% 9.25/5.24         => ( ! [I2: set_nat] :
% 9.25/5.24                ( ( member_set_nat @ I2 @ I4 )
% 9.25/5.24               => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 9.25/5.24           => ( ord_less_eq_rat
% 9.25/5.24              @ ( abs_abs_rat
% 9.25/5.24                @ ( minus_minus_rat
% 9.25/5.24                  @ ( groups7659867448343625626at_rat
% 9.25/5.24                    @ ^ [I3: set_nat] : ( times_times_rat @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.25/5.24                    @ I4 )
% 9.25/5.24                  @ B ) )
% 9.25/5.24              @ Delta ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7050_convex__sum__bound__le,axiom,
% 9.25/5.24      ! [I4: set_set_nat,X: set_nat > int,A: set_nat > int,B: int,Delta: int] :
% 9.25/5.24        ( ! [I2: set_nat] :
% 9.25/5.24            ( ( member_set_nat @ I2 @ I4 )
% 9.25/5.24           => ( ord_less_eq_int @ zero_zero_int @ ( X @ I2 ) ) )
% 9.25/5.24       => ( ( ( groups8292507037921071086at_int @ X @ I4 )
% 9.25/5.24            = one_one_int )
% 9.25/5.24         => ( ! [I2: set_nat] :
% 9.25/5.24                ( ( member_set_nat @ I2 @ I4 )
% 9.25/5.24               => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 9.25/5.24           => ( ord_less_eq_int
% 9.25/5.24              @ ( abs_abs_int
% 9.25/5.24                @ ( minus_minus_int
% 9.25/5.24                  @ ( groups8292507037921071086at_int
% 9.25/5.24                    @ ^ [I3: set_nat] : ( times_times_int @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.25/5.24                    @ I4 )
% 9.25/5.24                  @ B ) )
% 9.25/5.24              @ Delta ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7051_convex__sum__bound__le,axiom,
% 9.25/5.24      ! [I4: set_se6260736226359567993nt_int,X: set_Pr958786334691620121nt_int > code_integer,A: set_Pr958786334691620121nt_int > code_integer,B: code_integer,Delta: code_integer] :
% 9.25/5.24        ( ! [I2: set_Pr958786334691620121nt_int] :
% 9.25/5.24            ( ( member2340774599025711042nt_int @ I2 @ I4 )
% 9.25/5.24           => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I2 ) ) )
% 9.25/5.24       => ( ( ( groups3738144136874984124nteger @ X @ I4 )
% 9.25/5.24            = one_one_Code_integer )
% 9.25/5.24         => ( ! [I2: set_Pr958786334691620121nt_int] :
% 9.25/5.24                ( ( member2340774599025711042nt_int @ I2 @ I4 )
% 9.25/5.24               => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I2 ) @ B ) ) @ Delta ) )
% 9.25/5.24           => ( ord_le3102999989581377725nteger
% 9.25/5.24              @ ( abs_abs_Code_integer
% 9.25/5.24                @ ( minus_8373710615458151222nteger
% 9.25/5.24                  @ ( groups3738144136874984124nteger
% 9.25/5.24                    @ ^ [I3: set_Pr958786334691620121nt_int] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X @ I3 ) )
% 9.25/5.24                    @ I4 )
% 9.25/5.24                  @ B ) )
% 9.25/5.24              @ Delta ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7052_abs__sum__abs,axiom,
% 9.25/5.24      ! [F2: int > int,A2: set_int] :
% 9.25/5.24        ( ( abs_abs_int
% 9.25/5.24          @ ( groups4538972089207619220nt_int
% 9.25/5.24            @ ^ [A3: int] : ( abs_abs_int @ ( F2 @ A3 ) )
% 9.25/5.24            @ A2 ) )
% 9.25/5.24        = ( groups4538972089207619220nt_int
% 9.25/5.24          @ ^ [A3: int] : ( abs_abs_int @ ( F2 @ A3 ) )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7053_sum_Oneutral__const,axiom,
% 9.25/5.24      ! [A2: set_nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [Uu: nat] : zero_zero_nat
% 9.25/5.24          @ A2 )
% 9.25/5.24        = zero_zero_nat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7054_sum_Oneutral__const,axiom,
% 9.25/5.24      ! [A2: set_int] :
% 9.25/5.24        ( ( groups4538972089207619220nt_int
% 9.25/5.24          @ ^ [Uu: int] : zero_zero_int
% 9.25/5.24          @ A2 )
% 9.25/5.24        = zero_zero_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7055_sum__diff1__nat,axiom,
% 9.25/5.24      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,F2: produc3843707927480180839at_nat > nat] :
% 9.25/5.24        ( ( ( member8757157785044589968at_nat @ A @ A2 )
% 9.25/5.24         => ( ( groups3860910324918113789at_nat @ F2 @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) )
% 9.25/5.24            = ( minus_minus_nat @ ( groups3860910324918113789at_nat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.24        & ( ~ ( member8757157785044589968at_nat @ A @ A2 )
% 9.25/5.24         => ( ( groups3860910324918113789at_nat @ F2 @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) )
% 9.25/5.24            = ( groups3860910324918113789at_nat @ F2 @ A2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7056_sum__diff1__nat,axiom,
% 9.25/5.24      ! [A: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,F2: set_Pr958786334691620121nt_int > nat] :
% 9.25/5.24        ( ( ( member2340774599025711042nt_int @ A @ A2 )
% 9.25/5.24         => ( ( groups185207323561075247nt_nat @ F2 @ ( minus_2612819937483484256nt_int @ A2 @ ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) )
% 9.25/5.24            = ( minus_minus_nat @ ( groups185207323561075247nt_nat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.24        & ( ~ ( member2340774599025711042nt_int @ A @ A2 )
% 9.25/5.24         => ( ( groups185207323561075247nt_nat @ F2 @ ( minus_2612819937483484256nt_int @ A2 @ ( insert8897473484851387113nt_int @ A @ bot_bo1488462491386950373nt_int ) ) )
% 9.25/5.24            = ( groups185207323561075247nt_nat @ F2 @ A2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7057_sum__diff1__nat,axiom,
% 9.25/5.24      ! [A: set_nat,A2: set_set_nat,F2: set_nat > nat] :
% 9.25/5.24        ( ( ( member_set_nat @ A @ A2 )
% 9.25/5.24         => ( ( groups8294997508430121362at_nat @ F2 @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 9.25/5.24            = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.24        & ( ~ ( member_set_nat @ A @ A2 )
% 9.25/5.24         => ( ( groups8294997508430121362at_nat @ F2 @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 9.25/5.24            = ( groups8294997508430121362at_nat @ F2 @ A2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7058_sum__diff1__nat,axiom,
% 9.25/5.24      ! [A: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,F2: ( produc3658429121746597890et_nat > $o ) > nat] :
% 9.25/5.24        ( ( ( member6576561426505652726_nat_o @ A @ A2 )
% 9.25/5.24         => ( ( groups6742167275697360483_o_nat @ F2 @ ( minus_1801376950450012436_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ) )
% 9.25/5.24            = ( minus_minus_nat @ ( groups6742167275697360483_o_nat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.24        & ( ~ ( member6576561426505652726_nat_o @ A @ A2 )
% 9.25/5.24         => ( ( groups6742167275697360483_o_nat @ F2 @ ( minus_1801376950450012436_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ A @ bot_bo7824918357723582233_nat_o ) ) )
% 9.25/5.24            = ( groups6742167275697360483_o_nat @ F2 @ A2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7059_sum__diff1__nat,axiom,
% 9.25/5.24      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > nat] :
% 9.25/5.24        ( ( ( member8440522571783428010at_nat @ A @ A2 )
% 9.25/5.24         => ( ( groups977919841031483927at_nat @ F2 @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 9.25/5.24            = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.24        & ( ~ ( member8440522571783428010at_nat @ A @ A2 )
% 9.25/5.24         => ( ( groups977919841031483927at_nat @ F2 @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 9.25/5.24            = ( groups977919841031483927at_nat @ F2 @ A2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7060_sum__diff1__nat,axiom,
% 9.25/5.24      ! [A: $o,A2: set_o,F2: $o > nat] :
% 9.25/5.24        ( ( ( member_o @ A @ A2 )
% 9.25/5.24         => ( ( groups8507830703676809646_o_nat @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 9.25/5.24            = ( minus_minus_nat @ ( groups8507830703676809646_o_nat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.24        & ( ~ ( member_o @ A @ A2 )
% 9.25/5.24         => ( ( groups8507830703676809646_o_nat @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 9.25/5.24            = ( groups8507830703676809646_o_nat @ F2 @ A2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7061_sum__diff1__nat,axiom,
% 9.25/5.24      ! [A: int,A2: set_int,F2: int > nat] :
% 9.25/5.24        ( ( ( member_int @ A @ A2 )
% 9.25/5.24         => ( ( groups4541462559716669496nt_nat @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.25/5.24            = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.24        & ( ~ ( member_int @ A @ A2 )
% 9.25/5.24         => ( ( groups4541462559716669496nt_nat @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.25/5.24            = ( groups4541462559716669496nt_nat @ F2 @ A2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7062_sum__diff1__nat,axiom,
% 9.25/5.24      ! [A: nat,A2: set_nat,F2: nat > nat] :
% 9.25/5.24        ( ( ( member_nat @ A @ A2 )
% 9.25/5.24         => ( ( groups3542108847815614940at_nat @ F2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.25/5.24            = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.24        & ( ~ ( member_nat @ A @ A2 )
% 9.25/5.24         => ( ( groups3542108847815614940at_nat @ F2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.25/5.24            = ( groups3542108847815614940at_nat @ F2 @ A2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7063_sum_Oswap,axiom,
% 9.25/5.24      ! [G2: nat > nat > nat,B2: set_nat,A2: set_nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [I3: nat] : ( groups3542108847815614940at_nat @ ( G2 @ I3 ) @ B2 )
% 9.25/5.24          @ A2 )
% 9.25/5.24        = ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [J3: nat] :
% 9.25/5.24              ( groups3542108847815614940at_nat
% 9.25/5.24              @ ^ [I3: nat] : ( G2 @ I3 @ J3 )
% 9.25/5.24              @ A2 )
% 9.25/5.24          @ B2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7064_sum_Oswap,axiom,
% 9.25/5.24      ! [G2: int > int > int,B2: set_int,A2: set_int] :
% 9.25/5.24        ( ( groups4538972089207619220nt_int
% 9.25/5.24          @ ^ [I3: int] : ( groups4538972089207619220nt_int @ ( G2 @ I3 ) @ B2 )
% 9.25/5.24          @ A2 )
% 9.25/5.24        = ( groups4538972089207619220nt_int
% 9.25/5.24          @ ^ [J3: int] :
% 9.25/5.24              ( groups4538972089207619220nt_int
% 9.25/5.24              @ ^ [I3: int] : ( G2 @ I3 @ J3 )
% 9.25/5.24              @ A2 )
% 9.25/5.24          @ B2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7065_sum__mono,axiom,
% 9.25/5.24      ! [K5: set_nat,F2: nat > rat,G2: nat > rat] :
% 9.25/5.24        ( ! [I2: nat] :
% 9.25/5.24            ( ( member_nat @ I2 @ K5 )
% 9.25/5.24           => ( ord_less_eq_rat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) )
% 9.25/5.24       => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ K5 ) @ ( groups2906978787729119204at_rat @ G2 @ K5 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7066_sum__mono,axiom,
% 9.25/5.24      ! [K5: set_int,F2: int > rat,G2: int > rat] :
% 9.25/5.24        ( ! [I2: int] :
% 9.25/5.24            ( ( member_int @ I2 @ K5 )
% 9.25/5.24           => ( ord_less_eq_rat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) )
% 9.25/5.24       => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ K5 ) @ ( groups3906332499630173760nt_rat @ G2 @ K5 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7067_sum__mono,axiom,
% 9.25/5.24      ! [K5: set_int,F2: int > nat,G2: int > nat] :
% 9.25/5.24        ( ! [I2: int] :
% 9.25/5.24            ( ( member_int @ I2 @ K5 )
% 9.25/5.24           => ( ord_less_eq_nat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) )
% 9.25/5.24       => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F2 @ K5 ) @ ( groups4541462559716669496nt_nat @ G2 @ K5 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7068_sum__mono,axiom,
% 9.25/5.24      ! [K5: set_nat,F2: nat > int,G2: nat > int] :
% 9.25/5.24        ( ! [I2: nat] :
% 9.25/5.24            ( ( member_nat @ I2 @ K5 )
% 9.25/5.24           => ( ord_less_eq_int @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) )
% 9.25/5.24       => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F2 @ K5 ) @ ( groups3539618377306564664at_int @ G2 @ K5 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7069_sum__mono,axiom,
% 9.25/5.24      ! [K5: set_nat,F2: nat > nat,G2: nat > nat] :
% 9.25/5.24        ( ! [I2: nat] :
% 9.25/5.24            ( ( member_nat @ I2 @ K5 )
% 9.25/5.24           => ( ord_less_eq_nat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) )
% 9.25/5.24       => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F2 @ K5 ) @ ( groups3542108847815614940at_nat @ G2 @ K5 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7070_sum__mono,axiom,
% 9.25/5.24      ! [K5: set_int,F2: int > int,G2: int > int] :
% 9.25/5.24        ( ! [I2: int] :
% 9.25/5.24            ( ( member_int @ I2 @ K5 )
% 9.25/5.24           => ( ord_less_eq_int @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) )
% 9.25/5.24       => ( ord_less_eq_int @ ( groups4538972089207619220nt_int @ F2 @ K5 ) @ ( groups4538972089207619220nt_int @ G2 @ K5 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7071_sum__mono,axiom,
% 9.25/5.24      ! [K5: set_set_nat,F2: set_nat > rat,G2: set_nat > rat] :
% 9.25/5.24        ( ! [I2: set_nat] :
% 9.25/5.24            ( ( member_set_nat @ I2 @ K5 )
% 9.25/5.24           => ( ord_less_eq_rat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) )
% 9.25/5.24       => ( ord_less_eq_rat @ ( groups7659867448343625626at_rat @ F2 @ K5 ) @ ( groups7659867448343625626at_rat @ G2 @ K5 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7072_sum__mono,axiom,
% 9.25/5.24      ! [K5: set_set_nat,F2: set_nat > nat,G2: set_nat > nat] :
% 9.25/5.24        ( ! [I2: set_nat] :
% 9.25/5.24            ( ( member_set_nat @ I2 @ K5 )
% 9.25/5.24           => ( ord_less_eq_nat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) )
% 9.25/5.24       => ( ord_less_eq_nat @ ( groups8294997508430121362at_nat @ F2 @ K5 ) @ ( groups8294997508430121362at_nat @ G2 @ K5 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7073_sum__mono,axiom,
% 9.25/5.24      ! [K5: set_set_nat,F2: set_nat > int,G2: set_nat > int] :
% 9.25/5.24        ( ! [I2: set_nat] :
% 9.25/5.24            ( ( member_set_nat @ I2 @ K5 )
% 9.25/5.24           => ( ord_less_eq_int @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) )
% 9.25/5.24       => ( ord_less_eq_int @ ( groups8292507037921071086at_int @ F2 @ K5 ) @ ( groups8292507037921071086at_int @ G2 @ K5 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7074_sum__mono,axiom,
% 9.25/5.24      ! [K5: set_se6260736226359567993nt_int,F2: set_Pr958786334691620121nt_int > rat,G2: set_Pr958786334691620121nt_int > rat] :
% 9.25/5.24        ( ! [I2: set_Pr958786334691620121nt_int] :
% 9.25/5.24            ( ( member2340774599025711042nt_int @ I2 @ K5 )
% 9.25/5.24           => ( ord_less_eq_rat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) )
% 9.25/5.24       => ( ord_less_eq_rat @ ( groups8773449300329355319nt_rat @ F2 @ K5 ) @ ( groups8773449300329355319nt_rat @ G2 @ K5 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7075_sum_Odistrib,axiom,
% 9.25/5.24      ! [G2: nat > nat,H3: nat > nat,A2: set_nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [X3: nat] : ( plus_plus_nat @ ( G2 @ X3 ) @ ( H3 @ X3 ) )
% 9.25/5.24          @ A2 )
% 9.25/5.24        = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ A2 ) @ ( groups3542108847815614940at_nat @ H3 @ A2 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7076_sum_Odistrib,axiom,
% 9.25/5.24      ! [G2: int > int,H3: int > int,A2: set_int] :
% 9.25/5.24        ( ( groups4538972089207619220nt_int
% 9.25/5.24          @ ^ [X3: int] : ( plus_plus_int @ ( G2 @ X3 ) @ ( H3 @ X3 ) )
% 9.25/5.24          @ A2 )
% 9.25/5.24        = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G2 @ A2 ) @ ( groups4538972089207619220nt_int @ H3 @ A2 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7077_sum__product,axiom,
% 9.25/5.24      ! [F2: nat > nat,A2: set_nat,G2: nat > nat,B2: set_nat] :
% 9.25/5.24        ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F2 @ A2 ) @ ( groups3542108847815614940at_nat @ G2 @ B2 ) )
% 9.25/5.24        = ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [I3: nat] :
% 9.25/5.24              ( groups3542108847815614940at_nat
% 9.25/5.24              @ ^ [J3: nat] : ( times_times_nat @ ( F2 @ I3 ) @ ( G2 @ J3 ) )
% 9.25/5.24              @ B2 )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7078_sum__product,axiom,
% 9.25/5.24      ! [F2: int > int,A2: set_int,G2: int > int,B2: set_int] :
% 9.25/5.24        ( ( times_times_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) @ ( groups4538972089207619220nt_int @ G2 @ B2 ) )
% 9.25/5.24        = ( groups4538972089207619220nt_int
% 9.25/5.24          @ ^ [I3: int] :
% 9.25/5.24              ( groups4538972089207619220nt_int
% 9.25/5.24              @ ^ [J3: int] : ( times_times_int @ ( F2 @ I3 ) @ ( G2 @ J3 ) )
% 9.25/5.24              @ B2 )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7079_sum__distrib__right,axiom,
% 9.25/5.24      ! [F2: nat > nat,A2: set_nat,R3: nat] :
% 9.25/5.24        ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F2 @ A2 ) @ R3 )
% 9.25/5.24        = ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [N2: nat] : ( times_times_nat @ ( F2 @ N2 ) @ R3 )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7080_sum__distrib__right,axiom,
% 9.25/5.24      ! [F2: int > int,A2: set_int,R3: int] :
% 9.25/5.24        ( ( times_times_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) @ R3 )
% 9.25/5.24        = ( groups4538972089207619220nt_int
% 9.25/5.24          @ ^ [N2: int] : ( times_times_int @ ( F2 @ N2 ) @ R3 )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7081_sum__distrib__left,axiom,
% 9.25/5.24      ! [R3: nat,F2: nat > nat,A2: set_nat] :
% 9.25/5.24        ( ( times_times_nat @ R3 @ ( groups3542108847815614940at_nat @ F2 @ A2 ) )
% 9.25/5.24        = ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [N2: nat] : ( times_times_nat @ R3 @ ( F2 @ N2 ) )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7082_sum__distrib__left,axiom,
% 9.25/5.24      ! [R3: int,F2: int > int,A2: set_int] :
% 9.25/5.24        ( ( times_times_int @ R3 @ ( groups4538972089207619220nt_int @ F2 @ A2 ) )
% 9.25/5.24        = ( groups4538972089207619220nt_int
% 9.25/5.24          @ ^ [N2: int] : ( times_times_int @ R3 @ ( F2 @ N2 ) )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7083_sum__subtractf,axiom,
% 9.25/5.24      ! [F2: int > int,G2: int > int,A2: set_int] :
% 9.25/5.24        ( ( groups4538972089207619220nt_int
% 9.25/5.24          @ ^ [X3: int] : ( minus_minus_int @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.24          @ A2 )
% 9.25/5.24        = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) @ ( groups4538972089207619220nt_int @ G2 @ A2 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7084_sum__negf,axiom,
% 9.25/5.24      ! [F2: int > int,A2: set_int] :
% 9.25/5.24        ( ( groups4538972089207619220nt_int
% 9.25/5.24          @ ^ [X3: int] : ( uminus_uminus_int @ ( F2 @ X3 ) )
% 9.25/5.24          @ A2 )
% 9.25/5.24        = ( uminus_uminus_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7085_sum__subtractf__nat,axiom,
% 9.25/5.24      ! [A2: set_se6260736226359567993nt_int,G2: set_Pr958786334691620121nt_int > nat,F2: set_Pr958786334691620121nt_int > nat] :
% 9.25/5.24        ( ! [X2: set_Pr958786334691620121nt_int] :
% 9.25/5.24            ( ( member2340774599025711042nt_int @ X2 @ A2 )
% 9.25/5.24           => ( ord_less_eq_nat @ ( G2 @ X2 ) @ ( F2 @ X2 ) ) )
% 9.25/5.24       => ( ( groups185207323561075247nt_nat
% 9.25/5.24            @ ^ [X3: set_Pr958786334691620121nt_int] : ( minus_minus_nat @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.24            @ A2 )
% 9.25/5.24          = ( minus_minus_nat @ ( groups185207323561075247nt_nat @ F2 @ A2 ) @ ( groups185207323561075247nt_nat @ G2 @ A2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7086_sum__subtractf__nat,axiom,
% 9.25/5.24      ! [A2: set_set_nat,G2: set_nat > nat,F2: set_nat > nat] :
% 9.25/5.24        ( ! [X2: set_nat] :
% 9.25/5.24            ( ( member_set_nat @ X2 @ A2 )
% 9.25/5.24           => ( ord_less_eq_nat @ ( G2 @ X2 ) @ ( F2 @ X2 ) ) )
% 9.25/5.24       => ( ( groups8294997508430121362at_nat
% 9.25/5.24            @ ^ [X3: set_nat] : ( minus_minus_nat @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.24            @ A2 )
% 9.25/5.24          = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F2 @ A2 ) @ ( groups8294997508430121362at_nat @ G2 @ A2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7087_sum__subtractf__nat,axiom,
% 9.25/5.24      ! [A2: set_int,G2: int > nat,F2: int > nat] :
% 9.25/5.24        ( ! [X2: int] :
% 9.25/5.24            ( ( member_int @ X2 @ A2 )
% 9.25/5.24           => ( ord_less_eq_nat @ ( G2 @ X2 ) @ ( F2 @ X2 ) ) )
% 9.25/5.24       => ( ( groups4541462559716669496nt_nat
% 9.25/5.24            @ ^ [X3: int] : ( minus_minus_nat @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.24            @ A2 )
% 9.25/5.24          = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F2 @ A2 ) @ ( groups4541462559716669496nt_nat @ G2 @ A2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7088_sum__subtractf__nat,axiom,
% 9.25/5.24      ! [A2: set_Pr4532377907799695533_nat_o,G2: ( produc3658429121746597890et_nat > $o ) > nat,F2: ( produc3658429121746597890et_nat > $o ) > nat] :
% 9.25/5.24        ( ! [X2: produc3658429121746597890et_nat > $o] :
% 9.25/5.24            ( ( member6576561426505652726_nat_o @ X2 @ A2 )
% 9.25/5.24           => ( ord_less_eq_nat @ ( G2 @ X2 ) @ ( F2 @ X2 ) ) )
% 9.25/5.24       => ( ( groups6742167275697360483_o_nat
% 9.25/5.24            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( minus_minus_nat @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.24            @ A2 )
% 9.25/5.24          = ( minus_minus_nat @ ( groups6742167275697360483_o_nat @ F2 @ A2 ) @ ( groups6742167275697360483_o_nat @ G2 @ A2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7089_sum__subtractf__nat,axiom,
% 9.25/5.24      ! [A2: set_nat,G2: nat > nat,F2: nat > nat] :
% 9.25/5.24        ( ! [X2: nat] :
% 9.25/5.24            ( ( member_nat @ X2 @ A2 )
% 9.25/5.24           => ( ord_less_eq_nat @ ( G2 @ X2 ) @ ( F2 @ X2 ) ) )
% 9.25/5.24       => ( ( groups3542108847815614940at_nat
% 9.25/5.24            @ ^ [X3: nat] : ( minus_minus_nat @ ( F2 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.24            @ A2 )
% 9.25/5.24          = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F2 @ A2 ) @ ( groups3542108847815614940at_nat @ G2 @ A2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7090_divmod__integer__code,axiom,
% 9.25/5.24      ( code_divmod_integer
% 9.25/5.24      = ( ^ [K4: code_integer,L2: code_integer] :
% 9.25/5.24            ( if_Pro6119634080678213985nteger @ ( K4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 9.25/5.24            @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L2 )
% 9.25/5.24              @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K4 ) @ ( code_divmod_abs @ K4 @ L2 )
% 9.25/5.24                @ ( produc6916734918728496179nteger
% 9.25/5.24                  @ ^ [R4: code_integer,S2: code_integer] : ( if_Pro6119634080678213985nteger @ ( S2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R4 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L2 @ S2 ) ) )
% 9.25/5.24                  @ ( code_divmod_abs @ K4 @ L2 ) ) )
% 9.25/5.24              @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K4 )
% 9.25/5.24                @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 9.25/5.24                  @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K4 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K4 @ L2 )
% 9.25/5.24                    @ ( produc6916734918728496179nteger
% 9.25/5.24                      @ ^ [R4: code_integer,S2: code_integer] : ( if_Pro6119634080678213985nteger @ ( S2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R4 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L2 ) @ S2 ) ) )
% 9.25/5.24                      @ ( code_divmod_abs @ K4 @ L2 ) ) ) ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7091_Sum__Icc__nat,axiom,
% 9.25/5.24      ! [M: nat,N: nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [X3: nat] : X3
% 9.25/5.24          @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.24        = ( 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 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7092_arith__series__nat,axiom,
% 9.25/5.24      ! [A: nat,D2: nat,N: nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I3 @ D2 ) )
% 9.25/5.24          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.25/5.24        = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7093_Sum__Icc__int,axiom,
% 9.25/5.24      ! [M: int,N: int] :
% 9.25/5.24        ( ( ord_less_eq_int @ M @ N )
% 9.25/5.24       => ( ( groups4538972089207619220nt_int
% 9.25/5.24            @ ^ [X3: int] : X3
% 9.25/5.24            @ ( set_or1266510415728281911st_int @ M @ N ) )
% 9.25/5.24          = ( 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 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7094_Sum__Ico__nat,axiom,
% 9.25/5.24      ! [M: nat,N: nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [X3: nat] : X3
% 9.25/5.24          @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 9.25/5.24        = ( 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 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7095_sum__power2,axiom,
% 9.25/5.24      ! [K: nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 9.25/5.24        = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7096_gauss__sum__nat,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [X3: nat] : X3
% 9.25/5.24          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.25/5.24        = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7097_apsnd__conv,axiom,
% 9.25/5.24      ! [F2: produc8923325533196201883nteger > produc8923325533196201883nteger,X: produc6241069584506657477e_term > option6357759511663192854e_term,Y: produc8923325533196201883nteger] :
% 9.25/5.24        ( ( produc717174245515237944e_term @ F2 @ ( produc8603105652947943368nteger @ X @ Y ) )
% 9.25/5.24        = ( produc8603105652947943368nteger @ X @ ( F2 @ Y ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7098_apsnd__conv,axiom,
% 9.25/5.24      ! [F2: produc3658429121746597890et_nat > produc3658429121746597890et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 9.25/5.24        ( ( produc8750854537940449737_nat_o @ F2 @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 9.25/5.24        = ( produc5001842942810119800et_nat @ X @ ( F2 @ Y ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7099_apsnd__conv,axiom,
% 9.25/5.24      ! [F2: produc3658429121746597890et_nat > produc3925858234332021118et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3658429121746597890et_nat] :
% 9.25/5.24        ( ( produc7714581247149323085_nat_o @ F2 @ ( produc5001842942810119800et_nat @ X @ Y ) )
% 9.25/5.24        = ( produc2245416461498447860et_nat @ X @ ( F2 @ Y ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7100_apsnd__conv,axiom,
% 9.25/5.24      ! [F2: produc3925858234332021118et_nat > produc3658429121746597890et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 9.25/5.24        ( ( produc1515462096303866701_nat_o @ F2 @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 9.25/5.24        = ( produc5001842942810119800et_nat @ X @ ( F2 @ Y ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7101_apsnd__conv,axiom,
% 9.25/5.24      ! [F2: produc3925858234332021118et_nat > produc3925858234332021118et_nat,X: produc3658429121746597890et_nat > $o,Y: produc3925858234332021118et_nat] :
% 9.25/5.24        ( ( produc969530845752564945_nat_o @ F2 @ ( produc2245416461498447860et_nat @ X @ Y ) )
% 9.25/5.24        = ( produc2245416461498447860et_nat @ X @ ( F2 @ Y ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7102_apsnd__conv,axiom,
% 9.25/5.24      ! [F2: product_prod_int_int > product_prod_int_int,X: produc8551481072490612790e_term > option6357759511663192854e_term,Y: product_prod_int_int] :
% 9.25/5.24        ( ( produc4973430039190721449e_term @ F2 @ ( produc5700946648718959541nt_int @ X @ Y ) )
% 9.25/5.24        = ( produc5700946648718959541nt_int @ X @ ( F2 @ Y ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7103_apsnd__conv,axiom,
% 9.25/5.24      ! [F2: product_prod_int_int > product_prod_int_int,X: int > option6357759511663192854e_term,Y: product_prod_int_int] :
% 9.25/5.24        ( ( produc7011684061226097695e_term @ F2 @ ( produc4305682042979456191nt_int @ X @ Y ) )
% 9.25/5.24        = ( produc4305682042979456191nt_int @ X @ ( F2 @ Y ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7104_apsnd__conv,axiom,
% 9.25/5.24      ! [F2: code_integer > code_integer,X: code_integer,Y: code_integer] :
% 9.25/5.24        ( ( produc6499014454317279255nteger @ F2 @ ( produc1086072967326762835nteger @ X @ Y ) )
% 9.25/5.24        = ( produc1086072967326762835nteger @ X @ ( F2 @ Y ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7105_atLeastatMost__empty__iff,axiom,
% 9.25/5.24      ! [A: $o,B: $o] :
% 9.25/5.24        ( ( ( set_or8904488021354931149Most_o @ A @ B )
% 9.25/5.24          = bot_bot_set_o )
% 9.25/5.24        = ( ~ ( ord_less_eq_o @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7106_atLeastatMost__empty__iff,axiom,
% 9.25/5.24      ! [A: filter_nat,B: filter_nat] :
% 9.25/5.24        ( ( ( set_or1955772592623580779er_nat @ A @ B )
% 9.25/5.24          = bot_bo498966703094740906er_nat )
% 9.25/5.24        = ( ~ ( ord_le2510731241096832064er_nat @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7107_atLeastatMost__empty__iff,axiom,
% 9.25/5.24      ! [A: set_nat,B: set_nat] :
% 9.25/5.24        ( ( ( set_or4548717258645045905et_nat @ A @ B )
% 9.25/5.24          = bot_bot_set_set_nat )
% 9.25/5.24        = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7108_atLeastatMost__empty__iff,axiom,
% 9.25/5.24      ! [A: rat,B: rat] :
% 9.25/5.24        ( ( ( set_or633870826150836451st_rat @ A @ B )
% 9.25/5.24          = bot_bot_set_rat )
% 9.25/5.24        = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7109_atLeastatMost__empty__iff,axiom,
% 9.25/5.24      ! [A: nat,B: nat] :
% 9.25/5.24        ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 9.25/5.24          = bot_bot_set_nat )
% 9.25/5.24        = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7110_atLeastatMost__empty__iff,axiom,
% 9.25/5.24      ! [A: int,B: int] :
% 9.25/5.24        ( ( ( set_or1266510415728281911st_int @ A @ B )
% 9.25/5.24          = bot_bot_set_int )
% 9.25/5.24        = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7111_atLeastatMost__empty__iff,axiom,
% 9.25/5.24      ! [A: code_integer,B: code_integer] :
% 9.25/5.24        ( ( ( set_or189985376899183464nteger @ A @ B )
% 9.25/5.24          = bot_bo3990330152332043303nteger )
% 9.25/5.24        = ( ~ ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7112_atLeastatMost__empty__iff2,axiom,
% 9.25/5.24      ! [A: $o,B: $o] :
% 9.25/5.24        ( ( bot_bot_set_o
% 9.25/5.24          = ( set_or8904488021354931149Most_o @ A @ B ) )
% 9.25/5.24        = ( ~ ( ord_less_eq_o @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7113_atLeastatMost__empty__iff2,axiom,
% 9.25/5.24      ! [A: filter_nat,B: filter_nat] :
% 9.25/5.24        ( ( bot_bo498966703094740906er_nat
% 9.25/5.24          = ( set_or1955772592623580779er_nat @ A @ B ) )
% 9.25/5.24        = ( ~ ( ord_le2510731241096832064er_nat @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7114_atLeastatMost__empty__iff2,axiom,
% 9.25/5.24      ! [A: set_nat,B: set_nat] :
% 9.25/5.24        ( ( bot_bot_set_set_nat
% 9.25/5.24          = ( set_or4548717258645045905et_nat @ A @ B ) )
% 9.25/5.24        = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7115_atLeastatMost__empty__iff2,axiom,
% 9.25/5.24      ! [A: rat,B: rat] :
% 9.25/5.24        ( ( bot_bot_set_rat
% 9.25/5.24          = ( set_or633870826150836451st_rat @ A @ B ) )
% 9.25/5.24        = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7116_atLeastatMost__empty__iff2,axiom,
% 9.25/5.24      ! [A: nat,B: nat] :
% 9.25/5.24        ( ( bot_bot_set_nat
% 9.25/5.24          = ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.25/5.24        = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7117_atLeastatMost__empty__iff2,axiom,
% 9.25/5.24      ! [A: int,B: int] :
% 9.25/5.24        ( ( bot_bot_set_int
% 9.25/5.24          = ( set_or1266510415728281911st_int @ A @ B ) )
% 9.25/5.24        = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7118_atLeastatMost__empty__iff2,axiom,
% 9.25/5.24      ! [A: code_integer,B: code_integer] :
% 9.25/5.24        ( ( bot_bo3990330152332043303nteger
% 9.25/5.24          = ( set_or189985376899183464nteger @ A @ B ) )
% 9.25/5.24        = ( ~ ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7119_atLeastatMost__empty,axiom,
% 9.25/5.24      ! [B: $o,A: $o] :
% 9.25/5.24        ( ( ord_less_o @ B @ A )
% 9.25/5.24       => ( ( set_or8904488021354931149Most_o @ A @ B )
% 9.25/5.24          = bot_bot_set_o ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7120_atLeastatMost__empty,axiom,
% 9.25/5.24      ! [B: literal,A: literal] :
% 9.25/5.24        ( ( ord_less_literal @ B @ A )
% 9.25/5.24       => ( ( set_or8436436507035938825iteral @ A @ B )
% 9.25/5.24          = bot_bot_set_literal ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7121_atLeastatMost__empty,axiom,
% 9.25/5.24      ! [B: rat,A: rat] :
% 9.25/5.24        ( ( ord_less_rat @ B @ A )
% 9.25/5.24       => ( ( set_or633870826150836451st_rat @ A @ B )
% 9.25/5.24          = bot_bot_set_rat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7122_atLeastatMost__empty,axiom,
% 9.25/5.24      ! [B: nat,A: nat] :
% 9.25/5.24        ( ( ord_less_nat @ B @ A )
% 9.25/5.24       => ( ( set_or1269000886237332187st_nat @ A @ B )
% 9.25/5.24          = bot_bot_set_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7123_atLeastatMost__empty,axiom,
% 9.25/5.24      ! [B: int,A: int] :
% 9.25/5.24        ( ( ord_less_int @ B @ A )
% 9.25/5.24       => ( ( set_or1266510415728281911st_int @ A @ B )
% 9.25/5.24          = bot_bot_set_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7124_atLeastatMost__empty,axiom,
% 9.25/5.24      ! [B: code_integer,A: code_integer] :
% 9.25/5.24        ( ( ord_le6747313008572928689nteger @ B @ A )
% 9.25/5.24       => ( ( set_or189985376899183464nteger @ A @ B )
% 9.25/5.24          = bot_bo3990330152332043303nteger ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7125_atLeastLessThan__empty,axiom,
% 9.25/5.24      ! [B: $o,A: $o] :
% 9.25/5.24        ( ( ord_less_eq_o @ B @ A )
% 9.25/5.24       => ( ( set_or7139685690850216873Than_o @ A @ B )
% 9.25/5.24          = bot_bot_set_o ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7126_atLeastLessThan__empty,axiom,
% 9.25/5.24      ! [B: filter_nat,A: filter_nat] :
% 9.25/5.24        ( ( ord_le2510731241096832064er_nat @ B @ A )
% 9.25/5.24       => ( ( set_or1773934645810362255er_nat @ A @ B )
% 9.25/5.24          = bot_bo498966703094740906er_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7127_atLeastLessThan__empty,axiom,
% 9.25/5.24      ! [B: set_nat,A: set_nat] :
% 9.25/5.24        ( ( ord_less_eq_set_nat @ B @ A )
% 9.25/5.24       => ( ( set_or3540276404033026485et_nat @ A @ B )
% 9.25/5.24          = bot_bot_set_set_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7128_atLeastLessThan__empty,axiom,
% 9.25/5.24      ! [B: rat,A: rat] :
% 9.25/5.24        ( ( ord_less_eq_rat @ B @ A )
% 9.25/5.24       => ( ( set_or4029947393144176647an_rat @ A @ B )
% 9.25/5.24          = bot_bot_set_rat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7129_atLeastLessThan__empty,axiom,
% 9.25/5.24      ! [B: nat,A: nat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ B @ A )
% 9.25/5.24       => ( ( set_or4665077453230672383an_nat @ A @ B )
% 9.25/5.24          = bot_bot_set_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7130_atLeastLessThan__empty,axiom,
% 9.25/5.24      ! [B: code_integer,A: code_integer] :
% 9.25/5.24        ( ( ord_le3102999989581377725nteger @ B @ A )
% 9.25/5.24       => ( ( set_or8404916559141939852nteger @ A @ B )
% 9.25/5.24          = bot_bo3990330152332043303nteger ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7131_atLeastLessThan__empty,axiom,
% 9.25/5.24      ! [B: int,A: int] :
% 9.25/5.24        ( ( ord_less_eq_int @ B @ A )
% 9.25/5.24       => ( ( set_or4662586982721622107an_int @ A @ B )
% 9.25/5.24          = bot_bot_set_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7132_atLeastLessThan__empty__iff,axiom,
% 9.25/5.24      ! [A: $o,B: $o] :
% 9.25/5.24        ( ( ( set_or7139685690850216873Than_o @ A @ B )
% 9.25/5.24          = bot_bot_set_o )
% 9.25/5.24        = ( ~ ( ord_less_o @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7133_atLeastLessThan__empty__iff,axiom,
% 9.25/5.24      ! [A: literal,B: literal] :
% 9.25/5.24        ( ( ( set_or4828121863581493221iteral @ A @ B )
% 9.25/5.24          = bot_bot_set_literal )
% 9.25/5.24        = ( ~ ( ord_less_literal @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7134_atLeastLessThan__empty__iff,axiom,
% 9.25/5.24      ! [A: rat,B: rat] :
% 9.25/5.24        ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 9.25/5.24          = bot_bot_set_rat )
% 9.25/5.24        = ( ~ ( ord_less_rat @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7135_atLeastLessThan__empty__iff,axiom,
% 9.25/5.24      ! [A: nat,B: nat] :
% 9.25/5.24        ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 9.25/5.24          = bot_bot_set_nat )
% 9.25/5.24        = ( ~ ( ord_less_nat @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7136_atLeastLessThan__empty__iff,axiom,
% 9.25/5.24      ! [A: code_integer,B: code_integer] :
% 9.25/5.24        ( ( ( set_or8404916559141939852nteger @ A @ B )
% 9.25/5.24          = bot_bo3990330152332043303nteger )
% 9.25/5.24        = ( ~ ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7137_atLeastLessThan__empty__iff,axiom,
% 9.25/5.24      ! [A: int,B: int] :
% 9.25/5.24        ( ( ( set_or4662586982721622107an_int @ A @ B )
% 9.25/5.24          = bot_bot_set_int )
% 9.25/5.24        = ( ~ ( ord_less_int @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7138_atLeastLessThan__empty__iff2,axiom,
% 9.25/5.24      ! [A: $o,B: $o] :
% 9.25/5.24        ( ( bot_bot_set_o
% 9.25/5.24          = ( set_or7139685690850216873Than_o @ A @ B ) )
% 9.25/5.24        = ( ~ ( ord_less_o @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7139_atLeastLessThan__empty__iff2,axiom,
% 9.25/5.24      ! [A: literal,B: literal] :
% 9.25/5.24        ( ( bot_bot_set_literal
% 9.25/5.24          = ( set_or4828121863581493221iteral @ A @ B ) )
% 9.25/5.24        = ( ~ ( ord_less_literal @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7140_atLeastLessThan__empty__iff2,axiom,
% 9.25/5.24      ! [A: rat,B: rat] :
% 9.25/5.24        ( ( bot_bot_set_rat
% 9.25/5.24          = ( set_or4029947393144176647an_rat @ A @ B ) )
% 9.25/5.24        = ( ~ ( ord_less_rat @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7141_atLeastLessThan__empty__iff2,axiom,
% 9.25/5.24      ! [A: nat,B: nat] :
% 9.25/5.24        ( ( bot_bot_set_nat
% 9.25/5.24          = ( set_or4665077453230672383an_nat @ A @ B ) )
% 9.25/5.24        = ( ~ ( ord_less_nat @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7142_atLeastLessThan__empty__iff2,axiom,
% 9.25/5.24      ! [A: code_integer,B: code_integer] :
% 9.25/5.24        ( ( bot_bo3990330152332043303nteger
% 9.25/5.24          = ( set_or8404916559141939852nteger @ A @ B ) )
% 9.25/5.24        = ( ~ ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7143_atLeastLessThan__empty__iff2,axiom,
% 9.25/5.24      ! [A: int,B: int] :
% 9.25/5.24        ( ( bot_bot_set_int
% 9.25/5.24          = ( set_or4662586982721622107an_int @ A @ B ) )
% 9.25/5.24        = ( ~ ( ord_less_int @ A @ B ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7144_atLeastAtMost__singleton,axiom,
% 9.25/5.24      ! [A: $o] :
% 9.25/5.24        ( ( set_or8904488021354931149Most_o @ A @ A )
% 9.25/5.24        = ( insert_o @ A @ bot_bot_set_o ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7145_atLeastAtMost__singleton,axiom,
% 9.25/5.24      ! [A: nat] :
% 9.25/5.24        ( ( set_or1269000886237332187st_nat @ A @ A )
% 9.25/5.24        = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7146_atLeastAtMost__singleton,axiom,
% 9.25/5.24      ! [A: int] :
% 9.25/5.24        ( ( set_or1266510415728281911st_int @ A @ A )
% 9.25/5.24        = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7147_atLeastAtMost__singleton,axiom,
% 9.25/5.24      ! [A: code_integer] :
% 9.25/5.24        ( ( set_or189985376899183464nteger @ A @ A )
% 9.25/5.24        = ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7148_atLeastAtMost__singleton__iff,axiom,
% 9.25/5.24      ! [A: $o,B: $o,C: $o] :
% 9.25/5.24        ( ( ( set_or8904488021354931149Most_o @ A @ B )
% 9.25/5.24          = ( insert_o @ C @ bot_bot_set_o ) )
% 9.25/5.24        = ( ( A = B )
% 9.25/5.24          & ( B = C ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7149_atLeastAtMost__singleton__iff,axiom,
% 9.25/5.24      ! [A: nat,B: nat,C: nat] :
% 9.25/5.24        ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 9.25/5.24          = ( insert_nat @ C @ bot_bot_set_nat ) )
% 9.25/5.24        = ( ( A = B )
% 9.25/5.24          & ( B = C ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7150_atLeastAtMost__singleton__iff,axiom,
% 9.25/5.24      ! [A: int,B: int,C: int] :
% 9.25/5.24        ( ( ( set_or1266510415728281911st_int @ A @ B )
% 9.25/5.24          = ( insert_int @ C @ bot_bot_set_int ) )
% 9.25/5.24        = ( ( A = B )
% 9.25/5.24          & ( B = C ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7151_atLeastAtMost__singleton__iff,axiom,
% 9.25/5.24      ! [A: code_integer,B: code_integer,C: code_integer] :
% 9.25/5.24        ( ( ( set_or189985376899183464nteger @ A @ B )
% 9.25/5.24          = ( insert_Code_integer @ C @ bot_bo3990330152332043303nteger ) )
% 9.25/5.24        = ( ( A = B )
% 9.25/5.24          & ( B = C ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7152_atLeastLessThan__singleton,axiom,
% 9.25/5.24      ! [M: nat] :
% 9.25/5.24        ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 9.25/5.24        = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7153_ivl__disj__un__two_I7_J,axiom,
% 9.25/5.24      ! [L: rat,M: rat,U: rat] :
% 9.25/5.24        ( ( ord_less_eq_rat @ L @ M )
% 9.25/5.24       => ( ( ord_less_eq_rat @ M @ U )
% 9.25/5.24         => ( ( sup_sup_set_rat @ ( set_or4029947393144176647an_rat @ L @ M ) @ ( set_or633870826150836451st_rat @ M @ U ) )
% 9.25/5.24            = ( set_or633870826150836451st_rat @ L @ U ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7154_ivl__disj__un__two_I7_J,axiom,
% 9.25/5.24      ! [L: nat,M: nat,U: nat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ L @ M )
% 9.25/5.24       => ( ( ord_less_eq_nat @ M @ U )
% 9.25/5.24         => ( ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ L @ M ) @ ( set_or1269000886237332187st_nat @ M @ U ) )
% 9.25/5.24            = ( set_or1269000886237332187st_nat @ L @ U ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7155_ivl__disj__un__two_I7_J,axiom,
% 9.25/5.24      ! [L: code_integer,M: code_integer,U: code_integer] :
% 9.25/5.24        ( ( ord_le3102999989581377725nteger @ L @ M )
% 9.25/5.24       => ( ( ord_le3102999989581377725nteger @ M @ U )
% 9.25/5.24         => ( ( sup_su848401254843788991nteger @ ( set_or8404916559141939852nteger @ L @ M ) @ ( set_or189985376899183464nteger @ M @ U ) )
% 9.25/5.24            = ( set_or189985376899183464nteger @ L @ U ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7156_ivl__disj__un__two_I7_J,axiom,
% 9.25/5.24      ! [L: int,M: int,U: int] :
% 9.25/5.24        ( ( ord_less_eq_int @ L @ M )
% 9.25/5.24       => ( ( ord_less_eq_int @ M @ U )
% 9.25/5.24         => ( ( sup_sup_set_int @ ( set_or4662586982721622107an_int @ L @ M ) @ ( set_or1266510415728281911st_int @ M @ U ) )
% 9.25/5.24            = ( set_or1266510415728281911st_int @ L @ U ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7157_ivl__disj__int__two_I7_J,axiom,
% 9.25/5.24      ! [L: $o,M: $o,U: $o] :
% 9.25/5.24        ( ( inf_inf_set_o @ ( set_or7139685690850216873Than_o @ L @ M ) @ ( set_or8904488021354931149Most_o @ M @ U ) )
% 9.25/5.24        = bot_bot_set_o ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7158_ivl__disj__int__two_I7_J,axiom,
% 9.25/5.24      ! [L: nat,M: nat,U: nat] :
% 9.25/5.24        ( ( inf_inf_set_nat @ ( set_or4665077453230672383an_nat @ L @ M ) @ ( set_or1269000886237332187st_nat @ M @ U ) )
% 9.25/5.24        = bot_bot_set_nat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7159_ivl__disj__int__two_I7_J,axiom,
% 9.25/5.24      ! [L: code_integer,M: code_integer,U: code_integer] :
% 9.25/5.24        ( ( inf_in1364745209274528805nteger @ ( set_or8404916559141939852nteger @ L @ M ) @ ( set_or189985376899183464nteger @ M @ U ) )
% 9.25/5.24        = bot_bo3990330152332043303nteger ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7160_ivl__disj__int__two_I7_J,axiom,
% 9.25/5.24      ! [L: int,M: int,U: int] :
% 9.25/5.24        ( ( inf_inf_set_int @ ( set_or4662586982721622107an_int @ L @ M ) @ ( set_or1266510415728281911st_int @ M @ U ) )
% 9.25/5.24        = bot_bot_set_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7161_not__UNIV__eq__Icc,axiom,
% 9.25/5.24      ! [L4: rat,H4: rat] :
% 9.25/5.24        ( top_top_set_rat
% 9.25/5.24       != ( set_or633870826150836451st_rat @ L4 @ H4 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7162_not__UNIV__eq__Icc,axiom,
% 9.25/5.24      ! [L4: nat,H4: nat] :
% 9.25/5.24        ( top_top_set_nat
% 9.25/5.24       != ( set_or1269000886237332187st_nat @ L4 @ H4 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7163_not__UNIV__eq__Icc,axiom,
% 9.25/5.24      ! [L4: int,H4: int] :
% 9.25/5.24        ( top_top_set_int
% 9.25/5.24       != ( set_or1266510415728281911st_int @ L4 @ H4 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7164_ivl__disj__un__two__touch_I2_J,axiom,
% 9.25/5.24      ! [L: literal,M: literal,U: literal] :
% 9.25/5.24        ( ( ord_less_eq_literal @ L @ M )
% 9.25/5.24       => ( ( ord_less_literal @ M @ U )
% 9.25/5.24         => ( ( sup_sup_set_literal @ ( set_or8436436507035938825iteral @ L @ M ) @ ( set_or4828121863581493221iteral @ M @ U ) )
% 9.25/5.24            = ( set_or4828121863581493221iteral @ L @ U ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7165_ivl__disj__un__two__touch_I2_J,axiom,
% 9.25/5.24      ! [L: rat,M: rat,U: rat] :
% 9.25/5.24        ( ( ord_less_eq_rat @ L @ M )
% 9.25/5.24       => ( ( ord_less_rat @ M @ U )
% 9.25/5.24         => ( ( sup_sup_set_rat @ ( set_or633870826150836451st_rat @ L @ M ) @ ( set_or4029947393144176647an_rat @ M @ U ) )
% 9.25/5.24            = ( set_or4029947393144176647an_rat @ L @ U ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7166_ivl__disj__un__two__touch_I2_J,axiom,
% 9.25/5.24      ! [L: nat,M: nat,U: nat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ L @ M )
% 9.25/5.24       => ( ( ord_less_nat @ M @ U )
% 9.25/5.24         => ( ( sup_sup_set_nat @ ( set_or1269000886237332187st_nat @ L @ M ) @ ( set_or4665077453230672383an_nat @ M @ U ) )
% 9.25/5.24            = ( set_or4665077453230672383an_nat @ L @ U ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7167_ivl__disj__un__two__touch_I2_J,axiom,
% 9.25/5.24      ! [L: code_integer,M: code_integer,U: code_integer] :
% 9.25/5.24        ( ( ord_le3102999989581377725nteger @ L @ M )
% 9.25/5.24       => ( ( ord_le6747313008572928689nteger @ M @ U )
% 9.25/5.24         => ( ( sup_su848401254843788991nteger @ ( set_or189985376899183464nteger @ L @ M ) @ ( set_or8404916559141939852nteger @ M @ U ) )
% 9.25/5.24            = ( set_or8404916559141939852nteger @ L @ U ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7168_ivl__disj__un__two__touch_I2_J,axiom,
% 9.25/5.24      ! [L: int,M: int,U: int] :
% 9.25/5.24        ( ( ord_less_eq_int @ L @ M )
% 9.25/5.24       => ( ( ord_less_int @ M @ U )
% 9.25/5.24         => ( ( sup_sup_set_int @ ( set_or1266510415728281911st_int @ L @ M ) @ ( set_or4662586982721622107an_int @ M @ U ) )
% 9.25/5.24            = ( set_or4662586982721622107an_int @ L @ U ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7169_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
% 9.25/5.24      ( set_or7139685690850216873Than_o
% 9.25/5.24      = ( ^ [A3: $o,B3: $o] : ( minus_minus_set_o @ ( set_or8904488021354931149Most_o @ A3 @ B3 ) @ ( insert_o @ B3 @ bot_bot_set_o ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7170_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
% 9.25/5.24      ( set_or4665077453230672383an_nat
% 9.25/5.24      = ( ^ [A3: nat,B3: nat] : ( minus_minus_set_nat @ ( set_or1269000886237332187st_nat @ A3 @ B3 ) @ ( insert_nat @ B3 @ bot_bot_set_nat ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7171_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
% 9.25/5.24      ( set_or8404916559141939852nteger
% 9.25/5.24      = ( ^ [A3: code_integer,B3: code_integer] : ( minus_2355218937544613996nteger @ ( set_or189985376899183464nteger @ A3 @ B3 ) @ ( insert_Code_integer @ B3 @ bot_bo3990330152332043303nteger ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7172_atLeastLessThan__eq__atLeastAtMost__diff,axiom,
% 9.25/5.24      ( set_or4662586982721622107an_int
% 9.25/5.24      = ( ^ [A3: int,B3: int] : ( minus_minus_set_int @ ( set_or1266510415728281911st_int @ A3 @ B3 ) @ ( insert_int @ B3 @ bot_bot_set_int ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7173_sum_Onested__swap,axiom,
% 9.25/5.24      ! [A: nat > nat > nat,N: nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [I3: nat] : ( groups3542108847815614940at_nat @ ( A @ I3 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I3 ) )
% 9.25/5.24          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.25/5.24        = ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [J3: nat] :
% 9.25/5.24              ( groups3542108847815614940at_nat
% 9.25/5.24              @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 9.25/5.24              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 9.25/5.24          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7174_ivl__disj__un__singleton_I6_J,axiom,
% 9.25/5.24      ! [L: $o,U: $o] :
% 9.25/5.24        ( ( ord_less_eq_o @ L @ U )
% 9.25/5.24       => ( ( sup_sup_set_o @ ( set_or7139685690850216873Than_o @ L @ U ) @ ( insert_o @ U @ bot_bot_set_o ) )
% 9.25/5.24          = ( set_or8904488021354931149Most_o @ L @ U ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7175_ivl__disj__un__singleton_I6_J,axiom,
% 9.25/5.24      ! [L: rat,U: rat] :
% 9.25/5.24        ( ( ord_less_eq_rat @ L @ U )
% 9.25/5.24       => ( ( sup_sup_set_rat @ ( set_or4029947393144176647an_rat @ L @ U ) @ ( insert_rat @ U @ bot_bot_set_rat ) )
% 9.25/5.24          = ( set_or633870826150836451st_rat @ L @ U ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7176_ivl__disj__un__singleton_I6_J,axiom,
% 9.25/5.24      ! [L: nat,U: nat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ L @ U )
% 9.25/5.24       => ( ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ L @ U ) @ ( insert_nat @ U @ bot_bot_set_nat ) )
% 9.25/5.24          = ( set_or1269000886237332187st_nat @ L @ U ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7177_ivl__disj__un__singleton_I6_J,axiom,
% 9.25/5.24      ! [L: code_integer,U: code_integer] :
% 9.25/5.24        ( ( ord_le3102999989581377725nteger @ L @ U )
% 9.25/5.24       => ( ( sup_su848401254843788991nteger @ ( set_or8404916559141939852nteger @ L @ U ) @ ( insert_Code_integer @ U @ bot_bo3990330152332043303nteger ) )
% 9.25/5.24          = ( set_or189985376899183464nteger @ L @ U ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7178_ivl__disj__un__singleton_I6_J,axiom,
% 9.25/5.24      ! [L: int,U: int] :
% 9.25/5.24        ( ( ord_less_eq_int @ L @ U )
% 9.25/5.24       => ( ( sup_sup_set_int @ ( set_or4662586982721622107an_int @ L @ U ) @ ( insert_int @ U @ bot_bot_set_int ) )
% 9.25/5.24          = ( set_or1266510415728281911st_int @ L @ U ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7179_ivl__disj__un__two__touch_I4_J,axiom,
% 9.25/5.24      ! [L: rat,M: rat,U: rat] :
% 9.25/5.24        ( ( ord_less_eq_rat @ L @ M )
% 9.25/5.24       => ( ( ord_less_eq_rat @ M @ U )
% 9.25/5.24         => ( ( sup_sup_set_rat @ ( set_or633870826150836451st_rat @ L @ M ) @ ( set_or633870826150836451st_rat @ M @ U ) )
% 9.25/5.24            = ( set_or633870826150836451st_rat @ L @ U ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7180_ivl__disj__un__two__touch_I4_J,axiom,
% 9.25/5.24      ! [L: nat,M: nat,U: nat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ L @ M )
% 9.25/5.24       => ( ( ord_less_eq_nat @ M @ U )
% 9.25/5.24         => ( ( sup_sup_set_nat @ ( set_or1269000886237332187st_nat @ L @ M ) @ ( set_or1269000886237332187st_nat @ M @ U ) )
% 9.25/5.24            = ( set_or1269000886237332187st_nat @ L @ U ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7181_ivl__disj__un__two__touch_I4_J,axiom,
% 9.25/5.24      ! [L: int,M: int,U: int] :
% 9.25/5.24        ( ( ord_less_eq_int @ L @ M )
% 9.25/5.24       => ( ( ord_less_eq_int @ M @ U )
% 9.25/5.24         => ( ( sup_sup_set_int @ ( set_or1266510415728281911st_int @ L @ M ) @ ( set_or1266510415728281911st_int @ M @ U ) )
% 9.25/5.24            = ( set_or1266510415728281911st_int @ L @ U ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7182_ivl__disj__un__two__touch_I4_J,axiom,
% 9.25/5.24      ! [L: code_integer,M: code_integer,U: code_integer] :
% 9.25/5.24        ( ( ord_le3102999989581377725nteger @ L @ M )
% 9.25/5.24       => ( ( ord_le3102999989581377725nteger @ M @ U )
% 9.25/5.24         => ( ( sup_su848401254843788991nteger @ ( set_or189985376899183464nteger @ L @ M ) @ ( set_or189985376899183464nteger @ M @ U ) )
% 9.25/5.24            = ( set_or189985376899183464nteger @ L @ U ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7183_atLeastAtMost__singleton_H,axiom,
% 9.25/5.24      ! [A: $o,B: $o] :
% 9.25/5.24        ( ( A = B )
% 9.25/5.24       => ( ( set_or8904488021354931149Most_o @ A @ B )
% 9.25/5.24          = ( insert_o @ A @ bot_bot_set_o ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7184_atLeastAtMost__singleton_H,axiom,
% 9.25/5.24      ! [A: nat,B: nat] :
% 9.25/5.24        ( ( A = B )
% 9.25/5.24       => ( ( set_or1269000886237332187st_nat @ A @ B )
% 9.25/5.24          = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7185_atLeastAtMost__singleton_H,axiom,
% 9.25/5.24      ! [A: int,B: int] :
% 9.25/5.24        ( ( A = B )
% 9.25/5.24       => ( ( set_or1266510415728281911st_int @ A @ B )
% 9.25/5.24          = ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7186_atLeastAtMost__singleton_H,axiom,
% 9.25/5.24      ! [A: code_integer,B: code_integer] :
% 9.25/5.24        ( ( A = B )
% 9.25/5.24       => ( ( set_or189985376899183464nteger @ A @ B )
% 9.25/5.24          = ( insert_Code_integer @ A @ bot_bo3990330152332043303nteger ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7187_not__UNIV__le__Icc,axiom,
% 9.25/5.24      ! [L: rat,H3: rat] :
% 9.25/5.24        ~ ( ord_less_eq_set_rat @ top_top_set_rat @ ( set_or633870826150836451st_rat @ L @ H3 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7188_not__UNIV__le__Icc,axiom,
% 9.25/5.24      ! [L: nat,H3: nat] :
% 9.25/5.24        ~ ( ord_less_eq_set_nat @ top_top_set_nat @ ( set_or1269000886237332187st_nat @ L @ H3 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7189_not__UNIV__le__Icc,axiom,
% 9.25/5.24      ! [L: int,H3: int] :
% 9.25/5.24        ~ ( ord_less_eq_set_int @ top_top_set_int @ ( set_or1266510415728281911st_int @ L @ H3 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7190_ivl__disj__un__two_I3_J,axiom,
% 9.25/5.24      ! [L: rat,M: rat,U: rat] :
% 9.25/5.24        ( ( ord_less_eq_rat @ L @ M )
% 9.25/5.24       => ( ( ord_less_eq_rat @ M @ U )
% 9.25/5.24         => ( ( sup_sup_set_rat @ ( set_or4029947393144176647an_rat @ L @ M ) @ ( set_or4029947393144176647an_rat @ M @ U ) )
% 9.25/5.24            = ( set_or4029947393144176647an_rat @ L @ U ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7191_ivl__disj__un__two_I3_J,axiom,
% 9.25/5.24      ! [L: nat,M: nat,U: nat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ L @ M )
% 9.25/5.24       => ( ( ord_less_eq_nat @ M @ U )
% 9.25/5.24         => ( ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ L @ M ) @ ( set_or4665077453230672383an_nat @ M @ U ) )
% 9.25/5.24            = ( set_or4665077453230672383an_nat @ L @ U ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7192_ivl__disj__un__two_I3_J,axiom,
% 9.25/5.24      ! [L: code_integer,M: code_integer,U: code_integer] :
% 9.25/5.24        ( ( ord_le3102999989581377725nteger @ L @ M )
% 9.25/5.24       => ( ( ord_le3102999989581377725nteger @ M @ U )
% 9.25/5.24         => ( ( sup_su848401254843788991nteger @ ( set_or8404916559141939852nteger @ L @ M ) @ ( set_or8404916559141939852nteger @ M @ U ) )
% 9.25/5.24            = ( set_or8404916559141939852nteger @ L @ U ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7193_ivl__disj__un__two_I3_J,axiom,
% 9.25/5.24      ! [L: int,M: int,U: int] :
% 9.25/5.24        ( ( ord_less_eq_int @ L @ M )
% 9.25/5.24       => ( ( ord_less_eq_int @ M @ U )
% 9.25/5.24         => ( ( sup_sup_set_int @ ( set_or4662586982721622107an_int @ L @ M ) @ ( set_or4662586982721622107an_int @ M @ U ) )
% 9.25/5.24            = ( set_or4662586982721622107an_int @ L @ U ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7194_ivl__disj__int__two_I3_J,axiom,
% 9.25/5.24      ! [L: $o,M: $o,U: $o] :
% 9.25/5.24        ( ( inf_inf_set_o @ ( set_or7139685690850216873Than_o @ L @ M ) @ ( set_or7139685690850216873Than_o @ M @ U ) )
% 9.25/5.24        = bot_bot_set_o ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7195_ivl__disj__int__two_I3_J,axiom,
% 9.25/5.24      ! [L: nat,M: nat,U: nat] :
% 9.25/5.24        ( ( inf_inf_set_nat @ ( set_or4665077453230672383an_nat @ L @ M ) @ ( set_or4665077453230672383an_nat @ M @ U ) )
% 9.25/5.24        = bot_bot_set_nat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7196_ivl__disj__int__two_I3_J,axiom,
% 9.25/5.24      ! [L: code_integer,M: code_integer,U: code_integer] :
% 9.25/5.24        ( ( inf_in1364745209274528805nteger @ ( set_or8404916559141939852nteger @ L @ M ) @ ( set_or8404916559141939852nteger @ M @ U ) )
% 9.25/5.24        = bot_bo3990330152332043303nteger ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7197_ivl__disj__int__two_I3_J,axiom,
% 9.25/5.24      ! [L: int,M: int,U: int] :
% 9.25/5.24        ( ( inf_inf_set_int @ ( set_or4662586982721622107an_int @ L @ M ) @ ( set_or4662586982721622107an_int @ M @ U ) )
% 9.25/5.24        = bot_bot_set_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7198_sum_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 9.25/5.24      ! [G2: nat > nat,N: nat,M: nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat @ G2 @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 9.25/5.24        = ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 9.25/5.24          @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7199_atLeastLessThan0,axiom,
% 9.25/5.24      ! [M: nat] :
% 9.25/5.24        ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 9.25/5.24        = bot_bot_set_nat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7200_sum_Oshift__bounds__Suc__ivl,axiom,
% 9.25/5.24      ! [G2: nat > nat,M: nat,N: nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat @ G2 @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 9.25/5.24        = ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.24          @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7201_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 9.25/5.24      ! [G2: nat > nat,M: nat,N: nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 9.25/5.24        = ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.24          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7202_sum_Oshift__bounds__nat__ivl,axiom,
% 9.25/5.24      ! [G2: nat > nat,M: nat,K: nat,N: nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat @ G2 @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 9.25/5.24        = ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [I3: nat] : ( G2 @ ( plus_plus_nat @ I3 @ K ) )
% 9.25/5.24          @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7203_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 9.25/5.24      ! [G2: nat > nat,M: nat,K: nat,N: nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 9.25/5.24        = ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [I3: nat] : ( G2 @ ( plus_plus_nat @ I3 @ K ) )
% 9.25/5.24          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7204_atLeastAtMost__eq__UNIV__iff,axiom,
% 9.25/5.24      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.25/5.24        ( ( ( set_or2784603332384507286at_nat @ X @ Y )
% 9.25/5.24          = top_to7629004291339433233at_nat )
% 9.25/5.24        = ( ( X = bot_bo2099793752762293965at_nat )
% 9.25/5.24          & ( Y = top_to4669805908274784177at_nat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7205_atLeastAtMost__eq__UNIV__iff,axiom,
% 9.25/5.24      ! [X: set_list_nat,Y: set_list_nat] :
% 9.25/5.24        ( ( ( set_or1270514513317581473st_nat @ X @ Y )
% 9.25/5.24          = top_to1619013496918823676st_nat )
% 9.25/5.24        = ( ( X = bot_bot_set_list_nat )
% 9.25/5.24          & ( Y = top_top_set_list_nat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7206_atLeastAtMost__eq__UNIV__iff,axiom,
% 9.25/5.24      ! [X: set_o,Y: set_o] :
% 9.25/5.24        ( ( ( set_or266616469461849773_set_o @ X @ Y )
% 9.25/5.24          = top_top_set_set_o )
% 9.25/5.24        = ( ( X = bot_bot_set_o )
% 9.25/5.24          & ( Y = top_top_set_o ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7207_atLeastAtMost__eq__UNIV__iff,axiom,
% 9.25/5.24      ! [X: set_rat,Y: set_rat] :
% 9.25/5.24        ( ( ( set_or1040488700251649177et_rat @ X @ Y )
% 9.25/5.24          = top_top_set_set_rat )
% 9.25/5.24        = ( ( X = bot_bot_set_rat )
% 9.25/5.24          & ( Y = top_top_set_rat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7208_atLeastAtMost__eq__UNIV__iff,axiom,
% 9.25/5.24      ! [X: set_nat,Y: set_nat] :
% 9.25/5.24        ( ( ( set_or4548717258645045905et_nat @ X @ Y )
% 9.25/5.24          = top_top_set_set_nat )
% 9.25/5.24        = ( ( X = bot_bot_set_nat )
% 9.25/5.24          & ( Y = top_top_set_nat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7209_atLeastAtMost__eq__UNIV__iff,axiom,
% 9.25/5.24      ! [X: set_int,Y: set_int] :
% 9.25/5.24        ( ( ( set_or370866239135849197et_int @ X @ Y )
% 9.25/5.24          = top_top_set_set_int )
% 9.25/5.24        = ( ( X = bot_bot_set_int )
% 9.25/5.24          & ( Y = top_top_set_int ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7210_atLeastAtMost__eq__UNIV__iff,axiom,
% 9.25/5.24      ! [X: $o,Y: $o] :
% 9.25/5.24        ( ( ( set_or8904488021354931149Most_o @ X @ Y )
% 9.25/5.24          = top_top_set_o )
% 9.25/5.24        = ( ( X = bot_bot_o )
% 9.25/5.24          & ( Y = top_top_o ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7211_aset_I2_J,axiom,
% 9.25/5.24      ! [D3: int,A2: set_int,P: int > $o,Q2: int > $o] :
% 9.25/5.24        ( ! [X2: int] :
% 9.25/5.24            ( ! [Xa2: int] :
% 9.25/5.24                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24               => ! [Xb2: int] :
% 9.25/5.24                    ( ( member_int @ Xb2 @ A2 )
% 9.25/5.24                   => ( X2
% 9.25/5.24                     != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 9.25/5.24           => ( ( P @ X2 )
% 9.25/5.24             => ( P @ ( plus_plus_int @ X2 @ D3 ) ) ) )
% 9.25/5.24       => ( ! [X2: int] :
% 9.25/5.24              ( ! [Xa2: int] :
% 9.25/5.24                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                 => ! [Xb2: int] :
% 9.25/5.24                      ( ( member_int @ Xb2 @ A2 )
% 9.25/5.24                     => ( X2
% 9.25/5.24                       != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 9.25/5.24             => ( ( Q2 @ X2 )
% 9.25/5.24               => ( Q2 @ ( plus_plus_int @ X2 @ D3 ) ) ) )
% 9.25/5.24         => ! [X5: int] :
% 9.25/5.24              ( ! [Xa3: int] :
% 9.25/5.24                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                 => ! [Xb3: int] :
% 9.25/5.24                      ( ( member_int @ Xb3 @ A2 )
% 9.25/5.24                     => ( X5
% 9.25/5.24                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.25/5.24             => ( ( ( P @ X5 )
% 9.25/5.24                  | ( Q2 @ X5 ) )
% 9.25/5.24               => ( ( P @ ( plus_plus_int @ X5 @ D3 ) )
% 9.25/5.24                  | ( Q2 @ ( plus_plus_int @ X5 @ D3 ) ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7212_aset_I1_J,axiom,
% 9.25/5.24      ! [D3: int,A2: set_int,P: int > $o,Q2: int > $o] :
% 9.25/5.24        ( ! [X2: int] :
% 9.25/5.24            ( ! [Xa2: int] :
% 9.25/5.24                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24               => ! [Xb2: int] :
% 9.25/5.24                    ( ( member_int @ Xb2 @ A2 )
% 9.25/5.24                   => ( X2
% 9.25/5.24                     != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 9.25/5.24           => ( ( P @ X2 )
% 9.25/5.24             => ( P @ ( plus_plus_int @ X2 @ D3 ) ) ) )
% 9.25/5.24       => ( ! [X2: int] :
% 9.25/5.24              ( ! [Xa2: int] :
% 9.25/5.24                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                 => ! [Xb2: int] :
% 9.25/5.24                      ( ( member_int @ Xb2 @ A2 )
% 9.25/5.24                     => ( X2
% 9.25/5.24                       != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 9.25/5.24             => ( ( Q2 @ X2 )
% 9.25/5.24               => ( Q2 @ ( plus_plus_int @ X2 @ D3 ) ) ) )
% 9.25/5.24         => ! [X5: int] :
% 9.25/5.24              ( ! [Xa3: int] :
% 9.25/5.24                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                 => ! [Xb3: int] :
% 9.25/5.24                      ( ( member_int @ Xb3 @ A2 )
% 9.25/5.24                     => ( X5
% 9.25/5.24                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.25/5.24             => ( ( ( P @ X5 )
% 9.25/5.24                  & ( Q2 @ X5 ) )
% 9.25/5.24               => ( ( P @ ( plus_plus_int @ X5 @ D3 ) )
% 9.25/5.24                  & ( Q2 @ ( plus_plus_int @ X5 @ D3 ) ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7213_bset_I2_J,axiom,
% 9.25/5.24      ! [D3: int,B2: set_int,P: int > $o,Q2: int > $o] :
% 9.25/5.24        ( ! [X2: int] :
% 9.25/5.24            ( ! [Xa2: int] :
% 9.25/5.24                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24               => ! [Xb2: int] :
% 9.25/5.24                    ( ( member_int @ Xb2 @ B2 )
% 9.25/5.24                   => ( X2
% 9.25/5.24                     != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 9.25/5.24           => ( ( P @ X2 )
% 9.25/5.24             => ( P @ ( minus_minus_int @ X2 @ D3 ) ) ) )
% 9.25/5.24       => ( ! [X2: int] :
% 9.25/5.24              ( ! [Xa2: int] :
% 9.25/5.24                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                 => ! [Xb2: int] :
% 9.25/5.24                      ( ( member_int @ Xb2 @ B2 )
% 9.25/5.24                     => ( X2
% 9.25/5.24                       != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 9.25/5.24             => ( ( Q2 @ X2 )
% 9.25/5.24               => ( Q2 @ ( minus_minus_int @ X2 @ D3 ) ) ) )
% 9.25/5.24         => ! [X5: int] :
% 9.25/5.24              ( ! [Xa3: int] :
% 9.25/5.24                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                 => ! [Xb3: int] :
% 9.25/5.24                      ( ( member_int @ Xb3 @ B2 )
% 9.25/5.24                     => ( X5
% 9.25/5.24                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.25/5.24             => ( ( ( P @ X5 )
% 9.25/5.24                  | ( Q2 @ X5 ) )
% 9.25/5.24               => ( ( P @ ( minus_minus_int @ X5 @ D3 ) )
% 9.25/5.24                  | ( Q2 @ ( minus_minus_int @ X5 @ D3 ) ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7214_bset_I1_J,axiom,
% 9.25/5.24      ! [D3: int,B2: set_int,P: int > $o,Q2: int > $o] :
% 9.25/5.24        ( ! [X2: int] :
% 9.25/5.24            ( ! [Xa2: int] :
% 9.25/5.24                ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24               => ! [Xb2: int] :
% 9.25/5.24                    ( ( member_int @ Xb2 @ B2 )
% 9.25/5.24                   => ( X2
% 9.25/5.24                     != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 9.25/5.24           => ( ( P @ X2 )
% 9.25/5.24             => ( P @ ( minus_minus_int @ X2 @ D3 ) ) ) )
% 9.25/5.24       => ( ! [X2: int] :
% 9.25/5.24              ( ! [Xa2: int] :
% 9.25/5.24                  ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                 => ! [Xb2: int] :
% 9.25/5.24                      ( ( member_int @ Xb2 @ B2 )
% 9.25/5.24                     => ( X2
% 9.25/5.24                       != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 9.25/5.24             => ( ( Q2 @ X2 )
% 9.25/5.24               => ( Q2 @ ( minus_minus_int @ X2 @ D3 ) ) ) )
% 9.25/5.24         => ! [X5: int] :
% 9.25/5.24              ( ! [Xa3: int] :
% 9.25/5.24                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                 => ! [Xb3: int] :
% 9.25/5.24                      ( ( member_int @ Xb3 @ B2 )
% 9.25/5.24                     => ( X5
% 9.25/5.24                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.25/5.24             => ( ( ( P @ X5 )
% 9.25/5.24                  & ( Q2 @ X5 ) )
% 9.25/5.24               => ( ( P @ ( minus_minus_int @ X5 @ D3 ) )
% 9.25/5.24                  & ( Q2 @ ( minus_minus_int @ X5 @ D3 ) ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7215_atLeastLessThanSuc,axiom,
% 9.25/5.24      ! [M: nat,N: nat] :
% 9.25/5.24        ( ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 9.25/5.24            = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 9.25/5.24        & ( ~ ( ord_less_eq_nat @ M @ N )
% 9.25/5.24         => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 9.25/5.24            = bot_bot_set_nat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7216_atLeastLessThan__add__Un,axiom,
% 9.25/5.24      ! [I: nat,J: nat,K: nat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ I @ J )
% 9.25/5.24       => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 9.25/5.24          = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7217_sum_OatLeastAtMost__rev,axiom,
% 9.25/5.24      ! [G2: nat > nat,N: nat,M: nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 9.25/5.24        = ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 9.25/5.24          @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7218_aset_I10_J,axiom,
% 9.25/5.24      ! [D2: int,D3: int,A2: set_int,T3: int] :
% 9.25/5.24        ( ( dvd_dvd_int @ D2 @ D3 )
% 9.25/5.24       => ! [X5: int] :
% 9.25/5.24            ( ! [Xa3: int] :
% 9.25/5.24                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24               => ! [Xb3: int] :
% 9.25/5.24                    ( ( member_int @ Xb3 @ A2 )
% 9.25/5.24                   => ( X5
% 9.25/5.24                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.25/5.24           => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T3 ) )
% 9.25/5.24             => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X5 @ D3 ) @ T3 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7219_aset_I9_J,axiom,
% 9.25/5.24      ! [D2: int,D3: int,A2: set_int,T3: int] :
% 9.25/5.24        ( ( dvd_dvd_int @ D2 @ D3 )
% 9.25/5.24       => ! [X5: int] :
% 9.25/5.24            ( ! [Xa3: int] :
% 9.25/5.24                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24               => ! [Xb3: int] :
% 9.25/5.24                    ( ( member_int @ Xb3 @ A2 )
% 9.25/5.24                   => ( X5
% 9.25/5.24                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.25/5.24           => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T3 ) )
% 9.25/5.24             => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( plus_plus_int @ X5 @ D3 ) @ T3 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7220_bset_I10_J,axiom,
% 9.25/5.24      ! [D2: int,D3: int,B2: set_int,T3: int] :
% 9.25/5.24        ( ( dvd_dvd_int @ D2 @ D3 )
% 9.25/5.24       => ! [X5: int] :
% 9.25/5.24            ( ! [Xa3: int] :
% 9.25/5.24                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24               => ! [Xb3: int] :
% 9.25/5.24                    ( ( member_int @ Xb3 @ B2 )
% 9.25/5.24                   => ( X5
% 9.25/5.24                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.25/5.24           => ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T3 ) )
% 9.25/5.24             => ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X5 @ D3 ) @ T3 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7221_bset_I9_J,axiom,
% 9.25/5.24      ! [D2: int,D3: int,B2: set_int,T3: int] :
% 9.25/5.24        ( ( dvd_dvd_int @ D2 @ D3 )
% 9.25/5.24       => ! [X5: int] :
% 9.25/5.24            ( ! [Xa3: int] :
% 9.25/5.24                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24               => ! [Xb3: int] :
% 9.25/5.24                    ( ( member_int @ Xb3 @ B2 )
% 9.25/5.24                   => ( X5
% 9.25/5.24                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.25/5.24           => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X5 @ T3 ) )
% 9.25/5.24             => ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X5 @ D3 ) @ T3 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7222_atLeastAtMostPlus1__int__conv,axiom,
% 9.25/5.24      ! [M: int,N: int] :
% 9.25/5.24        ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 9.25/5.24       => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 9.25/5.24          = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M @ N ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7223_atLeastLessThan__nat__numeral,axiom,
% 9.25/5.24      ! [M: nat,K: num] :
% 9.25/5.24        ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 9.25/5.24         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 9.25/5.24            = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 9.25/5.24        & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 9.25/5.24         => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 9.25/5.24            = bot_bot_set_nat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7224_sum__Suc__diff_H,axiom,
% 9.25/5.24      ! [M: nat,N: nat,F2: nat > rat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24       => ( ( groups2906978787729119204at_rat
% 9.25/5.24            @ ^ [I3: nat] : ( minus_minus_rat @ ( F2 @ ( suc @ I3 ) ) @ ( F2 @ I3 ) )
% 9.25/5.24            @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 9.25/5.24          = ( minus_minus_rat @ ( F2 @ N ) @ ( F2 @ M ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7225_sum__Suc__diff_H,axiom,
% 9.25/5.24      ! [M: nat,N: nat,F2: nat > int] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24       => ( ( groups3539618377306564664at_int
% 9.25/5.24            @ ^ [I3: nat] : ( minus_minus_int @ ( F2 @ ( suc @ I3 ) ) @ ( F2 @ I3 ) )
% 9.25/5.24            @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 9.25/5.24          = ( minus_minus_int @ ( F2 @ N ) @ ( F2 @ M ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7226_sum_OSuc__reindex__ivl,axiom,
% 9.25/5.24      ! [M: nat,N: nat,G2: nat > rat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24       => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 9.25/5.24          = ( plus_plus_rat @ ( G2 @ M )
% 9.25/5.24            @ ( groups2906978787729119204at_rat
% 9.25/5.24              @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.24              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7227_sum_OSuc__reindex__ivl,axiom,
% 9.25/5.24      ! [M: nat,N: nat,G2: nat > int] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24       => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 9.25/5.24          = ( plus_plus_int @ ( G2 @ M )
% 9.25/5.24            @ ( groups3539618377306564664at_int
% 9.25/5.24              @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.24              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7228_sum_OSuc__reindex__ivl,axiom,
% 9.25/5.24      ! [M: nat,N: nat,G2: nat > nat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24       => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 9.25/5.24          = ( plus_plus_nat @ ( G2 @ M )
% 9.25/5.24            @ ( groups3542108847815614940at_nat
% 9.25/5.24              @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.24              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7229_sum__Suc__diff,axiom,
% 9.25/5.24      ! [M: nat,N: nat,F2: nat > rat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.25/5.24       => ( ( groups2906978787729119204at_rat
% 9.25/5.24            @ ^ [I3: nat] : ( minus_minus_rat @ ( F2 @ ( suc @ I3 ) ) @ ( F2 @ I3 ) )
% 9.25/5.24            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.24          = ( minus_minus_rat @ ( F2 @ ( suc @ N ) ) @ ( F2 @ M ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7230_sum__Suc__diff,axiom,
% 9.25/5.24      ! [M: nat,N: nat,F2: nat > int] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.25/5.24       => ( ( groups3539618377306564664at_int
% 9.25/5.24            @ ^ [I3: nat] : ( minus_minus_int @ ( F2 @ ( suc @ I3 ) ) @ ( F2 @ I3 ) )
% 9.25/5.24            @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.24          = ( minus_minus_int @ ( F2 @ ( suc @ N ) ) @ ( F2 @ M ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7231_sum_OatLeastLessThan__rev,axiom,
% 9.25/5.24      ! [G2: nat > nat,N: nat,M: nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat @ G2 @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 9.25/5.24        = ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ ( suc @ I3 ) ) )
% 9.25/5.24          @ ( set_or4665077453230672383an_nat @ N @ M ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7232_sum__atLeastAtMost__code,axiom,
% 9.25/5.24      ! [F2: nat > code_integer,A: nat,B: nat] :
% 9.25/5.24        ( ( groups7501900531339628137nteger @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.25/5.24        = ( set_fo1084959871951514735nteger
% 9.25/5.24          @ ^ [A3: nat] : ( plus_p5714425477246183910nteger @ ( F2 @ A3 ) )
% 9.25/5.24          @ A
% 9.25/5.24          @ B
% 9.25/5.24          @ zero_z3403309356797280102nteger ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7233_sum__atLeastAtMost__code,axiom,
% 9.25/5.24      ! [F2: nat > multis2468970476368604999at_nat,A: nat,B: nat] :
% 9.25/5.24        ( ( groups6857163185585827899at_nat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.25/5.24        = ( set_fo4497565046347964853at_nat
% 9.25/5.24          @ ^ [A3: nat] : ( plus_p7104986032573967614at_nat @ ( F2 @ A3 ) )
% 9.25/5.24          @ A
% 9.25/5.24          @ B
% 9.25/5.24          @ zero_z1048942125864253310at_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7234_sum__atLeastAtMost__code,axiom,
% 9.25/5.24      ! [F2: nat > rat,A: nat,B: nat] :
% 9.25/5.24        ( ( groups2906978787729119204at_rat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.25/5.24        = ( set_fo1949268297981939178at_rat
% 9.25/5.24          @ ^ [A3: nat] : ( plus_plus_rat @ ( F2 @ A3 ) )
% 9.25/5.24          @ A
% 9.25/5.24          @ B
% 9.25/5.24          @ zero_zero_rat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7235_sum__atLeastAtMost__code,axiom,
% 9.25/5.24      ! [F2: nat > int,A: nat,B: nat] :
% 9.25/5.24        ( ( groups3539618377306564664at_int @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.25/5.24        = ( set_fo2581907887559384638at_int
% 9.25/5.24          @ ^ [A3: nat] : ( plus_plus_int @ ( F2 @ A3 ) )
% 9.25/5.24          @ A
% 9.25/5.24          @ B
% 9.25/5.24          @ zero_zero_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7236_sum__atLeastAtMost__code,axiom,
% 9.25/5.24      ! [F2: nat > nat,A: nat,B: nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.25/5.24        = ( set_fo2584398358068434914at_nat
% 9.25/5.24          @ ^ [A3: nat] : ( plus_plus_nat @ ( F2 @ A3 ) )
% 9.25/5.24          @ A
% 9.25/5.24          @ B
% 9.25/5.24          @ zero_zero_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7237_periodic__finite__ex,axiom,
% 9.25/5.24      ! [D2: int,P: int > $o] :
% 9.25/5.24        ( ( ord_less_int @ zero_zero_int @ D2 )
% 9.25/5.24       => ( ! [X2: int,K2: int] :
% 9.25/5.24              ( ( P @ X2 )
% 9.25/5.24              = ( P @ ( minus_minus_int @ X2 @ ( times_times_int @ K2 @ D2 ) ) ) )
% 9.25/5.24         => ( ( ? [X4: int] : ( P @ X4 ) )
% 9.25/5.24            = ( ? [X3: int] :
% 9.25/5.24                  ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D2 ) )
% 9.25/5.24                  & ( P @ X3 ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7238_aset_I7_J,axiom,
% 9.25/5.24      ! [D3: int,A2: set_int,T3: int] :
% 9.25/5.24        ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.25/5.24       => ! [X5: int] :
% 9.25/5.24            ( ! [Xa3: int] :
% 9.25/5.24                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24               => ! [Xb3: int] :
% 9.25/5.24                    ( ( member_int @ Xb3 @ A2 )
% 9.25/5.24                   => ( X5
% 9.25/5.24                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.25/5.24           => ( ( ord_less_int @ T3 @ X5 )
% 9.25/5.24             => ( ord_less_int @ T3 @ ( plus_plus_int @ X5 @ D3 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7239_aset_I5_J,axiom,
% 9.25/5.24      ! [D3: int,T3: int,A2: set_int] :
% 9.25/5.24        ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.25/5.24       => ( ( member_int @ T3 @ A2 )
% 9.25/5.24         => ! [X5: int] :
% 9.25/5.24              ( ! [Xa3: int] :
% 9.25/5.24                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                 => ! [Xb3: int] :
% 9.25/5.24                      ( ( member_int @ Xb3 @ A2 )
% 9.25/5.24                     => ( X5
% 9.25/5.24                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.25/5.24             => ( ( ord_less_int @ X5 @ T3 )
% 9.25/5.24               => ( ord_less_int @ ( plus_plus_int @ X5 @ D3 ) @ T3 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7240_aset_I4_J,axiom,
% 9.25/5.24      ! [D3: int,T3: int,A2: set_int] :
% 9.25/5.24        ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.25/5.24       => ( ( member_int @ T3 @ A2 )
% 9.25/5.24         => ! [X5: int] :
% 9.25/5.24              ( ! [Xa3: int] :
% 9.25/5.24                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                 => ! [Xb3: int] :
% 9.25/5.24                      ( ( member_int @ Xb3 @ A2 )
% 9.25/5.24                     => ( X5
% 9.25/5.24                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.25/5.24             => ( ( X5 != T3 )
% 9.25/5.24               => ( ( plus_plus_int @ X5 @ D3 )
% 9.25/5.24                 != T3 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7241_aset_I3_J,axiom,
% 9.25/5.24      ! [D3: int,T3: int,A2: set_int] :
% 9.25/5.24        ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.25/5.24       => ( ( member_int @ ( plus_plus_int @ T3 @ one_one_int ) @ A2 )
% 9.25/5.24         => ! [X5: int] :
% 9.25/5.24              ( ! [Xa3: int] :
% 9.25/5.24                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                 => ! [Xb3: int] :
% 9.25/5.24                      ( ( member_int @ Xb3 @ A2 )
% 9.25/5.24                     => ( X5
% 9.25/5.24                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.25/5.24             => ( ( X5 = T3 )
% 9.25/5.24               => ( ( plus_plus_int @ X5 @ D3 )
% 9.25/5.24                  = T3 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7242_bset_I7_J,axiom,
% 9.25/5.24      ! [D3: int,T3: int,B2: set_int] :
% 9.25/5.24        ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.25/5.24       => ( ( member_int @ T3 @ B2 )
% 9.25/5.24         => ! [X5: int] :
% 9.25/5.24              ( ! [Xa3: int] :
% 9.25/5.24                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                 => ! [Xb3: int] :
% 9.25/5.24                      ( ( member_int @ Xb3 @ B2 )
% 9.25/5.24                     => ( X5
% 9.25/5.24                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.25/5.24             => ( ( ord_less_int @ T3 @ X5 )
% 9.25/5.24               => ( ord_less_int @ T3 @ ( minus_minus_int @ X5 @ D3 ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7243_bset_I5_J,axiom,
% 9.25/5.24      ! [D3: int,B2: set_int,T3: int] :
% 9.25/5.24        ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.25/5.24       => ! [X5: int] :
% 9.25/5.24            ( ! [Xa3: int] :
% 9.25/5.24                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24               => ! [Xb3: int] :
% 9.25/5.24                    ( ( member_int @ Xb3 @ B2 )
% 9.25/5.24                   => ( X5
% 9.25/5.24                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.25/5.24           => ( ( ord_less_int @ X5 @ T3 )
% 9.25/5.24             => ( ord_less_int @ ( minus_minus_int @ X5 @ D3 ) @ T3 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7244_bset_I4_J,axiom,
% 9.25/5.24      ! [D3: int,T3: int,B2: set_int] :
% 9.25/5.24        ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.25/5.24       => ( ( member_int @ T3 @ B2 )
% 9.25/5.24         => ! [X5: int] :
% 9.25/5.24              ( ! [Xa3: int] :
% 9.25/5.24                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                 => ! [Xb3: int] :
% 9.25/5.24                      ( ( member_int @ Xb3 @ B2 )
% 9.25/5.24                     => ( X5
% 9.25/5.24                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.25/5.24             => ( ( X5 != T3 )
% 9.25/5.24               => ( ( minus_minus_int @ X5 @ D3 )
% 9.25/5.24                 != T3 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7245_bset_I3_J,axiom,
% 9.25/5.24      ! [D3: int,T3: int,B2: set_int] :
% 9.25/5.24        ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.25/5.24       => ( ( member_int @ ( minus_minus_int @ T3 @ one_one_int ) @ B2 )
% 9.25/5.24         => ! [X5: int] :
% 9.25/5.24              ( ! [Xa3: int] :
% 9.25/5.24                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                 => ! [Xb3: int] :
% 9.25/5.24                      ( ( member_int @ Xb3 @ B2 )
% 9.25/5.24                     => ( X5
% 9.25/5.24                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.25/5.24             => ( ( X5 = T3 )
% 9.25/5.24               => ( ( minus_minus_int @ X5 @ D3 )
% 9.25/5.24                  = T3 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7246_sum_Oub__add__nat,axiom,
% 9.25/5.24      ! [M: nat,N: nat,G2: nat > rat,P4: nat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 9.25/5.24       => ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 9.25/5.24          = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7247_sum_Oub__add__nat,axiom,
% 9.25/5.24      ! [M: nat,N: nat,G2: nat > int,P4: nat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 9.25/5.24       => ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 9.25/5.24          = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7248_sum_Oub__add__nat,axiom,
% 9.25/5.24      ! [M: nat,N: nat,G2: nat > nat,P4: nat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 9.25/5.24       => ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 9.25/5.24          = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7249_simp__from__to,axiom,
% 9.25/5.24      ( set_or1266510415728281911st_int
% 9.25/5.24      = ( ^ [I3: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I3 ) @ bot_bot_set_int @ ( insert_int @ I3 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7250_aset_I8_J,axiom,
% 9.25/5.24      ! [D3: int,A2: set_int,T3: int] :
% 9.25/5.24        ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.25/5.24       => ! [X5: int] :
% 9.25/5.24            ( ! [Xa3: int] :
% 9.25/5.24                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24               => ! [Xb3: int] :
% 9.25/5.24                    ( ( member_int @ Xb3 @ A2 )
% 9.25/5.24                   => ( X5
% 9.25/5.24                     != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.25/5.24           => ( ( ord_less_eq_int @ T3 @ X5 )
% 9.25/5.24             => ( ord_less_eq_int @ T3 @ ( plus_plus_int @ X5 @ D3 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7251_aset_I6_J,axiom,
% 9.25/5.24      ! [D3: int,T3: int,A2: set_int] :
% 9.25/5.24        ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.25/5.24       => ( ( member_int @ ( plus_plus_int @ T3 @ one_one_int ) @ A2 )
% 9.25/5.24         => ! [X5: int] :
% 9.25/5.24              ( ! [Xa3: int] :
% 9.25/5.24                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                 => ! [Xb3: int] :
% 9.25/5.24                      ( ( member_int @ Xb3 @ A2 )
% 9.25/5.24                     => ( X5
% 9.25/5.24                       != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 9.25/5.24             => ( ( ord_less_eq_int @ X5 @ T3 )
% 9.25/5.24               => ( ord_less_eq_int @ ( plus_plus_int @ X5 @ D3 ) @ T3 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7252_bset_I8_J,axiom,
% 9.25/5.24      ! [D3: int,T3: int,B2: set_int] :
% 9.25/5.24        ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.25/5.24       => ( ( member_int @ ( minus_minus_int @ T3 @ one_one_int ) @ B2 )
% 9.25/5.24         => ! [X5: int] :
% 9.25/5.24              ( ! [Xa3: int] :
% 9.25/5.24                  ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                 => ! [Xb3: int] :
% 9.25/5.24                      ( ( member_int @ Xb3 @ B2 )
% 9.25/5.24                     => ( X5
% 9.25/5.24                       != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.25/5.24             => ( ( ord_less_eq_int @ T3 @ X5 )
% 9.25/5.24               => ( ord_less_eq_int @ T3 @ ( minus_minus_int @ X5 @ D3 ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7253_bset_I6_J,axiom,
% 9.25/5.24      ! [D3: int,B2: set_int,T3: int] :
% 9.25/5.24        ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.25/5.24       => ! [X5: int] :
% 9.25/5.24            ( ! [Xa3: int] :
% 9.25/5.24                ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24               => ! [Xb3: int] :
% 9.25/5.24                    ( ( member_int @ Xb3 @ B2 )
% 9.25/5.24                   => ( X5
% 9.25/5.24                     != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 9.25/5.24           => ( ( ord_less_eq_int @ X5 @ T3 )
% 9.25/5.24             => ( ord_less_eq_int @ ( minus_minus_int @ X5 @ D3 ) @ T3 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7254_cpmi,axiom,
% 9.25/5.24      ! [D3: int,P: int > $o,P7: int > $o,B2: set_int] :
% 9.25/5.24        ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.25/5.24       => ( ? [Z7: int] :
% 9.25/5.24            ! [X2: int] :
% 9.25/5.24              ( ( ord_less_int @ X2 @ Z7 )
% 9.25/5.24             => ( ( P @ X2 )
% 9.25/5.24                = ( P7 @ X2 ) ) )
% 9.25/5.24         => ( ! [X2: int] :
% 9.25/5.24                ( ! [Xa2: int] :
% 9.25/5.24                    ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                   => ! [Xb2: int] :
% 9.25/5.24                        ( ( member_int @ Xb2 @ B2 )
% 9.25/5.24                       => ( X2
% 9.25/5.24                         != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 9.25/5.24               => ( ( P @ X2 )
% 9.25/5.24                 => ( P @ ( minus_minus_int @ X2 @ D3 ) ) ) )
% 9.25/5.24           => ( ! [X2: int,K2: int] :
% 9.25/5.24                  ( ( P7 @ X2 )
% 9.25/5.24                  = ( P7 @ ( minus_minus_int @ X2 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 9.25/5.24             => ( ( ? [X4: int] : ( P @ X4 ) )
% 9.25/5.24                = ( ? [X3: int] :
% 9.25/5.24                      ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                      & ( P7 @ X3 ) )
% 9.25/5.24                  | ? [X3: int] :
% 9.25/5.24                      ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                      & ? [Y3: int] :
% 9.25/5.24                          ( ( member_int @ Y3 @ B2 )
% 9.25/5.24                          & ( P @ ( plus_plus_int @ Y3 @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7255_cppi,axiom,
% 9.25/5.24      ! [D3: int,P: int > $o,P7: int > $o,A2: set_int] :
% 9.25/5.24        ( ( ord_less_int @ zero_zero_int @ D3 )
% 9.25/5.24       => ( ? [Z7: int] :
% 9.25/5.24            ! [X2: int] :
% 9.25/5.24              ( ( ord_less_int @ Z7 @ X2 )
% 9.25/5.24             => ( ( P @ X2 )
% 9.25/5.24                = ( P7 @ X2 ) ) )
% 9.25/5.24         => ( ! [X2: int] :
% 9.25/5.24                ( ! [Xa2: int] :
% 9.25/5.24                    ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                   => ! [Xb2: int] :
% 9.25/5.24                        ( ( member_int @ Xb2 @ A2 )
% 9.25/5.24                       => ( X2
% 9.25/5.24                         != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 9.25/5.24               => ( ( P @ X2 )
% 9.25/5.24                 => ( P @ ( plus_plus_int @ X2 @ D3 ) ) ) )
% 9.25/5.24           => ( ! [X2: int,K2: int] :
% 9.25/5.24                  ( ( P7 @ X2 )
% 9.25/5.24                  = ( P7 @ ( minus_minus_int @ X2 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 9.25/5.24             => ( ( ? [X4: int] : ( P @ X4 ) )
% 9.25/5.24                = ( ? [X3: int] :
% 9.25/5.24                      ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                      & ( P7 @ X3 ) )
% 9.25/5.24                  | ? [X3: int] :
% 9.25/5.24                      ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 9.25/5.24                      & ? [Y3: int] :
% 9.25/5.24                          ( ( member_int @ Y3 @ A2 )
% 9.25/5.24                          & ( P @ ( minus_minus_int @ Y3 @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7256_sum__natinterval__diff,axiom,
% 9.25/5.24      ! [M: nat,N: nat,F2: nat > code_integer] :
% 9.25/5.24        ( ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24         => ( ( groups7501900531339628137nteger
% 9.25/5.24              @ ^ [K4: nat] : ( minus_8373710615458151222nteger @ ( F2 @ K4 ) @ ( F2 @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 9.25/5.24              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.24            = ( minus_8373710615458151222nteger @ ( F2 @ M ) @ ( F2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 9.25/5.24        & ( ~ ( ord_less_eq_nat @ M @ N )
% 9.25/5.24         => ( ( groups7501900531339628137nteger
% 9.25/5.24              @ ^ [K4: nat] : ( minus_8373710615458151222nteger @ ( F2 @ K4 ) @ ( F2 @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 9.25/5.24              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.24            = zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7257_sum__natinterval__diff,axiom,
% 9.25/5.24      ! [M: nat,N: nat,F2: nat > rat] :
% 9.25/5.24        ( ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24         => ( ( groups2906978787729119204at_rat
% 9.25/5.24              @ ^ [K4: nat] : ( minus_minus_rat @ ( F2 @ K4 ) @ ( F2 @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 9.25/5.24              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.24            = ( minus_minus_rat @ ( F2 @ M ) @ ( F2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 9.25/5.24        & ( ~ ( ord_less_eq_nat @ M @ N )
% 9.25/5.24         => ( ( groups2906978787729119204at_rat
% 9.25/5.24              @ ^ [K4: nat] : ( minus_minus_rat @ ( F2 @ K4 ) @ ( F2 @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 9.25/5.24              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.24            = zero_zero_rat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7258_sum__natinterval__diff,axiom,
% 9.25/5.24      ! [M: nat,N: nat,F2: nat > int] :
% 9.25/5.24        ( ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24         => ( ( groups3539618377306564664at_int
% 9.25/5.24              @ ^ [K4: nat] : ( minus_minus_int @ ( F2 @ K4 ) @ ( F2 @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 9.25/5.24              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.24            = ( minus_minus_int @ ( F2 @ M ) @ ( F2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 9.25/5.24        & ( ~ ( ord_less_eq_nat @ M @ N )
% 9.25/5.24         => ( ( groups3539618377306564664at_int
% 9.25/5.24              @ ^ [K4: nat] : ( minus_minus_int @ ( F2 @ K4 ) @ ( F2 @ ( plus_plus_nat @ K4 @ one_one_nat ) ) )
% 9.25/5.24              @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.24            = zero_zero_int ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7259_sum__telescope_H_H,axiom,
% 9.25/5.24      ! [M: nat,N: nat,F2: nat > rat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24       => ( ( groups2906978787729119204at_rat
% 9.25/5.24            @ ^ [K4: nat] : ( minus_minus_rat @ ( F2 @ K4 ) @ ( F2 @ ( minus_minus_nat @ K4 @ one_one_nat ) ) )
% 9.25/5.24            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 9.25/5.24          = ( minus_minus_rat @ ( F2 @ N ) @ ( F2 @ M ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7260_sum__telescope_H_H,axiom,
% 9.25/5.24      ! [M: nat,N: nat,F2: nat > int] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24       => ( ( groups3539618377306564664at_int
% 9.25/5.24            @ ^ [K4: nat] : ( minus_minus_int @ ( F2 @ K4 ) @ ( F2 @ ( minus_minus_nat @ K4 @ one_one_nat ) ) )
% 9.25/5.24            @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 9.25/5.24          = ( minus_minus_int @ ( F2 @ N ) @ ( F2 @ M ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7261_sum__gp__multiplied,axiom,
% 9.25/5.24      ! [M: nat,N: nat,X: code_integer] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24       => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 9.25/5.24          = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ M ) @ ( power_8256067586552552935nteger @ X @ ( suc @ N ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7262_sum__gp__multiplied,axiom,
% 9.25/5.24      ! [M: nat,N: nat,X: rat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24       => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 9.25/5.24          = ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7263_sum__gp__multiplied,axiom,
% 9.25/5.24      ! [M: nat,N: nat,X: int] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24       => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 9.25/5.24          = ( minus_minus_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ ( suc @ N ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7264_sum_Oin__pairs,axiom,
% 9.25/5.24      ! [G2: nat > rat,M: nat,N: nat] :
% 9.25/5.24        ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.25/5.24        = ( groups2906978787729119204at_rat
% 9.25/5.24          @ ^ [I3: nat] : ( plus_plus_rat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.25/5.24          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7265_sum_Oin__pairs,axiom,
% 9.25/5.24      ! [G2: nat > int,M: nat,N: nat] :
% 9.25/5.24        ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.25/5.24        = ( groups3539618377306564664at_int
% 9.25/5.24          @ ^ [I3: nat] : ( plus_plus_int @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.25/5.24          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7266_sum_Oin__pairs,axiom,
% 9.25/5.24      ! [G2: nat > nat,M: nat,N: nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.25/5.24        = ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [I3: nat] : ( plus_plus_nat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.25/5.24          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7267_sum__gp,axiom,
% 9.25/5.24      ! [N: nat,M: nat,X: rat] :
% 9.25/5.24        ( ( ( ord_less_nat @ N @ M )
% 9.25/5.24         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.24            = zero_zero_rat ) )
% 9.25/5.24        & ( ~ ( ord_less_nat @ N @ M )
% 9.25/5.24         => ( ( ( X = one_one_rat )
% 9.25/5.24             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.24                = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 9.25/5.24            & ( ( X != one_one_rat )
% 9.25/5.24             => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.24                = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7268_gauss__sum__from__Suc__0,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 9.25/5.24        = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7269_gauss__sum__from__Suc__0,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 9.25/5.24        = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N ) @ one_one_Code_natural ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7270_gauss__sum__from__Suc__0,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 9.25/5.24        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7271_gauss__sum__from__Suc__0,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 9.25/5.24        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7272_sum__gp__offset,axiom,
% 9.25/5.24      ! [X: rat,M: nat,N: nat] :
% 9.25/5.24        ( ( ( X = one_one_rat )
% 9.25/5.24         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 9.25/5.24            = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) )
% 9.25/5.24        & ( ( X != one_one_rat )
% 9.25/5.24         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 9.25/5.24            = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7273_arith__series,axiom,
% 9.25/5.24      ! [A: code_integer,D2: code_integer,N: nat] :
% 9.25/5.24        ( ( groups7501900531339628137nteger
% 9.25/5.24          @ ^ [I3: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I3 ) @ D2 ) )
% 9.25/5.24          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.25/5.24        = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ D2 ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7274_arith__series,axiom,
% 9.25/5.24      ! [A: code_natural,D2: code_natural,N: nat] :
% 9.25/5.24        ( ( groups6325495683096345652atural
% 9.25/5.24          @ ^ [I3: nat] : ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ I3 ) @ D2 ) )
% 9.25/5.24          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.25/5.24        = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N ) @ one_one_Code_natural ) @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N ) @ D2 ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7275_arith__series,axiom,
% 9.25/5.24      ! [A: int,D2: int,N: nat] :
% 9.25/5.24        ( ( groups3539618377306564664at_int
% 9.25/5.24          @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D2 ) )
% 9.25/5.24          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.25/5.24        = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7276_arith__series,axiom,
% 9.25/5.24      ! [A: nat,D2: nat,N: nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D2 ) )
% 9.25/5.24          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.25/5.24        = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7277_gauss__sum,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.25/5.24        = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7278_gauss__sum,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.25/5.24        = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N ) @ one_one_Code_natural ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7279_gauss__sum,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.25/5.24        = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7280_gauss__sum,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.25/5.24        = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7281_double__gauss__sum__from__Suc__0,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 9.25/5.24        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7282_double__gauss__sum__from__Suc__0,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 9.25/5.24        = ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N ) @ one_one_Code_natural ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7283_double__gauss__sum__from__Suc__0,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 9.25/5.24        = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7284_double__gauss__sum__from__Suc__0,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 9.25/5.24        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7285_double__gauss__sum__from__Suc__0,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 9.25/5.24        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7286_double__arith__series,axiom,
% 9.25/5.24      ! [A: code_integer,D2: code_integer,N: nat] :
% 9.25/5.24        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 9.25/5.24          @ ( groups7501900531339628137nteger
% 9.25/5.24            @ ^ [I3: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I3 ) @ D2 ) )
% 9.25/5.24            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 9.25/5.24        = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ D2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7287_double__arith__series,axiom,
% 9.25/5.24      ! [A: code_natural,D2: code_natural,N: nat] :
% 9.25/5.24        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) )
% 9.25/5.24          @ ( groups6325495683096345652atural
% 9.25/5.24            @ ^ [I3: nat] : ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ I3 ) @ D2 ) )
% 9.25/5.24            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 9.25/5.24        = ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N ) @ one_one_Code_natural ) @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N ) @ D2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7288_double__arith__series,axiom,
% 9.25/5.24      ! [A: int,D2: int,N: nat] :
% 9.25/5.24        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 9.25/5.24          @ ( groups3539618377306564664at_int
% 9.25/5.24            @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D2 ) )
% 9.25/5.24            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 9.25/5.24        = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7289_double__arith__series,axiom,
% 9.25/5.24      ! [A: rat,D2: rat,N: nat] :
% 9.25/5.24        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 9.25/5.24          @ ( groups2906978787729119204at_rat
% 9.25/5.24            @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I3 ) @ D2 ) )
% 9.25/5.24            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 9.25/5.24        = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ D2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7290_double__arith__series,axiom,
% 9.25/5.24      ! [A: nat,D2: nat,N: nat] :
% 9.25/5.24        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.25/5.24          @ ( groups3542108847815614940at_nat
% 9.25/5.24            @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D2 ) )
% 9.25/5.24            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 9.25/5.24        = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7291_negative__eq__positive,axiom,
% 9.25/5.24      ! [N: nat,M: nat] :
% 9.25/5.24        ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
% 9.25/5.24          = ( semiri1314217659103216013at_int @ M ) )
% 9.25/5.24        = ( ( N = zero_zero_nat )
% 9.25/5.24          & ( M = zero_zero_nat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7292_negative__zle,axiom,
% 9.25/5.24      ! [N: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7293_of__nat__mult,axiom,
% 9.25/5.24      ! [M: nat,N: nat] :
% 9.25/5.24        ( ( semiri4939895301339042750nteger @ ( times_times_nat @ M @ N ) )
% 9.25/5.24        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7294_of__nat__mult,axiom,
% 9.25/5.24      ! [M: nat,N: nat] :
% 9.25/5.24        ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 9.25/5.24        = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7295_of__nat__mult,axiom,
% 9.25/5.24      ! [M: nat,N: nat] :
% 9.25/5.24        ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 9.25/5.24        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7296_of__nat__mult,axiom,
% 9.25/5.24      ! [M: nat,N: nat] :
% 9.25/5.24        ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N ) )
% 9.25/5.24        = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7297_of__nat__1,axiom,
% 9.25/5.24      ( ( semiri4939895301339042750nteger @ one_one_nat )
% 9.25/5.24      = one_one_Code_integer ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7298_of__nat__1,axiom,
% 9.25/5.24      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 9.25/5.24      = one_one_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7299_of__nat__1,axiom,
% 9.25/5.24      ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 9.25/5.24      = one_one_nat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7300_of__nat__1,axiom,
% 9.25/5.24      ( ( semiri681578069525770553at_rat @ one_one_nat )
% 9.25/5.24      = one_one_rat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7301_of__nat__1__eq__iff,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( one_one_Code_integer
% 9.25/5.24          = ( semiri4939895301339042750nteger @ N ) )
% 9.25/5.24        = ( N = one_one_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7302_of__nat__1__eq__iff,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( one_one_int
% 9.25/5.24          = ( semiri1314217659103216013at_int @ N ) )
% 9.25/5.24        = ( N = one_one_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7303_of__nat__1__eq__iff,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( one_one_nat
% 9.25/5.24          = ( semiri1316708129612266289at_nat @ N ) )
% 9.25/5.24        = ( N = one_one_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7304_of__nat__1__eq__iff,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( one_one_rat
% 9.25/5.24          = ( semiri681578069525770553at_rat @ N ) )
% 9.25/5.24        = ( N = one_one_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7305_of__nat__eq__1__iff,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( ( semiri4939895301339042750nteger @ N )
% 9.25/5.24          = one_one_Code_integer )
% 9.25/5.24        = ( N = one_one_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7306_of__nat__eq__1__iff,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( ( semiri1314217659103216013at_int @ N )
% 9.25/5.24          = one_one_int )
% 9.25/5.24        = ( N = one_one_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7307_of__nat__eq__1__iff,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( ( semiri1316708129612266289at_nat @ N )
% 9.25/5.24          = one_one_nat )
% 9.25/5.24        = ( N = one_one_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7308_of__nat__eq__1__iff,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( ( semiri681578069525770553at_rat @ N )
% 9.25/5.24          = one_one_rat )
% 9.25/5.24        = ( N = one_one_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7309_negative__zless,axiom,
% 9.25/5.24      ! [N: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7310_of__nat__sum,axiom,
% 9.25/5.24      ! [F2: int > nat,A2: set_int] :
% 9.25/5.24        ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F2 @ A2 ) )
% 9.25/5.24        = ( groups4538972089207619220nt_int
% 9.25/5.24          @ ^ [X3: int] : ( semiri1314217659103216013at_int @ ( F2 @ X3 ) )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7311_of__nat__sum,axiom,
% 9.25/5.24      ! [F2: nat > nat,A2: set_nat] :
% 9.25/5.24        ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F2 @ A2 ) )
% 9.25/5.24        = ( groups3539618377306564664at_int
% 9.25/5.24          @ ^ [X3: nat] : ( semiri1314217659103216013at_int @ ( F2 @ X3 ) )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7312_of__nat__sum,axiom,
% 9.25/5.24      ! [F2: nat > nat,A2: set_nat] :
% 9.25/5.24        ( ( semiri681578069525770553at_rat @ ( groups3542108847815614940at_nat @ F2 @ A2 ) )
% 9.25/5.24        = ( groups2906978787729119204at_rat
% 9.25/5.24          @ ^ [X3: nat] : ( semiri681578069525770553at_rat @ ( F2 @ X3 ) )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7313_of__nat__sum,axiom,
% 9.25/5.24      ! [F2: nat > nat,A2: set_nat] :
% 9.25/5.24        ( ( semiri1316708129612266289at_nat @ ( groups3542108847815614940at_nat @ F2 @ A2 ) )
% 9.25/5.24        = ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [X3: nat] : ( semiri1316708129612266289at_nat @ ( F2 @ X3 ) )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7314_of__nat__Suc,axiom,
% 9.25/5.24      ! [M: nat] :
% 9.25/5.24        ( ( semiri4939895301339042750nteger @ ( suc @ M ) )
% 9.25/5.24        = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( semiri4939895301339042750nteger @ M ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7315_of__nat__Suc,axiom,
% 9.25/5.24      ! [M: nat] :
% 9.25/5.24        ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 9.25/5.24        = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7316_of__nat__Suc,axiom,
% 9.25/5.24      ! [M: nat] :
% 9.25/5.24        ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 9.25/5.24        = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7317_of__nat__Suc,axiom,
% 9.25/5.24      ! [M: nat] :
% 9.25/5.24        ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 9.25/5.24        = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7318_mult__of__nat__commute,axiom,
% 9.25/5.24      ! [X: nat,Y: code_integer] :
% 9.25/5.24        ( ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ X ) @ Y )
% 9.25/5.24        = ( times_3573771949741848930nteger @ Y @ ( semiri4939895301339042750nteger @ X ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7319_mult__of__nat__commute,axiom,
% 9.25/5.24      ! [X: nat,Y: int] :
% 9.25/5.24        ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y )
% 9.25/5.24        = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7320_mult__of__nat__commute,axiom,
% 9.25/5.24      ! [X: nat,Y: nat] :
% 9.25/5.24        ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
% 9.25/5.24        = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7321_mult__of__nat__commute,axiom,
% 9.25/5.24      ! [X: nat,Y: rat] :
% 9.25/5.24        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X ) @ Y )
% 9.25/5.24        = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7322_atLeastLessThanPlusOne__atLeastAtMost__integer,axiom,
% 9.25/5.24      ! [L: code_integer,U: code_integer] :
% 9.25/5.24        ( ( set_or8404916559141939852nteger @ L @ ( plus_p5714425477246183910nteger @ U @ one_one_Code_integer ) )
% 9.25/5.24        = ( set_or189985376899183464nteger @ L @ U ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7323_int__cases2,axiom,
% 9.25/5.24      ! [Z: int] :
% 9.25/5.24        ( ! [N3: nat] :
% 9.25/5.24            ( Z
% 9.25/5.24           != ( semiri1314217659103216013at_int @ N3 ) )
% 9.25/5.24       => ~ ! [N3: nat] :
% 9.25/5.24              ( Z
% 9.25/5.24             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7324_div__mult2__eq_H,axiom,
% 9.25/5.24      ! [A: code_integer,M: nat,N: nat] :
% 9.25/5.24        ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 9.25/5.24        = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7325_div__mult2__eq_H,axiom,
% 9.25/5.24      ! [A: code_natural,M: nat,N: nat] :
% 9.25/5.24        ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) ) )
% 9.25/5.24        = ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ ( semiri3763490453095760265atural @ M ) ) @ ( semiri3763490453095760265atural @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7326_div__mult2__eq_H,axiom,
% 9.25/5.24      ! [A: int,M: nat,N: nat] :
% 9.25/5.24        ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 9.25/5.24        = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7327_div__mult2__eq_H,axiom,
% 9.25/5.24      ! [A: nat,M: nat,N: nat] :
% 9.25/5.24        ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 9.25/5.24        = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7328_int__cases,axiom,
% 9.25/5.24      ! [Z: int] :
% 9.25/5.24        ( ! [N3: nat] :
% 9.25/5.24            ( Z
% 9.25/5.24           != ( semiri1314217659103216013at_int @ N3 ) )
% 9.25/5.24       => ~ ! [N3: nat] :
% 9.25/5.24              ( Z
% 9.25/5.24             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7329_int__of__nat__induct,axiom,
% 9.25/5.24      ! [P: int > $o,Z: int] :
% 9.25/5.24        ( ! [N3: nat] : ( P @ ( semiri1314217659103216013at_int @ N3 ) )
% 9.25/5.24       => ( ! [N3: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) )
% 9.25/5.24         => ( P @ Z ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7330_int__ops_I2_J,axiom,
% 9.25/5.24      ( ( semiri1314217659103216013at_int @ one_one_nat )
% 9.25/5.24      = one_one_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7331_not__int__zless__negative,axiom,
% 9.25/5.24      ! [N: nat,M: nat] :
% 9.25/5.24        ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7332_nat__less__as__int,axiom,
% 9.25/5.24      ( ord_less_nat
% 9.25/5.24      = ( ^ [A3: nat,B3: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7333_nat__leq__as__int,axiom,
% 9.25/5.24      ( ord_less_eq_nat
% 9.25/5.24      = ( ^ [A3: nat,B3: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7334_ex__less__of__nat__mult,axiom,
% 9.25/5.24      ! [X: rat,Y: rat] :
% 9.25/5.24        ( ( ord_less_rat @ zero_zero_rat @ X )
% 9.25/5.24       => ? [N3: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7335_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 9.25/5.24      ! [L: int,U: int] :
% 9.25/5.24        ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 9.25/5.24        = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7336_int__cases4,axiom,
% 9.25/5.24      ! [M: int] :
% 9.25/5.24        ( ! [N3: nat] :
% 9.25/5.24            ( M
% 9.25/5.24           != ( semiri1314217659103216013at_int @ N3 ) )
% 9.25/5.24       => ~ ! [N3: nat] :
% 9.25/5.24              ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 9.25/5.24             => ( M
% 9.25/5.24               != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7337_int__zle__neg,axiom,
% 9.25/5.24      ! [N: nat,M: nat] :
% 9.25/5.24        ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 9.25/5.24        = ( ( N = zero_zero_nat )
% 9.25/5.24          & ( M = zero_zero_nat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7338_int__Suc,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 9.25/5.24        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7339_int__ops_I4_J,axiom,
% 9.25/5.24      ! [A: nat] :
% 9.25/5.24        ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 9.25/5.24        = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7340_negative__zle__0,axiom,
% 9.25/5.24      ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7341_nonpos__int__cases,axiom,
% 9.25/5.24      ! [K: int] :
% 9.25/5.24        ( ( ord_less_eq_int @ K @ zero_zero_int )
% 9.25/5.24       => ~ ! [N3: nat] :
% 9.25/5.24              ( K
% 9.25/5.24             != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7342_int__sum,axiom,
% 9.25/5.24      ! [F2: int > nat,A2: set_int] :
% 9.25/5.24        ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F2 @ A2 ) )
% 9.25/5.24        = ( groups4538972089207619220nt_int
% 9.25/5.24          @ ^ [X3: int] : ( semiri1314217659103216013at_int @ ( F2 @ X3 ) )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7343_int__sum,axiom,
% 9.25/5.24      ! [F2: nat > nat,A2: set_nat] :
% 9.25/5.24        ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F2 @ A2 ) )
% 9.25/5.24        = ( groups3539618377306564664at_int
% 9.25/5.24          @ ^ [X3: nat] : ( semiri1314217659103216013at_int @ ( F2 @ X3 ) )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7344_mod__mult2__eq_H,axiom,
% 9.25/5.24      ! [A: code_integer,M: nat,N: nat] :
% 9.25/5.24        ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 9.25/5.24        = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7345_mod__mult2__eq_H,axiom,
% 9.25/5.24      ! [A: code_natural,M: nat,N: nat] :
% 9.25/5.24        ( ( modulo8411746178871703098atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N ) ) )
% 9.25/5.24        = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M ) @ ( modulo8411746178871703098atural @ ( divide5121882707175180666atural @ A @ ( semiri3763490453095760265atural @ M ) ) @ ( semiri3763490453095760265atural @ N ) ) ) @ ( modulo8411746178871703098atural @ A @ ( semiri3763490453095760265atural @ M ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7346_mod__mult2__eq_H,axiom,
% 9.25/5.24      ! [A: int,M: nat,N: nat] :
% 9.25/5.24        ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 9.25/5.24        = ( 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 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7347_mod__mult2__eq_H,axiom,
% 9.25/5.24      ! [A: nat,M: nat,N: nat] :
% 9.25/5.24        ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 9.25/5.24        = ( 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 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7348_int__cases3,axiom,
% 9.25/5.24      ! [K: int] :
% 9.25/5.24        ( ( K != zero_zero_int )
% 9.25/5.24       => ( ! [N3: nat] :
% 9.25/5.24              ( ( K
% 9.25/5.24                = ( semiri1314217659103216013at_int @ N3 ) )
% 9.25/5.24             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 9.25/5.24         => ~ ! [N3: nat] :
% 9.25/5.24                ( ( K
% 9.25/5.24                  = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 9.25/5.24               => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7349_not__zle__0__negative,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7350_negD,axiom,
% 9.25/5.24      ! [X: int] :
% 9.25/5.24        ( ( ord_less_int @ X @ zero_zero_int )
% 9.25/5.24       => ? [N3: nat] :
% 9.25/5.24            ( X
% 9.25/5.24            = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7351_negative__zless__0,axiom,
% 9.25/5.24      ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7352_nat__approx__posE,axiom,
% 9.25/5.24      ! [E2: rat] :
% 9.25/5.24        ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 9.25/5.24       => ~ ! [N3: nat] :
% 9.25/5.24              ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7353_neg__int__cases,axiom,
% 9.25/5.24      ! [K: int] :
% 9.25/5.24        ( ( ord_less_int @ K @ zero_zero_int )
% 9.25/5.24       => ~ ! [N3: nat] :
% 9.25/5.24              ( ( K
% 9.25/5.24                = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 9.25/5.24             => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7354_double__gauss__sum,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 9.25/5.24        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7355_double__gauss__sum,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 9.25/5.24        = ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N ) @ one_one_Code_natural ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7356_double__gauss__sum,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 9.25/5.24        = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7357_double__gauss__sum,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 9.25/5.24        = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7358_double__gauss__sum,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 9.25/5.24        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7359_pochhammer__double,axiom,
% 9.25/5.24      ! [Z: rat,N: nat] :
% 9.25/5.24        ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.24        = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7360_of__nat__code,axiom,
% 9.25/5.24      ( semiri4939895301339042750nteger
% 9.25/5.24      = ( ^ [N2: nat] :
% 9.25/5.24            ( semiri4055485073559036834nteger
% 9.25/5.24            @ ^ [I3: code_integer] : ( plus_p5714425477246183910nteger @ I3 @ one_one_Code_integer )
% 9.25/5.24            @ N2
% 9.25/5.24            @ zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7361_of__nat__code,axiom,
% 9.25/5.24      ( semiri1314217659103216013at_int
% 9.25/5.24      = ( ^ [N2: nat] :
% 9.25/5.24            ( semiri8420488043553186161ux_int
% 9.25/5.24            @ ^ [I3: int] : ( plus_plus_int @ I3 @ one_one_int )
% 9.25/5.24            @ N2
% 9.25/5.24            @ zero_zero_int ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7362_of__nat__code,axiom,
% 9.25/5.24      ( semiri1316708129612266289at_nat
% 9.25/5.24      = ( ^ [N2: nat] :
% 9.25/5.24            ( semiri8422978514062236437ux_nat
% 9.25/5.24            @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ one_one_nat )
% 9.25/5.24            @ N2
% 9.25/5.24            @ zero_zero_nat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7363_of__nat__code,axiom,
% 9.25/5.24      ( semiri681578069525770553at_rat
% 9.25/5.24      = ( ^ [N2: nat] :
% 9.25/5.24            ( semiri7787848453975740701ux_rat
% 9.25/5.24            @ ^ [I3: rat] : ( plus_plus_rat @ I3 @ one_one_rat )
% 9.25/5.24            @ N2
% 9.25/5.24            @ zero_zero_rat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7364_pochhammer__code,axiom,
% 9.25/5.24      ( comm_s8582702949713902594nteger
% 9.25/5.24      = ( ^ [A3: code_integer,N2: nat] :
% 9.25/5.24            ( if_Code_integer @ ( N2 = zero_zero_nat ) @ one_one_Code_integer
% 9.25/5.24            @ ( set_fo1084959871951514735nteger
% 9.25/5.24              @ ^ [O: nat] : ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A3 @ ( semiri4939895301339042750nteger @ O ) ) )
% 9.25/5.24              @ zero_zero_nat
% 9.25/5.24              @ ( minus_minus_nat @ N2 @ one_one_nat )
% 9.25/5.24              @ one_one_Code_integer ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7365_pochhammer__code,axiom,
% 9.25/5.24      ( comm_s4660882817536571857er_int
% 9.25/5.24      = ( ^ [A3: int,N2: nat] :
% 9.25/5.24            ( if_int @ ( N2 = zero_zero_nat ) @ one_one_int
% 9.25/5.24            @ ( set_fo2581907887559384638at_int
% 9.25/5.24              @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ O ) ) )
% 9.25/5.24              @ zero_zero_nat
% 9.25/5.24              @ ( minus_minus_nat @ N2 @ one_one_nat )
% 9.25/5.24              @ one_one_int ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7366_pochhammer__code,axiom,
% 9.25/5.24      ( comm_s4028243227959126397er_rat
% 9.25/5.24      = ( ^ [A3: rat,N2: nat] :
% 9.25/5.24            ( if_rat @ ( N2 = zero_zero_nat ) @ one_one_rat
% 9.25/5.24            @ ( set_fo1949268297981939178at_rat
% 9.25/5.24              @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ O ) ) )
% 9.25/5.24              @ zero_zero_nat
% 9.25/5.24              @ ( minus_minus_nat @ N2 @ one_one_nat )
% 9.25/5.24              @ one_one_rat ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7367_pochhammer__code,axiom,
% 9.25/5.24      ( comm_s4663373288045622133er_nat
% 9.25/5.24      = ( ^ [A3: nat,N2: nat] :
% 9.25/5.24            ( if_nat @ ( N2 = zero_zero_nat ) @ one_one_nat
% 9.25/5.24            @ ( set_fo2584398358068434914at_nat
% 9.25/5.24              @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 9.25/5.24              @ zero_zero_nat
% 9.25/5.24              @ ( minus_minus_nat @ N2 @ one_one_nat )
% 9.25/5.24              @ one_one_nat ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7368_sum__gp0,axiom,
% 9.25/5.24      ! [X: rat,N: nat] :
% 9.25/5.24        ( ( ( X = one_one_rat )
% 9.25/5.24         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.24            = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 9.25/5.24        & ( ( X != one_one_rat )
% 9.25/5.24         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.24            = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7369_gchoose__row__sum__weighted,axiom,
% 9.25/5.24      ! [R3: rat,M: nat] :
% 9.25/5.24        ( ( groups2906978787729119204at_rat
% 9.25/5.24          @ ^ [K4: nat] : ( times_times_rat @ ( gbinomial_rat @ R3 @ K4 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K4 ) ) )
% 9.25/5.24          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 9.25/5.24        = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R3 @ ( suc @ M ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7370_case__nat__add__eq__if,axiom,
% 9.25/5.24      ! [A: $o,F2: nat > $o,V: num,N: nat] :
% 9.25/5.24        ( ( case_nat_o @ A @ F2 @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 9.25/5.24        = ( F2 @ ( plus_plus_nat @ ( pred_numeral @ V ) @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7371_case__nat__add__eq__if,axiom,
% 9.25/5.24      ! [A: nat,F2: nat > nat,V: num,N: nat] :
% 9.25/5.24        ( ( case_nat_nat @ A @ F2 @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 9.25/5.24        = ( F2 @ ( plus_plus_nat @ ( pred_numeral @ V ) @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7372_case__nat__add__eq__if,axiom,
% 9.25/5.24      ! [A: option_num,F2: nat > option_num,V: num,N: nat] :
% 9.25/5.24        ( ( case_nat_option_num @ A @ F2 @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 9.25/5.24        = ( F2 @ ( plus_plus_nat @ ( pred_numeral @ V ) @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7373_gbinomial__0_I1_J,axiom,
% 9.25/5.24      ! [A: code_integer] :
% 9.25/5.24        ( ( gbinom8545251970709558553nteger @ A @ zero_zero_nat )
% 9.25/5.24        = one_one_Code_integer ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7374_gbinomial__0_I1_J,axiom,
% 9.25/5.24      ! [A: rat] :
% 9.25/5.24        ( ( gbinomial_rat @ A @ zero_zero_nat )
% 9.25/5.24        = one_one_rat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7375_gbinomial__0_I1_J,axiom,
% 9.25/5.24      ! [A: nat] :
% 9.25/5.24        ( ( gbinomial_nat @ A @ zero_zero_nat )
% 9.25/5.24        = one_one_nat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7376_gbinomial__0_I1_J,axiom,
% 9.25/5.24      ! [A: int] :
% 9.25/5.24        ( ( gbinomial_int @ A @ zero_zero_nat )
% 9.25/5.24        = one_one_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7377_pochhammer__0,axiom,
% 9.25/5.24      ! [A: code_integer] :
% 9.25/5.24        ( ( comm_s8582702949713902594nteger @ A @ zero_zero_nat )
% 9.25/5.24        = one_one_Code_integer ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7378_pochhammer__0,axiom,
% 9.25/5.24      ! [A: rat] :
% 9.25/5.24        ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 9.25/5.24        = one_one_rat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7379_pochhammer__0,axiom,
% 9.25/5.24      ! [A: nat] :
% 9.25/5.24        ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 9.25/5.24        = one_one_nat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7380_pochhammer__0,axiom,
% 9.25/5.24      ! [A: int] :
% 9.25/5.24        ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 9.25/5.24        = one_one_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7381_case__nat__numeral,axiom,
% 9.25/5.24      ! [A: $o,F2: nat > $o,V: num] :
% 9.25/5.24        ( ( case_nat_o @ A @ F2 @ ( numeral_numeral_nat @ V ) )
% 9.25/5.24        = ( F2 @ ( pred_numeral @ V ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7382_case__nat__numeral,axiom,
% 9.25/5.24      ! [A: nat,F2: nat > nat,V: num] :
% 9.25/5.24        ( ( case_nat_nat @ A @ F2 @ ( numeral_numeral_nat @ V ) )
% 9.25/5.24        = ( F2 @ ( pred_numeral @ V ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7383_case__nat__numeral,axiom,
% 9.25/5.24      ! [A: option_num,F2: nat > option_num,V: num] :
% 9.25/5.24        ( ( case_nat_option_num @ A @ F2 @ ( numeral_numeral_nat @ V ) )
% 9.25/5.24        = ( F2 @ ( pred_numeral @ V ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7384_atMost__0,axiom,
% 9.25/5.24      ( ( set_ord_atMost_nat @ zero_zero_nat )
% 9.25/5.24      = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7385_nat_Ocase__distrib,axiom,
% 9.25/5.24      ! [H3: $o > $o,F1: $o,F22: nat > $o,Nat: nat] :
% 9.25/5.24        ( ( H3 @ ( case_nat_o @ F1 @ F22 @ Nat ) )
% 9.25/5.24        = ( case_nat_o @ ( H3 @ F1 )
% 9.25/5.24          @ ^ [X3: nat] : ( H3 @ ( F22 @ X3 ) )
% 9.25/5.24          @ Nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7386_nat_Ocase__distrib,axiom,
% 9.25/5.24      ! [H3: $o > nat,F1: $o,F22: nat > $o,Nat: nat] :
% 9.25/5.24        ( ( H3 @ ( case_nat_o @ F1 @ F22 @ Nat ) )
% 9.25/5.24        = ( case_nat_nat @ ( H3 @ F1 )
% 9.25/5.24          @ ^ [X3: nat] : ( H3 @ ( F22 @ X3 ) )
% 9.25/5.24          @ Nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7387_nat_Ocase__distrib,axiom,
% 9.25/5.24      ! [H3: $o > option_num,F1: $o,F22: nat > $o,Nat: nat] :
% 9.25/5.24        ( ( H3 @ ( case_nat_o @ F1 @ F22 @ Nat ) )
% 9.25/5.24        = ( case_nat_option_num @ ( H3 @ F1 )
% 9.25/5.24          @ ^ [X3: nat] : ( H3 @ ( F22 @ X3 ) )
% 9.25/5.24          @ Nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7388_nat_Ocase__distrib,axiom,
% 9.25/5.24      ! [H3: nat > $o,F1: nat,F22: nat > nat,Nat: nat] :
% 9.25/5.24        ( ( H3 @ ( case_nat_nat @ F1 @ F22 @ Nat ) )
% 9.25/5.24        = ( case_nat_o @ ( H3 @ F1 )
% 9.25/5.24          @ ^ [X3: nat] : ( H3 @ ( F22 @ X3 ) )
% 9.25/5.24          @ Nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7389_nat_Ocase__distrib,axiom,
% 9.25/5.24      ! [H3: nat > nat,F1: nat,F22: nat > nat,Nat: nat] :
% 9.25/5.24        ( ( H3 @ ( case_nat_nat @ F1 @ F22 @ Nat ) )
% 9.25/5.24        = ( case_nat_nat @ ( H3 @ F1 )
% 9.25/5.24          @ ^ [X3: nat] : ( H3 @ ( F22 @ X3 ) )
% 9.25/5.24          @ Nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7390_nat_Ocase__distrib,axiom,
% 9.25/5.24      ! [H3: nat > option_num,F1: nat,F22: nat > nat,Nat: nat] :
% 9.25/5.24        ( ( H3 @ ( case_nat_nat @ F1 @ F22 @ Nat ) )
% 9.25/5.24        = ( case_nat_option_num @ ( H3 @ F1 )
% 9.25/5.24          @ ^ [X3: nat] : ( H3 @ ( F22 @ X3 ) )
% 9.25/5.24          @ Nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7391_nat_Ocase__distrib,axiom,
% 9.25/5.24      ! [H3: option_num > $o,F1: option_num,F22: nat > option_num,Nat: nat] :
% 9.25/5.24        ( ( H3 @ ( case_nat_option_num @ F1 @ F22 @ Nat ) )
% 9.25/5.24        = ( case_nat_o @ ( H3 @ F1 )
% 9.25/5.24          @ ^ [X3: nat] : ( H3 @ ( F22 @ X3 ) )
% 9.25/5.24          @ Nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7392_nat_Ocase__distrib,axiom,
% 9.25/5.24      ! [H3: option_num > nat,F1: option_num,F22: nat > option_num,Nat: nat] :
% 9.25/5.24        ( ( H3 @ ( case_nat_option_num @ F1 @ F22 @ Nat ) )
% 9.25/5.24        = ( case_nat_nat @ ( H3 @ F1 )
% 9.25/5.24          @ ^ [X3: nat] : ( H3 @ ( F22 @ X3 ) )
% 9.25/5.24          @ Nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7393_nat_Ocase__distrib,axiom,
% 9.25/5.24      ! [H3: option_num > option_num,F1: option_num,F22: nat > option_num,Nat: nat] :
% 9.25/5.24        ( ( H3 @ ( case_nat_option_num @ F1 @ F22 @ Nat ) )
% 9.25/5.24        = ( case_nat_option_num @ ( H3 @ F1 )
% 9.25/5.24          @ ^ [X3: nat] : ( H3 @ ( F22 @ X3 ) )
% 9.25/5.24          @ Nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7394_not__empty__eq__Iic__eq__empty,axiom,
% 9.25/5.24      ! [H3: $o] :
% 9.25/5.24        ( bot_bot_set_o
% 9.25/5.24       != ( set_ord_atMost_o @ H3 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7395_not__empty__eq__Iic__eq__empty,axiom,
% 9.25/5.24      ! [H3: int] :
% 9.25/5.24        ( bot_bot_set_int
% 9.25/5.24       != ( set_ord_atMost_int @ H3 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7396_not__empty__eq__Iic__eq__empty,axiom,
% 9.25/5.24      ! [H3: nat] :
% 9.25/5.24        ( bot_bot_set_nat
% 9.25/5.24       != ( set_ord_atMost_nat @ H3 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7397_not__UNIV__eq__Iic,axiom,
% 9.25/5.24      ! [H4: rat] :
% 9.25/5.24        ( top_top_set_rat
% 9.25/5.24       != ( set_ord_atMost_rat @ H4 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7398_not__UNIV__eq__Iic,axiom,
% 9.25/5.24      ! [H4: int] :
% 9.25/5.24        ( top_top_set_int
% 9.25/5.24       != ( set_ord_atMost_int @ H4 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7399_not__UNIV__eq__Iic,axiom,
% 9.25/5.24      ! [H4: nat] :
% 9.25/5.24        ( top_top_set_nat
% 9.25/5.24       != ( set_ord_atMost_nat @ H4 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7400_atMost__def,axiom,
% 9.25/5.24      ( set_or2459421552957432928nt_int
% 9.25/5.24      = ( ^ [U2: set_Pr958786334691620121nt_int] :
% 9.25/5.24            ( collec5210948495886036740nt_int
% 9.25/5.24            @ ^ [X3: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ X3 @ U2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7401_atMost__def,axiom,
% 9.25/5.24      ( set_or1537382583742010260_nat_o
% 9.25/5.24      = ( ^ [U2: produc3658429121746597890et_nat > $o] :
% 9.25/5.24            ( collec939566748876313656_nat_o
% 9.25/5.24            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( ord_le729326519192465773_nat_o @ X3 @ U2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7402_atMost__def,axiom,
% 9.25/5.24      ( set_or9144418160755794905er_nat
% 9.25/5.24      = ( ^ [U2: filter_nat] :
% 9.25/5.24            ( collect_filter_nat
% 9.25/5.24            @ ^ [X3: filter_nat] : ( ord_le2510731241096832064er_nat @ X3 @ U2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7403_atMost__def,axiom,
% 9.25/5.24      ( set_or4236626031148496127et_nat
% 9.25/5.24      = ( ^ [U2: set_nat] :
% 9.25/5.24            ( collect_set_nat
% 9.25/5.24            @ ^ [X3: set_nat] : ( ord_less_eq_set_nat @ X3 @ U2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7404_atMost__def,axiom,
% 9.25/5.24      ( set_ord_atMost_rat
% 9.25/5.24      = ( ^ [U2: rat] :
% 9.25/5.24            ( collect_rat
% 9.25/5.24            @ ^ [X3: rat] : ( ord_less_eq_rat @ X3 @ U2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7405_atMost__def,axiom,
% 9.25/5.24      ( set_ord_atMost_int
% 9.25/5.24      = ( ^ [U2: int] :
% 9.25/5.24            ( collect_int
% 9.25/5.24            @ ^ [X3: int] : ( ord_less_eq_int @ X3 @ U2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7406_atMost__def,axiom,
% 9.25/5.24      ( set_ord_atMost_nat
% 9.25/5.24      = ( ^ [U2: nat] :
% 9.25/5.24            ( collect_nat
% 9.25/5.24            @ ^ [X3: nat] : ( ord_less_eq_nat @ X3 @ U2 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7407_gbinomial__parallel__sum,axiom,
% 9.25/5.24      ! [A: rat,N: nat] :
% 9.25/5.24        ( ( groups2906978787729119204at_rat
% 9.25/5.24          @ ^ [K4: nat] : ( gbinomial_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K4 ) ) @ K4 )
% 9.25/5.24          @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.24        = ( gbinomial_rat @ ( plus_plus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ N ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7408_gbinomial__Suc__Suc,axiom,
% 9.25/5.24      ! [A: rat,K: nat] :
% 9.25/5.24        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 9.25/5.24        = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7409_nat_Odisc__eq__case_I2_J,axiom,
% 9.25/5.24      ! [Nat: nat] :
% 9.25/5.24        ( ( Nat != zero_zero_nat )
% 9.25/5.24        = ( case_nat_o @ $false
% 9.25/5.24          @ ^ [Uu: nat] : $true
% 9.25/5.24          @ Nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7410_nat_Odisc__eq__case_I1_J,axiom,
% 9.25/5.24      ! [Nat: nat] :
% 9.25/5.24        ( ( Nat = zero_zero_nat )
% 9.25/5.24        = ( case_nat_o @ $true
% 9.25/5.24          @ ^ [Uu: nat] : $false
% 9.25/5.24          @ Nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7411_not__UNIV__le__Iic,axiom,
% 9.25/5.24      ! [H3: rat] :
% 9.25/5.24        ~ ( ord_less_eq_set_rat @ top_top_set_rat @ ( set_ord_atMost_rat @ H3 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7412_not__UNIV__le__Iic,axiom,
% 9.25/5.24      ! [H3: int] :
% 9.25/5.24        ~ ( ord_less_eq_set_int @ top_top_set_int @ ( set_ord_atMost_int @ H3 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7413_not__UNIV__le__Iic,axiom,
% 9.25/5.24      ! [H3: nat] :
% 9.25/5.24        ~ ( ord_less_eq_set_nat @ top_top_set_nat @ ( set_ord_atMost_nat @ H3 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7414_atMost__eq__UNIV__iff,axiom,
% 9.25/5.24      ! [X: set_list_nat] :
% 9.25/5.24        ( ( ( set_or2492388921469580815st_nat @ X )
% 9.25/5.24          = top_to1619013496918823676st_nat )
% 9.25/5.24        = ( X = top_top_set_list_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7415_atMost__eq__UNIV__iff,axiom,
% 9.25/5.24      ! [X: set_o] :
% 9.25/5.24        ( ( ( set_ord_atMost_set_o @ X )
% 9.25/5.24          = top_top_set_set_o )
% 9.25/5.24        = ( X = top_top_set_o ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7416_atMost__eq__UNIV__iff,axiom,
% 9.25/5.24      ! [X: set_rat] :
% 9.25/5.24        ( ( ( set_or728397472755099399et_rat @ X )
% 9.25/5.24          = top_top_set_set_rat )
% 9.25/5.24        = ( X = top_top_set_rat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7417_atMost__eq__UNIV__iff,axiom,
% 9.25/5.24      ! [X: set_nat] :
% 9.25/5.24        ( ( ( set_or4236626031148496127et_nat @ X )
% 9.25/5.24          = top_top_set_set_nat )
% 9.25/5.24        = ( X = top_top_set_nat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7418_atMost__eq__UNIV__iff,axiom,
% 9.25/5.24      ! [X: set_int] :
% 9.25/5.24        ( ( ( set_or58775011639299419et_int @ X )
% 9.25/5.24          = top_top_set_set_int )
% 9.25/5.24        = ( X = top_top_set_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7419_atMost__eq__UNIV__iff,axiom,
% 9.25/5.24      ! [X: $o] :
% 9.25/5.24        ( ( ( set_ord_atMost_o @ X )
% 9.25/5.24          = top_top_set_o )
% 9.25/5.24        = ( X = top_top_o ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7420_gbinomial__sum__lower__neg,axiom,
% 9.25/5.24      ! [A: rat,M: nat] :
% 9.25/5.24        ( ( groups2906978787729119204at_rat
% 9.25/5.24          @ ^ [K4: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K4 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K4 ) )
% 9.25/5.24          @ ( set_ord_atMost_nat @ M ) )
% 9.25/5.24        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ M ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7421_gbinomial__addition__formula,axiom,
% 9.25/5.24      ! [A: rat,K: nat] :
% 9.25/5.24        ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 9.25/5.24        = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7422_gbinomial__absorb__comp,axiom,
% 9.25/5.24      ! [A: rat,K: nat] :
% 9.25/5.24        ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 9.25/5.24        = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7423_gbinomial__mult__1,axiom,
% 9.25/5.24      ! [A: rat,K: nat] :
% 9.25/5.24        ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 9.25/5.24        = ( 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 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7424_gbinomial__mult__1_H,axiom,
% 9.25/5.24      ! [A: rat,K: nat] :
% 9.25/5.24        ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 9.25/5.24        = ( 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 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7425_gbinomial__partial__sum__poly,axiom,
% 9.25/5.24      ! [M: nat,A: rat,X: rat,Y: rat] :
% 9.25/5.24        ( ( groups2906978787729119204at_rat
% 9.25/5.24          @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K4 ) @ ( power_power_rat @ X @ K4 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M @ K4 ) ) )
% 9.25/5.24          @ ( set_ord_atMost_nat @ M ) )
% 9.25/5.24        = ( groups2906978787729119204at_rat
% 9.25/5.24          @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K4 ) @ ( power_power_rat @ ( uminus_uminus_rat @ X ) @ K4 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_nat @ M @ K4 ) ) )
% 9.25/5.24          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7426_pochhammer__0__left,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( ( N = zero_zero_nat )
% 9.25/5.24         => ( ( comm_s8582702949713902594nteger @ zero_z3403309356797280102nteger @ N )
% 9.25/5.24            = one_one_Code_integer ) )
% 9.25/5.24        & ( ( N != zero_zero_nat )
% 9.25/5.24         => ( ( comm_s8582702949713902594nteger @ zero_z3403309356797280102nteger @ N )
% 9.25/5.24            = zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7427_pochhammer__0__left,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( ( N = zero_zero_nat )
% 9.25/5.24         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 9.25/5.24            = one_one_rat ) )
% 9.25/5.24        & ( ( N != zero_zero_nat )
% 9.25/5.24         => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 9.25/5.24            = zero_zero_rat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7428_pochhammer__0__left,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( ( N = zero_zero_nat )
% 9.25/5.24         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 9.25/5.24            = one_one_nat ) )
% 9.25/5.24        & ( ( N != zero_zero_nat )
% 9.25/5.24         => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 9.25/5.24            = zero_zero_nat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7429_pochhammer__0__left,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( ( N = zero_zero_nat )
% 9.25/5.24         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 9.25/5.24            = one_one_int ) )
% 9.25/5.24        & ( ( N != zero_zero_nat )
% 9.25/5.24         => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 9.25/5.24            = zero_zero_int ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7430_gbinomial__partial__sum__poly__xpos,axiom,
% 9.25/5.24      ! [M: nat,A: rat,X: rat,Y: rat] :
% 9.25/5.24        ( ( groups2906978787729119204at_rat
% 9.25/5.24          @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K4 ) @ ( power_power_rat @ X @ K4 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M @ K4 ) ) )
% 9.25/5.24          @ ( set_ord_atMost_nat @ M ) )
% 9.25/5.24        = ( groups2906978787729119204at_rat
% 9.25/5.24          @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ K4 ) @ A ) @ one_one_rat ) @ K4 ) @ ( power_power_rat @ X @ K4 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_nat @ M @ K4 ) ) )
% 9.25/5.24          @ ( set_ord_atMost_nat @ M ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7431_gbinomial__sum__nat__pow2,axiom,
% 9.25/5.24      ! [M: nat] :
% 9.25/5.24        ( ( groups2906978787729119204at_rat
% 9.25/5.24          @ ^ [K4: nat] : ( divide_divide_rat @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ K4 ) ) @ K4 ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ K4 ) )
% 9.25/5.24          @ ( set_ord_atMost_nat @ M ) )
% 9.25/5.24        = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ M ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7432_Suc__times__gbinomial,axiom,
% 9.25/5.24      ! [K: nat,A: rat] :
% 9.25/5.24        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 9.25/5.24        = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7433_gbinomial__absorption,axiom,
% 9.25/5.24      ! [K: nat,A: rat] :
% 9.25/5.24        ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 9.25/5.24        = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7434_less__eq__nat_Osimps_I2_J,axiom,
% 9.25/5.24      ! [M: nat,N: nat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 9.25/5.24        = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7435_gbinomial__trinomial__revision,axiom,
% 9.25/5.24      ! [K: nat,M: nat,A: rat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ K @ M )
% 9.25/5.24       => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 9.25/5.24          = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7436_sum_OatMost__Suc__shift,axiom,
% 9.25/5.24      ! [G2: nat > rat,N: nat] :
% 9.25/5.24        ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 9.25/5.24        = ( plus_plus_rat @ ( G2 @ zero_zero_nat )
% 9.25/5.24          @ ( groups2906978787729119204at_rat
% 9.25/5.24            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.24            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7437_sum_OatMost__Suc__shift,axiom,
% 9.25/5.24      ! [G2: nat > int,N: nat] :
% 9.25/5.24        ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 9.25/5.24        = ( plus_plus_int @ ( G2 @ zero_zero_nat )
% 9.25/5.24          @ ( groups3539618377306564664at_int
% 9.25/5.24            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.24            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7438_sum_OatMost__Suc__shift,axiom,
% 9.25/5.24      ! [G2: nat > nat,N: nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 9.25/5.24        = ( plus_plus_nat @ ( G2 @ zero_zero_nat )
% 9.25/5.24          @ ( groups3542108847815614940at_nat
% 9.25/5.24            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.24            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7439_sum__telescope,axiom,
% 9.25/5.24      ! [F2: nat > rat,I: nat] :
% 9.25/5.24        ( ( groups2906978787729119204at_rat
% 9.25/5.24          @ ^ [I3: nat] : ( minus_minus_rat @ ( F2 @ I3 ) @ ( F2 @ ( suc @ I3 ) ) )
% 9.25/5.24          @ ( set_ord_atMost_nat @ I ) )
% 9.25/5.24        = ( minus_minus_rat @ ( F2 @ zero_zero_nat ) @ ( F2 @ ( suc @ I ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7440_sum__telescope,axiom,
% 9.25/5.24      ! [F2: nat > int,I: nat] :
% 9.25/5.24        ( ( groups3539618377306564664at_int
% 9.25/5.24          @ ^ [I3: nat] : ( minus_minus_int @ ( F2 @ I3 ) @ ( F2 @ ( suc @ I3 ) ) )
% 9.25/5.24          @ ( set_ord_atMost_nat @ I ) )
% 9.25/5.24        = ( minus_minus_int @ ( F2 @ zero_zero_nat ) @ ( F2 @ ( suc @ I ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7441_pochhammer__rec,axiom,
% 9.25/5.24      ! [A: code_integer,N: nat] :
% 9.25/5.24        ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N ) )
% 9.25/5.24        = ( times_3573771949741848930nteger @ A @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7442_pochhammer__rec,axiom,
% 9.25/5.24      ! [A: rat,N: nat] :
% 9.25/5.24        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 9.25/5.24        = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7443_pochhammer__rec,axiom,
% 9.25/5.24      ! [A: nat,N: nat] :
% 9.25/5.24        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 9.25/5.24        = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7444_pochhammer__rec,axiom,
% 9.25/5.24      ! [A: int,N: nat] :
% 9.25/5.24        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 9.25/5.24        = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7445_pochhammer__Suc,axiom,
% 9.25/5.24      ! [A: code_integer,N: nat] :
% 9.25/5.24        ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N ) )
% 9.25/5.24        = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ A @ N ) @ ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ N ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7446_pochhammer__Suc,axiom,
% 9.25/5.24      ! [A: int,N: nat] :
% 9.25/5.24        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 9.25/5.24        = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7447_pochhammer__Suc,axiom,
% 9.25/5.24      ! [A: nat,N: nat] :
% 9.25/5.24        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 9.25/5.24        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7448_pochhammer__Suc,axiom,
% 9.25/5.24      ! [A: rat,N: nat] :
% 9.25/5.24        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 9.25/5.24        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7449_pochhammer__rec_H,axiom,
% 9.25/5.24      ! [Z: code_integer,N: nat] :
% 9.25/5.24        ( ( comm_s8582702949713902594nteger @ Z @ ( suc @ N ) )
% 9.25/5.24        = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ N ) ) @ ( comm_s8582702949713902594nteger @ Z @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7450_pochhammer__rec_H,axiom,
% 9.25/5.24      ! [Z: int,N: nat] :
% 9.25/5.24        ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N ) )
% 9.25/5.24        = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7451_pochhammer__rec_H,axiom,
% 9.25/5.24      ! [Z: nat,N: nat] :
% 9.25/5.24        ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N ) )
% 9.25/5.24        = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7452_pochhammer__rec_H,axiom,
% 9.25/5.24      ! [Z: rat,N: nat] :
% 9.25/5.24        ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) )
% 9.25/5.24        = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7453_pochhammer__of__nat__eq__0__lemma,axiom,
% 9.25/5.24      ! [N: nat,K: nat] :
% 9.25/5.24        ( ( ord_less_nat @ N @ K )
% 9.25/5.24       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 9.25/5.24          = zero_z3403309356797280102nteger ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7454_pochhammer__of__nat__eq__0__lemma,axiom,
% 9.25/5.24      ! [N: nat,K: nat] :
% 9.25/5.24        ( ( ord_less_nat @ N @ K )
% 9.25/5.24       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 9.25/5.24          = zero_zero_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7455_pochhammer__of__nat__eq__0__lemma,axiom,
% 9.25/5.24      ! [N: nat,K: nat] :
% 9.25/5.24        ( ( ord_less_nat @ N @ K )
% 9.25/5.24       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 9.25/5.24          = zero_zero_rat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7456_pochhammer__of__nat__eq__0__iff,axiom,
% 9.25/5.24      ! [N: nat,K: nat] :
% 9.25/5.24        ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 9.25/5.24          = zero_z3403309356797280102nteger )
% 9.25/5.24        = ( ord_less_nat @ N @ K ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7457_pochhammer__of__nat__eq__0__iff,axiom,
% 9.25/5.24      ! [N: nat,K: nat] :
% 9.25/5.24        ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 9.25/5.24          = zero_zero_int )
% 9.25/5.24        = ( ord_less_nat @ N @ K ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7458_pochhammer__of__nat__eq__0__iff,axiom,
% 9.25/5.24      ! [N: nat,K: nat] :
% 9.25/5.24        ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 9.25/5.24          = zero_zero_rat )
% 9.25/5.24        = ( ord_less_nat @ N @ K ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7459_pochhammer__eq__0__iff,axiom,
% 9.25/5.24      ! [A: rat,N: nat] :
% 9.25/5.24        ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 9.25/5.24          = zero_zero_rat )
% 9.25/5.24        = ( ? [K4: nat] :
% 9.25/5.24              ( ( ord_less_nat @ K4 @ N )
% 9.25/5.24              & ( A
% 9.25/5.24                = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K4 ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7460_gbinomial__rec,axiom,
% 9.25/5.24      ! [A: rat,K: nat] :
% 9.25/5.24        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 9.25/5.24        = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7461_gbinomial__factors,axiom,
% 9.25/5.24      ! [A: rat,K: nat] :
% 9.25/5.24        ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 9.25/5.24        = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7462_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 9.25/5.24      ! [K: nat,N: nat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ K @ N )
% 9.25/5.24       => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K )
% 9.25/5.24         != zero_z3403309356797280102nteger ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7463_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 9.25/5.24      ! [K: nat,N: nat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ K @ N )
% 9.25/5.24       => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K )
% 9.25/5.24         != zero_zero_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7464_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 9.25/5.24      ! [K: nat,N: nat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ K @ N )
% 9.25/5.24       => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K )
% 9.25/5.24         != zero_zero_rat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7465_pochhammer__product_H,axiom,
% 9.25/5.24      ! [Z: code_integer,N: nat,M: nat] :
% 9.25/5.24        ( ( comm_s8582702949713902594nteger @ Z @ ( plus_plus_nat @ N @ M ) )
% 9.25/5.24        = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z @ N ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ N ) ) @ M ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7466_pochhammer__product_H,axiom,
% 9.25/5.24      ! [Z: int,N: nat,M: nat] :
% 9.25/5.24        ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N @ M ) )
% 9.25/5.24        = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N ) ) @ M ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7467_pochhammer__product_H,axiom,
% 9.25/5.24      ! [Z: nat,N: nat,M: nat] :
% 9.25/5.24        ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N @ M ) )
% 9.25/5.24        = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N ) ) @ M ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7468_pochhammer__product_H,axiom,
% 9.25/5.24      ! [Z: rat,N: nat,M: nat] :
% 9.25/5.24        ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N @ M ) )
% 9.25/5.24        = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N ) ) @ M ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7469_gbinomial__negated__upper,axiom,
% 9.25/5.24      ( gbinomial_rat
% 9.25/5.24      = ( ^ [A3: rat,K4: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K4 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K4 ) @ A3 ) @ one_one_rat ) @ K4 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7470_gbinomial__index__swap,axiom,
% 9.25/5.24      ! [K: nat,N: nat] :
% 9.25/5.24        ( ( 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 ) )
% 9.25/5.24        = ( 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 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7471_gbinomial__r__part__sum,axiom,
% 9.25/5.24      ! [M: nat] :
% 9.25/5.24        ( ( groups2906978787729119204at_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M ) ) @ one_one_rat ) ) @ ( set_ord_atMost_nat @ M ) )
% 9.25/5.24        = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7472_diff__Suc,axiom,
% 9.25/5.24      ! [M: nat,N: nat] :
% 9.25/5.24        ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 9.25/5.24        = ( case_nat_nat @ zero_zero_nat
% 9.25/5.24          @ ^ [K4: nat] : K4
% 9.25/5.24          @ ( minus_minus_nat @ M @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7473_gbinomial__partial__row__sum,axiom,
% 9.25/5.24      ! [A: rat,M: nat] :
% 9.25/5.24        ( ( groups2906978787729119204at_rat
% 9.25/5.24          @ ^ [K4: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K4 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K4 ) ) )
% 9.25/5.24          @ ( set_ord_atMost_nat @ M ) )
% 9.25/5.24        = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ one_one_rat ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7474_Nitpick_Ocase__nat__unfold,axiom,
% 9.25/5.24      ( case_nat_o
% 9.25/5.24      = ( ^ [X3: $o,F: nat > $o,N2: nat] :
% 9.25/5.24            ( ( ( N2 = zero_zero_nat )
% 9.25/5.24             => X3 )
% 9.25/5.24            & ( ( N2 != zero_zero_nat )
% 9.25/5.24             => ( F @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7475_Nitpick_Ocase__nat__unfold,axiom,
% 9.25/5.24      ( case_nat_nat
% 9.25/5.24      = ( ^ [X3: nat,F: nat > nat,N2: nat] : ( if_nat @ ( N2 = zero_zero_nat ) @ X3 @ ( F @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7476_Nitpick_Ocase__nat__unfold,axiom,
% 9.25/5.24      ( case_nat_option_num
% 9.25/5.24      = ( ^ [X3: option_num,F: nat > option_num,N2: nat] : ( if_option_num @ ( N2 = zero_zero_nat ) @ X3 @ ( F @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7477_gbinomial__minus,axiom,
% 9.25/5.24      ! [A: rat,K: nat] :
% 9.25/5.24        ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 9.25/5.24        = ( 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 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7478_atLeast1__atMost__eq__remove0,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 9.25/5.24        = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7479_gbinomial__reduce__nat,axiom,
% 9.25/5.24      ! [K: nat,A: rat] :
% 9.25/5.24        ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.25/5.24       => ( ( gbinomial_rat @ A @ K )
% 9.25/5.24          = ( 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 ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7480_sum_Otriangle__reindex__eq,axiom,
% 9.25/5.24      ! [G2: nat > nat > nat,N: nat] :
% 9.25/5.24        ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G2 )
% 9.25/5.24          @ ( collec3392354462482085612at_nat
% 9.25/5.24            @ ( produc6081775807080527818_nat_o
% 9.25/5.24              @ ^ [I3: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 9.25/5.24        = ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [K4: nat] :
% 9.25/5.24              ( groups3542108847815614940at_nat
% 9.25/5.24              @ ^ [I3: nat] : ( G2 @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 9.25/5.24              @ ( set_ord_atMost_nat @ K4 ) )
% 9.25/5.24          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7481_pochhammer__product,axiom,
% 9.25/5.24      ! [M: nat,N: nat,Z: code_integer] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24       => ( ( comm_s8582702949713902594nteger @ Z @ N )
% 9.25/5.24          = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z @ M ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7482_pochhammer__product,axiom,
% 9.25/5.24      ! [M: nat,N: nat,Z: int] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24       => ( ( comm_s4660882817536571857er_int @ Z @ N )
% 9.25/5.24          = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7483_pochhammer__product,axiom,
% 9.25/5.24      ! [M: nat,N: nat,Z: nat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24       => ( ( comm_s4663373288045622133er_nat @ Z @ N )
% 9.25/5.24          = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7484_pochhammer__product,axiom,
% 9.25/5.24      ! [M: nat,N: nat,Z: rat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24       => ( ( comm_s4028243227959126397er_rat @ Z @ N )
% 9.25/5.24          = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7485_sum__gp__basic,axiom,
% 9.25/5.24      ! [X: code_integer,N: nat] :
% 9.25/5.24        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 9.25/5.24        = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ ( suc @ N ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7486_sum__gp__basic,axiom,
% 9.25/5.24      ! [X: rat,N: nat] :
% 9.25/5.24        ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 9.25/5.24        = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7487_sum__gp__basic,axiom,
% 9.25/5.24      ! [X: int,N: nat] :
% 9.25/5.24        ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 9.25/5.24        = ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ ( suc @ N ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7488_sum__power__shift,axiom,
% 9.25/5.24      ! [M: nat,N: nat,X: code_integer] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24       => ( ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.24          = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ M ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7489_sum__power__shift,axiom,
% 9.25/5.24      ! [M: nat,N: nat,X: rat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24       => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.24          = ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7490_sum__power__shift,axiom,
% 9.25/5.24      ! [M: nat,N: nat,X: int] :
% 9.25/5.24        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.24       => ( ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.24          = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7491_gbinomial__sum__up__index,axiom,
% 9.25/5.24      ! [K: nat,N: nat] :
% 9.25/5.24        ( ( groups2906978787729119204at_rat
% 9.25/5.24          @ ^ [J3: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J3 ) @ K )
% 9.25/5.24          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.25/5.24        = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7492_pochhammer__absorb__comp,axiom,
% 9.25/5.24      ! [R3: code_integer,K: nat] :
% 9.25/5.24        ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R3 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R3 ) @ K ) )
% 9.25/5.24        = ( times_3573771949741848930nteger @ R3 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R3 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7493_pochhammer__absorb__comp,axiom,
% 9.25/5.24      ! [R3: int,K: nat] :
% 9.25/5.24        ( ( times_times_int @ ( minus_minus_int @ R3 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R3 ) @ K ) )
% 9.25/5.24        = ( times_times_int @ R3 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R3 ) @ one_one_int ) @ K ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7494_pochhammer__absorb__comp,axiom,
% 9.25/5.24      ! [R3: rat,K: nat] :
% 9.25/5.24        ( ( times_times_rat @ ( minus_minus_rat @ R3 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R3 ) @ K ) )
% 9.25/5.24        = ( times_times_rat @ R3 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R3 ) @ one_one_rat ) @ K ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7495_gbinomial__absorption_H,axiom,
% 9.25/5.24      ! [K: nat,A: rat] :
% 9.25/5.24        ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.25/5.24       => ( ( gbinomial_rat @ A @ K )
% 9.25/5.24          = ( 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 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7496_sum_Oin__pairs__0,axiom,
% 9.25/5.24      ! [G2: nat > rat,N: nat] :
% 9.25/5.24        ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.25/5.24        = ( groups2906978787729119204at_rat
% 9.25/5.24          @ ^ [I3: nat] : ( plus_plus_rat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.25/5.24          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7497_sum_Oin__pairs__0,axiom,
% 9.25/5.24      ! [G2: nat > int,N: nat] :
% 9.25/5.24        ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.25/5.24        = ( groups3539618377306564664at_int
% 9.25/5.24          @ ^ [I3: nat] : ( plus_plus_int @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.25/5.24          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7498_sum_Oin__pairs__0,axiom,
% 9.25/5.24      ! [G2: nat > nat,N: nat] :
% 9.25/5.24        ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.25/5.24        = ( groups3542108847815614940at_nat
% 9.25/5.24          @ ^ [I3: nat] : ( plus_plus_nat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.25/5.24          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7499_pochhammer__minus_H,axiom,
% 9.25/5.24      ! [B: code_integer,K: nat] :
% 9.25/5.24        ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 9.25/5.24        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7500_pochhammer__minus_H,axiom,
% 9.25/5.24      ! [B: int,K: nat] :
% 9.25/5.24        ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 9.25/5.24        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7501_pochhammer__minus_H,axiom,
% 9.25/5.24      ! [B: rat,K: nat] :
% 9.25/5.24        ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 9.25/5.24        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7502_pochhammer__minus,axiom,
% 9.25/5.24      ! [B: code_integer,K: nat] :
% 9.25/5.24        ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 9.25/5.24        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7503_pochhammer__minus,axiom,
% 9.25/5.24      ! [B: int,K: nat] :
% 9.25/5.24        ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 9.25/5.24        = ( 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 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7504_pochhammer__minus,axiom,
% 9.25/5.24      ! [B: rat,K: nat] :
% 9.25/5.24        ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 9.25/5.24        = ( 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 ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7505_sum_Ozero__middle,axiom,
% 9.25/5.24      ! [P4: nat,K: nat,G2: nat > code_integer,H3: nat > code_integer] :
% 9.25/5.24        ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 9.25/5.24       => ( ( ord_less_eq_nat @ K @ P4 )
% 9.25/5.24         => ( ( groups7501900531339628137nteger
% 9.25/5.24              @ ^ [J3: nat] : ( if_Code_integer @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( if_Code_integer @ ( J3 = K ) @ zero_z3403309356797280102nteger @ ( H3 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.25/5.24              @ ( set_ord_atMost_nat @ P4 ) )
% 9.25/5.24            = ( groups7501900531339628137nteger
% 9.25/5.24              @ ^ [J3: nat] : ( if_Code_integer @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( H3 @ J3 ) )
% 9.25/5.24              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7506_sum_Ozero__middle,axiom,
% 9.25/5.24      ! [P4: nat,K: nat,G2: nat > multis2468970476368604999at_nat,H3: nat > multis2468970476368604999at_nat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 9.25/5.24       => ( ( ord_less_eq_nat @ K @ P4 )
% 9.25/5.24         => ( ( groups6857163185585827899at_nat
% 9.25/5.24              @ ^ [J3: nat] : ( if_mul8430962117462786573at_nat @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( if_mul8430962117462786573at_nat @ ( J3 = K ) @ zero_z1048942125864253310at_nat @ ( H3 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.25/5.24              @ ( set_ord_atMost_nat @ P4 ) )
% 9.25/5.24            = ( groups6857163185585827899at_nat
% 9.25/5.24              @ ^ [J3: nat] : ( if_mul8430962117462786573at_nat @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( H3 @ J3 ) )
% 9.25/5.24              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7507_sum_Ozero__middle,axiom,
% 9.25/5.24      ! [P4: nat,K: nat,G2: nat > rat,H3: nat > rat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 9.25/5.24       => ( ( ord_less_eq_nat @ K @ P4 )
% 9.25/5.24         => ( ( groups2906978787729119204at_rat
% 9.25/5.24              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( if_rat @ ( J3 = K ) @ zero_zero_rat @ ( H3 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.25/5.24              @ ( set_ord_atMost_nat @ P4 ) )
% 9.25/5.24            = ( groups2906978787729119204at_rat
% 9.25/5.24              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( H3 @ J3 ) )
% 9.25/5.24              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7508_sum_Ozero__middle,axiom,
% 9.25/5.24      ! [P4: nat,K: nat,G2: nat > int,H3: nat > int] :
% 9.25/5.24        ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 9.25/5.24       => ( ( ord_less_eq_nat @ K @ P4 )
% 9.25/5.24         => ( ( groups3539618377306564664at_int
% 9.25/5.24              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( if_int @ ( J3 = K ) @ zero_zero_int @ ( H3 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.25/5.24              @ ( set_ord_atMost_nat @ P4 ) )
% 9.25/5.24            = ( groups3539618377306564664at_int
% 9.25/5.24              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( H3 @ J3 ) )
% 9.25/5.24              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7509_sum_Ozero__middle,axiom,
% 9.25/5.24      ! [P4: nat,K: nat,G2: nat > nat,H3: nat > nat] :
% 9.25/5.24        ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 9.25/5.24       => ( ( ord_less_eq_nat @ K @ P4 )
% 9.25/5.24         => ( ( groups3542108847815614940at_nat
% 9.25/5.24              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( if_nat @ ( J3 = K ) @ zero_zero_nat @ ( H3 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.25/5.24              @ ( set_ord_atMost_nat @ P4 ) )
% 9.25/5.24            = ( groups3542108847815614940at_nat
% 9.25/5.24              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( H3 @ J3 ) )
% 9.25/5.24              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7510_pochhammer__times__pochhammer__half,axiom,
% 9.25/5.24      ! [Z: rat,N: nat] :
% 9.25/5.24        ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 9.25/5.24        = ( groups73079841787564623at_rat
% 9.25/5.24          @ ^ [K4: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K4 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 9.25/5.24          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7511_choose__odd__sum,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.24       => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 9.25/5.24            @ ( groups7501900531339628137nteger
% 9.25/5.24              @ ^ [I3: nat] :
% 9.25/5.24                  ( if_Code_integer
% 9.25/5.24                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 9.25/5.24                  @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I3 ) )
% 9.25/5.24                  @ zero_z3403309356797280102nteger )
% 9.25/5.24              @ ( set_ord_atMost_nat @ N ) ) )
% 9.25/5.24          = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7512_choose__odd__sum,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.24       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 9.25/5.24            @ ( groups3539618377306564664at_int
% 9.25/5.24              @ ^ [I3: nat] :
% 9.25/5.24                  ( if_int
% 9.25/5.24                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 9.25/5.24                  @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I3 ) )
% 9.25/5.24                  @ zero_zero_int )
% 9.25/5.24              @ ( set_ord_atMost_nat @ N ) ) )
% 9.25/5.24          = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7513_choose__odd__sum,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.24       => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 9.25/5.24            @ ( groups2906978787729119204at_rat
% 9.25/5.24              @ ^ [I3: nat] :
% 9.25/5.24                  ( if_rat
% 9.25/5.24                  @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 9.25/5.24                  @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I3 ) )
% 9.25/5.24                  @ zero_zero_rat )
% 9.25/5.24              @ ( set_ord_atMost_nat @ N ) ) )
% 9.25/5.24          = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7514_choose__even__sum,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.24       => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 9.25/5.24            @ ( groups7501900531339628137nteger
% 9.25/5.24              @ ^ [I3: nat] : ( if_Code_integer @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I3 ) ) @ zero_z3403309356797280102nteger )
% 9.25/5.24              @ ( set_ord_atMost_nat @ N ) ) )
% 9.25/5.24          = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7515_choose__even__sum,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.24       => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 9.25/5.24            @ ( groups3539618377306564664at_int
% 9.25/5.24              @ ^ [I3: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I3 ) ) @ zero_zero_int )
% 9.25/5.24              @ ( set_ord_atMost_nat @ N ) ) )
% 9.25/5.24          = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7516_choose__even__sum,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.24       => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 9.25/5.24            @ ( groups2906978787729119204at_rat
% 9.25/5.24              @ ^ [I3: nat] : ( if_rat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I3 ) ) @ zero_zero_rat )
% 9.25/5.24              @ ( set_ord_atMost_nat @ N ) ) )
% 9.25/5.24          = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7517_gbinomial__code,axiom,
% 9.25/5.24      ( gbinomial_rat
% 9.25/5.24      = ( ^ [A3: rat,K4: nat] :
% 9.25/5.24            ( if_rat @ ( K4 = zero_zero_nat ) @ one_one_rat
% 9.25/5.24            @ ( divide_divide_rat
% 9.25/5.24              @ ( set_fo1949268297981939178at_rat
% 9.25/5.24                @ ^ [L2: nat] : ( times_times_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ L2 ) ) )
% 9.25/5.24                @ zero_zero_nat
% 9.25/5.24                @ ( minus_minus_nat @ K4 @ one_one_nat )
% 9.25/5.24                @ one_one_rat )
% 9.25/5.24              @ ( semiri773545260158071498ct_rat @ K4 ) ) ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7518_fact__double,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 9.25/5.24        = ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7519_choose__alternating__sum,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.24       => ( ( groups7501900531339628137nteger
% 9.25/5.24            @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I3 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I3 ) ) )
% 9.25/5.24            @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.24          = zero_z3403309356797280102nteger ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7520_choose__alternating__sum,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.24       => ( ( groups3539618377306564664at_int
% 9.25/5.24            @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I3 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I3 ) ) )
% 9.25/5.24            @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.24          = zero_zero_int ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7521_choose__alternating__sum,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.24       => ( ( groups2906978787729119204at_rat
% 9.25/5.24            @ ^ [I3: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I3 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I3 ) ) )
% 9.25/5.24            @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.24          = zero_zero_rat ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7522_atMost__UNIV__triv,axiom,
% 9.25/5.24      ( ( set_or2492388921469580815st_nat @ top_top_set_list_nat )
% 9.25/5.24      = top_to1619013496918823676st_nat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7523_atMost__UNIV__triv,axiom,
% 9.25/5.24      ( ( set_ord_atMost_set_o @ top_top_set_o )
% 9.25/5.24      = top_top_set_set_o ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7524_atMost__UNIV__triv,axiom,
% 9.25/5.24      ( ( set_or728397472755099399et_rat @ top_top_set_rat )
% 9.25/5.24      = top_top_set_set_rat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7525_atMost__UNIV__triv,axiom,
% 9.25/5.24      ( ( set_or4236626031148496127et_nat @ top_top_set_nat )
% 9.25/5.24      = top_top_set_set_nat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7526_atMost__UNIV__triv,axiom,
% 9.25/5.24      ( ( set_or58775011639299419et_int @ top_top_set_int )
% 9.25/5.24      = top_top_set_set_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7527_binomial__n__n,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( binomial @ N @ N )
% 9.25/5.24        = one_one_nat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7528_prod_Oneutral__const,axiom,
% 9.25/5.24      ! [A2: set_nat] :
% 9.25/5.24        ( ( groups708209901874060359at_nat
% 9.25/5.24          @ ^ [Uu: nat] : one_one_nat
% 9.25/5.24          @ A2 )
% 9.25/5.24        = one_one_nat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7529_prod_Oneutral__const,axiom,
% 9.25/5.24      ! [A2: set_nat] :
% 9.25/5.24        ( ( groups705719431365010083at_int
% 9.25/5.24          @ ^ [Uu: nat] : one_one_int
% 9.25/5.24          @ A2 )
% 9.25/5.24        = one_one_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7530_prod_Oneutral__const,axiom,
% 9.25/5.24      ! [A2: set_int] :
% 9.25/5.24        ( ( groups1705073143266064639nt_int
% 9.25/5.24          @ ^ [Uu: int] : one_one_int
% 9.25/5.24          @ A2 )
% 9.25/5.24        = one_one_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7531_of__nat__prod,axiom,
% 9.25/5.24      ! [F2: int > nat,A2: set_int] :
% 9.25/5.24        ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F2 @ A2 ) )
% 9.25/5.24        = ( groups1705073143266064639nt_int
% 9.25/5.24          @ ^ [X3: int] : ( semiri1314217659103216013at_int @ ( F2 @ X3 ) )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7532_of__nat__prod,axiom,
% 9.25/5.24      ! [F2: nat > nat,A2: set_nat] :
% 9.25/5.24        ( ( semiri681578069525770553at_rat @ ( groups708209901874060359at_nat @ F2 @ A2 ) )
% 9.25/5.24        = ( groups73079841787564623at_rat
% 9.25/5.24          @ ^ [X3: nat] : ( semiri681578069525770553at_rat @ ( F2 @ X3 ) )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7533_of__nat__prod,axiom,
% 9.25/5.24      ! [F2: nat > nat,A2: set_nat] :
% 9.25/5.24        ( ( semiri1316708129612266289at_nat @ ( groups708209901874060359at_nat @ F2 @ A2 ) )
% 9.25/5.24        = ( groups708209901874060359at_nat
% 9.25/5.24          @ ^ [X3: nat] : ( semiri1316708129612266289at_nat @ ( F2 @ X3 ) )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7534_of__nat__prod,axiom,
% 9.25/5.24      ! [F2: nat > nat,A2: set_nat] :
% 9.25/5.24        ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F2 @ A2 ) )
% 9.25/5.24        = ( groups705719431365010083at_int
% 9.25/5.24          @ ^ [X3: nat] : ( semiri1314217659103216013at_int @ ( F2 @ X3 ) )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7535_of__int__prod,axiom,
% 9.25/5.24      ! [F2: nat > int,A2: set_nat] :
% 9.25/5.24        ( ( ring_1_of_int_rat @ ( groups705719431365010083at_int @ F2 @ A2 ) )
% 9.25/5.24        = ( groups73079841787564623at_rat
% 9.25/5.24          @ ^ [X3: nat] : ( ring_1_of_int_rat @ ( F2 @ X3 ) )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7536_of__int__prod,axiom,
% 9.25/5.24      ! [F2: nat > int,A2: set_nat] :
% 9.25/5.24        ( ( ring_1_of_int_int @ ( groups705719431365010083at_int @ F2 @ A2 ) )
% 9.25/5.24        = ( groups705719431365010083at_int
% 9.25/5.24          @ ^ [X3: nat] : ( ring_1_of_int_int @ ( F2 @ X3 ) )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7537_of__int__prod,axiom,
% 9.25/5.24      ! [F2: int > int,A2: set_int] :
% 9.25/5.24        ( ( ring_1_of_int_rat @ ( groups1705073143266064639nt_int @ F2 @ A2 ) )
% 9.25/5.24        = ( groups1072433553688619179nt_rat
% 9.25/5.24          @ ^ [X3: int] : ( ring_1_of_int_rat @ ( F2 @ X3 ) )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7538_of__int__prod,axiom,
% 9.25/5.24      ! [F2: int > int,A2: set_int] :
% 9.25/5.24        ( ( ring_1_of_int_int @ ( groups1705073143266064639nt_int @ F2 @ A2 ) )
% 9.25/5.24        = ( groups1705073143266064639nt_int
% 9.25/5.24          @ ^ [X3: int] : ( ring_1_of_int_int @ ( F2 @ X3 ) )
% 9.25/5.24          @ A2 ) ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7539_prod_Oempty,axiom,
% 9.25/5.24      ! [G2: $o > code_integer] :
% 9.25/5.24        ( ( groups7694694392188491536nteger @ G2 @ bot_bot_set_o )
% 9.25/5.24        = one_one_Code_integer ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7540_prod_Oempty,axiom,
% 9.25/5.24      ! [G2: $o > assn] :
% 9.25/5.24        ( ( groups5301882518646026715o_assn @ G2 @ bot_bot_set_o )
% 9.25/5.24        = one_one_assn ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7541_prod_Oempty,axiom,
% 9.25/5.24      ! [G2: $o > rat] :
% 9.25/5.24        ( ( groups2869687844427037835_o_rat @ G2 @ bot_bot_set_o )
% 9.25/5.24        = one_one_rat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7542_prod_Oempty,axiom,
% 9.25/5.24      ! [G2: $o > nat] :
% 9.25/5.24        ( ( groups3504817904513533571_o_nat @ G2 @ bot_bot_set_o )
% 9.25/5.24        = one_one_nat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7543_prod_Oempty,axiom,
% 9.25/5.24      ! [G2: $o > int] :
% 9.25/5.24        ( ( groups3502327434004483295_o_int @ G2 @ bot_bot_set_o )
% 9.25/5.24        = one_one_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7544_prod_Oempty,axiom,
% 9.25/5.24      ! [G2: nat > code_integer] :
% 9.25/5.24        ( ( groups3455450783089532116nteger @ G2 @ bot_bot_set_nat )
% 9.25/5.24        = one_one_Code_integer ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7545_prod_Oempty,axiom,
% 9.25/5.24      ! [G2: nat > assn] :
% 9.25/5.24        ( ( groups6906906614972039071t_assn @ G2 @ bot_bot_set_nat )
% 9.25/5.24        = one_one_assn ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7546_prod_Oempty,axiom,
% 9.25/5.24      ! [G2: nat > rat] :
% 9.25/5.24        ( ( groups73079841787564623at_rat @ G2 @ bot_bot_set_nat )
% 9.25/5.24        = one_one_rat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7547_prod_Oempty,axiom,
% 9.25/5.24      ! [G2: int > code_integer] :
% 9.25/5.24        ( ( groups3827104343326376752nteger @ G2 @ bot_bot_set_int )
% 9.25/5.24        = one_one_Code_integer ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7548_prod_Oempty,axiom,
% 9.25/5.24      ! [G2: int > assn] :
% 9.25/5.24        ( ( groups7882442080178216443t_assn @ G2 @ bot_bot_set_int )
% 9.25/5.24        = one_one_assn ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7549_fact__0,axiom,
% 9.25/5.24      ( ( semiri3624122377584611663nteger @ zero_zero_nat )
% 9.25/5.24      = one_one_Code_integer ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7550_fact__0,axiom,
% 9.25/5.24      ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 9.25/5.24      = one_one_rat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7551_fact__0,axiom,
% 9.25/5.24      ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 9.25/5.24      = one_one_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7552_fact__0,axiom,
% 9.25/5.24      ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 9.25/5.24      = one_one_nat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7553_fact__1,axiom,
% 9.25/5.24      ( ( semiri3624122377584611663nteger @ one_one_nat )
% 9.25/5.24      = one_one_Code_integer ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7554_fact__1,axiom,
% 9.25/5.24      ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 9.25/5.24      = one_one_rat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7555_fact__1,axiom,
% 9.25/5.24      ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 9.25/5.24      = one_one_int ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7556_fact__1,axiom,
% 9.25/5.24      ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 9.25/5.24      = one_one_nat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7557_binomial__n__0,axiom,
% 9.25/5.24      ! [N: nat] :
% 9.25/5.24        ( ( binomial @ N @ zero_zero_nat )
% 9.25/5.24        = one_one_nat ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7558_fact__Suc__0,axiom,
% 9.25/5.24      ( ( semiri3624122377584611663nteger @ ( suc @ zero_zero_nat ) )
% 9.25/5.24      = one_one_Code_integer ) ).
% 9.25/5.24  
% 9.25/5.24  thf(fact_7559_fact__Suc__0,axiom,
% 9.25/5.24      ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 9.25/5.25      = one_one_rat ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7560_fact__Suc__0,axiom,
% 9.25/5.25      ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 9.25/5.25      = one_one_int ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7561_fact__Suc__0,axiom,
% 9.25/5.25      ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 9.25/5.25      = one_one_nat ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7562_fact__Suc,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( semiri3624122377584611663nteger @ ( suc @ N ) )
% 9.25/5.25        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( suc @ N ) ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7563_fact__Suc,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( semiri1406184849735516958ct_int @ ( suc @ N ) )
% 9.25/5.25        = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7564_fact__Suc,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( semiri773545260158071498ct_rat @ ( suc @ N ) )
% 9.25/5.25        = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7565_fact__Suc,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( semiri1408675320244567234ct_nat @ ( suc @ N ) )
% 9.25/5.25        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7566_prod_OatMost__Suc,axiom,
% 9.25/5.25      ! [G2: nat > code_integer,N: nat] :
% 9.25/5.25        ( ( groups3455450783089532116nteger @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7567_prod_OatMost__Suc,axiom,
% 9.25/5.25      ! [G2: nat > assn,N: nat] :
% 9.25/5.25        ( ( groups6906906614972039071t_assn @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7568_prod_OatMost__Suc,axiom,
% 9.25/5.25      ! [G2: nat > rat,N: nat] :
% 9.25/5.25        ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7569_prod_OatMost__Suc,axiom,
% 9.25/5.25      ! [G2: nat > nat,N: nat] :
% 9.25/5.25        ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7570_prod_OatMost__Suc,axiom,
% 9.25/5.25      ! [G2: nat > int,N: nat] :
% 9.25/5.25        ( ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7571_prod_Ocl__ivl__Suc,axiom,
% 9.25/5.25      ! [N: nat,M: nat,G2: nat > code_integer] :
% 9.25/5.25        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 9.25/5.25         => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25            = one_one_Code_integer ) )
% 9.25/5.25        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 9.25/5.25         => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25            = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7572_prod_Ocl__ivl__Suc,axiom,
% 9.25/5.25      ! [N: nat,M: nat,G2: nat > assn] :
% 9.25/5.25        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 9.25/5.25         => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25            = one_one_assn ) )
% 9.25/5.25        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 9.25/5.25         => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25            = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7573_prod_Ocl__ivl__Suc,axiom,
% 9.25/5.25      ! [N: nat,M: nat,G2: nat > rat] :
% 9.25/5.25        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 9.25/5.25         => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25            = one_one_rat ) )
% 9.25/5.25        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 9.25/5.25         => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25            = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7574_prod_Ocl__ivl__Suc,axiom,
% 9.25/5.25      ! [N: nat,M: nat,G2: nat > nat] :
% 9.25/5.25        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 9.25/5.25         => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25            = one_one_nat ) )
% 9.25/5.25        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 9.25/5.25         => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25            = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7575_prod_Ocl__ivl__Suc,axiom,
% 9.25/5.25      ! [N: nat,M: nat,G2: nat > int] :
% 9.25/5.25        ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 9.25/5.25         => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25            = one_one_int ) )
% 9.25/5.25        & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 9.25/5.25         => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25            = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7576_prod_Oop__ivl__Suc,axiom,
% 9.25/5.25      ! [N: nat,M: nat,G2: nat > code_integer] :
% 9.25/5.25        ( ( ( ord_less_nat @ N @ M )
% 9.25/5.25         => ( ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25            = one_one_Code_integer ) )
% 9.25/5.25        & ( ~ ( ord_less_nat @ N @ M )
% 9.25/5.25         => ( ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25            = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G2 @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7577_prod_Oop__ivl__Suc,axiom,
% 9.25/5.25      ! [N: nat,M: nat,G2: nat > assn] :
% 9.25/5.25        ( ( ( ord_less_nat @ N @ M )
% 9.25/5.25         => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25            = one_one_assn ) )
% 9.25/5.25        & ( ~ ( ord_less_nat @ N @ M )
% 9.25/5.25         => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25            = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G2 @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7578_prod_Oop__ivl__Suc,axiom,
% 9.25/5.25      ! [N: nat,M: nat,G2: nat > rat] :
% 9.25/5.25        ( ( ( ord_less_nat @ N @ M )
% 9.25/5.25         => ( ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25            = one_one_rat ) )
% 9.25/5.25        & ( ~ ( ord_less_nat @ N @ M )
% 9.25/5.25         => ( ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25            = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G2 @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7579_prod_Oop__ivl__Suc,axiom,
% 9.25/5.25      ! [N: nat,M: nat,G2: nat > nat] :
% 9.25/5.25        ( ( ( ord_less_nat @ N @ M )
% 9.25/5.25         => ( ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25            = one_one_nat ) )
% 9.25/5.25        & ( ~ ( ord_less_nat @ N @ M )
% 9.25/5.25         => ( ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25            = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G2 @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7580_prod_Oop__ivl__Suc,axiom,
% 9.25/5.25      ! [N: nat,M: nat,G2: nat > int] :
% 9.25/5.25        ( ( ( ord_less_nat @ N @ M )
% 9.25/5.25         => ( ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25            = one_one_int ) )
% 9.25/5.25        & ( ~ ( ord_less_nat @ N @ M )
% 9.25/5.25         => ( ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25            = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G2 @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7581_prod_Oswap,axiom,
% 9.25/5.25      ! [G2: nat > nat > nat,B2: set_nat,A2: set_nat] :
% 9.25/5.25        ( ( groups708209901874060359at_nat
% 9.25/5.25          @ ^ [I3: nat] : ( groups708209901874060359at_nat @ ( G2 @ I3 ) @ B2 )
% 9.25/5.25          @ A2 )
% 9.25/5.25        = ( groups708209901874060359at_nat
% 9.25/5.25          @ ^ [J3: nat] :
% 9.25/5.25              ( groups708209901874060359at_nat
% 9.25/5.25              @ ^ [I3: nat] : ( G2 @ I3 @ J3 )
% 9.25/5.25              @ A2 )
% 9.25/5.25          @ B2 ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7582_prod_Oswap,axiom,
% 9.25/5.25      ! [G2: nat > nat > int,B2: set_nat,A2: set_nat] :
% 9.25/5.25        ( ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [I3: nat] : ( groups705719431365010083at_int @ ( G2 @ I3 ) @ B2 )
% 9.25/5.25          @ A2 )
% 9.25/5.25        = ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [J3: nat] :
% 9.25/5.25              ( groups705719431365010083at_int
% 9.25/5.25              @ ^ [I3: nat] : ( G2 @ I3 @ J3 )
% 9.25/5.25              @ A2 )
% 9.25/5.25          @ B2 ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7583_prod_Oswap,axiom,
% 9.25/5.25      ! [G2: nat > int > int,B2: set_int,A2: set_nat] :
% 9.25/5.25        ( ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [I3: nat] : ( groups1705073143266064639nt_int @ ( G2 @ I3 ) @ B2 )
% 9.25/5.25          @ A2 )
% 9.25/5.25        = ( groups1705073143266064639nt_int
% 9.25/5.25          @ ^ [J3: int] :
% 9.25/5.25              ( groups705719431365010083at_int
% 9.25/5.25              @ ^ [I3: nat] : ( G2 @ I3 @ J3 )
% 9.25/5.25              @ A2 )
% 9.25/5.25          @ B2 ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7584_prod_Oswap,axiom,
% 9.25/5.25      ! [G2: int > nat > int,B2: set_nat,A2: set_int] :
% 9.25/5.25        ( ( groups1705073143266064639nt_int
% 9.25/5.25          @ ^ [I3: int] : ( groups705719431365010083at_int @ ( G2 @ I3 ) @ B2 )
% 9.25/5.25          @ A2 )
% 9.25/5.25        = ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [J3: nat] :
% 9.25/5.25              ( groups1705073143266064639nt_int
% 9.25/5.25              @ ^ [I3: int] : ( G2 @ I3 @ J3 )
% 9.25/5.25              @ A2 )
% 9.25/5.25          @ B2 ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7585_prod_Oswap,axiom,
% 9.25/5.25      ! [G2: int > int > int,B2: set_int,A2: set_int] :
% 9.25/5.25        ( ( groups1705073143266064639nt_int
% 9.25/5.25          @ ^ [I3: int] : ( groups1705073143266064639nt_int @ ( G2 @ I3 ) @ B2 )
% 9.25/5.25          @ A2 )
% 9.25/5.25        = ( groups1705073143266064639nt_int
% 9.25/5.25          @ ^ [J3: int] :
% 9.25/5.25              ( groups1705073143266064639nt_int
% 9.25/5.25              @ ^ [I3: int] : ( G2 @ I3 @ J3 )
% 9.25/5.25              @ A2 )
% 9.25/5.25          @ B2 ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7586_prod_Oneutral,axiom,
% 9.25/5.25      ! [A2: set_nat,G2: nat > nat] :
% 9.25/5.25        ( ! [X2: nat] :
% 9.25/5.25            ( ( member_nat @ X2 @ A2 )
% 9.25/5.25           => ( ( G2 @ X2 )
% 9.25/5.25              = one_one_nat ) )
% 9.25/5.25       => ( ( groups708209901874060359at_nat @ G2 @ A2 )
% 9.25/5.25          = one_one_nat ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7587_prod_Oneutral,axiom,
% 9.25/5.25      ! [A2: set_nat,G2: nat > int] :
% 9.25/5.25        ( ! [X2: nat] :
% 9.25/5.25            ( ( member_nat @ X2 @ A2 )
% 9.25/5.25           => ( ( G2 @ X2 )
% 9.25/5.25              = one_one_int ) )
% 9.25/5.25       => ( ( groups705719431365010083at_int @ G2 @ A2 )
% 9.25/5.25          = one_one_int ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7588_prod_Oneutral,axiom,
% 9.25/5.25      ! [A2: set_int,G2: int > int] :
% 9.25/5.25        ( ! [X2: int] :
% 9.25/5.25            ( ( member_int @ X2 @ A2 )
% 9.25/5.25           => ( ( G2 @ X2 )
% 9.25/5.25              = one_one_int ) )
% 9.25/5.25       => ( ( groups1705073143266064639nt_int @ G2 @ A2 )
% 9.25/5.25          = one_one_int ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7589_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.25/5.25      ! [G2: nat > code_integer,A2: set_nat] :
% 9.25/5.25        ( ( ( groups3455450783089532116nteger @ G2 @ A2 )
% 9.25/5.25         != one_one_Code_integer )
% 9.25/5.25       => ~ ! [A6: nat] :
% 9.25/5.25              ( ( member_nat @ A6 @ A2 )
% 9.25/5.25             => ( ( G2 @ A6 )
% 9.25/5.25                = one_one_Code_integer ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7590_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.25/5.25      ! [G2: int > code_integer,A2: set_int] :
% 9.25/5.25        ( ( ( groups3827104343326376752nteger @ G2 @ A2 )
% 9.25/5.25         != one_one_Code_integer )
% 9.25/5.25       => ~ ! [A6: int] :
% 9.25/5.25              ( ( member_int @ A6 @ A2 )
% 9.25/5.25             => ( ( G2 @ A6 )
% 9.25/5.25                = one_one_Code_integer ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7591_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.25/5.25      ! [G2: nat > assn,A2: set_nat] :
% 9.25/5.25        ( ( ( groups6906906614972039071t_assn @ G2 @ A2 )
% 9.25/5.25         != one_one_assn )
% 9.25/5.25       => ~ ! [A6: nat] :
% 9.25/5.25              ( ( member_nat @ A6 @ A2 )
% 9.25/5.25             => ( ( G2 @ A6 )
% 9.25/5.25                = one_one_assn ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7592_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.25/5.25      ! [G2: int > assn,A2: set_int] :
% 9.25/5.25        ( ( ( groups7882442080178216443t_assn @ G2 @ A2 )
% 9.25/5.25         != one_one_assn )
% 9.25/5.25       => ~ ! [A6: int] :
% 9.25/5.25              ( ( member_int @ A6 @ A2 )
% 9.25/5.25             => ( ( G2 @ A6 )
% 9.25/5.25                = one_one_assn ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7593_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.25/5.25      ! [G2: nat > rat,A2: set_nat] :
% 9.25/5.25        ( ( ( groups73079841787564623at_rat @ G2 @ A2 )
% 9.25/5.25         != one_one_rat )
% 9.25/5.25       => ~ ! [A6: nat] :
% 9.25/5.25              ( ( member_nat @ A6 @ A2 )
% 9.25/5.25             => ( ( G2 @ A6 )
% 9.25/5.25                = one_one_rat ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7594_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.25/5.25      ! [G2: int > rat,A2: set_int] :
% 9.25/5.25        ( ( ( groups1072433553688619179nt_rat @ G2 @ A2 )
% 9.25/5.25         != one_one_rat )
% 9.25/5.25       => ~ ! [A6: int] :
% 9.25/5.25              ( ( member_int @ A6 @ A2 )
% 9.25/5.25             => ( ( G2 @ A6 )
% 9.25/5.25                = one_one_rat ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7595_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.25/5.25      ! [G2: int > nat,A2: set_int] :
% 9.25/5.25        ( ( ( groups1707563613775114915nt_nat @ G2 @ A2 )
% 9.25/5.25         != one_one_nat )
% 9.25/5.25       => ~ ! [A6: int] :
% 9.25/5.25              ( ( member_int @ A6 @ A2 )
% 9.25/5.25             => ( ( G2 @ A6 )
% 9.25/5.25                = one_one_nat ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7596_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.25/5.25      ! [G2: nat > nat,A2: set_nat] :
% 9.25/5.25        ( ( ( groups708209901874060359at_nat @ G2 @ A2 )
% 9.25/5.25         != one_one_nat )
% 9.25/5.25       => ~ ! [A6: nat] :
% 9.25/5.25              ( ( member_nat @ A6 @ A2 )
% 9.25/5.25             => ( ( G2 @ A6 )
% 9.25/5.25                = one_one_nat ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7597_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.25/5.25      ! [G2: nat > int,A2: set_nat] :
% 9.25/5.25        ( ( ( groups705719431365010083at_int @ G2 @ A2 )
% 9.25/5.25         != one_one_int )
% 9.25/5.25       => ~ ! [A6: nat] :
% 9.25/5.25              ( ( member_nat @ A6 @ A2 )
% 9.25/5.25             => ( ( G2 @ A6 )
% 9.25/5.25                = one_one_int ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7598_prod_Onot__neutral__contains__not__neutral,axiom,
% 9.25/5.25      ! [G2: int > int,A2: set_int] :
% 9.25/5.25        ( ( ( groups1705073143266064639nt_int @ G2 @ A2 )
% 9.25/5.25         != one_one_int )
% 9.25/5.25       => ~ ! [A6: int] :
% 9.25/5.25              ( ( member_int @ A6 @ A2 )
% 9.25/5.25             => ( ( G2 @ A6 )
% 9.25/5.25                = one_one_int ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7599_choose__one,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( binomial @ N @ one_one_nat )
% 9.25/5.25        = N ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7600_prod_Odistrib,axiom,
% 9.25/5.25      ! [G2: nat > nat,H3: nat > nat,A2: set_nat] :
% 9.25/5.25        ( ( groups708209901874060359at_nat
% 9.25/5.25          @ ^ [X3: nat] : ( times_times_nat @ ( G2 @ X3 ) @ ( H3 @ X3 ) )
% 9.25/5.25          @ A2 )
% 9.25/5.25        = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ A2 ) @ ( groups708209901874060359at_nat @ H3 @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7601_prod_Odistrib,axiom,
% 9.25/5.25      ! [G2: nat > int,H3: nat > int,A2: set_nat] :
% 9.25/5.25        ( ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [X3: nat] : ( times_times_int @ ( G2 @ X3 ) @ ( H3 @ X3 ) )
% 9.25/5.25          @ A2 )
% 9.25/5.25        = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ A2 ) @ ( groups705719431365010083at_int @ H3 @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7602_prod_Odistrib,axiom,
% 9.25/5.25      ! [G2: int > int,H3: int > int,A2: set_int] :
% 9.25/5.25        ( ( groups1705073143266064639nt_int
% 9.25/5.25          @ ^ [X3: int] : ( times_times_int @ ( G2 @ X3 ) @ ( H3 @ X3 ) )
% 9.25/5.25          @ A2 )
% 9.25/5.25        = ( times_times_int @ ( groups1705073143266064639nt_int @ G2 @ A2 ) @ ( groups1705073143266064639nt_int @ H3 @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7603_prod__power__distrib,axiom,
% 9.25/5.25      ! [F2: nat > nat,A2: set_nat,N: nat] :
% 9.25/5.25        ( ( power_power_nat @ ( groups708209901874060359at_nat @ F2 @ A2 ) @ N )
% 9.25/5.25        = ( groups708209901874060359at_nat
% 9.25/5.25          @ ^ [X3: nat] : ( power_power_nat @ ( F2 @ X3 ) @ N )
% 9.25/5.25          @ A2 ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7604_prod__power__distrib,axiom,
% 9.25/5.25      ! [F2: nat > int,A2: set_nat,N: nat] :
% 9.25/5.25        ( ( power_power_int @ ( groups705719431365010083at_int @ F2 @ A2 ) @ N )
% 9.25/5.25        = ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [X3: nat] : ( power_power_int @ ( F2 @ X3 ) @ N )
% 9.25/5.25          @ A2 ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7605_prod__power__distrib,axiom,
% 9.25/5.25      ! [F2: int > int,A2: set_int,N: nat] :
% 9.25/5.25        ( ( power_power_int @ ( groups1705073143266064639nt_int @ F2 @ A2 ) @ N )
% 9.25/5.25        = ( groups1705073143266064639nt_int
% 9.25/5.25          @ ^ [X3: int] : ( power_power_int @ ( F2 @ X3 ) @ N )
% 9.25/5.25          @ A2 ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7606_mod__prod__eq,axiom,
% 9.25/5.25      ! [F2: nat > nat,A: nat,A2: set_nat] :
% 9.25/5.25        ( ( modulo_modulo_nat
% 9.25/5.25          @ ( groups708209901874060359at_nat
% 9.25/5.25            @ ^ [I3: nat] : ( modulo_modulo_nat @ ( F2 @ I3 ) @ A )
% 9.25/5.25            @ A2 )
% 9.25/5.25          @ A )
% 9.25/5.25        = ( modulo_modulo_nat @ ( groups708209901874060359at_nat @ F2 @ A2 ) @ A ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7607_mod__prod__eq,axiom,
% 9.25/5.25      ! [F2: nat > int,A: int,A2: set_nat] :
% 9.25/5.25        ( ( modulo_modulo_int
% 9.25/5.25          @ ( groups705719431365010083at_int
% 9.25/5.25            @ ^ [I3: nat] : ( modulo_modulo_int @ ( F2 @ I3 ) @ A )
% 9.25/5.25            @ A2 )
% 9.25/5.25          @ A )
% 9.25/5.25        = ( modulo_modulo_int @ ( groups705719431365010083at_int @ F2 @ A2 ) @ A ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7608_mod__prod__eq,axiom,
% 9.25/5.25      ! [F2: int > int,A: int,A2: set_int] :
% 9.25/5.25        ( ( modulo_modulo_int
% 9.25/5.25          @ ( groups1705073143266064639nt_int
% 9.25/5.25            @ ^ [I3: int] : ( modulo_modulo_int @ ( F2 @ I3 ) @ A )
% 9.25/5.25            @ A2 )
% 9.25/5.25          @ A )
% 9.25/5.25        = ( modulo_modulo_int @ ( groups1705073143266064639nt_int @ F2 @ A2 ) @ A ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7609_fact__prod,axiom,
% 9.25/5.25      ( semiri1406184849735516958ct_int
% 9.25/5.25      = ( ^ [N2: nat] :
% 9.25/5.25            ( semiri1314217659103216013at_int
% 9.25/5.25            @ ( groups708209901874060359at_nat
% 9.25/5.25              @ ^ [X3: nat] : X3
% 9.25/5.25              @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7610_fact__prod,axiom,
% 9.25/5.25      ( semiri773545260158071498ct_rat
% 9.25/5.25      = ( ^ [N2: nat] :
% 9.25/5.25            ( semiri681578069525770553at_rat
% 9.25/5.25            @ ( groups708209901874060359at_nat
% 9.25/5.25              @ ^ [X3: nat] : X3
% 9.25/5.25              @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7611_fact__prod,axiom,
% 9.25/5.25      ( semiri1408675320244567234ct_nat
% 9.25/5.25      = ( ^ [N2: nat] :
% 9.25/5.25            ( semiri1316708129612266289at_nat
% 9.25/5.25            @ ( groups708209901874060359at_nat
% 9.25/5.25              @ ^ [X3: nat] : X3
% 9.25/5.25              @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7612_prod__ge__1,axiom,
% 9.25/5.25      ! [A2: set_nat,F2: nat > code_integer] :
% 9.25/5.25        ( ! [X2: nat] :
% 9.25/5.25            ( ( member_nat @ X2 @ A2 )
% 9.25/5.25           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ X2 ) ) )
% 9.25/5.25       => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F2 @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7613_prod__ge__1,axiom,
% 9.25/5.25      ! [A2: set_int,F2: int > code_integer] :
% 9.25/5.25        ( ! [X2: int] :
% 9.25/5.25            ( ( member_int @ X2 @ A2 )
% 9.25/5.25           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ X2 ) ) )
% 9.25/5.25       => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F2 @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7614_prod__ge__1,axiom,
% 9.25/5.25      ! [A2: set_nat,F2: nat > rat] :
% 9.25/5.25        ( ! [X2: nat] :
% 9.25/5.25            ( ( member_nat @ X2 @ A2 )
% 9.25/5.25           => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ X2 ) ) )
% 9.25/5.25       => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F2 @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7615_prod__ge__1,axiom,
% 9.25/5.25      ! [A2: set_int,F2: int > rat] :
% 9.25/5.25        ( ! [X2: int] :
% 9.25/5.25            ( ( member_int @ X2 @ A2 )
% 9.25/5.25           => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ X2 ) ) )
% 9.25/5.25       => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F2 @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7616_prod__ge__1,axiom,
% 9.25/5.25      ! [A2: set_int,F2: int > nat] :
% 9.25/5.25        ( ! [X2: int] :
% 9.25/5.25            ( ( member_int @ X2 @ A2 )
% 9.25/5.25           => ( ord_less_eq_nat @ one_one_nat @ ( F2 @ X2 ) ) )
% 9.25/5.25       => ( ord_less_eq_nat @ one_one_nat @ ( groups1707563613775114915nt_nat @ F2 @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7617_prod__ge__1,axiom,
% 9.25/5.25      ! [A2: set_nat,F2: nat > nat] :
% 9.25/5.25        ( ! [X2: nat] :
% 9.25/5.25            ( ( member_nat @ X2 @ A2 )
% 9.25/5.25           => ( ord_less_eq_nat @ one_one_nat @ ( F2 @ X2 ) ) )
% 9.25/5.25       => ( ord_less_eq_nat @ one_one_nat @ ( groups708209901874060359at_nat @ F2 @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7618_prod__ge__1,axiom,
% 9.25/5.25      ! [A2: set_nat,F2: nat > int] :
% 9.25/5.25        ( ! [X2: nat] :
% 9.25/5.25            ( ( member_nat @ X2 @ A2 )
% 9.25/5.25           => ( ord_less_eq_int @ one_one_int @ ( F2 @ X2 ) ) )
% 9.25/5.25       => ( ord_less_eq_int @ one_one_int @ ( groups705719431365010083at_int @ F2 @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7619_prod__ge__1,axiom,
% 9.25/5.25      ! [A2: set_int,F2: int > int] :
% 9.25/5.25        ( ! [X2: int] :
% 9.25/5.25            ( ( member_int @ X2 @ A2 )
% 9.25/5.25           => ( ord_less_eq_int @ one_one_int @ ( F2 @ X2 ) ) )
% 9.25/5.25       => ( ord_less_eq_int @ one_one_int @ ( groups1705073143266064639nt_int @ F2 @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7620_prod__ge__1,axiom,
% 9.25/5.25      ! [A2: set_set_nat,F2: set_nat > code_integer] :
% 9.25/5.25        ( ! [X2: set_nat] :
% 9.25/5.25            ( ( member_set_nat @ X2 @ A2 )
% 9.25/5.25           => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ X2 ) ) )
% 9.25/5.25       => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups2761809935038513290nteger @ F2 @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7621_prod__ge__1,axiom,
% 9.25/5.25      ! [A2: set_set_nat,F2: set_nat > rat] :
% 9.25/5.25        ( ! [X2: set_nat] :
% 9.25/5.25            ( ( member_set_nat @ X2 @ A2 )
% 9.25/5.25           => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ X2 ) ) )
% 9.25/5.25       => ( ord_less_eq_rat @ one_one_rat @ ( groups3613417700093529605at_rat @ F2 @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7622_fact__eq__fact__times,axiom,
% 9.25/5.25      ! [N: nat,M: nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ N @ M )
% 9.25/5.25       => ( ( semiri1408675320244567234ct_nat @ M )
% 9.25/5.25          = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 9.25/5.25            @ ( groups708209901874060359at_nat
% 9.25/5.25              @ ^ [X3: nat] : X3
% 9.25/5.25              @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7623_fact__prod__rev,axiom,
% 9.25/5.25      ( semiri1406184849735516958ct_int
% 9.25/5.25      = ( ^ [N2: nat] : ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ ( minus_minus_nat @ N2 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7624_fact__prod__rev,axiom,
% 9.25/5.25      ( semiri773545260158071498ct_rat
% 9.25/5.25      = ( ^ [N2: nat] : ( semiri681578069525770553at_rat @ ( groups708209901874060359at_nat @ ( minus_minus_nat @ N2 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7625_fact__prod__rev,axiom,
% 9.25/5.25      ( semiri1408675320244567234ct_nat
% 9.25/5.25      = ( ^ [N2: nat] : ( semiri1316708129612266289at_nat @ ( groups708209901874060359at_nat @ ( minus_minus_nat @ N2 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7626_fact__ge__1,axiom,
% 9.25/5.25      ! [N: nat] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( semiri3624122377584611663nteger @ N ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7627_fact__ge__1,axiom,
% 9.25/5.25      ! [N: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7628_fact__ge__1,axiom,
% 9.25/5.25      ! [N: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7629_fact__ge__1,axiom,
% 9.25/5.25      ! [N: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7630_pochhammer__fact,axiom,
% 9.25/5.25      ( semiri3624122377584611663nteger
% 9.25/5.25      = ( comm_s8582702949713902594nteger @ one_one_Code_integer ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7631_pochhammer__fact,axiom,
% 9.25/5.25      ( semiri773545260158071498ct_rat
% 9.25/5.25      = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7632_pochhammer__fact,axiom,
% 9.25/5.25      ( semiri1406184849735516958ct_int
% 9.25/5.25      = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7633_pochhammer__fact,axiom,
% 9.25/5.25      ( semiri1408675320244567234ct_nat
% 9.25/5.25      = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7634_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 9.25/5.25      ! [G2: nat > nat,M: nat,N: nat] :
% 9.25/5.25        ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 9.25/5.25        = ( groups708209901874060359at_nat
% 9.25/5.25          @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.25          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7635_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 9.25/5.25      ! [G2: nat > int,M: nat,N: nat] :
% 9.25/5.25        ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 9.25/5.25        = ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.25          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7636_prod_Oshift__bounds__Suc__ivl,axiom,
% 9.25/5.25      ! [G2: nat > nat,M: nat,N: nat] :
% 9.25/5.25        ( ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 9.25/5.25        = ( groups708209901874060359at_nat
% 9.25/5.25          @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.25          @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7637_prod_Oshift__bounds__Suc__ivl,axiom,
% 9.25/5.25      ! [G2: nat > int,M: nat,N: nat] :
% 9.25/5.25        ( ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 9.25/5.25        = ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.25          @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7638_power__sum,axiom,
% 9.25/5.25      ! [C: nat,F2: nat > nat,A2: set_nat] :
% 9.25/5.25        ( ( power_power_nat @ C @ ( groups3542108847815614940at_nat @ F2 @ A2 ) )
% 9.25/5.25        = ( groups708209901874060359at_nat
% 9.25/5.25          @ ^ [A3: nat] : ( power_power_nat @ C @ ( F2 @ A3 ) )
% 9.25/5.25          @ A2 ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7639_power__sum,axiom,
% 9.25/5.25      ! [C: int,F2: nat > nat,A2: set_nat] :
% 9.25/5.25        ( ( power_power_int @ C @ ( groups3542108847815614940at_nat @ F2 @ A2 ) )
% 9.25/5.25        = ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [A3: nat] : ( power_power_int @ C @ ( F2 @ A3 ) )
% 9.25/5.25          @ A2 ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7640_power__sum,axiom,
% 9.25/5.25      ! [C: int,F2: int > nat,A2: set_int] :
% 9.25/5.25        ( ( power_power_int @ C @ ( groups4541462559716669496nt_nat @ F2 @ A2 ) )
% 9.25/5.25        = ( groups1705073143266064639nt_int
% 9.25/5.25          @ ^ [A3: int] : ( power_power_int @ C @ ( F2 @ A3 ) )
% 9.25/5.25          @ A2 ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7641_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 9.25/5.25      ! [G2: nat > nat,M: nat,K: nat,N: nat] :
% 9.25/5.25        ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 9.25/5.25        = ( groups708209901874060359at_nat
% 9.25/5.25          @ ^ [I3: nat] : ( G2 @ ( plus_plus_nat @ I3 @ K ) )
% 9.25/5.25          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7642_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 9.25/5.25      ! [G2: nat > int,M: nat,K: nat,N: nat] :
% 9.25/5.25        ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 9.25/5.25        = ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [I3: nat] : ( G2 @ ( plus_plus_nat @ I3 @ K ) )
% 9.25/5.25          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7643_prod_Oshift__bounds__nat__ivl,axiom,
% 9.25/5.25      ! [G2: nat > nat,M: nat,K: nat,N: nat] :
% 9.25/5.25        ( ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 9.25/5.25        = ( groups708209901874060359at_nat
% 9.25/5.25          @ ^ [I3: nat] : ( G2 @ ( plus_plus_nat @ I3 @ K ) )
% 9.25/5.25          @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7644_prod_Oshift__bounds__nat__ivl,axiom,
% 9.25/5.25      ! [G2: nat > int,M: nat,K: nat,N: nat] :
% 9.25/5.25        ( ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 9.25/5.25        = ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [I3: nat] : ( G2 @ ( plus_plus_nat @ I3 @ K ) )
% 9.25/5.25          @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7645_fact__binomial,axiom,
% 9.25/5.25      ! [K: nat,N: nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ K @ N )
% 9.25/5.25       => ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) ) )
% 9.25/5.25          = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7646_binomial__fact,axiom,
% 9.25/5.25      ! [K: nat,N: nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ K @ N )
% 9.25/5.25       => ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) )
% 9.25/5.25          = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7647_fact__div__fact,axiom,
% 9.25/5.25      ! [N: nat,M: nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ N @ M )
% 9.25/5.25       => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 9.25/5.25          = ( groups708209901874060359at_nat
% 9.25/5.25            @ ^ [X3: nat] : X3
% 9.25/5.25            @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7648_prod__le__1,axiom,
% 9.25/5.25      ! [A2: set_nat,F2: nat > code_integer] :
% 9.25/5.25        ( ! [X2: nat] :
% 9.25/5.25            ( ( member_nat @ X2 @ A2 )
% 9.25/5.25           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X2 ) )
% 9.25/5.25              & ( ord_le3102999989581377725nteger @ ( F2 @ X2 ) @ one_one_Code_integer ) ) )
% 9.25/5.25       => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F2 @ A2 ) @ one_one_Code_integer ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7649_prod__le__1,axiom,
% 9.25/5.25      ! [A2: set_int,F2: int > code_integer] :
% 9.25/5.25        ( ! [X2: int] :
% 9.25/5.25            ( ( member_int @ X2 @ A2 )
% 9.25/5.25           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X2 ) )
% 9.25/5.25              & ( ord_le3102999989581377725nteger @ ( F2 @ X2 ) @ one_one_Code_integer ) ) )
% 9.25/5.25       => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F2 @ A2 ) @ one_one_Code_integer ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7650_prod__le__1,axiom,
% 9.25/5.25      ! [A2: set_nat,F2: nat > rat] :
% 9.25/5.25        ( ! [X2: nat] :
% 9.25/5.25            ( ( member_nat @ X2 @ A2 )
% 9.25/5.25           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X2 ) )
% 9.25/5.25              & ( ord_less_eq_rat @ ( F2 @ X2 ) @ one_one_rat ) ) )
% 9.25/5.25       => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F2 @ A2 ) @ one_one_rat ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7651_prod__le__1,axiom,
% 9.25/5.25      ! [A2: set_int,F2: int > rat] :
% 9.25/5.25        ( ! [X2: int] :
% 9.25/5.25            ( ( member_int @ X2 @ A2 )
% 9.25/5.25           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X2 ) )
% 9.25/5.25              & ( ord_less_eq_rat @ ( F2 @ X2 ) @ one_one_rat ) ) )
% 9.25/5.25       => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F2 @ A2 ) @ one_one_rat ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7652_prod__le__1,axiom,
% 9.25/5.25      ! [A2: set_int,F2: int > nat] :
% 9.25/5.25        ( ! [X2: int] :
% 9.25/5.25            ( ( member_int @ X2 @ A2 )
% 9.25/5.25           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X2 ) )
% 9.25/5.25              & ( ord_less_eq_nat @ ( F2 @ X2 ) @ one_one_nat ) ) )
% 9.25/5.25       => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F2 @ A2 ) @ one_one_nat ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7653_prod__le__1,axiom,
% 9.25/5.25      ! [A2: set_nat,F2: nat > nat] :
% 9.25/5.25        ( ! [X2: nat] :
% 9.25/5.25            ( ( member_nat @ X2 @ A2 )
% 9.25/5.25           => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X2 ) )
% 9.25/5.25              & ( ord_less_eq_nat @ ( F2 @ X2 ) @ one_one_nat ) ) )
% 9.25/5.25       => ( ord_less_eq_nat @ ( groups708209901874060359at_nat @ F2 @ A2 ) @ one_one_nat ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7654_prod__le__1,axiom,
% 9.25/5.25      ! [A2: set_nat,F2: nat > int] :
% 9.25/5.25        ( ! [X2: nat] :
% 9.25/5.25            ( ( member_nat @ X2 @ A2 )
% 9.25/5.25           => ( ( ord_less_eq_int @ zero_zero_int @ ( F2 @ X2 ) )
% 9.25/5.25              & ( ord_less_eq_int @ ( F2 @ X2 ) @ one_one_int ) ) )
% 9.25/5.25       => ( ord_less_eq_int @ ( groups705719431365010083at_int @ F2 @ A2 ) @ one_one_int ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7655_prod__le__1,axiom,
% 9.25/5.25      ! [A2: set_int,F2: int > int] :
% 9.25/5.25        ( ! [X2: int] :
% 9.25/5.25            ( ( member_int @ X2 @ A2 )
% 9.25/5.25           => ( ( ord_less_eq_int @ zero_zero_int @ ( F2 @ X2 ) )
% 9.25/5.25              & ( ord_less_eq_int @ ( F2 @ X2 ) @ one_one_int ) ) )
% 9.25/5.25       => ( ord_less_eq_int @ ( groups1705073143266064639nt_int @ F2 @ A2 ) @ one_one_int ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7656_prod__le__1,axiom,
% 9.25/5.25      ! [A2: set_set_nat,F2: set_nat > code_integer] :
% 9.25/5.25        ( ! [X2: set_nat] :
% 9.25/5.25            ( ( member_set_nat @ X2 @ A2 )
% 9.25/5.25           => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X2 ) )
% 9.25/5.25              & ( ord_le3102999989581377725nteger @ ( F2 @ X2 ) @ one_one_Code_integer ) ) )
% 9.25/5.25       => ( ord_le3102999989581377725nteger @ ( groups2761809935038513290nteger @ F2 @ A2 ) @ one_one_Code_integer ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7657_prod__le__1,axiom,
% 9.25/5.25      ! [A2: set_set_nat,F2: set_nat > rat] :
% 9.25/5.25        ( ! [X2: set_nat] :
% 9.25/5.25            ( ( member_set_nat @ X2 @ A2 )
% 9.25/5.25           => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X2 ) )
% 9.25/5.25              & ( ord_less_eq_rat @ ( F2 @ X2 ) @ one_one_rat ) ) )
% 9.25/5.25       => ( ord_less_eq_rat @ ( groups3613417700093529605at_rat @ F2 @ A2 ) @ one_one_rat ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7658_fact__split,axiom,
% 9.25/5.25      ! [K: nat,N: nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ K @ N )
% 9.25/5.25       => ( ( semiri3624122377584611663nteger @ N )
% 9.25/5.25          = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ N @ K ) @ N ) ) ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7659_fact__split,axiom,
% 9.25/5.25      ! [K: nat,N: nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ K @ N )
% 9.25/5.25       => ( ( semiri1406184849735516958ct_int @ N )
% 9.25/5.25          = ( times_times_int @ ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ N @ K ) @ N ) ) ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7660_fact__split,axiom,
% 9.25/5.25      ! [K: nat,N: nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ K @ N )
% 9.25/5.25       => ( ( semiri773545260158071498ct_rat @ N )
% 9.25/5.25          = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ N @ K ) @ N ) ) ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7661_fact__split,axiom,
% 9.25/5.25      ! [K: nat,N: nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ K @ N )
% 9.25/5.25       => ( ( semiri1408675320244567234ct_nat @ N )
% 9.25/5.25          = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ N @ K ) @ N ) ) ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7662_prod_OatLeastLessThan__concat,axiom,
% 9.25/5.25      ! [M: nat,N: nat,P4: nat,G2: nat > code_integer] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25       => ( ( ord_less_eq_nat @ N @ P4 )
% 9.25/5.25         => ( ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ N @ P4 ) ) )
% 9.25/5.25            = ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ M @ P4 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7663_prod_OatLeastLessThan__concat,axiom,
% 9.25/5.25      ! [M: nat,N: nat,P4: nat,G2: nat > assn] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25       => ( ( ord_less_eq_nat @ N @ P4 )
% 9.25/5.25         => ( ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ N @ P4 ) ) )
% 9.25/5.25            = ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ M @ P4 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7664_prod_OatLeastLessThan__concat,axiom,
% 9.25/5.25      ! [M: nat,N: nat,P4: nat,G2: nat > rat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25       => ( ( ord_less_eq_nat @ N @ P4 )
% 9.25/5.25         => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ N @ P4 ) ) )
% 9.25/5.25            = ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ M @ P4 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7665_prod_OatLeastLessThan__concat,axiom,
% 9.25/5.25      ! [M: nat,N: nat,P4: nat,G2: nat > nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25       => ( ( ord_less_eq_nat @ N @ P4 )
% 9.25/5.25         => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ N @ P4 ) ) )
% 9.25/5.25            = ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ M @ P4 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7666_prod_OatLeastLessThan__concat,axiom,
% 9.25/5.25      ! [M: nat,N: nat,P4: nat,G2: nat > int] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25       => ( ( ord_less_eq_nat @ N @ P4 )
% 9.25/5.25         => ( ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ N @ P4 ) ) )
% 9.25/5.25            = ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ M @ P4 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7667_binomial__altdef__of__nat,axiom,
% 9.25/5.25      ! [K: nat,N: nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ K @ N )
% 9.25/5.25       => ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K ) )
% 9.25/5.25          = ( groups73079841787564623at_rat
% 9.25/5.25            @ ^ [I3: nat] : ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I3 ) ) @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ K @ I3 ) ) )
% 9.25/5.25            @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7668_binomial__absorb__comp,axiom,
% 9.25/5.25      ! [N: nat,K: nat] :
% 9.25/5.25        ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 9.25/5.25        = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7669_dvd__fact,axiom,
% 9.25/5.25      ! [M: nat,N: nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 9.25/5.25       => ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25         => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7670_gbinomial__mult__fact_H,axiom,
% 9.25/5.25      ! [A: rat,K: nat] :
% 9.25/5.25        ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( semiri773545260158071498ct_rat @ K ) )
% 9.25/5.25        = ( groups73079841787564623at_rat
% 9.25/5.25          @ ^ [I3: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I3 ) )
% 9.25/5.25          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7671_gbinomial__mult__fact,axiom,
% 9.25/5.25      ! [K: nat,A: rat] :
% 9.25/5.25        ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( gbinomial_rat @ A @ K ) )
% 9.25/5.25        = ( groups73079841787564623at_rat
% 9.25/5.25          @ ^ [I3: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I3 ) )
% 9.25/5.25          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7672_gbinomial__prod__rev,axiom,
% 9.25/5.25      ( gbinom8545251970709558553nteger
% 9.25/5.25      = ( ^ [A3: code_integer,K4: nat] :
% 9.25/5.25            ( divide6298287555418463151nteger
% 9.25/5.25            @ ( groups3455450783089532116nteger
% 9.25/5.25              @ ^ [I3: nat] : ( minus_8373710615458151222nteger @ A3 @ ( semiri4939895301339042750nteger @ I3 ) )
% 9.25/5.25              @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K4 ) )
% 9.25/5.25            @ ( semiri3624122377584611663nteger @ K4 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7673_gbinomial__prod__rev,axiom,
% 9.25/5.25      ( gbinom7368847122466276068atural
% 9.25/5.25      = ( ^ [A3: code_natural,K4: nat] :
% 9.25/5.25            ( divide5121882707175180666atural
% 9.25/5.25            @ ( groups2279045934846249631atural
% 9.25/5.25              @ ^ [I3: nat] : ( minus_7197305767214868737atural @ A3 @ ( semiri3763490453095760265atural @ I3 ) )
% 9.25/5.25              @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K4 ) )
% 9.25/5.25            @ ( semiri2447717529341329178atural @ K4 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7674_gbinomial__prod__rev,axiom,
% 9.25/5.25      ( gbinomial_rat
% 9.25/5.25      = ( ^ [A3: rat,K4: nat] :
% 9.25/5.25            ( divide_divide_rat
% 9.25/5.25            @ ( groups73079841787564623at_rat
% 9.25/5.25              @ ^ [I3: nat] : ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ I3 ) )
% 9.25/5.25              @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K4 ) )
% 9.25/5.25            @ ( semiri773545260158071498ct_rat @ K4 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7675_gbinomial__prod__rev,axiom,
% 9.25/5.25      ( gbinomial_nat
% 9.25/5.25      = ( ^ [A3: nat,K4: nat] :
% 9.25/5.25            ( divide_divide_nat
% 9.25/5.25            @ ( groups708209901874060359at_nat
% 9.25/5.25              @ ^ [I3: nat] : ( minus_minus_nat @ A3 @ ( semiri1316708129612266289at_nat @ I3 ) )
% 9.25/5.25              @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K4 ) )
% 9.25/5.25            @ ( semiri1408675320244567234ct_nat @ K4 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7676_gbinomial__prod__rev,axiom,
% 9.25/5.25      ( gbinomial_int
% 9.25/5.25      = ( ^ [A3: int,K4: nat] :
% 9.25/5.25            ( divide_divide_int
% 9.25/5.25            @ ( groups705719431365010083at_int
% 9.25/5.25              @ ^ [I3: nat] : ( minus_minus_int @ A3 @ ( semiri1314217659103216013at_int @ I3 ) )
% 9.25/5.25              @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K4 ) )
% 9.25/5.25            @ ( semiri1406184849735516958ct_int @ K4 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7677_fact__fact__dvd__fact,axiom,
% 9.25/5.25      ! [K: nat,N: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7678_fact__fact__dvd__fact,axiom,
% 9.25/5.25      ! [K: nat,N: nat] : ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ N ) ) @ ( semiri773545260158071498ct_rat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7679_fact__fact__dvd__fact,axiom,
% 9.25/5.25      ! [K: nat,N: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7680_fact__fact__dvd__fact,axiom,
% 9.25/5.25      ! [K: nat,N: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7681_prod_OatLeastAtMost__rev,axiom,
% 9.25/5.25      ! [G2: nat > nat,N: nat,M: nat] :
% 9.25/5.25        ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 9.25/5.25        = ( groups708209901874060359at_nat
% 9.25/5.25          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 9.25/5.25          @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7682_prod_OatLeastAtMost__rev,axiom,
% 9.25/5.25      ! [G2: nat > int,N: nat,M: nat] :
% 9.25/5.25        ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 9.25/5.25        = ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 9.25/5.25          @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7683_gbinomial__Suc,axiom,
% 9.25/5.25      ! [A: code_integer,K: nat] :
% 9.25/5.25        ( ( gbinom8545251970709558553nteger @ A @ ( suc @ K ) )
% 9.25/5.25        = ( divide6298287555418463151nteger
% 9.25/5.25          @ ( groups3455450783089532116nteger
% 9.25/5.25            @ ^ [I3: nat] : ( minus_8373710615458151222nteger @ A @ ( semiri4939895301339042750nteger @ I3 ) )
% 9.25/5.25            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 9.25/5.25          @ ( semiri3624122377584611663nteger @ ( suc @ K ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7684_gbinomial__Suc,axiom,
% 9.25/5.25      ! [A: code_natural,K: nat] :
% 9.25/5.25        ( ( gbinom7368847122466276068atural @ A @ ( suc @ K ) )
% 9.25/5.25        = ( divide5121882707175180666atural
% 9.25/5.25          @ ( groups2279045934846249631atural
% 9.25/5.25            @ ^ [I3: nat] : ( minus_7197305767214868737atural @ A @ ( semiri3763490453095760265atural @ I3 ) )
% 9.25/5.25            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 9.25/5.25          @ ( semiri2447717529341329178atural @ ( suc @ K ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7685_gbinomial__Suc,axiom,
% 9.25/5.25      ! [A: rat,K: nat] :
% 9.25/5.25        ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 9.25/5.25        = ( divide_divide_rat
% 9.25/5.25          @ ( groups73079841787564623at_rat
% 9.25/5.25            @ ^ [I3: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I3 ) )
% 9.25/5.25            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 9.25/5.25          @ ( semiri773545260158071498ct_rat @ ( suc @ K ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7686_gbinomial__Suc,axiom,
% 9.25/5.25      ! [A: nat,K: nat] :
% 9.25/5.25        ( ( gbinomial_nat @ A @ ( suc @ K ) )
% 9.25/5.25        = ( divide_divide_nat
% 9.25/5.25          @ ( groups708209901874060359at_nat
% 9.25/5.25            @ ^ [I3: nat] : ( minus_minus_nat @ A @ ( semiri1316708129612266289at_nat @ I3 ) )
% 9.25/5.25            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 9.25/5.25          @ ( semiri1408675320244567234ct_nat @ ( suc @ K ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7687_gbinomial__Suc,axiom,
% 9.25/5.25      ! [A: int,K: nat] :
% 9.25/5.25        ( ( gbinomial_int @ A @ ( suc @ K ) )
% 9.25/5.25        = ( divide_divide_int
% 9.25/5.25          @ ( groups705719431365010083at_int
% 9.25/5.25            @ ^ [I3: nat] : ( minus_minus_int @ A @ ( semiri1314217659103216013at_int @ I3 ) )
% 9.25/5.25            @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 9.25/5.25          @ ( semiri1406184849735516958ct_int @ ( suc @ K ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7688_sum__choose__upper,axiom,
% 9.25/5.25      ! [M: nat,N: nat] :
% 9.25/5.25        ( ( groups3542108847815614940at_nat
% 9.25/5.25          @ ^ [K4: nat] : ( binomial @ K4 @ M )
% 9.25/5.25          @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.25        = ( binomial @ ( suc @ N ) @ ( suc @ M ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7689_prod_OatLeast0__atMost__Suc,axiom,
% 9.25/5.25      ! [G2: nat > code_integer,N: nat] :
% 9.25/5.25        ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7690_prod_OatLeast0__atMost__Suc,axiom,
% 9.25/5.25      ! [G2: nat > assn,N: nat] :
% 9.25/5.25        ( ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7691_prod_OatLeast0__atMost__Suc,axiom,
% 9.25/5.25      ! [G2: nat > rat,N: nat] :
% 9.25/5.25        ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7692_prod_OatLeast0__atMost__Suc,axiom,
% 9.25/5.25      ! [G2: nat > nat,N: nat] :
% 9.25/5.25        ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7693_prod_OatLeast0__atMost__Suc,axiom,
% 9.25/5.25      ! [G2: nat > int,N: nat] :
% 9.25/5.25        ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7694_prod_OatLeast0__lessThan__Suc,axiom,
% 9.25/5.25      ! [G2: nat > code_integer,N: nat] :
% 9.25/5.25        ( ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7695_prod_OatLeast0__lessThan__Suc,axiom,
% 9.25/5.25      ! [G2: nat > assn,N: nat] :
% 9.25/5.25        ( ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7696_prod_OatLeast0__lessThan__Suc,axiom,
% 9.25/5.25      ! [G2: nat > rat,N: nat] :
% 9.25/5.25        ( ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7697_prod_OatLeast0__lessThan__Suc,axiom,
% 9.25/5.25      ! [G2: nat > nat,N: nat] :
% 9.25/5.25        ( ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7698_prod_OatLeast0__lessThan__Suc,axiom,
% 9.25/5.25      ! [G2: nat > int,N: nat] :
% 9.25/5.25        ( ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7699_prod_OatLeast__Suc__lessThan,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > code_integer] :
% 9.25/5.25        ( ( ord_less_nat @ M @ N )
% 9.25/5.25       => ( ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 9.25/5.25          = ( times_3573771949741848930nteger @ ( G2 @ M ) @ ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7700_prod_OatLeast__Suc__lessThan,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > assn] :
% 9.25/5.25        ( ( ord_less_nat @ M @ N )
% 9.25/5.25       => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 9.25/5.25          = ( times_times_assn @ ( G2 @ M ) @ ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7701_prod_OatLeast__Suc__lessThan,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > rat] :
% 9.25/5.25        ( ( ord_less_nat @ M @ N )
% 9.25/5.25       => ( ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 9.25/5.25          = ( times_times_rat @ ( G2 @ M ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7702_prod_OatLeast__Suc__lessThan,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > nat] :
% 9.25/5.25        ( ( ord_less_nat @ M @ N )
% 9.25/5.25       => ( ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 9.25/5.25          = ( times_times_nat @ ( G2 @ M ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7703_prod_OatLeast__Suc__lessThan,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > int] :
% 9.25/5.25        ( ( ord_less_nat @ M @ N )
% 9.25/5.25       => ( ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 9.25/5.25          = ( times_times_int @ ( G2 @ M ) @ ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7704_prod_Onat__ivl__Suc_H,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > code_integer] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.25/5.25       => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25          = ( times_3573771949741848930nteger @ ( G2 @ ( suc @ N ) ) @ ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7705_prod_Onat__ivl__Suc_H,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > assn] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.25/5.25       => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25          = ( times_times_assn @ ( G2 @ ( suc @ N ) ) @ ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7706_prod_Onat__ivl__Suc_H,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > rat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.25/5.25       => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25          = ( times_times_rat @ ( G2 @ ( suc @ N ) ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7707_prod_Onat__ivl__Suc_H,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.25/5.25       => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25          = ( times_times_nat @ ( G2 @ ( suc @ N ) ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7708_prod_Onat__ivl__Suc_H,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > int] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 9.25/5.25       => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 9.25/5.25          = ( times_times_int @ ( G2 @ ( suc @ N ) ) @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7709_prod_OatLeast__Suc__atMost,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > code_integer] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25       => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.25          = ( times_3573771949741848930nteger @ ( G2 @ M ) @ ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7710_prod_OatLeast__Suc__atMost,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > assn] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25       => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.25          = ( times_times_assn @ ( G2 @ M ) @ ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7711_prod_OatLeast__Suc__atMost,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > rat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25       => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.25          = ( times_times_rat @ ( G2 @ M ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7712_prod_OatLeast__Suc__atMost,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25       => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.25          = ( times_times_nat @ ( G2 @ M ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7713_prod_OatLeast__Suc__atMost,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > int] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25       => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.25          = ( times_times_int @ ( G2 @ M ) @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7714_prod_OatLeastLessThan__Suc,axiom,
% 9.25/5.25      ! [A: nat,B: nat,G2: nat > code_integer] :
% 9.25/5.25        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.25       => ( ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 9.25/5.25          = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G2 @ B ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7715_prod_OatLeastLessThan__Suc,axiom,
% 9.25/5.25      ! [A: nat,B: nat,G2: nat > assn] :
% 9.25/5.25        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.25       => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 9.25/5.25          = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G2 @ B ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7716_prod_OatLeastLessThan__Suc,axiom,
% 9.25/5.25      ! [A: nat,B: nat,G2: nat > rat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.25       => ( ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 9.25/5.25          = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G2 @ B ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7717_prod_OatLeastLessThan__Suc,axiom,
% 9.25/5.25      ! [A: nat,B: nat,G2: nat > nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.25       => ( ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 9.25/5.25          = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G2 @ B ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7718_prod_OatLeastLessThan__Suc,axiom,
% 9.25/5.25      ! [A: nat,B: nat,G2: nat > int] :
% 9.25/5.25        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.25       => ( ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 9.25/5.25          = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G2 @ B ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7719_prod_Olast__plus,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > code_integer] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25       => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.25          = ( times_3573771949741848930nteger @ ( G2 @ N ) @ ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7720_prod_Olast__plus,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > assn] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25       => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.25          = ( times_times_assn @ ( G2 @ N ) @ ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7721_prod_Olast__plus,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > rat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25       => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.25          = ( times_times_rat @ ( G2 @ N ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7722_prod_Olast__plus,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25       => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.25          = ( times_times_nat @ ( G2 @ N ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7723_prod_Olast__plus,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > int] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25       => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.25          = ( times_times_int @ ( G2 @ N ) @ ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7724_binomial__absorption,axiom,
% 9.25/5.25      ! [K: nat,N: nat] :
% 9.25/5.25        ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 9.25/5.25        = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7725_prod_OSuc__reindex__ivl,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > code_integer] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25       => ( ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 9.25/5.25          = ( times_3573771949741848930nteger @ ( G2 @ M )
% 9.25/5.25            @ ( groups3455450783089532116nteger
% 9.25/5.25              @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.25              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7726_prod_OSuc__reindex__ivl,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > assn] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25       => ( ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 9.25/5.25          = ( times_times_assn @ ( G2 @ M )
% 9.25/5.25            @ ( groups6906906614972039071t_assn
% 9.25/5.25              @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.25              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7727_prod_OSuc__reindex__ivl,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > rat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25       => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 9.25/5.25          = ( times_times_rat @ ( G2 @ M )
% 9.25/5.25            @ ( groups73079841787564623at_rat
% 9.25/5.25              @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.25              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7728_prod_OSuc__reindex__ivl,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25       => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 9.25/5.25          = ( times_times_nat @ ( G2 @ M )
% 9.25/5.25            @ ( groups708209901874060359at_nat
% 9.25/5.25              @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.25              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7729_prod_OSuc__reindex__ivl,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > int] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25       => ( ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 9.25/5.25          = ( times_times_int @ ( G2 @ M )
% 9.25/5.25            @ ( groups705719431365010083at_int
% 9.25/5.25              @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.25              @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7730_prod_OatMost__Suc__shift,axiom,
% 9.25/5.25      ! [G2: nat > code_integer,N: nat] :
% 9.25/5.25        ( ( groups3455450783089532116nteger @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_3573771949741848930nteger @ ( G2 @ zero_zero_nat )
% 9.25/5.25          @ ( groups3455450783089532116nteger
% 9.25/5.25            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.25            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7731_prod_OatMost__Suc__shift,axiom,
% 9.25/5.25      ! [G2: nat > assn,N: nat] :
% 9.25/5.25        ( ( groups6906906614972039071t_assn @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_times_assn @ ( G2 @ zero_zero_nat )
% 9.25/5.25          @ ( groups6906906614972039071t_assn
% 9.25/5.25            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.25            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7732_prod_OatMost__Suc__shift,axiom,
% 9.25/5.25      ! [G2: nat > rat,N: nat] :
% 9.25/5.25        ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_times_rat @ ( G2 @ zero_zero_nat )
% 9.25/5.25          @ ( groups73079841787564623at_rat
% 9.25/5.25            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.25            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7733_prod_OatMost__Suc__shift,axiom,
% 9.25/5.25      ! [G2: nat > nat,N: nat] :
% 9.25/5.25        ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_times_nat @ ( G2 @ zero_zero_nat )
% 9.25/5.25          @ ( groups708209901874060359at_nat
% 9.25/5.25            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.25            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7734_prod_OatMost__Suc__shift,axiom,
% 9.25/5.25      ! [G2: nat > int,N: nat] :
% 9.25/5.25        ( ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_times_int @ ( G2 @ zero_zero_nat )
% 9.25/5.25          @ ( groups705719431365010083at_int
% 9.25/5.25            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.25            @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7735_prod_OatLeastLessThan__rev,axiom,
% 9.25/5.25      ! [G2: nat > nat,N: nat,M: nat] :
% 9.25/5.25        ( ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 9.25/5.25        = ( groups708209901874060359at_nat
% 9.25/5.25          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ ( suc @ I3 ) ) )
% 9.25/5.25          @ ( set_or4665077453230672383an_nat @ N @ M ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7736_prod_OatLeastLessThan__rev,axiom,
% 9.25/5.25      ! [G2: nat > int,N: nat,M: nat] :
% 9.25/5.25        ( ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 9.25/5.25        = ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ ( suc @ I3 ) ) )
% 9.25/5.25          @ ( set_or4665077453230672383an_nat @ N @ M ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7737_choose__dvd,axiom,
% 9.25/5.25      ! [K: nat,N: nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ K @ N )
% 9.25/5.25       => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7738_choose__dvd,axiom,
% 9.25/5.25      ! [K: nat,N: nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ K @ N )
% 9.25/5.25       => ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7739_choose__dvd,axiom,
% 9.25/5.25      ! [K: nat,N: nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ K @ N )
% 9.25/5.25       => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7740_choose__dvd,axiom,
% 9.25/5.25      ! [K: nat,N: nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ K @ N )
% 9.25/5.25       => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7741_prod_Onested__swap,axiom,
% 9.25/5.25      ! [A: nat > nat > nat,N: nat] :
% 9.25/5.25        ( ( groups708209901874060359at_nat
% 9.25/5.25          @ ^ [I3: nat] : ( groups708209901874060359at_nat @ ( A @ I3 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I3 ) )
% 9.25/5.25          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.25/5.25        = ( groups708209901874060359at_nat
% 9.25/5.25          @ ^ [J3: nat] :
% 9.25/5.25              ( groups708209901874060359at_nat
% 9.25/5.25              @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 9.25/5.25              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 9.25/5.25          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7742_prod_Onested__swap,axiom,
% 9.25/5.25      ! [A: nat > nat > int,N: nat] :
% 9.25/5.25        ( ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [I3: nat] : ( groups705719431365010083at_int @ ( A @ I3 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I3 ) )
% 9.25/5.25          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 9.25/5.25        = ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [J3: nat] :
% 9.25/5.25              ( groups705719431365010083at_int
% 9.25/5.25              @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 9.25/5.25              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 9.25/5.25          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7743_fact__numeral,axiom,
% 9.25/5.25      ! [K: num] :
% 9.25/5.25        ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 9.25/5.25        = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7744_fact__numeral,axiom,
% 9.25/5.25      ! [K: num] :
% 9.25/5.25        ( ( semiri3624122377584611663nteger @ ( numeral_numeral_nat @ K ) )
% 9.25/5.25        = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ K ) @ ( semiri3624122377584611663nteger @ ( pred_numeral @ K ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7745_fact__numeral,axiom,
% 9.25/5.25      ! [K: num] :
% 9.25/5.25        ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ K ) )
% 9.25/5.25        = ( times_times_rat @ ( numeral_numeral_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( pred_numeral @ K ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7746_fact__numeral,axiom,
% 9.25/5.25      ! [K: num] :
% 9.25/5.25        ( ( semiri2447717529341329178atural @ ( numeral_numeral_nat @ K ) )
% 9.25/5.25        = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ K ) @ ( semiri2447717529341329178atural @ ( pred_numeral @ K ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7747_fact__numeral,axiom,
% 9.25/5.25      ! [K: num] :
% 9.25/5.25        ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 9.25/5.25        = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7748_prod__atLeastAtMost__code,axiom,
% 9.25/5.25      ! [F2: nat > code_integer,A: nat,B: nat] :
% 9.25/5.25        ( ( groups3455450783089532116nteger @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.25/5.25        = ( set_fo1084959871951514735nteger
% 9.25/5.25          @ ^ [A3: nat] : ( times_3573771949741848930nteger @ ( F2 @ A3 ) )
% 9.25/5.25          @ A
% 9.25/5.25          @ B
% 9.25/5.25          @ one_one_Code_integer ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7749_prod__atLeastAtMost__code,axiom,
% 9.25/5.25      ! [F2: nat > assn,A: nat,B: nat] :
% 9.25/5.25        ( ( groups6906906614972039071t_assn @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.25/5.25        = ( set_fo1959793692361082170t_assn
% 9.25/5.25          @ ^ [A3: nat] : ( times_times_assn @ ( F2 @ A3 ) )
% 9.25/5.25          @ A
% 9.25/5.25          @ B
% 9.25/5.25          @ one_one_assn ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7750_prod__atLeastAtMost__code,axiom,
% 9.25/5.25      ! [F2: nat > rat,A: nat,B: nat] :
% 9.25/5.25        ( ( groups73079841787564623at_rat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.25/5.25        = ( set_fo1949268297981939178at_rat
% 9.25/5.25          @ ^ [A3: nat] : ( times_times_rat @ ( F2 @ A3 ) )
% 9.25/5.25          @ A
% 9.25/5.25          @ B
% 9.25/5.25          @ one_one_rat ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7751_prod__atLeastAtMost__code,axiom,
% 9.25/5.25      ! [F2: nat > nat,A: nat,B: nat] :
% 9.25/5.25        ( ( groups708209901874060359at_nat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.25/5.25        = ( set_fo2584398358068434914at_nat
% 9.25/5.25          @ ^ [A3: nat] : ( times_times_nat @ ( F2 @ A3 ) )
% 9.25/5.25          @ A
% 9.25/5.25          @ B
% 9.25/5.25          @ one_one_nat ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7752_prod__atLeastAtMost__code,axiom,
% 9.25/5.25      ! [F2: nat > int,A: nat,B: nat] :
% 9.25/5.25        ( ( groups705719431365010083at_int @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 9.25/5.25        = ( set_fo2581907887559384638at_int
% 9.25/5.25          @ ^ [A3: nat] : ( times_times_int @ ( F2 @ A3 ) )
% 9.25/5.25          @ A
% 9.25/5.25          @ B
% 9.25/5.25          @ one_one_int ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7753_sum__choose__lower,axiom,
% 9.25/5.25      ! [R3: nat,N: nat] :
% 9.25/5.25        ( ( groups3542108847815614940at_nat
% 9.25/5.25          @ ^ [K4: nat] : ( binomial @ ( plus_plus_nat @ R3 @ K4 ) @ K4 )
% 9.25/5.25          @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.25        = ( binomial @ ( suc @ ( plus_plus_nat @ R3 @ N ) ) @ N ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7754_choose__rising__sum_I2_J,axiom,
% 9.25/5.25      ! [N: nat,M: nat] :
% 9.25/5.25        ( ( groups3542108847815614940at_nat
% 9.25/5.25          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 9.25/5.25          @ ( set_ord_atMost_nat @ M ) )
% 9.25/5.25        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ M ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7755_choose__rising__sum_I1_J,axiom,
% 9.25/5.25      ! [N: nat,M: nat] :
% 9.25/5.25        ( ( groups3542108847815614940at_nat
% 9.25/5.25          @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 9.25/5.25          @ ( set_ord_atMost_nat @ M ) )
% 9.25/5.25        = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7756_binomial__code,axiom,
% 9.25/5.25      ( binomial
% 9.25/5.25      = ( ^ [N2: nat,K4: nat] : ( if_nat @ ( ord_less_nat @ N2 @ K4 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K4 ) ) @ ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K4 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N2 @ K4 ) @ one_one_nat ) @ N2 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K4 ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7757_prod_Ohead__if,axiom,
% 9.25/5.25      ! [N: nat,M: nat,G2: nat > code_integer] :
% 9.25/5.25        ( ( ( ord_less_nat @ N @ M )
% 9.25/5.25         => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.25            = one_one_Code_integer ) )
% 9.25/5.25        & ( ~ ( ord_less_nat @ N @ M )
% 9.25/5.25         => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.25            = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G2 @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7758_prod_Ohead__if,axiom,
% 9.25/5.25      ! [N: nat,M: nat,G2: nat > assn] :
% 9.25/5.25        ( ( ( ord_less_nat @ N @ M )
% 9.25/5.25         => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.25            = one_one_assn ) )
% 9.25/5.25        & ( ~ ( ord_less_nat @ N @ M )
% 9.25/5.25         => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.25            = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G2 @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7759_prod_Ohead__if,axiom,
% 9.25/5.25      ! [N: nat,M: nat,G2: nat > rat] :
% 9.25/5.25        ( ( ( ord_less_nat @ N @ M )
% 9.25/5.25         => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.25            = one_one_rat ) )
% 9.25/5.25        & ( ~ ( ord_less_nat @ N @ M )
% 9.25/5.25         => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.25            = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G2 @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7760_prod_Ohead__if,axiom,
% 9.25/5.25      ! [N: nat,M: nat,G2: nat > nat] :
% 9.25/5.25        ( ( ( ord_less_nat @ N @ M )
% 9.25/5.25         => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.25            = one_one_nat ) )
% 9.25/5.25        & ( ~ ( ord_less_nat @ N @ M )
% 9.25/5.25         => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.25            = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G2 @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7761_prod_Ohead__if,axiom,
% 9.25/5.25      ! [N: nat,M: nat,G2: nat > int] :
% 9.25/5.25        ( ( ( ord_less_nat @ N @ M )
% 9.25/5.25         => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.25            = one_one_int ) )
% 9.25/5.25        & ( ~ ( ord_less_nat @ N @ M )
% 9.25/5.25         => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 9.25/5.25            = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ M @ N ) ) @ ( G2 @ N ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7762_prod_Oub__add__nat,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > code_integer,P4: nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 9.25/5.25       => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 9.25/5.25          = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7763_prod_Oub__add__nat,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > assn,P4: nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 9.25/5.25       => ( ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 9.25/5.25          = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7764_prod_Oub__add__nat,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > rat,P4: nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 9.25/5.25       => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 9.25/5.25          = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7765_prod_Oub__add__nat,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > nat,P4: nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 9.25/5.25       => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 9.25/5.25          = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7766_prod_Oub__add__nat,axiom,
% 9.25/5.25      ! [M: nat,N: nat,G2: nat > int,P4: nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 9.25/5.25       => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P4 ) ) )
% 9.25/5.25          = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P4 ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7767_choose__reduce__nat,axiom,
% 9.25/5.25      ! [N: nat,K: nat] :
% 9.25/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.25       => ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.25/5.25         => ( ( binomial @ N @ K )
% 9.25/5.25            = ( 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 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7768_times__binomial__minus1__eq,axiom,
% 9.25/5.25      ! [K: nat,N: nat] :
% 9.25/5.25        ( ( ord_less_nat @ zero_zero_nat @ K )
% 9.25/5.25       => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 9.25/5.25          = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7769_prod_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 9.25/5.25      ! [G2: nat > nat,N: nat,M: nat] :
% 9.25/5.25        ( ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 9.25/5.25        = ( groups708209901874060359at_nat
% 9.25/5.25          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 9.25/5.25          @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7770_prod_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 9.25/5.25      ! [G2: nat > int,N: nat,M: nat] :
% 9.25/5.25        ( ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ N @ M ) )
% 9.25/5.25        = ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I3 ) )
% 9.25/5.25          @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7771_pochhammer__prod,axiom,
% 9.25/5.25      ( comm_s4028243227959126397er_rat
% 9.25/5.25      = ( ^ [A3: rat,N2: nat] :
% 9.25/5.25            ( groups73079841787564623at_rat
% 9.25/5.25            @ ^ [I3: nat] : ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ I3 ) )
% 9.25/5.25            @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7772_pochhammer__prod,axiom,
% 9.25/5.25      ( comm_s4663373288045622133er_nat
% 9.25/5.25      = ( ^ [A3: nat,N2: nat] :
% 9.25/5.25            ( groups708209901874060359at_nat
% 9.25/5.25            @ ^ [I3: nat] : ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ I3 ) )
% 9.25/5.25            @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7773_pochhammer__prod,axiom,
% 9.25/5.25      ( comm_s4660882817536571857er_int
% 9.25/5.25      = ( ^ [A3: int,N2: nat] :
% 9.25/5.25            ( groups705719431365010083at_int
% 9.25/5.25            @ ^ [I3: nat] : ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ I3 ) )
% 9.25/5.25            @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7774_sum__choose__diagonal,axiom,
% 9.25/5.25      ! [M: nat,N: nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.25       => ( ( groups3542108847815614940at_nat
% 9.25/5.25            @ ^ [K4: nat] : ( binomial @ ( minus_minus_nat @ N @ K4 ) @ ( minus_minus_nat @ M @ K4 ) )
% 9.25/5.25            @ ( set_ord_atMost_nat @ M ) )
% 9.25/5.25          = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7775_vandermonde,axiom,
% 9.25/5.25      ! [M: nat,N: nat,R3: nat] :
% 9.25/5.25        ( ( groups3542108847815614940at_nat
% 9.25/5.25          @ ^ [K4: nat] : ( times_times_nat @ ( binomial @ M @ K4 ) @ ( binomial @ N @ ( minus_minus_nat @ R3 @ K4 ) ) )
% 9.25/5.25          @ ( set_ord_atMost_nat @ R3 ) )
% 9.25/5.25        = ( binomial @ ( plus_plus_nat @ M @ N ) @ R3 ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7776_binomial__addition__formula,axiom,
% 9.25/5.25      ! [N: nat,K: nat] :
% 9.25/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.25       => ( ( binomial @ N @ ( suc @ K ) )
% 9.25/5.25          = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7777_pochhammer__Suc__prod,axiom,
% 9.25/5.25      ! [A: rat,N: nat] :
% 9.25/5.25        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 9.25/5.25        = ( groups73079841787564623at_rat
% 9.25/5.25          @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I3 ) )
% 9.25/5.25          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7778_pochhammer__Suc__prod,axiom,
% 9.25/5.25      ! [A: nat,N: nat] :
% 9.25/5.25        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 9.25/5.25        = ( groups708209901874060359at_nat
% 9.25/5.25          @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I3 ) )
% 9.25/5.25          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7779_pochhammer__Suc__prod,axiom,
% 9.25/5.25      ! [A: int,N: nat] :
% 9.25/5.25        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 9.25/5.25        = ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [I3: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I3 ) )
% 9.25/5.25          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7780_pochhammer__prod__rev,axiom,
% 9.25/5.25      ( comm_s4028243227959126397er_rat
% 9.25/5.25      = ( ^ [A3: rat,N2: nat] :
% 9.25/5.25            ( groups73079841787564623at_rat
% 9.25/5.25            @ ^ [I3: nat] : ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 9.25/5.25            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7781_pochhammer__prod__rev,axiom,
% 9.25/5.25      ( comm_s4663373288045622133er_nat
% 9.25/5.25      = ( ^ [A3: nat,N2: nat] :
% 9.25/5.25            ( groups708209901874060359at_nat
% 9.25/5.25            @ ^ [I3: nat] : ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 9.25/5.25            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7782_pochhammer__prod__rev,axiom,
% 9.25/5.25      ( comm_s4660882817536571857er_int
% 9.25/5.25      = ( ^ [A3: int,N2: nat] :
% 9.25/5.25            ( groups705719431365010083at_int
% 9.25/5.25            @ ^ [I3: nat] : ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ I3 ) ) )
% 9.25/5.25            @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7783_fact__num__eq__if,axiom,
% 9.25/5.25      ( semiri3624122377584611663nteger
% 9.25/5.25      = ( ^ [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 ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7784_fact__num__eq__if,axiom,
% 9.25/5.25      ( semiri1406184849735516958ct_int
% 9.25/5.25      = ( ^ [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 ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7785_fact__num__eq__if,axiom,
% 9.25/5.25      ( semiri773545260158071498ct_rat
% 9.25/5.25      = ( ^ [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 ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7786_fact__num__eq__if,axiom,
% 9.25/5.25      ( semiri1408675320244567234ct_nat
% 9.25/5.25      = ( ^ [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 ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7787_fact__reduce,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.25       => ( ( semiri3624122377584611663nteger @ N )
% 9.25/5.25          = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7788_fact__reduce,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.25       => ( ( semiri1406184849735516958ct_int @ N )
% 9.25/5.25          = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7789_fact__reduce,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.25       => ( ( semiri773545260158071498ct_rat @ N )
% 9.25/5.25          = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7790_fact__reduce,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.25       => ( ( semiri1408675320244567234ct_nat @ N )
% 9.25/5.25          = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7791_fact__code,axiom,
% 9.25/5.25      ( semiri1406184849735516958ct_int
% 9.25/5.25      = ( ^ [N2: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7792_fact__code,axiom,
% 9.25/5.25      ( semiri773545260158071498ct_rat
% 9.25/5.25      = ( ^ [N2: nat] : ( semiri681578069525770553at_rat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7793_fact__code,axiom,
% 9.25/5.25      ( semiri1408675320244567234ct_nat
% 9.25/5.25      = ( ^ [N2: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 @ one_one_nat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7794_pochhammer__same,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ N )
% 9.25/5.25        = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7795_pochhammer__same,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ N )
% 9.25/5.25        = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7796_pochhammer__same,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ N )
% 9.25/5.25        = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7797_choose__row__sum,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.25        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7798_binomial,axiom,
% 9.25/5.25      ! [A: nat,B: nat,N: nat] :
% 9.25/5.25        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 9.25/5.25        = ( groups3542108847815614940at_nat
% 9.25/5.25          @ ^ [K4: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K4 ) ) @ ( power_power_nat @ A @ K4 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K4 ) ) )
% 9.25/5.25          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7799_choose__two,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.25        = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7800_prod_Oin__pairs,axiom,
% 9.25/5.25      ! [G2: nat > code_integer,M: nat,N: nat] :
% 9.25/5.25        ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.25/5.25        = ( groups3455450783089532116nteger
% 9.25/5.25          @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.25/5.25          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7801_prod_Oin__pairs,axiom,
% 9.25/5.25      ! [G2: nat > assn,M: nat,N: nat] :
% 9.25/5.25        ( ( groups6906906614972039071t_assn @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.25/5.25        = ( groups6906906614972039071t_assn
% 9.25/5.25          @ ^ [I3: nat] : ( times_times_assn @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.25/5.25          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7802_prod_Oin__pairs,axiom,
% 9.25/5.25      ! [G2: nat > rat,M: nat,N: nat] :
% 9.25/5.25        ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.25/5.25        = ( groups73079841787564623at_rat
% 9.25/5.25          @ ^ [I3: nat] : ( times_times_rat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.25/5.25          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7803_prod_Oin__pairs,axiom,
% 9.25/5.25      ! [G2: nat > nat,M: nat,N: nat] :
% 9.25/5.25        ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.25/5.25        = ( groups708209901874060359at_nat
% 9.25/5.25          @ ^ [I3: nat] : ( times_times_nat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.25/5.25          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7804_prod_Oin__pairs,axiom,
% 9.25/5.25      ! [G2: nat > int,M: nat,N: nat] :
% 9.25/5.25        ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.25/5.25        = ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [I3: nat] : ( times_times_int @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.25/5.25          @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7805_prod_Oin__pairs__0,axiom,
% 9.25/5.25      ! [G2: nat > code_integer,N: nat] :
% 9.25/5.25        ( ( groups3455450783089532116nteger @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.25/5.25        = ( groups3455450783089532116nteger
% 9.25/5.25          @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.25/5.25          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7806_prod_Oin__pairs__0,axiom,
% 9.25/5.25      ! [G2: nat > assn,N: nat] :
% 9.25/5.25        ( ( groups6906906614972039071t_assn @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.25/5.25        = ( groups6906906614972039071t_assn
% 9.25/5.25          @ ^ [I3: nat] : ( times_times_assn @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.25/5.25          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7807_prod_Oin__pairs__0,axiom,
% 9.25/5.25      ! [G2: nat > rat,N: nat] :
% 9.25/5.25        ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.25/5.25        = ( groups73079841787564623at_rat
% 9.25/5.25          @ ^ [I3: nat] : ( times_times_rat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.25/5.25          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7808_prod_Oin__pairs__0,axiom,
% 9.25/5.25      ! [G2: nat > nat,N: nat] :
% 9.25/5.25        ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.25/5.25        = ( groups708209901874060359at_nat
% 9.25/5.25          @ ^ [I3: nat] : ( times_times_nat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.25/5.25          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7809_prod_Oin__pairs__0,axiom,
% 9.25/5.25      ! [G2: nat > int,N: nat] :
% 9.25/5.25        ( ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 9.25/5.25        = ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [I3: nat] : ( times_times_int @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) ) ) )
% 9.25/5.25          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7810_gbinomial__altdef__of__nat,axiom,
% 9.25/5.25      ( gbinomial_rat
% 9.25/5.25      = ( ^ [A3: rat,K4: nat] :
% 9.25/5.25            ( groups73079841787564623at_rat
% 9.25/5.25            @ ^ [I3: nat] : ( divide_divide_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ I3 ) ) @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ K4 @ I3 ) ) )
% 9.25/5.25            @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K4 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7811_pochhammer__Suc__prod__rev,axiom,
% 9.25/5.25      ! [A: rat,N: nat] :
% 9.25/5.25        ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 9.25/5.25        = ( groups73079841787564623at_rat
% 9.25/5.25          @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I3 ) ) )
% 9.25/5.25          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7812_pochhammer__Suc__prod__rev,axiom,
% 9.25/5.25      ! [A: nat,N: nat] :
% 9.25/5.25        ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 9.25/5.25        = ( groups708209901874060359at_nat
% 9.25/5.25          @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I3 ) ) )
% 9.25/5.25          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7813_pochhammer__Suc__prod__rev,axiom,
% 9.25/5.25      ! [A: int,N: nat] :
% 9.25/5.25        ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 9.25/5.25        = ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [I3: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I3 ) ) )
% 9.25/5.25          @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7814_binomial__ring,axiom,
% 9.25/5.25      ! [A: code_integer,B: code_integer,N: nat] :
% 9.25/5.25        ( ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ N )
% 9.25/5.25        = ( groups7501900531339628137nteger
% 9.25/5.25          @ ^ [K4: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( binomial @ N @ K4 ) ) @ ( power_8256067586552552935nteger @ A @ K4 ) ) @ ( power_8256067586552552935nteger @ B @ ( minus_minus_nat @ N @ K4 ) ) )
% 9.25/5.25          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7815_binomial__ring,axiom,
% 9.25/5.25      ! [A: int,B: int,N: nat] :
% 9.25/5.25        ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N )
% 9.25/5.25        = ( groups3539618377306564664at_int
% 9.25/5.25          @ ^ [K4: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K4 ) ) @ ( power_power_int @ A @ K4 ) ) @ ( power_power_int @ B @ ( minus_minus_nat @ N @ K4 ) ) )
% 9.25/5.25          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7816_binomial__ring,axiom,
% 9.25/5.25      ! [A: rat,B: rat,N: nat] :
% 9.25/5.25        ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 9.25/5.25        = ( groups2906978787729119204at_rat
% 9.25/5.25          @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K4 ) ) @ ( power_power_rat @ A @ K4 ) ) @ ( power_power_rat @ B @ ( minus_minus_nat @ N @ K4 ) ) )
% 9.25/5.25          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7817_binomial__ring,axiom,
% 9.25/5.25      ! [A: nat,B: nat,N: nat] :
% 9.25/5.25        ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 9.25/5.25        = ( groups3542108847815614940at_nat
% 9.25/5.25          @ ^ [K4: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K4 ) ) @ ( power_power_nat @ A @ K4 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K4 ) ) )
% 9.25/5.25          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7818_pochhammer__binomial__sum,axiom,
% 9.25/5.25      ! [A: code_integer,B: code_integer,N: nat] :
% 9.25/5.25        ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ N )
% 9.25/5.25        = ( groups7501900531339628137nteger
% 9.25/5.25          @ ^ [K4: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( binomial @ N @ K4 ) ) @ ( comm_s8582702949713902594nteger @ A @ K4 ) ) @ ( comm_s8582702949713902594nteger @ B @ ( minus_minus_nat @ N @ K4 ) ) )
% 9.25/5.25          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7819_pochhammer__binomial__sum,axiom,
% 9.25/5.25      ! [A: int,B: int,N: nat] :
% 9.25/5.25        ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N )
% 9.25/5.25        = ( groups3539618377306564664at_int
% 9.25/5.25          @ ^ [K4: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K4 ) ) @ ( comm_s4660882817536571857er_int @ A @ K4 ) ) @ ( comm_s4660882817536571857er_int @ B @ ( minus_minus_nat @ N @ K4 ) ) )
% 9.25/5.25          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7820_pochhammer__binomial__sum,axiom,
% 9.25/5.25      ! [A: rat,B: rat,N: nat] :
% 9.25/5.25        ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 9.25/5.25        = ( groups2906978787729119204at_rat
% 9.25/5.25          @ ^ [K4: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K4 ) ) @ ( comm_s4028243227959126397er_rat @ A @ K4 ) ) @ ( comm_s4028243227959126397er_rat @ B @ ( minus_minus_nat @ N @ K4 ) ) )
% 9.25/5.25          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7821_gbinomial__pochhammer_H,axiom,
% 9.25/5.25      ( gbinomial_rat
% 9.25/5.25      = ( ^ [A3: rat,K4: nat] : ( divide_divide_rat @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ K4 ) ) @ one_one_rat ) @ K4 ) @ ( semiri773545260158071498ct_rat @ K4 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7822_choose__square__sum,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( groups3542108847815614940at_nat
% 9.25/5.25          @ ^ [K4: nat] : ( power_power_nat @ ( binomial @ N @ K4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.25          @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.25        = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7823_gbinomial__pochhammer,axiom,
% 9.25/5.25      ( gbinomial_rat
% 9.25/5.25      = ( ^ [A3: rat,K4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K4 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ A3 ) @ K4 ) ) @ ( semiri773545260158071498ct_rat @ K4 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7824_prod_Ozero__middle,axiom,
% 9.25/5.25      ! [P4: nat,K: nat,G2: nat > code_integer,H3: nat > code_integer] :
% 9.25/5.25        ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 9.25/5.25       => ( ( ord_less_eq_nat @ K @ P4 )
% 9.25/5.25         => ( ( groups3455450783089532116nteger
% 9.25/5.25              @ ^ [J3: nat] : ( if_Code_integer @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( if_Code_integer @ ( J3 = K ) @ one_one_Code_integer @ ( H3 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.25/5.25              @ ( set_ord_atMost_nat @ P4 ) )
% 9.25/5.25            = ( groups3455450783089532116nteger
% 9.25/5.25              @ ^ [J3: nat] : ( if_Code_integer @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( H3 @ J3 ) )
% 9.25/5.25              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7825_prod_Ozero__middle,axiom,
% 9.25/5.25      ! [P4: nat,K: nat,G2: nat > assn,H3: nat > assn] :
% 9.25/5.25        ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 9.25/5.25       => ( ( ord_less_eq_nat @ K @ P4 )
% 9.25/5.25         => ( ( groups6906906614972039071t_assn
% 9.25/5.25              @ ^ [J3: nat] : ( if_assn @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( if_assn @ ( J3 = K ) @ one_one_assn @ ( H3 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.25/5.25              @ ( set_ord_atMost_nat @ P4 ) )
% 9.25/5.25            = ( groups6906906614972039071t_assn
% 9.25/5.25              @ ^ [J3: nat] : ( if_assn @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( H3 @ J3 ) )
% 9.25/5.25              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7826_prod_Ozero__middle,axiom,
% 9.25/5.25      ! [P4: nat,K: nat,G2: nat > rat,H3: nat > rat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 9.25/5.25       => ( ( ord_less_eq_nat @ K @ P4 )
% 9.25/5.25         => ( ( groups73079841787564623at_rat
% 9.25/5.25              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( if_rat @ ( J3 = K ) @ one_one_rat @ ( H3 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.25/5.25              @ ( set_ord_atMost_nat @ P4 ) )
% 9.25/5.25            = ( groups73079841787564623at_rat
% 9.25/5.25              @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( H3 @ J3 ) )
% 9.25/5.25              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7827_prod_Ozero__middle,axiom,
% 9.25/5.25      ! [P4: nat,K: nat,G2: nat > nat,H3: nat > nat] :
% 9.25/5.25        ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 9.25/5.25       => ( ( ord_less_eq_nat @ K @ P4 )
% 9.25/5.25         => ( ( groups708209901874060359at_nat
% 9.25/5.25              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( if_nat @ ( J3 = K ) @ one_one_nat @ ( H3 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.25/5.25              @ ( set_ord_atMost_nat @ P4 ) )
% 9.25/5.25            = ( groups708209901874060359at_nat
% 9.25/5.25              @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( H3 @ J3 ) )
% 9.25/5.25              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7828_prod_Ozero__middle,axiom,
% 9.25/5.25      ! [P4: nat,K: nat,G2: nat > int,H3: nat > int] :
% 9.25/5.25        ( ( ord_less_eq_nat @ one_one_nat @ P4 )
% 9.25/5.25       => ( ( ord_less_eq_nat @ K @ P4 )
% 9.25/5.25         => ( ( groups705719431365010083at_int
% 9.25/5.25              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( if_int @ ( J3 = K ) @ one_one_int @ ( H3 @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 9.25/5.25              @ ( set_ord_atMost_nat @ P4 ) )
% 9.25/5.25            = ( groups705719431365010083at_int
% 9.25/5.25              @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G2 @ J3 ) @ ( H3 @ J3 ) )
% 9.25/5.25              @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P4 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7829_choose__alternating__linear__sum,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( N != one_one_nat )
% 9.25/5.25       => ( ( groups7501900531339628137nteger
% 9.25/5.25            @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I3 ) @ ( semiri4939895301339042750nteger @ I3 ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I3 ) ) )
% 9.25/5.25            @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.25          = zero_z3403309356797280102nteger ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7830_choose__alternating__linear__sum,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( N != one_one_nat )
% 9.25/5.25       => ( ( groups3539618377306564664at_int
% 9.25/5.25            @ ^ [I3: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I3 ) @ ( semiri1314217659103216013at_int @ I3 ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I3 ) ) )
% 9.25/5.25            @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.25          = zero_zero_int ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7831_choose__alternating__linear__sum,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( N != one_one_nat )
% 9.25/5.25       => ( ( groups2906978787729119204at_rat
% 9.25/5.25            @ ^ [I3: nat] : ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I3 ) @ ( semiri681578069525770553at_rat @ I3 ) ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I3 ) ) )
% 9.25/5.25            @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.25          = zero_zero_rat ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7832_binomial__r__part__sum,axiom,
% 9.25/5.25      ! [M: nat] :
% 9.25/5.25        ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 9.25/5.25        = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7833_choose__linear__sum,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( groups3542108847815614940at_nat
% 9.25/5.25          @ ^ [I3: nat] : ( times_times_nat @ I3 @ ( binomial @ N @ I3 ) )
% 9.25/5.25          @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.25        = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7834_sum_Otriangle__reindex,axiom,
% 9.25/5.25      ! [G2: nat > nat > nat,N: nat] :
% 9.25/5.25        ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G2 )
% 9.25/5.25          @ ( collec3392354462482085612at_nat
% 9.25/5.25            @ ( produc6081775807080527818_nat_o
% 9.25/5.25              @ ^ [I3: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 9.25/5.25        = ( groups3542108847815614940at_nat
% 9.25/5.25          @ ^ [K4: nat] :
% 9.25/5.25              ( groups3542108847815614940at_nat
% 9.25/5.25              @ ^ [I3: nat] : ( G2 @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 9.25/5.25              @ ( set_ord_atMost_nat @ K4 ) )
% 9.25/5.25          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7835_divide__int__unfold,axiom,
% 9.25/5.25      ! [L: int,K: int,N: nat,M: nat] :
% 9.25/5.25        ( ( ( ( ( sgn_sgn_int @ L )
% 9.25/5.25              = zero_zero_int )
% 9.25/5.25            | ( ( sgn_sgn_int @ K )
% 9.25/5.25              = zero_zero_int )
% 9.25/5.25            | ( N = zero_zero_nat ) )
% 9.25/5.25         => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 9.25/5.25            = zero_zero_int ) )
% 9.25/5.25        & ( ~ ( ( ( sgn_sgn_int @ L )
% 9.25/5.25                = zero_zero_int )
% 9.25/5.25              | ( ( sgn_sgn_int @ K )
% 9.25/5.25                = zero_zero_int )
% 9.25/5.25              | ( N = zero_zero_nat ) )
% 9.25/5.25         => ( ( ( ( sgn_sgn_int @ K )
% 9.25/5.25                = ( sgn_sgn_int @ L ) )
% 9.25/5.25             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 9.25/5.25                = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 9.25/5.25            & ( ( ( sgn_sgn_int @ K )
% 9.25/5.25               != ( sgn_sgn_int @ L ) )
% 9.25/5.25             => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 9.25/5.25                = ( uminus_uminus_int
% 9.25/5.25                  @ ( semiri1314217659103216013at_int
% 9.25/5.25                    @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 9.25/5.25                      @ ( zero_n2687167440665602831ol_nat
% 9.25/5.25                        @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7836_sum__zero__power_H,axiom,
% 9.25/5.25      ! [A2: set_nat,C: nat > rat,D2: nat > rat] :
% 9.25/5.25        ( ( ( ( finite_finite_nat @ A2 )
% 9.25/5.25            & ( member_nat @ zero_zero_nat @ A2 ) )
% 9.25/5.25         => ( ( groups2906978787729119204at_rat
% 9.25/5.25              @ ^ [I3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) ) @ ( D2 @ I3 ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( divide_divide_rat @ ( C @ zero_zero_nat ) @ ( D2 @ zero_zero_nat ) ) ) )
% 9.25/5.25        & ( ~ ( ( finite_finite_nat @ A2 )
% 9.25/5.25              & ( member_nat @ zero_zero_nat @ A2 ) )
% 9.25/5.25         => ( ( groups2906978787729119204at_rat
% 9.25/5.25              @ ^ [I3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) ) @ ( D2 @ I3 ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = zero_zero_rat ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7837_bezw__0,axiom,
% 9.25/5.25      ! [X: nat] :
% 9.25/5.25        ( ( bezw @ X @ zero_zero_nat )
% 9.25/5.25        = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7838_drop__bit__numeral__minus__bit1,axiom,
% 9.25/5.25      ! [L: num,K: num] :
% 9.25/5.25        ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 9.25/5.25        = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7839_sgn__1,axiom,
% 9.25/5.25      ( ( sgn_sgn_int @ one_one_int )
% 9.25/5.25      = one_one_int ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7840_sgn__1,axiom,
% 9.25/5.25      ( ( sgn_sgn_Code_integer @ one_one_Code_integer )
% 9.25/5.25      = one_one_Code_integer ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7841_sgn__1,axiom,
% 9.25/5.25      ( ( sgn_sgn_rat @ one_one_rat )
% 9.25/5.25      = one_one_rat ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7842_sgn__minus,axiom,
% 9.25/5.25      ! [A: int] :
% 9.25/5.25        ( ( sgn_sgn_int @ ( uminus_uminus_int @ A ) )
% 9.25/5.25        = ( uminus_uminus_int @ ( sgn_sgn_int @ A ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7843_sgn__minus,axiom,
% 9.25/5.25      ! [A: code_integer] :
% 9.25/5.25        ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 9.25/5.25        = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ A ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7844_sgn__minus,axiom,
% 9.25/5.25      ! [A: rat] :
% 9.25/5.25        ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ A ) )
% 9.25/5.25        = ( uminus_uminus_rat @ ( sgn_sgn_rat @ A ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7845_prod_Oinfinite,axiom,
% 9.25/5.25      ! [A2: set_nat,G2: nat > code_integer] :
% 9.25/5.25        ( ~ ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups3455450783089532116nteger @ G2 @ A2 )
% 9.25/5.25          = one_one_Code_integer ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7846_prod_Oinfinite,axiom,
% 9.25/5.25      ! [A2: set_int,G2: int > code_integer] :
% 9.25/5.25        ( ~ ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups3827104343326376752nteger @ G2 @ A2 )
% 9.25/5.25          = one_one_Code_integer ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7847_prod_Oinfinite,axiom,
% 9.25/5.25      ! [A2: set_nat,G2: nat > assn] :
% 9.25/5.25        ( ~ ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups6906906614972039071t_assn @ G2 @ A2 )
% 9.25/5.25          = one_one_assn ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7848_prod_Oinfinite,axiom,
% 9.25/5.25      ! [A2: set_int,G2: int > assn] :
% 9.25/5.25        ( ~ ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups7882442080178216443t_assn @ G2 @ A2 )
% 9.25/5.25          = one_one_assn ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7849_prod_Oinfinite,axiom,
% 9.25/5.25      ! [A2: set_nat,G2: nat > rat] :
% 9.25/5.25        ( ~ ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups73079841787564623at_rat @ G2 @ A2 )
% 9.25/5.25          = one_one_rat ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7850_prod_Oinfinite,axiom,
% 9.25/5.25      ! [A2: set_int,G2: int > rat] :
% 9.25/5.25        ( ~ ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups1072433553688619179nt_rat @ G2 @ A2 )
% 9.25/5.25          = one_one_rat ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7851_prod_Oinfinite,axiom,
% 9.25/5.25      ! [A2: set_int,G2: int > nat] :
% 9.25/5.25        ( ~ ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups1707563613775114915nt_nat @ G2 @ A2 )
% 9.25/5.25          = one_one_nat ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7852_prod_Oinfinite,axiom,
% 9.25/5.25      ! [A2: set_nat,G2: nat > nat] :
% 9.25/5.25        ( ~ ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups708209901874060359at_nat @ G2 @ A2 )
% 9.25/5.25          = one_one_nat ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7853_prod_Oinfinite,axiom,
% 9.25/5.25      ! [A2: set_nat,G2: nat > int] :
% 9.25/5.25        ( ~ ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups705719431365010083at_int @ G2 @ A2 )
% 9.25/5.25          = one_one_int ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7854_prod_Oinfinite,axiom,
% 9.25/5.25      ! [A2: set_int,G2: int > int] :
% 9.25/5.25        ( ~ ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups1705073143266064639nt_int @ G2 @ A2 )
% 9.25/5.25          = one_one_int ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7855_divide__sgn,axiom,
% 9.25/5.25      ! [A: rat,B: rat] :
% 9.25/5.25        ( ( divide_divide_rat @ A @ ( sgn_sgn_rat @ B ) )
% 9.25/5.25        = ( times_times_rat @ A @ ( sgn_sgn_rat @ B ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7856_lessThan__0,axiom,
% 9.25/5.25      ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 9.25/5.25      = bot_bot_set_nat ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7857_drop__bit__minus__one,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.25        = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7858_sum_Odelta_H,axiom,
% 9.25/5.25      ! [S: set_nat,A: nat,B: nat > code_integer] :
% 9.25/5.25        ( ( finite_finite_nat @ S )
% 9.25/5.25       => ( ( ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups7501900531339628137nteger
% 9.25/5.25                @ ^ [K4: nat] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups7501900531339628137nteger
% 9.25/5.25                @ ^ [K4: nat] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 9.25/5.25                @ S )
% 9.25/5.25              = zero_z3403309356797280102nteger ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7859_sum_Odelta_H,axiom,
% 9.25/5.25      ! [S: set_int,A: int,B: int > code_integer] :
% 9.25/5.25        ( ( finite_finite_int @ S )
% 9.25/5.25       => ( ( ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups7873554091576472773nteger
% 9.25/5.25                @ ^ [K4: int] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups7873554091576472773nteger
% 9.25/5.25                @ ^ [K4: int] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 9.25/5.25                @ S )
% 9.25/5.25              = zero_z3403309356797280102nteger ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7860_sum_Odelta_H,axiom,
% 9.25/5.25      ! [S: set_nat,A: nat,B: nat > rat] :
% 9.25/5.25        ( ( finite_finite_nat @ S )
% 9.25/5.25       => ( ( ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups2906978787729119204at_rat
% 9.25/5.25                @ ^ [K4: nat] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_rat )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups2906978787729119204at_rat
% 9.25/5.25                @ ^ [K4: nat] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_rat )
% 9.25/5.25                @ S )
% 9.25/5.25              = zero_zero_rat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7861_sum_Odelta_H,axiom,
% 9.25/5.25      ! [S: set_int,A: int,B: int > rat] :
% 9.25/5.25        ( ( finite_finite_int @ S )
% 9.25/5.25       => ( ( ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups3906332499630173760nt_rat
% 9.25/5.25                @ ^ [K4: int] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_rat )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups3906332499630173760nt_rat
% 9.25/5.25                @ ^ [K4: int] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_rat )
% 9.25/5.25                @ S )
% 9.25/5.25              = zero_zero_rat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7862_sum_Odelta_H,axiom,
% 9.25/5.25      ! [S: set_int,A: int,B: int > nat] :
% 9.25/5.25        ( ( finite_finite_int @ S )
% 9.25/5.25       => ( ( ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups4541462559716669496nt_nat
% 9.25/5.25                @ ^ [K4: int] : ( if_nat @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_nat )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups4541462559716669496nt_nat
% 9.25/5.25                @ ^ [K4: int] : ( if_nat @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_nat )
% 9.25/5.25                @ S )
% 9.25/5.25              = zero_zero_nat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7863_sum_Odelta_H,axiom,
% 9.25/5.25      ! [S: set_nat,A: nat,B: nat > int] :
% 9.25/5.25        ( ( finite_finite_nat @ S )
% 9.25/5.25       => ( ( ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups3539618377306564664at_int
% 9.25/5.25                @ ^ [K4: nat] : ( if_int @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_int )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups3539618377306564664at_int
% 9.25/5.25                @ ^ [K4: nat] : ( if_int @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_int )
% 9.25/5.25                @ S )
% 9.25/5.25              = zero_zero_int ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7864_sum_Odelta_H,axiom,
% 9.25/5.25      ! [S: set_nat,A: nat,B: nat > nat] :
% 9.25/5.25        ( ( finite_finite_nat @ S )
% 9.25/5.25       => ( ( ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups3542108847815614940at_nat
% 9.25/5.25                @ ^ [K4: nat] : ( if_nat @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_nat )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups3542108847815614940at_nat
% 9.25/5.25                @ ^ [K4: nat] : ( if_nat @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_nat )
% 9.25/5.25                @ S )
% 9.25/5.25              = zero_zero_nat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7865_sum_Odelta_H,axiom,
% 9.25/5.25      ! [S: set_int,A: int,B: int > int] :
% 9.25/5.25        ( ( finite_finite_int @ S )
% 9.25/5.25       => ( ( ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups4538972089207619220nt_int
% 9.25/5.25                @ ^ [K4: int] : ( if_int @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_int )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups4538972089207619220nt_int
% 9.25/5.25                @ ^ [K4: int] : ( if_int @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_int )
% 9.25/5.25                @ S )
% 9.25/5.25              = zero_zero_int ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7866_sum_Odelta_H,axiom,
% 9.25/5.25      ! [S: set_set_nat,A: set_nat,B: set_nat > code_integer] :
% 9.25/5.25        ( ( finite1152437895449049373et_nat @ S )
% 9.25/5.25       => ( ( ( member_set_nat @ A @ S )
% 9.25/5.25           => ( ( groups9190459664516455967nteger
% 9.25/5.25                @ ^ [K4: set_nat] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_set_nat @ A @ S )
% 9.25/5.25           => ( ( groups9190459664516455967nteger
% 9.25/5.25                @ ^ [K4: set_nat] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 9.25/5.25                @ S )
% 9.25/5.25              = zero_z3403309356797280102nteger ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7867_sum_Odelta_H,axiom,
% 9.25/5.25      ! [S: set_set_nat,A: set_nat,B: set_nat > rat] :
% 9.25/5.25        ( ( finite1152437895449049373et_nat @ S )
% 9.25/5.25       => ( ( ( member_set_nat @ A @ S )
% 9.25/5.25           => ( ( groups7659867448343625626at_rat
% 9.25/5.25                @ ^ [K4: set_nat] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_rat )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_set_nat @ A @ S )
% 9.25/5.25           => ( ( groups7659867448343625626at_rat
% 9.25/5.25                @ ^ [K4: set_nat] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ zero_zero_rat )
% 9.25/5.25                @ S )
% 9.25/5.25              = zero_zero_rat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7868_sum_Odelta,axiom,
% 9.25/5.25      ! [S: set_nat,A: nat,B: nat > code_integer] :
% 9.25/5.25        ( ( finite_finite_nat @ S )
% 9.25/5.25       => ( ( ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups7501900531339628137nteger
% 9.25/5.25                @ ^ [K4: nat] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups7501900531339628137nteger
% 9.25/5.25                @ ^ [K4: nat] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 9.25/5.25                @ S )
% 9.25/5.25              = zero_z3403309356797280102nteger ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7869_sum_Odelta,axiom,
% 9.25/5.25      ! [S: set_int,A: int,B: int > code_integer] :
% 9.25/5.25        ( ( finite_finite_int @ S )
% 9.25/5.25       => ( ( ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups7873554091576472773nteger
% 9.25/5.25                @ ^ [K4: int] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups7873554091576472773nteger
% 9.25/5.25                @ ^ [K4: int] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 9.25/5.25                @ S )
% 9.25/5.25              = zero_z3403309356797280102nteger ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7870_sum_Odelta,axiom,
% 9.25/5.25      ! [S: set_nat,A: nat,B: nat > rat] :
% 9.25/5.25        ( ( finite_finite_nat @ S )
% 9.25/5.25       => ( ( ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups2906978787729119204at_rat
% 9.25/5.25                @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_rat )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups2906978787729119204at_rat
% 9.25/5.25                @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_rat )
% 9.25/5.25                @ S )
% 9.25/5.25              = zero_zero_rat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7871_sum_Odelta,axiom,
% 9.25/5.25      ! [S: set_int,A: int,B: int > rat] :
% 9.25/5.25        ( ( finite_finite_int @ S )
% 9.25/5.25       => ( ( ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups3906332499630173760nt_rat
% 9.25/5.25                @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_rat )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups3906332499630173760nt_rat
% 9.25/5.25                @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_rat )
% 9.25/5.25                @ S )
% 9.25/5.25              = zero_zero_rat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7872_sum_Odelta,axiom,
% 9.25/5.25      ! [S: set_int,A: int,B: int > nat] :
% 9.25/5.25        ( ( finite_finite_int @ S )
% 9.25/5.25       => ( ( ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups4541462559716669496nt_nat
% 9.25/5.25                @ ^ [K4: int] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_nat )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups4541462559716669496nt_nat
% 9.25/5.25                @ ^ [K4: int] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_nat )
% 9.25/5.25                @ S )
% 9.25/5.25              = zero_zero_nat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7873_sum_Odelta,axiom,
% 9.25/5.25      ! [S: set_nat,A: nat,B: nat > int] :
% 9.25/5.25        ( ( finite_finite_nat @ S )
% 9.25/5.25       => ( ( ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups3539618377306564664at_int
% 9.25/5.25                @ ^ [K4: nat] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_int )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups3539618377306564664at_int
% 9.25/5.25                @ ^ [K4: nat] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_int )
% 9.25/5.25                @ S )
% 9.25/5.25              = zero_zero_int ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7874_sum_Odelta,axiom,
% 9.25/5.25      ! [S: set_nat,A: nat,B: nat > nat] :
% 9.25/5.25        ( ( finite_finite_nat @ S )
% 9.25/5.25       => ( ( ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups3542108847815614940at_nat
% 9.25/5.25                @ ^ [K4: nat] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_nat )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups3542108847815614940at_nat
% 9.25/5.25                @ ^ [K4: nat] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_nat )
% 9.25/5.25                @ S )
% 9.25/5.25              = zero_zero_nat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7875_sum_Odelta,axiom,
% 9.25/5.25      ! [S: set_int,A: int,B: int > int] :
% 9.25/5.25        ( ( finite_finite_int @ S )
% 9.25/5.25       => ( ( ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups4538972089207619220nt_int
% 9.25/5.25                @ ^ [K4: int] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_int )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups4538972089207619220nt_int
% 9.25/5.25                @ ^ [K4: int] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_int )
% 9.25/5.25                @ S )
% 9.25/5.25              = zero_zero_int ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7876_sum_Odelta,axiom,
% 9.25/5.25      ! [S: set_set_nat,A: set_nat,B: set_nat > code_integer] :
% 9.25/5.25        ( ( finite1152437895449049373et_nat @ S )
% 9.25/5.25       => ( ( ( member_set_nat @ A @ S )
% 9.25/5.25           => ( ( groups9190459664516455967nteger
% 9.25/5.25                @ ^ [K4: set_nat] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_set_nat @ A @ S )
% 9.25/5.25           => ( ( groups9190459664516455967nteger
% 9.25/5.25                @ ^ [K4: set_nat] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ zero_z3403309356797280102nteger )
% 9.25/5.25                @ S )
% 9.25/5.25              = zero_z3403309356797280102nteger ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7877_sum_Odelta,axiom,
% 9.25/5.25      ! [S: set_set_nat,A: set_nat,B: set_nat > rat] :
% 9.25/5.25        ( ( finite1152437895449049373et_nat @ S )
% 9.25/5.25       => ( ( ( member_set_nat @ A @ S )
% 9.25/5.25           => ( ( groups7659867448343625626at_rat
% 9.25/5.25                @ ^ [K4: set_nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_rat )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_set_nat @ A @ S )
% 9.25/5.25           => ( ( groups7659867448343625626at_rat
% 9.25/5.25                @ ^ [K4: set_nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ zero_zero_rat )
% 9.25/5.25                @ S )
% 9.25/5.25              = zero_zero_rat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7878_prod__eq__1__iff,axiom,
% 9.25/5.25      ! [A2: set_int,F2: int > nat] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( ( groups1707563613775114915nt_nat @ F2 @ A2 )
% 9.25/5.25            = one_one_nat )
% 9.25/5.25          = ( ! [X3: int] :
% 9.25/5.25                ( ( member_int @ X3 @ A2 )
% 9.25/5.25               => ( ( F2 @ X3 )
% 9.25/5.25                  = one_one_nat ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7879_prod__eq__1__iff,axiom,
% 9.25/5.25      ! [A2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > nat] :
% 9.25/5.25        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.25       => ( ( ( groups4077766827762148844at_nat @ F2 @ A2 )
% 9.25/5.25            = one_one_nat )
% 9.25/5.25          = ( ! [X3: product_prod_nat_nat] :
% 9.25/5.25                ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 9.25/5.25               => ( ( F2 @ X3 )
% 9.25/5.25                  = one_one_nat ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7880_prod__eq__1__iff,axiom,
% 9.25/5.25      ! [A2: set_nat,F2: nat > nat] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( ( groups708209901874060359at_nat @ F2 @ A2 )
% 9.25/5.25            = one_one_nat )
% 9.25/5.25          = ( ! [X3: nat] :
% 9.25/5.25                ( ( member_nat @ X3 @ A2 )
% 9.25/5.25               => ( ( F2 @ X3 )
% 9.25/5.25                  = one_one_nat ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7881_prod_Odelta,axiom,
% 9.25/5.25      ! [S: set_nat,A: nat,B: nat > code_integer] :
% 9.25/5.25        ( ( finite_finite_nat @ S )
% 9.25/5.25       => ( ( ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups3455450783089532116nteger
% 9.25/5.25                @ ^ [K4: nat] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups3455450783089532116nteger
% 9.25/5.25                @ ^ [K4: nat] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.25/5.25                @ S )
% 9.25/5.25              = one_one_Code_integer ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7882_prod_Odelta,axiom,
% 9.25/5.25      ! [S: set_int,A: int,B: int > code_integer] :
% 9.25/5.25        ( ( finite_finite_int @ S )
% 9.25/5.25       => ( ( ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups3827104343326376752nteger
% 9.25/5.25                @ ^ [K4: int] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups3827104343326376752nteger
% 9.25/5.25                @ ^ [K4: int] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.25/5.25                @ S )
% 9.25/5.25              = one_one_Code_integer ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7883_prod_Odelta,axiom,
% 9.25/5.25      ! [S: set_nat,A: nat,B: nat > assn] :
% 9.25/5.25        ( ( finite_finite_nat @ S )
% 9.25/5.25       => ( ( ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups6906906614972039071t_assn
% 9.25/5.25                @ ^ [K4: nat] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups6906906614972039071t_assn
% 9.25/5.25                @ ^ [K4: nat] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 9.25/5.25                @ S )
% 9.25/5.25              = one_one_assn ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7884_prod_Odelta,axiom,
% 9.25/5.25      ! [S: set_int,A: int,B: int > assn] :
% 9.25/5.25        ( ( finite_finite_int @ S )
% 9.25/5.25       => ( ( ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups7882442080178216443t_assn
% 9.25/5.25                @ ^ [K4: int] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups7882442080178216443t_assn
% 9.25/5.25                @ ^ [K4: int] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ one_one_assn )
% 9.25/5.25                @ S )
% 9.25/5.25              = one_one_assn ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7885_prod_Odelta,axiom,
% 9.25/5.25      ! [S: set_nat,A: nat,B: nat > rat] :
% 9.25/5.25        ( ( finite_finite_nat @ S )
% 9.25/5.25       => ( ( ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups73079841787564623at_rat
% 9.25/5.25                @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_rat )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups73079841787564623at_rat
% 9.25/5.25                @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_rat )
% 9.25/5.25                @ S )
% 9.25/5.25              = one_one_rat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7886_prod_Odelta,axiom,
% 9.25/5.25      ! [S: set_int,A: int,B: int > rat] :
% 9.25/5.25        ( ( finite_finite_int @ S )
% 9.25/5.25       => ( ( ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups1072433553688619179nt_rat
% 9.25/5.25                @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_rat )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups1072433553688619179nt_rat
% 9.25/5.25                @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_rat )
% 9.25/5.25                @ S )
% 9.25/5.25              = one_one_rat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7887_prod_Odelta,axiom,
% 9.25/5.25      ! [S: set_int,A: int,B: int > nat] :
% 9.25/5.25        ( ( finite_finite_int @ S )
% 9.25/5.25       => ( ( ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups1707563613775114915nt_nat
% 9.25/5.25                @ ^ [K4: int] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_nat )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups1707563613775114915nt_nat
% 9.25/5.25                @ ^ [K4: int] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_nat )
% 9.25/5.25                @ S )
% 9.25/5.25              = one_one_nat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7888_prod_Odelta,axiom,
% 9.25/5.25      ! [S: set_nat,A: nat,B: nat > nat] :
% 9.25/5.25        ( ( finite_finite_nat @ S )
% 9.25/5.25       => ( ( ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups708209901874060359at_nat
% 9.25/5.25                @ ^ [K4: nat] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_nat )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups708209901874060359at_nat
% 9.25/5.25                @ ^ [K4: nat] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ one_one_nat )
% 9.25/5.25                @ S )
% 9.25/5.25              = one_one_nat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7889_prod_Odelta,axiom,
% 9.25/5.25      ! [S: set_nat,A: nat,B: nat > int] :
% 9.25/5.25        ( ( finite_finite_nat @ S )
% 9.25/5.25       => ( ( ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups705719431365010083at_int
% 9.25/5.25                @ ^ [K4: nat] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ one_one_int )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups705719431365010083at_int
% 9.25/5.25                @ ^ [K4: nat] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ one_one_int )
% 9.25/5.25                @ S )
% 9.25/5.25              = one_one_int ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7890_prod_Odelta,axiom,
% 9.25/5.25      ! [S: set_int,A: int,B: int > int] :
% 9.25/5.25        ( ( finite_finite_int @ S )
% 9.25/5.25       => ( ( ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups1705073143266064639nt_int
% 9.25/5.25                @ ^ [K4: int] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ one_one_int )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups1705073143266064639nt_int
% 9.25/5.25                @ ^ [K4: int] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ one_one_int )
% 9.25/5.25                @ S )
% 9.25/5.25              = one_one_int ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7891_prod_Odelta_H,axiom,
% 9.25/5.25      ! [S: set_nat,A: nat,B: nat > code_integer] :
% 9.25/5.25        ( ( finite_finite_nat @ S )
% 9.25/5.25       => ( ( ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups3455450783089532116nteger
% 9.25/5.25                @ ^ [K4: nat] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups3455450783089532116nteger
% 9.25/5.25                @ ^ [K4: nat] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.25/5.25                @ S )
% 9.25/5.25              = one_one_Code_integer ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7892_prod_Odelta_H,axiom,
% 9.25/5.25      ! [S: set_int,A: int,B: int > code_integer] :
% 9.25/5.25        ( ( finite_finite_int @ S )
% 9.25/5.25       => ( ( ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups3827104343326376752nteger
% 9.25/5.25                @ ^ [K4: int] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups3827104343326376752nteger
% 9.25/5.25                @ ^ [K4: int] : ( if_Code_integer @ ( A = K4 ) @ ( B @ K4 ) @ one_one_Code_integer )
% 9.25/5.25                @ S )
% 9.25/5.25              = one_one_Code_integer ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7893_prod_Odelta_H,axiom,
% 9.25/5.25      ! [S: set_nat,A: nat,B: nat > assn] :
% 9.25/5.25        ( ( finite_finite_nat @ S )
% 9.25/5.25       => ( ( ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups6906906614972039071t_assn
% 9.25/5.25                @ ^ [K4: nat] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups6906906614972039071t_assn
% 9.25/5.25                @ ^ [K4: nat] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 9.25/5.25                @ S )
% 9.25/5.25              = one_one_assn ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7894_prod_Odelta_H,axiom,
% 9.25/5.25      ! [S: set_int,A: int,B: int > assn] :
% 9.25/5.25        ( ( finite_finite_int @ S )
% 9.25/5.25       => ( ( ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups7882442080178216443t_assn
% 9.25/5.25                @ ^ [K4: int] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups7882442080178216443t_assn
% 9.25/5.25                @ ^ [K4: int] : ( if_assn @ ( A = K4 ) @ ( B @ K4 ) @ one_one_assn )
% 9.25/5.25                @ S )
% 9.25/5.25              = one_one_assn ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7895_prod_Odelta_H,axiom,
% 9.25/5.25      ! [S: set_nat,A: nat,B: nat > rat] :
% 9.25/5.25        ( ( finite_finite_nat @ S )
% 9.25/5.25       => ( ( ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups73079841787564623at_rat
% 9.25/5.25                @ ^ [K4: nat] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_rat )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups73079841787564623at_rat
% 9.25/5.25                @ ^ [K4: nat] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_rat )
% 9.25/5.25                @ S )
% 9.25/5.25              = one_one_rat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7896_prod_Odelta_H,axiom,
% 9.25/5.25      ! [S: set_int,A: int,B: int > rat] :
% 9.25/5.25        ( ( finite_finite_int @ S )
% 9.25/5.25       => ( ( ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups1072433553688619179nt_rat
% 9.25/5.25                @ ^ [K4: int] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_rat )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups1072433553688619179nt_rat
% 9.25/5.25                @ ^ [K4: int] : ( if_rat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_rat )
% 9.25/5.25                @ S )
% 9.25/5.25              = one_one_rat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7897_prod_Odelta_H,axiom,
% 9.25/5.25      ! [S: set_int,A: int,B: int > nat] :
% 9.25/5.25        ( ( finite_finite_int @ S )
% 9.25/5.25       => ( ( ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups1707563613775114915nt_nat
% 9.25/5.25                @ ^ [K4: int] : ( if_nat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_nat )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups1707563613775114915nt_nat
% 9.25/5.25                @ ^ [K4: int] : ( if_nat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_nat )
% 9.25/5.25                @ S )
% 9.25/5.25              = one_one_nat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7898_prod_Odelta_H,axiom,
% 9.25/5.25      ! [S: set_nat,A: nat,B: nat > nat] :
% 9.25/5.25        ( ( finite_finite_nat @ S )
% 9.25/5.25       => ( ( ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups708209901874060359at_nat
% 9.25/5.25                @ ^ [K4: nat] : ( if_nat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_nat )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups708209901874060359at_nat
% 9.25/5.25                @ ^ [K4: nat] : ( if_nat @ ( A = K4 ) @ ( B @ K4 ) @ one_one_nat )
% 9.25/5.25                @ S )
% 9.25/5.25              = one_one_nat ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7899_prod_Odelta_H,axiom,
% 9.25/5.25      ! [S: set_nat,A: nat,B: nat > int] :
% 9.25/5.25        ( ( finite_finite_nat @ S )
% 9.25/5.25       => ( ( ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups705719431365010083at_int
% 9.25/5.25                @ ^ [K4: nat] : ( if_int @ ( A = K4 ) @ ( B @ K4 ) @ one_one_int )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_nat @ A @ S )
% 9.25/5.25           => ( ( groups705719431365010083at_int
% 9.25/5.25                @ ^ [K4: nat] : ( if_int @ ( A = K4 ) @ ( B @ K4 ) @ one_one_int )
% 9.25/5.25                @ S )
% 9.25/5.25              = one_one_int ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7900_prod_Odelta_H,axiom,
% 9.25/5.25      ! [S: set_int,A: int,B: int > int] :
% 9.25/5.25        ( ( finite_finite_int @ S )
% 9.25/5.25       => ( ( ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups1705073143266064639nt_int
% 9.25/5.25                @ ^ [K4: int] : ( if_int @ ( A = K4 ) @ ( B @ K4 ) @ one_one_int )
% 9.25/5.25                @ S )
% 9.25/5.25              = ( B @ A ) ) )
% 9.25/5.25          & ( ~ ( member_int @ A @ S )
% 9.25/5.25           => ( ( groups1705073143266064639nt_int
% 9.25/5.25                @ ^ [K4: int] : ( if_int @ ( A = K4 ) @ ( B @ K4 ) @ one_one_int )
% 9.25/5.25                @ S )
% 9.25/5.25              = one_one_int ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7901_sgn__pos,axiom,
% 9.25/5.25      ! [A: code_integer] :
% 9.25/5.25        ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 9.25/5.25       => ( ( sgn_sgn_Code_integer @ A )
% 9.25/5.25          = one_one_Code_integer ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7902_sgn__pos,axiom,
% 9.25/5.25      ! [A: rat] :
% 9.25/5.25        ( ( ord_less_rat @ zero_zero_rat @ A )
% 9.25/5.25       => ( ( sgn_sgn_rat @ A )
% 9.25/5.25          = one_one_rat ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7903_sgn__pos,axiom,
% 9.25/5.25      ! [A: int] :
% 9.25/5.25        ( ( ord_less_int @ zero_zero_int @ A )
% 9.25/5.25       => ( ( sgn_sgn_int @ A )
% 9.25/5.25          = one_one_int ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7904_prod_Oinsert,axiom,
% 9.25/5.25      ! [A2: set_o,X: $o,G2: $o > code_integer] :
% 9.25/5.25        ( ( finite_finite_o @ A2 )
% 9.25/5.25       => ( ~ ( member_o @ X @ A2 )
% 9.25/5.25         => ( ( groups7694694392188491536nteger @ G2 @ ( insert_o @ X @ A2 ) )
% 9.25/5.25            = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups7694694392188491536nteger @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7905_prod_Oinsert,axiom,
% 9.25/5.25      ! [A2: set_nat,X: nat,G2: nat > code_integer] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ~ ( member_nat @ X @ A2 )
% 9.25/5.25         => ( ( groups3455450783089532116nteger @ G2 @ ( insert_nat @ X @ A2 ) )
% 9.25/5.25            = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups3455450783089532116nteger @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7906_prod_Oinsert,axiom,
% 9.25/5.25      ! [A2: set_int,X: int,G2: int > code_integer] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ~ ( member_int @ X @ A2 )
% 9.25/5.25         => ( ( groups3827104343326376752nteger @ G2 @ ( insert_int @ X @ A2 ) )
% 9.25/5.25            = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups3827104343326376752nteger @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7907_prod_Oinsert,axiom,
% 9.25/5.25      ! [A2: set_o,X: $o,G2: $o > assn] :
% 9.25/5.25        ( ( finite_finite_o @ A2 )
% 9.25/5.25       => ( ~ ( member_o @ X @ A2 )
% 9.25/5.25         => ( ( groups5301882518646026715o_assn @ G2 @ ( insert_o @ X @ A2 ) )
% 9.25/5.25            = ( times_times_assn @ ( G2 @ X ) @ ( groups5301882518646026715o_assn @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7908_prod_Oinsert,axiom,
% 9.25/5.25      ! [A2: set_nat,X: nat,G2: nat > assn] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ~ ( member_nat @ X @ A2 )
% 9.25/5.25         => ( ( groups6906906614972039071t_assn @ G2 @ ( insert_nat @ X @ A2 ) )
% 9.25/5.25            = ( times_times_assn @ ( G2 @ X ) @ ( groups6906906614972039071t_assn @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7909_prod_Oinsert,axiom,
% 9.25/5.25      ! [A2: set_int,X: int,G2: int > assn] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ~ ( member_int @ X @ A2 )
% 9.25/5.25         => ( ( groups7882442080178216443t_assn @ G2 @ ( insert_int @ X @ A2 ) )
% 9.25/5.25            = ( times_times_assn @ ( G2 @ X ) @ ( groups7882442080178216443t_assn @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7910_prod_Oinsert,axiom,
% 9.25/5.25      ! [A2: set_o,X: $o,G2: $o > rat] :
% 9.25/5.25        ( ( finite_finite_o @ A2 )
% 9.25/5.25       => ( ~ ( member_o @ X @ A2 )
% 9.25/5.25         => ( ( groups2869687844427037835_o_rat @ G2 @ ( insert_o @ X @ A2 ) )
% 9.25/5.25            = ( times_times_rat @ ( G2 @ X ) @ ( groups2869687844427037835_o_rat @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7911_prod_Oinsert,axiom,
% 9.25/5.25      ! [A2: set_nat,X: nat,G2: nat > rat] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ~ ( member_nat @ X @ A2 )
% 9.25/5.25         => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A2 ) )
% 9.25/5.25            = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7912_prod_Oinsert,axiom,
% 9.25/5.25      ! [A2: set_int,X: int,G2: int > rat] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ~ ( member_int @ X @ A2 )
% 9.25/5.25         => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A2 ) )
% 9.25/5.25            = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7913_prod_Oinsert,axiom,
% 9.25/5.25      ! [A2: set_o,X: $o,G2: $o > nat] :
% 9.25/5.25        ( ( finite_finite_o @ A2 )
% 9.25/5.25       => ( ~ ( member_o @ X @ A2 )
% 9.25/5.25         => ( ( groups3504817904513533571_o_nat @ G2 @ ( insert_o @ X @ A2 ) )
% 9.25/5.25            = ( times_times_nat @ ( G2 @ X ) @ ( groups3504817904513533571_o_nat @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7914_abs__sgn__eq__1,axiom,
% 9.25/5.25      ! [A: code_integer] :
% 9.25/5.25        ( ( A != zero_z3403309356797280102nteger )
% 9.25/5.25       => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 9.25/5.25          = one_one_Code_integer ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7915_abs__sgn__eq__1,axiom,
% 9.25/5.25      ! [A: rat] :
% 9.25/5.25        ( ( A != zero_zero_rat )
% 9.25/5.25       => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 9.25/5.25          = one_one_rat ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7916_abs__sgn__eq__1,axiom,
% 9.25/5.25      ! [A: int] :
% 9.25/5.25        ( ( A != zero_zero_int )
% 9.25/5.25       => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 9.25/5.25          = one_one_int ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7917_single__Diff__lessThan,axiom,
% 9.25/5.25      ! [K: $o] :
% 9.25/5.25        ( ( minus_minus_set_o @ ( insert_o @ K @ bot_bot_set_o ) @ ( set_ord_lessThan_o @ K ) )
% 9.25/5.25        = ( insert_o @ K @ bot_bot_set_o ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7918_single__Diff__lessThan,axiom,
% 9.25/5.25      ! [K: int] :
% 9.25/5.25        ( ( minus_minus_set_int @ ( insert_int @ K @ bot_bot_set_int ) @ ( set_ord_lessThan_int @ K ) )
% 9.25/5.25        = ( insert_int @ K @ bot_bot_set_int ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7919_single__Diff__lessThan,axiom,
% 9.25/5.25      ! [K: nat] :
% 9.25/5.25        ( ( minus_minus_set_nat @ ( insert_nat @ K @ bot_bot_set_nat ) @ ( set_ord_lessThan_nat @ K ) )
% 9.25/5.25        = ( insert_nat @ K @ bot_bot_set_nat ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7920_sgn__mult__self__eq,axiom,
% 9.25/5.25      ! [A: code_integer] :
% 9.25/5.25        ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 9.25/5.25        = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7921_sgn__mult__self__eq,axiom,
% 9.25/5.25      ! [A: rat] :
% 9.25/5.25        ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 9.25/5.25        = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7922_sgn__mult__self__eq,axiom,
% 9.25/5.25      ! [A: int] :
% 9.25/5.25        ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ A ) )
% 9.25/5.25        = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7923_drop__bit__of__1,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( bit_se3928097537394005634nteger @ N @ one_one_Code_integer )
% 9.25/5.25        = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7924_drop__bit__of__1,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( bit_se8570568707652914677it_nat @ N @ one_one_nat )
% 9.25/5.25        = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7925_drop__bit__of__1,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( bit_se8568078237143864401it_int @ N @ one_one_int )
% 9.25/5.25        = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7926_prod_OlessThan__Suc,axiom,
% 9.25/5.25      ! [G2: nat > code_integer,N: nat] :
% 9.25/5.25        ( ( groups3455450783089532116nteger @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7927_prod_OlessThan__Suc,axiom,
% 9.25/5.25      ! [G2: nat > assn,N: nat] :
% 9.25/5.25        ( ( groups6906906614972039071t_assn @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7928_prod_OlessThan__Suc,axiom,
% 9.25/5.25      ! [G2: nat > rat,N: nat] :
% 9.25/5.25        ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7929_prod_OlessThan__Suc,axiom,
% 9.25/5.25      ! [G2: nat > nat,N: nat] :
% 9.25/5.25        ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7930_prod_OlessThan__Suc,axiom,
% 9.25/5.25      ! [G2: nat > int,N: nat] :
% 9.25/5.25        ( ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.25/5.25        = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7931_sgn__neg,axiom,
% 9.25/5.25      ! [A: int] :
% 9.25/5.25        ( ( ord_less_int @ A @ zero_zero_int )
% 9.25/5.25       => ( ( sgn_sgn_int @ A )
% 9.25/5.25          = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7932_sgn__neg,axiom,
% 9.25/5.25      ! [A: code_integer] :
% 9.25/5.25        ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 9.25/5.25       => ( ( sgn_sgn_Code_integer @ A )
% 9.25/5.25          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7933_sgn__neg,axiom,
% 9.25/5.25      ! [A: rat] :
% 9.25/5.25        ( ( ord_less_rat @ A @ zero_zero_rat )
% 9.25/5.25       => ( ( sgn_sgn_rat @ A )
% 9.25/5.25          = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7934_drop__bit__Suc__minus__bit0,axiom,
% 9.25/5.25      ! [N: nat,K: num] :
% 9.25/5.25        ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 9.25/5.25        = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7935_sum__mult__of__bool__eq,axiom,
% 9.25/5.25      ! [A2: set_int,F2: int > code_integer,P: int > $o] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups7873554091576472773nteger
% 9.25/5.25            @ ^ [X3: int] : ( times_3573771949741848930nteger @ ( F2 @ X3 ) @ ( zero_n356916108424825756nteger @ ( P @ X3 ) ) )
% 9.25/5.25            @ A2 )
% 9.25/5.25          = ( groups7873554091576472773nteger @ F2 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7936_sum__mult__of__bool__eq,axiom,
% 9.25/5.25      ! [A2: set_nat,F2: nat > code_integer,P: nat > $o] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups7501900531339628137nteger
% 9.25/5.25            @ ^ [X3: nat] : ( times_3573771949741848930nteger @ ( F2 @ X3 ) @ ( zero_n356916108424825756nteger @ ( P @ X3 ) ) )
% 9.25/5.25            @ A2 )
% 9.25/5.25          = ( groups7501900531339628137nteger @ F2 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7937_sum__mult__of__bool__eq,axiom,
% 9.25/5.25      ! [A2: set_int,F2: int > rat,P: int > $o] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups3906332499630173760nt_rat
% 9.25/5.25            @ ^ [X3: int] : ( times_times_rat @ ( F2 @ X3 ) @ ( zero_n2052037380579107095ol_rat @ ( P @ X3 ) ) )
% 9.25/5.25            @ A2 )
% 9.25/5.25          = ( groups3906332499630173760nt_rat @ F2 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7938_sum__mult__of__bool__eq,axiom,
% 9.25/5.25      ! [A2: set_nat,F2: nat > rat,P: nat > $o] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups2906978787729119204at_rat
% 9.25/5.25            @ ^ [X3: nat] : ( times_times_rat @ ( F2 @ X3 ) @ ( zero_n2052037380579107095ol_rat @ ( P @ X3 ) ) )
% 9.25/5.25            @ A2 )
% 9.25/5.25          = ( groups2906978787729119204at_rat @ F2 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7939_sum__mult__of__bool__eq,axiom,
% 9.25/5.25      ! [A2: set_nat,F2: nat > int,P: nat > $o] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups3539618377306564664at_int
% 9.25/5.25            @ ^ [X3: nat] : ( times_times_int @ ( F2 @ X3 ) @ ( zero_n2684676970156552555ol_int @ ( P @ X3 ) ) )
% 9.25/5.25            @ A2 )
% 9.25/5.25          = ( groups3539618377306564664at_int @ F2 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7940_sum__mult__of__bool__eq,axiom,
% 9.25/5.25      ! [A2: set_int,F2: int > nat,P: int > $o] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups4541462559716669496nt_nat
% 9.25/5.25            @ ^ [X3: int] : ( times_times_nat @ ( F2 @ X3 ) @ ( zero_n2687167440665602831ol_nat @ ( P @ X3 ) ) )
% 9.25/5.25            @ A2 )
% 9.25/5.25          = ( groups4541462559716669496nt_nat @ F2 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7941_sum__mult__of__bool__eq,axiom,
% 9.25/5.25      ! [A2: set_nat,F2: nat > nat,P: nat > $o] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups3542108847815614940at_nat
% 9.25/5.25            @ ^ [X3: nat] : ( times_times_nat @ ( F2 @ X3 ) @ ( zero_n2687167440665602831ol_nat @ ( P @ X3 ) ) )
% 9.25/5.25            @ A2 )
% 9.25/5.25          = ( groups3542108847815614940at_nat @ F2 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7942_sum__mult__of__bool__eq,axiom,
% 9.25/5.25      ! [A2: set_int,F2: int > int,P: int > $o] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups4538972089207619220nt_int
% 9.25/5.25            @ ^ [X3: int] : ( times_times_int @ ( F2 @ X3 ) @ ( zero_n2684676970156552555ol_int @ ( P @ X3 ) ) )
% 9.25/5.25            @ A2 )
% 9.25/5.25          = ( groups4538972089207619220nt_int @ F2 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7943_sum__mult__of__bool__eq,axiom,
% 9.25/5.25      ! [A2: set_set_nat,F2: set_nat > code_integer,P: set_nat > $o] :
% 9.25/5.25        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.25       => ( ( groups9190459664516455967nteger
% 9.25/5.25            @ ^ [X3: set_nat] : ( times_3573771949741848930nteger @ ( F2 @ X3 ) @ ( zero_n356916108424825756nteger @ ( P @ X3 ) ) )
% 9.25/5.25            @ A2 )
% 9.25/5.25          = ( groups9190459664516455967nteger @ F2 @ ( inf_inf_set_set_nat @ A2 @ ( collect_set_nat @ P ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7944_sum__mult__of__bool__eq,axiom,
% 9.25/5.25      ! [A2: set_set_nat,F2: set_nat > rat,P: set_nat > $o] :
% 9.25/5.25        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.25       => ( ( groups7659867448343625626at_rat
% 9.25/5.25            @ ^ [X3: set_nat] : ( times_times_rat @ ( F2 @ X3 ) @ ( zero_n2052037380579107095ol_rat @ ( P @ X3 ) ) )
% 9.25/5.25            @ A2 )
% 9.25/5.25          = ( groups7659867448343625626at_rat @ F2 @ ( inf_inf_set_set_nat @ A2 @ ( collect_set_nat @ P ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7945_sum__of__bool__mult__eq,axiom,
% 9.25/5.25      ! [A2: set_int,P: int > $o,F2: int > code_integer] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups7873554091576472773nteger
% 9.25/5.25            @ ^ [X3: int] : ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( P @ X3 ) ) @ ( F2 @ X3 ) )
% 9.25/5.25            @ A2 )
% 9.25/5.25          = ( groups7873554091576472773nteger @ F2 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7946_sum__of__bool__mult__eq,axiom,
% 9.25/5.25      ! [A2: set_nat,P: nat > $o,F2: nat > code_integer] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups7501900531339628137nteger
% 9.25/5.25            @ ^ [X3: nat] : ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( P @ X3 ) ) @ ( F2 @ X3 ) )
% 9.25/5.25            @ A2 )
% 9.25/5.25          = ( groups7501900531339628137nteger @ F2 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7947_sum__of__bool__mult__eq,axiom,
% 9.25/5.25      ! [A2: set_int,P: int > $o,F2: int > rat] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups3906332499630173760nt_rat
% 9.25/5.25            @ ^ [X3: int] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P @ X3 ) ) @ ( F2 @ X3 ) )
% 9.25/5.25            @ A2 )
% 9.25/5.25          = ( groups3906332499630173760nt_rat @ F2 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7948_sum__of__bool__mult__eq,axiom,
% 9.25/5.25      ! [A2: set_nat,P: nat > $o,F2: nat > rat] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups2906978787729119204at_rat
% 9.25/5.25            @ ^ [X3: nat] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P @ X3 ) ) @ ( F2 @ X3 ) )
% 9.25/5.25            @ A2 )
% 9.25/5.25          = ( groups2906978787729119204at_rat @ F2 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7949_sum__of__bool__mult__eq,axiom,
% 9.25/5.25      ! [A2: set_nat,P: nat > $o,F2: nat > int] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups3539618377306564664at_int
% 9.25/5.25            @ ^ [X3: nat] : ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( P @ X3 ) ) @ ( F2 @ X3 ) )
% 9.25/5.25            @ A2 )
% 9.25/5.25          = ( groups3539618377306564664at_int @ F2 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7950_sum__of__bool__mult__eq,axiom,
% 9.25/5.25      ! [A2: set_int,P: int > $o,F2: int > nat] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups4541462559716669496nt_nat
% 9.25/5.25            @ ^ [X3: int] : ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( P @ X3 ) ) @ ( F2 @ X3 ) )
% 9.25/5.25            @ A2 )
% 9.25/5.25          = ( groups4541462559716669496nt_nat @ F2 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7951_sum__of__bool__mult__eq,axiom,
% 9.25/5.25      ! [A2: set_nat,P: nat > $o,F2: nat > nat] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups3542108847815614940at_nat
% 9.25/5.25            @ ^ [X3: nat] : ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( P @ X3 ) ) @ ( F2 @ X3 ) )
% 9.25/5.25            @ A2 )
% 9.25/5.25          = ( groups3542108847815614940at_nat @ F2 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7952_sum__of__bool__mult__eq,axiom,
% 9.25/5.25      ! [A2: set_int,P: int > $o,F2: int > int] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups4538972089207619220nt_int
% 9.25/5.25            @ ^ [X3: int] : ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( P @ X3 ) ) @ ( F2 @ X3 ) )
% 9.25/5.25            @ A2 )
% 9.25/5.25          = ( groups4538972089207619220nt_int @ F2 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7953_sum__of__bool__mult__eq,axiom,
% 9.25/5.25      ! [A2: set_set_nat,P: set_nat > $o,F2: set_nat > code_integer] :
% 9.25/5.25        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.25       => ( ( groups9190459664516455967nteger
% 9.25/5.25            @ ^ [X3: set_nat] : ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( P @ X3 ) ) @ ( F2 @ X3 ) )
% 9.25/5.25            @ A2 )
% 9.25/5.25          = ( groups9190459664516455967nteger @ F2 @ ( inf_inf_set_set_nat @ A2 @ ( collect_set_nat @ P ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7954_sum__of__bool__mult__eq,axiom,
% 9.25/5.25      ! [A2: set_set_nat,P: set_nat > $o,F2: set_nat > rat] :
% 9.25/5.25        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.25       => ( ( groups7659867448343625626at_rat
% 9.25/5.25            @ ^ [X3: set_nat] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P @ X3 ) ) @ ( F2 @ X3 ) )
% 9.25/5.25            @ A2 )
% 9.25/5.25          = ( groups7659867448343625626at_rat @ F2 @ ( inf_inf_set_set_nat @ A2 @ ( collect_set_nat @ P ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7955_drop__bit__numeral__minus__bit0,axiom,
% 9.25/5.25      ! [L: num,K: num] :
% 9.25/5.25        ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 9.25/5.25        = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7956_sum__zero__power,axiom,
% 9.25/5.25      ! [A2: set_nat,C: nat > rat] :
% 9.25/5.25        ( ( ( ( finite_finite_nat @ A2 )
% 9.25/5.25            & ( member_nat @ zero_zero_nat @ A2 ) )
% 9.25/5.25         => ( ( groups2906978787729119204at_rat
% 9.25/5.25              @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( C @ zero_zero_nat ) ) )
% 9.25/5.25        & ( ~ ( ( finite_finite_nat @ A2 )
% 9.25/5.25              & ( member_nat @ zero_zero_nat @ A2 ) )
% 9.25/5.25         => ( ( groups2906978787729119204at_rat
% 9.25/5.25              @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ zero_zero_rat @ I3 ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = zero_zero_rat ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7957_drop__bit__Suc__minus__bit1,axiom,
% 9.25/5.25      ! [N: nat,K: num] :
% 9.25/5.25        ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 9.25/5.25        = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7958_int__prod,axiom,
% 9.25/5.25      ! [F2: int > nat,A2: set_int] :
% 9.25/5.25        ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F2 @ A2 ) )
% 9.25/5.25        = ( groups1705073143266064639nt_int
% 9.25/5.25          @ ^ [X3: int] : ( semiri1314217659103216013at_int @ ( F2 @ X3 ) )
% 9.25/5.25          @ A2 ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7959_int__prod,axiom,
% 9.25/5.25      ! [F2: nat > nat,A2: set_nat] :
% 9.25/5.25        ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F2 @ A2 ) )
% 9.25/5.25        = ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [X3: nat] : ( semiri1314217659103216013at_int @ ( F2 @ X3 ) )
% 9.25/5.25          @ A2 ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7960_finite__if__eq__beyond__finite,axiom,
% 9.25/5.25      ! [S: set_Pr958786334691620121nt_int,S5: set_Pr958786334691620121nt_int] :
% 9.25/5.25        ( ( finite2998713641127702882nt_int @ S )
% 9.25/5.25       => ( finite8744585540193469122nt_int
% 9.25/5.25          @ ( collec5210948495886036740nt_int
% 9.25/5.25            @ ^ [S2: set_Pr958786334691620121nt_int] :
% 9.25/5.25                ( ( minus_1052850069191792384nt_int @ S2 @ S )
% 9.25/5.25                = ( minus_1052850069191792384nt_int @ S5 @ S ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7961_finite__if__eq__beyond__finite,axiom,
% 9.25/5.25      ! [S: set_int,S5: set_int] :
% 9.25/5.25        ( ( finite_finite_int @ S )
% 9.25/5.25       => ( finite6197958912794628473et_int
% 9.25/5.25          @ ( collect_set_int
% 9.25/5.25            @ ^ [S2: set_int] :
% 9.25/5.25                ( ( minus_minus_set_int @ S2 @ S )
% 9.25/5.25                = ( minus_minus_set_int @ S5 @ S ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7962_finite__if__eq__beyond__finite,axiom,
% 9.25/5.25      ! [S: set_Pr1261947904930325089at_nat,S5: set_Pr1261947904930325089at_nat] :
% 9.25/5.25        ( ( finite6177210948735845034at_nat @ S )
% 9.25/5.25       => ( finite9047747110432174090at_nat
% 9.25/5.25          @ ( collec5514110066124741708at_nat
% 9.25/5.25            @ ^ [S2: set_Pr1261947904930325089at_nat] :
% 9.25/5.25                ( ( minus_1356011639430497352at_nat @ S2 @ S )
% 9.25/5.25                = ( minus_1356011639430497352at_nat @ S5 @ S ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7963_finite__if__eq__beyond__finite,axiom,
% 9.25/5.25      ! [S: set_nat,S5: set_nat] :
% 9.25/5.25        ( ( finite_finite_nat @ S )
% 9.25/5.25       => ( finite1152437895449049373et_nat
% 9.25/5.25          @ ( collect_set_nat
% 9.25/5.25            @ ^ [S2: set_nat] :
% 9.25/5.25                ( ( minus_minus_set_nat @ S2 @ S )
% 9.25/5.25                = ( minus_minus_set_nat @ S5 @ S ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7964_sgn__mult,axiom,
% 9.25/5.25      ! [A: code_integer,B: code_integer] :
% 9.25/5.25        ( ( sgn_sgn_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 9.25/5.25        = ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ B ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7965_sgn__mult,axiom,
% 9.25/5.25      ! [A: rat,B: rat] :
% 9.25/5.25        ( ( sgn_sgn_rat @ ( times_times_rat @ A @ B ) )
% 9.25/5.25        = ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7966_sgn__mult,axiom,
% 9.25/5.25      ! [A: int,B: int] :
% 9.25/5.25        ( ( sgn_sgn_int @ ( times_times_int @ A @ B ) )
% 9.25/5.25        = ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7967_lessThan__non__empty,axiom,
% 9.25/5.25      ! [X: int] :
% 9.25/5.25        ( ( set_ord_lessThan_int @ X )
% 9.25/5.25       != bot_bot_set_int ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7968_finite__M__bounded__by__nat,axiom,
% 9.25/5.25      ! [P: nat > $o,I: nat] :
% 9.25/5.25        ( finite_finite_nat
% 9.25/5.25        @ ( collect_nat
% 9.25/5.25          @ ^ [K4: nat] :
% 9.25/5.25              ( ( P @ K4 )
% 9.25/5.25              & ( ord_less_nat @ K4 @ I ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7969_finite__less__ub,axiom,
% 9.25/5.25      ! [F2: nat > nat,U: nat] :
% 9.25/5.25        ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F2 @ N3 ) )
% 9.25/5.25       => ( finite_finite_nat
% 9.25/5.25          @ ( collect_nat
% 9.25/5.25            @ ^ [N2: nat] : ( ord_less_eq_nat @ ( F2 @ N2 ) @ U ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7970_sum_Oswap__restrict,axiom,
% 9.25/5.25      ! [A2: set_int,B2: set_nat,G2: int > nat > nat,R: int > nat > $o] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( finite_finite_nat @ B2 )
% 9.25/5.25         => ( ( groups4541462559716669496nt_nat
% 9.25/5.25              @ ^ [X3: int] :
% 9.25/5.25                  ( groups3542108847815614940at_nat @ ( G2 @ X3 )
% 9.25/5.25                  @ ( collect_nat
% 9.25/5.25                    @ ^ [Y3: nat] :
% 9.25/5.25                        ( ( member_nat @ Y3 @ B2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( groups3542108847815614940at_nat
% 9.25/5.25              @ ^ [Y3: nat] :
% 9.25/5.25                  ( groups4541462559716669496nt_nat
% 9.25/5.25                  @ ^ [X3: int] : ( G2 @ X3 @ Y3 )
% 9.25/5.25                  @ ( collect_int
% 9.25/5.25                    @ ^ [X3: int] :
% 9.25/5.25                        ( ( member_int @ X3 @ A2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ B2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7971_sum_Oswap__restrict,axiom,
% 9.25/5.25      ! [A2: set_nat,B2: set_int,G2: nat > int > int,R: nat > int > $o] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( finite_finite_int @ B2 )
% 9.25/5.25         => ( ( groups3539618377306564664at_int
% 9.25/5.25              @ ^ [X3: nat] :
% 9.25/5.25                  ( groups4538972089207619220nt_int @ ( G2 @ X3 )
% 9.25/5.25                  @ ( collect_int
% 9.25/5.25                    @ ^ [Y3: int] :
% 9.25/5.25                        ( ( member_int @ Y3 @ B2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( groups4538972089207619220nt_int
% 9.25/5.25              @ ^ [Y3: int] :
% 9.25/5.25                  ( groups3539618377306564664at_int
% 9.25/5.25                  @ ^ [X3: nat] : ( G2 @ X3 @ Y3 )
% 9.25/5.25                  @ ( collect_nat
% 9.25/5.25                    @ ^ [X3: nat] :
% 9.25/5.25                        ( ( member_nat @ X3 @ A2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ B2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7972_sum_Oswap__restrict,axiom,
% 9.25/5.25      ! [A2: set_nat,B2: set_int,G2: nat > int > nat,R: nat > int > $o] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( finite_finite_int @ B2 )
% 9.25/5.25         => ( ( groups3542108847815614940at_nat
% 9.25/5.25              @ ^ [X3: nat] :
% 9.25/5.25                  ( groups4541462559716669496nt_nat @ ( G2 @ X3 )
% 9.25/5.25                  @ ( collect_int
% 9.25/5.25                    @ ^ [Y3: int] :
% 9.25/5.25                        ( ( member_int @ Y3 @ B2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( groups4541462559716669496nt_nat
% 9.25/5.25              @ ^ [Y3: int] :
% 9.25/5.25                  ( groups3542108847815614940at_nat
% 9.25/5.25                  @ ^ [X3: nat] : ( G2 @ X3 @ Y3 )
% 9.25/5.25                  @ ( collect_nat
% 9.25/5.25                    @ ^ [X3: nat] :
% 9.25/5.25                        ( ( member_nat @ X3 @ A2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ B2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7973_sum_Oswap__restrict,axiom,
% 9.25/5.25      ! [A2: set_nat,B2: set_nat,G2: nat > nat > nat,R: nat > nat > $o] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( finite_finite_nat @ B2 )
% 9.25/5.25         => ( ( groups3542108847815614940at_nat
% 9.25/5.25              @ ^ [X3: nat] :
% 9.25/5.25                  ( groups3542108847815614940at_nat @ ( G2 @ X3 )
% 9.25/5.25                  @ ( collect_nat
% 9.25/5.25                    @ ^ [Y3: nat] :
% 9.25/5.25                        ( ( member_nat @ Y3 @ B2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( groups3542108847815614940at_nat
% 9.25/5.25              @ ^ [Y3: nat] :
% 9.25/5.25                  ( groups3542108847815614940at_nat
% 9.25/5.25                  @ ^ [X3: nat] : ( G2 @ X3 @ Y3 )
% 9.25/5.25                  @ ( collect_nat
% 9.25/5.25                    @ ^ [X3: nat] :
% 9.25/5.25                        ( ( member_nat @ X3 @ A2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ B2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7974_sum_Oswap__restrict,axiom,
% 9.25/5.25      ! [A2: set_int,B2: set_nat,G2: int > nat > int,R: int > nat > $o] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( finite_finite_nat @ B2 )
% 9.25/5.25         => ( ( groups4538972089207619220nt_int
% 9.25/5.25              @ ^ [X3: int] :
% 9.25/5.25                  ( groups3539618377306564664at_int @ ( G2 @ X3 )
% 9.25/5.25                  @ ( collect_nat
% 9.25/5.25                    @ ^ [Y3: nat] :
% 9.25/5.25                        ( ( member_nat @ Y3 @ B2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( groups3539618377306564664at_int
% 9.25/5.25              @ ^ [Y3: nat] :
% 9.25/5.25                  ( groups4538972089207619220nt_int
% 9.25/5.25                  @ ^ [X3: int] : ( G2 @ X3 @ Y3 )
% 9.25/5.25                  @ ( collect_int
% 9.25/5.25                    @ ^ [X3: int] :
% 9.25/5.25                        ( ( member_int @ X3 @ A2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ B2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7975_sum_Oswap__restrict,axiom,
% 9.25/5.25      ! [A2: set_int,B2: set_int,G2: int > int > int,R: int > int > $o] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( finite_finite_int @ B2 )
% 9.25/5.25         => ( ( groups4538972089207619220nt_int
% 9.25/5.25              @ ^ [X3: int] :
% 9.25/5.25                  ( groups4538972089207619220nt_int @ ( G2 @ X3 )
% 9.25/5.25                  @ ( collect_int
% 9.25/5.25                    @ ^ [Y3: int] :
% 9.25/5.25                        ( ( member_int @ Y3 @ B2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( groups4538972089207619220nt_int
% 9.25/5.25              @ ^ [Y3: int] :
% 9.25/5.25                  ( groups4538972089207619220nt_int
% 9.25/5.25                  @ ^ [X3: int] : ( G2 @ X3 @ Y3 )
% 9.25/5.25                  @ ( collect_int
% 9.25/5.25                    @ ^ [X3: int] :
% 9.25/5.25                        ( ( member_int @ X3 @ A2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ B2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7976_sum_Oswap__restrict,axiom,
% 9.25/5.25      ! [A2: set_set_nat,B2: set_nat,G2: set_nat > nat > nat,R: set_nat > nat > $o] :
% 9.25/5.25        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.25       => ( ( finite_finite_nat @ B2 )
% 9.25/5.25         => ( ( groups8294997508430121362at_nat
% 9.25/5.25              @ ^ [X3: set_nat] :
% 9.25/5.25                  ( groups3542108847815614940at_nat @ ( G2 @ X3 )
% 9.25/5.25                  @ ( collect_nat
% 9.25/5.25                    @ ^ [Y3: nat] :
% 9.25/5.25                        ( ( member_nat @ Y3 @ B2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( groups3542108847815614940at_nat
% 9.25/5.25              @ ^ [Y3: nat] :
% 9.25/5.25                  ( groups8294997508430121362at_nat
% 9.25/5.25                  @ ^ [X3: set_nat] : ( G2 @ X3 @ Y3 )
% 9.25/5.25                  @ ( collect_set_nat
% 9.25/5.25                    @ ^ [X3: set_nat] :
% 9.25/5.25                        ( ( member_set_nat @ X3 @ A2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ B2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7977_sum_Oswap__restrict,axiom,
% 9.25/5.25      ! [A2: set_set_nat,B2: set_int,G2: set_nat > int > int,R: set_nat > int > $o] :
% 9.25/5.25        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.25       => ( ( finite_finite_int @ B2 )
% 9.25/5.25         => ( ( groups8292507037921071086at_int
% 9.25/5.25              @ ^ [X3: set_nat] :
% 9.25/5.25                  ( groups4538972089207619220nt_int @ ( G2 @ X3 )
% 9.25/5.25                  @ ( collect_int
% 9.25/5.25                    @ ^ [Y3: int] :
% 9.25/5.25                        ( ( member_int @ Y3 @ B2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( groups4538972089207619220nt_int
% 9.25/5.25              @ ^ [Y3: int] :
% 9.25/5.25                  ( groups8292507037921071086at_int
% 9.25/5.25                  @ ^ [X3: set_nat] : ( G2 @ X3 @ Y3 )
% 9.25/5.25                  @ ( collect_set_nat
% 9.25/5.25                    @ ^ [X3: set_nat] :
% 9.25/5.25                        ( ( member_set_nat @ X3 @ A2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ B2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7978_sum_Oswap__restrict,axiom,
% 9.25/5.25      ! [A2: set_nat,B2: set_set_nat,G2: nat > set_nat > nat,R: nat > set_nat > $o] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( finite1152437895449049373et_nat @ B2 )
% 9.25/5.25         => ( ( groups3542108847815614940at_nat
% 9.25/5.25              @ ^ [X3: nat] :
% 9.25/5.25                  ( groups8294997508430121362at_nat @ ( G2 @ X3 )
% 9.25/5.25                  @ ( collect_set_nat
% 9.25/5.25                    @ ^ [Y3: set_nat] :
% 9.25/5.25                        ( ( member_set_nat @ Y3 @ B2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( groups8294997508430121362at_nat
% 9.25/5.25              @ ^ [Y3: set_nat] :
% 9.25/5.25                  ( groups3542108847815614940at_nat
% 9.25/5.25                  @ ^ [X3: nat] : ( G2 @ X3 @ Y3 )
% 9.25/5.25                  @ ( collect_nat
% 9.25/5.25                    @ ^ [X3: nat] :
% 9.25/5.25                        ( ( member_nat @ X3 @ A2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ B2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7979_sum_Oswap__restrict,axiom,
% 9.25/5.25      ! [A2: set_int,B2: set_set_nat,G2: int > set_nat > int,R: int > set_nat > $o] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( finite1152437895449049373et_nat @ B2 )
% 9.25/5.25         => ( ( groups4538972089207619220nt_int
% 9.25/5.25              @ ^ [X3: int] :
% 9.25/5.25                  ( groups8292507037921071086at_int @ ( G2 @ X3 )
% 9.25/5.25                  @ ( collect_set_nat
% 9.25/5.25                    @ ^ [Y3: set_nat] :
% 9.25/5.25                        ( ( member_set_nat @ Y3 @ B2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( groups8292507037921071086at_int
% 9.25/5.25              @ ^ [Y3: set_nat] :
% 9.25/5.25                  ( groups4538972089207619220nt_int
% 9.25/5.25                  @ ^ [X3: int] : ( G2 @ X3 @ Y3 )
% 9.25/5.25                  @ ( collect_int
% 9.25/5.25                    @ ^ [X3: int] :
% 9.25/5.25                        ( ( member_int @ X3 @ A2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ B2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7980_prod_Oswap__restrict,axiom,
% 9.25/5.25      ! [A2: set_int,B2: set_nat,G2: int > nat > nat,R: int > nat > $o] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( finite_finite_nat @ B2 )
% 9.25/5.25         => ( ( groups1707563613775114915nt_nat
% 9.25/5.25              @ ^ [X3: int] :
% 9.25/5.25                  ( groups708209901874060359at_nat @ ( G2 @ X3 )
% 9.25/5.25                  @ ( collect_nat
% 9.25/5.25                    @ ^ [Y3: nat] :
% 9.25/5.25                        ( ( member_nat @ Y3 @ B2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( groups708209901874060359at_nat
% 9.25/5.25              @ ^ [Y3: nat] :
% 9.25/5.25                  ( groups1707563613775114915nt_nat
% 9.25/5.25                  @ ^ [X3: int] : ( G2 @ X3 @ Y3 )
% 9.25/5.25                  @ ( collect_int
% 9.25/5.25                    @ ^ [X3: int] :
% 9.25/5.25                        ( ( member_int @ X3 @ A2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ B2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7981_prod_Oswap__restrict,axiom,
% 9.25/5.25      ! [A2: set_nat,B2: set_int,G2: nat > int > nat,R: nat > int > $o] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( finite_finite_int @ B2 )
% 9.25/5.25         => ( ( groups708209901874060359at_nat
% 9.25/5.25              @ ^ [X3: nat] :
% 9.25/5.25                  ( groups1707563613775114915nt_nat @ ( G2 @ X3 )
% 9.25/5.25                  @ ( collect_int
% 9.25/5.25                    @ ^ [Y3: int] :
% 9.25/5.25                        ( ( member_int @ Y3 @ B2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( groups1707563613775114915nt_nat
% 9.25/5.25              @ ^ [Y3: int] :
% 9.25/5.25                  ( groups708209901874060359at_nat
% 9.25/5.25                  @ ^ [X3: nat] : ( G2 @ X3 @ Y3 )
% 9.25/5.25                  @ ( collect_nat
% 9.25/5.25                    @ ^ [X3: nat] :
% 9.25/5.25                        ( ( member_nat @ X3 @ A2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ B2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7982_prod_Oswap__restrict,axiom,
% 9.25/5.25      ! [A2: set_nat,B2: set_nat,G2: nat > nat > nat,R: nat > nat > $o] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( finite_finite_nat @ B2 )
% 9.25/5.25         => ( ( groups708209901874060359at_nat
% 9.25/5.25              @ ^ [X3: nat] :
% 9.25/5.25                  ( groups708209901874060359at_nat @ ( G2 @ X3 )
% 9.25/5.25                  @ ( collect_nat
% 9.25/5.25                    @ ^ [Y3: nat] :
% 9.25/5.25                        ( ( member_nat @ Y3 @ B2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( groups708209901874060359at_nat
% 9.25/5.25              @ ^ [Y3: nat] :
% 9.25/5.25                  ( groups708209901874060359at_nat
% 9.25/5.25                  @ ^ [X3: nat] : ( G2 @ X3 @ Y3 )
% 9.25/5.25                  @ ( collect_nat
% 9.25/5.25                    @ ^ [X3: nat] :
% 9.25/5.25                        ( ( member_nat @ X3 @ A2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ B2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7983_prod_Oswap__restrict,axiom,
% 9.25/5.25      ! [A2: set_nat,B2: set_nat,G2: nat > nat > int,R: nat > nat > $o] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( finite_finite_nat @ B2 )
% 9.25/5.25         => ( ( groups705719431365010083at_int
% 9.25/5.25              @ ^ [X3: nat] :
% 9.25/5.25                  ( groups705719431365010083at_int @ ( G2 @ X3 )
% 9.25/5.25                  @ ( collect_nat
% 9.25/5.25                    @ ^ [Y3: nat] :
% 9.25/5.25                        ( ( member_nat @ Y3 @ B2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( groups705719431365010083at_int
% 9.25/5.25              @ ^ [Y3: nat] :
% 9.25/5.25                  ( groups705719431365010083at_int
% 9.25/5.25                  @ ^ [X3: nat] : ( G2 @ X3 @ Y3 )
% 9.25/5.25                  @ ( collect_nat
% 9.25/5.25                    @ ^ [X3: nat] :
% 9.25/5.25                        ( ( member_nat @ X3 @ A2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ B2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7984_prod_Oswap__restrict,axiom,
% 9.25/5.25      ! [A2: set_nat,B2: set_int,G2: nat > int > int,R: nat > int > $o] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( finite_finite_int @ B2 )
% 9.25/5.25         => ( ( groups705719431365010083at_int
% 9.25/5.25              @ ^ [X3: nat] :
% 9.25/5.25                  ( groups1705073143266064639nt_int @ ( G2 @ X3 )
% 9.25/5.25                  @ ( collect_int
% 9.25/5.25                    @ ^ [Y3: int] :
% 9.25/5.25                        ( ( member_int @ Y3 @ B2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( groups1705073143266064639nt_int
% 9.25/5.25              @ ^ [Y3: int] :
% 9.25/5.25                  ( groups705719431365010083at_int
% 9.25/5.25                  @ ^ [X3: nat] : ( G2 @ X3 @ Y3 )
% 9.25/5.25                  @ ( collect_nat
% 9.25/5.25                    @ ^ [X3: nat] :
% 9.25/5.25                        ( ( member_nat @ X3 @ A2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ B2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7985_prod_Oswap__restrict,axiom,
% 9.25/5.25      ! [A2: set_int,B2: set_nat,G2: int > nat > int,R: int > nat > $o] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( finite_finite_nat @ B2 )
% 9.25/5.25         => ( ( groups1705073143266064639nt_int
% 9.25/5.25              @ ^ [X3: int] :
% 9.25/5.25                  ( groups705719431365010083at_int @ ( G2 @ X3 )
% 9.25/5.25                  @ ( collect_nat
% 9.25/5.25                    @ ^ [Y3: nat] :
% 9.25/5.25                        ( ( member_nat @ Y3 @ B2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( groups705719431365010083at_int
% 9.25/5.25              @ ^ [Y3: nat] :
% 9.25/5.25                  ( groups1705073143266064639nt_int
% 9.25/5.25                  @ ^ [X3: int] : ( G2 @ X3 @ Y3 )
% 9.25/5.25                  @ ( collect_int
% 9.25/5.25                    @ ^ [X3: int] :
% 9.25/5.25                        ( ( member_int @ X3 @ A2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ B2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7986_prod_Oswap__restrict,axiom,
% 9.25/5.25      ! [A2: set_int,B2: set_int,G2: int > int > int,R: int > int > $o] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( finite_finite_int @ B2 )
% 9.25/5.25         => ( ( groups1705073143266064639nt_int
% 9.25/5.25              @ ^ [X3: int] :
% 9.25/5.25                  ( groups1705073143266064639nt_int @ ( G2 @ X3 )
% 9.25/5.25                  @ ( collect_int
% 9.25/5.25                    @ ^ [Y3: int] :
% 9.25/5.25                        ( ( member_int @ Y3 @ B2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( groups1705073143266064639nt_int
% 9.25/5.25              @ ^ [Y3: int] :
% 9.25/5.25                  ( groups1705073143266064639nt_int
% 9.25/5.25                  @ ^ [X3: int] : ( G2 @ X3 @ Y3 )
% 9.25/5.25                  @ ( collect_int
% 9.25/5.25                    @ ^ [X3: int] :
% 9.25/5.25                        ( ( member_int @ X3 @ A2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ B2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7987_prod_Oswap__restrict,axiom,
% 9.25/5.25      ! [A2: set_set_nat,B2: set_nat,G2: set_nat > nat > nat,R: set_nat > nat > $o] :
% 9.25/5.25        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.25       => ( ( finite_finite_nat @ B2 )
% 9.25/5.25         => ( ( groups4248547760180025341at_nat
% 9.25/5.25              @ ^ [X3: set_nat] :
% 9.25/5.25                  ( groups708209901874060359at_nat @ ( G2 @ X3 )
% 9.25/5.25                  @ ( collect_nat
% 9.25/5.25                    @ ^ [Y3: nat] :
% 9.25/5.25                        ( ( member_nat @ Y3 @ B2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( groups708209901874060359at_nat
% 9.25/5.25              @ ^ [Y3: nat] :
% 9.25/5.25                  ( groups4248547760180025341at_nat
% 9.25/5.25                  @ ^ [X3: set_nat] : ( G2 @ X3 @ Y3 )
% 9.25/5.25                  @ ( collect_set_nat
% 9.25/5.25                    @ ^ [X3: set_nat] :
% 9.25/5.25                        ( ( member_set_nat @ X3 @ A2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ B2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7988_prod_Oswap__restrict,axiom,
% 9.25/5.25      ! [A2: set_set_nat,B2: set_nat,G2: set_nat > nat > int,R: set_nat > nat > $o] :
% 9.25/5.25        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.25       => ( ( finite_finite_nat @ B2 )
% 9.25/5.25         => ( ( groups4246057289670975065at_int
% 9.25/5.25              @ ^ [X3: set_nat] :
% 9.25/5.25                  ( groups705719431365010083at_int @ ( G2 @ X3 )
% 9.25/5.25                  @ ( collect_nat
% 9.25/5.25                    @ ^ [Y3: nat] :
% 9.25/5.25                        ( ( member_nat @ Y3 @ B2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( groups705719431365010083at_int
% 9.25/5.25              @ ^ [Y3: nat] :
% 9.25/5.25                  ( groups4246057289670975065at_int
% 9.25/5.25                  @ ^ [X3: set_nat] : ( G2 @ X3 @ Y3 )
% 9.25/5.25                  @ ( collect_set_nat
% 9.25/5.25                    @ ^ [X3: set_nat] :
% 9.25/5.25                        ( ( member_set_nat @ X3 @ A2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ B2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7989_prod_Oswap__restrict,axiom,
% 9.25/5.25      ! [A2: set_set_nat,B2: set_int,G2: set_nat > int > int,R: set_nat > int > $o] :
% 9.25/5.25        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.25       => ( ( finite_finite_int @ B2 )
% 9.25/5.25         => ( ( groups4246057289670975065at_int
% 9.25/5.25              @ ^ [X3: set_nat] :
% 9.25/5.25                  ( groups1705073143266064639nt_int @ ( G2 @ X3 )
% 9.25/5.25                  @ ( collect_int
% 9.25/5.25                    @ ^ [Y3: int] :
% 9.25/5.25                        ( ( member_int @ Y3 @ B2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ A2 )
% 9.25/5.25            = ( groups1705073143266064639nt_int
% 9.25/5.25              @ ^ [Y3: int] :
% 9.25/5.25                  ( groups4246057289670975065at_int
% 9.25/5.25                  @ ^ [X3: set_nat] : ( G2 @ X3 @ Y3 )
% 9.25/5.25                  @ ( collect_set_nat
% 9.25/5.25                    @ ^ [X3: set_nat] :
% 9.25/5.25                        ( ( member_set_nat @ X3 @ A2 )
% 9.25/5.25                        & ( R @ X3 @ Y3 ) ) ) )
% 9.25/5.25              @ B2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7990_lessThan__def,axiom,
% 9.25/5.25      ( set_or4940836740269066044nt_int
% 9.25/5.25      = ( ^ [U2: set_Pr958786334691620121nt_int] :
% 9.25/5.25            ( collec5210948495886036740nt_int
% 9.25/5.25            @ ^ [X3: set_Pr958786334691620121nt_int] : ( ord_le7563427860532173253nt_int @ X3 @ U2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7991_lessThan__def,axiom,
% 9.25/5.25      ( set_or890127255671739683et_nat
% 9.25/5.25      = ( ^ [U2: set_nat] :
% 9.25/5.25            ( collect_set_nat
% 9.25/5.25            @ ^ [X3: set_nat] : ( ord_less_set_nat @ X3 @ U2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7992_lessThan__def,axiom,
% 9.25/5.25      ( set_or7240481858991947888_nat_o
% 9.25/5.25      = ( ^ [U2: produc3658429121746597890et_nat > $o] :
% 9.25/5.25            ( collec939566748876313656_nat_o
% 9.25/5.25            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( ord_le8176553561544679545_nat_o @ X3 @ U2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7993_lessThan__def,axiom,
% 9.25/5.25      ( set_or2436086697161274615iteral
% 9.25/5.25      = ( ^ [U2: literal] :
% 9.25/5.25            ( collect_literal
% 9.25/5.25            @ ^ [X3: literal] : ( ord_less_literal @ X3 @ U2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7994_lessThan__def,axiom,
% 9.25/5.25      ( set_ord_lessThan_rat
% 9.25/5.25      = ( ^ [U2: rat] :
% 9.25/5.25            ( collect_rat
% 9.25/5.25            @ ^ [X3: rat] : ( ord_less_rat @ X3 @ U2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7995_lessThan__def,axiom,
% 9.25/5.25      ( set_ord_lessThan_int
% 9.25/5.25      = ( ^ [U2: int] :
% 9.25/5.25            ( collect_int
% 9.25/5.25            @ ^ [X3: int] : ( ord_less_int @ X3 @ U2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7996_lessThan__def,axiom,
% 9.25/5.25      ( set_ord_lessThan_nat
% 9.25/5.25      = ( ^ [U2: nat] :
% 9.25/5.25            ( collect_nat
% 9.25/5.25            @ ^ [X3: nat] : ( ord_less_nat @ X3 @ U2 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7997_lessThan__empty__iff,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( ( set_ord_lessThan_nat @ N )
% 9.25/5.25          = bot_bot_set_nat )
% 9.25/5.25        = ( N = zero_zero_nat ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7998_sgn__not__eq__imp,axiom,
% 9.25/5.25      ! [B: int,A: int] :
% 9.25/5.25        ( ( ( sgn_sgn_int @ B )
% 9.25/5.25         != ( sgn_sgn_int @ A ) )
% 9.25/5.25       => ( ( ( sgn_sgn_int @ A )
% 9.25/5.25           != zero_zero_int )
% 9.25/5.25         => ( ( ( sgn_sgn_int @ B )
% 9.25/5.25             != zero_zero_int )
% 9.25/5.25           => ( ( sgn_sgn_int @ A )
% 9.25/5.25              = ( uminus_uminus_int @ ( sgn_sgn_int @ B ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_7999_sgn__not__eq__imp,axiom,
% 9.25/5.25      ! [B: code_integer,A: code_integer] :
% 9.25/5.25        ( ( ( sgn_sgn_Code_integer @ B )
% 9.25/5.25         != ( sgn_sgn_Code_integer @ A ) )
% 9.25/5.25       => ( ( ( sgn_sgn_Code_integer @ A )
% 9.25/5.25           != zero_z3403309356797280102nteger )
% 9.25/5.25         => ( ( ( sgn_sgn_Code_integer @ B )
% 9.25/5.25             != zero_z3403309356797280102nteger )
% 9.25/5.25           => ( ( sgn_sgn_Code_integer @ A )
% 9.25/5.25              = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ B ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8000_sgn__not__eq__imp,axiom,
% 9.25/5.25      ! [B: rat,A: rat] :
% 9.25/5.25        ( ( ( sgn_sgn_rat @ B )
% 9.25/5.25         != ( sgn_sgn_rat @ A ) )
% 9.25/5.25       => ( ( ( sgn_sgn_rat @ A )
% 9.25/5.25           != zero_zero_rat )
% 9.25/5.25         => ( ( ( sgn_sgn_rat @ B )
% 9.25/5.25             != zero_zero_rat )
% 9.25/5.25           => ( ( sgn_sgn_rat @ A )
% 9.25/5.25              = ( uminus_uminus_rat @ ( sgn_sgn_rat @ B ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8001_sgn__minus__1,axiom,
% 9.25/5.25      ( ( sgn_sgn_int @ ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.25      = ( uminus_uminus_int @ one_one_int ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8002_sgn__minus__1,axiom,
% 9.25/5.25      ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.25      = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8003_sgn__minus__1,axiom,
% 9.25/5.25      ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.25/5.25      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8004_mult__sgn__abs,axiom,
% 9.25/5.25      ! [X: code_integer] :
% 9.25/5.25        ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ X ) @ ( abs_abs_Code_integer @ X ) )
% 9.25/5.25        = X ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8005_mult__sgn__abs,axiom,
% 9.25/5.25      ! [X: rat] :
% 9.25/5.25        ( ( times_times_rat @ ( sgn_sgn_rat @ X ) @ ( abs_abs_rat @ X ) )
% 9.25/5.25        = X ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8006_mult__sgn__abs,axiom,
% 9.25/5.25      ! [X: int] :
% 9.25/5.25        ( ( times_times_int @ ( sgn_sgn_int @ X ) @ ( abs_abs_int @ X ) )
% 9.25/5.25        = X ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8007_sgn__mult__abs,axiom,
% 9.25/5.25      ! [A: code_integer] :
% 9.25/5.25        ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 9.25/5.25        = A ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8008_sgn__mult__abs,axiom,
% 9.25/5.25      ! [A: rat] :
% 9.25/5.25        ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( abs_abs_rat @ A ) )
% 9.25/5.25        = A ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8009_sgn__mult__abs,axiom,
% 9.25/5.25      ! [A: int] :
% 9.25/5.25        ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( abs_abs_int @ A ) )
% 9.25/5.25        = A ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8010_abs__mult__sgn,axiom,
% 9.25/5.25      ! [A: code_integer] :
% 9.25/5.25        ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 9.25/5.25        = A ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8011_abs__mult__sgn,axiom,
% 9.25/5.25      ! [A: rat] :
% 9.25/5.25        ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 9.25/5.25        = A ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8012_abs__mult__sgn,axiom,
% 9.25/5.25      ! [A: int] :
% 9.25/5.25        ( ( times_times_int @ ( abs_abs_int @ A ) @ ( sgn_sgn_int @ A ) )
% 9.25/5.25        = A ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8013_linordered__idom__class_Oabs__sgn,axiom,
% 9.25/5.25      ( abs_abs_Code_integer
% 9.25/5.25      = ( ^ [K4: code_integer] : ( times_3573771949741848930nteger @ K4 @ ( sgn_sgn_Code_integer @ K4 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8014_linordered__idom__class_Oabs__sgn,axiom,
% 9.25/5.25      ( abs_abs_rat
% 9.25/5.25      = ( ^ [K4: rat] : ( times_times_rat @ K4 @ ( sgn_sgn_rat @ K4 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8015_linordered__idom__class_Oabs__sgn,axiom,
% 9.25/5.25      ( abs_abs_int
% 9.25/5.25      = ( ^ [K4: int] : ( times_times_int @ K4 @ ( sgn_sgn_int @ K4 ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8016_Iio__eq__empty__iff,axiom,
% 9.25/5.25      ! [N: $o] :
% 9.25/5.25        ( ( ( set_ord_lessThan_o @ N )
% 9.25/5.25          = bot_bot_set_o )
% 9.25/5.25        = ( N = bot_bot_o ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8017_Iio__eq__empty__iff,axiom,
% 9.25/5.25      ! [N: nat] :
% 9.25/5.25        ( ( ( set_ord_lessThan_nat @ N )
% 9.25/5.25          = bot_bot_set_nat )
% 9.25/5.25        = ( N = bot_bot_nat ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8018_sum_Ofinite__Collect__op,axiom,
% 9.25/5.25      ! [I4: set_nat,X: nat > code_integer,Y: nat > code_integer] :
% 9.25/5.25        ( ( finite_finite_nat
% 9.25/5.25          @ ( collect_nat
% 9.25/5.25            @ ^ [I3: nat] :
% 9.25/5.25                ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                & ( ( X @ I3 )
% 9.25/5.25                 != zero_z3403309356797280102nteger ) ) ) )
% 9.25/5.25       => ( ( finite_finite_nat
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [I3: nat] :
% 9.25/5.25                  ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( Y @ I3 )
% 9.25/5.25                   != zero_z3403309356797280102nteger ) ) ) )
% 9.25/5.25         => ( finite_finite_nat
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [I3: nat] :
% 9.25/5.25                  ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( plus_p5714425477246183910nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.25/5.25                   != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8019_sum_Ofinite__Collect__op,axiom,
% 9.25/5.25      ! [I4: set_int,X: int > code_integer,Y: int > code_integer] :
% 9.25/5.25        ( ( finite_finite_int
% 9.25/5.25          @ ( collect_int
% 9.25/5.25            @ ^ [I3: int] :
% 9.25/5.25                ( ( member_int @ I3 @ I4 )
% 9.25/5.25                & ( ( X @ I3 )
% 9.25/5.25                 != zero_z3403309356797280102nteger ) ) ) )
% 9.25/5.25       => ( ( finite_finite_int
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [I3: int] :
% 9.25/5.25                  ( ( member_int @ I3 @ I4 )
% 9.25/5.25                  & ( ( Y @ I3 )
% 9.25/5.25                   != zero_z3403309356797280102nteger ) ) ) )
% 9.25/5.25         => ( finite_finite_int
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [I3: int] :
% 9.25/5.25                  ( ( member_int @ I3 @ I4 )
% 9.25/5.25                  & ( ( plus_p5714425477246183910nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.25/5.25                   != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8020_sum_Ofinite__Collect__op,axiom,
% 9.25/5.25      ! [I4: set_nat,X: nat > rat,Y: nat > rat] :
% 9.25/5.25        ( ( finite_finite_nat
% 9.25/5.25          @ ( collect_nat
% 9.25/5.25            @ ^ [I3: nat] :
% 9.25/5.25                ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                & ( ( X @ I3 )
% 9.25/5.25                 != zero_zero_rat ) ) ) )
% 9.25/5.25       => ( ( finite_finite_nat
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [I3: nat] :
% 9.25/5.25                  ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( Y @ I3 )
% 9.25/5.25                   != zero_zero_rat ) ) ) )
% 9.25/5.25         => ( finite_finite_nat
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [I3: nat] :
% 9.25/5.25                  ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.25/5.25                   != zero_zero_rat ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8021_sum_Ofinite__Collect__op,axiom,
% 9.25/5.25      ! [I4: set_int,X: int > rat,Y: int > rat] :
% 9.25/5.25        ( ( finite_finite_int
% 9.25/5.25          @ ( collect_int
% 9.25/5.25            @ ^ [I3: int] :
% 9.25/5.25                ( ( member_int @ I3 @ I4 )
% 9.25/5.25                & ( ( X @ I3 )
% 9.25/5.25                 != zero_zero_rat ) ) ) )
% 9.25/5.25       => ( ( finite_finite_int
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [I3: int] :
% 9.25/5.25                  ( ( member_int @ I3 @ I4 )
% 9.25/5.25                  & ( ( Y @ I3 )
% 9.25/5.25                   != zero_zero_rat ) ) ) )
% 9.25/5.25         => ( finite_finite_int
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [I3: int] :
% 9.25/5.25                  ( ( member_int @ I3 @ I4 )
% 9.25/5.25                  & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.25/5.25                   != zero_zero_rat ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8022_sum_Ofinite__Collect__op,axiom,
% 9.25/5.25      ! [I4: set_nat,X: nat > nat,Y: nat > nat] :
% 9.25/5.25        ( ( finite_finite_nat
% 9.25/5.25          @ ( collect_nat
% 9.25/5.25            @ ^ [I3: nat] :
% 9.25/5.25                ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                & ( ( X @ I3 )
% 9.25/5.25                 != zero_zero_nat ) ) ) )
% 9.25/5.25       => ( ( finite_finite_nat
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [I3: nat] :
% 9.25/5.25                  ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( Y @ I3 )
% 9.25/5.25                   != zero_zero_nat ) ) ) )
% 9.25/5.25         => ( finite_finite_nat
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [I3: nat] :
% 9.25/5.25                  ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( plus_plus_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.25/5.25                   != zero_zero_nat ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8023_sum_Ofinite__Collect__op,axiom,
% 9.25/5.25      ! [I4: set_int,X: int > nat,Y: int > nat] :
% 9.25/5.25        ( ( finite_finite_int
% 9.25/5.25          @ ( collect_int
% 9.25/5.25            @ ^ [I3: int] :
% 9.25/5.25                ( ( member_int @ I3 @ I4 )
% 9.25/5.25                & ( ( X @ I3 )
% 9.25/5.25                 != zero_zero_nat ) ) ) )
% 9.25/5.25       => ( ( finite_finite_int
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [I3: int] :
% 9.25/5.25                  ( ( member_int @ I3 @ I4 )
% 9.25/5.25                  & ( ( Y @ I3 )
% 9.25/5.25                   != zero_zero_nat ) ) ) )
% 9.25/5.25         => ( finite_finite_int
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [I3: int] :
% 9.25/5.25                  ( ( member_int @ I3 @ I4 )
% 9.25/5.25                  & ( ( plus_plus_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.25/5.25                   != zero_zero_nat ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8024_sum_Ofinite__Collect__op,axiom,
% 9.25/5.25      ! [I4: set_nat,X: nat > int,Y: nat > int] :
% 9.25/5.25        ( ( finite_finite_nat
% 9.25/5.25          @ ( collect_nat
% 9.25/5.25            @ ^ [I3: nat] :
% 9.25/5.25                ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                & ( ( X @ I3 )
% 9.25/5.25                 != zero_zero_int ) ) ) )
% 9.25/5.25       => ( ( finite_finite_nat
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [I3: nat] :
% 9.25/5.25                  ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( Y @ I3 )
% 9.25/5.25                   != zero_zero_int ) ) ) )
% 9.25/5.25         => ( finite_finite_nat
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [I3: nat] :
% 9.25/5.25                  ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( plus_plus_int @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.25/5.25                   != zero_zero_int ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8025_sum_Ofinite__Collect__op,axiom,
% 9.25/5.25      ! [I4: set_int,X: int > int,Y: int > int] :
% 9.25/5.25        ( ( finite_finite_int
% 9.25/5.25          @ ( collect_int
% 9.25/5.25            @ ^ [I3: int] :
% 9.25/5.25                ( ( member_int @ I3 @ I4 )
% 9.25/5.25                & ( ( X @ I3 )
% 9.25/5.25                 != zero_zero_int ) ) ) )
% 9.25/5.25       => ( ( finite_finite_int
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [I3: int] :
% 9.25/5.25                  ( ( member_int @ I3 @ I4 )
% 9.25/5.25                  & ( ( Y @ I3 )
% 9.25/5.25                   != zero_zero_int ) ) ) )
% 9.25/5.25         => ( finite_finite_int
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [I3: int] :
% 9.25/5.25                  ( ( member_int @ I3 @ I4 )
% 9.25/5.25                  & ( ( plus_plus_int @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.25/5.25                   != zero_zero_int ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8026_sum_Ofinite__Collect__op,axiom,
% 9.25/5.25      ! [I4: set_set_nat,X: set_nat > code_integer,Y: set_nat > code_integer] :
% 9.25/5.25        ( ( finite1152437895449049373et_nat
% 9.25/5.25          @ ( collect_set_nat
% 9.25/5.25            @ ^ [I3: set_nat] :
% 9.25/5.25                ( ( member_set_nat @ I3 @ I4 )
% 9.25/5.25                & ( ( X @ I3 )
% 9.25/5.25                 != zero_z3403309356797280102nteger ) ) ) )
% 9.25/5.25       => ( ( finite1152437895449049373et_nat
% 9.25/5.25            @ ( collect_set_nat
% 9.25/5.25              @ ^ [I3: set_nat] :
% 9.25/5.25                  ( ( member_set_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( Y @ I3 )
% 9.25/5.25                   != zero_z3403309356797280102nteger ) ) ) )
% 9.25/5.25         => ( finite1152437895449049373et_nat
% 9.25/5.25            @ ( collect_set_nat
% 9.25/5.25              @ ^ [I3: set_nat] :
% 9.25/5.25                  ( ( member_set_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( plus_p5714425477246183910nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.25/5.25                   != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8027_sum_Ofinite__Collect__op,axiom,
% 9.25/5.25      ! [I4: set_set_nat,X: set_nat > rat,Y: set_nat > rat] :
% 9.25/5.25        ( ( finite1152437895449049373et_nat
% 9.25/5.25          @ ( collect_set_nat
% 9.25/5.25            @ ^ [I3: set_nat] :
% 9.25/5.25                ( ( member_set_nat @ I3 @ I4 )
% 9.25/5.25                & ( ( X @ I3 )
% 9.25/5.25                 != zero_zero_rat ) ) ) )
% 9.25/5.25       => ( ( finite1152437895449049373et_nat
% 9.25/5.25            @ ( collect_set_nat
% 9.25/5.25              @ ^ [I3: set_nat] :
% 9.25/5.25                  ( ( member_set_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( Y @ I3 )
% 9.25/5.25                   != zero_zero_rat ) ) ) )
% 9.25/5.25         => ( finite1152437895449049373et_nat
% 9.25/5.25            @ ( collect_set_nat
% 9.25/5.25              @ ^ [I3: set_nat] :
% 9.25/5.25                  ( ( member_set_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( plus_plus_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.25/5.25                   != zero_zero_rat ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8028_prod_Ofinite__Collect__op,axiom,
% 9.25/5.25      ! [I4: set_nat,X: nat > code_integer,Y: nat > code_integer] :
% 9.25/5.25        ( ( finite_finite_nat
% 9.25/5.25          @ ( collect_nat
% 9.25/5.25            @ ^ [I3: nat] :
% 9.25/5.25                ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                & ( ( X @ I3 )
% 9.25/5.25                 != one_one_Code_integer ) ) ) )
% 9.25/5.25       => ( ( finite_finite_nat
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [I3: nat] :
% 9.25/5.25                  ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( Y @ I3 )
% 9.25/5.25                   != one_one_Code_integer ) ) ) )
% 9.25/5.25         => ( finite_finite_nat
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [I3: nat] :
% 9.25/5.25                  ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( times_3573771949741848930nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.25/5.25                   != one_one_Code_integer ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8029_prod_Ofinite__Collect__op,axiom,
% 9.25/5.25      ! [I4: set_int,X: int > code_integer,Y: int > code_integer] :
% 9.25/5.25        ( ( finite_finite_int
% 9.25/5.25          @ ( collect_int
% 9.25/5.25            @ ^ [I3: int] :
% 9.25/5.25                ( ( member_int @ I3 @ I4 )
% 9.25/5.25                & ( ( X @ I3 )
% 9.25/5.25                 != one_one_Code_integer ) ) ) )
% 9.25/5.25       => ( ( finite_finite_int
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [I3: int] :
% 9.25/5.25                  ( ( member_int @ I3 @ I4 )
% 9.25/5.25                  & ( ( Y @ I3 )
% 9.25/5.25                   != one_one_Code_integer ) ) ) )
% 9.25/5.25         => ( finite_finite_int
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [I3: int] :
% 9.25/5.25                  ( ( member_int @ I3 @ I4 )
% 9.25/5.25                  & ( ( times_3573771949741848930nteger @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.25/5.25                   != one_one_Code_integer ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8030_prod_Ofinite__Collect__op,axiom,
% 9.25/5.25      ! [I4: set_nat,X: nat > assn,Y: nat > assn] :
% 9.25/5.25        ( ( finite_finite_nat
% 9.25/5.25          @ ( collect_nat
% 9.25/5.25            @ ^ [I3: nat] :
% 9.25/5.25                ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                & ( ( X @ I3 )
% 9.25/5.25                 != one_one_assn ) ) ) )
% 9.25/5.25       => ( ( finite_finite_nat
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [I3: nat] :
% 9.25/5.25                  ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( Y @ I3 )
% 9.25/5.25                   != one_one_assn ) ) ) )
% 9.25/5.25         => ( finite_finite_nat
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [I3: nat] :
% 9.25/5.25                  ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( times_times_assn @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.25/5.25                   != one_one_assn ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8031_prod_Ofinite__Collect__op,axiom,
% 9.25/5.25      ! [I4: set_int,X: int > assn,Y: int > assn] :
% 9.25/5.25        ( ( finite_finite_int
% 9.25/5.25          @ ( collect_int
% 9.25/5.25            @ ^ [I3: int] :
% 9.25/5.25                ( ( member_int @ I3 @ I4 )
% 9.25/5.25                & ( ( X @ I3 )
% 9.25/5.25                 != one_one_assn ) ) ) )
% 9.25/5.25       => ( ( finite_finite_int
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [I3: int] :
% 9.25/5.25                  ( ( member_int @ I3 @ I4 )
% 9.25/5.25                  & ( ( Y @ I3 )
% 9.25/5.25                   != one_one_assn ) ) ) )
% 9.25/5.25         => ( finite_finite_int
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [I3: int] :
% 9.25/5.25                  ( ( member_int @ I3 @ I4 )
% 9.25/5.25                  & ( ( times_times_assn @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.25/5.25                   != one_one_assn ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8032_prod_Ofinite__Collect__op,axiom,
% 9.25/5.25      ! [I4: set_nat,X: nat > rat,Y: nat > rat] :
% 9.25/5.25        ( ( finite_finite_nat
% 9.25/5.25          @ ( collect_nat
% 9.25/5.25            @ ^ [I3: nat] :
% 9.25/5.25                ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                & ( ( X @ I3 )
% 9.25/5.25                 != one_one_rat ) ) ) )
% 9.25/5.25       => ( ( finite_finite_nat
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [I3: nat] :
% 9.25/5.25                  ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( Y @ I3 )
% 9.25/5.25                   != one_one_rat ) ) ) )
% 9.25/5.25         => ( finite_finite_nat
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [I3: nat] :
% 9.25/5.25                  ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.25/5.25                   != one_one_rat ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8033_prod_Ofinite__Collect__op,axiom,
% 9.25/5.25      ! [I4: set_int,X: int > rat,Y: int > rat] :
% 9.25/5.25        ( ( finite_finite_int
% 9.25/5.25          @ ( collect_int
% 9.25/5.25            @ ^ [I3: int] :
% 9.25/5.25                ( ( member_int @ I3 @ I4 )
% 9.25/5.25                & ( ( X @ I3 )
% 9.25/5.25                 != one_one_rat ) ) ) )
% 9.25/5.25       => ( ( finite_finite_int
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [I3: int] :
% 9.25/5.25                  ( ( member_int @ I3 @ I4 )
% 9.25/5.25                  & ( ( Y @ I3 )
% 9.25/5.25                   != one_one_rat ) ) ) )
% 9.25/5.25         => ( finite_finite_int
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [I3: int] :
% 9.25/5.25                  ( ( member_int @ I3 @ I4 )
% 9.25/5.25                  & ( ( times_times_rat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.25/5.25                   != one_one_rat ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8034_prod_Ofinite__Collect__op,axiom,
% 9.25/5.25      ! [I4: set_nat,X: nat > nat,Y: nat > nat] :
% 9.25/5.25        ( ( finite_finite_nat
% 9.25/5.25          @ ( collect_nat
% 9.25/5.25            @ ^ [I3: nat] :
% 9.25/5.25                ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                & ( ( X @ I3 )
% 9.25/5.25                 != one_one_nat ) ) ) )
% 9.25/5.25       => ( ( finite_finite_nat
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [I3: nat] :
% 9.25/5.25                  ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( Y @ I3 )
% 9.25/5.25                   != one_one_nat ) ) ) )
% 9.25/5.25         => ( finite_finite_nat
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [I3: nat] :
% 9.25/5.25                  ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( times_times_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.25/5.25                   != one_one_nat ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8035_prod_Ofinite__Collect__op,axiom,
% 9.25/5.25      ! [I4: set_int,X: int > nat,Y: int > nat] :
% 9.25/5.25        ( ( finite_finite_int
% 9.25/5.25          @ ( collect_int
% 9.25/5.25            @ ^ [I3: int] :
% 9.25/5.25                ( ( member_int @ I3 @ I4 )
% 9.25/5.25                & ( ( X @ I3 )
% 9.25/5.25                 != one_one_nat ) ) ) )
% 9.25/5.25       => ( ( finite_finite_int
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [I3: int] :
% 9.25/5.25                  ( ( member_int @ I3 @ I4 )
% 9.25/5.25                  & ( ( Y @ I3 )
% 9.25/5.25                   != one_one_nat ) ) ) )
% 9.25/5.25         => ( finite_finite_int
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [I3: int] :
% 9.25/5.25                  ( ( member_int @ I3 @ I4 )
% 9.25/5.25                  & ( ( times_times_nat @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.25/5.25                   != one_one_nat ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8036_prod_Ofinite__Collect__op,axiom,
% 9.25/5.25      ! [I4: set_nat,X: nat > int,Y: nat > int] :
% 9.25/5.25        ( ( finite_finite_nat
% 9.25/5.25          @ ( collect_nat
% 9.25/5.25            @ ^ [I3: nat] :
% 9.25/5.25                ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                & ( ( X @ I3 )
% 9.25/5.25                 != one_one_int ) ) ) )
% 9.25/5.25       => ( ( finite_finite_nat
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [I3: nat] :
% 9.25/5.25                  ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( Y @ I3 )
% 9.25/5.25                   != one_one_int ) ) ) )
% 9.25/5.25         => ( finite_finite_nat
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [I3: nat] :
% 9.25/5.25                  ( ( member_nat @ I3 @ I4 )
% 9.25/5.25                  & ( ( times_times_int @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.25/5.25                   != one_one_int ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8037_prod_Ofinite__Collect__op,axiom,
% 9.25/5.25      ! [I4: set_int,X: int > int,Y: int > int] :
% 9.25/5.25        ( ( finite_finite_int
% 9.25/5.25          @ ( collect_int
% 9.25/5.25            @ ^ [I3: int] :
% 9.25/5.25                ( ( member_int @ I3 @ I4 )
% 9.25/5.25                & ( ( X @ I3 )
% 9.25/5.25                 != one_one_int ) ) ) )
% 9.25/5.25       => ( ( finite_finite_int
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [I3: int] :
% 9.25/5.25                  ( ( member_int @ I3 @ I4 )
% 9.25/5.25                  & ( ( Y @ I3 )
% 9.25/5.25                   != one_one_int ) ) ) )
% 9.25/5.25         => ( finite_finite_int
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [I3: int] :
% 9.25/5.25                  ( ( member_int @ I3 @ I4 )
% 9.25/5.25                  & ( ( times_times_int @ ( X @ I3 ) @ ( Y @ I3 ) )
% 9.25/5.25                   != one_one_int ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8038_sum_Ointer__filter,axiom,
% 9.25/5.25      ! [A2: set_nat,G2: nat > code_integer,P: nat > $o] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups7501900531339628137nteger @ G2
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [X3: nat] :
% 9.25/5.25                  ( ( member_nat @ X3 @ A2 )
% 9.25/5.25                  & ( P @ X3 ) ) ) )
% 9.25/5.25          = ( groups7501900531339628137nteger
% 9.25/5.25            @ ^ [X3: nat] : ( if_Code_integer @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_z3403309356797280102nteger )
% 9.25/5.25            @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8039_sum_Ointer__filter,axiom,
% 9.25/5.25      ! [A2: set_int,G2: int > code_integer,P: int > $o] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups7873554091576472773nteger @ G2
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [X3: int] :
% 9.25/5.25                  ( ( member_int @ X3 @ A2 )
% 9.25/5.25                  & ( P @ X3 ) ) ) )
% 9.25/5.25          = ( groups7873554091576472773nteger
% 9.25/5.25            @ ^ [X3: int] : ( if_Code_integer @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_z3403309356797280102nteger )
% 9.25/5.25            @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8040_sum_Ointer__filter,axiom,
% 9.25/5.25      ! [A2: set_nat,G2: nat > rat,P: nat > $o] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups2906978787729119204at_rat @ G2
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [X3: nat] :
% 9.25/5.25                  ( ( member_nat @ X3 @ A2 )
% 9.25/5.25                  & ( P @ X3 ) ) ) )
% 9.25/5.25          = ( groups2906978787729119204at_rat
% 9.25/5.25            @ ^ [X3: nat] : ( if_rat @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_rat )
% 9.25/5.25            @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8041_sum_Ointer__filter,axiom,
% 9.25/5.25      ! [A2: set_int,G2: int > rat,P: int > $o] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups3906332499630173760nt_rat @ G2
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [X3: int] :
% 9.25/5.25                  ( ( member_int @ X3 @ A2 )
% 9.25/5.25                  & ( P @ X3 ) ) ) )
% 9.25/5.25          = ( groups3906332499630173760nt_rat
% 9.25/5.25            @ ^ [X3: int] : ( if_rat @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_rat )
% 9.25/5.25            @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8042_sum_Ointer__filter,axiom,
% 9.25/5.25      ! [A2: set_int,G2: int > nat,P: int > $o] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups4541462559716669496nt_nat @ G2
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [X3: int] :
% 9.25/5.25                  ( ( member_int @ X3 @ A2 )
% 9.25/5.25                  & ( P @ X3 ) ) ) )
% 9.25/5.25          = ( groups4541462559716669496nt_nat
% 9.25/5.25            @ ^ [X3: int] : ( if_nat @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_nat )
% 9.25/5.25            @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8043_sum_Ointer__filter,axiom,
% 9.25/5.25      ! [A2: set_nat,G2: nat > int,P: nat > $o] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups3539618377306564664at_int @ G2
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [X3: nat] :
% 9.25/5.25                  ( ( member_nat @ X3 @ A2 )
% 9.25/5.25                  & ( P @ X3 ) ) ) )
% 9.25/5.25          = ( groups3539618377306564664at_int
% 9.25/5.25            @ ^ [X3: nat] : ( if_int @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_int )
% 9.25/5.25            @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8044_sum_Ointer__filter,axiom,
% 9.25/5.25      ! [A2: set_nat,G2: nat > nat,P: nat > $o] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups3542108847815614940at_nat @ G2
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [X3: nat] :
% 9.25/5.25                  ( ( member_nat @ X3 @ A2 )
% 9.25/5.25                  & ( P @ X3 ) ) ) )
% 9.25/5.25          = ( groups3542108847815614940at_nat
% 9.25/5.25            @ ^ [X3: nat] : ( if_nat @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_nat )
% 9.25/5.25            @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8045_sum_Ointer__filter,axiom,
% 9.25/5.25      ! [A2: set_int,G2: int > int,P: int > $o] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups4538972089207619220nt_int @ G2
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [X3: int] :
% 9.25/5.25                  ( ( member_int @ X3 @ A2 )
% 9.25/5.25                  & ( P @ X3 ) ) ) )
% 9.25/5.25          = ( groups4538972089207619220nt_int
% 9.25/5.25            @ ^ [X3: int] : ( if_int @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_int )
% 9.25/5.25            @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8046_sum_Ointer__filter,axiom,
% 9.25/5.25      ! [A2: set_set_nat,G2: set_nat > code_integer,P: set_nat > $o] :
% 9.25/5.25        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.25       => ( ( groups9190459664516455967nteger @ G2
% 9.25/5.25            @ ( collect_set_nat
% 9.25/5.25              @ ^ [X3: set_nat] :
% 9.25/5.25                  ( ( member_set_nat @ X3 @ A2 )
% 9.25/5.25                  & ( P @ X3 ) ) ) )
% 9.25/5.25          = ( groups9190459664516455967nteger
% 9.25/5.25            @ ^ [X3: set_nat] : ( if_Code_integer @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_z3403309356797280102nteger )
% 9.25/5.25            @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8047_sum_Ointer__filter,axiom,
% 9.25/5.25      ! [A2: set_set_nat,G2: set_nat > rat,P: set_nat > $o] :
% 9.25/5.25        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.25       => ( ( groups7659867448343625626at_rat @ G2
% 9.25/5.25            @ ( collect_set_nat
% 9.25/5.25              @ ^ [X3: set_nat] :
% 9.25/5.25                  ( ( member_set_nat @ X3 @ A2 )
% 9.25/5.25                  & ( P @ X3 ) ) ) )
% 9.25/5.25          = ( groups7659867448343625626at_rat
% 9.25/5.25            @ ^ [X3: set_nat] : ( if_rat @ ( P @ X3 ) @ ( G2 @ X3 ) @ zero_zero_rat )
% 9.25/5.25            @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8048_prod_Ointer__filter,axiom,
% 9.25/5.25      ! [A2: set_nat,G2: nat > code_integer,P: nat > $o] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups3455450783089532116nteger @ G2
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [X3: nat] :
% 9.25/5.25                  ( ( member_nat @ X3 @ A2 )
% 9.25/5.25                  & ( P @ X3 ) ) ) )
% 9.25/5.25          = ( groups3455450783089532116nteger
% 9.25/5.25            @ ^ [X3: nat] : ( if_Code_integer @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_Code_integer )
% 9.25/5.25            @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8049_prod_Ointer__filter,axiom,
% 9.25/5.25      ! [A2: set_int,G2: int > code_integer,P: int > $o] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups3827104343326376752nteger @ G2
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [X3: int] :
% 9.25/5.25                  ( ( member_int @ X3 @ A2 )
% 9.25/5.25                  & ( P @ X3 ) ) ) )
% 9.25/5.25          = ( groups3827104343326376752nteger
% 9.25/5.25            @ ^ [X3: int] : ( if_Code_integer @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_Code_integer )
% 9.25/5.25            @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8050_prod_Ointer__filter,axiom,
% 9.25/5.25      ! [A2: set_nat,G2: nat > assn,P: nat > $o] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups6906906614972039071t_assn @ G2
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [X3: nat] :
% 9.25/5.25                  ( ( member_nat @ X3 @ A2 )
% 9.25/5.25                  & ( P @ X3 ) ) ) )
% 9.25/5.25          = ( groups6906906614972039071t_assn
% 9.25/5.25            @ ^ [X3: nat] : ( if_assn @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_assn )
% 9.25/5.25            @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8051_prod_Ointer__filter,axiom,
% 9.25/5.25      ! [A2: set_int,G2: int > assn,P: int > $o] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups7882442080178216443t_assn @ G2
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [X3: int] :
% 9.25/5.25                  ( ( member_int @ X3 @ A2 )
% 9.25/5.25                  & ( P @ X3 ) ) ) )
% 9.25/5.25          = ( groups7882442080178216443t_assn
% 9.25/5.25            @ ^ [X3: int] : ( if_assn @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_assn )
% 9.25/5.25            @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8052_prod_Ointer__filter,axiom,
% 9.25/5.25      ! [A2: set_nat,G2: nat > rat,P: nat > $o] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups73079841787564623at_rat @ G2
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [X3: nat] :
% 9.25/5.25                  ( ( member_nat @ X3 @ A2 )
% 9.25/5.25                  & ( P @ X3 ) ) ) )
% 9.25/5.25          = ( groups73079841787564623at_rat
% 9.25/5.25            @ ^ [X3: nat] : ( if_rat @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_rat )
% 9.25/5.25            @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8053_prod_Ointer__filter,axiom,
% 9.25/5.25      ! [A2: set_int,G2: int > rat,P: int > $o] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups1072433553688619179nt_rat @ G2
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [X3: int] :
% 9.25/5.25                  ( ( member_int @ X3 @ A2 )
% 9.25/5.25                  & ( P @ X3 ) ) ) )
% 9.25/5.25          = ( groups1072433553688619179nt_rat
% 9.25/5.25            @ ^ [X3: int] : ( if_rat @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_rat )
% 9.25/5.25            @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8054_prod_Ointer__filter,axiom,
% 9.25/5.25      ! [A2: set_int,G2: int > nat,P: int > $o] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups1707563613775114915nt_nat @ G2
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [X3: int] :
% 9.25/5.25                  ( ( member_int @ X3 @ A2 )
% 9.25/5.25                  & ( P @ X3 ) ) ) )
% 9.25/5.25          = ( groups1707563613775114915nt_nat
% 9.25/5.25            @ ^ [X3: int] : ( if_nat @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_nat )
% 9.25/5.25            @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8055_prod_Ointer__filter,axiom,
% 9.25/5.25      ! [A2: set_nat,G2: nat > nat,P: nat > $o] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups708209901874060359at_nat @ G2
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [X3: nat] :
% 9.25/5.25                  ( ( member_nat @ X3 @ A2 )
% 9.25/5.25                  & ( P @ X3 ) ) ) )
% 9.25/5.25          = ( groups708209901874060359at_nat
% 9.25/5.25            @ ^ [X3: nat] : ( if_nat @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_nat )
% 9.25/5.25            @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8056_prod_Ointer__filter,axiom,
% 9.25/5.25      ! [A2: set_nat,G2: nat > int,P: nat > $o] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( groups705719431365010083at_int @ G2
% 9.25/5.25            @ ( collect_nat
% 9.25/5.25              @ ^ [X3: nat] :
% 9.25/5.25                  ( ( member_nat @ X3 @ A2 )
% 9.25/5.25                  & ( P @ X3 ) ) ) )
% 9.25/5.25          = ( groups705719431365010083at_int
% 9.25/5.25            @ ^ [X3: nat] : ( if_int @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_int )
% 9.25/5.25            @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8057_prod_Ointer__filter,axiom,
% 9.25/5.25      ! [A2: set_int,G2: int > int,P: int > $o] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( groups1705073143266064639nt_int @ G2
% 9.25/5.25            @ ( collect_int
% 9.25/5.25              @ ^ [X3: int] :
% 9.25/5.25                  ( ( member_int @ X3 @ A2 )
% 9.25/5.25                  & ( P @ X3 ) ) ) )
% 9.25/5.25          = ( groups1705073143266064639nt_int
% 9.25/5.25            @ ^ [X3: int] : ( if_int @ ( P @ X3 ) @ ( G2 @ X3 ) @ one_one_int )
% 9.25/5.25            @ A2 ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8058_sum__strict__mono,axiom,
% 9.25/5.25      ! [A2: set_o,F2: $o > rat,G2: $o > rat] :
% 9.25/5.25        ( ( finite_finite_o @ A2 )
% 9.25/5.25       => ( ( A2 != bot_bot_set_o )
% 9.25/5.25         => ( ! [X2: $o] :
% 9.25/5.25                ( ( member_o @ X2 @ A2 )
% 9.25/5.25               => ( ord_less_rat @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) )
% 9.25/5.25           => ( ord_less_rat @ ( groups7872700643590313910_o_rat @ F2 @ A2 ) @ ( groups7872700643590313910_o_rat @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8059_sum__strict__mono,axiom,
% 9.25/5.25      ! [A2: set_nat,F2: nat > rat,G2: nat > rat] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( A2 != bot_bot_set_nat )
% 9.25/5.25         => ( ! [X2: nat] :
% 9.25/5.25                ( ( member_nat @ X2 @ A2 )
% 9.25/5.25               => ( ord_less_rat @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) )
% 9.25/5.25           => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F2 @ A2 ) @ ( groups2906978787729119204at_rat @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8060_sum__strict__mono,axiom,
% 9.25/5.25      ! [A2: set_int,F2: int > rat,G2: int > rat] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( A2 != bot_bot_set_int )
% 9.25/5.25         => ( ! [X2: int] :
% 9.25/5.25                ( ( member_int @ X2 @ A2 )
% 9.25/5.25               => ( ord_less_rat @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) )
% 9.25/5.25           => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F2 @ A2 ) @ ( groups3906332499630173760nt_rat @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8061_sum__strict__mono,axiom,
% 9.25/5.25      ! [A2: set_o,F2: $o > nat,G2: $o > nat] :
% 9.25/5.25        ( ( finite_finite_o @ A2 )
% 9.25/5.25       => ( ( A2 != bot_bot_set_o )
% 9.25/5.25         => ( ! [X2: $o] :
% 9.25/5.25                ( ( member_o @ X2 @ A2 )
% 9.25/5.25               => ( ord_less_nat @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) )
% 9.25/5.25           => ( ord_less_nat @ ( groups8507830703676809646_o_nat @ F2 @ A2 ) @ ( groups8507830703676809646_o_nat @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8062_sum__strict__mono,axiom,
% 9.25/5.25      ! [A2: set_int,F2: int > nat,G2: int > nat] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( A2 != bot_bot_set_int )
% 9.25/5.25         => ( ! [X2: int] :
% 9.25/5.25                ( ( member_int @ X2 @ A2 )
% 9.25/5.25               => ( ord_less_nat @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) )
% 9.25/5.25           => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F2 @ A2 ) @ ( groups4541462559716669496nt_nat @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8063_sum__strict__mono,axiom,
% 9.25/5.25      ! [A2: set_o,F2: $o > int,G2: $o > int] :
% 9.25/5.25        ( ( finite_finite_o @ A2 )
% 9.25/5.25       => ( ( A2 != bot_bot_set_o )
% 9.25/5.25         => ( ! [X2: $o] :
% 9.25/5.25                ( ( member_o @ X2 @ A2 )
% 9.25/5.25               => ( ord_less_int @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) )
% 9.25/5.25           => ( ord_less_int @ ( groups8505340233167759370_o_int @ F2 @ A2 ) @ ( groups8505340233167759370_o_int @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8064_sum__strict__mono,axiom,
% 9.25/5.25      ! [A2: set_nat,F2: nat > int,G2: nat > int] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( A2 != bot_bot_set_nat )
% 9.25/5.25         => ( ! [X2: nat] :
% 9.25/5.25                ( ( member_nat @ X2 @ A2 )
% 9.25/5.25               => ( ord_less_int @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) )
% 9.25/5.25           => ( ord_less_int @ ( groups3539618377306564664at_int @ F2 @ A2 ) @ ( groups3539618377306564664at_int @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8065_sum__strict__mono,axiom,
% 9.25/5.25      ! [A2: set_nat,F2: nat > nat,G2: nat > nat] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( A2 != bot_bot_set_nat )
% 9.25/5.25         => ( ! [X2: nat] :
% 9.25/5.25                ( ( member_nat @ X2 @ A2 )
% 9.25/5.25               => ( ord_less_nat @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) )
% 9.25/5.25           => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F2 @ A2 ) @ ( groups3542108847815614940at_nat @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8066_sum__strict__mono,axiom,
% 9.25/5.25      ! [A2: set_int,F2: int > int,G2: int > int] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( A2 != bot_bot_set_int )
% 9.25/5.25         => ( ! [X2: int] :
% 9.25/5.25                ( ( member_int @ X2 @ A2 )
% 9.25/5.25               => ( ord_less_int @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) )
% 9.25/5.25           => ( ord_less_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) @ ( groups4538972089207619220nt_int @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8067_sum__strict__mono,axiom,
% 9.25/5.25      ! [A2: set_set_nat,F2: set_nat > rat,G2: set_nat > rat] :
% 9.25/5.25        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.25       => ( ( A2 != bot_bot_set_set_nat )
% 9.25/5.25         => ( ! [X2: set_nat] :
% 9.25/5.25                ( ( member_set_nat @ X2 @ A2 )
% 9.25/5.25               => ( ord_less_rat @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) )
% 9.25/5.25           => ( ord_less_rat @ ( groups7659867448343625626at_rat @ F2 @ A2 ) @ ( groups7659867448343625626at_rat @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8068_sgn__1__pos,axiom,
% 9.25/5.25      ! [A: code_integer] :
% 9.25/5.25        ( ( ( sgn_sgn_Code_integer @ A )
% 9.25/5.25          = one_one_Code_integer )
% 9.25/5.25        = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8069_sgn__1__pos,axiom,
% 9.25/5.25      ! [A: rat] :
% 9.25/5.25        ( ( ( sgn_sgn_rat @ A )
% 9.25/5.25          = one_one_rat )
% 9.25/5.25        = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8070_sgn__1__pos,axiom,
% 9.25/5.25      ! [A: int] :
% 9.25/5.25        ( ( ( sgn_sgn_int @ A )
% 9.25/5.25          = one_one_int )
% 9.25/5.25        = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8071_prod_Orelated,axiom,
% 9.25/5.25      ! [R: code_integer > code_integer > $o,S: set_nat,H3: nat > code_integer,G2: nat > code_integer] :
% 9.25/5.25        ( ( R @ one_one_Code_integer @ one_one_Code_integer )
% 9.25/5.25       => ( ! [X13: code_integer,Y12: code_integer,X24: code_integer,Y23: code_integer] :
% 9.25/5.25              ( ( ( R @ X13 @ X24 )
% 9.25/5.25                & ( R @ Y12 @ Y23 ) )
% 9.25/5.25             => ( R @ ( times_3573771949741848930nteger @ X13 @ Y12 ) @ ( times_3573771949741848930nteger @ X24 @ Y23 ) ) )
% 9.25/5.25         => ( ( finite_finite_nat @ S )
% 9.25/5.25           => ( ! [X2: nat] :
% 9.25/5.25                  ( ( member_nat @ X2 @ S )
% 9.25/5.25                 => ( R @ ( H3 @ X2 ) @ ( G2 @ X2 ) ) )
% 9.25/5.25             => ( R @ ( groups3455450783089532116nteger @ H3 @ S ) @ ( groups3455450783089532116nteger @ G2 @ S ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8072_prod_Orelated,axiom,
% 9.25/5.25      ! [R: code_integer > code_integer > $o,S: set_int,H3: int > code_integer,G2: int > code_integer] :
% 9.25/5.25        ( ( R @ one_one_Code_integer @ one_one_Code_integer )
% 9.25/5.25       => ( ! [X13: code_integer,Y12: code_integer,X24: code_integer,Y23: code_integer] :
% 9.25/5.25              ( ( ( R @ X13 @ X24 )
% 9.25/5.25                & ( R @ Y12 @ Y23 ) )
% 9.25/5.25             => ( R @ ( times_3573771949741848930nteger @ X13 @ Y12 ) @ ( times_3573771949741848930nteger @ X24 @ Y23 ) ) )
% 9.25/5.25         => ( ( finite_finite_int @ S )
% 9.25/5.25           => ( ! [X2: int] :
% 9.25/5.25                  ( ( member_int @ X2 @ S )
% 9.25/5.25                 => ( R @ ( H3 @ X2 ) @ ( G2 @ X2 ) ) )
% 9.25/5.25             => ( R @ ( groups3827104343326376752nteger @ H3 @ S ) @ ( groups3827104343326376752nteger @ G2 @ S ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8073_prod_Orelated,axiom,
% 9.25/5.25      ! [R: assn > assn > $o,S: set_nat,H3: nat > assn,G2: nat > assn] :
% 9.25/5.25        ( ( R @ one_one_assn @ one_one_assn )
% 9.25/5.25       => ( ! [X13: assn,Y12: assn,X24: assn,Y23: assn] :
% 9.25/5.25              ( ( ( R @ X13 @ X24 )
% 9.25/5.25                & ( R @ Y12 @ Y23 ) )
% 9.25/5.25             => ( R @ ( times_times_assn @ X13 @ Y12 ) @ ( times_times_assn @ X24 @ Y23 ) ) )
% 9.25/5.25         => ( ( finite_finite_nat @ S )
% 9.25/5.25           => ( ! [X2: nat] :
% 9.25/5.25                  ( ( member_nat @ X2 @ S )
% 9.25/5.25                 => ( R @ ( H3 @ X2 ) @ ( G2 @ X2 ) ) )
% 9.25/5.25             => ( R @ ( groups6906906614972039071t_assn @ H3 @ S ) @ ( groups6906906614972039071t_assn @ G2 @ S ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8074_prod_Orelated,axiom,
% 9.25/5.25      ! [R: assn > assn > $o,S: set_int,H3: int > assn,G2: int > assn] :
% 9.25/5.25        ( ( R @ one_one_assn @ one_one_assn )
% 9.25/5.25       => ( ! [X13: assn,Y12: assn,X24: assn,Y23: assn] :
% 9.25/5.25              ( ( ( R @ X13 @ X24 )
% 9.25/5.25                & ( R @ Y12 @ Y23 ) )
% 9.25/5.25             => ( R @ ( times_times_assn @ X13 @ Y12 ) @ ( times_times_assn @ X24 @ Y23 ) ) )
% 9.25/5.25         => ( ( finite_finite_int @ S )
% 9.25/5.25           => ( ! [X2: int] :
% 9.25/5.25                  ( ( member_int @ X2 @ S )
% 9.25/5.25                 => ( R @ ( H3 @ X2 ) @ ( G2 @ X2 ) ) )
% 9.25/5.25             => ( R @ ( groups7882442080178216443t_assn @ H3 @ S ) @ ( groups7882442080178216443t_assn @ G2 @ S ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8075_prod_Orelated,axiom,
% 9.25/5.25      ! [R: rat > rat > $o,S: set_nat,H3: nat > rat,G2: nat > rat] :
% 9.25/5.25        ( ( R @ one_one_rat @ one_one_rat )
% 9.25/5.25       => ( ! [X13: rat,Y12: rat,X24: rat,Y23: rat] :
% 9.25/5.25              ( ( ( R @ X13 @ X24 )
% 9.25/5.25                & ( R @ Y12 @ Y23 ) )
% 9.25/5.25             => ( R @ ( times_times_rat @ X13 @ Y12 ) @ ( times_times_rat @ X24 @ Y23 ) ) )
% 9.25/5.25         => ( ( finite_finite_nat @ S )
% 9.25/5.25           => ( ! [X2: nat] :
% 9.25/5.25                  ( ( member_nat @ X2 @ S )
% 9.25/5.25                 => ( R @ ( H3 @ X2 ) @ ( G2 @ X2 ) ) )
% 9.25/5.25             => ( R @ ( groups73079841787564623at_rat @ H3 @ S ) @ ( groups73079841787564623at_rat @ G2 @ S ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8076_prod_Orelated,axiom,
% 9.25/5.25      ! [R: rat > rat > $o,S: set_int,H3: int > rat,G2: int > rat] :
% 9.25/5.25        ( ( R @ one_one_rat @ one_one_rat )
% 9.25/5.25       => ( ! [X13: rat,Y12: rat,X24: rat,Y23: rat] :
% 9.25/5.25              ( ( ( R @ X13 @ X24 )
% 9.25/5.25                & ( R @ Y12 @ Y23 ) )
% 9.25/5.25             => ( R @ ( times_times_rat @ X13 @ Y12 ) @ ( times_times_rat @ X24 @ Y23 ) ) )
% 9.25/5.25         => ( ( finite_finite_int @ S )
% 9.25/5.25           => ( ! [X2: int] :
% 9.25/5.25                  ( ( member_int @ X2 @ S )
% 9.25/5.25                 => ( R @ ( H3 @ X2 ) @ ( G2 @ X2 ) ) )
% 9.25/5.25             => ( R @ ( groups1072433553688619179nt_rat @ H3 @ S ) @ ( groups1072433553688619179nt_rat @ G2 @ S ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8077_prod_Orelated,axiom,
% 9.25/5.25      ! [R: nat > nat > $o,S: set_int,H3: int > nat,G2: int > nat] :
% 9.25/5.25        ( ( R @ one_one_nat @ one_one_nat )
% 9.25/5.25       => ( ! [X13: nat,Y12: nat,X24: nat,Y23: nat] :
% 9.25/5.25              ( ( ( R @ X13 @ X24 )
% 9.25/5.25                & ( R @ Y12 @ Y23 ) )
% 9.25/5.25             => ( R @ ( times_times_nat @ X13 @ Y12 ) @ ( times_times_nat @ X24 @ Y23 ) ) )
% 9.25/5.25         => ( ( finite_finite_int @ S )
% 9.25/5.25           => ( ! [X2: int] :
% 9.25/5.25                  ( ( member_int @ X2 @ S )
% 9.25/5.25                 => ( R @ ( H3 @ X2 ) @ ( G2 @ X2 ) ) )
% 9.25/5.25             => ( R @ ( groups1707563613775114915nt_nat @ H3 @ S ) @ ( groups1707563613775114915nt_nat @ G2 @ S ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8078_prod_Orelated,axiom,
% 9.25/5.25      ! [R: nat > nat > $o,S: set_nat,H3: nat > nat,G2: nat > nat] :
% 9.25/5.25        ( ( R @ one_one_nat @ one_one_nat )
% 9.25/5.25       => ( ! [X13: nat,Y12: nat,X24: nat,Y23: nat] :
% 9.25/5.25              ( ( ( R @ X13 @ X24 )
% 9.25/5.25                & ( R @ Y12 @ Y23 ) )
% 9.25/5.25             => ( R @ ( times_times_nat @ X13 @ Y12 ) @ ( times_times_nat @ X24 @ Y23 ) ) )
% 9.25/5.25         => ( ( finite_finite_nat @ S )
% 9.25/5.25           => ( ! [X2: nat] :
% 9.25/5.25                  ( ( member_nat @ X2 @ S )
% 9.25/5.25                 => ( R @ ( H3 @ X2 ) @ ( G2 @ X2 ) ) )
% 9.25/5.25             => ( R @ ( groups708209901874060359at_nat @ H3 @ S ) @ ( groups708209901874060359at_nat @ G2 @ S ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8079_prod_Orelated,axiom,
% 9.25/5.25      ! [R: int > int > $o,S: set_nat,H3: nat > int,G2: nat > int] :
% 9.25/5.25        ( ( R @ one_one_int @ one_one_int )
% 9.25/5.25       => ( ! [X13: int,Y12: int,X24: int,Y23: int] :
% 9.25/5.25              ( ( ( R @ X13 @ X24 )
% 9.25/5.25                & ( R @ Y12 @ Y23 ) )
% 9.25/5.25             => ( R @ ( times_times_int @ X13 @ Y12 ) @ ( times_times_int @ X24 @ Y23 ) ) )
% 9.25/5.25         => ( ( finite_finite_nat @ S )
% 9.25/5.25           => ( ! [X2: nat] :
% 9.25/5.25                  ( ( member_nat @ X2 @ S )
% 9.25/5.25                 => ( R @ ( H3 @ X2 ) @ ( G2 @ X2 ) ) )
% 9.25/5.25             => ( R @ ( groups705719431365010083at_int @ H3 @ S ) @ ( groups705719431365010083at_int @ G2 @ S ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8080_prod_Orelated,axiom,
% 9.25/5.25      ! [R: int > int > $o,S: set_int,H3: int > int,G2: int > int] :
% 9.25/5.25        ( ( R @ one_one_int @ one_one_int )
% 9.25/5.25       => ( ! [X13: int,Y12: int,X24: int,Y23: int] :
% 9.25/5.25              ( ( ( R @ X13 @ X24 )
% 9.25/5.25                & ( R @ Y12 @ Y23 ) )
% 9.25/5.25             => ( R @ ( times_times_int @ X13 @ Y12 ) @ ( times_times_int @ X24 @ Y23 ) ) )
% 9.25/5.25         => ( ( finite_finite_int @ S )
% 9.25/5.25           => ( ! [X2: int] :
% 9.25/5.25                  ( ( member_int @ X2 @ S )
% 9.25/5.25                 => ( R @ ( H3 @ X2 ) @ ( G2 @ X2 ) ) )
% 9.25/5.25             => ( R @ ( groups1705073143266064639nt_int @ H3 @ S ) @ ( groups1705073143266064639nt_int @ G2 @ S ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8081_prod_Oinsert__if,axiom,
% 9.25/5.25      ! [A2: set_o,X: $o,G2: $o > code_integer] :
% 9.25/5.25        ( ( finite_finite_o @ A2 )
% 9.25/5.25       => ( ( ( member_o @ X @ A2 )
% 9.25/5.25           => ( ( groups7694694392188491536nteger @ G2 @ ( insert_o @ X @ A2 ) )
% 9.25/5.25              = ( groups7694694392188491536nteger @ G2 @ A2 ) ) )
% 9.25/5.25          & ( ~ ( member_o @ X @ A2 )
% 9.25/5.25           => ( ( groups7694694392188491536nteger @ G2 @ ( insert_o @ X @ A2 ) )
% 9.25/5.25              = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups7694694392188491536nteger @ G2 @ A2 ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8082_prod_Oinsert__if,axiom,
% 9.25/5.25      ! [A2: set_nat,X: nat,G2: nat > code_integer] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( ( member_nat @ X @ A2 )
% 9.25/5.25           => ( ( groups3455450783089532116nteger @ G2 @ ( insert_nat @ X @ A2 ) )
% 9.25/5.25              = ( groups3455450783089532116nteger @ G2 @ A2 ) ) )
% 9.25/5.25          & ( ~ ( member_nat @ X @ A2 )
% 9.25/5.25           => ( ( groups3455450783089532116nteger @ G2 @ ( insert_nat @ X @ A2 ) )
% 9.25/5.25              = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups3455450783089532116nteger @ G2 @ A2 ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8083_prod_Oinsert__if,axiom,
% 9.25/5.25      ! [A2: set_int,X: int,G2: int > code_integer] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( ( member_int @ X @ A2 )
% 9.25/5.25           => ( ( groups3827104343326376752nteger @ G2 @ ( insert_int @ X @ A2 ) )
% 9.25/5.25              = ( groups3827104343326376752nteger @ G2 @ A2 ) ) )
% 9.25/5.25          & ( ~ ( member_int @ X @ A2 )
% 9.25/5.25           => ( ( groups3827104343326376752nteger @ G2 @ ( insert_int @ X @ A2 ) )
% 9.25/5.25              = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups3827104343326376752nteger @ G2 @ A2 ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8084_prod_Oinsert__if,axiom,
% 9.25/5.25      ! [A2: set_o,X: $o,G2: $o > assn] :
% 9.25/5.25        ( ( finite_finite_o @ A2 )
% 9.25/5.25       => ( ( ( member_o @ X @ A2 )
% 9.25/5.25           => ( ( groups5301882518646026715o_assn @ G2 @ ( insert_o @ X @ A2 ) )
% 9.25/5.25              = ( groups5301882518646026715o_assn @ G2 @ A2 ) ) )
% 9.25/5.25          & ( ~ ( member_o @ X @ A2 )
% 9.25/5.25           => ( ( groups5301882518646026715o_assn @ G2 @ ( insert_o @ X @ A2 ) )
% 9.25/5.25              = ( times_times_assn @ ( G2 @ X ) @ ( groups5301882518646026715o_assn @ G2 @ A2 ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8085_prod_Oinsert__if,axiom,
% 9.25/5.25      ! [A2: set_nat,X: nat,G2: nat > assn] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( ( member_nat @ X @ A2 )
% 9.25/5.25           => ( ( groups6906906614972039071t_assn @ G2 @ ( insert_nat @ X @ A2 ) )
% 9.25/5.25              = ( groups6906906614972039071t_assn @ G2 @ A2 ) ) )
% 9.25/5.25          & ( ~ ( member_nat @ X @ A2 )
% 9.25/5.25           => ( ( groups6906906614972039071t_assn @ G2 @ ( insert_nat @ X @ A2 ) )
% 9.25/5.25              = ( times_times_assn @ ( G2 @ X ) @ ( groups6906906614972039071t_assn @ G2 @ A2 ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8086_prod_Oinsert__if,axiom,
% 9.25/5.25      ! [A2: set_int,X: int,G2: int > assn] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( ( member_int @ X @ A2 )
% 9.25/5.25           => ( ( groups7882442080178216443t_assn @ G2 @ ( insert_int @ X @ A2 ) )
% 9.25/5.25              = ( groups7882442080178216443t_assn @ G2 @ A2 ) ) )
% 9.25/5.25          & ( ~ ( member_int @ X @ A2 )
% 9.25/5.25           => ( ( groups7882442080178216443t_assn @ G2 @ ( insert_int @ X @ A2 ) )
% 9.25/5.25              = ( times_times_assn @ ( G2 @ X ) @ ( groups7882442080178216443t_assn @ G2 @ A2 ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8087_prod_Oinsert__if,axiom,
% 9.25/5.25      ! [A2: set_o,X: $o,G2: $o > rat] :
% 9.25/5.25        ( ( finite_finite_o @ A2 )
% 9.25/5.25       => ( ( ( member_o @ X @ A2 )
% 9.25/5.25           => ( ( groups2869687844427037835_o_rat @ G2 @ ( insert_o @ X @ A2 ) )
% 9.25/5.25              = ( groups2869687844427037835_o_rat @ G2 @ A2 ) ) )
% 9.25/5.25          & ( ~ ( member_o @ X @ A2 )
% 9.25/5.25           => ( ( groups2869687844427037835_o_rat @ G2 @ ( insert_o @ X @ A2 ) )
% 9.25/5.25              = ( times_times_rat @ ( G2 @ X ) @ ( groups2869687844427037835_o_rat @ G2 @ A2 ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8088_prod_Oinsert__if,axiom,
% 9.25/5.25      ! [A2: set_nat,X: nat,G2: nat > rat] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( ( member_nat @ X @ A2 )
% 9.25/5.25           => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A2 ) )
% 9.25/5.25              = ( groups73079841787564623at_rat @ G2 @ A2 ) ) )
% 9.25/5.25          & ( ~ ( member_nat @ X @ A2 )
% 9.25/5.25           => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A2 ) )
% 9.25/5.25              = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ A2 ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8089_prod_Oinsert__if,axiom,
% 9.25/5.25      ! [A2: set_int,X: int,G2: int > rat] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( ( member_int @ X @ A2 )
% 9.25/5.25           => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A2 ) )
% 9.25/5.25              = ( groups1072433553688619179nt_rat @ G2 @ A2 ) ) )
% 9.25/5.25          & ( ~ ( member_int @ X @ A2 )
% 9.25/5.25           => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A2 ) )
% 9.25/5.25              = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ A2 ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8090_prod_Oinsert__if,axiom,
% 9.25/5.25      ! [A2: set_o,X: $o,G2: $o > nat] :
% 9.25/5.25        ( ( finite_finite_o @ A2 )
% 9.25/5.25       => ( ( ( member_o @ X @ A2 )
% 9.25/5.25           => ( ( groups3504817904513533571_o_nat @ G2 @ ( insert_o @ X @ A2 ) )
% 9.25/5.25              = ( groups3504817904513533571_o_nat @ G2 @ A2 ) ) )
% 9.25/5.25          & ( ~ ( member_o @ X @ A2 )
% 9.25/5.25           => ( ( groups3504817904513533571_o_nat @ G2 @ ( insert_o @ X @ A2 ) )
% 9.25/5.25              = ( times_times_nat @ ( G2 @ X ) @ ( groups3504817904513533571_o_nat @ G2 @ A2 ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8091_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.25/5.25      ! [S4: set_int,T4: set_int,S: set_int,I: int > int,J: int > int,T: set_int,G2: int > code_integer,H3: int > code_integer] :
% 9.25/5.25        ( ( finite_finite_int @ S4 )
% 9.25/5.25       => ( ( finite_finite_int @ T4 )
% 9.25/5.25         => ( ! [A6: int] :
% 9.25/5.25                ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 9.25/5.25               => ( ( I @ ( J @ A6 ) )
% 9.25/5.25                  = A6 ) )
% 9.25/5.25           => ( ! [A6: int] :
% 9.25/5.25                  ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 9.25/5.25                 => ( member_int @ ( J @ A6 ) @ ( minus_minus_set_int @ T @ T4 ) ) )
% 9.25/5.25             => ( ! [B6: int] :
% 9.25/5.25                    ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 9.25/5.25                   => ( ( J @ ( I @ B6 ) )
% 9.25/5.25                      = B6 ) )
% 9.25/5.25               => ( ! [B6: int] :
% 9.25/5.25                      ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 9.25/5.25                     => ( member_int @ ( I @ B6 ) @ ( minus_minus_set_int @ S @ S4 ) ) )
% 9.25/5.25                 => ( ! [A6: int] :
% 9.25/5.25                        ( ( member_int @ A6 @ S4 )
% 9.25/5.25                       => ( ( G2 @ A6 )
% 9.25/5.25                          = one_one_Code_integer ) )
% 9.25/5.25                   => ( ! [B6: int] :
% 9.25/5.25                          ( ( member_int @ B6 @ T4 )
% 9.25/5.25                         => ( ( H3 @ B6 )
% 9.25/5.25                            = one_one_Code_integer ) )
% 9.25/5.25                     => ( ! [A6: int] :
% 9.25/5.25                            ( ( member_int @ A6 @ S )
% 9.25/5.25                           => ( ( H3 @ ( J @ A6 ) )
% 9.25/5.25                              = ( G2 @ A6 ) ) )
% 9.25/5.25                       => ( ( groups3827104343326376752nteger @ G2 @ S )
% 9.25/5.25                          = ( groups3827104343326376752nteger @ H3 @ T ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8092_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.25/5.25      ! [S4: set_int,T4: set_int,S: set_int,I: int > int,J: int > int,T: set_int,G2: int > assn,H3: int > assn] :
% 9.25/5.25        ( ( finite_finite_int @ S4 )
% 9.25/5.25       => ( ( finite_finite_int @ T4 )
% 9.25/5.25         => ( ! [A6: int] :
% 9.25/5.25                ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 9.25/5.25               => ( ( I @ ( J @ A6 ) )
% 9.25/5.25                  = A6 ) )
% 9.25/5.25           => ( ! [A6: int] :
% 9.25/5.25                  ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 9.25/5.25                 => ( member_int @ ( J @ A6 ) @ ( minus_minus_set_int @ T @ T4 ) ) )
% 9.25/5.25             => ( ! [B6: int] :
% 9.25/5.25                    ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 9.25/5.25                   => ( ( J @ ( I @ B6 ) )
% 9.25/5.25                      = B6 ) )
% 9.25/5.25               => ( ! [B6: int] :
% 9.25/5.25                      ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 9.25/5.25                     => ( member_int @ ( I @ B6 ) @ ( minus_minus_set_int @ S @ S4 ) ) )
% 9.25/5.25                 => ( ! [A6: int] :
% 9.25/5.25                        ( ( member_int @ A6 @ S4 )
% 9.25/5.25                       => ( ( G2 @ A6 )
% 9.25/5.25                          = one_one_assn ) )
% 9.25/5.25                   => ( ! [B6: int] :
% 9.25/5.25                          ( ( member_int @ B6 @ T4 )
% 9.25/5.25                         => ( ( H3 @ B6 )
% 9.25/5.25                            = one_one_assn ) )
% 9.25/5.25                     => ( ! [A6: int] :
% 9.25/5.25                            ( ( member_int @ A6 @ S )
% 9.25/5.25                           => ( ( H3 @ ( J @ A6 ) )
% 9.25/5.25                              = ( G2 @ A6 ) ) )
% 9.25/5.25                       => ( ( groups7882442080178216443t_assn @ G2 @ S )
% 9.25/5.25                          = ( groups7882442080178216443t_assn @ H3 @ T ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8093_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.25/5.25      ! [S4: set_int,T4: set_int,S: set_int,I: int > int,J: int > int,T: set_int,G2: int > rat,H3: int > rat] :
% 9.25/5.25        ( ( finite_finite_int @ S4 )
% 9.25/5.25       => ( ( finite_finite_int @ T4 )
% 9.25/5.25         => ( ! [A6: int] :
% 9.25/5.25                ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 9.25/5.25               => ( ( I @ ( J @ A6 ) )
% 9.25/5.25                  = A6 ) )
% 9.25/5.25           => ( ! [A6: int] :
% 9.25/5.25                  ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 9.25/5.25                 => ( member_int @ ( J @ A6 ) @ ( minus_minus_set_int @ T @ T4 ) ) )
% 9.25/5.25             => ( ! [B6: int] :
% 9.25/5.25                    ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 9.25/5.25                   => ( ( J @ ( I @ B6 ) )
% 9.25/5.25                      = B6 ) )
% 9.25/5.25               => ( ! [B6: int] :
% 9.25/5.25                      ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 9.25/5.25                     => ( member_int @ ( I @ B6 ) @ ( minus_minus_set_int @ S @ S4 ) ) )
% 9.25/5.25                 => ( ! [A6: int] :
% 9.25/5.25                        ( ( member_int @ A6 @ S4 )
% 9.25/5.25                       => ( ( G2 @ A6 )
% 9.25/5.25                          = one_one_rat ) )
% 9.25/5.25                   => ( ! [B6: int] :
% 9.25/5.25                          ( ( member_int @ B6 @ T4 )
% 9.25/5.25                         => ( ( H3 @ B6 )
% 9.25/5.25                            = one_one_rat ) )
% 9.25/5.25                     => ( ! [A6: int] :
% 9.25/5.25                            ( ( member_int @ A6 @ S )
% 9.25/5.25                           => ( ( H3 @ ( J @ A6 ) )
% 9.25/5.25                              = ( G2 @ A6 ) ) )
% 9.25/5.25                       => ( ( groups1072433553688619179nt_rat @ G2 @ S )
% 9.25/5.25                          = ( groups1072433553688619179nt_rat @ H3 @ T ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8094_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.25/5.25      ! [S4: set_int,T4: set_int,S: set_int,I: int > int,J: int > int,T: set_int,G2: int > nat,H3: int > nat] :
% 9.25/5.25        ( ( finite_finite_int @ S4 )
% 9.25/5.25       => ( ( finite_finite_int @ T4 )
% 9.25/5.25         => ( ! [A6: int] :
% 9.25/5.25                ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 9.25/5.25               => ( ( I @ ( J @ A6 ) )
% 9.25/5.25                  = A6 ) )
% 9.25/5.25           => ( ! [A6: int] :
% 9.25/5.25                  ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 9.25/5.25                 => ( member_int @ ( J @ A6 ) @ ( minus_minus_set_int @ T @ T4 ) ) )
% 9.25/5.25             => ( ! [B6: int] :
% 9.25/5.25                    ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 9.25/5.25                   => ( ( J @ ( I @ B6 ) )
% 9.25/5.25                      = B6 ) )
% 9.25/5.25               => ( ! [B6: int] :
% 9.25/5.25                      ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 9.25/5.25                     => ( member_int @ ( I @ B6 ) @ ( minus_minus_set_int @ S @ S4 ) ) )
% 9.25/5.25                 => ( ! [A6: int] :
% 9.25/5.25                        ( ( member_int @ A6 @ S4 )
% 9.25/5.25                       => ( ( G2 @ A6 )
% 9.25/5.25                          = one_one_nat ) )
% 9.25/5.25                   => ( ! [B6: int] :
% 9.25/5.25                          ( ( member_int @ B6 @ T4 )
% 9.25/5.25                         => ( ( H3 @ B6 )
% 9.25/5.25                            = one_one_nat ) )
% 9.25/5.25                     => ( ! [A6: int] :
% 9.25/5.25                            ( ( member_int @ A6 @ S )
% 9.25/5.25                           => ( ( H3 @ ( J @ A6 ) )
% 9.25/5.25                              = ( G2 @ A6 ) ) )
% 9.25/5.25                       => ( ( groups1707563613775114915nt_nat @ G2 @ S )
% 9.25/5.25                          = ( groups1707563613775114915nt_nat @ H3 @ T ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8095_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.25/5.25      ! [S4: set_int,T4: set_nat,S: set_int,I: nat > int,J: int > nat,T: set_nat,G2: int > code_integer,H3: nat > code_integer] :
% 9.25/5.25        ( ( finite_finite_int @ S4 )
% 9.25/5.25       => ( ( finite_finite_nat @ T4 )
% 9.25/5.25         => ( ! [A6: int] :
% 9.25/5.25                ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 9.25/5.25               => ( ( I @ ( J @ A6 ) )
% 9.25/5.25                  = A6 ) )
% 9.25/5.25           => ( ! [A6: int] :
% 9.25/5.25                  ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 9.25/5.25                 => ( member_nat @ ( J @ A6 ) @ ( minus_minus_set_nat @ T @ T4 ) ) )
% 9.25/5.25             => ( ! [B6: nat] :
% 9.25/5.25                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ T @ T4 ) )
% 9.25/5.25                   => ( ( J @ ( I @ B6 ) )
% 9.25/5.25                      = B6 ) )
% 9.25/5.25               => ( ! [B6: nat] :
% 9.25/5.25                      ( ( member_nat @ B6 @ ( minus_minus_set_nat @ T @ T4 ) )
% 9.25/5.25                     => ( member_int @ ( I @ B6 ) @ ( minus_minus_set_int @ S @ S4 ) ) )
% 9.25/5.25                 => ( ! [A6: int] :
% 9.25/5.25                        ( ( member_int @ A6 @ S4 )
% 9.25/5.25                       => ( ( G2 @ A6 )
% 9.25/5.25                          = one_one_Code_integer ) )
% 9.25/5.25                   => ( ! [B6: nat] :
% 9.25/5.25                          ( ( member_nat @ B6 @ T4 )
% 9.25/5.25                         => ( ( H3 @ B6 )
% 9.25/5.25                            = one_one_Code_integer ) )
% 9.25/5.25                     => ( ! [A6: int] :
% 9.25/5.25                            ( ( member_int @ A6 @ S )
% 9.25/5.25                           => ( ( H3 @ ( J @ A6 ) )
% 9.25/5.25                              = ( G2 @ A6 ) ) )
% 9.25/5.25                       => ( ( groups3827104343326376752nteger @ G2 @ S )
% 9.25/5.25                          = ( groups3455450783089532116nteger @ H3 @ T ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8096_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.25/5.25      ! [S4: set_int,T4: set_nat,S: set_int,I: nat > int,J: int > nat,T: set_nat,G2: int > assn,H3: nat > assn] :
% 9.25/5.25        ( ( finite_finite_int @ S4 )
% 9.25/5.25       => ( ( finite_finite_nat @ T4 )
% 9.25/5.25         => ( ! [A6: int] :
% 9.25/5.25                ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 9.25/5.25               => ( ( I @ ( J @ A6 ) )
% 9.25/5.25                  = A6 ) )
% 9.25/5.25           => ( ! [A6: int] :
% 9.25/5.25                  ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 9.25/5.25                 => ( member_nat @ ( J @ A6 ) @ ( minus_minus_set_nat @ T @ T4 ) ) )
% 9.25/5.25             => ( ! [B6: nat] :
% 9.25/5.25                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ T @ T4 ) )
% 9.25/5.25                   => ( ( J @ ( I @ B6 ) )
% 9.25/5.25                      = B6 ) )
% 9.25/5.25               => ( ! [B6: nat] :
% 9.25/5.25                      ( ( member_nat @ B6 @ ( minus_minus_set_nat @ T @ T4 ) )
% 9.25/5.25                     => ( member_int @ ( I @ B6 ) @ ( minus_minus_set_int @ S @ S4 ) ) )
% 9.25/5.25                 => ( ! [A6: int] :
% 9.25/5.25                        ( ( member_int @ A6 @ S4 )
% 9.25/5.25                       => ( ( G2 @ A6 )
% 9.25/5.25                          = one_one_assn ) )
% 9.25/5.25                   => ( ! [B6: nat] :
% 9.25/5.25                          ( ( member_nat @ B6 @ T4 )
% 9.25/5.25                         => ( ( H3 @ B6 )
% 9.25/5.25                            = one_one_assn ) )
% 9.25/5.25                     => ( ! [A6: int] :
% 9.25/5.25                            ( ( member_int @ A6 @ S )
% 9.25/5.25                           => ( ( H3 @ ( J @ A6 ) )
% 9.25/5.25                              = ( G2 @ A6 ) ) )
% 9.25/5.25                       => ( ( groups7882442080178216443t_assn @ G2 @ S )
% 9.25/5.25                          = ( groups6906906614972039071t_assn @ H3 @ T ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8097_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.25/5.25      ! [S4: set_int,T4: set_nat,S: set_int,I: nat > int,J: int > nat,T: set_nat,G2: int > rat,H3: nat > rat] :
% 9.25/5.25        ( ( finite_finite_int @ S4 )
% 9.25/5.25       => ( ( finite_finite_nat @ T4 )
% 9.25/5.25         => ( ! [A6: int] :
% 9.25/5.25                ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 9.25/5.25               => ( ( I @ ( J @ A6 ) )
% 9.25/5.25                  = A6 ) )
% 9.25/5.25           => ( ! [A6: int] :
% 9.25/5.25                  ( ( member_int @ A6 @ ( minus_minus_set_int @ S @ S4 ) )
% 9.25/5.25                 => ( member_nat @ ( J @ A6 ) @ ( minus_minus_set_nat @ T @ T4 ) ) )
% 9.25/5.25             => ( ! [B6: nat] :
% 9.25/5.25                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ T @ T4 ) )
% 9.25/5.25                   => ( ( J @ ( I @ B6 ) )
% 9.25/5.25                      = B6 ) )
% 9.25/5.25               => ( ! [B6: nat] :
% 9.25/5.25                      ( ( member_nat @ B6 @ ( minus_minus_set_nat @ T @ T4 ) )
% 9.25/5.25                     => ( member_int @ ( I @ B6 ) @ ( minus_minus_set_int @ S @ S4 ) ) )
% 9.25/5.25                 => ( ! [A6: int] :
% 9.25/5.25                        ( ( member_int @ A6 @ S4 )
% 9.25/5.25                       => ( ( G2 @ A6 )
% 9.25/5.25                          = one_one_rat ) )
% 9.25/5.25                   => ( ! [B6: nat] :
% 9.25/5.25                          ( ( member_nat @ B6 @ T4 )
% 9.25/5.25                         => ( ( H3 @ B6 )
% 9.25/5.25                            = one_one_rat ) )
% 9.25/5.25                     => ( ! [A6: int] :
% 9.25/5.25                            ( ( member_int @ A6 @ S )
% 9.25/5.25                           => ( ( H3 @ ( J @ A6 ) )
% 9.25/5.25                              = ( G2 @ A6 ) ) )
% 9.25/5.25                       => ( ( groups1072433553688619179nt_rat @ G2 @ S )
% 9.25/5.25                          = ( groups73079841787564623at_rat @ H3 @ T ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8098_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.25/5.25      ! [S4: set_nat,T4: set_int,S: set_nat,I: int > nat,J: nat > int,T: set_int,G2: nat > code_integer,H3: int > code_integer] :
% 9.25/5.25        ( ( finite_finite_nat @ S4 )
% 9.25/5.25       => ( ( finite_finite_int @ T4 )
% 9.25/5.25         => ( ! [A6: nat] :
% 9.25/5.25                ( ( member_nat @ A6 @ ( minus_minus_set_nat @ S @ S4 ) )
% 9.25/5.25               => ( ( I @ ( J @ A6 ) )
% 9.25/5.25                  = A6 ) )
% 9.25/5.25           => ( ! [A6: nat] :
% 9.25/5.25                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ S @ S4 ) )
% 9.25/5.25                 => ( member_int @ ( J @ A6 ) @ ( minus_minus_set_int @ T @ T4 ) ) )
% 9.25/5.25             => ( ! [B6: int] :
% 9.25/5.25                    ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 9.25/5.25                   => ( ( J @ ( I @ B6 ) )
% 9.25/5.25                      = B6 ) )
% 9.25/5.25               => ( ! [B6: int] :
% 9.25/5.25                      ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 9.25/5.25                     => ( member_nat @ ( I @ B6 ) @ ( minus_minus_set_nat @ S @ S4 ) ) )
% 9.25/5.25                 => ( ! [A6: nat] :
% 9.25/5.25                        ( ( member_nat @ A6 @ S4 )
% 9.25/5.25                       => ( ( G2 @ A6 )
% 9.25/5.25                          = one_one_Code_integer ) )
% 9.25/5.25                   => ( ! [B6: int] :
% 9.25/5.25                          ( ( member_int @ B6 @ T4 )
% 9.25/5.25                         => ( ( H3 @ B6 )
% 9.25/5.25                            = one_one_Code_integer ) )
% 9.25/5.25                     => ( ! [A6: nat] :
% 9.25/5.25                            ( ( member_nat @ A6 @ S )
% 9.25/5.25                           => ( ( H3 @ ( J @ A6 ) )
% 9.25/5.25                              = ( G2 @ A6 ) ) )
% 9.25/5.25                       => ( ( groups3455450783089532116nteger @ G2 @ S )
% 9.25/5.25                          = ( groups3827104343326376752nteger @ H3 @ T ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8099_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.25/5.25      ! [S4: set_nat,T4: set_int,S: set_nat,I: int > nat,J: nat > int,T: set_int,G2: nat > assn,H3: int > assn] :
% 9.25/5.25        ( ( finite_finite_nat @ S4 )
% 9.25/5.25       => ( ( finite_finite_int @ T4 )
% 9.25/5.25         => ( ! [A6: nat] :
% 9.25/5.25                ( ( member_nat @ A6 @ ( minus_minus_set_nat @ S @ S4 ) )
% 9.25/5.25               => ( ( I @ ( J @ A6 ) )
% 9.25/5.25                  = A6 ) )
% 9.25/5.25           => ( ! [A6: nat] :
% 9.25/5.25                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ S @ S4 ) )
% 9.25/5.25                 => ( member_int @ ( J @ A6 ) @ ( minus_minus_set_int @ T @ T4 ) ) )
% 9.25/5.25             => ( ! [B6: int] :
% 9.25/5.25                    ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 9.25/5.25                   => ( ( J @ ( I @ B6 ) )
% 9.25/5.25                      = B6 ) )
% 9.25/5.25               => ( ! [B6: int] :
% 9.25/5.25                      ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 9.25/5.25                     => ( member_nat @ ( I @ B6 ) @ ( minus_minus_set_nat @ S @ S4 ) ) )
% 9.25/5.25                 => ( ! [A6: nat] :
% 9.25/5.25                        ( ( member_nat @ A6 @ S4 )
% 9.25/5.25                       => ( ( G2 @ A6 )
% 9.25/5.25                          = one_one_assn ) )
% 9.25/5.25                   => ( ! [B6: int] :
% 9.25/5.25                          ( ( member_int @ B6 @ T4 )
% 9.25/5.25                         => ( ( H3 @ B6 )
% 9.25/5.25                            = one_one_assn ) )
% 9.25/5.25                     => ( ! [A6: nat] :
% 9.25/5.25                            ( ( member_nat @ A6 @ S )
% 9.25/5.25                           => ( ( H3 @ ( J @ A6 ) )
% 9.25/5.25                              = ( G2 @ A6 ) ) )
% 9.25/5.25                       => ( ( groups6906906614972039071t_assn @ G2 @ S )
% 9.25/5.25                          = ( groups7882442080178216443t_assn @ H3 @ T ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8100_prod_Oreindex__bij__witness__not__neutral,axiom,
% 9.25/5.25      ! [S4: set_nat,T4: set_int,S: set_nat,I: int > nat,J: nat > int,T: set_int,G2: nat > rat,H3: int > rat] :
% 9.25/5.25        ( ( finite_finite_nat @ S4 )
% 9.25/5.25       => ( ( finite_finite_int @ T4 )
% 9.25/5.25         => ( ! [A6: nat] :
% 9.25/5.25                ( ( member_nat @ A6 @ ( minus_minus_set_nat @ S @ S4 ) )
% 9.25/5.25               => ( ( I @ ( J @ A6 ) )
% 9.25/5.25                  = A6 ) )
% 9.25/5.25           => ( ! [A6: nat] :
% 9.25/5.25                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ S @ S4 ) )
% 9.25/5.25                 => ( member_int @ ( J @ A6 ) @ ( minus_minus_set_int @ T @ T4 ) ) )
% 9.25/5.25             => ( ! [B6: int] :
% 9.25/5.25                    ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 9.25/5.25                   => ( ( J @ ( I @ B6 ) )
% 9.25/5.25                      = B6 ) )
% 9.25/5.25               => ( ! [B6: int] :
% 9.25/5.25                      ( ( member_int @ B6 @ ( minus_minus_set_int @ T @ T4 ) )
% 9.25/5.25                     => ( member_nat @ ( I @ B6 ) @ ( minus_minus_set_nat @ S @ S4 ) ) )
% 9.25/5.25                 => ( ! [A6: nat] :
% 9.25/5.25                        ( ( member_nat @ A6 @ S4 )
% 9.25/5.25                       => ( ( G2 @ A6 )
% 9.25/5.25                          = one_one_rat ) )
% 9.25/5.25                   => ( ! [B6: int] :
% 9.25/5.25                          ( ( member_int @ B6 @ T4 )
% 9.25/5.25                         => ( ( H3 @ B6 )
% 9.25/5.25                            = one_one_rat ) )
% 9.25/5.25                     => ( ! [A6: nat] :
% 9.25/5.25                            ( ( member_nat @ A6 @ S )
% 9.25/5.25                           => ( ( H3 @ ( J @ A6 ) )
% 9.25/5.25                              = ( G2 @ A6 ) ) )
% 9.25/5.25                       => ( ( groups73079841787564623at_rat @ G2 @ S )
% 9.25/5.25                          = ( groups1072433553688619179nt_rat @ H3 @ T ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8101_abs__sgn__eq,axiom,
% 9.25/5.25      ! [A: code_integer] :
% 9.25/5.25        ( ( ( A = zero_z3403309356797280102nteger )
% 9.25/5.25         => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 9.25/5.25            = zero_z3403309356797280102nteger ) )
% 9.25/5.25        & ( ( A != zero_z3403309356797280102nteger )
% 9.25/5.25         => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 9.25/5.25            = one_one_Code_integer ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8102_abs__sgn__eq,axiom,
% 9.25/5.25      ! [A: rat] :
% 9.25/5.25        ( ( ( A = zero_zero_rat )
% 9.25/5.25         => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 9.25/5.25            = zero_zero_rat ) )
% 9.25/5.25        & ( ( A != zero_zero_rat )
% 9.25/5.25         => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 9.25/5.25            = one_one_rat ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8103_abs__sgn__eq,axiom,
% 9.25/5.25      ! [A: int] :
% 9.25/5.25        ( ( ( A = zero_zero_int )
% 9.25/5.25         => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 9.25/5.25            = zero_zero_int ) )
% 9.25/5.25        & ( ( A != zero_zero_int )
% 9.25/5.25         => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 9.25/5.25            = one_one_int ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8104_sum_Onat__diff__reindex,axiom,
% 9.25/5.25      ! [G2: nat > nat,N: nat] :
% 9.25/5.25        ( ( groups3542108847815614940at_nat
% 9.25/5.25          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 9.25/5.25          @ ( set_ord_lessThan_nat @ N ) )
% 9.25/5.25        = ( groups3542108847815614940at_nat @ G2 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8105_prod_Onat__diff__reindex,axiom,
% 9.25/5.25      ! [G2: nat > nat,N: nat] :
% 9.25/5.25        ( ( groups708209901874060359at_nat
% 9.25/5.25          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 9.25/5.25          @ ( set_ord_lessThan_nat @ N ) )
% 9.25/5.25        = ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8106_prod_Onat__diff__reindex,axiom,
% 9.25/5.25      ! [G2: nat > int,N: nat] :
% 9.25/5.25        ( ( groups705719431365010083at_int
% 9.25/5.25          @ ^ [I3: nat] : ( G2 @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 9.25/5.25          @ ( set_ord_lessThan_nat @ N ) )
% 9.25/5.25        = ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8107_sum__eq__1__iff,axiom,
% 9.25/5.25      ! [A2: set_int,F2: int > nat] :
% 9.25/5.25        ( ( finite_finite_int @ A2 )
% 9.25/5.25       => ( ( ( groups4541462559716669496nt_nat @ F2 @ A2 )
% 9.25/5.25            = one_one_nat )
% 9.25/5.25          = ( ? [X3: int] :
% 9.25/5.25                ( ( member_int @ X3 @ A2 )
% 9.25/5.25                & ( ( F2 @ X3 )
% 9.25/5.25                  = one_one_nat )
% 9.25/5.25                & ! [Y3: int] :
% 9.25/5.25                    ( ( member_int @ Y3 @ A2 )
% 9.25/5.25                   => ( ( X3 != Y3 )
% 9.25/5.25                     => ( ( F2 @ Y3 )
% 9.25/5.25                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8108_sum__eq__1__iff,axiom,
% 9.25/5.25      ! [A2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > nat] :
% 9.25/5.25        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.25       => ( ( ( groups977919841031483927at_nat @ F2 @ A2 )
% 9.25/5.25            = one_one_nat )
% 9.25/5.25          = ( ? [X3: product_prod_nat_nat] :
% 9.25/5.25                ( ( member8440522571783428010at_nat @ X3 @ A2 )
% 9.25/5.25                & ( ( F2 @ X3 )
% 9.25/5.25                  = one_one_nat )
% 9.25/5.25                & ! [Y3: product_prod_nat_nat] :
% 9.25/5.25                    ( ( member8440522571783428010at_nat @ Y3 @ A2 )
% 9.25/5.25                   => ( ( X3 != Y3 )
% 9.25/5.25                     => ( ( F2 @ Y3 )
% 9.25/5.25                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8109_sum__eq__1__iff,axiom,
% 9.25/5.25      ! [A2: set_nat,F2: nat > nat] :
% 9.25/5.25        ( ( finite_finite_nat @ A2 )
% 9.25/5.25       => ( ( ( groups3542108847815614940at_nat @ F2 @ A2 )
% 9.25/5.25            = one_one_nat )
% 9.25/5.25          = ( ? [X3: nat] :
% 9.25/5.25                ( ( member_nat @ X3 @ A2 )
% 9.25/5.25                & ( ( F2 @ X3 )
% 9.25/5.25                  = one_one_nat )
% 9.25/5.25                & ! [Y3: nat] :
% 9.25/5.25                    ( ( member_nat @ Y3 @ A2 )
% 9.25/5.25                   => ( ( X3 != Y3 )
% 9.25/5.25                     => ( ( F2 @ Y3 )
% 9.25/5.25                        = zero_zero_nat ) ) ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8110_prod__int__eq,axiom,
% 9.25/5.25      ! [I: nat,J: nat] :
% 9.25/5.25        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 9.25/5.25        = ( groups1705073143266064639nt_int
% 9.25/5.25          @ ^ [X3: int] : X3
% 9.25/5.25          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8111_div__push__bit__of__1__eq__drop__bit,axiom,
% 9.25/5.25      ! [A: code_integer,N: nat] :
% 9.25/5.25        ( ( divide6298287555418463151nteger @ A @ ( bit_se7788150548672797655nteger @ N @ one_one_Code_integer ) )
% 9.25/5.25        = ( bit_se3928097537394005634nteger @ N @ A ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8112_div__push__bit__of__1__eq__drop__bit,axiom,
% 9.25/5.25      ! [A: code_natural,N: nat] :
% 9.25/5.25        ( ( divide5121882707175180666atural @ A @ ( bit_se6611745700429515170atural @ N @ one_one_Code_natural ) )
% 9.25/5.25        = ( bit_se2751692689150723149atural @ N @ A ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8113_div__push__bit__of__1__eq__drop__bit,axiom,
% 9.25/5.25      ! [A: int,N: nat] :
% 9.25/5.25        ( ( divide_divide_int @ A @ ( bit_se545348938243370406it_int @ N @ one_one_int ) )
% 9.25/5.25        = ( bit_se8568078237143864401it_int @ N @ A ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8114_div__push__bit__of__1__eq__drop__bit,axiom,
% 9.25/5.25      ! [A: nat,N: nat] :
% 9.25/5.25        ( ( divide_divide_nat @ A @ ( bit_se547839408752420682it_nat @ N @ one_one_nat ) )
% 9.25/5.25        = ( bit_se8570568707652914677it_nat @ N @ A ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8115_sum__nonneg__leq__bound,axiom,
% 9.25/5.25      ! [S3: set_nat,F2: nat > code_integer,B2: code_integer,I: nat] :
% 9.25/5.25        ( ( finite_finite_nat @ S3 )
% 9.25/5.25       => ( ! [I2: nat] :
% 9.25/5.25              ( ( member_nat @ I2 @ S3 )
% 9.25/5.25             => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) ) )
% 9.25/5.25         => ( ( ( groups7501900531339628137nteger @ F2 @ S3 )
% 9.25/5.25              = B2 )
% 9.25/5.25           => ( ( member_nat @ I @ S3 )
% 9.25/5.25             => ( ord_le3102999989581377725nteger @ ( F2 @ I ) @ B2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8116_sum__nonneg__leq__bound,axiom,
% 9.25/5.25      ! [S3: set_int,F2: int > code_integer,B2: code_integer,I: int] :
% 9.25/5.25        ( ( finite_finite_int @ S3 )
% 9.25/5.25       => ( ! [I2: int] :
% 9.25/5.25              ( ( member_int @ I2 @ S3 )
% 9.25/5.25             => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) ) )
% 9.25/5.25         => ( ( ( groups7873554091576472773nteger @ F2 @ S3 )
% 9.25/5.25              = B2 )
% 9.25/5.25           => ( ( member_int @ I @ S3 )
% 9.25/5.25             => ( ord_le3102999989581377725nteger @ ( F2 @ I ) @ B2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8117_sum__nonneg__leq__bound,axiom,
% 9.25/5.25      ! [S3: set_nat,F2: nat > rat,B2: rat,I: nat] :
% 9.25/5.25        ( ( finite_finite_nat @ S3 )
% 9.25/5.25       => ( ! [I2: nat] :
% 9.25/5.25              ( ( member_nat @ I2 @ S3 )
% 9.25/5.25             => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I2 ) ) )
% 9.25/5.25         => ( ( ( groups2906978787729119204at_rat @ F2 @ S3 )
% 9.25/5.25              = B2 )
% 9.25/5.25           => ( ( member_nat @ I @ S3 )
% 9.25/5.25             => ( ord_less_eq_rat @ ( F2 @ I ) @ B2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8118_sum__nonneg__leq__bound,axiom,
% 9.25/5.25      ! [S3: set_int,F2: int > rat,B2: rat,I: int] :
% 9.25/5.25        ( ( finite_finite_int @ S3 )
% 9.25/5.25       => ( ! [I2: int] :
% 9.25/5.25              ( ( member_int @ I2 @ S3 )
% 9.25/5.25             => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I2 ) ) )
% 9.25/5.25         => ( ( ( groups3906332499630173760nt_rat @ F2 @ S3 )
% 9.25/5.25              = B2 )
% 9.25/5.25           => ( ( member_int @ I @ S3 )
% 9.25/5.25             => ( ord_less_eq_rat @ ( F2 @ I ) @ B2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8119_sum__nonneg__leq__bound,axiom,
% 9.25/5.25      ! [S3: set_int,F2: int > nat,B2: nat,I: int] :
% 9.25/5.25        ( ( finite_finite_int @ S3 )
% 9.25/5.25       => ( ! [I2: int] :
% 9.25/5.25              ( ( member_int @ I2 @ S3 )
% 9.25/5.25             => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I2 ) ) )
% 9.25/5.25         => ( ( ( groups4541462559716669496nt_nat @ F2 @ S3 )
% 9.25/5.25              = B2 )
% 9.25/5.25           => ( ( member_int @ I @ S3 )
% 9.25/5.25             => ( ord_less_eq_nat @ ( F2 @ I ) @ B2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8120_sum__nonneg__leq__bound,axiom,
% 9.25/5.25      ! [S3: set_nat,F2: nat > int,B2: int,I: nat] :
% 9.25/5.25        ( ( finite_finite_nat @ S3 )
% 9.25/5.25       => ( ! [I2: nat] :
% 9.25/5.25              ( ( member_nat @ I2 @ S3 )
% 9.25/5.25             => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ I2 ) ) )
% 9.25/5.25         => ( ( ( groups3539618377306564664at_int @ F2 @ S3 )
% 9.25/5.25              = B2 )
% 9.25/5.25           => ( ( member_nat @ I @ S3 )
% 9.25/5.25             => ( ord_less_eq_int @ ( F2 @ I ) @ B2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8121_sum__nonneg__leq__bound,axiom,
% 9.25/5.25      ! [S3: set_nat,F2: nat > nat,B2: nat,I: nat] :
% 9.25/5.25        ( ( finite_finite_nat @ S3 )
% 9.25/5.25       => ( ! [I2: nat] :
% 9.25/5.25              ( ( member_nat @ I2 @ S3 )
% 9.25/5.25             => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I2 ) ) )
% 9.25/5.25         => ( ( ( groups3542108847815614940at_nat @ F2 @ S3 )
% 9.25/5.25              = B2 )
% 9.25/5.25           => ( ( member_nat @ I @ S3 )
% 9.25/5.25             => ( ord_less_eq_nat @ ( F2 @ I ) @ B2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8122_sum__nonneg__leq__bound,axiom,
% 9.25/5.25      ! [S3: set_int,F2: int > int,B2: int,I: int] :
% 9.25/5.25        ( ( finite_finite_int @ S3 )
% 9.25/5.25       => ( ! [I2: int] :
% 9.25/5.25              ( ( member_int @ I2 @ S3 )
% 9.25/5.25             => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ I2 ) ) )
% 9.25/5.25         => ( ( ( groups4538972089207619220nt_int @ F2 @ S3 )
% 9.25/5.25              = B2 )
% 9.25/5.25           => ( ( member_int @ I @ S3 )
% 9.25/5.25             => ( ord_less_eq_int @ ( F2 @ I ) @ B2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8123_sum__nonneg__leq__bound,axiom,
% 9.25/5.25      ! [S3: set_set_nat,F2: set_nat > code_integer,B2: code_integer,I: set_nat] :
% 9.25/5.25        ( ( finite1152437895449049373et_nat @ S3 )
% 9.25/5.25       => ( ! [I2: set_nat] :
% 9.25/5.25              ( ( member_set_nat @ I2 @ S3 )
% 9.25/5.25             => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) ) )
% 9.25/5.25         => ( ( ( groups9190459664516455967nteger @ F2 @ S3 )
% 9.25/5.25              = B2 )
% 9.25/5.25           => ( ( member_set_nat @ I @ S3 )
% 9.25/5.25             => ( ord_le3102999989581377725nteger @ ( F2 @ I ) @ B2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8124_sum__nonneg__leq__bound,axiom,
% 9.25/5.25      ! [S3: set_set_nat,F2: set_nat > rat,B2: rat,I: set_nat] :
% 9.25/5.25        ( ( finite1152437895449049373et_nat @ S3 )
% 9.25/5.25       => ( ! [I2: set_nat] :
% 9.25/5.25              ( ( member_set_nat @ I2 @ S3 )
% 9.25/5.25             => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I2 ) ) )
% 9.25/5.25         => ( ( ( groups7659867448343625626at_rat @ F2 @ S3 )
% 9.25/5.25              = B2 )
% 9.25/5.25           => ( ( member_set_nat @ I @ S3 )
% 9.25/5.25             => ( ord_less_eq_rat @ ( F2 @ I ) @ B2 ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8125_sum__nonneg__0,axiom,
% 9.25/5.25      ! [S3: set_nat,F2: nat > code_integer,I: nat] :
% 9.25/5.25        ( ( finite_finite_nat @ S3 )
% 9.25/5.25       => ( ! [I2: nat] :
% 9.25/5.25              ( ( member_nat @ I2 @ S3 )
% 9.25/5.25             => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) ) )
% 9.25/5.25         => ( ( ( groups7501900531339628137nteger @ F2 @ S3 )
% 9.25/5.25              = zero_z3403309356797280102nteger )
% 9.25/5.25           => ( ( member_nat @ I @ S3 )
% 9.25/5.25             => ( ( F2 @ I )
% 9.25/5.25                = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8126_sum__nonneg__0,axiom,
% 9.25/5.25      ! [S3: set_int,F2: int > code_integer,I: int] :
% 9.25/5.25        ( ( finite_finite_int @ S3 )
% 9.25/5.25       => ( ! [I2: int] :
% 9.25/5.25              ( ( member_int @ I2 @ S3 )
% 9.25/5.25             => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) ) )
% 9.25/5.25         => ( ( ( groups7873554091576472773nteger @ F2 @ S3 )
% 9.25/5.25              = zero_z3403309356797280102nteger )
% 9.25/5.25           => ( ( member_int @ I @ S3 )
% 9.25/5.25             => ( ( F2 @ I )
% 9.25/5.25                = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 9.25/5.25  
% 9.25/5.25  thf(fact_8127_sum__nonneg__0,axiom,
% 9.25/5.25      ! [S3: set_nat,F2: nat > rat,I: nat] :
% 9.25/5.26        ( ( finite_finite_nat @ S3 )
% 9.25/5.26       => ( ! [I2: nat] :
% 9.25/5.26              ( ( member_nat @ I2 @ S3 )
% 9.25/5.26             => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I2 ) ) )
% 9.25/5.26         => ( ( ( groups2906978787729119204at_rat @ F2 @ S3 )
% 9.25/5.26              = zero_zero_rat )
% 9.25/5.26           => ( ( member_nat @ I @ S3 )
% 9.25/5.26             => ( ( F2 @ I )
% 9.25/5.26                = zero_zero_rat ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8128_sum__nonneg__0,axiom,
% 9.25/5.26      ! [S3: set_int,F2: int > rat,I: int] :
% 9.25/5.26        ( ( finite_finite_int @ S3 )
% 9.25/5.26       => ( ! [I2: int] :
% 9.25/5.26              ( ( member_int @ I2 @ S3 )
% 9.25/5.26             => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I2 ) ) )
% 9.25/5.26         => ( ( ( groups3906332499630173760nt_rat @ F2 @ S3 )
% 9.25/5.26              = zero_zero_rat )
% 9.25/5.26           => ( ( member_int @ I @ S3 )
% 9.25/5.26             => ( ( F2 @ I )
% 9.25/5.26                = zero_zero_rat ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8129_sum__nonneg__0,axiom,
% 9.25/5.26      ! [S3: set_int,F2: int > nat,I: int] :
% 9.25/5.26        ( ( finite_finite_int @ S3 )
% 9.25/5.26       => ( ! [I2: int] :
% 9.25/5.26              ( ( member_int @ I2 @ S3 )
% 9.25/5.26             => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I2 ) ) )
% 9.25/5.26         => ( ( ( groups4541462559716669496nt_nat @ F2 @ S3 )
% 9.25/5.26              = zero_zero_nat )
% 9.25/5.26           => ( ( member_int @ I @ S3 )
% 9.25/5.26             => ( ( F2 @ I )
% 9.25/5.26                = zero_zero_nat ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8130_sum__nonneg__0,axiom,
% 9.25/5.26      ! [S3: set_nat,F2: nat > int,I: nat] :
% 9.25/5.26        ( ( finite_finite_nat @ S3 )
% 9.25/5.26       => ( ! [I2: nat] :
% 9.25/5.26              ( ( member_nat @ I2 @ S3 )
% 9.25/5.26             => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ I2 ) ) )
% 9.25/5.26         => ( ( ( groups3539618377306564664at_int @ F2 @ S3 )
% 9.25/5.26              = zero_zero_int )
% 9.25/5.26           => ( ( member_nat @ I @ S3 )
% 9.25/5.26             => ( ( F2 @ I )
% 9.25/5.26                = zero_zero_int ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8131_sum__nonneg__0,axiom,
% 9.25/5.26      ! [S3: set_nat,F2: nat > nat,I: nat] :
% 9.25/5.26        ( ( finite_finite_nat @ S3 )
% 9.25/5.26       => ( ! [I2: nat] :
% 9.25/5.26              ( ( member_nat @ I2 @ S3 )
% 9.25/5.26             => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I2 ) ) )
% 9.25/5.26         => ( ( ( groups3542108847815614940at_nat @ F2 @ S3 )
% 9.25/5.26              = zero_zero_nat )
% 9.25/5.26           => ( ( member_nat @ I @ S3 )
% 9.25/5.26             => ( ( F2 @ I )
% 9.25/5.26                = zero_zero_nat ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8132_sum__nonneg__0,axiom,
% 9.25/5.26      ! [S3: set_int,F2: int > int,I: int] :
% 9.25/5.26        ( ( finite_finite_int @ S3 )
% 9.25/5.26       => ( ! [I2: int] :
% 9.25/5.26              ( ( member_int @ I2 @ S3 )
% 9.25/5.26             => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ I2 ) ) )
% 9.25/5.26         => ( ( ( groups4538972089207619220nt_int @ F2 @ S3 )
% 9.25/5.26              = zero_zero_int )
% 9.25/5.26           => ( ( member_int @ I @ S3 )
% 9.25/5.26             => ( ( F2 @ I )
% 9.25/5.26                = zero_zero_int ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8133_sum__nonneg__0,axiom,
% 9.25/5.26      ! [S3: set_set_nat,F2: set_nat > code_integer,I: set_nat] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ S3 )
% 9.25/5.26       => ( ! [I2: set_nat] :
% 9.25/5.26              ( ( member_set_nat @ I2 @ S3 )
% 9.25/5.26             => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) ) )
% 9.25/5.26         => ( ( ( groups9190459664516455967nteger @ F2 @ S3 )
% 9.25/5.26              = zero_z3403309356797280102nteger )
% 9.25/5.26           => ( ( member_set_nat @ I @ S3 )
% 9.25/5.26             => ( ( F2 @ I )
% 9.25/5.26                = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8134_sum__nonneg__0,axiom,
% 9.25/5.26      ! [S3: set_set_nat,F2: set_nat > rat,I: set_nat] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ S3 )
% 9.25/5.26       => ( ! [I2: set_nat] :
% 9.25/5.26              ( ( member_set_nat @ I2 @ S3 )
% 9.25/5.26             => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I2 ) ) )
% 9.25/5.26         => ( ( ( groups7659867448343625626at_rat @ F2 @ S3 )
% 9.25/5.26              = zero_zero_rat )
% 9.25/5.26           => ( ( member_set_nat @ I @ S3 )
% 9.25/5.26             => ( ( F2 @ I )
% 9.25/5.26                = zero_zero_rat ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8135_ivl__disj__un__one_I2_J,axiom,
% 9.25/5.26      ! [L: rat,U: rat] :
% 9.25/5.26        ( ( ord_less_eq_rat @ L @ U )
% 9.25/5.26       => ( ( sup_sup_set_rat @ ( set_ord_lessThan_rat @ L ) @ ( set_or4029947393144176647an_rat @ L @ U ) )
% 9.25/5.26          = ( set_ord_lessThan_rat @ U ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8136_ivl__disj__un__one_I2_J,axiom,
% 9.25/5.26      ! [L: nat,U: nat] :
% 9.25/5.26        ( ( ord_less_eq_nat @ L @ U )
% 9.25/5.26       => ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 9.25/5.26          = ( set_ord_lessThan_nat @ U ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8137_ivl__disj__un__one_I2_J,axiom,
% 9.25/5.26      ! [L: code_integer,U: code_integer] :
% 9.25/5.26        ( ( ord_le3102999989581377725nteger @ L @ U )
% 9.25/5.26       => ( ( sup_su848401254843788991nteger @ ( set_or5754767410780653050nteger @ L ) @ ( set_or8404916559141939852nteger @ L @ U ) )
% 9.25/5.26          = ( set_or5754767410780653050nteger @ U ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8138_ivl__disj__un__one_I2_J,axiom,
% 9.25/5.26      ! [L: int,U: int] :
% 9.25/5.26        ( ( ord_less_eq_int @ L @ U )
% 9.25/5.26       => ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or4662586982721622107an_int @ L @ U ) )
% 9.25/5.26          = ( set_ord_lessThan_int @ U ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8139_ivl__disj__int__one_I4_J,axiom,
% 9.25/5.26      ! [L: $o,U: $o] :
% 9.25/5.26        ( ( inf_inf_set_o @ ( set_ord_lessThan_o @ L ) @ ( set_or8904488021354931149Most_o @ L @ U ) )
% 9.25/5.26        = bot_bot_set_o ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8140_ivl__disj__int__one_I4_J,axiom,
% 9.25/5.26      ! [L: nat,U: nat] :
% 9.25/5.26        ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 9.25/5.26        = bot_bot_set_nat ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8141_ivl__disj__int__one_I4_J,axiom,
% 9.25/5.26      ! [L: int,U: int] :
% 9.25/5.26        ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or1266510415728281911st_int @ L @ U ) )
% 9.25/5.26        = bot_bot_set_int ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8142_ivl__disj__int__one_I4_J,axiom,
% 9.25/5.26      ! [L: code_integer,U: code_integer] :
% 9.25/5.26        ( ( inf_in1364745209274528805nteger @ ( set_or5754767410780653050nteger @ L ) @ ( set_or189985376899183464nteger @ L @ U ) )
% 9.25/5.26        = bot_bo3990330152332043303nteger ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8143_prod_Otriangle__reindex,axiom,
% 9.25/5.26      ! [G2: nat > nat > nat,N: nat] :
% 9.25/5.26        ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G2 )
% 9.25/5.26          @ ( collec3392354462482085612at_nat
% 9.25/5.26            @ ( produc6081775807080527818_nat_o
% 9.25/5.26              @ ^ [I3: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 9.25/5.26        = ( groups708209901874060359at_nat
% 9.25/5.26          @ ^ [K4: nat] :
% 9.25/5.26              ( groups708209901874060359at_nat
% 9.25/5.26              @ ^ [I3: nat] : ( G2 @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 9.25/5.26              @ ( set_ord_atMost_nat @ K4 ) )
% 9.25/5.26          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8144_prod_Otriangle__reindex,axiom,
% 9.25/5.26      ! [G2: nat > nat > int,N: nat] :
% 9.25/5.26        ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G2 )
% 9.25/5.26          @ ( collec3392354462482085612at_nat
% 9.25/5.26            @ ( produc6081775807080527818_nat_o
% 9.25/5.26              @ ^ [I3: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 9.25/5.26        = ( groups705719431365010083at_int
% 9.25/5.26          @ ^ [K4: nat] :
% 9.25/5.26              ( groups705719431365010083at_int
% 9.25/5.26              @ ^ [I3: nat] : ( G2 @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 9.25/5.26              @ ( set_ord_atMost_nat @ K4 ) )
% 9.25/5.26          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8145_ivl__disj__int__one_I2_J,axiom,
% 9.25/5.26      ! [L: $o,U: $o] :
% 9.25/5.26        ( ( inf_inf_set_o @ ( set_ord_lessThan_o @ L ) @ ( set_or7139685690850216873Than_o @ L @ U ) )
% 9.25/5.26        = bot_bot_set_o ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8146_ivl__disj__int__one_I2_J,axiom,
% 9.25/5.26      ! [L: nat,U: nat] :
% 9.25/5.26        ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 9.25/5.26        = bot_bot_set_nat ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8147_ivl__disj__int__one_I2_J,axiom,
% 9.25/5.26      ! [L: code_integer,U: code_integer] :
% 9.25/5.26        ( ( inf_in1364745209274528805nteger @ ( set_or5754767410780653050nteger @ L ) @ ( set_or8404916559141939852nteger @ L @ U ) )
% 9.25/5.26        = bot_bo3990330152332043303nteger ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8148_ivl__disj__int__one_I2_J,axiom,
% 9.25/5.26      ! [L: int,U: int] :
% 9.25/5.26        ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or4662586982721622107an_int @ L @ U ) )
% 9.25/5.26        = bot_bot_set_int ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8149_sum_Ointer__restrict,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > code_integer,B2: set_int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups7873554091576472773nteger @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.26          = ( groups7873554091576472773nteger
% 9.25/5.26            @ ^ [X3: int] : ( if_Code_integer @ ( member_int @ X3 @ B2 ) @ ( G2 @ X3 ) @ zero_z3403309356797280102nteger )
% 9.25/5.26            @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8150_sum_Ointer__restrict,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > rat,B2: set_int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups3906332499630173760nt_rat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.26          = ( groups3906332499630173760nt_rat
% 9.25/5.26            @ ^ [X3: int] : ( if_rat @ ( member_int @ X3 @ B2 ) @ ( G2 @ X3 ) @ zero_zero_rat )
% 9.25/5.26            @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8151_sum_Ointer__restrict,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > nat,B2: set_int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups4541462559716669496nt_nat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.26          = ( groups4541462559716669496nt_nat
% 9.25/5.26            @ ^ [X3: int] : ( if_nat @ ( member_int @ X3 @ B2 ) @ ( G2 @ X3 ) @ zero_zero_nat )
% 9.25/5.26            @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8152_sum_Ointer__restrict,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > code_integer,B2: set_nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups7501900531339628137nteger @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.26          = ( groups7501900531339628137nteger
% 9.25/5.26            @ ^ [X3: nat] : ( if_Code_integer @ ( member_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ zero_z3403309356797280102nteger )
% 9.25/5.26            @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8153_sum_Ointer__restrict,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > rat,B2: set_nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups2906978787729119204at_rat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.26          = ( groups2906978787729119204at_rat
% 9.25/5.26            @ ^ [X3: nat] : ( if_rat @ ( member_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ zero_zero_rat )
% 9.25/5.26            @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8154_sum_Ointer__restrict,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > int,B2: set_nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups3539618377306564664at_int @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.26          = ( groups3539618377306564664at_int
% 9.25/5.26            @ ^ [X3: nat] : ( if_int @ ( member_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ zero_zero_int )
% 9.25/5.26            @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8155_sum_Ointer__restrict,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > nat,B2: set_nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups3542108847815614940at_nat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.26          = ( groups3542108847815614940at_nat
% 9.25/5.26            @ ^ [X3: nat] : ( if_nat @ ( member_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ zero_zero_nat )
% 9.25/5.26            @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8156_sum_Ointer__restrict,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > int,B2: set_int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups4538972089207619220nt_int @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.26          = ( groups4538972089207619220nt_int
% 9.25/5.26            @ ^ [X3: int] : ( if_int @ ( member_int @ X3 @ B2 ) @ ( G2 @ X3 ) @ zero_zero_int )
% 9.25/5.26            @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8157_sum_Ointer__restrict,axiom,
% 9.25/5.26      ! [A2: set_set_nat,G2: set_nat > code_integer,B2: set_set_nat] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.26       => ( ( groups9190459664516455967nteger @ G2 @ ( inf_inf_set_set_nat @ A2 @ B2 ) )
% 9.25/5.26          = ( groups9190459664516455967nteger
% 9.25/5.26            @ ^ [X3: set_nat] : ( if_Code_integer @ ( member_set_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ zero_z3403309356797280102nteger )
% 9.25/5.26            @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8158_sum_Ointer__restrict,axiom,
% 9.25/5.26      ! [A2: set_set_nat,G2: set_nat > rat,B2: set_set_nat] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.26       => ( ( groups7659867448343625626at_rat @ G2 @ ( inf_inf_set_set_nat @ A2 @ B2 ) )
% 9.25/5.26          = ( groups7659867448343625626at_rat
% 9.25/5.26            @ ^ [X3: set_nat] : ( if_rat @ ( member_set_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ zero_zero_rat )
% 9.25/5.26            @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8159_sum_Osetdiff__irrelevant,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups7873554091576472773nteger @ G2
% 9.25/5.26            @ ( minus_minus_set_int @ A2
% 9.25/5.26              @ ( collect_int
% 9.25/5.26                @ ^ [X3: int] :
% 9.25/5.26                    ( ( G2 @ X3 )
% 9.25/5.26                    = zero_z3403309356797280102nteger ) ) ) )
% 9.25/5.26          = ( groups7873554091576472773nteger @ G2 @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8160_sum_Osetdiff__irrelevant,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups3906332499630173760nt_rat @ G2
% 9.25/5.26            @ ( minus_minus_set_int @ A2
% 9.25/5.26              @ ( collect_int
% 9.25/5.26                @ ^ [X3: int] :
% 9.25/5.26                    ( ( G2 @ X3 )
% 9.25/5.26                    = zero_zero_rat ) ) ) )
% 9.25/5.26          = ( groups3906332499630173760nt_rat @ G2 @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8161_sum_Osetdiff__irrelevant,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups4541462559716669496nt_nat @ G2
% 9.25/5.26            @ ( minus_minus_set_int @ A2
% 9.25/5.26              @ ( collect_int
% 9.25/5.26                @ ^ [X3: int] :
% 9.25/5.26                    ( ( G2 @ X3 )
% 9.25/5.26                    = zero_zero_nat ) ) ) )
% 9.25/5.26          = ( groups4541462559716669496nt_nat @ G2 @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8162_sum_Osetdiff__irrelevant,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups7501900531339628137nteger @ G2
% 9.25/5.26            @ ( minus_minus_set_nat @ A2
% 9.25/5.26              @ ( collect_nat
% 9.25/5.26                @ ^ [X3: nat] :
% 9.25/5.26                    ( ( G2 @ X3 )
% 9.25/5.26                    = zero_z3403309356797280102nteger ) ) ) )
% 9.25/5.26          = ( groups7501900531339628137nteger @ G2 @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8163_sum_Osetdiff__irrelevant,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups2906978787729119204at_rat @ G2
% 9.25/5.26            @ ( minus_minus_set_nat @ A2
% 9.25/5.26              @ ( collect_nat
% 9.25/5.26                @ ^ [X3: nat] :
% 9.25/5.26                    ( ( G2 @ X3 )
% 9.25/5.26                    = zero_zero_rat ) ) ) )
% 9.25/5.26          = ( groups2906978787729119204at_rat @ G2 @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8164_sum_Osetdiff__irrelevant,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups3539618377306564664at_int @ G2
% 9.25/5.26            @ ( minus_minus_set_nat @ A2
% 9.25/5.26              @ ( collect_nat
% 9.25/5.26                @ ^ [X3: nat] :
% 9.25/5.26                    ( ( G2 @ X3 )
% 9.25/5.26                    = zero_zero_int ) ) ) )
% 9.25/5.26          = ( groups3539618377306564664at_int @ G2 @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8165_sum_Osetdiff__irrelevant,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups3542108847815614940at_nat @ G2
% 9.25/5.26            @ ( minus_minus_set_nat @ A2
% 9.25/5.26              @ ( collect_nat
% 9.25/5.26                @ ^ [X3: nat] :
% 9.25/5.26                    ( ( G2 @ X3 )
% 9.25/5.26                    = zero_zero_nat ) ) ) )
% 9.25/5.26          = ( groups3542108847815614940at_nat @ G2 @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8166_sum_Osetdiff__irrelevant,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups4538972089207619220nt_int @ G2
% 9.25/5.26            @ ( minus_minus_set_int @ A2
% 9.25/5.26              @ ( collect_int
% 9.25/5.26                @ ^ [X3: int] :
% 9.25/5.26                    ( ( G2 @ X3 )
% 9.25/5.26                    = zero_zero_int ) ) ) )
% 9.25/5.26          = ( groups4538972089207619220nt_int @ G2 @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8167_sum_Osetdiff__irrelevant,axiom,
% 9.25/5.26      ! [A2: set_set_nat,G2: set_nat > code_integer] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.26       => ( ( groups9190459664516455967nteger @ G2
% 9.25/5.26            @ ( minus_2163939370556025621et_nat @ A2
% 9.25/5.26              @ ( collect_set_nat
% 9.25/5.26                @ ^ [X3: set_nat] :
% 9.25/5.26                    ( ( G2 @ X3 )
% 9.25/5.26                    = zero_z3403309356797280102nteger ) ) ) )
% 9.25/5.26          = ( groups9190459664516455967nteger @ G2 @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8168_sum_Osetdiff__irrelevant,axiom,
% 9.25/5.26      ! [A2: set_set_nat,G2: set_nat > rat] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.26       => ( ( groups7659867448343625626at_rat @ G2
% 9.25/5.26            @ ( minus_2163939370556025621et_nat @ A2
% 9.25/5.26              @ ( collect_set_nat
% 9.25/5.26                @ ^ [X3: set_nat] :
% 9.25/5.26                    ( ( G2 @ X3 )
% 9.25/5.26                    = zero_zero_rat ) ) ) )
% 9.25/5.26          = ( groups7659867448343625626at_rat @ G2 @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8169_prod_Ointer__restrict,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > code_integer,B2: set_int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups3827104343326376752nteger @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.26          = ( groups3827104343326376752nteger
% 9.25/5.26            @ ^ [X3: int] : ( if_Code_integer @ ( member_int @ X3 @ B2 ) @ ( G2 @ X3 ) @ one_one_Code_integer )
% 9.25/5.26            @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8170_prod_Ointer__restrict,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > assn,B2: set_int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups7882442080178216443t_assn @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.26          = ( groups7882442080178216443t_assn
% 9.25/5.26            @ ^ [X3: int] : ( if_assn @ ( member_int @ X3 @ B2 ) @ ( G2 @ X3 ) @ one_one_assn )
% 9.25/5.26            @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8171_prod_Ointer__restrict,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > rat,B2: set_int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.26          = ( groups1072433553688619179nt_rat
% 9.25/5.26            @ ^ [X3: int] : ( if_rat @ ( member_int @ X3 @ B2 ) @ ( G2 @ X3 ) @ one_one_rat )
% 9.25/5.26            @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8172_prod_Ointer__restrict,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > nat,B2: set_int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.26          = ( groups1707563613775114915nt_nat
% 9.25/5.26            @ ^ [X3: int] : ( if_nat @ ( member_int @ X3 @ B2 ) @ ( G2 @ X3 ) @ one_one_nat )
% 9.25/5.26            @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8173_prod_Ointer__restrict,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > code_integer,B2: set_nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups3455450783089532116nteger @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.26          = ( groups3455450783089532116nteger
% 9.25/5.26            @ ^ [X3: nat] : ( if_Code_integer @ ( member_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ one_one_Code_integer )
% 9.25/5.26            @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8174_prod_Ointer__restrict,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > assn,B2: set_nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups6906906614972039071t_assn @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.26          = ( groups6906906614972039071t_assn
% 9.25/5.26            @ ^ [X3: nat] : ( if_assn @ ( member_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ one_one_assn )
% 9.25/5.26            @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8175_prod_Ointer__restrict,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > rat,B2: set_nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.26          = ( groups73079841787564623at_rat
% 9.25/5.26            @ ^ [X3: nat] : ( if_rat @ ( member_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ one_one_rat )
% 9.25/5.26            @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8176_prod_Ointer__restrict,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > nat,B2: set_nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups708209901874060359at_nat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.26          = ( groups708209901874060359at_nat
% 9.25/5.26            @ ^ [X3: nat] : ( if_nat @ ( member_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ one_one_nat )
% 9.25/5.26            @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8177_prod_Ointer__restrict,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > int,B2: set_nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups705719431365010083at_int @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.26          = ( groups705719431365010083at_int
% 9.25/5.26            @ ^ [X3: nat] : ( if_int @ ( member_nat @ X3 @ B2 ) @ ( G2 @ X3 ) @ one_one_int )
% 9.25/5.26            @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8178_prod_Ointer__restrict,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > int,B2: set_int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups1705073143266064639nt_int @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.26          = ( groups1705073143266064639nt_int
% 9.25/5.26            @ ^ [X3: int] : ( if_int @ ( member_int @ X3 @ B2 ) @ ( G2 @ X3 ) @ one_one_int )
% 9.25/5.26            @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8179_prod_Osetdiff__irrelevant,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups3827104343326376752nteger @ G2
% 9.25/5.26            @ ( minus_minus_set_int @ A2
% 9.25/5.26              @ ( collect_int
% 9.25/5.26                @ ^ [X3: int] :
% 9.25/5.26                    ( ( G2 @ X3 )
% 9.25/5.26                    = one_one_Code_integer ) ) ) )
% 9.25/5.26          = ( groups3827104343326376752nteger @ G2 @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8180_prod_Osetdiff__irrelevant,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > assn] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups7882442080178216443t_assn @ G2
% 9.25/5.26            @ ( minus_minus_set_int @ A2
% 9.25/5.26              @ ( collect_int
% 9.25/5.26                @ ^ [X3: int] :
% 9.25/5.26                    ( ( G2 @ X3 )
% 9.25/5.26                    = one_one_assn ) ) ) )
% 9.25/5.26          = ( groups7882442080178216443t_assn @ G2 @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8181_prod_Osetdiff__irrelevant,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups1072433553688619179nt_rat @ G2
% 9.25/5.26            @ ( minus_minus_set_int @ A2
% 9.25/5.26              @ ( collect_int
% 9.25/5.26                @ ^ [X3: int] :
% 9.25/5.26                    ( ( G2 @ X3 )
% 9.25/5.26                    = one_one_rat ) ) ) )
% 9.25/5.26          = ( groups1072433553688619179nt_rat @ G2 @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8182_prod_Osetdiff__irrelevant,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups1707563613775114915nt_nat @ G2
% 9.25/5.26            @ ( minus_minus_set_int @ A2
% 9.25/5.26              @ ( collect_int
% 9.25/5.26                @ ^ [X3: int] :
% 9.25/5.26                    ( ( G2 @ X3 )
% 9.25/5.26                    = one_one_nat ) ) ) )
% 9.25/5.26          = ( groups1707563613775114915nt_nat @ G2 @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8183_prod_Osetdiff__irrelevant,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups3455450783089532116nteger @ G2
% 9.25/5.26            @ ( minus_minus_set_nat @ A2
% 9.25/5.26              @ ( collect_nat
% 9.25/5.26                @ ^ [X3: nat] :
% 9.25/5.26                    ( ( G2 @ X3 )
% 9.25/5.26                    = one_one_Code_integer ) ) ) )
% 9.25/5.26          = ( groups3455450783089532116nteger @ G2 @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8184_prod_Osetdiff__irrelevant,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > assn] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups6906906614972039071t_assn @ G2
% 9.25/5.26            @ ( minus_minus_set_nat @ A2
% 9.25/5.26              @ ( collect_nat
% 9.25/5.26                @ ^ [X3: nat] :
% 9.25/5.26                    ( ( G2 @ X3 )
% 9.25/5.26                    = one_one_assn ) ) ) )
% 9.25/5.26          = ( groups6906906614972039071t_assn @ G2 @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8185_prod_Osetdiff__irrelevant,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups73079841787564623at_rat @ G2
% 9.25/5.26            @ ( minus_minus_set_nat @ A2
% 9.25/5.26              @ ( collect_nat
% 9.25/5.26                @ ^ [X3: nat] :
% 9.25/5.26                    ( ( G2 @ X3 )
% 9.25/5.26                    = one_one_rat ) ) ) )
% 9.25/5.26          = ( groups73079841787564623at_rat @ G2 @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8186_prod_Osetdiff__irrelevant,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups708209901874060359at_nat @ G2
% 9.25/5.26            @ ( minus_minus_set_nat @ A2
% 9.25/5.26              @ ( collect_nat
% 9.25/5.26                @ ^ [X3: nat] :
% 9.25/5.26                    ( ( G2 @ X3 )
% 9.25/5.26                    = one_one_nat ) ) ) )
% 9.25/5.26          = ( groups708209901874060359at_nat @ G2 @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8187_prod_Osetdiff__irrelevant,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups705719431365010083at_int @ G2
% 9.25/5.26            @ ( minus_minus_set_nat @ A2
% 9.25/5.26              @ ( collect_nat
% 9.25/5.26                @ ^ [X3: nat] :
% 9.25/5.26                    ( ( G2 @ X3 )
% 9.25/5.26                    = one_one_int ) ) ) )
% 9.25/5.26          = ( groups705719431365010083at_int @ G2 @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8188_prod_Osetdiff__irrelevant,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups1705073143266064639nt_int @ G2
% 9.25/5.26            @ ( minus_minus_set_int @ A2
% 9.25/5.26              @ ( collect_int
% 9.25/5.26                @ ^ [X3: int] :
% 9.25/5.26                    ( ( G2 @ X3 )
% 9.25/5.26                    = one_one_int ) ) ) )
% 9.25/5.26          = ( groups1705073143266064639nt_int @ G2 @ A2 ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8189_finite__divisors__nat,axiom,
% 9.25/5.26      ! [M: nat] :
% 9.25/5.26        ( ( ord_less_nat @ zero_zero_nat @ M )
% 9.25/5.26       => ( finite_finite_nat
% 9.25/5.26          @ ( collect_nat
% 9.25/5.26            @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8190_zsgn__def,axiom,
% 9.25/5.26      ( sgn_sgn_int
% 9.25/5.26      = ( ^ [I3: int] : ( if_int @ ( I3 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I3 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8191_sum__diff__distrib,axiom,
% 9.25/5.26      ! [Q2: nat > nat,P: nat > nat,N: nat] :
% 9.25/5.26        ( ! [X2: nat] : ( ord_less_eq_nat @ ( Q2 @ X2 ) @ ( P @ X2 ) )
% 9.25/5.26       => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q2 @ ( set_ord_lessThan_nat @ N ) ) )
% 9.25/5.26          = ( groups3542108847815614940at_nat
% 9.25/5.26            @ ^ [X3: nat] : ( minus_minus_nat @ ( P @ X3 ) @ ( Q2 @ X3 ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8192_sum__pos,axiom,
% 9.25/5.26      ! [I4: set_o,F2: $o > code_integer] :
% 9.25/5.26        ( ( finite_finite_o @ I4 )
% 9.25/5.26       => ( ( I4 != bot_bot_set_o )
% 9.25/5.26         => ( ! [I2: $o] :
% 9.25/5.26                ( ( member_o @ I2 @ I4 )
% 9.25/5.26               => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) ) )
% 9.25/5.26           => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups4406642042086082107nteger @ F2 @ I4 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8193_sum__pos,axiom,
% 9.25/5.26      ! [I4: set_nat,F2: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ I4 )
% 9.25/5.26       => ( ( I4 != bot_bot_set_nat )
% 9.25/5.26         => ( ! [I2: nat] :
% 9.25/5.26                ( ( member_nat @ I2 @ I4 )
% 9.25/5.26               => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) ) )
% 9.25/5.26           => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups7501900531339628137nteger @ F2 @ I4 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8194_sum__pos,axiom,
% 9.25/5.26      ! [I4: set_int,F2: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ I4 )
% 9.25/5.26       => ( ( I4 != bot_bot_set_int )
% 9.25/5.26         => ( ! [I2: int] :
% 9.25/5.26                ( ( member_int @ I2 @ I4 )
% 9.25/5.26               => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) ) )
% 9.25/5.26           => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups7873554091576472773nteger @ F2 @ I4 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8195_sum__pos,axiom,
% 9.25/5.26      ! [I4: set_o,F2: $o > rat] :
% 9.25/5.26        ( ( finite_finite_o @ I4 )
% 9.25/5.26       => ( ( I4 != bot_bot_set_o )
% 9.25/5.26         => ( ! [I2: $o] :
% 9.25/5.26                ( ( member_o @ I2 @ I4 )
% 9.25/5.26               => ( ord_less_rat @ zero_zero_rat @ ( F2 @ I2 ) ) )
% 9.25/5.26           => ( ord_less_rat @ zero_zero_rat @ ( groups7872700643590313910_o_rat @ F2 @ I4 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8196_sum__pos,axiom,
% 9.25/5.26      ! [I4: set_nat,F2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ I4 )
% 9.25/5.26       => ( ( I4 != bot_bot_set_nat )
% 9.25/5.26         => ( ! [I2: nat] :
% 9.25/5.26                ( ( member_nat @ I2 @ I4 )
% 9.25/5.26               => ( ord_less_rat @ zero_zero_rat @ ( F2 @ I2 ) ) )
% 9.25/5.26           => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F2 @ I4 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8197_sum__pos,axiom,
% 9.25/5.26      ! [I4: set_int,F2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ I4 )
% 9.25/5.26       => ( ( I4 != bot_bot_set_int )
% 9.25/5.26         => ( ! [I2: int] :
% 9.25/5.26                ( ( member_int @ I2 @ I4 )
% 9.25/5.26               => ( ord_less_rat @ zero_zero_rat @ ( F2 @ I2 ) ) )
% 9.25/5.26           => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F2 @ I4 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8198_sum__pos,axiom,
% 9.25/5.26      ! [I4: set_o,F2: $o > nat] :
% 9.25/5.26        ( ( finite_finite_o @ I4 )
% 9.25/5.26       => ( ( I4 != bot_bot_set_o )
% 9.25/5.26         => ( ! [I2: $o] :
% 9.25/5.26                ( ( member_o @ I2 @ I4 )
% 9.25/5.26               => ( ord_less_nat @ zero_zero_nat @ ( F2 @ I2 ) ) )
% 9.25/5.26           => ( ord_less_nat @ zero_zero_nat @ ( groups8507830703676809646_o_nat @ F2 @ I4 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8199_sum__pos,axiom,
% 9.25/5.26      ! [I4: set_int,F2: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ I4 )
% 9.25/5.26       => ( ( I4 != bot_bot_set_int )
% 9.25/5.26         => ( ! [I2: int] :
% 9.25/5.26                ( ( member_int @ I2 @ I4 )
% 9.25/5.26               => ( ord_less_nat @ zero_zero_nat @ ( F2 @ I2 ) ) )
% 9.25/5.26           => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F2 @ I4 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8200_sum__pos,axiom,
% 9.25/5.26      ! [I4: set_o,F2: $o > int] :
% 9.25/5.26        ( ( finite_finite_o @ I4 )
% 9.25/5.26       => ( ( I4 != bot_bot_set_o )
% 9.25/5.26         => ( ! [I2: $o] :
% 9.25/5.26                ( ( member_o @ I2 @ I4 )
% 9.25/5.26               => ( ord_less_int @ zero_zero_int @ ( F2 @ I2 ) ) )
% 9.25/5.26           => ( ord_less_int @ zero_zero_int @ ( groups8505340233167759370_o_int @ F2 @ I4 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8201_sum__pos,axiom,
% 9.25/5.26      ! [I4: set_nat,F2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ I4 )
% 9.25/5.26       => ( ( I4 != bot_bot_set_nat )
% 9.25/5.26         => ( ! [I2: nat] :
% 9.25/5.26                ( ( member_nat @ I2 @ I4 )
% 9.25/5.26               => ( ord_less_int @ zero_zero_int @ ( F2 @ I2 ) ) )
% 9.25/5.26           => ( ord_less_int @ zero_zero_int @ ( groups3539618377306564664at_int @ F2 @ I4 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8202_less__1__prod2,axiom,
% 9.25/5.26      ! [I4: set_nat,I: nat,F2: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ I4 )
% 9.25/5.26       => ( ( member_nat @ I @ I4 )
% 9.25/5.26         => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I ) )
% 9.25/5.26           => ( ! [I2: nat] :
% 9.25/5.26                  ( ( member_nat @ I2 @ I4 )
% 9.25/5.26                 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ I2 ) ) )
% 9.25/5.26             => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F2 @ I4 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8203_less__1__prod2,axiom,
% 9.25/5.26      ! [I4: set_int,I: int,F2: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ I4 )
% 9.25/5.26       => ( ( member_int @ I @ I4 )
% 9.25/5.26         => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I ) )
% 9.25/5.26           => ( ! [I2: int] :
% 9.25/5.26                  ( ( member_int @ I2 @ I4 )
% 9.25/5.26                 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ I2 ) ) )
% 9.25/5.26             => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F2 @ I4 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8204_less__1__prod2,axiom,
% 9.25/5.26      ! [I4: set_nat,I: nat,F2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ I4 )
% 9.25/5.26       => ( ( member_nat @ I @ I4 )
% 9.25/5.26         => ( ( ord_less_rat @ one_one_rat @ ( F2 @ I ) )
% 9.25/5.26           => ( ! [I2: nat] :
% 9.25/5.26                  ( ( member_nat @ I2 @ I4 )
% 9.25/5.26                 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ I2 ) ) )
% 9.25/5.26             => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F2 @ I4 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8205_less__1__prod2,axiom,
% 9.25/5.26      ! [I4: set_int,I: int,F2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ I4 )
% 9.25/5.26       => ( ( member_int @ I @ I4 )
% 9.25/5.26         => ( ( ord_less_rat @ one_one_rat @ ( F2 @ I ) )
% 9.25/5.26           => ( ! [I2: int] :
% 9.25/5.26                  ( ( member_int @ I2 @ I4 )
% 9.25/5.26                 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ I2 ) ) )
% 9.25/5.26             => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F2 @ I4 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8206_less__1__prod2,axiom,
% 9.25/5.26      ! [I4: set_nat,I: nat,F2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ I4 )
% 9.25/5.26       => ( ( member_nat @ I @ I4 )
% 9.25/5.26         => ( ( ord_less_int @ one_one_int @ ( F2 @ I ) )
% 9.25/5.26           => ( ! [I2: nat] :
% 9.25/5.26                  ( ( member_nat @ I2 @ I4 )
% 9.25/5.26                 => ( ord_less_eq_int @ one_one_int @ ( F2 @ I2 ) ) )
% 9.25/5.26             => ( ord_less_int @ one_one_int @ ( groups705719431365010083at_int @ F2 @ I4 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8207_less__1__prod2,axiom,
% 9.25/5.26      ! [I4: set_int,I: int,F2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ I4 )
% 9.25/5.26       => ( ( member_int @ I @ I4 )
% 9.25/5.26         => ( ( ord_less_int @ one_one_int @ ( F2 @ I ) )
% 9.25/5.26           => ( ! [I2: int] :
% 9.25/5.26                  ( ( member_int @ I2 @ I4 )
% 9.25/5.26                 => ( ord_less_eq_int @ one_one_int @ ( F2 @ I2 ) ) )
% 9.25/5.26             => ( ord_less_int @ one_one_int @ ( groups1705073143266064639nt_int @ F2 @ I4 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8208_less__1__prod2,axiom,
% 9.25/5.26      ! [I4: set_set_nat,I: set_nat,F2: set_nat > code_integer] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ I4 )
% 9.25/5.26       => ( ( member_set_nat @ I @ I4 )
% 9.25/5.26         => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I ) )
% 9.25/5.26           => ( ! [I2: set_nat] :
% 9.25/5.26                  ( ( member_set_nat @ I2 @ I4 )
% 9.25/5.26                 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ I2 ) ) )
% 9.25/5.26             => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups2761809935038513290nteger @ F2 @ I4 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8209_less__1__prod2,axiom,
% 9.25/5.26      ! [I4: set_set_nat,I: set_nat,F2: set_nat > rat] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ I4 )
% 9.25/5.26       => ( ( member_set_nat @ I @ I4 )
% 9.25/5.26         => ( ( ord_less_rat @ one_one_rat @ ( F2 @ I ) )
% 9.25/5.26           => ( ! [I2: set_nat] :
% 9.25/5.26                  ( ( member_set_nat @ I2 @ I4 )
% 9.25/5.26                 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ I2 ) ) )
% 9.25/5.26             => ( ord_less_rat @ one_one_rat @ ( groups3613417700093529605at_rat @ F2 @ I4 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8210_less__1__prod2,axiom,
% 9.25/5.26      ! [I4: set_set_nat,I: set_nat,F2: set_nat > int] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ I4 )
% 9.25/5.26       => ( ( member_set_nat @ I @ I4 )
% 9.25/5.26         => ( ( ord_less_int @ one_one_int @ ( F2 @ I ) )
% 9.25/5.26           => ( ! [I2: set_nat] :
% 9.25/5.26                  ( ( member_set_nat @ I2 @ I4 )
% 9.25/5.26                 => ( ord_less_eq_int @ one_one_int @ ( F2 @ I2 ) ) )
% 9.25/5.26             => ( ord_less_int @ one_one_int @ ( groups4246057289670975065at_int @ F2 @ I4 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8211_less__1__prod2,axiom,
% 9.25/5.26      ! [I4: set_Pr1261947904930325089at_nat,I: product_prod_nat_nat,F2: product_prod_nat_nat > code_integer] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ I4 )
% 9.25/5.26       => ( ( member8440522571783428010at_nat @ I @ I4 )
% 9.25/5.26         => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I ) )
% 9.25/5.26           => ( ! [I2: product_prod_nat_nat] :
% 9.25/5.26                  ( ( member8440522571783428010at_nat @ I2 @ I4 )
% 9.25/5.26                 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ I2 ) ) )
% 9.25/5.26             => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups1230400874837758585nteger @ F2 @ I4 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8212_less__1__prod,axiom,
% 9.25/5.26      ! [I4: set_o,F2: $o > code_integer] :
% 9.25/5.26        ( ( finite_finite_o @ I4 )
% 9.25/5.26       => ( ( I4 != bot_bot_set_o )
% 9.25/5.26         => ( ! [I2: $o] :
% 9.25/5.26                ( ( member_o @ I2 @ I4 )
% 9.25/5.26               => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I2 ) ) )
% 9.25/5.26           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups7694694392188491536nteger @ F2 @ I4 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8213_less__1__prod,axiom,
% 9.25/5.26      ! [I4: set_nat,F2: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ I4 )
% 9.25/5.26       => ( ( I4 != bot_bot_set_nat )
% 9.25/5.26         => ( ! [I2: nat] :
% 9.25/5.26                ( ( member_nat @ I2 @ I4 )
% 9.25/5.26               => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I2 ) ) )
% 9.25/5.26           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F2 @ I4 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8214_less__1__prod,axiom,
% 9.25/5.26      ! [I4: set_int,F2: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ I4 )
% 9.25/5.26       => ( ( I4 != bot_bot_set_int )
% 9.25/5.26         => ( ! [I2: int] :
% 9.25/5.26                ( ( member_int @ I2 @ I4 )
% 9.25/5.26               => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I2 ) ) )
% 9.25/5.26           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F2 @ I4 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8215_less__1__prod,axiom,
% 9.25/5.26      ! [I4: set_o,F2: $o > rat] :
% 9.25/5.26        ( ( finite_finite_o @ I4 )
% 9.25/5.26       => ( ( I4 != bot_bot_set_o )
% 9.25/5.26         => ( ! [I2: $o] :
% 9.25/5.26                ( ( member_o @ I2 @ I4 )
% 9.25/5.26               => ( ord_less_rat @ one_one_rat @ ( F2 @ I2 ) ) )
% 9.25/5.26           => ( ord_less_rat @ one_one_rat @ ( groups2869687844427037835_o_rat @ F2 @ I4 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8216_less__1__prod,axiom,
% 9.25/5.26      ! [I4: set_nat,F2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ I4 )
% 9.25/5.26       => ( ( I4 != bot_bot_set_nat )
% 9.25/5.26         => ( ! [I2: nat] :
% 9.25/5.26                ( ( member_nat @ I2 @ I4 )
% 9.25/5.26               => ( ord_less_rat @ one_one_rat @ ( F2 @ I2 ) ) )
% 9.25/5.26           => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F2 @ I4 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8217_less__1__prod,axiom,
% 9.25/5.26      ! [I4: set_int,F2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ I4 )
% 9.25/5.26       => ( ( I4 != bot_bot_set_int )
% 9.25/5.26         => ( ! [I2: int] :
% 9.25/5.26                ( ( member_int @ I2 @ I4 )
% 9.25/5.26               => ( ord_less_rat @ one_one_rat @ ( F2 @ I2 ) ) )
% 9.25/5.26           => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F2 @ I4 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8218_less__1__prod,axiom,
% 9.25/5.26      ! [I4: set_o,F2: $o > int] :
% 9.25/5.26        ( ( finite_finite_o @ I4 )
% 9.25/5.26       => ( ( I4 != bot_bot_set_o )
% 9.25/5.26         => ( ! [I2: $o] :
% 9.25/5.26                ( ( member_o @ I2 @ I4 )
% 9.25/5.26               => ( ord_less_int @ one_one_int @ ( F2 @ I2 ) ) )
% 9.25/5.26           => ( ord_less_int @ one_one_int @ ( groups3502327434004483295_o_int @ F2 @ I4 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8219_less__1__prod,axiom,
% 9.25/5.26      ! [I4: set_nat,F2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ I4 )
% 9.25/5.26       => ( ( I4 != bot_bot_set_nat )
% 9.25/5.26         => ( ! [I2: nat] :
% 9.25/5.26                ( ( member_nat @ I2 @ I4 )
% 9.25/5.26               => ( ord_less_int @ one_one_int @ ( F2 @ I2 ) ) )
% 9.25/5.26           => ( ord_less_int @ one_one_int @ ( groups705719431365010083at_int @ F2 @ I4 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8220_less__1__prod,axiom,
% 9.25/5.26      ! [I4: set_int,F2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ I4 )
% 9.25/5.26       => ( ( I4 != bot_bot_set_int )
% 9.25/5.26         => ( ! [I2: int] :
% 9.25/5.26                ( ( member_int @ I2 @ I4 )
% 9.25/5.26               => ( ord_less_int @ one_one_int @ ( F2 @ I2 ) ) )
% 9.25/5.26           => ( ord_less_int @ one_one_int @ ( groups1705073143266064639nt_int @ F2 @ I4 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8221_less__1__prod,axiom,
% 9.25/5.26      ! [I4: set_set_nat,F2: set_nat > code_integer] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ I4 )
% 9.25/5.26       => ( ( I4 != bot_bot_set_set_nat )
% 9.25/5.26         => ( ! [I2: set_nat] :
% 9.25/5.26                ( ( member_set_nat @ I2 @ I4 )
% 9.25/5.26               => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I2 ) ) )
% 9.25/5.26           => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups2761809935038513290nteger @ F2 @ I4 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8222_sum_OlessThan__Suc__shift,axiom,
% 9.25/5.26      ! [G2: nat > rat,N: nat] :
% 9.25/5.26        ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.25/5.26        = ( plus_plus_rat @ ( G2 @ zero_zero_nat )
% 9.25/5.26          @ ( groups2906978787729119204at_rat
% 9.25/5.26            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8223_sum_OlessThan__Suc__shift,axiom,
% 9.25/5.26      ! [G2: nat > int,N: nat] :
% 9.25/5.26        ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.25/5.26        = ( plus_plus_int @ ( G2 @ zero_zero_nat )
% 9.25/5.26          @ ( groups3539618377306564664at_int
% 9.25/5.26            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8224_sum_OlessThan__Suc__shift,axiom,
% 9.25/5.26      ! [G2: nat > nat,N: nat] :
% 9.25/5.26        ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.25/5.26        = ( plus_plus_nat @ ( G2 @ zero_zero_nat )
% 9.25/5.26          @ ( groups3542108847815614940at_nat
% 9.25/5.26            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8225_sum__lessThan__telescope_H,axiom,
% 9.25/5.26      ! [F2: nat > rat,M: nat] :
% 9.25/5.26        ( ( groups2906978787729119204at_rat
% 9.25/5.26          @ ^ [N2: nat] : ( minus_minus_rat @ ( F2 @ N2 ) @ ( F2 @ ( suc @ N2 ) ) )
% 9.25/5.26          @ ( set_ord_lessThan_nat @ M ) )
% 9.25/5.26        = ( minus_minus_rat @ ( F2 @ zero_zero_nat ) @ ( F2 @ M ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8226_sum__lessThan__telescope_H,axiom,
% 9.25/5.26      ! [F2: nat > int,M: nat] :
% 9.25/5.26        ( ( groups3539618377306564664at_int
% 9.25/5.26          @ ^ [N2: nat] : ( minus_minus_int @ ( F2 @ N2 ) @ ( F2 @ ( suc @ N2 ) ) )
% 9.25/5.26          @ ( set_ord_lessThan_nat @ M ) )
% 9.25/5.26        = ( minus_minus_int @ ( F2 @ zero_zero_nat ) @ ( F2 @ M ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8227_sum__lessThan__telescope,axiom,
% 9.25/5.26      ! [F2: nat > rat,M: nat] :
% 9.25/5.26        ( ( groups2906978787729119204at_rat
% 9.25/5.26          @ ^ [N2: nat] : ( minus_minus_rat @ ( F2 @ ( suc @ N2 ) ) @ ( F2 @ N2 ) )
% 9.25/5.26          @ ( set_ord_lessThan_nat @ M ) )
% 9.25/5.26        = ( minus_minus_rat @ ( F2 @ M ) @ ( F2 @ zero_zero_nat ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8228_sum__lessThan__telescope,axiom,
% 9.25/5.26      ! [F2: nat > int,M: nat] :
% 9.25/5.26        ( ( groups3539618377306564664at_int
% 9.25/5.26          @ ^ [N2: nat] : ( minus_minus_int @ ( F2 @ ( suc @ N2 ) ) @ ( F2 @ N2 ) )
% 9.25/5.26          @ ( set_ord_lessThan_nat @ M ) )
% 9.25/5.26        = ( minus_minus_int @ ( F2 @ M ) @ ( F2 @ zero_zero_nat ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8229_sgn__1__neg,axiom,
% 9.25/5.26      ! [A: int] :
% 9.25/5.26        ( ( ( sgn_sgn_int @ A )
% 9.25/5.26          = ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.26        = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8230_sgn__1__neg,axiom,
% 9.25/5.26      ! [A: code_integer] :
% 9.25/5.26        ( ( ( sgn_sgn_Code_integer @ A )
% 9.25/5.26          = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 9.25/5.26        = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8231_sgn__1__neg,axiom,
% 9.25/5.26      ! [A: rat] :
% 9.25/5.26        ( ( ( sgn_sgn_rat @ A )
% 9.25/5.26          = ( uminus_uminus_rat @ one_one_rat ) )
% 9.25/5.26        = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8232_sgn__if,axiom,
% 9.25/5.26      ( sgn_sgn_int
% 9.25/5.26      = ( ^ [X3: int] : ( if_int @ ( X3 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ X3 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8233_sgn__if,axiom,
% 9.25/5.26      ( sgn_sgn_Code_integer
% 9.25/5.26      = ( ^ [X3: code_integer] : ( if_Code_integer @ ( X3 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X3 ) @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8234_sgn__if,axiom,
% 9.25/5.26      ( sgn_sgn_rat
% 9.25/5.26      = ( ^ [X3: rat] : ( if_rat @ ( X3 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ X3 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8235_prod_OlessThan__Suc__shift,axiom,
% 9.25/5.26      ! [G2: nat > code_integer,N: nat] :
% 9.25/5.26        ( ( groups3455450783089532116nteger @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.25/5.26        = ( times_3573771949741848930nteger @ ( G2 @ zero_zero_nat )
% 9.25/5.26          @ ( groups3455450783089532116nteger
% 9.25/5.26            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8236_prod_OlessThan__Suc__shift,axiom,
% 9.25/5.26      ! [G2: nat > assn,N: nat] :
% 9.25/5.26        ( ( groups6906906614972039071t_assn @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.25/5.26        = ( times_times_assn @ ( G2 @ zero_zero_nat )
% 9.25/5.26          @ ( groups6906906614972039071t_assn
% 9.25/5.26            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8237_prod_OlessThan__Suc__shift,axiom,
% 9.25/5.26      ! [G2: nat > rat,N: nat] :
% 9.25/5.26        ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.25/5.26        = ( times_times_rat @ ( G2 @ zero_zero_nat )
% 9.25/5.26          @ ( groups73079841787564623at_rat
% 9.25/5.26            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8238_prod_OlessThan__Suc__shift,axiom,
% 9.25/5.26      ! [G2: nat > nat,N: nat] :
% 9.25/5.26        ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.25/5.26        = ( times_times_nat @ ( G2 @ zero_zero_nat )
% 9.25/5.26          @ ( groups708209901874060359at_nat
% 9.25/5.26            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8239_prod_OlessThan__Suc__shift,axiom,
% 9.25/5.26      ! [G2: nat > int,N: nat] :
% 9.25/5.26        ( ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 9.25/5.26        = ( times_times_int @ ( G2 @ zero_zero_nat )
% 9.25/5.26          @ ( groups705719431365010083at_int
% 9.25/5.26            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8240_sum_Omono__neutral__cong,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,H3: int > code_integer,G2: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( finite_finite_int @ S )
% 9.25/5.26         => ( ! [I2: int] :
% 9.25/5.26                ( ( member_int @ I2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ I2 )
% 9.25/5.26                  = zero_z3403309356797280102nteger ) )
% 9.25/5.26           => ( ! [I2: int] :
% 9.25/5.26                  ( ( member_int @ I2 @ ( minus_minus_set_int @ S @ T ) )
% 9.25/5.26                 => ( ( G2 @ I2 )
% 9.25/5.26                    = zero_z3403309356797280102nteger ) )
% 9.25/5.26             => ( ! [X2: int] :
% 9.25/5.26                    ( ( member_int @ X2 @ ( inf_inf_set_int @ S @ T ) )
% 9.25/5.26                   => ( ( G2 @ X2 )
% 9.25/5.26                      = ( H3 @ X2 ) ) )
% 9.25/5.26               => ( ( groups7873554091576472773nteger @ G2 @ S )
% 9.25/5.26                  = ( groups7873554091576472773nteger @ H3 @ T ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8241_sum_Omono__neutral__cong,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,H3: int > rat,G2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( finite_finite_int @ S )
% 9.25/5.26         => ( ! [I2: int] :
% 9.25/5.26                ( ( member_int @ I2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ I2 )
% 9.25/5.26                  = zero_zero_rat ) )
% 9.25/5.26           => ( ! [I2: int] :
% 9.25/5.26                  ( ( member_int @ I2 @ ( minus_minus_set_int @ S @ T ) )
% 9.25/5.26                 => ( ( G2 @ I2 )
% 9.25/5.26                    = zero_zero_rat ) )
% 9.25/5.26             => ( ! [X2: int] :
% 9.25/5.26                    ( ( member_int @ X2 @ ( inf_inf_set_int @ S @ T ) )
% 9.25/5.26                   => ( ( G2 @ X2 )
% 9.25/5.26                      = ( H3 @ X2 ) ) )
% 9.25/5.26               => ( ( groups3906332499630173760nt_rat @ G2 @ S )
% 9.25/5.26                  = ( groups3906332499630173760nt_rat @ H3 @ T ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8242_sum_Omono__neutral__cong,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,H3: int > nat,G2: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( finite_finite_int @ S )
% 9.25/5.26         => ( ! [I2: int] :
% 9.25/5.26                ( ( member_int @ I2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ I2 )
% 9.25/5.26                  = zero_zero_nat ) )
% 9.25/5.26           => ( ! [I2: int] :
% 9.25/5.26                  ( ( member_int @ I2 @ ( minus_minus_set_int @ S @ T ) )
% 9.25/5.26                 => ( ( G2 @ I2 )
% 9.25/5.26                    = zero_zero_nat ) )
% 9.25/5.26             => ( ! [X2: int] :
% 9.25/5.26                    ( ( member_int @ X2 @ ( inf_inf_set_int @ S @ T ) )
% 9.25/5.26                   => ( ( G2 @ X2 )
% 9.25/5.26                      = ( H3 @ X2 ) ) )
% 9.25/5.26               => ( ( groups4541462559716669496nt_nat @ G2 @ S )
% 9.25/5.26                  = ( groups4541462559716669496nt_nat @ H3 @ T ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8243_sum_Omono__neutral__cong,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,H3: nat > code_integer,G2: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( finite_finite_nat @ S )
% 9.25/5.26         => ( ! [I2: nat] :
% 9.25/5.26                ( ( member_nat @ I2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ I2 )
% 9.25/5.26                  = zero_z3403309356797280102nteger ) )
% 9.25/5.26           => ( ! [I2: nat] :
% 9.25/5.26                  ( ( member_nat @ I2 @ ( minus_minus_set_nat @ S @ T ) )
% 9.25/5.26                 => ( ( G2 @ I2 )
% 9.25/5.26                    = zero_z3403309356797280102nteger ) )
% 9.25/5.26             => ( ! [X2: nat] :
% 9.25/5.26                    ( ( member_nat @ X2 @ ( inf_inf_set_nat @ S @ T ) )
% 9.25/5.26                   => ( ( G2 @ X2 )
% 9.25/5.26                      = ( H3 @ X2 ) ) )
% 9.25/5.26               => ( ( groups7501900531339628137nteger @ G2 @ S )
% 9.25/5.26                  = ( groups7501900531339628137nteger @ H3 @ T ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8244_sum_Omono__neutral__cong,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,H3: nat > rat,G2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( finite_finite_nat @ S )
% 9.25/5.26         => ( ! [I2: nat] :
% 9.25/5.26                ( ( member_nat @ I2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ I2 )
% 9.25/5.26                  = zero_zero_rat ) )
% 9.25/5.26           => ( ! [I2: nat] :
% 9.25/5.26                  ( ( member_nat @ I2 @ ( minus_minus_set_nat @ S @ T ) )
% 9.25/5.26                 => ( ( G2 @ I2 )
% 9.25/5.26                    = zero_zero_rat ) )
% 9.25/5.26             => ( ! [X2: nat] :
% 9.25/5.26                    ( ( member_nat @ X2 @ ( inf_inf_set_nat @ S @ T ) )
% 9.25/5.26                   => ( ( G2 @ X2 )
% 9.25/5.26                      = ( H3 @ X2 ) ) )
% 9.25/5.26               => ( ( groups2906978787729119204at_rat @ G2 @ S )
% 9.25/5.26                  = ( groups2906978787729119204at_rat @ H3 @ T ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8245_sum_Omono__neutral__cong,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,H3: nat > int,G2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( finite_finite_nat @ S )
% 9.25/5.26         => ( ! [I2: nat] :
% 9.25/5.26                ( ( member_nat @ I2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ I2 )
% 9.25/5.26                  = zero_zero_int ) )
% 9.25/5.26           => ( ! [I2: nat] :
% 9.25/5.26                  ( ( member_nat @ I2 @ ( minus_minus_set_nat @ S @ T ) )
% 9.25/5.26                 => ( ( G2 @ I2 )
% 9.25/5.26                    = zero_zero_int ) )
% 9.25/5.26             => ( ! [X2: nat] :
% 9.25/5.26                    ( ( member_nat @ X2 @ ( inf_inf_set_nat @ S @ T ) )
% 9.25/5.26                   => ( ( G2 @ X2 )
% 9.25/5.26                      = ( H3 @ X2 ) ) )
% 9.25/5.26               => ( ( groups3539618377306564664at_int @ G2 @ S )
% 9.25/5.26                  = ( groups3539618377306564664at_int @ H3 @ T ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8246_sum_Omono__neutral__cong,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,H3: nat > nat,G2: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( finite_finite_nat @ S )
% 9.25/5.26         => ( ! [I2: nat] :
% 9.25/5.26                ( ( member_nat @ I2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ I2 )
% 9.25/5.26                  = zero_zero_nat ) )
% 9.25/5.26           => ( ! [I2: nat] :
% 9.25/5.26                  ( ( member_nat @ I2 @ ( minus_minus_set_nat @ S @ T ) )
% 9.25/5.26                 => ( ( G2 @ I2 )
% 9.25/5.26                    = zero_zero_nat ) )
% 9.25/5.26             => ( ! [X2: nat] :
% 9.25/5.26                    ( ( member_nat @ X2 @ ( inf_inf_set_nat @ S @ T ) )
% 9.25/5.26                   => ( ( G2 @ X2 )
% 9.25/5.26                      = ( H3 @ X2 ) ) )
% 9.25/5.26               => ( ( groups3542108847815614940at_nat @ G2 @ S )
% 9.25/5.26                  = ( groups3542108847815614940at_nat @ H3 @ T ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8247_sum_Omono__neutral__cong,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,H3: int > int,G2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( finite_finite_int @ S )
% 9.25/5.26         => ( ! [I2: int] :
% 9.25/5.26                ( ( member_int @ I2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ I2 )
% 9.25/5.26                  = zero_zero_int ) )
% 9.25/5.26           => ( ! [I2: int] :
% 9.25/5.26                  ( ( member_int @ I2 @ ( minus_minus_set_int @ S @ T ) )
% 9.25/5.26                 => ( ( G2 @ I2 )
% 9.25/5.26                    = zero_zero_int ) )
% 9.25/5.26             => ( ! [X2: int] :
% 9.25/5.26                    ( ( member_int @ X2 @ ( inf_inf_set_int @ S @ T ) )
% 9.25/5.26                   => ( ( G2 @ X2 )
% 9.25/5.26                      = ( H3 @ X2 ) ) )
% 9.25/5.26               => ( ( groups4538972089207619220nt_int @ G2 @ S )
% 9.25/5.26                  = ( groups4538972089207619220nt_int @ H3 @ T ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8248_sum_Omono__neutral__cong,axiom,
% 9.25/5.26      ! [T: set_set_nat,S: set_set_nat,H3: set_nat > code_integer,G2: set_nat > code_integer] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ T )
% 9.25/5.26       => ( ( finite1152437895449049373et_nat @ S )
% 9.25/5.26         => ( ! [I2: set_nat] :
% 9.25/5.26                ( ( member_set_nat @ I2 @ ( minus_2163939370556025621et_nat @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ I2 )
% 9.25/5.26                  = zero_z3403309356797280102nteger ) )
% 9.25/5.26           => ( ! [I2: set_nat] :
% 9.25/5.26                  ( ( member_set_nat @ I2 @ ( minus_2163939370556025621et_nat @ S @ T ) )
% 9.25/5.26                 => ( ( G2 @ I2 )
% 9.25/5.26                    = zero_z3403309356797280102nteger ) )
% 9.25/5.26             => ( ! [X2: set_nat] :
% 9.25/5.26                    ( ( member_set_nat @ X2 @ ( inf_inf_set_set_nat @ S @ T ) )
% 9.25/5.26                   => ( ( G2 @ X2 )
% 9.25/5.26                      = ( H3 @ X2 ) ) )
% 9.25/5.26               => ( ( groups9190459664516455967nteger @ G2 @ S )
% 9.25/5.26                  = ( groups9190459664516455967nteger @ H3 @ T ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8249_sum_Omono__neutral__cong,axiom,
% 9.25/5.26      ! [T: set_set_nat,S: set_set_nat,H3: set_nat > rat,G2: set_nat > rat] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ T )
% 9.25/5.26       => ( ( finite1152437895449049373et_nat @ S )
% 9.25/5.26         => ( ! [I2: set_nat] :
% 9.25/5.26                ( ( member_set_nat @ I2 @ ( minus_2163939370556025621et_nat @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ I2 )
% 9.25/5.26                  = zero_zero_rat ) )
% 9.25/5.26           => ( ! [I2: set_nat] :
% 9.25/5.26                  ( ( member_set_nat @ I2 @ ( minus_2163939370556025621et_nat @ S @ T ) )
% 9.25/5.26                 => ( ( G2 @ I2 )
% 9.25/5.26                    = zero_zero_rat ) )
% 9.25/5.26             => ( ! [X2: set_nat] :
% 9.25/5.26                    ( ( member_set_nat @ X2 @ ( inf_inf_set_set_nat @ S @ T ) )
% 9.25/5.26                   => ( ( G2 @ X2 )
% 9.25/5.26                      = ( H3 @ X2 ) ) )
% 9.25/5.26               => ( ( groups7659867448343625626at_rat @ G2 @ S )
% 9.25/5.26                  = ( groups7659867448343625626at_rat @ H3 @ T ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8250_prod_Osubset__diff,axiom,
% 9.25/5.26      ! [B2: set_int,A2: set_int,G2: int > code_integer] :
% 9.25/5.26        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ A2 )
% 9.25/5.26         => ( ( groups3827104343326376752nteger @ G2 @ A2 )
% 9.25/5.26            = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups3827104343326376752nteger @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8251_prod_Osubset__diff,axiom,
% 9.25/5.26      ! [B2: set_int,A2: set_int,G2: int > assn] :
% 9.25/5.26        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ A2 )
% 9.25/5.26         => ( ( groups7882442080178216443t_assn @ G2 @ A2 )
% 9.25/5.26            = ( times_times_assn @ ( groups7882442080178216443t_assn @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups7882442080178216443t_assn @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8252_prod_Osubset__diff,axiom,
% 9.25/5.26      ! [B2: set_int,A2: set_int,G2: int > rat] :
% 9.25/5.26        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ A2 )
% 9.25/5.26         => ( ( groups1072433553688619179nt_rat @ G2 @ A2 )
% 9.25/5.26            = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups1072433553688619179nt_rat @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8253_prod_Osubset__diff,axiom,
% 9.25/5.26      ! [B2: set_int,A2: set_int,G2: int > nat] :
% 9.25/5.26        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ A2 )
% 9.25/5.26         => ( ( groups1707563613775114915nt_nat @ G2 @ A2 )
% 9.25/5.26            = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups1707563613775114915nt_nat @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8254_prod_Osubset__diff,axiom,
% 9.25/5.26      ! [B2: set_nat,A2: set_nat,G2: nat > code_integer] :
% 9.25/5.26        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ A2 )
% 9.25/5.26         => ( ( groups3455450783089532116nteger @ G2 @ A2 )
% 9.25/5.26            = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups3455450783089532116nteger @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8255_prod_Osubset__diff,axiom,
% 9.25/5.26      ! [B2: set_nat,A2: set_nat,G2: nat > assn] :
% 9.25/5.26        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ A2 )
% 9.25/5.26         => ( ( groups6906906614972039071t_assn @ G2 @ A2 )
% 9.25/5.26            = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups6906906614972039071t_assn @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8256_prod_Osubset__diff,axiom,
% 9.25/5.26      ! [B2: set_nat,A2: set_nat,G2: nat > rat] :
% 9.25/5.26        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ A2 )
% 9.25/5.26         => ( ( groups73079841787564623at_rat @ G2 @ A2 )
% 9.25/5.26            = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups73079841787564623at_rat @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8257_prod_Osubset__diff,axiom,
% 9.25/5.26      ! [B2: set_nat,A2: set_nat,G2: nat > nat] :
% 9.25/5.26        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ A2 )
% 9.25/5.26         => ( ( groups708209901874060359at_nat @ G2 @ A2 )
% 9.25/5.26            = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups708209901874060359at_nat @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8258_prod_Osubset__diff,axiom,
% 9.25/5.26      ! [B2: set_nat,A2: set_nat,G2: nat > int] :
% 9.25/5.26        ( ( ord_less_eq_set_nat @ B2 @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ A2 )
% 9.25/5.26         => ( ( groups705719431365010083at_int @ G2 @ A2 )
% 9.25/5.26            = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups705719431365010083at_int @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8259_prod_Osubset__diff,axiom,
% 9.25/5.26      ! [B2: set_int,A2: set_int,G2: int > int] :
% 9.25/5.26        ( ( ord_less_eq_set_int @ B2 @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ A2 )
% 9.25/5.26         => ( ( groups1705073143266064639nt_int @ G2 @ A2 )
% 9.25/5.26            = ( times_times_int @ ( groups1705073143266064639nt_int @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups1705073143266064639nt_int @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8260_prod_Omono__neutral__cong__right,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,G2: int > code_integer,H3: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ S @ T )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_Code_integer ) )
% 9.25/5.26           => ( ! [X2: int] :
% 9.25/5.26                  ( ( member_int @ X2 @ S )
% 9.25/5.26                 => ( ( G2 @ X2 )
% 9.25/5.26                    = ( H3 @ X2 ) ) )
% 9.25/5.26             => ( ( groups3827104343326376752nteger @ G2 @ T )
% 9.25/5.26                = ( groups3827104343326376752nteger @ H3 @ S ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8261_prod_Omono__neutral__cong__right,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,G2: int > assn,H3: int > assn] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ S @ T )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_assn ) )
% 9.25/5.26           => ( ! [X2: int] :
% 9.25/5.26                  ( ( member_int @ X2 @ S )
% 9.25/5.26                 => ( ( G2 @ X2 )
% 9.25/5.26                    = ( H3 @ X2 ) ) )
% 9.25/5.26             => ( ( groups7882442080178216443t_assn @ G2 @ T )
% 9.25/5.26                = ( groups7882442080178216443t_assn @ H3 @ S ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8262_prod_Omono__neutral__cong__right,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,G2: int > rat,H3: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ S @ T )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_rat ) )
% 9.25/5.26           => ( ! [X2: int] :
% 9.25/5.26                  ( ( member_int @ X2 @ S )
% 9.25/5.26                 => ( ( G2 @ X2 )
% 9.25/5.26                    = ( H3 @ X2 ) ) )
% 9.25/5.26             => ( ( groups1072433553688619179nt_rat @ G2 @ T )
% 9.25/5.26                = ( groups1072433553688619179nt_rat @ H3 @ S ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8263_prod_Omono__neutral__cong__right,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,G2: int > nat,H3: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ S @ T )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_nat ) )
% 9.25/5.26           => ( ! [X2: int] :
% 9.25/5.26                  ( ( member_int @ X2 @ S )
% 9.25/5.26                 => ( ( G2 @ X2 )
% 9.25/5.26                    = ( H3 @ X2 ) ) )
% 9.25/5.26             => ( ( groups1707563613775114915nt_nat @ G2 @ T )
% 9.25/5.26                = ( groups1707563613775114915nt_nat @ H3 @ S ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8264_prod_Omono__neutral__cong__right,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,G2: nat > code_integer,H3: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ S @ T )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_Code_integer ) )
% 9.25/5.26           => ( ! [X2: nat] :
% 9.25/5.26                  ( ( member_nat @ X2 @ S )
% 9.25/5.26                 => ( ( G2 @ X2 )
% 9.25/5.26                    = ( H3 @ X2 ) ) )
% 9.25/5.26             => ( ( groups3455450783089532116nteger @ G2 @ T )
% 9.25/5.26                = ( groups3455450783089532116nteger @ H3 @ S ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8265_prod_Omono__neutral__cong__right,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,G2: nat > assn,H3: nat > assn] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ S @ T )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_assn ) )
% 9.25/5.26           => ( ! [X2: nat] :
% 9.25/5.26                  ( ( member_nat @ X2 @ S )
% 9.25/5.26                 => ( ( G2 @ X2 )
% 9.25/5.26                    = ( H3 @ X2 ) ) )
% 9.25/5.26             => ( ( groups6906906614972039071t_assn @ G2 @ T )
% 9.25/5.26                = ( groups6906906614972039071t_assn @ H3 @ S ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8266_prod_Omono__neutral__cong__right,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,G2: nat > rat,H3: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ S @ T )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_rat ) )
% 9.25/5.26           => ( ! [X2: nat] :
% 9.25/5.26                  ( ( member_nat @ X2 @ S )
% 9.25/5.26                 => ( ( G2 @ X2 )
% 9.25/5.26                    = ( H3 @ X2 ) ) )
% 9.25/5.26             => ( ( groups73079841787564623at_rat @ G2 @ T )
% 9.25/5.26                = ( groups73079841787564623at_rat @ H3 @ S ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8267_prod_Omono__neutral__cong__right,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,G2: nat > nat,H3: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ S @ T )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_nat ) )
% 9.25/5.26           => ( ! [X2: nat] :
% 9.25/5.26                  ( ( member_nat @ X2 @ S )
% 9.25/5.26                 => ( ( G2 @ X2 )
% 9.25/5.26                    = ( H3 @ X2 ) ) )
% 9.25/5.26             => ( ( groups708209901874060359at_nat @ G2 @ T )
% 9.25/5.26                = ( groups708209901874060359at_nat @ H3 @ S ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8268_prod_Omono__neutral__cong__right,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,G2: nat > int,H3: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ S @ T )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_int ) )
% 9.25/5.26           => ( ! [X2: nat] :
% 9.25/5.26                  ( ( member_nat @ X2 @ S )
% 9.25/5.26                 => ( ( G2 @ X2 )
% 9.25/5.26                    = ( H3 @ X2 ) ) )
% 9.25/5.26             => ( ( groups705719431365010083at_int @ G2 @ T )
% 9.25/5.26                = ( groups705719431365010083at_int @ H3 @ S ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8269_prod_Omono__neutral__cong__right,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,G2: int > int,H3: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ S @ T )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_int ) )
% 9.25/5.26           => ( ! [X2: int] :
% 9.25/5.26                  ( ( member_int @ X2 @ S )
% 9.25/5.26                 => ( ( G2 @ X2 )
% 9.25/5.26                    = ( H3 @ X2 ) ) )
% 9.25/5.26             => ( ( groups1705073143266064639nt_int @ G2 @ T )
% 9.25/5.26                = ( groups1705073143266064639nt_int @ H3 @ S ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8270_prod_Omono__neutral__cong__left,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,H3: int > code_integer,G2: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ S @ T )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ X2 )
% 9.25/5.26                  = one_one_Code_integer ) )
% 9.25/5.26           => ( ! [X2: int] :
% 9.25/5.26                  ( ( member_int @ X2 @ S )
% 9.25/5.26                 => ( ( G2 @ X2 )
% 9.25/5.26                    = ( H3 @ X2 ) ) )
% 9.25/5.26             => ( ( groups3827104343326376752nteger @ G2 @ S )
% 9.25/5.26                = ( groups3827104343326376752nteger @ H3 @ T ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8271_prod_Omono__neutral__cong__left,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,H3: int > assn,G2: int > assn] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ S @ T )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ X2 )
% 9.25/5.26                  = one_one_assn ) )
% 9.25/5.26           => ( ! [X2: int] :
% 9.25/5.26                  ( ( member_int @ X2 @ S )
% 9.25/5.26                 => ( ( G2 @ X2 )
% 9.25/5.26                    = ( H3 @ X2 ) ) )
% 9.25/5.26             => ( ( groups7882442080178216443t_assn @ G2 @ S )
% 9.25/5.26                = ( groups7882442080178216443t_assn @ H3 @ T ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8272_prod_Omono__neutral__cong__left,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,H3: int > rat,G2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ S @ T )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ X2 )
% 9.25/5.26                  = one_one_rat ) )
% 9.25/5.26           => ( ! [X2: int] :
% 9.25/5.26                  ( ( member_int @ X2 @ S )
% 9.25/5.26                 => ( ( G2 @ X2 )
% 9.25/5.26                    = ( H3 @ X2 ) ) )
% 9.25/5.26             => ( ( groups1072433553688619179nt_rat @ G2 @ S )
% 9.25/5.26                = ( groups1072433553688619179nt_rat @ H3 @ T ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8273_prod_Omono__neutral__cong__left,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,H3: int > nat,G2: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ S @ T )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ X2 )
% 9.25/5.26                  = one_one_nat ) )
% 9.25/5.26           => ( ! [X2: int] :
% 9.25/5.26                  ( ( member_int @ X2 @ S )
% 9.25/5.26                 => ( ( G2 @ X2 )
% 9.25/5.26                    = ( H3 @ X2 ) ) )
% 9.25/5.26             => ( ( groups1707563613775114915nt_nat @ G2 @ S )
% 9.25/5.26                = ( groups1707563613775114915nt_nat @ H3 @ T ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8274_prod_Omono__neutral__cong__left,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,H3: nat > code_integer,G2: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ S @ T )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ X2 )
% 9.25/5.26                  = one_one_Code_integer ) )
% 9.25/5.26           => ( ! [X2: nat] :
% 9.25/5.26                  ( ( member_nat @ X2 @ S )
% 9.25/5.26                 => ( ( G2 @ X2 )
% 9.25/5.26                    = ( H3 @ X2 ) ) )
% 9.25/5.26             => ( ( groups3455450783089532116nteger @ G2 @ S )
% 9.25/5.26                = ( groups3455450783089532116nteger @ H3 @ T ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8275_prod_Omono__neutral__cong__left,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,H3: nat > assn,G2: nat > assn] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ S @ T )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ X2 )
% 9.25/5.26                  = one_one_assn ) )
% 9.25/5.26           => ( ! [X2: nat] :
% 9.25/5.26                  ( ( member_nat @ X2 @ S )
% 9.25/5.26                 => ( ( G2 @ X2 )
% 9.25/5.26                    = ( H3 @ X2 ) ) )
% 9.25/5.26             => ( ( groups6906906614972039071t_assn @ G2 @ S )
% 9.25/5.26                = ( groups6906906614972039071t_assn @ H3 @ T ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8276_prod_Omono__neutral__cong__left,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,H3: nat > rat,G2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ S @ T )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ X2 )
% 9.25/5.26                  = one_one_rat ) )
% 9.25/5.26           => ( ! [X2: nat] :
% 9.25/5.26                  ( ( member_nat @ X2 @ S )
% 9.25/5.26                 => ( ( G2 @ X2 )
% 9.25/5.26                    = ( H3 @ X2 ) ) )
% 9.25/5.26             => ( ( groups73079841787564623at_rat @ G2 @ S )
% 9.25/5.26                = ( groups73079841787564623at_rat @ H3 @ T ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8277_prod_Omono__neutral__cong__left,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,H3: nat > nat,G2: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ S @ T )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ X2 )
% 9.25/5.26                  = one_one_nat ) )
% 9.25/5.26           => ( ! [X2: nat] :
% 9.25/5.26                  ( ( member_nat @ X2 @ S )
% 9.25/5.26                 => ( ( G2 @ X2 )
% 9.25/5.26                    = ( H3 @ X2 ) ) )
% 9.25/5.26             => ( ( groups708209901874060359at_nat @ G2 @ S )
% 9.25/5.26                = ( groups708209901874060359at_nat @ H3 @ T ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8278_prod_Omono__neutral__cong__left,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,H3: nat > int,G2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ S @ T )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ X2 )
% 9.25/5.26                  = one_one_int ) )
% 9.25/5.26           => ( ! [X2: nat] :
% 9.25/5.26                  ( ( member_nat @ X2 @ S )
% 9.25/5.26                 => ( ( G2 @ X2 )
% 9.25/5.26                    = ( H3 @ X2 ) ) )
% 9.25/5.26             => ( ( groups705719431365010083at_int @ G2 @ S )
% 9.25/5.26                = ( groups705719431365010083at_int @ H3 @ T ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8279_prod_Omono__neutral__cong__left,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,H3: int > int,G2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ S @ T )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ X2 )
% 9.25/5.26                  = one_one_int ) )
% 9.25/5.26           => ( ! [X2: int] :
% 9.25/5.26                  ( ( member_int @ X2 @ S )
% 9.25/5.26                 => ( ( G2 @ X2 )
% 9.25/5.26                    = ( H3 @ X2 ) ) )
% 9.25/5.26             => ( ( groups1705073143266064639nt_int @ G2 @ S )
% 9.25/5.26                = ( groups1705073143266064639nt_int @ H3 @ T ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8280_prod_Omono__neutral__right,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,G2: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ S @ T )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_Code_integer ) )
% 9.25/5.26           => ( ( groups3827104343326376752nteger @ G2 @ T )
% 9.25/5.26              = ( groups3827104343326376752nteger @ G2 @ S ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8281_prod_Omono__neutral__right,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,G2: int > assn] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ S @ T )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_assn ) )
% 9.25/5.26           => ( ( groups7882442080178216443t_assn @ G2 @ T )
% 9.25/5.26              = ( groups7882442080178216443t_assn @ G2 @ S ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8282_prod_Omono__neutral__right,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,G2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ S @ T )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_rat ) )
% 9.25/5.26           => ( ( groups1072433553688619179nt_rat @ G2 @ T )
% 9.25/5.26              = ( groups1072433553688619179nt_rat @ G2 @ S ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8283_prod_Omono__neutral__right,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,G2: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ S @ T )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_nat ) )
% 9.25/5.26           => ( ( groups1707563613775114915nt_nat @ G2 @ T )
% 9.25/5.26              = ( groups1707563613775114915nt_nat @ G2 @ S ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8284_prod_Omono__neutral__right,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,G2: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ S @ T )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_Code_integer ) )
% 9.25/5.26           => ( ( groups3455450783089532116nteger @ G2 @ T )
% 9.25/5.26              = ( groups3455450783089532116nteger @ G2 @ S ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8285_prod_Omono__neutral__right,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,G2: nat > assn] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ S @ T )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_assn ) )
% 9.25/5.26           => ( ( groups6906906614972039071t_assn @ G2 @ T )
% 9.25/5.26              = ( groups6906906614972039071t_assn @ G2 @ S ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8286_prod_Omono__neutral__right,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,G2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ S @ T )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_rat ) )
% 9.25/5.26           => ( ( groups73079841787564623at_rat @ G2 @ T )
% 9.25/5.26              = ( groups73079841787564623at_rat @ G2 @ S ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8287_prod_Omono__neutral__right,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,G2: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ S @ T )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_nat ) )
% 9.25/5.26           => ( ( groups708209901874060359at_nat @ G2 @ T )
% 9.25/5.26              = ( groups708209901874060359at_nat @ G2 @ S ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8288_prod_Omono__neutral__right,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,G2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ S @ T )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_int ) )
% 9.25/5.26           => ( ( groups705719431365010083at_int @ G2 @ T )
% 9.25/5.26              = ( groups705719431365010083at_int @ G2 @ S ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8289_prod_Omono__neutral__right,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,G2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ S @ T )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_int ) )
% 9.25/5.26           => ( ( groups1705073143266064639nt_int @ G2 @ T )
% 9.25/5.26              = ( groups1705073143266064639nt_int @ G2 @ S ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8290_prod_Omono__neutral__left,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,G2: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ S @ T )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_Code_integer ) )
% 9.25/5.26           => ( ( groups3827104343326376752nteger @ G2 @ S )
% 9.25/5.26              = ( groups3827104343326376752nteger @ G2 @ T ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8291_prod_Omono__neutral__left,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,G2: int > assn] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ S @ T )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_assn ) )
% 9.25/5.26           => ( ( groups7882442080178216443t_assn @ G2 @ S )
% 9.25/5.26              = ( groups7882442080178216443t_assn @ G2 @ T ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8292_prod_Omono__neutral__left,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,G2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ S @ T )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_rat ) )
% 9.25/5.26           => ( ( groups1072433553688619179nt_rat @ G2 @ S )
% 9.25/5.26              = ( groups1072433553688619179nt_rat @ G2 @ T ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8293_prod_Omono__neutral__left,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,G2: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ S @ T )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_nat ) )
% 9.25/5.26           => ( ( groups1707563613775114915nt_nat @ G2 @ S )
% 9.25/5.26              = ( groups1707563613775114915nt_nat @ G2 @ T ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8294_prod_Omono__neutral__left,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,G2: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ S @ T )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_Code_integer ) )
% 9.25/5.26           => ( ( groups3455450783089532116nteger @ G2 @ S )
% 9.25/5.26              = ( groups3455450783089532116nteger @ G2 @ T ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8295_prod_Omono__neutral__left,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,G2: nat > assn] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ S @ T )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_assn ) )
% 9.25/5.26           => ( ( groups6906906614972039071t_assn @ G2 @ S )
% 9.25/5.26              = ( groups6906906614972039071t_assn @ G2 @ T ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8296_prod_Omono__neutral__left,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,G2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ S @ T )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_rat ) )
% 9.25/5.26           => ( ( groups73079841787564623at_rat @ G2 @ S )
% 9.25/5.26              = ( groups73079841787564623at_rat @ G2 @ T ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8297_prod_Omono__neutral__left,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,G2: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ S @ T )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_nat ) )
% 9.25/5.26           => ( ( groups708209901874060359at_nat @ G2 @ S )
% 9.25/5.26              = ( groups708209901874060359at_nat @ G2 @ T ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8298_prod_Omono__neutral__left,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,G2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ S @ T )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_int ) )
% 9.25/5.26           => ( ( groups705719431365010083at_int @ G2 @ S )
% 9.25/5.26              = ( groups705719431365010083at_int @ G2 @ T ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8299_prod_Omono__neutral__left,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,G2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ S @ T )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_int ) )
% 9.25/5.26           => ( ( groups1705073143266064639nt_int @ G2 @ S )
% 9.25/5.26              = ( groups1705073143266064639nt_int @ G2 @ T ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8300_prod_Osame__carrierI,axiom,
% 9.25/5.26      ! [C2: set_int,A2: set_int,B2: set_int,G2: int > code_integer,H3: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ C2 )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ A2 @ C2 )
% 9.25/5.26         => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 9.25/5.26           => ( ! [A6: int] :
% 9.25/5.26                  ( ( member_int @ A6 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 9.25/5.26                 => ( ( G2 @ A6 )
% 9.25/5.26                    = one_one_Code_integer ) )
% 9.25/5.26             => ( ! [B6: int] :
% 9.25/5.26                    ( ( member_int @ B6 @ ( minus_minus_set_int @ C2 @ B2 ) )
% 9.25/5.26                   => ( ( H3 @ B6 )
% 9.25/5.26                      = one_one_Code_integer ) )
% 9.25/5.26               => ( ( ( groups3827104343326376752nteger @ G2 @ C2 )
% 9.25/5.26                    = ( groups3827104343326376752nteger @ H3 @ C2 ) )
% 9.25/5.26                 => ( ( groups3827104343326376752nteger @ G2 @ A2 )
% 9.25/5.26                    = ( groups3827104343326376752nteger @ H3 @ B2 ) ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8301_prod_Osame__carrierI,axiom,
% 9.25/5.26      ! [C2: set_int,A2: set_int,B2: set_int,G2: int > assn,H3: int > assn] :
% 9.25/5.26        ( ( finite_finite_int @ C2 )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ A2 @ C2 )
% 9.25/5.26         => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 9.25/5.26           => ( ! [A6: int] :
% 9.25/5.26                  ( ( member_int @ A6 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 9.25/5.26                 => ( ( G2 @ A6 )
% 9.25/5.26                    = one_one_assn ) )
% 9.25/5.26             => ( ! [B6: int] :
% 9.25/5.26                    ( ( member_int @ B6 @ ( minus_minus_set_int @ C2 @ B2 ) )
% 9.25/5.26                   => ( ( H3 @ B6 )
% 9.25/5.26                      = one_one_assn ) )
% 9.25/5.26               => ( ( ( groups7882442080178216443t_assn @ G2 @ C2 )
% 9.25/5.26                    = ( groups7882442080178216443t_assn @ H3 @ C2 ) )
% 9.25/5.26                 => ( ( groups7882442080178216443t_assn @ G2 @ A2 )
% 9.25/5.26                    = ( groups7882442080178216443t_assn @ H3 @ B2 ) ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8302_prod_Osame__carrierI,axiom,
% 9.25/5.26      ! [C2: set_int,A2: set_int,B2: set_int,G2: int > rat,H3: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ C2 )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ A2 @ C2 )
% 9.25/5.26         => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 9.25/5.26           => ( ! [A6: int] :
% 9.25/5.26                  ( ( member_int @ A6 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 9.25/5.26                 => ( ( G2 @ A6 )
% 9.25/5.26                    = one_one_rat ) )
% 9.25/5.26             => ( ! [B6: int] :
% 9.25/5.26                    ( ( member_int @ B6 @ ( minus_minus_set_int @ C2 @ B2 ) )
% 9.25/5.26                   => ( ( H3 @ B6 )
% 9.25/5.26                      = one_one_rat ) )
% 9.25/5.26               => ( ( ( groups1072433553688619179nt_rat @ G2 @ C2 )
% 9.25/5.26                    = ( groups1072433553688619179nt_rat @ H3 @ C2 ) )
% 9.25/5.26                 => ( ( groups1072433553688619179nt_rat @ G2 @ A2 )
% 9.25/5.26                    = ( groups1072433553688619179nt_rat @ H3 @ B2 ) ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8303_prod_Osame__carrierI,axiom,
% 9.25/5.26      ! [C2: set_int,A2: set_int,B2: set_int,G2: int > nat,H3: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ C2 )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ A2 @ C2 )
% 9.25/5.26         => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 9.25/5.26           => ( ! [A6: int] :
% 9.25/5.26                  ( ( member_int @ A6 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 9.25/5.26                 => ( ( G2 @ A6 )
% 9.25/5.26                    = one_one_nat ) )
% 9.25/5.26             => ( ! [B6: int] :
% 9.25/5.26                    ( ( member_int @ B6 @ ( minus_minus_set_int @ C2 @ B2 ) )
% 9.25/5.26                   => ( ( H3 @ B6 )
% 9.25/5.26                      = one_one_nat ) )
% 9.25/5.26               => ( ( ( groups1707563613775114915nt_nat @ G2 @ C2 )
% 9.25/5.26                    = ( groups1707563613775114915nt_nat @ H3 @ C2 ) )
% 9.25/5.26                 => ( ( groups1707563613775114915nt_nat @ G2 @ A2 )
% 9.25/5.26                    = ( groups1707563613775114915nt_nat @ H3 @ B2 ) ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8304_prod_Osame__carrierI,axiom,
% 9.25/5.26      ! [C2: set_nat,A2: set_nat,B2: set_nat,G2: nat > code_integer,H3: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ C2 )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 9.25/5.26         => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 9.25/5.26           => ( ! [A6: nat] :
% 9.25/5.26                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 9.25/5.26                 => ( ( G2 @ A6 )
% 9.25/5.26                    = one_one_Code_integer ) )
% 9.25/5.26             => ( ! [B6: nat] :
% 9.25/5.26                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ C2 @ B2 ) )
% 9.25/5.26                   => ( ( H3 @ B6 )
% 9.25/5.26                      = one_one_Code_integer ) )
% 9.25/5.26               => ( ( ( groups3455450783089532116nteger @ G2 @ C2 )
% 9.25/5.26                    = ( groups3455450783089532116nteger @ H3 @ C2 ) )
% 9.25/5.26                 => ( ( groups3455450783089532116nteger @ G2 @ A2 )
% 9.25/5.26                    = ( groups3455450783089532116nteger @ H3 @ B2 ) ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8305_prod_Osame__carrierI,axiom,
% 9.25/5.26      ! [C2: set_nat,A2: set_nat,B2: set_nat,G2: nat > assn,H3: nat > assn] :
% 9.25/5.26        ( ( finite_finite_nat @ C2 )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 9.25/5.26         => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 9.25/5.26           => ( ! [A6: nat] :
% 9.25/5.26                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 9.25/5.26                 => ( ( G2 @ A6 )
% 9.25/5.26                    = one_one_assn ) )
% 9.25/5.26             => ( ! [B6: nat] :
% 9.25/5.26                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ C2 @ B2 ) )
% 9.25/5.26                   => ( ( H3 @ B6 )
% 9.25/5.26                      = one_one_assn ) )
% 9.25/5.26               => ( ( ( groups6906906614972039071t_assn @ G2 @ C2 )
% 9.25/5.26                    = ( groups6906906614972039071t_assn @ H3 @ C2 ) )
% 9.25/5.26                 => ( ( groups6906906614972039071t_assn @ G2 @ A2 )
% 9.25/5.26                    = ( groups6906906614972039071t_assn @ H3 @ B2 ) ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8306_prod_Osame__carrierI,axiom,
% 9.25/5.26      ! [C2: set_nat,A2: set_nat,B2: set_nat,G2: nat > rat,H3: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ C2 )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 9.25/5.26         => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 9.25/5.26           => ( ! [A6: nat] :
% 9.25/5.26                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 9.25/5.26                 => ( ( G2 @ A6 )
% 9.25/5.26                    = one_one_rat ) )
% 9.25/5.26             => ( ! [B6: nat] :
% 9.25/5.26                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ C2 @ B2 ) )
% 9.25/5.26                   => ( ( H3 @ B6 )
% 9.25/5.26                      = one_one_rat ) )
% 9.25/5.26               => ( ( ( groups73079841787564623at_rat @ G2 @ C2 )
% 9.25/5.26                    = ( groups73079841787564623at_rat @ H3 @ C2 ) )
% 9.25/5.26                 => ( ( groups73079841787564623at_rat @ G2 @ A2 )
% 9.25/5.26                    = ( groups73079841787564623at_rat @ H3 @ B2 ) ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8307_prod_Osame__carrierI,axiom,
% 9.25/5.26      ! [C2: set_nat,A2: set_nat,B2: set_nat,G2: nat > nat,H3: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ C2 )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 9.25/5.26         => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 9.25/5.26           => ( ! [A6: nat] :
% 9.25/5.26                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 9.25/5.26                 => ( ( G2 @ A6 )
% 9.25/5.26                    = one_one_nat ) )
% 9.25/5.26             => ( ! [B6: nat] :
% 9.25/5.26                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ C2 @ B2 ) )
% 9.25/5.26                   => ( ( H3 @ B6 )
% 9.25/5.26                      = one_one_nat ) )
% 9.25/5.26               => ( ( ( groups708209901874060359at_nat @ G2 @ C2 )
% 9.25/5.26                    = ( groups708209901874060359at_nat @ H3 @ C2 ) )
% 9.25/5.26                 => ( ( groups708209901874060359at_nat @ G2 @ A2 )
% 9.25/5.26                    = ( groups708209901874060359at_nat @ H3 @ B2 ) ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8308_prod_Osame__carrierI,axiom,
% 9.25/5.26      ! [C2: set_nat,A2: set_nat,B2: set_nat,G2: nat > int,H3: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ C2 )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 9.25/5.26         => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 9.25/5.26           => ( ! [A6: nat] :
% 9.25/5.26                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 9.25/5.26                 => ( ( G2 @ A6 )
% 9.25/5.26                    = one_one_int ) )
% 9.25/5.26             => ( ! [B6: nat] :
% 9.25/5.26                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ C2 @ B2 ) )
% 9.25/5.26                   => ( ( H3 @ B6 )
% 9.25/5.26                      = one_one_int ) )
% 9.25/5.26               => ( ( ( groups705719431365010083at_int @ G2 @ C2 )
% 9.25/5.26                    = ( groups705719431365010083at_int @ H3 @ C2 ) )
% 9.25/5.26                 => ( ( groups705719431365010083at_int @ G2 @ A2 )
% 9.25/5.26                    = ( groups705719431365010083at_int @ H3 @ B2 ) ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8309_prod_Osame__carrierI,axiom,
% 9.25/5.26      ! [C2: set_int,A2: set_int,B2: set_int,G2: int > int,H3: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ C2 )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ A2 @ C2 )
% 9.25/5.26         => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 9.25/5.26           => ( ! [A6: int] :
% 9.25/5.26                  ( ( member_int @ A6 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 9.25/5.26                 => ( ( G2 @ A6 )
% 9.25/5.26                    = one_one_int ) )
% 9.25/5.26             => ( ! [B6: int] :
% 9.25/5.26                    ( ( member_int @ B6 @ ( minus_minus_set_int @ C2 @ B2 ) )
% 9.25/5.26                   => ( ( H3 @ B6 )
% 9.25/5.26                      = one_one_int ) )
% 9.25/5.26               => ( ( ( groups1705073143266064639nt_int @ G2 @ C2 )
% 9.25/5.26                    = ( groups1705073143266064639nt_int @ H3 @ C2 ) )
% 9.25/5.26                 => ( ( groups1705073143266064639nt_int @ G2 @ A2 )
% 9.25/5.26                    = ( groups1705073143266064639nt_int @ H3 @ B2 ) ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8310_prod_Osame__carrier,axiom,
% 9.25/5.26      ! [C2: set_int,A2: set_int,B2: set_int,G2: int > code_integer,H3: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ C2 )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ A2 @ C2 )
% 9.25/5.26         => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 9.25/5.26           => ( ! [A6: int] :
% 9.25/5.26                  ( ( member_int @ A6 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 9.25/5.26                 => ( ( G2 @ A6 )
% 9.25/5.26                    = one_one_Code_integer ) )
% 9.25/5.26             => ( ! [B6: int] :
% 9.25/5.26                    ( ( member_int @ B6 @ ( minus_minus_set_int @ C2 @ B2 ) )
% 9.25/5.26                   => ( ( H3 @ B6 )
% 9.25/5.26                      = one_one_Code_integer ) )
% 9.25/5.26               => ( ( ( groups3827104343326376752nteger @ G2 @ A2 )
% 9.25/5.26                    = ( groups3827104343326376752nteger @ H3 @ B2 ) )
% 9.25/5.26                  = ( ( groups3827104343326376752nteger @ G2 @ C2 )
% 9.25/5.26                    = ( groups3827104343326376752nteger @ H3 @ C2 ) ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8311_prod_Osame__carrier,axiom,
% 9.25/5.26      ! [C2: set_int,A2: set_int,B2: set_int,G2: int > assn,H3: int > assn] :
% 9.25/5.26        ( ( finite_finite_int @ C2 )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ A2 @ C2 )
% 9.25/5.26         => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 9.25/5.26           => ( ! [A6: int] :
% 9.25/5.26                  ( ( member_int @ A6 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 9.25/5.26                 => ( ( G2 @ A6 )
% 9.25/5.26                    = one_one_assn ) )
% 9.25/5.26             => ( ! [B6: int] :
% 9.25/5.26                    ( ( member_int @ B6 @ ( minus_minus_set_int @ C2 @ B2 ) )
% 9.25/5.26                   => ( ( H3 @ B6 )
% 9.25/5.26                      = one_one_assn ) )
% 9.25/5.26               => ( ( ( groups7882442080178216443t_assn @ G2 @ A2 )
% 9.25/5.26                    = ( groups7882442080178216443t_assn @ H3 @ B2 ) )
% 9.25/5.26                  = ( ( groups7882442080178216443t_assn @ G2 @ C2 )
% 9.25/5.26                    = ( groups7882442080178216443t_assn @ H3 @ C2 ) ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8312_prod_Osame__carrier,axiom,
% 9.25/5.26      ! [C2: set_int,A2: set_int,B2: set_int,G2: int > rat,H3: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ C2 )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ A2 @ C2 )
% 9.25/5.26         => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 9.25/5.26           => ( ! [A6: int] :
% 9.25/5.26                  ( ( member_int @ A6 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 9.25/5.26                 => ( ( G2 @ A6 )
% 9.25/5.26                    = one_one_rat ) )
% 9.25/5.26             => ( ! [B6: int] :
% 9.25/5.26                    ( ( member_int @ B6 @ ( minus_minus_set_int @ C2 @ B2 ) )
% 9.25/5.26                   => ( ( H3 @ B6 )
% 9.25/5.26                      = one_one_rat ) )
% 9.25/5.26               => ( ( ( groups1072433553688619179nt_rat @ G2 @ A2 )
% 9.25/5.26                    = ( groups1072433553688619179nt_rat @ H3 @ B2 ) )
% 9.25/5.26                  = ( ( groups1072433553688619179nt_rat @ G2 @ C2 )
% 9.25/5.26                    = ( groups1072433553688619179nt_rat @ H3 @ C2 ) ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8313_prod_Osame__carrier,axiom,
% 9.25/5.26      ! [C2: set_int,A2: set_int,B2: set_int,G2: int > nat,H3: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ C2 )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ A2 @ C2 )
% 9.25/5.26         => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 9.25/5.26           => ( ! [A6: int] :
% 9.25/5.26                  ( ( member_int @ A6 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 9.25/5.26                 => ( ( G2 @ A6 )
% 9.25/5.26                    = one_one_nat ) )
% 9.25/5.26             => ( ! [B6: int] :
% 9.25/5.26                    ( ( member_int @ B6 @ ( minus_minus_set_int @ C2 @ B2 ) )
% 9.25/5.26                   => ( ( H3 @ B6 )
% 9.25/5.26                      = one_one_nat ) )
% 9.25/5.26               => ( ( ( groups1707563613775114915nt_nat @ G2 @ A2 )
% 9.25/5.26                    = ( groups1707563613775114915nt_nat @ H3 @ B2 ) )
% 9.25/5.26                  = ( ( groups1707563613775114915nt_nat @ G2 @ C2 )
% 9.25/5.26                    = ( groups1707563613775114915nt_nat @ H3 @ C2 ) ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8314_prod_Osame__carrier,axiom,
% 9.25/5.26      ! [C2: set_nat,A2: set_nat,B2: set_nat,G2: nat > code_integer,H3: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ C2 )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 9.25/5.26         => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 9.25/5.26           => ( ! [A6: nat] :
% 9.25/5.26                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 9.25/5.26                 => ( ( G2 @ A6 )
% 9.25/5.26                    = one_one_Code_integer ) )
% 9.25/5.26             => ( ! [B6: nat] :
% 9.25/5.26                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ C2 @ B2 ) )
% 9.25/5.26                   => ( ( H3 @ B6 )
% 9.25/5.26                      = one_one_Code_integer ) )
% 9.25/5.26               => ( ( ( groups3455450783089532116nteger @ G2 @ A2 )
% 9.25/5.26                    = ( groups3455450783089532116nteger @ H3 @ B2 ) )
% 9.25/5.26                  = ( ( groups3455450783089532116nteger @ G2 @ C2 )
% 9.25/5.26                    = ( groups3455450783089532116nteger @ H3 @ C2 ) ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8315_prod_Osame__carrier,axiom,
% 9.25/5.26      ! [C2: set_nat,A2: set_nat,B2: set_nat,G2: nat > assn,H3: nat > assn] :
% 9.25/5.26        ( ( finite_finite_nat @ C2 )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 9.25/5.26         => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 9.25/5.26           => ( ! [A6: nat] :
% 9.25/5.26                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 9.25/5.26                 => ( ( G2 @ A6 )
% 9.25/5.26                    = one_one_assn ) )
% 9.25/5.26             => ( ! [B6: nat] :
% 9.25/5.26                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ C2 @ B2 ) )
% 9.25/5.26                   => ( ( H3 @ B6 )
% 9.25/5.26                      = one_one_assn ) )
% 9.25/5.26               => ( ( ( groups6906906614972039071t_assn @ G2 @ A2 )
% 9.25/5.26                    = ( groups6906906614972039071t_assn @ H3 @ B2 ) )
% 9.25/5.26                  = ( ( groups6906906614972039071t_assn @ G2 @ C2 )
% 9.25/5.26                    = ( groups6906906614972039071t_assn @ H3 @ C2 ) ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8316_prod_Osame__carrier,axiom,
% 9.25/5.26      ! [C2: set_nat,A2: set_nat,B2: set_nat,G2: nat > rat,H3: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ C2 )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 9.25/5.26         => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 9.25/5.26           => ( ! [A6: nat] :
% 9.25/5.26                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 9.25/5.26                 => ( ( G2 @ A6 )
% 9.25/5.26                    = one_one_rat ) )
% 9.25/5.26             => ( ! [B6: nat] :
% 9.25/5.26                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ C2 @ B2 ) )
% 9.25/5.26                   => ( ( H3 @ B6 )
% 9.25/5.26                      = one_one_rat ) )
% 9.25/5.26               => ( ( ( groups73079841787564623at_rat @ G2 @ A2 )
% 9.25/5.26                    = ( groups73079841787564623at_rat @ H3 @ B2 ) )
% 9.25/5.26                  = ( ( groups73079841787564623at_rat @ G2 @ C2 )
% 9.25/5.26                    = ( groups73079841787564623at_rat @ H3 @ C2 ) ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8317_prod_Osame__carrier,axiom,
% 9.25/5.26      ! [C2: set_nat,A2: set_nat,B2: set_nat,G2: nat > nat,H3: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ C2 )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 9.25/5.26         => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 9.25/5.26           => ( ! [A6: nat] :
% 9.25/5.26                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 9.25/5.26                 => ( ( G2 @ A6 )
% 9.25/5.26                    = one_one_nat ) )
% 9.25/5.26             => ( ! [B6: nat] :
% 9.25/5.26                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ C2 @ B2 ) )
% 9.25/5.26                   => ( ( H3 @ B6 )
% 9.25/5.26                      = one_one_nat ) )
% 9.25/5.26               => ( ( ( groups708209901874060359at_nat @ G2 @ A2 )
% 9.25/5.26                    = ( groups708209901874060359at_nat @ H3 @ B2 ) )
% 9.25/5.26                  = ( ( groups708209901874060359at_nat @ G2 @ C2 )
% 9.25/5.26                    = ( groups708209901874060359at_nat @ H3 @ C2 ) ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8318_prod_Osame__carrier,axiom,
% 9.25/5.26      ! [C2: set_nat,A2: set_nat,B2: set_nat,G2: nat > int,H3: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ C2 )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ A2 @ C2 )
% 9.25/5.26         => ( ( ord_less_eq_set_nat @ B2 @ C2 )
% 9.25/5.26           => ( ! [A6: nat] :
% 9.25/5.26                  ( ( member_nat @ A6 @ ( minus_minus_set_nat @ C2 @ A2 ) )
% 9.25/5.26                 => ( ( G2 @ A6 )
% 9.25/5.26                    = one_one_int ) )
% 9.25/5.26             => ( ! [B6: nat] :
% 9.25/5.26                    ( ( member_nat @ B6 @ ( minus_minus_set_nat @ C2 @ B2 ) )
% 9.25/5.26                   => ( ( H3 @ B6 )
% 9.25/5.26                      = one_one_int ) )
% 9.25/5.26               => ( ( ( groups705719431365010083at_int @ G2 @ A2 )
% 9.25/5.26                    = ( groups705719431365010083at_int @ H3 @ B2 ) )
% 9.25/5.26                  = ( ( groups705719431365010083at_int @ G2 @ C2 )
% 9.25/5.26                    = ( groups705719431365010083at_int @ H3 @ C2 ) ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8319_prod_Osame__carrier,axiom,
% 9.25/5.26      ! [C2: set_int,A2: set_int,B2: set_int,G2: int > int,H3: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ C2 )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ A2 @ C2 )
% 9.25/5.26         => ( ( ord_less_eq_set_int @ B2 @ C2 )
% 9.25/5.26           => ( ! [A6: int] :
% 9.25/5.26                  ( ( member_int @ A6 @ ( minus_minus_set_int @ C2 @ A2 ) )
% 9.25/5.26                 => ( ( G2 @ A6 )
% 9.25/5.26                    = one_one_int ) )
% 9.25/5.26             => ( ! [B6: int] :
% 9.25/5.26                    ( ( member_int @ B6 @ ( minus_minus_set_int @ C2 @ B2 ) )
% 9.25/5.26                   => ( ( H3 @ B6 )
% 9.25/5.26                      = one_one_int ) )
% 9.25/5.26               => ( ( ( groups1705073143266064639nt_int @ G2 @ A2 )
% 9.25/5.26                    = ( groups1705073143266064639nt_int @ H3 @ B2 ) )
% 9.25/5.26                  = ( ( groups1705073143266064639nt_int @ G2 @ C2 )
% 9.25/5.26                    = ( groups1705073143266064639nt_int @ H3 @ C2 ) ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8320_sum_Ounion__inter,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) ) @ ( groups3906332499630173760nt_rat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) )
% 9.25/5.26            = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G2 @ A2 ) @ ( groups3906332499630173760nt_rat @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8321_sum_Ounion__inter,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) ) @ ( groups4541462559716669496nt_nat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) )
% 9.25/5.26            = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G2 @ A2 ) @ ( groups4541462559716669496nt_nat @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8322_sum_Ounion__inter,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ ( groups2906978787729119204at_rat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) )
% 9.25/5.26            = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ A2 ) @ ( groups2906978787729119204at_rat @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8323_sum_Ounion__inter,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ ( groups3539618377306564664at_int @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) )
% 9.25/5.26            = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ A2 ) @ ( groups3539618377306564664at_int @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8324_sum_Ounion__inter,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ ( groups3542108847815614940at_nat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) )
% 9.25/5.26            = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ A2 ) @ ( groups3542108847815614940at_nat @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8325_sum_Ounion__inter,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( plus_plus_int @ ( groups4538972089207619220nt_int @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) ) @ ( groups4538972089207619220nt_int @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) )
% 9.25/5.26            = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G2 @ A2 ) @ ( groups4538972089207619220nt_int @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8326_sum_Ounion__inter,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > rat] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.26       => ( ( finite6177210948735845034at_nat @ B2 )
% 9.25/5.26         => ( ( plus_plus_rat @ ( groups342789780944988191at_rat @ G2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) ) @ ( groups342789780944988191at_rat @ G2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) )
% 9.25/5.26            = ( plus_plus_rat @ ( groups342789780944988191at_rat @ G2 @ A2 ) @ ( groups342789780944988191at_rat @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8327_sum_Ounion__inter,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > nat] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.26       => ( ( finite6177210948735845034at_nat @ B2 )
% 9.25/5.26         => ( ( plus_plus_nat @ ( groups977919841031483927at_nat @ G2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) ) @ ( groups977919841031483927at_nat @ G2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) )
% 9.25/5.26            = ( plus_plus_nat @ ( groups977919841031483927at_nat @ G2 @ A2 ) @ ( groups977919841031483927at_nat @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8328_sum_Ounion__inter,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > int] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.26       => ( ( finite6177210948735845034at_nat @ B2 )
% 9.25/5.26         => ( ( plus_plus_int @ ( groups975429370522433651at_int @ G2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) ) @ ( groups975429370522433651at_int @ G2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) )
% 9.25/5.26            = ( plus_plus_int @ ( groups975429370522433651at_int @ G2 @ A2 ) @ ( groups975429370522433651at_int @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8329_sum_Ounion__inter,axiom,
% 9.25/5.26      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,G2: produc4166570645942440679at_nat > rat] :
% 9.25/5.26        ( ( finite1918287321285529104at_nat @ A2 )
% 9.25/5.26       => ( ( finite1918287321285529104at_nat @ B2 )
% 9.25/5.26         => ( ( plus_plus_rat @ ( groups6424767709179651461at_rat @ G2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) ) @ ( groups6424767709179651461at_rat @ G2 @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) ) )
% 9.25/5.26            = ( plus_plus_rat @ ( groups6424767709179651461at_rat @ G2 @ A2 ) @ ( groups6424767709179651461at_rat @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8330_sum_OInt__Diff,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > rat,B2: set_int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups3906332499630173760nt_rat @ G2 @ A2 )
% 9.25/5.26          = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) @ ( groups3906332499630173760nt_rat @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8331_sum_OInt__Diff,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > nat,B2: set_int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups4541462559716669496nt_nat @ G2 @ A2 )
% 9.25/5.26          = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) @ ( groups4541462559716669496nt_nat @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8332_sum_OInt__Diff,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > rat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.26       => ( ( groups342789780944988191at_rat @ G2 @ A2 )
% 9.25/5.26          = ( plus_plus_rat @ ( groups342789780944988191at_rat @ G2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) @ ( groups342789780944988191at_rat @ G2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8333_sum_OInt__Diff,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.26       => ( ( groups977919841031483927at_nat @ G2 @ A2 )
% 9.25/5.26          = ( plus_plus_nat @ ( groups977919841031483927at_nat @ G2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) @ ( groups977919841031483927at_nat @ G2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8334_sum_OInt__Diff,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > int,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.26       => ( ( groups975429370522433651at_int @ G2 @ A2 )
% 9.25/5.26          = ( plus_plus_int @ ( groups975429370522433651at_int @ G2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) @ ( groups975429370522433651at_int @ G2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8335_sum_OInt__Diff,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > rat,B2: set_nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups2906978787729119204at_rat @ G2 @ A2 )
% 9.25/5.26          = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) @ ( groups2906978787729119204at_rat @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8336_sum_OInt__Diff,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > int,B2: set_nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups3539618377306564664at_int @ G2 @ A2 )
% 9.25/5.26          = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) @ ( groups3539618377306564664at_int @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8337_sum_OInt__Diff,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > nat,B2: set_nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups3542108847815614940at_nat @ G2 @ A2 )
% 9.25/5.26          = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) @ ( groups3542108847815614940at_nat @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8338_sum_OInt__Diff,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > int,B2: set_int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups4538972089207619220nt_int @ G2 @ A2 )
% 9.25/5.26          = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) @ ( groups4538972089207619220nt_int @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8339_sum_OatLeast1__atMost__eq,axiom,
% 9.25/5.26      ! [G2: nat > nat,N: nat] :
% 9.25/5.26        ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 9.25/5.26        = ( groups3542108847815614940at_nat
% 9.25/5.26          @ ^ [K4: nat] : ( G2 @ ( suc @ K4 ) )
% 9.25/5.26          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8340_prod_Ounion__inter,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) ) @ ( groups3827104343326376752nteger @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) )
% 9.25/5.26            = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G2 @ A2 ) @ ( groups3827104343326376752nteger @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8341_prod_Ounion__inter,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ ( groups3455450783089532116nteger @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) )
% 9.25/5.26            = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ A2 ) @ ( groups3455450783089532116nteger @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8342_prod_Ounion__inter,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > assn] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( times_times_assn @ ( groups7882442080178216443t_assn @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) ) @ ( groups7882442080178216443t_assn @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) )
% 9.25/5.26            = ( times_times_assn @ ( groups7882442080178216443t_assn @ G2 @ A2 ) @ ( groups7882442080178216443t_assn @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8343_prod_Ounion__inter,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > assn] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ ( groups6906906614972039071t_assn @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) )
% 9.25/5.26            = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ A2 ) @ ( groups6906906614972039071t_assn @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8344_prod_Ounion__inter,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) )
% 9.25/5.26            = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ A2 ) @ ( groups1072433553688619179nt_rat @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8345_prod_Ounion__inter,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) )
% 9.25/5.26            = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ A2 ) @ ( groups73079841787564623at_rat @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8346_prod_Ounion__inter,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) )
% 9.25/5.26            = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ A2 ) @ ( groups1707563613775114915nt_nat @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8347_prod_Ounion__inter,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ ( groups708209901874060359at_nat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) )
% 9.25/5.26            = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ A2 ) @ ( groups708209901874060359at_nat @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8348_prod_Ounion__inter,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) ) @ ( groups705719431365010083at_int @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) )
% 9.25/5.26            = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ A2 ) @ ( groups705719431365010083at_int @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8349_prod_Ounion__inter,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( times_times_int @ ( groups1705073143266064639nt_int @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) ) @ ( groups1705073143266064639nt_int @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) )
% 9.25/5.26            = ( times_times_int @ ( groups1705073143266064639nt_int @ G2 @ A2 ) @ ( groups1705073143266064639nt_int @ G2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8350_prod_OInt__Diff,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > code_integer,B2: set_int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups3827104343326376752nteger @ G2 @ A2 )
% 9.25/5.26          = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) @ ( groups3827104343326376752nteger @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8351_prod_OInt__Diff,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > code_integer,B2: set_nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups3455450783089532116nteger @ G2 @ A2 )
% 9.25/5.26          = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) @ ( groups3455450783089532116nteger @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8352_prod_OInt__Diff,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > assn,B2: set_int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups7882442080178216443t_assn @ G2 @ A2 )
% 9.25/5.26          = ( times_times_assn @ ( groups7882442080178216443t_assn @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) @ ( groups7882442080178216443t_assn @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8353_prod_OInt__Diff,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > assn,B2: set_nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups6906906614972039071t_assn @ G2 @ A2 )
% 9.25/5.26          = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) @ ( groups6906906614972039071t_assn @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8354_prod_OInt__Diff,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > rat,B2: set_int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups1072433553688619179nt_rat @ G2 @ A2 )
% 9.25/5.26          = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8355_prod_OInt__Diff,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > rat,B2: set_nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups73079841787564623at_rat @ G2 @ A2 )
% 9.25/5.26          = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8356_prod_OInt__Diff,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > nat,B2: set_int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups1707563613775114915nt_nat @ G2 @ A2 )
% 9.25/5.26          = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8357_prod_OInt__Diff,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > nat,B2: set_nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups708209901874060359at_nat @ G2 @ A2 )
% 9.25/5.26          = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) @ ( groups708209901874060359at_nat @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8358_prod_OInt__Diff,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > int,B2: set_nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups705719431365010083at_int @ G2 @ A2 )
% 9.25/5.26          = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) @ ( groups705719431365010083at_int @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8359_prod_OInt__Diff,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > int,B2: set_int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups1705073143266064639nt_int @ G2 @ A2 )
% 9.25/5.26          = ( times_times_int @ ( groups1705073143266064639nt_int @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) @ ( groups1705073143266064639nt_int @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8360_prod_Omono__neutral__cong,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,H3: int > code_integer,G2: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( finite_finite_int @ S )
% 9.25/5.26         => ( ! [I2: int] :
% 9.25/5.26                ( ( member_int @ I2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ I2 )
% 9.25/5.26                  = one_one_Code_integer ) )
% 9.25/5.26           => ( ! [I2: int] :
% 9.25/5.26                  ( ( member_int @ I2 @ ( minus_minus_set_int @ S @ T ) )
% 9.25/5.26                 => ( ( G2 @ I2 )
% 9.25/5.26                    = one_one_Code_integer ) )
% 9.25/5.26             => ( ! [X2: int] :
% 9.25/5.26                    ( ( member_int @ X2 @ ( inf_inf_set_int @ S @ T ) )
% 9.25/5.26                   => ( ( G2 @ X2 )
% 9.25/5.26                      = ( H3 @ X2 ) ) )
% 9.25/5.26               => ( ( groups3827104343326376752nteger @ G2 @ S )
% 9.25/5.26                  = ( groups3827104343326376752nteger @ H3 @ T ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8361_prod_Omono__neutral__cong,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,H3: int > assn,G2: int > assn] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( finite_finite_int @ S )
% 9.25/5.26         => ( ! [I2: int] :
% 9.25/5.26                ( ( member_int @ I2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ I2 )
% 9.25/5.26                  = one_one_assn ) )
% 9.25/5.26           => ( ! [I2: int] :
% 9.25/5.26                  ( ( member_int @ I2 @ ( minus_minus_set_int @ S @ T ) )
% 9.25/5.26                 => ( ( G2 @ I2 )
% 9.25/5.26                    = one_one_assn ) )
% 9.25/5.26             => ( ! [X2: int] :
% 9.25/5.26                    ( ( member_int @ X2 @ ( inf_inf_set_int @ S @ T ) )
% 9.25/5.26                   => ( ( G2 @ X2 )
% 9.25/5.26                      = ( H3 @ X2 ) ) )
% 9.25/5.26               => ( ( groups7882442080178216443t_assn @ G2 @ S )
% 9.25/5.26                  = ( groups7882442080178216443t_assn @ H3 @ T ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8362_prod_Omono__neutral__cong,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,H3: int > rat,G2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( finite_finite_int @ S )
% 9.25/5.26         => ( ! [I2: int] :
% 9.25/5.26                ( ( member_int @ I2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ I2 )
% 9.25/5.26                  = one_one_rat ) )
% 9.25/5.26           => ( ! [I2: int] :
% 9.25/5.26                  ( ( member_int @ I2 @ ( minus_minus_set_int @ S @ T ) )
% 9.25/5.26                 => ( ( G2 @ I2 )
% 9.25/5.26                    = one_one_rat ) )
% 9.25/5.26             => ( ! [X2: int] :
% 9.25/5.26                    ( ( member_int @ X2 @ ( inf_inf_set_int @ S @ T ) )
% 9.25/5.26                   => ( ( G2 @ X2 )
% 9.25/5.26                      = ( H3 @ X2 ) ) )
% 9.25/5.26               => ( ( groups1072433553688619179nt_rat @ G2 @ S )
% 9.25/5.26                  = ( groups1072433553688619179nt_rat @ H3 @ T ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8363_prod_Omono__neutral__cong,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,H3: int > nat,G2: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( finite_finite_int @ S )
% 9.25/5.26         => ( ! [I2: int] :
% 9.25/5.26                ( ( member_int @ I2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ I2 )
% 9.25/5.26                  = one_one_nat ) )
% 9.25/5.26           => ( ! [I2: int] :
% 9.25/5.26                  ( ( member_int @ I2 @ ( minus_minus_set_int @ S @ T ) )
% 9.25/5.26                 => ( ( G2 @ I2 )
% 9.25/5.26                    = one_one_nat ) )
% 9.25/5.26             => ( ! [X2: int] :
% 9.25/5.26                    ( ( member_int @ X2 @ ( inf_inf_set_int @ S @ T ) )
% 9.25/5.26                   => ( ( G2 @ X2 )
% 9.25/5.26                      = ( H3 @ X2 ) ) )
% 9.25/5.26               => ( ( groups1707563613775114915nt_nat @ G2 @ S )
% 9.25/5.26                  = ( groups1707563613775114915nt_nat @ H3 @ T ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8364_prod_Omono__neutral__cong,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,H3: nat > code_integer,G2: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( finite_finite_nat @ S )
% 9.25/5.26         => ( ! [I2: nat] :
% 9.25/5.26                ( ( member_nat @ I2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ I2 )
% 9.25/5.26                  = one_one_Code_integer ) )
% 9.25/5.26           => ( ! [I2: nat] :
% 9.25/5.26                  ( ( member_nat @ I2 @ ( minus_minus_set_nat @ S @ T ) )
% 9.25/5.26                 => ( ( G2 @ I2 )
% 9.25/5.26                    = one_one_Code_integer ) )
% 9.25/5.26             => ( ! [X2: nat] :
% 9.25/5.26                    ( ( member_nat @ X2 @ ( inf_inf_set_nat @ S @ T ) )
% 9.25/5.26                   => ( ( G2 @ X2 )
% 9.25/5.26                      = ( H3 @ X2 ) ) )
% 9.25/5.26               => ( ( groups3455450783089532116nteger @ G2 @ S )
% 9.25/5.26                  = ( groups3455450783089532116nteger @ H3 @ T ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8365_prod_Omono__neutral__cong,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,H3: nat > assn,G2: nat > assn] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( finite_finite_nat @ S )
% 9.25/5.26         => ( ! [I2: nat] :
% 9.25/5.26                ( ( member_nat @ I2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ I2 )
% 9.25/5.26                  = one_one_assn ) )
% 9.25/5.26           => ( ! [I2: nat] :
% 9.25/5.26                  ( ( member_nat @ I2 @ ( minus_minus_set_nat @ S @ T ) )
% 9.25/5.26                 => ( ( G2 @ I2 )
% 9.25/5.26                    = one_one_assn ) )
% 9.25/5.26             => ( ! [X2: nat] :
% 9.25/5.26                    ( ( member_nat @ X2 @ ( inf_inf_set_nat @ S @ T ) )
% 9.25/5.26                   => ( ( G2 @ X2 )
% 9.25/5.26                      = ( H3 @ X2 ) ) )
% 9.25/5.26               => ( ( groups6906906614972039071t_assn @ G2 @ S )
% 9.25/5.26                  = ( groups6906906614972039071t_assn @ H3 @ T ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8366_prod_Omono__neutral__cong,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,H3: nat > rat,G2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( finite_finite_nat @ S )
% 9.25/5.26         => ( ! [I2: nat] :
% 9.25/5.26                ( ( member_nat @ I2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ I2 )
% 9.25/5.26                  = one_one_rat ) )
% 9.25/5.26           => ( ! [I2: nat] :
% 9.25/5.26                  ( ( member_nat @ I2 @ ( minus_minus_set_nat @ S @ T ) )
% 9.25/5.26                 => ( ( G2 @ I2 )
% 9.25/5.26                    = one_one_rat ) )
% 9.25/5.26             => ( ! [X2: nat] :
% 9.25/5.26                    ( ( member_nat @ X2 @ ( inf_inf_set_nat @ S @ T ) )
% 9.25/5.26                   => ( ( G2 @ X2 )
% 9.25/5.26                      = ( H3 @ X2 ) ) )
% 9.25/5.26               => ( ( groups73079841787564623at_rat @ G2 @ S )
% 9.25/5.26                  = ( groups73079841787564623at_rat @ H3 @ T ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8367_prod_Omono__neutral__cong,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,H3: nat > nat,G2: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( finite_finite_nat @ S )
% 9.25/5.26         => ( ! [I2: nat] :
% 9.25/5.26                ( ( member_nat @ I2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ I2 )
% 9.25/5.26                  = one_one_nat ) )
% 9.25/5.26           => ( ! [I2: nat] :
% 9.25/5.26                  ( ( member_nat @ I2 @ ( minus_minus_set_nat @ S @ T ) )
% 9.25/5.26                 => ( ( G2 @ I2 )
% 9.25/5.26                    = one_one_nat ) )
% 9.25/5.26             => ( ! [X2: nat] :
% 9.25/5.26                    ( ( member_nat @ X2 @ ( inf_inf_set_nat @ S @ T ) )
% 9.25/5.26                   => ( ( G2 @ X2 )
% 9.25/5.26                      = ( H3 @ X2 ) ) )
% 9.25/5.26               => ( ( groups708209901874060359at_nat @ G2 @ S )
% 9.25/5.26                  = ( groups708209901874060359at_nat @ H3 @ T ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8368_prod_Omono__neutral__cong,axiom,
% 9.25/5.26      ! [T: set_nat,S: set_nat,H3: nat > int,G2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ T )
% 9.25/5.26       => ( ( finite_finite_nat @ S )
% 9.25/5.26         => ( ! [I2: nat] :
% 9.25/5.26                ( ( member_nat @ I2 @ ( minus_minus_set_nat @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ I2 )
% 9.25/5.26                  = one_one_int ) )
% 9.25/5.26           => ( ! [I2: nat] :
% 9.25/5.26                  ( ( member_nat @ I2 @ ( minus_minus_set_nat @ S @ T ) )
% 9.25/5.26                 => ( ( G2 @ I2 )
% 9.25/5.26                    = one_one_int ) )
% 9.25/5.26             => ( ! [X2: nat] :
% 9.25/5.26                    ( ( member_nat @ X2 @ ( inf_inf_set_nat @ S @ T ) )
% 9.25/5.26                   => ( ( G2 @ X2 )
% 9.25/5.26                      = ( H3 @ X2 ) ) )
% 9.25/5.26               => ( ( groups705719431365010083at_int @ G2 @ S )
% 9.25/5.26                  = ( groups705719431365010083at_int @ H3 @ T ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8369_prod_Omono__neutral__cong,axiom,
% 9.25/5.26      ! [T: set_int,S: set_int,H3: int > int,G2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ T )
% 9.25/5.26       => ( ( finite_finite_int @ S )
% 9.25/5.26         => ( ! [I2: int] :
% 9.25/5.26                ( ( member_int @ I2 @ ( minus_minus_set_int @ T @ S ) )
% 9.25/5.26               => ( ( H3 @ I2 )
% 9.25/5.26                  = one_one_int ) )
% 9.25/5.26           => ( ! [I2: int] :
% 9.25/5.26                  ( ( member_int @ I2 @ ( minus_minus_set_int @ S @ T ) )
% 9.25/5.26                 => ( ( G2 @ I2 )
% 9.25/5.26                    = one_one_int ) )
% 9.25/5.26             => ( ! [X2: int] :
% 9.25/5.26                    ( ( member_int @ X2 @ ( inf_inf_set_int @ S @ T ) )
% 9.25/5.26                   => ( ( G2 @ X2 )
% 9.25/5.26                      = ( H3 @ X2 ) ) )
% 9.25/5.26               => ( ( groups1705073143266064639nt_int @ G2 @ S )
% 9.25/5.26                  = ( groups1705073143266064639nt_int @ H3 @ T ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8370_prod_OatLeast1__atMost__eq,axiom,
% 9.25/5.26      ! [G2: nat > nat,N: nat] :
% 9.25/5.26        ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 9.25/5.26        = ( groups708209901874060359at_nat
% 9.25/5.26          @ ^ [K4: nat] : ( G2 @ ( suc @ K4 ) )
% 9.25/5.26          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8371_prod_OatLeast1__atMost__eq,axiom,
% 9.25/5.26      ! [G2: nat > int,N: nat] :
% 9.25/5.26        ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 9.25/5.26        = ( groups705719431365010083at_int
% 9.25/5.26          @ ^ [K4: nat] : ( G2 @ ( suc @ K4 ) )
% 9.25/5.26          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8372_sum__bounds__lt__plus1,axiom,
% 9.25/5.26      ! [F2: nat > nat,Mm: nat] :
% 9.25/5.26        ( ( groups3542108847815614940at_nat
% 9.25/5.26          @ ^ [K4: nat] : ( F2 @ ( suc @ K4 ) )
% 9.25/5.26          @ ( set_ord_lessThan_nat @ Mm ) )
% 9.25/5.26        = ( groups3542108847815614940at_nat @ F2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8373_prod__int__plus__eq,axiom,
% 9.25/5.26      ! [I: nat,J: nat] :
% 9.25/5.26        ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 9.25/5.26        = ( groups1705073143266064639nt_int
% 9.25/5.26          @ ^ [X3: int] : X3
% 9.25/5.26          @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8374_sum_Onat__group,axiom,
% 9.25/5.26      ! [G2: nat > nat,K: nat,N: nat] :
% 9.25/5.26        ( ( groups3542108847815614940at_nat
% 9.25/5.26          @ ^ [M2: nat] : ( groups3542108847815614940at_nat @ G2 @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M2 @ K ) @ ( plus_plus_nat @ ( times_times_nat @ M2 @ K ) @ K ) ) )
% 9.25/5.26          @ ( set_ord_lessThan_nat @ N ) )
% 9.25/5.26        = ( groups3542108847815614940at_nat @ G2 @ ( set_ord_lessThan_nat @ ( times_times_nat @ N @ K ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8375_prod_Onat__group,axiom,
% 9.25/5.26      ! [G2: nat > nat,K: nat,N: nat] :
% 9.25/5.26        ( ( groups708209901874060359at_nat
% 9.25/5.26          @ ^ [M2: nat] : ( groups708209901874060359at_nat @ G2 @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M2 @ K ) @ ( plus_plus_nat @ ( times_times_nat @ M2 @ K ) @ K ) ) )
% 9.25/5.26          @ ( set_ord_lessThan_nat @ N ) )
% 9.25/5.26        = ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ ( times_times_nat @ N @ K ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8376_prod_Onat__group,axiom,
% 9.25/5.26      ! [G2: nat > int,K: nat,N: nat] :
% 9.25/5.26        ( ( groups705719431365010083at_int
% 9.25/5.26          @ ^ [M2: nat] : ( groups705719431365010083at_int @ G2 @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M2 @ K ) @ ( plus_plus_nat @ ( times_times_nat @ M2 @ K ) @ K ) ) )
% 9.25/5.26          @ ( set_ord_lessThan_nat @ N ) )
% 9.25/5.26        = ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ ( times_times_nat @ N @ K ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8377_sum_Onested__swap_H,axiom,
% 9.25/5.26      ! [A: nat > nat > nat,N: nat] :
% 9.25/5.26        ( ( groups3542108847815614940at_nat
% 9.25/5.26          @ ^ [I3: nat] : ( groups3542108847815614940at_nat @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 9.25/5.26          @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.26        = ( groups3542108847815614940at_nat
% 9.25/5.26          @ ^ [J3: nat] :
% 9.25/5.26              ( groups3542108847815614940at_nat
% 9.25/5.26              @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 9.25/5.26              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 9.25/5.26          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8378_prod_Onested__swap_H,axiom,
% 9.25/5.26      ! [A: nat > nat > nat,N: nat] :
% 9.25/5.26        ( ( groups708209901874060359at_nat
% 9.25/5.26          @ ^ [I3: nat] : ( groups708209901874060359at_nat @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 9.25/5.26          @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.26        = ( groups708209901874060359at_nat
% 9.25/5.26          @ ^ [J3: nat] :
% 9.25/5.26              ( groups708209901874060359at_nat
% 9.25/5.26              @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 9.25/5.26              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 9.25/5.26          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8379_prod_Onested__swap_H,axiom,
% 9.25/5.26      ! [A: nat > nat > int,N: nat] :
% 9.25/5.26        ( ( groups705719431365010083at_int
% 9.25/5.26          @ ^ [I3: nat] : ( groups705719431365010083at_int @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 9.25/5.26          @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.26        = ( groups705719431365010083at_int
% 9.25/5.26          @ ^ [J3: nat] :
% 9.25/5.26              ( groups705719431365010083at_int
% 9.25/5.26              @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 9.25/5.26              @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N ) )
% 9.25/5.26          @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8380_Iio__Int__singleton,axiom,
% 9.25/5.26      ! [X: $o,K: $o] :
% 9.25/5.26        ( ( ( ord_less_o @ X @ K )
% 9.25/5.26         => ( ( inf_inf_set_o @ ( set_ord_lessThan_o @ K ) @ ( insert_o @ X @ bot_bot_set_o ) )
% 9.25/5.26            = ( insert_o @ X @ bot_bot_set_o ) ) )
% 9.25/5.26        & ( ~ ( ord_less_o @ X @ K )
% 9.25/5.26         => ( ( inf_inf_set_o @ ( set_ord_lessThan_o @ K ) @ ( insert_o @ X @ bot_bot_set_o ) )
% 9.25/5.26            = bot_bot_set_o ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8381_Iio__Int__singleton,axiom,
% 9.25/5.26      ! [X: literal,K: literal] :
% 9.25/5.26        ( ( ( ord_less_literal @ X @ K )
% 9.25/5.26         => ( ( inf_inf_set_literal @ ( set_or2436086697161274615iteral @ K ) @ ( insert_literal @ X @ bot_bot_set_literal ) )
% 9.25/5.26            = ( insert_literal @ X @ bot_bot_set_literal ) ) )
% 9.25/5.26        & ( ~ ( ord_less_literal @ X @ K )
% 9.25/5.26         => ( ( inf_inf_set_literal @ ( set_or2436086697161274615iteral @ K ) @ ( insert_literal @ X @ bot_bot_set_literal ) )
% 9.25/5.26            = bot_bot_set_literal ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8382_Iio__Int__singleton,axiom,
% 9.25/5.26      ! [X: rat,K: rat] :
% 9.25/5.26        ( ( ( ord_less_rat @ X @ K )
% 9.25/5.26         => ( ( inf_inf_set_rat @ ( set_ord_lessThan_rat @ K ) @ ( insert_rat @ X @ bot_bot_set_rat ) )
% 9.25/5.26            = ( insert_rat @ X @ bot_bot_set_rat ) ) )
% 9.25/5.26        & ( ~ ( ord_less_rat @ X @ K )
% 9.25/5.26         => ( ( inf_inf_set_rat @ ( set_ord_lessThan_rat @ K ) @ ( insert_rat @ X @ bot_bot_set_rat ) )
% 9.25/5.26            = bot_bot_set_rat ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8383_Iio__Int__singleton,axiom,
% 9.25/5.26      ! [X: int,K: int] :
% 9.25/5.26        ( ( ( ord_less_int @ X @ K )
% 9.25/5.26         => ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ K ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 9.25/5.26            = ( insert_int @ X @ bot_bot_set_int ) ) )
% 9.25/5.26        & ( ~ ( ord_less_int @ X @ K )
% 9.25/5.26         => ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ K ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 9.25/5.26            = bot_bot_set_int ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8384_Iio__Int__singleton,axiom,
% 9.25/5.26      ! [X: nat,K: nat] :
% 9.25/5.26        ( ( ( ord_less_nat @ X @ K )
% 9.25/5.26         => ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ K ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 9.25/5.26            = ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 9.25/5.26        & ( ~ ( ord_less_nat @ X @ K )
% 9.25/5.26         => ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ K ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 9.25/5.26            = bot_bot_set_nat ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8385_ivl__disj__un__singleton_I2_J,axiom,
% 9.25/5.26      ! [U: $o] :
% 9.25/5.26        ( ( sup_sup_set_o @ ( set_ord_lessThan_o @ U ) @ ( insert_o @ U @ bot_bot_set_o ) )
% 9.25/5.26        = ( set_ord_atMost_o @ U ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8386_ivl__disj__un__singleton_I2_J,axiom,
% 9.25/5.26      ! [U: int] :
% 9.25/5.26        ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ U ) @ ( insert_int @ U @ bot_bot_set_int ) )
% 9.25/5.26        = ( set_ord_atMost_int @ U ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8387_ivl__disj__un__singleton_I2_J,axiom,
% 9.25/5.26      ! [U: nat] :
% 9.25/5.26        ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ U ) @ ( insert_nat @ U @ bot_bot_set_nat ) )
% 9.25/5.26        = ( set_ord_atMost_nat @ U ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8388_ivl__disj__un__one_I4_J,axiom,
% 9.25/5.26      ! [L: rat,U: rat] :
% 9.25/5.26        ( ( ord_less_eq_rat @ L @ U )
% 9.25/5.26       => ( ( sup_sup_set_rat @ ( set_ord_lessThan_rat @ L ) @ ( set_or633870826150836451st_rat @ L @ U ) )
% 9.25/5.26          = ( set_ord_atMost_rat @ U ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8389_ivl__disj__un__one_I4_J,axiom,
% 9.25/5.26      ! [L: nat,U: nat] :
% 9.25/5.26        ( ( ord_less_eq_nat @ L @ U )
% 9.25/5.26       => ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 9.25/5.26          = ( set_ord_atMost_nat @ U ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8390_ivl__disj__un__one_I4_J,axiom,
% 9.25/5.26      ! [L: int,U: int] :
% 9.25/5.26        ( ( ord_less_eq_int @ L @ U )
% 9.25/5.26       => ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or1266510415728281911st_int @ L @ U ) )
% 9.25/5.26          = ( set_ord_atMost_int @ U ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8391_ivl__disj__un__one_I4_J,axiom,
% 9.25/5.26      ! [L: code_integer,U: code_integer] :
% 9.25/5.26        ( ( ord_le3102999989581377725nteger @ L @ U )
% 9.25/5.26       => ( ( sup_su848401254843788991nteger @ ( set_or5754767410780653050nteger @ L ) @ ( set_or189985376899183464nteger @ L @ U ) )
% 9.25/5.26          = ( set_or9101266186257409494nteger @ U ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8392_sum_OIf__cases,axiom,
% 9.25/5.26      ! [A2: set_int,P: int > $o,H3: int > rat,G2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups3906332499630173760nt_rat
% 9.25/5.26            @ ^ [X3: int] : ( if_rat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.26            @ A2 )
% 9.25/5.26          = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ H3 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) @ ( groups3906332499630173760nt_rat @ G2 @ ( inf_inf_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8393_sum_OIf__cases,axiom,
% 9.25/5.26      ! [A2: set_int,P: int > $o,H3: int > nat,G2: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups4541462559716669496nt_nat
% 9.25/5.26            @ ^ [X3: int] : ( if_nat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.26            @ A2 )
% 9.25/5.26          = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ H3 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) @ ( groups4541462559716669496nt_nat @ G2 @ ( inf_inf_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8394_sum_OIf__cases,axiom,
% 9.25/5.26      ! [A2: set_nat,P: nat > $o,H3: nat > rat,G2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups2906978787729119204at_rat
% 9.25/5.26            @ ^ [X3: nat] : ( if_rat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.26            @ A2 )
% 9.25/5.26          = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ H3 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) @ ( groups2906978787729119204at_rat @ G2 @ ( inf_inf_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8395_sum_OIf__cases,axiom,
% 9.25/5.26      ! [A2: set_nat,P: nat > $o,H3: nat > int,G2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups3539618377306564664at_int
% 9.25/5.26            @ ^ [X3: nat] : ( if_int @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.26            @ A2 )
% 9.25/5.26          = ( plus_plus_int @ ( groups3539618377306564664at_int @ H3 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) @ ( groups3539618377306564664at_int @ G2 @ ( inf_inf_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8396_sum_OIf__cases,axiom,
% 9.25/5.26      ! [A2: set_nat,P: nat > $o,H3: nat > nat,G2: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups3542108847815614940at_nat
% 9.25/5.26            @ ^ [X3: nat] : ( if_nat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.26            @ A2 )
% 9.25/5.26          = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ H3 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) @ ( groups3542108847815614940at_nat @ G2 @ ( inf_inf_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8397_sum_OIf__cases,axiom,
% 9.25/5.26      ! [A2: set_int,P: int > $o,H3: int > int,G2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups4538972089207619220nt_int
% 9.25/5.26            @ ^ [X3: int] : ( if_int @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.26            @ A2 )
% 9.25/5.26          = ( plus_plus_int @ ( groups4538972089207619220nt_int @ H3 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) @ ( groups4538972089207619220nt_int @ G2 @ ( inf_inf_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8398_sum_OIf__cases,axiom,
% 9.25/5.26      ! [A2: set_set_nat,P: set_nat > $o,H3: set_nat > rat,G2: set_nat > rat] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.26       => ( ( groups7659867448343625626at_rat
% 9.25/5.26            @ ^ [X3: set_nat] : ( if_rat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.26            @ A2 )
% 9.25/5.26          = ( plus_plus_rat @ ( groups7659867448343625626at_rat @ H3 @ ( inf_inf_set_set_nat @ A2 @ ( collect_set_nat @ P ) ) ) @ ( groups7659867448343625626at_rat @ G2 @ ( inf_inf_set_set_nat @ A2 @ ( uminus613421341184616069et_nat @ ( collect_set_nat @ P ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8399_sum_OIf__cases,axiom,
% 9.25/5.26      ! [A2: set_set_nat,P: set_nat > $o,H3: set_nat > nat,G2: set_nat > nat] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.26       => ( ( groups8294997508430121362at_nat
% 9.25/5.26            @ ^ [X3: set_nat] : ( if_nat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.26            @ A2 )
% 9.25/5.26          = ( plus_plus_nat @ ( groups8294997508430121362at_nat @ H3 @ ( inf_inf_set_set_nat @ A2 @ ( collect_set_nat @ P ) ) ) @ ( groups8294997508430121362at_nat @ G2 @ ( inf_inf_set_set_nat @ A2 @ ( uminus613421341184616069et_nat @ ( collect_set_nat @ P ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8400_sum_OIf__cases,axiom,
% 9.25/5.26      ! [A2: set_set_nat,P: set_nat > $o,H3: set_nat > int,G2: set_nat > int] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.26       => ( ( groups8292507037921071086at_int
% 9.25/5.26            @ ^ [X3: set_nat] : ( if_int @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.26            @ A2 )
% 9.25/5.26          = ( plus_plus_int @ ( groups8292507037921071086at_int @ H3 @ ( inf_inf_set_set_nat @ A2 @ ( collect_set_nat @ P ) ) ) @ ( groups8292507037921071086at_int @ G2 @ ( inf_inf_set_set_nat @ A2 @ ( uminus613421341184616069et_nat @ ( collect_set_nat @ P ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8401_sum_OIf__cases,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o,H3: product_prod_nat_nat > rat,G2: product_prod_nat_nat > rat] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.26       => ( ( groups342789780944988191at_rat
% 9.25/5.26            @ ^ [X3: product_prod_nat_nat] : ( if_rat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.26            @ A2 )
% 9.25/5.26          = ( plus_plus_rat @ ( groups342789780944988191at_rat @ H3 @ ( inf_in2572325071724192079at_nat @ A2 @ ( collec3392354462482085612at_nat @ P ) ) ) @ ( groups342789780944988191at_rat @ G2 @ ( inf_in2572325071724192079at_nat @ A2 @ ( uminus6524753893492686040at_nat @ ( collec3392354462482085612at_nat @ P ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8402_prod_OIf__cases,axiom,
% 9.25/5.26      ! [A2: set_int,P: int > $o,H3: int > code_integer,G2: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups3827104343326376752nteger
% 9.25/5.26            @ ^ [X3: int] : ( if_Code_integer @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.26            @ A2 )
% 9.25/5.26          = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ H3 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) @ ( groups3827104343326376752nteger @ G2 @ ( inf_inf_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8403_prod_OIf__cases,axiom,
% 9.25/5.26      ! [A2: set_nat,P: nat > $o,H3: nat > code_integer,G2: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups3455450783089532116nteger
% 9.25/5.26            @ ^ [X3: nat] : ( if_Code_integer @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.26            @ A2 )
% 9.25/5.26          = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ H3 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) @ ( groups3455450783089532116nteger @ G2 @ ( inf_inf_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8404_prod_OIf__cases,axiom,
% 9.25/5.26      ! [A2: set_int,P: int > $o,H3: int > assn,G2: int > assn] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups7882442080178216443t_assn
% 9.25/5.26            @ ^ [X3: int] : ( if_assn @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.26            @ A2 )
% 9.25/5.26          = ( times_times_assn @ ( groups7882442080178216443t_assn @ H3 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) @ ( groups7882442080178216443t_assn @ G2 @ ( inf_inf_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8405_prod_OIf__cases,axiom,
% 9.25/5.26      ! [A2: set_nat,P: nat > $o,H3: nat > assn,G2: nat > assn] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups6906906614972039071t_assn
% 9.25/5.26            @ ^ [X3: nat] : ( if_assn @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.26            @ A2 )
% 9.25/5.26          = ( times_times_assn @ ( groups6906906614972039071t_assn @ H3 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) @ ( groups6906906614972039071t_assn @ G2 @ ( inf_inf_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8406_prod_OIf__cases,axiom,
% 9.25/5.26      ! [A2: set_int,P: int > $o,H3: int > rat,G2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups1072433553688619179nt_rat
% 9.25/5.26            @ ^ [X3: int] : ( if_rat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.26            @ A2 )
% 9.25/5.26          = ( times_times_rat @ ( groups1072433553688619179nt_rat @ H3 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8407_prod_OIf__cases,axiom,
% 9.25/5.26      ! [A2: set_nat,P: nat > $o,H3: nat > rat,G2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups73079841787564623at_rat
% 9.25/5.26            @ ^ [X3: nat] : ( if_rat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.26            @ A2 )
% 9.25/5.26          = ( times_times_rat @ ( groups73079841787564623at_rat @ H3 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) @ ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8408_prod_OIf__cases,axiom,
% 9.25/5.26      ! [A2: set_int,P: int > $o,H3: int > nat,G2: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups1707563613775114915nt_nat
% 9.25/5.26            @ ^ [X3: int] : ( if_nat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.26            @ A2 )
% 9.25/5.26          = ( times_times_nat @ ( groups1707563613775114915nt_nat @ H3 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8409_prod_OIf__cases,axiom,
% 9.25/5.26      ! [A2: set_nat,P: nat > $o,H3: nat > nat,G2: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups708209901874060359at_nat
% 9.25/5.26            @ ^ [X3: nat] : ( if_nat @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.26            @ A2 )
% 9.25/5.26          = ( times_times_nat @ ( groups708209901874060359at_nat @ H3 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) @ ( groups708209901874060359at_nat @ G2 @ ( inf_inf_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8410_prod_OIf__cases,axiom,
% 9.25/5.26      ! [A2: set_nat,P: nat > $o,H3: nat > int,G2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups705719431365010083at_int
% 9.25/5.26            @ ^ [X3: nat] : ( if_int @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.26            @ A2 )
% 9.25/5.26          = ( times_times_int @ ( groups705719431365010083at_int @ H3 @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) @ ( groups705719431365010083at_int @ G2 @ ( inf_inf_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8411_prod_OIf__cases,axiom,
% 9.25/5.26      ! [A2: set_int,P: int > $o,H3: int > int,G2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups1705073143266064639nt_int
% 9.25/5.26            @ ^ [X3: int] : ( if_int @ ( P @ X3 ) @ ( H3 @ X3 ) @ ( G2 @ X3 ) )
% 9.25/5.26            @ A2 )
% 9.25/5.26          = ( times_times_int @ ( groups1705073143266064639nt_int @ H3 @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) @ ( groups1705073143266064639nt_int @ G2 @ ( inf_inf_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8412_one__diff__power__eq,axiom,
% 9.25/5.26      ! [X: code_integer,N: nat] :
% 9.25/5.26        ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) )
% 9.25/5.26        = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8413_one__diff__power__eq,axiom,
% 9.25/5.26      ! [X: rat,N: nat] :
% 9.25/5.26        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 9.25/5.26        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8414_one__diff__power__eq,axiom,
% 9.25/5.26      ! [X: int,N: nat] :
% 9.25/5.26        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 9.25/5.26        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8415_power__diff__1__eq,axiom,
% 9.25/5.26      ! [X: code_integer,N: nat] :
% 9.25/5.26        ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ N ) @ one_one_Code_integer )
% 9.25/5.26        = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8416_power__diff__1__eq,axiom,
% 9.25/5.26      ! [X: rat,N: nat] :
% 9.25/5.26        ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat )
% 9.25/5.26        = ( times_times_rat @ ( minus_minus_rat @ X @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8417_power__diff__1__eq,axiom,
% 9.25/5.26      ! [X: int,N: nat] :
% 9.25/5.26        ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ one_one_int )
% 9.25/5.26        = ( times_times_int @ ( minus_minus_int @ X @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8418_geometric__sum,axiom,
% 9.25/5.26      ! [X: rat,N: nat] :
% 9.25/5.26        ( ( X != one_one_rat )
% 9.25/5.26       => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 9.25/5.26          = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8419_prod__mono__strict,axiom,
% 9.25/5.26      ! [A2: set_o,F2: $o > code_integer,G2: $o > code_integer] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ! [I2: $o] :
% 9.25/5.26              ( ( member_o @ I2 @ A2 )
% 9.25/5.26             => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) )
% 9.25/5.26                & ( ord_le6747313008572928689nteger @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) ) )
% 9.25/5.26         => ( ( A2 != bot_bot_set_o )
% 9.25/5.26           => ( ord_le6747313008572928689nteger @ ( groups7694694392188491536nteger @ F2 @ A2 ) @ ( groups7694694392188491536nteger @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8420_prod__mono__strict,axiom,
% 9.25/5.26      ! [A2: set_nat,F2: nat > code_integer,G2: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ! [I2: nat] :
% 9.25/5.26              ( ( member_nat @ I2 @ A2 )
% 9.25/5.26             => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) )
% 9.25/5.26                & ( ord_le6747313008572928689nteger @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) ) )
% 9.25/5.26         => ( ( A2 != bot_bot_set_nat )
% 9.25/5.26           => ( ord_le6747313008572928689nteger @ ( groups3455450783089532116nteger @ F2 @ A2 ) @ ( groups3455450783089532116nteger @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8421_prod__mono__strict,axiom,
% 9.25/5.26      ! [A2: set_int,F2: int > code_integer,G2: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ! [I2: int] :
% 9.25/5.26              ( ( member_int @ I2 @ A2 )
% 9.25/5.26             => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I2 ) )
% 9.25/5.26                & ( ord_le6747313008572928689nteger @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) ) )
% 9.25/5.26         => ( ( A2 != bot_bot_set_int )
% 9.25/5.26           => ( ord_le6747313008572928689nteger @ ( groups3827104343326376752nteger @ F2 @ A2 ) @ ( groups3827104343326376752nteger @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8422_prod__mono__strict,axiom,
% 9.25/5.26      ! [A2: set_o,F2: $o > rat,G2: $o > rat] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ! [I2: $o] :
% 9.25/5.26              ( ( member_o @ I2 @ A2 )
% 9.25/5.26             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I2 ) )
% 9.25/5.26                & ( ord_less_rat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) ) )
% 9.25/5.26         => ( ( A2 != bot_bot_set_o )
% 9.25/5.26           => ( ord_less_rat @ ( groups2869687844427037835_o_rat @ F2 @ A2 ) @ ( groups2869687844427037835_o_rat @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8423_prod__mono__strict,axiom,
% 9.25/5.26      ! [A2: set_nat,F2: nat > rat,G2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ! [I2: nat] :
% 9.25/5.26              ( ( member_nat @ I2 @ A2 )
% 9.25/5.26             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I2 ) )
% 9.25/5.26                & ( ord_less_rat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) ) )
% 9.25/5.26         => ( ( A2 != bot_bot_set_nat )
% 9.25/5.26           => ( ord_less_rat @ ( groups73079841787564623at_rat @ F2 @ A2 ) @ ( groups73079841787564623at_rat @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8424_prod__mono__strict,axiom,
% 9.25/5.26      ! [A2: set_int,F2: int > rat,G2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ! [I2: int] :
% 9.25/5.26              ( ( member_int @ I2 @ A2 )
% 9.25/5.26             => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I2 ) )
% 9.25/5.26                & ( ord_less_rat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) ) )
% 9.25/5.26         => ( ( A2 != bot_bot_set_int )
% 9.25/5.26           => ( ord_less_rat @ ( groups1072433553688619179nt_rat @ F2 @ A2 ) @ ( groups1072433553688619179nt_rat @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8425_prod__mono__strict,axiom,
% 9.25/5.26      ! [A2: set_o,F2: $o > nat,G2: $o > nat] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ! [I2: $o] :
% 9.25/5.26              ( ( member_o @ I2 @ A2 )
% 9.25/5.26             => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I2 ) )
% 9.25/5.26                & ( ord_less_nat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) ) )
% 9.25/5.26         => ( ( A2 != bot_bot_set_o )
% 9.25/5.26           => ( ord_less_nat @ ( groups3504817904513533571_o_nat @ F2 @ A2 ) @ ( groups3504817904513533571_o_nat @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8426_prod__mono__strict,axiom,
% 9.25/5.26      ! [A2: set_int,F2: int > nat,G2: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ! [I2: int] :
% 9.25/5.26              ( ( member_int @ I2 @ A2 )
% 9.25/5.26             => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I2 ) )
% 9.25/5.26                & ( ord_less_nat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) ) )
% 9.25/5.26         => ( ( A2 != bot_bot_set_int )
% 9.25/5.26           => ( ord_less_nat @ ( groups1707563613775114915nt_nat @ F2 @ A2 ) @ ( groups1707563613775114915nt_nat @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8427_prod__mono__strict,axiom,
% 9.25/5.26      ! [A2: set_o,F2: $o > int,G2: $o > int] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ! [I2: $o] :
% 9.25/5.26              ( ( member_o @ I2 @ A2 )
% 9.25/5.26             => ( ( ord_less_eq_int @ zero_zero_int @ ( F2 @ I2 ) )
% 9.25/5.26                & ( ord_less_int @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) ) )
% 9.25/5.26         => ( ( A2 != bot_bot_set_o )
% 9.25/5.26           => ( ord_less_int @ ( groups3502327434004483295_o_int @ F2 @ A2 ) @ ( groups3502327434004483295_o_int @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8428_prod__mono__strict,axiom,
% 9.25/5.26      ! [A2: set_nat,F2: nat > nat,G2: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ! [I2: nat] :
% 9.25/5.26              ( ( member_nat @ I2 @ A2 )
% 9.25/5.26             => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I2 ) )
% 9.25/5.26                & ( ord_less_nat @ ( F2 @ I2 ) @ ( G2 @ I2 ) ) ) )
% 9.25/5.26         => ( ( A2 != bot_bot_set_nat )
% 9.25/5.26           => ( ord_less_nat @ ( groups708209901874060359at_nat @ F2 @ A2 ) @ ( groups708209901874060359at_nat @ G2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8429_sum_OatMost__shift,axiom,
% 9.25/5.26      ! [G2: nat > rat,N: nat] :
% 9.25/5.26        ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.26        = ( plus_plus_rat @ ( G2 @ zero_zero_nat )
% 9.25/5.26          @ ( groups2906978787729119204at_rat
% 9.25/5.26            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8430_sum_OatMost__shift,axiom,
% 9.25/5.26      ! [G2: nat > int,N: nat] :
% 9.25/5.26        ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.26        = ( plus_plus_int @ ( G2 @ zero_zero_nat )
% 9.25/5.26          @ ( groups3539618377306564664at_int
% 9.25/5.26            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8431_sum_OatMost__shift,axiom,
% 9.25/5.26      ! [G2: nat > nat,N: nat] :
% 9.25/5.26        ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.26        = ( plus_plus_nat @ ( G2 @ zero_zero_nat )
% 9.25/5.26          @ ( groups3542108847815614940at_nat
% 9.25/5.26            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8432_sum_Ounion__inter__neutral,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = zero_z3403309356797280102nteger ) )
% 9.25/5.26           => ( ( groups7873554091576472773nteger @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26              = ( plus_p5714425477246183910nteger @ ( groups7873554091576472773nteger @ G2 @ A2 ) @ ( groups7873554091576472773nteger @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8433_sum_Ounion__inter__neutral,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = zero_zero_rat ) )
% 9.25/5.26           => ( ( groups3906332499630173760nt_rat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26              = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G2 @ A2 ) @ ( groups3906332499630173760nt_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8434_sum_Ounion__inter__neutral,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = zero_zero_nat ) )
% 9.25/5.26           => ( ( groups4541462559716669496nt_nat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26              = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G2 @ A2 ) @ ( groups4541462559716669496nt_nat @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8435_sum_Ounion__inter__neutral,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = zero_z3403309356797280102nteger ) )
% 9.25/5.26           => ( ( groups7501900531339628137nteger @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( plus_p5714425477246183910nteger @ ( groups7501900531339628137nteger @ G2 @ A2 ) @ ( groups7501900531339628137nteger @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8436_sum_Ounion__inter__neutral,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = zero_zero_rat ) )
% 9.25/5.26           => ( ( groups2906978787729119204at_rat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ A2 ) @ ( groups2906978787729119204at_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8437_sum_Ounion__inter__neutral,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = zero_zero_int ) )
% 9.25/5.26           => ( ( groups3539618377306564664at_int @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ A2 ) @ ( groups3539618377306564664at_int @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8438_sum_Ounion__inter__neutral,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = zero_zero_nat ) )
% 9.25/5.26           => ( ( groups3542108847815614940at_nat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ A2 ) @ ( groups3542108847815614940at_nat @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8439_sum_Ounion__inter__neutral,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = zero_zero_int ) )
% 9.25/5.26           => ( ( groups4538972089207619220nt_int @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26              = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G2 @ A2 ) @ ( groups4538972089207619220nt_int @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8440_sum_Ounion__inter__neutral,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > code_integer] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.26       => ( ( finite6177210948735845034at_nat @ B2 )
% 9.25/5.26         => ( ! [X2: product_prod_nat_nat] :
% 9.25/5.26                ( ( member8440522571783428010at_nat @ X2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = zero_z3403309356797280102nteger ) )
% 9.25/5.26           => ( ( groups196832835297161892nteger @ G2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( plus_p5714425477246183910nteger @ ( groups196832835297161892nteger @ G2 @ A2 ) @ ( groups196832835297161892nteger @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8441_sum_Ounion__inter__neutral,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > rat] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.26       => ( ( finite6177210948735845034at_nat @ B2 )
% 9.25/5.26         => ( ! [X2: product_prod_nat_nat] :
% 9.25/5.26                ( ( member8440522571783428010at_nat @ X2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = zero_zero_rat ) )
% 9.25/5.26           => ( ( groups342789780944988191at_rat @ G2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( plus_plus_rat @ ( groups342789780944988191at_rat @ G2 @ A2 ) @ ( groups342789780944988191at_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8442_sum_Oremove,axiom,
% 9.25/5.26      ! [A2: set_o,X: $o,G2: $o > rat] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( member_o @ X @ A2 )
% 9.25/5.26         => ( ( groups7872700643590313910_o_rat @ G2 @ A2 )
% 9.25/5.26            = ( plus_plus_rat @ ( G2 @ X ) @ ( groups7872700643590313910_o_rat @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8443_sum_Oremove,axiom,
% 9.25/5.26      ! [A2: set_o,X: $o,G2: $o > nat] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( member_o @ X @ A2 )
% 9.25/5.26         => ( ( groups8507830703676809646_o_nat @ G2 @ A2 )
% 9.25/5.26            = ( plus_plus_nat @ ( G2 @ X ) @ ( groups8507830703676809646_o_nat @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8444_sum_Oremove,axiom,
% 9.25/5.26      ! [A2: set_o,X: $o,G2: $o > int] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( member_o @ X @ A2 )
% 9.25/5.26         => ( ( groups8505340233167759370_o_int @ G2 @ A2 )
% 9.25/5.26            = ( plus_plus_int @ ( G2 @ X ) @ ( groups8505340233167759370_o_int @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8445_sum_Oremove,axiom,
% 9.25/5.26      ! [A2: set_int,X: int,G2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( member_int @ X @ A2 )
% 9.25/5.26         => ( ( groups3906332499630173760nt_rat @ G2 @ A2 )
% 9.25/5.26            = ( plus_plus_rat @ ( G2 @ X ) @ ( groups3906332499630173760nt_rat @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8446_sum_Oremove,axiom,
% 9.25/5.26      ! [A2: set_int,X: int,G2: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( member_int @ X @ A2 )
% 9.25/5.26         => ( ( groups4541462559716669496nt_nat @ G2 @ A2 )
% 9.25/5.26            = ( plus_plus_nat @ ( G2 @ X ) @ ( groups4541462559716669496nt_nat @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8447_sum_Oremove,axiom,
% 9.25/5.26      ! [A2: set_nat,X: nat,G2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( member_nat @ X @ A2 )
% 9.25/5.26         => ( ( groups2906978787729119204at_rat @ G2 @ A2 )
% 9.25/5.26            = ( plus_plus_rat @ ( G2 @ X ) @ ( groups2906978787729119204at_rat @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8448_sum_Oremove,axiom,
% 9.25/5.26      ! [A2: set_nat,X: nat,G2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( member_nat @ X @ A2 )
% 9.25/5.26         => ( ( groups3539618377306564664at_int @ G2 @ A2 )
% 9.25/5.26            = ( plus_plus_int @ ( G2 @ X ) @ ( groups3539618377306564664at_int @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8449_sum_Oremove,axiom,
% 9.25/5.26      ! [A2: set_nat,X: nat,G2: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( member_nat @ X @ A2 )
% 9.25/5.26         => ( ( groups3542108847815614940at_nat @ G2 @ A2 )
% 9.25/5.26            = ( plus_plus_nat @ ( G2 @ X ) @ ( groups3542108847815614940at_nat @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8450_sum_Oremove,axiom,
% 9.25/5.26      ! [A2: set_int,X: int,G2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( member_int @ X @ A2 )
% 9.25/5.26         => ( ( groups4538972089207619220nt_int @ G2 @ A2 )
% 9.25/5.26            = ( plus_plus_int @ ( G2 @ X ) @ ( groups4538972089207619220nt_int @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8451_sum_Oremove,axiom,
% 9.25/5.26      ! [A2: set_set_nat,X: set_nat,G2: set_nat > rat] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.26       => ( ( member_set_nat @ X @ A2 )
% 9.25/5.26         => ( ( groups7659867448343625626at_rat @ G2 @ A2 )
% 9.25/5.26            = ( plus_plus_rat @ ( G2 @ X ) @ ( groups7659867448343625626at_rat @ G2 @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8452_sum_Oinsert__remove,axiom,
% 9.25/5.26      ! [A2: set_o,G2: $o > rat,X: $o] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( groups7872700643590313910_o_rat @ G2 @ ( insert_o @ X @ A2 ) )
% 9.25/5.26          = ( plus_plus_rat @ ( G2 @ X ) @ ( groups7872700643590313910_o_rat @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8453_sum_Oinsert__remove,axiom,
% 9.25/5.26      ! [A2: set_o,G2: $o > nat,X: $o] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( groups8507830703676809646_o_nat @ G2 @ ( insert_o @ X @ A2 ) )
% 9.25/5.26          = ( plus_plus_nat @ ( G2 @ X ) @ ( groups8507830703676809646_o_nat @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8454_sum_Oinsert__remove,axiom,
% 9.25/5.26      ! [A2: set_o,G2: $o > int,X: $o] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( groups8505340233167759370_o_int @ G2 @ ( insert_o @ X @ A2 ) )
% 9.25/5.26          = ( plus_plus_int @ ( G2 @ X ) @ ( groups8505340233167759370_o_int @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8455_sum_Oinsert__remove,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > rat,X: int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups3906332499630173760nt_rat @ G2 @ ( insert_int @ X @ A2 ) )
% 9.25/5.26          = ( plus_plus_rat @ ( G2 @ X ) @ ( groups3906332499630173760nt_rat @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8456_sum_Oinsert__remove,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > nat,X: int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups4541462559716669496nt_nat @ G2 @ ( insert_int @ X @ A2 ) )
% 9.25/5.26          = ( plus_plus_nat @ ( G2 @ X ) @ ( groups4541462559716669496nt_nat @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8457_sum_Oinsert__remove,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > rat,X: nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups2906978787729119204at_rat @ G2 @ ( insert_nat @ X @ A2 ) )
% 9.25/5.26          = ( plus_plus_rat @ ( G2 @ X ) @ ( groups2906978787729119204at_rat @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8458_sum_Oinsert__remove,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > int,X: nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups3539618377306564664at_int @ G2 @ ( insert_nat @ X @ A2 ) )
% 9.25/5.26          = ( plus_plus_int @ ( G2 @ X ) @ ( groups3539618377306564664at_int @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8459_sum_Oinsert__remove,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > nat,X: nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups3542108847815614940at_nat @ G2 @ ( insert_nat @ X @ A2 ) )
% 9.25/5.26          = ( plus_plus_nat @ ( G2 @ X ) @ ( groups3542108847815614940at_nat @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8460_sum_Oinsert__remove,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > int,X: int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups4538972089207619220nt_int @ G2 @ ( insert_int @ X @ A2 ) )
% 9.25/5.26          = ( plus_plus_int @ ( G2 @ X ) @ ( groups4538972089207619220nt_int @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8461_sum_Oinsert__remove,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > rat,X: product_prod_nat_nat] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.26       => ( ( groups342789780944988191at_rat @ G2 @ ( insert8211810215607154385at_nat @ X @ A2 ) )
% 9.25/5.26          = ( plus_plus_rat @ ( G2 @ X ) @ ( groups342789780944988191at_rat @ G2 @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8462_prod_OatMost__shift,axiom,
% 9.25/5.26      ! [G2: nat > code_integer,N: nat] :
% 9.25/5.26        ( ( groups3455450783089532116nteger @ G2 @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.26        = ( times_3573771949741848930nteger @ ( G2 @ zero_zero_nat )
% 9.25/5.26          @ ( groups3455450783089532116nteger
% 9.25/5.26            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8463_prod_OatMost__shift,axiom,
% 9.25/5.26      ! [G2: nat > assn,N: nat] :
% 9.25/5.26        ( ( groups6906906614972039071t_assn @ G2 @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.26        = ( times_times_assn @ ( G2 @ zero_zero_nat )
% 9.25/5.26          @ ( groups6906906614972039071t_assn
% 9.25/5.26            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8464_prod_OatMost__shift,axiom,
% 9.25/5.26      ! [G2: nat > rat,N: nat] :
% 9.25/5.26        ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.26        = ( times_times_rat @ ( G2 @ zero_zero_nat )
% 9.25/5.26          @ ( groups73079841787564623at_rat
% 9.25/5.26            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8465_prod_OatMost__shift,axiom,
% 9.25/5.26      ! [G2: nat > nat,N: nat] :
% 9.25/5.26        ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.26        = ( times_times_nat @ ( G2 @ zero_zero_nat )
% 9.25/5.26          @ ( groups708209901874060359at_nat
% 9.25/5.26            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8466_prod_OatMost__shift,axiom,
% 9.25/5.26      ! [G2: nat > int,N: nat] :
% 9.25/5.26        ( ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.26        = ( times_times_int @ ( G2 @ zero_zero_nat )
% 9.25/5.26          @ ( groups705719431365010083at_int
% 9.25/5.26            @ ^ [I3: nat] : ( G2 @ ( suc @ I3 ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8467_sum__diff1,axiom,
% 9.25/5.26      ! [A2: set_o,A: $o,F2: $o > rat] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( ( member_o @ A @ A2 )
% 9.25/5.26           => ( ( groups7872700643590313910_o_rat @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 9.25/5.26              = ( minus_minus_rat @ ( groups7872700643590313910_o_rat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.26          & ( ~ ( member_o @ A @ A2 )
% 9.25/5.26           => ( ( groups7872700643590313910_o_rat @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 9.25/5.26              = ( groups7872700643590313910_o_rat @ F2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8468_sum__diff1,axiom,
% 9.25/5.26      ! [A2: set_int,A: int,F2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( ( member_int @ A @ A2 )
% 9.25/5.26           => ( ( groups3906332499630173760nt_rat @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.25/5.26              = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.26          & ( ~ ( member_int @ A @ A2 )
% 9.25/5.26           => ( ( groups3906332499630173760nt_rat @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.25/5.26              = ( groups3906332499630173760nt_rat @ F2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8469_sum__diff1,axiom,
% 9.25/5.26      ! [A2: set_o,A: $o,F2: $o > int] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( ( member_o @ A @ A2 )
% 9.25/5.26           => ( ( groups8505340233167759370_o_int @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 9.25/5.26              = ( minus_minus_int @ ( groups8505340233167759370_o_int @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.26          & ( ~ ( member_o @ A @ A2 )
% 9.25/5.26           => ( ( groups8505340233167759370_o_int @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 9.25/5.26              = ( groups8505340233167759370_o_int @ F2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8470_sum__diff1,axiom,
% 9.25/5.26      ! [A2: set_nat,A: nat,F2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( ( member_nat @ A @ A2 )
% 9.25/5.26           => ( ( groups2906978787729119204at_rat @ F2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.25/5.26              = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.26          & ( ~ ( member_nat @ A @ A2 )
% 9.25/5.26           => ( ( groups2906978787729119204at_rat @ F2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.25/5.26              = ( groups2906978787729119204at_rat @ F2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8471_sum__diff1,axiom,
% 9.25/5.26      ! [A2: set_nat,A: nat,F2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( ( member_nat @ A @ A2 )
% 9.25/5.26           => ( ( groups3539618377306564664at_int @ F2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.25/5.26              = ( minus_minus_int @ ( groups3539618377306564664at_int @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.26          & ( ~ ( member_nat @ A @ A2 )
% 9.25/5.26           => ( ( groups3539618377306564664at_int @ F2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.25/5.26              = ( groups3539618377306564664at_int @ F2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8472_sum__diff1,axiom,
% 9.25/5.26      ! [A2: set_int,A: int,F2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( ( member_int @ A @ A2 )
% 9.25/5.26           => ( ( groups4538972089207619220nt_int @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.25/5.26              = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.26          & ( ~ ( member_int @ A @ A2 )
% 9.25/5.26           => ( ( groups4538972089207619220nt_int @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.25/5.26              = ( groups4538972089207619220nt_int @ F2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8473_sum__diff1,axiom,
% 9.25/5.26      ! [A2: set_set_nat,A: set_nat,F2: set_nat > rat] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.26       => ( ( ( member_set_nat @ A @ A2 )
% 9.25/5.26           => ( ( groups7659867448343625626at_rat @ F2 @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 9.25/5.26              = ( minus_minus_rat @ ( groups7659867448343625626at_rat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.26          & ( ~ ( member_set_nat @ A @ A2 )
% 9.25/5.26           => ( ( groups7659867448343625626at_rat @ F2 @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 9.25/5.26              = ( groups7659867448343625626at_rat @ F2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8474_sum__diff1,axiom,
% 9.25/5.26      ! [A2: set_set_nat,A: set_nat,F2: set_nat > int] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.26       => ( ( ( member_set_nat @ A @ A2 )
% 9.25/5.26           => ( ( groups8292507037921071086at_int @ F2 @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 9.25/5.26              = ( minus_minus_int @ ( groups8292507037921071086at_int @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.26          & ( ~ ( member_set_nat @ A @ A2 )
% 9.25/5.26           => ( ( groups8292507037921071086at_int @ F2 @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 9.25/5.26              = ( groups8292507037921071086at_int @ F2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8475_sum__diff1,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,F2: product_prod_nat_nat > rat] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.26       => ( ( ( member8440522571783428010at_nat @ A @ A2 )
% 9.25/5.26           => ( ( groups342789780944988191at_rat @ F2 @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 9.25/5.26              = ( minus_minus_rat @ ( groups342789780944988191at_rat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.26          & ( ~ ( member8440522571783428010at_nat @ A @ A2 )
% 9.25/5.26           => ( ( groups342789780944988191at_rat @ F2 @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 9.25/5.26              = ( groups342789780944988191at_rat @ F2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8476_sum__diff1,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat,F2: product_prod_nat_nat > int] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.26       => ( ( ( member8440522571783428010at_nat @ A @ A2 )
% 9.25/5.26           => ( ( groups975429370522433651at_int @ F2 @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 9.25/5.26              = ( minus_minus_int @ ( groups975429370522433651at_int @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.26          & ( ~ ( member8440522571783428010at_nat @ A @ A2 )
% 9.25/5.26           => ( ( groups975429370522433651at_int @ F2 @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) )
% 9.25/5.26              = ( groups975429370522433651at_int @ F2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8477_sum__Un,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,F2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( groups3906332499630173760nt_rat @ F2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26            = ( minus_minus_rat @ ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ F2 @ A2 ) @ ( groups3906332499630173760nt_rat @ F2 @ B2 ) ) @ ( groups3906332499630173760nt_rat @ F2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8478_sum__Un,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > rat] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.26       => ( ( finite6177210948735845034at_nat @ B2 )
% 9.25/5.26         => ( ( groups342789780944988191at_rat @ F2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( minus_minus_rat @ ( plus_plus_rat @ ( groups342789780944988191at_rat @ F2 @ A2 ) @ ( groups342789780944988191at_rat @ F2 @ B2 ) ) @ ( groups342789780944988191at_rat @ F2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8479_sum__Un,axiom,
% 9.25/5.26      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,F2: produc4166570645942440679at_nat > rat] :
% 9.25/5.26        ( ( finite1918287321285529104at_nat @ A2 )
% 9.25/5.26       => ( ( finite1918287321285529104at_nat @ B2 )
% 9.25/5.26         => ( ( groups6424767709179651461at_rat @ F2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( minus_minus_rat @ ( plus_plus_rat @ ( groups6424767709179651461at_rat @ F2 @ A2 ) @ ( groups6424767709179651461at_rat @ F2 @ B2 ) ) @ ( groups6424767709179651461at_rat @ F2 @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8480_sum__Un,axiom,
% 9.25/5.26      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,F2: produc3843707927480180839at_nat > rat] :
% 9.25/5.26        ( ( finite4343798906461161616at_nat @ A2 )
% 9.25/5.26       => ( ( finite4343798906461161616at_nat @ B2 )
% 9.25/5.26         => ( ( groups3225780264831618053at_rat @ F2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( minus_minus_rat @ ( plus_plus_rat @ ( groups3225780264831618053at_rat @ F2 @ A2 ) @ ( groups3225780264831618053at_rat @ F2 @ B2 ) ) @ ( groups3225780264831618053at_rat @ F2 @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8481_sum__Un,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,F2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( groups2906978787729119204at_rat @ F2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( minus_minus_rat @ ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F2 @ A2 ) @ ( groups2906978787729119204at_rat @ F2 @ B2 ) ) @ ( groups2906978787729119204at_rat @ F2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8482_sum__Un,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > int] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.26       => ( ( finite6177210948735845034at_nat @ B2 )
% 9.25/5.26         => ( ( groups975429370522433651at_int @ F2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( minus_minus_int @ ( plus_plus_int @ ( groups975429370522433651at_int @ F2 @ A2 ) @ ( groups975429370522433651at_int @ F2 @ B2 ) ) @ ( groups975429370522433651at_int @ F2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8483_sum__Un,axiom,
% 9.25/5.26      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,F2: produc4166570645942440679at_nat > int] :
% 9.25/5.26        ( ( finite1918287321285529104at_nat @ A2 )
% 9.25/5.26       => ( ( finite1918287321285529104at_nat @ B2 )
% 9.25/5.26         => ( ( groups7057407298757096921at_int @ F2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( minus_minus_int @ ( plus_plus_int @ ( groups7057407298757096921at_int @ F2 @ A2 ) @ ( groups7057407298757096921at_int @ F2 @ B2 ) ) @ ( groups7057407298757096921at_int @ F2 @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8484_sum__Un,axiom,
% 9.25/5.26      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,F2: produc3843707927480180839at_nat > int] :
% 9.25/5.26        ( ( finite4343798906461161616at_nat @ A2 )
% 9.25/5.26       => ( ( finite4343798906461161616at_nat @ B2 )
% 9.25/5.26         => ( ( groups3858419854409063513at_int @ F2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( minus_minus_int @ ( plus_plus_int @ ( groups3858419854409063513at_int @ F2 @ A2 ) @ ( groups3858419854409063513at_int @ F2 @ B2 ) ) @ ( groups3858419854409063513at_int @ F2 @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8485_sum__Un,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,F2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( groups3539618377306564664at_int @ F2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( minus_minus_int @ ( plus_plus_int @ ( groups3539618377306564664at_int @ F2 @ A2 ) @ ( groups3539618377306564664at_int @ F2 @ B2 ) ) @ ( groups3539618377306564664at_int @ F2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8486_sum__Un,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,F2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( groups4538972089207619220nt_int @ F2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26            = ( minus_minus_int @ ( plus_plus_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) @ ( groups4538972089207619220nt_int @ F2 @ B2 ) ) @ ( groups4538972089207619220nt_int @ F2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8487_sum_Ounion__disjoint,axiom,
% 9.25/5.26      ! [A2: set_o,B2: set_o,G2: $o > rat] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( finite_finite_o @ B2 )
% 9.25/5.26         => ( ( ( inf_inf_set_o @ A2 @ B2 )
% 9.25/5.26              = bot_bot_set_o )
% 9.25/5.26           => ( ( groups7872700643590313910_o_rat @ G2 @ ( sup_sup_set_o @ A2 @ B2 ) )
% 9.25/5.26              = ( plus_plus_rat @ ( groups7872700643590313910_o_rat @ G2 @ A2 ) @ ( groups7872700643590313910_o_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8488_sum_Ounion__disjoint,axiom,
% 9.25/5.26      ! [A2: set_o,B2: set_o,G2: $o > nat] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( finite_finite_o @ B2 )
% 9.25/5.26         => ( ( ( inf_inf_set_o @ A2 @ B2 )
% 9.25/5.26              = bot_bot_set_o )
% 9.25/5.26           => ( ( groups8507830703676809646_o_nat @ G2 @ ( sup_sup_set_o @ A2 @ B2 ) )
% 9.25/5.26              = ( plus_plus_nat @ ( groups8507830703676809646_o_nat @ G2 @ A2 ) @ ( groups8507830703676809646_o_nat @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8489_sum_Ounion__disjoint,axiom,
% 9.25/5.26      ! [A2: set_o,B2: set_o,G2: $o > int] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( finite_finite_o @ B2 )
% 9.25/5.26         => ( ( ( inf_inf_set_o @ A2 @ B2 )
% 9.25/5.26              = bot_bot_set_o )
% 9.25/5.26           => ( ( groups8505340233167759370_o_int @ G2 @ ( sup_sup_set_o @ A2 @ B2 ) )
% 9.25/5.26              = ( plus_plus_int @ ( groups8505340233167759370_o_int @ G2 @ A2 ) @ ( groups8505340233167759370_o_int @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8490_sum_Ounion__disjoint,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 9.25/5.26              = bot_bot_set_nat )
% 9.25/5.26           => ( ( groups2906978787729119204at_rat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ A2 ) @ ( groups2906978787729119204at_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8491_sum_Ounion__disjoint,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 9.25/5.26              = bot_bot_set_nat )
% 9.25/5.26           => ( ( groups3539618377306564664at_int @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ A2 ) @ ( groups3539618377306564664at_int @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8492_sum_Ounion__disjoint,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( ( inf_inf_set_int @ A2 @ B2 )
% 9.25/5.26              = bot_bot_set_int )
% 9.25/5.26           => ( ( groups3906332499630173760nt_rat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26              = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G2 @ A2 ) @ ( groups3906332499630173760nt_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8493_sum_Ounion__disjoint,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( ( inf_inf_set_int @ A2 @ B2 )
% 9.25/5.26              = bot_bot_set_int )
% 9.25/5.26           => ( ( groups4541462559716669496nt_nat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26              = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G2 @ A2 ) @ ( groups4541462559716669496nt_nat @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8494_sum_Ounion__disjoint,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 9.25/5.26              = bot_bot_set_nat )
% 9.25/5.26           => ( ( groups3542108847815614940at_nat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ A2 ) @ ( groups3542108847815614940at_nat @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8495_sum_Ounion__disjoint,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( ( inf_inf_set_int @ A2 @ B2 )
% 9.25/5.26              = bot_bot_set_int )
% 9.25/5.26           => ( ( groups4538972089207619220nt_int @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26              = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G2 @ A2 ) @ ( groups4538972089207619220nt_int @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8496_sum_Ounion__disjoint,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > rat] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.26       => ( ( finite6177210948735845034at_nat @ B2 )
% 9.25/5.26         => ( ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 9.25/5.26              = bot_bo2099793752762293965at_nat )
% 9.25/5.26           => ( ( groups342789780944988191at_rat @ G2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( plus_plus_rat @ ( groups342789780944988191at_rat @ G2 @ A2 ) @ ( groups342789780944988191at_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8497_prod_Oremove,axiom,
% 9.25/5.26      ! [A2: set_o,X: $o,G2: $o > code_integer] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( member_o @ X @ A2 )
% 9.25/5.26         => ( ( groups7694694392188491536nteger @ G2 @ A2 )
% 9.25/5.26            = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups7694694392188491536nteger @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8498_prod_Oremove,axiom,
% 9.25/5.26      ! [A2: set_int,X: int,G2: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( member_int @ X @ A2 )
% 9.25/5.26         => ( ( groups3827104343326376752nteger @ G2 @ A2 )
% 9.25/5.26            = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups3827104343326376752nteger @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8499_prod_Oremove,axiom,
% 9.25/5.26      ! [A2: set_nat,X: nat,G2: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( member_nat @ X @ A2 )
% 9.25/5.26         => ( ( groups3455450783089532116nteger @ G2 @ A2 )
% 9.25/5.26            = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups3455450783089532116nteger @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8500_prod_Oremove,axiom,
% 9.25/5.26      ! [A2: set_o,X: $o,G2: $o > assn] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( member_o @ X @ A2 )
% 9.25/5.26         => ( ( groups5301882518646026715o_assn @ G2 @ A2 )
% 9.25/5.26            = ( times_times_assn @ ( G2 @ X ) @ ( groups5301882518646026715o_assn @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8501_prod_Oremove,axiom,
% 9.25/5.26      ! [A2: set_int,X: int,G2: int > assn] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( member_int @ X @ A2 )
% 9.25/5.26         => ( ( groups7882442080178216443t_assn @ G2 @ A2 )
% 9.25/5.26            = ( times_times_assn @ ( G2 @ X ) @ ( groups7882442080178216443t_assn @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8502_prod_Oremove,axiom,
% 9.25/5.26      ! [A2: set_nat,X: nat,G2: nat > assn] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( member_nat @ X @ A2 )
% 9.25/5.26         => ( ( groups6906906614972039071t_assn @ G2 @ A2 )
% 9.25/5.26            = ( times_times_assn @ ( G2 @ X ) @ ( groups6906906614972039071t_assn @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8503_prod_Oremove,axiom,
% 9.25/5.26      ! [A2: set_o,X: $o,G2: $o > rat] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( member_o @ X @ A2 )
% 9.25/5.26         => ( ( groups2869687844427037835_o_rat @ G2 @ A2 )
% 9.25/5.26            = ( times_times_rat @ ( G2 @ X ) @ ( groups2869687844427037835_o_rat @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8504_prod_Oremove,axiom,
% 9.25/5.26      ! [A2: set_int,X: int,G2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( member_int @ X @ A2 )
% 9.25/5.26         => ( ( groups1072433553688619179nt_rat @ G2 @ A2 )
% 9.25/5.26            = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8505_prod_Oremove,axiom,
% 9.25/5.26      ! [A2: set_nat,X: nat,G2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( member_nat @ X @ A2 )
% 9.25/5.26         => ( ( groups73079841787564623at_rat @ G2 @ A2 )
% 9.25/5.26            = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8506_prod_Oremove,axiom,
% 9.25/5.26      ! [A2: set_o,X: $o,G2: $o > nat] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( member_o @ X @ A2 )
% 9.25/5.26         => ( ( groups3504817904513533571_o_nat @ G2 @ A2 )
% 9.25/5.26            = ( times_times_nat @ ( G2 @ X ) @ ( groups3504817904513533571_o_nat @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8507_prod_Oinsert__remove,axiom,
% 9.25/5.26      ! [A2: set_o,G2: $o > code_integer,X: $o] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( groups7694694392188491536nteger @ G2 @ ( insert_o @ X @ A2 ) )
% 9.25/5.26          = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups7694694392188491536nteger @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8508_prod_Oinsert__remove,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > code_integer,X: int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups3827104343326376752nteger @ G2 @ ( insert_int @ X @ A2 ) )
% 9.25/5.26          = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups3827104343326376752nteger @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8509_prod_Oinsert__remove,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > code_integer,X: nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups3455450783089532116nteger @ G2 @ ( insert_nat @ X @ A2 ) )
% 9.25/5.26          = ( times_3573771949741848930nteger @ ( G2 @ X ) @ ( groups3455450783089532116nteger @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8510_prod_Oinsert__remove,axiom,
% 9.25/5.26      ! [A2: set_o,G2: $o > assn,X: $o] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( groups5301882518646026715o_assn @ G2 @ ( insert_o @ X @ A2 ) )
% 9.25/5.26          = ( times_times_assn @ ( G2 @ X ) @ ( groups5301882518646026715o_assn @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8511_prod_Oinsert__remove,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > assn,X: int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups7882442080178216443t_assn @ G2 @ ( insert_int @ X @ A2 ) )
% 9.25/5.26          = ( times_times_assn @ ( G2 @ X ) @ ( groups7882442080178216443t_assn @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8512_prod_Oinsert__remove,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > assn,X: nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups6906906614972039071t_assn @ G2 @ ( insert_nat @ X @ A2 ) )
% 9.25/5.26          = ( times_times_assn @ ( G2 @ X ) @ ( groups6906906614972039071t_assn @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8513_prod_Oinsert__remove,axiom,
% 9.25/5.26      ! [A2: set_o,G2: $o > rat,X: $o] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( groups2869687844427037835_o_rat @ G2 @ ( insert_o @ X @ A2 ) )
% 9.25/5.26          = ( times_times_rat @ ( G2 @ X ) @ ( groups2869687844427037835_o_rat @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8514_prod_Oinsert__remove,axiom,
% 9.25/5.26      ! [A2: set_int,G2: int > rat,X: int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A2 ) )
% 9.25/5.26          = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8515_prod_Oinsert__remove,axiom,
% 9.25/5.26      ! [A2: set_nat,G2: nat > rat,X: nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A2 ) )
% 9.25/5.26          = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8516_prod_Oinsert__remove,axiom,
% 9.25/5.26      ! [A2: set_o,G2: $o > nat,X: $o] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( groups3504817904513533571_o_nat @ G2 @ ( insert_o @ X @ A2 ) )
% 9.25/5.26          = ( times_times_nat @ ( G2 @ X ) @ ( groups3504817904513533571_o_nat @ G2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ X @ bot_bot_set_o ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8517_prod_Ounion__inter__neutral,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_Code_integer ) )
% 9.25/5.26           => ( ( groups3827104343326376752nteger @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26              = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G2 @ A2 ) @ ( groups3827104343326376752nteger @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8518_prod_Ounion__inter__neutral,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_Code_integer ) )
% 9.25/5.26           => ( ( groups3455450783089532116nteger @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ A2 ) @ ( groups3455450783089532116nteger @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8519_prod_Ounion__inter__neutral,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > assn] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_assn ) )
% 9.25/5.26           => ( ( groups7882442080178216443t_assn @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26              = ( times_times_assn @ ( groups7882442080178216443t_assn @ G2 @ A2 ) @ ( groups7882442080178216443t_assn @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8520_prod_Ounion__inter__neutral,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > assn] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_assn ) )
% 9.25/5.26           => ( ( groups6906906614972039071t_assn @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ A2 ) @ ( groups6906906614972039071t_assn @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8521_prod_Ounion__inter__neutral,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_rat ) )
% 9.25/5.26           => ( ( groups1072433553688619179nt_rat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26              = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ A2 ) @ ( groups1072433553688619179nt_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8522_prod_Ounion__inter__neutral,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_rat ) )
% 9.25/5.26           => ( ( groups73079841787564623at_rat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ A2 ) @ ( groups73079841787564623at_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8523_prod_Ounion__inter__neutral,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_nat ) )
% 9.25/5.26           => ( ( groups1707563613775114915nt_nat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26              = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ A2 ) @ ( groups1707563613775114915nt_nat @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8524_prod_Ounion__inter__neutral,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_nat ) )
% 9.25/5.26           => ( ( groups708209901874060359at_nat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ A2 ) @ ( groups708209901874060359at_nat @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8525_prod_Ounion__inter__neutral,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_int ) )
% 9.25/5.26           => ( ( groups705719431365010083at_int @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ A2 ) @ ( groups705719431365010083at_int @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8526_prod_Ounion__inter__neutral,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.26               => ( ( G2 @ X2 )
% 9.25/5.26                  = one_one_int ) )
% 9.25/5.26           => ( ( groups1705073143266064639nt_int @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26              = ( times_times_int @ ( groups1705073143266064639nt_int @ G2 @ A2 ) @ ( groups1705073143266064639nt_int @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8527_prod_Ounion__disjoint,axiom,
% 9.25/5.26      ! [A2: set_o,B2: set_o,G2: $o > code_integer] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( finite_finite_o @ B2 )
% 9.25/5.26         => ( ( ( inf_inf_set_o @ A2 @ B2 )
% 9.25/5.26              = bot_bot_set_o )
% 9.25/5.26           => ( ( groups7694694392188491536nteger @ G2 @ ( sup_sup_set_o @ A2 @ B2 ) )
% 9.25/5.26              = ( times_3573771949741848930nteger @ ( groups7694694392188491536nteger @ G2 @ A2 ) @ ( groups7694694392188491536nteger @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8528_prod_Ounion__disjoint,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 9.25/5.26              = bot_bot_set_nat )
% 9.25/5.26           => ( ( groups3455450783089532116nteger @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ A2 ) @ ( groups3455450783089532116nteger @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8529_prod_Ounion__disjoint,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( ( inf_inf_set_int @ A2 @ B2 )
% 9.25/5.26              = bot_bot_set_int )
% 9.25/5.26           => ( ( groups3827104343326376752nteger @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26              = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G2 @ A2 ) @ ( groups3827104343326376752nteger @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8530_prod_Ounion__disjoint,axiom,
% 9.25/5.26      ! [A2: set_o,B2: set_o,G2: $o > assn] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( finite_finite_o @ B2 )
% 9.25/5.26         => ( ( ( inf_inf_set_o @ A2 @ B2 )
% 9.25/5.26              = bot_bot_set_o )
% 9.25/5.26           => ( ( groups5301882518646026715o_assn @ G2 @ ( sup_sup_set_o @ A2 @ B2 ) )
% 9.25/5.26              = ( times_times_assn @ ( groups5301882518646026715o_assn @ G2 @ A2 ) @ ( groups5301882518646026715o_assn @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8531_prod_Ounion__disjoint,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > assn] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 9.25/5.26              = bot_bot_set_nat )
% 9.25/5.26           => ( ( groups6906906614972039071t_assn @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ A2 ) @ ( groups6906906614972039071t_assn @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8532_prod_Ounion__disjoint,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > assn] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( ( inf_inf_set_int @ A2 @ B2 )
% 9.25/5.26              = bot_bot_set_int )
% 9.25/5.26           => ( ( groups7882442080178216443t_assn @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26              = ( times_times_assn @ ( groups7882442080178216443t_assn @ G2 @ A2 ) @ ( groups7882442080178216443t_assn @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8533_prod_Ounion__disjoint,axiom,
% 9.25/5.26      ! [A2: set_o,B2: set_o,G2: $o > rat] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( finite_finite_o @ B2 )
% 9.25/5.26         => ( ( ( inf_inf_set_o @ A2 @ B2 )
% 9.25/5.26              = bot_bot_set_o )
% 9.25/5.26           => ( ( groups2869687844427037835_o_rat @ G2 @ ( sup_sup_set_o @ A2 @ B2 ) )
% 9.25/5.26              = ( times_times_rat @ ( groups2869687844427037835_o_rat @ G2 @ A2 ) @ ( groups2869687844427037835_o_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8534_prod_Ounion__disjoint,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 9.25/5.26              = bot_bot_set_nat )
% 9.25/5.26           => ( ( groups73079841787564623at_rat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ A2 ) @ ( groups73079841787564623at_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8535_prod_Ounion__disjoint,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( ( inf_inf_set_int @ A2 @ B2 )
% 9.25/5.26              = bot_bot_set_int )
% 9.25/5.26           => ( ( groups1072433553688619179nt_rat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26              = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ A2 ) @ ( groups1072433553688619179nt_rat @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8536_prod_Ounion__disjoint,axiom,
% 9.25/5.26      ! [A2: set_o,B2: set_o,G2: $o > nat] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( finite_finite_o @ B2 )
% 9.25/5.26         => ( ( ( inf_inf_set_o @ A2 @ B2 )
% 9.25/5.26              = bot_bot_set_o )
% 9.25/5.26           => ( ( groups3504817904513533571_o_nat @ G2 @ ( sup_sup_set_o @ A2 @ B2 ) )
% 9.25/5.26              = ( times_times_nat @ ( groups3504817904513533571_o_nat @ G2 @ A2 ) @ ( groups3504817904513533571_o_nat @ G2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8537_sum_Ounion__diff2,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( groups3906332499630173760nt_rat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26            = ( plus_plus_rat @ ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups3906332499630173760nt_rat @ G2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups3906332499630173760nt_rat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8538_sum_Ounion__diff2,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( groups4541462559716669496nt_nat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26            = ( plus_plus_nat @ ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups4541462559716669496nt_nat @ G2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups4541462559716669496nt_nat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8539_sum_Ounion__diff2,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( groups2906978787729119204at_rat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( plus_plus_rat @ ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups2906978787729119204at_rat @ G2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups2906978787729119204at_rat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8540_sum_Ounion__diff2,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( groups3539618377306564664at_int @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( plus_plus_int @ ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups3539618377306564664at_int @ G2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups3539618377306564664at_int @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8541_sum_Ounion__diff2,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( groups3542108847815614940at_nat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( plus_plus_nat @ ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups3542108847815614940at_nat @ G2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups3542108847815614940at_nat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8542_sum_Ounion__diff2,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( groups4538972089207619220nt_int @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26            = ( plus_plus_int @ ( plus_plus_int @ ( groups4538972089207619220nt_int @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups4538972089207619220nt_int @ G2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups4538972089207619220nt_int @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8543_sum_Ounion__diff2,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > rat] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.26       => ( ( finite6177210948735845034at_nat @ B2 )
% 9.25/5.26         => ( ( groups342789780944988191at_rat @ G2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( plus_plus_rat @ ( plus_plus_rat @ ( groups342789780944988191at_rat @ G2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) @ ( groups342789780944988191at_rat @ G2 @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) ) ) @ ( groups342789780944988191at_rat @ G2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8544_sum_Ounion__diff2,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > nat] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.26       => ( ( finite6177210948735845034at_nat @ B2 )
% 9.25/5.26         => ( ( groups977919841031483927at_nat @ G2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( plus_plus_nat @ ( plus_plus_nat @ ( groups977919841031483927at_nat @ G2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) @ ( groups977919841031483927at_nat @ G2 @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) ) ) @ ( groups977919841031483927at_nat @ G2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8545_sum_Ounion__diff2,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,G2: product_prod_nat_nat > int] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.26       => ( ( finite6177210948735845034at_nat @ B2 )
% 9.25/5.26         => ( ( groups975429370522433651at_int @ G2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( plus_plus_int @ ( plus_plus_int @ ( groups975429370522433651at_int @ G2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) @ ( groups975429370522433651at_int @ G2 @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) ) ) @ ( groups975429370522433651at_int @ G2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8546_sum_Ounion__diff2,axiom,
% 9.25/5.26      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,G2: produc4166570645942440679at_nat > rat] :
% 9.25/5.26        ( ( finite1918287321285529104at_nat @ A2 )
% 9.25/5.26       => ( ( finite1918287321285529104at_nat @ B2 )
% 9.25/5.26         => ( ( groups6424767709179651461at_rat @ G2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( plus_plus_rat @ ( plus_plus_rat @ ( groups6424767709179651461at_rat @ G2 @ ( minus_5060654252129873198at_nat @ A2 @ B2 ) ) @ ( groups6424767709179651461at_rat @ G2 @ ( minus_5060654252129873198at_nat @ B2 @ A2 ) ) ) @ ( groups6424767709179651461at_rat @ G2 @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8547_sum__Un2,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,F2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26       => ( ( groups3906332499630173760nt_rat @ F2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26          = ( plus_plus_rat @ ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ F2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups3906332499630173760nt_rat @ F2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups3906332499630173760nt_rat @ F2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8548_sum__Un2,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,F2: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26       => ( ( groups4541462559716669496nt_nat @ F2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26          = ( plus_plus_nat @ ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ F2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups4541462559716669496nt_nat @ F2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups4541462559716669496nt_nat @ F2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8549_sum__Un2,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,F2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26       => ( ( groups2906978787729119204at_rat @ F2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26          = ( plus_plus_rat @ ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups2906978787729119204at_rat @ F2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups2906978787729119204at_rat @ F2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8550_sum__Un2,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,F2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26       => ( ( groups3539618377306564664at_int @ F2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26          = ( plus_plus_int @ ( plus_plus_int @ ( groups3539618377306564664at_int @ F2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups3539618377306564664at_int @ F2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups3539618377306564664at_int @ F2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8551_sum__Un2,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,F2: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26       => ( ( groups3542108847815614940at_nat @ F2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26          = ( plus_plus_nat @ ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups3542108847815614940at_nat @ F2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups3542108847815614940at_nat @ F2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8552_sum__Un2,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,F2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26       => ( ( groups4538972089207619220nt_int @ F2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26          = ( plus_plus_int @ ( plus_plus_int @ ( groups4538972089207619220nt_int @ F2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups4538972089207619220nt_int @ F2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups4538972089207619220nt_int @ F2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8553_sum__Un2,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > rat] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 9.25/5.26       => ( ( groups342789780944988191at_rat @ F2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 9.25/5.26          = ( plus_plus_rat @ ( plus_plus_rat @ ( groups342789780944988191at_rat @ F2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) @ ( groups342789780944988191at_rat @ F2 @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) ) ) @ ( groups342789780944988191at_rat @ F2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8554_sum__Un2,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > nat] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 9.25/5.26       => ( ( groups977919841031483927at_nat @ F2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 9.25/5.26          = ( plus_plus_nat @ ( plus_plus_nat @ ( groups977919841031483927at_nat @ F2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) @ ( groups977919841031483927at_nat @ F2 @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) ) ) @ ( groups977919841031483927at_nat @ F2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8555_sum__Un2,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > int] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 9.25/5.26       => ( ( groups975429370522433651at_int @ F2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 9.25/5.26          = ( plus_plus_int @ ( plus_plus_int @ ( groups975429370522433651at_int @ F2 @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) @ ( groups975429370522433651at_int @ F2 @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) ) ) @ ( groups975429370522433651at_int @ F2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8556_sum__Un2,axiom,
% 9.25/5.26      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,F2: produc4166570645942440679at_nat > rat] :
% 9.25/5.26        ( ( finite1918287321285529104at_nat @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 9.25/5.26       => ( ( groups6424767709179651461at_rat @ F2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 9.25/5.26          = ( plus_plus_rat @ ( plus_plus_rat @ ( groups6424767709179651461at_rat @ F2 @ ( minus_5060654252129873198at_nat @ A2 @ B2 ) ) @ ( groups6424767709179651461at_rat @ F2 @ ( minus_5060654252129873198at_nat @ B2 @ A2 ) ) ) @ ( groups6424767709179651461at_rat @ F2 @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8557_prod_Ounion__diff2,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( groups3827104343326376752nteger @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26            = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups3827104343326376752nteger @ G2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups3827104343326376752nteger @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8558_prod_Ounion__diff2,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( groups3455450783089532116nteger @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups3455450783089532116nteger @ G2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups3455450783089532116nteger @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8559_prod_Ounion__diff2,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > assn] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( groups7882442080178216443t_assn @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26            = ( times_times_assn @ ( times_times_assn @ ( groups7882442080178216443t_assn @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups7882442080178216443t_assn @ G2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups7882442080178216443t_assn @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8560_prod_Ounion__diff2,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > assn] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( groups6906906614972039071t_assn @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( times_times_assn @ ( times_times_assn @ ( groups6906906614972039071t_assn @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups6906906614972039071t_assn @ G2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups6906906614972039071t_assn @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8561_prod_Ounion__diff2,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( groups1072433553688619179nt_rat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26            = ( times_times_rat @ ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8562_prod_Ounion__diff2,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( groups73079841787564623at_rat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( times_times_rat @ ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8563_prod_Ounion__diff2,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( groups1707563613775114915nt_nat @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26            = ( times_times_nat @ ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8564_prod_Ounion__diff2,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( groups708209901874060359at_nat @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( times_times_nat @ ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups708209901874060359at_nat @ G2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups708209901874060359at_nat @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8565_prod_Ounion__diff2,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,G2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( groups705719431365010083at_int @ G2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( times_times_int @ ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ ( groups705719431365010083at_int @ G2 @ ( minus_minus_set_nat @ B2 @ A2 ) ) ) @ ( groups705719431365010083at_int @ G2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8566_prod_Ounion__diff2,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,G2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( groups1705073143266064639nt_int @ G2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26            = ( times_times_int @ ( times_times_int @ ( groups1705073143266064639nt_int @ G2 @ ( minus_minus_set_int @ A2 @ B2 ) ) @ ( groups1705073143266064639nt_int @ G2 @ ( minus_minus_set_int @ B2 @ A2 ) ) ) @ ( groups1705073143266064639nt_int @ G2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8567_sum__Un__nat,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,F2: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ( groups4541462559716669496nt_nat @ F2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26            = ( minus_minus_nat @ ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ F2 @ A2 ) @ ( groups4541462559716669496nt_nat @ F2 @ B2 ) ) @ ( groups4541462559716669496nt_nat @ F2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8568_sum__Un__nat,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > nat] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.26       => ( ( finite6177210948735845034at_nat @ B2 )
% 9.25/5.26         => ( ( groups977919841031483927at_nat @ F2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( minus_minus_nat @ ( plus_plus_nat @ ( groups977919841031483927at_nat @ F2 @ A2 ) @ ( groups977919841031483927at_nat @ F2 @ B2 ) ) @ ( groups977919841031483927at_nat @ F2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8569_sum__Un__nat,axiom,
% 9.25/5.26      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,F2: produc4166570645942440679at_nat > nat] :
% 9.25/5.26        ( ( finite1918287321285529104at_nat @ A2 )
% 9.25/5.26       => ( ( finite1918287321285529104at_nat @ B2 )
% 9.25/5.26         => ( ( groups7059897769266147197at_nat @ F2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( minus_minus_nat @ ( plus_plus_nat @ ( groups7059897769266147197at_nat @ F2 @ A2 ) @ ( groups7059897769266147197at_nat @ F2 @ B2 ) ) @ ( groups7059897769266147197at_nat @ F2 @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8570_sum__Un__nat,axiom,
% 9.25/5.26      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,F2: produc3843707927480180839at_nat > nat] :
% 9.25/5.26        ( ( finite4343798906461161616at_nat @ A2 )
% 9.25/5.26       => ( ( finite4343798906461161616at_nat @ B2 )
% 9.25/5.26         => ( ( groups3860910324918113789at_nat @ F2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( minus_minus_nat @ ( plus_plus_nat @ ( groups3860910324918113789at_nat @ F2 @ A2 ) @ ( groups3860910324918113789at_nat @ F2 @ B2 ) ) @ ( groups3860910324918113789at_nat @ F2 @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8571_sum__Un__nat,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,F2: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ( groups3542108847815614940at_nat @ F2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26            = ( minus_minus_nat @ ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F2 @ A2 ) @ ( groups3542108847815614940at_nat @ F2 @ B2 ) ) @ ( groups3542108847815614940at_nat @ F2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8572_sum_Odelta__remove,axiom,
% 9.25/5.26      ! [S: set_o,A: $o,B: $o > rat,C: $o > rat] :
% 9.25/5.26        ( ( finite_finite_o @ S )
% 9.25/5.26       => ( ( ( member_o @ A @ S )
% 9.25/5.26           => ( ( groups7872700643590313910_o_rat
% 9.25/5.26                @ ^ [K4: $o] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( plus_plus_rat @ ( B @ A ) @ ( groups7872700643590313910_o_rat @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 9.25/5.26          & ( ~ ( member_o @ A @ S )
% 9.25/5.26           => ( ( groups7872700643590313910_o_rat
% 9.25/5.26                @ ^ [K4: $o] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( groups7872700643590313910_o_rat @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8573_sum_Odelta__remove,axiom,
% 9.25/5.26      ! [S: set_o,A: $o,B: $o > nat,C: $o > nat] :
% 9.25/5.26        ( ( finite_finite_o @ S )
% 9.25/5.26       => ( ( ( member_o @ A @ S )
% 9.25/5.26           => ( ( groups8507830703676809646_o_nat
% 9.25/5.26                @ ^ [K4: $o] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( plus_plus_nat @ ( B @ A ) @ ( groups8507830703676809646_o_nat @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 9.25/5.26          & ( ~ ( member_o @ A @ S )
% 9.25/5.26           => ( ( groups8507830703676809646_o_nat
% 9.25/5.26                @ ^ [K4: $o] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( groups8507830703676809646_o_nat @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8574_sum_Odelta__remove,axiom,
% 9.25/5.26      ! [S: set_o,A: $o,B: $o > int,C: $o > int] :
% 9.25/5.26        ( ( finite_finite_o @ S )
% 9.25/5.26       => ( ( ( member_o @ A @ S )
% 9.25/5.26           => ( ( groups8505340233167759370_o_int
% 9.25/5.26                @ ^ [K4: $o] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( plus_plus_int @ ( B @ A ) @ ( groups8505340233167759370_o_int @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 9.25/5.26          & ( ~ ( member_o @ A @ S )
% 9.25/5.26           => ( ( groups8505340233167759370_o_int
% 9.25/5.26                @ ^ [K4: $o] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( groups8505340233167759370_o_int @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8575_sum_Odelta__remove,axiom,
% 9.25/5.26      ! [S: set_int,A: int,B: int > rat,C: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ S )
% 9.25/5.26       => ( ( ( member_int @ A @ S )
% 9.25/5.26           => ( ( groups3906332499630173760nt_rat
% 9.25/5.26                @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( plus_plus_rat @ ( B @ A ) @ ( groups3906332499630173760nt_rat @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 9.25/5.26          & ( ~ ( member_int @ A @ S )
% 9.25/5.26           => ( ( groups3906332499630173760nt_rat
% 9.25/5.26                @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( groups3906332499630173760nt_rat @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8576_sum_Odelta__remove,axiom,
% 9.25/5.26      ! [S: set_int,A: int,B: int > nat,C: int > nat] :
% 9.25/5.26        ( ( finite_finite_int @ S )
% 9.25/5.26       => ( ( ( member_int @ A @ S )
% 9.25/5.26           => ( ( groups4541462559716669496nt_nat
% 9.25/5.26                @ ^ [K4: int] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( plus_plus_nat @ ( B @ A ) @ ( groups4541462559716669496nt_nat @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 9.25/5.26          & ( ~ ( member_int @ A @ S )
% 9.25/5.26           => ( ( groups4541462559716669496nt_nat
% 9.25/5.26                @ ^ [K4: int] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( groups4541462559716669496nt_nat @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8577_sum_Odelta__remove,axiom,
% 9.25/5.26      ! [S: set_nat,A: nat,B: nat > rat,C: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ S )
% 9.25/5.26       => ( ( ( member_nat @ A @ S )
% 9.25/5.26           => ( ( groups2906978787729119204at_rat
% 9.25/5.26                @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( plus_plus_rat @ ( B @ A ) @ ( groups2906978787729119204at_rat @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 9.25/5.26          & ( ~ ( member_nat @ A @ S )
% 9.25/5.26           => ( ( groups2906978787729119204at_rat
% 9.25/5.26                @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( groups2906978787729119204at_rat @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8578_sum_Odelta__remove,axiom,
% 9.25/5.26      ! [S: set_nat,A: nat,B: nat > int,C: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ S )
% 9.25/5.26       => ( ( ( member_nat @ A @ S )
% 9.25/5.26           => ( ( groups3539618377306564664at_int
% 9.25/5.26                @ ^ [K4: nat] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( plus_plus_int @ ( B @ A ) @ ( groups3539618377306564664at_int @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 9.25/5.26          & ( ~ ( member_nat @ A @ S )
% 9.25/5.26           => ( ( groups3539618377306564664at_int
% 9.25/5.26                @ ^ [K4: nat] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( groups3539618377306564664at_int @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8579_sum_Odelta__remove,axiom,
% 9.25/5.26      ! [S: set_nat,A: nat,B: nat > nat,C: nat > nat] :
% 9.25/5.26        ( ( finite_finite_nat @ S )
% 9.25/5.26       => ( ( ( member_nat @ A @ S )
% 9.25/5.26           => ( ( groups3542108847815614940at_nat
% 9.25/5.26                @ ^ [K4: nat] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( plus_plus_nat @ ( B @ A ) @ ( groups3542108847815614940at_nat @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 9.25/5.26          & ( ~ ( member_nat @ A @ S )
% 9.25/5.26           => ( ( groups3542108847815614940at_nat
% 9.25/5.26                @ ^ [K4: nat] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( groups3542108847815614940at_nat @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8580_sum_Odelta__remove,axiom,
% 9.25/5.26      ! [S: set_int,A: int,B: int > int,C: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ S )
% 9.25/5.26       => ( ( ( member_int @ A @ S )
% 9.25/5.26           => ( ( groups4538972089207619220nt_int
% 9.25/5.26                @ ^ [K4: int] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( plus_plus_int @ ( B @ A ) @ ( groups4538972089207619220nt_int @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 9.25/5.26          & ( ~ ( member_int @ A @ S )
% 9.25/5.26           => ( ( groups4538972089207619220nt_int
% 9.25/5.26                @ ^ [K4: int] : ( if_int @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( groups4538972089207619220nt_int @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8581_sum_Odelta__remove,axiom,
% 9.25/5.26      ! [S: set_set_nat,A: set_nat,B: set_nat > rat,C: set_nat > rat] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ S )
% 9.25/5.26       => ( ( ( member_set_nat @ A @ S )
% 9.25/5.26           => ( ( groups7659867448343625626at_rat
% 9.25/5.26                @ ^ [K4: set_nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( plus_plus_rat @ ( B @ A ) @ ( groups7659867448343625626at_rat @ C @ ( minus_2163939370556025621et_nat @ S @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ) ) ) )
% 9.25/5.26          & ( ~ ( member_set_nat @ A @ S )
% 9.25/5.26           => ( ( groups7659867448343625626at_rat
% 9.25/5.26                @ ^ [K4: set_nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( groups7659867448343625626at_rat @ C @ ( minus_2163939370556025621et_nat @ S @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8582_sum__div__partition,axiom,
% 9.25/5.26      ! [A2: set_int,F2: int > nat,B: nat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( divide_divide_nat @ ( groups4541462559716669496nt_nat @ F2 @ A2 ) @ B )
% 9.25/5.26          = ( plus_plus_nat
% 9.25/5.26            @ ( groups4541462559716669496nt_nat
% 9.25/5.26              @ ^ [A3: int] : ( divide_divide_nat @ ( F2 @ A3 ) @ B )
% 9.25/5.26              @ ( inf_inf_set_int @ A2
% 9.25/5.26                @ ( collect_int
% 9.25/5.26                  @ ^ [A3: int] : ( dvd_dvd_nat @ B @ ( F2 @ A3 ) ) ) ) )
% 9.25/5.26            @ ( divide_divide_nat
% 9.25/5.26              @ ( groups4541462559716669496nt_nat @ F2
% 9.25/5.26                @ ( inf_inf_set_int @ A2
% 9.25/5.26                  @ ( collect_int
% 9.25/5.26                    @ ^ [A3: int] :
% 9.25/5.26                        ~ ( dvd_dvd_nat @ B @ ( F2 @ A3 ) ) ) ) )
% 9.25/5.26              @ B ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8583_sum__div__partition,axiom,
% 9.25/5.26      ! [A2: set_nat,F2: nat > int,B: int] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( divide_divide_int @ ( groups3539618377306564664at_int @ F2 @ A2 ) @ B )
% 9.25/5.26          = ( plus_plus_int
% 9.25/5.26            @ ( groups3539618377306564664at_int
% 9.25/5.26              @ ^ [A3: nat] : ( divide_divide_int @ ( F2 @ A3 ) @ B )
% 9.25/5.26              @ ( inf_inf_set_nat @ A2
% 9.25/5.26                @ ( collect_nat
% 9.25/5.26                  @ ^ [A3: nat] : ( dvd_dvd_int @ B @ ( F2 @ A3 ) ) ) ) )
% 9.25/5.26            @ ( divide_divide_int
% 9.25/5.26              @ ( groups3539618377306564664at_int @ F2
% 9.25/5.26                @ ( inf_inf_set_nat @ A2
% 9.25/5.26                  @ ( collect_nat
% 9.25/5.26                    @ ^ [A3: nat] :
% 9.25/5.26                        ~ ( dvd_dvd_int @ B @ ( F2 @ A3 ) ) ) ) )
% 9.25/5.26              @ B ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8584_sum__div__partition,axiom,
% 9.25/5.26      ! [A2: set_int,F2: int > code_integer,B: code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( divide6298287555418463151nteger @ ( groups7873554091576472773nteger @ F2 @ A2 ) @ B )
% 9.25/5.26          = ( plus_p5714425477246183910nteger
% 9.25/5.26            @ ( groups7873554091576472773nteger
% 9.25/5.26              @ ^ [A3: int] : ( divide6298287555418463151nteger @ ( F2 @ A3 ) @ B )
% 9.25/5.26              @ ( inf_inf_set_int @ A2
% 9.25/5.26                @ ( collect_int
% 9.25/5.26                  @ ^ [A3: int] : ( dvd_dvd_Code_integer @ B @ ( F2 @ A3 ) ) ) ) )
% 9.25/5.26            @ ( divide6298287555418463151nteger
% 9.25/5.26              @ ( groups7873554091576472773nteger @ F2
% 9.25/5.26                @ ( inf_inf_set_int @ A2
% 9.25/5.26                  @ ( collect_int
% 9.25/5.26                    @ ^ [A3: int] :
% 9.25/5.26                        ~ ( dvd_dvd_Code_integer @ B @ ( F2 @ A3 ) ) ) ) )
% 9.25/5.26              @ B ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8585_sum__div__partition,axiom,
% 9.25/5.26      ! [A2: set_nat,F2: nat > code_integer,B: code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( divide6298287555418463151nteger @ ( groups7501900531339628137nteger @ F2 @ A2 ) @ B )
% 9.25/5.26          = ( plus_p5714425477246183910nteger
% 9.25/5.26            @ ( groups7501900531339628137nteger
% 9.25/5.26              @ ^ [A3: nat] : ( divide6298287555418463151nteger @ ( F2 @ A3 ) @ B )
% 9.25/5.26              @ ( inf_inf_set_nat @ A2
% 9.25/5.26                @ ( collect_nat
% 9.25/5.26                  @ ^ [A3: nat] : ( dvd_dvd_Code_integer @ B @ ( F2 @ A3 ) ) ) ) )
% 9.25/5.26            @ ( divide6298287555418463151nteger
% 9.25/5.26              @ ( groups7501900531339628137nteger @ F2
% 9.25/5.26                @ ( inf_inf_set_nat @ A2
% 9.25/5.26                  @ ( collect_nat
% 9.25/5.26                    @ ^ [A3: nat] :
% 9.25/5.26                        ~ ( dvd_dvd_Code_integer @ B @ ( F2 @ A3 ) ) ) ) )
% 9.25/5.26              @ B ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8586_sum__div__partition,axiom,
% 9.25/5.26      ! [A2: set_int,F2: int > code_natural,B: code_natural] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( divide5121882707175180666atural @ ( groups6697149243333190288atural @ F2 @ A2 ) @ B )
% 9.25/5.26          = ( plus_p4538020629002901425atural
% 9.25/5.26            @ ( groups6697149243333190288atural
% 9.25/5.26              @ ^ [A3: int] : ( divide5121882707175180666atural @ ( F2 @ A3 ) @ B )
% 9.25/5.26              @ ( inf_inf_set_int @ A2
% 9.25/5.26                @ ( collect_int
% 9.25/5.26                  @ ^ [A3: int] : ( dvd_dvd_Code_natural @ B @ ( F2 @ A3 ) ) ) ) )
% 9.25/5.26            @ ( divide5121882707175180666atural
% 9.25/5.26              @ ( groups6697149243333190288atural @ F2
% 9.25/5.26                @ ( inf_inf_set_int @ A2
% 9.25/5.26                  @ ( collect_int
% 9.25/5.26                    @ ^ [A3: int] :
% 9.25/5.26                        ~ ( dvd_dvd_Code_natural @ B @ ( F2 @ A3 ) ) ) ) )
% 9.25/5.26              @ B ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8587_sum__div__partition,axiom,
% 9.25/5.26      ! [A2: set_nat,F2: nat > code_natural,B: code_natural] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( divide5121882707175180666atural @ ( groups6325495683096345652atural @ F2 @ A2 ) @ B )
% 9.25/5.26          = ( plus_p4538020629002901425atural
% 9.25/5.26            @ ( groups6325495683096345652atural
% 9.25/5.26              @ ^ [A3: nat] : ( divide5121882707175180666atural @ ( F2 @ A3 ) @ B )
% 9.25/5.26              @ ( inf_inf_set_nat @ A2
% 9.25/5.26                @ ( collect_nat
% 9.25/5.26                  @ ^ [A3: nat] : ( dvd_dvd_Code_natural @ B @ ( F2 @ A3 ) ) ) ) )
% 9.25/5.26            @ ( divide5121882707175180666atural
% 9.25/5.26              @ ( groups6325495683096345652atural @ F2
% 9.25/5.26                @ ( inf_inf_set_nat @ A2
% 9.25/5.26                  @ ( collect_nat
% 9.25/5.26                    @ ^ [A3: nat] :
% 9.25/5.26                        ~ ( dvd_dvd_Code_natural @ B @ ( F2 @ A3 ) ) ) ) )
% 9.25/5.26              @ B ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8588_sum__div__partition,axiom,
% 9.25/5.26      ! [A2: set_nat,F2: nat > nat,B: nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( divide_divide_nat @ ( groups3542108847815614940at_nat @ F2 @ A2 ) @ B )
% 9.25/5.26          = ( plus_plus_nat
% 9.25/5.26            @ ( groups3542108847815614940at_nat
% 9.25/5.26              @ ^ [A3: nat] : ( divide_divide_nat @ ( F2 @ A3 ) @ B )
% 9.25/5.26              @ ( inf_inf_set_nat @ A2
% 9.25/5.26                @ ( collect_nat
% 9.25/5.26                  @ ^ [A3: nat] : ( dvd_dvd_nat @ B @ ( F2 @ A3 ) ) ) ) )
% 9.25/5.26            @ ( divide_divide_nat
% 9.25/5.26              @ ( groups3542108847815614940at_nat @ F2
% 9.25/5.26                @ ( inf_inf_set_nat @ A2
% 9.25/5.26                  @ ( collect_nat
% 9.25/5.26                    @ ^ [A3: nat] :
% 9.25/5.26                        ~ ( dvd_dvd_nat @ B @ ( F2 @ A3 ) ) ) ) )
% 9.25/5.26              @ B ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8589_sum__div__partition,axiom,
% 9.25/5.26      ! [A2: set_int,F2: int > int,B: int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( divide_divide_int @ ( groups4538972089207619220nt_int @ F2 @ A2 ) @ B )
% 9.25/5.26          = ( plus_plus_int
% 9.25/5.26            @ ( groups4538972089207619220nt_int
% 9.25/5.26              @ ^ [A3: int] : ( divide_divide_int @ ( F2 @ A3 ) @ B )
% 9.25/5.26              @ ( inf_inf_set_int @ A2
% 9.25/5.26                @ ( collect_int
% 9.25/5.26                  @ ^ [A3: int] : ( dvd_dvd_int @ B @ ( F2 @ A3 ) ) ) ) )
% 9.25/5.26            @ ( divide_divide_int
% 9.25/5.26              @ ( groups4538972089207619220nt_int @ F2
% 9.25/5.26                @ ( inf_inf_set_int @ A2
% 9.25/5.26                  @ ( collect_int
% 9.25/5.26                    @ ^ [A3: int] :
% 9.25/5.26                        ~ ( dvd_dvd_int @ B @ ( F2 @ A3 ) ) ) ) )
% 9.25/5.26              @ B ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8590_sum__div__partition,axiom,
% 9.25/5.26      ! [A2: set_set_nat,F2: set_nat > nat,B: nat] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.26       => ( ( divide_divide_nat @ ( groups8294997508430121362at_nat @ F2 @ A2 ) @ B )
% 9.25/5.26          = ( plus_plus_nat
% 9.25/5.26            @ ( groups8294997508430121362at_nat
% 9.25/5.26              @ ^ [A3: set_nat] : ( divide_divide_nat @ ( F2 @ A3 ) @ B )
% 9.25/5.26              @ ( inf_inf_set_set_nat @ A2
% 9.25/5.26                @ ( collect_set_nat
% 9.25/5.26                  @ ^ [A3: set_nat] : ( dvd_dvd_nat @ B @ ( F2 @ A3 ) ) ) ) )
% 9.25/5.26            @ ( divide_divide_nat
% 9.25/5.26              @ ( groups8294997508430121362at_nat @ F2
% 9.25/5.26                @ ( inf_inf_set_set_nat @ A2
% 9.25/5.26                  @ ( collect_set_nat
% 9.25/5.26                    @ ^ [A3: set_nat] :
% 9.25/5.26                        ~ ( dvd_dvd_nat @ B @ ( F2 @ A3 ) ) ) ) )
% 9.25/5.26              @ B ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8591_sum__div__partition,axiom,
% 9.25/5.26      ! [A2: set_set_nat,F2: set_nat > int,B: int] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.26       => ( ( divide_divide_int @ ( groups8292507037921071086at_int @ F2 @ A2 ) @ B )
% 9.25/5.26          = ( plus_plus_int
% 9.25/5.26            @ ( groups8292507037921071086at_int
% 9.25/5.26              @ ^ [A3: set_nat] : ( divide_divide_int @ ( F2 @ A3 ) @ B )
% 9.25/5.26              @ ( inf_inf_set_set_nat @ A2
% 9.25/5.26                @ ( collect_set_nat
% 9.25/5.26                  @ ^ [A3: set_nat] : ( dvd_dvd_int @ B @ ( F2 @ A3 ) ) ) ) )
% 9.25/5.26            @ ( divide_divide_int
% 9.25/5.26              @ ( groups8292507037921071086at_int @ F2
% 9.25/5.26                @ ( inf_inf_set_set_nat @ A2
% 9.25/5.26                  @ ( collect_set_nat
% 9.25/5.26                    @ ^ [A3: set_nat] :
% 9.25/5.26                        ~ ( dvd_dvd_int @ B @ ( F2 @ A3 ) ) ) ) )
% 9.25/5.26              @ B ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8592_prod_Odelta__remove,axiom,
% 9.25/5.26      ! [S: set_o,A: $o,B: $o > code_integer,C: $o > code_integer] :
% 9.25/5.26        ( ( finite_finite_o @ S )
% 9.25/5.26       => ( ( ( member_o @ A @ S )
% 9.25/5.26           => ( ( groups7694694392188491536nteger
% 9.25/5.26                @ ^ [K4: $o] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( times_3573771949741848930nteger @ ( B @ A ) @ ( groups7694694392188491536nteger @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 9.25/5.26          & ( ~ ( member_o @ A @ S )
% 9.25/5.26           => ( ( groups7694694392188491536nteger
% 9.25/5.26                @ ^ [K4: $o] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( groups7694694392188491536nteger @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8593_prod_Odelta__remove,axiom,
% 9.25/5.26      ! [S: set_int,A: int,B: int > code_integer,C: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ S )
% 9.25/5.26       => ( ( ( member_int @ A @ S )
% 9.25/5.26           => ( ( groups3827104343326376752nteger
% 9.25/5.26                @ ^ [K4: int] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( times_3573771949741848930nteger @ ( B @ A ) @ ( groups3827104343326376752nteger @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 9.25/5.26          & ( ~ ( member_int @ A @ S )
% 9.25/5.26           => ( ( groups3827104343326376752nteger
% 9.25/5.26                @ ^ [K4: int] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( groups3827104343326376752nteger @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8594_prod_Odelta__remove,axiom,
% 9.25/5.26      ! [S: set_nat,A: nat,B: nat > code_integer,C: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ S )
% 9.25/5.26       => ( ( ( member_nat @ A @ S )
% 9.25/5.26           => ( ( groups3455450783089532116nteger
% 9.25/5.26                @ ^ [K4: nat] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( times_3573771949741848930nteger @ ( B @ A ) @ ( groups3455450783089532116nteger @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 9.25/5.26          & ( ~ ( member_nat @ A @ S )
% 9.25/5.26           => ( ( groups3455450783089532116nteger
% 9.25/5.26                @ ^ [K4: nat] : ( if_Code_integer @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( groups3455450783089532116nteger @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8595_prod_Odelta__remove,axiom,
% 9.25/5.26      ! [S: set_o,A: $o,B: $o > assn,C: $o > assn] :
% 9.25/5.26        ( ( finite_finite_o @ S )
% 9.25/5.26       => ( ( ( member_o @ A @ S )
% 9.25/5.26           => ( ( groups5301882518646026715o_assn
% 9.25/5.26                @ ^ [K4: $o] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( times_times_assn @ ( B @ A ) @ ( groups5301882518646026715o_assn @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 9.25/5.26          & ( ~ ( member_o @ A @ S )
% 9.25/5.26           => ( ( groups5301882518646026715o_assn
% 9.25/5.26                @ ^ [K4: $o] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( groups5301882518646026715o_assn @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8596_prod_Odelta__remove,axiom,
% 9.25/5.26      ! [S: set_int,A: int,B: int > assn,C: int > assn] :
% 9.25/5.26        ( ( finite_finite_int @ S )
% 9.25/5.26       => ( ( ( member_int @ A @ S )
% 9.25/5.26           => ( ( groups7882442080178216443t_assn
% 9.25/5.26                @ ^ [K4: int] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( times_times_assn @ ( B @ A ) @ ( groups7882442080178216443t_assn @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 9.25/5.26          & ( ~ ( member_int @ A @ S )
% 9.25/5.26           => ( ( groups7882442080178216443t_assn
% 9.25/5.26                @ ^ [K4: int] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( groups7882442080178216443t_assn @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8597_prod_Odelta__remove,axiom,
% 9.25/5.26      ! [S: set_nat,A: nat,B: nat > assn,C: nat > assn] :
% 9.25/5.26        ( ( finite_finite_nat @ S )
% 9.25/5.26       => ( ( ( member_nat @ A @ S )
% 9.25/5.26           => ( ( groups6906906614972039071t_assn
% 9.25/5.26                @ ^ [K4: nat] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( times_times_assn @ ( B @ A ) @ ( groups6906906614972039071t_assn @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 9.25/5.26          & ( ~ ( member_nat @ A @ S )
% 9.25/5.26           => ( ( groups6906906614972039071t_assn
% 9.25/5.26                @ ^ [K4: nat] : ( if_assn @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( groups6906906614972039071t_assn @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8598_prod_Odelta__remove,axiom,
% 9.25/5.26      ! [S: set_o,A: $o,B: $o > rat,C: $o > rat] :
% 9.25/5.26        ( ( finite_finite_o @ S )
% 9.25/5.26       => ( ( ( member_o @ A @ S )
% 9.25/5.26           => ( ( groups2869687844427037835_o_rat
% 9.25/5.26                @ ^ [K4: $o] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( times_times_rat @ ( B @ A ) @ ( groups2869687844427037835_o_rat @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 9.25/5.26          & ( ~ ( member_o @ A @ S )
% 9.25/5.26           => ( ( groups2869687844427037835_o_rat
% 9.25/5.26                @ ^ [K4: $o] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( groups2869687844427037835_o_rat @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8599_prod_Odelta__remove,axiom,
% 9.25/5.26      ! [S: set_int,A: int,B: int > rat,C: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ S )
% 9.25/5.26       => ( ( ( member_int @ A @ S )
% 9.25/5.26           => ( ( groups1072433553688619179nt_rat
% 9.25/5.26                @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( times_times_rat @ ( B @ A ) @ ( groups1072433553688619179nt_rat @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 9.25/5.26          & ( ~ ( member_int @ A @ S )
% 9.25/5.26           => ( ( groups1072433553688619179nt_rat
% 9.25/5.26                @ ^ [K4: int] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( groups1072433553688619179nt_rat @ C @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8600_prod_Odelta__remove,axiom,
% 9.25/5.26      ! [S: set_nat,A: nat,B: nat > rat,C: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ S )
% 9.25/5.26       => ( ( ( member_nat @ A @ S )
% 9.25/5.26           => ( ( groups73079841787564623at_rat
% 9.25/5.26                @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( times_times_rat @ ( B @ A ) @ ( groups73079841787564623at_rat @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 9.25/5.26          & ( ~ ( member_nat @ A @ S )
% 9.25/5.26           => ( ( groups73079841787564623at_rat
% 9.25/5.26                @ ^ [K4: nat] : ( if_rat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( groups73079841787564623at_rat @ C @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8601_prod_Odelta__remove,axiom,
% 9.25/5.26      ! [S: set_o,A: $o,B: $o > nat,C: $o > nat] :
% 9.25/5.26        ( ( finite_finite_o @ S )
% 9.25/5.26       => ( ( ( member_o @ A @ S )
% 9.25/5.26           => ( ( groups3504817904513533571_o_nat
% 9.25/5.26                @ ^ [K4: $o] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( times_times_nat @ ( B @ A ) @ ( groups3504817904513533571_o_nat @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) )
% 9.25/5.26          & ( ~ ( member_o @ A @ S )
% 9.25/5.26           => ( ( groups3504817904513533571_o_nat
% 9.25/5.26                @ ^ [K4: $o] : ( if_nat @ ( K4 = A ) @ ( B @ K4 ) @ ( C @ K4 ) )
% 9.25/5.26                @ S )
% 9.25/5.26              = ( groups3504817904513533571_o_nat @ C @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8602_sum__gp__strict,axiom,
% 9.25/5.26      ! [X: rat,N: nat] :
% 9.25/5.26        ( ( ( X = one_one_rat )
% 9.25/5.26         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 9.25/5.26            = ( semiri681578069525770553at_rat @ N ) ) )
% 9.25/5.26        & ( ( X != one_one_rat )
% 9.25/5.26         => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 9.25/5.26            = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8603_power__diff__sumr2,axiom,
% 9.25/5.26      ! [X: code_integer,N: nat,Y: code_integer] :
% 9.25/5.26        ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y @ N ) )
% 9.25/5.26        = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X @ Y )
% 9.25/5.26          @ ( groups7501900531339628137nteger
% 9.25/5.26            @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ Y @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_8256067586552552935nteger @ X @ I3 ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8604_power__diff__sumr2,axiom,
% 9.25/5.26      ! [X: rat,N: nat,Y: rat] :
% 9.25/5.26        ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y @ N ) )
% 9.25/5.26        = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 9.25/5.26          @ ( groups2906978787729119204at_rat
% 9.25/5.26            @ ^ [I3: nat] : ( times_times_rat @ ( power_power_rat @ Y @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_rat @ X @ I3 ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8605_power__diff__sumr2,axiom,
% 9.25/5.26      ! [X: int,N: nat,Y: int] :
% 9.25/5.26        ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 9.25/5.26        = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 9.25/5.26          @ ( groups3539618377306564664at_int
% 9.25/5.26            @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) ) @ ( power_power_int @ X @ I3 ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8606_diff__power__eq__sum,axiom,
% 9.25/5.26      ! [X: code_integer,N: nat,Y: code_integer] :
% 9.25/5.26        ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ ( suc @ N ) ) @ ( power_8256067586552552935nteger @ Y @ ( suc @ N ) ) )
% 9.25/5.26        = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X @ Y )
% 9.25/5.26          @ ( groups7501900531339628137nteger
% 9.25/5.26            @ ^ [P6: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ P6 ) @ ( power_8256067586552552935nteger @ Y @ ( minus_minus_nat @ N @ P6 ) ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8607_diff__power__eq__sum,axiom,
% 9.25/5.26      ! [X: rat,N: nat,Y: rat] :
% 9.25/5.26        ( ( minus_minus_rat @ ( power_power_rat @ X @ ( suc @ N ) ) @ ( power_power_rat @ Y @ ( suc @ N ) ) )
% 9.25/5.26        = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 9.25/5.26          @ ( groups2906978787729119204at_rat
% 9.25/5.26            @ ^ [P6: nat] : ( times_times_rat @ ( power_power_rat @ X @ P6 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ N @ P6 ) ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8608_diff__power__eq__sum,axiom,
% 9.25/5.26      ! [X: int,N: nat,Y: int] :
% 9.25/5.26        ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N ) ) @ ( power_power_int @ Y @ ( suc @ N ) ) )
% 9.25/5.26        = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 9.25/5.26          @ ( groups3539618377306564664at_int
% 9.25/5.26            @ ^ [P6: nat] : ( times_times_int @ ( power_power_int @ X @ P6 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ P6 ) ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8609_eucl__rel__int__remainderI,axiom,
% 9.25/5.26      ! [R3: int,L: int,K: int,Q4: int] :
% 9.25/5.26        ( ( ( sgn_sgn_int @ R3 )
% 9.25/5.26          = ( sgn_sgn_int @ L ) )
% 9.25/5.26       => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ L ) )
% 9.25/5.26         => ( ( K
% 9.25/5.26              = ( plus_plus_int @ ( times_times_int @ Q4 @ L ) @ R3 ) )
% 9.25/5.26           => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q4 @ R3 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8610_member__le__sum,axiom,
% 9.25/5.26      ! [I: $o,A2: set_o,F2: $o > code_integer] :
% 9.25/5.26        ( ( member_o @ I @ A2 )
% 9.25/5.26       => ( ! [X2: $o] :
% 9.25/5.26              ( ( member_o @ X2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 9.25/5.26             => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X2 ) ) )
% 9.25/5.26         => ( ( finite_finite_o @ A2 )
% 9.25/5.26           => ( ord_le3102999989581377725nteger @ ( F2 @ I ) @ ( groups4406642042086082107nteger @ F2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8611_member__le__sum,axiom,
% 9.25/5.26      ! [I: int,A2: set_int,F2: int > code_integer] :
% 9.25/5.26        ( ( member_int @ I @ A2 )
% 9.25/5.26       => ( ! [X2: int] :
% 9.25/5.26              ( ( member_int @ X2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 9.25/5.26             => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X2 ) ) )
% 9.25/5.26         => ( ( finite_finite_int @ A2 )
% 9.25/5.26           => ( ord_le3102999989581377725nteger @ ( F2 @ I ) @ ( groups7873554091576472773nteger @ F2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8612_member__le__sum,axiom,
% 9.25/5.26      ! [I: nat,A2: set_nat,F2: nat > code_integer] :
% 9.25/5.26        ( ( member_nat @ I @ A2 )
% 9.25/5.26       => ( ! [X2: nat] :
% 9.25/5.26              ( ( member_nat @ X2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 9.25/5.26             => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X2 ) ) )
% 9.25/5.26         => ( ( finite_finite_nat @ A2 )
% 9.25/5.26           => ( ord_le3102999989581377725nteger @ ( F2 @ I ) @ ( groups7501900531339628137nteger @ F2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8613_member__le__sum,axiom,
% 9.25/5.26      ! [I: $o,A2: set_o,F2: $o > rat] :
% 9.25/5.26        ( ( member_o @ I @ A2 )
% 9.25/5.26       => ( ! [X2: $o] :
% 9.25/5.26              ( ( member_o @ X2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 9.25/5.26             => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X2 ) ) )
% 9.25/5.26         => ( ( finite_finite_o @ A2 )
% 9.25/5.26           => ( ord_less_eq_rat @ ( F2 @ I ) @ ( groups7872700643590313910_o_rat @ F2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8614_member__le__sum,axiom,
% 9.25/5.26      ! [I: int,A2: set_int,F2: int > rat] :
% 9.25/5.26        ( ( member_int @ I @ A2 )
% 9.25/5.26       => ( ! [X2: int] :
% 9.25/5.26              ( ( member_int @ X2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 9.25/5.26             => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X2 ) ) )
% 9.25/5.26         => ( ( finite_finite_int @ A2 )
% 9.25/5.26           => ( ord_less_eq_rat @ ( F2 @ I ) @ ( groups3906332499630173760nt_rat @ F2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8615_member__le__sum,axiom,
% 9.25/5.26      ! [I: nat,A2: set_nat,F2: nat > rat] :
% 9.25/5.26        ( ( member_nat @ I @ A2 )
% 9.25/5.26       => ( ! [X2: nat] :
% 9.25/5.26              ( ( member_nat @ X2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 9.25/5.26             => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X2 ) ) )
% 9.25/5.26         => ( ( finite_finite_nat @ A2 )
% 9.25/5.26           => ( ord_less_eq_rat @ ( F2 @ I ) @ ( groups2906978787729119204at_rat @ F2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8616_member__le__sum,axiom,
% 9.25/5.26      ! [I: $o,A2: set_o,F2: $o > nat] :
% 9.25/5.26        ( ( member_o @ I @ A2 )
% 9.25/5.26       => ( ! [X2: $o] :
% 9.25/5.26              ( ( member_o @ X2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 9.25/5.26             => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X2 ) ) )
% 9.25/5.26         => ( ( finite_finite_o @ A2 )
% 9.25/5.26           => ( ord_less_eq_nat @ ( F2 @ I ) @ ( groups8507830703676809646_o_nat @ F2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8617_member__le__sum,axiom,
% 9.25/5.26      ! [I: int,A2: set_int,F2: int > nat] :
% 9.25/5.26        ( ( member_int @ I @ A2 )
% 9.25/5.26       => ( ! [X2: int] :
% 9.25/5.26              ( ( member_int @ X2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 9.25/5.26             => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X2 ) ) )
% 9.25/5.26         => ( ( finite_finite_int @ A2 )
% 9.25/5.26           => ( ord_less_eq_nat @ ( F2 @ I ) @ ( groups4541462559716669496nt_nat @ F2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8618_member__le__sum,axiom,
% 9.25/5.26      ! [I: $o,A2: set_o,F2: $o > int] :
% 9.25/5.26        ( ( member_o @ I @ A2 )
% 9.25/5.26       => ( ! [X2: $o] :
% 9.25/5.26              ( ( member_o @ X2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 9.25/5.26             => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ X2 ) ) )
% 9.25/5.26         => ( ( finite_finite_o @ A2 )
% 9.25/5.26           => ( ord_less_eq_int @ ( F2 @ I ) @ ( groups8505340233167759370_o_int @ F2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8619_member__le__sum,axiom,
% 9.25/5.26      ! [I: nat,A2: set_nat,F2: nat > int] :
% 9.25/5.26        ( ( member_nat @ I @ A2 )
% 9.25/5.26       => ( ! [X2: nat] :
% 9.25/5.26              ( ( member_nat @ X2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 9.25/5.26             => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ X2 ) ) )
% 9.25/5.26         => ( ( finite_finite_nat @ A2 )
% 9.25/5.26           => ( ord_less_eq_int @ ( F2 @ I ) @ ( groups3539618377306564664at_int @ F2 @ A2 ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8620_prod__mono2,axiom,
% 9.25/5.26      ! [B2: set_int,A2: set_int,F2: int > code_integer] :
% 9.25/5.26        ( ( finite_finite_int @ B2 )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 9.25/5.26         => ( ! [B6: int] :
% 9.25/5.26                ( ( member_int @ B6 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 9.25/5.26               => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ B6 ) ) )
% 9.25/5.26           => ( ! [A6: int] :
% 9.25/5.26                  ( ( member_int @ A6 @ A2 )
% 9.25/5.26                 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ A6 ) ) )
% 9.25/5.26             => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F2 @ A2 ) @ ( groups3827104343326376752nteger @ F2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8621_prod__mono2,axiom,
% 9.25/5.26      ! [B2: set_int,A2: set_int,F2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ B2 )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 9.25/5.26         => ( ! [B6: int] :
% 9.25/5.26                ( ( member_int @ B6 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 9.25/5.26               => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ B6 ) ) )
% 9.25/5.26           => ( ! [A6: int] :
% 9.25/5.26                  ( ( member_int @ A6 @ A2 )
% 9.25/5.26                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ A6 ) ) )
% 9.25/5.26             => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F2 @ A2 ) @ ( groups1072433553688619179nt_rat @ F2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8622_prod__mono2,axiom,
% 9.25/5.26      ! [B2: set_nat,A2: set_nat,F2: nat > code_integer] :
% 9.25/5.26        ( ( finite_finite_nat @ B2 )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 9.25/5.26         => ( ! [B6: nat] :
% 9.25/5.26                ( ( member_nat @ B6 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 9.25/5.26               => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ B6 ) ) )
% 9.25/5.26           => ( ! [A6: nat] :
% 9.25/5.26                  ( ( member_nat @ A6 @ A2 )
% 9.25/5.26                 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ A6 ) ) )
% 9.25/5.26             => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F2 @ A2 ) @ ( groups3455450783089532116nteger @ F2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8623_prod__mono2,axiom,
% 9.25/5.26      ! [B2: set_nat,A2: set_nat,F2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ B2 )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 9.25/5.26         => ( ! [B6: nat] :
% 9.25/5.26                ( ( member_nat @ B6 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 9.25/5.26               => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ B6 ) ) )
% 9.25/5.26           => ( ! [A6: nat] :
% 9.25/5.26                  ( ( member_nat @ A6 @ A2 )
% 9.25/5.26                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ A6 ) ) )
% 9.25/5.26             => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F2 @ A2 ) @ ( groups73079841787564623at_rat @ F2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8624_prod__mono2,axiom,
% 9.25/5.26      ! [B2: set_nat,A2: set_nat,F2: nat > int] :
% 9.25/5.26        ( ( finite_finite_nat @ B2 )
% 9.25/5.26       => ( ( ord_less_eq_set_nat @ A2 @ B2 )
% 9.25/5.26         => ( ! [B6: nat] :
% 9.25/5.26                ( ( member_nat @ B6 @ ( minus_minus_set_nat @ B2 @ A2 ) )
% 9.25/5.26               => ( ord_less_eq_int @ one_one_int @ ( F2 @ B6 ) ) )
% 9.25/5.26           => ( ! [A6: nat] :
% 9.25/5.26                  ( ( member_nat @ A6 @ A2 )
% 9.25/5.26                 => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ A6 ) ) )
% 9.25/5.26             => ( ord_less_eq_int @ ( groups705719431365010083at_int @ F2 @ A2 ) @ ( groups705719431365010083at_int @ F2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8625_prod__mono2,axiom,
% 9.25/5.26      ! [B2: set_int,A2: set_int,F2: int > int] :
% 9.25/5.26        ( ( finite_finite_int @ B2 )
% 9.25/5.26       => ( ( ord_less_eq_set_int @ A2 @ B2 )
% 9.25/5.26         => ( ! [B6: int] :
% 9.25/5.26                ( ( member_int @ B6 @ ( minus_minus_set_int @ B2 @ A2 ) )
% 9.25/5.26               => ( ord_less_eq_int @ one_one_int @ ( F2 @ B6 ) ) )
% 9.25/5.26           => ( ! [A6: int] :
% 9.25/5.26                  ( ( member_int @ A6 @ A2 )
% 9.25/5.26                 => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ A6 ) ) )
% 9.25/5.26             => ( ord_less_eq_int @ ( groups1705073143266064639nt_int @ F2 @ A2 ) @ ( groups1705073143266064639nt_int @ F2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8626_prod__mono2,axiom,
% 9.25/5.26      ! [B2: set_set_nat,A2: set_set_nat,F2: set_nat > code_integer] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ B2 )
% 9.25/5.26       => ( ( ord_le6893508408891458716et_nat @ A2 @ B2 )
% 9.25/5.26         => ( ! [B6: set_nat] :
% 9.25/5.26                ( ( member_set_nat @ B6 @ ( minus_2163939370556025621et_nat @ B2 @ A2 ) )
% 9.25/5.26               => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ B6 ) ) )
% 9.25/5.26           => ( ! [A6: set_nat] :
% 9.25/5.26                  ( ( member_set_nat @ A6 @ A2 )
% 9.25/5.26                 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ A6 ) ) )
% 9.25/5.26             => ( ord_le3102999989581377725nteger @ ( groups2761809935038513290nteger @ F2 @ A2 ) @ ( groups2761809935038513290nteger @ F2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8627_prod__mono2,axiom,
% 9.25/5.26      ! [B2: set_set_nat,A2: set_set_nat,F2: set_nat > rat] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ B2 )
% 9.25/5.26       => ( ( ord_le6893508408891458716et_nat @ A2 @ B2 )
% 9.25/5.26         => ( ! [B6: set_nat] :
% 9.25/5.26                ( ( member_set_nat @ B6 @ ( minus_2163939370556025621et_nat @ B2 @ A2 ) )
% 9.25/5.26               => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ B6 ) ) )
% 9.25/5.26           => ( ! [A6: set_nat] :
% 9.25/5.26                  ( ( member_set_nat @ A6 @ A2 )
% 9.25/5.26                 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ A6 ) ) )
% 9.25/5.26             => ( ord_less_eq_rat @ ( groups3613417700093529605at_rat @ F2 @ A2 ) @ ( groups3613417700093529605at_rat @ F2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8628_prod__mono2,axiom,
% 9.25/5.26      ! [B2: set_set_nat,A2: set_set_nat,F2: set_nat > int] :
% 9.25/5.26        ( ( finite1152437895449049373et_nat @ B2 )
% 9.25/5.26       => ( ( ord_le6893508408891458716et_nat @ A2 @ B2 )
% 9.25/5.26         => ( ! [B6: set_nat] :
% 9.25/5.26                ( ( member_set_nat @ B6 @ ( minus_2163939370556025621et_nat @ B2 @ A2 ) )
% 9.25/5.26               => ( ord_less_eq_int @ one_one_int @ ( F2 @ B6 ) ) )
% 9.25/5.26           => ( ! [A6: set_nat] :
% 9.25/5.26                  ( ( member_set_nat @ A6 @ A2 )
% 9.25/5.26                 => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ A6 ) ) )
% 9.25/5.26             => ( ord_less_eq_int @ ( groups4246057289670975065at_int @ F2 @ A2 ) @ ( groups4246057289670975065at_int @ F2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8629_prod__mono2,axiom,
% 9.25/5.26      ! [B2: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > code_integer] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ B2 )
% 9.25/5.26       => ( ( ord_le3146513528884898305at_nat @ A2 @ B2 )
% 9.25/5.26         => ( ! [B6: product_prod_nat_nat] :
% 9.25/5.26                ( ( member8440522571783428010at_nat @ B6 @ ( minus_1356011639430497352at_nat @ B2 @ A2 ) )
% 9.25/5.26               => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ B6 ) ) )
% 9.25/5.26           => ( ! [A6: product_prod_nat_nat] :
% 9.25/5.26                  ( ( member8440522571783428010at_nat @ A6 @ A2 )
% 9.25/5.26                 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ A6 ) ) )
% 9.25/5.26             => ( ord_le3102999989581377725nteger @ ( groups1230400874837758585nteger @ F2 @ A2 ) @ ( groups1230400874837758585nteger @ F2 @ B2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8630_prod__diff1,axiom,
% 9.25/5.26      ! [A2: set_o,F2: $o > nat,A: $o] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( ( F2 @ A )
% 9.25/5.26           != zero_zero_nat )
% 9.25/5.26         => ( ( ( member_o @ A @ A2 )
% 9.25/5.26             => ( ( groups3504817904513533571_o_nat @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 9.25/5.26                = ( divide_divide_nat @ ( groups3504817904513533571_o_nat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.26            & ( ~ ( member_o @ A @ A2 )
% 9.25/5.26             => ( ( groups3504817904513533571_o_nat @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 9.25/5.26                = ( groups3504817904513533571_o_nat @ F2 @ A2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8631_prod__diff1,axiom,
% 9.25/5.26      ! [A2: set_int,F2: int > nat,A: int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( ( F2 @ A )
% 9.25/5.26           != zero_zero_nat )
% 9.25/5.26         => ( ( ( member_int @ A @ A2 )
% 9.25/5.26             => ( ( groups1707563613775114915nt_nat @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.25/5.26                = ( divide_divide_nat @ ( groups1707563613775114915nt_nat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.26            & ( ~ ( member_int @ A @ A2 )
% 9.25/5.26             => ( ( groups1707563613775114915nt_nat @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.25/5.26                = ( groups1707563613775114915nt_nat @ F2 @ A2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8632_prod__diff1,axiom,
% 9.25/5.26      ! [A2: set_o,F2: $o > int,A: $o] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( ( F2 @ A )
% 9.25/5.26           != zero_zero_int )
% 9.25/5.26         => ( ( ( member_o @ A @ A2 )
% 9.25/5.26             => ( ( groups3502327434004483295_o_int @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 9.25/5.26                = ( divide_divide_int @ ( groups3502327434004483295_o_int @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.26            & ( ~ ( member_o @ A @ A2 )
% 9.25/5.26             => ( ( groups3502327434004483295_o_int @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 9.25/5.26                = ( groups3502327434004483295_o_int @ F2 @ A2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8633_prod__diff1,axiom,
% 9.25/5.26      ! [A2: set_o,F2: $o > code_integer,A: $o] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( ( F2 @ A )
% 9.25/5.26           != zero_z3403309356797280102nteger )
% 9.25/5.26         => ( ( ( member_o @ A @ A2 )
% 9.25/5.26             => ( ( groups7694694392188491536nteger @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 9.25/5.26                = ( divide6298287555418463151nteger @ ( groups7694694392188491536nteger @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.26            & ( ~ ( member_o @ A @ A2 )
% 9.25/5.26             => ( ( groups7694694392188491536nteger @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 9.25/5.26                = ( groups7694694392188491536nteger @ F2 @ A2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8634_prod__diff1,axiom,
% 9.25/5.26      ! [A2: set_int,F2: int > code_integer,A: int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( ( F2 @ A )
% 9.25/5.26           != zero_z3403309356797280102nteger )
% 9.25/5.26         => ( ( ( member_int @ A @ A2 )
% 9.25/5.26             => ( ( groups3827104343326376752nteger @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.25/5.26                = ( divide6298287555418463151nteger @ ( groups3827104343326376752nteger @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.26            & ( ~ ( member_int @ A @ A2 )
% 9.25/5.26             => ( ( groups3827104343326376752nteger @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.25/5.26                = ( groups3827104343326376752nteger @ F2 @ A2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8635_prod__diff1,axiom,
% 9.25/5.26      ! [A2: set_nat,F2: nat > code_integer,A: nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( ( F2 @ A )
% 9.25/5.26           != zero_z3403309356797280102nteger )
% 9.25/5.26         => ( ( ( member_nat @ A @ A2 )
% 9.25/5.26             => ( ( groups3455450783089532116nteger @ F2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.25/5.26                = ( divide6298287555418463151nteger @ ( groups3455450783089532116nteger @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.26            & ( ~ ( member_nat @ A @ A2 )
% 9.25/5.26             => ( ( groups3455450783089532116nteger @ F2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.25/5.26                = ( groups3455450783089532116nteger @ F2 @ A2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8636_prod__diff1,axiom,
% 9.25/5.26      ! [A2: set_o,F2: $o > rat,A: $o] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( ( F2 @ A )
% 9.25/5.26           != zero_zero_rat )
% 9.25/5.26         => ( ( ( member_o @ A @ A2 )
% 9.25/5.26             => ( ( groups2869687844427037835_o_rat @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 9.25/5.26                = ( divide_divide_rat @ ( groups2869687844427037835_o_rat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.26            & ( ~ ( member_o @ A @ A2 )
% 9.25/5.26             => ( ( groups2869687844427037835_o_rat @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 9.25/5.26                = ( groups2869687844427037835_o_rat @ F2 @ A2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8637_prod__diff1,axiom,
% 9.25/5.26      ! [A2: set_int,F2: int > rat,A: int] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( ( F2 @ A )
% 9.25/5.26           != zero_zero_rat )
% 9.25/5.26         => ( ( ( member_int @ A @ A2 )
% 9.25/5.26             => ( ( groups1072433553688619179nt_rat @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.25/5.26                = ( divide_divide_rat @ ( groups1072433553688619179nt_rat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.26            & ( ~ ( member_int @ A @ A2 )
% 9.25/5.26             => ( ( groups1072433553688619179nt_rat @ F2 @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 9.25/5.26                = ( groups1072433553688619179nt_rat @ F2 @ A2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8638_prod__diff1,axiom,
% 9.25/5.26      ! [A2: set_nat,F2: nat > rat,A: nat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( ( F2 @ A )
% 9.25/5.26           != zero_zero_rat )
% 9.25/5.26         => ( ( ( member_nat @ A @ A2 )
% 9.25/5.26             => ( ( groups73079841787564623at_rat @ F2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.25/5.26                = ( divide_divide_rat @ ( groups73079841787564623at_rat @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.26            & ( ~ ( member_nat @ A @ A2 )
% 9.25/5.26             => ( ( groups73079841787564623at_rat @ F2 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 9.25/5.26                = ( groups73079841787564623at_rat @ F2 @ A2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8639_prod__diff1,axiom,
% 9.25/5.26      ! [A2: set_o,F2: $o > code_natural,A: $o] :
% 9.25/5.26        ( ( finite_finite_o @ A2 )
% 9.25/5.26       => ( ( ( F2 @ A )
% 9.25/5.26           != zero_z2226904508553997617atural )
% 9.25/5.26         => ( ( ( member_o @ A @ A2 )
% 9.25/5.26             => ( ( groups6518289543945209051atural @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 9.25/5.26                = ( divide5121882707175180666atural @ ( groups6518289543945209051atural @ F2 @ A2 ) @ ( F2 @ A ) ) ) )
% 9.25/5.26            & ( ~ ( member_o @ A @ A2 )
% 9.25/5.26             => ( ( groups6518289543945209051atural @ F2 @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ bot_bot_set_o ) ) )
% 9.25/5.26                = ( groups6518289543945209051atural @ F2 @ A2 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8640_prod__Un,axiom,
% 9.25/5.26      ! [A2: set_int,B2: set_int,F2: int > rat] :
% 9.25/5.26        ( ( finite_finite_int @ A2 )
% 9.25/5.26       => ( ( finite_finite_int @ B2 )
% 9.25/5.26         => ( ! [X2: int] :
% 9.25/5.26                ( ( member_int @ X2 @ ( inf_inf_set_int @ A2 @ B2 ) )
% 9.25/5.26               => ( ( F2 @ X2 )
% 9.25/5.26                 != zero_zero_rat ) )
% 9.25/5.26           => ( ( groups1072433553688619179nt_rat @ F2 @ ( sup_sup_set_int @ A2 @ B2 ) )
% 9.25/5.26              = ( divide_divide_rat @ ( times_times_rat @ ( groups1072433553688619179nt_rat @ F2 @ A2 ) @ ( groups1072433553688619179nt_rat @ F2 @ B2 ) ) @ ( groups1072433553688619179nt_rat @ F2 @ ( inf_inf_set_int @ A2 @ B2 ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8641_prod__Un,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > rat] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.26       => ( ( finite6177210948735845034at_nat @ B2 )
% 9.25/5.26         => ( ! [X2: product_prod_nat_nat] :
% 9.25/5.26                ( ( member8440522571783428010at_nat @ X2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) )
% 9.25/5.26               => ( ( F2 @ X2 )
% 9.25/5.26                 != zero_zero_rat ) )
% 9.25/5.26           => ( ( groups3442636767675653108at_rat @ F2 @ ( sup_su6327502436637775413at_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( divide_divide_rat @ ( times_times_rat @ ( groups3442636767675653108at_rat @ F2 @ A2 ) @ ( groups3442636767675653108at_rat @ F2 @ B2 ) ) @ ( groups3442636767675653108at_rat @ F2 @ ( inf_in2572325071724192079at_nat @ A2 @ B2 ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8642_prod__Un,axiom,
% 9.25/5.26      ! [A2: set_Pr8551490117392284871at_nat,B2: set_Pr8551490117392284871at_nat,F2: produc4166570645942440679at_nat > rat] :
% 9.25/5.26        ( ( finite1918287321285529104at_nat @ A2 )
% 9.25/5.26       => ( ( finite1918287321285529104at_nat @ B2 )
% 9.25/5.26         => ( ! [X2: produc4166570645942440679at_nat] :
% 9.25/5.26                ( ( member6689249552917799696at_nat @ X2 @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) )
% 9.25/5.26               => ( ( F2 @ X2 )
% 9.25/5.26                 != zero_zero_rat ) )
% 9.25/5.26           => ( ( groups5938585286922990810at_rat @ F2 @ ( sup_su3035147773818789531at_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( divide_divide_rat @ ( times_times_rat @ ( groups5938585286922990810at_rat @ F2 @ A2 ) @ ( groups5938585286922990810at_rat @ F2 @ B2 ) ) @ ( groups5938585286922990810at_rat @ F2 @ ( inf_in1697001100524423349at_nat @ A2 @ B2 ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8643_prod__Un,axiom,
% 9.25/5.26      ! [A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat,F2: produc3843707927480180839at_nat > rat] :
% 9.25/5.26        ( ( finite4343798906461161616at_nat @ A2 )
% 9.25/5.26       => ( ( finite4343798906461161616at_nat @ B2 )
% 9.25/5.26         => ( ! [X2: produc3843707927480180839at_nat] :
% 9.25/5.26                ( ( member8757157785044589968at_nat @ X2 @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) )
% 9.25/5.26               => ( ( F2 @ X2 )
% 9.25/5.26                 != zero_zero_rat ) )
% 9.25/5.26           => ( ( groups8874911130973611098at_rat @ F2 @ ( sup_su5525570899277871387at_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( divide_divide_rat @ ( times_times_rat @ ( groups8874911130973611098at_rat @ F2 @ A2 ) @ ( groups8874911130973611098at_rat @ F2 @ B2 ) ) @ ( groups8874911130973611098at_rat @ F2 @ ( inf_in7913087082777306421at_nat @ A2 @ B2 ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8644_prod__Un,axiom,
% 9.25/5.26      ! [A2: set_nat,B2: set_nat,F2: nat > rat] :
% 9.25/5.26        ( ( finite_finite_nat @ A2 )
% 9.25/5.26       => ( ( finite_finite_nat @ B2 )
% 9.25/5.26         => ( ! [X2: nat] :
% 9.25/5.26                ( ( member_nat @ X2 @ ( inf_inf_set_nat @ A2 @ B2 ) )
% 9.25/5.26               => ( ( F2 @ X2 )
% 9.25/5.26                 != zero_zero_rat ) )
% 9.25/5.26           => ( ( groups73079841787564623at_rat @ F2 @ ( sup_sup_set_nat @ A2 @ B2 ) )
% 9.25/5.26              = ( divide_divide_rat @ ( times_times_rat @ ( groups73079841787564623at_rat @ F2 @ A2 ) @ ( groups73079841787564623at_rat @ F2 @ B2 ) ) @ ( groups73079841787564623at_rat @ F2 @ ( inf_inf_set_nat @ A2 @ B2 ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8645_atLeast1__lessThan__eq__remove0,axiom,
% 9.25/5.26      ! [N: nat] :
% 9.25/5.26        ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 9.25/5.26        = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8646_one__diff__power__eq_H,axiom,
% 9.25/5.26      ! [X: code_integer,N: nat] :
% 9.25/5.26        ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) )
% 9.25/5.26        = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X )
% 9.25/5.26          @ ( groups7501900531339628137nteger
% 9.25/5.26            @ ^ [I3: nat] : ( power_8256067586552552935nteger @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8647_one__diff__power__eq_H,axiom,
% 9.25/5.26      ! [X: rat,N: nat] :
% 9.25/5.26        ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 9.25/5.26        = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X )
% 9.25/5.26          @ ( groups2906978787729119204at_rat
% 9.25/5.26            @ ^ [I3: nat] : ( power_power_rat @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8648_one__diff__power__eq_H,axiom,
% 9.25/5.26      ! [X: int,N: nat] :
% 9.25/5.26        ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 9.25/5.26        = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 9.25/5.26          @ ( groups3539618377306564664at_int
% 9.25/5.26            @ ^ [I3: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N @ ( suc @ I3 ) ) )
% 9.25/5.26            @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8649_eucl__rel__int_Ocases,axiom,
% 9.25/5.26      ! [A1: int,A22: int,A32: product_prod_int_int] :
% 9.25/5.26        ( ( eucl_rel_int @ A1 @ A22 @ A32 )
% 9.25/5.26       => ( ( ( A22 = zero_zero_int )
% 9.25/5.26           => ( A32
% 9.25/5.26             != ( product_Pair_int_int @ zero_zero_int @ A1 ) ) )
% 9.25/5.26         => ( ! [Q7: int] :
% 9.25/5.26                ( ( A32
% 9.25/5.26                  = ( product_Pair_int_int @ Q7 @ zero_zero_int ) )
% 9.25/5.26               => ( ( A22 != zero_zero_int )
% 9.25/5.26                 => ( A1
% 9.25/5.26                   != ( times_times_int @ Q7 @ A22 ) ) ) )
% 9.25/5.26           => ~ ! [R6: int,Q7: int] :
% 9.25/5.26                  ( ( A32
% 9.25/5.26                    = ( product_Pair_int_int @ Q7 @ R6 ) )
% 9.25/5.26                 => ( ( ( sgn_sgn_int @ R6 )
% 9.25/5.26                      = ( sgn_sgn_int @ A22 ) )
% 9.25/5.26                   => ( ( ord_less_int @ ( abs_abs_int @ R6 ) @ ( abs_abs_int @ A22 ) )
% 9.25/5.26                     => ( A1
% 9.25/5.26                       != ( plus_plus_int @ ( times_times_int @ Q7 @ A22 ) @ R6 ) ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8650_eucl__rel__int_Osimps,axiom,
% 9.25/5.26      ( eucl_rel_int
% 9.25/5.26      = ( ^ [A12: int,A23: int,A33: product_prod_int_int] :
% 9.25/5.26            ( ? [K4: int] :
% 9.25/5.26                ( ( A12 = K4 )
% 9.25/5.26                & ( A23 = zero_zero_int )
% 9.25/5.26                & ( A33
% 9.25/5.26                  = ( product_Pair_int_int @ zero_zero_int @ K4 ) ) )
% 9.25/5.26            | ? [L2: int,K4: int,Q5: int] :
% 9.25/5.26                ( ( A12 = K4 )
% 9.25/5.26                & ( A23 = L2 )
% 9.25/5.26                & ( A33
% 9.25/5.26                  = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 9.25/5.26                & ( L2 != zero_zero_int )
% 9.25/5.26                & ( K4
% 9.25/5.26                  = ( times_times_int @ Q5 @ L2 ) ) )
% 9.25/5.26            | ? [R4: int,L2: int,K4: int,Q5: int] :
% 9.25/5.26                ( ( A12 = K4 )
% 9.25/5.26                & ( A23 = L2 )
% 9.25/5.26                & ( A33
% 9.25/5.26                  = ( product_Pair_int_int @ Q5 @ R4 ) )
% 9.25/5.26                & ( ( sgn_sgn_int @ R4 )
% 9.25/5.26                  = ( sgn_sgn_int @ L2 ) )
% 9.25/5.26                & ( ord_less_int @ ( abs_abs_int @ R4 ) @ ( abs_abs_int @ L2 ) )
% 9.25/5.26                & ( K4
% 9.25/5.26                  = ( plus_plus_int @ ( times_times_int @ Q5 @ L2 ) @ R4 ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8651_div__noneq__sgn__abs,axiom,
% 9.25/5.26      ! [L: int,K: int] :
% 9.25/5.26        ( ( L != zero_zero_int )
% 9.25/5.26       => ( ( ( sgn_sgn_int @ K )
% 9.25/5.26           != ( sgn_sgn_int @ L ) )
% 9.25/5.26         => ( ( divide_divide_int @ K @ L )
% 9.25/5.26            = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) )
% 9.25/5.26              @ ( zero_n2684676970156552555ol_int
% 9.25/5.26                @ ~ ( dvd_dvd_int @ L @ K ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8652_prod_Otriangle__reindex__eq,axiom,
% 9.25/5.26      ! [G2: nat > nat > nat,N: nat] :
% 9.25/5.26        ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G2 )
% 9.25/5.26          @ ( collec3392354462482085612at_nat
% 9.25/5.26            @ ( produc6081775807080527818_nat_o
% 9.25/5.26              @ ^ [I3: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 9.25/5.26        = ( groups708209901874060359at_nat
% 9.25/5.26          @ ^ [K4: nat] :
% 9.25/5.26              ( groups708209901874060359at_nat
% 9.25/5.26              @ ^ [I3: nat] : ( G2 @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 9.25/5.26              @ ( set_ord_atMost_nat @ K4 ) )
% 9.25/5.26          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8653_prod_Otriangle__reindex__eq,axiom,
% 9.25/5.26      ! [G2: nat > nat > int,N: nat] :
% 9.25/5.26        ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G2 )
% 9.25/5.26          @ ( collec3392354462482085612at_nat
% 9.25/5.26            @ ( produc6081775807080527818_nat_o
% 9.25/5.26              @ ^ [I3: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J3 ) @ N ) ) ) )
% 9.25/5.26        = ( groups705719431365010083at_int
% 9.25/5.26          @ ^ [K4: nat] :
% 9.25/5.26              ( groups705719431365010083at_int
% 9.25/5.26              @ ^ [I3: nat] : ( G2 @ I3 @ ( minus_minus_nat @ K4 @ I3 ) )
% 9.25/5.26              @ ( set_ord_atMost_nat @ K4 ) )
% 9.25/5.26          @ ( set_ord_atMost_nat @ N ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8654_drop__bit__rec,axiom,
% 9.25/5.26      ( bit_se8570568707652914677it_nat
% 9.25/5.26      = ( ^ [N2: nat,A3: nat] : ( if_nat @ ( N2 = zero_zero_nat ) @ A3 @ ( bit_se8570568707652914677it_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8655_drop__bit__rec,axiom,
% 9.25/5.26      ( bit_se3928097537394005634nteger
% 9.25/5.26      = ( ^ [N2: nat,A3: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ A3 @ ( bit_se3928097537394005634nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8656_drop__bit__rec,axiom,
% 9.25/5.26      ( bit_se2751692689150723149atural
% 9.25/5.26      = ( ^ [N2: nat,A3: code_natural] : ( if_Code_natural @ ( N2 = zero_zero_nat ) @ A3 @ ( bit_se2751692689150723149atural @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide5121882707175180666atural @ A3 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8657_drop__bit__rec,axiom,
% 9.25/5.26      ( bit_se8568078237143864401it_int
% 9.25/5.26      = ( ^ [N2: nat,A3: int] : ( if_int @ ( N2 = zero_zero_nat ) @ A3 @ ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8658_finite__compl,axiom,
% 9.25/5.26      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.26        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.26       => ( ( finite6177210948735845034at_nat @ ( uminus6524753893492686040at_nat @ A2 ) )
% 9.25/5.26          = ( finite6177210948735845034at_nat @ top_to4669805908274784177at_nat ) ) ) ).
% 9.25/5.26  
% 9.25/5.26  thf(fact_8659_finite__compl,axiom,
% 9.25/5.26      ! [A2: set_list_nat] :
% 9.25/5.26        ( ( finite8100373058378681591st_nat @ A2 )
% 9.25/5.26       => ( ( finite8100373058378681591st_nat @ ( uminus3195874150345416415st_nat @ A2 ) )
% 9.25/5.27          = ( finite8100373058378681591st_nat @ top_top_set_list_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8660_finite__compl,axiom,
% 9.25/5.27      ! [A2: set_o] :
% 9.25/5.27        ( ( finite_finite_o @ A2 )
% 9.25/5.27       => ( ( finite_finite_o @ ( uminus_uminus_set_o @ A2 ) )
% 9.25/5.27          = ( finite_finite_o @ top_top_set_o ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8661_finite__compl,axiom,
% 9.25/5.27      ! [A2: set_rat] :
% 9.25/5.27        ( ( finite_finite_rat @ A2 )
% 9.25/5.27       => ( ( finite_finite_rat @ ( uminus2201863774496077783et_rat @ A2 ) )
% 9.25/5.27          = ( finite_finite_rat @ top_top_set_rat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8662_finite__compl,axiom,
% 9.25/5.27      ! [A2: set_nat] :
% 9.25/5.27        ( ( finite_finite_nat @ A2 )
% 9.25/5.27       => ( ( finite_finite_nat @ ( uminus5710092332889474511et_nat @ A2 ) )
% 9.25/5.27          = ( finite_finite_nat @ top_top_set_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8663_finite__compl,axiom,
% 9.25/5.27      ! [A2: set_int] :
% 9.25/5.27        ( ( finite_finite_int @ A2 )
% 9.25/5.27       => ( ( finite_finite_int @ ( uminus1532241313380277803et_int @ A2 ) )
% 9.25/5.27          = ( finite_finite_int @ top_top_set_int ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8664_finite__Collect__le__nat,axiom,
% 9.25/5.27      ! [K: nat] :
% 9.25/5.27        ( finite_finite_nat
% 9.25/5.27        @ ( collect_nat
% 9.25/5.27          @ ^ [N2: nat] : ( ord_less_eq_nat @ N2 @ K ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8665_finite__Collect__less__nat,axiom,
% 9.25/5.27      ! [K: nat] :
% 9.25/5.27        ( finite_finite_nat
% 9.25/5.27        @ ( collect_nat
% 9.25/5.27          @ ^ [N2: nat] : ( ord_less_nat @ N2 @ K ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8666_finite__Collect__not,axiom,
% 9.25/5.27      ! [P: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.27        ( ( finite8744585540193469122nt_int @ ( collec5210948495886036740nt_int @ P ) )
% 9.25/5.27       => ( ( finite8744585540193469122nt_int
% 9.25/5.27            @ ( collec5210948495886036740nt_int
% 9.25/5.27              @ ^ [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.27                  ~ ( P @ X3 ) ) )
% 9.25/5.27          = ( finite8744585540193469122nt_int @ top_to6034159466715884489nt_int ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8667_finite__Collect__not,axiom,
% 9.25/5.27      ! [P: set_nat > $o] :
% 9.25/5.27        ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 9.25/5.27       => ( ( finite1152437895449049373et_nat
% 9.25/5.27            @ ( collect_set_nat
% 9.25/5.27              @ ^ [X3: set_nat] :
% 9.25/5.27                  ~ ( P @ X3 ) ) )
% 9.25/5.27          = ( finite1152437895449049373et_nat @ top_top_set_set_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8668_finite__Collect__not,axiom,
% 9.25/5.27      ! [P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.27        ( ( finite3252695134891459830_nat_o @ ( collec939566748876313656_nat_o @ P ) )
% 9.25/5.27       => ( ( finite3252695134891459830_nat_o
% 9.25/5.27            @ ( collec939566748876313656_nat_o
% 9.25/5.27              @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.27                  ~ ( P @ X3 ) ) )
% 9.25/5.27          = ( finite3252695134891459830_nat_o @ top_to4869887016220417533_nat_o ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8669_finite__Collect__not,axiom,
% 9.25/5.27      ! [P: product_prod_nat_nat > $o] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ P ) )
% 9.25/5.27       => ( ( finite6177210948735845034at_nat
% 9.25/5.27            @ ( collec3392354462482085612at_nat
% 9.25/5.27              @ ^ [X3: product_prod_nat_nat] :
% 9.25/5.27                  ~ ( P @ X3 ) ) )
% 9.25/5.27          = ( finite6177210948735845034at_nat @ top_to4669805908274784177at_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8670_finite__Collect__not,axiom,
% 9.25/5.27      ! [P: list_nat > $o] :
% 9.25/5.27        ( ( finite8100373058378681591st_nat @ ( collect_list_nat @ P ) )
% 9.25/5.27       => ( ( finite8100373058378681591st_nat
% 9.25/5.27            @ ( collect_list_nat
% 9.25/5.27              @ ^ [X3: list_nat] :
% 9.25/5.27                  ~ ( P @ X3 ) ) )
% 9.25/5.27          = ( finite8100373058378681591st_nat @ top_top_set_list_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8671_finite__Collect__not,axiom,
% 9.25/5.27      ! [P: $o > $o] :
% 9.25/5.27        ( ( finite_finite_o @ ( collect_o @ P ) )
% 9.25/5.27       => ( ( finite_finite_o
% 9.25/5.27            @ ( collect_o
% 9.25/5.27              @ ^ [X3: $o] :
% 9.25/5.27                  ~ ( P @ X3 ) ) )
% 9.25/5.27          = ( finite_finite_o @ top_top_set_o ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8672_finite__Collect__not,axiom,
% 9.25/5.27      ! [P: rat > $o] :
% 9.25/5.27        ( ( finite_finite_rat @ ( collect_rat @ P ) )
% 9.25/5.27       => ( ( finite_finite_rat
% 9.25/5.27            @ ( collect_rat
% 9.25/5.27              @ ^ [X3: rat] :
% 9.25/5.27                  ~ ( P @ X3 ) ) )
% 9.25/5.27          = ( finite_finite_rat @ top_top_set_rat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8673_finite__Collect__not,axiom,
% 9.25/5.27      ! [P: nat > $o] :
% 9.25/5.27        ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 9.25/5.27       => ( ( finite_finite_nat
% 9.25/5.27            @ ( collect_nat
% 9.25/5.27              @ ^ [X3: nat] :
% 9.25/5.27                  ~ ( P @ X3 ) ) )
% 9.25/5.27          = ( finite_finite_nat @ top_top_set_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8674_finite__Collect__not,axiom,
% 9.25/5.27      ! [P: int > $o] :
% 9.25/5.27        ( ( finite_finite_int @ ( collect_int @ P ) )
% 9.25/5.27       => ( ( finite_finite_int
% 9.25/5.27            @ ( collect_int
% 9.25/5.27              @ ^ [X3: int] :
% 9.25/5.27                  ~ ( P @ X3 ) ) )
% 9.25/5.27          = ( finite_finite_int @ top_top_set_int ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8675_finite__Collect__subsets,axiom,
% 9.25/5.27      ! [A2: set_Pr958786334691620121nt_int] :
% 9.25/5.27        ( ( finite2998713641127702882nt_int @ A2 )
% 9.25/5.27       => ( finite8744585540193469122nt_int
% 9.25/5.27          @ ( collec5210948495886036740nt_int
% 9.25/5.27            @ ^ [B4: set_Pr958786334691620121nt_int] : ( ord_le2843351958646193337nt_int @ B4 @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8676_finite__Collect__subsets,axiom,
% 9.25/5.27      ! [A2: set_int] :
% 9.25/5.27        ( ( finite_finite_int @ A2 )
% 9.25/5.27       => ( finite6197958912794628473et_int
% 9.25/5.27          @ ( collect_set_int
% 9.25/5.27            @ ^ [B4: set_int] : ( ord_less_eq_set_int @ B4 @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8677_finite__Collect__subsets,axiom,
% 9.25/5.27      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.27       => ( finite9047747110432174090at_nat
% 9.25/5.27          @ ( collec5514110066124741708at_nat
% 9.25/5.27            @ ^ [B4: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ B4 @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8678_finite__Collect__subsets,axiom,
% 9.25/5.27      ! [A2: set_nat] :
% 9.25/5.27        ( ( finite_finite_nat @ A2 )
% 9.25/5.27       => ( finite1152437895449049373et_nat
% 9.25/5.27          @ ( collect_set_nat
% 9.25/5.27            @ ^ [B4: set_nat] : ( ord_less_eq_set_nat @ B4 @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8679_finite__finite__vimage__IntI,axiom,
% 9.25/5.27      ! [F4: set_o,H3: int > $o,A2: set_int] :
% 9.25/5.27        ( ( finite_finite_o @ F4 )
% 9.25/5.27       => ( ! [Y2: $o] :
% 9.25/5.27              ( ( member_o @ Y2 @ F4 )
% 9.25/5.27             => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_o @ H3 @ ( insert_o @ Y2 @ bot_bot_set_o ) ) @ A2 ) ) )
% 9.25/5.27         => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_o @ H3 @ F4 ) @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8680_finite__finite__vimage__IntI,axiom,
% 9.25/5.27      ! [F4: set_o,H3: nat > $o,A2: set_nat] :
% 9.25/5.27        ( ( finite_finite_o @ F4 )
% 9.25/5.27       => ( ! [Y2: $o] :
% 9.25/5.27              ( ( member_o @ Y2 @ F4 )
% 9.25/5.27             => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_o @ H3 @ ( insert_o @ Y2 @ bot_bot_set_o ) ) @ A2 ) ) )
% 9.25/5.27         => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_o @ H3 @ F4 ) @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8681_finite__finite__vimage__IntI,axiom,
% 9.25/5.27      ! [F4: set_nat,H3: int > nat,A2: set_int] :
% 9.25/5.27        ( ( finite_finite_nat @ F4 )
% 9.25/5.27       => ( ! [Y2: nat] :
% 9.25/5.27              ( ( member_nat @ Y2 @ F4 )
% 9.25/5.27             => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_nat @ H3 @ ( insert_nat @ Y2 @ bot_bot_set_nat ) ) @ A2 ) ) )
% 9.25/5.27         => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_nat @ H3 @ F4 ) @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8682_finite__finite__vimage__IntI,axiom,
% 9.25/5.27      ! [F4: set_nat,H3: nat > nat,A2: set_nat] :
% 9.25/5.27        ( ( finite_finite_nat @ F4 )
% 9.25/5.27       => ( ! [Y2: nat] :
% 9.25/5.27              ( ( member_nat @ Y2 @ F4 )
% 9.25/5.27             => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_nat @ H3 @ ( insert_nat @ Y2 @ bot_bot_set_nat ) ) @ A2 ) ) )
% 9.25/5.27         => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_nat @ H3 @ F4 ) @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8683_finite__finite__vimage__IntI,axiom,
% 9.25/5.27      ! [F4: set_int,H3: int > int,A2: set_int] :
% 9.25/5.27        ( ( finite_finite_int @ F4 )
% 9.25/5.27       => ( ! [Y2: int] :
% 9.25/5.27              ( ( member_int @ Y2 @ F4 )
% 9.25/5.27             => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_int @ H3 @ ( insert_int @ Y2 @ bot_bot_set_int ) ) @ A2 ) ) )
% 9.25/5.27         => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_int @ H3 @ F4 ) @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8684_finite__finite__vimage__IntI,axiom,
% 9.25/5.27      ! [F4: set_int,H3: nat > int,A2: set_nat] :
% 9.25/5.27        ( ( finite_finite_int @ F4 )
% 9.25/5.27       => ( ! [Y2: int] :
% 9.25/5.27              ( ( member_int @ Y2 @ F4 )
% 9.25/5.27             => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_int @ H3 @ ( insert_int @ Y2 @ bot_bot_set_int ) ) @ A2 ) ) )
% 9.25/5.27         => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_int @ H3 @ F4 ) @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8685_finite__finite__vimage__IntI,axiom,
% 9.25/5.27      ! [F4: set_set_nat,H3: int > set_nat,A2: set_int] :
% 9.25/5.27        ( ( finite1152437895449049373et_nat @ F4 )
% 9.25/5.27       => ( ! [Y2: set_nat] :
% 9.25/5.27              ( ( member_set_nat @ Y2 @ F4 )
% 9.25/5.27             => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_set_nat @ H3 @ ( insert_set_nat @ Y2 @ bot_bot_set_set_nat ) ) @ A2 ) ) )
% 9.25/5.27         => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage_int_set_nat @ H3 @ F4 ) @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8686_finite__finite__vimage__IntI,axiom,
% 9.25/5.27      ! [F4: set_set_nat,H3: nat > set_nat,A2: set_nat] :
% 9.25/5.27        ( ( finite1152437895449049373et_nat @ F4 )
% 9.25/5.27       => ( ! [Y2: set_nat] :
% 9.25/5.27              ( ( member_set_nat @ Y2 @ F4 )
% 9.25/5.27             => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_set_nat @ H3 @ ( insert_set_nat @ Y2 @ bot_bot_set_set_nat ) ) @ A2 ) ) )
% 9.25/5.27         => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage_nat_set_nat @ H3 @ F4 ) @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8687_finite__finite__vimage__IntI,axiom,
% 9.25/5.27      ! [F4: set_Pr1261947904930325089at_nat,H3: int > product_prod_nat_nat,A2: set_int] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat @ F4 )
% 9.25/5.27       => ( ! [Y2: product_prod_nat_nat] :
% 9.25/5.27              ( ( member8440522571783428010at_nat @ Y2 @ F4 )
% 9.25/5.27             => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage1827798767263827160at_nat @ H3 @ ( insert8211810215607154385at_nat @ Y2 @ bot_bo2099793752762293965at_nat ) ) @ A2 ) ) )
% 9.25/5.27         => ( finite_finite_int @ ( inf_inf_set_int @ ( vimage1827798767263827160at_nat @ H3 @ F4 ) @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8688_finite__finite__vimage__IntI,axiom,
% 9.25/5.27      ! [F4: set_Pr1261947904930325089at_nat,H3: nat > product_prod_nat_nat,A2: set_nat] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat @ F4 )
% 9.25/5.27       => ( ! [Y2: product_prod_nat_nat] :
% 9.25/5.27              ( ( member8440522571783428010at_nat @ Y2 @ F4 )
% 9.25/5.27             => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage8013328719654469172at_nat @ H3 @ ( insert8211810215607154385at_nat @ Y2 @ bot_bo2099793752762293965at_nat ) ) @ A2 ) ) )
% 9.25/5.27         => ( finite_finite_nat @ ( inf_inf_set_nat @ ( vimage8013328719654469172at_nat @ H3 @ F4 ) @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8689_finite__Collect__conjI,axiom,
% 9.25/5.27      ! [P: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.27        ( ( ( finite8744585540193469122nt_int @ ( collec5210948495886036740nt_int @ P ) )
% 9.25/5.27          | ( finite8744585540193469122nt_int @ ( collec5210948495886036740nt_int @ Q2 ) ) )
% 9.25/5.27       => ( finite8744585540193469122nt_int
% 9.25/5.27          @ ( collec5210948495886036740nt_int
% 9.25/5.27            @ ^ [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.27                ( ( P @ X3 )
% 9.25/5.27                & ( Q2 @ X3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8690_finite__Collect__conjI,axiom,
% 9.25/5.27      ! [P: set_nat > $o,Q2: set_nat > $o] :
% 9.25/5.27        ( ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 9.25/5.27          | ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q2 ) ) )
% 9.25/5.27       => ( finite1152437895449049373et_nat
% 9.25/5.27          @ ( collect_set_nat
% 9.25/5.27            @ ^ [X3: set_nat] :
% 9.25/5.27                ( ( P @ X3 )
% 9.25/5.27                & ( Q2 @ X3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8691_finite__Collect__conjI,axiom,
% 9.25/5.27      ! [P: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.27        ( ( ( finite3252695134891459830_nat_o @ ( collec939566748876313656_nat_o @ P ) )
% 9.25/5.27          | ( finite3252695134891459830_nat_o @ ( collec939566748876313656_nat_o @ Q2 ) ) )
% 9.25/5.27       => ( finite3252695134891459830_nat_o
% 9.25/5.27          @ ( collec939566748876313656_nat_o
% 9.25/5.27            @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.27                ( ( P @ X3 )
% 9.25/5.27                & ( Q2 @ X3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8692_finite__Collect__conjI,axiom,
% 9.25/5.27      ! [P: nat > $o,Q2: nat > $o] :
% 9.25/5.27        ( ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 9.25/5.27          | ( finite_finite_nat @ ( collect_nat @ Q2 ) ) )
% 9.25/5.27       => ( finite_finite_nat
% 9.25/5.27          @ ( collect_nat
% 9.25/5.27            @ ^ [X3: nat] :
% 9.25/5.27                ( ( P @ X3 )
% 9.25/5.27                & ( Q2 @ X3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8693_finite__Collect__conjI,axiom,
% 9.25/5.27      ! [P: int > $o,Q2: int > $o] :
% 9.25/5.27        ( ( ( finite_finite_int @ ( collect_int @ P ) )
% 9.25/5.27          | ( finite_finite_int @ ( collect_int @ Q2 ) ) )
% 9.25/5.27       => ( finite_finite_int
% 9.25/5.27          @ ( collect_int
% 9.25/5.27            @ ^ [X3: int] :
% 9.25/5.27                ( ( P @ X3 )
% 9.25/5.27                & ( Q2 @ X3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8694_finite__Collect__conjI,axiom,
% 9.25/5.27      ! [P: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > $o] :
% 9.25/5.27        ( ( ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ P ) )
% 9.25/5.27          | ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ Q2 ) ) )
% 9.25/5.27       => ( finite6177210948735845034at_nat
% 9.25/5.27          @ ( collec3392354462482085612at_nat
% 9.25/5.27            @ ^ [X3: product_prod_nat_nat] :
% 9.25/5.27                ( ( P @ X3 )
% 9.25/5.27                & ( Q2 @ X3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8695_finite__Collect__disjI,axiom,
% 9.25/5.27      ! [P: set_Pr958786334691620121nt_int > $o,Q2: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.27        ( ( finite8744585540193469122nt_int
% 9.25/5.27          @ ( collec5210948495886036740nt_int
% 9.25/5.27            @ ^ [X3: set_Pr958786334691620121nt_int] :
% 9.25/5.27                ( ( P @ X3 )
% 9.25/5.27                | ( Q2 @ X3 ) ) ) )
% 9.25/5.27        = ( ( finite8744585540193469122nt_int @ ( collec5210948495886036740nt_int @ P ) )
% 9.25/5.27          & ( finite8744585540193469122nt_int @ ( collec5210948495886036740nt_int @ Q2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8696_finite__Collect__disjI,axiom,
% 9.25/5.27      ! [P: set_nat > $o,Q2: set_nat > $o] :
% 9.25/5.27        ( ( finite1152437895449049373et_nat
% 9.25/5.27          @ ( collect_set_nat
% 9.25/5.27            @ ^ [X3: set_nat] :
% 9.25/5.27                ( ( P @ X3 )
% 9.25/5.27                | ( Q2 @ X3 ) ) ) )
% 9.25/5.27        = ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 9.25/5.27          & ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8697_finite__Collect__disjI,axiom,
% 9.25/5.27      ! [P: ( produc3658429121746597890et_nat > $o ) > $o,Q2: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.27        ( ( finite3252695134891459830_nat_o
% 9.25/5.27          @ ( collec939566748876313656_nat_o
% 9.25/5.27            @ ^ [X3: produc3658429121746597890et_nat > $o] :
% 9.25/5.27                ( ( P @ X3 )
% 9.25/5.27                | ( Q2 @ X3 ) ) ) )
% 9.25/5.27        = ( ( finite3252695134891459830_nat_o @ ( collec939566748876313656_nat_o @ P ) )
% 9.25/5.27          & ( finite3252695134891459830_nat_o @ ( collec939566748876313656_nat_o @ Q2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8698_finite__Collect__disjI,axiom,
% 9.25/5.27      ! [P: nat > $o,Q2: nat > $o] :
% 9.25/5.27        ( ( finite_finite_nat
% 9.25/5.27          @ ( collect_nat
% 9.25/5.27            @ ^ [X3: nat] :
% 9.25/5.27                ( ( P @ X3 )
% 9.25/5.27                | ( Q2 @ X3 ) ) ) )
% 9.25/5.27        = ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 9.25/5.27          & ( finite_finite_nat @ ( collect_nat @ Q2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8699_finite__Collect__disjI,axiom,
% 9.25/5.27      ! [P: int > $o,Q2: int > $o] :
% 9.25/5.27        ( ( finite_finite_int
% 9.25/5.27          @ ( collect_int
% 9.25/5.27            @ ^ [X3: int] :
% 9.25/5.27                ( ( P @ X3 )
% 9.25/5.27                | ( Q2 @ X3 ) ) ) )
% 9.25/5.27        = ( ( finite_finite_int @ ( collect_int @ P ) )
% 9.25/5.27          & ( finite_finite_int @ ( collect_int @ Q2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8700_finite__Collect__disjI,axiom,
% 9.25/5.27      ! [P: product_prod_nat_nat > $o,Q2: product_prod_nat_nat > $o] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat
% 9.25/5.27          @ ( collec3392354462482085612at_nat
% 9.25/5.27            @ ^ [X3: product_prod_nat_nat] :
% 9.25/5.27                ( ( P @ X3 )
% 9.25/5.27                | ( Q2 @ X3 ) ) ) )
% 9.25/5.27        = ( ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ P ) )
% 9.25/5.27          & ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ Q2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8701_finite__interval__int1,axiom,
% 9.25/5.27      ! [A: int,B: int] :
% 9.25/5.27        ( finite_finite_int
% 9.25/5.27        @ ( collect_int
% 9.25/5.27          @ ^ [I3: int] :
% 9.25/5.27              ( ( ord_less_eq_int @ A @ I3 )
% 9.25/5.27              & ( ord_less_eq_int @ I3 @ B ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8702_finite__interval__int4,axiom,
% 9.25/5.27      ! [A: int,B: int] :
% 9.25/5.27        ( finite_finite_int
% 9.25/5.27        @ ( collect_int
% 9.25/5.27          @ ^ [I3: int] :
% 9.25/5.27              ( ( ord_less_int @ A @ I3 )
% 9.25/5.27              & ( ord_less_int @ I3 @ B ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8703_finite__Plus__UNIV__iff,axiom,
% 9.25/5.27      ( ( finite6699802884135759036um_o_o @ top_to1686961084667892491um_o_o )
% 9.25/5.27      = ( ( finite_finite_o @ top_top_set_o )
% 9.25/5.27        & ( finite_finite_o @ top_top_set_o ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8704_finite__Plus__UNIV__iff,axiom,
% 9.25/5.27      ( ( finite2301497163391418442_o_rat @ top_to8915897456388626257_o_rat )
% 9.25/5.27      = ( ( finite_finite_o @ top_top_set_o )
% 9.25/5.27        & ( finite_finite_rat @ top_top_set_rat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8705_finite__Plus__UNIV__iff,axiom,
% 9.25/5.27      ( ( finite5809725721784815170_o_nat @ top_to6072511757011528009_o_nat )
% 9.25/5.27      = ( ( finite_finite_o @ top_top_set_o )
% 9.25/5.27        & ( finite_finite_nat @ top_top_set_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8706_finite__Plus__UNIV__iff,axiom,
% 9.25/5.27      ( ( finite1631874702275618462_o_int @ top_to3582428612079801253_o_int )
% 9.25/5.27      = ( ( finite_finite_o @ top_top_set_o )
% 9.25/5.27        & ( finite_finite_int @ top_top_set_int ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8707_finite__Plus__UNIV__iff,axiom,
% 9.25/5.27      ( ( finite5580927318523740128_rat_o @ top_to6370680384054995943_rat_o )
% 9.25/5.27      = ( ( finite_finite_rat @ top_top_set_rat )
% 9.25/5.27        & ( finite_finite_o @ top_top_set_o ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8708_finite__Plus__UNIV__iff,axiom,
% 9.25/5.27      ( ( finite2362923481445498406at_rat @ top_to5104522503381003637at_rat )
% 9.25/5.27      = ( ( finite_finite_rat @ top_top_set_rat )
% 9.25/5.27        & ( finite_finite_rat @ top_top_set_rat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8709_finite__Plus__UNIV__iff,axiom,
% 9.25/5.27      ( ( finite5871152039838895134at_nat @ top_to2261136804003905389at_nat )
% 9.25/5.27      = ( ( finite_finite_rat @ top_top_set_rat )
% 9.25/5.27        & ( finite_finite_nat @ top_top_set_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8710_finite__Plus__UNIV__iff,axiom,
% 9.25/5.27      ( ( finite1693301020329698426at_int @ top_to8994425695926954441at_int )
% 9.25/5.27      = ( ( finite_finite_rat @ top_top_set_rat )
% 9.25/5.27        & ( finite_finite_int @ top_top_set_int ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8711_finite__Plus__UNIV__iff,axiom,
% 9.25/5.27      ( ( finite94888208985532392_nat_o @ top_to7120114879189831663_nat_o )
% 9.25/5.27      = ( ( finite_finite_nat @ top_top_set_nat )
% 9.25/5.27        & ( finite_finite_o @ top_top_set_o ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8712_finite__Plus__UNIV__iff,axiom,
% 9.25/5.27      ( ( finite2679478125380364318at_rat @ top_to281834657035230061at_rat )
% 9.25/5.27      = ( ( finite_finite_nat @ top_top_set_nat )
% 9.25/5.27        & ( finite_finite_rat @ top_top_set_rat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8713_finite__Int,axiom,
% 9.25/5.27      ! [F4: set_int,G3: set_int] :
% 9.25/5.27        ( ( ( finite_finite_int @ F4 )
% 9.25/5.27          | ( finite_finite_int @ G3 ) )
% 9.25/5.27       => ( finite_finite_int @ ( inf_inf_set_int @ F4 @ G3 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8714_finite__Int,axiom,
% 9.25/5.27      ! [F4: set_Pr1261947904930325089at_nat,G3: set_Pr1261947904930325089at_nat] :
% 9.25/5.27        ( ( ( finite6177210948735845034at_nat @ F4 )
% 9.25/5.27          | ( finite6177210948735845034at_nat @ G3 ) )
% 9.25/5.27       => ( finite6177210948735845034at_nat @ ( inf_in2572325071724192079at_nat @ F4 @ G3 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8715_finite__Int,axiom,
% 9.25/5.27      ! [F4: set_nat,G3: set_nat] :
% 9.25/5.27        ( ( ( finite_finite_nat @ F4 )
% 9.25/5.27          | ( finite_finite_nat @ G3 ) )
% 9.25/5.27       => ( finite_finite_nat @ ( inf_inf_set_nat @ F4 @ G3 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8716_finite__Un,axiom,
% 9.25/5.27      ! [F4: set_int,G3: set_int] :
% 9.25/5.27        ( ( finite_finite_int @ ( sup_sup_set_int @ F4 @ G3 ) )
% 9.25/5.27        = ( ( finite_finite_int @ F4 )
% 9.25/5.27          & ( finite_finite_int @ G3 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8717_finite__Un,axiom,
% 9.25/5.27      ! [F4: set_Pr1261947904930325089at_nat,G3: set_Pr1261947904930325089at_nat] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ F4 @ G3 ) )
% 9.25/5.27        = ( ( finite6177210948735845034at_nat @ F4 )
% 9.25/5.27          & ( finite6177210948735845034at_nat @ G3 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8718_finite__Un,axiom,
% 9.25/5.27      ! [F4: set_Pr8551490117392284871at_nat,G3: set_Pr8551490117392284871at_nat] :
% 9.25/5.27        ( ( finite1918287321285529104at_nat @ ( sup_su3035147773818789531at_nat @ F4 @ G3 ) )
% 9.25/5.27        = ( ( finite1918287321285529104at_nat @ F4 )
% 9.25/5.27          & ( finite1918287321285529104at_nat @ G3 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8719_finite__Un,axiom,
% 9.25/5.27      ! [F4: set_Pr4329608150637261639at_nat,G3: set_Pr4329608150637261639at_nat] :
% 9.25/5.27        ( ( finite4343798906461161616at_nat @ ( sup_su5525570899277871387at_nat @ F4 @ G3 ) )
% 9.25/5.27        = ( ( finite4343798906461161616at_nat @ F4 )
% 9.25/5.27          & ( finite4343798906461161616at_nat @ G3 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8720_finite__Un,axiom,
% 9.25/5.27      ! [F4: set_nat,G3: set_nat] :
% 9.25/5.27        ( ( finite_finite_nat @ ( sup_sup_set_nat @ F4 @ G3 ) )
% 9.25/5.27        = ( ( finite_finite_nat @ F4 )
% 9.25/5.27          & ( finite_finite_nat @ G3 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8721_finite__interval__int2,axiom,
% 9.25/5.27      ! [A: int,B: int] :
% 9.25/5.27        ( finite_finite_int
% 9.25/5.27        @ ( collect_int
% 9.25/5.27          @ ^ [I3: int] :
% 9.25/5.27              ( ( ord_less_eq_int @ A @ I3 )
% 9.25/5.27              & ( ord_less_int @ I3 @ B ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8722_finite__interval__int3,axiom,
% 9.25/5.27      ! [A: int,B: int] :
% 9.25/5.27        ( finite_finite_int
% 9.25/5.27        @ ( collect_int
% 9.25/5.27          @ ^ [I3: int] :
% 9.25/5.27              ( ( ord_less_int @ A @ I3 )
% 9.25/5.27              & ( ord_less_eq_int @ I3 @ B ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8723_infinite__UNIV__int,axiom,
% 9.25/5.27      ~ ( finite_finite_int @ top_top_set_int ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8724_finite__divisors__int,axiom,
% 9.25/5.27      ! [I: int] :
% 9.25/5.27        ( ( I != zero_zero_int )
% 9.25/5.27       => ( finite_finite_int
% 9.25/5.27          @ ( collect_int
% 9.25/5.27            @ ^ [D4: int] : ( dvd_dvd_int @ D4 @ I ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8725_infinite__UNIV__nat,axiom,
% 9.25/5.27      ~ ( finite_finite_nat @ top_top_set_nat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8726_not__finite__existsD,axiom,
% 9.25/5.27      ! [P: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.27        ( ~ ( finite8744585540193469122nt_int @ ( collec5210948495886036740nt_int @ P ) )
% 9.25/5.27       => ? [X_1: set_Pr958786334691620121nt_int] : ( P @ X_1 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8727_not__finite__existsD,axiom,
% 9.25/5.27      ! [P: set_nat > $o] :
% 9.25/5.27        ( ~ ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 9.25/5.27       => ? [X_1: set_nat] : ( P @ X_1 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8728_not__finite__existsD,axiom,
% 9.25/5.27      ! [P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.27        ( ~ ( finite3252695134891459830_nat_o @ ( collec939566748876313656_nat_o @ P ) )
% 9.25/5.27       => ? [X_1: produc3658429121746597890et_nat > $o] : ( P @ X_1 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8729_not__finite__existsD,axiom,
% 9.25/5.27      ! [P: nat > $o] :
% 9.25/5.27        ( ~ ( finite_finite_nat @ ( collect_nat @ P ) )
% 9.25/5.27       => ? [X_1: nat] : ( P @ X_1 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8730_not__finite__existsD,axiom,
% 9.25/5.27      ! [P: int > $o] :
% 9.25/5.27        ( ~ ( finite_finite_int @ ( collect_int @ P ) )
% 9.25/5.27       => ? [X_1: int] : ( P @ X_1 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8731_not__finite__existsD,axiom,
% 9.25/5.27      ! [P: product_prod_nat_nat > $o] :
% 9.25/5.27        ( ~ ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ P ) )
% 9.25/5.27       => ? [X_1: product_prod_nat_nat] : ( P @ X_1 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8732_pigeonhole__infinite__rel,axiom,
% 9.25/5.27      ! [A2: set_nat,B2: set_nat,R: nat > nat > $o] :
% 9.25/5.27        ( ~ ( finite_finite_nat @ A2 )
% 9.25/5.27       => ( ( finite_finite_nat @ B2 )
% 9.25/5.27         => ( ! [X2: nat] :
% 9.25/5.27                ( ( member_nat @ X2 @ A2 )
% 9.25/5.27               => ? [Xa2: nat] :
% 9.25/5.27                    ( ( member_nat @ Xa2 @ B2 )
% 9.25/5.27                    & ( R @ X2 @ Xa2 ) ) )
% 9.25/5.27           => ? [X2: nat] :
% 9.25/5.27                ( ( member_nat @ X2 @ B2 )
% 9.25/5.27                & ~ ( finite_finite_nat
% 9.25/5.27                    @ ( collect_nat
% 9.25/5.27                      @ ^ [A3: nat] :
% 9.25/5.27                          ( ( member_nat @ A3 @ A2 )
% 9.25/5.27                          & ( R @ A3 @ X2 ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8733_pigeonhole__infinite__rel,axiom,
% 9.25/5.27      ! [A2: set_nat,B2: set_int,R: nat > int > $o] :
% 9.25/5.27        ( ~ ( finite_finite_nat @ A2 )
% 9.25/5.27       => ( ( finite_finite_int @ B2 )
% 9.25/5.27         => ( ! [X2: nat] :
% 9.25/5.27                ( ( member_nat @ X2 @ A2 )
% 9.25/5.27               => ? [Xa2: int] :
% 9.25/5.27                    ( ( member_int @ Xa2 @ B2 )
% 9.25/5.27                    & ( R @ X2 @ Xa2 ) ) )
% 9.25/5.27           => ? [X2: int] :
% 9.25/5.27                ( ( member_int @ X2 @ B2 )
% 9.25/5.27                & ~ ( finite_finite_nat
% 9.25/5.27                    @ ( collect_nat
% 9.25/5.27                      @ ^ [A3: nat] :
% 9.25/5.27                          ( ( member_nat @ A3 @ A2 )
% 9.25/5.27                          & ( R @ A3 @ X2 ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8734_pigeonhole__infinite__rel,axiom,
% 9.25/5.27      ! [A2: set_int,B2: set_nat,R: int > nat > $o] :
% 9.25/5.27        ( ~ ( finite_finite_int @ A2 )
% 9.25/5.27       => ( ( finite_finite_nat @ B2 )
% 9.25/5.27         => ( ! [X2: int] :
% 9.25/5.27                ( ( member_int @ X2 @ A2 )
% 9.25/5.27               => ? [Xa2: nat] :
% 9.25/5.27                    ( ( member_nat @ Xa2 @ B2 )
% 9.25/5.27                    & ( R @ X2 @ Xa2 ) ) )
% 9.25/5.27           => ? [X2: nat] :
% 9.25/5.27                ( ( member_nat @ X2 @ B2 )
% 9.25/5.27                & ~ ( finite_finite_int
% 9.25/5.27                    @ ( collect_int
% 9.25/5.27                      @ ^ [A3: int] :
% 9.25/5.27                          ( ( member_int @ A3 @ A2 )
% 9.25/5.27                          & ( R @ A3 @ X2 ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8735_pigeonhole__infinite__rel,axiom,
% 9.25/5.27      ! [A2: set_int,B2: set_int,R: int > int > $o] :
% 9.25/5.27        ( ~ ( finite_finite_int @ A2 )
% 9.25/5.27       => ( ( finite_finite_int @ B2 )
% 9.25/5.27         => ( ! [X2: int] :
% 9.25/5.27                ( ( member_int @ X2 @ A2 )
% 9.25/5.27               => ? [Xa2: int] :
% 9.25/5.27                    ( ( member_int @ Xa2 @ B2 )
% 9.25/5.27                    & ( R @ X2 @ Xa2 ) ) )
% 9.25/5.27           => ? [X2: int] :
% 9.25/5.27                ( ( member_int @ X2 @ B2 )
% 9.25/5.27                & ~ ( finite_finite_int
% 9.25/5.27                    @ ( collect_int
% 9.25/5.27                      @ ^ [A3: int] :
% 9.25/5.27                          ( ( member_int @ A3 @ A2 )
% 9.25/5.27                          & ( R @ A3 @ X2 ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8736_pigeonhole__infinite__rel,axiom,
% 9.25/5.27      ! [A2: set_set_nat,B2: set_nat,R: set_nat > nat > $o] :
% 9.25/5.27        ( ~ ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.27       => ( ( finite_finite_nat @ B2 )
% 9.25/5.27         => ( ! [X2: set_nat] :
% 9.25/5.27                ( ( member_set_nat @ X2 @ A2 )
% 9.25/5.27               => ? [Xa2: nat] :
% 9.25/5.27                    ( ( member_nat @ Xa2 @ B2 )
% 9.25/5.27                    & ( R @ X2 @ Xa2 ) ) )
% 9.25/5.27           => ? [X2: nat] :
% 9.25/5.27                ( ( member_nat @ X2 @ B2 )
% 9.25/5.27                & ~ ( finite1152437895449049373et_nat
% 9.25/5.27                    @ ( collect_set_nat
% 9.25/5.27                      @ ^ [A3: set_nat] :
% 9.25/5.27                          ( ( member_set_nat @ A3 @ A2 )
% 9.25/5.27                          & ( R @ A3 @ X2 ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8737_pigeonhole__infinite__rel,axiom,
% 9.25/5.27      ! [A2: set_set_nat,B2: set_int,R: set_nat > int > $o] :
% 9.25/5.27        ( ~ ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.27       => ( ( finite_finite_int @ B2 )
% 9.25/5.27         => ( ! [X2: set_nat] :
% 9.25/5.27                ( ( member_set_nat @ X2 @ A2 )
% 9.25/5.27               => ? [Xa2: int] :
% 9.25/5.27                    ( ( member_int @ Xa2 @ B2 )
% 9.25/5.27                    & ( R @ X2 @ Xa2 ) ) )
% 9.25/5.27           => ? [X2: int] :
% 9.25/5.27                ( ( member_int @ X2 @ B2 )
% 9.25/5.27                & ~ ( finite1152437895449049373et_nat
% 9.25/5.27                    @ ( collect_set_nat
% 9.25/5.27                      @ ^ [A3: set_nat] :
% 9.25/5.27                          ( ( member_set_nat @ A3 @ A2 )
% 9.25/5.27                          & ( R @ A3 @ X2 ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8738_pigeonhole__infinite__rel,axiom,
% 9.25/5.27      ! [A2: set_nat,B2: set_Pr1261947904930325089at_nat,R: nat > product_prod_nat_nat > $o] :
% 9.25/5.27        ( ~ ( finite_finite_nat @ A2 )
% 9.25/5.27       => ( ( finite6177210948735845034at_nat @ B2 )
% 9.25/5.27         => ( ! [X2: nat] :
% 9.25/5.27                ( ( member_nat @ X2 @ A2 )
% 9.25/5.27               => ? [Xa2: product_prod_nat_nat] :
% 9.25/5.27                    ( ( member8440522571783428010at_nat @ Xa2 @ B2 )
% 9.25/5.27                    & ( R @ X2 @ Xa2 ) ) )
% 9.25/5.27           => ? [X2: product_prod_nat_nat] :
% 9.25/5.27                ( ( member8440522571783428010at_nat @ X2 @ B2 )
% 9.25/5.27                & ~ ( finite_finite_nat
% 9.25/5.27                    @ ( collect_nat
% 9.25/5.27                      @ ^ [A3: nat] :
% 9.25/5.27                          ( ( member_nat @ A3 @ A2 )
% 9.25/5.27                          & ( R @ A3 @ X2 ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8739_pigeonhole__infinite__rel,axiom,
% 9.25/5.27      ! [A2: set_int,B2: set_Pr1261947904930325089at_nat,R: int > product_prod_nat_nat > $o] :
% 9.25/5.27        ( ~ ( finite_finite_int @ A2 )
% 9.25/5.27       => ( ( finite6177210948735845034at_nat @ B2 )
% 9.25/5.27         => ( ! [X2: int] :
% 9.25/5.27                ( ( member_int @ X2 @ A2 )
% 9.25/5.27               => ? [Xa2: product_prod_nat_nat] :
% 9.25/5.27                    ( ( member8440522571783428010at_nat @ Xa2 @ B2 )
% 9.25/5.27                    & ( R @ X2 @ Xa2 ) ) )
% 9.25/5.27           => ? [X2: product_prod_nat_nat] :
% 9.25/5.27                ( ( member8440522571783428010at_nat @ X2 @ B2 )
% 9.25/5.27                & ~ ( finite_finite_int
% 9.25/5.27                    @ ( collect_int
% 9.25/5.27                      @ ^ [A3: int] :
% 9.25/5.27                          ( ( member_int @ A3 @ A2 )
% 9.25/5.27                          & ( R @ A3 @ X2 ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8740_pigeonhole__infinite__rel,axiom,
% 9.25/5.27      ! [A2: set_Pr1261947904930325089at_nat,B2: set_nat,R: product_prod_nat_nat > nat > $o] :
% 9.25/5.27        ( ~ ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.27       => ( ( finite_finite_nat @ B2 )
% 9.25/5.27         => ( ! [X2: product_prod_nat_nat] :
% 9.25/5.27                ( ( member8440522571783428010at_nat @ X2 @ A2 )
% 9.25/5.27               => ? [Xa2: nat] :
% 9.25/5.27                    ( ( member_nat @ Xa2 @ B2 )
% 9.25/5.27                    & ( R @ X2 @ Xa2 ) ) )
% 9.25/5.27           => ? [X2: nat] :
% 9.25/5.27                ( ( member_nat @ X2 @ B2 )
% 9.25/5.27                & ~ ( finite6177210948735845034at_nat
% 9.25/5.27                    @ ( collec3392354462482085612at_nat
% 9.25/5.27                      @ ^ [A3: product_prod_nat_nat] :
% 9.25/5.27                          ( ( member8440522571783428010at_nat @ A3 @ A2 )
% 9.25/5.27                          & ( R @ A3 @ X2 ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8741_pigeonhole__infinite__rel,axiom,
% 9.25/5.27      ! [A2: set_Pr1261947904930325089at_nat,B2: set_int,R: product_prod_nat_nat > int > $o] :
% 9.25/5.27        ( ~ ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.27       => ( ( finite_finite_int @ B2 )
% 9.25/5.27         => ( ! [X2: product_prod_nat_nat] :
% 9.25/5.27                ( ( member8440522571783428010at_nat @ X2 @ A2 )
% 9.25/5.27               => ? [Xa2: int] :
% 9.25/5.27                    ( ( member_int @ Xa2 @ B2 )
% 9.25/5.27                    & ( R @ X2 @ Xa2 ) ) )
% 9.25/5.27           => ? [X2: int] :
% 9.25/5.27                ( ( member_int @ X2 @ B2 )
% 9.25/5.27                & ~ ( finite6177210948735845034at_nat
% 9.25/5.27                    @ ( collec3392354462482085612at_nat
% 9.25/5.27                      @ ^ [A3: product_prod_nat_nat] :
% 9.25/5.27                          ( ( member8440522571783428010at_nat @ A3 @ A2 )
% 9.25/5.27                          & ( R @ A3 @ X2 ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8742_sgn__integer__code,axiom,
% 9.25/5.27      ( sgn_sgn_Code_integer
% 9.25/5.27      = ( ^ [K4: code_integer] : ( if_Code_integer @ ( K4 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K4 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8743_finite_OemptyI,axiom,
% 9.25/5.27      finite6177210948735845034at_nat @ bot_bo2099793752762293965at_nat ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8744_finite_OemptyI,axiom,
% 9.25/5.27      finite_finite_o @ bot_bot_set_o ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8745_finite_OemptyI,axiom,
% 9.25/5.27      finite_finite_nat @ bot_bot_set_nat ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8746_finite_OemptyI,axiom,
% 9.25/5.27      finite_finite_int @ bot_bot_set_int ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8747_infinite__imp__nonempty,axiom,
% 9.25/5.27      ! [S: set_Pr1261947904930325089at_nat] :
% 9.25/5.27        ( ~ ( finite6177210948735845034at_nat @ S )
% 9.25/5.27       => ( S != bot_bo2099793752762293965at_nat ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8748_infinite__imp__nonempty,axiom,
% 9.25/5.27      ! [S: set_o] :
% 9.25/5.27        ( ~ ( finite_finite_o @ S )
% 9.25/5.27       => ( S != bot_bot_set_o ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8749_infinite__imp__nonempty,axiom,
% 9.25/5.27      ! [S: set_nat] :
% 9.25/5.27        ( ~ ( finite_finite_nat @ S )
% 9.25/5.27       => ( S != bot_bot_set_nat ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8750_infinite__imp__nonempty,axiom,
% 9.25/5.27      ! [S: set_int] :
% 9.25/5.27        ( ~ ( finite_finite_int @ S )
% 9.25/5.27       => ( S != bot_bot_set_int ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8751_finite__UNIV,axiom,
% 9.25/5.27      finite_finite_o @ top_top_set_o ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8752_ex__new__if__finite,axiom,
% 9.25/5.27      ! [A2: set_se6260736226359567993nt_int] :
% 9.25/5.27        ( ~ ( finite8744585540193469122nt_int @ top_to6034159466715884489nt_int )
% 9.25/5.27       => ( ( finite8744585540193469122nt_int @ A2 )
% 9.25/5.27         => ? [A6: set_Pr958786334691620121nt_int] :
% 9.25/5.27              ~ ( member2340774599025711042nt_int @ A6 @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8753_ex__new__if__finite,axiom,
% 9.25/5.27      ! [A2: set_set_nat] :
% 9.25/5.27        ( ~ ( finite1152437895449049373et_nat @ top_top_set_set_nat )
% 9.25/5.27       => ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.27         => ? [A6: set_nat] :
% 9.25/5.27              ~ ( member_set_nat @ A6 @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8754_ex__new__if__finite,axiom,
% 9.25/5.27      ! [A2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.27        ( ~ ( finite3252695134891459830_nat_o @ top_to4869887016220417533_nat_o )
% 9.25/5.27       => ( ( finite3252695134891459830_nat_o @ A2 )
% 9.25/5.27         => ? [A6: produc3658429121746597890et_nat > $o] :
% 9.25/5.27              ~ ( member6576561426505652726_nat_o @ A6 @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8755_ex__new__if__finite,axiom,
% 9.25/5.27      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.27        ( ~ ( finite6177210948735845034at_nat @ top_to4669805908274784177at_nat )
% 9.25/5.27       => ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.27         => ? [A6: product_prod_nat_nat] :
% 9.25/5.27              ~ ( member8440522571783428010at_nat @ A6 @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8756_ex__new__if__finite,axiom,
% 9.25/5.27      ! [A2: set_list_nat] :
% 9.25/5.27        ( ~ ( finite8100373058378681591st_nat @ top_top_set_list_nat )
% 9.25/5.27       => ( ( finite8100373058378681591st_nat @ A2 )
% 9.25/5.27         => ? [A6: list_nat] :
% 9.25/5.27              ~ ( member_list_nat @ A6 @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8757_ex__new__if__finite,axiom,
% 9.25/5.27      ! [A2: set_o] :
% 9.25/5.27        ( ~ ( finite_finite_o @ top_top_set_o )
% 9.25/5.27       => ( ( finite_finite_o @ A2 )
% 9.25/5.27         => ? [A6: $o] :
% 9.25/5.27              ~ ( member_o @ A6 @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8758_ex__new__if__finite,axiom,
% 9.25/5.27      ! [A2: set_rat] :
% 9.25/5.27        ( ~ ( finite_finite_rat @ top_top_set_rat )
% 9.25/5.27       => ( ( finite_finite_rat @ A2 )
% 9.25/5.27         => ? [A6: rat] :
% 9.25/5.27              ~ ( member_rat @ A6 @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8759_ex__new__if__finite,axiom,
% 9.25/5.27      ! [A2: set_nat] :
% 9.25/5.27        ( ~ ( finite_finite_nat @ top_top_set_nat )
% 9.25/5.27       => ( ( finite_finite_nat @ A2 )
% 9.25/5.27         => ? [A6: nat] :
% 9.25/5.27              ~ ( member_nat @ A6 @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8760_ex__new__if__finite,axiom,
% 9.25/5.27      ! [A2: set_int] :
% 9.25/5.27        ( ~ ( finite_finite_int @ top_top_set_int )
% 9.25/5.27       => ( ( finite_finite_int @ A2 )
% 9.25/5.27         => ? [A6: int] :
% 9.25/5.27              ~ ( member_int @ A6 @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8761_infinite__UNIV__char__0,axiom,
% 9.25/5.27      ~ ( finite_finite_rat @ top_top_set_rat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8762_infinite__UNIV__char__0,axiom,
% 9.25/5.27      ~ ( finite_finite_nat @ top_top_set_nat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8763_infinite__UNIV__char__0,axiom,
% 9.25/5.27      ~ ( finite_finite_int @ top_top_set_int ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8764_finite__UnI,axiom,
% 9.25/5.27      ! [F4: set_int,G3: set_int] :
% 9.25/5.27        ( ( finite_finite_int @ F4 )
% 9.25/5.27       => ( ( finite_finite_int @ G3 )
% 9.25/5.27         => ( finite_finite_int @ ( sup_sup_set_int @ F4 @ G3 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8765_finite__UnI,axiom,
% 9.25/5.27      ! [F4: set_Pr1261947904930325089at_nat,G3: set_Pr1261947904930325089at_nat] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat @ F4 )
% 9.25/5.27       => ( ( finite6177210948735845034at_nat @ G3 )
% 9.25/5.27         => ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ F4 @ G3 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8766_finite__UnI,axiom,
% 9.25/5.27      ! [F4: set_Pr8551490117392284871at_nat,G3: set_Pr8551490117392284871at_nat] :
% 9.25/5.27        ( ( finite1918287321285529104at_nat @ F4 )
% 9.25/5.27       => ( ( finite1918287321285529104at_nat @ G3 )
% 9.25/5.27         => ( finite1918287321285529104at_nat @ ( sup_su3035147773818789531at_nat @ F4 @ G3 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8767_finite__UnI,axiom,
% 9.25/5.27      ! [F4: set_Pr4329608150637261639at_nat,G3: set_Pr4329608150637261639at_nat] :
% 9.25/5.27        ( ( finite4343798906461161616at_nat @ F4 )
% 9.25/5.27       => ( ( finite4343798906461161616at_nat @ G3 )
% 9.25/5.27         => ( finite4343798906461161616at_nat @ ( sup_su5525570899277871387at_nat @ F4 @ G3 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8768_finite__UnI,axiom,
% 9.25/5.27      ! [F4: set_nat,G3: set_nat] :
% 9.25/5.27        ( ( finite_finite_nat @ F4 )
% 9.25/5.27       => ( ( finite_finite_nat @ G3 )
% 9.25/5.27         => ( finite_finite_nat @ ( sup_sup_set_nat @ F4 @ G3 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8769_Un__infinite,axiom,
% 9.25/5.27      ! [S: set_int,T: set_int] :
% 9.25/5.27        ( ~ ( finite_finite_int @ S )
% 9.25/5.27       => ~ ( finite_finite_int @ ( sup_sup_set_int @ S @ T ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8770_Un__infinite,axiom,
% 9.25/5.27      ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 9.25/5.27        ( ~ ( finite6177210948735845034at_nat @ S )
% 9.25/5.27       => ~ ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ S @ T ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8771_Un__infinite,axiom,
% 9.25/5.27      ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 9.25/5.27        ( ~ ( finite1918287321285529104at_nat @ S )
% 9.25/5.27       => ~ ( finite1918287321285529104at_nat @ ( sup_su3035147773818789531at_nat @ S @ T ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8772_Un__infinite,axiom,
% 9.25/5.27      ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 9.25/5.27        ( ~ ( finite4343798906461161616at_nat @ S )
% 9.25/5.27       => ~ ( finite4343798906461161616at_nat @ ( sup_su5525570899277871387at_nat @ S @ T ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8773_Un__infinite,axiom,
% 9.25/5.27      ! [S: set_nat,T: set_nat] :
% 9.25/5.27        ( ~ ( finite_finite_nat @ S )
% 9.25/5.27       => ~ ( finite_finite_nat @ ( sup_sup_set_nat @ S @ T ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8774_infinite__Un,axiom,
% 9.25/5.27      ! [S: set_int,T: set_int] :
% 9.25/5.27        ( ( ~ ( finite_finite_int @ ( sup_sup_set_int @ S @ T ) ) )
% 9.25/5.27        = ( ~ ( finite_finite_int @ S )
% 9.25/5.27          | ~ ( finite_finite_int @ T ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8775_infinite__Un,axiom,
% 9.25/5.27      ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 9.25/5.27        ( ( ~ ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ S @ T ) ) )
% 9.25/5.27        = ( ~ ( finite6177210948735845034at_nat @ S )
% 9.25/5.27          | ~ ( finite6177210948735845034at_nat @ T ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8776_infinite__Un,axiom,
% 9.25/5.27      ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 9.25/5.27        ( ( ~ ( finite1918287321285529104at_nat @ ( sup_su3035147773818789531at_nat @ S @ T ) ) )
% 9.25/5.27        = ( ~ ( finite1918287321285529104at_nat @ S )
% 9.25/5.27          | ~ ( finite1918287321285529104at_nat @ T ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8777_infinite__Un,axiom,
% 9.25/5.27      ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 9.25/5.27        ( ( ~ ( finite4343798906461161616at_nat @ ( sup_su5525570899277871387at_nat @ S @ T ) ) )
% 9.25/5.27        = ( ~ ( finite4343798906461161616at_nat @ S )
% 9.25/5.27          | ~ ( finite4343798906461161616at_nat @ T ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8778_infinite__Un,axiom,
% 9.25/5.27      ! [S: set_nat,T: set_nat] :
% 9.25/5.27        ( ( ~ ( finite_finite_nat @ ( sup_sup_set_nat @ S @ T ) ) )
% 9.25/5.27        = ( ~ ( finite_finite_nat @ S )
% 9.25/5.27          | ~ ( finite_finite_nat @ T ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8779_finite__has__minimal,axiom,
% 9.25/5.27      ! [A2: set_o] :
% 9.25/5.27        ( ( finite_finite_o @ A2 )
% 9.25/5.27       => ( ( A2 != bot_bot_set_o )
% 9.25/5.27         => ? [X2: $o] :
% 9.25/5.27              ( ( member_o @ X2 @ A2 )
% 9.25/5.27              & ! [Xa2: $o] :
% 9.25/5.27                  ( ( member_o @ Xa2 @ A2 )
% 9.25/5.27                 => ( ( ord_less_eq_o @ Xa2 @ X2 )
% 9.25/5.27                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8780_finite__has__minimal,axiom,
% 9.25/5.27      ! [A2: set_filter_nat] :
% 9.25/5.27        ( ( finite2119507909894593271er_nat @ A2 )
% 9.25/5.27       => ( ( A2 != bot_bo498966703094740906er_nat )
% 9.25/5.27         => ? [X2: filter_nat] :
% 9.25/5.27              ( ( member_filter_nat @ X2 @ A2 )
% 9.25/5.27              & ! [Xa2: filter_nat] :
% 9.25/5.27                  ( ( member_filter_nat @ Xa2 @ A2 )
% 9.25/5.27                 => ( ( ord_le2510731241096832064er_nat @ Xa2 @ X2 )
% 9.25/5.27                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8781_finite__has__minimal,axiom,
% 9.25/5.27      ! [A2: set_set_nat] :
% 9.25/5.27        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.27       => ( ( A2 != bot_bot_set_set_nat )
% 9.25/5.27         => ? [X2: set_nat] :
% 9.25/5.27              ( ( member_set_nat @ X2 @ A2 )
% 9.25/5.27              & ! [Xa2: set_nat] :
% 9.25/5.27                  ( ( member_set_nat @ Xa2 @ A2 )
% 9.25/5.27                 => ( ( ord_less_eq_set_nat @ Xa2 @ X2 )
% 9.25/5.27                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8782_finite__has__minimal,axiom,
% 9.25/5.27      ! [A2: set_rat] :
% 9.25/5.27        ( ( finite_finite_rat @ A2 )
% 9.25/5.27       => ( ( A2 != bot_bot_set_rat )
% 9.25/5.27         => ? [X2: rat] :
% 9.25/5.27              ( ( member_rat @ X2 @ A2 )
% 9.25/5.27              & ! [Xa2: rat] :
% 9.25/5.27                  ( ( member_rat @ Xa2 @ A2 )
% 9.25/5.27                 => ( ( ord_less_eq_rat @ Xa2 @ X2 )
% 9.25/5.27                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8783_finite__has__minimal,axiom,
% 9.25/5.27      ! [A2: set_nat] :
% 9.25/5.27        ( ( finite_finite_nat @ A2 )
% 9.25/5.27       => ( ( A2 != bot_bot_set_nat )
% 9.25/5.27         => ? [X2: nat] :
% 9.25/5.27              ( ( member_nat @ X2 @ A2 )
% 9.25/5.27              & ! [Xa2: nat] :
% 9.25/5.27                  ( ( member_nat @ Xa2 @ A2 )
% 9.25/5.27                 => ( ( ord_less_eq_nat @ Xa2 @ X2 )
% 9.25/5.27                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8784_finite__has__minimal,axiom,
% 9.25/5.27      ! [A2: set_int] :
% 9.25/5.27        ( ( finite_finite_int @ A2 )
% 9.25/5.27       => ( ( A2 != bot_bot_set_int )
% 9.25/5.27         => ? [X2: int] :
% 9.25/5.27              ( ( member_int @ X2 @ A2 )
% 9.25/5.27              & ! [Xa2: int] :
% 9.25/5.27                  ( ( member_int @ Xa2 @ A2 )
% 9.25/5.27                 => ( ( ord_less_eq_int @ Xa2 @ X2 )
% 9.25/5.27                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8785_finite__has__maximal,axiom,
% 9.25/5.27      ! [A2: set_o] :
% 9.25/5.27        ( ( finite_finite_o @ A2 )
% 9.25/5.27       => ( ( A2 != bot_bot_set_o )
% 9.25/5.27         => ? [X2: $o] :
% 9.25/5.27              ( ( member_o @ X2 @ A2 )
% 9.25/5.27              & ! [Xa2: $o] :
% 9.25/5.27                  ( ( member_o @ Xa2 @ A2 )
% 9.25/5.27                 => ( ( ord_less_eq_o @ X2 @ Xa2 )
% 9.25/5.27                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8786_finite__has__maximal,axiom,
% 9.25/5.27      ! [A2: set_filter_nat] :
% 9.25/5.27        ( ( finite2119507909894593271er_nat @ A2 )
% 9.25/5.27       => ( ( A2 != bot_bo498966703094740906er_nat )
% 9.25/5.27         => ? [X2: filter_nat] :
% 9.25/5.27              ( ( member_filter_nat @ X2 @ A2 )
% 9.25/5.27              & ! [Xa2: filter_nat] :
% 9.25/5.27                  ( ( member_filter_nat @ Xa2 @ A2 )
% 9.25/5.27                 => ( ( ord_le2510731241096832064er_nat @ X2 @ Xa2 )
% 9.25/5.27                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8787_finite__has__maximal,axiom,
% 9.25/5.27      ! [A2: set_set_nat] :
% 9.25/5.27        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.27       => ( ( A2 != bot_bot_set_set_nat )
% 9.25/5.27         => ? [X2: set_nat] :
% 9.25/5.27              ( ( member_set_nat @ X2 @ A2 )
% 9.25/5.27              & ! [Xa2: set_nat] :
% 9.25/5.27                  ( ( member_set_nat @ Xa2 @ A2 )
% 9.25/5.27                 => ( ( ord_less_eq_set_nat @ X2 @ Xa2 )
% 9.25/5.27                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8788_finite__has__maximal,axiom,
% 9.25/5.27      ! [A2: set_rat] :
% 9.25/5.27        ( ( finite_finite_rat @ A2 )
% 9.25/5.27       => ( ( A2 != bot_bot_set_rat )
% 9.25/5.27         => ? [X2: rat] :
% 9.25/5.27              ( ( member_rat @ X2 @ A2 )
% 9.25/5.27              & ! [Xa2: rat] :
% 9.25/5.27                  ( ( member_rat @ Xa2 @ A2 )
% 9.25/5.27                 => ( ( ord_less_eq_rat @ X2 @ Xa2 )
% 9.25/5.27                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8789_finite__has__maximal,axiom,
% 9.25/5.27      ! [A2: set_nat] :
% 9.25/5.27        ( ( finite_finite_nat @ A2 )
% 9.25/5.27       => ( ( A2 != bot_bot_set_nat )
% 9.25/5.27         => ? [X2: nat] :
% 9.25/5.27              ( ( member_nat @ X2 @ A2 )
% 9.25/5.27              & ! [Xa2: nat] :
% 9.25/5.27                  ( ( member_nat @ Xa2 @ A2 )
% 9.25/5.27                 => ( ( ord_less_eq_nat @ X2 @ Xa2 )
% 9.25/5.27                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8790_finite__has__maximal,axiom,
% 9.25/5.27      ! [A2: set_int] :
% 9.25/5.27        ( ( finite_finite_int @ A2 )
% 9.25/5.27       => ( ( A2 != bot_bot_set_int )
% 9.25/5.27         => ? [X2: int] :
% 9.25/5.27              ( ( member_int @ X2 @ A2 )
% 9.25/5.27              & ! [Xa2: int] :
% 9.25/5.27                  ( ( member_int @ Xa2 @ A2 )
% 9.25/5.27                 => ( ( ord_less_eq_int @ X2 @ Xa2 )
% 9.25/5.27                   => ( X2 = Xa2 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8791_finite_Ocases,axiom,
% 9.25/5.27      ! [A: set_Pr4329608150637261639at_nat] :
% 9.25/5.27        ( ( finite4343798906461161616at_nat @ A )
% 9.25/5.27       => ( ( A != bot_bo228742789529271731at_nat )
% 9.25/5.27         => ~ ! [A8: set_Pr4329608150637261639at_nat] :
% 9.25/5.27                ( ? [A6: produc3843707927480180839at_nat] :
% 9.25/5.27                    ( A
% 9.25/5.27                    = ( insert9069300056098147895at_nat @ A6 @ A8 ) )
% 9.25/5.27               => ~ ( finite4343798906461161616at_nat @ A8 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8792_finite_Ocases,axiom,
% 9.25/5.27      ! [A: set_Pr1261947904930325089at_nat] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat @ A )
% 9.25/5.27       => ( ( A != bot_bo2099793752762293965at_nat )
% 9.25/5.27         => ~ ! [A8: set_Pr1261947904930325089at_nat] :
% 9.25/5.27                ( ? [A6: product_prod_nat_nat] :
% 9.25/5.27                    ( A
% 9.25/5.27                    = ( insert8211810215607154385at_nat @ A6 @ A8 ) )
% 9.25/5.27               => ~ ( finite6177210948735845034at_nat @ A8 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8793_finite_Ocases,axiom,
% 9.25/5.27      ! [A: set_o] :
% 9.25/5.27        ( ( finite_finite_o @ A )
% 9.25/5.27       => ( ( A != bot_bot_set_o )
% 9.25/5.27         => ~ ! [A8: set_o] :
% 9.25/5.27                ( ? [A6: $o] :
% 9.25/5.27                    ( A
% 9.25/5.27                    = ( insert_o @ A6 @ A8 ) )
% 9.25/5.27               => ~ ( finite_finite_o @ A8 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8794_finite_Ocases,axiom,
% 9.25/5.27      ! [A: set_nat] :
% 9.25/5.27        ( ( finite_finite_nat @ A )
% 9.25/5.27       => ( ( A != bot_bot_set_nat )
% 9.25/5.27         => ~ ! [A8: set_nat] :
% 9.25/5.27                ( ? [A6: nat] :
% 9.25/5.27                    ( A
% 9.25/5.27                    = ( insert_nat @ A6 @ A8 ) )
% 9.25/5.27               => ~ ( finite_finite_nat @ A8 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8795_finite_Ocases,axiom,
% 9.25/5.27      ! [A: set_int] :
% 9.25/5.27        ( ( finite_finite_int @ A )
% 9.25/5.27       => ( ( A != bot_bot_set_int )
% 9.25/5.27         => ~ ! [A8: set_int] :
% 9.25/5.27                ( ? [A6: int] :
% 9.25/5.27                    ( A
% 9.25/5.27                    = ( insert_int @ A6 @ A8 ) )
% 9.25/5.27               => ~ ( finite_finite_int @ A8 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8796_finite_Osimps,axiom,
% 9.25/5.27      ( finite4343798906461161616at_nat
% 9.25/5.27      = ( ^ [A3: set_Pr4329608150637261639at_nat] :
% 9.25/5.27            ( ( A3 = bot_bo228742789529271731at_nat )
% 9.25/5.27            | ? [A4: set_Pr4329608150637261639at_nat,B3: produc3843707927480180839at_nat] :
% 9.25/5.27                ( ( A3
% 9.25/5.27                  = ( insert9069300056098147895at_nat @ B3 @ A4 ) )
% 9.25/5.27                & ( finite4343798906461161616at_nat @ A4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8797_finite_Osimps,axiom,
% 9.25/5.27      ( finite6177210948735845034at_nat
% 9.25/5.27      = ( ^ [A3: set_Pr1261947904930325089at_nat] :
% 9.25/5.27            ( ( A3 = bot_bo2099793752762293965at_nat )
% 9.25/5.27            | ? [A4: set_Pr1261947904930325089at_nat,B3: product_prod_nat_nat] :
% 9.25/5.27                ( ( A3
% 9.25/5.27                  = ( insert8211810215607154385at_nat @ B3 @ A4 ) )
% 9.25/5.27                & ( finite6177210948735845034at_nat @ A4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8798_finite_Osimps,axiom,
% 9.25/5.27      ( finite_finite_o
% 9.25/5.27      = ( ^ [A3: set_o] :
% 9.25/5.27            ( ( A3 = bot_bot_set_o )
% 9.25/5.27            | ? [A4: set_o,B3: $o] :
% 9.25/5.27                ( ( A3
% 9.25/5.27                  = ( insert_o @ B3 @ A4 ) )
% 9.25/5.27                & ( finite_finite_o @ A4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8799_finite_Osimps,axiom,
% 9.25/5.27      ( finite_finite_nat
% 9.25/5.27      = ( ^ [A3: set_nat] :
% 9.25/5.27            ( ( A3 = bot_bot_set_nat )
% 9.25/5.27            | ? [A4: set_nat,B3: nat] :
% 9.25/5.27                ( ( A3
% 9.25/5.27                  = ( insert_nat @ B3 @ A4 ) )
% 9.25/5.27                & ( finite_finite_nat @ A4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8800_finite_Osimps,axiom,
% 9.25/5.27      ( finite_finite_int
% 9.25/5.27      = ( ^ [A3: set_int] :
% 9.25/5.27            ( ( A3 = bot_bot_set_int )
% 9.25/5.27            | ? [A4: set_int,B3: int] :
% 9.25/5.27                ( ( A3
% 9.25/5.27                  = ( insert_int @ B3 @ A4 ) )
% 9.25/5.27                & ( finite_finite_int @ A4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8801_finite__induct,axiom,
% 9.25/5.27      ! [F4: set_Pr4329608150637261639at_nat,P: set_Pr4329608150637261639at_nat > $o] :
% 9.25/5.27        ( ( finite4343798906461161616at_nat @ F4 )
% 9.25/5.27       => ( ( P @ bot_bo228742789529271731at_nat )
% 9.25/5.27         => ( ! [X2: produc3843707927480180839at_nat,F5: set_Pr4329608150637261639at_nat] :
% 9.25/5.27                ( ( finite4343798906461161616at_nat @ F5 )
% 9.25/5.27               => ( ~ ( member8757157785044589968at_nat @ X2 @ F5 )
% 9.25/5.27                 => ( ( P @ F5 )
% 9.25/5.27                   => ( P @ ( insert9069300056098147895at_nat @ X2 @ F5 ) ) ) ) )
% 9.25/5.27           => ( P @ F4 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8802_finite__induct,axiom,
% 9.25/5.27      ! [F4: set_se6260736226359567993nt_int,P: set_se6260736226359567993nt_int > $o] :
% 9.25/5.27        ( ( finite8744585540193469122nt_int @ F4 )
% 9.25/5.27       => ( ( P @ bot_bo1488462491386950373nt_int )
% 9.25/5.27         => ( ! [X2: set_Pr958786334691620121nt_int,F5: set_se6260736226359567993nt_int] :
% 9.25/5.27                ( ( finite8744585540193469122nt_int @ F5 )
% 9.25/5.27               => ( ~ ( member2340774599025711042nt_int @ X2 @ F5 )
% 9.25/5.27                 => ( ( P @ F5 )
% 9.25/5.27                   => ( P @ ( insert8897473484851387113nt_int @ X2 @ F5 ) ) ) ) )
% 9.25/5.27           => ( P @ F4 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8803_finite__induct,axiom,
% 9.25/5.27      ! [F4: set_set_nat,P: set_set_nat > $o] :
% 9.25/5.27        ( ( finite1152437895449049373et_nat @ F4 )
% 9.25/5.27       => ( ( P @ bot_bot_set_set_nat )
% 9.25/5.27         => ( ! [X2: set_nat,F5: set_set_nat] :
% 9.25/5.27                ( ( finite1152437895449049373et_nat @ F5 )
% 9.25/5.27               => ( ~ ( member_set_nat @ X2 @ F5 )
% 9.25/5.27                 => ( ( P @ F5 )
% 9.25/5.27                   => ( P @ ( insert_set_nat @ X2 @ F5 ) ) ) ) )
% 9.25/5.27           => ( P @ F4 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8804_finite__induct,axiom,
% 9.25/5.27      ! [F4: set_Pr4532377907799695533_nat_o,P: set_Pr4532377907799695533_nat_o > $o] :
% 9.25/5.27        ( ( finite3252695134891459830_nat_o @ F4 )
% 9.25/5.27       => ( ( P @ bot_bo7824918357723582233_nat_o )
% 9.25/5.27         => ( ! [X2: produc3658429121746597890et_nat > $o,F5: set_Pr4532377907799695533_nat_o] :
% 9.25/5.27                ( ( finite3252695134891459830_nat_o @ F5 )
% 9.25/5.27               => ( ~ ( member6576561426505652726_nat_o @ X2 @ F5 )
% 9.25/5.27                 => ( ( P @ F5 )
% 9.25/5.27                   => ( P @ ( insert5175938949040314269_nat_o @ X2 @ F5 ) ) ) ) )
% 9.25/5.27           => ( P @ F4 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8805_finite__induct,axiom,
% 9.25/5.27      ! [F4: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat @ F4 )
% 9.25/5.27       => ( ( P @ bot_bo2099793752762293965at_nat )
% 9.25/5.27         => ( ! [X2: product_prod_nat_nat,F5: set_Pr1261947904930325089at_nat] :
% 9.25/5.27                ( ( finite6177210948735845034at_nat @ F5 )
% 9.25/5.27               => ( ~ ( member8440522571783428010at_nat @ X2 @ F5 )
% 9.25/5.27                 => ( ( P @ F5 )
% 9.25/5.27                   => ( P @ ( insert8211810215607154385at_nat @ X2 @ F5 ) ) ) ) )
% 9.25/5.27           => ( P @ F4 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8806_finite__induct,axiom,
% 9.25/5.27      ! [F4: set_o,P: set_o > $o] :
% 9.25/5.27        ( ( finite_finite_o @ F4 )
% 9.25/5.27       => ( ( P @ bot_bot_set_o )
% 9.25/5.27         => ( ! [X2: $o,F5: set_o] :
% 9.25/5.27                ( ( finite_finite_o @ F5 )
% 9.25/5.27               => ( ~ ( member_o @ X2 @ F5 )
% 9.25/5.27                 => ( ( P @ F5 )
% 9.25/5.27                   => ( P @ ( insert_o @ X2 @ F5 ) ) ) ) )
% 9.25/5.27           => ( P @ F4 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8807_finite__induct,axiom,
% 9.25/5.27      ! [F4: set_nat,P: set_nat > $o] :
% 9.25/5.27        ( ( finite_finite_nat @ F4 )
% 9.25/5.27       => ( ( P @ bot_bot_set_nat )
% 9.25/5.27         => ( ! [X2: nat,F5: set_nat] :
% 9.25/5.27                ( ( finite_finite_nat @ F5 )
% 9.25/5.27               => ( ~ ( member_nat @ X2 @ F5 )
% 9.25/5.27                 => ( ( P @ F5 )
% 9.25/5.27                   => ( P @ ( insert_nat @ X2 @ F5 ) ) ) ) )
% 9.25/5.27           => ( P @ F4 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8808_finite__induct,axiom,
% 9.25/5.27      ! [F4: set_int,P: set_int > $o] :
% 9.25/5.27        ( ( finite_finite_int @ F4 )
% 9.25/5.27       => ( ( P @ bot_bot_set_int )
% 9.25/5.27         => ( ! [X2: int,F5: set_int] :
% 9.25/5.27                ( ( finite_finite_int @ F5 )
% 9.25/5.27               => ( ~ ( member_int @ X2 @ F5 )
% 9.25/5.27                 => ( ( P @ F5 )
% 9.25/5.27                   => ( P @ ( insert_int @ X2 @ F5 ) ) ) ) )
% 9.25/5.27           => ( P @ F4 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8809_finite__ne__induct,axiom,
% 9.25/5.27      ! [F4: set_Pr4329608150637261639at_nat,P: set_Pr4329608150637261639at_nat > $o] :
% 9.25/5.27        ( ( finite4343798906461161616at_nat @ F4 )
% 9.25/5.27       => ( ( F4 != bot_bo228742789529271731at_nat )
% 9.25/5.27         => ( ! [X2: produc3843707927480180839at_nat] : ( P @ ( insert9069300056098147895at_nat @ X2 @ bot_bo228742789529271731at_nat ) )
% 9.25/5.27           => ( ! [X2: produc3843707927480180839at_nat,F5: set_Pr4329608150637261639at_nat] :
% 9.25/5.27                  ( ( finite4343798906461161616at_nat @ F5 )
% 9.25/5.27                 => ( ( F5 != bot_bo228742789529271731at_nat )
% 9.25/5.27                   => ( ~ ( member8757157785044589968at_nat @ X2 @ F5 )
% 9.25/5.27                     => ( ( P @ F5 )
% 9.25/5.27                       => ( P @ ( insert9069300056098147895at_nat @ X2 @ F5 ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8810_finite__ne__induct,axiom,
% 9.25/5.27      ! [F4: set_se6260736226359567993nt_int,P: set_se6260736226359567993nt_int > $o] :
% 9.25/5.27        ( ( finite8744585540193469122nt_int @ F4 )
% 9.25/5.27       => ( ( F4 != bot_bo1488462491386950373nt_int )
% 9.25/5.27         => ( ! [X2: set_Pr958786334691620121nt_int] : ( P @ ( insert8897473484851387113nt_int @ X2 @ bot_bo1488462491386950373nt_int ) )
% 9.25/5.27           => ( ! [X2: set_Pr958786334691620121nt_int,F5: set_se6260736226359567993nt_int] :
% 9.25/5.27                  ( ( finite8744585540193469122nt_int @ F5 )
% 9.25/5.27                 => ( ( F5 != bot_bo1488462491386950373nt_int )
% 9.25/5.27                   => ( ~ ( member2340774599025711042nt_int @ X2 @ F5 )
% 9.25/5.27                     => ( ( P @ F5 )
% 9.25/5.27                       => ( P @ ( insert8897473484851387113nt_int @ X2 @ F5 ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8811_finite__ne__induct,axiom,
% 9.25/5.27      ! [F4: set_set_nat,P: set_set_nat > $o] :
% 9.25/5.27        ( ( finite1152437895449049373et_nat @ F4 )
% 9.25/5.27       => ( ( F4 != bot_bot_set_set_nat )
% 9.25/5.27         => ( ! [X2: set_nat] : ( P @ ( insert_set_nat @ X2 @ bot_bot_set_set_nat ) )
% 9.25/5.27           => ( ! [X2: set_nat,F5: set_set_nat] :
% 9.25/5.27                  ( ( finite1152437895449049373et_nat @ F5 )
% 9.25/5.27                 => ( ( F5 != bot_bot_set_set_nat )
% 9.25/5.27                   => ( ~ ( member_set_nat @ X2 @ F5 )
% 9.25/5.27                     => ( ( P @ F5 )
% 9.25/5.27                       => ( P @ ( insert_set_nat @ X2 @ F5 ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8812_finite__ne__induct,axiom,
% 9.25/5.27      ! [F4: set_Pr4532377907799695533_nat_o,P: set_Pr4532377907799695533_nat_o > $o] :
% 9.25/5.27        ( ( finite3252695134891459830_nat_o @ F4 )
% 9.25/5.27       => ( ( F4 != bot_bo7824918357723582233_nat_o )
% 9.25/5.27         => ( ! [X2: produc3658429121746597890et_nat > $o] : ( P @ ( insert5175938949040314269_nat_o @ X2 @ bot_bo7824918357723582233_nat_o ) )
% 9.25/5.27           => ( ! [X2: produc3658429121746597890et_nat > $o,F5: set_Pr4532377907799695533_nat_o] :
% 9.25/5.27                  ( ( finite3252695134891459830_nat_o @ F5 )
% 9.25/5.27                 => ( ( F5 != bot_bo7824918357723582233_nat_o )
% 9.25/5.27                   => ( ~ ( member6576561426505652726_nat_o @ X2 @ F5 )
% 9.25/5.27                     => ( ( P @ F5 )
% 9.25/5.27                       => ( P @ ( insert5175938949040314269_nat_o @ X2 @ F5 ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8813_finite__ne__induct,axiom,
% 9.25/5.27      ! [F4: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat @ F4 )
% 9.25/5.27       => ( ( F4 != bot_bo2099793752762293965at_nat )
% 9.25/5.27         => ( ! [X2: product_prod_nat_nat] : ( P @ ( insert8211810215607154385at_nat @ X2 @ bot_bo2099793752762293965at_nat ) )
% 9.25/5.27           => ( ! [X2: product_prod_nat_nat,F5: set_Pr1261947904930325089at_nat] :
% 9.25/5.27                  ( ( finite6177210948735845034at_nat @ F5 )
% 9.25/5.27                 => ( ( F5 != bot_bo2099793752762293965at_nat )
% 9.25/5.27                   => ( ~ ( member8440522571783428010at_nat @ X2 @ F5 )
% 9.25/5.27                     => ( ( P @ F5 )
% 9.25/5.27                       => ( P @ ( insert8211810215607154385at_nat @ X2 @ F5 ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8814_finite__ne__induct,axiom,
% 9.25/5.27      ! [F4: set_o,P: set_o > $o] :
% 9.25/5.27        ( ( finite_finite_o @ F4 )
% 9.25/5.27       => ( ( F4 != bot_bot_set_o )
% 9.25/5.27         => ( ! [X2: $o] : ( P @ ( insert_o @ X2 @ bot_bot_set_o ) )
% 9.25/5.27           => ( ! [X2: $o,F5: set_o] :
% 9.25/5.27                  ( ( finite_finite_o @ F5 )
% 9.25/5.27                 => ( ( F5 != bot_bot_set_o )
% 9.25/5.27                   => ( ~ ( member_o @ X2 @ F5 )
% 9.25/5.27                     => ( ( P @ F5 )
% 9.25/5.27                       => ( P @ ( insert_o @ X2 @ F5 ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8815_finite__ne__induct,axiom,
% 9.25/5.27      ! [F4: set_nat,P: set_nat > $o] :
% 9.25/5.27        ( ( finite_finite_nat @ F4 )
% 9.25/5.27       => ( ( F4 != bot_bot_set_nat )
% 9.25/5.27         => ( ! [X2: nat] : ( P @ ( insert_nat @ X2 @ bot_bot_set_nat ) )
% 9.25/5.27           => ( ! [X2: nat,F5: set_nat] :
% 9.25/5.27                  ( ( finite_finite_nat @ F5 )
% 9.25/5.27                 => ( ( F5 != bot_bot_set_nat )
% 9.25/5.27                   => ( ~ ( member_nat @ X2 @ F5 )
% 9.25/5.27                     => ( ( P @ F5 )
% 9.25/5.27                       => ( P @ ( insert_nat @ X2 @ F5 ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8816_finite__ne__induct,axiom,
% 9.25/5.27      ! [F4: set_int,P: set_int > $o] :
% 9.25/5.27        ( ( finite_finite_int @ F4 )
% 9.25/5.27       => ( ( F4 != bot_bot_set_int )
% 9.25/5.27         => ( ! [X2: int] : ( P @ ( insert_int @ X2 @ bot_bot_set_int ) )
% 9.25/5.27           => ( ! [X2: int,F5: set_int] :
% 9.25/5.27                  ( ( finite_finite_int @ F5 )
% 9.25/5.27                 => ( ( F5 != bot_bot_set_int )
% 9.25/5.27                   => ( ~ ( member_int @ X2 @ F5 )
% 9.25/5.27                     => ( ( P @ F5 )
% 9.25/5.27                       => ( P @ ( insert_int @ X2 @ F5 ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8817_infinite__finite__induct,axiom,
% 9.25/5.27      ! [P: set_Pr4329608150637261639at_nat > $o,A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.27        ( ! [A8: set_Pr4329608150637261639at_nat] :
% 9.25/5.27            ( ~ ( finite4343798906461161616at_nat @ A8 )
% 9.25/5.27           => ( P @ A8 ) )
% 9.25/5.27       => ( ( P @ bot_bo228742789529271731at_nat )
% 9.25/5.27         => ( ! [X2: produc3843707927480180839at_nat,F5: set_Pr4329608150637261639at_nat] :
% 9.25/5.27                ( ( finite4343798906461161616at_nat @ F5 )
% 9.25/5.27               => ( ~ ( member8757157785044589968at_nat @ X2 @ F5 )
% 9.25/5.27                 => ( ( P @ F5 )
% 9.25/5.27                   => ( P @ ( insert9069300056098147895at_nat @ X2 @ F5 ) ) ) ) )
% 9.25/5.27           => ( P @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8818_infinite__finite__induct,axiom,
% 9.25/5.27      ! [P: set_se6260736226359567993nt_int > $o,A2: set_se6260736226359567993nt_int] :
% 9.25/5.27        ( ! [A8: set_se6260736226359567993nt_int] :
% 9.25/5.27            ( ~ ( finite8744585540193469122nt_int @ A8 )
% 9.25/5.27           => ( P @ A8 ) )
% 9.25/5.27       => ( ( P @ bot_bo1488462491386950373nt_int )
% 9.25/5.27         => ( ! [X2: set_Pr958786334691620121nt_int,F5: set_se6260736226359567993nt_int] :
% 9.25/5.27                ( ( finite8744585540193469122nt_int @ F5 )
% 9.25/5.27               => ( ~ ( member2340774599025711042nt_int @ X2 @ F5 )
% 9.25/5.27                 => ( ( P @ F5 )
% 9.25/5.27                   => ( P @ ( insert8897473484851387113nt_int @ X2 @ F5 ) ) ) ) )
% 9.25/5.27           => ( P @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8819_infinite__finite__induct,axiom,
% 9.25/5.27      ! [P: set_set_nat > $o,A2: set_set_nat] :
% 9.25/5.27        ( ! [A8: set_set_nat] :
% 9.25/5.27            ( ~ ( finite1152437895449049373et_nat @ A8 )
% 9.25/5.27           => ( P @ A8 ) )
% 9.25/5.27       => ( ( P @ bot_bot_set_set_nat )
% 9.25/5.27         => ( ! [X2: set_nat,F5: set_set_nat] :
% 9.25/5.27                ( ( finite1152437895449049373et_nat @ F5 )
% 9.25/5.27               => ( ~ ( member_set_nat @ X2 @ F5 )
% 9.25/5.27                 => ( ( P @ F5 )
% 9.25/5.27                   => ( P @ ( insert_set_nat @ X2 @ F5 ) ) ) ) )
% 9.25/5.27           => ( P @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8820_infinite__finite__induct,axiom,
% 9.25/5.27      ! [P: set_Pr4532377907799695533_nat_o > $o,A2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.27        ( ! [A8: set_Pr4532377907799695533_nat_o] :
% 9.25/5.27            ( ~ ( finite3252695134891459830_nat_o @ A8 )
% 9.25/5.27           => ( P @ A8 ) )
% 9.25/5.27       => ( ( P @ bot_bo7824918357723582233_nat_o )
% 9.25/5.27         => ( ! [X2: produc3658429121746597890et_nat > $o,F5: set_Pr4532377907799695533_nat_o] :
% 9.25/5.27                ( ( finite3252695134891459830_nat_o @ F5 )
% 9.25/5.27               => ( ~ ( member6576561426505652726_nat_o @ X2 @ F5 )
% 9.25/5.27                 => ( ( P @ F5 )
% 9.25/5.27                   => ( P @ ( insert5175938949040314269_nat_o @ X2 @ F5 ) ) ) ) )
% 9.25/5.27           => ( P @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8821_infinite__finite__induct,axiom,
% 9.25/5.27      ! [P: set_Pr1261947904930325089at_nat > $o,A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.27        ( ! [A8: set_Pr1261947904930325089at_nat] :
% 9.25/5.27            ( ~ ( finite6177210948735845034at_nat @ A8 )
% 9.25/5.27           => ( P @ A8 ) )
% 9.25/5.27       => ( ( P @ bot_bo2099793752762293965at_nat )
% 9.25/5.27         => ( ! [X2: product_prod_nat_nat,F5: set_Pr1261947904930325089at_nat] :
% 9.25/5.27                ( ( finite6177210948735845034at_nat @ F5 )
% 9.25/5.27               => ( ~ ( member8440522571783428010at_nat @ X2 @ F5 )
% 9.25/5.27                 => ( ( P @ F5 )
% 9.25/5.27                   => ( P @ ( insert8211810215607154385at_nat @ X2 @ F5 ) ) ) ) )
% 9.25/5.27           => ( P @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8822_infinite__finite__induct,axiom,
% 9.25/5.27      ! [P: set_o > $o,A2: set_o] :
% 9.25/5.27        ( ! [A8: set_o] :
% 9.25/5.27            ( ~ ( finite_finite_o @ A8 )
% 9.25/5.27           => ( P @ A8 ) )
% 9.25/5.27       => ( ( P @ bot_bot_set_o )
% 9.25/5.27         => ( ! [X2: $o,F5: set_o] :
% 9.25/5.27                ( ( finite_finite_o @ F5 )
% 9.25/5.27               => ( ~ ( member_o @ X2 @ F5 )
% 9.25/5.27                 => ( ( P @ F5 )
% 9.25/5.27                   => ( P @ ( insert_o @ X2 @ F5 ) ) ) ) )
% 9.25/5.27           => ( P @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8823_infinite__finite__induct,axiom,
% 9.25/5.27      ! [P: set_nat > $o,A2: set_nat] :
% 9.25/5.27        ( ! [A8: set_nat] :
% 9.25/5.27            ( ~ ( finite_finite_nat @ A8 )
% 9.25/5.27           => ( P @ A8 ) )
% 9.25/5.27       => ( ( P @ bot_bot_set_nat )
% 9.25/5.27         => ( ! [X2: nat,F5: set_nat] :
% 9.25/5.27                ( ( finite_finite_nat @ F5 )
% 9.25/5.27               => ( ~ ( member_nat @ X2 @ F5 )
% 9.25/5.27                 => ( ( P @ F5 )
% 9.25/5.27                   => ( P @ ( insert_nat @ X2 @ F5 ) ) ) ) )
% 9.25/5.27           => ( P @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8824_infinite__finite__induct,axiom,
% 9.25/5.27      ! [P: set_int > $o,A2: set_int] :
% 9.25/5.27        ( ! [A8: set_int] :
% 9.25/5.27            ( ~ ( finite_finite_int @ A8 )
% 9.25/5.27           => ( P @ A8 ) )
% 9.25/5.27       => ( ( P @ bot_bot_set_int )
% 9.25/5.27         => ( ! [X2: int,F5: set_int] :
% 9.25/5.27                ( ( finite_finite_int @ F5 )
% 9.25/5.27               => ( ~ ( member_int @ X2 @ F5 )
% 9.25/5.27                 => ( ( P @ F5 )
% 9.25/5.27                   => ( P @ ( insert_int @ X2 @ F5 ) ) ) ) )
% 9.25/5.27           => ( P @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8825_finite__prod,axiom,
% 9.25/5.27      ( ( finite6120865539452801872od_o_o @ top_to7721136755696657239od_o_o )
% 9.25/5.27      = ( ( finite_finite_o @ top_top_set_o )
% 9.25/5.27        & ( finite_finite_o @ top_top_set_o ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8826_finite__prod,axiom,
% 9.25/5.27      ( ( finite7561617386449315510_o_rat @ top_to642698169864860165_o_rat )
% 9.25/5.27      = ( ( finite_finite_o @ top_top_set_o )
% 9.25/5.27        & ( finite_finite_rat @ top_top_set_rat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8827_finite__prod,axiom,
% 9.25/5.27      ( ( finite1846473907987936430_o_nat @ top_to7022684507342537725_o_nat )
% 9.25/5.27      = ( ( finite_finite_o @ top_top_set_o )
% 9.25/5.27        & ( finite_finite_nat @ top_top_set_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8828_finite__prod,axiom,
% 9.25/5.27      ( ( finite6891994925333515530_o_int @ top_to4532601362410810969_o_int )
% 9.25/5.27      = ( ( finite_finite_o @ top_top_set_o )
% 9.25/5.27        & ( finite_finite_int @ top_top_set_int ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8829_finite__prod,axiom,
% 9.25/5.27      ( ( finite1617675504726861388_rat_o @ top_to7320853134386005659_rat_o )
% 9.25/5.27      = ( ( finite_finite_rat @ top_top_set_rat )
% 9.25/5.27        & ( finite_finite_o @ top_top_set_o ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8830_finite__prod,axiom,
% 9.25/5.27      ( ( finite2352427746407582394at_rat @ top_to3112507417142880193at_rat )
% 9.25/5.27      = ( ( finite_finite_rat @ top_top_set_rat )
% 9.25/5.27        & ( finite_finite_rat @ top_top_set_rat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8831_finite__prod,axiom,
% 9.25/5.27      ( ( finite5860656304800979122at_nat @ top_to269121717765781945at_nat )
% 9.25/5.27      = ( ( finite_finite_rat @ top_top_set_rat )
% 9.25/5.27        & ( finite_finite_nat @ top_top_set_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8832_finite__prod,axiom,
% 9.25/5.27      ( ( finite1682805285291782414at_int @ top_to7002410609688830997at_int )
% 9.25/5.27      = ( ( finite_finite_rat @ top_top_set_rat )
% 9.25/5.27        & ( finite_finite_int @ top_top_set_int ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8833_finite__prod,axiom,
% 9.25/5.27      ( ( finite5355008432043429460_nat_o @ top_to8070287629520841379_nat_o )
% 9.25/5.27      = ( ( finite_finite_nat @ top_top_set_nat )
% 9.25/5.27        & ( finite_finite_o @ top_top_set_o ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8834_finite__prod,axiom,
% 9.25/5.27      ( ( finite2668982390342448306at_rat @ top_to7513191607651882425at_rat )
% 9.25/5.27      = ( ( finite_finite_nat @ top_top_set_nat )
% 9.25/5.27        & ( finite_finite_rat @ top_top_set_rat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8835_finite__Prod__UNIV,axiom,
% 9.25/5.27      ( ( finite_finite_o @ top_top_set_o )
% 9.25/5.27     => ( ( finite_finite_o @ top_top_set_o )
% 9.25/5.27       => ( finite6120865539452801872od_o_o @ top_to7721136755696657239od_o_o ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8836_finite__Prod__UNIV,axiom,
% 9.25/5.27      ( ( finite_finite_o @ top_top_set_o )
% 9.25/5.27     => ( ( finite_finite_rat @ top_top_set_rat )
% 9.25/5.27       => ( finite7561617386449315510_o_rat @ top_to642698169864860165_o_rat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8837_finite__Prod__UNIV,axiom,
% 9.25/5.27      ( ( finite_finite_o @ top_top_set_o )
% 9.25/5.27     => ( ( finite_finite_nat @ top_top_set_nat )
% 9.25/5.27       => ( finite1846473907987936430_o_nat @ top_to7022684507342537725_o_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8838_finite__Prod__UNIV,axiom,
% 9.25/5.27      ( ( finite_finite_o @ top_top_set_o )
% 9.25/5.27     => ( ( finite_finite_int @ top_top_set_int )
% 9.25/5.27       => ( finite6891994925333515530_o_int @ top_to4532601362410810969_o_int ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8839_finite__Prod__UNIV,axiom,
% 9.25/5.27      ( ( finite_finite_rat @ top_top_set_rat )
% 9.25/5.27     => ( ( finite_finite_o @ top_top_set_o )
% 9.25/5.27       => ( finite1617675504726861388_rat_o @ top_to7320853134386005659_rat_o ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8840_finite__Prod__UNIV,axiom,
% 9.25/5.27      ( ( finite_finite_rat @ top_top_set_rat )
% 9.25/5.27     => ( ( finite_finite_rat @ top_top_set_rat )
% 9.25/5.27       => ( finite2352427746407582394at_rat @ top_to3112507417142880193at_rat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8841_finite__Prod__UNIV,axiom,
% 9.25/5.27      ( ( finite_finite_rat @ top_top_set_rat )
% 9.25/5.27     => ( ( finite_finite_nat @ top_top_set_nat )
% 9.25/5.27       => ( finite5860656304800979122at_nat @ top_to269121717765781945at_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8842_finite__Prod__UNIV,axiom,
% 9.25/5.27      ( ( finite_finite_rat @ top_top_set_rat )
% 9.25/5.27     => ( ( finite_finite_int @ top_top_set_int )
% 9.25/5.27       => ( finite1682805285291782414at_int @ top_to7002410609688830997at_int ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8843_finite__Prod__UNIV,axiom,
% 9.25/5.27      ( ( finite_finite_nat @ top_top_set_nat )
% 9.25/5.27     => ( ( finite_finite_o @ top_top_set_o )
% 9.25/5.27       => ( finite5355008432043429460_nat_o @ top_to8070287629520841379_nat_o ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8844_finite__Prod__UNIV,axiom,
% 9.25/5.27      ( ( finite_finite_nat @ top_top_set_nat )
% 9.25/5.27     => ( ( finite_finite_rat @ top_top_set_rat )
% 9.25/5.27       => ( finite2668982390342448306at_rat @ top_to7513191607651882425at_rat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8845_Finite__Set_Ofinite__set,axiom,
% 9.25/5.27      ( ( finite9047747110432174090at_nat @ top_to7629004291339433233at_nat )
% 9.25/5.27      = ( finite6177210948735845034at_nat @ top_to4669805908274784177at_nat ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8846_Finite__Set_Ofinite__set,axiom,
% 9.25/5.27      ( ( finite7047420756378620717st_nat @ top_to1619013496918823676st_nat )
% 9.25/5.27      = ( finite8100373058378681591st_nat @ top_top_set_list_nat ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8847_Finite__Set_Ofinite__set,axiom,
% 9.25/5.27      ( ( finite_finite_set_o @ top_top_set_set_o )
% 9.25/5.27      = ( finite_finite_o @ top_top_set_o ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8848_Finite__Set_Ofinite__set,axiom,
% 9.25/5.27      ( ( finite6867581373910428453et_rat @ top_top_set_set_rat )
% 9.25/5.27      = ( finite_finite_rat @ top_top_set_rat ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8849_Finite__Set_Ofinite__set,axiom,
% 9.25/5.27      ( ( finite1152437895449049373et_nat @ top_top_set_set_nat )
% 9.25/5.27      = ( finite_finite_nat @ top_top_set_nat ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8850_Finite__Set_Ofinite__set,axiom,
% 9.25/5.27      ( ( finite6197958912794628473et_int @ top_top_set_set_int )
% 9.25/5.27      = ( finite_finite_int @ top_top_set_int ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8851_finite__subset__induct_H,axiom,
% 9.25/5.27      ! [F4: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,P: set_Pr4329608150637261639at_nat > $o] :
% 9.25/5.27        ( ( finite4343798906461161616at_nat @ F4 )
% 9.25/5.27       => ( ( ord_le1268244103169919719at_nat @ F4 @ A2 )
% 9.25/5.27         => ( ( P @ bot_bo228742789529271731at_nat )
% 9.25/5.27           => ( ! [A6: produc3843707927480180839at_nat,F5: set_Pr4329608150637261639at_nat] :
% 9.25/5.27                  ( ( finite4343798906461161616at_nat @ F5 )
% 9.25/5.27                 => ( ( member8757157785044589968at_nat @ A6 @ A2 )
% 9.25/5.27                   => ( ( ord_le1268244103169919719at_nat @ F5 @ A2 )
% 9.25/5.27                     => ( ~ ( member8757157785044589968at_nat @ A6 @ F5 )
% 9.25/5.27                       => ( ( P @ F5 )
% 9.25/5.27                         => ( P @ ( insert9069300056098147895at_nat @ A6 @ F5 ) ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8852_finite__subset__induct_H,axiom,
% 9.25/5.27      ! [F4: set_se6260736226359567993nt_int,A2: set_se6260736226359567993nt_int,P: set_se6260736226359567993nt_int > $o] :
% 9.25/5.27        ( ( finite8744585540193469122nt_int @ F4 )
% 9.25/5.27       => ( ( ord_le483042692224249369nt_int @ F4 @ A2 )
% 9.25/5.27         => ( ( P @ bot_bo1488462491386950373nt_int )
% 9.25/5.27           => ( ! [A6: set_Pr958786334691620121nt_int,F5: set_se6260736226359567993nt_int] :
% 9.25/5.27                  ( ( finite8744585540193469122nt_int @ F5 )
% 9.25/5.27                 => ( ( member2340774599025711042nt_int @ A6 @ A2 )
% 9.25/5.27                   => ( ( ord_le483042692224249369nt_int @ F5 @ A2 )
% 9.25/5.27                     => ( ~ ( member2340774599025711042nt_int @ A6 @ F5 )
% 9.25/5.27                       => ( ( P @ F5 )
% 9.25/5.27                         => ( P @ ( insert8897473484851387113nt_int @ A6 @ F5 ) ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8853_finite__subset__induct_H,axiom,
% 9.25/5.27      ! [F4: set_set_nat,A2: set_set_nat,P: set_set_nat > $o] :
% 9.25/5.27        ( ( finite1152437895449049373et_nat @ F4 )
% 9.25/5.27       => ( ( ord_le6893508408891458716et_nat @ F4 @ A2 )
% 9.25/5.27         => ( ( P @ bot_bot_set_set_nat )
% 9.25/5.27           => ( ! [A6: set_nat,F5: set_set_nat] :
% 9.25/5.27                  ( ( finite1152437895449049373et_nat @ F5 )
% 9.25/5.27                 => ( ( member_set_nat @ A6 @ A2 )
% 9.25/5.27                   => ( ( ord_le6893508408891458716et_nat @ F5 @ A2 )
% 9.25/5.27                     => ( ~ ( member_set_nat @ A6 @ F5 )
% 9.25/5.27                       => ( ( P @ F5 )
% 9.25/5.27                         => ( P @ ( insert_set_nat @ A6 @ F5 ) ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8854_finite__subset__induct_H,axiom,
% 9.25/5.27      ! [F4: set_Pr4532377907799695533_nat_o,A2: set_Pr4532377907799695533_nat_o,P: set_Pr4532377907799695533_nat_o > $o] :
% 9.25/5.27        ( ( finite3252695134891459830_nat_o @ F4 )
% 9.25/5.27       => ( ( ord_le2965882846123202637_nat_o @ F4 @ A2 )
% 9.25/5.27         => ( ( P @ bot_bo7824918357723582233_nat_o )
% 9.25/5.27           => ( ! [A6: produc3658429121746597890et_nat > $o,F5: set_Pr4532377907799695533_nat_o] :
% 9.25/5.27                  ( ( finite3252695134891459830_nat_o @ F5 )
% 9.25/5.27                 => ( ( member6576561426505652726_nat_o @ A6 @ A2 )
% 9.25/5.27                   => ( ( ord_le2965882846123202637_nat_o @ F5 @ A2 )
% 9.25/5.27                     => ( ~ ( member6576561426505652726_nat_o @ A6 @ F5 )
% 9.25/5.27                       => ( ( P @ F5 )
% 9.25/5.27                         => ( P @ ( insert5175938949040314269_nat_o @ A6 @ F5 ) ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8855_finite__subset__induct_H,axiom,
% 9.25/5.27      ! [F4: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat @ F4 )
% 9.25/5.27       => ( ( ord_le3146513528884898305at_nat @ F4 @ A2 )
% 9.25/5.27         => ( ( P @ bot_bo2099793752762293965at_nat )
% 9.25/5.27           => ( ! [A6: product_prod_nat_nat,F5: set_Pr1261947904930325089at_nat] :
% 9.25/5.27                  ( ( finite6177210948735845034at_nat @ F5 )
% 9.25/5.27                 => ( ( member8440522571783428010at_nat @ A6 @ A2 )
% 9.25/5.27                   => ( ( ord_le3146513528884898305at_nat @ F5 @ A2 )
% 9.25/5.27                     => ( ~ ( member8440522571783428010at_nat @ A6 @ F5 )
% 9.25/5.27                       => ( ( P @ F5 )
% 9.25/5.27                         => ( P @ ( insert8211810215607154385at_nat @ A6 @ F5 ) ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8856_finite__subset__induct_H,axiom,
% 9.25/5.27      ! [F4: set_o,A2: set_o,P: set_o > $o] :
% 9.25/5.27        ( ( finite_finite_o @ F4 )
% 9.25/5.27       => ( ( ord_less_eq_set_o @ F4 @ A2 )
% 9.25/5.27         => ( ( P @ bot_bot_set_o )
% 9.25/5.27           => ( ! [A6: $o,F5: set_o] :
% 9.25/5.27                  ( ( finite_finite_o @ F5 )
% 9.25/5.27                 => ( ( member_o @ A6 @ A2 )
% 9.25/5.27                   => ( ( ord_less_eq_set_o @ F5 @ A2 )
% 9.25/5.27                     => ( ~ ( member_o @ A6 @ F5 )
% 9.25/5.27                       => ( ( P @ F5 )
% 9.25/5.27                         => ( P @ ( insert_o @ A6 @ F5 ) ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8857_finite__subset__induct_H,axiom,
% 9.25/5.27      ! [F4: set_int,A2: set_int,P: set_int > $o] :
% 9.25/5.27        ( ( finite_finite_int @ F4 )
% 9.25/5.27       => ( ( ord_less_eq_set_int @ F4 @ A2 )
% 9.25/5.27         => ( ( P @ bot_bot_set_int )
% 9.25/5.27           => ( ! [A6: int,F5: set_int] :
% 9.25/5.27                  ( ( finite_finite_int @ F5 )
% 9.25/5.27                 => ( ( member_int @ A6 @ A2 )
% 9.25/5.27                   => ( ( ord_less_eq_set_int @ F5 @ A2 )
% 9.25/5.27                     => ( ~ ( member_int @ A6 @ F5 )
% 9.25/5.27                       => ( ( P @ F5 )
% 9.25/5.27                         => ( P @ ( insert_int @ A6 @ F5 ) ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8858_finite__subset__induct_H,axiom,
% 9.25/5.27      ! [F4: set_nat,A2: set_nat,P: set_nat > $o] :
% 9.25/5.27        ( ( finite_finite_nat @ F4 )
% 9.25/5.27       => ( ( ord_less_eq_set_nat @ F4 @ A2 )
% 9.25/5.27         => ( ( P @ bot_bot_set_nat )
% 9.25/5.27           => ( ! [A6: nat,F5: set_nat] :
% 9.25/5.27                  ( ( finite_finite_nat @ F5 )
% 9.25/5.27                 => ( ( member_nat @ A6 @ A2 )
% 9.25/5.27                   => ( ( ord_less_eq_set_nat @ F5 @ A2 )
% 9.25/5.27                     => ( ~ ( member_nat @ A6 @ F5 )
% 9.25/5.27                       => ( ( P @ F5 )
% 9.25/5.27                         => ( P @ ( insert_nat @ A6 @ F5 ) ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8859_finite__subset__induct,axiom,
% 9.25/5.27      ! [F4: set_Pr4329608150637261639at_nat,A2: set_Pr4329608150637261639at_nat,P: set_Pr4329608150637261639at_nat > $o] :
% 9.25/5.27        ( ( finite4343798906461161616at_nat @ F4 )
% 9.25/5.27       => ( ( ord_le1268244103169919719at_nat @ F4 @ A2 )
% 9.25/5.27         => ( ( P @ bot_bo228742789529271731at_nat )
% 9.25/5.27           => ( ! [A6: produc3843707927480180839at_nat,F5: set_Pr4329608150637261639at_nat] :
% 9.25/5.27                  ( ( finite4343798906461161616at_nat @ F5 )
% 9.25/5.27                 => ( ( member8757157785044589968at_nat @ A6 @ A2 )
% 9.25/5.27                   => ( ~ ( member8757157785044589968at_nat @ A6 @ F5 )
% 9.25/5.27                     => ( ( P @ F5 )
% 9.25/5.27                       => ( P @ ( insert9069300056098147895at_nat @ A6 @ F5 ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8860_finite__subset__induct,axiom,
% 9.25/5.27      ! [F4: set_se6260736226359567993nt_int,A2: set_se6260736226359567993nt_int,P: set_se6260736226359567993nt_int > $o] :
% 9.25/5.27        ( ( finite8744585540193469122nt_int @ F4 )
% 9.25/5.27       => ( ( ord_le483042692224249369nt_int @ F4 @ A2 )
% 9.25/5.27         => ( ( P @ bot_bo1488462491386950373nt_int )
% 9.25/5.27           => ( ! [A6: set_Pr958786334691620121nt_int,F5: set_se6260736226359567993nt_int] :
% 9.25/5.27                  ( ( finite8744585540193469122nt_int @ F5 )
% 9.25/5.27                 => ( ( member2340774599025711042nt_int @ A6 @ A2 )
% 9.25/5.27                   => ( ~ ( member2340774599025711042nt_int @ A6 @ F5 )
% 9.25/5.27                     => ( ( P @ F5 )
% 9.25/5.27                       => ( P @ ( insert8897473484851387113nt_int @ A6 @ F5 ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8861_finite__subset__induct,axiom,
% 9.25/5.27      ! [F4: set_set_nat,A2: set_set_nat,P: set_set_nat > $o] :
% 9.25/5.27        ( ( finite1152437895449049373et_nat @ F4 )
% 9.25/5.27       => ( ( ord_le6893508408891458716et_nat @ F4 @ A2 )
% 9.25/5.27         => ( ( P @ bot_bot_set_set_nat )
% 9.25/5.27           => ( ! [A6: set_nat,F5: set_set_nat] :
% 9.25/5.27                  ( ( finite1152437895449049373et_nat @ F5 )
% 9.25/5.27                 => ( ( member_set_nat @ A6 @ A2 )
% 9.25/5.27                   => ( ~ ( member_set_nat @ A6 @ F5 )
% 9.25/5.27                     => ( ( P @ F5 )
% 9.25/5.27                       => ( P @ ( insert_set_nat @ A6 @ F5 ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8862_finite__subset__induct,axiom,
% 9.25/5.27      ! [F4: set_Pr4532377907799695533_nat_o,A2: set_Pr4532377907799695533_nat_o,P: set_Pr4532377907799695533_nat_o > $o] :
% 9.25/5.27        ( ( finite3252695134891459830_nat_o @ F4 )
% 9.25/5.27       => ( ( ord_le2965882846123202637_nat_o @ F4 @ A2 )
% 9.25/5.27         => ( ( P @ bot_bo7824918357723582233_nat_o )
% 9.25/5.27           => ( ! [A6: produc3658429121746597890et_nat > $o,F5: set_Pr4532377907799695533_nat_o] :
% 9.25/5.27                  ( ( finite3252695134891459830_nat_o @ F5 )
% 9.25/5.27                 => ( ( member6576561426505652726_nat_o @ A6 @ A2 )
% 9.25/5.27                   => ( ~ ( member6576561426505652726_nat_o @ A6 @ F5 )
% 9.25/5.27                     => ( ( P @ F5 )
% 9.25/5.27                       => ( P @ ( insert5175938949040314269_nat_o @ A6 @ F5 ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8863_finite__subset__induct,axiom,
% 9.25/5.27      ! [F4: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat @ F4 )
% 9.25/5.27       => ( ( ord_le3146513528884898305at_nat @ F4 @ A2 )
% 9.25/5.27         => ( ( P @ bot_bo2099793752762293965at_nat )
% 9.25/5.27           => ( ! [A6: product_prod_nat_nat,F5: set_Pr1261947904930325089at_nat] :
% 9.25/5.27                  ( ( finite6177210948735845034at_nat @ F5 )
% 9.25/5.27                 => ( ( member8440522571783428010at_nat @ A6 @ A2 )
% 9.25/5.27                   => ( ~ ( member8440522571783428010at_nat @ A6 @ F5 )
% 9.25/5.27                     => ( ( P @ F5 )
% 9.25/5.27                       => ( P @ ( insert8211810215607154385at_nat @ A6 @ F5 ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8864_finite__subset__induct,axiom,
% 9.25/5.27      ! [F4: set_o,A2: set_o,P: set_o > $o] :
% 9.25/5.27        ( ( finite_finite_o @ F4 )
% 9.25/5.27       => ( ( ord_less_eq_set_o @ F4 @ A2 )
% 9.25/5.27         => ( ( P @ bot_bot_set_o )
% 9.25/5.27           => ( ! [A6: $o,F5: set_o] :
% 9.25/5.27                  ( ( finite_finite_o @ F5 )
% 9.25/5.27                 => ( ( member_o @ A6 @ A2 )
% 9.25/5.27                   => ( ~ ( member_o @ A6 @ F5 )
% 9.25/5.27                     => ( ( P @ F5 )
% 9.25/5.27                       => ( P @ ( insert_o @ A6 @ F5 ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8865_finite__subset__induct,axiom,
% 9.25/5.27      ! [F4: set_int,A2: set_int,P: set_int > $o] :
% 9.25/5.27        ( ( finite_finite_int @ F4 )
% 9.25/5.27       => ( ( ord_less_eq_set_int @ F4 @ A2 )
% 9.25/5.27         => ( ( P @ bot_bot_set_int )
% 9.25/5.27           => ( ! [A6: int,F5: set_int] :
% 9.25/5.27                  ( ( finite_finite_int @ F5 )
% 9.25/5.27                 => ( ( member_int @ A6 @ A2 )
% 9.25/5.27                   => ( ~ ( member_int @ A6 @ F5 )
% 9.25/5.27                     => ( ( P @ F5 )
% 9.25/5.27                       => ( P @ ( insert_int @ A6 @ F5 ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8866_finite__subset__induct,axiom,
% 9.25/5.27      ! [F4: set_nat,A2: set_nat,P: set_nat > $o] :
% 9.25/5.27        ( ( finite_finite_nat @ F4 )
% 9.25/5.27       => ( ( ord_less_eq_set_nat @ F4 @ A2 )
% 9.25/5.27         => ( ( P @ bot_bot_set_nat )
% 9.25/5.27           => ( ! [A6: nat,F5: set_nat] :
% 9.25/5.27                  ( ( finite_finite_nat @ F5 )
% 9.25/5.27                 => ( ( member_nat @ A6 @ A2 )
% 9.25/5.27                   => ( ~ ( member_nat @ A6 @ F5 )
% 9.25/5.27                     => ( ( P @ F5 )
% 9.25/5.27                       => ( P @ ( insert_nat @ A6 @ F5 ) ) ) ) ) )
% 9.25/5.27             => ( P @ F4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8867_infinite__remove,axiom,
% 9.25/5.27      ! [S: set_Pr4329608150637261639at_nat,A: produc3843707927480180839at_nat] :
% 9.25/5.27        ( ~ ( finite4343798906461161616at_nat @ S )
% 9.25/5.27       => ~ ( finite4343798906461161616at_nat @ ( minus_3314409938677909166at_nat @ S @ ( insert9069300056098147895at_nat @ A @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8868_infinite__remove,axiom,
% 9.25/5.27      ! [S: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
% 9.25/5.27        ( ~ ( finite6177210948735845034at_nat @ S )
% 9.25/5.27       => ~ ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ S @ ( insert8211810215607154385at_nat @ A @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8869_infinite__remove,axiom,
% 9.25/5.27      ! [S: set_o,A: $o] :
% 9.25/5.27        ( ~ ( finite_finite_o @ S )
% 9.25/5.27       => ~ ( finite_finite_o @ ( minus_minus_set_o @ S @ ( insert_o @ A @ bot_bot_set_o ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8870_infinite__remove,axiom,
% 9.25/5.27      ! [S: set_int,A: int] :
% 9.25/5.27        ( ~ ( finite_finite_int @ S )
% 9.25/5.27       => ~ ( finite_finite_int @ ( minus_minus_set_int @ S @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8871_infinite__remove,axiom,
% 9.25/5.27      ! [S: set_nat,A: nat] :
% 9.25/5.27        ( ~ ( finite_finite_nat @ S )
% 9.25/5.27       => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8872_infinite__coinduct,axiom,
% 9.25/5.27      ! [X7: set_Pr4329608150637261639at_nat > $o,A2: set_Pr4329608150637261639at_nat] :
% 9.25/5.27        ( ( X7 @ A2 )
% 9.25/5.27       => ( ! [A8: set_Pr4329608150637261639at_nat] :
% 9.25/5.27              ( ( X7 @ A8 )
% 9.25/5.27             => ? [X5: produc3843707927480180839at_nat] :
% 9.25/5.27                  ( ( member8757157785044589968at_nat @ X5 @ A8 )
% 9.25/5.27                  & ( ( X7 @ ( minus_3314409938677909166at_nat @ A8 @ ( insert9069300056098147895at_nat @ X5 @ bot_bo228742789529271731at_nat ) ) )
% 9.25/5.27                    | ~ ( finite4343798906461161616at_nat @ ( minus_3314409938677909166at_nat @ A8 @ ( insert9069300056098147895at_nat @ X5 @ bot_bo228742789529271731at_nat ) ) ) ) ) )
% 9.25/5.27         => ~ ( finite4343798906461161616at_nat @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8873_infinite__coinduct,axiom,
% 9.25/5.27      ! [X7: set_Pr1261947904930325089at_nat > $o,A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.27        ( ( X7 @ A2 )
% 9.25/5.27       => ( ! [A8: set_Pr1261947904930325089at_nat] :
% 9.25/5.27              ( ( X7 @ A8 )
% 9.25/5.27             => ? [X5: product_prod_nat_nat] :
% 9.25/5.27                  ( ( member8440522571783428010at_nat @ X5 @ A8 )
% 9.25/5.27                  & ( ( X7 @ ( minus_1356011639430497352at_nat @ A8 @ ( insert8211810215607154385at_nat @ X5 @ bot_bo2099793752762293965at_nat ) ) )
% 9.25/5.27                    | ~ ( finite6177210948735845034at_nat @ ( minus_1356011639430497352at_nat @ A8 @ ( insert8211810215607154385at_nat @ X5 @ bot_bo2099793752762293965at_nat ) ) ) ) ) )
% 9.25/5.27         => ~ ( finite6177210948735845034at_nat @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8874_infinite__coinduct,axiom,
% 9.25/5.27      ! [X7: set_o > $o,A2: set_o] :
% 9.25/5.27        ( ( X7 @ A2 )
% 9.25/5.27       => ( ! [A8: set_o] :
% 9.25/5.27              ( ( X7 @ A8 )
% 9.25/5.27             => ? [X5: $o] :
% 9.25/5.27                  ( ( member_o @ X5 @ A8 )
% 9.25/5.27                  & ( ( X7 @ ( minus_minus_set_o @ A8 @ ( insert_o @ X5 @ bot_bot_set_o ) ) )
% 9.25/5.27                    | ~ ( finite_finite_o @ ( minus_minus_set_o @ A8 @ ( insert_o @ X5 @ bot_bot_set_o ) ) ) ) ) )
% 9.25/5.27         => ~ ( finite_finite_o @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8875_infinite__coinduct,axiom,
% 9.25/5.27      ! [X7: set_int > $o,A2: set_int] :
% 9.25/5.27        ( ( X7 @ A2 )
% 9.25/5.27       => ( ! [A8: set_int] :
% 9.25/5.27              ( ( X7 @ A8 )
% 9.25/5.27             => ? [X5: int] :
% 9.25/5.27                  ( ( member_int @ X5 @ A8 )
% 9.25/5.27                  & ( ( X7 @ ( minus_minus_set_int @ A8 @ ( insert_int @ X5 @ bot_bot_set_int ) ) )
% 9.25/5.27                    | ~ ( finite_finite_int @ ( minus_minus_set_int @ A8 @ ( insert_int @ X5 @ bot_bot_set_int ) ) ) ) ) )
% 9.25/5.27         => ~ ( finite_finite_int @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8876_infinite__coinduct,axiom,
% 9.25/5.27      ! [X7: set_nat > $o,A2: set_nat] :
% 9.25/5.27        ( ( X7 @ A2 )
% 9.25/5.27       => ( ! [A8: set_nat] :
% 9.25/5.27              ( ( X7 @ A8 )
% 9.25/5.27             => ? [X5: nat] :
% 9.25/5.27                  ( ( member_nat @ X5 @ A8 )
% 9.25/5.27                  & ( ( X7 @ ( minus_minus_set_nat @ A8 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) )
% 9.25/5.27                    | ~ ( finite_finite_nat @ ( minus_minus_set_nat @ A8 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) ) ) )
% 9.25/5.27         => ~ ( finite_finite_nat @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8877_finite__empty__induct,axiom,
% 9.25/5.27      ! [A2: set_Pr4329608150637261639at_nat,P: set_Pr4329608150637261639at_nat > $o] :
% 9.25/5.27        ( ( finite4343798906461161616at_nat @ A2 )
% 9.25/5.27       => ( ( P @ A2 )
% 9.25/5.27         => ( ! [A6: produc3843707927480180839at_nat,A8: set_Pr4329608150637261639at_nat] :
% 9.25/5.27                ( ( finite4343798906461161616at_nat @ A8 )
% 9.25/5.27               => ( ( member8757157785044589968at_nat @ A6 @ A8 )
% 9.25/5.27                 => ( ( P @ A8 )
% 9.25/5.27                   => ( P @ ( minus_3314409938677909166at_nat @ A8 @ ( insert9069300056098147895at_nat @ A6 @ bot_bo228742789529271731at_nat ) ) ) ) ) )
% 9.25/5.27           => ( P @ bot_bo228742789529271731at_nat ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8878_finite__empty__induct,axiom,
% 9.25/5.27      ! [A2: set_se6260736226359567993nt_int,P: set_se6260736226359567993nt_int > $o] :
% 9.25/5.27        ( ( finite8744585540193469122nt_int @ A2 )
% 9.25/5.27       => ( ( P @ A2 )
% 9.25/5.27         => ( ! [A6: set_Pr958786334691620121nt_int,A8: set_se6260736226359567993nt_int] :
% 9.25/5.27                ( ( finite8744585540193469122nt_int @ A8 )
% 9.25/5.27               => ( ( member2340774599025711042nt_int @ A6 @ A8 )
% 9.25/5.27                 => ( ( P @ A8 )
% 9.25/5.27                   => ( P @ ( minus_2612819937483484256nt_int @ A8 @ ( insert8897473484851387113nt_int @ A6 @ bot_bo1488462491386950373nt_int ) ) ) ) ) )
% 9.25/5.27           => ( P @ bot_bo1488462491386950373nt_int ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8879_finite__empty__induct,axiom,
% 9.25/5.27      ! [A2: set_set_nat,P: set_set_nat > $o] :
% 9.25/5.27        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.27       => ( ( P @ A2 )
% 9.25/5.27         => ( ! [A6: set_nat,A8: set_set_nat] :
% 9.25/5.27                ( ( finite1152437895449049373et_nat @ A8 )
% 9.25/5.27               => ( ( member_set_nat @ A6 @ A8 )
% 9.25/5.27                 => ( ( P @ A8 )
% 9.25/5.27                   => ( P @ ( minus_2163939370556025621et_nat @ A8 @ ( insert_set_nat @ A6 @ bot_bot_set_set_nat ) ) ) ) ) )
% 9.25/5.27           => ( P @ bot_bot_set_set_nat ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8880_finite__empty__induct,axiom,
% 9.25/5.27      ! [A2: set_Pr4532377907799695533_nat_o,P: set_Pr4532377907799695533_nat_o > $o] :
% 9.25/5.27        ( ( finite3252695134891459830_nat_o @ A2 )
% 9.25/5.27       => ( ( P @ A2 )
% 9.25/5.27         => ( ! [A6: produc3658429121746597890et_nat > $o,A8: set_Pr4532377907799695533_nat_o] :
% 9.25/5.27                ( ( finite3252695134891459830_nat_o @ A8 )
% 9.25/5.27               => ( ( member6576561426505652726_nat_o @ A6 @ A8 )
% 9.25/5.27                 => ( ( P @ A8 )
% 9.25/5.27                   => ( P @ ( minus_1801376950450012436_nat_o @ A8 @ ( insert5175938949040314269_nat_o @ A6 @ bot_bo7824918357723582233_nat_o ) ) ) ) ) )
% 9.25/5.27           => ( P @ bot_bo7824918357723582233_nat_o ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8881_finite__empty__induct,axiom,
% 9.25/5.27      ! [A2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.27       => ( ( P @ A2 )
% 9.25/5.27         => ( ! [A6: product_prod_nat_nat,A8: set_Pr1261947904930325089at_nat] :
% 9.25/5.27                ( ( finite6177210948735845034at_nat @ A8 )
% 9.25/5.27               => ( ( member8440522571783428010at_nat @ A6 @ A8 )
% 9.25/5.27                 => ( ( P @ A8 )
% 9.25/5.27                   => ( P @ ( minus_1356011639430497352at_nat @ A8 @ ( insert8211810215607154385at_nat @ A6 @ bot_bo2099793752762293965at_nat ) ) ) ) ) )
% 9.25/5.27           => ( P @ bot_bo2099793752762293965at_nat ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8882_finite__empty__induct,axiom,
% 9.25/5.27      ! [A2: set_o,P: set_o > $o] :
% 9.25/5.27        ( ( finite_finite_o @ A2 )
% 9.25/5.27       => ( ( P @ A2 )
% 9.25/5.27         => ( ! [A6: $o,A8: set_o] :
% 9.25/5.27                ( ( finite_finite_o @ A8 )
% 9.25/5.27               => ( ( member_o @ A6 @ A8 )
% 9.25/5.27                 => ( ( P @ A8 )
% 9.25/5.27                   => ( P @ ( minus_minus_set_o @ A8 @ ( insert_o @ A6 @ bot_bot_set_o ) ) ) ) ) )
% 9.25/5.27           => ( P @ bot_bot_set_o ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8883_finite__empty__induct,axiom,
% 9.25/5.27      ! [A2: set_int,P: set_int > $o] :
% 9.25/5.27        ( ( finite_finite_int @ A2 )
% 9.25/5.27       => ( ( P @ A2 )
% 9.25/5.27         => ( ! [A6: int,A8: set_int] :
% 9.25/5.27                ( ( finite_finite_int @ A8 )
% 9.25/5.27               => ( ( member_int @ A6 @ A8 )
% 9.25/5.27                 => ( ( P @ A8 )
% 9.25/5.27                   => ( P @ ( minus_minus_set_int @ A8 @ ( insert_int @ A6 @ bot_bot_set_int ) ) ) ) ) )
% 9.25/5.27           => ( P @ bot_bot_set_int ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8884_finite__empty__induct,axiom,
% 9.25/5.27      ! [A2: set_nat,P: set_nat > $o] :
% 9.25/5.27        ( ( finite_finite_nat @ A2 )
% 9.25/5.27       => ( ( P @ A2 )
% 9.25/5.27         => ( ! [A6: nat,A8: set_nat] :
% 9.25/5.27                ( ( finite_finite_nat @ A8 )
% 9.25/5.27               => ( ( member_nat @ A6 @ A8 )
% 9.25/5.27                 => ( ( P @ A8 )
% 9.25/5.27                   => ( P @ ( minus_minus_set_nat @ A8 @ ( insert_nat @ A6 @ bot_bot_set_nat ) ) ) ) ) )
% 9.25/5.27           => ( P @ bot_bot_set_nat ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8885_finite__remove__induct,axiom,
% 9.25/5.27      ! [B2: set_Pr4329608150637261639at_nat,P: set_Pr4329608150637261639at_nat > $o] :
% 9.25/5.27        ( ( finite4343798906461161616at_nat @ B2 )
% 9.25/5.27       => ( ( P @ bot_bo228742789529271731at_nat )
% 9.25/5.27         => ( ! [A8: set_Pr4329608150637261639at_nat] :
% 9.25/5.27                ( ( finite4343798906461161616at_nat @ A8 )
% 9.25/5.27               => ( ( A8 != bot_bo228742789529271731at_nat )
% 9.25/5.27                 => ( ( ord_le1268244103169919719at_nat @ A8 @ B2 )
% 9.25/5.27                   => ( ! [X5: produc3843707927480180839at_nat] :
% 9.25/5.27                          ( ( member8757157785044589968at_nat @ X5 @ A8 )
% 9.25/5.27                         => ( P @ ( minus_3314409938677909166at_nat @ A8 @ ( insert9069300056098147895at_nat @ X5 @ bot_bo228742789529271731at_nat ) ) ) )
% 9.25/5.27                     => ( P @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ B2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8886_finite__remove__induct,axiom,
% 9.25/5.27      ! [B2: set_se6260736226359567993nt_int,P: set_se6260736226359567993nt_int > $o] :
% 9.25/5.27        ( ( finite8744585540193469122nt_int @ B2 )
% 9.25/5.27       => ( ( P @ bot_bo1488462491386950373nt_int )
% 9.25/5.27         => ( ! [A8: set_se6260736226359567993nt_int] :
% 9.25/5.27                ( ( finite8744585540193469122nt_int @ A8 )
% 9.25/5.27               => ( ( A8 != bot_bo1488462491386950373nt_int )
% 9.25/5.27                 => ( ( ord_le483042692224249369nt_int @ A8 @ B2 )
% 9.25/5.27                   => ( ! [X5: set_Pr958786334691620121nt_int] :
% 9.25/5.27                          ( ( member2340774599025711042nt_int @ X5 @ A8 )
% 9.25/5.27                         => ( P @ ( minus_2612819937483484256nt_int @ A8 @ ( insert8897473484851387113nt_int @ X5 @ bot_bo1488462491386950373nt_int ) ) ) )
% 9.25/5.27                     => ( P @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ B2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8887_finite__remove__induct,axiom,
% 9.25/5.27      ! [B2: set_set_nat,P: set_set_nat > $o] :
% 9.25/5.27        ( ( finite1152437895449049373et_nat @ B2 )
% 9.25/5.27       => ( ( P @ bot_bot_set_set_nat )
% 9.25/5.27         => ( ! [A8: set_set_nat] :
% 9.25/5.27                ( ( finite1152437895449049373et_nat @ A8 )
% 9.25/5.27               => ( ( A8 != bot_bot_set_set_nat )
% 9.25/5.27                 => ( ( ord_le6893508408891458716et_nat @ A8 @ B2 )
% 9.25/5.27                   => ( ! [X5: set_nat] :
% 9.25/5.27                          ( ( member_set_nat @ X5 @ A8 )
% 9.25/5.27                         => ( P @ ( minus_2163939370556025621et_nat @ A8 @ ( insert_set_nat @ X5 @ bot_bot_set_set_nat ) ) ) )
% 9.25/5.27                     => ( P @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ B2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8888_finite__remove__induct,axiom,
% 9.25/5.27      ! [B2: set_Pr4532377907799695533_nat_o,P: set_Pr4532377907799695533_nat_o > $o] :
% 9.25/5.27        ( ( finite3252695134891459830_nat_o @ B2 )
% 9.25/5.27       => ( ( P @ bot_bo7824918357723582233_nat_o )
% 9.25/5.27         => ( ! [A8: set_Pr4532377907799695533_nat_o] :
% 9.25/5.27                ( ( finite3252695134891459830_nat_o @ A8 )
% 9.25/5.27               => ( ( A8 != bot_bo7824918357723582233_nat_o )
% 9.25/5.27                 => ( ( ord_le2965882846123202637_nat_o @ A8 @ B2 )
% 9.25/5.27                   => ( ! [X5: produc3658429121746597890et_nat > $o] :
% 9.25/5.27                          ( ( member6576561426505652726_nat_o @ X5 @ A8 )
% 9.25/5.27                         => ( P @ ( minus_1801376950450012436_nat_o @ A8 @ ( insert5175938949040314269_nat_o @ X5 @ bot_bo7824918357723582233_nat_o ) ) ) )
% 9.25/5.27                     => ( P @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ B2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8889_finite__remove__induct,axiom,
% 9.25/5.27      ! [B2: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat @ B2 )
% 9.25/5.27       => ( ( P @ bot_bo2099793752762293965at_nat )
% 9.25/5.27         => ( ! [A8: set_Pr1261947904930325089at_nat] :
% 9.25/5.27                ( ( finite6177210948735845034at_nat @ A8 )
% 9.25/5.27               => ( ( A8 != bot_bo2099793752762293965at_nat )
% 9.25/5.27                 => ( ( ord_le3146513528884898305at_nat @ A8 @ B2 )
% 9.25/5.27                   => ( ! [X5: product_prod_nat_nat] :
% 9.25/5.27                          ( ( member8440522571783428010at_nat @ X5 @ A8 )
% 9.25/5.27                         => ( P @ ( minus_1356011639430497352at_nat @ A8 @ ( insert8211810215607154385at_nat @ X5 @ bot_bo2099793752762293965at_nat ) ) ) )
% 9.25/5.27                     => ( P @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ B2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8890_finite__remove__induct,axiom,
% 9.25/5.27      ! [B2: set_o,P: set_o > $o] :
% 9.25/5.27        ( ( finite_finite_o @ B2 )
% 9.25/5.27       => ( ( P @ bot_bot_set_o )
% 9.25/5.27         => ( ! [A8: set_o] :
% 9.25/5.27                ( ( finite_finite_o @ A8 )
% 9.25/5.27               => ( ( A8 != bot_bot_set_o )
% 9.25/5.27                 => ( ( ord_less_eq_set_o @ A8 @ B2 )
% 9.25/5.27                   => ( ! [X5: $o] :
% 9.25/5.27                          ( ( member_o @ X5 @ A8 )
% 9.25/5.27                         => ( P @ ( minus_minus_set_o @ A8 @ ( insert_o @ X5 @ bot_bot_set_o ) ) ) )
% 9.25/5.27                     => ( P @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ B2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8891_finite__remove__induct,axiom,
% 9.25/5.27      ! [B2: set_int,P: set_int > $o] :
% 9.25/5.27        ( ( finite_finite_int @ B2 )
% 9.25/5.27       => ( ( P @ bot_bot_set_int )
% 9.25/5.27         => ( ! [A8: set_int] :
% 9.25/5.27                ( ( finite_finite_int @ A8 )
% 9.25/5.27               => ( ( A8 != bot_bot_set_int )
% 9.25/5.27                 => ( ( ord_less_eq_set_int @ A8 @ B2 )
% 9.25/5.27                   => ( ! [X5: int] :
% 9.25/5.27                          ( ( member_int @ X5 @ A8 )
% 9.25/5.27                         => ( P @ ( minus_minus_set_int @ A8 @ ( insert_int @ X5 @ bot_bot_set_int ) ) ) )
% 9.25/5.27                     => ( P @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ B2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8892_finite__remove__induct,axiom,
% 9.25/5.27      ! [B2: set_nat,P: set_nat > $o] :
% 9.25/5.27        ( ( finite_finite_nat @ B2 )
% 9.25/5.27       => ( ( P @ bot_bot_set_nat )
% 9.25/5.27         => ( ! [A8: set_nat] :
% 9.25/5.27                ( ( finite_finite_nat @ A8 )
% 9.25/5.27               => ( ( A8 != bot_bot_set_nat )
% 9.25/5.27                 => ( ( ord_less_eq_set_nat @ A8 @ B2 )
% 9.25/5.27                   => ( ! [X5: nat] :
% 9.25/5.27                          ( ( member_nat @ X5 @ A8 )
% 9.25/5.27                         => ( P @ ( minus_minus_set_nat @ A8 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) )
% 9.25/5.27                     => ( P @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ B2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8893_remove__induct,axiom,
% 9.25/5.27      ! [P: set_Pr4329608150637261639at_nat > $o,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.27        ( ( P @ bot_bo228742789529271731at_nat )
% 9.25/5.27       => ( ( ~ ( finite4343798906461161616at_nat @ B2 )
% 9.25/5.27           => ( P @ B2 ) )
% 9.25/5.27         => ( ! [A8: set_Pr4329608150637261639at_nat] :
% 9.25/5.27                ( ( finite4343798906461161616at_nat @ A8 )
% 9.25/5.27               => ( ( A8 != bot_bo228742789529271731at_nat )
% 9.25/5.27                 => ( ( ord_le1268244103169919719at_nat @ A8 @ B2 )
% 9.25/5.27                   => ( ! [X5: produc3843707927480180839at_nat] :
% 9.25/5.27                          ( ( member8757157785044589968at_nat @ X5 @ A8 )
% 9.25/5.27                         => ( P @ ( minus_3314409938677909166at_nat @ A8 @ ( insert9069300056098147895at_nat @ X5 @ bot_bo228742789529271731at_nat ) ) ) )
% 9.25/5.27                     => ( P @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ B2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8894_remove__induct,axiom,
% 9.25/5.27      ! [P: set_se6260736226359567993nt_int > $o,B2: set_se6260736226359567993nt_int] :
% 9.25/5.27        ( ( P @ bot_bo1488462491386950373nt_int )
% 9.25/5.27       => ( ( ~ ( finite8744585540193469122nt_int @ B2 )
% 9.25/5.27           => ( P @ B2 ) )
% 9.25/5.27         => ( ! [A8: set_se6260736226359567993nt_int] :
% 9.25/5.27                ( ( finite8744585540193469122nt_int @ A8 )
% 9.25/5.27               => ( ( A8 != bot_bo1488462491386950373nt_int )
% 9.25/5.27                 => ( ( ord_le483042692224249369nt_int @ A8 @ B2 )
% 9.25/5.27                   => ( ! [X5: set_Pr958786334691620121nt_int] :
% 9.25/5.27                          ( ( member2340774599025711042nt_int @ X5 @ A8 )
% 9.25/5.27                         => ( P @ ( minus_2612819937483484256nt_int @ A8 @ ( insert8897473484851387113nt_int @ X5 @ bot_bo1488462491386950373nt_int ) ) ) )
% 9.25/5.27                     => ( P @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ B2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8895_remove__induct,axiom,
% 9.25/5.27      ! [P: set_set_nat > $o,B2: set_set_nat] :
% 9.25/5.27        ( ( P @ bot_bot_set_set_nat )
% 9.25/5.27       => ( ( ~ ( finite1152437895449049373et_nat @ B2 )
% 9.25/5.27           => ( P @ B2 ) )
% 9.25/5.27         => ( ! [A8: set_set_nat] :
% 9.25/5.27                ( ( finite1152437895449049373et_nat @ A8 )
% 9.25/5.27               => ( ( A8 != bot_bot_set_set_nat )
% 9.25/5.27                 => ( ( ord_le6893508408891458716et_nat @ A8 @ B2 )
% 9.25/5.27                   => ( ! [X5: set_nat] :
% 9.25/5.27                          ( ( member_set_nat @ X5 @ A8 )
% 9.25/5.27                         => ( P @ ( minus_2163939370556025621et_nat @ A8 @ ( insert_set_nat @ X5 @ bot_bot_set_set_nat ) ) ) )
% 9.25/5.27                     => ( P @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ B2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8896_remove__induct,axiom,
% 9.25/5.27      ! [P: set_Pr4532377907799695533_nat_o > $o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.27        ( ( P @ bot_bo7824918357723582233_nat_o )
% 9.25/5.27       => ( ( ~ ( finite3252695134891459830_nat_o @ B2 )
% 9.25/5.27           => ( P @ B2 ) )
% 9.25/5.27         => ( ! [A8: set_Pr4532377907799695533_nat_o] :
% 9.25/5.27                ( ( finite3252695134891459830_nat_o @ A8 )
% 9.25/5.27               => ( ( A8 != bot_bo7824918357723582233_nat_o )
% 9.25/5.27                 => ( ( ord_le2965882846123202637_nat_o @ A8 @ B2 )
% 9.25/5.27                   => ( ! [X5: produc3658429121746597890et_nat > $o] :
% 9.25/5.27                          ( ( member6576561426505652726_nat_o @ X5 @ A8 )
% 9.25/5.27                         => ( P @ ( minus_1801376950450012436_nat_o @ A8 @ ( insert5175938949040314269_nat_o @ X5 @ bot_bo7824918357723582233_nat_o ) ) ) )
% 9.25/5.27                     => ( P @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ B2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8897_remove__induct,axiom,
% 9.25/5.27      ! [P: set_Pr1261947904930325089at_nat > $o,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.27        ( ( P @ bot_bo2099793752762293965at_nat )
% 9.25/5.27       => ( ( ~ ( finite6177210948735845034at_nat @ B2 )
% 9.25/5.27           => ( P @ B2 ) )
% 9.25/5.27         => ( ! [A8: set_Pr1261947904930325089at_nat] :
% 9.25/5.27                ( ( finite6177210948735845034at_nat @ A8 )
% 9.25/5.27               => ( ( A8 != bot_bo2099793752762293965at_nat )
% 9.25/5.27                 => ( ( ord_le3146513528884898305at_nat @ A8 @ B2 )
% 9.25/5.27                   => ( ! [X5: product_prod_nat_nat] :
% 9.25/5.27                          ( ( member8440522571783428010at_nat @ X5 @ A8 )
% 9.25/5.27                         => ( P @ ( minus_1356011639430497352at_nat @ A8 @ ( insert8211810215607154385at_nat @ X5 @ bot_bo2099793752762293965at_nat ) ) ) )
% 9.25/5.27                     => ( P @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ B2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8898_remove__induct,axiom,
% 9.25/5.27      ! [P: set_o > $o,B2: set_o] :
% 9.25/5.27        ( ( P @ bot_bot_set_o )
% 9.25/5.27       => ( ( ~ ( finite_finite_o @ B2 )
% 9.25/5.27           => ( P @ B2 ) )
% 9.25/5.27         => ( ! [A8: set_o] :
% 9.25/5.27                ( ( finite_finite_o @ A8 )
% 9.25/5.27               => ( ( A8 != bot_bot_set_o )
% 9.25/5.27                 => ( ( ord_less_eq_set_o @ A8 @ B2 )
% 9.25/5.27                   => ( ! [X5: $o] :
% 9.25/5.27                          ( ( member_o @ X5 @ A8 )
% 9.25/5.27                         => ( P @ ( minus_minus_set_o @ A8 @ ( insert_o @ X5 @ bot_bot_set_o ) ) ) )
% 9.25/5.27                     => ( P @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ B2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8899_remove__induct,axiom,
% 9.25/5.27      ! [P: set_int > $o,B2: set_int] :
% 9.25/5.27        ( ( P @ bot_bot_set_int )
% 9.25/5.27       => ( ( ~ ( finite_finite_int @ B2 )
% 9.25/5.27           => ( P @ B2 ) )
% 9.25/5.27         => ( ! [A8: set_int] :
% 9.25/5.27                ( ( finite_finite_int @ A8 )
% 9.25/5.27               => ( ( A8 != bot_bot_set_int )
% 9.25/5.27                 => ( ( ord_less_eq_set_int @ A8 @ B2 )
% 9.25/5.27                   => ( ! [X5: int] :
% 9.25/5.27                          ( ( member_int @ X5 @ A8 )
% 9.25/5.27                         => ( P @ ( minus_minus_set_int @ A8 @ ( insert_int @ X5 @ bot_bot_set_int ) ) ) )
% 9.25/5.27                     => ( P @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ B2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8900_remove__induct,axiom,
% 9.25/5.27      ! [P: set_nat > $o,B2: set_nat] :
% 9.25/5.27        ( ( P @ bot_bot_set_nat )
% 9.25/5.27       => ( ( ~ ( finite_finite_nat @ B2 )
% 9.25/5.27           => ( P @ B2 ) )
% 9.25/5.27         => ( ! [A8: set_nat] :
% 9.25/5.27                ( ( finite_finite_nat @ A8 )
% 9.25/5.27               => ( ( A8 != bot_bot_set_nat )
% 9.25/5.27                 => ( ( ord_less_eq_set_nat @ A8 @ B2 )
% 9.25/5.27                   => ( ! [X5: nat] :
% 9.25/5.27                          ( ( member_nat @ X5 @ A8 )
% 9.25/5.27                         => ( P @ ( minus_minus_set_nat @ A8 @ ( insert_nat @ X5 @ bot_bot_set_nat ) ) ) )
% 9.25/5.27                     => ( P @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ B2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8901_finite__induct__select,axiom,
% 9.25/5.27      ! [S: set_Pr4329608150637261639at_nat,P: set_Pr4329608150637261639at_nat > $o] :
% 9.25/5.27        ( ( finite4343798906461161616at_nat @ S )
% 9.25/5.27       => ( ( P @ bot_bo228742789529271731at_nat )
% 9.25/5.27         => ( ! [T5: set_Pr4329608150637261639at_nat] :
% 9.25/5.27                ( ( ord_le2604355607129572851at_nat @ T5 @ S )
% 9.25/5.27               => ( ( P @ T5 )
% 9.25/5.27                 => ? [X5: produc3843707927480180839at_nat] :
% 9.25/5.27                      ( ( member8757157785044589968at_nat @ X5 @ ( minus_3314409938677909166at_nat @ S @ T5 ) )
% 9.25/5.27                      & ( P @ ( insert9069300056098147895at_nat @ X5 @ T5 ) ) ) ) )
% 9.25/5.27           => ( P @ S ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8902_finite__induct__select,axiom,
% 9.25/5.27      ! [S: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat @ S )
% 9.25/5.27       => ( ( P @ bot_bo2099793752762293965at_nat )
% 9.25/5.27         => ( ! [T5: set_Pr1261947904930325089at_nat] :
% 9.25/5.27                ( ( ord_le7866589430770878221at_nat @ T5 @ S )
% 9.25/5.27               => ( ( P @ T5 )
% 9.25/5.27                 => ? [X5: product_prod_nat_nat] :
% 9.25/5.27                      ( ( member8440522571783428010at_nat @ X5 @ ( minus_1356011639430497352at_nat @ S @ T5 ) )
% 9.25/5.27                      & ( P @ ( insert8211810215607154385at_nat @ X5 @ T5 ) ) ) ) )
% 9.25/5.27           => ( P @ S ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8903_finite__induct__select,axiom,
% 9.25/5.27      ! [S: set_o,P: set_o > $o] :
% 9.25/5.27        ( ( finite_finite_o @ S )
% 9.25/5.27       => ( ( P @ bot_bot_set_o )
% 9.25/5.27         => ( ! [T5: set_o] :
% 9.25/5.27                ( ( ord_less_set_o @ T5 @ S )
% 9.25/5.27               => ( ( P @ T5 )
% 9.25/5.27                 => ? [X5: $o] :
% 9.25/5.27                      ( ( member_o @ X5 @ ( minus_minus_set_o @ S @ T5 ) )
% 9.25/5.27                      & ( P @ ( insert_o @ X5 @ T5 ) ) ) ) )
% 9.25/5.27           => ( P @ S ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8904_finite__induct__select,axiom,
% 9.25/5.27      ! [S: set_int,P: set_int > $o] :
% 9.25/5.27        ( ( finite_finite_int @ S )
% 9.25/5.27       => ( ( P @ bot_bot_set_int )
% 9.25/5.27         => ( ! [T5: set_int] :
% 9.25/5.27                ( ( ord_less_set_int @ T5 @ S )
% 9.25/5.27               => ( ( P @ T5 )
% 9.25/5.27                 => ? [X5: int] :
% 9.25/5.27                      ( ( member_int @ X5 @ ( minus_minus_set_int @ S @ T5 ) )
% 9.25/5.27                      & ( P @ ( insert_int @ X5 @ T5 ) ) ) ) )
% 9.25/5.27           => ( P @ S ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8905_finite__induct__select,axiom,
% 9.25/5.27      ! [S: set_nat,P: set_nat > $o] :
% 9.25/5.27        ( ( finite_finite_nat @ S )
% 9.25/5.27       => ( ( P @ bot_bot_set_nat )
% 9.25/5.27         => ( ! [T5: set_nat] :
% 9.25/5.27                ( ( ord_less_set_nat @ T5 @ S )
% 9.25/5.27               => ( ( P @ T5 )
% 9.25/5.27                 => ? [X5: nat] :
% 9.25/5.27                      ( ( member_nat @ X5 @ ( minus_minus_set_nat @ S @ T5 ) )
% 9.25/5.27                      & ( P @ ( insert_nat @ X5 @ T5 ) ) ) ) )
% 9.25/5.27           => ( P @ S ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8906_finite__option__UNIV,axiom,
% 9.25/5.27      ( ( finite6732403688824079472at_nat @ top_to3251141154256563319at_nat )
% 9.25/5.27      = ( finite6177210948735845034at_nat @ top_to4669805908274784177at_nat ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8907_finite__option__UNIV,axiom,
% 9.25/5.27      ( ( finite7857960318081769799st_nat @ top_to1113147461230312982st_nat )
% 9.25/5.27      = ( finite8100373058378681591st_nat @ top_top_set_list_nat ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8908_finite__option__UNIV,axiom,
% 9.25/5.27      ( ( finite4093902646404507527tion_o @ top_top_set_option_o )
% 9.25/5.27      = ( finite_finite_o @ top_top_set_o ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8909_finite__option__UNIV,axiom,
% 9.25/5.27      ( ( finite2014924581280026175on_rat @ top_to2540212048668676366on_rat )
% 9.25/5.27      = ( finite_finite_rat @ top_top_set_rat ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8910_finite__option__UNIV,axiom,
% 9.25/5.27      ( ( finite5523153139673422903on_nat @ top_to8920198386146353926on_nat )
% 9.25/5.27      = ( finite_finite_nat @ top_top_set_nat ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8911_finite__option__UNIV,axiom,
% 9.25/5.27      ( ( finite1345302120164226195on_int @ top_to6430115241214627170on_int )
% 9.25/5.27      = ( finite_finite_int @ top_top_set_int ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8912_diff__preserves__multiset,axiom,
% 9.25/5.27      ! [M4: set_Pr958786334691620121nt_int > nat,N4: set_Pr958786334691620121nt_int > nat] :
% 9.25/5.27        ( ( finite8744585540193469122nt_int
% 9.25/5.27          @ ( collec5210948495886036740nt_int
% 9.25/5.27            @ ^ [X3: set_Pr958786334691620121nt_int] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 9.25/5.27       => ( finite8744585540193469122nt_int
% 9.25/5.27          @ ( collec5210948495886036740nt_int
% 9.25/5.27            @ ^ [X3: set_Pr958786334691620121nt_int] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M4 @ X3 ) @ ( N4 @ X3 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8913_diff__preserves__multiset,axiom,
% 9.25/5.27      ! [M4: set_nat > nat,N4: set_nat > nat] :
% 9.25/5.27        ( ( finite1152437895449049373et_nat
% 9.25/5.27          @ ( collect_set_nat
% 9.25/5.27            @ ^ [X3: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 9.25/5.27       => ( finite1152437895449049373et_nat
% 9.25/5.27          @ ( collect_set_nat
% 9.25/5.27            @ ^ [X3: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M4 @ X3 ) @ ( N4 @ X3 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8914_diff__preserves__multiset,axiom,
% 9.25/5.27      ! [M4: ( produc3658429121746597890et_nat > $o ) > nat,N4: ( produc3658429121746597890et_nat > $o ) > nat] :
% 9.25/5.27        ( ( finite3252695134891459830_nat_o
% 9.25/5.27          @ ( collec939566748876313656_nat_o
% 9.25/5.27            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 9.25/5.27       => ( finite3252695134891459830_nat_o
% 9.25/5.27          @ ( collec939566748876313656_nat_o
% 9.25/5.27            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M4 @ X3 ) @ ( N4 @ X3 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8915_diff__preserves__multiset,axiom,
% 9.25/5.27      ! [M4: nat > nat,N4: nat > nat] :
% 9.25/5.27        ( ( finite_finite_nat
% 9.25/5.27          @ ( collect_nat
% 9.25/5.27            @ ^ [X3: nat] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 9.25/5.27       => ( finite_finite_nat
% 9.25/5.27          @ ( collect_nat
% 9.25/5.27            @ ^ [X3: nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M4 @ X3 ) @ ( N4 @ X3 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8916_diff__preserves__multiset,axiom,
% 9.25/5.27      ! [M4: int > nat,N4: int > nat] :
% 9.25/5.27        ( ( finite_finite_int
% 9.25/5.27          @ ( collect_int
% 9.25/5.27            @ ^ [X3: int] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 9.25/5.27       => ( finite_finite_int
% 9.25/5.27          @ ( collect_int
% 9.25/5.27            @ ^ [X3: int] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M4 @ X3 ) @ ( N4 @ X3 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8917_diff__preserves__multiset,axiom,
% 9.25/5.27      ! [M4: product_prod_nat_nat > nat,N4: product_prod_nat_nat > nat] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat
% 9.25/5.27          @ ( collec3392354462482085612at_nat
% 9.25/5.27            @ ^ [X3: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 9.25/5.27       => ( finite6177210948735845034at_nat
% 9.25/5.27          @ ( collec3392354462482085612at_nat
% 9.25/5.27            @ ^ [X3: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M4 @ X3 ) @ ( N4 @ X3 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8918_add__mset__in__multiset,axiom,
% 9.25/5.27      ! [M4: set_Pr958786334691620121nt_int > nat,A: set_Pr958786334691620121nt_int] :
% 9.25/5.27        ( ( finite8744585540193469122nt_int
% 9.25/5.27          @ ( collec5210948495886036740nt_int
% 9.25/5.27            @ ^ [X3: set_Pr958786334691620121nt_int] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 9.25/5.27       => ( finite8744585540193469122nt_int
% 9.25/5.27          @ ( collec5210948495886036740nt_int
% 9.25/5.27            @ ^ [X3: set_Pr958786334691620121nt_int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X3 = A ) @ ( suc @ ( M4 @ X3 ) ) @ ( M4 @ X3 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8919_add__mset__in__multiset,axiom,
% 9.25/5.27      ! [M4: set_nat > nat,A: set_nat] :
% 9.25/5.27        ( ( finite1152437895449049373et_nat
% 9.25/5.27          @ ( collect_set_nat
% 9.25/5.27            @ ^ [X3: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 9.25/5.27       => ( finite1152437895449049373et_nat
% 9.25/5.27          @ ( collect_set_nat
% 9.25/5.27            @ ^ [X3: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X3 = A ) @ ( suc @ ( M4 @ X3 ) ) @ ( M4 @ X3 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8920_add__mset__in__multiset,axiom,
% 9.25/5.27      ! [M4: ( produc3658429121746597890et_nat > $o ) > nat,A: produc3658429121746597890et_nat > $o] :
% 9.25/5.27        ( ( finite3252695134891459830_nat_o
% 9.25/5.27          @ ( collec939566748876313656_nat_o
% 9.25/5.27            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 9.25/5.27       => ( finite3252695134891459830_nat_o
% 9.25/5.27          @ ( collec939566748876313656_nat_o
% 9.25/5.27            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X3 = A ) @ ( suc @ ( M4 @ X3 ) ) @ ( M4 @ X3 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8921_add__mset__in__multiset,axiom,
% 9.25/5.27      ! [M4: nat > nat,A: nat] :
% 9.25/5.27        ( ( finite_finite_nat
% 9.25/5.27          @ ( collect_nat
% 9.25/5.27            @ ^ [X3: nat] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 9.25/5.27       => ( finite_finite_nat
% 9.25/5.27          @ ( collect_nat
% 9.25/5.27            @ ^ [X3: nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X3 = A ) @ ( suc @ ( M4 @ X3 ) ) @ ( M4 @ X3 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8922_add__mset__in__multiset,axiom,
% 9.25/5.27      ! [M4: int > nat,A: int] :
% 9.25/5.27        ( ( finite_finite_int
% 9.25/5.27          @ ( collect_int
% 9.25/5.27            @ ^ [X3: int] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 9.25/5.27       => ( finite_finite_int
% 9.25/5.27          @ ( collect_int
% 9.25/5.27            @ ^ [X3: int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X3 = A ) @ ( suc @ ( M4 @ X3 ) ) @ ( M4 @ X3 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8923_add__mset__in__multiset,axiom,
% 9.25/5.27      ! [M4: product_prod_nat_nat > nat,A: product_prod_nat_nat] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat
% 9.25/5.27          @ ( collec3392354462482085612at_nat
% 9.25/5.27            @ ^ [X3: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 9.25/5.27       => ( finite6177210948735845034at_nat
% 9.25/5.27          @ ( collec3392354462482085612at_nat
% 9.25/5.27            @ ^ [X3: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X3 = A ) @ ( suc @ ( M4 @ X3 ) ) @ ( M4 @ X3 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8924_finite__linorder__min__induct,axiom,
% 9.25/5.27      ! [A2: set_o,P: set_o > $o] :
% 9.25/5.27        ( ( finite_finite_o @ A2 )
% 9.25/5.27       => ( ( P @ bot_bot_set_o )
% 9.25/5.27         => ( ! [B6: $o,A8: set_o] :
% 9.25/5.27                ( ( finite_finite_o @ A8 )
% 9.25/5.27               => ( ! [X5: $o] :
% 9.25/5.27                      ( ( member_o @ X5 @ A8 )
% 9.25/5.27                     => ( ord_less_o @ B6 @ X5 ) )
% 9.25/5.27                 => ( ( P @ A8 )
% 9.25/5.27                   => ( P @ ( insert_o @ B6 @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8925_finite__linorder__min__induct,axiom,
% 9.25/5.27      ! [A2: set_literal,P: set_literal > $o] :
% 9.25/5.27        ( ( finite5847741373460823677iteral @ A2 )
% 9.25/5.27       => ( ( P @ bot_bot_set_literal )
% 9.25/5.27         => ( ! [B6: literal,A8: set_literal] :
% 9.25/5.27                ( ( finite5847741373460823677iteral @ A8 )
% 9.25/5.27               => ( ! [X5: literal] :
% 9.25/5.27                      ( ( member_literal @ X5 @ A8 )
% 9.25/5.27                     => ( ord_less_literal @ B6 @ X5 ) )
% 9.25/5.27                 => ( ( P @ A8 )
% 9.25/5.27                   => ( P @ ( insert_literal @ B6 @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8926_finite__linorder__min__induct,axiom,
% 9.25/5.27      ! [A2: set_rat,P: set_rat > $o] :
% 9.25/5.27        ( ( finite_finite_rat @ A2 )
% 9.25/5.27       => ( ( P @ bot_bot_set_rat )
% 9.25/5.27         => ( ! [B6: rat,A8: set_rat] :
% 9.25/5.27                ( ( finite_finite_rat @ A8 )
% 9.25/5.27               => ( ! [X5: rat] :
% 9.25/5.27                      ( ( member_rat @ X5 @ A8 )
% 9.25/5.27                     => ( ord_less_rat @ B6 @ X5 ) )
% 9.25/5.27                 => ( ( P @ A8 )
% 9.25/5.27                   => ( P @ ( insert_rat @ B6 @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8927_finite__linorder__min__induct,axiom,
% 9.25/5.27      ! [A2: set_nat,P: set_nat > $o] :
% 9.25/5.27        ( ( finite_finite_nat @ A2 )
% 9.25/5.27       => ( ( P @ bot_bot_set_nat )
% 9.25/5.27         => ( ! [B6: nat,A8: set_nat] :
% 9.25/5.27                ( ( finite_finite_nat @ A8 )
% 9.25/5.27               => ( ! [X5: nat] :
% 9.25/5.27                      ( ( member_nat @ X5 @ A8 )
% 9.25/5.27                     => ( ord_less_nat @ B6 @ X5 ) )
% 9.25/5.27                 => ( ( P @ A8 )
% 9.25/5.27                   => ( P @ ( insert_nat @ B6 @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8928_finite__linorder__min__induct,axiom,
% 9.25/5.27      ! [A2: set_int,P: set_int > $o] :
% 9.25/5.27        ( ( finite_finite_int @ A2 )
% 9.25/5.27       => ( ( P @ bot_bot_set_int )
% 9.25/5.27         => ( ! [B6: int,A8: set_int] :
% 9.25/5.27                ( ( finite_finite_int @ A8 )
% 9.25/5.27               => ( ! [X5: int] :
% 9.25/5.27                      ( ( member_int @ X5 @ A8 )
% 9.25/5.27                     => ( ord_less_int @ B6 @ X5 ) )
% 9.25/5.27                 => ( ( P @ A8 )
% 9.25/5.27                   => ( P @ ( insert_int @ B6 @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8929_finite__linorder__max__induct,axiom,
% 9.25/5.27      ! [A2: set_o,P: set_o > $o] :
% 9.25/5.27        ( ( finite_finite_o @ A2 )
% 9.25/5.27       => ( ( P @ bot_bot_set_o )
% 9.25/5.27         => ( ! [B6: $o,A8: set_o] :
% 9.25/5.27                ( ( finite_finite_o @ A8 )
% 9.25/5.27               => ( ! [X5: $o] :
% 9.25/5.27                      ( ( member_o @ X5 @ A8 )
% 9.25/5.27                     => ( ord_less_o @ X5 @ B6 ) )
% 9.25/5.27                 => ( ( P @ A8 )
% 9.25/5.27                   => ( P @ ( insert_o @ B6 @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8930_finite__linorder__max__induct,axiom,
% 9.25/5.27      ! [A2: set_literal,P: set_literal > $o] :
% 9.25/5.27        ( ( finite5847741373460823677iteral @ A2 )
% 9.25/5.27       => ( ( P @ bot_bot_set_literal )
% 9.25/5.27         => ( ! [B6: literal,A8: set_literal] :
% 9.25/5.27                ( ( finite5847741373460823677iteral @ A8 )
% 9.25/5.27               => ( ! [X5: literal] :
% 9.25/5.27                      ( ( member_literal @ X5 @ A8 )
% 9.25/5.27                     => ( ord_less_literal @ X5 @ B6 ) )
% 9.25/5.27                 => ( ( P @ A8 )
% 9.25/5.27                   => ( P @ ( insert_literal @ B6 @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8931_finite__linorder__max__induct,axiom,
% 9.25/5.27      ! [A2: set_rat,P: set_rat > $o] :
% 9.25/5.27        ( ( finite_finite_rat @ A2 )
% 9.25/5.27       => ( ( P @ bot_bot_set_rat )
% 9.25/5.27         => ( ! [B6: rat,A8: set_rat] :
% 9.25/5.27                ( ( finite_finite_rat @ A8 )
% 9.25/5.27               => ( ! [X5: rat] :
% 9.25/5.27                      ( ( member_rat @ X5 @ A8 )
% 9.25/5.27                     => ( ord_less_rat @ X5 @ B6 ) )
% 9.25/5.27                 => ( ( P @ A8 )
% 9.25/5.27                   => ( P @ ( insert_rat @ B6 @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8932_finite__linorder__max__induct,axiom,
% 9.25/5.27      ! [A2: set_nat,P: set_nat > $o] :
% 9.25/5.27        ( ( finite_finite_nat @ A2 )
% 9.25/5.27       => ( ( P @ bot_bot_set_nat )
% 9.25/5.27         => ( ! [B6: nat,A8: set_nat] :
% 9.25/5.27                ( ( finite_finite_nat @ A8 )
% 9.25/5.27               => ( ! [X5: nat] :
% 9.25/5.27                      ( ( member_nat @ X5 @ A8 )
% 9.25/5.27                     => ( ord_less_nat @ X5 @ B6 ) )
% 9.25/5.27                 => ( ( P @ A8 )
% 9.25/5.27                   => ( P @ ( insert_nat @ B6 @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8933_finite__linorder__max__induct,axiom,
% 9.25/5.27      ! [A2: set_int,P: set_int > $o] :
% 9.25/5.27        ( ( finite_finite_int @ A2 )
% 9.25/5.27       => ( ( P @ bot_bot_set_int )
% 9.25/5.27         => ( ! [B6: int,A8: set_int] :
% 9.25/5.27                ( ( finite_finite_int @ A8 )
% 9.25/5.27               => ( ! [X5: int] :
% 9.25/5.27                      ( ( member_int @ X5 @ A8 )
% 9.25/5.27                     => ( ord_less_int @ X5 @ B6 ) )
% 9.25/5.27                 => ( ( P @ A8 )
% 9.25/5.27                   => ( P @ ( insert_int @ B6 @ A8 ) ) ) ) )
% 9.25/5.27           => ( P @ A2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8934_finite__ranking__induct,axiom,
% 9.25/5.27      ! [S: set_o,P: set_o > $o,F2: $o > rat] :
% 9.25/5.27        ( ( finite_finite_o @ S )
% 9.25/5.27       => ( ( P @ bot_bot_set_o )
% 9.25/5.27         => ( ! [X2: $o,S6: set_o] :
% 9.25/5.27                ( ( finite_finite_o @ S6 )
% 9.25/5.27               => ( ! [Y5: $o] :
% 9.25/5.27                      ( ( member_o @ Y5 @ S6 )
% 9.25/5.27                     => ( ord_less_eq_rat @ ( F2 @ Y5 ) @ ( F2 @ X2 ) ) )
% 9.25/5.27                 => ( ( P @ S6 )
% 9.25/5.27                   => ( P @ ( insert_o @ X2 @ S6 ) ) ) ) )
% 9.25/5.27           => ( P @ S ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8935_finite__ranking__induct,axiom,
% 9.25/5.27      ! [S: set_nat,P: set_nat > $o,F2: nat > rat] :
% 9.25/5.27        ( ( finite_finite_nat @ S )
% 9.25/5.27       => ( ( P @ bot_bot_set_nat )
% 9.25/5.27         => ( ! [X2: nat,S6: set_nat] :
% 9.25/5.27                ( ( finite_finite_nat @ S6 )
% 9.25/5.27               => ( ! [Y5: nat] :
% 9.25/5.27                      ( ( member_nat @ Y5 @ S6 )
% 9.25/5.27                     => ( ord_less_eq_rat @ ( F2 @ Y5 ) @ ( F2 @ X2 ) ) )
% 9.25/5.27                 => ( ( P @ S6 )
% 9.25/5.27                   => ( P @ ( insert_nat @ X2 @ S6 ) ) ) ) )
% 9.25/5.27           => ( P @ S ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8936_finite__ranking__induct,axiom,
% 9.25/5.27      ! [S: set_int,P: set_int > $o,F2: int > rat] :
% 9.25/5.27        ( ( finite_finite_int @ S )
% 9.25/5.27       => ( ( P @ bot_bot_set_int )
% 9.25/5.27         => ( ! [X2: int,S6: set_int] :
% 9.25/5.27                ( ( finite_finite_int @ S6 )
% 9.25/5.27               => ( ! [Y5: int] :
% 9.25/5.27                      ( ( member_int @ Y5 @ S6 )
% 9.25/5.27                     => ( ord_less_eq_rat @ ( F2 @ Y5 ) @ ( F2 @ X2 ) ) )
% 9.25/5.27                 => ( ( P @ S6 )
% 9.25/5.27                   => ( P @ ( insert_int @ X2 @ S6 ) ) ) ) )
% 9.25/5.27           => ( P @ S ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8937_finite__ranking__induct,axiom,
% 9.25/5.27      ! [S: set_o,P: set_o > $o,F2: $o > nat] :
% 9.25/5.27        ( ( finite_finite_o @ S )
% 9.25/5.27       => ( ( P @ bot_bot_set_o )
% 9.25/5.27         => ( ! [X2: $o,S6: set_o] :
% 9.25/5.27                ( ( finite_finite_o @ S6 )
% 9.25/5.27               => ( ! [Y5: $o] :
% 9.25/5.27                      ( ( member_o @ Y5 @ S6 )
% 9.25/5.27                     => ( ord_less_eq_nat @ ( F2 @ Y5 ) @ ( F2 @ X2 ) ) )
% 9.25/5.27                 => ( ( P @ S6 )
% 9.25/5.27                   => ( P @ ( insert_o @ X2 @ S6 ) ) ) ) )
% 9.25/5.27           => ( P @ S ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8938_finite__ranking__induct,axiom,
% 9.25/5.27      ! [S: set_nat,P: set_nat > $o,F2: nat > nat] :
% 9.25/5.27        ( ( finite_finite_nat @ S )
% 9.25/5.27       => ( ( P @ bot_bot_set_nat )
% 9.25/5.27         => ( ! [X2: nat,S6: set_nat] :
% 9.25/5.27                ( ( finite_finite_nat @ S6 )
% 9.25/5.27               => ( ! [Y5: nat] :
% 9.25/5.27                      ( ( member_nat @ Y5 @ S6 )
% 9.25/5.27                     => ( ord_less_eq_nat @ ( F2 @ Y5 ) @ ( F2 @ X2 ) ) )
% 9.25/5.27                 => ( ( P @ S6 )
% 9.25/5.27                   => ( P @ ( insert_nat @ X2 @ S6 ) ) ) ) )
% 9.25/5.27           => ( P @ S ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8939_finite__ranking__induct,axiom,
% 9.25/5.27      ! [S: set_int,P: set_int > $o,F2: int > nat] :
% 9.25/5.27        ( ( finite_finite_int @ S )
% 9.25/5.27       => ( ( P @ bot_bot_set_int )
% 9.25/5.27         => ( ! [X2: int,S6: set_int] :
% 9.25/5.27                ( ( finite_finite_int @ S6 )
% 9.25/5.27               => ( ! [Y5: int] :
% 9.25/5.27                      ( ( member_int @ Y5 @ S6 )
% 9.25/5.27                     => ( ord_less_eq_nat @ ( F2 @ Y5 ) @ ( F2 @ X2 ) ) )
% 9.25/5.27                 => ( ( P @ S6 )
% 9.25/5.27                   => ( P @ ( insert_int @ X2 @ S6 ) ) ) ) )
% 9.25/5.27           => ( P @ S ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8940_finite__ranking__induct,axiom,
% 9.25/5.27      ! [S: set_o,P: set_o > $o,F2: $o > int] :
% 9.25/5.27        ( ( finite_finite_o @ S )
% 9.25/5.27       => ( ( P @ bot_bot_set_o )
% 9.25/5.27         => ( ! [X2: $o,S6: set_o] :
% 9.25/5.27                ( ( finite_finite_o @ S6 )
% 9.25/5.27               => ( ! [Y5: $o] :
% 9.25/5.27                      ( ( member_o @ Y5 @ S6 )
% 9.25/5.27                     => ( ord_less_eq_int @ ( F2 @ Y5 ) @ ( F2 @ X2 ) ) )
% 9.25/5.27                 => ( ( P @ S6 )
% 9.25/5.27                   => ( P @ ( insert_o @ X2 @ S6 ) ) ) ) )
% 9.25/5.27           => ( P @ S ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8941_finite__ranking__induct,axiom,
% 9.25/5.27      ! [S: set_nat,P: set_nat > $o,F2: nat > int] :
% 9.25/5.27        ( ( finite_finite_nat @ S )
% 9.25/5.27       => ( ( P @ bot_bot_set_nat )
% 9.25/5.27         => ( ! [X2: nat,S6: set_nat] :
% 9.25/5.27                ( ( finite_finite_nat @ S6 )
% 9.25/5.27               => ( ! [Y5: nat] :
% 9.25/5.27                      ( ( member_nat @ Y5 @ S6 )
% 9.25/5.27                     => ( ord_less_eq_int @ ( F2 @ Y5 ) @ ( F2 @ X2 ) ) )
% 9.25/5.27                 => ( ( P @ S6 )
% 9.25/5.27                   => ( P @ ( insert_nat @ X2 @ S6 ) ) ) ) )
% 9.25/5.27           => ( P @ S ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8942_finite__ranking__induct,axiom,
% 9.25/5.27      ! [S: set_int,P: set_int > $o,F2: int > int] :
% 9.25/5.27        ( ( finite_finite_int @ S )
% 9.25/5.27       => ( ( P @ bot_bot_set_int )
% 9.25/5.27         => ( ! [X2: int,S6: set_int] :
% 9.25/5.27                ( ( finite_finite_int @ S6 )
% 9.25/5.27               => ( ! [Y5: int] :
% 9.25/5.27                      ( ( member_int @ Y5 @ S6 )
% 9.25/5.27                     => ( ord_less_eq_int @ ( F2 @ Y5 ) @ ( F2 @ X2 ) ) )
% 9.25/5.27                 => ( ( P @ S6 )
% 9.25/5.27                   => ( P @ ( insert_int @ X2 @ S6 ) ) ) ) )
% 9.25/5.27           => ( P @ S ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8943_finite__ranking__induct,axiom,
% 9.25/5.27      ! [S: set_set_nat,P: set_set_nat > $o,F2: set_nat > rat] :
% 9.25/5.27        ( ( finite1152437895449049373et_nat @ S )
% 9.25/5.27       => ( ( P @ bot_bot_set_set_nat )
% 9.25/5.27         => ( ! [X2: set_nat,S6: set_set_nat] :
% 9.25/5.27                ( ( finite1152437895449049373et_nat @ S6 )
% 9.25/5.27               => ( ! [Y5: set_nat] :
% 9.25/5.27                      ( ( member_set_nat @ Y5 @ S6 )
% 9.25/5.27                     => ( ord_less_eq_rat @ ( F2 @ Y5 ) @ ( F2 @ X2 ) ) )
% 9.25/5.27                 => ( ( P @ S6 )
% 9.25/5.27                   => ( P @ ( insert_set_nat @ X2 @ S6 ) ) ) ) )
% 9.25/5.27           => ( P @ S ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8944_infinite__growing,axiom,
% 9.25/5.27      ! [X7: set_o] :
% 9.25/5.27        ( ( X7 != bot_bot_set_o )
% 9.25/5.27       => ( ! [X2: $o] :
% 9.25/5.27              ( ( member_o @ X2 @ X7 )
% 9.25/5.27             => ? [Xa2: $o] :
% 9.25/5.27                  ( ( member_o @ Xa2 @ X7 )
% 9.25/5.27                  & ( ord_less_o @ X2 @ Xa2 ) ) )
% 9.25/5.27         => ~ ( finite_finite_o @ X7 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8945_infinite__growing,axiom,
% 9.25/5.27      ! [X7: set_literal] :
% 9.25/5.27        ( ( X7 != bot_bot_set_literal )
% 9.25/5.27       => ( ! [X2: literal] :
% 9.25/5.27              ( ( member_literal @ X2 @ X7 )
% 9.25/5.27             => ? [Xa2: literal] :
% 9.25/5.27                  ( ( member_literal @ Xa2 @ X7 )
% 9.25/5.27                  & ( ord_less_literal @ X2 @ Xa2 ) ) )
% 9.25/5.27         => ~ ( finite5847741373460823677iteral @ X7 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8946_infinite__growing,axiom,
% 9.25/5.27      ! [X7: set_rat] :
% 9.25/5.27        ( ( X7 != bot_bot_set_rat )
% 9.25/5.27       => ( ! [X2: rat] :
% 9.25/5.27              ( ( member_rat @ X2 @ X7 )
% 9.25/5.27             => ? [Xa2: rat] :
% 9.25/5.27                  ( ( member_rat @ Xa2 @ X7 )
% 9.25/5.27                  & ( ord_less_rat @ X2 @ Xa2 ) ) )
% 9.25/5.27         => ~ ( finite_finite_rat @ X7 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8947_infinite__growing,axiom,
% 9.25/5.27      ! [X7: set_nat] :
% 9.25/5.27        ( ( X7 != bot_bot_set_nat )
% 9.25/5.27       => ( ! [X2: nat] :
% 9.25/5.27              ( ( member_nat @ X2 @ X7 )
% 9.25/5.27             => ? [Xa2: nat] :
% 9.25/5.27                  ( ( member_nat @ Xa2 @ X7 )
% 9.25/5.27                  & ( ord_less_nat @ X2 @ Xa2 ) ) )
% 9.25/5.27         => ~ ( finite_finite_nat @ X7 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8948_infinite__growing,axiom,
% 9.25/5.27      ! [X7: set_int] :
% 9.25/5.27        ( ( X7 != bot_bot_set_int )
% 9.25/5.27       => ( ! [X2: int] :
% 9.25/5.27              ( ( member_int @ X2 @ X7 )
% 9.25/5.27             => ? [Xa2: int] :
% 9.25/5.27                  ( ( member_int @ Xa2 @ X7 )
% 9.25/5.27                  & ( ord_less_int @ X2 @ Xa2 ) ) )
% 9.25/5.27         => ~ ( finite_finite_int @ X7 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8949_ex__min__if__finite,axiom,
% 9.25/5.27      ! [S: set_o] :
% 9.25/5.27        ( ( finite_finite_o @ S )
% 9.25/5.27       => ( ( S != bot_bot_set_o )
% 9.25/5.27         => ? [X2: $o] :
% 9.25/5.27              ( ( member_o @ X2 @ S )
% 9.25/5.27              & ~ ? [Xa2: $o] :
% 9.25/5.27                    ( ( member_o @ Xa2 @ S )
% 9.25/5.27                    & ( ord_less_o @ Xa2 @ X2 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8950_ex__min__if__finite,axiom,
% 9.25/5.27      ! [S: set_literal] :
% 9.25/5.27        ( ( finite5847741373460823677iteral @ S )
% 9.25/5.27       => ( ( S != bot_bot_set_literal )
% 9.25/5.27         => ? [X2: literal] :
% 9.25/5.27              ( ( member_literal @ X2 @ S )
% 9.25/5.27              & ~ ? [Xa2: literal] :
% 9.25/5.27                    ( ( member_literal @ Xa2 @ S )
% 9.25/5.27                    & ( ord_less_literal @ Xa2 @ X2 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8951_ex__min__if__finite,axiom,
% 9.25/5.27      ! [S: set_rat] :
% 9.25/5.27        ( ( finite_finite_rat @ S )
% 9.25/5.27       => ( ( S != bot_bot_set_rat )
% 9.25/5.27         => ? [X2: rat] :
% 9.25/5.27              ( ( member_rat @ X2 @ S )
% 9.25/5.27              & ~ ? [Xa2: rat] :
% 9.25/5.27                    ( ( member_rat @ Xa2 @ S )
% 9.25/5.27                    & ( ord_less_rat @ Xa2 @ X2 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8952_ex__min__if__finite,axiom,
% 9.25/5.27      ! [S: set_nat] :
% 9.25/5.27        ( ( finite_finite_nat @ S )
% 9.25/5.27       => ( ( S != bot_bot_set_nat )
% 9.25/5.27         => ? [X2: nat] :
% 9.25/5.27              ( ( member_nat @ X2 @ S )
% 9.25/5.27              & ~ ? [Xa2: nat] :
% 9.25/5.27                    ( ( member_nat @ Xa2 @ S )
% 9.25/5.27                    & ( ord_less_nat @ Xa2 @ X2 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8953_ex__min__if__finite,axiom,
% 9.25/5.27      ! [S: set_int] :
% 9.25/5.27        ( ( finite_finite_int @ S )
% 9.25/5.27       => ( ( S != bot_bot_set_int )
% 9.25/5.27         => ? [X2: int] :
% 9.25/5.27              ( ( member_int @ X2 @ S )
% 9.25/5.27              & ~ ? [Xa2: int] :
% 9.25/5.27                    ( ( member_int @ Xa2 @ S )
% 9.25/5.27                    & ( ord_less_int @ Xa2 @ X2 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8954_filter__preserves__multiset,axiom,
% 9.25/5.27      ! [M4: set_Pr958786334691620121nt_int > nat,P: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.27        ( ( finite8744585540193469122nt_int
% 9.25/5.27          @ ( collec5210948495886036740nt_int
% 9.25/5.27            @ ^ [X3: set_Pr958786334691620121nt_int] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 9.25/5.27       => ( finite8744585540193469122nt_int
% 9.25/5.27          @ ( collec5210948495886036740nt_int
% 9.25/5.27            @ ^ [X3: set_Pr958786334691620121nt_int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X3 ) @ ( M4 @ X3 ) @ zero_zero_nat ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8955_filter__preserves__multiset,axiom,
% 9.25/5.27      ! [M4: set_nat > nat,P: set_nat > $o] :
% 9.25/5.27        ( ( finite1152437895449049373et_nat
% 9.25/5.27          @ ( collect_set_nat
% 9.25/5.27            @ ^ [X3: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 9.25/5.27       => ( finite1152437895449049373et_nat
% 9.25/5.27          @ ( collect_set_nat
% 9.25/5.27            @ ^ [X3: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X3 ) @ ( M4 @ X3 ) @ zero_zero_nat ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8956_filter__preserves__multiset,axiom,
% 9.25/5.27      ! [M4: ( produc3658429121746597890et_nat > $o ) > nat,P: ( produc3658429121746597890et_nat > $o ) > $o] :
% 9.25/5.27        ( ( finite3252695134891459830_nat_o
% 9.25/5.27          @ ( collec939566748876313656_nat_o
% 9.25/5.27            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 9.25/5.27       => ( finite3252695134891459830_nat_o
% 9.25/5.27          @ ( collec939566748876313656_nat_o
% 9.25/5.27            @ ^ [X3: produc3658429121746597890et_nat > $o] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X3 ) @ ( M4 @ X3 ) @ zero_zero_nat ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8957_filter__preserves__multiset,axiom,
% 9.25/5.27      ! [M4: nat > nat,P: nat > $o] :
% 9.25/5.27        ( ( finite_finite_nat
% 9.25/5.27          @ ( collect_nat
% 9.25/5.27            @ ^ [X3: nat] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 9.25/5.27       => ( finite_finite_nat
% 9.25/5.27          @ ( collect_nat
% 9.25/5.27            @ ^ [X3: nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X3 ) @ ( M4 @ X3 ) @ zero_zero_nat ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8958_filter__preserves__multiset,axiom,
% 9.25/5.27      ! [M4: int > nat,P: int > $o] :
% 9.25/5.27        ( ( finite_finite_int
% 9.25/5.27          @ ( collect_int
% 9.25/5.27            @ ^ [X3: int] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 9.25/5.27       => ( finite_finite_int
% 9.25/5.27          @ ( collect_int
% 9.25/5.27            @ ^ [X3: int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X3 ) @ ( M4 @ X3 ) @ zero_zero_nat ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8959_filter__preserves__multiset,axiom,
% 9.25/5.27      ! [M4: product_prod_nat_nat > nat,P: product_prod_nat_nat > $o] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat
% 9.25/5.27          @ ( collec3392354462482085612at_nat
% 9.25/5.27            @ ^ [X3: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( M4 @ X3 ) ) ) )
% 9.25/5.27       => ( finite6177210948735845034at_nat
% 9.25/5.27          @ ( collec3392354462482085612at_nat
% 9.25/5.27            @ ^ [X3: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X3 ) @ ( M4 @ X3 ) @ zero_zero_nat ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8960_divide__int__def,axiom,
% 9.25/5.27      ( divide_divide_int
% 9.25/5.27      = ( ^ [K4: int,L2: int] :
% 9.25/5.27            ( if_int @ ( L2 = zero_zero_int ) @ zero_zero_int
% 9.25/5.27            @ ( if_int
% 9.25/5.27              @ ( ( sgn_sgn_int @ K4 )
% 9.25/5.27                = ( sgn_sgn_int @ L2 ) )
% 9.25/5.27              @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K4 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) )
% 9.25/5.27              @ ( uminus_uminus_int
% 9.25/5.27                @ ( semiri1314217659103216013at_int
% 9.25/5.27                  @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K4 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) )
% 9.25/5.27                    @ ( zero_n2687167440665602831ol_nat
% 9.25/5.27                      @ ~ ( dvd_dvd_int @ L2 @ K4 ) ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8961_sum__diff1_H__aux,axiom,
% 9.25/5.27      ! [F4: set_o,I4: set_o,F2: $o > code_integer,I: $o] :
% 9.25/5.27        ( ( finite_finite_o @ F4 )
% 9.25/5.27       => ( ( ord_less_eq_set_o
% 9.25/5.27            @ ( collect_o
% 9.25/5.27              @ ^ [I3: $o] :
% 9.25/5.27                  ( ( member_o @ I3 @ I4 )
% 9.25/5.27                  & ( ( F2 @ I3 )
% 9.25/5.27                   != zero_z3403309356797280102nteger ) ) )
% 9.25/5.27            @ F4 )
% 9.25/5.27         => ( ( ( member_o @ I @ I4 )
% 9.25/5.27             => ( ( groups1402912129352969042nteger @ F2 @ ( minus_minus_set_o @ I4 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 9.25/5.27                = ( minus_8373710615458151222nteger @ ( groups1402912129352969042nteger @ F2 @ I4 ) @ ( F2 @ I ) ) ) )
% 9.25/5.27            & ( ~ ( member_o @ I @ I4 )
% 9.25/5.27             => ( ( groups1402912129352969042nteger @ F2 @ ( minus_minus_set_o @ I4 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 9.25/5.27                = ( groups1402912129352969042nteger @ F2 @ I4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8962_sum__diff1_H__aux,axiom,
% 9.25/5.27      ! [F4: set_int,I4: set_int,F2: int > code_integer,I: int] :
% 9.25/5.27        ( ( finite_finite_int @ F4 )
% 9.25/5.27       => ( ( ord_less_eq_set_int
% 9.25/5.27            @ ( collect_int
% 9.25/5.27              @ ^ [I3: int] :
% 9.25/5.27                  ( ( member_int @ I3 @ I4 )
% 9.25/5.27                  & ( ( F2 @ I3 )
% 9.25/5.27                   != zero_z3403309356797280102nteger ) ) )
% 9.25/5.27            @ F4 )
% 9.25/5.27         => ( ( ( member_int @ I @ I4 )
% 9.25/5.27             => ( ( groups926780983652909934nteger @ F2 @ ( minus_minus_set_int @ I4 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 9.25/5.27                = ( minus_8373710615458151222nteger @ ( groups926780983652909934nteger @ F2 @ I4 ) @ ( F2 @ I ) ) ) )
% 9.25/5.27            & ( ~ ( member_int @ I @ I4 )
% 9.25/5.27             => ( ( groups926780983652909934nteger @ F2 @ ( minus_minus_set_int @ I4 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 9.25/5.27                = ( groups926780983652909934nteger @ F2 @ I4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8963_sum__diff1_H__aux,axiom,
% 9.25/5.27      ! [F4: set_o,I4: set_o,F2: $o > rat,I: $o] :
% 9.25/5.27        ( ( finite_finite_o @ F4 )
% 9.25/5.27       => ( ( ord_less_eq_set_o
% 9.25/5.27            @ ( collect_o
% 9.25/5.27              @ ^ [I3: $o] :
% 9.25/5.27                  ( ( member_o @ I3 @ I4 )
% 9.25/5.27                  & ( ( F2 @ I3 )
% 9.25/5.27                   != zero_zero_rat ) ) )
% 9.25/5.27            @ F4 )
% 9.25/5.27         => ( ( ( member_o @ I @ I4 )
% 9.25/5.27             => ( ( groups3921277224699582669_o_rat @ F2 @ ( minus_minus_set_o @ I4 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 9.25/5.27                = ( minus_minus_rat @ ( groups3921277224699582669_o_rat @ F2 @ I4 ) @ ( F2 @ I ) ) ) )
% 9.25/5.27            & ( ~ ( member_o @ I @ I4 )
% 9.25/5.27             => ( ( groups3921277224699582669_o_rat @ F2 @ ( minus_minus_set_o @ I4 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 9.25/5.27                = ( groups3921277224699582669_o_rat @ F2 @ I4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8964_sum__diff1_H__aux,axiom,
% 9.25/5.27      ! [F4: set_int,I4: set_int,F2: int > rat,I: int] :
% 9.25/5.27        ( ( finite_finite_int @ F4 )
% 9.25/5.27       => ( ( ord_less_eq_set_int
% 9.25/5.27            @ ( collect_int
% 9.25/5.27              @ ^ [I3: int] :
% 9.25/5.27                  ( ( member_int @ I3 @ I4 )
% 9.25/5.27                  & ( ( F2 @ I3 )
% 9.25/5.27                   != zero_zero_rat ) ) )
% 9.25/5.27            @ F4 )
% 9.25/5.27         => ( ( ( member_int @ I @ I4 )
% 9.25/5.27             => ( ( groups2350640619554545897nt_rat @ F2 @ ( minus_minus_set_int @ I4 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 9.25/5.27                = ( minus_minus_rat @ ( groups2350640619554545897nt_rat @ F2 @ I4 ) @ ( F2 @ I ) ) ) )
% 9.25/5.27            & ( ~ ( member_int @ I @ I4 )
% 9.25/5.27             => ( ( groups2350640619554545897nt_rat @ F2 @ ( minus_minus_set_int @ I4 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 9.25/5.27                = ( groups2350640619554545897nt_rat @ F2 @ I4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8965_sum__diff1_H__aux,axiom,
% 9.25/5.27      ! [F4: set_o,I4: set_o,F2: $o > int,I: $o] :
% 9.25/5.27        ( ( finite_finite_o @ F4 )
% 9.25/5.27       => ( ( ord_less_eq_set_o
% 9.25/5.27            @ ( collect_o
% 9.25/5.27              @ ^ [I3: $o] :
% 9.25/5.27                  ( ( member_o @ I3 @ I4 )
% 9.25/5.27                  & ( ( F2 @ I3 )
% 9.25/5.27                   != zero_zero_int ) ) )
% 9.25/5.27            @ F4 )
% 9.25/5.27         => ( ( ( member_o @ I @ I4 )
% 9.25/5.27             => ( ( groups4553916814277028129_o_int @ F2 @ ( minus_minus_set_o @ I4 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 9.25/5.27                = ( minus_minus_int @ ( groups4553916814277028129_o_int @ F2 @ I4 ) @ ( F2 @ I ) ) ) )
% 9.25/5.27            & ( ~ ( member_o @ I @ I4 )
% 9.25/5.27             => ( ( groups4553916814277028129_o_int @ F2 @ ( minus_minus_set_o @ I4 @ ( insert_o @ I @ bot_bot_set_o ) ) )
% 9.25/5.27                = ( groups4553916814277028129_o_int @ F2 @ I4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8966_sum__diff1_H__aux,axiom,
% 9.25/5.27      ! [F4: set_int,I4: set_int,F2: int > int,I: int] :
% 9.25/5.27        ( ( finite_finite_int @ F4 )
% 9.25/5.27       => ( ( ord_less_eq_set_int
% 9.25/5.27            @ ( collect_int
% 9.25/5.27              @ ^ [I3: int] :
% 9.25/5.27                  ( ( member_int @ I3 @ I4 )
% 9.25/5.27                  & ( ( F2 @ I3 )
% 9.25/5.27                   != zero_zero_int ) ) )
% 9.25/5.27            @ F4 )
% 9.25/5.27         => ( ( ( member_int @ I @ I4 )
% 9.25/5.27             => ( ( groups2983280209131991357nt_int @ F2 @ ( minus_minus_set_int @ I4 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 9.25/5.27                = ( minus_minus_int @ ( groups2983280209131991357nt_int @ F2 @ I4 ) @ ( F2 @ I ) ) ) )
% 9.25/5.27            & ( ~ ( member_int @ I @ I4 )
% 9.25/5.27             => ( ( groups2983280209131991357nt_int @ F2 @ ( minus_minus_set_int @ I4 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 9.25/5.27                = ( groups2983280209131991357nt_int @ F2 @ I4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8967_sum__diff1_H__aux,axiom,
% 9.25/5.27      ! [F4: set_nat,I4: set_nat,F2: nat > code_integer,I: nat] :
% 9.25/5.27        ( ( finite_finite_nat @ F4 )
% 9.25/5.27       => ( ( ord_less_eq_set_nat
% 9.25/5.27            @ ( collect_nat
% 9.25/5.27              @ ^ [I3: nat] :
% 9.25/5.27                  ( ( member_nat @ I3 @ I4 )
% 9.25/5.27                  & ( ( F2 @ I3 )
% 9.25/5.27                   != zero_z3403309356797280102nteger ) ) )
% 9.25/5.27            @ F4 )
% 9.25/5.27         => ( ( ( member_nat @ I @ I4 )
% 9.25/5.27             => ( ( groups555127423416065298nteger @ F2 @ ( minus_minus_set_nat @ I4 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 9.25/5.27                = ( minus_8373710615458151222nteger @ ( groups555127423416065298nteger @ F2 @ I4 ) @ ( F2 @ I ) ) ) )
% 9.25/5.27            & ( ~ ( member_nat @ I @ I4 )
% 9.25/5.27             => ( ( groups555127423416065298nteger @ F2 @ ( minus_minus_set_nat @ I4 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 9.25/5.27                = ( groups555127423416065298nteger @ F2 @ I4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8968_sum__diff1_H__aux,axiom,
% 9.25/5.27      ! [F4: set_nat,I4: set_nat,F2: nat > rat,I: nat] :
% 9.25/5.27        ( ( finite_finite_nat @ F4 )
% 9.25/5.27       => ( ( ord_less_eq_set_nat
% 9.25/5.27            @ ( collect_nat
% 9.25/5.27              @ ^ [I3: nat] :
% 9.25/5.27                  ( ( member_nat @ I3 @ I4 )
% 9.25/5.27                  & ( ( F2 @ I3 )
% 9.25/5.27                   != zero_zero_rat ) ) )
% 9.25/5.27            @ F4 )
% 9.25/5.27         => ( ( ( member_nat @ I @ I4 )
% 9.25/5.27             => ( ( groups1351286907653491341at_rat @ F2 @ ( minus_minus_set_nat @ I4 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 9.25/5.27                = ( minus_minus_rat @ ( groups1351286907653491341at_rat @ F2 @ I4 ) @ ( F2 @ I ) ) ) )
% 9.25/5.27            & ( ~ ( member_nat @ I @ I4 )
% 9.25/5.27             => ( ( groups1351286907653491341at_rat @ F2 @ ( minus_minus_set_nat @ I4 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 9.25/5.27                = ( groups1351286907653491341at_rat @ F2 @ I4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8969_sum__diff1_H__aux,axiom,
% 9.25/5.27      ! [F4: set_nat,I4: set_nat,F2: nat > int,I: nat] :
% 9.25/5.27        ( ( finite_finite_nat @ F4 )
% 9.25/5.27       => ( ( ord_less_eq_set_nat
% 9.25/5.27            @ ( collect_nat
% 9.25/5.27              @ ^ [I3: nat] :
% 9.25/5.27                  ( ( member_nat @ I3 @ I4 )
% 9.25/5.27                  & ( ( F2 @ I3 )
% 9.25/5.27                   != zero_zero_int ) ) )
% 9.25/5.27            @ F4 )
% 9.25/5.27         => ( ( ( member_nat @ I @ I4 )
% 9.25/5.27             => ( ( groups1983926497230936801at_int @ F2 @ ( minus_minus_set_nat @ I4 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 9.25/5.27                = ( minus_minus_int @ ( groups1983926497230936801at_int @ F2 @ I4 ) @ ( F2 @ I ) ) ) )
% 9.25/5.27            & ( ~ ( member_nat @ I @ I4 )
% 9.25/5.27             => ( ( groups1983926497230936801at_int @ F2 @ ( minus_minus_set_nat @ I4 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 9.25/5.27                = ( groups1983926497230936801at_int @ F2 @ I4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8970_sum__diff1_H__aux,axiom,
% 9.25/5.27      ! [F4: set_set_nat,I4: set_set_nat,F2: set_nat > code_integer,I: set_nat] :
% 9.25/5.27        ( ( finite1152437895449049373et_nat @ F4 )
% 9.25/5.27       => ( ( ord_le6893508408891458716et_nat
% 9.25/5.27            @ ( collect_set_nat
% 9.25/5.27              @ ^ [I3: set_nat] :
% 9.25/5.27                  ( ( member_set_nat @ I3 @ I4 )
% 9.25/5.27                  & ( ( F2 @ I3 )
% 9.25/5.27                   != zero_z3403309356797280102nteger ) ) )
% 9.25/5.27            @ F4 )
% 9.25/5.27         => ( ( ( member_set_nat @ I @ I4 )
% 9.25/5.27             => ( ( groups9221925307898054856nteger @ F2 @ ( minus_2163939370556025621et_nat @ I4 @ ( insert_set_nat @ I @ bot_bot_set_set_nat ) ) )
% 9.25/5.27                = ( minus_8373710615458151222nteger @ ( groups9221925307898054856nteger @ F2 @ I4 ) @ ( F2 @ I ) ) ) )
% 9.25/5.27            & ( ~ ( member_set_nat @ I @ I4 )
% 9.25/5.27             => ( ( groups9221925307898054856nteger @ F2 @ ( minus_2163939370556025621et_nat @ I4 @ ( insert_set_nat @ I @ bot_bot_set_set_nat ) ) )
% 9.25/5.27                = ( groups9221925307898054856nteger @ F2 @ I4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8971_even__sum__iff,axiom,
% 9.25/5.27      ! [A2: set_o,F2: $o > nat] :
% 9.25/5.27        ( ( finite_finite_o @ A2 )
% 9.25/5.27       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups8507830703676809646_o_nat @ F2 @ A2 ) )
% 9.25/5.27          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.25/5.27            @ ( finite_card_o
% 9.25/5.27              @ ( collect_o
% 9.25/5.27                @ ^ [A3: $o] :
% 9.25/5.27                    ( ( member_o @ A3 @ A2 )
% 9.25/5.27                    & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F2 @ A3 ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8972_even__sum__iff,axiom,
% 9.25/5.27      ! [A2: set_int,F2: int > nat] :
% 9.25/5.27        ( ( finite_finite_int @ A2 )
% 9.25/5.27       => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups4541462559716669496nt_nat @ F2 @ A2 ) )
% 9.25/5.27          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.25/5.27            @ ( finite_card_int
% 9.25/5.27              @ ( collect_int
% 9.25/5.27                @ ^ [A3: int] :
% 9.25/5.27                    ( ( member_int @ A3 @ A2 )
% 9.25/5.27                    & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F2 @ A3 ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8973_even__sum__iff,axiom,
% 9.25/5.27      ! [A2: set_o,F2: $o > int] :
% 9.25/5.27        ( ( finite_finite_o @ A2 )
% 9.25/5.27       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups8505340233167759370_o_int @ F2 @ A2 ) )
% 9.25/5.27          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.25/5.27            @ ( finite_card_o
% 9.25/5.27              @ ( collect_o
% 9.25/5.27                @ ^ [A3: $o] :
% 9.25/5.27                    ( ( member_o @ A3 @ A2 )
% 9.25/5.27                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F2 @ A3 ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8974_even__sum__iff,axiom,
% 9.25/5.27      ! [A2: set_nat,F2: nat > int] :
% 9.25/5.27        ( ( finite_finite_nat @ A2 )
% 9.25/5.27       => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ F2 @ A2 ) )
% 9.25/5.27          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.25/5.27            @ ( finite_card_nat
% 9.25/5.27              @ ( collect_nat
% 9.25/5.27                @ ^ [A3: nat] :
% 9.25/5.27                    ( ( member_nat @ A3 @ A2 )
% 9.25/5.27                    & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F2 @ A3 ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8975_even__sum__iff,axiom,
% 9.25/5.27      ! [A2: set_o,F2: $o > code_integer] :
% 9.25/5.27        ( ( finite_finite_o @ A2 )
% 9.25/5.27       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups4406642042086082107nteger @ F2 @ A2 ) )
% 9.25/5.27          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.25/5.27            @ ( finite_card_o
% 9.25/5.27              @ ( collect_o
% 9.25/5.27                @ ^ [A3: $o] :
% 9.25/5.27                    ( ( member_o @ A3 @ A2 )
% 9.25/5.27                    & ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F2 @ A3 ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8976_even__sum__iff,axiom,
% 9.25/5.27      ! [A2: set_nat,F2: nat > code_integer] :
% 9.25/5.27        ( ( finite_finite_nat @ A2 )
% 9.25/5.27       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ F2 @ A2 ) )
% 9.25/5.27          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.25/5.27            @ ( finite_card_nat
% 9.25/5.27              @ ( collect_nat
% 9.25/5.27                @ ^ [A3: nat] :
% 9.25/5.27                    ( ( member_nat @ A3 @ A2 )
% 9.25/5.27                    & ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F2 @ A3 ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8977_even__sum__iff,axiom,
% 9.25/5.27      ! [A2: set_int,F2: int > code_integer] :
% 9.25/5.27        ( ( finite_finite_int @ A2 )
% 9.25/5.27       => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7873554091576472773nteger @ F2 @ A2 ) )
% 9.25/5.27          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.25/5.27            @ ( finite_card_int
% 9.25/5.27              @ ( collect_int
% 9.25/5.27                @ ^ [A3: int] :
% 9.25/5.27                    ( ( member_int @ A3 @ A2 )
% 9.25/5.27                    & ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F2 @ A3 ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8978_even__sum__iff,axiom,
% 9.25/5.27      ! [A2: set_o,F2: $o > code_natural] :
% 9.25/5.27        ( ( finite_finite_o @ A2 )
% 9.25/5.27       => ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups3230237193842799622atural @ F2 @ A2 ) )
% 9.25/5.27          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.25/5.27            @ ( finite_card_o
% 9.25/5.27              @ ( collect_o
% 9.25/5.27                @ ^ [A3: $o] :
% 9.25/5.27                    ( ( member_o @ A3 @ A2 )
% 9.25/5.27                    & ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( F2 @ A3 ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8979_even__sum__iff,axiom,
% 9.25/5.27      ! [A2: set_nat,F2: nat > code_natural] :
% 9.25/5.27        ( ( finite_finite_nat @ A2 )
% 9.25/5.27       => ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups6325495683096345652atural @ F2 @ A2 ) )
% 9.25/5.27          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.25/5.27            @ ( finite_card_nat
% 9.25/5.27              @ ( collect_nat
% 9.25/5.27                @ ^ [A3: nat] :
% 9.25/5.27                    ( ( member_nat @ A3 @ A2 )
% 9.25/5.27                    & ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( F2 @ A3 ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8980_even__sum__iff,axiom,
% 9.25/5.27      ! [A2: set_int,F2: int > code_natural] :
% 9.25/5.27        ( ( finite_finite_int @ A2 )
% 9.25/5.27       => ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups6697149243333190288atural @ F2 @ A2 ) )
% 9.25/5.27          = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 9.25/5.27            @ ( finite_card_int
% 9.25/5.27              @ ( collect_int
% 9.25/5.27                @ ^ [A3: int] :
% 9.25/5.27                    ( ( member_int @ A3 @ A2 )
% 9.25/5.27                    & ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( F2 @ A3 ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8981_nat__not__finite,axiom,
% 9.25/5.27      ~ ( finite_finite_nat @ top_top_set_nat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8982_card__UNIV__unit,axiom,
% 9.25/5.27      ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 9.25/5.27      = one_one_nat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8983_card__Collect__less__nat,axiom,
% 9.25/5.27      ! [N: nat] :
% 9.25/5.27        ( ( finite_card_nat
% 9.25/5.27          @ ( collect_nat
% 9.25/5.27            @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N ) ) )
% 9.25/5.27        = N ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8984_card__eq__UNIV,axiom,
% 9.25/5.27      ! [S: set_o] :
% 9.25/5.27        ( ( ( finite_card_o @ S )
% 9.25/5.27          = ( finite_card_o @ top_top_set_o ) )
% 9.25/5.27        = ( S = top_top_set_o ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8985_card__eq__UNIV2,axiom,
% 9.25/5.27      ! [S: set_o] :
% 9.25/5.27        ( ( ( finite_card_o @ top_top_set_o )
% 9.25/5.27          = ( finite_card_o @ S ) )
% 9.25/5.27        = ( S = top_top_set_o ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8986_card__Collect__le__nat,axiom,
% 9.25/5.27      ! [N: nat] :
% 9.25/5.27        ( ( finite_card_nat
% 9.25/5.27          @ ( collect_nat
% 9.25/5.27            @ ^ [I3: nat] : ( ord_less_eq_nat @ I3 @ N ) ) )
% 9.25/5.27        = ( suc @ N ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8987_card__UNIV__bool,axiom,
% 9.25/5.27      ( ( finite_card_o @ top_top_set_o )
% 9.25/5.27      = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8988_card_Oempty,axiom,
% 9.25/5.27      ( ( finite_card_list_nat @ bot_bot_set_list_nat )
% 9.25/5.27      = zero_zero_nat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8989_card_Oempty,axiom,
% 9.25/5.27      ( ( finite_card_set_nat @ bot_bot_set_set_nat )
% 9.25/5.27      = zero_zero_nat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8990_card_Oempty,axiom,
% 9.25/5.27      ( ( finite711546835091564841at_nat @ bot_bo2099793752762293965at_nat )
% 9.25/5.27      = zero_zero_nat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8991_card_Oempty,axiom,
% 9.25/5.27      ( ( finite_card_o @ bot_bot_set_o )
% 9.25/5.27      = zero_zero_nat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8992_card_Oempty,axiom,
% 9.25/5.27      ( ( finite_card_nat @ bot_bot_set_nat )
% 9.25/5.27      = zero_zero_nat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8993_card_Oempty,axiom,
% 9.25/5.27      ( ( finite_card_int @ bot_bot_set_int )
% 9.25/5.27      = zero_zero_nat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8994_card__ge__UNIV,axiom,
% 9.25/5.27      ! [S: set_o] :
% 9.25/5.27        ( ( ord_less_eq_nat @ ( finite_card_o @ top_top_set_o ) @ ( finite_card_o @ S ) )
% 9.25/5.27        = ( S = top_top_set_o ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8995_sum_Oempty_H,axiom,
% 9.25/5.27      ! [P4: $o > code_integer] :
% 9.25/5.27        ( ( groups1402912129352969042nteger @ P4 @ bot_bot_set_o )
% 9.25/5.27        = zero_z3403309356797280102nteger ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8996_sum_Oempty_H,axiom,
% 9.25/5.27      ! [P4: $o > rat] :
% 9.25/5.27        ( ( groups3921277224699582669_o_rat @ P4 @ bot_bot_set_o )
% 9.25/5.27        = zero_zero_rat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8997_sum_Oempty_H,axiom,
% 9.25/5.27      ! [P4: $o > nat] :
% 9.25/5.27        ( ( groups4556407284786078405_o_nat @ P4 @ bot_bot_set_o )
% 9.25/5.27        = zero_zero_nat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8998_sum_Oempty_H,axiom,
% 9.25/5.27      ! [P4: $o > int] :
% 9.25/5.27        ( ( groups4553916814277028129_o_int @ P4 @ bot_bot_set_o )
% 9.25/5.27        = zero_zero_int ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_8999_sum_Oempty_H,axiom,
% 9.25/5.27      ! [P4: nat > code_integer] :
% 9.25/5.27        ( ( groups555127423416065298nteger @ P4 @ bot_bot_set_nat )
% 9.25/5.27        = zero_z3403309356797280102nteger ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9000_sum_Oempty_H,axiom,
% 9.25/5.27      ! [P4: nat > rat] :
% 9.25/5.27        ( ( groups1351286907653491341at_rat @ P4 @ bot_bot_set_nat )
% 9.25/5.27        = zero_zero_rat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9001_sum_Oempty_H,axiom,
% 9.25/5.27      ! [P4: nat > nat] :
% 9.25/5.27        ( ( groups1986416967739987077at_nat @ P4 @ bot_bot_set_nat )
% 9.25/5.27        = zero_zero_nat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9002_sum_Oempty_H,axiom,
% 9.25/5.27      ! [P4: nat > int] :
% 9.25/5.27        ( ( groups1983926497230936801at_int @ P4 @ bot_bot_set_nat )
% 9.25/5.27        = zero_zero_int ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9003_sum_Oempty_H,axiom,
% 9.25/5.27      ! [P4: int > code_integer] :
% 9.25/5.27        ( ( groups926780983652909934nteger @ P4 @ bot_bot_set_int )
% 9.25/5.27        = zero_z3403309356797280102nteger ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9004_sum_Oempty_H,axiom,
% 9.25/5.27      ! [P4: int > rat] :
% 9.25/5.27        ( ( groups2350640619554545897nt_rat @ P4 @ bot_bot_set_int )
% 9.25/5.27        = zero_zero_rat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9005_prod__constant,axiom,
% 9.25/5.27      ! [Y: int,A2: set_list_nat] :
% 9.25/5.27        ( ( groups2905156660866384563at_int
% 9.25/5.27          @ ^ [X3: list_nat] : Y
% 9.25/5.27          @ A2 )
% 9.25/5.27        = ( power_power_int @ Y @ ( finite_card_list_nat @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9006_prod__constant,axiom,
% 9.25/5.27      ! [Y: int,A2: set_o] :
% 9.25/5.27        ( ( groups3502327434004483295_o_int
% 9.25/5.27          @ ^ [X3: $o] : Y
% 9.25/5.27          @ A2 )
% 9.25/5.27        = ( power_power_int @ Y @ ( finite_card_o @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9007_prod__constant,axiom,
% 9.25/5.27      ! [Y: int,A2: set_set_nat] :
% 9.25/5.27        ( ( groups4246057289670975065at_int
% 9.25/5.27          @ ^ [X3: set_nat] : Y
% 9.25/5.27          @ A2 )
% 9.25/5.27        = ( power_power_int @ Y @ ( finite_card_set_nat @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9008_prod__constant,axiom,
% 9.25/5.27      ! [Y: nat,A2: set_list_nat] :
% 9.25/5.27        ( ( groups2907647131375434839at_nat
% 9.25/5.27          @ ^ [X3: list_nat] : Y
% 9.25/5.27          @ A2 )
% 9.25/5.27        = ( power_power_nat @ Y @ ( finite_card_list_nat @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9009_prod__constant,axiom,
% 9.25/5.27      ! [Y: nat,A2: set_o] :
% 9.25/5.27        ( ( groups3504817904513533571_o_nat
% 9.25/5.27          @ ^ [X3: $o] : Y
% 9.25/5.27          @ A2 )
% 9.25/5.27        = ( power_power_nat @ Y @ ( finite_card_o @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9010_prod__constant,axiom,
% 9.25/5.27      ! [Y: nat,A2: set_set_nat] :
% 9.25/5.27        ( ( groups4248547760180025341at_nat
% 9.25/5.27          @ ^ [X3: set_nat] : Y
% 9.25/5.27          @ A2 )
% 9.25/5.27        = ( power_power_nat @ Y @ ( finite_card_set_nat @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9011_prod__constant,axiom,
% 9.25/5.27      ! [Y: nat,A2: set_int] :
% 9.25/5.27        ( ( groups1707563613775114915nt_nat
% 9.25/5.27          @ ^ [X3: int] : Y
% 9.25/5.27          @ A2 )
% 9.25/5.27        = ( power_power_nat @ Y @ ( finite_card_int @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9012_prod__constant,axiom,
% 9.25/5.27      ! [Y: nat,A2: set_nat] :
% 9.25/5.27        ( ( groups708209901874060359at_nat
% 9.25/5.27          @ ^ [X3: nat] : Y
% 9.25/5.27          @ A2 )
% 9.25/5.27        = ( power_power_nat @ Y @ ( finite_card_nat @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9013_prod__constant,axiom,
% 9.25/5.27      ! [Y: int,A2: set_nat] :
% 9.25/5.27        ( ( groups705719431365010083at_int
% 9.25/5.27          @ ^ [X3: nat] : Y
% 9.25/5.27          @ A2 )
% 9.25/5.27        = ( power_power_int @ Y @ ( finite_card_nat @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9014_prod__constant,axiom,
% 9.25/5.27      ! [Y: int,A2: set_int] :
% 9.25/5.27        ( ( groups1705073143266064639nt_int
% 9.25/5.27          @ ^ [X3: int] : Y
% 9.25/5.27          @ A2 )
% 9.25/5.27        = ( power_power_int @ Y @ ( finite_card_int @ A2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9015_card__0__eq,axiom,
% 9.25/5.27      ! [A2: set_list_nat] :
% 9.25/5.27        ( ( finite8100373058378681591st_nat @ A2 )
% 9.25/5.27       => ( ( ( finite_card_list_nat @ A2 )
% 9.25/5.27            = zero_zero_nat )
% 9.25/5.27          = ( A2 = bot_bot_set_list_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9016_card__0__eq,axiom,
% 9.25/5.27      ! [A2: set_set_nat] :
% 9.25/5.27        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.27       => ( ( ( finite_card_set_nat @ A2 )
% 9.25/5.27            = zero_zero_nat )
% 9.25/5.27          = ( A2 = bot_bot_set_set_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9017_card__0__eq,axiom,
% 9.25/5.27      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.27       => ( ( ( finite711546835091564841at_nat @ A2 )
% 9.25/5.27            = zero_zero_nat )
% 9.25/5.27          = ( A2 = bot_bo2099793752762293965at_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9018_card__0__eq,axiom,
% 9.25/5.27      ! [A2: set_o] :
% 9.25/5.27        ( ( finite_finite_o @ A2 )
% 9.25/5.27       => ( ( ( finite_card_o @ A2 )
% 9.25/5.27            = zero_zero_nat )
% 9.25/5.27          = ( A2 = bot_bot_set_o ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9019_card__0__eq,axiom,
% 9.25/5.27      ! [A2: set_nat] :
% 9.25/5.27        ( ( finite_finite_nat @ A2 )
% 9.25/5.27       => ( ( ( finite_card_nat @ A2 )
% 9.25/5.27            = zero_zero_nat )
% 9.25/5.27          = ( A2 = bot_bot_set_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9020_card__0__eq,axiom,
% 9.25/5.27      ! [A2: set_int] :
% 9.25/5.27        ( ( finite_finite_int @ A2 )
% 9.25/5.27       => ( ( ( finite_card_int @ A2 )
% 9.25/5.27            = zero_zero_nat )
% 9.25/5.27          = ( A2 = bot_bot_set_int ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9021_nat__1,axiom,
% 9.25/5.27      ( ( nat2 @ one_one_int )
% 9.25/5.27      = ( suc @ zero_zero_nat ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9022_nat__neg__numeral,axiom,
% 9.25/5.27      ! [K: num] :
% 9.25/5.27        ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 9.25/5.27        = zero_zero_nat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9023_nat__zminus__int,axiom,
% 9.25/5.27      ! [N: nat] :
% 9.25/5.27        ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 9.25/5.27        = zero_zero_nat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9024_sum__constant,axiom,
% 9.25/5.27      ! [Y: code_integer,A2: set_o] :
% 9.25/5.27        ( ( groups4406642042086082107nteger
% 9.25/5.27          @ ^ [X3: $o] : Y
% 9.25/5.27          @ A2 )
% 9.25/5.27        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_o @ A2 ) ) @ Y ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9025_sum__constant,axiom,
% 9.25/5.27      ! [Y: code_integer,A2: set_nat] :
% 9.25/5.27        ( ( groups7501900531339628137nteger
% 9.25/5.27          @ ^ [X3: nat] : Y
% 9.25/5.27          @ A2 )
% 9.25/5.27        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_nat @ A2 ) ) @ Y ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9026_sum__constant,axiom,
% 9.25/5.27      ! [Y: code_integer,A2: set_int] :
% 9.25/5.27        ( ( groups7873554091576472773nteger
% 9.25/5.27          @ ^ [X3: int] : Y
% 9.25/5.27          @ A2 )
% 9.25/5.27        = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_int @ A2 ) ) @ Y ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9027_sum__constant,axiom,
% 9.25/5.27      ! [Y: int,A2: set_o] :
% 9.25/5.27        ( ( groups8505340233167759370_o_int
% 9.25/5.27          @ ^ [X3: $o] : Y
% 9.25/5.27          @ A2 )
% 9.25/5.27        = ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_o @ A2 ) ) @ Y ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9028_sum__constant,axiom,
% 9.25/5.27      ! [Y: int,A2: set_nat] :
% 9.25/5.27        ( ( groups3539618377306564664at_int
% 9.25/5.27          @ ^ [X3: nat] : Y
% 9.25/5.27          @ A2 )
% 9.25/5.27        = ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_nat @ A2 ) ) @ Y ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9029_sum__constant,axiom,
% 9.25/5.27      ! [Y: nat,A2: set_o] :
% 9.25/5.27        ( ( groups8507830703676809646_o_nat
% 9.25/5.27          @ ^ [X3: $o] : Y
% 9.25/5.27          @ A2 )
% 9.25/5.27        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_o @ A2 ) ) @ Y ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9030_sum__constant,axiom,
% 9.25/5.27      ! [Y: nat,A2: set_int] :
% 9.25/5.27        ( ( groups4541462559716669496nt_nat
% 9.25/5.27          @ ^ [X3: int] : Y
% 9.25/5.27          @ A2 )
% 9.25/5.27        = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_int @ A2 ) ) @ Y ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9031_sum__constant,axiom,
% 9.25/5.27      ! [Y: rat,A2: set_o] :
% 9.25/5.27        ( ( groups7872700643590313910_o_rat
% 9.25/5.27          @ ^ [X3: $o] : Y
% 9.25/5.27          @ A2 )
% 9.25/5.27        = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_o @ A2 ) ) @ Y ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9032_sum__constant,axiom,
% 9.25/5.27      ! [Y: rat,A2: set_nat] :
% 9.25/5.27        ( ( groups2906978787729119204at_rat
% 9.25/5.27          @ ^ [X3: nat] : Y
% 9.25/5.27          @ A2 )
% 9.25/5.27        = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A2 ) ) @ Y ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9033_sum__constant,axiom,
% 9.25/5.27      ! [Y: rat,A2: set_int] :
% 9.25/5.27        ( ( groups3906332499630173760nt_rat
% 9.25/5.27          @ ^ [X3: int] : Y
% 9.25/5.27          @ A2 )
% 9.25/5.27        = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A2 ) ) @ Y ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9034_card__Diff__insert,axiom,
% 9.25/5.27      ! [A: produc3843707927480180839at_nat,A2: set_Pr4329608150637261639at_nat,B2: set_Pr4329608150637261639at_nat] :
% 9.25/5.27        ( ( member8757157785044589968at_nat @ A @ A2 )
% 9.25/5.27       => ( ~ ( member8757157785044589968at_nat @ A @ B2 )
% 9.25/5.27         => ( ( finite3771342082235030671at_nat @ ( minus_3314409938677909166at_nat @ A2 @ ( insert9069300056098147895at_nat @ A @ B2 ) ) )
% 9.25/5.27            = ( minus_minus_nat @ ( finite3771342082235030671at_nat @ ( minus_3314409938677909166at_nat @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9035_card__Diff__insert,axiom,
% 9.25/5.27      ! [A: product_prod_nat_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 9.25/5.27        ( ( member8440522571783428010at_nat @ A @ A2 )
% 9.25/5.27       => ( ~ ( member8440522571783428010at_nat @ A @ B2 )
% 9.25/5.27         => ( ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ ( insert8211810215607154385at_nat @ A @ B2 ) ) )
% 9.25/5.27            = ( minus_minus_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9036_card__Diff__insert,axiom,
% 9.25/5.27      ! [A: set_Pr958786334691620121nt_int,A2: set_se6260736226359567993nt_int,B2: set_se6260736226359567993nt_int] :
% 9.25/5.27        ( ( member2340774599025711042nt_int @ A @ A2 )
% 9.25/5.27       => ( ~ ( member2340774599025711042nt_int @ A @ B2 )
% 9.25/5.27         => ( ( finite4053189226111446337nt_int @ ( minus_2612819937483484256nt_int @ A2 @ ( insert8897473484851387113nt_int @ A @ B2 ) ) )
% 9.25/5.27            = ( minus_minus_nat @ ( finite4053189226111446337nt_int @ ( minus_2612819937483484256nt_int @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9037_card__Diff__insert,axiom,
% 9.25/5.27      ! [A: produc3658429121746597890et_nat > $o,A2: set_Pr4532377907799695533_nat_o,B2: set_Pr4532377907799695533_nat_o] :
% 9.25/5.27        ( ( member6576561426505652726_nat_o @ A @ A2 )
% 9.25/5.27       => ( ~ ( member6576561426505652726_nat_o @ A @ B2 )
% 9.25/5.27         => ( ( finite1363419556375932405_nat_o @ ( minus_1801376950450012436_nat_o @ A2 @ ( insert5175938949040314269_nat_o @ A @ B2 ) ) )
% 9.25/5.27            = ( minus_minus_nat @ ( finite1363419556375932405_nat_o @ ( minus_1801376950450012436_nat_o @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9038_card__Diff__insert,axiom,
% 9.25/5.27      ! [A: list_nat,A2: set_list_nat,B2: set_list_nat] :
% 9.25/5.27        ( ( member_list_nat @ A @ A2 )
% 9.25/5.27       => ( ~ ( member_list_nat @ A @ B2 )
% 9.25/5.27         => ( ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ ( insert_list_nat @ A @ B2 ) ) )
% 9.25/5.27            = ( minus_minus_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9039_card__Diff__insert,axiom,
% 9.25/5.27      ! [A: $o,A2: set_o,B2: set_o] :
% 9.25/5.27        ( ( member_o @ A @ A2 )
% 9.25/5.27       => ( ~ ( member_o @ A @ B2 )
% 9.25/5.27         => ( ( finite_card_o @ ( minus_minus_set_o @ A2 @ ( insert_o @ A @ B2 ) ) )
% 9.25/5.27            = ( minus_minus_nat @ ( finite_card_o @ ( minus_minus_set_o @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9040_card__Diff__insert,axiom,
% 9.25/5.27      ! [A: set_nat,A2: set_set_nat,B2: set_set_nat] :
% 9.25/5.27        ( ( member_set_nat @ A @ A2 )
% 9.25/5.27       => ( ~ ( member_set_nat @ A @ B2 )
% 9.25/5.27         => ( ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ B2 ) ) )
% 9.25/5.27            = ( minus_minus_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9041_card__Diff__insert,axiom,
% 9.25/5.27      ! [A: int,A2: set_int,B2: set_int] :
% 9.25/5.27        ( ( member_int @ A @ A2 )
% 9.25/5.27       => ( ~ ( member_int @ A @ B2 )
% 9.25/5.27         => ( ( finite_card_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B2 ) ) )
% 9.25/5.27            = ( minus_minus_nat @ ( finite_card_int @ ( minus_minus_set_int @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9042_card__Diff__insert,axiom,
% 9.25/5.27      ! [A: nat,A2: set_nat,B2: set_nat] :
% 9.25/5.27        ( ( member_nat @ A @ A2 )
% 9.25/5.27       => ( ~ ( member_nat @ A @ B2 )
% 9.25/5.27         => ( ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B2 ) ) )
% 9.25/5.27            = ( minus_minus_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A2 @ B2 ) ) @ one_one_nat ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9043_card__atLeastAtMost__int,axiom,
% 9.25/5.27      ! [L: int,U: int] :
% 9.25/5.27        ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 9.25/5.27        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9044_sum_Oinsert_H,axiom,
% 9.25/5.27      ! [I4: set_o,P4: $o > code_integer,I: $o] :
% 9.25/5.27        ( ( finite_finite_o
% 9.25/5.27          @ ( collect_o
% 9.25/5.27            @ ^ [X3: $o] :
% 9.25/5.27                ( ( member_o @ X3 @ I4 )
% 9.25/5.27                & ( ( P4 @ X3 )
% 9.25/5.27                 != zero_z3403309356797280102nteger ) ) ) )
% 9.25/5.27       => ( ( ( member_o @ I @ I4 )
% 9.25/5.27           => ( ( groups1402912129352969042nteger @ P4 @ ( insert_o @ I @ I4 ) )
% 9.25/5.27              = ( groups1402912129352969042nteger @ P4 @ I4 ) ) )
% 9.25/5.27          & ( ~ ( member_o @ I @ I4 )
% 9.25/5.27           => ( ( groups1402912129352969042nteger @ P4 @ ( insert_o @ I @ I4 ) )
% 9.25/5.27              = ( plus_p5714425477246183910nteger @ ( P4 @ I ) @ ( groups1402912129352969042nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9045_sum_Oinsert_H,axiom,
% 9.25/5.27      ! [I4: set_nat,P4: nat > code_integer,I: nat] :
% 9.25/5.27        ( ( finite_finite_nat
% 9.25/5.27          @ ( collect_nat
% 9.25/5.27            @ ^ [X3: nat] :
% 9.25/5.27                ( ( member_nat @ X3 @ I4 )
% 9.25/5.27                & ( ( P4 @ X3 )
% 9.25/5.27                 != zero_z3403309356797280102nteger ) ) ) )
% 9.25/5.27       => ( ( ( member_nat @ I @ I4 )
% 9.25/5.27           => ( ( groups555127423416065298nteger @ P4 @ ( insert_nat @ I @ I4 ) )
% 9.25/5.27              = ( groups555127423416065298nteger @ P4 @ I4 ) ) )
% 9.25/5.27          & ( ~ ( member_nat @ I @ I4 )
% 9.25/5.27           => ( ( groups555127423416065298nteger @ P4 @ ( insert_nat @ I @ I4 ) )
% 9.25/5.27              = ( plus_p5714425477246183910nteger @ ( P4 @ I ) @ ( groups555127423416065298nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9046_sum_Oinsert_H,axiom,
% 9.25/5.27      ! [I4: set_int,P4: int > code_integer,I: int] :
% 9.25/5.27        ( ( finite_finite_int
% 9.25/5.27          @ ( collect_int
% 9.25/5.27            @ ^ [X3: int] :
% 9.25/5.27                ( ( member_int @ X3 @ I4 )
% 9.25/5.27                & ( ( P4 @ X3 )
% 9.25/5.27                 != zero_z3403309356797280102nteger ) ) ) )
% 9.25/5.27       => ( ( ( member_int @ I @ I4 )
% 9.25/5.27           => ( ( groups926780983652909934nteger @ P4 @ ( insert_int @ I @ I4 ) )
% 9.25/5.27              = ( groups926780983652909934nteger @ P4 @ I4 ) ) )
% 9.25/5.27          & ( ~ ( member_int @ I @ I4 )
% 9.25/5.27           => ( ( groups926780983652909934nteger @ P4 @ ( insert_int @ I @ I4 ) )
% 9.25/5.27              = ( plus_p5714425477246183910nteger @ ( P4 @ I ) @ ( groups926780983652909934nteger @ P4 @ I4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9047_sum_Oinsert_H,axiom,
% 9.25/5.27      ! [I4: set_o,P4: $o > rat,I: $o] :
% 9.25/5.27        ( ( finite_finite_o
% 9.25/5.27          @ ( collect_o
% 9.25/5.27            @ ^ [X3: $o] :
% 9.25/5.27                ( ( member_o @ X3 @ I4 )
% 9.25/5.27                & ( ( P4 @ X3 )
% 9.25/5.27                 != zero_zero_rat ) ) ) )
% 9.25/5.27       => ( ( ( member_o @ I @ I4 )
% 9.25/5.27           => ( ( groups3921277224699582669_o_rat @ P4 @ ( insert_o @ I @ I4 ) )
% 9.25/5.27              = ( groups3921277224699582669_o_rat @ P4 @ I4 ) ) )
% 9.25/5.27          & ( ~ ( member_o @ I @ I4 )
% 9.25/5.27           => ( ( groups3921277224699582669_o_rat @ P4 @ ( insert_o @ I @ I4 ) )
% 9.25/5.27              = ( plus_plus_rat @ ( P4 @ I ) @ ( groups3921277224699582669_o_rat @ P4 @ I4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9048_sum_Oinsert_H,axiom,
% 9.25/5.27      ! [I4: set_nat,P4: nat > rat,I: nat] :
% 9.25/5.27        ( ( finite_finite_nat
% 9.25/5.27          @ ( collect_nat
% 9.25/5.27            @ ^ [X3: nat] :
% 9.25/5.27                ( ( member_nat @ X3 @ I4 )
% 9.25/5.27                & ( ( P4 @ X3 )
% 9.25/5.27                 != zero_zero_rat ) ) ) )
% 9.25/5.27       => ( ( ( member_nat @ I @ I4 )
% 9.25/5.27           => ( ( groups1351286907653491341at_rat @ P4 @ ( insert_nat @ I @ I4 ) )
% 9.25/5.27              = ( groups1351286907653491341at_rat @ P4 @ I4 ) ) )
% 9.25/5.27          & ( ~ ( member_nat @ I @ I4 )
% 9.25/5.27           => ( ( groups1351286907653491341at_rat @ P4 @ ( insert_nat @ I @ I4 ) )
% 9.25/5.27              = ( plus_plus_rat @ ( P4 @ I ) @ ( groups1351286907653491341at_rat @ P4 @ I4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9049_sum_Oinsert_H,axiom,
% 9.25/5.27      ! [I4: set_int,P4: int > rat,I: int] :
% 9.25/5.27        ( ( finite_finite_int
% 9.25/5.27          @ ( collect_int
% 9.25/5.27            @ ^ [X3: int] :
% 9.25/5.27                ( ( member_int @ X3 @ I4 )
% 9.25/5.27                & ( ( P4 @ X3 )
% 9.25/5.27                 != zero_zero_rat ) ) ) )
% 9.25/5.27       => ( ( ( member_int @ I @ I4 )
% 9.25/5.27           => ( ( groups2350640619554545897nt_rat @ P4 @ ( insert_int @ I @ I4 ) )
% 9.25/5.27              = ( groups2350640619554545897nt_rat @ P4 @ I4 ) ) )
% 9.25/5.27          & ( ~ ( member_int @ I @ I4 )
% 9.25/5.27           => ( ( groups2350640619554545897nt_rat @ P4 @ ( insert_int @ I @ I4 ) )
% 9.25/5.27              = ( plus_plus_rat @ ( P4 @ I ) @ ( groups2350640619554545897nt_rat @ P4 @ I4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9050_sum_Oinsert_H,axiom,
% 9.25/5.27      ! [I4: set_o,P4: $o > nat,I: $o] :
% 9.25/5.27        ( ( finite_finite_o
% 9.25/5.27          @ ( collect_o
% 9.25/5.27            @ ^ [X3: $o] :
% 9.25/5.27                ( ( member_o @ X3 @ I4 )
% 9.25/5.27                & ( ( P4 @ X3 )
% 9.25/5.27                 != zero_zero_nat ) ) ) )
% 9.25/5.27       => ( ( ( member_o @ I @ I4 )
% 9.25/5.27           => ( ( groups4556407284786078405_o_nat @ P4 @ ( insert_o @ I @ I4 ) )
% 9.25/5.27              = ( groups4556407284786078405_o_nat @ P4 @ I4 ) ) )
% 9.25/5.27          & ( ~ ( member_o @ I @ I4 )
% 9.25/5.27           => ( ( groups4556407284786078405_o_nat @ P4 @ ( insert_o @ I @ I4 ) )
% 9.25/5.27              = ( plus_plus_nat @ ( P4 @ I ) @ ( groups4556407284786078405_o_nat @ P4 @ I4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9051_sum_Oinsert_H,axiom,
% 9.25/5.27      ! [I4: set_nat,P4: nat > nat,I: nat] :
% 9.25/5.27        ( ( finite_finite_nat
% 9.25/5.27          @ ( collect_nat
% 9.25/5.27            @ ^ [X3: nat] :
% 9.25/5.27                ( ( member_nat @ X3 @ I4 )
% 9.25/5.27                & ( ( P4 @ X3 )
% 9.25/5.27                 != zero_zero_nat ) ) ) )
% 9.25/5.27       => ( ( ( member_nat @ I @ I4 )
% 9.25/5.27           => ( ( groups1986416967739987077at_nat @ P4 @ ( insert_nat @ I @ I4 ) )
% 9.25/5.27              = ( groups1986416967739987077at_nat @ P4 @ I4 ) ) )
% 9.25/5.27          & ( ~ ( member_nat @ I @ I4 )
% 9.25/5.27           => ( ( groups1986416967739987077at_nat @ P4 @ ( insert_nat @ I @ I4 ) )
% 9.25/5.27              = ( plus_plus_nat @ ( P4 @ I ) @ ( groups1986416967739987077at_nat @ P4 @ I4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9052_sum_Oinsert_H,axiom,
% 9.25/5.27      ! [I4: set_int,P4: int > nat,I: int] :
% 9.25/5.27        ( ( finite_finite_int
% 9.25/5.27          @ ( collect_int
% 9.25/5.27            @ ^ [X3: int] :
% 9.25/5.27                ( ( member_int @ X3 @ I4 )
% 9.25/5.27                & ( ( P4 @ X3 )
% 9.25/5.27                 != zero_zero_nat ) ) ) )
% 9.25/5.27       => ( ( ( member_int @ I @ I4 )
% 9.25/5.27           => ( ( groups2985770679641041633nt_nat @ P4 @ ( insert_int @ I @ I4 ) )
% 9.25/5.27              = ( groups2985770679641041633nt_nat @ P4 @ I4 ) ) )
% 9.25/5.27          & ( ~ ( member_int @ I @ I4 )
% 9.25/5.27           => ( ( groups2985770679641041633nt_nat @ P4 @ ( insert_int @ I @ I4 ) )
% 9.25/5.27              = ( plus_plus_nat @ ( P4 @ I ) @ ( groups2985770679641041633nt_nat @ P4 @ I4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9053_sum_Oinsert_H,axiom,
% 9.25/5.27      ! [I4: set_o,P4: $o > int,I: $o] :
% 9.25/5.27        ( ( finite_finite_o
% 9.25/5.27          @ ( collect_o
% 9.25/5.27            @ ^ [X3: $o] :
% 9.25/5.27                ( ( member_o @ X3 @ I4 )
% 9.25/5.27                & ( ( P4 @ X3 )
% 9.25/5.27                 != zero_zero_int ) ) ) )
% 9.25/5.27       => ( ( ( member_o @ I @ I4 )
% 9.25/5.27           => ( ( groups4553916814277028129_o_int @ P4 @ ( insert_o @ I @ I4 ) )
% 9.25/5.27              = ( groups4553916814277028129_o_int @ P4 @ I4 ) ) )
% 9.25/5.27          & ( ~ ( member_o @ I @ I4 )
% 9.25/5.27           => ( ( groups4553916814277028129_o_int @ P4 @ ( insert_o @ I @ I4 ) )
% 9.25/5.27              = ( plus_plus_int @ ( P4 @ I ) @ ( groups4553916814277028129_o_int @ P4 @ I4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9054_card__doubleton__eq__2__iff,axiom,
% 9.25/5.27      ! [A: produc3843707927480180839at_nat,B: produc3843707927480180839at_nat] :
% 9.25/5.27        ( ( ( finite3771342082235030671at_nat @ ( insert9069300056098147895at_nat @ A @ ( insert9069300056098147895at_nat @ B @ bot_bo228742789529271731at_nat ) ) )
% 9.25/5.27          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.27        = ( A != B ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9055_card__doubleton__eq__2__iff,axiom,
% 9.25/5.27      ! [A: list_nat,B: list_nat] :
% 9.25/5.27        ( ( ( finite_card_list_nat @ ( insert_list_nat @ A @ ( insert_list_nat @ B @ bot_bot_set_list_nat ) ) )
% 9.25/5.27          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.27        = ( A != B ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9056_card__doubleton__eq__2__iff,axiom,
% 9.25/5.27      ! [A: set_nat,B: set_nat] :
% 9.25/5.27        ( ( ( finite_card_set_nat @ ( insert_set_nat @ A @ ( insert_set_nat @ B @ bot_bot_set_set_nat ) ) )
% 9.25/5.27          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.27        = ( A != B ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9057_card__doubleton__eq__2__iff,axiom,
% 9.25/5.27      ! [A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 9.25/5.27        ( ( ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ A @ ( insert8211810215607154385at_nat @ B @ bot_bo2099793752762293965at_nat ) ) )
% 9.25/5.27          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.27        = ( A != B ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9058_card__doubleton__eq__2__iff,axiom,
% 9.25/5.27      ! [A: $o,B: $o] :
% 9.25/5.27        ( ( ( finite_card_o @ ( insert_o @ A @ ( insert_o @ B @ bot_bot_set_o ) ) )
% 9.25/5.27          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.27        = ( A != B ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9059_card__doubleton__eq__2__iff,axiom,
% 9.25/5.27      ! [A: nat,B: nat] :
% 9.25/5.27        ( ( ( finite_card_nat @ ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 9.25/5.27          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.27        = ( A != B ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9060_card__doubleton__eq__2__iff,axiom,
% 9.25/5.27      ! [A: int,B: int] :
% 9.25/5.27        ( ( ( finite_card_int @ ( insert_int @ A @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 9.25/5.27          = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.27        = ( A != B ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9061_one__less__nat__eq,axiom,
% 9.25/5.27      ! [Z: int] :
% 9.25/5.27        ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 9.25/5.27        = ( ord_less_int @ one_one_int @ Z ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9062_sum__of__bool__eq,axiom,
% 9.25/5.27      ! [A2: set_o,P: $o > $o] :
% 9.25/5.27        ( ( finite_finite_o @ A2 )
% 9.25/5.27       => ( ( finite_finite_o @ A2 )
% 9.25/5.27         => ( ( groups7872700643590313910_o_rat
% 9.25/5.27              @ ^ [X3: $o] : ( zero_n2052037380579107095ol_rat @ ( P @ X3 ) )
% 9.25/5.27              @ A2 )
% 9.25/5.27            = ( semiri681578069525770553at_rat @ ( finite_card_o @ ( inf_inf_set_o @ A2 @ ( collect_o @ P ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9063_sum__of__bool__eq,axiom,
% 9.25/5.27      ! [A2: set_int,P: int > $o] :
% 9.25/5.27        ( ( finite_finite_int @ A2 )
% 9.25/5.27       => ( ( finite_finite_int @ A2 )
% 9.25/5.27         => ( ( groups3906332499630173760nt_rat
% 9.25/5.27              @ ^ [X3: int] : ( zero_n2052037380579107095ol_rat @ ( P @ X3 ) )
% 9.25/5.27              @ A2 )
% 9.25/5.27            = ( semiri681578069525770553at_rat @ ( finite_card_int @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9064_sum__of__bool__eq,axiom,
% 9.25/5.27      ! [A2: set_nat,P: nat > $o] :
% 9.25/5.27        ( ( finite_finite_nat @ A2 )
% 9.25/5.27       => ( ( finite_finite_nat @ A2 )
% 9.25/5.27         => ( ( groups2906978787729119204at_rat
% 9.25/5.27              @ ^ [X3: nat] : ( zero_n2052037380579107095ol_rat @ ( P @ X3 ) )
% 9.25/5.27              @ A2 )
% 9.25/5.27            = ( semiri681578069525770553at_rat @ ( finite_card_nat @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9065_sum__of__bool__eq,axiom,
% 9.25/5.27      ! [A2: set_o,P: $o > $o] :
% 9.25/5.27        ( ( finite_finite_o @ A2 )
% 9.25/5.27       => ( ( finite_finite_o @ A2 )
% 9.25/5.27         => ( ( groups8505340233167759370_o_int
% 9.25/5.27              @ ^ [X3: $o] : ( zero_n2684676970156552555ol_int @ ( P @ X3 ) )
% 9.25/5.27              @ A2 )
% 9.25/5.27            = ( semiri1314217659103216013at_int @ ( finite_card_o @ ( inf_inf_set_o @ A2 @ ( collect_o @ P ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9066_sum__of__bool__eq,axiom,
% 9.25/5.27      ! [A2: set_nat,P: nat > $o] :
% 9.25/5.27        ( ( finite_finite_nat @ A2 )
% 9.25/5.27       => ( ( finite_finite_nat @ A2 )
% 9.25/5.27         => ( ( groups3539618377306564664at_int
% 9.25/5.27              @ ^ [X3: nat] : ( zero_n2684676970156552555ol_int @ ( P @ X3 ) )
% 9.25/5.27              @ A2 )
% 9.25/5.27            = ( semiri1314217659103216013at_int @ ( finite_card_nat @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9067_sum__of__bool__eq,axiom,
% 9.25/5.27      ! [A2: set_o,P: $o > $o] :
% 9.25/5.27        ( ( finite_finite_o @ A2 )
% 9.25/5.27       => ( ( finite_finite_o @ A2 )
% 9.25/5.27         => ( ( groups8507830703676809646_o_nat
% 9.25/5.27              @ ^ [X3: $o] : ( zero_n2687167440665602831ol_nat @ ( P @ X3 ) )
% 9.25/5.27              @ A2 )
% 9.25/5.27            = ( semiri1316708129612266289at_nat @ ( finite_card_o @ ( inf_inf_set_o @ A2 @ ( collect_o @ P ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9068_sum__of__bool__eq,axiom,
% 9.25/5.27      ! [A2: set_int,P: int > $o] :
% 9.25/5.27        ( ( finite_finite_int @ A2 )
% 9.25/5.27       => ( ( finite_finite_int @ A2 )
% 9.25/5.27         => ( ( groups4541462559716669496nt_nat
% 9.25/5.27              @ ^ [X3: int] : ( zero_n2687167440665602831ol_nat @ ( P @ X3 ) )
% 9.25/5.27              @ A2 )
% 9.25/5.27            = ( semiri1316708129612266289at_nat @ ( finite_card_int @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9069_sum__of__bool__eq,axiom,
% 9.25/5.27      ! [A2: set_nat,P: nat > $o] :
% 9.25/5.27        ( ( finite_finite_nat @ A2 )
% 9.25/5.27       => ( ( finite_finite_nat @ A2 )
% 9.25/5.27         => ( ( groups3542108847815614940at_nat
% 9.25/5.27              @ ^ [X3: nat] : ( zero_n2687167440665602831ol_nat @ ( P @ X3 ) )
% 9.25/5.27              @ A2 )
% 9.25/5.27            = ( semiri1316708129612266289at_nat @ ( finite_card_nat @ ( inf_inf_set_nat @ A2 @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9070_sum__of__bool__eq,axiom,
% 9.25/5.27      ! [A2: set_int,P: int > $o] :
% 9.25/5.27        ( ( finite_finite_int @ A2 )
% 9.25/5.27       => ( ( finite_finite_int @ A2 )
% 9.25/5.27         => ( ( groups4538972089207619220nt_int
% 9.25/5.27              @ ^ [X3: int] : ( zero_n2684676970156552555ol_int @ ( P @ X3 ) )
% 9.25/5.27              @ A2 )
% 9.25/5.27            = ( semiri1314217659103216013at_int @ ( finite_card_int @ ( inf_inf_set_int @ A2 @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9071_sum__of__bool__eq,axiom,
% 9.25/5.27      ! [A2: set_list_nat,P: list_nat > $o] :
% 9.25/5.27        ( ( finite8100373058378681591st_nat @ A2 )
% 9.25/5.27       => ( ( finite8100373058378681591st_nat @ A2 )
% 9.25/5.27         => ( ( groups3760926236672600436at_rat
% 9.25/5.27              @ ^ [X3: list_nat] : ( zero_n2052037380579107095ol_rat @ ( P @ X3 ) )
% 9.25/5.27              @ A2 )
% 9.25/5.27            = ( semiri681578069525770553at_rat @ ( finite_card_list_nat @ ( inf_inf_set_list_nat @ A2 @ ( collect_list_nat @ P ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9072_nat__numeral__diff__1,axiom,
% 9.25/5.27      ! [V: num] :
% 9.25/5.27        ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 9.25/5.27        = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9073_n__subsets,axiom,
% 9.25/5.27      ! [A2: set_Pr958786334691620121nt_int,K: nat] :
% 9.25/5.27        ( ( finite2998713641127702882nt_int @ A2 )
% 9.25/5.27       => ( ( finite4053189226111446337nt_int
% 9.25/5.27            @ ( collec5210948495886036740nt_int
% 9.25/5.27              @ ^ [B4: set_Pr958786334691620121nt_int] :
% 9.25/5.27                  ( ( ord_le2843351958646193337nt_int @ B4 @ A2 )
% 9.25/5.27                  & ( ( finite6756421564338198497nt_int @ B4 )
% 9.25/5.27                    = K ) ) ) )
% 9.25/5.27          = ( binomial @ ( finite6756421564338198497nt_int @ A2 ) @ K ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9074_n__subsets,axiom,
% 9.25/5.27      ! [A2: set_list_nat,K: nat] :
% 9.25/5.27        ( ( finite8100373058378681591st_nat @ A2 )
% 9.25/5.27       => ( ( finite2364142230527598318st_nat
% 9.25/5.27            @ ( collect_set_list_nat
% 9.25/5.27              @ ^ [B4: set_list_nat] :
% 9.25/5.27                  ( ( ord_le6045566169113846134st_nat @ B4 @ A2 )
% 9.25/5.27                  & ( ( finite_card_list_nat @ B4 )
% 9.25/5.27                    = K ) ) ) )
% 9.25/5.27          = ( binomial @ ( finite_card_list_nat @ A2 ) @ K ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9075_n__subsets,axiom,
% 9.25/5.27      ! [A2: set_o,K: nat] :
% 9.25/5.27        ( ( finite_finite_o @ A2 )
% 9.25/5.27       => ( ( finite_card_set_o
% 9.25/5.27            @ ( collect_set_o
% 9.25/5.27              @ ^ [B4: set_o] :
% 9.25/5.27                  ( ( ord_less_eq_set_o @ B4 @ A2 )
% 9.25/5.27                  & ( ( finite_card_o @ B4 )
% 9.25/5.27                    = K ) ) ) )
% 9.25/5.27          = ( binomial @ ( finite_card_o @ A2 ) @ K ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9076_n__subsets,axiom,
% 9.25/5.27      ! [A2: set_set_nat,K: nat] :
% 9.25/5.27        ( ( finite1152437895449049373et_nat @ A2 )
% 9.25/5.27       => ( ( finite1149291290879098388et_nat
% 9.25/5.27            @ ( collect_set_set_nat
% 9.25/5.27              @ ^ [B4: set_set_nat] :
% 9.25/5.27                  ( ( ord_le6893508408891458716et_nat @ B4 @ A2 )
% 9.25/5.27                  & ( ( finite_card_set_nat @ B4 )
% 9.25/5.27                    = K ) ) ) )
% 9.25/5.27          = ( binomial @ ( finite_card_set_nat @ A2 ) @ K ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9077_n__subsets,axiom,
% 9.25/5.27      ! [A2: set_int,K: nat] :
% 9.25/5.27        ( ( finite_finite_int @ A2 )
% 9.25/5.27       => ( ( finite_card_set_int
% 9.25/5.27            @ ( collect_set_int
% 9.25/5.27              @ ^ [B4: set_int] :
% 9.25/5.27                  ( ( ord_less_eq_set_int @ B4 @ A2 )
% 9.25/5.27                  & ( ( finite_card_int @ B4 )
% 9.25/5.27                    = K ) ) ) )
% 9.25/5.27          = ( binomial @ ( finite_card_int @ A2 ) @ K ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9078_n__subsets,axiom,
% 9.25/5.27      ! [A2: set_Pr1261947904930325089at_nat,K: nat] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat @ A2 )
% 9.25/5.27       => ( ( finite4356350796350151305at_nat
% 9.25/5.27            @ ( collec5514110066124741708at_nat
% 9.25/5.27              @ ^ [B4: set_Pr1261947904930325089at_nat] :
% 9.25/5.27                  ( ( ord_le3146513528884898305at_nat @ B4 @ A2 )
% 9.25/5.27                  & ( ( finite711546835091564841at_nat @ B4 )
% 9.25/5.27                    = K ) ) ) )
% 9.25/5.27          = ( binomial @ ( finite711546835091564841at_nat @ A2 ) @ K ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9079_n__subsets,axiom,
% 9.25/5.27      ! [A2: set_nat,K: nat] :
% 9.25/5.27        ( ( finite_finite_nat @ A2 )
% 9.25/5.27       => ( ( finite_card_set_nat
% 9.25/5.27            @ ( collect_set_nat
% 9.25/5.27              @ ^ [B4: set_nat] :
% 9.25/5.27                  ( ( ord_less_eq_set_nat @ B4 @ A2 )
% 9.25/5.27                  & ( ( finite_card_nat @ B4 )
% 9.25/5.27                    = K ) ) ) )
% 9.25/5.27          = ( binomial @ ( finite_card_nat @ A2 ) @ K ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9080_sum_Onon__neutral_H,axiom,
% 9.25/5.27      ! [G2: nat > code_integer,I4: set_nat] :
% 9.25/5.27        ( ( groups555127423416065298nteger @ G2
% 9.25/5.27          @ ( collect_nat
% 9.25/5.27            @ ^ [X3: nat] :
% 9.25/5.27                ( ( member_nat @ X3 @ I4 )
% 9.25/5.27                & ( ( G2 @ X3 )
% 9.25/5.27                 != zero_z3403309356797280102nteger ) ) ) )
% 9.25/5.27        = ( groups555127423416065298nteger @ G2 @ I4 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9081_sum_Onon__neutral_H,axiom,
% 9.25/5.27      ! [G2: int > code_integer,I4: set_int] :
% 9.25/5.27        ( ( groups926780983652909934nteger @ G2
% 9.25/5.27          @ ( collect_int
% 9.25/5.27            @ ^ [X3: int] :
% 9.25/5.27                ( ( member_int @ X3 @ I4 )
% 9.25/5.27                & ( ( G2 @ X3 )
% 9.25/5.27                 != zero_z3403309356797280102nteger ) ) ) )
% 9.25/5.27        = ( groups926780983652909934nteger @ G2 @ I4 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9082_sum_Onon__neutral_H,axiom,
% 9.25/5.27      ! [G2: nat > rat,I4: set_nat] :
% 9.25/5.27        ( ( groups1351286907653491341at_rat @ G2
% 9.25/5.27          @ ( collect_nat
% 9.25/5.27            @ ^ [X3: nat] :
% 9.25/5.27                ( ( member_nat @ X3 @ I4 )
% 9.25/5.27                & ( ( G2 @ X3 )
% 9.25/5.27                 != zero_zero_rat ) ) ) )
% 9.25/5.27        = ( groups1351286907653491341at_rat @ G2 @ I4 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9083_sum_Onon__neutral_H,axiom,
% 9.25/5.27      ! [G2: int > rat,I4: set_int] :
% 9.25/5.27        ( ( groups2350640619554545897nt_rat @ G2
% 9.25/5.27          @ ( collect_int
% 9.25/5.27            @ ^ [X3: int] :
% 9.25/5.27                ( ( member_int @ X3 @ I4 )
% 9.25/5.27                & ( ( G2 @ X3 )
% 9.25/5.27                 != zero_zero_rat ) ) ) )
% 9.25/5.27        = ( groups2350640619554545897nt_rat @ G2 @ I4 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9084_sum_Onon__neutral_H,axiom,
% 9.25/5.27      ! [G2: nat > nat,I4: set_nat] :
% 9.25/5.27        ( ( groups1986416967739987077at_nat @ G2
% 9.25/5.27          @ ( collect_nat
% 9.25/5.27            @ ^ [X3: nat] :
% 9.25/5.27                ( ( member_nat @ X3 @ I4 )
% 9.25/5.27                & ( ( G2 @ X3 )
% 9.25/5.27                 != zero_zero_nat ) ) ) )
% 9.25/5.27        = ( groups1986416967739987077at_nat @ G2 @ I4 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9085_sum_Onon__neutral_H,axiom,
% 9.25/5.27      ! [G2: int > nat,I4: set_int] :
% 9.25/5.27        ( ( groups2985770679641041633nt_nat @ G2
% 9.25/5.27          @ ( collect_int
% 9.25/5.27            @ ^ [X3: int] :
% 9.25/5.27                ( ( member_int @ X3 @ I4 )
% 9.25/5.27                & ( ( G2 @ X3 )
% 9.25/5.27                 != zero_zero_nat ) ) ) )
% 9.25/5.27        = ( groups2985770679641041633nt_nat @ G2 @ I4 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9086_sum_Onon__neutral_H,axiom,
% 9.25/5.27      ! [G2: nat > int,I4: set_nat] :
% 9.25/5.27        ( ( groups1983926497230936801at_int @ G2
% 9.25/5.27          @ ( collect_nat
% 9.25/5.27            @ ^ [X3: nat] :
% 9.25/5.27                ( ( member_nat @ X3 @ I4 )
% 9.25/5.27                & ( ( G2 @ X3 )
% 9.25/5.27                 != zero_zero_int ) ) ) )
% 9.25/5.27        = ( groups1983926497230936801at_int @ G2 @ I4 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9087_sum_Onon__neutral_H,axiom,
% 9.25/5.27      ! [G2: int > int,I4: set_int] :
% 9.25/5.27        ( ( groups2983280209131991357nt_int @ G2
% 9.25/5.27          @ ( collect_int
% 9.25/5.27            @ ^ [X3: int] :
% 9.25/5.27                ( ( member_int @ X3 @ I4 )
% 9.25/5.27                & ( ( G2 @ X3 )
% 9.25/5.27                 != zero_zero_int ) ) ) )
% 9.25/5.27        = ( groups2983280209131991357nt_int @ G2 @ I4 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9088_sum_Onon__neutral_H,axiom,
% 9.25/5.27      ! [G2: set_nat > code_integer,I4: set_set_nat] :
% 9.25/5.27        ( ( groups9221925307898054856nteger @ G2
% 9.25/5.27          @ ( collect_set_nat
% 9.25/5.27            @ ^ [X3: set_nat] :
% 9.25/5.27                ( ( member_set_nat @ X3 @ I4 )
% 9.25/5.27                & ( ( G2 @ X3 )
% 9.25/5.27                 != zero_z3403309356797280102nteger ) ) ) )
% 9.25/5.27        = ( groups9221925307898054856nteger @ G2 @ I4 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9089_sum_Onon__neutral_H,axiom,
% 9.25/5.27      ! [G2: set_nat > rat,I4: set_set_nat] :
% 9.25/5.27        ( ( groups713094340420062787at_rat @ G2
% 9.25/5.27          @ ( collect_set_nat
% 9.25/5.27            @ ^ [X3: set_nat] :
% 9.25/5.27                ( ( member_set_nat @ X3 @ I4 )
% 9.25/5.27                & ( ( G2 @ X3 )
% 9.25/5.27                 != zero_zero_rat ) ) ) )
% 9.25/5.27        = ( groups713094340420062787at_rat @ G2 @ I4 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9090_card__eq__UNIV__imp__eq__UNIV,axiom,
% 9.25/5.27      ! [A2: set_set_nat] :
% 9.25/5.27        ( ( finite1152437895449049373et_nat @ top_top_set_set_nat )
% 9.25/5.27       => ( ( ( finite_card_set_nat @ A2 )
% 9.25/5.27            = ( finite_card_set_nat @ top_top_set_set_nat ) )
% 9.25/5.27         => ( A2 = top_top_set_set_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9091_card__eq__UNIV__imp__eq__UNIV,axiom,
% 9.25/5.27      ! [A2: set_Pr1261947904930325089at_nat] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat @ top_to4669805908274784177at_nat )
% 9.25/5.27       => ( ( ( finite711546835091564841at_nat @ A2 )
% 9.25/5.27            = ( finite711546835091564841at_nat @ top_to4669805908274784177at_nat ) )
% 9.25/5.27         => ( A2 = top_to4669805908274784177at_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9092_card__eq__UNIV__imp__eq__UNIV,axiom,
% 9.25/5.27      ! [A2: set_list_nat] :
% 9.25/5.27        ( ( finite8100373058378681591st_nat @ top_top_set_list_nat )
% 9.25/5.27       => ( ( ( finite_card_list_nat @ A2 )
% 9.25/5.27            = ( finite_card_list_nat @ top_top_set_list_nat ) )
% 9.25/5.27         => ( A2 = top_top_set_list_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9093_card__eq__UNIV__imp__eq__UNIV,axiom,
% 9.25/5.27      ! [A2: set_o] :
% 9.25/5.27        ( ( finite_finite_o @ top_top_set_o )
% 9.25/5.27       => ( ( ( finite_card_o @ A2 )
% 9.25/5.27            = ( finite_card_o @ top_top_set_o ) )
% 9.25/5.27         => ( A2 = top_top_set_o ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9094_card__eq__UNIV__imp__eq__UNIV,axiom,
% 9.25/5.27      ! [A2: set_rat] :
% 9.25/5.27        ( ( finite_finite_rat @ top_top_set_rat )
% 9.25/5.27       => ( ( ( finite_card_rat @ A2 )
% 9.25/5.27            = ( finite_card_rat @ top_top_set_rat ) )
% 9.25/5.27         => ( A2 = top_top_set_rat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9095_card__eq__UNIV__imp__eq__UNIV,axiom,
% 9.25/5.27      ! [A2: set_nat] :
% 9.25/5.27        ( ( finite_finite_nat @ top_top_set_nat )
% 9.25/5.27       => ( ( ( finite_card_nat @ A2 )
% 9.25/5.27            = ( finite_card_nat @ top_top_set_nat ) )
% 9.25/5.27         => ( A2 = top_top_set_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9096_card__eq__UNIV__imp__eq__UNIV,axiom,
% 9.25/5.27      ! [A2: set_int] :
% 9.25/5.27        ( ( finite_finite_int @ top_top_set_int )
% 9.25/5.27       => ( ( ( finite_card_int @ A2 )
% 9.25/5.27            = ( finite_card_int @ top_top_set_int ) )
% 9.25/5.27         => ( A2 = top_top_set_int ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9097_nat__one__as__int,axiom,
% 9.25/5.27      ( one_one_nat
% 9.25/5.27      = ( nat2 @ one_one_int ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9098_sum__multicount__gen,axiom,
% 9.25/5.27      ! [S3: set_o,T3: set_nat,R: $o > nat > $o,K: nat > nat] :
% 9.25/5.27        ( ( finite_finite_o @ S3 )
% 9.25/5.27       => ( ( finite_finite_nat @ T3 )
% 9.25/5.27         => ( ! [X2: nat] :
% 9.25/5.27                ( ( member_nat @ X2 @ T3 )
% 9.25/5.27               => ( ( finite_card_o
% 9.25/5.27                    @ ( collect_o
% 9.25/5.27                      @ ^ [I3: $o] :
% 9.25/5.27                          ( ( member_o @ I3 @ S3 )
% 9.25/5.27                          & ( R @ I3 @ X2 ) ) ) )
% 9.25/5.27                  = ( K @ X2 ) ) )
% 9.25/5.27           => ( ( groups8507830703676809646_o_nat
% 9.25/5.27                @ ^ [I3: $o] :
% 9.25/5.27                    ( finite_card_nat
% 9.25/5.27                    @ ( collect_nat
% 9.25/5.27                      @ ^ [J3: nat] :
% 9.25/5.27                          ( ( member_nat @ J3 @ T3 )
% 9.25/5.27                          & ( R @ I3 @ J3 ) ) ) )
% 9.25/5.27                @ S3 )
% 9.25/5.27              = ( groups3542108847815614940at_nat @ K @ T3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9099_sum__multicount__gen,axiom,
% 9.25/5.27      ! [S3: set_int,T3: set_nat,R: int > nat > $o,K: nat > nat] :
% 9.25/5.27        ( ( finite_finite_int @ S3 )
% 9.25/5.27       => ( ( finite_finite_nat @ T3 )
% 9.25/5.27         => ( ! [X2: nat] :
% 9.25/5.27                ( ( member_nat @ X2 @ T3 )
% 9.25/5.27               => ( ( finite_card_int
% 9.25/5.27                    @ ( collect_int
% 9.25/5.27                      @ ^ [I3: int] :
% 9.25/5.27                          ( ( member_int @ I3 @ S3 )
% 9.25/5.27                          & ( R @ I3 @ X2 ) ) ) )
% 9.25/5.27                  = ( K @ X2 ) ) )
% 9.25/5.27           => ( ( groups4541462559716669496nt_nat
% 9.25/5.27                @ ^ [I3: int] :
% 9.25/5.27                    ( finite_card_nat
% 9.25/5.27                    @ ( collect_nat
% 9.25/5.27                      @ ^ [J3: nat] :
% 9.25/5.27                          ( ( member_nat @ J3 @ T3 )
% 9.25/5.27                          & ( R @ I3 @ J3 ) ) ) )
% 9.25/5.27                @ S3 )
% 9.25/5.27              = ( groups3542108847815614940at_nat @ K @ T3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9100_sum__multicount__gen,axiom,
% 9.25/5.27      ! [S3: set_nat,T3: set_o,R: nat > $o > $o,K: $o > nat] :
% 9.25/5.27        ( ( finite_finite_nat @ S3 )
% 9.25/5.27       => ( ( finite_finite_o @ T3 )
% 9.25/5.27         => ( ! [X2: $o] :
% 9.25/5.27                ( ( member_o @ X2 @ T3 )
% 9.25/5.27               => ( ( finite_card_nat
% 9.25/5.27                    @ ( collect_nat
% 9.25/5.27                      @ ^ [I3: nat] :
% 9.25/5.27                          ( ( member_nat @ I3 @ S3 )
% 9.25/5.27                          & ( R @ I3 @ X2 ) ) ) )
% 9.25/5.27                  = ( K @ X2 ) ) )
% 9.25/5.27           => ( ( groups3542108847815614940at_nat
% 9.25/5.27                @ ^ [I3: nat] :
% 9.25/5.27                    ( finite_card_o
% 9.25/5.27                    @ ( collect_o
% 9.25/5.27                      @ ^ [J3: $o] :
% 9.25/5.27                          ( ( member_o @ J3 @ T3 )
% 9.25/5.27                          & ( R @ I3 @ J3 ) ) ) )
% 9.25/5.27                @ S3 )
% 9.25/5.27              = ( groups8507830703676809646_o_nat @ K @ T3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9101_sum__multicount__gen,axiom,
% 9.25/5.27      ! [S3: set_nat,T3: set_int,R: nat > int > $o,K: int > nat] :
% 9.25/5.27        ( ( finite_finite_nat @ S3 )
% 9.25/5.27       => ( ( finite_finite_int @ T3 )
% 9.25/5.27         => ( ! [X2: int] :
% 9.25/5.27                ( ( member_int @ X2 @ T3 )
% 9.25/5.27               => ( ( finite_card_nat
% 9.25/5.27                    @ ( collect_nat
% 9.25/5.27                      @ ^ [I3: nat] :
% 9.25/5.27                          ( ( member_nat @ I3 @ S3 )
% 9.25/5.27                          & ( R @ I3 @ X2 ) ) ) )
% 9.25/5.27                  = ( K @ X2 ) ) )
% 9.25/5.27           => ( ( groups3542108847815614940at_nat
% 9.25/5.27                @ ^ [I3: nat] :
% 9.25/5.27                    ( finite_card_int
% 9.25/5.27                    @ ( collect_int
% 9.25/5.27                      @ ^ [J3: int] :
% 9.25/5.27                          ( ( member_int @ J3 @ T3 )
% 9.25/5.27                          & ( R @ I3 @ J3 ) ) ) )
% 9.25/5.27                @ S3 )
% 9.25/5.27              = ( groups4541462559716669496nt_nat @ K @ T3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9102_sum__multicount__gen,axiom,
% 9.25/5.27      ! [S3: set_nat,T3: set_nat,R: nat > nat > $o,K: nat > nat] :
% 9.25/5.27        ( ( finite_finite_nat @ S3 )
% 9.25/5.27       => ( ( finite_finite_nat @ T3 )
% 9.25/5.27         => ( ! [X2: nat] :
% 9.25/5.27                ( ( member_nat @ X2 @ T3 )
% 9.25/5.27               => ( ( finite_card_nat
% 9.25/5.27                    @ ( collect_nat
% 9.25/5.27                      @ ^ [I3: nat] :
% 9.25/5.27                          ( ( member_nat @ I3 @ S3 )
% 9.25/5.27                          & ( R @ I3 @ X2 ) ) ) )
% 9.25/5.27                  = ( K @ X2 ) ) )
% 9.25/5.27           => ( ( groups3542108847815614940at_nat
% 9.25/5.27                @ ^ [I3: nat] :
% 9.25/5.27                    ( finite_card_nat
% 9.25/5.27                    @ ( collect_nat
% 9.25/5.27                      @ ^ [J3: nat] :
% 9.25/5.27                          ( ( member_nat @ J3 @ T3 )
% 9.25/5.27                          & ( R @ I3 @ J3 ) ) ) )
% 9.25/5.27                @ S3 )
% 9.25/5.27              = ( groups3542108847815614940at_nat @ K @ T3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9103_sum__multicount__gen,axiom,
% 9.25/5.27      ! [S3: set_list_nat,T3: set_nat,R: list_nat > nat > $o,K: nat > nat] :
% 9.25/5.27        ( ( finite8100373058378681591st_nat @ S3 )
% 9.25/5.27       => ( ( finite_finite_nat @ T3 )
% 9.25/5.27         => ( ! [X2: nat] :
% 9.25/5.27                ( ( member_nat @ X2 @ T3 )
% 9.25/5.27               => ( ( finite_card_list_nat
% 9.25/5.27                    @ ( collect_list_nat
% 9.25/5.27                      @ ^ [I3: list_nat] :
% 9.25/5.27                          ( ( member_list_nat @ I3 @ S3 )
% 9.25/5.27                          & ( R @ I3 @ X2 ) ) ) )
% 9.25/5.27                  = ( K @ X2 ) ) )
% 9.25/5.27           => ( ( groups4396056296759096172at_nat
% 9.25/5.27                @ ^ [I3: list_nat] :
% 9.25/5.27                    ( finite_card_nat
% 9.25/5.27                    @ ( collect_nat
% 9.25/5.27                      @ ^ [J3: nat] :
% 9.25/5.27                          ( ( member_nat @ J3 @ T3 )
% 9.25/5.27                          & ( R @ I3 @ J3 ) ) ) )
% 9.25/5.27                @ S3 )
% 9.25/5.27              = ( groups3542108847815614940at_nat @ K @ T3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9104_sum__multicount__gen,axiom,
% 9.25/5.27      ! [S3: set_set_nat,T3: set_nat,R: set_nat > nat > $o,K: nat > nat] :
% 9.25/5.27        ( ( finite1152437895449049373et_nat @ S3 )
% 9.25/5.27       => ( ( finite_finite_nat @ T3 )
% 9.25/5.27         => ( ! [X2: nat] :
% 9.25/5.27                ( ( member_nat @ X2 @ T3 )
% 9.25/5.27               => ( ( finite_card_set_nat
% 9.25/5.27                    @ ( collect_set_nat
% 9.25/5.27                      @ ^ [I3: set_nat] :
% 9.25/5.27                          ( ( member_set_nat @ I3 @ S3 )
% 9.25/5.27                          & ( R @ I3 @ X2 ) ) ) )
% 9.25/5.27                  = ( K @ X2 ) ) )
% 9.25/5.27           => ( ( groups8294997508430121362at_nat
% 9.25/5.27                @ ^ [I3: set_nat] :
% 9.25/5.27                    ( finite_card_nat
% 9.25/5.27                    @ ( collect_nat
% 9.25/5.27                      @ ^ [J3: nat] :
% 9.25/5.27                          ( ( member_nat @ J3 @ T3 )
% 9.25/5.27                          & ( R @ I3 @ J3 ) ) ) )
% 9.25/5.27                @ S3 )
% 9.25/5.27              = ( groups3542108847815614940at_nat @ K @ T3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9105_sum__multicount__gen,axiom,
% 9.25/5.27      ! [S3: set_nat,T3: set_list_nat,R: nat > list_nat > $o,K: list_nat > nat] :
% 9.25/5.27        ( ( finite_finite_nat @ S3 )
% 9.25/5.27       => ( ( finite8100373058378681591st_nat @ T3 )
% 9.25/5.27         => ( ! [X2: list_nat] :
% 9.25/5.27                ( ( member_list_nat @ X2 @ T3 )
% 9.25/5.27               => ( ( finite_card_nat
% 9.25/5.27                    @ ( collect_nat
% 9.25/5.27                      @ ^ [I3: nat] :
% 9.25/5.27                          ( ( member_nat @ I3 @ S3 )
% 9.25/5.27                          & ( R @ I3 @ X2 ) ) ) )
% 9.25/5.27                  = ( K @ X2 ) ) )
% 9.25/5.27           => ( ( groups3542108847815614940at_nat
% 9.25/5.27                @ ^ [I3: nat] :
% 9.25/5.27                    ( finite_card_list_nat
% 9.25/5.27                    @ ( collect_list_nat
% 9.25/5.27                      @ ^ [J3: list_nat] :
% 9.25/5.27                          ( ( member_list_nat @ J3 @ T3 )
% 9.25/5.27                          & ( R @ I3 @ J3 ) ) ) )
% 9.25/5.27                @ S3 )
% 9.25/5.27              = ( groups4396056296759096172at_nat @ K @ T3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9106_sum__multicount__gen,axiom,
% 9.25/5.27      ! [S3: set_nat,T3: set_set_nat,R: nat > set_nat > $o,K: set_nat > nat] :
% 9.25/5.27        ( ( finite_finite_nat @ S3 )
% 9.25/5.27       => ( ( finite1152437895449049373et_nat @ T3 )
% 9.25/5.27         => ( ! [X2: set_nat] :
% 9.25/5.27                ( ( member_set_nat @ X2 @ T3 )
% 9.25/5.27               => ( ( finite_card_nat
% 9.25/5.27                    @ ( collect_nat
% 9.25/5.27                      @ ^ [I3: nat] :
% 9.25/5.27                          ( ( member_nat @ I3 @ S3 )
% 9.25/5.27                          & ( R @ I3 @ X2 ) ) ) )
% 9.25/5.27                  = ( K @ X2 ) ) )
% 9.25/5.27           => ( ( groups3542108847815614940at_nat
% 9.25/5.27                @ ^ [I3: nat] :
% 9.25/5.27                    ( finite_card_set_nat
% 9.25/5.27                    @ ( collect_set_nat
% 9.25/5.27                      @ ^ [J3: set_nat] :
% 9.25/5.27                          ( ( member_set_nat @ J3 @ T3 )
% 9.25/5.27                          & ( R @ I3 @ J3 ) ) ) )
% 9.25/5.27                @ S3 )
% 9.25/5.27              = ( groups8294997508430121362at_nat @ K @ T3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9107_sum__multicount__gen,axiom,
% 9.25/5.27      ! [S3: set_Pr1261947904930325089at_nat,T3: set_nat,R: product_prod_nat_nat > nat > $o,K: nat > nat] :
% 9.25/5.27        ( ( finite6177210948735845034at_nat @ S3 )
% 9.25/5.27       => ( ( finite_finite_nat @ T3 )
% 9.25/5.27         => ( ! [X2: nat] :
% 9.25/5.27                ( ( member_nat @ X2 @ T3 )
% 9.25/5.27               => ( ( finite711546835091564841at_nat
% 9.25/5.27                    @ ( collec3392354462482085612at_nat
% 9.25/5.27                      @ ^ [I3: product_prod_nat_nat] :
% 9.25/5.27                          ( ( member8440522571783428010at_nat @ I3 @ S3 )
% 9.25/5.27                          & ( R @ I3 @ X2 ) ) ) )
% 9.25/5.27                  = ( K @ X2 ) ) )
% 9.25/5.27           => ( ( groups977919841031483927at_nat
% 9.25/5.27                @ ^ [I3: product_prod_nat_nat] :
% 9.25/5.27                    ( finite_card_nat
% 9.25/5.27                    @ ( collect_nat
% 9.25/5.27                      @ ^ [J3: nat] :
% 9.25/5.27                          ( ( member_nat @ J3 @ T3 )
% 9.25/5.27                          & ( R @ I3 @ J3 ) ) ) )
% 9.25/5.27                @ S3 )
% 9.25/5.27              = ( groups3542108847815614940at_nat @ K @ T3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9108_card__less,axiom,
% 9.25/5.27      ! [M4: set_nat,I: nat] :
% 9.25/5.27        ( ( member_nat @ zero_zero_nat @ M4 )
% 9.25/5.27       => ( ( finite_card_nat
% 9.25/5.27            @ ( collect_nat
% 9.25/5.27              @ ^ [K4: nat] :
% 9.25/5.27                  ( ( member_nat @ K4 @ M4 )
% 9.25/5.27                  & ( ord_less_nat @ K4 @ ( suc @ I ) ) ) ) )
% 9.25/5.27         != zero_zero_nat ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9109_card__less__Suc,axiom,
% 9.25/5.27      ! [M4: set_nat,I: nat] :
% 9.25/5.27        ( ( member_nat @ zero_zero_nat @ M4 )
% 9.25/5.27       => ( ( suc
% 9.25/5.27            @ ( finite_card_nat
% 9.25/5.27              @ ( collect_nat
% 9.25/5.27                @ ^ [K4: nat] :
% 9.25/5.27                    ( ( member_nat @ ( suc @ K4 ) @ M4 )
% 9.25/5.27                    & ( ord_less_nat @ K4 @ I ) ) ) ) )
% 9.25/5.27          = ( finite_card_nat
% 9.25/5.27            @ ( collect_nat
% 9.25/5.27              @ ^ [K4: nat] :
% 9.25/5.27                  ( ( member_nat @ K4 @ M4 )
% 9.25/5.27                  & ( ord_less_nat @ K4 @ ( suc @ I ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9110_card__less__Suc2,axiom,
% 9.25/5.27      ! [M4: set_nat,I: nat] :
% 9.25/5.27        ( ~ ( member_nat @ zero_zero_nat @ M4 )
% 9.25/5.27       => ( ( finite_card_nat
% 9.25/5.27            @ ( collect_nat
% 9.25/5.27              @ ^ [K4: nat] :
% 9.25/5.27                  ( ( member_nat @ ( suc @ K4 ) @ M4 )
% 9.25/5.27                  & ( ord_less_nat @ K4 @ I ) ) ) )
% 9.25/5.27          = ( finite_card_nat
% 9.25/5.27            @ ( collect_nat
% 9.25/5.27              @ ^ [K4: nat] :
% 9.25/5.27                  ( ( member_nat @ K4 @ M4 )
% 9.25/5.27                  & ( ord_less_nat @ K4 @ ( suc @ I ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9111_nat__plus__as__int,axiom,
% 9.25/5.27      ( plus_plus_nat
% 9.25/5.27      = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9112_nat__times__as__int,axiom,
% 9.25/5.27      ( times_times_nat
% 9.25/5.27      = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9113_nat__minus__as__int,axiom,
% 9.25/5.27      ( minus_minus_nat
% 9.25/5.27      = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9114_nat__div__as__int,axiom,
% 9.25/5.27      ( divide_divide_nat
% 9.25/5.27      = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9115_nat__mod__as__int,axiom,
% 9.25/5.27      ( modulo_modulo_nat
% 9.25/5.27      = ( ^ [A3: nat,B3: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9116_Suc__as__int,axiom,
% 9.25/5.27      ( suc
% 9.25/5.27      = ( ^ [A3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ one_one_int ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9117_card__sum__le__nat__sum,axiom,
% 9.25/5.27      ! [S: set_nat] :
% 9.25/5.27        ( ord_less_eq_nat
% 9.25/5.27        @ ( groups3542108847815614940at_nat
% 9.25/5.27          @ ^ [X3: nat] : X3
% 9.25/5.27          @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S ) ) )
% 9.25/5.27        @ ( groups3542108847815614940at_nat
% 9.25/5.27          @ ^ [X3: nat] : X3
% 9.25/5.27          @ S ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9118_Suc__nat__eq__nat__zadd1,axiom,
% 9.25/5.27      ! [Z: int] :
% 9.25/5.27        ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 9.25/5.27       => ( ( suc @ ( nat2 @ Z ) )
% 9.25/5.27          = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9119_nat__mult__distrib__neg,axiom,
% 9.25/5.27      ! [Z: int,Z8: int] :
% 9.25/5.27        ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 9.25/5.27       => ( ( nat2 @ ( times_times_int @ Z @ Z8 ) )
% 9.25/5.27          = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z8 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9120_diff__nat__eq__if,axiom,
% 9.25/5.27      ! [Z8: int,Z: int] :
% 9.25/5.27        ( ( ( ord_less_int @ Z8 @ zero_zero_int )
% 9.25/5.27         => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z8 ) )
% 9.25/5.27            = ( nat2 @ Z ) ) )
% 9.25/5.27        & ( ~ ( ord_less_int @ Z8 @ zero_zero_int )
% 9.25/5.27         => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z8 ) )
% 9.25/5.27            = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z8 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z8 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9121_card__UNIV__char,axiom,
% 9.25/5.27      ( ( finite_card_char @ top_top_set_char )
% 9.25/5.27      = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9122_divmod__integer__eq__cases,axiom,
% 9.25/5.27      ( code_divmod_integer
% 9.25/5.27      = ( ^ [K4: code_integer,L2: code_integer] :
% 9.25/5.27            ( if_Pro6119634080678213985nteger @ ( K4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 9.25/5.27            @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K4 )
% 9.25/5.27              @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L2
% 9.25/5.27                @ ( if_Pro6119634080678213985nteger
% 9.25/5.27                  @ ( ( sgn_sgn_Code_integer @ K4 )
% 9.25/5.27                    = ( sgn_sgn_Code_integer @ L2 ) )
% 9.25/5.27                  @ ( code_divmod_abs @ K4 @ L2 )
% 9.25/5.27                  @ ( produc6916734918728496179nteger
% 9.25/5.27                    @ ^ [R4: code_integer,S2: code_integer] : ( if_Pro6119634080678213985nteger @ ( S2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R4 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L2 ) @ S2 ) ) )
% 9.25/5.27                    @ ( code_divmod_abs @ K4 @ L2 ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9123_or__minus__numerals_I2_J,axiom,
% 9.25/5.27      ! [N: num] :
% 9.25/5.27        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 9.25/5.27        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9124_or__minus__numerals_I6_J,axiom,
% 9.25/5.27      ! [N: num] :
% 9.25/5.27        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 9.25/5.27        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9125_or__minus__minus__numerals,axiom,
% 9.25/5.27      ! [M: num,N: num] :
% 9.25/5.27        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.27        = ( 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 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9126_and__minus__minus__numerals,axiom,
% 9.25/5.27      ! [M: num,N: num] :
% 9.25/5.27        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.27        = ( 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 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9127_UNIV__bool,axiom,
% 9.25/5.27      ( top_top_set_o
% 9.25/5.27      = ( insert_o @ $false @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9128_set__bit__int__def,axiom,
% 9.25/5.27      ( bit_se7879613467334960850it_int
% 9.25/5.27      = ( ^ [N2: nat,K4: int] : ( bit_se1409905431419307370or_int @ K4 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9129_set__bit__nat__def,axiom,
% 9.25/5.27      ( bit_se7882103937844011126it_nat
% 9.25/5.27      = ( ^ [M2: nat,N2: nat] : ( bit_se1412395901928357646or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M2 @ one_one_nat ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9130_or__not__numerals_I1_J,axiom,
% 9.25/5.27      ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 9.25/5.27      = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9131_or__not__numerals_I2_J,axiom,
% 9.25/5.27      ! [N: num] :
% 9.25/5.27        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 9.25/5.27        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9132_or__not__numerals_I4_J,axiom,
% 9.25/5.27      ! [M: num] :
% 9.25/5.27        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 9.25/5.27        = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9133_or__not__numerals_I3_J,axiom,
% 9.25/5.27      ! [N: num] :
% 9.25/5.27        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 9.25/5.27        = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9134_or__not__numerals_I7_J,axiom,
% 9.25/5.27      ! [M: num] :
% 9.25/5.27        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 9.25/5.27        = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9135_or__not__numerals_I5_J,axiom,
% 9.25/5.27      ! [M: num,N: num] :
% 9.25/5.27        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 9.25/5.27        = ( 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 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9136_or__not__numerals_I9_J,axiom,
% 9.25/5.27      ! [M: num,N: num] :
% 9.25/5.27        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 9.25/5.27        = ( 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 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9137_or__not__numerals_I8_J,axiom,
% 9.25/5.27      ! [M: num,N: num] :
% 9.25/5.27        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 9.25/5.27        = ( 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 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9138_or__int__unfold,axiom,
% 9.25/5.27      ( bit_se1409905431419307370or_int
% 9.25/5.27      = ( ^ [K4: int,L2: int] :
% 9.25/5.27            ( if_int
% 9.25/5.27            @ ( ( K4
% 9.25/5.27                = ( uminus_uminus_int @ one_one_int ) )
% 9.25/5.27              | ( L2
% 9.25/5.27                = ( uminus_uminus_int @ one_one_int ) ) )
% 9.25/5.27            @ ( uminus_uminus_int @ one_one_int )
% 9.25/5.27            @ ( if_int @ ( K4 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K4 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K4 @ ( 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 @ K4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9139_or__minus__numerals_I5_J,axiom,
% 9.25/5.27      ! [N: num] :
% 9.25/5.27        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 9.25/5.27        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9140_or__minus__numerals_I1_J,axiom,
% 9.25/5.27      ! [N: num] :
% 9.25/5.27        ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 9.25/5.27        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9141_card__greaterThanLessThan__int,axiom,
% 9.25/5.27      ! [L: int,U: int] :
% 9.25/5.27        ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 9.25/5.27        = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9142_or__minus__numerals_I8_J,axiom,
% 9.25/5.27      ! [N: num,M: num] :
% 9.25/5.27        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 9.25/5.27        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9143_or__minus__numerals_I4_J,axiom,
% 9.25/5.27      ! [M: num,N: num] :
% 9.25/5.27        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 9.25/5.27        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9144_or__minus__numerals_I3_J,axiom,
% 9.25/5.27      ! [M: num,N: num] :
% 9.25/5.27        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 9.25/5.27        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9145_or__minus__numerals_I7_J,axiom,
% 9.25/5.27      ! [N: num,M: num] :
% 9.25/5.27        ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 9.25/5.27        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9146_sup__int__def,axiom,
% 9.25/5.27      sup_sup_int = ord_max_int ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9147_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 9.25/5.27      ! [L: int,U: int] :
% 9.25/5.27        ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 9.25/5.27        = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9148_int__numeral__or__not__num__neg,axiom,
% 9.25/5.27      ! [M: num,N: num] :
% 9.25/5.27        ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.27        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9149_int__numeral__not__or__num__neg,axiom,
% 9.25/5.27      ! [M: num,N: num] :
% 9.25/5.27        ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 9.25/5.27        = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N @ M ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9150_numeral__or__not__num__eq,axiom,
% 9.25/5.27      ! [M: num,N: num] :
% 9.25/5.27        ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) )
% 9.25/5.27        = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9151_Sup__nat__empty,axiom,
% 9.25/5.27      ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 9.25/5.27      = zero_zero_nat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9152_max__nat_Osemilattice__neutr__axioms,axiom,
% 9.25/5.27      semila9081495762789891438tr_nat @ ord_max_nat @ zero_zero_nat ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9153_max__nat_Ocomm__monoid__axioms,axiom,
% 9.25/5.27      comm_monoid_nat @ ord_max_nat @ zero_zero_nat ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9154_max__nat_Omonoid__axioms,axiom,
% 9.25/5.27      monoid_nat @ ord_max_nat @ zero_zero_nat ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9155_max__Suc2,axiom,
% 9.25/5.27      ! [M: nat,N: nat] :
% 9.25/5.27        ( ( ord_max_nat @ M @ ( suc @ N ) )
% 9.25/5.27        = ( case_nat_nat @ ( suc @ N )
% 9.25/5.27          @ ^ [M5: nat] : ( suc @ ( ord_max_nat @ M5 @ N ) )
% 9.25/5.27          @ M ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9156_max__Suc1,axiom,
% 9.25/5.27      ! [N: nat,M: nat] :
% 9.25/5.27        ( ( ord_max_nat @ ( suc @ N ) @ M )
% 9.25/5.27        = ( case_nat_nat @ ( suc @ N )
% 9.25/5.27          @ ^ [M5: nat] : ( suc @ ( ord_max_nat @ N @ M5 ) )
% 9.25/5.27          @ M ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9157_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 9.25/5.27      ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 9.25/5.27      @ ^ [X3: nat,Y3: nat] : ( ord_less_eq_nat @ Y3 @ X3 )
% 9.25/5.27      @ ^ [X3: nat,Y3: nat] : ( ord_less_nat @ Y3 @ X3 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9158_atLeastPlusOneLessThan__greaterThanLessThan__integer,axiom,
% 9.25/5.27      ! [L: code_integer,U: code_integer] :
% 9.25/5.27        ( ( set_or8404916559141939852nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 9.25/5.27        = ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9159_Code__Numeral_Onegative__def,axiom,
% 9.25/5.27      ( code_negative
% 9.25/5.27      = ( comp_C3531382070062128313er_num @ uminus1351360451143612070nteger @ numera6620942414471956472nteger ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9160_sup__nat__def,axiom,
% 9.25/5.27      sup_sup_nat = ord_max_nat ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9161_UN__atMost__UNIV,axiom,
% 9.25/5.27      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 9.25/5.27      = top_top_set_nat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9162_UN__lessThan__UNIV,axiom,
% 9.25/5.27      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 9.25/5.27      = top_top_set_nat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9163_Inf__int__def,axiom,
% 9.25/5.27      ( complete_Inf_Inf_int
% 9.25/5.27      = ( ^ [X4: set_int] : ( uminus_uminus_int @ ( complete_Sup_Sup_int @ ( image_int_int @ uminus_uminus_int @ X4 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9164_Inf__nat__def1,axiom,
% 9.25/5.27      ! [K5: set_nat] :
% 9.25/5.27        ( ( K5 != bot_bot_set_nat )
% 9.25/5.27       => ( member_nat @ ( complete_Inf_Inf_nat @ K5 ) @ K5 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9165_int__in__range__abs,axiom,
% 9.25/5.27      ! [N: nat] : ( member_int @ ( semiri1314217659103216013at_int @ N ) @ ( image_int_int @ abs_abs_int @ top_top_set_int ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9166_image__Suc__atMost,axiom,
% 9.25/5.27      ! [N: nat] :
% 9.25/5.27        ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 9.25/5.27        = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9167_image__Suc__lessThan,axiom,
% 9.25/5.27      ! [N: nat] :
% 9.25/5.27        ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 9.25/5.27        = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9168_image__add__int__atLeastLessThan,axiom,
% 9.25/5.27      ! [L: int,U: int] :
% 9.25/5.27        ( ( image_int_int
% 9.25/5.27          @ ^ [X3: int] : ( plus_plus_int @ X3 @ L )
% 9.25/5.27          @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 9.25/5.27        = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9169_image__add__integer__atLeastLessThan,axiom,
% 9.25/5.27      ! [L: code_integer,U: code_integer] :
% 9.25/5.27        ( ( image_4470545334726330049nteger
% 9.25/5.27          @ ^ [X3: code_integer] : ( plus_p5714425477246183910nteger @ X3 @ L )
% 9.25/5.27          @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ U @ L ) ) )
% 9.25/5.27        = ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9170_range__mod,axiom,
% 9.25/5.27      ! [N: nat] :
% 9.25/5.27        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.27       => ( ( image_nat_nat
% 9.25/5.27            @ ^ [M2: nat] : ( modulo_modulo_nat @ M2 @ N )
% 9.25/5.27            @ top_top_set_nat )
% 9.25/5.27          = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9171_image__minus__const__atLeastLessThan__nat,axiom,
% 9.25/5.27      ! [C: nat,Y: nat,X: nat] :
% 9.25/5.27        ( ( ( ord_less_nat @ C @ Y )
% 9.25/5.27         => ( ( image_nat_nat
% 9.25/5.27              @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 9.25/5.27              @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 9.25/5.27            = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 9.25/5.27        & ( ~ ( ord_less_nat @ C @ Y )
% 9.25/5.27         => ( ( ( ord_less_nat @ X @ Y )
% 9.25/5.27             => ( ( image_nat_nat
% 9.25/5.27                  @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 9.25/5.27                  @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 9.25/5.27                = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 9.25/5.27            & ( ~ ( ord_less_nat @ X @ Y )
% 9.25/5.27             => ( ( image_nat_nat
% 9.25/5.27                  @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 9.25/5.27                  @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 9.25/5.27                = bot_bot_set_nat ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9172_UNIV__char__of__nat,axiom,
% 9.25/5.27      ( top_top_set_char
% 9.25/5.27      = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9173_range__nat__of__char,axiom,
% 9.25/5.27      ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 9.25/5.27      = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9174_pred__def,axiom,
% 9.25/5.27      ( pred
% 9.25/5.27      = ( case_nat_nat @ zero_zero_nat
% 9.25/5.27        @ ^ [X23: nat] : X23 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9175_range__abs__Nats,axiom,
% 9.25/5.27      ( ( image_int_int @ abs_abs_int @ top_top_set_int )
% 9.25/5.27      = semiring_1_Nats_int ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9176_binomial__def,axiom,
% 9.25/5.27      ( binomial
% 9.25/5.27      = ( ^ [N2: nat,K4: nat] :
% 9.25/5.27            ( finite_card_set_nat
% 9.25/5.27            @ ( collect_set_nat
% 9.25/5.27              @ ^ [K6: set_nat] :
% 9.25/5.27                  ( ( member_set_nat @ K6 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) )
% 9.25/5.27                  & ( ( finite_card_nat @ K6 )
% 9.25/5.27                    = K4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9177_times__int_Oabs__eq,axiom,
% 9.25/5.27      ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 9.25/5.27        ( ( times_times_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 9.25/5.27        = ( abs_Integ
% 9.25/5.27          @ ( produc27273713700761075at_nat
% 9.25/5.27            @ ^ [X3: nat,Y3: nat] :
% 9.25/5.27                ( produc2626176000494625587at_nat
% 9.25/5.27                @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V2 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) )
% 9.25/5.27            @ Xa
% 9.25/5.27            @ X ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9178_rat__minus__code,axiom,
% 9.25/5.27      ! [P4: rat,Q4: rat] :
% 9.25/5.27        ( ( quotient_of @ ( minus_minus_rat @ P4 @ Q4 ) )
% 9.25/5.27        = ( produc4245557441103728435nt_int
% 9.25/5.27          @ ^ [A3: int,C4: int] :
% 9.25/5.27              ( produc4245557441103728435nt_int
% 9.25/5.27              @ ^ [B3: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A3 @ D4 ) @ ( times_times_int @ B3 @ C4 ) ) @ ( times_times_int @ C4 @ D4 ) ) )
% 9.25/5.27              @ ( quotient_of @ Q4 ) )
% 9.25/5.27          @ ( quotient_of @ P4 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9179_rat__one__code,axiom,
% 9.25/5.27      ( ( quotient_of @ one_one_rat )
% 9.25/5.27      = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9180_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 9.25/5.27      ! [W: num,N: nat] :
% 9.25/5.27        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N ) )
% 9.25/5.27        = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9181_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 9.25/5.27      ! [W: num,N: nat] :
% 9.25/5.27        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N ) )
% 9.25/5.27        = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9182_rat__zero__code,axiom,
% 9.25/5.27      ( ( quotient_of @ zero_zero_rat )
% 9.25/5.27      = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9183_quotient__of__number_I3_J,axiom,
% 9.25/5.27      ! [K: num] :
% 9.25/5.27        ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 9.25/5.27        = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9184_quotient__of__number_I4_J,axiom,
% 9.25/5.27      ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 9.25/5.27      = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9185_bit__minus__numeral__int_I1_J,axiom,
% 9.25/5.27      ! [W: num,N: num] :
% 9.25/5.27        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 9.25/5.27        = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9186_bit__minus__numeral__int_I2_J,axiom,
% 9.25/5.27      ! [W: num,N: num] :
% 9.25/5.27        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 9.25/5.27        = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9187_quotient__of__number_I5_J,axiom,
% 9.25/5.27      ! [K: num] :
% 9.25/5.27        ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 9.25/5.27        = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9188_diff__rat__def,axiom,
% 9.25/5.27      ( minus_minus_rat
% 9.25/5.27      = ( ^ [Q5: rat,R4: rat] : ( plus_plus_rat @ Q5 @ ( uminus_uminus_rat @ R4 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9189_quotient__of__div,axiom,
% 9.25/5.27      ! [R3: rat,N: int,D2: int] :
% 9.25/5.27        ( ( ( quotient_of @ R3 )
% 9.25/5.27          = ( product_Pair_int_int @ N @ D2 ) )
% 9.25/5.27       => ( R3
% 9.25/5.27          = ( divide_divide_rat @ ( ring_1_of_int_rat @ N ) @ ( ring_1_of_int_rat @ D2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9190_eq__Abs__Integ,axiom,
% 9.25/5.27      ! [Z: int] :
% 9.25/5.27        ~ ! [X2: nat,Y2: nat] :
% 9.25/5.27            ( Z
% 9.25/5.27           != ( abs_Integ @ ( product_Pair_nat_nat @ X2 @ Y2 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9191_bit__not__int__iff_H,axiom,
% 9.25/5.27      ! [K: int,N: nat] :
% 9.25/5.27        ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 9.25/5.27        = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9192_quotient__of__denom__pos,axiom,
% 9.25/5.27      ! [R3: rat,P4: int,Q4: int] :
% 9.25/5.27        ( ( ( quotient_of @ R3 )
% 9.25/5.27          = ( product_Pair_int_int @ P4 @ Q4 ) )
% 9.25/5.27       => ( ord_less_int @ zero_zero_int @ Q4 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9193_zero__int__def,axiom,
% 9.25/5.27      ( zero_zero_int
% 9.25/5.27      = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9194_int__def,axiom,
% 9.25/5.27      ( semiri1314217659103216013at_int
% 9.25/5.27      = ( ^ [N2: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N2 @ zero_zero_nat ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9195_bit__minus__int__iff,axiom,
% 9.25/5.27      ! [K: int,N: nat] :
% 9.25/5.27        ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 9.25/5.27        = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9196_rat__floor__code,axiom,
% 9.25/5.27      ( archim3151403230148437115or_rat
% 9.25/5.27      = ( ^ [P6: rat] : ( produc8211389475949308722nt_int @ divide_divide_int @ ( quotient_of @ P6 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9197_rat__uminus__code,axiom,
% 9.25/5.27      ! [P4: rat] :
% 9.25/5.27        ( ( quotient_of @ ( uminus_uminus_rat @ P4 ) )
% 9.25/5.27        = ( produc4245557441103728435nt_int
% 9.25/5.27          @ ^ [A3: int] : ( product_Pair_int_int @ ( uminus_uminus_int @ A3 ) )
% 9.25/5.27          @ ( quotient_of @ P4 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9198_rat__abs__code,axiom,
% 9.25/5.27      ! [P4: rat] :
% 9.25/5.27        ( ( quotient_of @ ( abs_abs_rat @ P4 ) )
% 9.25/5.27        = ( produc4245557441103728435nt_int
% 9.25/5.27          @ ^ [A3: int] : ( product_Pair_int_int @ ( abs_abs_int @ A3 ) )
% 9.25/5.27          @ ( quotient_of @ P4 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9199_rat__less__eq__code,axiom,
% 9.25/5.27      ( ord_less_eq_rat
% 9.25/5.27      = ( ^ [P6: rat,Q5: rat] :
% 9.25/5.27            ( produc4947309494688390418_int_o
% 9.25/5.27            @ ^ [A3: int,C4: int] :
% 9.25/5.27                ( produc4947309494688390418_int_o
% 9.25/5.27                @ ^ [B3: int,D4: int] : ( ord_less_eq_int @ ( times_times_int @ A3 @ D4 ) @ ( times_times_int @ C4 @ B3 ) )
% 9.25/5.27                @ ( quotient_of @ Q5 ) )
% 9.25/5.27            @ ( quotient_of @ P6 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9200_rat__less__code,axiom,
% 9.25/5.27      ( ord_less_rat
% 9.25/5.27      = ( ^ [P6: rat,Q5: rat] :
% 9.25/5.27            ( produc4947309494688390418_int_o
% 9.25/5.27            @ ^ [A3: int,C4: int] :
% 9.25/5.27                ( produc4947309494688390418_int_o
% 9.25/5.27                @ ^ [B3: int,D4: int] : ( ord_less_int @ ( times_times_int @ A3 @ D4 ) @ ( times_times_int @ C4 @ B3 ) )
% 9.25/5.27                @ ( quotient_of @ Q5 ) )
% 9.25/5.27            @ ( quotient_of @ P6 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9201_uminus__int_Oabs__eq,axiom,
% 9.25/5.27      ! [X: product_prod_nat_nat] :
% 9.25/5.27        ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 9.25/5.27        = ( abs_Integ
% 9.25/5.27          @ ( produc2626176000494625587at_nat
% 9.25/5.27            @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 )
% 9.25/5.27            @ X ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9202_int__bit__bound,axiom,
% 9.25/5.27      ! [K: int] :
% 9.25/5.27        ~ ! [N3: nat] :
% 9.25/5.27            ( ! [M6: nat] :
% 9.25/5.27                ( ( ord_less_eq_nat @ N3 @ M6 )
% 9.25/5.27               => ( ( bit_se1146084159140164899it_int @ K @ M6 )
% 9.25/5.27                  = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 9.25/5.27           => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 9.25/5.27               => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 9.25/5.27                  = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9203_one__int__def,axiom,
% 9.25/5.27      ( one_one_int
% 9.25/5.27      = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9204_less__int_Oabs__eq,axiom,
% 9.25/5.27      ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 9.25/5.27        ( ( ord_less_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 9.25/5.27        = ( produc8739625826339149834_nat_o
% 9.25/5.27          @ ^ [X3: nat,Y3: nat] :
% 9.25/5.27              ( produc6081775807080527818_nat_o
% 9.25/5.27              @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) )
% 9.25/5.27          @ Xa
% 9.25/5.27          @ X ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9205_less__eq__int_Oabs__eq,axiom,
% 9.25/5.27      ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 9.25/5.27        ( ( ord_less_eq_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 9.25/5.27        = ( produc8739625826339149834_nat_o
% 9.25/5.27          @ ^ [X3: nat,Y3: nat] :
% 9.25/5.27              ( produc6081775807080527818_nat_o
% 9.25/5.27              @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) )
% 9.25/5.27          @ Xa
% 9.25/5.27          @ X ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9206_plus__int_Oabs__eq,axiom,
% 9.25/5.27      ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 9.25/5.27        ( ( plus_plus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 9.25/5.27        = ( abs_Integ
% 9.25/5.27          @ ( produc27273713700761075at_nat
% 9.25/5.27            @ ^ [X3: nat,Y3: nat] :
% 9.25/5.27                ( produc2626176000494625587at_nat
% 9.25/5.27                @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V2 ) ) )
% 9.25/5.27            @ Xa
% 9.25/5.27            @ X ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9207_minus__int_Oabs__eq,axiom,
% 9.25/5.27      ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 9.25/5.27        ( ( minus_minus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 9.25/5.27        = ( abs_Integ
% 9.25/5.27          @ ( produc27273713700761075at_nat
% 9.25/5.27            @ ^ [X3: nat,Y3: nat] :
% 9.25/5.27                ( produc2626176000494625587at_nat
% 9.25/5.27                @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) )
% 9.25/5.27            @ Xa
% 9.25/5.27            @ X ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9208_rat__divide__code,axiom,
% 9.25/5.27      ! [P4: rat,Q4: rat] :
% 9.25/5.27        ( ( quotient_of @ ( divide_divide_rat @ P4 @ Q4 ) )
% 9.25/5.27        = ( produc4245557441103728435nt_int
% 9.25/5.27          @ ^ [A3: int,C4: int] :
% 9.25/5.27              ( produc4245557441103728435nt_int
% 9.25/5.27              @ ^ [B3: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ D4 ) @ ( times_times_int @ C4 @ B3 ) ) )
% 9.25/5.27              @ ( quotient_of @ Q4 ) )
% 9.25/5.27          @ ( quotient_of @ P4 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9209_rat__times__code,axiom,
% 9.25/5.27      ! [P4: rat,Q4: rat] :
% 9.25/5.27        ( ( quotient_of @ ( times_times_rat @ P4 @ Q4 ) )
% 9.25/5.27        = ( produc4245557441103728435nt_int
% 9.25/5.27          @ ^ [A3: int,C4: int] :
% 9.25/5.27              ( produc4245557441103728435nt_int
% 9.25/5.27              @ ^ [B3: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ B3 ) @ ( times_times_int @ C4 @ D4 ) ) )
% 9.25/5.27              @ ( quotient_of @ Q4 ) )
% 9.25/5.27          @ ( quotient_of @ P4 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9210_rat__plus__code,axiom,
% 9.25/5.27      ! [P4: rat,Q4: rat] :
% 9.25/5.27        ( ( quotient_of @ ( plus_plus_rat @ P4 @ Q4 ) )
% 9.25/5.27        = ( produc4245557441103728435nt_int
% 9.25/5.27          @ ^ [A3: int,C4: int] :
% 9.25/5.27              ( produc4245557441103728435nt_int
% 9.25/5.27              @ ^ [B3: int,D4: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A3 @ D4 ) @ ( times_times_int @ B3 @ C4 ) ) @ ( times_times_int @ C4 @ D4 ) ) )
% 9.25/5.27              @ ( quotient_of @ Q4 ) )
% 9.25/5.27          @ ( quotient_of @ P4 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9211_quotient__of__int,axiom,
% 9.25/5.27      ! [A: int] :
% 9.25/5.27        ( ( quotient_of @ ( of_int @ A ) )
% 9.25/5.27        = ( product_Pair_int_int @ A @ one_one_int ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9212_rat__inverse__code,axiom,
% 9.25/5.27      ! [P4: rat] :
% 9.25/5.27        ( ( quotient_of @ ( inverse_inverse_rat @ P4 ) )
% 9.25/5.27        = ( produc4245557441103728435nt_int
% 9.25/5.27          @ ^ [A3: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( A3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A3 ) @ B3 ) @ ( abs_abs_int @ A3 ) ) )
% 9.25/5.27          @ ( quotient_of @ P4 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9213_abs__rat__def,axiom,
% 9.25/5.27      ( abs_abs_rat
% 9.25/5.27      = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9214_sgn__rat__def,axiom,
% 9.25/5.27      ( sgn_sgn_rat
% 9.25/5.27      = ( ^ [A3: rat] : ( if_rat @ ( A3 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A3 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9215_char__of__integer__code,axiom,
% 9.25/5.27      ( char_of_integer
% 9.25/5.27      = ( ^ [K4: code_integer] :
% 9.25/5.27            ( produc4188289175737317920o_char
% 9.25/5.27            @ ^ [Q0: code_integer,B0: $o] :
% 9.25/5.27                ( produc4188289175737317920o_char
% 9.25/5.27                @ ^ [Q1: code_integer,B1: $o] :
% 9.25/5.27                    ( produc4188289175737317920o_char
% 9.25/5.27                    @ ^ [Q22: code_integer,B22: $o] :
% 9.25/5.27                        ( produc4188289175737317920o_char
% 9.25/5.27                        @ ^ [Q32: code_integer,B32: $o] :
% 9.25/5.27                            ( produc4188289175737317920o_char
% 9.25/5.27                            @ ^ [Q42: code_integer,B42: $o] :
% 9.25/5.27                                ( produc4188289175737317920o_char
% 9.25/5.27                                @ ^ [Q52: code_integer,B52: $o] :
% 9.25/5.27                                    ( produc4188289175737317920o_char
% 9.25/5.27                                    @ ^ [Q62: code_integer,B62: $o] :
% 9.25/5.27                                        ( produc4188289175737317920o_char
% 9.25/5.27                                        @ ^ [Uu: code_integer] : ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 )
% 9.25/5.27                                        @ ( code_bit_cut_integer @ Q62 ) )
% 9.25/5.27                                    @ ( code_bit_cut_integer @ Q52 ) )
% 9.25/5.27                                @ ( code_bit_cut_integer @ Q42 ) )
% 9.25/5.27                            @ ( code_bit_cut_integer @ Q32 ) )
% 9.25/5.27                        @ ( code_bit_cut_integer @ Q22 ) )
% 9.25/5.27                    @ ( code_bit_cut_integer @ Q1 ) )
% 9.25/5.27                @ ( code_bit_cut_integer @ Q0 ) )
% 9.25/5.27            @ ( code_bit_cut_integer @ K4 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9216_Frct__code__post_I5_J,axiom,
% 9.25/5.27      ! [K: num] :
% 9.25/5.27        ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 9.25/5.27        = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9217_floor__rat__def,axiom,
% 9.25/5.27      ( archim3151403230148437115or_rat
% 9.25/5.27      = ( ^ [X3: rat] :
% 9.25/5.27            ( the_int
% 9.25/5.27            @ ^ [Z3: int] :
% 9.25/5.27                ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X3 )
% 9.25/5.27                & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9218_Frct__code__post_I9_J,axiom,
% 9.25/5.27      ! [Q4: product_prod_int_int] :
% 9.25/5.27        ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ ( frct @ Q4 ) ) )
% 9.25/5.27        = ( frct @ Q4 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9219_Frct__code__post_I1_J,axiom,
% 9.25/5.27      ! [A: int] :
% 9.25/5.27        ( ( frct @ ( product_Pair_int_int @ zero_zero_int @ A ) )
% 9.25/5.27        = zero_zero_rat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9220_Frct__code__post_I2_J,axiom,
% 9.25/5.27      ! [A: int] :
% 9.25/5.27        ( ( frct @ ( product_Pair_int_int @ A @ zero_zero_int ) )
% 9.25/5.27        = zero_zero_rat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9221_Frct__code__post_I3_J,axiom,
% 9.25/5.27      ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 9.25/5.27      = one_one_rat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9222_Frct__code__post_I7_J,axiom,
% 9.25/5.27      ! [A: int,B: int] :
% 9.25/5.27        ( ( frct @ ( product_Pair_int_int @ ( uminus_uminus_int @ A ) @ B ) )
% 9.25/5.27        = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9223_Frct__code__post_I8_J,axiom,
% 9.25/5.27      ! [A: int,B: int] :
% 9.25/5.27        ( ( frct @ ( product_Pair_int_int @ A @ ( uminus_uminus_int @ B ) ) )
% 9.25/5.27        = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9224_Frct__code__post_I4_J,axiom,
% 9.25/5.27      ! [K: num] :
% 9.25/5.27        ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 9.25/5.27        = ( numeral_numeral_rat @ K ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9225_Frct__code__post_I6_J,axiom,
% 9.25/5.27      ! [K: num,L: num] :
% 9.25/5.27        ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L ) ) )
% 9.25/5.27        = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9226_less__eq__int_Orep__eq,axiom,
% 9.25/5.27      ( ord_less_eq_int
% 9.25/5.27      = ( ^ [X3: int,Xa4: int] :
% 9.25/5.27            ( produc8739625826339149834_nat_o
% 9.25/5.27            @ ^ [Y3: nat,Z3: nat] :
% 9.25/5.27                ( produc6081775807080527818_nat_o
% 9.25/5.27                @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y3 @ V2 ) @ ( plus_plus_nat @ U2 @ Z3 ) ) )
% 9.25/5.27            @ ( rep_Integ @ X3 )
% 9.25/5.27            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9227_less__int_Orep__eq,axiom,
% 9.25/5.27      ( ord_less_int
% 9.25/5.27      = ( ^ [X3: int,Xa4: int] :
% 9.25/5.27            ( produc8739625826339149834_nat_o
% 9.25/5.27            @ ^ [Y3: nat,Z3: nat] :
% 9.25/5.27                ( produc6081775807080527818_nat_o
% 9.25/5.27                @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y3 @ V2 ) @ ( plus_plus_nat @ U2 @ Z3 ) ) )
% 9.25/5.27            @ ( rep_Integ @ X3 )
% 9.25/5.27            @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9228_uminus__int__def,axiom,
% 9.25/5.27      ( uminus_uminus_int
% 9.25/5.27      = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 9.25/5.27        @ ( produc2626176000494625587at_nat
% 9.25/5.27          @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9229_pred__nat__def,axiom,
% 9.25/5.27      ( pred_nat
% 9.25/5.27      = ( collec3392354462482085612at_nat
% 9.25/5.27        @ ( produc6081775807080527818_nat_o
% 9.25/5.27          @ ^ [M2: nat,N2: nat] :
% 9.25/5.27              ( N2
% 9.25/5.27              = ( suc @ M2 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9230_less__eq,axiom,
% 9.25/5.27      ! [M: nat,N: nat] :
% 9.25/5.27        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 9.25/5.27        = ( ord_less_nat @ M @ N ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9231_pred__nat__trancl__eq__le,axiom,
% 9.25/5.27      ! [M: nat,N: nat] :
% 9.25/5.27        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 9.25/5.27        = ( ord_less_eq_nat @ M @ N ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9232_times__int__def,axiom,
% 9.25/5.27      ( times_times_int
% 9.25/5.27      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 9.25/5.27        @ ( produc27273713700761075at_nat
% 9.25/5.27          @ ^ [X3: nat,Y3: nat] :
% 9.25/5.27              ( produc2626176000494625587at_nat
% 9.25/5.27              @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V2 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9233_natLess__def,axiom,
% 9.25/5.27      ( bNF_Ca8459412986667044542atLess
% 9.25/5.27      = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9234_minus__int__def,axiom,
% 9.25/5.27      ( minus_minus_int
% 9.25/5.27      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 9.25/5.27        @ ( produc27273713700761075at_nat
% 9.25/5.27          @ ^ [X3: nat,Y3: nat] :
% 9.25/5.27              ( produc2626176000494625587at_nat
% 9.25/5.27              @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9235_plus__int__def,axiom,
% 9.25/5.27      ( plus_plus_int
% 9.25/5.27      = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 9.25/5.27        @ ( produc27273713700761075at_nat
% 9.25/5.27          @ ^ [X3: nat,Y3: nat] :
% 9.25/5.27              ( produc2626176000494625587at_nat
% 9.25/5.27              @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V2 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9236_Gcd__remove0__nat,axiom,
% 9.25/5.27      ! [M4: set_nat] :
% 9.25/5.27        ( ( finite_finite_nat @ M4 )
% 9.25/5.27       => ( ( gcd_Gcd_nat @ M4 )
% 9.25/5.27          = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M4 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9237_take__bit__numeral__minus__numeral__int,axiom,
% 9.25/5.27      ! [M: num,N: num] :
% 9.25/5.27        ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.27        = ( case_option_int_num @ zero_zero_int
% 9.25/5.27          @ ^ [Q5: num] : ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_int @ Q5 ) ) )
% 9.25/5.27          @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9238_rat__floor__lemma,axiom,
% 9.25/5.27      ! [A: int,B: int] :
% 9.25/5.27        ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 9.25/5.27        & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9239_minus__rat__cancel,axiom,
% 9.25/5.27      ! [A: int,B: int] :
% 9.25/5.27        ( ( fract @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 9.25/5.27        = ( fract @ A @ B ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9240_minus__rat,axiom,
% 9.25/5.27      ! [A: int,B: int] :
% 9.25/5.27        ( ( uminus_uminus_rat @ ( fract @ A @ B ) )
% 9.25/5.27        = ( fract @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9241_Gcd__nat__eq__one,axiom,
% 9.25/5.27      ! [N4: set_nat] :
% 9.25/5.27        ( ( member_nat @ one_one_nat @ N4 )
% 9.25/5.27       => ( ( gcd_Gcd_nat @ N4 )
% 9.25/5.27          = one_one_nat ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9242_eq__rat_I2_J,axiom,
% 9.25/5.27      ! [A: int] :
% 9.25/5.27        ( ( fract @ A @ zero_zero_int )
% 9.25/5.27        = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9243_Fract__of__nat__eq,axiom,
% 9.25/5.27      ! [K: nat] :
% 9.25/5.27        ( ( fract @ ( semiri1314217659103216013at_int @ K ) @ one_one_int )
% 9.25/5.27        = ( semiri681578069525770553at_rat @ K ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9244_quotient__of__eq,axiom,
% 9.25/5.27      ! [A: int,B: int,P4: int,Q4: int] :
% 9.25/5.27        ( ( ( quotient_of @ ( fract @ A @ B ) )
% 9.25/5.27          = ( product_Pair_int_int @ P4 @ Q4 ) )
% 9.25/5.27       => ( ( fract @ P4 @ Q4 )
% 9.25/5.27          = ( fract @ A @ B ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9245_One__rat__def,axiom,
% 9.25/5.27      ( one_one_rat
% 9.25/5.27      = ( fract @ one_one_int @ one_one_int ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9246_Fract__of__int__eq,axiom,
% 9.25/5.27      ! [K: int] :
% 9.25/5.27        ( ( fract @ K @ one_one_int )
% 9.25/5.27        = ( ring_1_of_int_rat @ K ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9247_normalize__eq,axiom,
% 9.25/5.27      ! [A: int,B: int,P4: int,Q4: int] :
% 9.25/5.27        ( ( ( normalize @ ( product_Pair_int_int @ A @ B ) )
% 9.25/5.27          = ( product_Pair_int_int @ P4 @ Q4 ) )
% 9.25/5.27       => ( ( fract @ P4 @ Q4 )
% 9.25/5.27          = ( fract @ A @ B ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9248_Zero__rat__def,axiom,
% 9.25/5.27      ( zero_zero_rat
% 9.25/5.27      = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9249_rat__number__expand_I3_J,axiom,
% 9.25/5.27      ( numeral_numeral_rat
% 9.25/5.27      = ( ^ [K4: num] : ( fract @ ( numeral_numeral_int @ K4 ) @ one_one_int ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9250_rat__number__collapse_I3_J,axiom,
% 9.25/5.27      ! [W: num] :
% 9.25/5.27        ( ( fract @ ( numeral_numeral_int @ W ) @ one_one_int )
% 9.25/5.27        = ( numeral_numeral_rat @ W ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9251_quotient__of__Fract,axiom,
% 9.25/5.27      ! [A: int,B: int] :
% 9.25/5.27        ( ( quotient_of @ ( fract @ A @ B ) )
% 9.25/5.27        = ( normalize @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9252_one__less__Fract__iff,axiom,
% 9.25/5.27      ! [B: int,A: int] :
% 9.25/5.27        ( ( ord_less_int @ zero_zero_int @ B )
% 9.25/5.27       => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 9.25/5.27          = ( ord_less_int @ B @ A ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9253_Fract__less__one__iff,axiom,
% 9.25/5.27      ! [B: int,A: int] :
% 9.25/5.27        ( ( ord_less_int @ zero_zero_int @ B )
% 9.25/5.27       => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 9.25/5.27          = ( ord_less_int @ A @ B ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9254_rat__number__collapse_I5_J,axiom,
% 9.25/5.27      ( ( fract @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 9.25/5.27      = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9255_Fract__add__one,axiom,
% 9.25/5.27      ! [N: int,M: int] :
% 9.25/5.27        ( ( N != zero_zero_int )
% 9.25/5.27       => ( ( fract @ ( plus_plus_int @ M @ N ) @ N )
% 9.25/5.27          = ( plus_plus_rat @ ( fract @ M @ N ) @ one_one_rat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9256_one__le__Fract__iff,axiom,
% 9.25/5.27      ! [B: int,A: int] :
% 9.25/5.27        ( ( ord_less_int @ zero_zero_int @ B )
% 9.25/5.27       => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 9.25/5.27          = ( ord_less_eq_int @ B @ A ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9257_Fract__le__one__iff,axiom,
% 9.25/5.27      ! [B: int,A: int] :
% 9.25/5.27        ( ( ord_less_int @ zero_zero_int @ B )
% 9.25/5.27       => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 9.25/5.27          = ( ord_less_eq_int @ A @ B ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9258_rat__number__collapse_I4_J,axiom,
% 9.25/5.27      ! [W: num] :
% 9.25/5.27        ( ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ one_one_int )
% 9.25/5.27        = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9259_rat__number__expand_I5_J,axiom,
% 9.25/5.27      ! [K: num] :
% 9.25/5.27        ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) )
% 9.25/5.27        = ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9260_and__minus__numerals_I3_J,axiom,
% 9.25/5.27      ! [M: num,N: num] :
% 9.25/5.27        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 9.25/5.27        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9261_and__minus__numerals_I7_J,axiom,
% 9.25/5.27      ! [N: num,M: num] :
% 9.25/5.27        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 9.25/5.27        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9262_and__minus__numerals_I8_J,axiom,
% 9.25/5.27      ! [N: num,M: num] :
% 9.25/5.27        ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 9.25/5.27        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9263_and__minus__numerals_I4_J,axiom,
% 9.25/5.27      ! [M: num,N: num] :
% 9.25/5.27        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 9.25/5.27        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9264_Gcd__int__eq,axiom,
% 9.25/5.27      ! [N4: set_nat] :
% 9.25/5.27        ( ( gcd_Gcd_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N4 ) )
% 9.25/5.27        = ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ N4 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9265_Gcd__abs__eq,axiom,
% 9.25/5.27      ! [K5: set_int] :
% 9.25/5.27        ( ( gcd_Gcd_int @ ( image_int_int @ abs_abs_int @ K5 ) )
% 9.25/5.27        = ( gcd_Gcd_int @ K5 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9266_Gcd__nat__abs__eq,axiom,
% 9.25/5.27      ! [K5: set_int] :
% 9.25/5.27        ( ( gcd_Gcd_nat
% 9.25/5.27          @ ( image_int_nat
% 9.25/5.27            @ ^ [K4: int] : ( nat2 @ ( abs_abs_int @ K4 ) )
% 9.25/5.27            @ K5 ) )
% 9.25/5.27        = ( nat2 @ ( gcd_Gcd_int @ K5 ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9267_Gcd__int__def,axiom,
% 9.25/5.27      ( gcd_Gcd_int
% 9.25/5.27      = ( ^ [K6: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K6 ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9268_int__numeral__and__not__num,axiom,
% 9.25/5.27      ! [M: num,N: num] :
% 9.25/5.27        ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.27        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9269_int__numeral__not__and__num,axiom,
% 9.25/5.27      ! [M: num,N: num] :
% 9.25/5.27        ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 9.25/5.27        = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N @ M ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9270_Gcd__eq__Max,axiom,
% 9.25/5.27      ! [M4: set_nat] :
% 9.25/5.27        ( ( finite_finite_nat @ M4 )
% 9.25/5.27       => ( ( M4 != bot_bot_set_nat )
% 9.25/5.27         => ( ~ ( member_nat @ zero_zero_nat @ M4 )
% 9.25/5.27           => ( ( gcd_Gcd_nat @ M4 )
% 9.25/5.27              = ( lattic8265883725875713057ax_nat
% 9.25/5.27                @ ( comple7806235888213564991et_nat
% 9.25/5.27                  @ ( image_nat_set_nat
% 9.25/5.27                    @ ^ [M2: nat] :
% 9.25/5.27                        ( collect_nat
% 9.25/5.27                        @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ M2 ) )
% 9.25/5.27                    @ M4 ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9271_take__bit__num__simps_I7_J,axiom,
% 9.25/5.27      ! [R3: num,M: num] :
% 9.25/5.27        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R3 ) @ ( bit1 @ M ) )
% 9.25/5.27        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R3 ) @ M ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9272_set__decode__def,axiom,
% 9.25/5.27      ( nat_set_decode
% 9.25/5.27      = ( ^ [X3: nat] :
% 9.25/5.27            ( collect_nat
% 9.25/5.27            @ ^ [N2: nat] :
% 9.25/5.27                ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9273_set__decode__zero,axiom,
% 9.25/5.27      ( ( nat_set_decode @ zero_zero_nat )
% 9.25/5.27      = bot_bot_set_nat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9274_Max__divisors__self__nat,axiom,
% 9.25/5.27      ! [N: nat] :
% 9.25/5.27        ( ( N != zero_zero_nat )
% 9.25/5.27       => ( ( lattic8265883725875713057ax_nat
% 9.25/5.27            @ ( collect_nat
% 9.25/5.27              @ ^ [D4: nat] : ( dvd_dvd_nat @ D4 @ N ) ) )
% 9.25/5.27          = N ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9275_take__bit__num__simps_I4_J,axiom,
% 9.25/5.27      ! [N: nat,M: num] :
% 9.25/5.27        ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 9.25/5.27        = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9276_prod__decode__aux_Ocases,axiom,
% 9.25/5.27      ! [X: product_prod_nat_nat] :
% 9.25/5.27        ~ ! [K2: nat,M3: nat] :
% 9.25/5.27            ( X
% 9.25/5.27           != ( product_Pair_nat_nat @ K2 @ M3 ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9277_Sup__nat__def,axiom,
% 9.25/5.27      ( complete_Sup_Sup_nat
% 9.25/5.27      = ( ^ [X4: set_nat] : ( if_nat @ ( X4 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X4 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9278_and__not__num_Osimps_I8_J,axiom,
% 9.25/5.27      ! [M: num,N: num] :
% 9.25/5.27        ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 9.25/5.27        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 9.25/5.27          @ ^ [N5: num] : ( some_num @ ( bit1 @ N5 ) )
% 9.25/5.27          @ ( bit_and_not_num @ M @ N ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9279_divide__nat__def,axiom,
% 9.25/5.27      ( divide_divide_nat
% 9.25/5.27      = ( ^ [M2: nat,N2: nat] :
% 9.25/5.27            ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 9.25/5.27            @ ( lattic8265883725875713057ax_nat
% 9.25/5.27              @ ( collect_nat
% 9.25/5.27                @ ^ [K4: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K4 @ N2 ) @ M2 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9280_Max__divisors__self__int,axiom,
% 9.25/5.27      ! [N: int] :
% 9.25/5.27        ( ( N != zero_zero_int )
% 9.25/5.27       => ( ( lattic8263393255366662781ax_int
% 9.25/5.27            @ ( collect_int
% 9.25/5.27              @ ^ [D4: int] : ( dvd_dvd_int @ D4 @ N ) ) )
% 9.25/5.27          = ( abs_abs_int @ N ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9281_take__bit__num__simps_I6_J,axiom,
% 9.25/5.27      ! [R3: num,M: num] :
% 9.25/5.27        ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R3 ) @ ( bit0 @ M ) )
% 9.25/5.27        = ( case_o6005452278849405969um_num @ none_num
% 9.25/5.27          @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 9.25/5.27          @ ( bit_take_bit_num @ ( pred_numeral @ R3 ) @ M ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9282_surj__int__encode,axiom,
% 9.25/5.27      ( ( image_int_nat @ nat_int_encode @ top_top_set_int )
% 9.25/5.27      = top_top_set_nat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9283_prod__decode__aux_Oelims,axiom,
% 9.25/5.27      ! [X: nat,Xa: nat,Y: product_prod_nat_nat] :
% 9.25/5.27        ( ( ( nat_prod_decode_aux @ X @ Xa )
% 9.25/5.27          = Y )
% 9.25/5.27       => ( ( ( ord_less_eq_nat @ Xa @ X )
% 9.25/5.27           => ( Y
% 9.25/5.27              = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X @ Xa ) ) ) )
% 9.25/5.27          & ( ~ ( ord_less_eq_nat @ Xa @ X )
% 9.25/5.27           => ( Y
% 9.25/5.27              = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa @ ( suc @ X ) ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9284_take__bit__num__simps_I3_J,axiom,
% 9.25/5.27      ! [N: nat,M: num] :
% 9.25/5.27        ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 9.25/5.27        = ( case_o6005452278849405969um_num @ none_num
% 9.25/5.27          @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 9.25/5.27          @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9285_prod__decode__aux_Osimps,axiom,
% 9.25/5.27      ( nat_prod_decode_aux
% 9.25/5.27      = ( ^ [K4: nat,M2: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M2 @ K4 ) @ ( product_Pair_nat_nat @ M2 @ ( minus_minus_nat @ K4 @ M2 ) ) @ ( nat_prod_decode_aux @ ( suc @ K4 ) @ ( minus_minus_nat @ M2 @ ( suc @ K4 ) ) ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9286_take__bit__num__code,axiom,
% 9.25/5.27      ( bit_take_bit_num
% 9.25/5.27      = ( ^ [N2: nat,M2: num] :
% 9.25/5.27            ( produc478579273971653890on_num
% 9.25/5.27            @ ^ [A3: nat,X3: num] :
% 9.25/5.27                ( case_nat_option_num @ none_num
% 9.25/5.27                @ ^ [O: nat] :
% 9.25/5.27                    ( case_num_option_num @ ( some_num @ one )
% 9.25/5.27                    @ ^ [P6: num] :
% 9.25/5.27                        ( case_o6005452278849405969um_num @ none_num
% 9.25/5.27                        @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 9.25/5.27                        @ ( bit_take_bit_num @ O @ P6 ) )
% 9.25/5.27                    @ ^ [P6: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P6 ) ) )
% 9.25/5.27                    @ X3 )
% 9.25/5.27                @ A3 )
% 9.25/5.27            @ ( product_Pair_nat_num @ N2 @ M2 ) ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9287_INT__greaterThan__UNIV,axiom,
% 9.25/5.27      ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 9.25/5.27      = bot_bot_set_nat ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9288_greaterThan__0,axiom,
% 9.25/5.27      ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 9.25/5.27      = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9289_greaterThan__Suc,axiom,
% 9.25/5.27      ! [K: nat] :
% 9.25/5.27        ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 9.25/5.27        = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 9.25/5.27  
% 9.25/5.27  thf(fact_9290_and__not__num_Oelims,axiom,
% 9.25/5.27      ! [X: num,Xa: num,Y: option_num] :
% 9.25/5.27        ( ( ( bit_and_not_num @ X @ Xa )
% 9.25/5.27          = Y )
% 9.25/5.27       => ( ( ( X = one )
% 9.25/5.27           => ( ( Xa = one )
% 9.25/5.27             => ( Y != none_num ) ) )
% 9.25/5.27         => ( ( ( X = one )
% 9.25/5.27             => ( ? [N3: num] :
% 9.25/5.27                    ( Xa
% 9.25/5.27                    = ( bit0 @ N3 ) )
% 9.25/5.27               => ( Y
% 9.25/5.27                 != ( some_num @ one ) ) ) )
% 9.25/5.27           => ( ( ( X = one )
% 9.25/5.27               => ( ? [N3: num] :
% 9.25/5.27                      ( Xa
% 9.25/5.27                      = ( bit1 @ N3 ) )
% 9.25/5.27                 => ( Y != none_num ) ) )
% 9.25/5.27             => ( ! [M3: num] :
% 9.25/5.27                    ( ( X
% 9.25/5.27                      = ( bit0 @ M3 ) )
% 9.25/5.27                   => ( ( Xa = one )
% 9.25/5.27                     => ( Y
% 9.25/5.27                       != ( some_num @ ( bit0 @ M3 ) ) ) ) )
% 9.25/5.27               => ( ! [M3: num] :
% 9.25/5.27                      ( ( X
% 9.25/5.27                        = ( bit0 @ M3 ) )
% 9.25/5.27                     => ! [N3: num] :
% 9.25/5.27                          ( ( Xa
% 9.25/5.27                            = ( bit0 @ N3 ) )
% 9.25/5.27                         => ( Y
% 9.25/5.27                           != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N3 ) ) ) ) )
% 9.25/5.27                 => ( ! [M3: num] :
% 9.25/5.27                        ( ( X
% 9.25/5.27                          = ( bit0 @ M3 ) )
% 9.25/5.27                       => ! [N3: num] :
% 9.25/5.27                            ( ( Xa
% 9.25/5.27                              = ( bit1 @ N3 ) )
% 9.25/5.27                           => ( Y
% 9.25/5.27                             != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N3 ) ) ) ) )
% 9.25/5.27                   => ( ! [M3: num] :
% 9.25/5.27                          ( ( X
% 9.25/5.27                            = ( bit1 @ M3 ) )
% 9.25/5.27                         => ( ( Xa = one )
% 9.25/5.27                           => ( Y
% 9.25/5.27                             != ( some_num @ ( bit0 @ M3 ) ) ) ) )
% 9.25/5.27                     => ( ! [M3: num] :
% 9.25/5.27                            ( ( X
% 9.25/5.27                              = ( bit1 @ M3 ) )
% 9.25/5.28                           => ! [N3: num] :
% 9.25/5.28                                ( ( Xa
% 9.25/5.28                                  = ( bit0 @ N3 ) )
% 9.25/5.28                               => ( Y
% 9.25/5.28                                 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 9.25/5.28                                    @ ^ [N5: num] : ( some_num @ ( bit1 @ N5 ) )
% 9.25/5.28                                    @ ( bit_and_not_num @ M3 @ N3 ) ) ) ) )
% 9.25/5.28                       => ~ ! [M3: num] :
% 9.25/5.28                              ( ( X
% 9.25/5.28                                = ( bit1 @ M3 ) )
% 9.25/5.28                             => ! [N3: num] :
% 9.25/5.28                                  ( ( Xa
% 9.25/5.28                                    = ( bit1 @ N3 ) )
% 9.25/5.28                                 => ( Y
% 9.25/5.28                                   != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9291_surj__int__decode,axiom,
% 9.25/5.28      ( ( image_nat_int @ nat_int_decode @ top_top_set_nat )
% 9.25/5.28      = top_top_set_int ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9292_mono__ge2__power__minus__self,axiom,
% 9.25/5.28      ! [K: nat] :
% 9.25/5.28        ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 9.25/5.28       => ( order_mono_nat_nat
% 9.25/5.28          @ ^ [M2: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M2 ) @ M2 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9293_and__num_Oelims,axiom,
% 9.25/5.28      ! [X: num,Xa: num,Y: option_num] :
% 9.25/5.28        ( ( ( bit_un7362597486090784418nd_num @ X @ Xa )
% 9.25/5.28          = Y )
% 9.25/5.28       => ( ( ( X = one )
% 9.25/5.28           => ( ( Xa = one )
% 9.25/5.28             => ( Y
% 9.25/5.28               != ( some_num @ one ) ) ) )
% 9.25/5.28         => ( ( ( X = one )
% 9.25/5.28             => ( ? [N3: num] :
% 9.25/5.28                    ( Xa
% 9.25/5.28                    = ( bit0 @ N3 ) )
% 9.25/5.28               => ( Y != none_num ) ) )
% 9.25/5.28           => ( ( ( X = one )
% 9.25/5.28               => ( ? [N3: num] :
% 9.25/5.28                      ( Xa
% 9.25/5.28                      = ( bit1 @ N3 ) )
% 9.25/5.28                 => ( Y
% 9.25/5.28                   != ( some_num @ one ) ) ) )
% 9.25/5.28             => ( ( ? [M3: num] :
% 9.25/5.28                      ( X
% 9.25/5.28                      = ( bit0 @ M3 ) )
% 9.25/5.28                 => ( ( Xa = one )
% 9.25/5.28                   => ( Y != none_num ) ) )
% 9.25/5.28               => ( ! [M3: num] :
% 9.25/5.28                      ( ( X
% 9.25/5.28                        = ( bit0 @ M3 ) )
% 9.25/5.28                     => ! [N3: num] :
% 9.25/5.28                          ( ( Xa
% 9.25/5.28                            = ( bit0 @ N3 ) )
% 9.25/5.28                         => ( Y
% 9.25/5.28                           != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N3 ) ) ) ) )
% 9.25/5.28                 => ( ! [M3: num] :
% 9.25/5.28                        ( ( X
% 9.25/5.28                          = ( bit0 @ M3 ) )
% 9.25/5.28                       => ! [N3: num] :
% 9.25/5.28                            ( ( Xa
% 9.25/5.28                              = ( bit1 @ N3 ) )
% 9.25/5.28                           => ( Y
% 9.25/5.28                             != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N3 ) ) ) ) )
% 9.25/5.28                   => ( ( ? [M3: num] :
% 9.25/5.28                            ( X
% 9.25/5.28                            = ( bit1 @ M3 ) )
% 9.25/5.28                       => ( ( Xa = one )
% 9.25/5.28                         => ( Y
% 9.25/5.28                           != ( some_num @ one ) ) ) )
% 9.25/5.28                     => ( ! [M3: num] :
% 9.25/5.28                            ( ( X
% 9.25/5.28                              = ( bit1 @ M3 ) )
% 9.25/5.28                           => ! [N3: num] :
% 9.25/5.28                                ( ( Xa
% 9.25/5.28                                  = ( bit0 @ N3 ) )
% 9.25/5.28                               => ( Y
% 9.25/5.28                                 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N3 ) ) ) ) )
% 9.25/5.28                       => ~ ! [M3: num] :
% 9.25/5.28                              ( ( X
% 9.25/5.28                                = ( bit1 @ M3 ) )
% 9.25/5.28                             => ! [N3: num] :
% 9.25/5.28                                  ( ( Xa
% 9.25/5.28                                    = ( bit1 @ N3 ) )
% 9.25/5.28                                 => ( Y
% 9.25/5.28                                   != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 9.25/5.28                                      @ ^ [N5: num] : ( some_num @ ( bit1 @ N5 ) )
% 9.25/5.28                                      @ ( bit_un7362597486090784418nd_num @ M3 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9294_nat__def,axiom,
% 9.25/5.28      ( nat2
% 9.25/5.28      = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9295_less__int__def,axiom,
% 9.25/5.28      ( ord_less_int
% 9.25/5.28      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 9.25/5.28        @ ( produc8739625826339149834_nat_o
% 9.25/5.28          @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28              ( produc6081775807080527818_nat_o
% 9.25/5.28              @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9296_less__eq__int__def,axiom,
% 9.25/5.28      ( ord_less_eq_int
% 9.25/5.28      = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 9.25/5.28        @ ( produc8739625826339149834_nat_o
% 9.25/5.28          @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28              ( produc6081775807080527818_nat_o
% 9.25/5.28              @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9297_and__num_Osimps_I9_J,axiom,
% 9.25/5.28      ! [M: num,N: num] :
% 9.25/5.28        ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 9.25/5.28        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 9.25/5.28          @ ^ [N5: num] : ( some_num @ ( bit1 @ N5 ) )
% 9.25/5.28          @ ( bit_un7362597486090784418nd_num @ M @ N ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9298_uminus__integer__def,axiom,
% 9.25/5.28      ( uminus1351360451143612070nteger
% 9.25/5.28      = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int @ uminus_uminus_int ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9299_inf__nat__def,axiom,
% 9.25/5.28      inf_inf_nat = ord_min_nat ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9300_min__Suc2,axiom,
% 9.25/5.28      ! [M: nat,N: nat] :
% 9.25/5.28        ( ( ord_min_nat @ M @ ( suc @ N ) )
% 9.25/5.28        = ( case_nat_nat @ zero_zero_nat
% 9.25/5.28          @ ^ [M5: nat] : ( suc @ ( ord_min_nat @ M5 @ N ) )
% 9.25/5.28          @ M ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9301_min__Suc1,axiom,
% 9.25/5.28      ! [N: nat,M: nat] :
% 9.25/5.28        ( ( ord_min_nat @ ( suc @ N ) @ M )
% 9.25/5.28        = ( case_nat_nat @ zero_zero_nat
% 9.25/5.28          @ ^ [M5: nat] : ( suc @ ( ord_min_nat @ N @ M5 ) )
% 9.25/5.28          @ M ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9302_Code__Numeral_Odup__def,axiom,
% 9.25/5.28      ( code_dup
% 9.25/5.28      = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int
% 9.25/5.28        @ ^ [K4: int] : ( plus_plus_int @ K4 @ K4 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9303_Code__Numeral_Osub__code_I9_J,axiom,
% 9.25/5.28      ! [M: num,N: num] :
% 9.25/5.28        ( ( code_sub @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 9.25/5.28        = ( minus_8373710615458151222nteger @ ( code_dup @ ( code_sub @ M @ N ) ) @ one_one_Code_integer ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9304_Code__Numeral_Osub__code_I8_J,axiom,
% 9.25/5.28      ! [M: num,N: num] :
% 9.25/5.28        ( ( code_sub @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 9.25/5.28        = ( plus_p5714425477246183910nteger @ ( code_dup @ ( code_sub @ M @ N ) ) @ one_one_Code_integer ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9305_Code__Numeral_Osub__def,axiom,
% 9.25/5.28      ( code_sub
% 9.25/5.28      = ( map_fu6891787308814931657nteger @ id_num @ ( map_fu8638147718074629079nteger @ id_num @ code_integer_of_int )
% 9.25/5.28        @ ^ [M2: num,N2: num] : ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9306_and__not__num_Opelims,axiom,
% 9.25/5.28      ! [X: num,Xa: num,Y: option_num] :
% 9.25/5.28        ( ( ( bit_and_not_num @ X @ Xa )
% 9.25/5.28          = Y )
% 9.25/5.28       => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 9.25/5.28         => ( ( ( X = one )
% 9.25/5.28             => ( ( Xa = one )
% 9.25/5.28               => ( ( Y = none_num )
% 9.25/5.28                 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 9.25/5.28           => ( ( ( X = one )
% 9.25/5.28               => ! [N3: num] :
% 9.25/5.28                    ( ( Xa
% 9.25/5.28                      = ( bit0 @ N3 ) )
% 9.25/5.28                   => ( ( Y
% 9.25/5.28                        = ( some_num @ one ) )
% 9.25/5.28                     => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 9.25/5.28             => ( ( ( X = one )
% 9.25/5.28                 => ! [N3: num] :
% 9.25/5.28                      ( ( Xa
% 9.25/5.28                        = ( bit1 @ N3 ) )
% 9.25/5.28                     => ( ( Y = none_num )
% 9.25/5.28                       => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 9.25/5.28               => ( ! [M3: num] :
% 9.25/5.28                      ( ( X
% 9.25/5.28                        = ( bit0 @ M3 ) )
% 9.25/5.28                     => ( ( Xa = one )
% 9.25/5.28                       => ( ( Y
% 9.25/5.28                            = ( some_num @ ( bit0 @ M3 ) ) )
% 9.25/5.28                         => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ one ) ) ) ) )
% 9.25/5.28                 => ( ! [M3: num] :
% 9.25/5.28                        ( ( X
% 9.25/5.28                          = ( bit0 @ M3 ) )
% 9.25/5.28                       => ! [N3: num] :
% 9.25/5.28                            ( ( Xa
% 9.25/5.28                              = ( bit0 @ N3 ) )
% 9.25/5.28                           => ( ( Y
% 9.25/5.28                                = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N3 ) ) )
% 9.25/5.28                             => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 9.25/5.28                   => ( ! [M3: num] :
% 9.25/5.28                          ( ( X
% 9.25/5.28                            = ( bit0 @ M3 ) )
% 9.25/5.28                         => ! [N3: num] :
% 9.25/5.28                              ( ( Xa
% 9.25/5.28                                = ( bit1 @ N3 ) )
% 9.25/5.28                             => ( ( Y
% 9.25/5.28                                  = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N3 ) ) )
% 9.25/5.28                               => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 9.25/5.28                     => ( ! [M3: num] :
% 9.25/5.28                            ( ( X
% 9.25/5.28                              = ( bit1 @ M3 ) )
% 9.25/5.28                           => ( ( Xa = one )
% 9.25/5.28                             => ( ( Y
% 9.25/5.28                                  = ( some_num @ ( bit0 @ M3 ) ) )
% 9.25/5.28                               => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ one ) ) ) ) )
% 9.25/5.28                       => ( ! [M3: num] :
% 9.25/5.28                              ( ( X
% 9.25/5.28                                = ( bit1 @ M3 ) )
% 9.25/5.28                             => ! [N3: num] :
% 9.25/5.28                                  ( ( Xa
% 9.25/5.28                                    = ( bit0 @ N3 ) )
% 9.25/5.28                                 => ( ( Y
% 9.25/5.28                                      = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 9.25/5.28                                        @ ^ [N5: num] : ( some_num @ ( bit1 @ N5 ) )
% 9.25/5.28                                        @ ( bit_and_not_num @ M3 @ N3 ) ) )
% 9.25/5.28                                   => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 9.25/5.28                         => ~ ! [M3: num] :
% 9.25/5.28                                ( ( X
% 9.25/5.28                                  = ( bit1 @ M3 ) )
% 9.25/5.28                               => ! [N3: num] :
% 9.25/5.28                                    ( ( Xa
% 9.25/5.28                                      = ( bit1 @ N3 ) )
% 9.25/5.28                                   => ( ( Y
% 9.25/5.28                                        = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M3 @ N3 ) ) )
% 9.25/5.28                                     => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9307_and__num_Opelims,axiom,
% 9.25/5.28      ! [X: num,Xa: num,Y: option_num] :
% 9.25/5.28        ( ( ( bit_un7362597486090784418nd_num @ X @ Xa )
% 9.25/5.28          = Y )
% 9.25/5.28       => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 9.25/5.28         => ( ( ( X = one )
% 9.25/5.28             => ( ( Xa = one )
% 9.25/5.28               => ( ( Y
% 9.25/5.28                    = ( some_num @ one ) )
% 9.25/5.28                 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 9.25/5.28           => ( ( ( X = one )
% 9.25/5.28               => ! [N3: num] :
% 9.25/5.28                    ( ( Xa
% 9.25/5.28                      = ( bit0 @ N3 ) )
% 9.25/5.28                   => ( ( Y = none_num )
% 9.25/5.28                     => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 9.25/5.28             => ( ( ( X = one )
% 9.25/5.28                 => ! [N3: num] :
% 9.25/5.28                      ( ( Xa
% 9.25/5.28                        = ( bit1 @ N3 ) )
% 9.25/5.28                     => ( ( Y
% 9.25/5.28                          = ( some_num @ one ) )
% 9.25/5.28                       => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 9.25/5.28               => ( ! [M3: num] :
% 9.25/5.28                      ( ( X
% 9.25/5.28                        = ( bit0 @ M3 ) )
% 9.25/5.28                     => ( ( Xa = one )
% 9.25/5.28                       => ( ( Y = none_num )
% 9.25/5.28                         => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ one ) ) ) ) )
% 9.25/5.28                 => ( ! [M3: num] :
% 9.25/5.28                        ( ( X
% 9.25/5.28                          = ( bit0 @ M3 ) )
% 9.25/5.28                       => ! [N3: num] :
% 9.25/5.28                            ( ( Xa
% 9.25/5.28                              = ( bit0 @ N3 ) )
% 9.25/5.28                           => ( ( Y
% 9.25/5.28                                = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N3 ) ) )
% 9.25/5.28                             => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 9.25/5.28                   => ( ! [M3: num] :
% 9.25/5.28                          ( ( X
% 9.25/5.28                            = ( bit0 @ M3 ) )
% 9.25/5.28                         => ! [N3: num] :
% 9.25/5.28                              ( ( Xa
% 9.25/5.28                                = ( bit1 @ N3 ) )
% 9.25/5.28                             => ( ( Y
% 9.25/5.28                                  = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N3 ) ) )
% 9.25/5.28                               => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 9.25/5.28                     => ( ! [M3: num] :
% 9.25/5.28                            ( ( X
% 9.25/5.28                              = ( bit1 @ M3 ) )
% 9.25/5.28                           => ( ( Xa = one )
% 9.25/5.28                             => ( ( Y
% 9.25/5.28                                  = ( some_num @ one ) )
% 9.25/5.28                               => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ one ) ) ) ) )
% 9.25/5.28                       => ( ! [M3: num] :
% 9.25/5.28                              ( ( X
% 9.25/5.28                                = ( bit1 @ M3 ) )
% 9.25/5.28                             => ! [N3: num] :
% 9.25/5.28                                  ( ( Xa
% 9.25/5.28                                    = ( bit0 @ N3 ) )
% 9.25/5.28                                 => ( ( Y
% 9.25/5.28                                      = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M3 @ N3 ) ) )
% 9.25/5.28                                   => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 9.25/5.28                         => ~ ! [M3: num] :
% 9.25/5.28                                ( ( X
% 9.25/5.28                                  = ( bit1 @ M3 ) )
% 9.25/5.28                               => ! [N3: num] :
% 9.25/5.28                                    ( ( Xa
% 9.25/5.28                                      = ( bit1 @ N3 ) )
% 9.25/5.28                                   => ( ( Y
% 9.25/5.28                                        = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 9.25/5.28                                          @ ^ [N5: num] : ( some_num @ ( bit1 @ N5 ) )
% 9.25/5.28                                          @ ( bit_un7362597486090784418nd_num @ M3 @ N3 ) ) )
% 9.25/5.28                                     => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9308_or__not__num__neg_Opelims,axiom,
% 9.25/5.28      ! [X: num,Xa: num,Y: num] :
% 9.25/5.28        ( ( ( bit_or_not_num_neg @ X @ Xa )
% 9.25/5.28          = Y )
% 9.25/5.28       => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 9.25/5.28         => ( ( ( X = one )
% 9.25/5.28             => ( ( Xa = one )
% 9.25/5.28               => ( ( Y = one )
% 9.25/5.28                 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 9.25/5.28           => ( ( ( X = one )
% 9.25/5.28               => ! [M3: num] :
% 9.25/5.28                    ( ( Xa
% 9.25/5.28                      = ( bit0 @ M3 ) )
% 9.25/5.28                   => ( ( Y
% 9.25/5.28                        = ( bit1 @ M3 ) )
% 9.25/5.28                     => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M3 ) ) ) ) ) )
% 9.25/5.28             => ( ( ( X = one )
% 9.25/5.28                 => ! [M3: num] :
% 9.25/5.28                      ( ( Xa
% 9.25/5.28                        = ( bit1 @ M3 ) )
% 9.25/5.28                     => ( ( Y
% 9.25/5.28                          = ( bit1 @ M3 ) )
% 9.25/5.28                       => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M3 ) ) ) ) ) )
% 9.25/5.28               => ( ! [N3: num] :
% 9.25/5.28                      ( ( X
% 9.25/5.28                        = ( bit0 @ N3 ) )
% 9.25/5.28                     => ( ( Xa = one )
% 9.25/5.28                       => ( ( Y
% 9.25/5.28                            = ( bit0 @ one ) )
% 9.25/5.28                         => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ one ) ) ) ) )
% 9.25/5.28                 => ( ! [N3: num] :
% 9.25/5.28                        ( ( X
% 9.25/5.28                          = ( bit0 @ N3 ) )
% 9.25/5.28                       => ! [M3: num] :
% 9.25/5.28                            ( ( Xa
% 9.25/5.28                              = ( bit0 @ M3 ) )
% 9.25/5.28                           => ( ( Y
% 9.25/5.28                                = ( bitM @ ( bit_or_not_num_neg @ N3 @ M3 ) ) )
% 9.25/5.28                             => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit0 @ M3 ) ) ) ) ) )
% 9.25/5.28                   => ( ! [N3: num] :
% 9.25/5.28                          ( ( X
% 9.25/5.28                            = ( bit0 @ N3 ) )
% 9.25/5.28                         => ! [M3: num] :
% 9.25/5.28                              ( ( Xa
% 9.25/5.28                                = ( bit1 @ M3 ) )
% 9.25/5.28                             => ( ( Y
% 9.25/5.28                                  = ( bit0 @ ( bit_or_not_num_neg @ N3 @ M3 ) ) )
% 9.25/5.28                               => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit1 @ M3 ) ) ) ) ) )
% 9.25/5.28                     => ( ! [N3: num] :
% 9.25/5.28                            ( ( X
% 9.25/5.28                              = ( bit1 @ N3 ) )
% 9.25/5.28                           => ( ( Xa = one )
% 9.25/5.28                             => ( ( Y = one )
% 9.25/5.28                               => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ one ) ) ) ) )
% 9.25/5.28                       => ( ! [N3: num] :
% 9.25/5.28                              ( ( X
% 9.25/5.28                                = ( bit1 @ N3 ) )
% 9.25/5.28                             => ! [M3: num] :
% 9.25/5.28                                  ( ( Xa
% 9.25/5.28                                    = ( bit0 @ M3 ) )
% 9.25/5.28                                 => ( ( Y
% 9.25/5.28                                      = ( bitM @ ( bit_or_not_num_neg @ N3 @ M3 ) ) )
% 9.25/5.28                                   => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit0 @ M3 ) ) ) ) ) )
% 9.25/5.28                         => ~ ! [N3: num] :
% 9.25/5.28                                ( ( X
% 9.25/5.28                                  = ( bit1 @ N3 ) )
% 9.25/5.28                               => ! [M3: num] :
% 9.25/5.28                                    ( ( Xa
% 9.25/5.28                                      = ( bit1 @ M3 ) )
% 9.25/5.28                                   => ( ( Y
% 9.25/5.28                                        = ( bitM @ ( bit_or_not_num_neg @ N3 @ M3 ) ) )
% 9.25/5.28                                     => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit1 @ M3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9309_xor__num_Opelims,axiom,
% 9.25/5.28      ! [X: num,Xa: num,Y: option_num] :
% 9.25/5.28        ( ( ( bit_un2480387367778600638or_num @ X @ Xa )
% 9.25/5.28          = Y )
% 9.25/5.28       => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 9.25/5.28         => ( ( ( X = one )
% 9.25/5.28             => ( ( Xa = one )
% 9.25/5.28               => ( ( Y = none_num )
% 9.25/5.28                 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 9.25/5.28           => ( ( ( X = one )
% 9.25/5.28               => ! [N3: num] :
% 9.25/5.28                    ( ( Xa
% 9.25/5.28                      = ( bit0 @ N3 ) )
% 9.25/5.28                   => ( ( Y
% 9.25/5.28                        = ( some_num @ ( bit1 @ N3 ) ) )
% 9.25/5.28                     => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 9.25/5.28             => ( ( ( X = one )
% 9.25/5.28                 => ! [N3: num] :
% 9.25/5.28                      ( ( Xa
% 9.25/5.28                        = ( bit1 @ N3 ) )
% 9.25/5.28                     => ( ( Y
% 9.25/5.28                          = ( some_num @ ( bit0 @ N3 ) ) )
% 9.25/5.28                       => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 9.25/5.28               => ( ! [M3: num] :
% 9.25/5.28                      ( ( X
% 9.25/5.28                        = ( bit0 @ M3 ) )
% 9.25/5.28                     => ( ( Xa = one )
% 9.25/5.28                       => ( ( Y
% 9.25/5.28                            = ( some_num @ ( bit1 @ M3 ) ) )
% 9.25/5.28                         => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ one ) ) ) ) )
% 9.25/5.28                 => ( ! [M3: num] :
% 9.25/5.28                        ( ( X
% 9.25/5.28                          = ( bit0 @ M3 ) )
% 9.25/5.28                       => ! [N3: num] :
% 9.25/5.28                            ( ( Xa
% 9.25/5.28                              = ( bit0 @ N3 ) )
% 9.25/5.28                           => ( ( Y
% 9.25/5.28                                = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M3 @ N3 ) ) )
% 9.25/5.28                             => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 9.25/5.28                   => ( ! [M3: num] :
% 9.25/5.28                          ( ( X
% 9.25/5.28                            = ( bit0 @ M3 ) )
% 9.25/5.28                         => ! [N3: num] :
% 9.25/5.28                              ( ( Xa
% 9.25/5.28                                = ( bit1 @ N3 ) )
% 9.25/5.28                             => ( ( Y
% 9.25/5.28                                  = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M3 @ N3 ) ) ) )
% 9.25/5.28                               => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 9.25/5.28                     => ( ! [M3: num] :
% 9.25/5.28                            ( ( X
% 9.25/5.28                              = ( bit1 @ M3 ) )
% 9.25/5.28                           => ( ( Xa = one )
% 9.25/5.28                             => ( ( Y
% 9.25/5.28                                  = ( some_num @ ( bit0 @ M3 ) ) )
% 9.25/5.28                               => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ one ) ) ) ) )
% 9.25/5.28                       => ( ! [M3: num] :
% 9.25/5.28                              ( ( X
% 9.25/5.28                                = ( bit1 @ M3 ) )
% 9.25/5.28                             => ! [N3: num] :
% 9.25/5.28                                  ( ( Xa
% 9.25/5.28                                    = ( bit0 @ N3 ) )
% 9.25/5.28                                 => ( ( Y
% 9.25/5.28                                      = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M3 @ N3 ) ) ) )
% 9.25/5.28                                   => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 9.25/5.28                         => ~ ! [M3: num] :
% 9.25/5.28                                ( ( X
% 9.25/5.28                                  = ( bit1 @ M3 ) )
% 9.25/5.28                               => ! [N3: num] :
% 9.25/5.28                                    ( ( Xa
% 9.25/5.28                                      = ( bit1 @ N3 ) )
% 9.25/5.28                                   => ( ( Y
% 9.25/5.28                                        = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M3 @ N3 ) ) )
% 9.25/5.28                                     => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9310_Field__natLeq__on,axiom,
% 9.25/5.28      ! [N: nat] :
% 9.25/5.28        ( ( field_nat
% 9.25/5.28          @ ( collec3392354462482085612at_nat
% 9.25/5.28            @ ( produc6081775807080527818_nat_o
% 9.25/5.28              @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28                  ( ( ord_less_nat @ X3 @ N )
% 9.25/5.28                  & ( ord_less_nat @ Y3 @ N )
% 9.25/5.28                  & ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) )
% 9.25/5.28        = ( collect_nat
% 9.25/5.28          @ ^ [X3: nat] : ( ord_less_nat @ X3 @ N ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9311_range__enumerate,axiom,
% 9.25/5.28      ! [S: set_nat] :
% 9.25/5.28        ( ~ ( finite_finite_nat @ S )
% 9.25/5.28       => ( ( image_nat_nat @ ( infini8530281810654367211te_nat @ S ) @ top_top_set_nat )
% 9.25/5.28          = S ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9312_Inf__nat__def,axiom,
% 9.25/5.28      ( complete_Inf_Inf_nat
% 9.25/5.28      = ( ^ [X4: set_nat] :
% 9.25/5.28            ( ord_Least_nat
% 9.25/5.28            @ ^ [N2: nat] : ( member_nat @ N2 @ X4 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9313_wf__less,axiom,
% 9.25/5.28      wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9314_Least__Suc,axiom,
% 9.25/5.28      ! [P: nat > $o,N: nat] :
% 9.25/5.28        ( ( P @ N )
% 9.25/5.28       => ( ~ ( P @ zero_zero_nat )
% 9.25/5.28         => ( ( ord_Least_nat @ P )
% 9.25/5.28            = ( suc
% 9.25/5.28              @ ( ord_Least_nat
% 9.25/5.28                @ ^ [M2: nat] : ( P @ ( suc @ M2 ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9315_rat__sgn__code,axiom,
% 9.25/5.28      ! [P4: rat] :
% 9.25/5.28        ( ( quotient_of @ ( sgn_sgn_rat @ P4 ) )
% 9.25/5.28        = ( product_Pair_int_int @ ( sgn_sgn_int @ ( product_fst_int_int @ ( quotient_of @ P4 ) ) ) @ one_one_int ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9316_bezw_Oelims,axiom,
% 9.25/5.28      ! [X: nat,Xa: nat,Y: product_prod_int_int] :
% 9.25/5.28        ( ( ( bezw @ X @ Xa )
% 9.25/5.28          = Y )
% 9.25/5.28       => ( ( ( Xa = zero_zero_nat )
% 9.25/5.28           => ( Y
% 9.25/5.28              = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 9.25/5.28          & ( ( Xa != zero_zero_nat )
% 9.25/5.28           => ( Y
% 9.25/5.28              = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa ) ) ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9317_bezw_Osimps,axiom,
% 9.25/5.28      ( bezw
% 9.25/5.28      = ( ^ [X3: nat,Y3: nat] : ( if_Pro3027730157355071871nt_int @ ( Y3 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X3 @ Y3 ) ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9318_bezw__non__0,axiom,
% 9.25/5.28      ! [Y: nat,X: nat] :
% 9.25/5.28        ( ( ord_less_nat @ zero_zero_nat @ Y )
% 9.25/5.28       => ( ( bezw @ X @ Y )
% 9.25/5.28          = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9319_one__mod__minus__numeral,axiom,
% 9.25/5.28      ! [N: num] :
% 9.25/5.28        ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.28        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9320_minus__one__mod__numeral,axiom,
% 9.25/5.28      ! [N: num] :
% 9.25/5.28        ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 9.25/5.28        = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9321_minus__numeral__mod__numeral,axiom,
% 9.25/5.28      ! [M: num,N: num] :
% 9.25/5.28        ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 9.25/5.28        = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9322_numeral__mod__minus__numeral,axiom,
% 9.25/5.28      ! [M: num,N: num] :
% 9.25/5.28        ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.28        = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9323_bezw_Opelims,axiom,
% 9.25/5.28      ! [X: nat,Xa: nat,Y: product_prod_int_int] :
% 9.25/5.28        ( ( ( bezw @ X @ Xa )
% 9.25/5.28          = Y )
% 9.25/5.28       => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 9.25/5.28         => ~ ( ( ( ( Xa = zero_zero_nat )
% 9.25/5.28                 => ( Y
% 9.25/5.28                    = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 9.25/5.28                & ( ( Xa != zero_zero_nat )
% 9.25/5.28                 => ( Y
% 9.25/5.28                    = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa ) ) ) ) ) ) ) )
% 9.25/5.28             => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9324_normalize__def,axiom,
% 9.25/5.28      ( normalize
% 9.25/5.28      = ( ^ [P6: product_prod_int_int] :
% 9.25/5.28            ( 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 ) ) ) )
% 9.25/5.28            @ ( if_Pro3027730157355071871nt_int
% 9.25/5.28              @ ( ( product_snd_int_int @ P6 )
% 9.25/5.28                = zero_zero_int )
% 9.25/5.28              @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 9.25/5.28              @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9325_gcd__1__int,axiom,
% 9.25/5.28      ! [M: int] :
% 9.25/5.28        ( ( gcd_gcd_int @ M @ one_one_int )
% 9.25/5.28        = one_one_int ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9326_gcd__neg1__int,axiom,
% 9.25/5.28      ! [X: int,Y: int] :
% 9.25/5.28        ( ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ Y )
% 9.25/5.28        = ( gcd_gcd_int @ X @ Y ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9327_gcd__neg2__int,axiom,
% 9.25/5.28      ! [X: int,Y: int] :
% 9.25/5.28        ( ( gcd_gcd_int @ X @ ( uminus_uminus_int @ Y ) )
% 9.25/5.28        = ( gcd_gcd_int @ X @ Y ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9328_gcd__neg__numeral__2__int,axiom,
% 9.25/5.28      ! [X: int,N: num] :
% 9.25/5.28        ( ( gcd_gcd_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.28        = ( gcd_gcd_int @ X @ ( numeral_numeral_int @ N ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9329_gcd__neg__numeral__1__int,axiom,
% 9.25/5.28      ! [N: num,X: int] :
% 9.25/5.28        ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ X )
% 9.25/5.28        = ( gcd_gcd_int @ ( numeral_numeral_int @ N ) @ X ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9330_dup_Orsp,axiom,
% 9.25/5.28      ( bNF_re4712519889275205905nt_int
% 9.25/5.28      @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 9.25/5.28      @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 9.25/5.28      @ ^ [K4: int] : ( plus_plus_int @ K4 @ K4 )
% 9.25/5.28      @ ^ [K4: int] : ( plus_plus_int @ K4 @ K4 ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9331_sub_Orsp,axiom,
% 9.25/5.28      ( bNF_re8402795839162346335um_int
% 9.25/5.28      @ ^ [Y4: num,Z4: num] : ( Y4 = Z4 )
% 9.25/5.28      @ ( bNF_re1822329894187522285nt_int
% 9.25/5.28        @ ^ [Y4: num,Z4: num] : ( Y4 = Z4 )
% 9.25/5.28        @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 9.25/5.28      @ ^ [M2: num,N2: num] : ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 9.25/5.28      @ ^ [M2: num,N2: num] : ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9332_uminus__integer_Orsp,axiom,
% 9.25/5.28      ( bNF_re4712519889275205905nt_int
% 9.25/5.28      @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 9.25/5.28      @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 9.25/5.28      @ uminus_uminus_int
% 9.25/5.28      @ uminus_uminus_int ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9333_gcd__cases__int,axiom,
% 9.25/5.28      ! [X: int,Y: int,P: int > $o] :
% 9.25/5.28        ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.25/5.28         => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 9.25/5.28           => ( P @ ( gcd_gcd_int @ X @ Y ) ) ) )
% 9.25/5.28       => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.25/5.28           => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 9.25/5.28             => ( P @ ( gcd_gcd_int @ X @ ( uminus_uminus_int @ Y ) ) ) ) )
% 9.25/5.28         => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 9.25/5.28             => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 9.25/5.28               => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ Y ) ) ) )
% 9.25/5.28           => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 9.25/5.28               => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 9.25/5.28                 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 9.25/5.28             => ( P @ ( gcd_gcd_int @ X @ Y ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9334_gcd__is__Max__divisors__int,axiom,
% 9.25/5.28      ! [N: int,M: int] :
% 9.25/5.28        ( ( N != zero_zero_int )
% 9.25/5.28       => ( ( gcd_gcd_int @ M @ N )
% 9.25/5.28          = ( lattic8263393255366662781ax_int
% 9.25/5.28            @ ( collect_int
% 9.25/5.28              @ ^ [D4: int] :
% 9.25/5.28                  ( ( dvd_dvd_int @ D4 @ M )
% 9.25/5.28                  & ( dvd_dvd_int @ D4 @ N ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9335_prod__decode__aux_Opelims,axiom,
% 9.25/5.28      ! [X: nat,Xa: nat,Y: product_prod_nat_nat] :
% 9.25/5.28        ( ( ( nat_prod_decode_aux @ X @ Xa )
% 9.25/5.28          = Y )
% 9.25/5.28       => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 9.25/5.28         => ~ ( ( ( ( ord_less_eq_nat @ Xa @ X )
% 9.25/5.28                 => ( Y
% 9.25/5.28                    = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X @ Xa ) ) ) )
% 9.25/5.28                & ( ~ ( ord_less_eq_nat @ Xa @ X )
% 9.25/5.28                 => ( Y
% 9.25/5.28                    = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa @ ( suc @ X ) ) ) ) ) )
% 9.25/5.28             => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9336_plus__rat_Otransfer,axiom,
% 9.25/5.28      ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 9.25/5.28      @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) )
% 9.25/5.28      @ plus_plus_rat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9337_gcd__1__nat,axiom,
% 9.25/5.28      ! [M: nat] :
% 9.25/5.28        ( ( gcd_gcd_nat @ M @ one_one_nat )
% 9.25/5.28        = one_one_nat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9338_Gcd__in,axiom,
% 9.25/5.28      ! [A2: set_nat] :
% 9.25/5.28        ( ! [A6: nat,B6: nat] :
% 9.25/5.28            ( ( member_nat @ A6 @ A2 )
% 9.25/5.28           => ( ( member_nat @ B6 @ A2 )
% 9.25/5.28             => ( member_nat @ ( gcd_gcd_nat @ A6 @ B6 ) @ A2 ) ) )
% 9.25/5.28       => ( ( A2 != bot_bot_set_nat )
% 9.25/5.28         => ( member_nat @ ( gcd_Gcd_nat @ A2 ) @ A2 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9339_gcd__nat_Osemilattice__neutr__axioms,axiom,
% 9.25/5.28      semila9081495762789891438tr_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9340_gcd__nat_Ocomm__monoid__axioms,axiom,
% 9.25/5.28      comm_monoid_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9341_gcd__nat_Omonoid__axioms,axiom,
% 9.25/5.28      monoid_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9342_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 9.25/5.28      ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 9.25/5.28      @ ^ [M2: nat,N2: nat] :
% 9.25/5.28          ( ( dvd_dvd_nat @ M2 @ N2 )
% 9.25/5.28          & ( M2 != N2 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9343_one__rat_Otransfer,axiom,
% 9.25/5.28      pcr_rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ one_one_rat ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9344_gcd__is__Max__divisors__nat,axiom,
% 9.25/5.28      ! [N: nat,M: nat] :
% 9.25/5.28        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.28       => ( ( gcd_gcd_nat @ M @ N )
% 9.25/5.28          = ( lattic8265883725875713057ax_nat
% 9.25/5.28            @ ( collect_nat
% 9.25/5.28              @ ^ [D4: nat] :
% 9.25/5.28                  ( ( dvd_dvd_nat @ D4 @ M )
% 9.25/5.28                  & ( dvd_dvd_nat @ D4 @ N ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9345_zero__rat_Otransfer,axiom,
% 9.25/5.28      pcr_rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ zero_zero_rat ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9346_Fract_Otransfer,axiom,
% 9.25/5.28      ( bNF_re3461391660133120880nt_rat
% 9.25/5.28      @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 9.25/5.28      @ ( bNF_re2214769303045360666nt_rat
% 9.25/5.28        @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 9.25/5.28        @ pcr_rat )
% 9.25/5.28      @ ^ [A3: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( B3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A3 @ B3 ) )
% 9.25/5.28      @ fract ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9347_uminus__rat_Otransfer,axiom,
% 9.25/5.28      ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 9.25/5.28      @ ^ [X3: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X3 ) ) @ ( product_snd_int_int @ X3 ) )
% 9.25/5.28      @ uminus_uminus_rat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9348_times__rat_Otransfer,axiom,
% 9.25/5.28      ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 9.25/5.28      @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_fst_int_int @ Y3 ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) )
% 9.25/5.28      @ times_times_rat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9349_inverse__rat_Otransfer,axiom,
% 9.25/5.28      ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 9.25/5.28      @ ^ [X3: product_prod_int_int] :
% 9.25/5.28          ( if_Pro3027730157355071871nt_int
% 9.25/5.28          @ ( ( product_fst_int_int @ X3 )
% 9.25/5.28            = zero_zero_int )
% 9.25/5.28          @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 9.25/5.28          @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) )
% 9.25/5.28      @ inverse_inverse_rat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9350_gcd__nat_Opelims,axiom,
% 9.25/5.28      ! [X: nat,Xa: nat,Y: nat] :
% 9.25/5.28        ( ( ( gcd_gcd_nat @ X @ Xa )
% 9.25/5.28          = Y )
% 9.25/5.28       => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 9.25/5.28         => ~ ( ( ( ( Xa = zero_zero_nat )
% 9.25/5.28                 => ( Y = X ) )
% 9.25/5.28                & ( ( Xa != zero_zero_nat )
% 9.25/5.28                 => ( Y
% 9.25/5.28                    = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) ) )
% 9.25/5.28             => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9351_positive_Otransfer,axiom,
% 9.25/5.28      ( bNF_re1494630372529172596at_o_o @ pcr_rat
% 9.25/5.28      @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 9.25/5.28      @ ^ [X3: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) )
% 9.25/5.28      @ positive ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9352_times__int_Otransfer,axiom,
% 9.25/5.28      ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 9.25/5.28      @ ( produc27273713700761075at_nat
% 9.25/5.28        @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28            ( produc2626176000494625587at_nat
% 9.25/5.28            @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V2 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) ) )
% 9.25/5.28      @ times_times_int ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9353_zero__int_Otransfer,axiom,
% 9.25/5.28      pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9354_positive__minus,axiom,
% 9.25/5.28      ! [X: rat] :
% 9.25/5.28        ( ~ ( positive @ X )
% 9.25/5.28       => ( ( X != zero_zero_rat )
% 9.25/5.28         => ( positive @ ( uminus_uminus_rat @ X ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9355_int__transfer,axiom,
% 9.25/5.28      ( bNF_re6830278522597306478at_int
% 9.25/5.28      @ ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 )
% 9.25/5.28      @ pcr_int
% 9.25/5.28      @ ^ [N2: nat] : ( product_Pair_nat_nat @ N2 @ zero_zero_nat )
% 9.25/5.28      @ semiri1314217659103216013at_int ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9356_uminus__int_Otransfer,axiom,
% 9.25/5.28      ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 9.25/5.28      @ ( produc2626176000494625587at_nat
% 9.25/5.28        @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 ) )
% 9.25/5.28      @ uminus_uminus_int ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9357_nat_Otransfer,axiom,
% 9.25/5.28      ( bNF_re4555766996558763186at_nat @ pcr_int
% 9.25/5.28      @ ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 )
% 9.25/5.28      @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 9.25/5.28      @ nat2 ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9358_one__int_Otransfer,axiom,
% 9.25/5.28      pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9359_less__int_Otransfer,axiom,
% 9.25/5.28      ( bNF_re717283939379294677_int_o @ pcr_int
% 9.25/5.28      @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 9.25/5.28        @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 ) )
% 9.25/5.28      @ ( produc8739625826339149834_nat_o
% 9.25/5.28        @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28            ( produc6081775807080527818_nat_o
% 9.25/5.28            @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) )
% 9.25/5.28      @ ord_less_int ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9360_less__eq__int_Otransfer,axiom,
% 9.25/5.28      ( bNF_re717283939379294677_int_o @ pcr_int
% 9.25/5.28      @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 9.25/5.28        @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 ) )
% 9.25/5.28      @ ( produc8739625826339149834_nat_o
% 9.25/5.28        @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28            ( produc6081775807080527818_nat_o
% 9.25/5.28            @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) )
% 9.25/5.28      @ ord_less_eq_int ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9361_plus__int_Otransfer,axiom,
% 9.25/5.28      ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 9.25/5.28      @ ( produc27273713700761075at_nat
% 9.25/5.28        @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28            ( produc2626176000494625587at_nat
% 9.25/5.28            @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V2 ) ) ) )
% 9.25/5.28      @ plus_plus_int ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9362_minus__int_Otransfer,axiom,
% 9.25/5.28      ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 9.25/5.28      @ ( produc27273713700761075at_nat
% 9.25/5.28        @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28            ( produc2626176000494625587at_nat
% 9.25/5.28            @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) ) )
% 9.25/5.28      @ minus_minus_int ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9363_positive__def,axiom,
% 9.25/5.28      ( positive
% 9.25/5.28      = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 9.25/5.28        @ ^ [X3: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9364_plus__rat__def,axiom,
% 9.25/5.28      ( plus_plus_rat
% 9.25/5.28      = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 9.25/5.28        @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9365_inverse__rat__def,axiom,
% 9.25/5.28      ( inverse_inverse_rat
% 9.25/5.28      = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 9.25/5.28        @ ^ [X3: product_prod_int_int] :
% 9.25/5.28            ( if_Pro3027730157355071871nt_int
% 9.25/5.28            @ ( ( product_fst_int_int @ X3 )
% 9.25/5.28              = zero_zero_int )
% 9.25/5.28            @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 9.25/5.28            @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9366_times__rat__def,axiom,
% 9.25/5.28      ( times_times_rat
% 9.25/5.28      = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 9.25/5.28        @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_fst_int_int @ Y3 ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9367_uminus__rat__def,axiom,
% 9.25/5.28      ( uminus_uminus_rat
% 9.25/5.28      = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 9.25/5.28        @ ^ [X3: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X3 ) ) @ ( product_snd_int_int @ X3 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9368_one__rat__def,axiom,
% 9.25/5.28      ( one_one_rat
% 9.25/5.28      = ( abs_Rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9369_Fract_Oabs__eq,axiom,
% 9.25/5.28      ( fract
% 9.25/5.28      = ( ^ [Xa4: int,X3: int] : ( abs_Rat @ ( if_Pro3027730157355071871nt_int @ ( X3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ Xa4 @ X3 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9370_zero__rat__def,axiom,
% 9.25/5.28      ( zero_zero_rat
% 9.25/5.28      = ( abs_Rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9371_Fract__def,axiom,
% 9.25/5.28      ( fract
% 9.25/5.28      = ( map_fu7831380289885515383nt_rat @ id_int @ ( map_fu3424225382358772769nt_rat @ id_int @ abs_Rat )
% 9.25/5.28        @ ^ [A3: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( B3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A3 @ B3 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9372_plus__rat_Oabs__eq,axiom,
% 9.25/5.28      ! [Xa: product_prod_int_int,X: product_prod_int_int] :
% 9.25/5.28        ( ( ratrel @ Xa @ Xa )
% 9.25/5.28       => ( ( ratrel @ X @ X )
% 9.25/5.28         => ( ( plus_plus_rat @ ( abs_Rat @ Xa ) @ ( abs_Rat @ X ) )
% 9.25/5.28            = ( abs_Rat @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9373_inverse__rat_Oabs__eq,axiom,
% 9.25/5.28      ! [X: product_prod_int_int] :
% 9.25/5.28        ( ( ratrel @ X @ X )
% 9.25/5.28       => ( ( inverse_inverse_rat @ ( abs_Rat @ X ) )
% 9.25/5.28          = ( abs_Rat
% 9.25/5.28            @ ( if_Pro3027730157355071871nt_int
% 9.25/5.28              @ ( ( product_fst_int_int @ X )
% 9.25/5.28                = zero_zero_int )
% 9.25/5.28              @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 9.25/5.28              @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9374_times__rat_Oabs__eq,axiom,
% 9.25/5.28      ! [Xa: product_prod_int_int,X: product_prod_int_int] :
% 9.25/5.28        ( ( ratrel @ Xa @ Xa )
% 9.25/5.28       => ( ( ratrel @ X @ X )
% 9.25/5.28         => ( ( times_times_rat @ ( abs_Rat @ Xa ) @ ( abs_Rat @ X ) )
% 9.25/5.28            = ( abs_Rat @ ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ Xa ) @ ( product_fst_int_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9375_one__rat_Orsp,axiom,
% 9.25/5.28      ratrel @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9376_zero__rat_Orsp,axiom,
% 9.25/5.28      ratrel @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9377_Fract_Orsp,axiom,
% 9.25/5.28      ( bNF_re157797125943740599nt_int
% 9.25/5.28      @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 9.25/5.28      @ ( bNF_re6250860962936578807nt_int
% 9.25/5.28        @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 9.25/5.28        @ ratrel )
% 9.25/5.28      @ ^ [A3: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( B3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A3 @ B3 ) )
% 9.25/5.28      @ ^ [A3: int,B3: int] : ( if_Pro3027730157355071871nt_int @ ( B3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A3 @ B3 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9378_ratrel__def,axiom,
% 9.25/5.28      ( ratrel
% 9.25/5.28      = ( ^ [X3: product_prod_int_int,Y3: product_prod_int_int] :
% 9.25/5.28            ( ( ( product_snd_int_int @ X3 )
% 9.25/5.28             != zero_zero_int )
% 9.25/5.28            & ( ( product_snd_int_int @ Y3 )
% 9.25/5.28             != zero_zero_int )
% 9.25/5.28            & ( ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) )
% 9.25/5.28              = ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X3 ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9379_times__rat_Orsp,axiom,
% 9.25/5.28      ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 9.25/5.28      @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_fst_int_int @ Y3 ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) )
% 9.25/5.28      @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_fst_int_int @ Y3 ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9380_uminus__rat_Orsp,axiom,
% 9.25/5.28      ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 9.25/5.28      @ ^ [X3: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X3 ) ) @ ( product_snd_int_int @ X3 ) )
% 9.25/5.28      @ ^ [X3: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X3 ) ) @ ( product_snd_int_int @ X3 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9381_positive_Orsp,axiom,
% 9.25/5.28      ( bNF_re8699439704749558557nt_o_o @ ratrel
% 9.25/5.28      @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 9.25/5.28      @ ^ [X3: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) )
% 9.25/5.28      @ ^ [X3: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9382_inverse__rat_Orsp,axiom,
% 9.25/5.28      ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 9.25/5.28      @ ^ [X3: product_prod_int_int] :
% 9.25/5.28          ( if_Pro3027730157355071871nt_int
% 9.25/5.28          @ ( ( product_fst_int_int @ X3 )
% 9.25/5.28            = zero_zero_int )
% 9.25/5.28          @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 9.25/5.28          @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) )
% 9.25/5.28      @ ^ [X3: product_prod_int_int] :
% 9.25/5.28          ( if_Pro3027730157355071871nt_int
% 9.25/5.28          @ ( ( product_fst_int_int @ X3 )
% 9.25/5.28            = zero_zero_int )
% 9.25/5.28          @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 9.25/5.28          @ ( product_Pair_int_int @ ( product_snd_int_int @ X3 ) @ ( product_fst_int_int @ X3 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9383_plus__rat_Orsp,axiom,
% 9.25/5.28      ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 9.25/5.28      @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) )
% 9.25/5.28      @ ^ [X3: product_prod_int_int,Y3: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y3 ) @ ( product_snd_int_int @ X3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X3 ) @ ( product_snd_int_int @ Y3 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9384_uminus__rat_Oabs__eq,axiom,
% 9.25/5.28      ! [X: product_prod_int_int] :
% 9.25/5.28        ( ( ratrel @ X @ X )
% 9.25/5.28       => ( ( uminus_uminus_rat @ ( abs_Rat @ X ) )
% 9.25/5.28          = ( abs_Rat @ ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X ) ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9385_cr__rat__def,axiom,
% 9.25/5.28      ( cr_rat
% 9.25/5.28      = ( ^ [X3: product_prod_int_int,Y3: rat] :
% 9.25/5.28            ( ( ratrel @ X3 @ X3 )
% 9.25/5.28            & ( ( abs_Rat @ X3 )
% 9.25/5.28              = Y3 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9386_times__int_Orsp,axiom,
% 9.25/5.28      ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 9.25/5.28      @ ( produc27273713700761075at_nat
% 9.25/5.28        @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28            ( produc2626176000494625587at_nat
% 9.25/5.28            @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V2 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) ) )
% 9.25/5.28      @ ( produc27273713700761075at_nat
% 9.25/5.28        @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28            ( produc2626176000494625587at_nat
% 9.25/5.28            @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V2 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9387_intrel__iff,axiom,
% 9.25/5.28      ! [X: nat,Y: nat,U: nat,V: nat] :
% 9.25/5.28        ( ( intrel @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ U @ V ) )
% 9.25/5.28        = ( ( plus_plus_nat @ X @ V )
% 9.25/5.28          = ( plus_plus_nat @ U @ Y ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9388_zero__int_Orsp,axiom,
% 9.25/5.28      intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9389_uminus__int_Orsp,axiom,
% 9.25/5.28      ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 9.25/5.28      @ ( produc2626176000494625587at_nat
% 9.25/5.28        @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 ) )
% 9.25/5.28      @ ( produc2626176000494625587at_nat
% 9.25/5.28        @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9390_nat_Orsp,axiom,
% 9.25/5.28      ( bNF_re8246922863344978751at_nat @ intrel
% 9.25/5.28      @ ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 )
% 9.25/5.28      @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 9.25/5.28      @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9391_one__int_Orsp,axiom,
% 9.25/5.28      intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9392_intrel__def,axiom,
% 9.25/5.28      ( intrel
% 9.25/5.28      = ( produc8739625826339149834_nat_o
% 9.25/5.28        @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28            ( produc6081775807080527818_nat_o
% 9.25/5.28            @ ^ [U2: nat,V2: nat] :
% 9.25/5.28                ( ( plus_plus_nat @ X3 @ V2 )
% 9.25/5.28                = ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9393_less__int_Orsp,axiom,
% 9.25/5.28      ( bNF_re4202695980764964119_nat_o @ intrel
% 9.25/5.28      @ ( bNF_re3666534408544137501at_o_o @ intrel
% 9.25/5.28        @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 ) )
% 9.25/5.28      @ ( produc8739625826339149834_nat_o
% 9.25/5.28        @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28            ( produc6081775807080527818_nat_o
% 9.25/5.28            @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) )
% 9.25/5.28      @ ( produc8739625826339149834_nat_o
% 9.25/5.28        @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28            ( produc6081775807080527818_nat_o
% 9.25/5.28            @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9394_less__eq__int_Orsp,axiom,
% 9.25/5.28      ( bNF_re4202695980764964119_nat_o @ intrel
% 9.25/5.28      @ ( bNF_re3666534408544137501at_o_o @ intrel
% 9.25/5.28        @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 ) )
% 9.25/5.28      @ ( produc8739625826339149834_nat_o
% 9.25/5.28        @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28            ( produc6081775807080527818_nat_o
% 9.25/5.28            @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) )
% 9.25/5.28      @ ( produc8739625826339149834_nat_o
% 9.25/5.28        @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28            ( produc6081775807080527818_nat_o
% 9.25/5.28            @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9395_plus__int_Orsp,axiom,
% 9.25/5.28      ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 9.25/5.28      @ ( produc27273713700761075at_nat
% 9.25/5.28        @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28            ( produc2626176000494625587at_nat
% 9.25/5.28            @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V2 ) ) ) )
% 9.25/5.28      @ ( produc27273713700761075at_nat
% 9.25/5.28        @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28            ( produc2626176000494625587at_nat
% 9.25/5.28            @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V2 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9396_minus__int_Orsp,axiom,
% 9.25/5.28      ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 9.25/5.28      @ ( produc27273713700761075at_nat
% 9.25/5.28        @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28            ( produc2626176000494625587at_nat
% 9.25/5.28            @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) ) )
% 9.25/5.28      @ ( produc27273713700761075at_nat
% 9.25/5.28        @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28            ( produc2626176000494625587at_nat
% 9.25/5.28            @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V2 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9397_quotient__of__def,axiom,
% 9.25/5.28      ( quotient_of
% 9.25/5.28      = ( ^ [X3: rat] :
% 9.25/5.28            ( the_Pr4378521158711661632nt_int
% 9.25/5.28            @ ^ [Pair: product_prod_int_int] :
% 9.25/5.28                ( ( X3
% 9.25/5.28                  = ( fract @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) )
% 9.25/5.28                & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Pair ) )
% 9.25/5.28                & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9398_signed__take__bit__eq__concat__bit,axiom,
% 9.25/5.28      ( bit_ri631733984087533419it_int
% 9.25/5.28      = ( ^ [N2: nat,K4: int] : ( bit_concat_bit @ N2 @ K4 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K4 @ N2 ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9399_normalize__stable,axiom,
% 9.25/5.28      ! [Q4: int,P4: int] :
% 9.25/5.28        ( ( ord_less_int @ zero_zero_int @ Q4 )
% 9.25/5.28       => ( ( algebr932160517623751201me_int @ P4 @ Q4 )
% 9.25/5.28         => ( ( normalize @ ( product_Pair_int_int @ P4 @ Q4 ) )
% 9.25/5.28            = ( product_Pair_int_int @ P4 @ Q4 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9400_quotient__of__coprime,axiom,
% 9.25/5.28      ! [R3: rat,P4: int,Q4: int] :
% 9.25/5.28        ( ( ( quotient_of @ R3 )
% 9.25/5.28          = ( product_Pair_int_int @ P4 @ Q4 ) )
% 9.25/5.28       => ( algebr932160517623751201me_int @ P4 @ Q4 ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9401_normalize__coprime,axiom,
% 9.25/5.28      ! [R3: product_prod_int_int,P4: int,Q4: int] :
% 9.25/5.28        ( ( ( normalize @ R3 )
% 9.25/5.28          = ( product_Pair_int_int @ P4 @ Q4 ) )
% 9.25/5.28       => ( algebr932160517623751201me_int @ P4 @ Q4 ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9402_coprime__common__divisor__int,axiom,
% 9.25/5.28      ! [A: int,B: int,X: int] :
% 9.25/5.28        ( ( algebr932160517623751201me_int @ A @ B )
% 9.25/5.28       => ( ( dvd_dvd_int @ X @ A )
% 9.25/5.28         => ( ( dvd_dvd_int @ X @ B )
% 9.25/5.28           => ( ( abs_abs_int @ X )
% 9.25/5.28              = one_one_int ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9403_coprime__common__divisor__nat,axiom,
% 9.25/5.28      ! [A: nat,B: nat,X: nat] :
% 9.25/5.28        ( ( algebr934650988132801477me_nat @ A @ B )
% 9.25/5.28       => ( ( dvd_dvd_nat @ X @ A )
% 9.25/5.28         => ( ( dvd_dvd_nat @ X @ B )
% 9.25/5.28           => ( X = one_one_nat ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9404_coprime__diff__one__left__nat,axiom,
% 9.25/5.28      ! [N: nat] :
% 9.25/5.28        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.28       => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ N ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9405_coprime__diff__one__right__nat,axiom,
% 9.25/5.28      ! [N: nat] :
% 9.25/5.28        ( ( ord_less_nat @ zero_zero_nat @ N )
% 9.25/5.28       => ( algebr934650988132801477me_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9406_upto__aux__rec,axiom,
% 9.25/5.28      ( upto_aux
% 9.25/5.28      = ( ^ [I3: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I3 ) @ Js @ ( upto_aux @ I3 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9407_upto_Opsimps,axiom,
% 9.25/5.28      ! [I: int,J: int] :
% 9.25/5.28        ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 9.25/5.28       => ( ( ( ord_less_eq_int @ I @ J )
% 9.25/5.28           => ( ( upto @ I @ J )
% 9.25/5.28              = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 9.25/5.28          & ( ~ ( ord_less_eq_int @ I @ J )
% 9.25/5.28           => ( ( upto @ I @ J )
% 9.25/5.28              = nil_int ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9408_upto_Opelims,axiom,
% 9.25/5.28      ! [X: int,Xa: int,Y: list_int] :
% 9.25/5.28        ( ( ( upto @ X @ Xa )
% 9.25/5.28          = Y )
% 9.25/5.28       => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa ) )
% 9.25/5.28         => ~ ( ( ( ( ord_less_eq_int @ X @ Xa )
% 9.25/5.28                 => ( Y
% 9.25/5.28                    = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa ) ) ) )
% 9.25/5.28                & ( ~ ( ord_less_eq_int @ X @ Xa )
% 9.25/5.28                 => ( Y = nil_int ) ) )
% 9.25/5.28             => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9409_upto__rec__numeral_I4_J,axiom,
% 9.25/5.28      ! [M: num,N: num] :
% 9.25/5.28        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.28         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.28            = ( 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 ) ) ) ) ) )
% 9.25/5.28        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.28         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.28            = nil_int ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9410_upto__rec__numeral_I3_J,axiom,
% 9.25/5.28      ! [M: num,N: num] :
% 9.25/5.28        ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 9.25/5.28         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 9.25/5.28            = ( 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 ) ) ) ) )
% 9.25/5.28        & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 9.25/5.28         => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 9.25/5.28            = nil_int ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9411_length__upto,axiom,
% 9.25/5.28      ! [I: int,J: int] :
% 9.25/5.28        ( ( size_size_list_int @ ( upto @ I @ J ) )
% 9.25/5.28        = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9412_upto__rec__numeral_I1_J,axiom,
% 9.25/5.28      ! [M: num,N: num] :
% 9.25/5.28        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 9.25/5.28         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 9.25/5.28            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 9.25/5.28        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 9.25/5.28         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 9.25/5.28            = nil_int ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9413_upto__rec__numeral_I2_J,axiom,
% 9.25/5.28      ! [M: num,N: num] :
% 9.25/5.28        ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.28         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.28            = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 9.25/5.28        & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.28         => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 9.25/5.28            = nil_int ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9414_atLeastLessThan__upto,axiom,
% 9.25/5.28      ( set_or4662586982721622107an_int
% 9.25/5.28      = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ I3 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9415_upto_Oelims,axiom,
% 9.25/5.28      ! [X: int,Xa: int,Y: list_int] :
% 9.25/5.28        ( ( ( upto @ X @ Xa )
% 9.25/5.28          = Y )
% 9.25/5.28       => ( ( ( ord_less_eq_int @ X @ Xa )
% 9.25/5.28           => ( Y
% 9.25/5.28              = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa ) ) ) )
% 9.25/5.28          & ( ~ ( ord_less_eq_int @ X @ Xa )
% 9.25/5.28           => ( Y = nil_int ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9416_upto_Osimps,axiom,
% 9.25/5.28      ( upto
% 9.25/5.28      = ( ^ [I3: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I3 @ J3 ) @ ( cons_int @ I3 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9417_upto__rec1,axiom,
% 9.25/5.28      ! [I: int,J: int] :
% 9.25/5.28        ( ( ord_less_eq_int @ I @ J )
% 9.25/5.28       => ( ( upto @ I @ J )
% 9.25/5.28          = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9418_greaterThanLessThan__upto,axiom,
% 9.25/5.28      ( set_or5832277885323065728an_int
% 9.25/5.28      = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9419_upto__split2,axiom,
% 9.25/5.28      ! [I: int,J: int,K: int] :
% 9.25/5.28        ( ( ord_less_eq_int @ I @ J )
% 9.25/5.28       => ( ( ord_less_eq_int @ J @ K )
% 9.25/5.28         => ( ( upto @ I @ K )
% 9.25/5.28            = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9420_upto__split1,axiom,
% 9.25/5.28      ! [I: int,J: int,K: int] :
% 9.25/5.28        ( ( ord_less_eq_int @ I @ J )
% 9.25/5.28       => ( ( ord_less_eq_int @ J @ K )
% 9.25/5.28         => ( ( upto @ I @ K )
% 9.25/5.28            = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9421_upto__split3,axiom,
% 9.25/5.28      ! [I: int,J: int,K: int] :
% 9.25/5.28        ( ( ord_less_eq_int @ I @ J )
% 9.25/5.28       => ( ( ord_less_eq_int @ J @ K )
% 9.25/5.28         => ( ( upto @ I @ K )
% 9.25/5.28            = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9422_upto__rec2,axiom,
% 9.25/5.28      ! [I: int,J: int] :
% 9.25/5.28        ( ( ord_less_eq_int @ I @ J )
% 9.25/5.28       => ( ( upto @ I @ J )
% 9.25/5.28          = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9423_sort__upto,axiom,
% 9.25/5.28      ! [I: int,J: int] :
% 9.25/5.28        ( ( linord1735203802627413978nt_int
% 9.25/5.28          @ ^ [X3: int] : X3
% 9.25/5.28          @ ( upto @ I @ J ) )
% 9.25/5.28        = ( upto @ I @ J ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9424_sort__upt,axiom,
% 9.25/5.28      ! [M: nat,N: nat] :
% 9.25/5.28        ( ( linord738340561235409698at_nat
% 9.25/5.28          @ ^ [X3: nat] : X3
% 9.25/5.28          @ ( upt @ M @ N ) )
% 9.25/5.28        = ( upt @ M @ N ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9425_map__add__upt_H,axiom,
% 9.25/5.28      ! [Ofs: nat,A: nat,B: nat] :
% 9.25/5.28        ( ( map_nat_nat
% 9.25/5.28          @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ Ofs )
% 9.25/5.28          @ ( upt @ A @ B ) )
% 9.25/5.28        = ( upt @ ( plus_plus_nat @ A @ Ofs ) @ ( plus_plus_nat @ B @ Ofs ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9426_map__add__upt,axiom,
% 9.25/5.28      ! [N: nat,M: nat] :
% 9.25/5.28        ( ( map_nat_nat
% 9.25/5.28          @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ N )
% 9.25/5.28          @ ( upt @ zero_zero_nat @ M ) )
% 9.25/5.28        = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9427_upt__eq__Cons__conv,axiom,
% 9.25/5.28      ! [I: nat,J: nat,X: nat,Xs: list_nat] :
% 9.25/5.28        ( ( ( upt @ I @ J )
% 9.25/5.28          = ( cons_nat @ X @ Xs ) )
% 9.25/5.28        = ( ( ord_less_nat @ I @ J )
% 9.25/5.28          & ( I = X )
% 9.25/5.28          & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 9.25/5.28            = Xs ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9428_upt__filter__extend,axiom,
% 9.25/5.28      ! [U: nat,U3: nat,P: nat > $o] :
% 9.25/5.28        ( ( ord_less_eq_nat @ U @ U3 )
% 9.25/5.28       => ( ! [I2: nat] :
% 9.25/5.28              ( ( ( ord_less_eq_nat @ U @ I2 )
% 9.25/5.28                & ( ord_less_nat @ I2 @ U3 ) )
% 9.25/5.28             => ~ ( P @ I2 ) )
% 9.25/5.28         => ( ( filter_nat2 @ P @ ( upt @ zero_zero_nat @ U ) )
% 9.25/5.28            = ( filter_nat2 @ P @ ( upt @ zero_zero_nat @ U3 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9429_map__decr__upt,axiom,
% 9.25/5.28      ! [M: nat,N: nat] :
% 9.25/5.28        ( ( map_nat_nat
% 9.25/5.28          @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 9.25/5.28          @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 9.25/5.28        = ( upt @ M @ N ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9430_sum__list__upt,axiom,
% 9.25/5.28      ! [M: nat,N: nat] :
% 9.25/5.28        ( ( ord_less_eq_nat @ M @ N )
% 9.25/5.28       => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 9.25/5.28          = ( groups3542108847815614940at_nat
% 9.25/5.28            @ ^ [X3: nat] : X3
% 9.25/5.28            @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9431_card__length__sum__list__rec,axiom,
% 9.25/5.28      ! [M: nat,N4: nat] :
% 9.25/5.28        ( ( ord_less_eq_nat @ one_one_nat @ M )
% 9.25/5.28       => ( ( finite_card_list_nat
% 9.25/5.28            @ ( collect_list_nat
% 9.25/5.28              @ ^ [L2: list_nat] :
% 9.25/5.28                  ( ( ( size_size_list_nat @ L2 )
% 9.25/5.28                    = M )
% 9.25/5.28                  & ( ( groups4561878855575611511st_nat @ L2 )
% 9.25/5.28                    = N4 ) ) ) )
% 9.25/5.28          = ( plus_plus_nat
% 9.25/5.28            @ ( finite_card_list_nat
% 9.25/5.28              @ ( collect_list_nat
% 9.25/5.28                @ ^ [L2: list_nat] :
% 9.25/5.28                    ( ( ( size_size_list_nat @ L2 )
% 9.25/5.28                      = ( minus_minus_nat @ M @ one_one_nat ) )
% 9.25/5.28                    & ( ( groups4561878855575611511st_nat @ L2 )
% 9.25/5.28                      = N4 ) ) ) )
% 9.25/5.28            @ ( finite_card_list_nat
% 9.25/5.28              @ ( collect_list_nat
% 9.25/5.28                @ ^ [L2: list_nat] :
% 9.25/5.28                    ( ( ( size_size_list_nat @ L2 )
% 9.25/5.28                      = M )
% 9.25/5.28                    & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 9.25/5.28                      = N4 ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9432_card__length__sum__list,axiom,
% 9.25/5.28      ! [M: nat,N4: nat] :
% 9.25/5.28        ( ( finite_card_list_nat
% 9.25/5.28          @ ( collect_list_nat
% 9.25/5.28            @ ^ [L2: list_nat] :
% 9.25/5.28                ( ( ( size_size_list_nat @ L2 )
% 9.25/5.28                  = M )
% 9.25/5.28                & ( ( groups4561878855575611511st_nat @ L2 )
% 9.25/5.28                  = N4 ) ) ) )
% 9.25/5.28        = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N4 @ M ) @ one_one_nat ) @ N4 ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9433_inj__on__diff__nat,axiom,
% 9.25/5.28      ! [N4: set_nat,K: nat] :
% 9.25/5.28        ( ! [N3: nat] :
% 9.25/5.28            ( ( member_nat @ N3 @ N4 )
% 9.25/5.28           => ( ord_less_eq_nat @ K @ N3 ) )
% 9.25/5.28       => ( inj_on_nat_nat
% 9.25/5.28          @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ K )
% 9.25/5.28          @ N4 ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9434_rat__denum,axiom,
% 9.25/5.28      ? [F3: nat > rat] :
% 9.25/5.28        ( ( image_nat_rat @ F3 @ top_top_set_nat )
% 9.25/5.28        = top_top_set_rat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9435_surj__nat__to__rat__surj,axiom,
% 9.25/5.28      ( ( image_nat_rat @ nat_to_rat_surj @ top_top_set_nat )
% 9.25/5.28      = top_top_set_rat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9436_last__upt,axiom,
% 9.25/5.28      ! [I: nat,J: nat] :
% 9.25/5.28        ( ( ord_less_nat @ I @ J )
% 9.25/5.28       => ( ( last_nat @ ( upt @ I @ J ) )
% 9.25/5.28          = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9437_Sup__int__def,axiom,
% 9.25/5.28      ( complete_Sup_Sup_int
% 9.25/5.28      = ( ^ [X4: set_int] :
% 9.25/5.28            ( the_int
% 9.25/5.28            @ ^ [X3: int] :
% 9.25/5.28                ( ( member_int @ X3 @ X4 )
% 9.25/5.28                & ! [Y3: int] :
% 9.25/5.28                    ( ( member_int @ Y3 @ X4 )
% 9.25/5.28                   => ( ord_less_eq_int @ Y3 @ X3 ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9438_Rats__eq__range__nat__to__rat__surj,axiom,
% 9.25/5.28      ( field_6020823756834552118ts_rat
% 9.25/5.28      = ( image_nat_rat @ nat_to_rat_surj @ top_top_set_nat ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9439_nat__to__rat__surj__def,axiom,
% 9.25/5.28      ( nat_to_rat_surj
% 9.25/5.28      = ( ^ [N2: nat] :
% 9.25/5.28            ( produc6207742614233964070at_rat
% 9.25/5.28            @ ^ [A3: nat,B3: nat] : ( fract @ ( nat_int_decode @ A3 ) @ ( nat_int_decode @ B3 ) )
% 9.25/5.28            @ ( nat_prod_decode @ N2 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9440_surj__prod__decode,axiom,
% 9.25/5.28      ( ( image_5846123807819985514at_nat @ nat_prod_decode @ top_top_set_nat )
% 9.25/5.28      = top_to4669805908274784177at_nat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9441_list__decode_Oelims,axiom,
% 9.25/5.28      ! [X: nat,Y: list_nat] :
% 9.25/5.28        ( ( ( nat_list_decode @ X )
% 9.25/5.28          = Y )
% 9.25/5.28       => ( ( ( X = zero_zero_nat )
% 9.25/5.28           => ( Y != nil_nat ) )
% 9.25/5.28         => ~ ! [N3: nat] :
% 9.25/5.28                ( ( X
% 9.25/5.28                  = ( suc @ N3 ) )
% 9.25/5.28               => ( Y
% 9.25/5.28                 != ( produc2761476792215241774st_nat
% 9.25/5.28                    @ ^ [X3: nat,Y3: nat] : ( cons_nat @ X3 @ ( nat_list_decode @ Y3 ) )
% 9.25/5.28                    @ ( nat_prod_decode @ N3 ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9442_surj__list__decode,axiom,
% 9.25/5.28      ( ( image_nat_list_nat @ nat_list_decode @ top_top_set_nat )
% 9.25/5.28      = top_top_set_list_nat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9443_list__decode_Osimps_I2_J,axiom,
% 9.25/5.28      ! [N: nat] :
% 9.25/5.28        ( ( nat_list_decode @ ( suc @ N ) )
% 9.25/5.28        = ( produc2761476792215241774st_nat
% 9.25/5.28          @ ^ [X3: nat,Y3: nat] : ( cons_nat @ X3 @ ( nat_list_decode @ Y3 ) )
% 9.25/5.28          @ ( nat_prod_decode @ N ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9444_list__decode_Opelims,axiom,
% 9.25/5.28      ! [X: nat,Y: list_nat] :
% 9.25/5.28        ( ( ( nat_list_decode @ X )
% 9.25/5.28          = Y )
% 9.25/5.28       => ( ( accp_nat @ nat_list_decode_rel @ X )
% 9.25/5.28         => ( ( ( X = zero_zero_nat )
% 9.25/5.28             => ( ( Y = nil_nat )
% 9.25/5.28               => ~ ( accp_nat @ nat_list_decode_rel @ zero_zero_nat ) ) )
% 9.25/5.28           => ~ ! [N3: nat] :
% 9.25/5.28                  ( ( X
% 9.25/5.28                    = ( suc @ N3 ) )
% 9.25/5.28                 => ( ( Y
% 9.25/5.28                      = ( produc2761476792215241774st_nat
% 9.25/5.28                        @ ^ [X3: nat,Y3: nat] : ( cons_nat @ X3 @ ( nat_list_decode @ Y3 ) )
% 9.25/5.28                        @ ( nat_prod_decode @ N3 ) ) )
% 9.25/5.28                   => ~ ( accp_nat @ nat_list_decode_rel @ ( suc @ N3 ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9445_list__decode_Opinduct,axiom,
% 9.25/5.28      ! [A0: nat,P: nat > $o] :
% 9.25/5.28        ( ( accp_nat @ nat_list_decode_rel @ A0 )
% 9.25/5.28       => ( ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 9.25/5.28           => ( P @ zero_zero_nat ) )
% 9.25/5.28         => ( ! [N3: nat] :
% 9.25/5.28                ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N3 ) )
% 9.25/5.28               => ( ! [X5: nat,Y5: nat] :
% 9.25/5.28                      ( ( ( product_Pair_nat_nat @ X5 @ Y5 )
% 9.25/5.28                        = ( nat_prod_decode @ N3 ) )
% 9.25/5.28                     => ( P @ Y5 ) )
% 9.25/5.28                 => ( P @ ( suc @ N3 ) ) ) )
% 9.25/5.28           => ( P @ A0 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9446_list__decode_Opsimps_I2_J,axiom,
% 9.25/5.28      ! [N: nat] :
% 9.25/5.28        ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N ) )
% 9.25/5.28       => ( ( nat_list_decode @ ( suc @ N ) )
% 9.25/5.28          = ( produc2761476792215241774st_nat
% 9.25/5.28            @ ^ [X3: nat,Y3: nat] : ( cons_nat @ X3 @ ( nat_list_decode @ Y3 ) )
% 9.25/5.28            @ ( nat_prod_decode @ N ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9447_bij__int__decode,axiom,
% 9.25/5.28      bij_betw_nat_int @ nat_int_decode @ top_top_set_nat @ top_top_set_int ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9448_bij__enumerate,axiom,
% 9.25/5.28      ! [S: set_nat] :
% 9.25/5.28        ( ~ ( finite_finite_nat @ S )
% 9.25/5.28       => ( bij_betw_nat_nat @ ( infini8530281810654367211te_nat @ S ) @ top_top_set_nat @ S ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9449_bij__int__encode,axiom,
% 9.25/5.28      bij_betw_int_nat @ nat_int_encode @ top_top_set_int @ top_top_set_nat ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9450_bij__prod__decode,axiom,
% 9.25/5.28      bij_be8693218025023041337at_nat @ nat_prod_decode @ top_top_set_nat @ top_to4669805908274784177at_nat ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9451_bij__list__decode,axiom,
% 9.25/5.28      bij_be6293887246118711976st_nat @ nat_list_decode @ top_top_set_nat @ top_top_set_list_nat ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9452_Rep__unit,axiom,
% 9.25/5.28      ! [X: product_unit] : ( member_o @ ( product_Rep_unit @ X ) @ ( insert_o @ $true @ bot_bot_set_o ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9453_Rep__unit__induct,axiom,
% 9.25/5.28      ! [Y: $o,P: $o > $o] :
% 9.25/5.28        ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 9.25/5.28       => ( ! [X2: product_unit] : ( P @ ( product_Rep_unit @ X2 ) )
% 9.25/5.28         => ( P @ Y ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9454_Rep__unit__cases,axiom,
% 9.25/5.28      ! [Y: $o] :
% 9.25/5.28        ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 9.25/5.28       => ~ ! [X2: product_unit] :
% 9.25/5.28              ( Y
% 9.25/5.28              = ( ~ ( product_Rep_unit @ X2 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9455_type__definition__unit,axiom,
% 9.25/5.28      type_d6188575255521822967unit_o @ product_Rep_unit @ product_Abs_unit @ ( insert_o @ $true @ bot_bot_set_o ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9456_Abs__unit__inverse,axiom,
% 9.25/5.28      ! [Y: $o] :
% 9.25/5.28        ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 9.25/5.28       => ( ( product_Rep_unit @ ( product_Abs_unit @ Y ) )
% 9.25/5.28          = Y ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9457_Abs__unit__inject,axiom,
% 9.25/5.28      ! [X: $o,Y: $o] :
% 9.25/5.28        ( ( member_o @ X @ ( insert_o @ $true @ bot_bot_set_o ) )
% 9.25/5.28       => ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 9.25/5.28         => ( ( ( product_Abs_unit @ X )
% 9.25/5.28              = ( product_Abs_unit @ Y ) )
% 9.25/5.28            = ( X = Y ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9458_Abs__unit__cases,axiom,
% 9.25/5.28      ! [X: product_unit] :
% 9.25/5.28        ~ ! [Y2: $o] :
% 9.25/5.28            ( ( X
% 9.25/5.28              = ( product_Abs_unit @ Y2 ) )
% 9.25/5.28           => ~ ( member_o @ Y2 @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9459_Abs__unit__induct,axiom,
% 9.25/5.28      ! [P: product_unit > $o,X: product_unit] :
% 9.25/5.28        ( ! [Y2: $o] :
% 9.25/5.28            ( ( member_o @ Y2 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 9.25/5.28           => ( P @ ( product_Abs_unit @ Y2 ) ) )
% 9.25/5.28       => ( P @ X ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9460_natLeq__on__wo__rel,axiom,
% 9.25/5.28      ! [N: nat] :
% 9.25/5.28        ( bNF_We3818239936649020644el_nat
% 9.25/5.28        @ ( collec3392354462482085612at_nat
% 9.25/5.28          @ ( produc6081775807080527818_nat_o
% 9.25/5.28            @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28                ( ( ord_less_nat @ X3 @ N )
% 9.25/5.28                & ( ord_less_nat @ Y3 @ N )
% 9.25/5.28                & ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9461_pair__lessI2,axiom,
% 9.25/5.28      ! [A: nat,B: nat,S3: nat,T3: nat] :
% 9.25/5.28        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.28       => ( ( ord_less_nat @ S3 @ T3 )
% 9.25/5.28         => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S3 ) @ ( product_Pair_nat_nat @ B @ T3 ) ) @ fun_pair_less ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9462_pair__less__iff1,axiom,
% 9.25/5.28      ! [X: nat,Y: nat,Z: nat] :
% 9.25/5.28        ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ X @ Z ) ) @ fun_pair_less )
% 9.25/5.28        = ( ord_less_nat @ Y @ Z ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9463_butlast__upt,axiom,
% 9.25/5.28      ! [M: nat,N: nat] :
% 9.25/5.28        ( ( butlast_nat @ ( upt @ M @ N ) )
% 9.25/5.28        = ( upt @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9464_pair__lessI1,axiom,
% 9.25/5.28      ! [A: nat,B: nat,S3: nat,T3: nat] :
% 9.25/5.28        ( ( ord_less_nat @ A @ B )
% 9.25/5.28       => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S3 ) @ ( product_Pair_nat_nat @ B @ T3 ) ) @ fun_pair_less ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9465_smin__insertI,axiom,
% 9.25/5.28      ! [X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 9.25/5.28        ( ( member8440522571783428010at_nat @ X @ XS )
% 9.25/5.28       => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_less )
% 9.25/5.28         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_strict )
% 9.25/5.28           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y @ YS ) ) @ fun_min_strict ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9466_smin__emptyI,axiom,
% 9.25/5.28      ! [X7: set_Pr1261947904930325089at_nat] :
% 9.25/5.28        ( ( X7 != bot_bo2099793752762293965at_nat )
% 9.25/5.28       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X7 @ bot_bo2099793752762293965at_nat ) @ fun_min_strict ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9467_smax__insertI,axiom,
% 9.25/5.28      ! [Y: product_prod_nat_nat,Y6: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,X7: set_Pr1261947904930325089at_nat] :
% 9.25/5.28        ( ( member8440522571783428010at_nat @ Y @ Y6 )
% 9.25/5.28       => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_less )
% 9.25/5.28         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X7 @ Y6 ) @ fun_max_strict )
% 9.25/5.28           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X @ X7 ) @ Y6 ) @ fun_max_strict ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9468_pair__leqI2,axiom,
% 9.25/5.28      ! [A: nat,B: nat,S3: nat,T3: nat] :
% 9.25/5.28        ( ( ord_less_eq_nat @ A @ B )
% 9.25/5.28       => ( ( ord_less_eq_nat @ S3 @ T3 )
% 9.25/5.28         => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S3 ) @ ( product_Pair_nat_nat @ B @ T3 ) ) @ fun_pair_leq ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9469_eventually__sequentially__Suc,axiom,
% 9.25/5.28      ! [P: nat > $o] :
% 9.25/5.28        ( ( eventually_nat
% 9.25/5.28          @ ^ [I3: nat] : ( P @ ( suc @ I3 ) )
% 9.25/5.28          @ at_top_nat )
% 9.25/5.28        = ( eventually_nat @ P @ at_top_nat ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9470_eventually__sequentially__seg,axiom,
% 9.25/5.28      ! [P: nat > $o,K: nat] :
% 9.25/5.28        ( ( eventually_nat
% 9.25/5.28          @ ^ [N2: nat] : ( P @ ( plus_plus_nat @ N2 @ K ) )
% 9.25/5.28          @ at_top_nat )
% 9.25/5.28        = ( eventually_nat @ P @ at_top_nat ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9471_le__sequentially,axiom,
% 9.25/5.28      ! [F4: filter_nat] :
% 9.25/5.28        ( ( ord_le2510731241096832064er_nat @ F4 @ at_top_nat )
% 9.25/5.28        = ( ! [N6: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N6 ) @ F4 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9472_pair__leq__def,axiom,
% 9.25/5.28      ( fun_pair_leq
% 9.25/5.28      = ( sup_su718114333110466843at_nat @ fun_pair_less @ id_Pro2258643101195443293at_nat ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9473_smax__emptyI,axiom,
% 9.25/5.28      ! [Y6: set_Pr1261947904930325089at_nat] :
% 9.25/5.28        ( ( finite6177210948735845034at_nat @ Y6 )
% 9.25/5.28       => ( ( Y6 != bot_bo2099793752762293965at_nat )
% 9.25/5.28         => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ Y6 ) @ fun_max_strict ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9474_filterlim__atMost__at__top,axiom,
% 9.25/5.28      filter3212408913953519116et_nat @ set_ord_atMost_nat @ ( finite3254316476582989077op_nat @ top_top_set_nat ) @ at_top_nat ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9475_filterlim__lessThan__at__top,axiom,
% 9.25/5.28      filter3212408913953519116et_nat @ set_ord_lessThan_nat @ ( finite3254316476582989077op_nat @ top_top_set_nat ) @ at_top_nat ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9476_pair__leqI1,axiom,
% 9.25/5.28      ! [A: nat,B: nat,S3: nat,T3: nat] :
% 9.25/5.28        ( ( ord_less_nat @ A @ B )
% 9.25/5.28       => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S3 ) @ ( product_Pair_nat_nat @ B @ T3 ) ) @ fun_pair_leq ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9477_wmin__insertI,axiom,
% 9.25/5.28      ! [X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 9.25/5.28        ( ( member8440522571783428010at_nat @ X @ XS )
% 9.25/5.28       => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 9.25/5.28         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_weak )
% 9.25/5.28           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y @ YS ) ) @ fun_min_weak ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9478_wmax__insertI,axiom,
% 9.25/5.28      ! [Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat] :
% 9.25/5.28        ( ( member8440522571783428010at_nat @ Y @ YS )
% 9.25/5.28       => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 9.25/5.28         => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_max_weak )
% 9.25/5.28           => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X @ XS ) @ YS ) @ fun_max_weak ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9479_max__weak__def,axiom,
% 9.25/5.28      ( fun_max_weak
% 9.25/5.28      = ( sup_su5525570899277871387at_nat @ ( max_ex8135407076693332796at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9480_trivial__limit__sequentially,axiom,
% 9.25/5.28      at_top_nat != bot_bot_filter_nat ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9481_eventually__False__sequentially,axiom,
% 9.25/5.28      ~ ( eventually_nat
% 9.25/5.28        @ ^ [N2: nat] : $false
% 9.25/5.28        @ at_top_nat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9482_max__rpair__set,axiom,
% 9.25/5.28      fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_max_strict @ fun_max_weak ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9483_min__rpair__set,axiom,
% 9.25/5.28      fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_min_strict @ fun_min_weak ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9484_wmax__emptyI,axiom,
% 9.25/5.28      ! [X7: set_Pr1261947904930325089at_nat] :
% 9.25/5.28        ( ( finite6177210948735845034at_nat @ X7 )
% 9.25/5.28       => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ X7 ) @ fun_max_weak ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9485_wmin__emptyI,axiom,
% 9.25/5.28      ! [X7: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X7 @ bot_bo2099793752762293965at_nat ) @ fun_min_weak ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9486_min__weak__def,axiom,
% 9.25/5.28      ( fun_min_weak
% 9.25/5.28      = ( sup_su5525570899277871387at_nat @ ( min_ex6901939911449802026at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9487_atLeast__0,axiom,
% 9.25/5.28      ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 9.25/5.28      = top_top_set_nat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9488_atLeast__Suc,axiom,
% 9.25/5.28      ! [K: nat] :
% 9.25/5.28        ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 9.25/5.28        = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9489_UN__atLeast__UNIV,axiom,
% 9.25/5.28      ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 9.25/5.28      = top_top_set_nat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9490_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 9.25/5.28      ! [L: int,U: int] :
% 9.25/5.28        ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 9.25/5.28        = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9491_atLeastPlusOneAtMost__greaterThanAtMost__integer,axiom,
% 9.25/5.28      ! [L: code_integer,U: code_integer] :
% 9.25/5.28        ( ( set_or189985376899183464nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 9.25/5.28        = ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9492_greaterThanAtMost__upto,axiom,
% 9.25/5.28      ( set_or6656581121297822940st_int
% 9.25/5.28      = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9493_abs__division__segment,axiom,
% 9.25/5.28      ! [K: int] :
% 9.25/5.28        ( ( abs_abs_int @ ( euclid3395696857347342551nt_int @ K ) )
% 9.25/5.28        = one_one_int ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9494_division__segment__nat__def,axiom,
% 9.25/5.28      ( euclid3398187327856392827nt_nat
% 9.25/5.28      = ( ^ [N2: nat] : one_one_nat ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9495_division__segment__int__def,axiom,
% 9.25/5.28      ( euclid3395696857347342551nt_int
% 9.25/5.28      = ( ^ [K4: int] : ( if_int @ ( ord_less_eq_int @ zero_zero_int @ K4 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9496_less__than__iff,axiom,
% 9.25/5.28      ! [X: nat,Y: nat] :
% 9.25/5.28        ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ less_than )
% 9.25/5.28        = ( ord_less_nat @ X @ Y ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9497_total__less__than,axiom,
% 9.25/5.28      total_on_nat @ top_top_set_nat @ less_than ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9498_natLeq__on__well__order__on,axiom,
% 9.25/5.28      ! [N: nat] :
% 9.25/5.28        ( order_2888998067076097458on_nat
% 9.25/5.28        @ ( collect_nat
% 9.25/5.28          @ ^ [X3: nat] : ( ord_less_nat @ X3 @ N ) )
% 9.25/5.28        @ ( collec3392354462482085612at_nat
% 9.25/5.28          @ ( produc6081775807080527818_nat_o
% 9.25/5.28            @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28                ( ( ord_less_nat @ X3 @ N )
% 9.25/5.28                & ( ord_less_nat @ Y3 @ N )
% 9.25/5.28                & ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9499_natLeq__on__Well__order,axiom,
% 9.25/5.28      ! [N: nat] :
% 9.25/5.28        ( order_2888998067076097458on_nat
% 9.25/5.28        @ ( field_nat
% 9.25/5.28          @ ( collec3392354462482085612at_nat
% 9.25/5.28            @ ( produc6081775807080527818_nat_o
% 9.25/5.28              @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28                  ( ( ord_less_nat @ X3 @ N )
% 9.25/5.28                  & ( ord_less_nat @ Y3 @ N )
% 9.25/5.28                  & ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) )
% 9.25/5.28        @ ( collec3392354462482085612at_nat
% 9.25/5.28          @ ( produc6081775807080527818_nat_o
% 9.25/5.28            @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28                ( ( ord_less_nat @ X3 @ N )
% 9.25/5.28                & ( ord_less_nat @ Y3 @ N )
% 9.25/5.28                & ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9500_ctwo__Cnotzero,axiom,
% 9.25/5.28      ( ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ bNF_Cardinal_ctwo @ bNF_Cardinal_czero_o ) @ bNF_We2654380646378065620so_o_o )
% 9.25/5.28      & ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ bNF_Cardinal_ctwo ) @ bNF_Cardinal_ctwo ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9501_ctwo__def,axiom,
% 9.25/5.28      ( bNF_Cardinal_ctwo
% 9.25/5.28      = ( bNF_Ca3172636760949973492d_of_o @ top_top_set_o ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9502_ctwo__ordLess__natLeq,axiom,
% 9.25/5.28      member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ bNF_Cardinal_ctwo @ bNF_Ca8665028551170535155natLeq ) @ bNF_We8182288985678559134_o_nat ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9503_natLeq__card__order,axiom,
% 9.25/5.28      bNF_Ca1281551314933786834on_nat @ top_top_set_nat @ bNF_Ca8665028551170535155natLeq ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9504_natLeq__underS__less,axiom,
% 9.25/5.28      ! [N: nat] :
% 9.25/5.28        ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 9.25/5.28        = ( collect_nat
% 9.25/5.28          @ ^ [X3: nat] : ( ord_less_nat @ X3 @ N ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9505_Field__natLeq,axiom,
% 9.25/5.28      ( ( field_nat @ bNF_Ca8665028551170535155natLeq )
% 9.25/5.28      = top_top_set_nat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9506_natLeq__def,axiom,
% 9.25/5.28      ( bNF_Ca8665028551170535155natLeq
% 9.25/5.28      = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9507_Restr__natLeq2,axiom,
% 9.25/5.28      ! [N: nat] :
% 9.25/5.28        ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 9.25/5.28          @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 9.25/5.28            @ ^ [Uu: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N ) ) )
% 9.25/5.28        = ( collec3392354462482085612at_nat
% 9.25/5.28          @ ( produc6081775807080527818_nat_o
% 9.25/5.28            @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28                ( ( ord_less_nat @ X3 @ N )
% 9.25/5.28                & ( ord_less_nat @ Y3 @ N )
% 9.25/5.28                & ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9508_Restr__natLeq,axiom,
% 9.25/5.28      ! [N: nat] :
% 9.25/5.28        ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 9.25/5.28          @ ( produc457027306803732586at_nat
% 9.25/5.28            @ ( collect_nat
% 9.25/5.28              @ ^ [X3: nat] : ( ord_less_nat @ X3 @ N ) )
% 9.25/5.28            @ ^ [Uu: nat] :
% 9.25/5.28                ( collect_nat
% 9.25/5.28                @ ^ [X3: nat] : ( ord_less_nat @ X3 @ N ) ) ) )
% 9.25/5.28        = ( collec3392354462482085612at_nat
% 9.25/5.28          @ ( produc6081775807080527818_nat_o
% 9.25/5.28            @ ^ [X3: nat,Y3: nat] :
% 9.25/5.28                ( ( ord_less_nat @ X3 @ N )
% 9.25/5.28                & ( ord_less_nat @ Y3 @ N )
% 9.25/5.28                & ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9509_card__of__nat,axiom,
% 9.25/5.28      member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ top_top_set_nat ) @ bNF_Ca8665028551170535155natLeq ) @ bNF_We5258908940166488438at_nat ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9510_card__of__Field__natLeq,axiom,
% 9.25/5.28      member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) ) @ bNF_Ca8665028551170535155natLeq ) @ bNF_We5258908940166488438at_nat ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9511_num__of__nat__One,axiom,
% 9.25/5.28      ! [N: nat] :
% 9.25/5.28        ( ( ord_less_eq_nat @ N @ one_one_nat )
% 9.25/5.28       => ( ( num_of_nat @ N )
% 9.25/5.28          = one ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9512_eventually__prod__sequentially,axiom,
% 9.25/5.28      ! [P: product_prod_nat_nat > $o] :
% 9.25/5.28        ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 9.25/5.28        = ( ? [N6: nat] :
% 9.25/5.28            ! [M2: nat] :
% 9.25/5.28              ( ( ord_less_eq_nat @ N6 @ M2 )
% 9.25/5.28             => ! [N2: nat] :
% 9.25/5.28                  ( ( ord_less_eq_nat @ N6 @ N2 )
% 9.25/5.28                 => ( P @ ( product_Pair_nat_nat @ N2 @ M2 ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9513_set__encode__empty,axiom,
% 9.25/5.28      ( ( nat_set_encode @ bot_bot_set_nat )
% 9.25/5.28      = zero_zero_nat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9514_int_Oid__abs__transfer,axiom,
% 9.25/5.28      ( bNF_re7934895593101944656at_int
% 9.25/5.28      @ ( basic_5328504652464829177at_nat
% 9.25/5.28        @ ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 )
% 9.25/5.28        @ ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 ) )
% 9.25/5.28      @ pcr_int
% 9.25/5.28      @ ^ [X3: product_prod_nat_nat] : X3
% 9.25/5.28      @ abs_Integ ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9515_smsI,axiom,
% 9.25/5.28      ! [A2: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat,Z5: multis2468970476368604999at_nat] :
% 9.25/5.28        ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A2 ) @ ( set_ms8126754132646256062at_nat @ B2 ) ) @ fun_max_strict )
% 9.25/5.28       => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z5 @ A2 ) @ ( plus_p7104986032573967614at_nat @ Z5 @ B2 ) ) @ ms_strict ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9516_wmsI,axiom,
% 9.25/5.28      ! [A2: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat,Z5: multis2468970476368604999at_nat] :
% 9.25/5.28        ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A2 ) @ ( set_ms8126754132646256062at_nat @ B2 ) ) @ fun_max_strict )
% 9.25/5.28          | ( ( A2 = zero_z1048942125864253310at_nat )
% 9.25/5.28            & ( B2 = zero_z1048942125864253310at_nat ) ) )
% 9.25/5.28       => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z5 @ A2 ) @ ( plus_p7104986032573967614at_nat @ Z5 @ B2 ) ) @ ms_weak ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9517_ms__weak__def,axiom,
% 9.25/5.28      ( ms_weak
% 9.25/5.28      = ( sup_su3035147773818789531at_nat @ ms_strict @ id_mul2649389997224486051at_nat ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9518_ms__reduction__pair,axiom,
% 9.25/5.28      fun_re7357418987779152907at_nat @ ( produc5245064249948416855at_nat @ ms_strict @ ms_weak ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9519_ms__strictI,axiom,
% 9.25/5.28      ! [Z5: multis2468970476368604999at_nat,Z9: multis2468970476368604999at_nat,A2: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat] :
% 9.25/5.28        ( ( pw_leq @ Z5 @ Z9 )
% 9.25/5.28       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A2 ) @ ( set_ms8126754132646256062at_nat @ B2 ) ) @ fun_max_strict )
% 9.25/5.28         => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z5 @ A2 ) @ ( plus_p7104986032573967614at_nat @ Z9 @ B2 ) ) @ ms_strict ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9520_ms__weakI1,axiom,
% 9.25/5.28      ! [Z5: multis2468970476368604999at_nat,Z9: multis2468970476368604999at_nat,A2: multis2468970476368604999at_nat,B2: multis2468970476368604999at_nat] :
% 9.25/5.28        ( ( pw_leq @ Z5 @ Z9 )
% 9.25/5.28       => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A2 ) @ ( set_ms8126754132646256062at_nat @ B2 ) ) @ fun_max_strict )
% 9.25/5.28         => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z5 @ A2 ) @ ( plus_p7104986032573967614at_nat @ Z9 @ B2 ) ) @ ms_weak ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9521_pw__leq__lstep,axiom,
% 9.25/5.28      ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 9.25/5.28        ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 9.25/5.28       => ( pw_leq @ ( add_ms2612439473150266591at_nat @ X @ zero_z1048942125864253310at_nat ) @ ( add_ms2612439473150266591at_nat @ Y @ zero_z1048942125864253310at_nat ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9522_pw__leq_Ocases,axiom,
% 9.25/5.28      ! [A1: multis2468970476368604999at_nat,A22: multis2468970476368604999at_nat] :
% 9.25/5.28        ( ( pw_leq @ A1 @ A22 )
% 9.25/5.28       => ( ( ( A1 = zero_z1048942125864253310at_nat )
% 9.25/5.28           => ( A22 != zero_z1048942125864253310at_nat ) )
% 9.25/5.28         => ~ ! [X2: product_prod_nat_nat,Y2: product_prod_nat_nat,X8: multis2468970476368604999at_nat] :
% 9.25/5.28                ( ( A1
% 9.25/5.28                  = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ X2 @ zero_z1048942125864253310at_nat ) @ X8 ) )
% 9.25/5.28               => ! [Y7: multis2468970476368604999at_nat] :
% 9.25/5.28                    ( ( A22
% 9.25/5.28                      = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ Y2 @ zero_z1048942125864253310at_nat ) @ Y7 ) )
% 9.25/5.28                   => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X2 @ Y2 ) @ fun_pair_leq )
% 9.25/5.28                     => ~ ( pw_leq @ X8 @ Y7 ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9523_pw__leq_Osimps,axiom,
% 9.25/5.28      ( pw_leq
% 9.25/5.28      = ( ^ [A12: multis2468970476368604999at_nat,A23: multis2468970476368604999at_nat] :
% 9.25/5.28            ( ( ( A12 = zero_z1048942125864253310at_nat )
% 9.25/5.28              & ( A23 = zero_z1048942125864253310at_nat ) )
% 9.25/5.28            | ? [X3: product_prod_nat_nat,Y3: product_prod_nat_nat,X4: multis2468970476368604999at_nat,Y8: multis2468970476368604999at_nat] :
% 9.25/5.28                ( ( A12
% 9.25/5.28                  = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ X3 @ zero_z1048942125864253310at_nat ) @ X4 ) )
% 9.25/5.28                & ( A23
% 9.25/5.28                  = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ Y3 @ zero_z1048942125864253310at_nat ) @ Y8 ) )
% 9.25/5.28                & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y3 ) @ fun_pair_leq )
% 9.25/5.28                & ( pw_leq @ X4 @ Y8 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9524_pw__leq__step,axiom,
% 9.25/5.28      ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,X7: multis2468970476368604999at_nat,Y6: multis2468970476368604999at_nat] :
% 9.25/5.28        ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 9.25/5.28       => ( ( pw_leq @ X7 @ Y6 )
% 9.25/5.28         => ( pw_leq @ ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ X @ zero_z1048942125864253310at_nat ) @ X7 ) @ ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ Y @ zero_z1048942125864253310at_nat ) @ Y6 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9525_ms__weakI2,axiom,
% 9.25/5.28      ! [Z5: multis2468970476368604999at_nat,Z9: multis2468970476368604999at_nat] :
% 9.25/5.28        ( ( pw_leq @ Z5 @ Z9 )
% 9.25/5.28       => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z5 @ zero_z1048942125864253310at_nat ) @ ( plus_p7104986032573967614at_nat @ Z9 @ zero_z1048942125864253310at_nat ) ) @ ms_weak ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9526_pw__leq__split,axiom,
% 9.25/5.28      ! [X7: multis2468970476368604999at_nat,Y6: multis2468970476368604999at_nat] :
% 9.25/5.28        ( ( pw_leq @ X7 @ Y6 )
% 9.25/5.28       => ? [A8: multis2468970476368604999at_nat,B9: multis2468970476368604999at_nat,Z10: multis2468970476368604999at_nat] :
% 9.25/5.28            ( ( X7
% 9.25/5.28              = ( plus_p7104986032573967614at_nat @ A8 @ Z10 ) )
% 9.25/5.28            & ( Y6
% 9.25/5.28              = ( plus_p7104986032573967614at_nat @ B9 @ Z10 ) )
% 9.25/5.28            & ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A8 ) @ ( set_ms8126754132646256062at_nat @ B9 ) ) @ fun_max_strict )
% 9.25/5.28              | ( ( B9 = zero_z1048942125864253310at_nat )
% 9.25/5.28                & ( A8 = zero_z1048942125864253310at_nat ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9527_rat_Odomain,axiom,
% 9.25/5.28      ( ( domain9213661015745956397nt_rat @ pcr_rat )
% 9.25/5.28      = ( ^ [X3: product_prod_int_int] :
% 9.25/5.28          ? [Y3: product_prod_int_int] :
% 9.25/5.28            ( ( basic_4387203522000727145nt_int
% 9.25/5.28              @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 9.25/5.28              @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 9.25/5.28              @ X3
% 9.25/5.28              @ Y3 )
% 9.25/5.28            & ( ratrel @ Y3 @ Y3 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9528_rat_Odomain__par,axiom,
% 9.25/5.28      ! [DR1: int > $o,DR2: int > $o,P22: product_prod_int_int > $o] :
% 9.25/5.28        ( ( ( domainp_int_int
% 9.25/5.28            @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 9.25/5.28          = DR1 )
% 9.25/5.28       => ( ( ( domainp_int_int
% 9.25/5.28              @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 9.25/5.28            = DR2 )
% 9.25/5.28         => ( ( bNF_re8699439704749558557nt_o_o
% 9.25/5.28              @ ( basic_4387203522000727145nt_int
% 9.25/5.28                @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 9.25/5.28                @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 9.25/5.28              @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 9.25/5.28              @ P22
% 9.25/5.28              @ ^ [X3: product_prod_int_int] : ( ratrel @ X3 @ X3 ) )
% 9.25/5.28           => ( ( domain9213661015745956397nt_rat @ pcr_rat )
% 9.25/5.28              = ( inf_in3604695632404883862_int_o @ ( basic_1567116559311922317nt_int @ DR1 @ DR2 ) @ P22 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9529_rat_Odomain__par__left__total,axiom,
% 9.25/5.28      ! [P7: product_prod_int_int > $o] :
% 9.25/5.28        ( ( left_t3131394472396969446nt_int
% 9.25/5.28          @ ( basic_4387203522000727145nt_int
% 9.25/5.28            @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 9.25/5.28            @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) ) )
% 9.25/5.28       => ( ( bNF_re8699439704749558557nt_o_o
% 9.25/5.28            @ ( basic_4387203522000727145nt_int
% 9.25/5.28              @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 9.25/5.28              @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 ) )
% 9.25/5.28            @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 9.25/5.28            @ P7
% 9.25/5.28            @ ^ [X3: product_prod_int_int] : ( ratrel @ X3 @ X3 ) )
% 9.25/5.28         => ( ( domain9213661015745956397nt_rat @ pcr_rat )
% 9.25/5.28            = P7 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9530_Abs__rat__inject,axiom,
% 9.25/5.28      ! [X: set_Pr958786334691620121nt_int,Y: set_Pr958786334691620121nt_int] :
% 9.25/5.28        ( ( member2340774599025711042nt_int @ X
% 9.25/5.28          @ ( collec5210948495886036740nt_int
% 9.25/5.28            @ ^ [C4: set_Pr958786334691620121nt_int] :
% 9.25/5.28              ? [X3: product_prod_int_int] :
% 9.25/5.28                ( ( ratrel @ X3 @ X3 )
% 9.25/5.28                & ( C4
% 9.25/5.28                  = ( collec213857154873943460nt_int @ ( ratrel @ X3 ) ) ) ) ) )
% 9.25/5.28       => ( ( member2340774599025711042nt_int @ Y
% 9.25/5.28            @ ( collec5210948495886036740nt_int
% 9.25/5.28              @ ^ [C4: set_Pr958786334691620121nt_int] :
% 9.25/5.28                ? [X3: product_prod_int_int] :
% 9.25/5.28                  ( ( ratrel @ X3 @ X3 )
% 9.25/5.28                  & ( C4
% 9.25/5.28                    = ( collec213857154873943460nt_int @ ( ratrel @ X3 ) ) ) ) ) )
% 9.25/5.28         => ( ( ( abs_rat @ X )
% 9.25/5.28              = ( abs_rat @ Y ) )
% 9.25/5.28            = ( X = Y ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9531_Abs__rat__induct,axiom,
% 9.25/5.28      ! [P: rat > $o,X: rat] :
% 9.25/5.28        ( ! [Y2: set_Pr958786334691620121nt_int] :
% 9.25/5.28            ( ( member2340774599025711042nt_int @ Y2
% 9.25/5.28              @ ( collec5210948495886036740nt_int
% 9.25/5.28                @ ^ [C4: set_Pr958786334691620121nt_int] :
% 9.25/5.28                  ? [X3: product_prod_int_int] :
% 9.25/5.28                    ( ( ratrel @ X3 @ X3 )
% 9.25/5.28                    & ( C4
% 9.25/5.28                      = ( collec213857154873943460nt_int @ ( ratrel @ X3 ) ) ) ) ) )
% 9.25/5.28           => ( P @ ( abs_rat @ Y2 ) ) )
% 9.25/5.28       => ( P @ X ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9532_Abs__rat__cases,axiom,
% 9.25/5.28      ! [X: rat] :
% 9.25/5.28        ~ ! [Y2: set_Pr958786334691620121nt_int] :
% 9.25/5.28            ( ( X
% 9.25/5.28              = ( abs_rat @ Y2 ) )
% 9.25/5.28           => ~ ( member2340774599025711042nt_int @ Y2
% 9.25/5.28                @ ( collec5210948495886036740nt_int
% 9.25/5.28                  @ ^ [C4: set_Pr958786334691620121nt_int] :
% 9.25/5.28                    ? [X3: product_prod_int_int] :
% 9.25/5.28                      ( ( ratrel @ X3 @ X3 )
% 9.25/5.28                      & ( C4
% 9.25/5.28                        = ( collec213857154873943460nt_int @ ( ratrel @ X3 ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9533_type__definition__rat,axiom,
% 9.25/5.28      ( type_d8554052265237484179nt_int @ rep_rat @ abs_rat
% 9.25/5.28      @ ( collec5210948495886036740nt_int
% 9.25/5.28        @ ^ [C4: set_Pr958786334691620121nt_int] :
% 9.25/5.28          ? [X3: product_prod_int_int] :
% 9.25/5.28            ( ( ratrel @ X3 @ X3 )
% 9.25/5.28            & ( C4
% 9.25/5.28              = ( collec213857154873943460nt_int @ ( ratrel @ X3 ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9534_Abs__rat__inverse,axiom,
% 9.25/5.28      ! [Y: set_Pr958786334691620121nt_int] :
% 9.25/5.28        ( ( member2340774599025711042nt_int @ Y
% 9.25/5.28          @ ( collec5210948495886036740nt_int
% 9.25/5.28            @ ^ [C4: set_Pr958786334691620121nt_int] :
% 9.25/5.28              ? [X3: product_prod_int_int] :
% 9.25/5.28                ( ( ratrel @ X3 @ X3 )
% 9.25/5.28                & ( C4
% 9.25/5.28                  = ( collec213857154873943460nt_int @ ( ratrel @ X3 ) ) ) ) ) )
% 9.25/5.28       => ( ( rep_rat @ ( abs_rat @ Y ) )
% 9.25/5.28          = Y ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9535_Rep__rat__induct,axiom,
% 9.25/5.28      ! [Y: set_Pr958786334691620121nt_int,P: set_Pr958786334691620121nt_int > $o] :
% 9.25/5.28        ( ( member2340774599025711042nt_int @ Y
% 9.25/5.28          @ ( collec5210948495886036740nt_int
% 9.25/5.28            @ ^ [C4: set_Pr958786334691620121nt_int] :
% 9.25/5.28              ? [X3: product_prod_int_int] :
% 9.25/5.28                ( ( ratrel @ X3 @ X3 )
% 9.25/5.28                & ( C4
% 9.25/5.28                  = ( collec213857154873943460nt_int @ ( ratrel @ X3 ) ) ) ) ) )
% 9.25/5.28       => ( ! [X2: rat] : ( P @ ( rep_rat @ X2 ) )
% 9.25/5.28         => ( P @ Y ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9536_Rep__rat__cases,axiom,
% 9.25/5.28      ! [Y: set_Pr958786334691620121nt_int] :
% 9.25/5.28        ( ( member2340774599025711042nt_int @ Y
% 9.25/5.28          @ ( collec5210948495886036740nt_int
% 9.25/5.28            @ ^ [C4: set_Pr958786334691620121nt_int] :
% 9.25/5.28              ? [X3: product_prod_int_int] :
% 9.25/5.28                ( ( ratrel @ X3 @ X3 )
% 9.25/5.28                & ( C4
% 9.25/5.28                  = ( collec213857154873943460nt_int @ ( ratrel @ X3 ) ) ) ) ) )
% 9.25/5.28       => ~ ! [X2: rat] :
% 9.25/5.28              ( Y
% 9.25/5.28             != ( rep_rat @ X2 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9537_Rep__rat,axiom,
% 9.25/5.28      ! [X: rat] :
% 9.25/5.28        ( member2340774599025711042nt_int @ ( rep_rat @ X )
% 9.25/5.28        @ ( collec5210948495886036740nt_int
% 9.25/5.28          @ ^ [C4: set_Pr958786334691620121nt_int] :
% 9.25/5.28            ? [X3: product_prod_int_int] :
% 9.25/5.28              ( ( ratrel @ X3 @ X3 )
% 9.25/5.28              & ( C4
% 9.25/5.28                = ( collec213857154873943460nt_int @ ( ratrel @ X3 ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9538_cr__int__def,axiom,
% 9.25/5.28      ( cr_int
% 9.25/5.28      = ( ^ [X3: product_prod_nat_nat] :
% 9.25/5.28            ( ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 9.25/5.28            @ ( abs_Integ @ X3 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9539_in__range_Osimps,axiom,
% 9.25/5.28      ! [H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 9.25/5.28        ( ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) )
% 9.25/5.28        = ( ! [X3: nat] :
% 9.25/5.28              ( ( member_nat @ X3 @ As )
% 9.25/5.28             => ( ord_less_nat @ X3 @ ( lim_Product_unit @ H3 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9540_in__range_Oelims_I3_J,axiom,
% 9.25/5.28      ! [X: produc3658429121746597890et_nat] :
% 9.25/5.28        ( ~ ( in_range @ X )
% 9.25/5.28       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 9.25/5.28              ( ( X
% 9.25/5.28                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.28             => ! [X2: nat] :
% 9.25/5.28                  ( ( member_nat @ X2 @ As4 )
% 9.25/5.28                 => ( ord_less_nat @ X2 @ ( lim_Product_unit @ H ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9541_in__range_Oelims_I2_J,axiom,
% 9.25/5.28      ! [X: produc3658429121746597890et_nat] :
% 9.25/5.28        ( ( in_range @ X )
% 9.25/5.28       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 9.25/5.28              ( ( X
% 9.25/5.28                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.28             => ~ ! [X5: nat] :
% 9.25/5.28                    ( ( member_nat @ X5 @ As4 )
% 9.25/5.28                   => ( ord_less_nat @ X5 @ ( lim_Product_unit @ H ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9542_in__range_Oelims_I1_J,axiom,
% 9.25/5.28      ! [X: produc3658429121746597890et_nat,Y: $o] :
% 9.25/5.28        ( ( ( in_range @ X )
% 9.25/5.28          = Y )
% 9.25/5.28       => ~ ! [H: heap_e7401611519738050253t_unit,As4: set_nat] :
% 9.25/5.28              ( ( X
% 9.25/5.28                = ( produc7507926704131184380et_nat @ H @ As4 ) )
% 9.25/5.28             => ( Y
% 9.25/5.28                = ( ~ ! [X3: nat] :
% 9.25/5.28                        ( ( member_nat @ X3 @ As4 )
% 9.25/5.28                       => ( ord_less_nat @ X3 @ ( lim_Product_unit @ H ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9543_surj__prod__encode,axiom,
% 9.25/5.28      ( ( image_2486076414777270412at_nat @ nat_prod_encode @ top_to4669805908274784177at_nat )
% 9.25/5.28      = top_top_set_nat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9544_le__prod__encode__1,axiom,
% 9.25/5.28      ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9545_le__prod__encode__2,axiom,
% 9.25/5.28      ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9546_bij__prod__encode,axiom,
% 9.25/5.28      bij_be5333170631980326235at_nat @ nat_prod_encode @ top_to4669805908274784177at_nat @ top_top_set_nat ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9547_list__encode_Oelims,axiom,
% 9.25/5.28      ! [X: list_nat,Y: nat] :
% 9.25/5.28        ( ( ( nat_list_encode @ X )
% 9.25/5.28          = Y )
% 9.25/5.28       => ( ( ( X = nil_nat )
% 9.25/5.28           => ( Y != zero_zero_nat ) )
% 9.25/5.28         => ~ ! [X2: nat,Xs2: list_nat] :
% 9.25/5.28                ( ( X
% 9.25/5.28                  = ( cons_nat @ X2 @ Xs2 ) )
% 9.25/5.28               => ( Y
% 9.25/5.28                 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X2 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9548_prod__encode__def,axiom,
% 9.25/5.28      ( nat_prod_encode
% 9.25/5.28      = ( produc6842872674320459806at_nat
% 9.25/5.28        @ ^ [M2: nat,N2: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M2 @ N2 ) ) @ M2 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9549_surj__list__encode,axiom,
% 9.25/5.28      ( ( image_list_nat_nat @ nat_list_encode @ top_top_set_list_nat )
% 9.25/5.28      = top_top_set_nat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9550_bij__list__encode,axiom,
% 9.25/5.28      bij_be8532844293280997160at_nat @ nat_list_encode @ top_top_set_list_nat @ top_top_set_nat ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9551_list__encode_Osimps_I2_J,axiom,
% 9.25/5.28      ! [X: nat,Xs: list_nat] :
% 9.25/5.28        ( ( nat_list_encode @ ( cons_nat @ X @ Xs ) )
% 9.25/5.28        = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9552_list__encode_Opelims,axiom,
% 9.25/5.28      ! [X: list_nat,Y: nat] :
% 9.25/5.28        ( ( ( nat_list_encode @ X )
% 9.25/5.28          = Y )
% 9.25/5.28       => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 9.25/5.28         => ( ( ( X = nil_nat )
% 9.25/5.28             => ( ( Y = zero_zero_nat )
% 9.25/5.28               => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 9.25/5.28           => ~ ! [X2: nat,Xs2: list_nat] :
% 9.25/5.28                  ( ( X
% 9.25/5.28                    = ( cons_nat @ X2 @ Xs2 ) )
% 9.25/5.28                 => ( ( Y
% 9.25/5.28                      = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X2 @ ( nat_list_encode @ Xs2 ) ) ) ) )
% 9.25/5.28                   => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X2 @ Xs2 ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9553_String_Oless__literal__def,axiom,
% 9.25/5.28      ( ord_less_literal
% 9.25/5.28      = ( map_fu2661873803724901240eral_o @ explode @ ( map_fu6698795530259886495ar_o_o @ explode @ id_o )
% 9.25/5.28        @ ( lexordp_char
% 9.25/5.28          @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9554_less__literal_Orep__eq,axiom,
% 9.25/5.28      ( ord_less_literal
% 9.25/5.28      = ( ^ [X3: literal,Xa4: literal] :
% 9.25/5.28            ( lexordp_char
% 9.25/5.28            @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) )
% 9.25/5.28            @ ( explode @ X3 )
% 9.25/5.28            @ ( explode @ Xa4 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9555_String_Oless__eq__literal__def,axiom,
% 9.25/5.28      ( ord_less_eq_literal
% 9.25/5.28      = ( map_fu2661873803724901240eral_o @ explode @ ( map_fu6698795530259886495ar_o_o @ explode @ id_o )
% 9.25/5.28        @ ( lexordp_eq_char
% 9.25/5.28          @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9556_less__literal_Otransfer,axiom,
% 9.25/5.28      ( bNF_re7831395832754058691eral_o @ pcr_literal
% 9.25/5.28      @ ( bNF_re8730477052009823892al_o_o @ pcr_literal
% 9.25/5.28        @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 ) )
% 9.25/5.28      @ ( lexordp_char
% 9.25/5.28        @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) ) )
% 9.25/5.28      @ ord_less_literal ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9557_literal_Orep__transfer,axiom,
% 9.25/5.28      ( bNF_re4991257583289732696t_char @ pcr_literal
% 9.25/5.28      @ ( list_all2_char_char
% 9.25/5.28        @ ^ [Y4: char,Z4: char] : ( Y4 = Z4 ) )
% 9.25/5.28      @ ^ [X3: list_char] : X3
% 9.25/5.28      @ explode ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9558_less__eq__literal_Otransfer,axiom,
% 9.25/5.28      ( bNF_re7831395832754058691eral_o @ pcr_literal
% 9.25/5.28      @ ( bNF_re8730477052009823892al_o_o @ pcr_literal
% 9.25/5.28        @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 ) )
% 9.25/5.28      @ ( lexordp_eq_char
% 9.25/5.28        @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) ) )
% 9.25/5.28      @ ord_less_eq_literal ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9559_less__eq__literal_Orep__eq,axiom,
% 9.25/5.28      ( ord_less_eq_literal
% 9.25/5.28      = ( ^ [X3: literal,Xa4: literal] :
% 9.25/5.28            ( lexordp_eq_char
% 9.25/5.28            @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) )
% 9.25/5.28            @ ( explode @ X3 )
% 9.25/5.28            @ ( explode @ Xa4 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9560_String_Ocr__literal__def,axiom,
% 9.25/5.28      ( cr_literal
% 9.25/5.28      = ( ^ [X3: list_char,Y3: literal] :
% 9.25/5.28            ( X3
% 9.25/5.28            = ( explode @ Y3 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9561_MOST__SucD,axiom,
% 9.25/5.28      ! [P: nat > $o] :
% 9.25/5.28        ( ( eventually_nat
% 9.25/5.28          @ ^ [N2: nat] : ( P @ ( suc @ N2 ) )
% 9.25/5.28          @ cofinite_nat )
% 9.25/5.28       => ( eventually_nat @ P @ cofinite_nat ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9562_MOST__SucI,axiom,
% 9.25/5.28      ! [P: nat > $o] :
% 9.25/5.28        ( ( eventually_nat @ P @ cofinite_nat )
% 9.25/5.28       => ( eventually_nat
% 9.25/5.28          @ ^ [N2: nat] : ( P @ ( suc @ N2 ) )
% 9.25/5.28          @ cofinite_nat ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9563_MOST__Suc__iff,axiom,
% 9.25/5.28      ! [P: nat > $o] :
% 9.25/5.28        ( ( eventually_nat
% 9.25/5.28          @ ^ [N2: nat] : ( P @ ( suc @ N2 ) )
% 9.25/5.28          @ cofinite_nat )
% 9.25/5.28        = ( eventually_nat @ P @ cofinite_nat ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9564_MOST__nat,axiom,
% 9.25/5.28      ! [P: nat > $o] :
% 9.25/5.28        ( ( eventually_nat @ P @ cofinite_nat )
% 9.25/5.28        = ( ? [M2: nat] :
% 9.25/5.28            ! [N2: nat] :
% 9.25/5.28              ( ( ord_less_nat @ M2 @ N2 )
% 9.25/5.28             => ( P @ N2 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9565_MOST__ge__nat,axiom,
% 9.25/5.28      ! [M: nat] : ( eventually_nat @ ( ord_less_eq_nat @ M ) @ cofinite_nat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9566_MOST__nat__le,axiom,
% 9.25/5.28      ! [P: nat > $o] :
% 9.25/5.28        ( ( eventually_nat @ P @ cofinite_nat )
% 9.25/5.28        = ( ? [M2: nat] :
% 9.25/5.28            ! [N2: nat] :
% 9.25/5.28              ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.25/5.28             => ( P @ N2 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9567_less__literal_Orsp,axiom,
% 9.25/5.28      ( bNF_re7775871201573978401char_o
% 9.25/5.28      @ ( bNF_eq_onp_list_char
% 9.25/5.28        @ ^ [Cs: list_char] :
% 9.25/5.28          ! [X3: char] :
% 9.25/5.28            ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28           => ~ ( digit7 @ X3 ) ) )
% 9.25/5.28      @ ( bNF_re6668474094832959905ar_o_o
% 9.25/5.28        @ ( bNF_eq_onp_list_char
% 9.25/5.28          @ ^ [Cs: list_char] :
% 9.25/5.28            ! [X3: char] :
% 9.25/5.28              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28             => ~ ( digit7 @ X3 ) ) )
% 9.25/5.28        @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 ) )
% 9.25/5.28      @ ( lexordp_char
% 9.25/5.28        @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) ) )
% 9.25/5.28      @ ( lexordp_char
% 9.25/5.28        @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9568_plus__literal_Orsp,axiom,
% 9.25/5.28      ( bNF_re7399511318543894245t_char
% 9.25/5.28      @ ( bNF_eq_onp_list_char
% 9.25/5.28        @ ^ [Cs: list_char] :
% 9.25/5.28          ! [X3: char] :
% 9.25/5.28            ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28           => ~ ( digit7 @ X3 ) ) )
% 9.25/5.28      @ ( bNF_re1407854171455731685t_char
% 9.25/5.28        @ ( bNF_eq_onp_list_char
% 9.25/5.28          @ ^ [Cs: list_char] :
% 9.25/5.28            ! [X3: char] :
% 9.25/5.28              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28             => ~ ( digit7 @ X3 ) ) )
% 9.25/5.28        @ ( bNF_eq_onp_list_char
% 9.25/5.28          @ ^ [Cs: list_char] :
% 9.25/5.28            ! [X3: char] :
% 9.25/5.28              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28             => ~ ( digit7 @ X3 ) ) ) )
% 9.25/5.28      @ append_char
% 9.25/5.28      @ append_char ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9569_asciis__of__literal_Orsp,axiom,
% 9.25/5.28      ( bNF_re901197953848981245nteger
% 9.25/5.28      @ ( bNF_eq_onp_list_char
% 9.25/5.28        @ ^ [Cs: list_char] :
% 9.25/5.28          ! [X3: char] :
% 9.25/5.28            ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28           => ~ ( digit7 @ X3 ) ) )
% 9.25/5.28      @ ^ [Y4: list_Code_integer,Z4: list_Code_integer] : ( Y4 = Z4 )
% 9.25/5.28      @ ( map_ch5843194146513361140nteger @ comm_s4049598766089966537nteger )
% 9.25/5.28      @ ( map_ch5843194146513361140nteger @ comm_s4049598766089966537nteger ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9570_size__literal_Orsp,axiom,
% 9.25/5.28      ( bNF_re76688982720252355at_nat
% 9.25/5.28      @ ( bNF_eq_onp_list_char
% 9.25/5.28        @ ^ [Cs: list_char] :
% 9.25/5.28          ! [X3: char] :
% 9.25/5.28            ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28           => ~ ( digit7 @ X3 ) ) )
% 9.25/5.28      @ ^ [Y4: nat,Z4: nat] : ( Y4 = Z4 )
% 9.25/5.28      @ size_size_list_char
% 9.25/5.28      @ size_size_list_char ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9571_Literal_Orsp,axiom,
% 9.25/5.28      ( bNF_re5598663031114558885t_char
% 9.25/5.28      @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 9.25/5.28      @ ( bNF_re7347849368244578525t_char
% 9.25/5.28        @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 9.25/5.28        @ ( bNF_re7972843584066424825t_char
% 9.25/5.28          @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 9.25/5.28          @ ( bNF_re796896441190010845t_char
% 9.25/5.28            @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 9.25/5.28            @ ( bNF_re4583855572895197261t_char
% 9.25/5.28              @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 9.25/5.28              @ ( bNF_re441219624009962717t_char
% 9.25/5.28                @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 9.25/5.28                @ ( bNF_re6157522605288126113t_char
% 9.25/5.28                  @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 9.25/5.28                  @ ( bNF_re1407854171455731685t_char
% 9.25/5.28                    @ ( bNF_eq_onp_list_char
% 9.25/5.28                      @ ^ [Cs: list_char] :
% 9.25/5.28                        ! [X3: char] :
% 9.25/5.28                          ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28                         => ~ ( digit7 @ X3 ) ) )
% 9.25/5.28                    @ ( bNF_eq_onp_list_char
% 9.25/5.28                      @ ^ [Cs: list_char] :
% 9.25/5.28                        ! [X3: char] :
% 9.25/5.28                          ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28                         => ~ ( digit7 @ X3 ) ) ) ) ) ) ) ) ) )
% 9.25/5.28      @ ^ [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o] : ( cons_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ $false ) )
% 9.25/5.28      @ ^ [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o] : ( cons_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ $false ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9572_literal_Oexplode,axiom,
% 9.25/5.28      ! [X: literal] :
% 9.25/5.28        ( member_list_char @ ( explode @ X )
% 9.25/5.28        @ ( collect_list_char
% 9.25/5.28          @ ^ [Cs: list_char] :
% 9.25/5.28            ! [X3: char] :
% 9.25/5.28              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28             => ~ ( digit7 @ X3 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9573_literal_Oexplode__cases,axiom,
% 9.25/5.28      ! [Y: list_char] :
% 9.25/5.28        ( ( member_list_char @ Y
% 9.25/5.28          @ ( collect_list_char
% 9.25/5.28            @ ^ [Cs: list_char] :
% 9.25/5.28              ! [X3: char] :
% 9.25/5.28                ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28               => ~ ( digit7 @ X3 ) ) ) )
% 9.25/5.28       => ~ ! [X2: literal] :
% 9.25/5.28              ( Y
% 9.25/5.28             != ( explode @ X2 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9574_literal_Oexplode__induct,axiom,
% 9.25/5.28      ! [Y: list_char,P: list_char > $o] :
% 9.25/5.28        ( ( member_list_char @ Y
% 9.25/5.28          @ ( collect_list_char
% 9.25/5.28            @ ^ [Cs: list_char] :
% 9.25/5.28              ! [X3: char] :
% 9.25/5.28                ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28               => ~ ( digit7 @ X3 ) ) ) )
% 9.25/5.28       => ( ! [X2: literal] : ( P @ ( explode @ X2 ) )
% 9.25/5.28         => ( P @ Y ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9575_zero__literal_Orsp,axiom,
% 9.25/5.28      ( bNF_eq_onp_list_char
% 9.25/5.28      @ ^ [Cs: list_char] :
% 9.25/5.28        ! [X3: char] :
% 9.25/5.28          ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28         => ~ ( digit7 @ X3 ) )
% 9.25/5.28      @ nil_char
% 9.25/5.28      @ nil_char ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9576_literal_Odomain__eq,axiom,
% 9.25/5.28      ( ( domain7888411570377768909iteral @ pcr_literal )
% 9.25/5.28      = ( ^ [Cs: list_char] :
% 9.25/5.28          ! [X3: char] :
% 9.25/5.28            ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28           => ~ ( digit7 @ X3 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9577_literal_Odomain,axiom,
% 9.25/5.28      ( ( domain7888411570377768909iteral @ pcr_literal )
% 9.25/5.28      = ( ^ [X3: list_char] :
% 9.25/5.28          ? [Y3: list_char] :
% 9.25/5.28            ( ( list_all2_char_char
% 9.25/5.28              @ ^ [Y4: char,Z4: char] : ( Y4 = Z4 )
% 9.25/5.28              @ X3
% 9.25/5.28              @ Y3 )
% 9.25/5.28            & ! [Z3: char] :
% 9.25/5.28                ( ( member_char @ Z3 @ ( set_char2 @ Y3 ) )
% 9.25/5.28               => ~ ( digit7 @ Z3 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9578_less__eq__literal_Orsp,axiom,
% 9.25/5.28      ( bNF_re7775871201573978401char_o
% 9.25/5.28      @ ( bNF_eq_onp_list_char
% 9.25/5.28        @ ^ [Cs: list_char] :
% 9.25/5.28          ! [X3: char] :
% 9.25/5.28            ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28           => ~ ( digit7 @ X3 ) ) )
% 9.25/5.28      @ ( bNF_re6668474094832959905ar_o_o
% 9.25/5.28        @ ( bNF_eq_onp_list_char
% 9.25/5.28          @ ^ [Cs: list_char] :
% 9.25/5.28            ! [X3: char] :
% 9.25/5.28              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28             => ~ ( digit7 @ X3 ) ) )
% 9.25/5.28        @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 ) )
% 9.25/5.28      @ ( lexordp_eq_char
% 9.25/5.28        @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) ) )
% 9.25/5.28      @ ( lexordp_eq_char
% 9.25/5.28        @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9579_less__eq__literal_Oabs__eq,axiom,
% 9.25/5.28      ! [Xa: list_char,X: list_char] :
% 9.25/5.28        ( ( bNF_eq_onp_list_char
% 9.25/5.28          @ ^ [Cs: list_char] :
% 9.25/5.28            ! [X3: char] :
% 9.25/5.28              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28             => ~ ( digit7 @ X3 ) )
% 9.25/5.28          @ Xa
% 9.25/5.28          @ Xa )
% 9.25/5.28       => ( ( bNF_eq_onp_list_char
% 9.25/5.28            @ ^ [Cs: list_char] :
% 9.25/5.28              ! [X3: char] :
% 9.25/5.28                ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28               => ~ ( digit7 @ X3 ) )
% 9.25/5.28            @ X
% 9.25/5.28            @ X )
% 9.25/5.28         => ( ( ord_less_eq_literal @ ( abs_literal @ Xa ) @ ( abs_literal @ X ) )
% 9.25/5.28            = ( lexordp_eq_char
% 9.25/5.28              @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) )
% 9.25/5.28              @ Xa
% 9.25/5.28              @ X ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9580_less__literal_Oabs__eq,axiom,
% 9.25/5.28      ! [Xa: list_char,X: list_char] :
% 9.25/5.28        ( ( bNF_eq_onp_list_char
% 9.25/5.28          @ ^ [Cs: list_char] :
% 9.25/5.28            ! [X3: char] :
% 9.25/5.28              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28             => ~ ( digit7 @ X3 ) )
% 9.25/5.28          @ Xa
% 9.25/5.28          @ Xa )
% 9.25/5.28       => ( ( bNF_eq_onp_list_char
% 9.25/5.28            @ ^ [Cs: list_char] :
% 9.25/5.28              ! [X3: char] :
% 9.25/5.28                ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28               => ~ ( digit7 @ X3 ) )
% 9.25/5.28            @ X
% 9.25/5.28            @ X )
% 9.25/5.28         => ( ( ord_less_literal @ ( abs_literal @ Xa ) @ ( abs_literal @ X ) )
% 9.25/5.28            = ( lexordp_char
% 9.25/5.28              @ ^ [C4: char,D4: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C4 ) @ ( comm_s629917340098488124ar_nat @ D4 ) )
% 9.25/5.28              @ Xa
% 9.25/5.28              @ X ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9581_literal_OAbs__literal__cases,axiom,
% 9.25/5.28      ! [X: literal] :
% 9.25/5.28        ~ ! [Y2: list_char] :
% 9.25/5.28            ( ( X
% 9.25/5.28              = ( abs_literal @ Y2 ) )
% 9.25/5.28           => ~ ( member_list_char @ Y2
% 9.25/5.28                @ ( collect_list_char
% 9.25/5.28                  @ ^ [Cs: list_char] :
% 9.25/5.28                    ! [X3: char] :
% 9.25/5.28                      ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28                     => ~ ( digit7 @ X3 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9582_literal_OAbs__literal__induct,axiom,
% 9.25/5.28      ! [P: literal > $o,X: literal] :
% 9.25/5.28        ( ! [Y2: list_char] :
% 9.25/5.28            ( ( member_list_char @ Y2
% 9.25/5.28              @ ( collect_list_char
% 9.25/5.28                @ ^ [Cs: list_char] :
% 9.25/5.28                  ! [X3: char] :
% 9.25/5.28                    ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28                   => ~ ( digit7 @ X3 ) ) ) )
% 9.25/5.28           => ( P @ ( abs_literal @ Y2 ) ) )
% 9.25/5.28       => ( P @ X ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9583_literal_OAbs__literal__inject,axiom,
% 9.25/5.28      ! [X: list_char,Y: list_char] :
% 9.25/5.28        ( ( member_list_char @ X
% 9.25/5.28          @ ( collect_list_char
% 9.25/5.28            @ ^ [Cs: list_char] :
% 9.25/5.28              ! [X3: char] :
% 9.25/5.28                ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28               => ~ ( digit7 @ X3 ) ) ) )
% 9.25/5.28       => ( ( member_list_char @ Y
% 9.25/5.28            @ ( collect_list_char
% 9.25/5.28              @ ^ [Cs: list_char] :
% 9.25/5.28                ! [X3: char] :
% 9.25/5.28                  ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28                 => ~ ( digit7 @ X3 ) ) ) )
% 9.25/5.28         => ( ( ( abs_literal @ X )
% 9.25/5.28              = ( abs_literal @ Y ) )
% 9.25/5.28            = ( X = Y ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9584_literal_Otype__definition__literal,axiom,
% 9.25/5.28      ( type_d4752411451802217481t_char @ explode @ abs_literal
% 9.25/5.28      @ ( collect_list_char
% 9.25/5.28        @ ^ [Cs: list_char] :
% 9.25/5.28          ! [X3: char] :
% 9.25/5.28            ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28           => ~ ( digit7 @ X3 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9585_literal_OAbs__literal__inverse,axiom,
% 9.25/5.28      ! [Y: list_char] :
% 9.25/5.28        ( ( member_list_char @ Y
% 9.25/5.28          @ ( collect_list_char
% 9.25/5.28            @ ^ [Cs: list_char] :
% 9.25/5.28              ! [X3: char] :
% 9.25/5.28                ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28               => ~ ( digit7 @ X3 ) ) ) )
% 9.25/5.28       => ( ( explode @ ( abs_literal @ Y ) )
% 9.25/5.28          = Y ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9586_plus__literal_Oabs__eq,axiom,
% 9.25/5.28      ! [Xa: list_char,X: list_char] :
% 9.25/5.28        ( ( bNF_eq_onp_list_char
% 9.25/5.28          @ ^ [Cs: list_char] :
% 9.25/5.28            ! [X3: char] :
% 9.25/5.28              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28             => ~ ( digit7 @ X3 ) )
% 9.25/5.28          @ Xa
% 9.25/5.28          @ Xa )
% 9.25/5.28       => ( ( bNF_eq_onp_list_char
% 9.25/5.28            @ ^ [Cs: list_char] :
% 9.25/5.28              ! [X3: char] :
% 9.25/5.28                ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28               => ~ ( digit7 @ X3 ) )
% 9.25/5.28            @ X
% 9.25/5.28            @ X )
% 9.25/5.28         => ( ( plus_plus_literal @ ( abs_literal @ Xa ) @ ( abs_literal @ X ) )
% 9.25/5.28            = ( abs_literal @ ( append_char @ Xa @ X ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9587_String_OQuotient__literal,axiom,
% 9.25/5.28      ( quotie6109894551476798619iteral
% 9.25/5.28      @ ( bNF_eq_onp_list_char
% 9.25/5.28        @ ^ [Cs: list_char] :
% 9.25/5.28          ! [X3: char] :
% 9.25/5.28            ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28           => ~ ( digit7 @ X3 ) ) )
% 9.25/5.28      @ abs_literal
% 9.25/5.28      @ explode
% 9.25/5.28      @ cr_literal ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9588_asciis__of__literal_Oabs__eq,axiom,
% 9.25/5.28      ! [X: list_char] :
% 9.25/5.28        ( ( bNF_eq_onp_list_char
% 9.25/5.28          @ ^ [Cs: list_char] :
% 9.25/5.28            ! [X3: char] :
% 9.25/5.28              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28             => ~ ( digit7 @ X3 ) )
% 9.25/5.28          @ X
% 9.25/5.28          @ X )
% 9.25/5.28       => ( ( asciis_of_literal @ ( abs_literal @ X ) )
% 9.25/5.28          = ( map_ch5843194146513361140nteger @ comm_s4049598766089966537nteger @ X ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9589_size__literal_Oabs__eq,axiom,
% 9.25/5.28      ! [X: list_char] :
% 9.25/5.28        ( ( bNF_eq_onp_list_char
% 9.25/5.28          @ ^ [Cs: list_char] :
% 9.25/5.28            ! [X3: char] :
% 9.25/5.28              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28             => ~ ( digit7 @ X3 ) )
% 9.25/5.28          @ X
% 9.25/5.28          @ X )
% 9.25/5.28       => ( ( size_size_literal @ ( abs_literal @ X ) )
% 9.25/5.28          = ( size_size_list_char @ X ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9590_literal_Odomain__par__left__total,axiom,
% 9.25/5.28      ! [P7: list_char > $o] :
% 9.25/5.28        ( ( left_t8440299596084406506t_char
% 9.25/5.28          @ ( list_all2_char_char
% 9.25/5.28            @ ^ [Y4: char,Z4: char] : ( Y4 = Z4 ) ) )
% 9.25/5.28       => ( ( bNF_re6668474094832959905ar_o_o
% 9.25/5.28            @ ( list_all2_char_char
% 9.25/5.28              @ ^ [Y4: char,Z4: char] : ( Y4 = Z4 ) )
% 9.25/5.28            @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 9.25/5.28            @ P7
% 9.25/5.28            @ ^ [Cs: list_char] :
% 9.25/5.28              ! [X3: char] :
% 9.25/5.28                ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28               => ~ ( digit7 @ X3 ) ) )
% 9.25/5.28         => ( ( domain7888411570377768909iteral @ pcr_literal )
% 9.25/5.28            = P7 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9591_literal_Odomain__par,axiom,
% 9.25/5.28      ! [DR: char > $o,P22: list_char > $o] :
% 9.25/5.28        ( ( ( domainp_char_char
% 9.25/5.28            @ ^ [Y4: char,Z4: char] : ( Y4 = Z4 ) )
% 9.25/5.28          = DR )
% 9.25/5.28       => ( ( bNF_re6668474094832959905ar_o_o
% 9.25/5.28            @ ( list_all2_char_char
% 9.25/5.28              @ ^ [Y4: char,Z4: char] : ( Y4 = Z4 ) )
% 9.25/5.28            @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 9.25/5.28            @ P22
% 9.25/5.28            @ ^ [Cs: list_char] :
% 9.25/5.28              ! [X3: char] :
% 9.25/5.28                ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28               => ~ ( digit7 @ X3 ) ) )
% 9.25/5.28         => ( ( domain7888411570377768909iteral @ pcr_literal )
% 9.25/5.28            = ( inf_inf_list_char_o @ ( list_all_char @ DR ) @ P22 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9592_implode_Orsp,axiom,
% 9.25/5.28      ( bNF_re1407854171455731685t_char
% 9.25/5.28      @ ^ [Y4: list_char,Z4: list_char] : ( Y4 = Z4 )
% 9.25/5.28      @ ( bNF_eq_onp_list_char
% 9.25/5.28        @ ^ [Cs: list_char] :
% 9.25/5.28          ! [X3: char] :
% 9.25/5.28            ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28           => ~ ( digit7 @ X3 ) ) )
% 9.25/5.28      @ ( map_char_char @ ascii_of )
% 9.25/5.28      @ ( map_char_char @ ascii_of ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9593_literal__of__asciis_Orsp,axiom,
% 9.25/5.28      ( bNF_re5828396963709814525t_char
% 9.25/5.28      @ ^ [Y4: list_Code_integer,Z4: list_Code_integer] : ( Y4 = Z4 )
% 9.25/5.28      @ ( bNF_eq_onp_list_char
% 9.25/5.28        @ ^ [Cs: list_char] :
% 9.25/5.28          ! [X3: char] :
% 9.25/5.28            ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28           => ~ ( digit7 @ X3 ) ) )
% 9.25/5.28      @ ( map_Co843364623960961780r_char @ ( comp_c4562247934908617188nteger @ ascii_of @ unique1708501630192214702nteger ) )
% 9.25/5.28      @ ( map_Co843364623960961780r_char @ ( comp_c4562247934908617188nteger @ ascii_of @ unique1708501630192214702nteger ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9594_Literal_Oabs__eq,axiom,
% 9.25/5.28      ! [X: list_char,Xg: $o,Xf: $o,Xe: $o,Xd: $o,Xc: $o,Xb: $o,Xa: $o] :
% 9.25/5.28        ( ( bNF_eq_onp_list_char
% 9.25/5.28          @ ^ [Cs: list_char] :
% 9.25/5.28            ! [X3: char] :
% 9.25/5.28              ( ( member_char @ X3 @ ( set_char2 @ Cs ) )
% 9.25/5.28             => ~ ( digit7 @ X3 ) )
% 9.25/5.28          @ X
% 9.25/5.28          @ X )
% 9.25/5.28       => ( ( literal2 @ Xg @ Xf @ Xe @ Xd @ Xc @ Xb @ Xa @ ( abs_literal @ X ) )
% 9.25/5.28          = ( abs_literal @ ( cons_char @ ( char2 @ Xg @ Xf @ Xe @ Xd @ Xc @ Xb @ Xa @ $false ) @ X ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9595_String_OLiteral__def,axiom,
% 9.25/5.28      ( literal2
% 9.25/5.28      = ( map_fu1104370778922912482iteral @ id_o @ ( map_fu7309004089335677210iteral @ id_o @ ( map_fu1929762555066093878iteral @ id_o @ ( map_fu5333924603067766298iteral @ id_o @ ( map_fu1888220742600445322iteral @ id_o @ ( map_fu5700776415251466522iteral @ id_o @ ( map_fu4627020735845646302iteral @ id_o @ ( map_fu7398138089906338514iteral @ explode @ abs_literal ) ) ) ) ) ) )
% 9.25/5.28        @ ^ [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o] : ( cons_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ $false ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9596_Literal_Otransfer,axiom,
% 9.25/5.28      ( bNF_re8691941649098027561iteral
% 9.25/5.28      @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 9.25/5.28      @ ( bNF_re5719858693005739489iteral
% 9.25/5.28        @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 9.25/5.28        @ ( bNF_re136309367175754621iteral
% 9.25/5.28          @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 9.25/5.28          @ ( bNF_re2365650225897248225iteral
% 9.25/5.28            @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 9.25/5.28            @ ( bNF_re5778109699181701841iteral
% 9.25/5.28              @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 9.25/5.28              @ ( bNF_re1595102025518187489iteral
% 9.25/5.28                @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 9.25/5.28                @ ( bNF_re6148748351543924773iteral
% 9.25/5.28                  @ ^ [Y4: $o,Z4: $o] : ( Y4 = Z4 )
% 9.25/5.28                  @ ( bNF_re5453467372598631581iteral @ pcr_literal @ pcr_literal ) ) ) ) ) ) )
% 9.25/5.28      @ ^ [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o] : ( cons_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ $false ) )
% 9.25/5.28      @ literal2 ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9597_cr__integer__def,axiom,
% 9.25/5.28      ( code_cr_integer
% 9.25/5.28      = ( ^ [X3: int,Y3: code_integer] :
% 9.25/5.28            ( X3
% 9.25/5.28            = ( code_int_of_integer @ Y3 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9598_int__encode__def,axiom,
% 9.25/5.28      ( nat_int_encode
% 9.25/5.28      = ( ^ [I3: int] : ( nat_sum_encode @ ( if_Sum_sum_nat_nat @ ( ord_less_eq_int @ zero_zero_int @ I3 ) @ ( sum_Inl_nat_nat @ ( nat2 @ I3 ) ) @ ( sum_Inr_nat_nat @ ( nat2 @ ( minus_minus_int @ ( uminus_uminus_int @ I3 ) @ one_one_int ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9599_surj__sum__encode,axiom,
% 9.25/5.28      ( ( image_1320371278474632150at_nat @ nat_sum_encode @ top_to6661820994512907621at_nat )
% 9.25/5.28      = top_top_set_nat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9600_bij__sum__encode,axiom,
% 9.25/5.28      bij_be5432664580149595207at_nat @ nat_sum_encode @ top_to6661820994512907621at_nat @ top_top_set_nat ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9601_sum__encode__def,axiom,
% 9.25/5.28      ( nat_sum_encode
% 9.25/5.28      = ( sum_ca6763686470577984908at_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 9.25/5.28        @ ^ [B3: nat] : ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9602_surj__sum__decode,axiom,
% 9.25/5.28      ( ( image_678696785212003926at_nat @ nat_sum_decode @ top_top_set_nat )
% 9.25/5.28      = top_to6661820994512907621at_nat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9603_bij__sum__decode,axiom,
% 9.25/5.28      bij_be4790990086886966983at_nat @ nat_sum_decode @ top_top_set_nat @ top_to6661820994512907621at_nat ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9604_nth__item_Opinduct,axiom,
% 9.25/5.28      ! [A0: nat,P: nat > $o] :
% 9.25/5.28        ( ( accp_nat @ nth_item_rel @ A0 )
% 9.25/5.28       => ( ( ( accp_nat @ nth_item_rel @ zero_zero_nat )
% 9.25/5.28           => ( P @ zero_zero_nat ) )
% 9.25/5.28         => ( ! [N3: nat] :
% 9.25/5.28                ( ( accp_nat @ nth_item_rel @ ( suc @ N3 ) )
% 9.25/5.28               => ( ! [A9: nat,Aa: nat] :
% 9.25/5.28                      ( ( ( nat_sum_decode @ N3 )
% 9.25/5.28                        = ( sum_Inl_nat_nat @ A9 ) )
% 9.25/5.28                     => ( ( ( nat_sum_decode @ A9 )
% 9.25/5.28                          = ( sum_Inl_nat_nat @ Aa ) )
% 9.25/5.28                       => ( P @ Aa ) ) )
% 9.25/5.28                 => ( ! [A9: nat,B10: nat] :
% 9.25/5.28                        ( ( ( nat_sum_decode @ N3 )
% 9.25/5.28                          = ( sum_Inl_nat_nat @ A9 ) )
% 9.25/5.28                       => ( ( ( nat_sum_decode @ A9 )
% 9.25/5.28                            = ( sum_Inr_nat_nat @ B10 ) )
% 9.25/5.28                         => ( P @ B10 ) ) )
% 9.25/5.28                   => ( ! [B10: nat,Ba: nat,X5: nat,Y5: nat] :
% 9.25/5.28                          ( ( ( nat_sum_decode @ N3 )
% 9.25/5.28                            = ( sum_Inr_nat_nat @ B10 ) )
% 9.25/5.28                         => ( ( ( nat_sum_decode @ B10 )
% 9.25/5.28                              = ( sum_Inr_nat_nat @ Ba ) )
% 9.25/5.28                           => ( ( ( product_Pair_nat_nat @ X5 @ Y5 )
% 9.25/5.28                                = ( nat_prod_decode @ Ba ) )
% 9.25/5.28                             => ( P @ X5 ) ) ) )
% 9.25/5.28                     => ( ! [B10: nat,Ba: nat,X5: nat,Y5: nat] :
% 9.25/5.28                            ( ( ( nat_sum_decode @ N3 )
% 9.25/5.28                              = ( sum_Inr_nat_nat @ B10 ) )
% 9.25/5.28                           => ( ( ( nat_sum_decode @ B10 )
% 9.25/5.28                                = ( sum_Inr_nat_nat @ Ba ) )
% 9.25/5.28                             => ( ( ( product_Pair_nat_nat @ X5 @ Y5 )
% 9.25/5.28                                  = ( nat_prod_decode @ Ba ) )
% 9.25/5.28                               => ( P @ Y5 ) ) ) )
% 9.25/5.28                       => ( P @ ( suc @ N3 ) ) ) ) ) ) )
% 9.25/5.28           => ( P @ A0 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9605_int__decode__def,axiom,
% 9.25/5.28      ( nat_int_decode
% 9.25/5.28      = ( ^ [N2: nat] :
% 9.25/5.28            ( sum_ca7763040182479039464nt_nat @ semiri1314217659103216013at_int
% 9.25/5.28            @ ^ [B3: nat] : ( minus_minus_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ B3 ) ) @ one_one_int )
% 9.25/5.28            @ ( nat_sum_decode @ N2 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9606_sup__unit__def,axiom,
% 9.25/5.28      ( sup_sup_Product_unit
% 9.25/5.28      = ( ^ [Uu2: product_unit,Uv2: product_unit] : product_Unity ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9607_cone__def,axiom,
% 9.25/5.28      ( bNF_Cardinal_cone
% 9.25/5.28      = ( bNF_Ca7083678892733797993t_unit @ ( insert_Product_unit @ product_Unity @ bot_bo3957492148770167129t_unit ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9608_bot__unit__def,axiom,
% 9.25/5.28      bot_bot_Product_unit = product_Unity ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9609_uminus__unit__def,axiom,
% 9.25/5.28      ( uminus2952777764628376836t_unit
% 9.25/5.28      = ( ^ [Uu2: product_unit] : product_Unity ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9610_inf__unit__def,axiom,
% 9.25/5.28      ( inf_inf_Product_unit
% 9.25/5.28      = ( ^ [Uu2: product_unit,Uv2: product_unit] : product_Unity ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9611_top__unit__def,axiom,
% 9.25/5.28      top_top_Product_unit = product_Unity ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9612_UNIV__unit,axiom,
% 9.25/5.28      ( top_to1996260823553986621t_unit
% 9.25/5.28      = ( insert_Product_unit @ product_Unity @ bot_bo3957492148770167129t_unit ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9613_natural__zero__minus__one,axiom,
% 9.25/5.28      ( ( minus_7197305767214868737atural @ zero_z2226904508553997617atural @ one_one_Code_natural )
% 9.25/5.28      = zero_z2226904508553997617atural ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9614_log_Oelims,axiom,
% 9.25/5.28      ! [X: code_natural,Xa: code_natural,Y: code_natural] :
% 9.25/5.28        ( ( ( log @ X @ Xa )
% 9.25/5.28          = Y )
% 9.25/5.28       => ( ( ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 9.25/5.28              | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 9.25/5.28           => ( Y = one_one_Code_natural ) )
% 9.25/5.28          & ( ~ ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 9.25/5.28                | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 9.25/5.28           => ( Y
% 9.25/5.28              = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ X @ ( divide5121882707175180666atural @ Xa @ X ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9615_log_Osimps,axiom,
% 9.25/5.28      ( log
% 9.25/5.28      = ( ^ [B3: code_natural,I3: code_natural] :
% 9.25/5.28            ( if_Code_natural
% 9.25/5.28            @ ( ( ord_le1926595141338095240atural @ B3 @ one_one_Code_natural )
% 9.25/5.28              | ( ord_le5570908160329646204atural @ I3 @ B3 ) )
% 9.25/5.28            @ one_one_Code_natural
% 9.25/5.28            @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ B3 @ ( divide5121882707175180666atural @ I3 @ B3 ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9616_Random_Orange__def,axiom,
% 9.25/5.28      ( range
% 9.25/5.28      = ( ^ [K4: code_natural] :
% 9.25/5.28            ( produc5538323210962509403atural
% 9.25/5.28            @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ K4 )
% 9.25/5.28              @ ^ [L2: code_natural] :
% 9.25/5.28                  ( produc5538323210962509403atural @ next
% 9.25/5.28                  @ ^ [V2: code_natural] : ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ V2 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 9.25/5.28              @ one_one_Code_natural )
% 9.25/5.28            @ ^ [V2: code_natural] : ( produc6639722614265839536atural @ ( modulo8411746178871703098atural @ V2 @ K4 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9617_next_Osimps,axiom,
% 9.25/5.28      ! [V: code_natural,W: code_natural] :
% 9.25/5.28        ( ( next @ ( produc3574140220909816553atural @ V @ W ) )
% 9.25/5.28        = ( 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 @ W @ ( 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 @ W @ ( 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 @ W @ ( 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 @ W @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9618_log_Ocases,axiom,
% 9.25/5.28      ! [X: produc7822875418678951345atural] :
% 9.25/5.28        ~ ! [B6: code_natural,I2: code_natural] :
% 9.25/5.28            ( X
% 9.25/5.28           != ( produc3574140220909816553atural @ B6 @ I2 ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9619_full__exhaustive__natural_H_Ocases,axiom,
% 9.25/5.28      ! [X: produc989692990947075319atural] :
% 9.25/5.28        ~ ! [F3: produc4972180933644002618e_term > option6357759511663192854e_term,D: code_natural,I2: code_natural] :
% 9.25/5.28            ( X
% 9.25/5.28           != ( produc3831813291587773865atural @ F3 @ ( produc3574140220909816553atural @ D @ I2 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9620_exhaustive__natural_H_Ocases,axiom,
% 9.25/5.28      ! [X: produc8731074985263844745atural] :
% 9.25/5.28        ~ ! [F3: code_natural > option6357759511663192854e_term,D: code_natural,I2: code_natural] :
% 9.25/5.28            ( X
% 9.25/5.28           != ( produc2252593628808123835atural @ F3 @ ( produc3574140220909816553atural @ D @ I2 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9621_split__seed__def,axiom,
% 9.25/5.28      ( split_seed
% 9.25/5.28      = ( ^ [S2: produc7822875418678951345atural] :
% 9.25/5.28            ( produc8282080750456430313atural
% 9.25/5.28            @ ^ [V2: code_natural,W3: code_natural] :
% 9.25/5.28                ( produc8282080750456430313atural
% 9.25/5.28                @ ^ [V3: 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ V2 ) @ W4 ) @ ( produc3574140220909816553atural @ V3 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ W3 ) ) )
% 9.25/5.28                @ ( produc6591912806276919810atural @ ( next @ S2 ) ) )
% 9.25/5.28            @ S2 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9622_inc__shift__def,axiom,
% 9.25/5.28      ( inc_shift
% 9.25/5.28      = ( ^ [V2: code_natural,K4: code_natural] : ( if_Code_natural @ ( V2 = K4 ) @ one_one_Code_natural @ ( plus_p4538020629002901425atural @ K4 @ one_one_Code_natural ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9623_log_Opelims,axiom,
% 9.25/5.28      ! [X: code_natural,Xa: code_natural,Y: code_natural] :
% 9.25/5.28        ( ( ( log @ X @ Xa )
% 9.25/5.28          = Y )
% 9.25/5.28       => ( ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X @ Xa ) )
% 9.25/5.28         => ~ ( ( ( ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 9.25/5.28                    | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 9.25/5.28                 => ( Y = one_one_Code_natural ) )
% 9.25/5.28                & ( ~ ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 9.25/5.28                      | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 9.25/5.28                 => ( Y
% 9.25/5.28                    = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ X @ ( divide5121882707175180666atural @ Xa @ X ) ) ) ) ) )
% 9.25/5.28             => ~ ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X @ Xa ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9624_one__natural__def,axiom,
% 9.25/5.28      ( one_one_Code_natural
% 9.25/5.28      = ( code_natural_of_nat @ one_one_nat ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9625_natural__of__nat__cases,axiom,
% 9.25/5.28      ! [X: code_natural] :
% 9.25/5.28        ~ ! [Y2: nat] :
% 9.25/5.28            ( ( X
% 9.25/5.28              = ( code_natural_of_nat @ Y2 ) )
% 9.25/5.28           => ~ ( member_nat @ Y2 @ top_top_set_nat ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9626_natural__of__nat__induct,axiom,
% 9.25/5.28      ! [P: code_natural > $o,X: code_natural] :
% 9.25/5.28        ( ! [Y2: nat] :
% 9.25/5.28            ( ( member_nat @ Y2 @ top_top_set_nat )
% 9.25/5.28           => ( P @ ( code_natural_of_nat @ Y2 ) ) )
% 9.25/5.28       => ( P @ X ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9627_natural__of__nat__inject,axiom,
% 9.25/5.28      ! [X: nat,Y: nat] :
% 9.25/5.28        ( ( member_nat @ X @ top_top_set_nat )
% 9.25/5.28       => ( ( member_nat @ Y @ top_top_set_nat )
% 9.25/5.28         => ( ( ( code_natural_of_nat @ X )
% 9.25/5.28              = ( code_natural_of_nat @ Y ) )
% 9.25/5.28            = ( X = Y ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9628_one__natural_Orep__eq,axiom,
% 9.25/5.28      ( ( code_nat_of_natural @ one_one_Code_natural )
% 9.25/5.28      = one_one_nat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9629_type__definition__natural,axiom,
% 9.25/5.28      type_d4410041424927559462al_nat @ code_nat_of_natural @ code_natural_of_nat @ top_top_set_nat ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9630_natural__of__nat__inverse,axiom,
% 9.25/5.28      ! [Y: nat] :
% 9.25/5.28        ( ( member_nat @ Y @ top_top_set_nat )
% 9.25/5.28       => ( ( code_nat_of_natural @ ( code_natural_of_nat @ Y ) )
% 9.25/5.28          = Y ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9631_nat__of__natural__induct,axiom,
% 9.25/5.28      ! [Y: nat,P: nat > $o] :
% 9.25/5.28        ( ( member_nat @ Y @ top_top_set_nat )
% 9.25/5.28       => ( ! [X2: code_natural] : ( P @ ( code_nat_of_natural @ X2 ) )
% 9.25/5.28         => ( P @ Y ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9632_nat__of__natural__cases,axiom,
% 9.25/5.28      ! [Y: nat] :
% 9.25/5.28        ( ( member_nat @ Y @ top_top_set_nat )
% 9.25/5.28       => ~ ! [X2: code_natural] :
% 9.25/5.28              ( Y
% 9.25/5.28             != ( code_nat_of_natural @ X2 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9633_nat__of__natural,axiom,
% 9.25/5.28      ! [X: code_natural] : ( member_nat @ ( code_nat_of_natural @ X ) @ top_top_set_nat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9634_cr__natural__def,axiom,
% 9.25/5.28      ( code_cr_natural
% 9.25/5.28      = ( ^ [X3: nat,Y3: code_natural] :
% 9.25/5.28            ( X3
% 9.25/5.28            = ( code_nat_of_natural @ Y3 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9635_INFM__nat,axiom,
% 9.25/5.28      ! [P: nat > $o] :
% 9.25/5.28        ( ( frequently_nat @ P @ cofinite_nat )
% 9.25/5.28        = ( ! [M2: nat] :
% 9.25/5.28            ? [N2: nat] :
% 9.25/5.28              ( ( ord_less_nat @ M2 @ N2 )
% 9.25/5.28              & ( P @ N2 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9636_INFM__nat__le,axiom,
% 9.25/5.28      ! [P: nat > $o] :
% 9.25/5.28        ( ( frequently_nat @ P @ cofinite_nat )
% 9.25/5.28        = ( ! [M2: nat] :
% 9.25/5.28            ? [N2: nat] :
% 9.25/5.28              ( ( ord_less_eq_nat @ M2 @ N2 )
% 9.25/5.28              & ( P @ N2 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9637_INFM__nat__inductI,axiom,
% 9.25/5.28      ! [P: nat > $o,Q2: nat > $o] :
% 9.25/5.28        ( ( P @ zero_zero_nat )
% 9.25/5.28       => ( ! [I2: nat] :
% 9.25/5.28              ( ( P @ I2 )
% 9.25/5.28             => ? [J4: nat] :
% 9.25/5.28                  ( ( ord_less_nat @ I2 @ J4 )
% 9.25/5.28                  & ( P @ J4 )
% 9.25/5.28                  & ( Q2 @ J4 ) ) )
% 9.25/5.28         => ( frequently_nat @ Q2 @ cofinite_nat ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9638_integer__of__nat__1,axiom,
% 9.25/5.28      ( ( code_integer_of_nat @ one_one_nat )
% 9.25/5.28      = one_one_Code_integer ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9639_Lcm__abs__eq,axiom,
% 9.25/5.28      ! [K5: set_int] :
% 9.25/5.28        ( ( gcd_Lcm_int @ ( image_int_int @ abs_abs_int @ K5 ) )
% 9.25/5.28        = ( gcd_Lcm_int @ K5 ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9640_Lcm__int__eq,axiom,
% 9.25/5.28      ! [N4: set_nat] :
% 9.25/5.28        ( ( gcd_Lcm_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N4 ) )
% 9.25/5.28        = ( semiri1314217659103216013at_int @ ( gcd_Lcm_nat @ N4 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9641_Lcm__nat__abs__eq,axiom,
% 9.25/5.28      ! [K5: set_int] :
% 9.25/5.28        ( ( gcd_Lcm_nat
% 9.25/5.28          @ ( image_int_nat
% 9.25/5.28            @ ^ [K4: int] : ( nat2 @ ( abs_abs_int @ K4 ) )
% 9.25/5.28            @ K5 ) )
% 9.25/5.28        = ( nat2 @ ( gcd_Lcm_int @ K5 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9642_Lcm__nat__empty,axiom,
% 9.25/5.28      ( ( gcd_Lcm_nat @ bot_bot_set_nat )
% 9.25/5.28      = one_one_nat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9643_Gcd__nat__def,axiom,
% 9.25/5.28      ( gcd_Gcd_nat
% 9.25/5.28      = ( ^ [M7: set_nat] :
% 9.25/5.28            ( gcd_Lcm_nat
% 9.25/5.28            @ ( collect_nat
% 9.25/5.28              @ ^ [D4: nat] :
% 9.25/5.28                ! [X3: nat] :
% 9.25/5.28                  ( ( member_nat @ X3 @ M7 )
% 9.25/5.28                 => ( dvd_dvd_nat @ D4 @ X3 ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9644_Lcm__int__def,axiom,
% 9.25/5.28      ( gcd_Lcm_int
% 9.25/5.28      = ( ^ [K6: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Lcm_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K6 ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9645_Lcm__eq__Max__nat,axiom,
% 9.25/5.28      ! [M4: set_nat] :
% 9.25/5.28        ( ( finite_finite_nat @ M4 )
% 9.25/5.28       => ( ( M4 != bot_bot_set_nat )
% 9.25/5.28         => ( ~ ( member_nat @ zero_zero_nat @ M4 )
% 9.25/5.28           => ( ! [M3: nat,N3: nat] :
% 9.25/5.28                  ( ( member_nat @ M3 @ M4 )
% 9.25/5.28                 => ( ( member_nat @ N3 @ M4 )
% 9.25/5.28                   => ( member_nat @ ( gcd_lcm_nat @ M3 @ N3 ) @ M4 ) ) )
% 9.25/5.28             => ( ( gcd_Lcm_nat @ M4 )
% 9.25/5.28                = ( lattic8265883725875713057ax_nat @ M4 ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9646_Lcm__nat__set__eq__fold,axiom,
% 9.25/5.28      ! [Xs: list_nat] :
% 9.25/5.28        ( ( gcd_Lcm_nat @ ( set_nat2 @ Xs ) )
% 9.25/5.28        = ( fold_nat_nat @ gcd_lcm_nat @ Xs @ one_one_nat ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9647_Lcm__in__lcm__closed__set__nat,axiom,
% 9.25/5.28      ! [M4: set_nat] :
% 9.25/5.28        ( ( finite_finite_nat @ M4 )
% 9.25/5.28       => ( ( M4 != bot_bot_set_nat )
% 9.25/5.28         => ( ! [M3: nat,N3: nat] :
% 9.25/5.28                ( ( member_nat @ M3 @ M4 )
% 9.25/5.28               => ( ( member_nat @ N3 @ M4 )
% 9.25/5.28                 => ( member_nat @ ( gcd_lcm_nat @ M3 @ N3 ) @ M4 ) ) )
% 9.25/5.28           => ( member_nat @ ( gcd_Lcm_nat @ M4 ) @ M4 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9648_Lcm__nat__def,axiom,
% 9.25/5.28      ( gcd_Lcm_nat
% 9.25/5.28      = ( ^ [M7: set_nat] : ( if_nat @ ( finite_finite_nat @ M7 ) @ ( lattic7826324295020591184_F_nat @ gcd_lcm_nat @ one_one_nat @ M7 ) @ zero_zero_nat ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9649_lcm__1__iff__int,axiom,
% 9.25/5.28      ! [M: int,N: int] :
% 9.25/5.28        ( ( ( gcd_lcm_int @ M @ N )
% 9.25/5.28          = one_one_int )
% 9.25/5.28        = ( ( ( M = one_one_int )
% 9.25/5.28            | ( M
% 9.25/5.28              = ( uminus_uminus_int @ one_one_int ) ) )
% 9.25/5.28          & ( ( N = one_one_int )
% 9.25/5.28            | ( N
% 9.25/5.28              = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9650_lcm__neg1__int,axiom,
% 9.25/5.28      ! [X: int,Y: int] :
% 9.25/5.28        ( ( gcd_lcm_int @ ( uminus_uminus_int @ X ) @ Y )
% 9.25/5.28        = ( gcd_lcm_int @ X @ Y ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9651_lcm__neg2__int,axiom,
% 9.25/5.28      ! [X: int,Y: int] :
% 9.25/5.28        ( ( gcd_lcm_int @ X @ ( uminus_uminus_int @ Y ) )
% 9.25/5.28        = ( gcd_lcm_int @ X @ Y ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9652_lcm__cases__int,axiom,
% 9.25/5.28      ! [X: int,Y: int,P: int > $o] :
% 9.25/5.28        ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.25/5.28         => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 9.25/5.28           => ( P @ ( gcd_lcm_int @ X @ Y ) ) ) )
% 9.25/5.28       => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 9.25/5.28           => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 9.25/5.28             => ( P @ ( gcd_lcm_int @ X @ ( uminus_uminus_int @ Y ) ) ) ) )
% 9.25/5.28         => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 9.25/5.28             => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 9.25/5.28               => ( P @ ( gcd_lcm_int @ ( uminus_uminus_int @ X ) @ Y ) ) ) )
% 9.25/5.28           => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 9.25/5.28               => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 9.25/5.28                 => ( P @ ( gcd_lcm_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 9.25/5.28             => ( P @ ( gcd_lcm_int @ X @ Y ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9653_Lcm__int__set__eq__fold,axiom,
% 9.25/5.28      ! [Xs: list_int] :
% 9.25/5.28        ( ( gcd_Lcm_int @ ( set_int2 @ Xs ) )
% 9.25/5.28        = ( fold_int_int @ gcd_lcm_int @ Xs @ one_one_int ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9654_unit__factor__simps_I2_J,axiom,
% 9.25/5.28      ! [N: nat] :
% 9.25/5.28        ( ( unit_f2748546683901255202or_nat @ ( suc @ N ) )
% 9.25/5.28        = one_one_nat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9655_unit__factor__nat__def,axiom,
% 9.25/5.28      ( unit_f2748546683901255202or_nat
% 9.25/5.28      = ( ^ [N2: nat] : ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat @ one_one_nat ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9656_unit__pred__cases,axiom,
% 9.25/5.28      ! [P: pred_Product_unit > $o,Q2: pred_Product_unit] :
% 9.25/5.28        ( ( P @ bot_bo2717538794563056311t_unit )
% 9.25/5.28       => ( ( P @ ( single_Product_unit @ product_Unity ) )
% 9.25/5.28         => ( P @ Q2 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9657_Random__Pred_Onot__randompred__def,axiom,
% 9.25/5.28      ( random6974930770145893639ompred
% 9.25/5.28      = ( ^ [P2: produc7822875418678951345atural > produc4675096598859438275atural,S2: produc7822875418678951345atural] :
% 9.25/5.28            ( produc6665183775751917029atural
% 9.25/5.28            @ ^ [P8: pred_Product_unit,S7: produc7822875418678951345atural] : ( if_Pro3444522238938527101atural @ ( eval_Product_unit @ P8 @ product_Unity ) @ ( produc5069803637994805237atural @ bot_bo2717538794563056311t_unit @ S7 ) @ ( produc5069803637994805237atural @ ( single_Product_unit @ product_Unity ) @ S7 ) )
% 9.25/5.28            @ ( P2 @ S2 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9658_not__pred__eq,axiom,
% 9.25/5.28      ( not_pred
% 9.25/5.28      = ( ^ [P2: pred_Product_unit] : ( if_pred_Product_unit @ ( eval_Product_unit @ P2 @ product_Unity ) @ bot_bo2717538794563056311t_unit @ ( single_Product_unit @ product_Unity ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9659_if__pred__eq,axiom,
% 9.25/5.28      ( if_pred
% 9.25/5.28      = ( ^ [B3: $o] : ( if_pred_Product_unit @ B3 @ ( single_Product_unit @ product_Unity ) @ bot_bo2717538794563056311t_unit ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9660_not__predE,axiom,
% 9.25/5.28      ! [P: $o,X: product_unit] :
% 9.25/5.28        ( ( eval_Product_unit
% 9.25/5.28          @ ( not_pred
% 9.25/5.28            @ ( pred_Product_unit2
% 9.25/5.28              @ ^ [U2: product_unit] : P ) )
% 9.25/5.28          @ X )
% 9.25/5.28       => ~ P ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9661_not__predI,axiom,
% 9.25/5.28      ! [P: $o] :
% 9.25/5.28        ( ~ P
% 9.25/5.28       => ( eval_Product_unit
% 9.25/5.28          @ ( not_pred
% 9.25/5.28            @ ( pred_Product_unit2
% 9.25/5.28              @ ^ [U2: product_unit] : P ) )
% 9.25/5.28          @ product_Unity ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9662_nat__of__num__code_I3_J,axiom,
% 9.25/5.28      ! [N: num] :
% 9.25/5.28        ( ( nat_of_num @ ( bit1 @ N ) )
% 9.25/5.28        = ( suc @ ( plus_plus_nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9663_nat__of__num__code_I1_J,axiom,
% 9.25/5.28      ( ( nat_of_num @ one )
% 9.25/5.28      = one_one_nat ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9664_nat__of__num__code_I2_J,axiom,
% 9.25/5.28      ! [N: num] :
% 9.25/5.28        ( ( nat_of_num @ ( bit0 @ N ) )
% 9.25/5.28        = ( plus_plus_nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9665_Suc__natural__minus__one,axiom,
% 9.25/5.28      ! [N: code_natural] :
% 9.25/5.28        ( ( minus_7197305767214868737atural @ ( code_Suc @ N ) @ one_one_Code_natural )
% 9.25/5.28        = N ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9666_gcd__nat_Osemilattice__order__axioms,axiom,
% 9.25/5.28      ( semila1248733672344298208er_nat @ gcd_gcd_nat @ dvd_dvd_nat
% 9.25/5.28      @ ^ [M2: nat,N2: nat] :
% 9.25/5.28          ( ( dvd_dvd_nat @ M2 @ N2 )
% 9.25/5.28          & ( M2 != N2 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9667_random__aux__set_Ocases,axiom,
% 9.25/5.28      ! [X: produc7822875418678951345atural] :
% 9.25/5.28        ( ! [J2: code_natural] :
% 9.25/5.28            ( X
% 9.25/5.28           != ( produc3574140220909816553atural @ zero_z2226904508553997617atural @ J2 ) )
% 9.25/5.28       => ~ ! [I2: code_natural,J2: code_natural] :
% 9.25/5.28              ( X
% 9.25/5.28             != ( produc3574140220909816553atural @ ( code_Suc @ I2 ) @ J2 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9668_or__num_Opelims,axiom,
% 9.25/5.28      ! [X: num,Xa: num,Y: num] :
% 9.25/5.28        ( ( ( bit_un6697907153464112080or_num @ X @ Xa )
% 9.25/5.28          = Y )
% 9.25/5.28       => ( ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 9.25/5.28         => ( ( ( X = one )
% 9.25/5.28             => ( ( Xa = one )
% 9.25/5.28               => ( ( Y = one )
% 9.25/5.28                 => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 9.25/5.28           => ( ( ( X = one )
% 9.25/5.28               => ! [N3: num] :
% 9.25/5.28                    ( ( Xa
% 9.25/5.28                      = ( bit0 @ N3 ) )
% 9.25/5.28                   => ( ( Y
% 9.25/5.28                        = ( bit1 @ N3 ) )
% 9.25/5.28                     => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 9.25/5.28             => ( ( ( X = one )
% 9.25/5.28                 => ! [N3: num] :
% 9.25/5.28                      ( ( Xa
% 9.25/5.28                        = ( bit1 @ N3 ) )
% 9.25/5.28                     => ( ( Y
% 9.25/5.28                          = ( bit1 @ N3 ) )
% 9.25/5.28                       => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 9.25/5.28               => ( ! [M3: num] :
% 9.25/5.28                      ( ( X
% 9.25/5.28                        = ( bit0 @ M3 ) )
% 9.25/5.28                     => ( ( Xa = one )
% 9.25/5.28                       => ( ( Y
% 9.25/5.28                            = ( bit1 @ M3 ) )
% 9.25/5.28                         => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ one ) ) ) ) )
% 9.25/5.28                 => ( ! [M3: num] :
% 9.25/5.28                        ( ( X
% 9.25/5.28                          = ( bit0 @ M3 ) )
% 9.25/5.28                       => ! [N3: num] :
% 9.25/5.28                            ( ( Xa
% 9.25/5.28                              = ( bit0 @ N3 ) )
% 9.25/5.28                           => ( ( Y
% 9.25/5.28                                = ( bit0 @ ( bit_un6697907153464112080or_num @ M3 @ N3 ) ) )
% 9.25/5.28                             => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 9.25/5.28                   => ( ! [M3: num] :
% 9.25/5.28                          ( ( X
% 9.25/5.28                            = ( bit0 @ M3 ) )
% 9.25/5.28                         => ! [N3: num] :
% 9.25/5.28                              ( ( Xa
% 9.25/5.28                                = ( bit1 @ N3 ) )
% 9.25/5.28                             => ( ( Y
% 9.25/5.28                                  = ( bit1 @ ( bit_un6697907153464112080or_num @ M3 @ N3 ) ) )
% 9.25/5.28                               => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit0 @ M3 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 9.25/5.28                     => ( ! [M3: num] :
% 9.25/5.28                            ( ( X
% 9.25/5.28                              = ( bit1 @ M3 ) )
% 9.25/5.28                           => ( ( Xa = one )
% 9.25/5.28                             => ( ( Y
% 9.25/5.28                                  = ( bit1 @ M3 ) )
% 9.25/5.28                               => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ one ) ) ) ) )
% 9.25/5.28                       => ( ! [M3: num] :
% 9.25/5.28                              ( ( X
% 9.25/5.28                                = ( bit1 @ M3 ) )
% 9.25/5.28                             => ! [N3: num] :
% 9.25/5.28                                  ( ( Xa
% 9.25/5.28                                    = ( bit0 @ N3 ) )
% 9.25/5.28                                 => ( ( Y
% 9.25/5.28                                      = ( bit1 @ ( bit_un6697907153464112080or_num @ M3 @ N3 ) ) )
% 9.25/5.28                                   => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 9.25/5.28                         => ~ ! [M3: num] :
% 9.25/5.28                                ( ( X
% 9.25/5.28                                  = ( bit1 @ M3 ) )
% 9.25/5.28                               => ! [N3: num] :
% 9.25/5.28                                    ( ( Xa
% 9.25/5.28                                      = ( bit1 @ N3 ) )
% 9.25/5.28                                   => ( ( Y
% 9.25/5.28                                        = ( bit1 @ ( bit_un6697907153464112080or_num @ M3 @ N3 ) ) )
% 9.25/5.28                                     => ~ ( accp_P3113834385874906142um_num @ bit_un4773296044027857193um_rel @ ( product_Pair_num_num @ ( bit1 @ M3 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9669_less__nat__rel,axiom,
% 9.25/5.28      ( ord_less_nat
% 9.25/5.28      = ( transi2163837189807498211lp_nat
% 9.25/5.28        @ ^ [M2: nat,N2: nat] :
% 9.25/5.28            ( N2
% 9.25/5.28            = ( suc @ M2 ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9670_sub_Otransfer,axiom,
% 9.25/5.28      ( bNF_re7876454716742015248nteger
% 9.25/5.28      @ ^ [Y4: num,Z4: num] : ( Y4 = Z4 )
% 9.25/5.28      @ ( bNF_re6501075790457514782nteger
% 9.25/5.28        @ ^ [Y4: num,Z4: num] : ( Y4 = Z4 )
% 9.25/5.28        @ code_pcr_integer )
% 9.25/5.28      @ ^ [M2: num,N2: num] : ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N2 ) )
% 9.25/5.28      @ code_sub ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9671_uminus__integer_Otransfer,axiom,
% 9.25/5.28      bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer @ uminus_uminus_int @ uminus1351360451143612070nteger ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9672_integer_Oid__abs__transfer,axiom,
% 9.25/5.28      ( bNF_re982302072995117890nteger
% 9.25/5.28      @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 9.25/5.28      @ code_pcr_integer
% 9.25/5.28      @ ^ [X3: int] : X3
% 9.25/5.28      @ code_integer_of_int ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9673_integer_Orep__transfer,axiom,
% 9.25/5.28      ( bNF_re3804157879324367682nt_int @ code_pcr_integer
% 9.25/5.28      @ ^ [Y4: int,Z4: int] : ( Y4 = Z4 )
% 9.25/5.28      @ ^ [X3: int] : X3
% 9.25/5.28      @ code_int_of_integer ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9674_dup_Otransfer,axiom,
% 9.25/5.28      ( bNF_re3379532845092657523nteger @ code_pcr_integer @ code_pcr_integer
% 9.25/5.28      @ ^ [K4: int] : ( plus_plus_int @ K4 @ K4 )
% 9.25/5.28      @ code_dup ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9675_one__integer_Otransfer,axiom,
% 9.25/5.28      code_pcr_integer @ one_one_int @ one_one_Code_integer ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9676_gcd__nat_Oordering__axioms,axiom,
% 9.25/5.28      ( ordering_nat @ dvd_dvd_nat
% 9.25/5.28      @ ^ [M2: nat,N2: nat] :
% 9.25/5.28          ( ( dvd_dvd_nat @ M2 @ N2 )
% 9.25/5.28          & ( M2 != N2 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9677_Abs__int__cases,axiom,
% 9.25/5.28      ! [X: int] :
% 9.25/5.28        ~ ! [Y2: set_Pr1261947904930325089at_nat] :
% 9.25/5.28            ( ( X
% 9.25/5.28              = ( abs_int @ Y2 ) )
% 9.25/5.28           => ~ ( member2643936169264416010at_nat @ Y2
% 9.25/5.28                @ ( collec5514110066124741708at_nat
% 9.25/5.28                  @ ^ [C4: set_Pr1261947904930325089at_nat] :
% 9.25/5.28                    ? [X3: product_prod_nat_nat] :
% 9.25/5.28                      ( ( intrel @ X3 @ X3 )
% 9.25/5.28                      & ( C4
% 9.25/5.28                        = ( collec3392354462482085612at_nat @ ( intrel @ X3 ) ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9678_Abs__int__induct,axiom,
% 9.25/5.28      ! [P: int > $o,X: int] :
% 9.25/5.28        ( ! [Y2: set_Pr1261947904930325089at_nat] :
% 9.25/5.28            ( ( member2643936169264416010at_nat @ Y2
% 9.25/5.28              @ ( collec5514110066124741708at_nat
% 9.25/5.28                @ ^ [C4: set_Pr1261947904930325089at_nat] :
% 9.25/5.28                  ? [X3: product_prod_nat_nat] :
% 9.25/5.28                    ( ( intrel @ X3 @ X3 )
% 9.25/5.28                    & ( C4
% 9.25/5.28                      = ( collec3392354462482085612at_nat @ ( intrel @ X3 ) ) ) ) ) )
% 9.25/5.28           => ( P @ ( abs_int @ Y2 ) ) )
% 9.25/5.28       => ( P @ X ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9679_Abs__int__inject,axiom,
% 9.25/5.28      ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 9.25/5.28        ( ( member2643936169264416010at_nat @ X
% 9.25/5.28          @ ( collec5514110066124741708at_nat
% 9.25/5.28            @ ^ [C4: set_Pr1261947904930325089at_nat] :
% 9.25/5.28              ? [X3: product_prod_nat_nat] :
% 9.25/5.28                ( ( intrel @ X3 @ X3 )
% 9.25/5.28                & ( C4
% 9.25/5.28                  = ( collec3392354462482085612at_nat @ ( intrel @ X3 ) ) ) ) ) )
% 9.25/5.28       => ( ( member2643936169264416010at_nat @ Y
% 9.25/5.28            @ ( collec5514110066124741708at_nat
% 9.25/5.28              @ ^ [C4: set_Pr1261947904930325089at_nat] :
% 9.25/5.28                ? [X3: product_prod_nat_nat] :
% 9.25/5.28                  ( ( intrel @ X3 @ X3 )
% 9.25/5.28                  & ( C4
% 9.25/5.28                    = ( collec3392354462482085612at_nat @ ( intrel @ X3 ) ) ) ) ) )
% 9.25/5.28         => ( ( ( abs_int @ X )
% 9.25/5.28              = ( abs_int @ Y ) )
% 9.25/5.28            = ( X = Y ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9680_Abs__int__inverse,axiom,
% 9.25/5.28      ! [Y: set_Pr1261947904930325089at_nat] :
% 9.25/5.28        ( ( member2643936169264416010at_nat @ Y
% 9.25/5.28          @ ( collec5514110066124741708at_nat
% 9.25/5.28            @ ^ [C4: set_Pr1261947904930325089at_nat] :
% 9.25/5.28              ? [X3: product_prod_nat_nat] :
% 9.25/5.28                ( ( intrel @ X3 @ X3 )
% 9.25/5.28                & ( C4
% 9.25/5.28                  = ( collec3392354462482085612at_nat @ ( intrel @ X3 ) ) ) ) ) )
% 9.25/5.28       => ( ( rep_int @ ( abs_int @ Y ) )
% 9.25/5.28          = Y ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9681_type__definition__int,axiom,
% 9.25/5.28      ( type_d8752208705193531015at_nat @ rep_int @ abs_int
% 9.25/5.28      @ ( collec5514110066124741708at_nat
% 9.25/5.28        @ ^ [C4: set_Pr1261947904930325089at_nat] :
% 9.25/5.28          ? [X3: product_prod_nat_nat] :
% 9.25/5.28            ( ( intrel @ X3 @ X3 )
% 9.25/5.28            & ( C4
% 9.25/5.28              = ( collec3392354462482085612at_nat @ ( intrel @ X3 ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9682_Rep__int__induct,axiom,
% 9.25/5.28      ! [Y: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 9.25/5.28        ( ( member2643936169264416010at_nat @ Y
% 9.25/5.28          @ ( collec5514110066124741708at_nat
% 9.25/5.28            @ ^ [C4: set_Pr1261947904930325089at_nat] :
% 9.25/5.28              ? [X3: product_prod_nat_nat] :
% 9.25/5.28                ( ( intrel @ X3 @ X3 )
% 9.25/5.28                & ( C4
% 9.25/5.28                  = ( collec3392354462482085612at_nat @ ( intrel @ X3 ) ) ) ) ) )
% 9.25/5.28       => ( ! [X2: int] : ( P @ ( rep_int @ X2 ) )
% 9.25/5.28         => ( P @ Y ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9683_Rep__int__cases,axiom,
% 9.25/5.28      ! [Y: set_Pr1261947904930325089at_nat] :
% 9.25/5.28        ( ( member2643936169264416010at_nat @ Y
% 9.25/5.28          @ ( collec5514110066124741708at_nat
% 9.25/5.28            @ ^ [C4: set_Pr1261947904930325089at_nat] :
% 9.25/5.28              ? [X3: product_prod_nat_nat] :
% 9.25/5.28                ( ( intrel @ X3 @ X3 )
% 9.25/5.28                & ( C4
% 9.25/5.28                  = ( collec3392354462482085612at_nat @ ( intrel @ X3 ) ) ) ) ) )
% 9.25/5.28       => ~ ! [X2: int] :
% 9.25/5.28              ( Y
% 9.25/5.28             != ( rep_int @ X2 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9684_Rep__int,axiom,
% 9.25/5.28      ! [X: int] :
% 9.25/5.28        ( member2643936169264416010at_nat @ ( rep_int @ X )
% 9.25/5.28        @ ( collec5514110066124741708at_nat
% 9.25/5.28          @ ^ [C4: set_Pr1261947904930325089at_nat] :
% 9.25/5.28            ? [X3: product_prod_nat_nat] :
% 9.25/5.28              ( ( intrel @ X3 @ X3 )
% 9.25/5.28              & ( C4
% 9.25/5.28                = ( collec3392354462482085612at_nat @ ( intrel @ X3 ) ) ) ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9685_Int_Osub__code_I9_J,axiom,
% 9.25/5.28      ! [M: num,N: num] :
% 9.25/5.28        ( ( sub @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 9.25/5.28        = ( minus_minus_int @ ( dup @ ( sub @ M @ N ) ) @ one_one_int ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9686_Int_Osub__code_I8_J,axiom,
% 9.25/5.28      ! [M: num,N: num] :
% 9.25/5.28        ( ( sub @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 9.25/5.28        = ( plus_plus_int @ ( dup @ ( sub @ M @ N ) ) @ one_one_int ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(fact_9687_gcd__nat_Opreordering__axioms,axiom,
% 9.25/5.28      ( preordering_nat @ dvd_dvd_nat
% 9.25/5.28      @ ^ [M2: nat,N2: nat] :
% 9.25/5.28          ( ( dvd_dvd_nat @ M2 @ N2 )
% 9.25/5.28          & ( M2 != N2 ) ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 9.25/5.28      ! [X: int,Y: int] :
% 9.25/5.28        ( ( if_int @ $false @ X @ Y )
% 9.25/5.28        = Y ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 9.25/5.28      ! [X: int,Y: int] :
% 9.25/5.28        ( ( if_int @ $true @ X @ Y )
% 9.25/5.28        = X ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 9.25/5.28      ! [X: nat,Y: nat] :
% 9.25/5.28        ( ( if_nat @ $false @ X @ Y )
% 9.25/5.28        = Y ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 9.25/5.28      ! [X: nat,Y: nat] :
% 9.25/5.28        ( ( if_nat @ $true @ X @ Y )
% 9.25/5.28        = X ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 9.25/5.28      ! [X: num,Y: num] :
% 9.25/5.28        ( ( if_num @ $false @ X @ Y )
% 9.25/5.28        = Y ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 9.25/5.28      ! [X: num,Y: num] :
% 9.25/5.28        ( ( if_num @ $true @ X @ Y )
% 9.25/5.28        = X ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 9.25/5.28      ! [X: rat,Y: rat] :
% 9.25/5.28        ( ( if_rat @ $false @ X @ Y )
% 9.25/5.28        = Y ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 9.25/5.28      ! [X: rat,Y: rat] :
% 9.25/5.28        ( ( if_rat @ $true @ X @ Y )
% 9.25/5.28        = X ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_2_1_If_001t__Assertions__Oassn_T,axiom,
% 9.25/5.28      ! [X: assn,Y: assn] :
% 9.25/5.28        ( ( if_assn @ $false @ X @ Y )
% 9.25/5.28        = Y ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_1_1_If_001t__Assertions__Oassn_T,axiom,
% 9.25/5.28      ! [X: assn,Y: assn] :
% 9.25/5.28        ( ( if_assn @ $true @ X @ Y )
% 9.25/5.28        = X ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 9.25/5.28      ! [X: code_integer,Y: code_integer] :
% 9.25/5.28        ( ( if_Code_integer @ $false @ X @ Y )
% 9.25/5.28        = Y ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 9.25/5.28      ! [X: code_integer,Y: code_integer] :
% 9.25/5.28        ( ( if_Code_integer @ $true @ X @ Y )
% 9.25/5.28        = X ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_2_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 9.25/5.28      ! [X: code_natural,Y: code_natural] :
% 9.25/5.28        ( ( if_Code_natural @ $false @ X @ Y )
% 9.25/5.28        = Y ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_1_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 9.25/5.28      ! [X: code_natural,Y: code_natural] :
% 9.25/5.28        ( ( if_Code_natural @ $true @ X @ Y )
% 9.25/5.28        = X ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 9.25/5.28      ! [X: set_int,Y: set_int] :
% 9.25/5.28        ( ( if_set_int @ $false @ X @ Y )
% 9.25/5.28        = Y ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 9.25/5.28      ! [X: set_int,Y: set_int] :
% 9.25/5.28        ( ( if_set_int @ $true @ X @ Y )
% 9.25/5.28        = X ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 9.25/5.28      ! [X: list_int,Y: list_int] :
% 9.25/5.28        ( ( if_list_int @ $false @ X @ Y )
% 9.25/5.28        = Y ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 9.25/5.28      ! [X: list_int,Y: list_int] :
% 9.25/5.28        ( ( if_list_int @ $true @ X @ Y )
% 9.25/5.28        = X ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 9.25/5.28      ! [X: option_num,Y: option_num] :
% 9.25/5.28        ( ( if_option_num @ $false @ X @ Y )
% 9.25/5.28        = Y ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 9.25/5.28      ! [X: option_num,Y: option_num] :
% 9.25/5.28        ( ( if_option_num @ $true @ X @ Y )
% 9.25/5.28        = X ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_2_1_If_001t__Predicate__Opred_It__Product____Type__Ounit_J_T,axiom,
% 9.25/5.28      ! [X: pred_Product_unit,Y: pred_Product_unit] :
% 9.25/5.28        ( ( if_pred_Product_unit @ $false @ X @ Y )
% 9.25/5.28        = Y ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_1_1_If_001t__Predicate__Opred_It__Product____Type__Ounit_J_T,axiom,
% 9.25/5.28      ! [X: pred_Product_unit,Y: pred_Product_unit] :
% 9.25/5.28        ( ( if_pred_Product_unit @ $true @ X @ Y )
% 9.25/5.28        = X ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_2_1_If_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 9.25/5.28      ! [X: sum_sum_nat_nat,Y: sum_sum_nat_nat] :
% 9.25/5.28        ( ( if_Sum_sum_nat_nat @ $false @ X @ Y )
% 9.25/5.28        = Y ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_1_1_If_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 9.25/5.28      ! [X: sum_sum_nat_nat,Y: sum_sum_nat_nat] :
% 9.25/5.28        ( ( if_Sum_sum_nat_nat @ $true @ X @ Y )
% 9.25/5.28        = X ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 9.25/5.28      ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 9.25/5.28        ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 9.25/5.28        = Y ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 9.25/5.28      ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 9.25/5.28        ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 9.25/5.28        = X ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 9.25/5.28      ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 9.25/5.28        ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 9.25/5.28        = Y ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 9.25/5.28      ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 9.25/5.28        ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 9.25/5.28        = X ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 9.25/5.28      ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 9.25/5.28        ( ( if_Pro5737122678794959658eger_o @ $false @ X @ Y )
% 9.25/5.28        = Y ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 9.25/5.28      ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 9.25/5.28        ( ( if_Pro5737122678794959658eger_o @ $true @ X @ Y )
% 9.25/5.28        = X ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_2_1_If_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 9.25/5.28      ! [X: multis2468970476368604999at_nat,Y: multis2468970476368604999at_nat] :
% 9.25/5.28        ( ( if_mul8430962117462786573at_nat @ $false @ X @ Y )
% 9.25/5.28        = Y ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_1_1_If_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 9.25/5.28      ! [X: multis2468970476368604999at_nat,Y: multis2468970476368604999at_nat] :
% 9.25/5.28        ( ( if_mul8430962117462786573at_nat @ $true @ X @ Y )
% 9.25/5.28        = X ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 9.25/5.28      ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 9.25/5.28        ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y )
% 9.25/5.28        = Y ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 9.25/5.28      ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 9.25/5.28        ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y )
% 9.25/5.28        = X ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Predicate__Opred_It__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_T,axiom,
% 9.25/5.28      ! [P: $o] :
% 9.25/5.28        ( ( P = $true )
% 9.25/5.28        | ( P = $false ) ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Predicate__Opred_It__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_T,axiom,
% 9.25/5.28      ! [X: produc4675096598859438275atural,Y: produc4675096598859438275atural] :
% 9.25/5.28        ( ( if_Pro3444522238938527101atural @ $false @ X @ Y )
% 9.25/5.28        = Y ) ).
% 9.25/5.28  
% 9.25/5.28  thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Predicate__Opred_It__Product____Type__Ounit_J_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J_T,axiom,
% 9.25/5.28      ! [X: produc4675096598859438275atural,Y: produc4675096598859438275atural] :
% 9.25/5.28        ( ( if_Pro3444522238938527101atural @ $true @ X @ Y )
% 9.25/5.28        = X ) ).
% 9.25/5.28  
% 9.25/5.28  thf(conj_0,conjecture,
% 9.25/5.28      ( ( ( x
% 9.25/5.28          = ( abs_assn
% 9.25/5.28            @ ^ [H2: produc3658429121746597890et_nat] :
% 9.25/5.28                ( ( rep_assn @ x @ H2 )
% 9.25/5.28                & ( rep_assn @ y @ H2 ) ) ) )
% 9.25/5.28        & ( x != y ) )
% 9.25/5.28      = ( ( x
% 9.25/5.28          = ( abs_assn
% 9.25/5.28            @ ^ [H2: produc3658429121746597890et_nat] :
% 9.25/5.28                ( ( rep_assn @ x @ H2 )
% 9.25/5.28                & ( rep_assn @ y @ H2 ) ) ) )
% 9.25/5.28        & ( y
% 9.25/5.28         != ( abs_assn
% 9.25/5.28            @ ^ [H2: produc3658429121746597890et_nat] :
% 9.25/5.28                ( ( rep_assn @ y @ H2 )
% 9.25/5.28                & ( rep_assn @ x @ H2 ) ) ) ) ) ) ).
% 9.25/5.28  ------------------------
% 9.26/5.77  % (32271)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32141 for (2995ds/18Mi)
% 9.26/5.78  % (32266)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_32141 for (2995ds/4Mi)
% 9.26/5.78  % (32265)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32141 for (2995ds/183Mi)
% 9.26/5.78  % (32267)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_32141 for (2995ds/27Mi)
% 9.26/5.78  % (32268)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32141 for (2995ds/2Mi)
% 9.26/5.78  % (32269)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_32141 for (2995ds/2Mi)
% 9.26/5.78  % (32270)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_32141 for (2995ds/275Mi)
% 9.26/5.78  % (32268)Instruction limit reached!
% 9.26/5.78  % (32268)------------------------------
% 9.26/5.78  % (32268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.78  % (32268)Termination reason: Unknown
% 9.26/5.78  % (32268)Termination phase: shuffling
% 9.26/5.78  
% 9.26/5.78  % (32268)Memory used [KB]: 11897
% 9.26/5.78  % (32268)Time elapsed: 0.004 s
% 9.26/5.78  % (32268)Instructions burned: 2 (million)
% 9.26/5.78  % (32268)------------------------------
% 9.26/5.78  % (32268)------------------------------
% 9.26/5.78  % (32269)Instruction limit reached!
% 9.26/5.78  % (32269)------------------------------
% 9.26/5.78  % (32269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.78  % (32269)Termination reason: Unknown
% 9.26/5.78  % (32269)Termination phase: shuffling
% 9.26/5.78  
% 9.26/5.78  % (32269)Memory used [KB]: 11897
% 9.26/5.78  % (32269)Time elapsed: 0.004 s
% 9.26/5.78  % (32269)Instructions burned: 2 (million)
% 9.26/5.78  % (32269)------------------------------
% 9.26/5.78  % (32269)------------------------------
% 9.26/5.78  % (32266)Instruction limit reached!
% 9.26/5.78  % (32266)------------------------------
% 9.26/5.78  % (32266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.78  % (32266)Termination reason: Unknown
% 9.26/5.78  % (32266)Termination phase: shuffling
% 9.26/5.78  
% 9.26/5.78  % (32266)Memory used [KB]: 12025
% 9.26/5.78  % (32266)Time elapsed: 0.007 s
% 9.26/5.78  % (32266)Instructions burned: 4 (million)
% 9.26/5.78  % (32266)------------------------------
% 9.26/5.78  % (32266)------------------------------
% 9.26/5.78  % (32271)Instruction limit reached!
% 9.26/5.78  % (32271)------------------------------
% 9.26/5.78  % (32271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.78  % (32271)Termination reason: Unknown
% 9.26/5.78  % (32271)Termination phase: shuffling
% 9.26/5.78  
% 9.26/5.78  % (32271)Memory used [KB]: 13688
% 9.26/5.78  % (32271)Time elapsed: 0.016 s
% 9.26/5.78  % (32271)Instructions burned: 20 (million)
% 9.26/5.78  % (32271)------------------------------
% 9.26/5.78  % (32271)------------------------------
% 9.26/5.79  % (32275)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_32141 for (2994ds/3Mi)
% 9.26/5.80  % (32275)Instruction limit reached!
% 9.26/5.80  % (32275)------------------------------
% 9.26/5.80  % (32275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.80  % (32275)Termination reason: Unknown
% 9.26/5.80  % (32275)Termination phase: shuffling
% 9.26/5.80  
% 9.26/5.80  % (32275)Memory used [KB]: 12025
% 9.26/5.80  % (32275)Time elapsed: 0.004 s
% 9.26/5.80  % (32275)Instructions burned: 3 (million)
% 9.26/5.80  % (32275)------------------------------
% 9.26/5.80  % (32275)------------------------------
% 9.26/5.80  % (32272)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32141 for (2995ds/3Mi)
% 9.26/5.80  % (32273)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_32141 for (2995ds/37Mi)
% 9.26/5.80  % (32274)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_32141 for (2994ds/15Mi)
% 9.26/5.80  % (32272)Instruction limit reached!
% 9.26/5.80  % (32272)------------------------------
% 9.26/5.80  % (32272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.80  % (32272)Termination reason: Unknown
% 9.26/5.80  % (32272)Termination phase: shuffling
% 9.26/5.80  
% 9.26/5.80  % (32272)Memory used [KB]: 11897
% 9.26/5.80  % (32272)Time elapsed: 0.005 s
% 9.26/5.80  % (32272)Instructions burned: 3 (million)
% 9.26/5.80  % (32272)------------------------------
% 9.26/5.80  % (32272)------------------------------
% 9.26/5.80  % (32267)Instruction limit reached!
% 9.26/5.80  % (32267)------------------------------
% 9.26/5.80  % (32267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.80  % (32267)Termination reason: Unknown
% 9.26/5.80  % (32267)Termination phase: shuffling
% 9.26/5.80  
% 9.26/5.80  % (32267)Memory used [KB]: 13816
% 9.26/5.80  % (32267)Time elapsed: 0.030 s
% 9.26/5.80  % (32267)Instructions burned: 28 (million)
% 9.26/5.80  % (32267)------------------------------
% 9.26/5.80  % (32267)------------------------------
% 9.26/5.81  % (32276)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_32141 for (2994ds/1041Mi)
% 9.26/5.82  % (32274)Instruction limit reached!
% 9.26/5.82  % (32274)------------------------------
% 9.26/5.82  % (32274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.82  % (32277)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_32141 for (2994ds/7Mi)
% 9.26/5.82  % (32274)Termination reason: Unknown
% 9.26/5.82  % (32274)Termination phase: shuffling
% 9.26/5.82  
% 9.26/5.82  % (32274)Memory used [KB]: 13688
% 9.26/5.82  % (32274)Time elapsed: 0.022 s
% 9.26/5.82  % (32274)Instructions burned: 16 (million)
% 9.26/5.82  % (32274)------------------------------
% 9.26/5.82  % (32274)------------------------------
% 9.26/5.82  % (32278)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_32141 for (2994ds/16Mi)
% 9.26/5.83  % (32273)Instruction limit reached!
% 9.26/5.83  % (32273)------------------------------
% 9.26/5.83  % (32273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.83  % (32273)Termination reason: Unknown
% 9.26/5.83  % (32273)Termination phase: shuffling
% 9.26/5.83  
% 9.26/5.83  % (32273)Memory used [KB]: 13944
% 9.26/5.83  % (32273)Time elapsed: 0.033 s
% 9.26/5.83  % (32273)Instructions burned: 37 (million)
% 9.26/5.83  % (32273)------------------------------
% 9.26/5.83  % (32273)------------------------------
% 9.26/5.83  % (32277)Instruction limit reached!
% 9.26/5.83  % (32277)------------------------------
% 9.26/5.83  % (32277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.83  % (32277)Termination reason: Unknown
% 9.26/5.83  % (32277)Termination phase: shuffling
% 9.26/5.83  
% 9.26/5.83  % (32277)Memory used [KB]: 12281
% 9.26/5.83  % (32277)Time elapsed: 0.012 s
% 9.26/5.83  % (32277)Instructions burned: 7 (million)
% 9.26/5.83  % (32277)------------------------------
% 9.26/5.83  % (32277)------------------------------
% 9.26/5.84  % (32279)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_32141 for (2994ds/3Mi)
% 9.26/5.84  % (32279)Instruction limit reached!
% 9.26/5.84  % (32279)------------------------------
% 9.26/5.84  % (32279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.84  % (32279)Termination reason: Unknown
% 9.26/5.84  % (32279)Termination phase: shuffling
% 9.26/5.84  
% 9.26/5.84  % (32279)Memory used [KB]: 11897
% 9.26/5.84  % (32279)Time elapsed: 0.005 s
% 9.26/5.84  % (32279)Instructions burned: 3 (million)
% 9.26/5.84  % (32279)------------------------------
% 9.26/5.84  % (32279)------------------------------
% 9.26/5.84  % (32278)Instruction limit reached!
% 9.26/5.84  % (32278)------------------------------
% 9.26/5.84  % (32278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.84  % (32278)Termination reason: Unknown
% 9.26/5.84  % (32278)Termination phase: shuffling
% 9.26/5.84  
% 9.26/5.84  % (32278)Memory used [KB]: 13688
% 9.26/5.84  % (32278)Time elapsed: 0.023 s
% 9.26/5.84  % (32278)Instructions burned: 17 (million)
% 9.26/5.84  % (32278)------------------------------
% 9.26/5.84  % (32278)------------------------------
% 9.26/5.85  % (32280)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_32141 for (2994ds/3Mi)
% 9.26/5.85  % (32281)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_32141 for (2994ds/7Mi)
% 9.26/5.85  % (32280)Instruction limit reached!
% 9.26/5.85  % (32280)------------------------------
% 9.26/5.85  % (32280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.85  % (32280)Termination reason: Unknown
% 9.26/5.85  % (32280)Termination phase: shuffling
% 9.26/5.85  
% 9.26/5.85  % (32280)Memory used [KB]: 11897
% 9.26/5.85  % (32280)Time elapsed: 0.005 s
% 9.26/5.85  % (32280)Instructions burned: 3 (million)
% 9.26/5.85  % (32280)------------------------------
% 9.26/5.85  % (32280)------------------------------
% 9.26/5.86  % (32281)Instruction limit reached!
% 9.26/5.86  % (32281)------------------------------
% 9.26/5.86  % (32281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.86  % (32281)Termination reason: Unknown
% 9.26/5.86  % (32281)Termination phase: shuffling
% 9.26/5.86  
% 9.26/5.86  % (32281)Memory used [KB]: 12281
% 9.26/5.86  % (32281)Time elapsed: 0.011 s
% 9.26/5.86  % (32281)Instructions burned: 7 (million)
% 9.26/5.86  % (32281)------------------------------
% 9.26/5.86  % (32281)------------------------------
% 9.26/5.86  % (32282)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_32141 for (2994ds/3Mi)
% 9.26/5.86  % (32283)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_32141 for (2994ds/4Mi)
% 9.26/5.87  % (32282)Instruction limit reached!
% 9.26/5.87  % (32282)------------------------------
% 9.26/5.87  % (32282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.87  % (32282)Termination reason: Unknown
% 9.26/5.87  % (32282)Termination phase: shuffling
% 9.26/5.87  
% 9.26/5.87  % (32282)Memory used [KB]: 11897
% 9.26/5.87  % (32282)Time elapsed: 0.005 s
% 9.26/5.87  % (32282)Instructions burned: 3 (million)
% 9.26/5.87  % (32282)------------------------------
% 9.26/5.87  % (32282)------------------------------
% 9.26/5.87  % (32283)Instruction limit reached!
% 9.26/5.87  % (32283)------------------------------
% 9.26/5.87  % (32283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.87  % (32283)Termination reason: Unknown
% 9.26/5.87  % (32283)Termination phase: shuffling
% 9.26/5.87  
% 9.26/5.87  % (32283)Memory used [KB]: 12025
% 9.26/5.87  % (32283)Time elapsed: 0.006 s
% 9.26/5.87  % (32283)Instructions burned: 4 (million)
% 9.26/5.87  % (32283)------------------------------
% 9.26/5.87  % (32283)------------------------------
% 9.26/5.87  % (32284)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_32141 for (2994ds/18Mi)
% 9.26/5.88  % (32285)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_32141 for (2994ds/710Mi)
% 9.26/5.88  % (32286)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32141 for (2994ds/6Mi)
% 9.26/5.89  % (32287)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_32141 for (2994ds/902Mi)
% 9.26/5.89  % (32284)Instruction limit reached!
% 9.26/5.89  % (32284)------------------------------
% 9.26/5.89  % (32284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.89  % (32284)Termination reason: Unknown
% 9.26/5.89  % (32284)Termination phase: shuffling
% 9.26/5.89  
% 9.26/5.89  % (32284)Memory used [KB]: 13688
% 9.26/5.89  % (32284)Time elapsed: 0.020 s
% 9.26/5.89  % (32284)Instructions burned: 18 (million)
% 9.26/5.89  % (32284)------------------------------
% 9.26/5.89  % (32284)------------------------------
% 9.26/5.89  % (32286)Instruction limit reached!
% 9.26/5.89  % (32286)------------------------------
% 9.26/5.89  % (32286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.89  % (32286)Termination reason: Unknown
% 9.26/5.89  % (32286)Termination phase: shuffling
% 9.26/5.89  
% 9.26/5.89  % (32286)Memory used [KB]: 12153
% 9.26/5.89  % (32286)Time elapsed: 0.009 s
% 9.26/5.89  % (32286)Instructions burned: 6 (million)
% 9.26/5.89  % (32286)------------------------------
% 9.26/5.89  % (32286)------------------------------
% 9.26/5.89  % (32265)Instruction limit reached!
% 9.26/5.89  % (32265)------------------------------
% 9.26/5.89  % (32265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.89  % (32265)Termination reason: Unknown
% 9.26/5.89  % (32265)Termination phase: shuffling
% 9.26/5.89  
% 9.26/5.89  % (32265)Memory used [KB]: 15991
% 9.26/5.89  % (32265)Time elapsed: 0.117 s
% 9.26/5.89  % (32265)Instructions burned: 183 (million)
% 9.26/5.89  % (32265)------------------------------
% 9.26/5.89  % (32265)------------------------------
% 9.26/5.90  % (32288)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_32141 for (2994ds/21Mi)
% 9.26/5.90  % (32290)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_32141 for (2994ds/6Mi)
% 9.26/5.90  % (32289)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_32141 for (2994ds/5Mi)
% 9.26/5.90  % (32289)Instruction limit reached!
% 9.26/5.90  % (32289)------------------------------
% 9.26/5.90  % (32289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.90  % (32289)Termination reason: Unknown
% 9.26/5.90  % (32289)Termination phase: shuffling
% 9.26/5.90  
% 9.26/5.90  % (32289)Memory used [KB]: 12153
% 9.26/5.90  % (32289)Time elapsed: 0.005 s
% 9.26/5.90  % (32289)Instructions burned: 5 (million)
% 9.26/5.90  % (32289)------------------------------
% 9.26/5.90  % (32289)------------------------------
% 9.26/5.91  % (32290)Instruction limit reached!
% 9.26/5.91  % (32290)------------------------------
% 9.26/5.91  % (32290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.91  % (32290)Termination reason: Unknown
% 9.26/5.91  % (32290)Termination phase: shuffling
% 9.26/5.91  
% 9.26/5.91  % (32290)Memory used [KB]: 12153
% 9.26/5.91  % (32290)Time elapsed: 0.006 s
% 9.26/5.91  % (32290)Instructions burned: 6 (million)
% 9.26/5.91  % (32290)------------------------------
% 9.26/5.91  % (32290)------------------------------
% 9.26/5.91  % (32288)Instruction limit reached!
% 9.26/5.91  % (32288)------------------------------
% 9.26/5.91  % (32288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.91  % (32288)Termination reason: Unknown
% 9.26/5.91  % (32288)Termination phase: shuffling
% 9.26/5.91  
% 9.26/5.91  % (32288)Memory used [KB]: 13816
% 9.26/5.91  % (32288)Time elapsed: 0.016 s
% 9.26/5.91  % (32288)Instructions burned: 21 (million)
% 9.26/5.91  % (32288)------------------------------
% 9.26/5.91  % (32288)------------------------------
% 9.26/5.92  % (32292)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_32141 for (2993ds/779Mi)
% 9.26/5.92  % (32291)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_32141 for (2993ds/377Mi)
% 9.26/5.93  % (32293)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_32141 for (2993ds/19Mi)
% 9.26/5.93  % (32270)Instruction limit reached!
% 9.26/5.93  % (32270)------------------------------
% 9.26/5.93  % (32270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.93  % (32270)Termination reason: Unknown
% 9.26/5.93  % (32270)Termination phase: shuffling
% 9.26/5.93  
% 9.26/5.93  % (32270)Memory used [KB]: 17398
% 9.26/5.93  % (32270)Time elapsed: 0.156 s
% 9.26/5.93  % (32270)Instructions burned: 276 (million)
% 9.26/5.93  % (32270)------------------------------
% 9.26/5.93  % (32270)------------------------------
% 9.26/5.94  % (32293)Instruction limit reached!
% 9.26/5.94  % (32293)------------------------------
% 9.26/5.94  % (32293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.94  % (32293)Termination reason: Unknown
% 9.26/5.94  % (32293)Termination phase: shuffling
% 9.26/5.94  
% 9.26/5.94  % (32293)Memory used [KB]: 13688
% 9.26/5.94  % (32293)Time elapsed: 0.015 s
% 9.26/5.94  % (32293)Instructions burned: 19 (million)
% 9.26/5.94  % (32293)------------------------------
% 9.26/5.94  % (32293)------------------------------
% 9.26/5.94  % (32294)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_32141 for (2993ds/879Mi)
% 9.26/5.95  % (32295)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_32141 for (2993ds/17Mi)
% 9.26/5.96  % (32295)Instruction limit reached!
% 9.26/5.96  % (32295)------------------------------
% 9.26/5.96  % (32295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.96  % (32295)Termination reason: Unknown
% 9.26/5.96  % (32295)Termination phase: shuffling
% 9.26/5.96  
% 9.26/5.96  % (32295)Memory used [KB]: 13688
% 9.26/5.96  % (32295)Time elapsed: 0.015 s
% 9.26/5.96  % (32295)Instructions burned: 18 (million)
% 9.26/5.96  % (32295)------------------------------
% 9.26/5.96  % (32295)------------------------------
% 9.26/5.97  % (32296)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_32141 for (2993ds/3Mi)
% 9.26/5.98  % (32296)Instruction limit reached!
% 9.26/5.98  % (32296)------------------------------
% 9.26/5.98  % (32296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/5.98  % (32296)Termination reason: Unknown
% 9.26/5.98  % (32296)Termination phase: shuffling
% 9.26/5.98  
% 9.26/5.98  % (32296)Memory used [KB]: 11897
% 9.26/5.98  % (32296)Time elapsed: 0.004 s
% 9.26/5.98  % (32296)Instructions burned: 3 (million)
% 9.26/5.98  % (32296)------------------------------
% 9.26/5.98  % (32296)------------------------------
% 9.26/5.99  % (32297)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_32141 for (2993ds/30Mi)
% 9.26/6.00  % (32297)Instruction limit reached!
% 9.26/6.00  % (32297)------------------------------
% 9.26/6.00  % (32297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.26/6.00  % (32297)Termination reason: Unknown
% 9.26/6.00  % (32297)Termination phase: shuffling
% 9.26/6.00  
% 9.26/6.00  % (32297)Memory used [KB]: 13944
% 9.26/6.00  % (32297)Time elapsed: 0.019 s
% 9.26/6.00  % (32297)Instructions burned: 31 (million)
% 9.26/6.00  % (32297)------------------------------
% 9.26/6.00  % (32297)------------------------------
% 11.42/6.02  % (32298)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_32141 for (2992ds/127Mi)
% 11.42/6.06  % (32291)Instruction limit reached!
% 11.42/6.06  % (32291)------------------------------
% 11.42/6.06  % (32291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.42/6.06  % (32291)Termination reason: Unknown
% 11.42/6.06  % (32291)Termination phase: shuffling
% 11.42/6.06  
% 11.42/6.06  % (32291)Memory used [KB]: 18677
% 11.42/6.06  % (32291)Time elapsed: 0.141 s
% 11.42/6.06  % (32291)Instructions burned: 377 (million)
% 11.42/6.06  % (32291)------------------------------
% 11.42/6.06  % (32291)------------------------------
% 11.42/6.07  % (32299)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_32141 for (2992ds/100Mi)
% 11.42/6.08  % (32298)Instruction limit reached!
% 11.42/6.08  % (32298)------------------------------
% 11.42/6.08  % (32298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.42/6.08  % (32298)Termination reason: Unknown
% 11.42/6.08  % (32298)Termination phase: shuffling
% 11.42/6.08  
% 11.42/6.08  % (32298)Memory used [KB]: 15223
% 11.42/6.08  % (32298)Time elapsed: 0.055 s
% 11.42/6.08  % (32298)Instructions burned: 129 (million)
% 11.42/6.08  % (32298)------------------------------
% 11.42/6.08  % (32298)------------------------------
% 11.42/6.09  % (32300)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_32141 for (2992ds/3Mi)
% 11.42/6.09  % (32300)Instruction limit reached!
% 11.42/6.09  % (32300)------------------------------
% 11.42/6.09  % (32300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.42/6.09  % (32300)Termination reason: Unknown
% 11.42/6.09  % (32300)Termination phase: shuffling
% 11.42/6.09  
% 11.42/6.09  % (32300)Memory used [KB]: 11897
% 11.42/6.09  % (32300)Time elapsed: 0.004 s
% 11.42/6.09  % (32300)Instructions burned: 3 (million)
% 11.42/6.09  % (32300)------------------------------
% 11.42/6.09  % (32300)------------------------------
% 11.42/6.10  % (32301)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_32141 for (2992ds/20Mi)
% 11.42/6.10  % (32299)Instruction limit reached!
% 11.42/6.10  % (32299)------------------------------
% 11.42/6.10  % (32299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.42/6.10  % (32299)Termination reason: Unknown
% 11.42/6.10  % (32299)Termination phase: shuffling
% 11.42/6.10  
% 11.42/6.10  % (32299)Memory used [KB]: 14839
% 11.42/6.10  % (32299)Time elapsed: 0.037 s
% 11.42/6.10  % (32299)Instructions burned: 103 (million)
% 11.42/6.10  % (32299)------------------------------
% 11.42/6.10  % (32299)------------------------------
% 12.12/6.12  % (32302)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_32141 for (2991ds/86Mi)
% 12.12/6.12  % (32301)Instruction limit reached!
% 12.12/6.12  % (32301)------------------------------
% 12.12/6.12  % (32301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.12/6.12  % (32301)Termination reason: Unknown
% 12.12/6.12  % (32301)Termination phase: shuffling
% 12.12/6.12  
% 12.12/6.12  % (32301)Memory used [KB]: 13688
% 12.12/6.12  % (32301)Time elapsed: 0.017 s
% 12.12/6.12  % (32301)Instructions burned: 21 (million)
% 12.12/6.12  % (32301)------------------------------
% 12.12/6.12  % (32301)------------------------------
% 12.12/6.12  % (32276)Instruction limit reached!
% 12.12/6.12  % (32276)------------------------------
% 12.12/6.12  % (32276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.12/6.12  % (32276)Termination reason: Unknown
% 12.12/6.12  % (32276)Termination phase: shuffling
% 12.12/6.12  
% 12.12/6.12  % (32276)Memory used [KB]: 33901
% 12.12/6.12  % (32276)Time elapsed: 0.318 s
% 12.12/6.12  % (32276)Instructions burned: 1043 (million)
% 12.12/6.12  % (32276)------------------------------
% 12.12/6.12  % (32276)------------------------------
% 12.12/6.14  % (32303)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_32141 for (2991ds/107Mi)
% 12.12/6.14  % (32304)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_32141 for (2991ds/39Mi)
% 12.12/6.14  % (32292)Instruction limit reached!
% 12.12/6.14  % (32292)------------------------------
% 12.12/6.14  % (32292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.12/6.14  % (32292)Termination reason: Unknown
% 12.12/6.14  % (32292)Termination phase: shuffling
% 12.12/6.14  
% 12.12/6.14  % (32292)Memory used [KB]: 26353
% 12.12/6.14  % (32292)Time elapsed: 0.230 s
% 12.12/6.14  % (32292)Instructions burned: 780 (million)
% 12.12/6.14  % (32292)------------------------------
% 12.12/6.14  % (32292)------------------------------
% 12.12/6.15  % (32285)Instruction limit reached!
% 12.12/6.15  % (32285)------------------------------
% 12.12/6.15  % (32285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.12/6.15  % (32285)Termination reason: Unknown
% 12.12/6.15  % (32285)Termination phase: shuffling
% 12.12/6.15  
% 12.12/6.15  % (32285)Memory used [KB]: 25458
% 12.12/6.15  % (32285)Time elapsed: 0.272 s
% 12.12/6.15  % (32285)Instructions burned: 711 (million)
% 12.12/6.15  % (32285)------------------------------
% 12.12/6.15  % (32285)------------------------------
% 12.12/6.15  % (32302)Instruction limit reached!
% 12.12/6.15  % (32302)------------------------------
% 12.12/6.15  % (32302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.12/6.15  % (32302)Termination reason: Unknown
% 12.12/6.15  % (32302)Termination phase: shuffling
% 12.12/6.15  
% 12.12/6.15  % (32302)Memory used [KB]: 14583
% 12.12/6.15  % (32302)Time elapsed: 0.037 s
% 12.12/6.15  % (32302)Instructions burned: 86 (million)
% 12.12/6.15  % (32302)------------------------------
% 12.12/6.15  % (32302)------------------------------
% 12.12/6.16  % (32305)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_32141 for (2991ds/448Mi)
% 12.12/6.16  % (32304)Instruction limit reached!
% 12.12/6.16  % (32304)------------------------------
% 12.12/6.16  % (32304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.12/6.16  % (32304)Termination reason: Unknown
% 12.12/6.16  % (32304)Termination phase: shuffling
% 12.12/6.16  
% 12.12/6.16  % (32304)Memory used [KB]: 14072
% 12.12/6.16  % (32304)Time elapsed: 0.022 s
% 12.12/6.16  % (32304)Instructions burned: 40 (million)
% 12.12/6.16  % (32304)------------------------------
% 12.12/6.16  % (32304)------------------------------
% 12.12/6.16  % (32306)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_32141 for (2991ds/46Mi)
% 12.12/6.16  % (32307)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_32141 for (2991ds/98Mi)
% 12.12/6.17  % (32308)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_32141 for (2991ds/507Mi)
% 12.12/6.18  % (32306)Instruction limit reached!
% 12.12/6.18  % (32306)------------------------------
% 12.12/6.18  % (32306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.12/6.18  % (32306)Termination reason: Unknown
% 12.12/6.18  % (32306)Termination phase: shuffling
% 12.12/6.18  
% 12.12/6.18  % (32306)Memory used [KB]: 14072
% 12.12/6.18  % (32306)Time elapsed: 0.025 s
% 12.12/6.18  % (32306)Instructions burned: 46 (million)
% 12.12/6.18  % (32306)------------------------------
% 12.12/6.18  % (32306)------------------------------
% 12.12/6.19  % (32303)Instruction limit reached!
% 12.12/6.19  % (32303)------------------------------
% 12.12/6.19  % (32303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.12/6.19  % (32303)Termination reason: Unknown
% 12.12/6.19  % (32303)Termination phase: shuffling
% 12.12/6.19  
% 12.12/6.19  % (32303)Memory used [KB]: 14967
% 12.12/6.19  % (32303)Time elapsed: 0.054 s
% 12.12/6.19  % (32303)Instructions burned: 108 (million)
% 12.12/6.19  % (32303)------------------------------
% 12.12/6.19  % (32303)------------------------------
% 12.12/6.20  % (32309)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_32141 for (2991ds/149Mi)
% 12.60/6.20  % (32307)Instruction limit reached!
% 12.60/6.20  % (32307)------------------------------
% 12.60/6.20  % (32307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.60/6.20  % (32307)Termination reason: Unknown
% 12.60/6.20  % (32307)Termination phase: shuffling
% 12.60/6.20  
% 12.60/6.20  % (32307)Memory used [KB]: 14839
% 12.60/6.20  % (32307)Time elapsed: 0.037 s
% 12.60/6.20  % (32307)Instructions burned: 100 (million)
% 12.60/6.20  % (32307)------------------------------
% 12.60/6.20  % (32307)------------------------------
% 12.60/6.20  % (32310)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_32141 for (2990ds/39Mi)
% 12.60/6.21  % (32311)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_32141 for (2990ds/6Mi)
% 12.60/6.21  % (32287)Instruction limit reached!
% 12.60/6.21  % (32287)------------------------------
% 12.60/6.21  % (32287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.60/6.21  % (32287)Termination reason: Unknown
% 12.60/6.21  % (32287)Termination phase: Property scanning
% 12.60/6.21  
% 12.60/6.21  % (32287)Memory used [KB]: 25841
% 12.60/6.21  % (32287)Time elapsed: 0.330 s
% 12.60/6.21  % (32287)Instructions burned: 903 (million)
% 12.60/6.21  % (32287)------------------------------
% 12.60/6.21  % (32287)------------------------------
% 12.60/6.21  % (32311)Instruction limit reached!
% 12.60/6.21  % (32311)------------------------------
% 12.60/6.21  % (32311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.60/6.21  % (32311)Termination reason: Unknown
% 12.60/6.21  % (32311)Termination phase: shuffling
% 12.60/6.21  
% 12.60/6.21  % (32311)Memory used [KB]: 12153
% 12.60/6.21  % (32311)Time elapsed: 0.007 s
% 12.60/6.21  % (32311)Instructions burned: 6 (million)
% 12.60/6.21  % (32311)------------------------------
% 12.60/6.21  % (32311)------------------------------
% 12.60/6.22  % (32310)Instruction limit reached!
% 12.60/6.22  % (32310)------------------------------
% 12.60/6.22  % (32310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.60/6.22  % (32310)Termination reason: Unknown
% 12.60/6.22  % (32310)Termination phase: shuffling
% 12.60/6.22  
% 12.60/6.22  % (32310)Memory used [KB]: 13944
% 12.60/6.22  % (32310)Time elapsed: 0.023 s
% 12.60/6.22  % (32310)Instructions burned: 41 (million)
% 12.60/6.22  % (32310)------------------------------
% 12.60/6.22  % (32310)------------------------------
% 12.60/6.23  % (32312)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_32141 for (2990ds/1087Mi)
% 12.60/6.23  % (32313)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_32141 for (2990ds/47Mi)
% 12.60/6.23  % (32314)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_32141 for (2990ds/44Mi)
% 12.60/6.25  % (32294)Instruction limit reached!
% 12.60/6.25  % (32294)------------------------------
% 12.60/6.25  % (32294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.60/6.25  % (32294)Termination reason: Unknown
% 12.60/6.25  % (32294)Termination phase: Property scanning
% 12.60/6.25  
% 12.60/6.25  % (32294)Memory used [KB]: 25713
% 12.60/6.25  % (32294)Time elapsed: 0.301 s
% 12.60/6.25  % (32294)Instructions burned: 880 (million)
% 12.60/6.25  % (32294)------------------------------
% 12.60/6.25  % (32294)------------------------------
% 12.60/6.25  % (32313)Instruction limit reached!
% 12.60/6.25  % (32313)------------------------------
% 12.60/6.25  % (32313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.60/6.25  % (32313)Termination reason: Unknown
% 12.60/6.25  % (32313)Termination phase: shuffling
% 12.60/6.25  
% 12.60/6.25  % (32313)Memory used [KB]: 14072
% 12.60/6.25  % (32313)Time elapsed: 0.026 s
% 12.60/6.25  % (32313)Instructions burned: 49 (million)
% 12.60/6.25  % (32313)------------------------------
% 12.60/6.25  % (32313)------------------------------
% 12.60/6.25  % (32309)Instruction limit reached!
% 12.60/6.25  % (32309)------------------------------
% 12.60/6.25  % (32309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.60/6.25  % (32309)Termination reason: Unknown
% 12.60/6.25  % (32309)Termination phase: shuffling
% 12.60/6.25  
% 12.60/6.25  % (32309)Memory used [KB]: 15479
% 12.60/6.25  % (32309)Time elapsed: 0.061 s
% 12.60/6.25  % (32309)Instructions burned: 149 (million)
% 12.60/6.25  % (32309)------------------------------
% 12.60/6.25  % (32309)------------------------------
% 12.60/6.26  % (32314)Instruction limit reached!
% 12.60/6.26  % (32314)------------------------------
% 12.60/6.26  % (32314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.60/6.26  % (32314)Termination reason: Unknown
% 12.60/6.26  % (32314)Termination phase: shuffling
% 12.60/6.26  
% 12.60/6.26  % (32314)Memory used [KB]: 14072
% 12.60/6.26  % (32314)Time elapsed: 0.023 s
% 12.60/6.26  % (32314)Instructions burned: 44 (million)
% 12.60/6.26  % (32314)------------------------------
% 12.60/6.26  % (32314)------------------------------
% 12.60/6.26  % (32315)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_32141 for (2990ds/432Mi)
% 12.60/6.26  % (32316)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_32141 for (2990ds/62Mi)
% 12.60/6.27  % (32317)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_32141 for (2990ds/31Mi)
% 12.60/6.27  % (32318)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_32141 for (2990ds/96Mi)
% 12.60/6.28  % (32317)Instruction limit reached!
% 12.60/6.28  % (32317)------------------------------
% 12.60/6.28  % (32317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.60/6.28  % (32317)Termination reason: Unknown
% 12.60/6.28  % (32317)Termination phase: shuffling
% 12.60/6.28  
% 12.60/6.28  % (32317)Memory used [KB]: 13944
% 12.60/6.28  % (32317)Time elapsed: 0.019 s
% 12.60/6.28  % (32317)Instructions burned: 32 (million)
% 12.60/6.28  % (32317)------------------------------
% 12.60/6.28  % (32317)------------------------------
% 12.60/6.29  % (32316)Instruction limit reached!
% 12.60/6.29  % (32316)------------------------------
% 12.60/6.29  % (32316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.60/6.29  % (32316)Termination reason: Unknown
% 12.60/6.29  % (32316)Termination phase: shuffling
% 12.60/6.29  
% 12.60/6.29  % (32316)Memory used [KB]: 14328
% 12.60/6.29  % (32316)Time elapsed: 0.027 s
% 12.60/6.29  % (32316)Instructions burned: 64 (million)
% 12.60/6.29  % (32316)------------------------------
% 12.60/6.29  % (32316)------------------------------
% 12.60/6.29  % (32305)Instruction limit reached!
% 12.60/6.29  % (32305)------------------------------
% 12.60/6.29  % (32305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.60/6.29  % (32305)Termination reason: Unknown
% 12.60/6.29  % (32305)Termination phase: shuffling
% 12.60/6.29  
% 12.60/6.29  % (32305)Memory used [KB]: 21875
% 12.60/6.29  % (32305)Time elapsed: 0.137 s
% 12.60/6.29  % (32305)Instructions burned: 451 (million)
% 12.60/6.29  % (32305)------------------------------
% 12.60/6.29  % (32305)------------------------------
% 12.60/6.29  % (32319)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_32141 for (2990ds/453Mi)
% 13.15/6.30  % (32320)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_32141 for (2990ds/71Mi)
% 13.15/6.31  % (32321)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_32141 for (2989ds/83Mi)
% 13.15/6.31  % (32318)Instruction limit reached!
% 13.15/6.31  % (32318)------------------------------
% 13.15/6.31  % (32318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.15/6.31  % (32318)Termination reason: Unknown
% 13.15/6.31  % (32318)Termination phase: shuffling
% 13.15/6.31  
% 13.15/6.31  % (32318)Memory used [KB]: 14839
% 13.15/6.31  % (32318)Time elapsed: 0.041 s
% 13.15/6.31  % (32318)Instructions burned: 97 (million)
% 13.15/6.31  % (32318)------------------------------
% 13.15/6.31  % (32318)------------------------------
% 13.15/6.32  % (32322)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_32141 for (2989ds/11Mi)
% 13.15/6.33  % (32322)Instruction limit reached!
% 13.15/6.33  % (32322)------------------------------
% 13.15/6.33  % (32322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.15/6.33  % (32322)Termination reason: Unknown
% 13.15/6.33  % (32322)Termination phase: shuffling
% 13.15/6.33  
% 13.15/6.33  % (32322)Memory used [KB]: 12665
% 13.15/6.33  % (32322)Time elapsed: 0.011 s
% 13.15/6.33  % (32322)Instructions burned: 11 (million)
% 13.15/6.33  % (32322)------------------------------
% 13.15/6.33  % (32322)------------------------------
% 13.15/6.33  % (32320)Instruction limit reached!
% 13.15/6.33  % (32320)------------------------------
% 13.15/6.33  % (32320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.15/6.33  % (32320)Termination reason: Unknown
% 13.15/6.33  % (32320)Termination phase: shuffling
% 13.15/6.33  
% 13.15/6.33  % (32320)Memory used [KB]: 14328
% 13.15/6.33  % (32320)Time elapsed: 0.032 s
% 13.15/6.33  % (32320)Instructions burned: 71 (million)
% 13.15/6.33  % (32320)------------------------------
% 13.15/6.33  % (32320)------------------------------
% 13.15/6.34  % (32321)Instruction limit reached!
% 13.15/6.34  % (32321)------------------------------
% 13.15/6.34  % (32321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.15/6.34  % (32321)Termination reason: Unknown
% 13.15/6.34  % (32321)Termination phase: shuffling
% 13.15/6.34  
% 13.15/6.34  % (32321)Memory used [KB]: 14583
% 13.15/6.34  % (32321)Time elapsed: 0.036 s
% 13.15/6.34  % (32321)Instructions burned: 84 (million)
% 13.15/6.34  % (32321)------------------------------
% 13.15/6.34  % (32321)------------------------------
% 13.15/6.34  % (32323)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_32141 for (2989ds/41Mi)
% 13.15/6.34  % (32324)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32141 for (2989ds/6Mi)
% 13.15/6.35  % (32324)Instruction limit reached!
% 13.15/6.35  % (32324)------------------------------
% 13.15/6.35  % (32324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.15/6.35  % (32324)Termination reason: Unknown
% 13.15/6.35  % (32324)Termination phase: shuffling
% 13.15/6.35  
% 13.15/6.35  % (32324)Memory used [KB]: 12153
% 13.15/6.35  % (32324)Time elapsed: 0.006 s
% 13.15/6.35  % (32324)Instructions burned: 6 (million)
% 13.15/6.35  % (32324)------------------------------
% 13.15/6.35  % (32324)------------------------------
% 13.15/6.35  % (32325)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_32141 for (2989ds/150Mi)
% 13.15/6.35  % (32308)Instruction limit reached!
% 13.15/6.35  % (32308)------------------------------
% 13.15/6.35  % (32308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.15/6.35  % (32308)Termination reason: Unknown
% 13.15/6.35  % (32308)Termination phase: shuffling
% 13.15/6.35  
% 13.15/6.35  % (32308)Memory used [KB]: 20212
% 13.15/6.35  % (32308)Time elapsed: 0.183 s
% 13.15/6.35  % (32308)Instructions burned: 509 (million)
% 13.15/6.35  % (32308)------------------------------
% 13.15/6.35  % (32308)------------------------------
% 13.15/6.36  % (32326)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_32141 for (2989ds/343Mi)
% 13.15/6.36  % (32323)Instruction limit reached!
% 13.15/6.36  % (32323)------------------------------
% 13.15/6.36  % (32323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.15/6.36  % (32323)Termination reason: Unknown
% 13.15/6.36  % (32323)Termination phase: shuffling
% 13.15/6.36  
% 13.15/6.36  % (32323)Memory used [KB]: 14072
% 13.15/6.36  % (32323)Time elapsed: 0.021 s
% 13.15/6.36  % (32323)Instructions burned: 42 (million)
% 13.15/6.36  % (32323)------------------------------
% 13.15/6.36  % (32323)------------------------------
% 13.15/6.36  % (32327)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_32141 for (2989ds/109Mi)
% 13.15/6.37  % (32328)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_32141 for (2989ds/253Mi)
% 13.15/6.39  % (32315)Instruction limit reached!
% 13.15/6.39  % (32315)------------------------------
% 13.15/6.39  % (32315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.15/6.39  % (32315)Termination reason: Unknown
% 13.15/6.39  % (32315)Termination phase: shuffling
% 13.15/6.39  
% 13.15/6.39  % (32315)Memory used [KB]: 21620
% 13.15/6.39  % (32315)Time elapsed: 0.133 s
% 13.15/6.39  % (32315)Instructions burned: 434 (million)
% 13.15/6.39  % (32315)------------------------------
% 13.15/6.39  % (32315)------------------------------
% 13.69/6.41  % (32329)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_32141 for (2989ds/140Mi)
% 13.69/6.41  % (32325)Instruction limit reached!
% 13.69/6.41  % (32325)------------------------------
% 13.69/6.41  % (32325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/6.41  % (32325)Termination reason: Unknown
% 13.69/6.41  % (32325)Termination phase: shuffling
% 13.69/6.41  
% 13.69/6.41  % (32325)Memory used [KB]: 15479
% 13.69/6.41  % (32325)Time elapsed: 0.058 s
% 13.69/6.41  % (32325)Instructions burned: 150 (million)
% 13.69/6.41  % (32325)------------------------------
% 13.69/6.41  % (32325)------------------------------
% 13.69/6.41  % (32327)Instruction limit reached!
% 13.69/6.41  % (32327)------------------------------
% 13.69/6.41  % (32327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/6.41  % (32327)Termination reason: Unknown
% 13.69/6.41  % (32327)Termination phase: shuffling
% 13.69/6.41  
% 13.69/6.41  % (32327)Memory used [KB]: 14967
% 13.69/6.41  % (32327)Time elapsed: 0.045 s
% 13.69/6.41  % (32327)Instructions burned: 110 (million)
% 13.69/6.41  % (32327)------------------------------
% 13.69/6.41  % (32327)------------------------------
% 13.69/6.42  % (32330)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_32141 for (2988ds/614Mi)
% 13.69/6.42  % (32331)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_32141 for (2988ds/202Mi)
% 13.69/6.43  % (32319)Instruction limit reached!
% 13.69/6.43  % (32319)------------------------------
% 13.69/6.43  % (32319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/6.43  % (32319)Termination reason: Unknown
% 13.69/6.43  % (32319)Termination phase: shuffling
% 13.69/6.43  
% 13.69/6.43  % (32319)Memory used [KB]: 21875
% 13.69/6.43  % (32319)Time elapsed: 0.138 s
% 13.69/6.43  % (32319)Instructions burned: 454 (million)
% 13.69/6.43  % (32319)------------------------------
% 13.69/6.43  % (32319)------------------------------
% 13.69/6.44  % (32332)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_32141 for (2988ds/339Mi)
% 13.69/6.46  % (32329)Instruction limit reached!
% 13.69/6.46  % (32329)------------------------------
% 13.69/6.46  % (32329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/6.46  % (32329)Termination reason: Unknown
% 13.69/6.46  % (32329)Termination phase: shuffling
% 13.69/6.46  
% 13.69/6.46  % (32329)Memory used [KB]: 15351
% 13.69/6.46  % (32329)Time elapsed: 0.054 s
% 13.69/6.46  % (32329)Instructions burned: 140 (million)
% 13.69/6.46  % (32329)------------------------------
% 13.69/6.46  % (32329)------------------------------
% 13.69/6.46  % (32328)Instruction limit reached!
% 13.69/6.46  % (32328)------------------------------
% 13.69/6.46  % (32328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/6.46  % (32328)Termination reason: Unknown
% 13.69/6.46  % (32328)Termination phase: shuffling
% 13.69/6.46  
% 13.69/6.46  % (32328)Memory used [KB]: 17014
% 13.69/6.46  % (32328)Time elapsed: 0.095 s
% 13.69/6.46  % (32328)Instructions burned: 255 (million)
% 13.69/6.46  % (32328)------------------------------
% 13.69/6.46  % (32328)------------------------------
% 13.69/6.47  % (32333)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_32141 for (2988ds/283Mi)
% 13.69/6.47  % (32334)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_32141 for (2988ds/134Mi)
% 13.69/6.48  % (32326)Instruction limit reached!
% 13.69/6.48  % (32326)------------------------------
% 13.69/6.48  % (32326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/6.48  % (32326)Termination reason: Unknown
% 13.69/6.48  % (32326)Termination phase: shuffling
% 13.69/6.48  
% 13.69/6.48  % (32326)Memory used [KB]: 18293
% 13.69/6.48  % (32326)Time elapsed: 0.123 s
% 13.69/6.48  % (32326)Instructions burned: 345 (million)
% 13.69/6.48  % (32326)------------------------------
% 13.69/6.48  % (32326)------------------------------
% 13.69/6.49  % (32335)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_32141 for (2988ds/298Mi)
% 13.69/6.49  % (32331)Instruction limit reached!
% 13.69/6.49  % (32331)------------------------------
% 13.69/6.49  % (32331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/6.49  % (32331)Termination reason: Unknown
% 13.69/6.49  % (32331)Termination phase: shuffling
% 13.69/6.49  
% 13.69/6.49  % (32331)Memory used [KB]: 16375
% 13.69/6.49  % (32331)Time elapsed: 0.076 s
% 13.69/6.49  % (32331)Instructions burned: 202 (million)
% 13.69/6.49  % (32331)------------------------------
% 13.69/6.49  % (32331)------------------------------
% 14.35/6.50  % (32336)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_32141 for (2987ds/192Mi)
% 14.35/6.53  % (32334)Instruction limit reached!
% 14.35/6.53  % (32334)------------------------------
% 14.35/6.53  % (32334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.35/6.53  % (32334)Termination reason: Unknown
% 14.35/6.53  % (32334)Termination phase: shuffling
% 14.35/6.53  
% 14.35/6.53  % (32334)Memory used [KB]: 15351
% 14.35/6.53  % (32334)Time elapsed: 0.054 s
% 14.35/6.53  % (32334)Instructions burned: 135 (million)
% 14.35/6.53  % (32334)------------------------------
% 14.35/6.53  % (32334)------------------------------
% 14.35/6.54  % (32337)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_32141 for (2987ds/258Mi)
% 14.35/6.56  % (32333)Instruction limit reached!
% 14.35/6.56  % (32333)------------------------------
% 14.35/6.56  % (32333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.35/6.56  % (32333)Termination reason: Unknown
% 14.35/6.56  % (32333)Termination phase: shuffling
% 14.35/6.56  
% 14.35/6.56  % (32333)Memory used [KB]: 19445
% 14.35/6.56  % (32333)Time elapsed: 0.089 s
% 14.35/6.56  % (32333)Instructions burned: 285 (million)
% 14.35/6.56  % (32333)------------------------------
% 14.35/6.56  % (32333)------------------------------
% 14.35/6.56  % (32332)Instruction limit reached!
% 14.35/6.56  % (32332)------------------------------
% 14.35/6.56  % (32332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.35/6.56  % (32332)Termination reason: Unknown
% 14.35/6.56  % (32332)Termination phase: shuffling
% 14.35/6.56  
% 14.35/6.56  % (32332)Memory used [KB]: 18166
% 14.35/6.56  % (32332)Time elapsed: 0.120 s
% 14.35/6.56  % (32332)Instructions burned: 340 (million)
% 14.35/6.56  % (32332)------------------------------
% 14.35/6.56  % (32332)------------------------------
% 14.35/6.57  % (32338)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_32141 for (2987ds/90Mi)
% 14.35/6.57  % (32339)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_32141 for (2987ds/231Mi)
% 14.35/6.58  % (32336)Instruction limit reached!
% 14.35/6.58  % (32336)------------------------------
% 14.35/6.58  % (32336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.35/6.58  % (32336)Termination reason: Unknown
% 14.35/6.58  % (32336)Termination phase: shuffling
% 14.35/6.58  
% 14.35/6.58  % (32336)Memory used [KB]: 16119
% 14.35/6.58  % (32336)Time elapsed: 0.072 s
% 14.35/6.58  % (32336)Instructions burned: 193 (million)
% 14.35/6.58  % (32336)------------------------------
% 14.35/6.58  % (32336)------------------------------
% 14.35/6.58  % (32312)Instruction limit reached!
% 14.35/6.58  % (32312)------------------------------
% 14.35/6.58  % (32312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.35/6.58  % (32312)Termination reason: Unknown
% 14.35/6.58  % (32312)Termination phase: Property scanning
% 14.35/6.58  
% 14.35/6.58  % (32312)Memory used [KB]: 25713
% 14.35/6.58  % (32312)Time elapsed: 0.353 s
% 14.35/6.58  % (32312)Instructions burned: 1089 (million)
% 14.35/6.58  % (32312)------------------------------
% 14.35/6.58  % (32312)------------------------------
% 14.35/6.58  % (32335)Instruction limit reached!
% 14.35/6.58  % (32335)------------------------------
% 14.35/6.58  % (32335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.35/6.58  % (32335)Termination reason: Unknown
% 14.35/6.58  % (32335)Termination phase: shuffling
% 14.35/6.58  
% 14.35/6.58  % (32335)Memory used [KB]: 19701
% 14.35/6.58  % (32335)Time elapsed: 0.093 s
% 14.35/6.58  % (32335)Instructions burned: 301 (million)
% 14.35/6.58  % (32335)------------------------------
% 14.35/6.58  % (32335)------------------------------
% 14.35/6.59  % (32340)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_32141 for (2987ds/458Mi)
% 14.35/6.59  % (32341)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_32141 for (2987ds/31Mi)
% 14.35/6.59  % (32342)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_32141 for (2987ds/297Mi)
% 15.20/6.61  % (32341)Instruction limit reached!
% 15.20/6.61  % (32341)------------------------------
% 15.20/6.61  % (32341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.20/6.61  % (32341)Termination reason: Unknown
% 15.20/6.61  % (32341)Termination phase: shuffling
% 15.20/6.61  
% 15.20/6.61  % (32341)Memory used [KB]: 13944
% 15.20/6.61  % (32341)Time elapsed: 0.019 s
% 15.20/6.61  % (32341)Instructions burned: 32 (million)
% 15.20/6.61  % (32341)------------------------------
% 15.20/6.61  % (32341)------------------------------
% 15.20/6.61  % (32338)Instruction limit reached!
% 15.20/6.61  % (32338)------------------------------
% 15.20/6.61  % (32338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.20/6.61  % (32338)Termination reason: Unknown
% 15.20/6.61  % (32338)Termination phase: shuffling
% 15.20/6.61  
% 15.20/6.61  % (32338)Memory used [KB]: 14711
% 15.20/6.61  % (32338)Time elapsed: 0.038 s
% 15.20/6.61  % (32338)Instructions burned: 90 (million)
% 15.20/6.61  % (32338)------------------------------
% 15.20/6.61  % (32338)------------------------------
% 15.20/6.62  % (32343)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_32141 for (2986ds/987Mi)
% 15.20/6.62  % (32344)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_32141 for (2986ds/182Mi)
% 15.20/6.63  % (32330)Instruction limit reached!
% 15.20/6.63  % (32330)------------------------------
% 15.20/6.63  % (32330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.20/6.63  % (32330)Termination reason: Unknown
% 15.20/6.63  % (32330)Termination phase: shuffling
% 15.20/6.63  
% 15.20/6.63  % (32330)Memory used [KB]: 23922
% 15.20/6.63  % (32330)Time elapsed: 0.214 s
% 15.20/6.63  % (32330)Instructions burned: 616 (million)
% 15.20/6.63  % (32330)------------------------------
% 15.20/6.63  % (32330)------------------------------
% 15.20/6.63  % (32337)Instruction limit reached!
% 15.20/6.63  % (32337)------------------------------
% 15.20/6.63  % (32337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.20/6.63  % (32337)Termination reason: Unknown
% 15.20/6.63  % (32337)Termination phase: shuffling
% 15.20/6.63  
% 15.20/6.63  % (32337)Memory used [KB]: 17014
% 15.20/6.63  % (32337)Time elapsed: 0.094 s
% 15.20/6.63  % (32337)Instructions burned: 259 (million)
% 15.20/6.63  % (32337)------------------------------
% 15.20/6.63  % (32337)------------------------------
% 15.20/6.64  % (32346)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_32141 for (2986ds/154Mi)
% 15.20/6.64  % (32345)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_32141 for (2986ds/182Mi)
% 15.20/6.65  % (32339)Instruction limit reached!
% 15.20/6.65  % (32339)------------------------------
% 15.20/6.65  % (32339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.20/6.65  % (32339)Termination reason: Unknown
% 15.20/6.65  % (32339)Termination phase: shuffling
% 15.20/6.65  
% 15.20/6.65  % (32339)Memory used [KB]: 16758
% 15.20/6.65  % (32339)Time elapsed: 0.074 s
% 15.20/6.65  % (32339)Instructions burned: 232 (million)
% 15.20/6.65  % (32339)------------------------------
% 15.20/6.65  % (32339)------------------------------
% 15.20/6.66  % (32347)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_32141 for (2986ds/79Mi)
% 15.20/6.68  % (32342)Instruction limit reached!
% 15.20/6.68  % (32342)------------------------------
% 15.20/6.68  % (32342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.20/6.68  % (32342)Termination reason: Unknown
% 15.20/6.68  % (32342)Termination phase: shuffling
% 15.20/6.68  
% 15.20/6.68  % (32342)Memory used [KB]: 19701
% 15.20/6.68  % (32342)Time elapsed: 0.093 s
% 15.20/6.68  % (32342)Instructions burned: 297 (million)
% 15.20/6.68  % (32342)------------------------------
% 15.20/6.68  % (32342)------------------------------
% 15.20/6.69  % (32344)Instruction limit reached!
% 15.20/6.69  % (32344)------------------------------
% 15.20/6.69  % (32344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.20/6.69  % (32344)Termination reason: Unknown
% 15.20/6.69  % (32344)Termination phase: shuffling
% 15.20/6.69  
% 15.20/6.69  % (32344)Memory used [KB]: 16119
% 15.20/6.69  % (32344)Time elapsed: 0.069 s
% 15.20/6.69  % (32344)Instructions burned: 184 (million)
% 15.20/6.69  % (32344)------------------------------
% 15.20/6.69  % (32344)------------------------------
% 15.20/6.69  % (32347)Instruction limit reached!
% 15.20/6.69  % (32347)------------------------------
% 15.20/6.69  % (32347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.20/6.69  % (32347)Termination reason: Unknown
% 15.20/6.69  % (32347)Termination phase: shuffling
% 15.20/6.69  
% 15.20/6.69  % (32347)Memory used [KB]: 14456
% 15.20/6.69  % (32347)Time elapsed: 0.034 s
% 15.20/6.69  % (32347)Instructions burned: 79 (million)
% 15.20/6.69  % (32347)------------------------------
% 15.20/6.69  % (32347)------------------------------
% 15.20/6.69  % (32346)Instruction limit reached!
% 15.20/6.69  % (32346)------------------------------
% 15.20/6.69  % (32346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.20/6.69  % (32346)Termination reason: Unknown
% 15.20/6.69  % (32346)Termination phase: shuffling
% 15.20/6.69  
% 15.20/6.69  % (32346)Memory used [KB]: 15607
% 15.20/6.69  % (32346)Time elapsed: 0.052 s
% 15.20/6.69  % (32346)Instructions burned: 155 (million)
% 15.20/6.69  % (32346)------------------------------
% 15.20/6.69  % (32346)------------------------------
% 15.97/6.70  % (32348)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_32141 for (2986ds/216Mi)
% 15.97/6.70  % (32349)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_32141 for (2986ds/114Mi)
% 15.97/6.70  % (32350)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_32141 for (2985ds/922Mi)
% 15.97/6.71  % (32351)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_32141 for (2985ds/182Mi)
% 15.97/6.71  % (32345)Instruction limit reached!
% 15.97/6.71  % (32345)------------------------------
% 15.97/6.71  % (32345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.97/6.71  % (32345)Termination reason: Unknown
% 15.97/6.71  % (32345)Termination phase: shuffling
% 15.97/6.71  
% 15.97/6.71  % (32345)Memory used [KB]: 15991
% 15.97/6.71  % (32345)Time elapsed: 0.069 s
% 15.97/6.71  % (32345)Instructions burned: 182 (million)
% 15.97/6.71  % (32345)------------------------------
% 15.97/6.71  % (32345)------------------------------
% 15.97/6.72  % (32352)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_32141 for (2985ds/164Mi)
% 15.97/6.74  % (32349)Instruction limit reached!
% 15.97/6.74  % (32349)------------------------------
% 15.97/6.74  % (32349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.97/6.74  % (32349)Termination reason: Unknown
% 15.97/6.74  % (32349)Termination phase: shuffling
% 15.97/6.74  
% 15.97/6.74  % (32349)Memory used [KB]: 15095
% 15.97/6.74  % (32349)Time elapsed: 0.046 s
% 15.97/6.74  % (32349)Instructions burned: 114 (million)
% 15.97/6.74  % (32349)------------------------------
% 15.97/6.74  % (32349)------------------------------
% 15.97/6.75  % (32340)Instruction limit reached!
% 15.97/6.75  % (32340)------------------------------
% 15.97/6.75  % (32340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.97/6.75  % (32340)Termination reason: Unknown
% 15.97/6.75  % (32340)Termination phase: shuffling
% 15.97/6.75  
% 15.97/6.75  % (32340)Memory used [KB]: 19829
% 15.97/6.75  % (32340)Time elapsed: 0.161 s
% 15.97/6.75  % (32340)Instructions burned: 458 (million)
% 15.97/6.75  % (32340)------------------------------
% 15.97/6.75  % (32340)------------------------------
% 15.97/6.75  % (32353)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_32141 for (2985ds/50Mi)
% 15.97/6.76  % (32354)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_32141 for (2985ds/368Mi)
% 15.97/6.76  % (32351)Instruction limit reached!
% 15.97/6.76  % (32351)------------------------------
% 15.97/6.76  % (32351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.97/6.76  % (32351)Termination reason: Unknown
% 15.97/6.76  % (32351)Termination phase: shuffling
% 15.97/6.76  
% 15.97/6.76  % (32351)Memory used [KB]: 15991
% 15.97/6.76  % (32351)Time elapsed: 0.060 s
% 15.97/6.76  % (32351)Instructions burned: 183 (million)
% 15.97/6.76  % (32351)------------------------------
% 15.97/6.76  % (32351)------------------------------
% 15.97/6.76  % (32348)Instruction limit reached!
% 15.97/6.76  % (32348)------------------------------
% 15.97/6.76  % (32348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.97/6.76  % (32348)Termination reason: Unknown
% 15.97/6.76  % (32348)Termination phase: shuffling
% 15.97/6.76  
% 15.97/6.76  % (32348)Memory used [KB]: 16502
% 15.97/6.76  % (32348)Time elapsed: 0.069 s
% 15.97/6.76  % (32348)Instructions burned: 218 (million)
% 15.97/6.76  % (32348)------------------------------
% 15.97/6.76  % (32348)------------------------------
% 15.97/6.78  % (32353)Instruction limit reached!
% 15.97/6.78  % (32353)------------------------------
% 15.97/6.78  % (32353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.97/6.78  % (32353)Termination reason: Unknown
% 15.97/6.78  % (32353)Termination phase: shuffling
% 15.97/6.78  
% 15.97/6.78  % (32353)Memory used [KB]: 14200
% 15.97/6.78  % (32353)Time elapsed: 0.023 s
% 15.97/6.78  % (32353)Instructions burned: 51 (million)
% 15.97/6.78  % (32353)------------------------------
% 15.97/6.78  % (32353)------------------------------
% 15.97/6.78  % (32355)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_32141 for (2985ds/1021Mi)
% 15.97/6.78  % (32356)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_32141 for (2985ds/267Mi)
% 15.97/6.78  % (32352)Instruction limit reached!
% 15.97/6.78  % (32352)------------------------------
% 15.97/6.78  % (32352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.97/6.78  % (32352)Termination reason: Unknown
% 15.97/6.78  % (32352)Termination phase: shuffling
% 15.97/6.78  
% 15.97/6.78  % (32352)Memory used [KB]: 15863
% 15.97/6.78  % (32352)Time elapsed: 0.055 s
% 15.97/6.78  % (32352)Instructions burned: 164 (million)
% 15.97/6.78  % (32352)------------------------------
% 15.97/6.78  % (32352)------------------------------
% 15.97/6.79  % (32357)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_32141 for (2985ds/204Mi)
% 15.97/6.79  % (32358)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_32141 for (2985ds/26Mi)
% 16.52/6.80  % (32358)Instruction limit reached!
% 16.52/6.80  % (32358)------------------------------
% 16.52/6.80  % (32358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.52/6.80  % (32358)Termination reason: Unknown
% 16.52/6.80  % (32358)Termination phase: shuffling
% 16.52/6.80  
% 16.52/6.80  % (32358)Memory used [KB]: 13816
% 16.52/6.80  % (32358)Time elapsed: 0.017 s
% 16.52/6.80  % (32358)Instructions burned: 26 (million)
% 16.52/6.80  % (32358)------------------------------
% 16.52/6.80  % (32358)------------------------------
% 16.52/6.82  % (32359)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_32141 for (2984ds/53Mi)
% 16.52/6.84  % (32359)Instruction limit reached!
% 16.52/6.84  % (32359)------------------------------
% 16.52/6.84  % (32359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.52/6.84  % (32359)Termination reason: Unknown
% 16.52/6.84  % (32359)Termination phase: shuffling
% 16.52/6.84  
% 16.52/6.84  % (32359)Memory used [KB]: 14200
% 16.52/6.84  % (32359)Time elapsed: 0.024 s
% 16.52/6.84  % (32359)Instructions burned: 53 (million)
% 16.52/6.84  % (32359)------------------------------
% 16.52/6.84  % (32359)------------------------------
% 16.52/6.85  % (32360)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_32141 for (2984ds/4436Mi)
% 16.52/6.86  % (32356)Instruction limit reached!
% 16.52/6.86  % (32356)------------------------------
% 16.52/6.86  % (32356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.52/6.86  % (32356)Termination reason: Unknown
% 16.52/6.86  % (32356)Termination phase: shuffling
% 16.52/6.86  
% 16.52/6.86  % (32356)Memory used [KB]: 19317
% 16.52/6.86  % (32356)Time elapsed: 0.083 s
% 16.52/6.86  % (32356)Instructions burned: 267 (million)
% 16.52/6.86  % (32356)------------------------------
% 16.52/6.86  % (32356)------------------------------
% 16.52/6.86  % (32357)Instruction limit reached!
% 16.52/6.86  % (32357)------------------------------
% 16.52/6.86  % (32357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.52/6.86  % (32357)Termination reason: Unknown
% 16.52/6.86  % (32357)Termination phase: shuffling
% 16.52/6.86  
% 16.52/6.86  % (32357)Memory used [KB]: 16375
% 16.52/6.86  % (32357)Time elapsed: 0.077 s
% 16.52/6.86  % (32357)Instructions burned: 206 (million)
% 16.52/6.86  % (32357)------------------------------
% 16.52/6.86  % (32357)------------------------------
% 16.52/6.87  % (32361)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_32141 for (2984ds/1539Mi)
% 16.52/6.87  % (32362)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_32141 for (2984ds/408Mi)
% 16.52/6.89  % (32354)Instruction limit reached!
% 16.52/6.89  % (32354)------------------------------
% 16.52/6.89  % (32354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.52/6.89  % (32354)Termination reason: Unknown
% 16.52/6.89  % (32354)Termination phase: shuffling
% 16.52/6.89  
% 16.52/6.89  % (32354)Memory used [KB]: 18677
% 16.52/6.89  % (32354)Time elapsed: 0.131 s
% 16.52/6.89  % (32354)Instructions burned: 368 (million)
% 16.52/6.89  % (32354)------------------------------
% 16.52/6.89  % (32354)------------------------------
% 16.90/6.90  % (32363)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_32141 for (2983ds/5205Mi)
% 16.90/6.91  % (32343)Instruction limit reached!
% 16.90/6.91  % (32343)------------------------------
% 16.90/6.91  % (32343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.90/6.91  % (32343)Termination reason: Unknown
% 16.90/6.91  % (32343)Termination phase: shuffling
% 16.90/6.91  
% 16.90/6.91  % (32343)Memory used [KB]: 33133
% 16.90/6.91  % (32343)Time elapsed: 0.294 s
% 16.90/6.91  % (32343)Instructions burned: 988 (million)
% 16.90/6.91  % (32343)------------------------------
% 16.90/6.91  % (32343)------------------------------
% 16.90/6.92  % (32364)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_32141 for (2983ds/1913Mi)
% 16.90/7.01  % (32350)Instruction limit reached!
% 16.90/7.01  % (32350)------------------------------
% 16.90/7.01  % (32350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.90/7.01  % (32350)Termination reason: Unknown
% 16.90/7.01  % (32350)Termination phase: Property scanning
% 16.90/7.01  
% 16.90/7.01  % (32350)Memory used [KB]: 25713
% 16.90/7.01  % (32350)Time elapsed: 0.308 s
% 16.90/7.01  % (32350)Instructions burned: 924 (million)
% 16.90/7.01  % (32350)------------------------------
% 16.90/7.01  % (32350)------------------------------
% 18.42/7.02  % (32362)Instruction limit reached!
% 18.42/7.02  % (32362)------------------------------
% 18.42/7.02  % (32362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.42/7.02  % (32362)Termination reason: Unknown
% 18.42/7.02  % (32362)Termination phase: shuffling
% 18.42/7.02  
% 18.42/7.02  % (32362)Memory used [KB]: 19189
% 18.42/7.02  % (32362)Time elapsed: 0.146 s
% 18.42/7.02  % (32362)Instructions burned: 410 (million)
% 18.42/7.02  % (32362)------------------------------
% 18.42/7.02  % (32362)------------------------------
% 18.42/7.02  % (32365)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_32141 for (2982ds/4350Mi)
% 18.42/7.03  % (32366)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_32141 for (2982ds/68Mi)
% 18.42/7.06  % (32366)Instruction limit reached!
% 18.42/7.06  % (32366)------------------------------
% 18.42/7.06  % (32366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.42/7.06  % (32366)Termination reason: Unknown
% 18.42/7.06  % (32366)Termination phase: shuffling
% 18.42/7.06  
% 18.42/7.06  % (32366)Memory used [KB]: 14328
% 18.42/7.06  % (32366)Time elapsed: 0.031 s
% 18.42/7.06  % (32366)Instructions burned: 70 (million)
% 18.42/7.06  % (32366)------------------------------
% 18.42/7.06  % (32366)------------------------------
% 18.42/7.07  % (32367)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_32141 for (2982ds/358Mi)
% 18.42/7.11  % (32355)Instruction limit reached!
% 18.42/7.11  % (32355)------------------------------
% 18.42/7.11  % (32355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.42/7.11  % (32355)Termination reason: Unknown
% 18.42/7.11  % (32355)Termination phase: Property scanning
% 18.42/7.11  
% 18.42/7.11  % (32355)Memory used [KB]: 25841
% 18.42/7.11  % (32355)Time elapsed: 0.336 s
% 18.42/7.11  % (32355)Instructions burned: 1023 (million)
% 18.42/7.11  % (32355)------------------------------
% 18.42/7.11  % (32355)------------------------------
% 18.63/7.12  % (32368)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_32141 for (2981ds/31Mi)
% 18.63/7.14  % (32368)Instruction limit reached!
% 18.63/7.14  % (32368)------------------------------
% 18.63/7.14  % (32368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.63/7.14  % (32368)Termination reason: Unknown
% 18.63/7.14  % (32368)Termination phase: shuffling
% 18.63/7.14  
% 18.63/7.14  % (32368)Memory used [KB]: 13944
% 18.63/7.14  % (32368)Time elapsed: 0.019 s
% 18.63/7.14  % (32368)Instructions burned: 32 (million)
% 18.63/7.14  % (32368)------------------------------
% 18.63/7.14  % (32368)------------------------------
% 18.63/7.15  % (32369)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_32141 for (2981ds/279Mi)
% 19.34/7.20  % (32367)Instruction limit reached!
% 19.34/7.20  % (32367)------------------------------
% 19.34/7.20  % (32367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.34/7.20  % (32367)Termination reason: Unknown
% 19.34/7.20  % (32367)Termination phase: shuffling
% 19.34/7.20  
% 19.34/7.20  % (32367)Memory used [KB]: 18421
% 19.34/7.20  % (32367)Time elapsed: 0.130 s
% 19.34/7.20  % (32367)Instructions burned: 358 (million)
% 19.34/7.20  % (32367)------------------------------
% 19.34/7.20  % (32367)------------------------------
% 19.34/7.21  % (32370)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_32141 for (2980ds/258Mi)
% 19.34/7.24  % (32369)Instruction limit reached!
% 19.34/7.24  % (32369)------------------------------
% 19.34/7.24  % (32369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.34/7.24  % (32369)Termination reason: Unknown
% 19.34/7.24  % (32369)Termination phase: shuffling
% 19.34/7.24  
% 19.34/7.24  % (32369)Memory used [KB]: 19445
% 19.34/7.24  % (32369)Time elapsed: 0.089 s
% 19.34/7.24  % (32369)Instructions burned: 281 (million)
% 19.34/7.24  % (32369)------------------------------
% 19.34/7.24  % (32369)------------------------------
% 19.34/7.25  % (32371)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_32141 for (2980ds/26Mi)
% 19.34/7.27  % (32371)Instruction limit reached!
% 19.34/7.27  % (32371)------------------------------
% 19.34/7.27  % (32371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.34/7.27  % (32371)Termination reason: Unknown
% 19.34/7.27  % (32371)Termination phase: shuffling
% 19.34/7.27  
% 19.34/7.27  % (32371)Memory used [KB]: 13816
% 19.34/7.27  % (32371)Time elapsed: 0.016 s
% 19.34/7.27  % (32371)Instructions burned: 27 (million)
% 19.34/7.27  % (32371)------------------------------
% 19.34/7.27  % (32371)------------------------------
% 19.34/7.28  % (32372)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_32141 for (2980ds/995Mi)
% 20.01/7.30  % (32370)Instruction limit reached!
% 20.01/7.30  % (32370)------------------------------
% 20.01/7.30  % (32370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.01/7.30  % (32370)Termination reason: Unknown
% 20.01/7.30  % (32370)Termination phase: shuffling
% 20.01/7.30  
% 20.01/7.30  % (32370)Memory used [KB]: 17014
% 20.01/7.30  % (32370)Time elapsed: 0.093 s
% 20.01/7.30  % (32370)Instructions burned: 260 (million)
% 20.01/7.30  % (32370)------------------------------
% 20.01/7.30  % (32370)------------------------------
% 20.01/7.32  % (32373)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_32141 for (2979ds/373Mi)
% 20.01/7.36  % (32361)Instruction limit reached!
% 20.01/7.36  % (32361)------------------------------
% 20.01/7.36  % (32361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.01/7.36  % (32361)Termination reason: Unknown
% 20.01/7.36  % (32361)Termination phase: Preprocessing 1
% 20.01/7.36  
% 20.01/7.36  % (32361)Memory used [KB]: 26865
% 20.01/7.36  % (32361)Time elapsed: 0.495 s
% 20.01/7.36  % (32361)Instructions burned: 1541 (million)
% 20.01/7.36  % (32361)------------------------------
% 20.01/7.36  % (32361)------------------------------
% 20.01/7.38  % (32374)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_32141 for (2979ds/253Mi)
% 20.51/7.44  % (32373)Instruction limit reached!
% 20.51/7.44  % (32373)------------------------------
% 20.51/7.44  % (32373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.51/7.44  % (32373)Termination reason: Unknown
% 20.51/7.44  % (32373)Termination phase: shuffling
% 20.51/7.44  
% 20.51/7.44  % (32373)Memory used [KB]: 18677
% 20.51/7.45  % (32373)Time elapsed: 0.130 s
% 20.51/7.45  % (32373)Instructions burned: 373 (million)
% 20.51/7.45  % (32373)------------------------------
% 20.51/7.45  % (32373)------------------------------
% 20.51/7.45  % (32374)Instruction limit reached!
% 20.51/7.45  % (32374)------------------------------
% 20.51/7.45  % (32374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.51/7.45  % (32374)Termination reason: Unknown
% 20.51/7.45  % (32374)Termination phase: shuffling
% 20.51/7.45  
% 20.51/7.45  % (32374)Memory used [KB]: 17142
% 20.51/7.45  % (32374)Time elapsed: 0.079 s
% 20.51/7.45  % (32374)Instructions burned: 256 (million)
% 20.51/7.45  % (32374)------------------------------
% 20.51/7.45  % (32374)------------------------------
% 20.51/7.46  % (32375)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_32141 for (2978ds/832Mi)
% 20.51/7.46  % (32376)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_32141 for (2978ds/668Mi)
% 21.04/7.55  % (32364)Instruction limit reached!
% 21.04/7.55  % (32364)------------------------------
% 21.04/7.55  % (32364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.04/7.55  % (32364)Termination reason: Unknown
% 21.04/7.55  % (32364)Termination phase: Preprocessing 3
% 21.04/7.55  
% 21.04/7.55  % (32364)Memory used [KB]: 28144
% 21.04/7.55  % (32364)Time elapsed: 0.630 s
% 21.04/7.55  % (32364)Instructions burned: 1914 (million)
% 21.04/7.55  % (32364)------------------------------
% 21.04/7.55  % (32364)------------------------------
% 21.04/7.57  % (32377)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_32141 for (2977ds/40Mi)
% 21.04/7.58  % (32372)Instruction limit reached!
% 21.04/7.58  % (32372)------------------------------
% 21.04/7.58  % (32372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.04/7.58  % (32372)Termination reason: Unknown
% 21.04/7.58  % (32372)Termination phase: shuffling
% 21.04/7.58  
% 21.04/7.58  % (32372)Memory used [KB]: 33261
% 21.04/7.58  % (32372)Time elapsed: 0.298 s
% 21.04/7.58  % (32372)Instructions burned: 996 (million)
% 21.04/7.58  % (32372)------------------------------
% 21.04/7.58  % (32372)------------------------------
% 21.04/7.58  % (32365)First to succeed.
% 21.04/7.58  % (32377)Instruction limit reached!
% 21.04/7.58  % (32377)------------------------------
% 21.04/7.58  % (32377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.04/7.58  % (32377)Termination reason: Unknown
% 21.04/7.58  % (32377)Termination phase: shuffling
% 21.04/7.58  
% 21.04/7.58  % (32377)Memory used [KB]: 14072
% 21.04/7.58  % (32377)Time elapsed: 0.020 s
% 21.04/7.58  % (32377)Instructions burned: 40 (million)
% 21.04/7.58  % (32377)------------------------------
% 21.04/7.58  % (32377)------------------------------
% 21.04/7.59  % (32378)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_32141 for (2977ds/294Mi)
% 21.04/7.59  % (32365)Refutation found. Thanks to Tanya!
% 21.04/7.59  % SZS status Theorem for DTF2THF_32141
% 21.04/7.59  % SZS output start Proof for DTF2THF_32141
% 21.04/7.59  thf(type_def_5, type, rat: $tType).
% 21.04/7.59  thf(type_def_6, type, int: $tType).
% 21.04/7.59  thf(type_def_8, type, produc3658429121746597890et_nat: $tType).
% 21.04/7.59  thf(type_def_9, type, assn: $tType).
% 21.04/7.59  thf(type_def_10, type, set_nat: $tType).
% 21.04/7.59  thf(type_def_11, type, heap_e7401611519738050253t_unit: $tType).
% 21.04/7.59  thf(type_def_12, type, produc2732055786443039994et_nat: $tType).
% 21.04/7.59  thf(type_def_13, type, set_Pr5094982260447487303t_unit: $tType).
% 21.04/7.59  thf(type_def_14, type, set_Product_prod_o_o: $tType).
% 21.04/7.59  thf(type_def_15, type, set_o: $tType).
% 21.04/7.59  thf(type_def_16, type, set_Pr1261947904930325089at_nat: $tType).
% 21.04/7.59  thf(type_def_17, type, set_Product_unit: $tType).
% 21.04/7.59  thf(type_def_18, type, nat: $tType).
% 21.04/7.59  thf(type_def_19, type, product_prod_nat_nat: $tType).
% 21.04/7.59  thf(type_def_20, type, produc3843707927480180839at_nat: $tType).
% 21.04/7.59  thf(type_def_21, type, set_Pr958786334691620121nt_int: $tType).
% 21.04/7.59  thf(type_def_22, type, list_nat: $tType).
% 21.04/7.59  thf(type_def_23, type, list_char: $tType).
% 21.04/7.59  thf(type_def_24, type, literal: $tType).
% 21.04/7.59  thf(type_def_25, type, code_integer: $tType).
% 21.04/7.59  thf(type_def_26, type, product_prod_int_int: $tType).
% 21.04/7.59  thf(type_def_27, type, list_Code_integer: $tType).
% 21.04/7.59  thf(type_def_28, type, num: $tType).
% 21.04/7.59  thf(type_def_29, type, set_Pr1932065953672099015od_o_o: $tType).
% 21.04/7.59  thf(type_def_30, type, set_Pr4329608150637261639at_nat: $tType).
% 21.04/7.59  thf(type_def_31, type, set_Pr457366540195662369at_nat: $tType).
% 21.04/7.59  thf(type_def_32, type, code_natural: $tType).
% 21.04/7.59  thf(type_def_33, type, option_num: $tType).
% 21.04/7.59  thf(type_def_34, type, product_prod_num_num: $tType).
% 21.04/7.59  thf(type_def_35, type, product_unit: $tType).
% 21.04/7.59  thf(type_def_36, type, set_int: $tType).
% 21.04/7.59  thf(type_def_37, type, set_list_nat: $tType).
% 21.04/7.59  thf(type_def_38, type, set_Pr8551490117392284871at_nat: $tType).
% 21.04/7.59  thf(type_def_39, type, set_rat: $tType).
% 21.04/7.59  thf(type_def_40, type, produc6271795597528267376eger_o: $tType).
% 21.04/7.59  thf(type_def_41, type, produc8923325533196201883nteger: $tType).
% 21.04/7.59  thf(type_def_42, type, set_set_nat: $tType).
% 21.04/7.59  thf(type_def_43, type, filter_nat: $tType).
% 21.04/7.59  thf(type_def_44, type, filter1242075044329608583at_nat: $tType).
% 21.04/7.59  thf(type_def_45, type, filter_set_nat: $tType).
% 21.04/7.59  thf(type_def_46, type, set_Pr4532377907799695533_nat_o: $tType).
% 21.04/7.59  thf(type_def_47, type, set_set_o: $tType).
% 21.04/7.59  thf(type_def_48, type, set_set_int: $tType).
% 21.04/7.59  thf(type_def_49, type, set_set_list_nat: $tType).
% 21.04/7.59  thf(type_def_50, type, set_se6260736226359567993nt_int: $tType).
% 21.04/7.59  thf(type_def_51, type, set_se7855581050983116737at_nat: $tType).
% 21.04/7.59  thf(type_def_52, type, set_set_set_nat: $tType).
% 21.04/7.59  thf(type_def_53, type, set_char: $tType).
% 21.04/7.59  thf(type_def_54, type, set_filter_nat: $tType).
% 21.04/7.59  thf(type_def_55, type, set_option_o: $tType).
% 21.04/7.59  thf(type_def_56, type, set_option_int: $tType).
% 21.04/7.59  thf(type_def_57, type, set_option_list_nat: $tType).
% 21.04/7.59  thf(type_def_58, type, set_option_nat: $tType).
% 21.04/7.59  thf(type_def_59, type, set_op4508134149509766951at_nat: $tType).
% 21.04/7.59  thf(type_def_60, type, set_option_rat: $tType).
% 21.04/7.59  thf(type_def_61, type, set_Pr8834758594704517033_o_int: $tType).
% 21.04/7.59  thf(type_def_62, type, set_Pr2101469702781467981_o_nat: $tType).
% 21.04/7.59  thf(type_def_63, type, set_Pr4944855402158566229_o_rat: $tType).
% 21.04/7.59  thf(type_def_64, type, set_Pr3149072824959771635_nat_o: $tType).
% 21.04/7.59  thf(type_def_65, type, set_Pr4105333604307423337at_rat: $tType).
% 21.04/7.59  thf(type_def_66, type, set_Pr2399638329824935915_rat_o: $tType).
% 21.04/7.59  thf(type_def_67, type, set_Pr3594552606344371909at_int: $tType).
% 21.04/7.59  thf(type_def_68, type, set_Pr6084635751276098665at_nat: $tType).
% 21.04/7.59  thf(type_def_69, type, set_Pr8928021450653196913at_rat: $tType).
% 21.04/7.59  thf(type_def_70, type, set_set_rat: $tType).
% 21.04/7.59  thf(type_def_71, type, set_literal: $tType).
% 21.04/7.59  thf(type_def_72, type, set_Sum_sum_o_o: $tType).
% 21.04/7.59  thf(type_def_73, type, set_Sum_sum_o_int: $tType).
% 21.04/7.59  thf(type_def_74, type, set_Sum_sum_o_nat: $tType).
% 21.04/7.59  thf(type_def_75, type, set_Sum_sum_o_rat: $tType).
% 21.04/7.59  thf(type_def_76, type, set_Sum_sum_nat_o: $tType).
% 21.04/7.59  thf(type_def_77, type, set_Sum_sum_nat_rat: $tType).
% 21.04/7.59  thf(type_def_78, type, set_Sum_sum_rat_o: $tType).
% 21.04/7.59  thf(type_def_79, type, set_Sum_sum_rat_int: $tType).
% 21.04/7.59  thf(type_def_80, type, set_Sum_sum_rat_nat: $tType).
% 21.04/7.59  thf(type_def_81, type, set_Sum_sum_rat_rat: $tType).
% 21.04/7.59  thf(type_def_82, type, sum_sum_nat_nat: $tType).
% 21.04/7.59  thf(type_def_83, type, set_Sum_sum_nat_nat: $tType).
% 21.04/7.59  thf(type_def_84, type, char: $tType).
% 21.04/7.59  thf(type_def_85, type, set_Pr8693737435421807431at_nat: $tType).
% 21.04/7.59  thf(type_def_86, type, produc4193628355235574503at_nat: $tType).
% 21.04/7.59  thf(type_def_87, type, produc1319942482725812455at_nat: $tType).
% 21.04/7.59  thf(type_def_88, type, multis2468970476368604999at_nat: $tType).
% 21.04/7.59  thf(type_def_89, type, set_Code_integer: $tType).
% 21.04/7.59  thf(type_def_90, type, produc4166570645942440679at_nat: $tType).
% 21.04/7.59  thf(type_def_91, type, list_int: $tType).
% 21.04/7.59  thf(type_def_92, type, pred_Product_unit: $tType).
% 21.04/7.59  thf(type_def_93, type, produc4675096598859438275atural: $tType).
% 21.04/7.59  thf(type_def_94, type, option6357759511663192854e_term: $tType).
% 21.04/7.59  thf(type_def_95, type, produc6241069584506657477e_term: $tType).
% 21.04/7.59  thf(type_def_96, type, produc3925858234332021118et_nat: $tType).
% 21.04/7.59  thf(type_def_97, type, produc8551481072490612790e_term: $tType).
% 21.04/7.59  thf(type_def_98, type, set_list_char: $tType).
% 21.04/7.59  thf(type_def_99, type, set_Pr1872883991513573699nt_int: $tType).
% 21.04/7.59  thf(type_def_100, type, set_Pr1281608226676607948nteger: $tType).
% 21.04/7.59  thf(type_def_101, type, set_Pr8536935166611901872et_nat: $tType).
% 21.04/7.59  thf(type_def_102, type, set_Pr3286484037609594932et_nat: $tType).
% 21.04/7.59  thf(type_def_103, type, set_Pr9222295170931077689nt_int: $tType).
% 21.04/7.59  thf(type_def_104, type, produc6576344331059438605e_term: $tType).
% 21.04/7.59  thf(type_def_105, type, produc7773217078559923341nt_int: $tType).
% 21.04/7.59  thf(type_def_106, type, set_Pr2161125870931222855_nat_o: $tType).
% 21.04/7.59  thf(type_def_107, type, set_Pr4759807026041935047at_nat: $tType).
% 21.04/7.59  thf(type_def_108, type, set_Pr5564308138774400199at_nat: $tType).
% 21.04/7.59  thf(type_def_109, type, set_Pr5488025237498180813et_nat: $tType).
% 21.04/7.59  thf(type_def_110, type, set_Pr8057934254988874055nt_int: $tType).
% 21.04/7.59  thf(type_def_111, type, produc8763457246119570046nteger: $tType).
% 21.04/7.59  thf(type_def_112, type, produc7822875418678951345atural: $tType).
% 21.04/7.59  thf(type_def_113, type, produc8731074985263844745atural: $tType).
% 21.04/7.59  thf(type_def_114, type, produc7248412053542808358at_nat: $tType).
% 21.04/7.59  thf(type_def_115, type, produc4471711990508489141at_nat: $tType).
% 21.04/7.59  thf(type_def_116, type, produc1908205239877642774nteger: $tType).
% 21.04/7.59  thf(type_def_117, type, produc4972180933644002618e_term: $tType).
% 21.04/7.59  thf(type_def_118, type, produc989692990947075319atural: $tType).
% 21.04/7.59  thf(type_def_119, type, produc4928098042776334183_nat_o: $tType).
% 21.04/7.59  thf(type_def_120, type, produc2285326912895808259nt_int: $tType).
% 21.04/7.59  thf(type_def_121, type, produc5835291356934675326atural: $tType).
% 21.04/7.59  thf(type_def_122, type, product_prod_nat_num: $tType).
% 21.04/7.59  thf(type_def_123, type, produc6756470014200349799atural: $tType).
% 21.04/7.59  thf(type_def_124, type, produc859450856879609959at_nat: $tType).
% 21.04/7.59  thf(type_def_125, type, produc7819656566062154093et_nat: $tType).
% 21.04/7.59  thf(type_def_126, type, produc2934264451710624999od_o_o: $tType).
% 21.04/7.59  thf(type_def_127, type, produc732395585841259969at_nat: $tType).
% 21.04/7.59  thf(type_def_128, type, produc412284730452459111nt_int: $tType).
% 21.04/7.59  thf(func_def_0, type, set_Pr8536935166611901872et_nat: $tType).
% 21.04/7.59  thf(func_def_1, type, produc4193628355235574503at_nat: $tType).
% 21.04/7.59  thf(func_def_2, type, produc2732055786443039994et_nat: $tType).
% 21.04/7.59  thf(func_def_3, type, set_Pr4759807026041935047at_nat: $tType).
% 21.04/7.59  thf(func_def_4, type, produc1319942482725812455at_nat: $tType).
% 21.04/7.59  thf(func_def_5, type, set_Pr5564308138774400199at_nat: $tType).
% 21.04/7.59  thf(func_def_6, type, set_Pr1281608226676607948nteger: $tType).
% 21.04/7.59  thf(func_def_7, type, produc989692990947075319atural: $tType).
% 21.04/7.59  thf(func_def_8, type, produc1908205239877642774nteger: $tType).
% 21.04/7.59  thf(func_def_9, type, set_Pr9222295170931077689nt_int: $tType).
% 21.04/7.59  thf(func_def_10, type, set_Pr2161125870931222855_nat_o: $tType).
% 21.04/7.59  thf(func_def_11, type, produc2285326912895808259nt_int: $tType).
% 21.04/7.59  thf(func_def_12, type, set_Pr3286484037609594932et_nat: $tType).
% 21.04/7.59  thf(func_def_13, type, produc4928098042776334183_nat_o: $tType).
% 21.04/7.59  thf(func_def_14, type, produc3925858234332021118et_nat: $tType).
% 21.04/7.59  thf(func_def_15, type, produc8731074985263844745atural: $tType).
% 21.04/7.59  thf(func_def_16, type, produc8763457246119570046nteger: $tType).
% 21.04/7.59  thf(func_def_17, type, produc6576344331059438605e_term: $tType).
% 21.04/7.59  thf(func_def_18, type, set_Pr1872883991513573699nt_int: $tType).
% 21.04/7.59  thf(func_def_19, type, produc7773217078559923341nt_int: $tType).
% 21.04/7.59  thf(func_def_20, type, set_Pr8551490117392284871at_nat: $tType).
% 21.04/7.59  thf(func_def_21, type, produc6756470014200349799atural: $tType).
% 21.04/7.59  thf(func_def_22, type, produc4166570645942440679at_nat: $tType).
% 21.04/7.59  thf(func_def_23, type, set_Pr4329608150637261639at_nat: $tType).
% 21.04/7.59  thf(func_def_24, type, set_Pr8057934254988874055nt_int: $tType).
% 21.04/7.59  thf(func_def_25, type, produc4471711990508489141at_nat: $tType).
% 21.04/7.59  thf(func_def_26, type, produc3843707927480180839at_nat: $tType).
% 21.04/7.59  thf(func_def_27, type, produc412284730452459111nt_int: $tType).
% 21.04/7.59  thf(func_def_28, type, set_Pr457366540195662369at_nat: $tType).
% 21.04/7.59  thf(func_def_29, type, produc4675096598859438275atural: $tType).
% 21.04/7.59  thf(func_def_30, type, set_Pr8693737435421807431at_nat: $tType).
% 21.04/7.59  thf(func_def_31, type, produc732395585841259969at_nat: $tType).
% 21.04/7.59  thf(func_def_32, type, set_Pr1932065953672099015od_o_o: $tType).
% 21.04/7.59  thf(func_def_33, type, produc5835291356934675326atural: $tType).
% 21.04/7.59  thf(func_def_34, type, set_Pr4532377907799695533_nat_o: $tType).
% 21.04/7.59  thf(func_def_35, type, produc859450856879609959at_nat: $tType).
% 21.04/7.59  thf(func_def_36, type, produc2934264451710624999od_o_o: $tType).
% 21.04/7.59  thf(func_def_37, type, produc4972180933644002618e_term: $tType).
% 21.04/7.59  thf(func_def_38, type, produc6241069584506657477e_term: $tType).
% 21.04/7.59  thf(func_def_39, type, produc3658429121746597890et_nat: $tType).
% 21.04/7.59  thf(func_def_40, type, produc8551481072490612790e_term: $tType).
% 21.04/7.59  thf(func_def_41, type, set_Pr5488025237498180813et_nat: $tType).
% 21.04/7.59  thf(func_def_42, type, option6357759511663192854e_term: $tType).
% 21.04/7.59  thf(func_def_43, type, produc7248412053542808358at_nat: $tType).
% 21.04/7.59  thf(func_def_44, type, set_Pr5094982260447487303t_unit: $tType).
% 21.04/7.59  thf(func_def_45, type, set_op4508134149509766951at_nat: $tType).
% 21.04/7.59  thf(func_def_46, type, set_se7855581050983116737at_nat: $tType).
% 21.04/7.59  thf(func_def_47, type, set_se6260736226359567993nt_int: $tType).
% 21.04/7.59  thf(func_def_48, type, produc7819656566062154093et_nat: $tType).
% 21.04/7.59  thf(func_def_49, type, produc7822875418678951345atural: $tType).
% 21.04/7.59  thf(func_def_50, type, produc8923325533196201883nteger: $tType).
% 21.04/7.59  thf(func_def_51, type, multis2468970476368604999at_nat: $tType).
% 21.04/7.59  thf(func_def_52, type, filter1242075044329608583at_nat: $tType).
% 21.04/7.59  thf(func_def_53, type, set_Pr8928021450653196913at_rat: $tType).
% 21.04/7.59  thf(func_def_54, type, set_Pr6084635751276098665at_nat: $tType).
% 21.04/7.59  thf(func_def_55, type, set_Pr3594552606344371909at_int: $tType).
% 21.04/7.59  thf(func_def_56, type, set_Pr4105333604307423337at_rat: $tType).
% 21.04/7.59  thf(func_def_57, type, set_Pr1261947904930325089at_nat: $tType).
% 21.04/7.59  thf(func_def_58, type, set_Pr958786334691620121nt_int: $tType).
% 21.04/7.59  thf(func_def_59, type, set_option_list_nat: $tType).
% 21.04/7.59  thf(func_def_60, type, set_Sum_sum_rat_rat: $tType).
% 21.04/7.59  thf(func_def_61, type, set_Sum_sum_rat_nat: $tType).
% 21.04/7.59  thf(func_def_62, type, set_Sum_sum_rat_int: $tType).
% 21.04/7.59  thf(func_def_63, type, set_Sum_sum_nat_rat: $tType).
% 21.04/7.59  thf(func_def_64, type, set_Sum_sum_nat_nat: $tType).
% 21.04/7.59  thf(func_def_65, type, set_set_list_nat: $tType).
% 21.04/7.59  thf(func_def_66, type, set_Pr2399638329824935915_rat_o: $tType).
% 21.04/7.59  thf(func_def_67, type, set_Pr3149072824959771635_nat_o: $tType).
% 21.04/7.59  thf(func_def_68, type, set_Pr4944855402158566229_o_rat: $tType).
% 21.04/7.59  thf(func_def_69, type, set_Pr2101469702781467981_o_nat: $tType).
% 21.04/7.59  thf(func_def_70, type, set_Pr8834758594704517033_o_int: $tType).
% 21.04/7.59  thf(func_def_71, type, produc6271795597528267376eger_o: $tType).
% 21.04/7.59  thf(func_def_72, type, set_set_set_nat: $tType).
% 21.04/7.59  thf(func_def_73, type, set_Sum_sum_rat_o: $tType).
% 21.04/7.59  thf(func_def_74, type, set_Sum_sum_nat_o: $tType).
% 21.04/7.59  thf(func_def_75, type, set_Sum_sum_o_rat: $tType).
% 21.04/7.59  thf(func_def_76, type, set_Sum_sum_o_nat: $tType).
% 21.04/7.59  thf(func_def_77, type, set_Sum_sum_o_int: $tType).
% 21.04/7.59  thf(func_def_78, type, heap_e7401611519738050253t_unit: $tType).
% 21.04/7.59  thf(func_def_79, type, product_prod_num_num: $tType).
% 21.04/7.59  thf(func_def_80, type, product_prod_nat_num: $tType).
% 21.04/7.59  thf(func_def_81, type, product_prod_nat_nat: $tType).
% 21.04/7.59  thf(func_def_82, type, product_prod_int_int: $tType).
% 21.04/7.59  thf(func_def_83, type, set_Product_prod_o_o: $tType).
% 21.04/7.59  thf(func_def_84, type, sum_sum_nat_nat: $tType).
% 21.04/7.59  thf(func_def_85, type, set_option_rat: $tType).
% 21.04/7.59  thf(func_def_86, type, set_option_nat: $tType).
% 21.04/7.59  thf(func_def_87, type, set_option_int: $tType).
% 21.04/7.59  thf(func_def_88, type, set_list_char: $tType).
% 21.04/7.59  thf(func_def_89, type, set_filter_nat: $tType).
% 21.04/7.59  thf(func_def_90, type, filter_set_nat: $tType).
% 21.04/7.59  thf(func_def_91, type, set_Sum_sum_o_o: $tType).
% 21.04/7.59  thf(func_def_92, type, pred_Product_unit: $tType).
% 21.04/7.59  thf(func_def_93, type, set_list_nat: $tType).
% 21.04/7.59  thf(func_def_94, type, list_Code_integer: $tType).
% 21.04/7.59  thf(func_def_95, type, set_set_rat: $tType).
% 21.04/7.59  thf(func_def_96, type, set_set_nat: $tType).
% 21.04/7.59  thf(func_def_97, type, set_set_int: $tType).
% 21.04/7.59  thf(func_def_98, type, set_Code_integer: $tType).
% 21.04/7.59  thf(func_def_99, type, set_Product_unit: $tType).
% 21.04/7.59  thf(func_def_100, type, set_option_o: $tType).
% 21.04/7.59  thf(func_def_101, type, set_literal: $tType).
% 21.04/7.59  thf(func_def_102, type, set_set_o: $tType).
% 21.04/7.59  thf(func_def_103, type, option_num: $tType).
% 21.04/7.59  thf(func_def_104, type, list_char: $tType).
% 21.04/7.59  thf(func_def_105, type, filter_nat: $tType).
% 21.04/7.59  thf(func_def_106, type, set_char: $tType).
% 21.04/7.59  thf(func_def_107, type, list_nat: $tType).
% 21.04/7.59  thf(func_def_108, type, list_int: $tType).
% 21.04/7.59  thf(func_def_109, type, set_rat: $tType).
% 21.04/7.59  thf(func_def_110, type, set_nat: $tType).
% 21.04/7.59  thf(func_def_111, type, set_int: $tType).
% 21.04/7.59  thf(func_def_112, type, code_natural: $tType).
% 21.04/7.59  thf(func_def_113, type, code_integer: $tType).
% 21.04/7.59  thf(func_def_114, type, product_unit: $tType).
% 21.04/7.59  thf(func_def_115, type, assn: $tType).
% 21.04/7.59  thf(func_def_116, type, literal: $tType).
% 21.04/7.59  thf(func_def_117, type, set_o: $tType).
% 21.04/7.59  thf(func_def_118, type, char: $tType).
% 21.04/7.59  thf(func_def_119, type, rat: $tType).
% 21.04/7.59  thf(func_def_120, type, num: $tType).
% 21.04/7.59  thf(func_def_121, type, nat: $tType).
% 21.04/7.59  thf(func_def_122, type, int: $tType).
% 21.04/7.59  thf(func_def_123, type, archim2889992004027027881ng_rat: rat > int).
% 21.04/7.59  thf(func_def_124, type, archim3151403230148437115or_rat: rat > int).
% 21.04/7.59  thf(func_def_125, type, archimedean_frac_rat: rat > rat).
% 21.04/7.59  thf(func_def_126, type, archim7778729529865785530nd_rat: rat > int).
% 21.04/7.59  thf(func_def_127, type, abs_assn: (produc3658429121746597890et_nat > $o) > assn).
% 21.04/7.59  thf(func_def_128, type, rep_assn: assn > produc3658429121746597890et_nat > $o).
% 21.04/7.59  thf(func_def_129, type, in_range: produc3658429121746597890et_nat > $o).
% 21.04/7.59  thf(func_def_130, type, one_assn_raw: produc3658429121746597890et_nat > $o).
% 21.04/7.59  thf(func_def_131, type, proper: (produc3658429121746597890et_nat > $o) > $o).
% 21.04/7.59  thf(func_def_132, type, relH: set_nat > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o).
% 21.04/7.59  thf(func_def_133, type, times_assn_raw: (produc3658429121746597890et_nat > $o) > (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o).
% 21.04/7.59  thf(func_def_134, type, times_assn_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o).
% 21.04/7.59  thf(func_def_135, type, wand_assn: assn > assn > assn).
% 21.04/7.59  thf(func_def_136, type, wand_raw: (produc3658429121746597890et_nat > $o) > (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o).
% 21.04/7.59  thf(func_def_137, type, wand_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o).
% 21.04/7.59  thf(func_def_138, type, bNF_Cardinal_cone: set_Pr5094982260447487303t_unit).
% 21.04/7.59  thf(func_def_139, type, bNF_Cardinal_ctwo: set_Product_prod_o_o).
% 21.04/7.59  thf(func_def_140, type, bNF_Cardinal_czero_o: set_Product_prod_o_o).
% 21.04/7.59  thf(func_def_141, type, bNF_Ca3172636760949973492d_of_o: set_o > set_Product_prod_o_o).
% 21.04/7.59  thf(func_def_142, type, bNF_Ca3793111618940312692of_nat: set_nat > set_Pr1261947904930325089at_nat).
% 21.04/7.59  thf(func_def_143, type, bNF_Ca7083678892733797993t_unit: set_Product_unit > set_Pr5094982260447487303t_unit).
% 21.04/7.59  thf(func_def_144, type, bNF_Ca8331644756375544342r_on_o: set_o > set_Product_prod_o_o > $o).
% 21.04/7.59  thf(func_def_145, type, bNF_Ca1281551314933786834on_nat: set_nat > set_Pr1261947904930325089at_nat > $o).
% 21.04/7.59  thf(func_def_146, type, bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat).
% 21.04/7.59  thf(func_def_147, type, bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat).
% 21.04/7.59  thf(func_def_148, type, bNF_id2059982186938784458at_o_o: ((produc3658429121746597890et_nat > $o) > (produc3658429121746597890et_nat > $o) > $o) > (produc3658429121746597890et_nat > $o) > (produc3658429121746597890et_nat > $o) > $o).
% 21.04/7.59  thf(func_def_149, type, bNF_id4470576313039291732at_o_o: ((produc3658429121746597890et_nat > $o) > $o) > (produc3658429121746597890et_nat > $o) > $o).
% 21.04/7.59  thf(func_def_150, type, bNF_id_bnf_o_o_o: ($o > $o > $o) > $o > $o > $o).
% 21.04/7.59  thf(func_def_151, type, bNF_id_bnf_o_int_o: ($o > int > $o) > $o > int > $o).
% 21.04/7.59  thf(func_def_152, type, bNF_id_bnf_o_nat_o: ($o > nat > $o) > $o > nat > $o).
% 21.04/7.59  thf(func_def_153, type, bNF_id_bnf_o_o: ($o > $o) > $o > $o).
% 21.04/7.59  thf(func_def_154, type, bNF_id_bnf_int_o_o: (int > $o > $o) > int > $o > $o).
% 21.04/7.59  thf(func_def_155, type, bNF_id_bnf_int_int_o: (int > int > $o) > int > int > $o).
% 21.04/7.59  thf(func_def_156, type, bNF_id_bnf_int_nat_o: (int > nat > $o) > int > nat > $o).
% 21.04/7.59  thf(func_def_157, type, bNF_id_bnf_int_o: (int > $o) > int > $o).
% 21.04/7.59  thf(func_def_158, type, bNF_id_bnf_nat_o_o: (nat > $o > $o) > nat > $o > $o).
% 21.04/7.59  thf(func_def_159, type, bNF_id_bnf_nat_int_o: (nat > int > $o) > nat > int > $o).
% 21.04/7.59  thf(func_def_160, type, bNF_id_bnf_nat_nat_o: (nat > nat > $o) > nat > nat > $o).
% 21.04/7.59  thf(func_def_161, type, bNF_id_bnf_nat_o: (nat > $o) > nat > $o).
% 21.04/7.59  thf(func_def_162, type, bNF_id146787821168362314_nat_o: (product_prod_nat_nat > product_prod_nat_nat > $o) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 21.04/7.59  thf(func_def_163, type, bNF_id5045731369644952736_nat_o: (product_prod_nat_nat > $o) > product_prod_nat_nat > $o).
% 21.04/7.59  thf(func_def_164, type, bNF_id5557877041440844106_nat_o: (produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o) > produc3843707927480180839at_nat > produc3843707927480180839at_nat > $o).
% 21.04/7.59  thf(func_def_165, type, bNF_id1044457264471098170_nat_o: (produc3843707927480180839at_nat > $o) > produc3843707927480180839at_nat > $o).
% 21.04/7.59  thf(func_def_166, type, bNF_id1382368747416007662at_o_o: (set_nat > $o > $o) > set_nat > $o > $o).
% 21.04/7.59  thf(func_def_167, type, bNF_id293821497076346774_nat_o: (set_nat > set_nat > $o) > set_nat > set_nat > $o).
% 21.04/7.59  thf(func_def_168, type, bNF_id_bnf_set_nat_o: (set_nat > $o) > set_nat > $o).
% 21.04/7.59  thf(func_def_169, type, bNF_id745042670895148362_int_o: (set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o) > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o).
% 21.04/7.59  thf(func_def_170, type, bNF_id9176111459293603464_int_o: (set_Pr958786334691620121nt_int > $o) > set_Pr958786334691620121nt_int > $o).
% 21.04/7.59  thf(func_def_171, type, bNF_id_bnf_o: $o > $o).
% 21.04/7.59  thf(func_def_172, type, bNF_id_bnf_int: int > int).
% 21.04/7.59  thf(func_def_173, type, bNF_id_bnf_list_nat: list_nat > list_nat).
% 21.04/7.59  thf(func_def_174, type, bNF_id_bnf_nat: nat > nat).
% 21.04/7.59  thf(func_def_175, type, bNF_id_bnf_rat: rat > rat).
% 21.04/7.59  thf(func_def_176, type, bNF_eq_onp_list_char: (list_char > $o) > list_char > list_char > $o).
% 21.04/7.59  thf(func_def_177, type, bNF_re5598663031114558885t_char: ($o > $o > $o) > (($o > $o > $o > $o > $o > $o > list_char > list_char) > ($o > $o > $o > $o > $o > $o > list_char > list_char) > $o) > ($o > $o > $o > $o > $o > $o > $o > list_char > list_char) > ($o > $o > $o > $o > $o > $o > $o > list_char > list_char) > $o).
% 21.04/7.59  thf(func_def_178, type, bNF_re8691941649098027561iteral: ($o > $o > $o) > (($o > $o > $o > $o > $o > $o > list_char > list_char) > ($o > $o > $o > $o > $o > $o > literal > literal) > $o) > ($o > $o > $o > $o > $o > $o > $o > list_char > list_char) > ($o > $o > $o > $o > $o > $o > $o > literal > literal) > $o).
% 21.04/7.59  thf(func_def_179, type, bNF_re7347849368244578525t_char: ($o > $o > $o) > (($o > $o > $o > $o > $o > list_char > list_char) > ($o > $o > $o > $o > $o > list_char > list_char) > $o) > ($o > $o > $o > $o > $o > $o > list_char > list_char) > ($o > $o > $o > $o > $o > $o > list_char > list_char) > $o).
% 21.04/7.59  thf(func_def_180, type, bNF_re5719858693005739489iteral: ($o > $o > $o) > (($o > $o > $o > $o > $o > list_char > list_char) > ($o > $o > $o > $o > $o > literal > literal) > $o) > ($o > $o > $o > $o > $o > $o > list_char > list_char) > ($o > $o > $o > $o > $o > $o > literal > literal) > $o).
% 21.04/7.59  thf(func_def_181, type, bNF_re7972843584066424825t_char: ($o > $o > $o) > (($o > $o > $o > $o > list_char > list_char) > ($o > $o > $o > $o > list_char > list_char) > $o) > ($o > $o > $o > $o > $o > list_char > list_char) > ($o > $o > $o > $o > $o > list_char > list_char) > $o).
% 21.04/7.59  thf(func_def_182, type, bNF_re136309367175754621iteral: ($o > $o > $o) > (($o > $o > $o > $o > list_char > list_char) > ($o > $o > $o > $o > literal > literal) > $o) > ($o > $o > $o > $o > $o > list_char > list_char) > ($o > $o > $o > $o > $o > literal > literal) > $o).
% 21.04/7.59  thf(func_def_183, type, bNF_re796896441190010845t_char: ($o > $o > $o) > (($o > $o > $o > list_char > list_char) > ($o > $o > $o > list_char > list_char) > $o) > ($o > $o > $o > $o > list_char > list_char) > ($o > $o > $o > $o > list_char > list_char) > $o).
% 21.04/7.59  thf(func_def_184, type, bNF_re2365650225897248225iteral: ($o > $o > $o) > (($o > $o > $o > list_char > list_char) > ($o > $o > $o > literal > literal) > $o) > ($o > $o > $o > $o > list_char > list_char) > ($o > $o > $o > $o > literal > literal) > $o).
% 21.04/7.59  thf(func_def_185, type, bNF_re4583855572895197261t_char: ($o > $o > $o) > (($o > $o > list_char > list_char) > ($o > $o > list_char > list_char) > $o) > ($o > $o > $o > list_char > list_char) > ($o > $o > $o > list_char > list_char) > $o).
% 21.04/7.59  thf(func_def_186, type, bNF_re5778109699181701841iteral: ($o > $o > $o) > (($o > $o > list_char > list_char) > ($o > $o > literal > literal) > $o) > ($o > $o > $o > list_char > list_char) > ($o > $o > $o > literal > literal) > $o).
% 21.04/7.59  thf(func_def_187, type, bNF_re441219624009962717t_char: ($o > $o > $o) > (($o > list_char > list_char) > ($o > list_char > list_char) > $o) > ($o > $o > list_char > list_char) > ($o > $o > list_char > list_char) > $o).
% 21.04/7.59  thf(func_def_188, type, bNF_re1595102025518187489iteral: ($o > $o > $o) > (($o > list_char > list_char) > ($o > literal > literal) > $o) > ($o > $o > list_char > list_char) > ($o > $o > literal > literal) > $o).
% 21.04/7.59  thf(func_def_189, type, bNF_re6157522605288126113t_char: ($o > $o > $o) > ((list_char > list_char) > (list_char > list_char) > $o) > ($o > list_char > list_char) > ($o > list_char > list_char) > $o).
% 21.04/7.59  thf(func_def_190, type, bNF_re6148748351543924773iteral: ($o > $o > $o) > ((list_char > list_char) > (literal > literal) > $o) > ($o > list_char > list_char) > ($o > literal > literal) > $o).
% 21.04/7.59  thf(func_def_191, type, bNF_re3379532845092657523nteger: (int > code_integer > $o) > (int > code_integer > $o) > (int > int) > (code_integer > code_integer) > $o).
% 21.04/7.59  thf(func_def_192, type, bNF_re3804157879324367682nt_int: (int > code_integer > $o) > (int > int > $o) > (int > int) > (code_integer > int) > $o).
% 21.04/7.59  thf(func_def_193, 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).
% 21.04/7.59  thf(func_def_194, 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).
% 21.04/7.59  thf(func_def_195, type, bNF_re982302072995117890nteger: (int > int > $o) > (int > code_integer > $o) > (int > int) > (int > code_integer) > $o).
% 21.04/7.59  thf(func_def_196, type, bNF_re4712519889275205905nt_int: (int > int > $o) > (int > int > $o) > (int > int) > (int > int) > $o).
% 21.04/7.59  thf(func_def_197, 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).
% 21.04/7.59  thf(func_def_198, type, bNF_re2214769303045360666nt_rat: (int > int > $o) > (product_prod_int_int > rat > $o) > (int > product_prod_int_int) > (int > rat) > $o).
% 21.04/7.59  thf(func_def_199, type, bNF_re5828396963709814525t_char: (list_Code_integer > list_Code_integer > $o) > (list_char > list_char > $o) > (list_Code_integer > list_char) > (list_Code_integer > list_char) > $o).
% 21.04/7.59  thf(func_def_200, type, bNF_re7775871201573978401char_o: (list_char > list_char > $o) > ((list_char > $o) > (list_char > $o) > $o) > (list_char > list_char > $o) > (list_char > list_char > $o) > $o).
% 21.04/7.59  thf(func_def_201, type, bNF_re7399511318543894245t_char: (list_char > list_char > $o) > ((list_char > list_char) > (list_char > list_char) > $o) > (list_char > list_char > list_char) > (list_char > list_char > list_char) > $o).
% 21.04/7.59  thf(func_def_202, type, bNF_re6668474094832959905ar_o_o: (list_char > list_char > $o) > ($o > $o > $o) > (list_char > $o) > (list_char > $o) > $o).
% 21.04/7.59  thf(func_def_203, type, bNF_re901197953848981245nteger: (list_char > list_char > $o) > (list_Code_integer > list_Code_integer > $o) > (list_char > list_Code_integer) > (list_char > list_Code_integer) > $o).
% 21.04/7.59  thf(func_def_204, type, bNF_re1407854171455731685t_char: (list_char > list_char > $o) > (list_char > list_char > $o) > (list_char > list_char) > (list_char > list_char) > $o).
% 21.04/7.59  thf(func_def_205, type, bNF_re76688982720252355at_nat: (list_char > list_char > $o) > (nat > nat > $o) > (list_char > nat) > (list_char > nat) > $o).
% 21.04/7.59  thf(func_def_206, type, bNF_re7831395832754058691eral_o: (list_char > literal > $o) > ((list_char > $o) > (literal > $o) > $o) > (list_char > list_char > $o) > (literal > literal > $o) > $o).
% 21.04/7.59  thf(func_def_207, type, bNF_re8730477052009823892al_o_o: (list_char > literal > $o) > ($o > $o > $o) > (list_char > $o) > (literal > $o) > $o).
% 21.04/7.59  thf(func_def_208, type, bNF_re4991257583289732696t_char: (list_char > literal > $o) > (list_char > list_char > $o) > (list_char > list_char) > (literal > list_char) > $o).
% 21.04/7.59  thf(func_def_209, type, bNF_re5453467372598631581iteral: (list_char > literal > $o) > (list_char > literal > $o) > (list_char > list_char) > (literal > literal) > $o).
% 21.04/7.59  thf(func_def_210, type, bNF_re6830278522597306478at_int: (nat > nat > $o) > (product_prod_nat_nat > int > $o) > (nat > product_prod_nat_nat) > (nat > int) > $o).
% 21.04/7.59  thf(func_def_211, type, bNF_re7876454716742015248nteger: (num > num > $o) > ((num > int) > (num > code_integer) > $o) > (num > num > int) > (num > num > code_integer) > $o).
% 21.04/7.59  thf(func_def_212, type, bNF_re8402795839162346335um_int: (num > num > $o) > ((num > int) > (num > int) > $o) > (num > num > int) > (num > num > int) > $o).
% 21.04/7.59  thf(func_def_213, type, bNF_re6501075790457514782nteger: (num > num > $o) > (int > code_integer > $o) > (num > int) > (num > code_integer) > $o).
% 21.04/7.59  thf(func_def_214, type, bNF_re1822329894187522285nt_int: (num > num > $o) > (int > int > $o) > (num > int) > (num > int) > $o).
% 21.04/7.59  thf(func_def_215, 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).
% 21.04/7.59  thf(func_def_216, 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).
% 21.04/7.59  thf(func_def_217, 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).
% 21.04/7.59  thf(func_def_218, 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).
% 21.04/7.59  thf(func_def_219, type, bNF_re1494630372529172596at_o_o: (product_prod_int_int > rat > $o) > ($o > $o > $o) > (product_prod_int_int > $o) > (rat > $o) > $o).
% 21.04/7.59  thf(func_def_220, 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).
% 21.04/7.59  thf(func_def_221, 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).
% 21.04/7.59  thf(func_def_222, 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).
% 21.04/7.59  thf(func_def_223, type, bNF_re6644619430987730960nt_o_o: (product_prod_nat_nat > int > $o) > ($o > $o > $o) > (product_prod_nat_nat > $o) > (int > $o) > $o).
% 21.04/7.59  thf(func_def_224, type, bNF_re4555766996558763186at_nat: (product_prod_nat_nat > int > $o) > (nat > nat > $o) > (product_prod_nat_nat > nat) > (int > nat) > $o).
% 21.04/7.59  thf(func_def_225, 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).
% 21.04/7.59  thf(func_def_226, 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).
% 21.04/7.59  thf(func_def_227, 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).
% 21.04/7.59  thf(func_def_228, 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).
% 21.04/7.59  thf(func_def_229, 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).
% 21.04/7.59  thf(func_def_230, 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).
% 21.04/7.59  thf(func_def_231, 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).
% 21.04/7.59  thf(func_def_232, type, bNF_We2654380646378065620so_o_o: set_Pr1932065953672099015od_o_o).
% 21.04/7.59  thf(func_def_233, type, bNF_We5258908940166488438at_nat: set_Pr4329608150637261639at_nat).
% 21.04/7.59  thf(func_def_234, type, bNF_We8182288985678559134_o_nat: set_Pr457366540195662369at_nat).
% 21.04/7.59  thf(func_def_235, type, bNF_We3818239936649020644el_nat: set_Pr1261947904930325089at_nat > $o).
% 21.04/7.59  thf(func_def_236, type, basic_1567116559311922317nt_int: (int > $o) > (int > $o) > product_prod_int_int > $o).
% 21.04/7.59  thf(func_def_237, type, basic_4387203522000727145nt_int: (int > int > $o) > (int > int > $o) > product_prod_int_int > product_prod_int_int > $o).
% 21.04/7.59  thf(func_def_238, type, basic_5328504652464829177at_nat: (nat > nat > $o) > (nat > nat > $o) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 21.04/7.59  thf(func_def_239, type, binomial: nat > nat > nat).
% 21.04/7.59  thf(func_def_240, type, gbinom8545251970709558553nteger: code_integer > nat > code_integer).
% 21.04/7.59  thf(func_def_241, type, gbinom7368847122466276068atural: code_natural > nat > code_natural).
% 21.04/7.59  thf(func_def_242, type, gbinomial_int: int > nat > int).
% 21.04/7.59  thf(func_def_243, type, gbinomial_nat: nat > nat > nat).
% 21.04/7.59  thf(func_def_244, type, gbinomial_rat: rat > nat > rat).
% 21.04/7.59  thf(func_def_245, type, bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o).
% 21.04/7.59  thf(func_def_246, type, bit_and_not_num: num > num > option_num).
% 21.04/7.59  thf(func_def_247, type, bit_and_not_num_rel: product_prod_num_num > product_prod_num_num > $o).
% 21.04/7.59  thf(func_def_248, type, bit_concat_bit: nat > int > int > int).
% 21.04/7.59  thf(func_def_249, type, bit_or_not_num_neg: num > num > num).
% 21.04/7.59  thf(func_def_250, type, bit_or3848514188828904588eg_rel: product_prod_num_num > product_prod_num_num > $o).
% 21.04/7.59  thf(func_def_251, type, bit_ri7632146776885996613nteger: code_integer > code_integer).
% 21.04/7.59  thf(func_def_252, type, bit_ri7919022796975470100ot_int: int > int).
% 21.04/7.59  thf(func_def_253, type, bit_ri6519982836138164636nteger: nat > code_integer > code_integer).
% 21.04/7.59  thf(func_def_254, type, bit_ri631733984087533419it_int: nat > int > int).
% 21.04/7.59  thf(func_def_255, type, bit_se3949692690581998587nteger: code_integer > code_integer > code_integer).
% 21.04/7.59  thf(func_def_256, type, bit_se2773287842338716102atural: code_natural > code_natural > code_natural).
% 21.04/7.59  thf(func_def_257, type, bit_se725231765392027082nd_int: int > int > int).
% 21.04/7.59  thf(func_def_258, type, bit_se727722235901077358nd_nat: nat > nat > nat).
% 21.04/7.59  thf(func_def_259, type, bit_se3928097537394005634nteger: nat > code_integer > code_integer).
% 21.04/7.59  thf(func_def_260, type, bit_se2751692689150723149atural: nat > code_natural > code_natural).
% 21.04/7.59  thf(func_def_261, type, bit_se8568078237143864401it_int: nat > int > int).
% 21.04/7.59  thf(func_def_262, type, bit_se8570568707652914677it_nat: nat > nat > nat).
% 21.04/7.59  thf(func_def_263, type, bit_se1345352211410354436nteger: nat > code_integer > code_integer).
% 21.04/7.59  thf(func_def_264, type, bit_se168947363167071951atural: nat > code_natural > code_natural).
% 21.04/7.59  thf(func_def_265, type, bit_se2159334234014336723it_int: nat > int > int).
% 21.04/7.59  thf(func_def_266, type, bit_se2161824704523386999it_nat: nat > nat > nat).
% 21.04/7.59  thf(func_def_267, type, bit_se2119862282449309892nteger: nat > code_integer).
% 21.04/7.59  thf(func_def_268, type, bit_se943457434206027407atural: nat > code_natural).
% 21.04/7.59  thf(func_def_269, type, bit_se2000444600071755411sk_int: nat > int).
% 21.04/7.59  thf(func_def_270, type, bit_se2002935070580805687sk_nat: nat > nat).
% 21.04/7.59  thf(func_def_271, type, bit_se1409905431419307370or_int: int > int > int).
% 21.04/7.59  thf(func_def_272, type, bit_se1412395901928357646or_nat: nat > nat > nat).
% 21.04/7.59  thf(func_def_273, type, bit_se7788150548672797655nteger: nat > code_integer > code_integer).
% 21.04/7.59  thf(func_def_274, type, bit_se6611745700429515170atural: nat > code_natural > code_natural).
% 21.04/7.59  thf(func_def_275, type, bit_se545348938243370406it_int: nat > int > int).
% 21.04/7.59  thf(func_def_276, type, bit_se547839408752420682it_nat: nat > nat > nat).
% 21.04/7.59  thf(func_def_277, type, bit_se2793503036327961859nteger: nat > code_integer > code_integer).
% 21.04/7.59  thf(func_def_278, type, bit_se1617098188084679374atural: nat > code_natural > code_natural).
% 21.04/7.59  thf(func_def_279, type, bit_se7879613467334960850it_int: nat > int > int).
% 21.04/7.59  thf(func_def_280, type, bit_se7882103937844011126it_nat: nat > nat > nat).
% 21.04/7.59  thf(func_def_281, type, bit_se1745604003318907178nteger: nat > code_integer > code_integer).
% 21.04/7.59  thf(func_def_282, type, bit_se569199155075624693atural: nat > code_natural > code_natural).
% 21.04/7.59  thf(func_def_283, type, bit_se2923211474154528505it_int: nat > int > int).
% 21.04/7.59  thf(func_def_284, type, bit_se2925701944663578781it_nat: nat > nat > nat).
% 21.04/7.59  thf(func_def_285, type, bit_se8260200283734997820nteger: nat > code_integer > code_integer).
% 21.04/7.59  thf(func_def_286, type, bit_se7083795435491715335atural: nat > code_natural > code_natural).
% 21.04/7.59  thf(func_def_287, type, bit_se4203085406695923979it_int: nat > int > int).
% 21.04/7.59  thf(func_def_288, type, bit_se4205575877204974255it_nat: nat > nat > nat).
% 21.04/7.59  thf(func_def_289, type, bit_se3222712562003087583nteger: code_integer > code_integer > code_integer).
% 21.04/7.59  thf(func_def_290, type, bit_se2046307713759805098atural: code_natural > code_natural > code_natural).
% 21.04/7.59  thf(func_def_291, type, bit_se6526347334894502574or_int: int > int > int).
% 21.04/7.59  thf(func_def_292, type, bit_se6528837805403552850or_nat: nat > nat > nat).
% 21.04/7.59  thf(func_def_293, type, bit_se1146084159140164899it_int: int > nat > $o).
% 21.04/7.59  thf(func_def_294, type, bit_take_bit_num: nat > num > option_num).
% 21.04/7.59  thf(func_def_295, type, bit_un7362597486090784418nd_num: num > num > option_num).
% 21.04/7.59  thf(func_def_296, type, bit_un4731106466462545111um_rel: product_prod_num_num > product_prod_num_num > $o).
% 21.04/7.59  thf(func_def_297, type, bit_un6697907153464112080or_num: num > num > num).
% 21.04/7.59  thf(func_def_298, type, bit_un4773296044027857193um_rel: product_prod_num_num > product_prod_num_num > $o).
% 21.04/7.59  thf(func_def_299, type, bit_un2480387367778600638or_num: num > num > option_num).
% 21.04/7.59  thf(func_def_300, type, bit_un2901131394128224187um_rel: product_prod_num_num > product_prod_num_num > $o).
% 21.04/7.59  thf(func_def_301, type, boolea934052484356091300char_o: ((list_char > $o) > (list_char > $o) > list_char > $o) > ((list_char > $o) > (list_char > $o) > list_char > $o) > ((list_char > $o) > list_char > $o) > (list_char > $o) > (list_char > $o) > $o).
% 21.04/7.59  thf(func_def_302, type, boolea1849928419393854478_int_o: ((product_prod_int_int > $o) > (product_prod_int_int > $o) > product_prod_int_int > $o) > ((product_prod_int_int > $o) > (product_prod_int_int > $o) > product_prod_int_int > $o) > ((product_prod_int_int > $o) > product_prod_int_int > $o) > (product_prod_int_int > $o) > (product_prod_int_int > $o) > $o).
% 21.04/7.59  thf(func_def_303, type, boolea7165431671056489859t_unit: (product_unit > product_unit > product_unit) > (product_unit > product_unit > product_unit) > (product_unit > product_unit) > product_unit > product_unit > $o).
% 21.04/7.59  thf(func_def_304, type, boolea379910186789422830_set_o: (set_o > set_o > set_o) > (set_o > set_o > set_o) > (set_o > set_o) > set_o > set_o > $o).
% 21.04/7.59  thf(func_def_305, type, boolea5824373010784320748et_int: (set_int > set_int > set_int) > (set_int > set_int > set_int) > (set_int > set_int) > set_int > set_int > $o).
% 21.04/7.59  thf(func_def_306, type, boolea9074081411689916704st_nat: (set_list_nat > set_list_nat > set_list_nat) > (set_list_nat > set_list_nat > set_list_nat) > (set_list_nat > set_list_nat) > set_list_nat > set_list_nat > $o).
% 21.04/7.59  thf(func_def_307, type, boolea778851993438741648et_nat: (set_nat > set_nat > set_nat) > (set_nat > set_nat > set_nat) > (set_nat > set_nat) > set_nat > set_nat > $o).
% 21.04/7.59  thf(func_def_308, type, boolea51845251928480829at_nat: (set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat) > (set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat) > (set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat) > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > $o).
% 21.04/7.59  thf(func_def_309, type, boolea949959532490082519at_nat: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 21.04/7.59  thf(func_def_310, type, boolea6493995471900120728et_rat: (set_rat > set_rat > set_rat) > (set_rat > set_rat > set_rat) > (set_rat > set_rat) > set_rat > set_rat > $o).
% 21.04/7.59  thf(func_def_311, type, code_Suc: code_natural > code_natural).
% 21.04/7.59  thf(func_def_312, type, code_bit_cut_integer: code_integer > produc6271795597528267376eger_o).
% 21.04/7.59  thf(func_def_313, type, code_cr_integer: int > code_integer > $o).
% 21.04/7.59  thf(func_def_314, type, code_cr_natural: nat > code_natural > $o).
% 21.04/7.59  thf(func_def_315, type, code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger).
% 21.04/7.59  thf(func_def_316, type, code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger).
% 21.04/7.59  thf(func_def_317, type, code_dup: code_integer > code_integer).
% 21.04/7.59  thf(func_def_318, type, code_int_of_integer: code_integer > int).
% 21.04/7.59  thf(func_def_319, type, code_integer_of_int: int > code_integer).
% 21.04/7.59  thf(func_def_320, type, code_integer_of_nat: nat > code_integer).
% 21.04/7.59  thf(func_def_321, type, code_integer_of_num: num > code_integer).
% 21.04/7.59  thf(func_def_322, type, code_nat_of_integer: code_integer > nat).
% 21.04/7.59  thf(func_def_323, type, code_nat_of_natural: code_natural > nat).
% 21.04/7.59  thf(func_def_324, type, code_natural_of_nat: nat > code_natural).
% 21.04/7.59  thf(func_def_325, type, code_negative: num > code_integer).
% 21.04/7.59  thf(func_def_326, type, code_num_of_integer: code_integer > num).
% 21.04/7.59  thf(func_def_327, type, code_pcr_integer: int > code_integer > $o).
% 21.04/7.59  thf(func_def_328, type, code_sub: num > num > code_integer).
% 21.04/7.59  thf(func_def_329, type, complete_Inf_Inf_int: set_int > int).
% 21.04/7.59  thf(func_def_330, type, complete_Inf_Inf_nat: set_nat > nat).
% 21.04/7.59  thf(func_def_331, type, comple7806235888213564991et_nat: set_set_nat > set_nat).
% 21.04/7.59  thf(func_def_332, type, complete_Sup_Sup_int: set_int > int).
% 21.04/7.59  thf(func_def_333, type, complete_Sup_Sup_nat: set_nat > nat).
% 21.04/7.59  thf(func_def_334, type, comple7399068483239264473et_nat: set_set_nat > set_nat).
% 21.04/7.59  thf(func_def_335, type, nat_to_rat_surj: nat > rat).
% 21.04/7.59  thf(func_def_336, type, nth_item_rel: nat > nat > $o).
% 21.04/7.59  thf(func_def_337, type, adjust_div: product_prod_int_int > int).
% 21.04/7.59  thf(func_def_338, type, adjust_mod: int > int > int).
% 21.04/7.59  thf(func_def_339, type, divmod_nat: nat > nat > product_prod_nat_nat).
% 21.04/7.59  thf(func_def_340, type, eucl_rel_int: int > int > product_prod_int_int > $o).
% 21.04/7.59  thf(func_def_341, type, unique5706413561485394159nteger: produc8923325533196201883nteger > $o).
% 21.04/7.59  thf(func_def_342, type, unique6319869463603278526ux_int: product_prod_int_int > $o).
% 21.04/7.59  thf(func_def_343, type, unique6322359934112328802ux_nat: product_prod_nat_nat > $o).
% 21.04/7.59  thf(func_def_344, type, unique3479559517661332726nteger: num > num > produc8923325533196201883nteger).
% 21.04/7.59  thf(func_def_345, type, unique5052692396658037445od_int: num > num > product_prod_int_int).
% 21.04/7.59  thf(func_def_346, type, unique5055182867167087721od_nat: num > num > product_prod_nat_nat).
% 21.04/7.59  thf(func_def_347, type, unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 21.04/7.59  thf(func_def_348, type, unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int).
% 21.04/7.59  thf(func_def_349, type, unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat).
% 21.04/7.59  thf(func_def_350, type, euclid3395696857347342551nt_int: int > int).
% 21.04/7.59  thf(func_def_351, type, euclid3398187327856392827nt_nat: nat > nat).
% 21.04/7.59  thf(func_def_352, type, comm_s8582702949713902594nteger: code_integer > nat > code_integer).
% 21.04/7.59  thf(func_def_353, type, comm_s4660882817536571857er_int: int > nat > int).
% 21.04/7.59  thf(func_def_354, type, comm_s4663373288045622133er_nat: nat > nat > nat).
% 21.04/7.59  thf(func_def_355, type, comm_s4028243227959126397er_rat: rat > nat > rat).
% 21.04/7.59  thf(func_def_356, type, semiri3624122377584611663nteger: nat > code_integer).
% 21.04/7.59  thf(func_def_357, type, semiri2447717529341329178atural: nat > code_natural).
% 21.04/7.59  thf(func_def_358, type, semiri1406184849735516958ct_int: nat > int).
% 21.04/7.59  thf(func_def_359, type, semiri1408675320244567234ct_nat: nat > nat).
% 21.04/7.59  thf(func_def_360, type, semiri773545260158071498ct_rat: nat > rat).
% 21.04/7.59  thf(func_def_361, type, inverse_inverse_rat: rat > rat).
% 21.04/7.59  thf(func_def_362, type, at_top_nat: filter_nat).
% 21.04/7.59  thf(func_def_363, type, cofinite_nat: filter_nat).
% 21.04/7.59  thf(func_def_364, type, eventually_nat: (nat > $o) > filter_nat > $o).
% 21.04/7.59  thf(func_def_365, type, eventu1038000079068216329at_nat: (product_prod_nat_nat > $o) > filter1242075044329608583at_nat > $o).
% 21.04/7.59  thf(func_def_366, type, filter3212408913953519116et_nat: (nat > set_nat) > filter_set_nat > filter_nat > $o).
% 21.04/7.59  thf(func_def_367, type, finite3254316476582989077op_nat: set_nat > filter_set_nat).
% 21.04/7.59  thf(func_def_368, type, frequently_nat: (nat > $o) > filter_nat > $o).
% 21.04/7.59  thf(func_def_369, type, prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat).
% 21.04/7.59  thf(func_def_370, type, finite1363419556375932405_nat_o: set_Pr4532377907799695533_nat_o > nat).
% 21.04/7.59  thf(func_def_371, type, finite_card_o: set_o > nat).
% 21.04/7.59  thf(func_def_372, type, finite_card_int: set_int > nat).
% 21.04/7.59  thf(func_def_373, type, finite_card_list_nat: set_list_nat > nat).
% 21.04/7.59  thf(func_def_374, type, finite_card_nat: set_nat > nat).
% 21.04/7.59  thf(func_def_375, type, finite6756421564338198497nt_int: set_Pr958786334691620121nt_int > nat).
% 21.04/7.59  thf(func_def_376, type, finite711546835091564841at_nat: set_Pr1261947904930325089at_nat > nat).
% 21.04/7.59  thf(func_def_377, type, finite3771342082235030671at_nat: set_Pr4329608150637261639at_nat > nat).
% 21.04/7.59  thf(func_def_378, type, finite410649719033368117t_unit: set_Product_unit > nat).
% 21.04/7.59  thf(func_def_379, type, finite_card_rat: set_rat > nat).
% 21.04/7.59  thf(func_def_380, type, finite_card_set_o: set_set_o > nat).
% 21.04/7.59  thf(func_def_381, type, finite_card_set_int: set_set_int > nat).
% 21.04/7.59  thf(func_def_382, type, finite2364142230527598318st_nat: set_set_list_nat > nat).
% 21.04/7.59  thf(func_def_383, type, finite_card_set_nat: set_set_nat > nat).
% 21.04/7.59  thf(func_def_384, type, finite4053189226111446337nt_int: set_se6260736226359567993nt_int > nat).
% 21.04/7.59  thf(func_def_385, type, finite4356350796350151305at_nat: set_se7855581050983116737at_nat > nat).
% 21.04/7.59  thf(func_def_386, type, finite1149291290879098388et_nat: set_set_set_nat > nat).
% 21.04/7.59  thf(func_def_387, type, finite_card_char: set_char > nat).
% 21.04/7.59  thf(func_def_388, type, finite3252695134891459830_nat_o: set_Pr4532377907799695533_nat_o > $o).
% 21.04/7.59  thf(func_def_389, type, finite_finite_o: set_o > $o).
% 21.04/7.59  thf(func_def_390, type, finite2119507909894593271er_nat: set_filter_nat > $o).
% 21.04/7.59  thf(func_def_391, type, finite_finite_int: set_int > $o).
% 21.04/7.59  thf(func_def_392, type, finite8100373058378681591st_nat: set_list_nat > $o).
% 21.04/7.59  thf(func_def_393, type, finite_finite_nat: set_nat > $o).
% 21.04/7.59  thf(func_def_394, type, finite4093902646404507527tion_o: set_option_o > $o).
% 21.04/7.59  thf(func_def_395, type, finite1345302120164226195on_int: set_option_int > $o).
% 21.04/7.59  thf(func_def_396, type, finite7857960318081769799st_nat: set_option_list_nat > $o).
% 21.04/7.59  thf(func_def_397, type, finite5523153139673422903on_nat: set_option_nat > $o).
% 21.04/7.59  thf(func_def_398, type, finite6732403688824079472at_nat: set_op4508134149509766951at_nat > $o).
% 21.04/7.59  thf(func_def_399, type, finite2014924581280026175on_rat: set_option_rat > $o).
% 21.04/7.59  thf(func_def_400, type, finite6120865539452801872od_o_o: set_Product_prod_o_o > $o).
% 21.04/7.59  thf(func_def_401, type, finite6891994925333515530_o_int: set_Pr8834758594704517033_o_int > $o).
% 21.04/7.59  thf(func_def_402, type, finite1846473907987936430_o_nat: set_Pr2101469702781467981_o_nat > $o).
% 21.04/7.59  thf(func_def_403, type, finite7561617386449315510_o_rat: set_Pr4944855402158566229_o_rat > $o).
% 21.04/7.59  thf(func_def_404, type, finite2998713641127702882nt_int: set_Pr958786334691620121nt_int > $o).
% 21.04/7.59  thf(func_def_405, type, finite1918287321285529104at_nat: set_Pr8551490117392284871at_nat > $o).
% 21.04/7.59  thf(func_def_406, type, finite5355008432043429460_nat_o: set_Pr3149072824959771635_nat_o > $o).
% 21.04/7.59  thf(func_def_407, type, finite6177210948735845034at_nat: set_Pr1261947904930325089at_nat > $o).
% 21.04/7.59  thf(func_def_408, type, finite2668982390342448306at_rat: set_Pr4105333604307423337at_rat > $o).
% 21.04/7.59  thf(func_def_409, type, finite1617675504726861388_rat_o: set_Pr2399638329824935915_rat_o > $o).
% 21.04/7.59  thf(func_def_410, type, finite1682805285291782414at_int: set_Pr3594552606344371909at_int > $o).
% 21.04/7.59  thf(func_def_411, type, finite5860656304800979122at_nat: set_Pr6084635751276098665at_nat > $o).
% 21.04/7.59  thf(func_def_412, type, finite2352427746407582394at_rat: set_Pr8928021450653196913at_rat > $o).
% 21.04/7.59  thf(func_def_413, type, finite4343798906461161616at_nat: set_Pr4329608150637261639at_nat > $o).
% 21.04/7.59  thf(func_def_414, type, finite_finite_rat: set_rat > $o).
% 21.04/7.59  thf(func_def_415, type, finite_finite_set_o: set_set_o > $o).
% 21.04/7.59  thf(func_def_416, type, finite6197958912794628473et_int: set_set_int > $o).
% 21.04/7.59  thf(func_def_417, type, finite7047420756378620717st_nat: set_set_list_nat > $o).
% 21.04/7.59  thf(func_def_418, type, finite1152437895449049373et_nat: set_set_nat > $o).
% 21.04/7.59  thf(func_def_419, type, finite8744585540193469122nt_int: set_se6260736226359567993nt_int > $o).
% 21.04/7.59  thf(func_def_420, type, finite9047747110432174090at_nat: set_se7855581050983116737at_nat > $o).
% 21.04/7.59  thf(func_def_421, type, finite6867581373910428453et_rat: set_set_rat > $o).
% 21.04/7.59  thf(func_def_422, type, finite5847741373460823677iteral: set_literal > $o).
% 21.04/7.59  thf(func_def_423, type, finite6699802884135759036um_o_o: set_Sum_sum_o_o > $o).
% 21.04/7.59  thf(func_def_424, type, finite1631874702275618462_o_int: set_Sum_sum_o_int > $o).
% 21.04/7.59  thf(func_def_425, type, finite5809725721784815170_o_nat: set_Sum_sum_o_nat > $o).
% 21.04/7.59  thf(func_def_426, type, finite2301497163391418442_o_rat: set_Sum_sum_o_rat > $o).
% 21.04/7.59  thf(func_def_427, type, finite94888208985532392_nat_o: set_Sum_sum_nat_o > $o).
% 21.04/7.59  thf(func_def_428, type, finite2679478125380364318at_rat: set_Sum_sum_nat_rat > $o).
% 21.04/7.59  thf(func_def_429, type, finite5580927318523740128_rat_o: set_Sum_sum_rat_o > $o).
% 21.04/7.59  thf(func_def_430, type, finite1693301020329698426at_int: set_Sum_sum_rat_int > $o).
% 21.04/7.59  thf(func_def_431, type, finite5871152039838895134at_nat: set_Sum_sum_rat_nat > $o).
% 21.04/7.59  thf(func_def_432, type, finite2362923481445498406at_rat: set_Sum_sum_rat_rat > $o).
% 21.04/7.59  thf(func_def_433, type, bij_betw_int_nat: (int > nat) > set_int > set_nat > $o).
% 21.04/7.59  thf(func_def_434, type, bij_be8532844293280997160at_nat: (list_nat > nat) > set_list_nat > set_nat > $o).
% 21.04/7.59  thf(func_def_435, type, bij_betw_nat_int: (nat > int) > set_nat > set_int > $o).
% 21.04/7.59  thf(func_def_436, type, bij_be6293887246118711976st_nat: (nat > list_nat) > set_nat > set_list_nat > $o).
% 21.04/7.59  thf(func_def_437, type, bij_betw_nat_nat: (nat > nat) > set_nat > set_nat > $o).
% 21.04/7.59  thf(func_def_438, type, bij_be8693218025023041337at_nat: (nat > product_prod_nat_nat) > set_nat > set_Pr1261947904930325089at_nat > $o).
% 21.04/7.59  thf(func_def_439, type, bij_be4790990086886966983at_nat: (nat > sum_sum_nat_nat) > set_nat > set_Sum_sum_nat_nat > $o).
% 21.04/7.59  thf(func_def_440, type, bij_be5333170631980326235at_nat: (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat > set_nat > $o).
% 21.04/7.59  thf(func_def_441, type, bij_be5432664580149595207at_nat: (sum_sum_nat_nat > nat) > set_Sum_sum_nat_nat > set_nat > $o).
% 21.04/7.59  thf(func_def_442, type, comp_C8797469213163452608nteger: ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 21.04/7.59  thf(func_def_443, type, comp_C1593894019821074884nteger: (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 21.04/7.59  thf(func_def_444, type, comp_C3531382070062128313er_num: (code_integer > code_integer) > (num > code_integer) > num > code_integer).
% 21.04/7.59  thf(func_def_445, type, comp_int_nat_int: (int > nat) > (int > int) > int > nat).
% 21.04/7.59  thf(func_def_446, type, comp_c4562247934908617188nteger: (char > char) > (code_integer > char) > code_integer > char).
% 21.04/7.59  thf(func_def_447, type, id_o: $o > $o).
% 21.04/7.59  thf(func_def_448, type, id_int: int > int).
% 21.04/7.59  thf(func_def_449, type, id_nat: nat > nat).
% 21.04/7.59  thf(func_def_450, type, id_num: num > num).
% 21.04/7.59  thf(func_def_451, type, inj_on_nat_nat: (nat > nat) > set_nat > $o).
% 21.04/7.59  thf(func_def_452, type, map_fu1104370778922912482iteral: ($o > $o) > (($o > $o > $o > $o > $o > $o > list_char > list_char) > $o > $o > $o > $o > $o > $o > literal > literal) > ($o > $o > $o > $o > $o > $o > $o > list_char > list_char) > $o > $o > $o > $o > $o > $o > $o > literal > literal).
% 21.04/7.59  thf(func_def_453, type, map_fu7309004089335677210iteral: ($o > $o) > (($o > $o > $o > $o > $o > list_char > list_char) > $o > $o > $o > $o > $o > literal > literal) > ($o > $o > $o > $o > $o > $o > list_char > list_char) > $o > $o > $o > $o > $o > $o > literal > literal).
% 21.04/7.59  thf(func_def_454, type, map_fu1929762555066093878iteral: ($o > $o) > (($o > $o > $o > $o > list_char > list_char) > $o > $o > $o > $o > literal > literal) > ($o > $o > $o > $o > $o > list_char > list_char) > $o > $o > $o > $o > $o > literal > literal).
% 21.04/7.59  thf(func_def_455, type, map_fu5333924603067766298iteral: ($o > $o) > (($o > $o > $o > list_char > list_char) > $o > $o > $o > literal > literal) > ($o > $o > $o > $o > list_char > list_char) > $o > $o > $o > $o > literal > literal).
% 21.04/7.59  thf(func_def_456, type, map_fu1888220742600445322iteral: ($o > $o) > (($o > $o > list_char > list_char) > $o > $o > literal > literal) > ($o > $o > $o > list_char > list_char) > $o > $o > $o > literal > literal).
% 21.04/7.59  thf(func_def_457, type, map_fu5700776415251466522iteral: ($o > $o) > (($o > list_char > list_char) > $o > literal > literal) > ($o > $o > list_char > list_char) > $o > $o > literal > literal).
% 21.04/7.59  thf(func_def_458, type, map_fu4627020735845646302iteral: ($o > $o) > ((list_char > list_char) > literal > literal) > ($o > list_char > list_char) > $o > literal > literal).
% 21.04/7.59  thf(func_def_459, type, map_fu2599414010547811884nteger: (code_integer > int) > (int > code_integer) > (int > int) > code_integer > code_integer).
% 21.04/7.59  thf(func_def_460, type, map_fu7831380289885515383nt_rat: (int > int) > ((int > product_prod_int_int) > int > rat) > (int > int > product_prod_int_int) > int > int > rat).
% 21.04/7.59  thf(func_def_461, type, map_fu3424225382358772769nt_rat: (int > int) > (product_prod_int_int > rat) > (int > product_prod_int_int) > int > rat).
% 21.04/7.59  thf(func_def_462, 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 > $o).
% 21.04/7.59  thf(func_def_463, type, map_fu4960017516451851995nt_int: (int > product_prod_nat_nat) > ((product_prod_nat_nat > product_prod_nat_nat) > int > int) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > int > int > int).
% 21.04/7.59  thf(func_def_464, type, map_fu4826362097070443709at_o_o: (int > product_prod_nat_nat) > ($o > $o) > (product_prod_nat_nat > $o) > int > $o).
% 21.04/7.59  thf(func_def_465, type, map_fu2345160673673942751at_nat: (int > product_prod_nat_nat) > (nat > nat) > (product_prod_nat_nat > nat) > int > nat).
% 21.04/7.59  thf(func_def_466, type, map_fu3667384564859982768at_int: (int > product_prod_nat_nat) > (product_prod_nat_nat > int) > (product_prod_nat_nat > product_prod_nat_nat) > int > int).
% 21.04/7.59  thf(func_def_467, type, map_fu6891787308814931657nteger: (num > num) > ((num > int) > num > code_integer) > (num > num > int) > num > num > code_integer).
% 21.04/7.59  thf(func_def_468, type, map_fu8638147718074629079nteger: (num > num) > (int > code_integer) > (num > int) > num > code_integer).
% 21.04/7.59  thf(func_def_469, type, map_fu4333342158222067775at_rat: (rat > product_prod_int_int) > ((product_prod_int_int > product_prod_int_int) > rat > rat) > (product_prod_int_int > product_prod_int_int > product_prod_int_int) > rat > rat > rat).
% 21.04/7.59  thf(func_def_470, type, map_fu898904425404107465nt_o_o: (rat > product_prod_int_int) > ($o > $o) > (product_prod_int_int > $o) > rat > $o).
% 21.04/7.59  thf(func_def_471, type, map_fu5673905371560938248nt_rat: (rat > product_prod_int_int) > (product_prod_int_int > rat) > (product_prod_int_int > product_prod_int_int) > rat > rat).
% 21.04/7.59  thf(func_def_472, type, map_fu2661873803724901240eral_o: (literal > list_char) > ((list_char > $o) > literal > $o) > (list_char > list_char > $o) > literal > literal > $o).
% 21.04/7.59  thf(func_def_473, type, map_fu6698795530259886495ar_o_o: (literal > list_char) > ($o > $o) > (list_char > $o) > literal > $o).
% 21.04/7.59  thf(func_def_474, type, map_fu7398138089906338514iteral: (literal > list_char) > (list_char > literal) > (list_char > list_char) > literal > literal).
% 21.04/7.59  thf(func_def_475, type, fun_max_strict: set_Pr4329608150637261639at_nat).
% 21.04/7.59  thf(func_def_476, type, fun_max_weak: set_Pr4329608150637261639at_nat).
% 21.04/7.59  thf(func_def_477, type, fun_min_strict: set_Pr4329608150637261639at_nat).
% 21.04/7.59  thf(func_def_478, type, fun_min_weak: set_Pr4329608150637261639at_nat).
% 21.04/7.59  thf(func_def_479, type, fun_pair_leq: set_Pr8693737435421807431at_nat).
% 21.04/7.59  thf(func_def_480, type, fun_pair_less: set_Pr8693737435421807431at_nat).
% 21.04/7.59  thf(func_def_481, type, fun_re7357418987779152907at_nat: produc4193628355235574503at_nat > $o).
% 21.04/7.59  thf(func_def_482, type, fun_re2478310338295953701at_nat: produc1319942482725812455at_nat > $o).
% 21.04/7.59  thf(func_def_483, type, gcd_Gcd_int: set_int > int).
% 21.04/7.59  thf(func_def_484, type, gcd_Gcd_nat: set_nat > nat).
% 21.04/7.59  thf(func_def_485, type, gcd_Lcm_int: set_int > int).
% 21.04/7.59  thf(func_def_486, type, gcd_Lcm_nat: set_nat > nat).
% 21.04/7.59  thf(func_def_487, type, bezw: nat > nat > product_prod_int_int).
% 21.04/7.59  thf(func_def_488, type, bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 21.04/7.59  thf(func_def_489, type, gcd_gcd_int: int > int > int).
% 21.04/7.59  thf(func_def_490, type, gcd_gcd_nat: nat > nat > nat).
% 21.04/7.59  thf(func_def_491, type, gcd_lcm_int: int > int > int).
% 21.04/7.59  thf(func_def_492, type, gcd_lcm_nat: nat > nat > nat).
% 21.04/7.59  thf(func_def_493, type, gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 21.04/7.59  thf(func_def_494, type, abs_abs_Code_integer: code_integer > code_integer).
% 21.04/7.59  thf(func_def_495, type, abs_abs_int: int > int).
% 21.04/7.59  thf(func_def_496, type, abs_abs_rat: rat > rat).
% 21.04/7.59  thf(func_def_497, type, comm_m8764728085499324515char_o: ((list_char > $o) > (list_char > $o) > list_char > $o) > (list_char > $o) > $o).
% 21.04/7.59  thf(func_def_498, type, comm_m5839176995973721103_int_o: ((product_prod_int_int > $o) > (product_prod_int_int > $o) > product_prod_int_int > $o) > (product_prod_int_int > $o) > $o).
% 21.04/7.59  thf(func_def_499, type, comm_monoid_assn: (assn > assn > assn) > assn > $o).
% 21.04/7.59  thf(func_def_500, type, comm_m1654649897431166824nteger: (code_integer > code_integer > code_integer) > code_integer > $o).
% 21.04/7.59  thf(func_def_501, type, comm_monoid_int: (int > int > int) > int > $o).
% 21.04/7.59  thf(func_def_502, type, comm_m1862543879040115196at_nat: (multis2468970476368604999at_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat) > multis2468970476368604999at_nat > $o).
% 21.04/7.59  thf(func_def_503, type, comm_monoid_nat: (nat > nat > nat) > nat > $o).
% 21.04/7.59  thf(func_def_504, type, comm_monoid_rat: (rat > rat > rat) > rat > $o).
% 21.04/7.59  thf(func_def_505, type, comm_monoid_set_o: (set_o > set_o > set_o) > set_o > $o).
% 21.04/7.59  thf(func_def_506, type, comm_monoid_set_int: (set_int > set_int > set_int) > set_int > $o).
% 21.04/7.59  thf(func_def_507, type, comm_m4511514676032769697st_nat: (set_list_nat > set_list_nat > set_list_nat) > set_list_nat > $o).
% 21.04/7.59  thf(func_def_508, type, comm_monoid_set_nat: (set_nat > set_nat > set_nat) > set_nat > $o).
% 21.04/7.59  thf(func_def_509, type, comm_m4707310049023135612at_nat: (set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat) > set_Pr8551490117392284871at_nat > $o).
% 21.04/7.59  thf(func_def_510, type, comm_m5709050211238513046at_nat: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat > $o).
% 21.04/7.59  thf(func_def_511, type, comm_m2457627138559323900at_nat: (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat) > set_Pr4329608150637261639at_nat > $o).
% 21.04/7.59  thf(func_def_512, type, comm_monoid_set_rat: (set_rat > set_rat > set_rat) > set_rat > $o).
% 21.04/7.59  thf(func_def_513, type, minus_2803741817741520073at_o_o: ((produc3658429121746597890et_nat > $o) > $o) > ((produc3658429121746597890et_nat > $o) > $o) > (produc3658429121746597890et_nat > $o) > $o).
% 21.04/7.59  thf(func_def_514, type, minus_minus_int_o: (int > $o) > (int > $o) > int > $o).
% 21.04/7.59  thf(func_def_515, type, minus_6821098565838606101char_o: (list_char > $o) > (list_char > $o) > list_char > $o).
% 21.04/7.59  thf(func_def_516, type, minus_minus_nat_o: (nat > $o) > (nat > $o) > nat > $o).
% 21.04/7.59  thf(func_def_517, type, minus_711738161318947805_int_o: (product_prod_int_int > $o) > (product_prod_int_int > $o) > product_prod_int_int > $o).
% 21.04/7.59  thf(func_def_518, type, minus_6910147592129066416_nat_o: (set_nat > $o) > (set_nat > $o) > set_nat > $o).
% 21.04/7.59  thf(func_def_519, type, minus_357216186751819389_int_o: (set_Pr958786334691620121nt_int > $o) > (set_Pr958786334691620121nt_int > $o) > set_Pr958786334691620121nt_int > $o).
% 21.04/7.59  thf(func_def_520, type, minus_minus_assn: assn > assn > assn).
% 21.04/7.59  thf(func_def_521, type, minus_8373710615458151222nteger: code_integer > code_integer > code_integer).
% 21.04/7.59  thf(func_def_522, type, minus_7197305767214868737atural: code_natural > code_natural > code_natural).
% 21.04/7.59  thf(func_def_523, type, minus_minus_int: int > int > int).
% 21.04/7.59  thf(func_def_524, type, minus_4286766774447292334at_nat: multis2468970476368604999at_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat).
% 21.04/7.59  thf(func_def_525, type, minus_minus_nat: nat > nat > nat).
% 21.04/7.59  thf(func_def_526, type, minus_3524152463667985524t_unit: product_unit > product_unit > product_unit).
% 21.04/7.59  thf(func_def_527, type, minus_minus_rat: rat > rat > rat).
% 21.04/7.59  thf(func_def_528, type, minus_1801376950450012436_nat_o: set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o).
% 21.04/7.59  thf(func_def_529, type, minus_minus_set_o: set_o > set_o > set_o).
% 21.04/7.59  thf(func_def_530, type, minus_2355218937544613996nteger: set_Code_integer > set_Code_integer > set_Code_integer).
% 21.04/7.59  thf(func_def_531, type, minus_minus_set_int: set_int > set_int > set_int).
% 21.04/7.59  thf(func_def_532, type, minus_7954133019191499631st_nat: set_list_nat > set_list_nat > set_list_nat).
% 21.04/7.59  thf(func_def_533, type, minus_minus_set_nat: set_nat > set_nat > set_nat).
% 21.04/7.59  thf(func_def_534, type, minus_1052850069191792384nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int).
% 21.04/7.59  thf(func_def_535, type, minus_5060654252129873198at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat).
% 21.04/7.59  thf(func_def_536, type, minus_1356011639430497352at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 21.04/7.59  thf(func_def_537, type, minus_3314409938677909166at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 21.04/7.59  thf(func_def_538, type, minus_minus_set_rat: set_rat > set_rat > set_rat).
% 21.04/7.59  thf(func_def_539, type, minus_2163939370556025621et_nat: set_set_nat > set_set_nat > set_set_nat).
% 21.04/7.59  thf(func_def_540, type, minus_2612819937483484256nt_int: set_se6260736226359567993nt_int > set_se6260736226359567993nt_int > set_se6260736226359567993nt_int).
% 21.04/7.59  thf(func_def_541, type, monoid_list_char_o: ((list_char > $o) > (list_char > $o) > list_char > $o) > (list_char > $o) > $o).
% 21.04/7.59  thf(func_def_542, type, monoid6910981727789844035_int_o: ((product_prod_int_int > $o) > (product_prod_int_int > $o) > product_prod_int_int > $o) > (product_prod_int_int > $o) > $o).
% 21.04/7.59  thf(func_def_543, type, monoid_assn: (assn > assn > assn) > assn > $o).
% 21.04/7.59  thf(func_def_544, type, monoid_Code_integer: (code_integer > code_integer > code_integer) > code_integer > $o).
% 21.04/7.59  thf(func_def_545, type, monoid_int: (int > int > int) > int > $o).
% 21.04/7.59  thf(func_def_546, type, monoid66256789251010760at_nat: (multis2468970476368604999at_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat) > multis2468970476368604999at_nat > $o).
% 21.04/7.59  thf(func_def_547, type, monoid_nat: (nat > nat > nat) > nat > $o).
% 21.04/7.59  thf(func_def_548, type, monoid_rat: (rat > rat > rat) > rat > $o).
% 21.04/7.59  thf(func_def_549, type, monoid_set_o: (set_o > set_o > set_o) > set_o > $o).
% 21.04/7.59  thf(func_def_550, type, monoid_set_int: (set_int > set_int > set_int) > set_int > $o).
% 21.04/7.59  thf(func_def_551, type, monoid_set_list_nat: (set_list_nat > set_list_nat > set_list_nat) > set_list_nat > $o).
% 21.04/7.59  thf(func_def_552, type, monoid_set_nat: (set_nat > set_nat > set_nat) > set_nat > $o).
% 21.04/7.59  thf(func_def_553, type, monoid3323479476634721864at_nat: (set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat) > set_Pr8551490117392284871at_nat > $o).
% 21.04/7.59  thf(func_def_554, type, monoid1519094961268053602at_nat: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat > $o).
% 21.04/7.59  thf(func_def_555, type, monoid534952638934301128at_nat: (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat) > set_Pr4329608150637261639at_nat > $o).
% 21.04/7.59  thf(func_def_556, type, monoid_set_rat: (set_rat > set_rat > set_rat) > set_rat > $o).
% 21.04/7.59  thf(func_def_557, type, monoid_literal: (literal > literal > literal) > literal > $o).
% 21.04/7.59  thf(func_def_558, type, one_one_assn: assn).
% 21.04/7.59  thf(func_def_559, type, one_one_Code_integer: code_integer).
% 21.04/7.59  thf(func_def_560, type, one_one_Code_natural: code_natural).
% 21.04/7.59  thf(func_def_561, type, one_one_int: int).
% 21.04/7.59  thf(func_def_562, type, one_one_nat: nat).
% 21.04/7.59  thf(func_def_563, type, one_one_rat: rat).
% 21.04/7.59  thf(func_def_564, type, plus_p5714425477246183910nteger: code_integer > code_integer > code_integer).
% 21.04/7.59  thf(func_def_565, type, plus_p4538020629002901425atural: code_natural > code_natural > code_natural).
% 21.04/7.59  thf(func_def_566, type, plus_plus_int: int > int > int).
% 21.04/7.59  thf(func_def_567, type, plus_p7104986032573967614at_nat: multis2468970476368604999at_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat).
% 21.04/7.59  thf(func_def_568, type, plus_plus_nat: nat > nat > nat).
% 21.04/7.59  thf(func_def_569, type, plus_plus_num: num > num > num).
% 21.04/7.59  thf(func_def_570, type, plus_plus_rat: rat > rat > rat).
% 21.04/7.59  thf(func_def_571, type, plus_plus_literal: literal > literal > literal).
% 21.04/7.59  thf(func_def_572, type, sgn_sgn_Code_integer: code_integer > code_integer).
% 21.04/7.59  thf(func_def_573, type, sgn_sgn_int: int > int).
% 21.04/7.59  thf(func_def_574, type, sgn_sgn_rat: rat > rat).
% 21.04/7.59  thf(func_def_575, type, times_times_assn: assn > assn > assn).
% 21.04/7.59  thf(func_def_576, type, times_3573771949741848930nteger: code_integer > code_integer > code_integer).
% 21.04/7.59  thf(func_def_577, type, times_2397367101498566445atural: code_natural > code_natural > code_natural).
% 21.04/7.59  thf(func_def_578, type, times_times_int: int > int > int).
% 21.04/7.59  thf(func_def_579, type, times_times_nat: nat > nat > nat).
% 21.04/7.59  thf(func_def_580, type, times_times_num: num > num > num).
% 21.04/7.59  thf(func_def_581, type, times_times_rat: rat > rat > rat).
% 21.04/7.59  thf(func_def_582, type, uminus8928876914783121465at_o_o: ((produc3658429121746597890et_nat > $o) > $o) > (produc3658429121746597890et_nat > $o) > $o).
% 21.04/7.59  thf(func_def_583, type, uminus_uminus_int_o: (int > $o) > int > $o).
% 21.04/7.59  thf(func_def_584, type, uminus7154032370948614053char_o: (list_char > $o) > list_char > $o).
% 21.04/7.59  thf(func_def_585, type, uminus_uminus_nat_o: (nat > $o) > nat > $o).
% 21.04/7.59  thf(func_def_586, type, uminus7117520113953359693_int_o: (product_prod_int_int > $o) > product_prod_int_int > $o).
% 21.04/7.59  thf(func_def_587, type, uminus6401447641752708672_nat_o: (set_nat > $o) > set_nat > $o).
% 21.04/7.59  thf(func_def_588, type, uminus8147837162492574189_int_o: (set_Pr958786334691620121nt_int > $o) > set_Pr958786334691620121nt_int > $o).
% 21.04/7.59  thf(func_def_589, type, uminus_uminus_assn: assn > assn).
% 21.04/7.59  thf(func_def_590, type, uminus1351360451143612070nteger: code_integer > code_integer).
% 21.04/7.59  thf(func_def_591, type, uminus_uminus_int: int > int).
% 21.04/7.59  thf(func_def_592, type, uminus2952777764628376836t_unit: product_unit > product_unit).
% 21.04/7.59  thf(func_def_593, type, uminus_uminus_rat: rat > rat).
% 21.04/7.59  thf(func_def_594, type, uminus5254974436814262692_nat_o: set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o).
% 21.04/7.59  thf(func_def_595, type, uminus_uminus_set_o: set_o > set_o).
% 21.04/7.59  thf(func_def_596, type, uminus1532241313380277803et_int: set_int > set_int).
% 21.04/7.59  thf(func_def_597, type, uminus3195874150345416415st_nat: set_list_nat > set_list_nat).
% 21.04/7.59  thf(func_def_598, type, uminus5710092332889474511et_nat: set_nat > set_nat).
% 21.04/7.59  thf(func_def_599, type, uminus2330091110623919550at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat).
% 21.04/7.59  thf(func_def_600, type, uminus6524753893492686040at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 21.04/7.59  thf(func_def_601, type, uminus935396558254630718at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 21.04/7.59  thf(func_def_602, type, uminus2201863774496077783et_rat: set_rat > set_rat).
% 21.04/7.59  thf(func_def_603, type, uminus613421341184616069et_nat: set_set_nat > set_set_nat).
% 21.04/7.59  thf(func_def_604, type, uminus6423885277529793776nt_int: set_se6260736226359567993nt_int > set_se6260736226359567993nt_int).
% 21.04/7.59  thf(func_def_605, type, zero_z3403309356797280102nteger: code_integer).
% 21.04/7.59  thf(func_def_606, type, zero_z2226904508553997617atural: code_natural).
% 21.04/7.59  thf(func_def_607, type, zero_zero_int: int).
% 21.04/7.59  thf(func_def_608, type, zero_z1048942125864253310at_nat: multis2468970476368604999at_nat).
% 21.04/7.59  thf(func_def_609, type, zero_zero_nat: nat).
% 21.04/7.59  thf(func_def_610, type, zero_zero_rat: rat).
% 21.04/7.59  thf(func_def_611, type, zero_zero_literal: literal).
% 21.04/7.59  thf(func_def_612, type, groups6742167275697360483_o_nat: ((produc3658429121746597890et_nat > $o) > nat) > set_Pr4532377907799695533_nat_o > nat).
% 21.04/7.59  thf(func_def_613, type, groups4406642042086082107nteger: ($o > code_integer) > set_o > code_integer).
% 21.04/7.59  thf(func_def_614, type, groups3230237193842799622atural: ($o > code_natural) > set_o > code_natural).
% 21.04/7.59  thf(func_def_615, type, groups8505340233167759370_o_int: ($o > int) > set_o > int).
% 21.04/7.59  thf(func_def_616, type, groups8507830703676809646_o_nat: ($o > nat) > set_o > nat).
% 21.04/7.59  thf(func_def_617, type, groups7872700643590313910_o_rat: ($o > rat) > set_o > rat).
% 21.04/7.59  thf(func_def_618, type, groups7873554091576472773nteger: (int > code_integer) > set_int > code_integer).
% 21.04/7.59  thf(func_def_619, type, groups6697149243333190288atural: (int > code_natural) > set_int > code_natural).
% 21.04/7.59  thf(func_def_620, type, groups4538972089207619220nt_int: (int > int) > set_int > int).
% 21.04/7.59  thf(func_def_621, type, groups4541462559716669496nt_nat: (int > nat) > set_int > nat).
% 21.04/7.59  thf(func_def_622, type, groups3906332499630173760nt_rat: (int > rat) > set_int > rat).
% 21.04/7.59  thf(func_def_623, type, groups4396056296759096172at_nat: (list_nat > nat) > set_list_nat > nat).
% 21.04/7.59  thf(func_def_624, type, groups3760926236672600436at_rat: (list_nat > rat) > set_list_nat > rat).
% 21.04/7.59  thf(func_def_625, type, groups7501900531339628137nteger: (nat > code_integer) > set_nat > code_integer).
% 21.04/7.59  thf(func_def_626, type, groups6325495683096345652atural: (nat > code_natural) > set_nat > code_natural).
% 21.04/7.59  thf(func_def_627, type, groups3539618377306564664at_int: (nat > int) > set_nat > int).
% 21.04/7.59  thf(func_def_628, type, groups6857163185585827899at_nat: (nat > multis2468970476368604999at_nat) > set_nat > multis2468970476368604999at_nat).
% 21.04/7.59  thf(func_def_629, type, groups3542108847815614940at_nat: (nat > nat) > set_nat > nat).
% 21.04/7.59  thf(func_def_630, type, groups2906978787729119204at_rat: (nat > rat) > set_nat > rat).
% 21.04/7.59  thf(func_def_631, type, groups7057407298757096921at_int: (produc4166570645942440679at_nat > int) > set_Pr8551490117392284871at_nat > int).
% 21.04/7.59  thf(func_def_632, type, groups7059897769266147197at_nat: (produc4166570645942440679at_nat > nat) > set_Pr8551490117392284871at_nat > nat).
% 21.04/7.59  thf(func_def_633, type, groups6424767709179651461at_rat: (produc4166570645942440679at_nat > rat) > set_Pr8551490117392284871at_nat > rat).
% 21.04/7.59  thf(func_def_634, type, groups196832835297161892nteger: (product_prod_nat_nat > code_integer) > set_Pr1261947904930325089at_nat > code_integer).
% 21.04/7.59  thf(func_def_635, type, groups975429370522433651at_int: (product_prod_nat_nat > int) > set_Pr1261947904930325089at_nat > int).
% 21.04/7.59  thf(func_def_636, type, groups977919841031483927at_nat: (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat > nat).
% 21.04/7.59  thf(func_def_637, type, groups342789780944988191at_rat: (product_prod_nat_nat > rat) > set_Pr1261947904930325089at_nat > rat).
% 21.04/7.59  thf(func_def_638, type, groups3858419854409063513at_int: (produc3843707927480180839at_nat > int) > set_Pr4329608150637261639at_nat > int).
% 21.04/7.59  thf(func_def_639, type, groups3860910324918113789at_nat: (produc3843707927480180839at_nat > nat) > set_Pr4329608150637261639at_nat > nat).
% 21.04/7.59  thf(func_def_640, type, groups3225780264831618053at_rat: (produc3843707927480180839at_nat > rat) > set_Pr4329608150637261639at_nat > rat).
% 21.04/7.59  thf(func_def_641, type, groups9190459664516455967nteger: (set_nat > code_integer) > set_set_nat > code_integer).
% 21.04/7.59  thf(func_def_642, type, groups8292507037921071086at_int: (set_nat > int) > set_set_nat > int).
% 21.04/7.59  thf(func_def_643, type, groups8294997508430121362at_nat: (set_nat > nat) > set_set_nat > nat).
% 21.04/7.59  thf(func_def_644, type, groups7659867448343625626at_rat: (set_nat > rat) > set_set_nat > rat).
% 21.04/7.59  thf(func_def_645, type, groups3738144136874984124nteger: (set_Pr958786334691620121nt_int > code_integer) > set_se6260736226359567993nt_int > code_integer).
% 21.04/7.59  thf(func_def_646, type, groups185207323561075247nt_nat: (set_Pr958786334691620121nt_int > nat) > set_se6260736226359567993nt_int > nat).
% 21.04/7.59  thf(func_def_647, type, groups8773449300329355319nt_rat: (set_Pr958786334691620121nt_int > rat) > set_se6260736226359567993nt_int > rat).
% 21.04/7.59  thf(func_def_648, type, groups1402912129352969042nteger: ($o > code_integer) > set_o > code_integer).
% 21.04/7.59  thf(func_def_649, type, groups4553916814277028129_o_int: ($o > int) > set_o > int).
% 21.04/7.59  thf(func_def_650, type, groups4556407284786078405_o_nat: ($o > nat) > set_o > nat).
% 21.04/7.59  thf(func_def_651, type, groups3921277224699582669_o_rat: ($o > rat) > set_o > rat).
% 21.04/7.59  thf(func_def_652, type, groups926780983652909934nteger: (int > code_integer) > set_int > code_integer).
% 21.04/7.59  thf(func_def_653, type, groups2983280209131991357nt_int: (int > int) > set_int > int).
% 21.04/7.59  thf(func_def_654, type, groups2985770679641041633nt_nat: (int > nat) > set_int > nat).
% 21.04/7.59  thf(func_def_655, type, groups2350640619554545897nt_rat: (int > rat) > set_int > rat).
% 21.04/7.59  thf(func_def_656, type, groups555127423416065298nteger: (nat > code_integer) > set_nat > code_integer).
% 21.04/7.59  thf(func_def_657, type, groups1983926497230936801at_int: (nat > int) > set_nat > int).
% 21.04/7.59  thf(func_def_658, type, groups1986416967739987077at_nat: (nat > nat) > set_nat > nat).
% 21.04/7.59  thf(func_def_659, type, groups1351286907653491341at_rat: (nat > rat) > set_nat > rat).
% 21.04/7.59  thf(func_def_660, type, groups9221925307898054856nteger: (set_nat > code_integer) > set_set_nat > code_integer).
% 21.04/7.59  thf(func_def_661, type, groups713094340420062787at_rat: (set_nat > rat) > set_set_nat > rat).
% 21.04/7.59  thf(func_def_662, type, groups5301882518646026715o_assn: ($o > assn) > set_o > assn).
% 21.04/7.59  thf(func_def_663, type, groups7694694392188491536nteger: ($o > code_integer) > set_o > code_integer).
% 21.04/7.59  thf(func_def_664, type, groups6518289543945209051atural: ($o > code_natural) > set_o > code_natural).
% 21.04/7.59  thf(func_def_665, type, groups3502327434004483295_o_int: ($o > int) > set_o > int).
% 21.04/7.59  thf(func_def_666, type, groups3504817904513533571_o_nat: ($o > nat) > set_o > nat).
% 21.04/7.59  thf(func_def_667, type, groups2869687844427037835_o_rat: ($o > rat) > set_o > rat).
% 21.04/7.59  thf(func_def_668, type, groups7882442080178216443t_assn: (int > assn) > set_int > assn).
% 21.04/7.59  thf(func_def_669, type, groups3827104343326376752nteger: (int > code_integer) > set_int > code_integer).
% 21.04/7.59  thf(func_def_670, type, groups1705073143266064639nt_int: (int > int) > set_int > int).
% 21.04/7.59  thf(func_def_671, type, groups1707563613775114915nt_nat: (int > nat) > set_int > nat).
% 21.04/7.59  thf(func_def_672, type, groups1072433553688619179nt_rat: (int > rat) > set_int > rat).
% 21.04/7.59  thf(func_def_673, type, groups2905156660866384563at_int: (list_nat > int) > set_list_nat > int).
% 21.04/7.59  thf(func_def_674, type, groups2907647131375434839at_nat: (list_nat > nat) > set_list_nat > nat).
% 21.04/7.59  thf(func_def_675, type, groups6906906614972039071t_assn: (nat > assn) > set_nat > assn).
% 21.04/7.59  thf(func_def_676, type, groups3455450783089532116nteger: (nat > code_integer) > set_nat > code_integer).
% 21.04/7.59  thf(func_def_677, type, groups2279045934846249631atural: (nat > code_natural) > set_nat > code_natural).
% 21.04/7.59  thf(func_def_678, type, groups705719431365010083at_int: (nat > int) > set_nat > int).
% 21.04/7.59  thf(func_def_679, type, groups708209901874060359at_nat: (nat > nat) > set_nat > nat).
% 21.04/7.59  thf(func_def_680, type, groups73079841787564623at_rat: (nat > rat) > set_nat > rat).
% 21.04/7.59  thf(func_def_681, type, groups5938585286922990810at_rat: (produc4166570645942440679at_nat > rat) > set_Pr8551490117392284871at_nat > rat).
% 21.04/7.59  thf(func_def_682, type, groups1230400874837758585nteger: (product_prod_nat_nat > code_integer) > set_Pr1261947904930325089at_nat > code_integer).
% 21.04/7.59  thf(func_def_683, type, groups4075276357253098568at_int: (product_prod_nat_nat > int) > set_Pr1261947904930325089at_nat > int).
% 21.04/7.59  thf(func_def_684, type, groups4077766827762148844at_nat: (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat > nat).
% 21.04/7.59  thf(func_def_685, type, groups3442636767675653108at_rat: (product_prod_nat_nat > rat) > set_Pr1261947904930325089at_nat > rat).
% 21.04/7.59  thf(func_def_686, type, groups8874911130973611098at_rat: (produc3843707927480180839at_nat > rat) > set_Pr4329608150637261639at_nat > rat).
% 21.04/7.59  thf(func_def_687, type, groups2761809935038513290nteger: (set_nat > code_integer) > set_set_nat > code_integer).
% 21.04/7.59  thf(func_def_688, type, groups4246057289670975065at_int: (set_nat > int) > set_set_nat > int).
% 21.04/7.59  thf(func_def_689, type, groups4248547760180025341at_nat: (set_nat > nat) > set_set_nat > nat).
% 21.04/7.59  thf(func_def_690, type, groups3613417700093529605at_rat: (set_nat > rat) > set_set_nat > rat).
% 21.04/7.59  thf(func_def_691, type, groups4561878855575611511st_nat: list_nat > nat).
% 21.04/7.59  thf(func_def_692, type, nO_MAT8252062027627875367nteger: code_integer > code_integer > $o).
% 21.04/7.59  thf(func_def_693, type, nO_MAT8427913294028938742er_int: code_integer > int > $o).
% 21.04/7.59  thf(func_def_694, type, nO_MAT7795273704451493282er_rat: code_integer > rat > $o).
% 21.04/7.59  thf(func_def_695, type, nO_MAT9066612773553876470nteger: int > code_integer > $o).
% 21.04/7.59  thf(func_def_696, type, nO_MATCH_int_int: int > int > $o).
% 21.04/7.59  thf(func_def_697, type, nO_MATCH_int_nat: int > nat > $o).
% 21.04/7.59  thf(func_def_698, type, nO_MATCH_int_rat: int > rat > $o).
% 21.04/7.59  thf(func_def_699, type, nO_MAT8694959213317031834nteger: nat > code_integer > $o).
% 21.04/7.59  thf(func_def_700, type, nO_MATCH_nat_int: nat > int > $o).
% 21.04/7.59  thf(func_def_701, type, nO_MATCH_nat_nat: nat > nat > $o).
% 21.04/7.59  thf(func_def_702, type, nO_MATCH_nat_rat: nat > rat > $o).
% 21.04/7.59  thf(func_def_703, type, nO_MAT243659986023775650nteger: rat > code_integer > $o).
% 21.04/7.59  thf(func_def_704, type, nO_MATCH_rat_rat: rat > rat > $o).
% 21.04/7.59  thf(func_def_705, type, the_int: (int > $o) > int).
% 21.04/7.59  thf(func_def_706, type, the_Pr4378521158711661632nt_int: (product_prod_int_int > $o) > product_prod_int_int).
% 21.04/7.59  thf(func_def_707, type, lim_Product_unit: heap_e7401611519738050253t_unit > nat).
% 21.04/7.59  thf(func_def_708, type, if_assn: $o > assn > assn > assn).
% 21.04/7.59  thf(func_def_709, type, if_Code_integer: $o > code_integer > code_integer > code_integer).
% 21.04/7.59  thf(func_def_710, type, if_Code_natural: $o > code_natural > code_natural > code_natural).
% 21.04/7.59  thf(func_def_711, type, if_int: $o > int > int > int).
% 21.04/7.59  thf(func_def_712, type, if_list_int: $o > list_int > list_int > list_int).
% 21.04/7.59  thf(func_def_713, type, if_mul8430962117462786573at_nat: $o > multis2468970476368604999at_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat).
% 21.04/7.59  thf(func_def_714, type, if_nat: $o > nat > nat > nat).
% 21.04/7.59  thf(func_def_715, type, if_num: $o > num > num > num).
% 21.04/7.59  thf(func_def_716, type, if_option_num: $o > option_num > option_num > option_num).
% 21.04/7.59  thf(func_def_717, type, if_pred_Product_unit: $o > pred_Product_unit > pred_Product_unit > pred_Product_unit).
% 21.04/7.59  thf(func_def_718, type, if_Pro5737122678794959658eger_o: $o > produc6271795597528267376eger_o > produc6271795597528267376eger_o > produc6271795597528267376eger_o).
% 21.04/7.59  thf(func_def_719, type, if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 21.04/7.59  thf(func_def_720, type, if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int).
% 21.04/7.59  thf(func_def_721, type, if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 21.04/7.59  thf(func_def_722, type, if_Pro3444522238938527101atural: $o > produc4675096598859438275atural > produc4675096598859438275atural > produc4675096598859438275atural).
% 21.04/7.59  thf(func_def_723, type, if_rat: $o > rat > rat > rat).
% 21.04/7.59  thf(func_def_724, type, if_set_int: $o > set_int > set_int > set_int).
% 21.04/7.59  thf(func_def_725, type, if_Sum_sum_nat_nat: $o > sum_sum_nat_nat > sum_sum_nat_nat > sum_sum_nat_nat).
% 21.04/7.59  thf(func_def_726, type, infini8530281810654367211te_nat: set_nat > nat > nat).
% 21.04/7.59  thf(func_def_727, type, abs_Integ: product_prod_nat_nat > int).
% 21.04/7.59  thf(func_def_728, type, rep_Integ: int > product_prod_nat_nat).
% 21.04/7.59  thf(func_def_729, type, cr_int: product_prod_nat_nat > int > $o).
% 21.04/7.59  thf(func_def_730, type, dup: int > int).
% 21.04/7.59  thf(func_def_731, type, abs_int: set_Pr1261947904930325089at_nat > int).
% 21.04/7.59  thf(func_def_732, type, rep_int: int > set_Pr1261947904930325089at_nat).
% 21.04/7.59  thf(func_def_733, type, int_ge_less_than: int > set_Pr958786334691620121nt_int).
% 21.04/7.59  thf(func_def_734, type, int_ge_less_than2: int > set_Pr958786334691620121nt_int).
% 21.04/7.59  thf(func_def_735, type, intrel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 21.04/7.59  thf(func_def_736, type, nat2: int > nat).
% 21.04/7.59  thf(func_def_737, type, pcr_int: product_prod_nat_nat > int > $o).
% 21.04/7.59  thf(func_def_738, type, ring_18347121197199848620nteger: int > code_integer).
% 21.04/7.59  thf(func_def_739, type, ring_1_of_int_int: int > int).
% 21.04/7.59  thf(func_def_740, type, ring_1_of_int_rat: int > rat).
% 21.04/7.59  thf(func_def_741, type, sub: num > num > int).
% 21.04/7.59  thf(func_def_742, type, inf_in8201999774870019094_int_o: ((int > option6357759511663192854e_term) > product_prod_int_int > $o) > ((int > option6357759511663192854e_term) > product_prod_int_int > $o) > (int > option6357759511663192854e_term) > product_prod_int_int > $o).
% 21.04/7.59  thf(func_def_743, type, inf_in3563340378267265229eger_o: ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > (produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o).
% 21.04/7.59  thf(func_def_744, type, inf_in2641120393918057659_nat_o: ((produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o) > ((produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o) > (produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o).
% 21.04/7.59  thf(func_def_745, type, inf_in3295504058751909687_nat_o: ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o) > ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o) > (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o).
% 21.04/7.59  thf(func_def_746, type, inf_in9018898317438245890at_o_o: ((produc3658429121746597890et_nat > $o) > $o) > ((produc3658429121746597890et_nat > $o) > $o) > (produc3658429121746597890et_nat > $o) > $o).
% 21.04/7.59  thf(func_def_747, type, inf_in8045883074377559328_int_o: ((produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o) > ((produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o) > (produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o).
% 21.04/7.59  thf(func_def_748, type, inf_inf_int_o: (int > $o) > (int > $o) > int > $o).
% 21.04/7.59  thf(func_def_749, type, inf_inf_list_char_o: (list_char > $o) > (list_char > $o) > list_char > $o).
% 21.04/7.59  thf(func_def_750, type, inf_inf_nat_nat_o: (nat > nat > $o) > (nat > nat > $o) > nat > nat > $o).
% 21.04/7.59  thf(func_def_751, type, inf_inf_nat_o: (nat > $o) > (nat > $o) > nat > $o).
% 21.04/7.59  thf(func_def_752, type, inf_in3604695632404883862_int_o: (product_prod_int_int > $o) > (product_prod_int_int > $o) > product_prod_int_int > $o).
% 21.04/7.59  thf(func_def_753, type, inf_in5163264567034779214_nat_o: (product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > product_prod_nat_nat > $o).
% 21.04/7.59  thf(func_def_754, type, inf_inf_set_nat_o: (set_nat > $o) > (set_nat > $o) > set_nat > $o).
% 21.04/7.59  thf(func_def_755, type, inf_in5102985939729578038_int_o: (set_Pr958786334691620121nt_int > $o) > (set_Pr958786334691620121nt_int > $o) > set_Pr958786334691620121nt_int > $o).
% 21.04/7.59  thf(func_def_756, type, inf_inf_o: $o > $o > $o).
% 21.04/7.59  thf(func_def_757, type, inf_inf_assn: assn > assn > assn).
% 21.04/7.59  thf(func_def_758, type, inf_inf_filter_nat: filter_nat > filter_nat > filter_nat).
% 21.04/7.59  thf(func_def_759, type, inf_inf_int: int > int > int).
% 21.04/7.59  thf(func_def_760, type, inf_inf_nat: nat > nat > nat).
% 21.04/7.59  thf(func_def_761, type, inf_inf_Product_unit: product_unit > product_unit > product_unit).
% 21.04/7.59  thf(func_def_762, type, inf_inf_rat: rat > rat > rat).
% 21.04/7.59  thf(func_def_763, type, inf_in1906310914598751387_nat_o: set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o).
% 21.04/7.59  thf(func_def_764, type, inf_inf_set_o: set_o > set_o > set_o).
% 21.04/7.59  thf(func_def_765, type, inf_in1364745209274528805nteger: set_Code_integer > set_Code_integer > set_Code_integer).
% 21.04/7.60  thf(func_def_766, type, inf_inf_set_int: set_int > set_int > set_int).
% 21.04/7.60  thf(func_def_767, type, inf_inf_set_list_nat: set_list_nat > set_list_nat > set_list_nat).
% 21.04/7.60  thf(func_def_768, type, inf_in6177012701088388009t_char: set_list_char > set_list_char > set_list_char).
% 21.04/7.60  thf(func_def_769, type, inf_inf_set_nat: set_nat > set_nat > set_nat).
% 21.04/7.60  thf(func_def_770, type, inf_in8806012763027673301nt_int: set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int).
% 21.04/7.60  thf(func_def_771, type, inf_in3408396081536963678nteger: set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger).
% 21.04/7.60  thf(func_def_772, type, inf_in3088352823822785602et_nat: set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat).
% 21.04/7.60  thf(func_def_773, type, inf_in1768905781608824518et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat).
% 21.04/7.60  thf(func_def_774, type, inf_in2576786181675586251nt_int: set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int).
% 21.04/7.60  thf(func_def_775, type, inf_in2269163501485487111nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int).
% 21.04/7.60  thf(func_def_776, type, inf_in1697001100524423349at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat).
% 21.04/7.60  thf(func_def_777, type, inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 21.04/7.60  thf(func_def_778, type, inf_in7913087082777306421at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 21.04/7.60  thf(func_def_779, type, inf_inf_set_rat: set_rat > set_rat > set_rat).
% 21.04/7.60  thf(func_def_780, type, inf_inf_set_set_nat: set_set_nat > set_set_nat > set_set_nat).
% 21.04/7.60  thf(func_def_781, type, inf_in8396524679539076455nt_int: set_se6260736226359567993nt_int > set_se6260736226359567993nt_int > set_se6260736226359567993nt_int).
% 21.04/7.60  thf(func_def_782, type, inf_inf_set_literal: set_literal > set_literal > set_literal).
% 21.04/7.60  thf(func_def_783, type, semila3963277552210239504char_o: ((list_char > $o) > (list_char > $o) > list_char > $o) > (list_char > $o) > $o).
% 21.04/7.60  thf(func_def_784, type, semila6538661356715008162_int_o: ((product_prod_int_int > $o) > (product_prod_int_int > $o) > product_prod_int_int > $o) > (product_prod_int_int > $o) > $o).
% 21.04/7.60  thf(func_def_785, type, semila6106414119144251899nteger: (code_integer > code_integer > code_integer) > code_integer > $o).
% 21.04/7.60  thf(func_def_786, type, semila9079005292280841162tr_int: (int > int > int) > int > $o).
% 21.04/7.60  thf(func_def_787, type, semila9081495762789891438tr_nat: (nat > nat > nat) > nat > $o).
% 21.04/7.60  thf(func_def_788, type, semila1065760912024005978_set_o: (set_o > set_o > set_o) > set_o > $o).
% 21.04/7.60  thf(func_def_789, type, semila6287294981380917632et_int: (set_int > set_int > set_int) > set_int > $o).
% 21.04/7.60  thf(func_def_790, type, semila7136768128396663732st_nat: (set_list_nat > set_list_nat > set_list_nat) > set_list_nat > $o).
% 21.04/7.60  thf(func_def_791, type, semila1241773964035338532et_nat: (set_nat > set_nat > set_nat) > set_nat > $o).
% 21.04/7.60  thf(func_def_792, type, semila6683195626996185257at_nat: (set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat) > set_Pr8551490117392284871at_nat > $o).
% 21.04/7.60  thf(func_def_793, type, semila858173770281612099at_nat: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat > $o).
% 21.04/7.60  thf(func_def_794, type, semila3675781407871293737at_nat: (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat) > set_Pr4329608150637261639at_nat > $o).
% 21.04/7.60  thf(func_def_795, type, semila6956917442496717612et_rat: (set_rat > set_rat > set_rat) > set_rat > $o).
% 21.04/7.60  thf(func_def_796, type, semila3134969884451571676char_o: ((list_char > $o) > (list_char > $o) > list_char > $o) > (list_char > $o) > ((list_char > $o) > (list_char > $o) > $o) > ((list_char > $o) > (list_char > $o) > $o) > $o).
% 21.04/7.60  thf(func_def_797, type, semila8052717425514686422_int_o: ((product_prod_int_int > $o) > (product_prod_int_int > $o) > product_prod_int_int > $o) > (product_prod_int_int > $o) > ((product_prod_int_int > $o) > (product_prod_int_int > $o) > $o) > ((product_prod_int_int > $o) > (product_prod_int_int > $o) > $o) > $o).
% 21.04/7.60  thf(func_def_798, type, semila5926144314033625522er_nat: (filter_nat > filter_nat > filter_nat) > filter_nat > (filter_nat > filter_nat > $o) > (filter_nat > filter_nat > $o) > $o).
% 21.04/7.60  thf(func_def_799, type, semila1623282765462674594er_nat: (nat > nat > nat) > nat > (nat > nat > $o) > (nat > nat > $o) > $o).
% 21.04/7.60  thf(func_def_800, type, semila2554085542299052326_set_o: (set_o > set_o > set_o) > set_o > (set_o > set_o > $o) > (set_o > set_o > $o) > $o).
% 21.04/7.60  thf(func_def_801, type, semila6712789903965657268et_int: (set_int > set_int > set_int) > set_int > (set_int > set_int > $o) > (set_int > set_int > $o) > $o).
% 21.04/7.60  thf(func_def_802, type, semila2613578647866687720st_nat: (set_list_nat > set_list_nat > set_list_nat) > set_list_nat > (set_list_nat > set_list_nat > $o) > (set_list_nat > set_list_nat > $o) > $o).
% 21.04/7.60  thf(func_def_803, type, semila1667268886620078168et_nat: (set_nat > set_nat > set_nat) > set_nat > (set_nat > set_nat > $o) > (set_nat > set_nat > $o) > $o).
% 21.04/7.60  thf(func_def_804, type, semila5207306265035627125at_nat: (set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat) > set_Pr8551490117392284871at_nat > (set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > $o) > (set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > $o) > $o).
% 21.04/7.60  thf(func_def_805, type, semila4918476307565957903at_nat: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > $o).
% 21.04/7.60  thf(func_def_806, type, semila6534579987270727413at_nat: (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat) > set_Pr4329608150637261639at_nat > (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o) > (set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o) > $o).
% 21.04/7.60  thf(func_def_807, type, semila7382412365081457248et_rat: (set_rat > set_rat > set_rat) > set_rat > (set_rat > set_rat > $o) > (set_rat > set_rat > $o) > $o).
% 21.04/7.60  thf(func_def_808, type, semila1248733672344298208er_nat: (nat > nat > nat) > (nat > nat > $o) > (nat > nat > $o) > $o).
% 21.04/7.60  thf(func_def_809, type, sup_su600977994968626096_int_o: ((int > option6357759511663192854e_term) > product_prod_int_int > $o) > ((int > option6357759511663192854e_term) > product_prod_int_int > $o) > (int > option6357759511663192854e_term) > product_prod_int_int > $o).
% 21.04/7.60  thf(func_def_810, type, sup_su234547053653886311eger_o: ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > (produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o).
% 21.04/7.60  thf(func_def_811, type, sup_su6535292691877529429_nat_o: ((produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o) > ((produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o) > (produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o).
% 21.04/7.60  thf(func_def_812, type, sup_su1630790145277462993_nat_o: ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o) > ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o) > (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o).
% 21.04/7.60  thf(func_def_813, type, sup_su8003631835303541148at_o_o: ((produc3658429121746597890et_nat > $o) > $o) > ((produc3658429121746597890et_nat > $o) > $o) > (produc3658429121746597890et_nat > $o) > $o).
% 21.04/7.60  thf(func_def_814, type, sup_su4182031696650224058_int_o: ((produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o) > ((produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o) > (produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o).
% 21.04/7.60  thf(func_def_815, type, sup_sup_int_o: (int > $o) > (int > $o) > int > $o).
% 21.04/7.60  thf(func_def_816, type, sup_sup_list_char_o: (list_char > $o) > (list_char > $o) > list_char > $o).
% 21.04/7.60  thf(func_def_817, type, sup_su2200014604384089602_nat_o: (multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o) > (multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o) > multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o).
% 21.04/7.60  thf(func_def_818, type, sup_sup_nat_o: (nat > $o) > (nat > $o) > nat > $o).
% 21.04/7.60  thf(func_def_819, type, sup_su8463660629351352368_int_o: (product_prod_int_int > $o) > (product_prod_int_int > $o) > product_prod_int_int > $o).
% 21.04/7.60  thf(func_def_820, type, sup_su6256023009775730178_nat_o: (produc4166570645942440679at_nat > $o) > (produc4166570645942440679at_nat > $o) > produc4166570645942440679at_nat > $o).
% 21.04/7.60  thf(func_def_821, type, sup_su2080679670758317954_nat_o: (produc3843707927480180839at_nat > $o) > (produc3843707927480180839at_nat > $o) > produc3843707927480180839at_nat > $o).
% 21.04/7.60  thf(func_def_822, type, sup_sup_set_nat_o: (set_nat > $o) > (set_nat > $o) > set_nat > $o).
% 21.04/7.60  thf(func_def_823, type, sup_su1852724690005176016_int_o: (set_Pr958786334691620121nt_int > $o) > (set_Pr958786334691620121nt_int > $o) > set_Pr958786334691620121nt_int > $o).
% 21.04/7.60  thf(func_def_824, type, sup_su7519161239522478338_nat_o: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 21.04/7.60  thf(func_def_825, type, sup_sup_assn: assn > assn > assn).
% 21.04/7.60  thf(func_def_826, type, sup_sup_filter_nat: filter_nat > filter_nat > filter_nat).
% 21.04/7.60  thf(func_def_827, type, sup_sup_int: int > int > int).
% 21.04/7.60  thf(func_def_828, type, sup_sup_nat: nat > nat > nat).
% 21.04/7.60  thf(func_def_829, type, sup_sup_Product_unit: product_unit > product_unit > product_unit).
% 21.04/7.60  thf(func_def_830, type, sup_sup_rat: rat > rat > rat).
% 21.04/7.60  thf(func_def_831, type, sup_su5209123915105501825_nat_o: set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o).
% 21.04/7.60  thf(func_def_832, type, sup_sup_set_o: set_o > set_o > set_o).
% 21.04/7.60  thf(func_def_833, type, sup_su848401254843788991nteger: set_Code_integer > set_Code_integer > set_Code_integer).
% 21.04/7.60  thf(func_def_834, type, sup_sup_set_int: set_int > set_int > set_int).
% 21.04/7.60  thf(func_def_835, type, sup_sup_set_list_nat: set_list_nat > set_list_nat > set_list_nat).
% 21.04/7.60  thf(func_def_836, type, sup_sup_set_nat: set_nat > set_nat > set_nat).
% 21.04/7.60  thf(func_def_837, type, sup_su3298353300217089135nt_int: set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int).
% 21.04/7.60  thf(func_def_838, type, sup_su4591284015454442744nteger: set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger).
% 21.04/7.60  thf(func_def_839, type, sup_su8975264963432250076et_nat: set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat).
% 21.04/7.60  thf(func_def_840, type, sup_su7128418612487073120et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat).
% 21.04/7.60  thf(func_def_841, type, sup_su3382966977382714213nt_int: set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int).
% 21.04/7.60  thf(func_def_842, type, sup_su3035147773818789531at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat).
% 21.04/7.60  thf(func_def_843, type, sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 21.04/7.60  thf(func_def_844, type, sup_su718114333110466843at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat).
% 21.04/7.60  thf(func_def_845, type, sup_su5525570899277871387at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 21.04/7.60  thf(func_def_846, type, sup_sup_set_rat: set_rat > set_rat > set_rat).
% 21.04/7.60  thf(func_def_847, type, sup_sup_set_set_nat: set_set_nat > set_set_nat > set_set_nat).
% 21.04/7.60  thf(func_def_848, type, sup_su2047564715030645325nt_int: set_se6260736226359567993nt_int > set_se6260736226359567993nt_int > set_se6260736226359567993nt_int).
% 21.04/7.60  thf(func_def_849, type, sup_sup_set_literal: set_literal > set_literal > set_literal).
% 21.04/7.60  thf(func_def_850, type, lattic8263393255366662781ax_int: set_int > int).
% 21.04/7.60  thf(func_def_851, type, lattic8265883725875713057ax_nat: set_nat > nat).
% 21.04/7.60  thf(func_def_852, type, lattic7826324295020591184_F_nat: (nat > nat > nat) > nat > set_nat > nat).
% 21.04/7.60  thf(func_def_853, type, quotie6109894551476798619iteral: (list_char > list_char > $o) > (list_char > literal) > (literal > list_char) > (list_char > literal > $o) > $o).
% 21.04/7.60  thf(func_def_854, type, append_int: list_int > list_int > list_int).
% 21.04/7.60  thf(func_def_855, type, append_char: list_char > list_char > list_char).
% 21.04/7.60  thf(func_def_856, type, butlast_nat: list_nat > list_nat).
% 21.04/7.60  thf(func_def_857, type, filter_nat2: (nat > $o) > list_nat > list_nat).
% 21.04/7.60  thf(func_def_858, type, fold_int_int: (int > int > int) > list_int > int > int).
% 21.04/7.60  thf(func_def_859, type, fold_nat_nat: (nat > nat > nat) > list_nat > nat > nat).
% 21.04/7.60  thf(func_def_860, type, last_nat: list_nat > nat).
% 21.04/7.60  thf(func_def_861, type, linord1735203802627413978nt_int: (int > int) > list_int > list_int).
% 21.04/7.60  thf(func_def_862, type, linord738340561235409698at_nat: (nat > nat) > list_nat > list_nat).
% 21.04/7.60  thf(func_def_863, type, cons_int: int > list_int > list_int).
% 21.04/7.60  thf(func_def_864, type, cons_nat: nat > list_nat > list_nat).
% 21.04/7.60  thf(func_def_865, type, cons_char: char > list_char > list_char).
% 21.04/7.60  thf(func_def_866, type, nil_int: list_int).
% 21.04/7.60  thf(func_def_867, type, nil_nat: list_nat).
% 21.04/7.60  thf(func_def_868, type, nil_char: list_char).
% 21.04/7.60  thf(func_def_869, type, list_all2_char_char: (char > char > $o) > list_char > list_char > $o).
% 21.04/7.60  thf(func_def_870, type, list_all_char: (char > $o) > list_char > $o).
% 21.04/7.60  thf(func_def_871, type, map_Co843364623960961780r_char: (code_integer > char) > list_Code_integer > list_char).
% 21.04/7.60  thf(func_def_872, type, map_nat_nat: (nat > nat) > list_nat > list_nat).
% 21.04/7.60  thf(func_def_873, type, map_ch5843194146513361140nteger: (char > code_integer) > list_char > list_Code_integer).
% 21.04/7.60  thf(func_def_874, type, map_char_char: (char > char) > list_char > list_char).
% 21.04/7.60  thf(func_def_875, type, set_int2: list_int > set_int).
% 21.04/7.60  thf(func_def_876, type, set_nat2: list_nat > set_nat).
% 21.04/7.60  thf(func_def_877, type, set_char2: list_char > set_char).
% 21.04/7.60  thf(func_def_878, type, lexordp_char: (char > char > $o) > list_char > list_char > $o).
% 21.04/7.60  thf(func_def_879, type, lexordp_eq_char: (char > char > $o) > list_char > list_char > $o).
% 21.04/7.60  thf(func_def_880, type, upt: nat > nat > list_nat).
% 21.04/7.60  thf(func_def_881, type, upto: int > int > list_int).
% 21.04/7.60  thf(func_def_882, type, upto_aux: int > int > list_int > list_int).
% 21.04/7.60  thf(func_def_883, type, upto_rel: product_prod_int_int > product_prod_int_int > $o).
% 21.04/7.60  thf(func_def_884, type, biject576505603616484041nt_int: set_Pr1872883991513573699nt_int > $o).
% 21.04/7.60  thf(func_def_885, type, biject9051520373387432658nteger: set_Pr1281608226676607948nteger > $o).
% 21.04/7.60  thf(func_def_886, type, biject1468766312547416318et_nat: set_Pr8536935166611901872et_nat > $o).
% 21.04/7.60  thf(func_def_887, type, biject2615096655818420098et_nat: set_Pr3286484037609594932et_nat > $o).
% 21.04/7.60  thf(func_def_888, type, biject383251550997737151nt_int: set_Pr9222295170931077689nt_int > $o).
% 21.04/7.60  thf(func_def_889, type, bijective_nat_nat: set_Pr1261947904930325089at_nat > $o).
% 21.04/7.60  thf(func_def_890, type, pairse3534876335208825186e_term: (int > option6357759511663192854e_term) > product_prod_int_int > produc6576344331059438605e_term).
% 21.04/7.60  thf(func_def_891, type, pairse6848479906795794847e_term: produc7773217078559923341nt_int > produc7773217078559923341nt_int > $o).
% 21.04/7.60  thf(func_def_892, type, rel_re3331361160397388719_nat_o: set_Pr2161125870931222855_nat_o > set_Pr4532377907799695533_nat_o > set_Pr2161125870931222855_nat_o).
% 21.04/7.60  thf(func_def_893, type, rel_restrict_o: set_Product_prod_o_o > set_o > set_Product_prod_o_o).
% 21.04/7.60  thf(func_def_894, type, rel_restrict_int: set_Pr958786334691620121nt_int > set_int > set_Pr958786334691620121nt_int).
% 21.04/7.60  thf(func_def_895, type, rel_restrict_nat: set_Pr1261947904930325089at_nat > set_nat > set_Pr1261947904930325089at_nat).
% 21.04/7.60  thf(func_def_896, type, rel_re2197483123211154633at_nat: set_Pr4759807026041935047at_nat > set_Pr8551490117392284871at_nat > set_Pr4759807026041935047at_nat).
% 21.04/7.60  thf(func_def_897, type, rel_re36662636952045539at_nat: set_Pr8693737435421807431at_nat > set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat).
% 21.04/7.60  thf(func_def_898, type, rel_re2767227651283840073at_nat: set_Pr5564308138774400199at_nat > set_Pr4329608150637261639at_nat > set_Pr5564308138774400199at_nat).
% 21.04/7.60  thf(func_def_899, type, rel_restrict_set_nat: set_Pr5488025237498180813et_nat > set_set_nat > set_Pr5488025237498180813et_nat).
% 21.04/7.60  thf(func_def_900, type, rel_re4349003428253852667nt_int: set_Pr8057934254988874055nt_int > set_se6260736226359567993nt_int > set_Pr8057934254988874055nt_int).
% 21.04/7.60  thf(func_def_901, type, uncurry_int_int_o: (int > int > $o) > product_prod_int_int > $o).
% 21.04/7.60  thf(func_def_902, type, uncurry_int_int_int: (int > int > int) > product_prod_int_int > int).
% 21.04/7.60  thf(func_def_903, type, uncurr7650761721940715016nt_int: (int > int > product_prod_int_int) > product_prod_int_int > product_prod_int_int).
% 21.04/7.60  thf(func_def_904, type, uncurr7511940902602773877_nat_o: (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 21.04/7.60  thf(func_def_905, type, uncurr8011562610307062878at_nat: (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 21.04/7.60  thf(func_def_906, type, add_ms2612439473150266591at_nat: product_prod_nat_nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat).
% 21.04/7.60  thf(func_def_907, type, ms_strict: set_Pr8551490117392284871at_nat).
% 21.04/7.60  thf(func_def_908, type, ms_weak: set_Pr8551490117392284871at_nat).
% 21.04/7.60  thf(func_def_909, type, pw_leq: multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o).
% 21.04/7.60  thf(func_def_910, type, set_ms8126754132646256062at_nat: multis2468970476368604999at_nat > set_Pr1261947904930325089at_nat).
% 21.04/7.60  thf(func_def_911, type, suc: nat > nat).
% 21.04/7.60  thf(func_def_912, type, case_nat_o: $o > (nat > $o) > nat > $o).
% 21.04/7.60  thf(func_def_913, type, case_nat_nat: nat > (nat > nat) > nat > nat).
% 21.04/7.60  thf(func_def_914, type, case_nat_option_num: option_num > (nat > option_num) > nat > option_num).
% 21.04/7.60  thf(func_def_915, type, pred: nat > nat).
% 21.04/7.60  thf(func_def_916, type, semiring_1_Nats_int: set_int).
% 21.04/7.60  thf(func_def_917, type, semiri4939895301339042750nteger: nat > code_integer).
% 21.04/7.60  thf(func_def_918, type, semiri3763490453095760265atural: nat > code_natural).
% 21.04/7.60  thf(func_def_919, type, semiri1314217659103216013at_int: nat > int).
% 21.04/7.60  thf(func_def_920, type, semiri1316708129612266289at_nat: nat > nat).
% 21.04/7.60  thf(func_def_921, type, semiri681578069525770553at_rat: nat > rat).
% 21.04/7.60  thf(func_def_922, type, semiri4055485073559036834nteger: (code_integer > code_integer) > nat > code_integer > code_integer).
% 21.04/7.60  thf(func_def_923, type, semiri8420488043553186161ux_int: (int > int) > nat > int > int).
% 21.04/7.60  thf(func_def_924, type, semiri8422978514062236437ux_nat: (nat > nat) > nat > nat > nat).
% 21.04/7.60  thf(func_def_925, type, semiri7787848453975740701ux_rat: (rat > rat) > nat > rat > rat).
% 21.04/7.60  thf(func_def_926, type, size_size_list_int: list_int > nat).
% 21.04/7.60  thf(func_def_927, type, size_size_list_nat: list_nat > nat).
% 21.04/7.60  thf(func_def_928, type, size_size_list_char: list_char > nat).
% 21.04/7.60  thf(func_def_929, type, size_size_literal: literal > nat).
% 21.04/7.60  thf(func_def_930, type, nat_int_decode: nat > int).
% 21.04/7.60  thf(func_def_931, type, nat_int_encode: int > nat).
% 21.04/7.60  thf(func_def_932, type, nat_list_decode: nat > list_nat).
% 21.04/7.60  thf(func_def_933, type, nat_list_decode_rel: nat > nat > $o).
% 21.04/7.60  thf(func_def_934, type, nat_list_encode: list_nat > nat).
% 21.04/7.60  thf(func_def_935, type, nat_list_encode_rel: list_nat > list_nat > $o).
% 21.04/7.60  thf(func_def_936, type, nat_prod_decode: nat > product_prod_nat_nat).
% 21.04/7.60  thf(func_def_937, type, nat_prod_decode_aux: nat > nat > product_prod_nat_nat).
% 21.04/7.60  thf(func_def_938, type, nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 21.04/7.60  thf(func_def_939, type, nat_prod_encode: product_prod_nat_nat > nat).
% 21.04/7.60  thf(func_def_940, type, nat_set_decode: nat > set_nat).
% 21.04/7.60  thf(func_def_941, type, nat_set_encode: set_nat > nat).
% 21.04/7.60  thf(func_def_942, type, nat_sum_decode: nat > sum_sum_nat_nat).
% 21.04/7.60  thf(func_def_943, type, nat_sum_encode: sum_sum_nat_nat > nat).
% 21.04/7.60  thf(func_def_944, type, nat_triangle: nat > nat).
% 21.04/7.60  thf(func_def_945, type, bitM: num > num).
% 21.04/7.60  thf(func_def_946, type, inc: num > num).
% 21.04/7.60  thf(func_def_947, type, nat_of_num: num > nat).
% 21.04/7.60  thf(func_def_948, type, neg_nu8804712462038260780nteger: code_integer > code_integer).
% 21.04/7.60  thf(func_def_949, type, neg_numeral_dbl_int: int > int).
% 21.04/7.60  thf(func_def_950, type, neg_numeral_dbl_rat: rat > rat).
% 21.04/7.60  thf(func_def_951, type, neg_nu7757733837767384882nteger: code_integer > code_integer).
% 21.04/7.60  thf(func_def_952, type, neg_nu3811975205180677377ec_int: int > int).
% 21.04/7.60  thf(func_def_953, type, neg_nu3179335615603231917ec_rat: rat > rat).
% 21.04/7.60  thf(func_def_954, type, neg_nu5831290666863070958nteger: code_integer > code_integer).
% 21.04/7.60  thf(func_def_955, type, neg_nu5851722552734809277nc_int: int > int).
% 21.04/7.60  thf(func_def_956, type, neg_nu5219082963157363817nc_rat: rat > rat).
% 21.04/7.60  thf(func_def_957, type, neg_nu5755505904847501662nteger: num > num > code_integer).
% 21.04/7.60  thf(func_def_958, type, neg_numeral_sub_int: num > num > int).
% 21.04/7.60  thf(func_def_959, type, neg_numeral_sub_rat: num > num > rat).
% 21.04/7.60  thf(func_def_960, type, bit0: num > num).
% 21.04/7.60  thf(func_def_961, type, bit1: num > num).
% 21.04/7.60  thf(func_def_962, type, one: num).
% 21.04/7.60  thf(func_def_963, type, case_num_option_num: option_num > (num > option_num) > (num > option_num) > num > option_num).
% 21.04/7.60  thf(func_def_964, type, num_of_nat: nat > num).
% 21.04/7.60  thf(func_def_965, type, numera6620942414471956472nteger: num > code_integer).
% 21.04/7.60  thf(func_def_966, type, numera5444537566228673987atural: num > code_natural).
% 21.04/7.60  thf(func_def_967, type, numeral_numeral_int: num > int).
% 21.04/7.60  thf(func_def_968, type, numeral_numeral_nat: num > nat).
% 21.04/7.60  thf(func_def_969, type, numeral_numeral_rat: num > rat).
% 21.04/7.60  thf(func_def_970, type, pred_numeral: num > nat).
% 21.04/7.60  thf(func_def_971, type, ring_16219924574208605041nteger: code_integer > $o).
% 21.04/7.60  thf(func_def_972, type, ring_1_iszero_int: int > $o).
% 21.04/7.60  thf(func_def_973, type, ring_1_iszero_rat: rat > $o).
% 21.04/7.60  thf(func_def_974, type, none_num: option_num).
% 21.04/7.60  thf(func_def_975, type, some_num: num > option_num).
% 21.04/7.60  thf(func_def_976, type, case_option_int_num: int > (num > int) > option_num > int).
% 21.04/7.60  thf(func_def_977, type, case_option_num_num: num > (num > num) > option_num > num).
% 21.04/7.60  thf(func_def_978, type, case_o6005452278849405969um_num: option_num > (num > option_num) > option_num > option_num).
% 21.04/7.60  thf(func_def_979, type, map_option_num_num: (num > num) > option_num > option_num).
% 21.04/7.60  thf(func_def_980, type, order_underS_nat: set_Pr1261947904930325089at_nat > nat > set_nat).
% 21.04/7.60  thf(func_def_981, type, order_2888998067076097458on_nat: set_nat > set_Pr1261947904930325089at_nat > $o).
% 21.04/7.60  thf(func_def_982, type, bot_bo1403522918969695512_int_o: (int > option6357759511663192854e_term) > product_prod_int_int > $o).
% 21.04/7.60  thf(func_def_983, type, bot_bo3000040243691356879eger_o: (produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o).
% 21.04/7.60  thf(func_def_984, type, bot_bo3790638025767943357_nat_o: (produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o).
% 21.04/7.60  thf(func_def_985, type, bot_bo5580076615179976505_nat_o: (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o).
% 21.04/7.60  thf(func_def_986, type, bot_bo7963750851167320836at_o_o: (produc3658429121746597890et_nat > $o) > $o).
% 21.04/7.60  thf(func_def_987, type, bot_bo8662317086119403298_int_o: (produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o).
% 21.04/7.60  thf(func_def_988, type, bot_bot_o_o: $o > $o).
% 21.04/7.60  thf(func_def_989, type, bot_bot_int_o: int > $o).
% 21.04/7.60  thf(func_def_990, type, bot_bot_list_char_o: list_char > $o).
% 21.04/7.60  thf(func_def_991, type, bot_bot_nat_nat_o: nat > nat > $o).
% 21.04/7.60  thf(func_def_992, type, bot_bot_nat_o: nat > $o).
% 21.04/7.60  thf(func_def_993, type, bot_bo8147686125503663512_int_o: product_prod_int_int > $o).
% 21.04/7.60  thf(func_def_994, type, bot_bo482883023278783056_nat_o: product_prod_nat_nat > $o).
% 21.04/7.60  thf(func_def_995, type, bot_bot_set_nat_o: set_nat > $o).
% 21.04/7.60  thf(func_def_996, type, bot_bo2686080419298087992_int_o: set_Pr958786334691620121nt_int > $o).
% 21.04/7.60  thf(func_def_998, type, bot_bot_assn: assn).
% 21.04/7.60  thf(func_def_999, type, bot_bot_filter_nat: filter_nat).
% 21.04/7.60  thf(func_def_1000, type, bot_bot_nat: nat).
% 21.04/7.60  thf(func_def_1001, type, bot_bo2717538794563056311t_unit: pred_Product_unit).
% 21.04/7.60  thf(func_def_1002, type, bot_bot_Product_unit: product_unit).
% 21.04/7.60  thf(func_def_1003, type, bot_bo7824918357723582233_nat_o: set_Pr4532377907799695533_nat_o).
% 21.04/7.60  thf(func_def_1004, type, bot_bot_set_o: set_o).
% 21.04/7.60  thf(func_def_1005, type, bot_bo3990330152332043303nteger: set_Code_integer).
% 21.04/7.60  thf(func_def_1006, type, bot_bo498966703094740906er_nat: set_filter_nat).
% 21.04/7.60  thf(func_def_1007, type, bot_bot_set_int: set_int).
% 21.04/7.60  thf(func_def_1008, type, bot_bot_set_list_nat: set_list_nat).
% 21.04/7.60  thf(func_def_1009, type, bot_bot_set_nat: set_nat).
% 21.04/7.60  thf(func_def_1010, type, bot_bo4508923176915781079nt_int: set_Pr1872883991513573699nt_int).
% 21.04/7.60  thf(func_def_1011, type, bot_bo5443222936135328352nteger: set_Pr1281608226676607948nteger).
% 21.04/7.60  thf(func_def_1012, type, bot_bo5635537948650799172et_nat: set_Pr8536935166611901872et_nat).
% 21.04/7.60  thf(func_def_1013, type, bot_bo1481135142794719944et_nat: set_Pr3286484037609594932et_nat).
% 21.04/7.60  thf(func_def_1014, type, bot_bo572930865798478029nt_int: set_Pr9222295170931077689nt_int).
% 21.04/7.60  thf(func_def_1015, type, bot_bo7073875226086086771od_o_o: set_Product_prod_o_o).
% 21.04/7.60  thf(func_def_1016, type, bot_bo1796632182523588997nt_int: set_Pr958786334691620121nt_int).
% 21.04/7.60  thf(func_def_1017, type, bot_bo8422036546324065075at_nat: set_Pr8551490117392284871at_nat).
% 21.04/7.60  thf(func_def_1018, type, bot_bo2099793752762293965at_nat: set_Pr1261947904930325089at_nat).
% 21.04/7.60  thf(func_def_1019, type, bot_bo5327735625951526323at_nat: set_Pr8693737435421807431at_nat).
% 21.04/7.60  thf(func_def_1020, type, bot_bo228742789529271731at_nat: set_Pr4329608150637261639at_nat).
% 21.04/7.60  thf(func_def_1021, type, bot_bo3957492148770167129t_unit: set_Product_unit).
% 21.04/7.60  thf(func_def_1022, type, bot_bot_set_rat: set_rat).
% 21.04/7.60  thf(func_def_1023, type, bot_bot_set_set_nat: set_set_nat).
% 21.04/7.60  thf(func_def_1024, type, bot_bo1488462491386950373nt_int: set_se6260736226359567993nt_int).
% 21.04/7.60  thf(func_def_1025, type, bot_bot_set_literal: set_literal).
% 21.04/7.60  thf(func_def_1026, type, ord_Least_nat: (nat > $o) > nat).
% 21.04/7.60  thf(func_def_1027, type, ord_le5728734702541193924at_o_o: ((produc3658429121746597890et_nat > $o) > $o) > ((produc3658429121746597890et_nat > $o) > $o) > $o).
% 21.04/7.60  thf(func_def_1028, type, ord_less_int_o: (int > $o) > (int > $o) > $o).
% 21.04/7.60  thf(func_def_1029, type, ord_less_list_char_o: (list_char > $o) > (list_char > $o) > $o).
% 21.04/7.60  thf(func_def_1030, type, ord_less_nat_o: (nat > $o) > (nat > $o) > $o).
% 21.04/7.60  thf(func_def_1031, type, ord_le8176553561544679545_nat_o: (produc3658429121746597890et_nat > $o) > (produc3658429121746597890et_nat > $o) > $o).
% 21.04/7.60  thf(func_def_1032, type, ord_le8213806771718485336_int_o: (product_prod_int_int > $o) > (product_prod_int_int > $o) > $o).
% 21.04/7.60  thf(func_def_1033, type, ord_less_set_nat_o: (set_nat > $o) > (set_nat > $o) > $o).
% 21.04/7.60  thf(func_def_1034, type, ord_le2688692977766382584_int_o: (set_Pr958786334691620121nt_int > $o) > (set_Pr958786334691620121nt_int > $o) > $o).
% 21.04/7.60  thf(func_def_1035, type, ord_less_o: $o > $o > $o).
% 21.04/7.60  thf(func_def_1036, type, ord_less_assn: assn > assn > $o).
% 21.04/7.60  thf(func_def_1037, type, ord_le6747313008572928689nteger: code_integer > code_integer > $o).
% 21.04/7.60  thf(func_def_1038, type, ord_le5570908160329646204atural: code_natural > code_natural > $o).
% 21.04/7.60  thf(func_def_1039, type, ord_less_filter_nat: filter_nat > filter_nat > $o).
% 21.04/7.60  thf(func_def_1040, type, ord_less_int: int > int > $o).
% 21.04/7.60  thf(func_def_1041, type, ord_less_nat: nat > nat > $o).
% 21.04/7.60  thf(func_def_1042, type, ord_less_num: num > num > $o).
% 21.04/7.60  thf(func_def_1043, type, ord_le361264281704409273t_unit: product_unit > product_unit > $o).
% 21.04/7.60  thf(func_def_1044, type, ord_less_rat: rat > rat > $o).
% 21.04/7.60  thf(func_def_1045, type, ord_le2453136405763929_nat_o: set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o > $o).
% 21.04/7.60  thf(func_def_1046, type, ord_less_set_o: set_o > set_o > $o).
% 21.04/7.60  thf(func_def_1047, type, ord_le1307284697595431911nteger: set_Code_integer > set_Code_integer > $o).
% 21.04/7.60  thf(func_def_1048, type, ord_less_set_int: set_int > set_int > $o).
% 21.04/7.60  thf(func_def_1049, type, ord_le1190675801316882794st_nat: set_list_nat > set_list_nat > $o).
% 21.04/7.60  thf(func_def_1050, type, ord_less_set_nat: set_nat > set_nat > $o).
% 21.04/7.60  thf(func_def_1051, type, ord_le7563427860532173253nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o).
% 21.04/7.60  thf(func_def_1052, type, ord_le7642048601412989811at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > $o).
% 21.04/7.60  thf(func_def_1053, type, ord_le7866589430770878221at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 21.04/7.60  thf(func_def_1054, type, ord_le2604355607129572851at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o).
% 21.04/7.60  thf(func_def_1055, type, ord_less_set_rat: set_rat > set_rat > $o).
% 21.04/7.60  thf(func_def_1056, type, ord_less_set_set_nat: set_set_nat > set_set_nat > $o).
% 21.04/7.60  thf(func_def_1057, type, ord_le1924305788584680229nt_int: set_se6260736226359567993nt_int > set_se6260736226359567993nt_int > $o).
% 21.04/7.60  thf(func_def_1058, type, ord_less_literal: literal > literal > $o).
% 21.04/7.60  thf(func_def_1059, type, ord_le2124322318746777828_int_o: ((int > option6357759511663192854e_term) > product_prod_int_int > $o) > ((int > option6357759511663192854e_term) > product_prod_int_int > $o) > $o).
% 21.04/7.60  thf(func_def_1060, type, ord_le4340812435750786203eger_o: ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > $o).
% 21.04/7.60  thf(func_def_1061, type, ord_le6753239538765779593_nat_o: ((produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o) > ((produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o) > $o).
% 21.04/7.60  thf(func_def_1062, type, ord_le8000401564054156549_nat_o: ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o) > ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o) > $o).
% 21.04/7.60  thf(func_def_1063, type, ord_le1304494283415849680at_o_o: ((produc3658429121746597890et_nat > $o) > $o) > ((produc3658429121746597890et_nat > $o) > $o) > $o).
% 21.04/7.60  thf(func_def_1064, type, ord_le5643404153117327598_int_o: ((produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o) > ((produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o) > $o).
% 21.04/7.60  thf(func_def_1065, type, ord_less_eq_int_o: (int > $o) > (int > $o) > $o).
% 21.04/7.60  thf(func_def_1066, type, ord_le4796328588573674190char_o: (list_char > $o) > (list_char > $o) > $o).
% 21.04/7.60  thf(func_def_1067, type, ord_less_eq_nat_o: (nat > $o) > (nat > $o) > $o).
% 21.04/7.60  thf(func_def_1068, type, ord_le729326519192465773_nat_o: (produc3658429121746597890et_nat > $o) > (produc3658429121746597890et_nat > $o) > $o).
% 21.04/7.60  thf(func_def_1069, type, ord_le8369615600986905444_int_o: (product_prod_int_int > $o) > (product_prod_int_int > $o) > $o).
% 21.04/7.60  thf(func_def_1070, type, ord_le3964352015994296041_nat_o: (set_nat > $o) > (set_nat > $o) > $o).
% 21.04/7.60  thf(func_def_1071, type, ord_le8334417538754933252_int_o: (set_Pr958786334691620121nt_int > $o) > (set_Pr958786334691620121nt_int > $o) > $o).
% 21.04/7.60  thf(func_def_1072, type, ord_less_eq_o: $o > $o > $o).
% 21.04/7.60  thf(func_def_1073, type, ord_less_eq_assn: assn > assn > $o).
% 21.04/7.60  thf(func_def_1074, type, ord_le3102999989581377725nteger: code_integer > code_integer > $o).
% 21.04/7.60  thf(func_def_1075, type, ord_le1926595141338095240atural: code_natural > code_natural > $o).
% 21.04/7.60  thf(func_def_1076, type, ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o).
% 21.04/7.60  thf(func_def_1077, type, ord_less_eq_int: int > int > $o).
% 21.04/7.60  thf(func_def_1078, type, ord_less_eq_nat: nat > nat > $o).
% 21.04/7.60  thf(func_def_1079, type, ord_less_eq_num: num > num > $o).
% 21.04/7.60  thf(func_def_1080, type, ord_le3221252021190050221t_unit: product_unit > product_unit > $o).
% 21.04/7.60  thf(func_def_1081, type, ord_less_eq_rat: rat > rat > $o).
% 21.04/7.60  thf(func_def_1082, type, ord_le2965882846123202637_nat_o: set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o > $o).
% 21.04/7.60  thf(func_def_1083, type, ord_less_eq_set_o: set_o > set_o > $o).
% 21.04/7.60  thf(func_def_1084, type, ord_le7084787975880047091nteger: set_Code_integer > set_Code_integer > $o).
% 21.04/7.60  thf(func_def_1085, type, ord_less_eq_set_int: set_int > set_int > $o).
% 21.04/7.60  thf(func_def_1086, type, ord_le6045566169113846134st_nat: set_list_nat > set_list_nat > $o).
% 21.04/7.60  thf(func_def_1087, type, ord_less_eq_set_nat: set_nat > set_nat > $o).
% 21.04/7.60  thf(func_def_1088, type, ord_le135402666524580259nt_int: set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int > $o).
% 21.04/7.60  thf(func_def_1089, type, ord_le653643898420964396nteger: set_Pr1281608226676607948nteger > set_Pr1281608226676607948nteger > $o).
% 21.04/7.60  thf(func_def_1090, type, ord_le4763372923235995152et_nat: set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat > $o).
% 21.04/7.60  thf(func_def_1091, type, ord_le5966269811547037844et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > $o).
% 21.04/7.60  thf(func_def_1092, type, ord_le8725513860283290265nt_int: set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int > $o).
% 21.04/7.60  thf(func_def_1093, type, ord_le2843351958646193337nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o).
% 21.04/7.60  thf(func_def_1094, type, ord_le8081472938463900775at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > $o).
% 21.04/7.60  thf(func_def_1095, type, ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 21.04/7.60  thf(func_def_1096, type, ord_le1268244103169919719at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o).
% 21.04/7.60  thf(func_def_1097, type, ord_less_eq_set_rat: set_rat > set_rat > $o).
% 21.04/7.60  thf(func_def_1098, type, ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o).
% 21.04/7.60  thf(func_def_1099, type, ord_le483042692224249369nt_int: set_se6260736226359567993nt_int > set_se6260736226359567993nt_int > $o).
% 21.04/7.60  thf(func_def_1100, type, ord_less_eq_literal: literal > literal > $o).
% 21.04/7.60  thf(func_def_1101, type, ord_max_int: int > int > int).
% 21.04/7.60  thf(func_def_1102, type, ord_max_nat: nat > nat > nat).
% 21.04/7.60  thf(func_def_1103, type, ord_min_nat: nat > nat > nat).
% 21.04/7.60  thf(func_def_1104, type, order_mono_nat_nat: (nat > nat) > $o).
% 21.04/7.60  thf(func_def_1105, type, ordering_nat: (nat > nat > $o) > (nat > nat > $o) > $o).
% 21.04/7.60  thf(func_def_1106, type, orderi2807725203697798511er_nat: (filter_nat > filter_nat > $o) > (filter_nat > filter_nat > $o) > filter_nat > $o).
% 21.04/7.60  thf(func_def_1107, type, ordering_top_nat: (nat > nat > $o) > (nat > nat > $o) > nat > $o).
% 21.04/7.60  thf(func_def_1108, type, ordering_top_set_o: (set_o > set_o > $o) > (set_o > set_o > $o) > set_o > $o).
% 21.04/7.60  thf(func_def_1109, type, ordering_top_set_int: (set_int > set_int > $o) > (set_int > set_int > $o) > set_int > $o).
% 21.04/7.60  thf(func_def_1110, type, orderi7613023277850353061st_nat: (set_list_nat > set_list_nat > $o) > (set_list_nat > set_list_nat > $o) > set_list_nat > $o).
% 21.04/7.60  thf(func_def_1111, type, ordering_top_set_nat: (set_nat > set_nat > $o) > (set_nat > set_nat > $o) > set_nat > $o).
% 21.04/7.60  thf(func_def_1112, type, orderi2172309028950807442at_nat: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o) > set_Pr1261947904930325089at_nat > $o).
% 21.04/7.60  thf(func_def_1113, type, ordering_top_set_rat: (set_rat > set_rat > $o) > (set_rat > set_rat > $o) > set_rat > $o).
% 21.04/7.60  thf(func_def_1114, type, preordering_nat: (nat > nat > $o) > (nat > nat > $o) > $o).
% 21.04/7.60  thf(func_def_1115, type, top_to6513043852502318900_int_o: (int > option6357759511663192854e_term) > product_prod_int_int > $o).
% 21.04/7.60  thf(func_def_1116, type, top_to8112647782992986859eger_o: (produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o).
% 21.04/7.60  thf(func_def_1117, type, top_to7190503160269336793_nat_o: (produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o).
% 21.04/7.60  thf(func_def_1118, type, top_to2428096842796733269_nat_o: (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o).
% 21.04/7.60  thf(func_def_1119, type, top_to2462227307520033056at_o_o: (produc3658429121746597890et_nat > $o) > $o).
% 21.04/7.60  thf(func_def_1120, type, top_to6261655714344447806_int_o: (produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o).
% 21.04/7.60  thf(func_def_1121, type, top_top_o_o: $o > $o).
% 21.04/7.60  thf(func_def_1122, type, top_top_int_o: int > $o).
% 21.04/7.60  thf(func_def_1123, type, top_top_list_nat_o: list_nat > $o).
% 21.04/7.60  thf(func_def_1124, type, top_top_list_char_o: list_char > $o).
% 21.04/7.60  thf(func_def_1125, type, top_top_nat_o: nat > $o).
% 21.04/7.60  thf(func_def_1126, type, top_to1578927101902068148_int_o: product_prod_int_int > $o).
% 21.04/7.60  thf(func_def_1127, type, top_top_rat_o: rat > $o).
% 21.04/7.60  thf(func_def_1128, type, top_top_set_nat_o: set_nat > $o).
% 21.04/7.60  thf(func_def_1129, type, top_to6187514276045680724_int_o: set_Pr958786334691620121nt_int > $o).
% 21.04/7.60  thf(func_def_1131, type, top_top_assn: assn).
% 21.04/7.60  thf(func_def_1132, type, top_top_filter_nat: filter_nat).
% 21.04/7.60  thf(func_def_1133, type, top_top_Product_unit: product_unit).
% 21.04/7.60  thf(func_def_1134, type, top_to4869887016220417533_nat_o: set_Pr4532377907799695533_nat_o).
% 21.04/7.60  thf(func_def_1135, type, top_top_set_o: set_o).
% 21.04/7.60  thf(func_def_1136, type, top_top_set_int: set_int).
% 21.04/7.60  thf(func_def_1137, type, top_top_set_list_nat: set_list_nat).
% 21.04/7.60  thf(func_def_1138, type, top_to3190553582279535303t_char: set_list_char).
% 21.04/7.60  thf(func_def_1139, type, top_top_set_nat: set_nat).
% 21.04/7.60  thf(func_def_1140, type, top_top_set_option_o: set_option_o).
% 21.04/7.60  thf(func_def_1141, type, top_to6430115241214627170on_int: set_option_int).
% 21.04/7.60  thf(func_def_1142, type, top_to1113147461230312982st_nat: set_option_list_nat).
% 21.04/7.60  thf(func_def_1143, type, top_to8920198386146353926on_nat: set_option_nat).
% 21.04/7.60  thf(func_def_1144, type, top_to3251141154256563319at_nat: set_op4508134149509766951at_nat).
% 21.04/7.60  thf(func_def_1145, type, top_to2540212048668676366on_rat: set_option_rat).
% 21.04/7.60  thf(func_def_1146, type, top_to2069137843433766899nt_int: set_Pr1872883991513573699nt_int).
% 21.04/7.60  thf(func_def_1147, type, top_to7512759353274530428nteger: set_Pr1281608226676607948nteger).
% 21.04/7.60  thf(func_def_1148, type, top_to1599102959340997728et_nat: set_Pr8536935166611901872et_nat).
% 21.04/7.60  thf(func_def_1149, type, top_to8753217654552796900et_nat: set_Pr3286484037609594932et_nat).
% 21.04/7.60  thf(func_def_1150, type, top_to3181862456159035625nt_int: set_Pr9222295170931077689nt_int).
% 21.04/7.60  thf(func_def_1151, type, top_to7721136755696657239od_o_o: set_Product_prod_o_o).
% 21.04/7.60  thf(func_def_1152, type, top_to4532601362410810969_o_int: set_Pr8834758594704517033_o_int).
% 21.04/7.60  thf(func_def_1153, type, top_to7022684507342537725_o_nat: set_Pr2101469702781467981_o_nat).
% 21.04/7.60  thf(func_def_1154, type, top_to642698169864860165_o_rat: set_Pr4944855402158566229_o_rat).
% 21.04/7.60  thf(func_def_1155, type, top_to4366644338036079209nt_int: set_Pr958786334691620121nt_int).
% 21.04/7.60  thf(func_def_1156, type, top_to8764741339697478167at_nat: set_Pr8551490117392284871at_nat).
% 21.04/7.60  thf(func_def_1157, type, top_to8070287629520841379_nat_o: set_Pr3149072824959771635_nat_o).
% 21.04/7.60  thf(func_def_1158, type, top_to4669805908274784177at_nat: set_Pr1261947904930325089at_nat).
% 21.04/7.60  thf(func_def_1159, type, top_to7513191607651882425at_rat: set_Pr4105333604307423337at_rat).
% 21.04/7.60  thf(func_def_1160, type, top_to7320853134386005659_rat_o: set_Pr2399638329824935915_rat_o).
% 21.04/7.60  thf(func_def_1161, type, top_to7002410609688830997at_int: set_Pr3594552606344371909at_int).
% 21.04/7.60  thf(func_def_1162, type, top_to269121717765781945at_nat: set_Pr6084635751276098665at_nat).
% 21.04/7.60  thf(func_def_1163, type, top_to3112507417142880193at_rat: set_Pr8928021450653196913at_rat).
% 21.04/7.60  thf(func_def_1164, type, top_to6833984726390702231at_nat: set_Pr4329608150637261639at_nat).
% 21.04/7.60  thf(func_def_1165, type, top_to1996260823553986621t_unit: set_Product_unit).
% 21.04/7.60  thf(func_def_1166, type, top_top_set_rat: set_rat).
% 21.04/7.60  thf(func_def_1167, type, top_top_set_set_o: set_set_o).
% 21.04/7.60  thf(func_def_1168, type, top_top_set_set_int: set_set_int).
% 21.04/7.60  thf(func_def_1169, type, top_to1619013496918823676st_nat: set_set_list_nat).
% 21.04/7.60  thf(func_def_1170, type, top_top_set_set_nat: set_set_nat).
% 21.04/7.60  thf(func_def_1171, type, top_to6034159466715884489nt_int: set_se6260736226359567993nt_int).
% 21.04/7.60  thf(func_def_1172, type, top_to7629004291339433233at_nat: set_se7855581050983116737at_nat).
% 21.04/7.60  thf(func_def_1173, type, top_top_set_set_rat: set_set_rat).
% 21.04/7.60  thf(func_def_1174, type, top_top_set_char: set_char).
% 21.04/7.60  thf(func_def_1175, type, top_to1686961084667892491um_o_o: set_Sum_sum_o_o).
% 21.04/7.60  thf(func_def_1176, type, top_to3582428612079801253_o_int: set_Sum_sum_o_int).
% 21.04/7.60  thf(func_def_1177, type, top_to6072511757011528009_o_nat: set_Sum_sum_o_nat).
% 21.04/7.60  thf(func_def_1178, type, top_to8915897456388626257_o_rat: set_Sum_sum_o_rat).
% 21.04/7.60  thf(func_def_1179, type, top_to7120114879189831663_nat_o: set_Sum_sum_nat_o).
% 21.04/7.60  thf(func_def_1180, type, top_to6661820994512907621at_nat: set_Sum_sum_nat_nat).
% 21.04/7.60  thf(func_def_1181, type, top_to281834657035230061at_rat: set_Sum_sum_nat_rat).
% 21.04/7.60  thf(func_def_1182, type, top_to6370680384054995943_rat_o: set_Sum_sum_rat_o).
% 21.04/7.60  thf(func_def_1183, type, top_to8994425695926954441at_int: set_Sum_sum_rat_int).
% 21.04/7.60  thf(func_def_1184, type, top_to2261136804003905389at_nat: set_Sum_sum_rat_nat).
% 21.04/7.60  thf(func_def_1185, type, top_to5104522503381003637at_rat: set_Sum_sum_rat_rat).
% 21.04/7.60  thf(func_def_1186, type, power_power_assn: assn > nat > assn).
% 21.04/7.60  thf(func_def_1187, type, power_8256067586552552935nteger: code_integer > nat > code_integer).
% 21.04/7.60  thf(func_def_1188, type, power_7079662738309270450atural: code_natural > nat > code_natural).
% 21.04/7.60  thf(func_def_1189, type, power_power_int: int > nat > int).
% 21.04/7.60  thf(func_def_1190, type, power_power_nat: nat > nat > nat).
% 21.04/7.60  thf(func_def_1191, type, power_power_rat: rat > nat > rat).
% 21.04/7.60  thf(func_def_1192, type, if_pred: $o > pred_Product_unit).
% 21.04/7.60  thf(func_def_1193, type, not_pred: pred_Product_unit > pred_Product_unit).
% 21.04/7.60  thf(func_def_1194, type, pred_Product_unit2: (product_unit > $o) > pred_Product_unit).
% 21.04/7.60  thf(func_def_1195, type, eval_Product_unit: pred_Product_unit > product_unit > $o).
% 21.04/7.60  thf(func_def_1196, type, single_Product_unit: product_unit > pred_Product_unit).
% 21.04/7.60  thf(func_def_1197, type, produc6137756002093451184nteger: (code_integer > option6357759511663192854e_term) > produc8923325533196201883nteger > produc8763457246119570046nteger).
% 21.04/7.60  thf(func_def_1198, type, produc2252593628808123835atural: (code_natural > option6357759511663192854e_term) > produc7822875418678951345atural > produc8731074985263844745atural).
% 21.04/7.60  thf(func_def_1199, type, produc4305682042979456191nt_int: (int > option6357759511663192854e_term) > product_prod_int_int > produc7773217078559923341nt_int).
% 21.04/7.60  thf(func_def_1200, type, produc3209952032786966637at_nat: (nat > nat > nat) > produc7248412053542808358at_nat > produc4471711990508489141at_nat).
% 21.04/7.60  thf(func_def_1201, type, produc8603105652947943368nteger: (produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > produc1908205239877642774nteger).
% 21.04/7.60  thf(func_def_1202, type, produc3831813291587773865atural: (produc4972180933644002618e_term > option6357759511663192854e_term) > produc7822875418678951345atural > produc989692990947075319atural).
% 21.04/7.60  thf(func_def_1203, type, produc7368190662567826135_nat_o: (produc3658429121746597890et_nat > $o) > (produc3658429121746597890et_nat > $o) > produc4928098042776334183_nat_o).
% 21.04/7.60  thf(func_def_1204, type, produc2245416461498447860et_nat: (produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > produc2732055786443039994et_nat).
% 21.04/7.60  thf(func_def_1205, type, produc5001842942810119800et_nat: (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > produc3925858234332021118et_nat).
% 21.04/7.60  thf(func_def_1206, type, produc5700946648718959541nt_int: (produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > produc2285326912895808259nt_int).
% 21.04/7.60  thf(func_def_1207, type, produc6677183202524767010eger_o: code_integer > $o > produc6271795597528267376eger_o).
% 21.04/7.60  thf(func_def_1208, type, produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger).
% 21.04/7.60  thf(func_def_1209, type, produc3574140220909816553atural: code_natural > code_natural > produc7822875418678951345atural).
% 21.04/7.60  thf(func_def_1210, type, produc6639722614265839536atural: code_natural > produc7822875418678951345atural > produc5835291356934675326atural).
% 21.04/7.60  thf(func_def_1211, type, produc7507926704131184380et_nat: heap_e7401611519738050253t_unit > set_nat > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1212, type, product_Pair_int_int: int > int > product_prod_int_int).
% 21.04/7.60  thf(func_def_1213, type, produc4348348721325984599at_nat: multis2468970476368604999at_nat > multis2468970476368604999at_nat > produc4166570645942440679at_nat).
% 21.04/7.60  thf(func_def_1214, type, product_Pair_nat_nat: nat > nat > product_prod_nat_nat).
% 21.04/7.60  thf(func_def_1215, type, product_Pair_nat_num: nat > num > product_prod_nat_num).
% 21.04/7.60  thf(func_def_1216, type, produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat).
% 21.04/7.60  thf(func_def_1217, type, product_Pair_num_num: num > num > product_prod_num_num).
% 21.04/7.60  thf(func_def_1218, type, produc5950683997804057413e_term: option6357759511663192854e_term > option6357759511663192854e_term > produc6576344331059438605e_term).
% 21.04/7.60  thf(func_def_1219, type, produc5069803637994805237atural: pred_Product_unit > produc7822875418678951345atural > produc4675096598859438275atural).
% 21.04/7.60  thf(func_def_1220, type, produc4480994950612372183atural: produc7822875418678951345atural > produc7822875418678951345atural > produc6756470014200349799atural).
% 21.04/7.60  thf(func_def_1221, type, produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat).
% 21.04/7.60  thf(func_def_1222, type, produc4532415448927165861et_nat: set_nat > set_nat > produc7819656566062154093et_nat).
% 21.04/7.60  thf(func_def_1223, type, produc763777882069021527od_o_o: set_Product_prod_o_o > set_Product_prod_o_o > produc2934264451710624999od_o_o).
% 21.04/7.60  thf(func_def_1224, type, produc8517790099723286449at_nat: set_Product_prod_o_o > set_Pr1261947904930325089at_nat > produc732395585841259969at_nat).
% 21.04/7.60  thf(func_def_1225, type, produc782388162306416855nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > produc412284730452459111nt_int).
% 21.04/7.60  thf(func_def_1226, type, produc5245064249948416855at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > produc4193628355235574503at_nat).
% 21.04/7.60  thf(func_def_1227, type, produc2922128104949294807at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat).
% 21.04/7.60  thf(func_def_1228, type, produc9060074326276436823at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > produc1319942482725812455at_nat).
% 21.04/7.60  thf(func_def_1229, type, produc457027306803732586at_nat: set_nat > (nat > set_nat) > set_Pr1261947904930325089at_nat).
% 21.04/7.60  thf(func_def_1230, type, product_Unity: product_unit).
% 21.04/7.60  thf(func_def_1231, type, produc6499014454317279255nteger: (code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 21.04/7.60  thf(func_def_1232, type, produc969530845752564945_nat_o: (produc3925858234332021118et_nat > produc3925858234332021118et_nat) > produc2732055786443039994et_nat > produc2732055786443039994et_nat).
% 21.04/7.60  thf(func_def_1233, type, produc1515462096303866701_nat_o: (produc3925858234332021118et_nat > produc3658429121746597890et_nat) > produc2732055786443039994et_nat > produc3925858234332021118et_nat).
% 21.04/7.60  thf(func_def_1234, type, produc717174245515237944e_term: (produc8923325533196201883nteger > produc8923325533196201883nteger) > produc1908205239877642774nteger > produc1908205239877642774nteger).
% 21.04/7.60  thf(func_def_1235, type, produc7714581247149323085_nat_o: (produc3658429121746597890et_nat > produc3925858234332021118et_nat) > produc3925858234332021118et_nat > produc2732055786443039994et_nat).
% 21.04/7.60  thf(func_def_1236, type, produc8750854537940449737_nat_o: (produc3658429121746597890et_nat > produc3658429121746597890et_nat) > produc3925858234332021118et_nat > produc3925858234332021118et_nat).
% 21.04/7.60  thf(func_def_1237, type, produc7011684061226097695e_term: (product_prod_int_int > product_prod_int_int) > produc7773217078559923341nt_int > produc7773217078559923341nt_int).
% 21.04/7.60  thf(func_def_1238, type, produc4973430039190721449e_term: (product_prod_int_int > product_prod_int_int) > produc2285326912895808259nt_int > produc2285326912895808259nt_int).
% 21.04/7.60  thf(func_def_1239, type, produc2558449545302689196_int_o: ((int > option6357759511663192854e_term) > product_prod_int_int > $o) > produc7773217078559923341nt_int > $o).
% 21.04/7.60  thf(func_def_1240, type, produc5122537100556696953nt_int: ((int > option6357759511663192854e_term) > product_prod_int_int > produc7773217078559923341nt_int) > produc7773217078559923341nt_int > produc7773217078559923341nt_int).
% 21.04/7.60  thf(func_def_1241, type, produc4111701587417901774et_int: ((int > option6357759511663192854e_term) > product_prod_int_int > set_int) > produc7773217078559923341nt_int > set_int).
% 21.04/7.60  thf(func_def_1242, type, produc8289552606927098482et_nat: ((int > option6357759511663192854e_term) > product_prod_int_int > set_nat) > produc7773217078559923341nt_int > set_nat).
% 21.04/7.60  thf(func_def_1243, type, produc3577156405726439208et_nat: ((int > option6357759511663192854e_term) > product_prod_int_int > set_set_nat) > produc7773217078559923341nt_int > set_set_nat).
% 21.04/7.60  thf(func_def_1244, type, produc575502675617541261nt_int: ((int > option6357759511663192854e_term) > product_prod_int_int > set_se6260736226359567993nt_int) > produc7773217078559923341nt_int > set_se6260736226359567993nt_int).
% 21.04/7.60  thf(func_def_1245, type, produc6253627499356882019eger_o: ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > $o) > produc1908205239877642774nteger > $o).
% 21.04/7.60  thf(func_def_1246, type, produc6512950862096126219nteger: ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > produc1908205239877642774nteger) > produc1908205239877642774nteger > produc1908205239877642774nteger).
% 21.04/7.60  thf(func_def_1247, type, produc5700143819190870999et_int: ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > set_int) > produc1908205239877642774nteger > set_int).
% 21.04/7.60  thf(func_def_1248, type, produc654622801845291899et_nat: ((produc6241069584506657477e_term > option6357759511663192854e_term) > produc8923325533196201883nteger > set_nat) > produc1908205239877642774nteger > set_nat).
% 21.04/7.60  thf(func_def_1249, type, produc5150382289251079596at_o_o: ((produc3658429121746597890et_nat > $o) > (produc3658429121746597890et_nat > $o) > $o) > produc4928098042776334183_nat_o > $o).
% 21.04/7.60  thf(func_def_1250, type, produc838355143741117751_nat_o: ((produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o) > produc2732055786443039994et_nat > $o).
% 21.04/7.60  thf(func_def_1251, type, produc2377985495875741467et_nat: ((produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > produc2732055786443039994et_nat) > produc2732055786443039994et_nat > produc2732055786443039994et_nat).
% 21.04/7.60  thf(func_def_1252, type, produc1437786849005270451_nat_o: ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > $o) > produc3925858234332021118et_nat > $o).
% 21.04/7.60  thf(func_def_1253, type, produc4058941399401191971et_nat: ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > produc3925858234332021118et_nat) > produc3925858234332021118et_nat > produc3925858234332021118et_nat).
% 21.04/7.60  thf(func_def_1254, type, produc4627640435386541703et_int: ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > set_int) > produc3925858234332021118et_nat > set_int).
% 21.04/7.60  thf(func_def_1255, type, produc8805491454895738411et_nat: ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > set_nat) > produc3925858234332021118et_nat > set_nat).
% 21.04/7.60  thf(func_def_1256, type, produc2333231157791014625et_nat: ((produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat > set_set_nat) > produc3925858234332021118et_nat > set_set_nat).
% 21.04/7.60  thf(func_def_1257, type, produc1573362020775583542_int_o: ((produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > $o) > produc2285326912895808259nt_int > $o).
% 21.04/7.60  thf(func_def_1258, type, produc8492565224438309093nt_int: ((produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > produc2285326912895808259nt_int) > produc2285326912895808259nt_int > produc2285326912895808259nt_int).
% 21.04/7.60  thf(func_def_1259, type, produc3619988815162578792et_nat: ((produc8551481072490612790e_term > option6357759511663192854e_term) > product_prod_int_int > set_nat) > produc2285326912895808259nt_int > set_nat).
% 21.04/7.60  thf(func_def_1260, type, produc4188289175737317920o_char: (code_integer > $o > char) > produc6271795597528267376eger_o > char).
% 21.04/7.60  thf(func_def_1261, type, produc1553301316500091796er_int: (code_integer > code_integer > int) > produc8923325533196201883nteger > int).
% 21.04/7.60  thf(func_def_1262, type, produc1555791787009142072er_nat: (code_integer > code_integer > nat) > produc8923325533196201883nteger > nat).
% 21.04/7.60  thf(func_def_1263, type, produc7336495610019696514er_num: (code_integer > code_integer > num) > produc8923325533196201883nteger > num).
% 21.04/7.60  thf(func_def_1264, type, produc9125791028180074456eger_o: (code_integer > code_integer > produc6271795597528267376eger_o) > produc8923325533196201883nteger > produc6271795597528267376eger_o).
% 21.04/7.60  thf(func_def_1265, type, produc6916734918728496179nteger: (code_integer > code_integer > produc8923325533196201883nteger) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 21.04/7.60  thf(func_def_1266, type, produc8282080750456430313atural: (code_natural > code_natural > produc6756470014200349799atural) > produc7822875418678951345atural > produc6756470014200349799atural).
% 21.04/7.60  thf(func_def_1267, type, produc4947309494688390418_int_o: (int > int > $o) > product_prod_int_int > $o).
% 21.04/7.60  thf(func_def_1268, type, produc8211389475949308722nt_int: (int > int > int) > product_prod_int_int > int).
% 21.04/7.60  thf(func_def_1269, type, produc4245557441103728435nt_int: (int > int > product_prod_int_int) > product_prod_int_int > product_prod_int_int).
% 21.04/7.60  thf(func_def_1270, type, produc8739625826339149834_nat_o: (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 21.04/7.60  thf(func_def_1271, 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).
% 21.04/7.60  thf(func_def_1272, type, produc6081775807080527818_nat_o: (nat > nat > $o) > product_prod_nat_nat > $o).
% 21.04/7.60  thf(func_def_1273, type, produc6840382203811409530at_int: (nat > nat > int) > product_prod_nat_nat > int).
% 21.04/7.60  thf(func_def_1274, type, produc2761476792215241774st_nat: (nat > nat > list_nat) > product_prod_nat_nat > list_nat).
% 21.04/7.60  thf(func_def_1275, type, produc6842872674320459806at_nat: (nat > nat > nat) > product_prod_nat_nat > nat).
% 21.04/7.60  thf(func_def_1276, type, produc2626176000494625587at_nat: (nat > nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat).
% 21.04/7.60  thf(func_def_1277, type, produc6207742614233964070at_rat: (nat > nat > rat) > product_prod_nat_nat > rat).
% 21.04/7.60  thf(func_def_1278, type, produc478579273971653890on_num: (nat > num > option_num) > product_prod_nat_num > option_num).
% 21.04/7.60  thf(func_def_1279, type, produc6665183775751917029atural: (pred_Product_unit > produc7822875418678951345atural > produc4675096598859438275atural) > produc4675096598859438275atural > produc4675096598859438275atural).
% 21.04/7.60  thf(func_def_1280, type, produc6247414631856714078_nat_o: (set_nat > set_nat > $o) > produc7819656566062154093et_nat > $o).
% 21.04/7.60  thf(func_def_1281, type, produc1547782455048856492_int_o: (set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > $o) > produc412284730452459111nt_int > $o).
% 21.04/7.60  thf(func_def_1282, type, product_fst_int_int: product_prod_int_int > int).
% 21.04/7.60  thf(func_def_1283, type, produc6591912806276919810atural: produc5835291356934675326atural > produc7822875418678951345atural).
% 21.04/7.60  thf(func_def_1284, type, product_snd_int_int: product_prod_int_int > int).
% 21.04/7.60  thf(func_def_1285, type, produc5538323210962509403atural: (produc7822875418678951345atural > produc5835291356934675326atural) > (code_natural > produc7822875418678951345atural > produc5835291356934675326atural) > produc7822875418678951345atural > produc5835291356934675326atural).
% 21.04/7.60  thf(func_def_1286, type, product_Abs_unit: $o > product_unit).
% 21.04/7.60  thf(func_def_1287, type, product_Rep_unit: product_unit > $o).
% 21.04/7.60  thf(func_def_1288, type, inc_shift: code_natural > code_natural > code_natural).
% 21.04/7.60  thf(func_def_1289, type, iterat8892046348760725948atural: code_natural > (code_natural > produc7822875418678951345atural > produc5835291356934675326atural) > code_natural > produc7822875418678951345atural > produc5835291356934675326atural).
% 21.04/7.60  thf(func_def_1290, type, log: code_natural > code_natural > code_natural).
% 21.04/7.60  thf(func_def_1291, type, log_rel: produc7822875418678951345atural > produc7822875418678951345atural > $o).
% 21.04/7.60  thf(func_def_1292, type, minus_shift: code_natural > code_natural > code_natural > code_natural).
% 21.04/7.60  thf(func_def_1293, type, next: produc7822875418678951345atural > produc5835291356934675326atural).
% 21.04/7.60  thf(func_def_1294, type, range: code_natural > produc7822875418678951345atural > produc5835291356934675326atural).
% 21.04/7.60  thf(func_def_1295, type, split_seed: produc7822875418678951345atural > produc6756470014200349799atural).
% 21.04/7.60  thf(func_def_1296, type, random6974930770145893639ompred: (produc7822875418678951345atural > produc4675096598859438275atural) > produc7822875418678951345atural > produc4675096598859438275atural).
% 21.04/7.60  thf(func_def_1297, type, abs_Rat: product_prod_int_int > rat).
% 21.04/7.60  thf(func_def_1298, type, fract: int > int > rat).
% 21.04/7.60  thf(func_def_1299, type, frct: product_prod_int_int > rat).
% 21.04/7.60  thf(func_def_1300, type, rep_Rat: rat > product_prod_int_int).
% 21.04/7.60  thf(func_def_1301, type, cr_rat: product_prod_int_int > rat > $o).
% 21.04/7.60  thf(func_def_1302, type, field_6020823756834552118ts_rat: set_rat).
% 21.04/7.60  thf(func_def_1303, type, normalize: product_prod_int_int > product_prod_int_int).
% 21.04/7.60  thf(func_def_1304, type, of_int: int > rat).
% 21.04/7.60  thf(func_def_1305, type, pcr_rat: product_prod_int_int > rat > $o).
% 21.04/7.60  thf(func_def_1306, type, positive: rat > $o).
% 21.04/7.60  thf(func_def_1307, type, quotient_of: rat > product_prod_int_int).
% 21.04/7.60  thf(func_def_1308, type, abs_rat: set_Pr958786334691620121nt_int > rat).
% 21.04/7.60  thf(func_def_1309, type, rep_rat: rat > set_Pr958786334691620121nt_int).
% 21.04/7.60  thf(func_def_1310, type, ratrel: product_prod_int_int > product_prod_int_int > $o).
% 21.04/7.60  thf(func_def_1311, type, domainp_int_int: (int > int > $o) > int > $o).
% 21.04/7.60  thf(func_def_1312, type, domain7888411570377768909iteral: (list_char > literal > $o) > list_char > $o).
% 21.04/7.60  thf(func_def_1313, type, domain9213661015745956397nt_rat: (product_prod_int_int > rat > $o) > product_prod_int_int > $o).
% 21.04/7.60  thf(func_def_1314, type, domainp_char_char: (char > char > $o) > char > $o).
% 21.04/7.60  thf(func_def_1315, type, field_o: set_Product_prod_o_o > set_o).
% 21.04/7.60  thf(func_def_1316, type, field_nat: set_Pr1261947904930325089at_nat > set_nat).
% 21.04/7.60  thf(func_def_1317, type, id_mul2649389997224486051at_nat: set_Pr8551490117392284871at_nat).
% 21.04/7.60  thf(func_def_1318, type, id_Pro2258643101195443293at_nat: set_Pr8693737435421807431at_nat).
% 21.04/7.60  thf(func_def_1319, type, id_on_7438695062414216554_nat_o: set_Pr4532377907799695533_nat_o > set_Pr2161125870931222855_nat_o).
% 21.04/7.60  thf(func_def_1320, type, id_on_o: set_o > set_Product_prod_o_o).
% 21.04/7.60  thf(func_def_1321, type, id_on_int: set_int > set_Pr958786334691620121nt_int).
% 21.04/7.60  thf(func_def_1322, type, id_on_nat: set_nat > set_Pr1261947904930325089at_nat).
% 21.04/7.60  thf(func_def_1323, type, id_on_2554058798563519774at_nat: set_Pr1261947904930325089at_nat > set_Pr8693737435421807431at_nat).
% 21.04/7.60  thf(func_def_1324, type, id_on_set_nat: set_set_nat > set_Pr5488025237498180813et_nat).
% 21.04/7.60  thf(func_def_1325, type, id_on_6410342593070439734nt_int: set_se6260736226359567993nt_int > set_Pr8057934254988874055nt_int).
% 21.04/7.60  thf(func_def_1326, type, total_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o).
% 21.04/7.60  thf(func_def_1327, type, algebr932160517623751201me_int: int > int > $o).
% 21.04/7.60  thf(func_def_1328, type, algebr934650988132801477me_nat: nat > nat > $o).
% 21.04/7.60  thf(func_def_1329, type, divide6298287555418463151nteger: code_integer > code_integer > code_integer).
% 21.04/7.60  thf(func_def_1330, type, divide5121882707175180666atural: code_natural > code_natural > code_natural).
% 21.04/7.60  thf(func_def_1331, type, divide_divide_int: int > int > int).
% 21.04/7.60  thf(func_def_1332, type, divide_divide_nat: nat > nat > nat).
% 21.04/7.60  thf(func_def_1333, type, divide_divide_rat: rat > rat > rat).
% 21.04/7.60  thf(func_def_1334, type, dvd_dvd_assn: assn > assn > $o).
% 21.04/7.60  thf(func_def_1335, type, dvd_dvd_Code_integer: code_integer > code_integer > $o).
% 21.04/7.60  thf(func_def_1336, type, dvd_dvd_Code_natural: code_natural > code_natural > $o).
% 21.04/7.60  thf(func_def_1337, type, dvd_dvd_int: int > int > $o).
% 21.04/7.60  thf(func_def_1338, type, dvd_dvd_nat: nat > nat > $o).
% 21.04/7.60  thf(func_def_1339, type, dvd_dvd_rat: rat > rat > $o).
% 21.04/7.60  thf(func_def_1340, type, modulo364778990260209775nteger: code_integer > code_integer > code_integer).
% 21.04/7.60  thf(func_def_1341, type, modulo8411746178871703098atural: code_natural > code_natural > code_natural).
% 21.04/7.60  thf(func_def_1342, type, modulo_modulo_int: int > int > int).
% 21.04/7.60  thf(func_def_1343, type, modulo_modulo_nat: nat > nat > nat).
% 21.04/7.60  thf(func_def_1344, type, unit_f2748546683901255202or_nat: nat > nat).
% 21.04/7.60  thf(func_def_1345, type, zero_n356916108424825756nteger: $o > code_integer).
% 21.04/7.60  thf(func_def_1346, type, zero_n8403883297036319079atural: $o > code_natural).
% 21.04/7.60  thf(func_def_1347, type, zero_n2684676970156552555ol_int: $o > int).
% 21.04/7.60  thf(func_def_1348, type, zero_n2687167440665602831ol_nat: $o > nat).
% 21.04/7.60  thf(func_def_1349, type, zero_n2052037380579107095ol_rat: $o > rat).
% 21.04/7.60  thf(func_def_1350, type, collec939566748876313656_nat_o: ((produc3658429121746597890et_nat > $o) > $o) > set_Pr4532377907799695533_nat_o).
% 21.04/7.60  thf(func_def_1351, type, collect_o: ($o > $o) > set_o).
% 21.04/7.60  thf(func_def_1352, type, collect_Code_integer: (code_integer > $o) > set_Code_integer).
% 21.04/7.60  thf(func_def_1353, type, collect_filter_nat: (filter_nat > $o) > set_filter_nat).
% 21.04/7.60  thf(func_def_1354, type, collect_int: (int > $o) > set_int).
% 21.04/7.60  thf(func_def_1355, type, collect_list_nat: (list_nat > $o) > set_list_nat).
% 21.04/7.60  thf(func_def_1356, type, collect_list_char: (list_char > $o) > set_list_char).
% 21.04/7.60  thf(func_def_1357, type, collect_nat: (nat > $o) > set_nat).
% 21.04/7.60  thf(func_def_1358, type, collec7086185654880424402_nat_o: (produc4928098042776334183_nat_o > $o) > set_Pr2161125870931222855_nat_o).
% 21.04/7.60  thf(func_def_1359, type, collec213857154873943460nt_int: (product_prod_int_int > $o) > set_Pr958786334691620121nt_int).
% 21.04/7.60  thf(func_def_1360, type, collec5204685387357076818at_nat: (produc4166570645942440679at_nat > $o) > set_Pr8551490117392284871at_nat).
% 21.04/7.60  thf(func_def_1361, type, collec3392354462482085612at_nat: (product_prod_nat_nat > $o) > set_Pr1261947904930325089at_nat).
% 21.04/7.60  thf(func_def_1362, type, collec6662362479098859352et_nat: (produc7819656566062154093et_nat > $o) > set_Pr5488025237498180813et_nat).
% 21.04/7.60  thf(func_def_1363, type, collec2889756465124990930nt_int: (produc412284730452459111nt_int > $o) > set_Pr8057934254988874055nt_int).
% 21.04/7.60  thf(func_def_1364, type, collec6321179662152712658at_nat: (produc3843707927480180839at_nat > $o) > set_Pr4329608150637261639at_nat).
% 21.04/7.60  thf(func_def_1365, type, collect_rat: (rat > $o) > set_rat).
% 21.04/7.60  thf(func_def_1366, type, collect_set_o: (set_o > $o) > set_set_o).
% 21.04/7.60  thf(func_def_1367, type, collect_set_int: (set_int > $o) > set_set_int).
% 21.04/7.60  thf(func_def_1368, type, collect_set_list_nat: (set_list_nat > $o) > set_set_list_nat).
% 21.04/7.60  thf(func_def_1369, type, collect_set_nat: (set_nat > $o) > set_set_nat).
% 21.04/7.60  thf(func_def_1370, type, collec5210948495886036740nt_int: (set_Pr958786334691620121nt_int > $o) > set_se6260736226359567993nt_int).
% 21.04/7.60  thf(func_def_1371, type, collec5514110066124741708at_nat: (set_Pr1261947904930325089at_nat > $o) > set_se7855581050983116737at_nat).
% 21.04/7.60  thf(func_def_1372, type, collect_set_set_nat: (set_set_nat > $o) > set_set_set_nat).
% 21.04/7.60  thf(func_def_1373, type, collect_literal: (literal > $o) > set_literal).
% 21.04/7.60  thf(func_def_1374, type, pow_nat: set_nat > set_set_nat).
% 21.04/7.60  thf(func_def_1375, type, image_4470545334726330049nteger: (code_integer > code_integer) > set_Code_integer > set_Code_integer).
% 21.04/7.60  thf(func_def_1376, type, image_int_int: (int > int) > set_int > set_int).
% 21.04/7.60  thf(func_def_1377, type, image_int_nat: (int > nat) > set_int > set_nat).
% 21.04/7.60  thf(func_def_1378, type, image_list_nat_nat: (list_nat > nat) > set_list_nat > set_nat).
% 21.04/7.60  thf(func_def_1379, type, image_nat_int: (nat > int) > set_nat > set_int).
% 21.04/7.60  thf(func_def_1380, type, image_nat_list_nat: (nat > list_nat) > set_nat > set_list_nat).
% 21.04/7.60  thf(func_def_1381, type, image_nat_nat: (nat > nat) > set_nat > set_nat).
% 21.04/7.60  thf(func_def_1382, type, image_5846123807819985514at_nat: (nat > product_prod_nat_nat) > set_nat > set_Pr1261947904930325089at_nat).
% 21.04/7.60  thf(func_def_1383, type, image_nat_rat: (nat > rat) > set_nat > set_rat).
% 21.04/7.60  thf(func_def_1384, type, image_nat_set_nat: (nat > set_nat) > set_nat > set_set_nat).
% 21.04/7.60  thf(func_def_1385, type, image_nat_char: (nat > char) > set_nat > set_char).
% 21.04/7.60  thf(func_def_1386, type, image_678696785212003926at_nat: (nat > sum_sum_nat_nat) > set_nat > set_Sum_sum_nat_nat).
% 21.04/7.60  thf(func_def_1387, type, image_2486076414777270412at_nat: (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat > set_nat).
% 21.04/7.60  thf(func_def_1388, type, image_char_nat: (char > nat) > set_char > set_nat).
% 21.04/7.60  thf(func_def_1389, type, image_1320371278474632150at_nat: (sum_sum_nat_nat > nat) > set_Sum_sum_nat_nat > set_nat).
% 21.04/7.60  thf(func_def_1390, type, insert5175938949040314269_nat_o: (produc3658429121746597890et_nat > $o) > set_Pr4532377907799695533_nat_o > set_Pr4532377907799695533_nat_o).
% 21.04/7.60  thf(func_def_1391, type, insert_o: $o > set_o > set_o).
% 21.04/7.60  thf(func_def_1392, type, insert_Code_integer: code_integer > set_Code_integer > set_Code_integer).
% 21.04/7.60  thf(func_def_1393, type, insert_int: int > set_int > set_int).
% 21.04/7.60  thf(func_def_1394, type, insert_list_nat: list_nat > set_list_nat > set_list_nat).
% 21.04/7.60  thf(func_def_1395, type, insert_nat: nat > set_nat > set_nat).
% 21.04/7.60  thf(func_def_1396, type, insert6337962749363155127at_nat: produc4166570645942440679at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat).
% 21.04/7.60  thf(func_def_1397, type, insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 21.04/7.60  thf(func_def_1398, type, insert9069300056098147895at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 21.04/7.60  thf(func_def_1399, type, insert_Product_unit: product_unit > set_Product_unit > set_Product_unit).
% 21.04/7.60  thf(func_def_1400, type, insert_rat: rat > set_rat > set_rat).
% 21.04/7.60  thf(func_def_1401, type, insert_set_nat: set_nat > set_set_nat > set_set_nat).
% 21.04/7.60  thf(func_def_1402, type, insert8897473484851387113nt_int: set_Pr958786334691620121nt_int > set_se6260736226359567993nt_int > set_se6260736226359567993nt_int).
% 21.04/7.60  thf(func_def_1403, type, insert_literal: literal > set_literal > set_literal).
% 21.04/7.60  thf(func_def_1404, type, is_empty_o: set_o > $o).
% 21.04/7.60  thf(func_def_1405, type, is_empty_int: set_int > $o).
% 21.04/7.60  thf(func_def_1406, type, is_empty_nat: set_nat > $o).
% 21.04/7.60  thf(func_def_1407, type, is_emp1662574758705540307at_nat: set_Pr1261947904930325089at_nat > $o).
% 21.04/7.60  thf(func_def_1408, type, is_sin5180296473474724033_nat_o: set_Pr4532377907799695533_nat_o > $o).
% 21.04/7.60  thf(func_def_1409, type, is_singleton_o: set_o > $o).
% 21.04/7.60  thf(func_def_1410, type, is_singleton_int: set_int > $o).
% 21.04/7.60  thf(func_def_1411, type, is_singleton_nat: set_nat > $o).
% 21.04/7.60  thf(func_def_1412, type, is_sin2850979758926227957at_nat: set_Pr1261947904930325089at_nat > $o).
% 21.04/7.60  thf(func_def_1413, type, is_sin2937591304547752795at_nat: set_Pr4329608150637261639at_nat > $o).
% 21.04/7.60  thf(func_def_1414, type, is_singleton_set_nat: set_set_nat > $o).
% 21.04/7.60  thf(func_def_1415, type, is_sin6299389887212142093nt_int: set_se6260736226359567993nt_int > $o).
% 21.04/7.60  thf(func_def_1416, type, the_elem_o: set_o > $o).
% 21.04/7.60  thf(func_def_1417, type, the_elem_int: set_int > int).
% 21.04/7.60  thf(func_def_1418, type, the_elem_nat: set_nat > nat).
% 21.04/7.60  thf(func_def_1419, type, the_el2281957884133575798at_nat: set_Pr1261947904930325089at_nat > product_prod_nat_nat).
% 21.04/7.60  thf(func_def_1420, type, the_el221668144340439132at_nat: set_Pr4329608150637261639at_nat > produc3843707927480180839at_nat).
% 21.04/7.60  thf(func_def_1421, type, vimage_o_o: ($o > $o) > set_o > set_o).
% 21.04/7.60  thf(func_def_1422, type, vimage_o_int: ($o > int) > set_int > set_o).
% 21.04/7.60  thf(func_def_1423, type, vimage_o_nat: ($o > nat) > set_nat > set_o).
% 21.04/7.60  thf(func_def_1424, type, vimage2606541041029201316at_nat: ($o > product_prod_nat_nat) > set_Pr1261947904930325089at_nat > set_o).
% 21.04/7.60  thf(func_def_1425, type, vimage_o_rat: ($o > rat) > set_rat > set_o).
% 21.04/7.60  thf(func_def_1426, type, vimage_int_o: (int > $o) > set_o > set_int).
% 21.04/7.60  thf(func_def_1427, type, vimage_int_int: (int > int) > set_int > set_int).
% 21.04/7.60  thf(func_def_1428, type, vimage_int_nat: (int > nat) > set_nat > set_int).
% 21.04/7.60  thf(func_def_1429, type, vimage1827798767263827160at_nat: (int > product_prod_nat_nat) > set_Pr1261947904930325089at_nat > set_int).
% 21.04/7.60  thf(func_def_1430, type, vimage_int_rat: (int > rat) > set_rat > set_int).
% 21.04/7.60  thf(func_def_1431, type, vimage_int_set_nat: (int > set_nat) > set_set_nat > set_int).
% 21.04/7.60  thf(func_def_1432, type, vimage_list_nat_int: (list_nat > int) > set_int > set_list_nat).
% 21.04/7.60  thf(func_def_1433, type, vimage_list_nat_nat: (list_nat > nat) > set_nat > set_list_nat).
% 21.04/7.60  thf(func_def_1434, type, vimage_nat_o: (nat > $o) > set_o > set_nat).
% 21.04/7.60  thf(func_def_1435, type, vimage_nat_int: (nat > int) > set_int > set_nat).
% 21.04/7.60  thf(func_def_1436, type, vimage_nat_nat: (nat > nat) > set_nat > set_nat).
% 21.04/7.60  thf(func_def_1437, type, vimage7262694317370708122at_nat: (nat > produc4166570645942440679at_nat) > set_Pr8551490117392284871at_nat > set_nat).
% 21.04/7.60  thf(func_def_1438, type, vimage8013328719654469172at_nat: (nat > product_prod_nat_nat) > set_Pr1261947904930325089at_nat > set_nat).
% 21.04/7.60  thf(func_def_1439, type, vimage6435164912253009178at_nat: (nat > produc3843707927480180839at_nat) > set_Pr4329608150637261639at_nat > set_nat).
% 21.04/7.60  thf(func_def_1440, type, vimage_nat_rat: (nat > rat) > set_rat > set_nat).
% 21.04/7.60  thf(func_def_1441, type, vimage_nat_set_nat: (nat > set_nat) > set_set_nat > set_nat).
% 21.04/7.60  thf(func_def_1442, type, vimage2935056327143036492nt_int: (nat > set_Pr958786334691620121nt_int) > set_se6260736226359567993nt_int > set_nat).
% 21.04/7.60  thf(func_def_1443, type, vimage2280073292226551852_nat_o: (produc4166570645942440679at_nat > $o) > set_o > set_Pr8551490117392284871at_nat).
% 21.04/7.60  thf(func_def_1444, type, vimage7949981338974167704at_int: (produc4166570645942440679at_nat > int) > set_int > set_Pr8551490117392284871at_nat).
% 21.04/7.60  thf(func_def_1445, type, vimage7952471809483217980at_nat: (produc4166570645942440679at_nat > nat) > set_nat > set_Pr8551490117392284871at_nat).
% 21.04/7.60  thf(func_def_1446, type, vimage3529983231074640251at_nat: (produc4166570645942440679at_nat > produc4166570645942440679at_nat) > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat).
% 21.04/7.60  thf(func_def_1447, type, vimage5412736291816116987at_nat: (produc4166570645942440679at_nat > produc3843707927480180839at_nat) > set_Pr4329608150637261639at_nat > set_Pr8551490117392284871at_nat).
% 21.04/7.60  thf(func_def_1448, type, vimage4653281326611754070at_nat: (product_prod_nat_nat > nat) > set_nat > set_Pr1261947904930325089at_nat).
% 21.04/7.60  thf(func_def_1449, type, vimage2449269961533847803at_nat: (product_prod_nat_nat > product_prod_nat_nat) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 21.04/7.60  thf(func_def_1450, type, vimage3307185822755684012_nat_o: (produc3843707927480180839at_nat > $o) > set_o > set_Pr4329608150637261639at_nat).
% 21.04/7.60  thf(func_def_1451, type, vimage7134676753939176892at_nat: (produc3843707927480180839at_nat > nat) > set_nat > set_Pr4329608150637261639at_nat).
% 21.04/7.60  thf(func_def_1452, type, vimage2716263466903273467at_nat: (produc3843707927480180839at_nat > produc4166570645942440679at_nat) > set_Pr8551490117392284871at_nat > set_Pr4329608150637261639at_nat).
% 21.04/7.60  thf(func_def_1453, type, vimage6896080417876799867at_nat: (produc3843707927480180839at_nat > produc3843707927480180839at_nat) > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat).
% 21.04/7.60  thf(func_def_1454, type, vimage_rat_o: (rat > $o) > set_o > set_rat).
% 21.04/7.60  thf(func_def_1455, type, vimage_rat_int: (rat > int) > set_int > set_rat).
% 21.04/7.60  thf(func_def_1456, type, vimage_rat_nat: (rat > nat) > set_nat > set_rat).
% 21.04/7.60  thf(func_def_1457, type, vimage_rat_rat: (rat > rat) > set_rat > set_rat).
% 21.04/7.60  thf(func_def_1458, type, vimage_set_nat_o: (set_nat > $o) > set_o > set_set_nat).
% 21.04/7.60  thf(func_def_1459, type, vimage_set_nat_int: (set_nat > int) > set_int > set_set_nat).
% 21.04/7.60  thf(func_def_1460, type, vimage_set_nat_nat: (set_nat > nat) > set_nat > set_set_nat).
% 21.04/7.60  thf(func_def_1461, type, vimage4765135879290611145et_nat: (set_nat > set_nat) > set_set_nat > set_set_nat).
% 21.04/7.60  thf(func_def_1462, type, vimage928727498438615150nt_nat: (set_Pr958786334691620121nt_int > nat) > set_nat > set_se6260736226359567993nt_int).
% 21.04/7.60  thf(func_def_1463, type, set_fo1959793692361082170t_assn: (nat > assn > assn) > nat > nat > assn > assn).
% 21.04/7.60  thf(func_def_1464, type, set_fo1084959871951514735nteger: (nat > code_integer > code_integer) > nat > nat > code_integer > code_integer).
% 21.04/7.60  thf(func_def_1465, type, set_fo2581907887559384638at_int: (nat > int > int) > nat > nat > int > int).
% 21.04/7.60  thf(func_def_1466, type, set_fo4497565046347964853at_nat: (nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat) > nat > nat > multis2468970476368604999at_nat > multis2468970476368604999at_nat).
% 21.04/7.60  thf(func_def_1467, type, set_fo2584398358068434914at_nat: (nat > nat > nat) > nat > nat > nat > nat).
% 21.04/7.60  thf(func_def_1468, type, set_fo1949268297981939178at_rat: (nat > rat > rat) > nat > nat > rat > rat).
% 21.04/7.60  thf(func_def_1469, type, set_fo3699595496184130361el_nat: produc4471711990508489141at_nat > produc4471711990508489141at_nat > $o).
% 21.04/7.60  thf(func_def_1470, type, set_or8904488021354931149Most_o: $o > $o > set_o).
% 21.04/7.60  thf(func_def_1471, type, set_or189985376899183464nteger: code_integer > code_integer > set_Code_integer).
% 21.04/7.60  thf(func_def_1472, type, set_or1955772592623580779er_nat: filter_nat > filter_nat > set_filter_nat).
% 21.04/7.60  thf(func_def_1473, type, set_or1266510415728281911st_int: int > int > set_int).
% 21.04/7.60  thf(func_def_1474, type, set_or1269000886237332187st_nat: nat > nat > set_nat).
% 21.04/7.60  thf(func_def_1475, type, set_or633870826150836451st_rat: rat > rat > set_rat).
% 21.04/7.60  thf(func_def_1476, type, set_or266616469461849773_set_o: set_o > set_o > set_set_o).
% 21.04/7.60  thf(func_def_1477, type, set_or370866239135849197et_int: set_int > set_int > set_set_int).
% 21.04/7.60  thf(func_def_1478, type, set_or1270514513317581473st_nat: set_list_nat > set_list_nat > set_set_list_nat).
% 21.04/7.60  thf(func_def_1479, type, set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat).
% 21.04/7.60  thf(func_def_1480, type, set_or2784603332384507286at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat).
% 21.04/7.60  thf(func_def_1481, type, set_or1040488700251649177et_rat: set_rat > set_rat > set_set_rat).
% 21.04/7.60  thf(func_def_1482, type, set_or8436436507035938825iteral: literal > literal > set_literal).
% 21.04/7.60  thf(func_def_1483, type, set_or7139685690850216873Than_o: $o > $o > set_o).
% 21.04/7.60  thf(func_def_1484, type, set_or8404916559141939852nteger: code_integer > code_integer > set_Code_integer).
% 21.04/7.60  thf(func_def_1485, type, set_or1773934645810362255er_nat: filter_nat > filter_nat > set_filter_nat).
% 21.04/7.60  thf(func_def_1486, type, set_or4662586982721622107an_int: int > int > set_int).
% 21.04/7.60  thf(func_def_1487, type, set_or4665077453230672383an_nat: nat > nat > set_nat).
% 21.04/7.60  thf(func_def_1488, type, set_or4029947393144176647an_rat: rat > rat > set_rat).
% 21.04/7.60  thf(func_def_1489, type, set_or3540276404033026485et_nat: set_nat > set_nat > set_set_nat).
% 21.04/7.60  thf(func_def_1490, type, set_or4828121863581493221iteral: literal > literal > set_literal).
% 21.04/7.60  thf(func_def_1491, type, set_ord_atLeast_nat: nat > set_nat).
% 21.04/7.60  thf(func_def_1492, type, set_or1537382583742010260_nat_o: (produc3658429121746597890et_nat > $o) > set_Pr4532377907799695533_nat_o).
% 21.04/7.60  thf(func_def_1493, type, set_ord_atMost_o: $o > set_o).
% 21.04/7.60  thf(func_def_1494, type, set_or9101266186257409494nteger: code_integer > set_Code_integer).
% 21.04/7.60  thf(func_def_1495, type, set_or9144418160755794905er_nat: filter_nat > set_filter_nat).
% 21.04/7.60  thf(func_def_1496, type, set_ord_atMost_int: int > set_int).
% 21.04/7.60  thf(func_def_1497, type, set_ord_atMost_nat: nat > set_nat).
% 21.04/7.60  thf(func_def_1498, type, set_ord_atMost_rat: rat > set_rat).
% 21.04/7.60  thf(func_def_1499, type, set_ord_atMost_set_o: set_o > set_set_o).
% 21.04/7.60  thf(func_def_1500, type, set_or58775011639299419et_int: set_int > set_set_int).
% 21.04/7.60  thf(func_def_1501, type, set_or2492388921469580815st_nat: set_list_nat > set_set_list_nat).
% 21.04/7.60  thf(func_def_1502, type, set_or4236626031148496127et_nat: set_nat > set_set_nat).
% 21.04/7.60  thf(func_def_1503, type, set_or2459421552957432928nt_int: set_Pr958786334691620121nt_int > set_se6260736226359567993nt_int).
% 21.04/7.60  thf(func_def_1504, type, set_or728397472755099399et_rat: set_rat > set_set_rat).
% 21.04/7.60  thf(func_def_1505, type, set_or2715278749043346189nteger: code_integer > code_integer > set_Code_integer).
% 21.04/7.60  thf(func_def_1506, type, set_or6656581121297822940st_int: int > int > set_int).
% 21.04/7.60  thf(func_def_1507, type, set_or4266950643985792945nteger: code_integer > code_integer > set_Code_integer).
% 21.04/7.60  thf(func_def_1508, type, set_or5832277885323065728an_int: int > int > set_int).
% 21.04/7.60  thf(func_def_1509, type, set_or1210151606488870762an_nat: nat > set_nat).
% 21.04/7.60  thf(func_def_1510, type, set_or7240481858991947888_nat_o: (produc3658429121746597890et_nat > $o) > set_Pr4532377907799695533_nat_o).
% 21.04/7.60  thf(func_def_1511, type, set_ord_lessThan_o: $o > set_o).
% 21.04/7.60  thf(func_def_1512, type, set_or5754767410780653050nteger: code_integer > set_Code_integer).
% 21.04/7.60  thf(func_def_1513, type, set_ord_lessThan_int: int > set_int).
% 21.04/7.60  thf(func_def_1514, type, set_ord_lessThan_nat: nat > set_nat).
% 21.04/7.60  thf(func_def_1515, type, set_ord_lessThan_rat: rat > set_rat).
% 21.04/7.60  thf(func_def_1516, type, set_or890127255671739683et_nat: set_nat > set_set_nat).
% 21.04/7.60  thf(func_def_1517, type, set_or4940836740269066044nt_int: set_Pr958786334691620121nt_int > set_se6260736226359567993nt_int).
% 21.04/7.60  thf(func_def_1518, type, set_or2436086697161274615iteral: literal > set_literal).
% 21.04/7.60  thf(func_def_1519, type, literal2: $o > $o > $o > $o > $o > $o > $o > literal > literal).
% 21.04/7.60  thf(func_def_1520, type, ascii_of: char > char).
% 21.04/7.60  thf(func_def_1521, type, asciis_of_literal: literal > list_Code_integer).
% 21.04/7.60  thf(func_def_1522, type, char2: $o > $o > $o > $o > $o > $o > $o > $o > char).
% 21.04/7.60  thf(func_def_1523, type, digit7: char > $o).
% 21.04/7.60  thf(func_def_1524, type, char_of_integer: code_integer > char).
% 21.04/7.60  thf(func_def_1525, type, comm_s4049598766089966537nteger: char > code_integer).
% 21.04/7.60  thf(func_def_1526, type, comm_s629917340098488124ar_nat: char > nat).
% 21.04/7.60  thf(func_def_1527, type, cr_literal: list_char > literal > $o).
% 21.04/7.60  thf(func_def_1528, type, abs_literal: list_char > literal).
% 21.04/7.60  thf(func_def_1529, type, explode: literal > list_char).
% 21.04/7.60  thf(func_def_1530, type, pcr_literal: list_char > literal > $o).
% 21.04/7.60  thf(func_def_1531, type, unique1708501630192214702nteger: code_integer > char).
% 21.04/7.60  thf(func_def_1532, type, unique3096191561947761185of_nat: nat > char).
% 21.04/7.60  thf(func_def_1533, type, sum_Inl_nat_nat: nat > sum_sum_nat_nat).
% 21.04/7.60  thf(func_def_1534, type, sum_Inr_nat_nat: nat > sum_sum_nat_nat).
% 21.04/7.60  thf(func_def_1535, type, sum_ca7763040182479039464nt_nat: (nat > int) > (nat > int) > sum_sum_nat_nat > int).
% 21.04/7.60  thf(func_def_1536, type, sum_ca6763686470577984908at_nat: (nat > nat) > (nat > nat) > sum_sum_nat_nat > nat).
% 21.04/7.60  thf(func_def_1537, type, syntax7398250324933576852n_assn: assn > assn > $o).
% 21.04/7.60  thf(func_def_1538, type, syntax380677951125133566nteger: code_integer > code_integer > $o).
% 21.04/7.60  thf(func_def_1539, type, syntax5678989248478167196nt_int: int > int > $o).
% 21.04/7.60  thf(func_def_1540, type, syntax4682126007086162916at_nat: nat > nat > $o).
% 21.04/7.60  thf(func_def_1541, type, syntax3730441303064801268at_rat: rat > rat > $o).
% 21.04/7.60  thf(func_def_1542, type, left_t8440299596084406506t_char: (list_char > list_char > $o) > $o).
% 21.04/7.60  thf(func_def_1543, type, left_t3131394472396969446nt_int: (product_prod_int_int > product_prod_int_int > $o) > $o).
% 21.04/7.60  thf(func_def_1544, type, transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 21.04/7.60  thf(func_def_1545, type, transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 21.04/7.60  thf(func_def_1546, type, transi2163837189807498211lp_nat: (nat > nat > $o) > nat > nat > $o).
% 21.04/7.60  thf(func_def_1547, type, type_definition_o_o: ($o > $o) > ($o > $o) > set_o > $o).
% 21.04/7.60  thf(func_def_1548, type, type_d3909072315231072503_nat_o: (assn > produc3658429121746597890et_nat > $o) > ((produc3658429121746597890et_nat > $o) > assn) > set_Pr4532377907799695533_nat_o > $o).
% 21.04/7.60  thf(func_def_1549, type, type_d8366093980585677751er_int: (code_integer > int) > (int > code_integer) > set_int > $o).
% 21.04/7.60  thf(func_def_1550, type, type_d4410041424927559462al_nat: (code_natural > nat) > (nat > code_natural) > set_nat > $o).
% 21.04/7.60  thf(func_def_1551, type, type_d7247357190169752966nt_int: (int > int) > (int > int) > set_int > $o).
% 21.04/7.60  thf(func_def_1552, type, type_d8752208705193531015at_nat: (int > set_Pr1261947904930325089at_nat) > (set_Pr1261947904930325089at_nat > int) > set_se7855581050983116737at_nat > $o).
% 21.04/7.60  thf(func_def_1553, type, type_d5972188401318659438st_nat: (list_nat > list_nat) > (list_nat > list_nat) > set_list_nat > $o).
% 21.04/7.60  thf(func_def_1554, type, type_d6250493948777748686at_nat: (nat > nat) > (nat > nat) > set_nat > $o).
% 21.04/7.60  thf(func_def_1555, type, type_d6188575255521822967unit_o: (product_unit > $o) > ($o > product_unit) > set_o > $o).
% 21.04/7.60  thf(func_def_1556, type, type_d5298809244756387038at_rat: (rat > rat) > (rat > rat) > set_rat > $o).
% 21.04/7.60  thf(func_def_1557, type, type_d8554052265237484179nt_int: (rat > set_Pr958786334691620121nt_int) > (set_Pr958786334691620121nt_int > rat) > set_se6260736226359567993nt_int > $o).
% 21.04/7.60  thf(func_def_1558, type, type_d4752411451802217481t_char: (literal > list_char) > (list_char > literal) > set_list_char > $o).
% 21.04/7.60  thf(func_def_1559, type, accp_list_nat: (list_nat > list_nat > $o) > list_nat > $o).
% 21.04/7.60  thf(func_def_1560, type, accp_nat: (nat > nat > $o) > nat > $o).
% 21.04/7.60  thf(func_def_1561, type, accp_P8928870874622223812nt_int: (produc7773217078559923341nt_int > produc7773217078559923341nt_int > $o) > produc7773217078559923341nt_int > $o).
% 21.04/7.60  thf(func_def_1562, type, accp_P6019419558468335806at_nat: (produc4471711990508489141at_nat > produc4471711990508489141at_nat > $o) > produc4471711990508489141at_nat > $o).
% 21.04/7.60  thf(func_def_1563, type, accp_P1862375125659990705et_nat: (produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o) > produc2732055786443039994et_nat > $o).
% 21.04/7.60  thf(func_def_1564, type, accp_P8126237942716283194atural: (produc7822875418678951345atural > produc7822875418678951345atural > $o) > produc7822875418678951345atural > $o).
% 21.04/7.60  thf(func_def_1565, type, accp_P1096762738010456898nt_int: (product_prod_int_int > product_prod_int_int > $o) > product_prod_int_int > $o).
% 21.04/7.60  thf(func_def_1566, type, accp_P4275260045618599050at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > product_prod_nat_nat > $o).
% 21.04/7.60  thf(func_def_1567, type, accp_P3113834385874906142um_num: (product_prod_num_num > product_prod_num_num > $o) > product_prod_num_num > $o).
% 21.04/7.60  thf(func_def_1568, type, less_than: set_Pr1261947904930325089at_nat).
% 21.04/7.60  thf(func_def_1569, type, max_ex8135407076693332796at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat).
% 21.04/7.60  thf(func_def_1570, type, min_ex6901939911449802026at_nat: set_Pr8693737435421807431at_nat > set_Pr4329608150637261639at_nat).
% 21.04/7.60  thf(func_def_1571, type, pred_nat: set_Pr1261947904930325089at_nat).
% 21.04/7.60  thf(func_def_1572, type, wf_nat: set_Pr1261947904930325089at_nat > $o).
% 21.04/7.60  thf(func_def_1573, type, member6576561426505652726_nat_o: (produc3658429121746597890et_nat > $o) > set_Pr4532377907799695533_nat_o > $o).
% 21.04/7.60  thf(func_def_1574, type, member_o: $o > set_o > $o).
% 21.04/7.60  thf(func_def_1575, type, member_filter_nat: filter_nat > set_filter_nat > $o).
% 21.04/7.60  thf(func_def_1576, type, member_int: int > set_int > $o).
% 21.04/7.60  thf(func_def_1577, type, member_list_nat: list_nat > set_list_nat > $o).
% 21.04/7.60  thf(func_def_1578, type, member_list_char: list_char > set_list_char > $o).
% 21.04/7.60  thf(func_def_1579, type, member_nat: nat > set_nat > $o).
% 21.04/7.60  thf(func_def_1580, type, member7034335876925520548nt_int: produc7773217078559923341nt_int > set_Pr1872883991513573699nt_int > $o).
% 21.04/7.60  thf(func_def_1581, type, member4164122664394876845nteger: produc1908205239877642774nteger > set_Pr1281608226676607948nteger > $o).
% 21.04/7.60  thf(func_def_1582, type, member8781333585448626064_nat_o: produc4928098042776334183_nat_o > set_Pr2161125870931222855_nat_o > $o).
% 21.04/7.60  thf(func_def_1583, type, member6124377750444531601et_nat: produc2732055786443039994et_nat > set_Pr8536935166611901872et_nat > $o).
% 21.04/7.60  thf(func_def_1584, type, member1996754912294343701et_nat: produc3925858234332021118et_nat > set_Pr3286484037609594932et_nat > $o).
% 21.04/7.60  thf(func_def_1585, type, member7618704894036264090nt_int: produc2285326912895808259nt_int > set_Pr9222295170931077689nt_int > $o).
% 21.04/7.60  thf(func_def_1586, type, member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o).
% 21.04/7.60  thf(func_def_1587, type, member6689249552917799696at_nat: produc4166570645942440679at_nat > set_Pr8551490117392284871at_nat > $o).
% 21.04/7.60  thf(func_def_1588, type, member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o).
% 21.04/7.60  thf(func_def_1589, type, member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o).
% 21.04/7.60  thf(func_def_1590, type, member8277197624267554838et_nat: produc7819656566062154093et_nat > set_Pr5488025237498180813et_nat > $o).
% 21.04/7.60  thf(func_def_1591, type, member444158400953824016od_o_o: produc2934264451710624999od_o_o > set_Pr1932065953672099015od_o_o > $o).
% 21.04/7.60  thf(func_def_1592, type, member4095101504841534314at_nat: produc732395585841259969at_nat > set_Pr457366540195662369at_nat > $o).
% 21.04/7.60  thf(func_def_1593, type, member5325734588016868240nt_int: produc412284730452459111nt_int > set_Pr8057934254988874055nt_int > $o).
% 21.04/7.60  thf(func_def_1594, type, member8757157785044589968at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > $o).
% 21.04/7.60  thf(func_def_1595, type, member_rat: rat > set_rat > $o).
% 21.04/7.60  thf(func_def_1596, type, member_set_nat: set_nat > set_set_nat > $o).
% 21.04/7.60  thf(func_def_1597, type, member2340774599025711042nt_int: set_Pr958786334691620121nt_int > set_se6260736226359567993nt_int > $o).
% 21.04/7.60  thf(func_def_1598, type, member2643936169264416010at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat > $o).
% 21.04/7.60  thf(func_def_1599, type, member_char: char > set_char > $o).
% 21.04/7.60  thf(func_def_1600, type, member_literal: literal > set_literal > $o).
% 21.04/7.60  thf(func_def_1601, type, x: assn).
% 21.04/7.60  thf(func_def_1602, type, y: assn).
% 21.04/7.60  thf(func_def_1625, type, sK0: assn > assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1626, type, sK1: assn > assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1627, type, sK2: assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1628, type, sK3: assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1629, type, sK4: assn > (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1630, type, sK5: (produc3658429121746597890et_nat > $o) > assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1631, type, sK6: assn > produc3658429121746597890et_nat > $o).
% 21.04/7.60  thf(func_def_1632, type, sK7: (assn > $o) > produc3658429121746597890et_nat > $o).
% 21.04/7.60  thf(func_def_1634, type, ph9: !>[X0: $tType]:(X0)).
% 21.04/7.60  thf(func_def_1635, type, sK10: assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1636, type, sK11: assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1637, type, sK12: assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1638, type, sK13: assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1639, type, sK14: assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1640, type, sK15: assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1641, type, sK16: (assn > $o) > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1642, type, sK17: produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1643, type, sK18: (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1644, type, sK19: (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1645, type, sK20: assn > assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1646, type, sK21: assn > assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1647, type, sK22: assn > assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1648, type, sK23: assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1649, type, sK24: assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1650, type, sK25: assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1651, type, sK26: assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1652, type, sK27: (assn > $o) > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1653, type, sK28: produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1654, type, sK29: (produc3658429121746597890et_nat > $o) > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1655, type, sK30: assn > assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1656, type, sK31: assn > assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1657, type, sK32: assn > assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(func_def_1658, type, sK33: assn > assn > produc3658429121746597890et_nat).
% 21.04/7.60  thf(f24177,plain,(
% 21.04/7.60    $false),
% 21.04/7.60    inference(avatar_sat_refutation,[status(thm)],[f23046,f23051,f23053,f23536,f23549,f23554,f23557,f23715,f23788,f23815,f23994,f23995,f24005,f24067,f24174])).
% 21.04/7.60  thf(f24174,plain,(
% 21.04/7.60    ~spl8_32 | ~spl8_34),
% 21.04/7.60    inference(avatar_contradiction_clause,[status(thm)],[f24173])).
% 21.04/7.60  thf(f24173,plain,(
% 21.04/7.60    $false | (~spl8_32 | ~spl8_34)),
% 21.04/7.60    inference(trivial_inequality_removal,[status(thm)],[f24162])).
% 21.04/7.60  thf(f24162,plain,(
% 21.04/7.60    ($false = $true) | (~spl8_32 | ~spl8_34)),
% 21.04/7.60    inference(superposition,[status(thm)],[f23992,f24004])).
% 21.04/7.60  thf(f24004,plain,(
% 21.04/7.60    ($false = (rep_assn @ y @ sK28)) | ~spl8_34),
% 21.04/7.60    inference(avatar_component_clause,[status(thm)],[f24002])).
% 21.04/7.60  thf(f24002,definition,(
% 21.04/7.60    spl8_34 <=> ($false = (rep_assn @ y @ sK28))),
% 21.04/7.60    introduced(definition,[new_symbols(naming,[spl8_34])],[avatar_definition])).
% 21.04/7.60  thf(f23992,plain,(
% 21.04/7.60    ((rep_assn @ y @ sK28) = $true) | ~spl8_32),
% 21.04/7.60    inference(avatar_component_clause,[status(thm)],[f23990])).
% 21.04/7.60  thf(f23990,definition,(
% 21.04/7.60    spl8_32 <=> ((rep_assn @ y @ sK28) = $true)),
% 21.04/7.60    introduced(definition,[new_symbols(naming,[spl8_32])],[avatar_definition])).
% 21.04/7.60  thf(f24067,plain,(
% 21.04/7.60    ~spl8_31 | ~spl8_33),
% 21.04/7.60    inference(avatar_contradiction_clause,[status(thm)],[f24066])).
% 21.04/7.60  thf(f24066,plain,(
% 21.04/7.60    $false | (~spl8_31 | ~spl8_33)),
% 21.04/7.60    inference(trivial_inequality_removal,[status(thm)],[f24056])).
% 21.04/7.60  thf(f24056,plain,(
% 21.04/7.60    ($false = $true) | (~spl8_31 | ~spl8_33)),
% 21.04/7.60    inference(superposition,[status(thm)],[f23988,f24000])).
% 21.04/7.60  thf(f24000,plain,(
% 21.04/7.60    ($false = (rep_assn @ x @ sK28)) | ~spl8_33),
% 21.04/7.60    inference(avatar_component_clause,[status(thm)],[f23998])).
% 21.04/7.60  thf(f23998,definition,(
% 21.04/7.60    spl8_33 <=> ($false = (rep_assn @ x @ sK28))),
% 21.04/7.60    introduced(definition,[new_symbols(naming,[spl8_33])],[avatar_definition])).
% 21.04/7.60  thf(f23988,plain,(
% 21.04/7.60    ((rep_assn @ x @ sK28) = $true) | ~spl8_31),
% 21.04/7.60    inference(avatar_component_clause,[status(thm)],[f23986])).
% 21.04/7.60  thf(f23986,definition,(
% 21.04/7.60    spl8_31 <=> ((rep_assn @ x @ sK28) = $true)),
% 21.04/7.60    introduced(definition,[new_symbols(naming,[spl8_31])],[avatar_definition])).
% 21.04/7.60  thf(f24005,plain,(
% 21.04/7.60    spl8_33 | spl8_34 | spl8_2 | ~spl8_4),
% 21.04/7.60    inference(avatar_split_clause,[status(thm)],[f23976,f23048,f23038,f24002,f23998])).
% 21.04/7.60  thf(f23038,definition,(
% 21.04/7.60    spl8_2 <=> (x = (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0)))))),
% 21.04/7.60    introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition])).
% 21.04/7.60  thf(f23048,definition,(
% 21.04/7.60    spl8_4 <=> (x = (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))))),
% 21.04/7.60    introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition])).
% 21.04/7.60  thf(f23976,plain,(
% 21.04/7.60    ($false = (rep_assn @ y @ sK28)) | ($false = (rep_assn @ x @ sK28)) | (spl8_2 | ~spl8_4)),
% 21.04/7.60    inference(duplicate_literal_removal,[status(thm)],[f23975])).
% 21.04/7.60  thf(f23975,plain,(
% 21.04/7.60    ($false = (rep_assn @ x @ sK28)) | ($false = (rep_assn @ y @ sK28)) | ($false = (rep_assn @ x @ sK28)) | ($false = (rep_assn @ y @ sK28)) | (spl8_2 | ~spl8_4)),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23974])).
% 21.04/7.60  thf(f23974,plain,(
% 21.04/7.60    ($false = (rep_assn @ y @ sK28)) | ($false = (rep_assn @ x @ sK28)) | ($false = ((rep_assn @ x @ sK28) & (rep_assn @ y @ sK28))) | (spl8_2 | ~spl8_4)),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23973])).
% 21.04/7.60  thf(f23973,plain,(
% 21.04/7.60    ($false = ((rep_assn @ y @ sK28) & (rep_assn @ x @ sK28))) | ($false = ((rep_assn @ x @ sK28) & (rep_assn @ y @ sK28))) | (spl8_2 | ~spl8_4)),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23971])).
% 21.04/7.60  thf(f23971,plain,(
% 21.04/7.60    (((rep_assn @ x @ sK28) & (rep_assn @ y @ sK28)) != ((rep_assn @ y @ sK28) & (rep_assn @ x @ sK28))) | (spl8_2 | ~spl8_4)),
% 21.04/7.60    inference(beta_eta_normalization,[status(thm)],[f23969])).
% 21.04/7.60  thf(f23969,plain,(
% 21.04/7.60    (((^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0))) @ sK28) != ((^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0))) @ sK28)) | (spl8_2 | ~spl8_4)),
% 21.04/7.60    inference(negative_extensionality,[status(thm)],[f23835])).
% 21.04/7.60  thf(f23835,plain,(
% 21.04/7.60    ((^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0))) != (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) | (spl8_2 | ~spl8_4)),
% 21.04/7.60    inference(trivial_inequality_removal,[status(thm)],[f23818])).
% 21.04/7.60  thf(f23818,plain,(
% 21.04/7.60    (x != x) | ((^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0))) != (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) | (spl8_2 | ~spl8_4)),
% 21.04/7.60    inference(constrained_superposition,[status(thm)],[f23039,f23050])).
% 21.04/7.60  thf(f23050,plain,(
% 21.04/7.60    (x = (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0))))) | ~spl8_4),
% 21.04/7.60    inference(avatar_component_clause,[status(thm)],[f23048])).
% 21.04/7.60  thf(f23039,plain,(
% 21.04/7.60    (x != (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0))))) | spl8_2),
% 21.04/7.60    inference(avatar_component_clause,[status(thm)],[f23038])).
% 21.04/7.60  thf(f23995,plain,(
% 21.04/7.60    spl8_32 | spl8_2 | ~spl8_4),
% 21.04/7.60    inference(avatar_split_clause,[status(thm)],[f23981,f23048,f23038,f23990])).
% 21.04/7.60  thf(f23981,plain,(
% 21.04/7.60    ((rep_assn @ y @ sK28) = $true) | (spl8_2 | ~spl8_4)),
% 21.04/7.60    inference(duplicate_literal_removal,[status(thm)],[f23979])).
% 21.04/7.60  thf(f23979,plain,(
% 21.04/7.60    ((rep_assn @ y @ sK28) = $true) | ((rep_assn @ y @ sK28) = $true) | (spl8_2 | ~spl8_4)),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23978])).
% 21.04/7.60  thf(f23978,plain,(
% 21.04/7.60    ((rep_assn @ y @ sK28) = $true) | (((rep_assn @ x @ sK28) & (rep_assn @ y @ sK28)) = $true) | (spl8_2 | ~spl8_4)),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23972])).
% 21.04/7.60  thf(f23972,plain,(
% 21.04/7.60    (((rep_assn @ y @ sK28) & (rep_assn @ x @ sK28)) = $true) | (((rep_assn @ x @ sK28) & (rep_assn @ y @ sK28)) = $true) | (spl8_2 | ~spl8_4)),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23971])).
% 21.04/7.60  thf(f23994,plain,(
% 21.04/7.60    spl8_31 | spl8_2 | ~spl8_4),
% 21.04/7.60    inference(avatar_split_clause,[status(thm)],[f23984,f23048,f23038,f23986])).
% 21.04/7.60  thf(f23984,plain,(
% 21.04/7.60    ((rep_assn @ x @ sK28) = $true) | (spl8_2 | ~spl8_4)),
% 21.04/7.60    inference(duplicate_literal_removal,[status(thm)],[f23983])).
% 21.04/7.60  thf(f23983,plain,(
% 21.04/7.60    ((rep_assn @ x @ sK28) = $true) | ((rep_assn @ x @ sK28) = $true) | (spl8_2 | ~spl8_4)),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23977])).
% 21.04/7.60  thf(f23977,plain,(
% 21.04/7.60    (((rep_assn @ x @ sK28) & (rep_assn @ y @ sK28)) = $true) | ((rep_assn @ x @ sK28) = $true) | (spl8_2 | ~spl8_4)),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23972])).
% 21.04/7.60  thf(f23815,plain,(
% 21.04/7.60    ~spl8_1 | spl8_3 | ~spl8_4),
% 21.04/7.60    inference(avatar_contradiction_clause,[status(thm)],[f23814])).
% 21.04/7.60  thf(f23814,plain,(
% 21.04/7.60    $false | (~spl8_1 | spl8_3 | ~spl8_4)),
% 21.04/7.60    inference(subsumption_resolution,[status(thm)],[f23813,f23045])).
% 21.04/7.60  thf(f23045,plain,(
% 21.04/7.60    (x != y) | spl8_3),
% 21.04/7.60    inference(avatar_component_clause,[status(thm)],[f23043])).
% 21.04/7.60  thf(f23043,definition,(
% 21.04/7.60    spl8_3 <=> (x = y)),
% 21.04/7.60    introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition])).
% 21.04/7.60  thf(f23813,plain,(
% 21.04/7.60    (x = y) | (~spl8_1 | ~spl8_4)),
% 21.04/7.60    inference(forward_demodulation,[status(thm)],[f23035,f23050])).
% 21.04/7.60  thf(f23035,plain,(
% 21.04/7.60    (y = (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0))))) | ~spl8_1),
% 21.04/7.60    inference(avatar_component_clause,[status(thm)],[f23034])).
% 21.04/7.60  thf(f23034,definition,(
% 21.04/7.60    spl8_1 <=> (y = (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))))),
% 21.04/7.60    introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition])).
% 21.04/7.60  thf(f23788,plain,(
% 21.04/7.60    spl8_1 | ~spl8_3 | ~spl8_4),
% 21.04/7.60    inference(avatar_contradiction_clause,[status(thm)],[f23787])).
% 21.04/7.60  thf(f23787,plain,(
% 21.04/7.60    $false | (spl8_1 | ~spl8_3 | ~spl8_4)),
% 21.04/7.60    inference(subsumption_resolution,[status(thm)],[f23744,f23044])).
% 21.04/7.60  thf(f23044,plain,(
% 21.04/7.60    (x = y) | ~spl8_3),
% 21.04/7.60    inference(avatar_component_clause,[status(thm)],[f23043])).
% 21.04/7.60  thf(f23744,plain,(
% 21.04/7.60    (x != y) | (spl8_1 | ~spl8_4)),
% 21.04/7.60    inference(superposition,[status(thm)],[f23036,f23050])).
% 21.04/7.60  thf(f23036,plain,(
% 21.04/7.60    (y != (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0))))) | spl8_1),
% 21.04/7.60    inference(avatar_component_clause,[status(thm)],[f23034])).
% 21.04/7.60  thf(f23715,plain,(
% 21.04/7.60    ~spl8_23 | ~spl8_25),
% 21.04/7.60    inference(avatar_contradiction_clause,[status(thm)],[f23714])).
% 21.04/7.60  thf(f23714,plain,(
% 21.04/7.60    $false | (~spl8_23 | ~spl8_25)),
% 21.04/7.60    inference(trivial_inequality_removal,[status(thm)],[f23705])).
% 21.04/7.60  thf(f23705,plain,(
% 21.04/7.60    ($false = $true) | (~spl8_23 | ~spl8_25)),
% 21.04/7.60    inference(superposition,[status(thm)],[f23535,f23544])).
% 21.04/7.60  thf(f23544,plain,(
% 21.04/7.60    ((rep_assn @ x @ sK17) = $true) | ~spl8_25),
% 21.04/7.60    inference(avatar_component_clause,[status(thm)],[f23542])).
% 21.04/7.60  thf(f23542,definition,(
% 21.04/7.60    spl8_25 <=> ((rep_assn @ x @ sK17) = $true)),
% 21.04/7.60    introduced(definition,[new_symbols(naming,[spl8_25])],[avatar_definition])).
% 21.04/7.60  thf(f23535,plain,(
% 21.04/7.60    ($false = (rep_assn @ x @ sK17)) | ~spl8_23),
% 21.04/7.60    inference(avatar_component_clause,[status(thm)],[f23533])).
% 21.04/7.60  thf(f23533,definition,(
% 21.04/7.60    spl8_23 <=> ($false = (rep_assn @ x @ sK17))),
% 21.04/7.60    introduced(definition,[new_symbols(naming,[spl8_23])],[avatar_definition])).
% 21.04/7.60  thf(f23557,plain,(
% 21.04/7.60    ~spl8_22 | ~spl8_24),
% 21.04/7.60    inference(avatar_contradiction_clause,[status(thm)],[f23556])).
% 21.04/7.60  thf(f23556,plain,(
% 21.04/7.60    $false | (~spl8_22 | ~spl8_24)),
% 21.04/7.60    inference(trivial_inequality_removal,[status(thm)],[f23555])).
% 21.04/7.60  thf(f23555,plain,(
% 21.04/7.60    ($false = $true) | (~spl8_22 | ~spl8_24)),
% 21.04/7.60    inference(forward_demodulation,[status(thm)],[f23540,f23531])).
% 21.04/7.60  thf(f23531,plain,(
% 21.04/7.60    ($false = (rep_assn @ y @ sK17)) | ~spl8_22),
% 21.04/7.60    inference(avatar_component_clause,[status(thm)],[f23529])).
% 21.04/7.60  thf(f23529,definition,(
% 21.04/7.60    spl8_22 <=> ($false = (rep_assn @ y @ sK17))),
% 21.04/7.60    introduced(definition,[new_symbols(naming,[spl8_22])],[avatar_definition])).
% 21.04/7.60  thf(f23540,plain,(
% 21.04/7.60    ((rep_assn @ y @ sK17) = $true) | ~spl8_24),
% 21.04/7.60    inference(avatar_component_clause,[status(thm)],[f23538])).
% 21.04/7.60  thf(f23538,definition,(
% 21.04/7.60    spl8_24 <=> ((rep_assn @ y @ sK17) = $true)),
% 21.04/7.60    introduced(definition,[new_symbols(naming,[spl8_24])],[avatar_definition])).
% 21.04/7.60  thf(f23554,plain,(
% 21.04/7.60    spl8_25 | ~spl8_2 | spl8_4),
% 21.04/7.60    inference(avatar_split_clause,[status(thm)],[f23521,f23048,f23038,f23542])).
% 21.04/7.60  thf(f23521,plain,(
% 21.04/7.60    ((rep_assn @ x @ sK17) = $true) | (~spl8_2 | spl8_4)),
% 21.04/7.60    inference(duplicate_literal_removal,[status(thm)],[f23519])).
% 21.04/7.60  thf(f23519,plain,(
% 21.04/7.60    ((rep_assn @ x @ sK17) = $true) | ((rep_assn @ x @ sK17) = $true) | (~spl8_2 | spl8_4)),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23518])).
% 21.04/7.60  thf(f23518,plain,(
% 21.04/7.60    (((rep_assn @ y @ sK17) & (rep_assn @ x @ sK17)) = $true) | ((rep_assn @ x @ sK17) = $true) | (~spl8_2 | spl8_4)),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23512])).
% 21.04/7.60  thf(f23512,plain,(
% 21.04/7.60    (((rep_assn @ x @ sK17) & (rep_assn @ y @ sK17)) = $true) | (((rep_assn @ y @ sK17) & (rep_assn @ x @ sK17)) = $true) | (~spl8_2 | spl8_4)),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23511])).
% 21.04/7.60  thf(f23511,plain,(
% 21.04/7.60    (((rep_assn @ y @ sK17) & (rep_assn @ x @ sK17)) != ((rep_assn @ x @ sK17) & (rep_assn @ y @ sK17))) | (~spl8_2 | spl8_4)),
% 21.04/7.60    inference(beta_eta_normalization,[status(thm)],[f23509])).
% 21.04/7.60  thf(f23509,plain,(
% 21.04/7.60    (((^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0))) @ sK17) != ((^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0))) @ sK17)) | (~spl8_2 | spl8_4)),
% 21.04/7.60    inference(negative_extensionality,[status(thm)],[f23359])).
% 21.04/7.60  thf(f23359,plain,(
% 21.04/7.60    ((^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0))) != (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) | (~spl8_2 | spl8_4)),
% 21.04/7.60    inference(trivial_inequality_removal,[status(thm)],[f23354])).
% 21.04/7.60  thf(f23354,plain,(
% 21.04/7.60    (x != x) | ((^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0))) != (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) | (~spl8_2 | spl8_4)),
% 21.04/7.60    inference(constrained_superposition,[status(thm)],[f23049,f23040])).
% 21.04/7.60  thf(f23040,plain,(
% 21.04/7.60    (x = (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0))))) | ~spl8_2),
% 21.04/7.60    inference(avatar_component_clause,[status(thm)],[f23038])).
% 21.04/7.60  thf(f23049,plain,(
% 21.04/7.60    (x != (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0))))) | spl8_4),
% 21.04/7.60    inference(avatar_component_clause,[status(thm)],[f23048])).
% 21.04/7.60  thf(f23549,plain,(
% 21.04/7.60    spl8_24 | ~spl8_2 | spl8_4),
% 21.04/7.60    inference(avatar_split_clause,[status(thm)],[f23524,f23048,f23038,f23538])).
% 21.04/7.60  thf(f23524,plain,(
% 21.04/7.60    ((rep_assn @ y @ sK17) = $true) | (~spl8_2 | spl8_4)),
% 21.04/7.60    inference(duplicate_literal_removal,[status(thm)],[f23523])).
% 21.04/7.60  thf(f23523,plain,(
% 21.04/7.60    ((rep_assn @ y @ sK17) = $true) | ((rep_assn @ y @ sK17) = $true) | (~spl8_2 | spl8_4)),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23517])).
% 21.04/7.60  thf(f23517,plain,(
% 21.04/7.60    ((rep_assn @ y @ sK17) = $true) | (((rep_assn @ y @ sK17) & (rep_assn @ x @ sK17)) = $true) | (~spl8_2 | spl8_4)),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23512])).
% 21.04/7.60  thf(f23536,plain,(
% 21.04/7.60    spl8_22 | spl8_23 | ~spl8_2 | spl8_4),
% 21.04/7.60    inference(avatar_split_clause,[status(thm)],[f23516,f23048,f23038,f23533,f23529])).
% 21.04/7.60  thf(f23516,plain,(
% 21.04/7.60    ($false = (rep_assn @ x @ sK17)) | ($false = (rep_assn @ y @ sK17)) | (~spl8_2 | spl8_4)),
% 21.04/7.60    inference(duplicate_literal_removal,[status(thm)],[f23515])).
% 21.04/7.60  thf(f23515,plain,(
% 21.04/7.60    ($false = (rep_assn @ y @ sK17)) | ($false = (rep_assn @ x @ sK17)) | ($false = (rep_assn @ y @ sK17)) | ($false = (rep_assn @ x @ sK17)) | (~spl8_2 | spl8_4)),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23514])).
% 21.04/7.60  thf(f23514,plain,(
% 21.04/7.60    ($false = (rep_assn @ y @ sK17)) | ($false = (rep_assn @ x @ sK17)) | ($false = ((rep_assn @ y @ sK17) & (rep_assn @ x @ sK17))) | (~spl8_2 | spl8_4)),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23513])).
% 21.04/7.60  thf(f23513,plain,(
% 21.04/7.60    ($false = ((rep_assn @ x @ sK17) & (rep_assn @ y @ sK17))) | ($false = ((rep_assn @ y @ sK17) & (rep_assn @ x @ sK17))) | (~spl8_2 | spl8_4)),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23511])).
% 21.04/7.60  thf(f23053,plain,(
% 21.04/7.60    spl8_3 | ~spl8_4 | ~spl8_2 | spl8_1),
% 21.04/7.60    inference(avatar_split_clause,[status(thm)],[f23015,f23034,f23038,f23048,f23043])).
% 21.04/7.60  thf(f23015,plain,(
% 21.04/7.60    (x != (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0))))) | (x != (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0))))) | (y = (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0))))) | (x = y)),
% 21.04/7.60    inference(equality_proxy_clausification,[status(thm)],[f23014])).
% 21.04/7.60  thf(f23014,plain,(
% 21.04/7.60    (x != (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0))))) | (((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = y) = $true) | (x = y) | (x != (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0)))))),
% 21.04/7.60    inference(equality_proxy_clausification,[status(thm)],[f23013])).
% 21.04/7.60  thf(f23013,plain,(
% 21.04/7.60    (x != (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0))))) | ($true = (x = y)) | (((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = y) = $true) | (x != (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0)))))),
% 21.04/7.60    inference(not_proxy_clausification,[status(thm)],[f23012])).
% 21.04/7.60  thf(f23012,plain,(
% 21.04/7.60    (x != (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0))))) | (x != (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0))))) | ($false = (~ (x = y))) | (((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = y) = $true)),
% 21.04/7.60    inference(not_proxy_clausification,[status(thm)],[f23011])).
% 21.04/7.60  thf(f23011,plain,(
% 21.04/7.60    ($false = (~ ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = y))) | (x != (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0))))) | ($false = (~ (x = y))) | (x != (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))))),
% 21.04/7.60    inference(equality_proxy_clausification,[status(thm)],[f23010])).
% 21.04/7.60  thf(f23010,plain,(
% 21.04/7.60    (x != (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0))))) | ($false = ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0)))) = x)) | ($false = (~ (x = y))) | ($false = (~ ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = y)))),
% 21.04/7.60    inference(equality_proxy_clausification,[status(thm)],[f23009])).
% 21.04/7.60  thf(f23009,plain,(
% 21.04/7.60    ($false = ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = x)) | ($false = (~ ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = y))) | ($false = (~ (x = y))) | ($false = ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0)))) = x))),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23008])).
% 21.04/7.60  thf(f23008,plain,(
% 21.04/7.60    ($false = (((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = x) & (~ ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = y)))) | ($false = ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0)))) = x)) | ($false = (~ (x = y)))),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23007])).
% 21.04/7.60  thf(f23007,plain,(
% 21.04/7.60    ($false = ((~ (x = y)) & ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0)))) = x))) | ($false = (((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = x) & (~ ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = y))))),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f22968])).
% 21.04/7.60  thf(f22968,plain,(
% 21.04/7.60    (((~ (x = y)) & ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0)))) = x)) != (((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = x) & (~ ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = y))))),
% 21.04/7.60    inference(cnf_transformation,[status(thm)],[f22935])).
% 21.04/7.60  thf(f22935,plain,(
% 21.04/7.60    (((~ (x = y)) & ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0)))) = x)) != (((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = x) & (~ ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = y))))),
% 21.04/7.60    inference(flattening,[status(thm)],[f20009])).
% 21.04/7.60  thf(f20009,plain,(
% 21.04/7.60    ~(((~ (x = y)) & ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0)))) = x)) = (((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = x) & (~ ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = y))))),
% 21.04/7.60    inference(fool_elimination,[status(thm)],[f20008])).
% 21.04/7.60  thf(f20008,plain,(
% 21.04/7.60    ~(((abs_assn @ (^[X0 : produc3658429121746597890et_nat] : ((rep_assn @ y @ X0) & (rep_assn @ x @ X0)))) = x) & (x != y) = ((abs_assn @ (^[X1 : produc3658429121746597890et_nat] : ((rep_assn @ x @ X1) & (rep_assn @ y @ X1)))) != y) & ((abs_assn @ (^[X2 : produc3658429121746597890et_nat] : ((rep_assn @ x @ X2) & (rep_assn @ y @ X2)))) = x))),
% 21.04/7.60    inference(rectify,[status(thm)],[f9727])).
% 21.04/7.60  thf(f9727,negated_conjecture,(
% 21.04/7.60    ~(((abs_assn @ (^[X7 : produc3658429121746597890et_nat] : ((rep_assn @ y @ X7) & (rep_assn @ x @ X7)))) = x) & (x != y) = ((abs_assn @ (^[X7 : produc3658429121746597890et_nat] : ((rep_assn @ x @ X7) & (rep_assn @ y @ X7)))) != y) & ((abs_assn @ (^[X7 : produc3658429121746597890et_nat] : ((rep_assn @ x @ X7) & (rep_assn @ y @ X7)))) = x))),
% 21.04/7.60    inference(negated_conjecture,[status(cth)],[f9726])).
% 21.04/7.60  thf(f9726,conjecture,(
% 21.04/7.60    (((abs_assn @ (^[X7 : produc3658429121746597890et_nat] : ((rep_assn @ y @ X7) & (rep_assn @ x @ X7)))) = x) & (x != y) = ((abs_assn @ (^[X7 : produc3658429121746597890et_nat] : ((rep_assn @ x @ X7) & (rep_assn @ y @ X7)))) != y) & ((abs_assn @ (^[X7 : produc3658429121746597890et_nat] : ((rep_assn @ x @ X7) & (rep_assn @ y @ X7)))) = x))),
% 21.04/7.60    file('/export/starexec/sandbox2/tmp/tmp.q4ZIkRLcku/DTF2THF_32141.p',conj_0)).
% 21.04/7.60  thf(f23051,plain,(
% 21.04/7.60    spl8_4 | spl8_2),
% 21.04/7.60    inference(avatar_split_clause,[status(thm)],[f23023,f23038,f23048])).
% 21.04/7.60  thf(f23023,plain,(
% 21.04/7.60    (x = (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0))))) | (x = (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))))),
% 21.04/7.60    inference(equality_proxy_clausification,[status(thm)],[f23019])).
% 21.04/7.60  thf(f23019,plain,(
% 21.04/7.60    (((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0)))) = x) = $true) | (x = (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))))),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23018])).
% 21.04/7.60  thf(f23018,plain,(
% 21.04/7.60    (((~ (x = y)) & ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0)))) = x)) = $true) | (x = (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))))),
% 21.04/7.60    inference(equality_proxy_clausification,[status(thm)],[f23017])).
% 21.04/7.60  thf(f23017,plain,(
% 21.04/7.60    (((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = x) = $true) | (((~ (x = y)) & ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0)))) = x)) = $true)),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23006])).
% 21.04/7.60  thf(f23006,plain,(
% 21.04/7.60    ((((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = x) & (~ ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = y))) = $true) | (((~ (x = y)) & ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0)))) = x)) = $true)),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f22968])).
% 21.04/7.60  thf(f23046,plain,(
% 21.04/7.60    ~spl8_1 | ~spl8_3),
% 21.04/7.60    inference(avatar_split_clause,[status(thm)],[f23029,f23043,f23034])).
% 21.04/7.60  thf(f23029,plain,(
% 21.04/7.60    (y != (abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0))))) | (x != y)),
% 21.04/7.60    inference(equality_proxy_clausification,[status(thm)],[f23028])).
% 21.04/7.60  thf(f23028,plain,(
% 21.04/7.60    ($false = ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = y)) | (x != y)),
% 21.04/7.60    inference(equality_proxy_clausification,[status(thm)],[f23027])).
% 21.04/7.60  thf(f23027,plain,(
% 21.04/7.60    ($false = (x = y)) | ($false = ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = y))),
% 21.04/7.60    inference(not_proxy_clausification,[status(thm)],[f23026])).
% 21.04/7.60  thf(f23026,plain,(
% 21.04/7.60    ((~ ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = y)) = $true) | ($false = (x = y))),
% 21.04/7.60    inference(not_proxy_clausification,[status(thm)],[f23025])).
% 21.04/7.60  thf(f23025,plain,(
% 21.04/7.60    ((~ (x = y)) = $true) | ((~ ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = y)) = $true)),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23016])).
% 21.04/7.60  thf(f23016,plain,(
% 21.04/7.60    (((~ (x = y)) & ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ x @ Y0) & (rep_assn @ y @ Y0)))) = x)) = $true) | ((~ ((abs_assn @ (^[Y0 : produc3658429121746597890et_nat]: ((rep_assn @ y @ Y0) & (rep_assn @ x @ Y0)))) = y)) = $true)),
% 21.04/7.60    inference(binary_proxy_clausification,[status(thm)],[f23006])).
% 21.04/7.60  % SZS output end Proof for DTF2THF_32141
% 21.04/7.60  % (32365)------------------------------
% 21.04/7.60  % (32365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.04/7.60  % (32365)Termination reason: Refutation
% 21.04/7.60  
% 21.04/7.60  % (32365)Memory used [KB]: 31086
% 21.04/7.60  % (32365)Time elapsed: 0.568 s
% 21.04/7.60  % (32365)Instructions burned: 1758 (million)
% 21.04/7.60  % (32365)------------------------------
% 21.04/7.60  % (32365)------------------------------
% 21.04/7.60  % (32250)Success in time 2.302 s
%------------------------------------------------------------------------------